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ME 8501 - METROLOGY AND MEASUREMENTS

UNIT I .BASICS OF METROLOGY 9

Introduction to Metrology – Need – Elements – Work piece, Instruments – Persons Environment – their effect on Precision and Accuracy – Errors – Errors in Measurements – Types – Control – Types of standards.

UNIT II LINEAR AND ANGULAR MEASUREMENTS 9

Linear Measuring Instruments – Evolution – Types – Classification – Limit gauges – gauge design –terminology – procedure – concepts of interchange ability and selective assembly – Angular measuring instruments – Types – Bevel protractor clinometers angle gauges, spirit levels sine bar – Angle alignment telescope – Autocollimator – Applications.

UNIT III ADVANCES IN METROLOGY 9

Basic concept of lasers Advantages of lasers – laser Interferometers – types – DC and AC Lasers interferometer – Applications – Straightness – Alignment. Basic concept of CMM – Types of CMM – Constructional features – Probes – Accessories – Software – Applications – Basic concepts of Machine Vision System – Element –Applications.

UNIT IV FORM MEASUREMENT 9

Principles and Methods of straightness – Flatness measurement – Thread measurement, gear measurement, surface finish measurement, Roundness measurement – Applications.

UNIT V MEASUREMENT OF POWER, FLOW AND TEMPERATURE 9

Force, torque, power - mechanical , Pneumatic, Hydraulic and Electrical type. Flow measurement: Venturimeter, Orifice meter, rotameter, pitot tube – Temperature: bimetallic strip, thermocouples, electrical resistance thermometer – Reliability and Calibration – Readability and Reliability.

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UNIT – I-BASICS OF METROLOGY

Metrology is the name given to the science of puremeasurement. Engineering Metrology is restricted to measurements of length & angle.Need for Measurement To ensure that the part to be measured conforms to the established standard. To meet the interchangeability of manufacture. To provide customer satisfaction by ensuring that no faulty product reaches

the customers. To coordinate the functions of quality control, production, procurement & other

departments of the organization. To judge the possibility of making some of the defective parts acceptable after

minor repairs.

Precision & Accuracy of Measurement Precision : It is the degree which determines how well identically performed measurements agree with each other. It is the repeatability of the measuring process. It carries no meaning for only one measurement. It exists only when a set of observations is gathered for the same quantity under identical conditions. In such a set, the observations will scatter about a mean. The less is the scattering, the more precise is the measurement.

Basic units in SI system 1) For Length : Metre (m) which is equal to 1650763.73 wavelengths in vacuum ofthe red-orange radiation corresponding to the transition between the levels 2p10 & 5d5 of the krypton-86 atom. (Definition by wavelength standard) By Line standard, Metre is the distance between the axes of two lines engraved on a polished surface of the Platinum – Iridium bar ‗M‘ (90% platinum & 10% iridium) kept at Bureau of Weights & Measures (BIPM) at Sevres near Paris at 0C, the bar kept under normal atmospheric pressure, supported by two rollers of at least 1 cm diameter symmetrically situated in the same horizontal plane at a distance of 588.9 mm (Airy points) so as to give minimum deflection. 2) For Mass: Kilogram (kg) which is equal to the mass of International prototype ofthe kilogram. 3) For Time : Second (s) which is equal to the duration of 9192631770 periods of theradiation corresponding to the transition between the hyper fine levels of the ground state of the Caesium 133 atom. 4) For Current : Ampere (A) is that constant current which, if maintained in twostraight parallel conductors of infinite length of negligible circular cross section & placed one metre apart in vacuum would produce between these conductors, a force equal to 2 x 10-7 Newton per unit length. 5) For Temperature: Kelvin (K) is the fraction 1/273 of thermodynamic temperature ofthe triple point of water. 6) For Luminous intensity: Candela (cd) is the luminous intensity in the perpendiculardirection of a surface of 1/6,00,000 m2 of a black body at the temperature of freezing platinum under a pressure of 101325 N/m2. 7) For amount of substance: Mole (mol) is the amount of substance of a systemwhich contains as many elementary entities as there are atoms in 0.012 kg of Carbon-12. Supplementary SI units:

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1) For Plane angle: Radian (rad)2) For Solid angle: Steradian (sr)Derived SI units: 1) For Frequency: Hertz (1 Hz = 1 cycle per second)2) For Force: Newton (1 N = 1 kg-m/s2)3) For Energy: Joule (1 J = 1 N-m)4) For Power: Watt (1 W = 1 J/s)

Errors In Measurements:-

During measurement several types of error may arise as indicated and these error can be broadly classified into two categories.

a) Controllable Errors :

These are controllable in both their magnitude and sense. These can be determined and reduced, if attempts are made to analyse them. These are also known as systematic errors. These can be due to :

1.Calibration Errors :

The actual length of standards such as slip gauges and engraved scales will vary from nominal value by small amount. Sometimes the instrument inertia and hysteresis effects do not let the instrument translate with complete fidelity. Often signal transmission errors such as a drop in voltage along the wires between the transducer and the electric meter occur. For high order accuracy these variations have positive significance and to minimize such variations calibration curves much be used.

2. Ambient Conditions :

Variations in the ambient conditions from internationally agreed standard value of 20oC, barometric pressure 760mm of mercury and 10mm of mercury vapour pressure, can give rise to errors in the measured size of the component. Temperature is by far the most significant of these ambient conditions and due correction is needed to obtain error free results.

1.Stylus Pressure :

Error induced due to stylus pressure are also appreciable. Whenever any component in measured under a definite stylus pressure both the deformation of the workpiece surface and deflection of the workpiece shape will occur.

Avoidable Errors :

These error include the errors due to Parallel and the effect of misalignment of the workpiece centers. Instrument location errors such as placing a thermometer is sunlight when attempting to measure air temperature also being to this category.

b) Random Errors :

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These occur randomly and the specific causes of such errors cannot be determined, but likely sources of this type of error are small variations in the position of setting standards and workpiece, slight displacement of lever joints in the measuring joints in the measuring instrument, transient flaction in the friction in the measuring instrument and operator errors in reading scale and pointer type displays or in reading engraved scale positions. From the above, it is clear that systematic errors are those which are repeated consistently with repetition of the experiment, where as random errors are those which are accidental and whose magnitude and sign cannot be predicted from a knowledge of the measuring system and condition of measurement. Systematic error and random error:- For statistical study and the study of accumulation of errors, errors are categorized as controllable errors and random errors. (a) Systematic or controllable errors: Systematic error is just a euphemism for experimental mistakes. These are controllable in both their magnitude and sense. These can be determined and reduced, if attempts are made to analyse them. However, they can not be revealed by repeated observations. These errors either have a constant value or a value changing according to a definite law. These can be due to:

1. Calibration Errors: The actual length of standards such as slip gauges and engraved scales will vary from nominal value by small amount. Sometimes the instrument inertia, hysteresis effects do not let the instrument translate with complete fidelity. Often signal transmission errors such as drop in voltage along the wires between the transducer and the electric meter occur. For high order accuracy these variations have positive significance and to minimize such variations calibration curves must be used.

2. Ambient Conditions: Variations in the ambient conditions from internationally

agreed standard value of 20C, barometric pressure 760 mm of mercury, and 10mm of mercury vapour pressure, can give rise to errors in the measured size of the component. Temperature is by far the most significant of these ambient conditions and due correction is needed to obtain error free results.

3. Styles Pressure: Error induced due to styles pressure is also appreciable. Whenever any component is measured under a definite stylus pressure both the deformation of the workpiece surface and deflection of the workpiece shape will occur.

4. Avoidable Errors: These errors include the errors due to parallax and the effect of misalignment of the workpiece centre. Instrument location errors such as placing a thermometer in sunlight when attempting to measure air temperature also belong to this category.

5. Experimental arrangement being different from that assumed in theory. 6. Incorrect theory i.e., the presence of effects not taken into account.

(b) Random Errors:

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These occur randomly and the specific cases of such errors cannot be determined, but likely sources of this type of errors are small variations in the position of setting standard and workpiece, slight displacement of lever joints in the measuring joints in measuring instrument, transient fluctuation in the friction in the measuring instrument, and operator errors in reading scale and pointer type displays or in reading engraved scale positions. Characteristics of random errors: The various characteristics of random errors are: These are due to large number of unpredictable and fluctuating causes that

can not be controlled by the experimenter. Hence they are sometimes positive and sometimes negative and of variable magnitude. Accordingly they get revealed by repeated observations.

These are caused by friction and play in the instrument‘s linkages, estimation of reading by judging fractional part of a scale division, by errors in position the measured object, etc.

These are variable in magnitude and sign and are introduced by the very process of observation itself.

The frequency of the occurrence of random errors depends on the occurrence probability for different values of random errors.

Random errors show up as various indication values within the specified limits of error in a series of measurements of a given dimension.

The probability of occurrence is equal for positive and negative errors of the same absolute value since random errors follow normal frequency distribution.

Random errors of larger absolute value are rather than those of smaller values.

The arithmetic mean of random errors in a given series of measurements approaches zero as the number of measurements increases.

For each method of measurement, random errors do not exceed a certain definite value. Errors exceeding this value are regarded as gross errors (errors which greatly distort the results and need to be ignored).

The most reliable value of the size being sought in a series of measurements is the arithmetic mean of the results obtained.

The main characteristic of random errors, which is used to determine the maximum measuring error, is the standard deviation.

The maximum error for a given method of measurement is determined as three times the standard deviation.

The maximum error determines the spread of possible random error values The standard deviation and the maximum error determine the accuracy of a

single measurement in given series.

From the above, it is clear that systematic errors are those which are repeated consistently with repetition of the experiment, whereas Random Errors are those which are accidental and whose magnitude and sign cannot be predicted from knowledge of measuring system and conditions of measurement.

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classification of measurements:- In the precision measurements, various methods of measurement are followed depending upon the accuracy required and the amount of permissible error. The various methods of measurement are classified as follow :-

Direct method of measurement Indirect method of measurement Absolute method of measurement Comparative method of measurement Contact method of measurement Contact less method of measurement

The direct method of measurement is one in which the measurement value in determined directly where as in the indirect method of measurement the dimension in determined by measuring the values functionally related to the required value. The direct method of measurement is simple and most widely employed in production. In many cases, for example, as when checking the pitch diameter of treads, the direct method may lead to large errors in measurement. In this case, it is more expedient to make indirect measurement. An absolute method of measurement in one in which the zero division of the measuring tool or instrument corresponding zero value of the measured dimension. eg. Steel rule, vernier Caliper, micrometer, Screw gauge). By absolute method the full value of the dimension is determined. In the comparative method, only the deviation of the measured dimension from a master gauge are determined (eg. Dial comparator). In contact methods of measurement, the measuring tip of the instrument actually touches the surface to be measured, eg. By dial comparator, screw gauges etc. In such cases arrangements for constant contact pressure should be provided in order to prevent errors due to excess contact pressure. In Contact less method of measurement, no contact is required. Such instruments include tool maker's micrometer and projection comparator. According to the functions, the measuring instruments classified as. Length measuring instruments Angle measuring instruments Instrument for checking deviation from geometrical forms Instrument for determining the quality of surface finish.

According to the accuracy of measurement, the measuring instrument are classified as follows.

Most accurate instrument eg : light – interference instruments. Second group consists of less accurate instruments. Such as tool room

Microscopes, comparator optimeter etc.

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Third group consists of , still less accurate instruments eg: dial indicators, vernier caliper and rules with vernier skills.

Measuring instrument are also classified in accordance with then metrological proper ties, such as range of instrument, scale graduation value, scale spacing, sensitivity and reading accuracy.

Range of Measurement : It indicates the size values between which measurements may be made on the given instrument. Scale Spacing : It is the distance between the axis of two adjacent graduations on the scale. Scale division Value : It the measured value corresponding to one division of the instrument scale, eg. For Vernier Caliper the scale division value 0.1mm.

Sensitivity (amplification or gearing ratio ): It is the ratio of the scale spacing to the space division value. It would also be expressed as the ratio of the product of all the larger lever arms and the product of all the smaller lever arms. Sensitivity Threshold : It is defined as the minimum measured value which may cause any movement whatsoever of the indicating hand..

Reading Accuracy : It is the accuracy that may be attained in using a measuring instrument. Reading Error : It is defined as the difference between the reading of the instrument and the actual value of the dimension being measured. Mention a few important precautions for use of instruments towards achieving accuracy in measurement are as follows : The measurement must be made at right angles to the surfaces of the component. The component must be supported so that it does not collapse under the measuring

pressure or under its own weight. The work piece must be cleaned before being measured, and coated with oil or a

corruption inhibitor after inspection. Measuring instrument must be handled with care so that they are not damaged or

strained. They must be kept in their cases when not in use and kept clean and lightly oiled on the bright surfaces. They should be regularly checked to ensure that they have not lost their mutual accuracy.

It must be emphasized that it is not good practice to rely on the accuracy of the

instruments and on the readings taken – readings should be double checked and

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the instruments should be periodically checked against the appropriate standards. Measuring instruments are produced to a high degree of accuracy, form the engineer's common rule to the most complex optical instrument, and they should be treated accordingly. Instruments are easily damaged, and very often the damage is not noticeable. Always handle instrument with great care, and report immediately any accidental damage. Protect highly polished surfaces from corrosion by handling them as little as possible and by covering them with petroleum jelly when not in use.

Sources of errors in precision measurement:- Failure to consider the following factors may introduce errors in measurement :

Alignment Principle Location of the measured part Temperature Parallax.

Alignment Principle (Abbe's Principle) : Abbe's principle of alignment states that " the axis or line of measurement of the measured part should consider with the measuring scale or axis or measurement of measuring instrument ". The effect of simple scale alignment error is shown in fig. L L Q JCL if Q = angle of scale misalignment L = apparent length Loose = true length if e = induced error then, e = L-L cose = L(1-CoseC) An alignment error of 2o over iN introduces an error of approximately 0.6mm. Error in introduced to dial indicator readings if the plunger axis does not coincide with the axis or line of measurement. Q

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If e = Induced error L = change in indicator reading, reading. L case = Surface displacement \ e = L (1-Cose) Line or axis of measure Dial gauge axis. To ensure correct displacement readings on the dial indicator the plunger must, of course be normal to the surface in both mutually perpendicular planes. A second source of error will illustrated by the vernier Caliper and similar instruments or circumstance is associated with measuring pressure or "feel". The measuring pressure in applied by the adjusting screw which is adjacent and parallel to the scale. A bending moment in introduced equal to the product of the force applied by the adjusting screw and the perpendicular distance between the screw centre line and the line of measurement as in Fig. Variation of force applied at the screw are augmented at the line of measurement and a hot unusual form of damage to Vernier Caliper is permanent distortion to the measuring jaws presumably from this source as in fig. Location :

when using a sensitive comparator, the measured part in located on a table which forms the datum for comparison with the standard. The comparator reading in thus an indication of the displacement of the upper surface of the measured part from the datum. Faults at the location surface of the part damage, geometrical variations from part to part or the presence of foreign matter are also transmitted to the indicator. This provides false information regarding the true length of the part by introducing both sine and cosine error. Where location conditions may not be ideal, ex:- inter stage measurement during production, sensors, operating on each side of the component can be used which eliminate the more serious sine type error. A two probe system measures length rather than surface displacement and highly sensitive electronic comparators of this type are used for slip gauge measurement. Temperature :- The standard reference temp. at which line and end standards are said to be at their true length is 20o and for highest accuracy in measurement this temp.

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Should be maintained. When this is not possible and the length at reference temp. must be known, a correction is made to allow for the difference between ambient and reference temp. The correction value required to – 0.001375mm, when steel object exactly 25mm long at 20oC and Co-efficient of linear expansion 11Mm c/m in measured at 25oC, Which is rather larger than the increment step the M88/2 stip gauge set. However, for less stringent measurement requirements it is not essential that correction to reference temperature is made provided that the following precautions and conditions are observed. a) The temp. at which measurement is made is not changing significantly. b) The gauge and work being compared are at the same temp and the temp is the same as ambient temp. c) The gauge and work have the same Co-efficient of linear expansion. Conditions a) and b) can be met if gauge and work allowed sufficient time to reach equal temp with surrounding after being arranged in the measuring positions. If the measurement can be carried out on the surface of a large mass, eg: Surface plate, then temp. equalization will be family vapid as heat will be conducted away form the work and gauge but will not contribute any significant temp. change to the plate. A component having a co-efficient of linear expansion significantly different from the gauge may be said to correct to size only at a given temp. Parallax Effect :

On most dials the indicating finger or pointer lies in a plane parallel to the scale but displaced a small distance away to allow free movement of the pointer. It is then essential to observe the pointer along a line normal to the scale otherwise a reading error will occur. This effect is shown in fig. Where a dial is shown observed from three positions where the pointer is set at zero on the scale, observed from position 1) ie, from the left, the pointer appears to indicate some value, to the right off zero, and from position 2) Some value slightly to the left of zero, while only at position. 3) With the pointer Coincide with zero on the scale. Rules and micrometer thimbles are beveled to reduce this effect and on dials the indicates may be arranged to lie in the same plane as the scale, thus completely eliminating parallax, or a silvered reflector may be incorporated on the scale so that the line between the of eye and pointer is normal to the scale only when the pointer obscures in own image in the reflector.

Classifications of Methods of Measurements In precision measurements various methods of measurement are followed depending upon the accuracy required and the amount of permissible error. There are numerous ways in which a quantity can be measured. Any method of measurements should be defined in such a detail and followed by such a standard

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practice that there is little scope for uncertainty. The nature of the procedure in some of the most common measurements is described below. Actual measurements may employ one or more combinations of the following.

(i) Direct method of measurement: In this method the value of a quantity of obtained directly by comparing the unknown with the standard. It involves no mathematical calculations to arrive at the results, for example, measurement of length by a graduated scale. The method is not very accurate because it depends on human insensitiveness in making judgement.

(ii) Indirect method of measurement: In this method several parameters (to which the quantity to be measured is linked with) are measured directly and then the value is determined by mathematical relationship. For example, measurement of density by measuring mass and geometrical dimensions.

(iii) Fundamental method of measurement: Also known as the absolute method of measurement, it is based on the measurement of the base quantities used to define the quantity. For example, measuring a quantity directly in accordance with the definition of that quantity, or measuring a quantity indirectly by direct measurement of the quantities linked with the definition of the quantity to be measured.

(iv) Comparison method of measurement: This method involves comparison with either a known value of the same quantity or another quantity which is function of the quantity to be measured.

(v) Substitution method of measurement: In this method, the quantity to be measured is measured by direct comparison on an indicating device by replacing the measuring quantity with some other known quantity which produce same effect on the indicating device. For example, determination of mass by Borda method.

(vi) Transposition method of measurement: This is a method of measurement by direct comparison in which the value of the quantity to be measured is first balanced by a initial known value A of the same quantity; next the value of the quantity to be measured is put in the place of that known value and is balanced again by a second known value B. When the balance indicating device gives the same indication in both cases, the

value of the quantity to be measured is AB . For example, determination of a mass by means of a balance and known weights, using the Gauss double weighing method.

(vii) Differential or comparison method of measurement: This method involves measuring the difference between the given quantity and a known master of near about the same value. For example, determination of diameter with master cylinder on a comparator.

(viii) Coincidence method of measurement: In this differential method of measurement the very small difference between the given quantity and the reference is determined is determined by the observation of the coincidence of scale marks. For example, measurement on vernier caliper.

(ix) Null method of measurement: In this method the quantity to be measured is compared with a known source and the difference between these two is made zero.

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(x) Deflection method of measurement: In this method, the value of the quantity is directly indicated by deflection of a pointer on a calibrated scale.

(xi) Interpolation method of measurement: In this method, the given quantity is compared with two or more known value of near about same value ensuring at least one smaller and one bigger than the quantity to be measured and the readings interpolated.

(xii) Extrapolation method of measurement: In this method, the given quantity is compared with two or more known smaller values and extrapolating the reading.

(xiii) Complimentary method of measurement: This is the method of measurement by comparison in which the value of the quantity to be measured is combined with a known value of the same quantity so adjusted that the sum of these two values is equal to predetermined comparison value. For example, determination of the volume of a solid by liquid displacement.

(xiv) Composite method of measurement: In involves the comparison of the actual contour of a component to be checked with its contours in maximum and minimum tolerable limits. This method provides for the checking of the cumulative errors of the interconnected elements of the component which are controlled through a combined tolerance. This method is most reliable to ensure inter-changeability and is usually effected through the use of composite ―Go‖ gauges, for example, checking of the thread of a nut with a screw plug ―GO‖ gauge.

(xv) Element method: In this method, the several related dimensions are gauged individually, i.e., each component element is checked separately. For example, in the case of thread, the pitch diameter, pitch, and flank angle are checked separately and then the virtual pitch diameter is calculated. It may be noted that value of virtual pitch diameter depends on the deviations of the above thread elements. The functioning of thread depends on virtual pitch diameter lying within the specified tolerable limits. In case of composite method, all the three elements need not be checked separately and is thus useful for checking the product parts. Element method is used for checking tools and for detecting the causes of rejects in the product.

(xvi) Contact and contact less methods of measurements: In contact methods of measurements, the measuring tip of the instrument actually touches the surface to be measured. In such cases, arrangements for constant contact pressure should be provided in order to prevent errors due to excess contact pressure. In contactless method of measurements, no contact is required. Such instruments include tool – maker‘s microscope and projection comparator, etc.

For every method of measurement a detailed definition of the equipment to be

used, a sequential list of operations to be performed, the surrounding environmental conditions and descriptions of all factors influencing accuracy of measurement at the required level must be prepared and followed.

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Metrological characteristics of Measuring Instruments:- Measuring instruments are usually specified by their metrological properties,

such as range of measurement, scale graduation value, scale spacing, sensitivity and reading accuracy. Range of Measurement: It indicates the size values between which measurements may be made on the given instrument. Scale range: It is the difference between the values of the measured quantities corresponding to the terminal scale marks. Instrument range: It is the capacity or total range of values which an instrument is capable of measuring. For example, a micrometer screw gauge with capacity of 25 to 50mm has instrument range of 25 to 50mm but scale range is 25mm. Scale Spacing: It is the distance between the axes of two adjacent graduations on the scale. Most instruments have a constant value of scale spacing throughout the scale. Such scales are said to be linear. In case of non – linear scales, the scale spacing value is variable within the limits of the scale. Scale Division Value: It is the measured value of the measured quantity corresponding to one division of the instrument, e.g. for ordinary scale, the scale division value is 1mm. As a rule, the scale division should not be smaller in value than the permissible indication error of an instrument. Sensitivity (Amplication or gearing ratio): It is the ratio of the scale spacing to the division value. It could also be expressed as the ratio of the product of all the larger lever arms and the product of all the smaller lever arms. It is the property of a measuring instrument to respond to changes in the measurement quantity. Sensitivity Threshold: It is defined as the minimum measured value which may cause any movement whatsoever of the indicating hand. It is also called the discrimination or resolving power of an instrument and is the minimum change in the quantity being measured which produces a perceptible movement of the index. Reading Accuracy: It is the accuracy that may be attained in using a measuring instrument. Reading Error: It is defined as the difference between the reading of the instrument and the actual value of the dimension being measured. Accuracy of observation: It is accuracy attainable in reading the scale of an instrument. It depends on the quality of the scale marks, the width or the pointer / index, the space between the pointer and the scale, the illumination of the scale, and the skill of the inspector. The width of scale mark is usually kept one – tenth of the scale spacing for accurate reading of indications.

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Parallax: It is apparent change in the position of the index relative to the scale marks, when the scale is observed in a direction other than perpendicular to its plane. Repeatability: It is the variation of indications in repeated measurements of the same dimension. The variations may be due to clearances, friction and distortions in the instrument‘s mechanism. Repeatability represents the reproducibility of the readings of an instrument when a series of measurements in carried out under fixed conditions of use. Measuring force: It is the force produced by an instrument and acting upon the measured surface in the direction of measurement. It is usually developed by springs whose deformation and pressure change with the displacement of the instrument‘s measuring spindle. Precision and Accuracy:- The agreement of the measured value with the true value of the measured quantity is called accuracy. If the measurement of a dimensions of a part approximates very closely to the true value of that dimension, it is said to be accurate. Thus the term accuracy denotes the closeness of the measured value with the true value. The difference between the measured value and the true value is the error of measurement. The lesser the error, more is the accuracy. Precision, The terms precision and accuracy are used in connection with the performance of the instrument. Precision is the repeatability of the measuring process. It refers to the group of measurements for the same characteristics taken under identical conditions. It indicates to what extent the identically performed measurements agree with each other. If the instrument is not precise it will give different (widely varying) results for the same dimension when measured again and again. The set of observations will scatter about the mean. The scatter of these

measurements is designated as , the standard deviation. It is used as an index of precision. The less the scattering more precise is the instrument. Thus, lower, the

value of , the more precise is the instrument. Accuracy: Accuracy is the degree to which the measured value of the quality characteristic agrees with the true value. The difference between the true value and the measured value is known as error of measurement. Distinction between Precision and Accuracy Accuracy is very often confused with precision though much different. The distinction between the precision and accuracy will become clear by the following example. Several measurements are made on a component by different types of instruments (A, B and C respectively) and the results are plotted. In any set of measurements, the individual measurements are scattered about the mean, and the precision signifies how well the various measurements performed by same instrument on the same quality characteristics agree with each other.

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The difference between the mean of set of readings of the same quality characteristic and the true value is called as error. Less the error more accurate is the instrument. Figure shows that the instrument A is precise since the results of number of measurements are close to the average value. However, there is a large difference (error) between the true value and the average value hence it is not accurate. The readings taken by the instruments are scattered much from the average value and hence it is not precise but accurate as there is a small difference between the average value and true value. Figure shows that the instrument is accurate as well as precise. Factors affecting the accuracy of the measuring system:- The basic components of an accuracy evaluation are the five elements of a measuring system such as:

1. Factors affecting the calibration standards 2. Factors affecting the workpiece 3. Factors affecting the inherent characteristics of the instrument 4. Factors affecting the person, who carries out the measurements, and 5. Factors affecting the environment.

1. Factors affecting the standard. It may be affected by:

a. Coefficient of thermal expansion,

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b. Calibration interval, c. Stability with time, d. Elastic properties, e. Geometric compatibility

2. Factors affecting the Workpiece, these are: a. Cleanliness, surface finish, waviness, scratch, surface defects etc., b. Hidden geometry, c. Elastic properties, d. Adequate datum on the workpiece e. Arrangement of supporting workpiece f. Thermal equalization etc.

3. Factors affecting the inherent characteristics of Instrument a. Adequate amplification for accuracy objective, b. Scale error, c. Effect of friction, backlash, hysteresis, zero drift error, d. Deformation in handling or use, when heavy workpieces are measured e. Calibration errors, f. Mechanical parts (slides, guide ways or moving elements) g. Repeatability and readability h. Contact geometry for both workpiece and standard

4. Factors affecting person: a. Training, skill b. Sense of precision appreciation, c. Ability to select measuring instruments and standards d. Sensible appreciation of measuring cost, e. Attitude towards personal accuracy achievements f. Planning measurement techniques for minimum cost, consistent with

precision requirements etc

5. Factors affecting Environment: a. Temperature, humidity etc., b. Clean surrounding and minimum vibration enhance precision, c. Adequate illumination d. Temperature equalization between standard, workpiece, and

instrument, e. Thermal expansion effects due to heat radiation from lights, heating

elements, sunlight and people, f. Manual handling may also introduce thermal expansion.

Higher accuracy can be achieved only if, all the sources of error due to the above five elements in the measuring system are analysed and steps taken to eliminate them. The above analysis of five basic metrology elements can be composed into the acronym. SWIPE, for convenient reference Where, S – STANDARD

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W - WORKPIECE I - INSTRUMENT P - PERSON E - ENVIRONMENT Terms of measuring systems:-

(i) Sensitivity (ii) Readability (iii) Calibration (iv) Repeatability

Sensitivity Sensitivity may be defined as the rate of displacement of the indicating device of a instrument, with respect to the measured quantity. In other words, sensitivity of an instrument is the ratio of the scale spacing to the scale division value. For example, if on a dial indicator, the scale spacing is 1.0 mm and the scale division value is 0.01 mm, then sensitivity is 100. It is also called as amplification factor or gearing ratio.

If we now consider sensitivity over the full range o instrument reading with respect to measured quantities as shown in Fig., the sensitivity at any value of

dyy

dx where dx and dy are increments of x and y, taken over the full instrument

scale, the sensitivity is the slope of the curve at any value of y.

The sensitivity may be constant or variable along the scale. In the first case we get linear transmission and in the second non-linear transmission and in the second non-linear transmission. Sensitivity refers to the ability of measuring device to detect small difference in a quantity being measured. High sensitivity instruments may lead to drifts due to thermal or other effects, and indications of lower sensitivity. Readability Readability refers to the ease with which the readings of a measuring instrument can be read. It is the susceptibility of a measuring device to have its

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indications converted into meaningful number. Fine and widely spaced graduation lines ordinarily improve the readability. If the graduation lines are very finely spaced, the scale will be more readable by using the microscope, however, with the naked eye the readability will be poor. To make micrometers more readable they are provided with vernier scale. It can also be improved by using magnifying devices. Calibration: The calibration of any measuring instrument is necessary to measure the quantity in terms of standard unit. It is the process of framing the scale of the instrument by applying some standardized signals. Calibration is a premeasurement process, generally carried out by manufactures. It is carried out by making adjustments such that the read out device produces zero output for zero measured input. Similarly, it should display an output equivalent to the known measured input near the full scale input value. The accuracy of the instrument depends upon the calibration. Constant uses of instruments affect heir accuracy. If the accuracy is to be maintained, the instruments must be checked and recalibrated if necessary. The schedule of such calibration depends upon the severity of use, environmental conditions, accuracy of measurement required etc. as far as possible calibration should be performed under environmental conditions which are vary close to the conditions under which actual measurements are carried out. If the output of a measuring system is linear and repeatable, it can be easily calibrated. Repeatability, It is the ability of the measuring instrument to repeat the same results for the measurements for the same quantity, when the measurement are carried out

- by the same observer - With the same instrument - Under the same conditions. - Without any change in location.

Standards:- Line and End Measurements A length may be measured as the distance between two lines or as he distance between two parallel faces. So, the instruments for direct measurement of linear dimensions fall into two categories

1. Line standards 2. End standards Line standards. When the length is measured as the distance between

centres of two engraved lines, it is called line standard. Both material standards yard

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and metre are line standards. The most common example of line measurement is the rule with divisions shown as lines marked on it. Characteristics of Line Standard

1. Scales can be accurately engraved but the engraved lines them selves

possess thickness and it is not possible to take measurements with high accuracy.

2. A scale is a quick and easy to use over a wide range. 3. The scale markings are not subjected to wear. However, he leading ends

are subjected to wear and this may lead to undersize measurements. 4. A scale does not posses a ―built in ― datum. Therefore it is not possible to

align the scale with the axis of measurement. 5. Scales are subjected to parallax error. 6. Also, the assistance of magnifying glass or microscope is required if

sufficient accuracy is to be achieved. End standards: When length is expressed as the distance between two flat parallel faces, it is known as ends standard. Examples: Measurement by slip gauges, end bars, ends of micrometer anvils, vernier calipers etc. the end faces are hardened, lapped flat and parallel to a very high degree of accuracy. Characteristics of End Standards:

1. These standards are highly accurate and used for measurement of close tolerance in precision engineering as well as in standard laboratories, tool rooms, inspection departments etc.

2. They require more time for measurements and measure only one

dimension at a time. 3. They are subjected to wear on their measuring faces. 4. Group of slips can be ―wrung‖ together to build up a given size; faulty

wringing and careless use may lead to inaccurate results. 5. End standards have built in datum since their measuring faces are flat and

parallel and can positively locked on datum surface. 6. They are not subjected to parallax effect as their use depends on feel.

The accuracy of both these standards is affected by temperature change and

both are originally calibrated at 201

C.2 It is also necessary to take utmost case in

their manufacture to ensure that the change of shape with time, secular change is reduced to negligible.

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line and end standard measurements: Comparison between line standards and End Standards: Sr. No.

Characteristics

Line standard End standard

1. Principle Length is expressed as the distance between two lines

Length is expressed as the distance between two flat parallel faces

2. Accuracy

Limited to is 0.2 mm for high accuracy, scales have to be used in conjunction with magnifying glass or microscope.

Highly accurate for measurement of close

tolerances up to 0.001 mm.

3. Ease and time of and easy.

Measurement is quick and easy.

Use of end standard requires skill and is time consuming.

4. Effect of wear

Scale markings are not subject to wear. However, significant wear may occur on leading ends. Thus it may be difficult to assume zero of scale as datum.

These are subjected to wear on their measuring surfaces.

5. Alignment Cannot be easily aligned with the axis of measurement.

Can be easily aligned with the axis of measurement.

6. Manufacture and cost

Simple to manufacture at low cost.

Manufacturing process is complex and cost is high

7. Parallax effect

They are subjected to parallax error.

They are not subjected to parallax error.

8. Examples Scale (yard, metre etc.,) Slip gauges, end bars, V. caliper, micrometers etc.

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UNIT – II-LINEAR AND ANGULAR MEASUREMENTS

Measurement of Engineering Components Gauges are used mainly to check the Engineering Components produced on

mass scale, where the job is usually handled by semi-skilled workers. This type of measurement cannot be relied upon where accuracy is more important. The different methods and instruments used for precision & accurate (linear & angular) measurements are discussed in this unit. Comparator

It is a precision instrument employed to compare the dimension of a given component with a working standard (generally slip gauges). It does not measure the actual dimension but indicates how much it differs from the basic dimension (working standard). Uses of Comparator : For calibrating the working gauges Used as working gauges Used as final inspection gauges Essential characteristics of a good Comparator : Robust design and construction Linear characteristics of scale High magnification Quick in results Versatility Minimum wear of contact point Free from back lash Quick insertion of work piece Provision for compensation from temperature effects Provision for means to prevent damage during use. Classification of comparators 1) Mechanical comparator a) Dial indicator b) Johansson ‗Mikrokator‘ comparator c) Sigma comparator d) Reed type mechanical comparator 2) Optical comparator a) Zeiss Ultra optimeter b) Zeiss optotest comparator 3) Mechanical – Optical comparator 4) Electrical comparator 5) Fluid displacement comparator 6) Pneumatic comparator a) Back pressure comparator b) Flow – velocity Pneumatic comparator In addition, the comparators used in standards room for calibration of gauges are : 7) Brookes Level comparator 8) Eden-Rolt ‗Millionth‘ Comparator

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Basic principle of operation of comparator The comparator is first adjusted to zero on its dial or recording device with a

gauge block in position. The gauge block (slip gauges) is of dimension which the work piece should have. The work piece to be checked is then placed in position and the comparator gives the difference in dimension in relation to the gauge block. The dimension of the work piece may be less than, equal to, or greater than the standard dimension. The difference in the dimension will be shown in the dial or in the recording device of the comparator. Mechanical Comparators: Various mechanical comparators are discussed next. Dial indicator It is the simplest type of mechanical comparator. It consists of a base with a rigid column and an arm carrying dial gauge (dial indicator). The arm can be adjusted vertically up and down along the column. The arm can be swivelled and the dial gauge also can be locked in any position along its arm. The whole set up is placed on the surface place which is used as a datum surface. uses, characteristics and classification of a comparator. (i) Uses of Comparator The various ways in which comparators can be used are:

1. Laboratory Standards: Comparators are used as laboratory standards from which working or inspection gauges are sent and co-related.

2. Working Gauges: They are also used as working gauges to prevent work spoilage and to maintain required tolerance at all important stages of manufacture. 3. Final Inspection Gauges: Comparators may be used as final inspection gauges where selective assembly, of production parts is necessary.

4. Receiving Inspection Gauges: As receiving inspection gauges comparators are used for checking parts received from outside sources.

5. For checking newly purchased gauges: The use of comparators enables the checking of the parts (components in mass production at a very fast rate)

(ii) Essential characteristics of a good comparator

1. Robust design and construction: The design and construction of the comparator should be robust so that it can withstand the effects of ordinary uses without affecting its measuring accuracy.

2. Linear characteristics of scale: Recording or measuring scale should be linear and uniform (straight line characteristic) and its indications should be clear.

3. High magnification: The magnification of the comparator should be such that a smallest deviation in size of components can be easily detected.

4. Quick in results: The indicating system should be such that the readings are obtained in least possible time.

5. Versatility: Instruments should be designed that it can be used for wide range of measurements.

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6. Minimum wear of contact point. The measuring plunger should have hardened steel contact or diamond to minimize wear effects. Further the contact pressure should be low and uniform.

7. Free from oscillations: The pointer should come rapidly to rest and should be free from oscillations.

8. Free from back lash: System should be free from back lash and unnecessary friction and it should have minimum inertia.

9. Quick insertion of workpiece: Means should be provided for lifting the plunger for quick insertion of work.

10. Adjustable Table: The table of the instrument should, preferably, be adjustable in a vertical sense.

11. Compensation from temperature effects: The indicator should be provided with maximum compensation for temperature effects.

12. Means to prevent damage: Suitable means should be provided for preventing damage of the instrument in the event of the plunger moving through a greater distance than that corresponding to the range of its measuring scale.

(iii) Classification A wide variety of comparators are commercially available at present. They are classified according to the method used for amplifying and recording the variations measured into the following types.

1. Mechanical comparators 2. Optical comparators 3. Mechanical-Optical comparators 4. Electrical and Electronics comparators 5. Pneumatic comparators 6. Fluid displacement comparators 7. Projection comparators. 8. Multi check comparators 9. Automatic Gauging Machines 10. Electro-Mech. Comparators.

In addition to above, comparators of particularly high sensitivity and

magnification, used in standard rooms for calibration of gauge include. 1. The Brookes Level comparator 2. The Eden-Rolt‘millionth‘ comparator.

Slip Gauges

Slip gauges or gauge blocks are universally accepted end standard of length in industry. These were introduced by Johnson, a Sweedish engineer, and are also called as Johnson Gauges.

Slip gauges are rectangular blocks of high grade steel with exceptionally close tolerances. These blocks are suitably hardened though out to ensure maximum resistance to wear. They are then stabilized by heating and cooling successively in

24

stages so that hardening stresses are removed.

After being hardened they are carefully finished by high grade lapping to a high degree of finish, flatness and accuracy. For successful use of slip gauges their working face are made truly flat and parallel. A slip gauge are also made from tungsten carbide which is extremely hard and wear resistance.

The cross- sections of these gauges are 9mm 30mm for sizes up to 10mm and

9mm35mm for larger sizes. Any two slips when perfectly clean may be wrung together. The dimensions are permanently marked on one of the measuring faces of gauge blocks. Gauges blocks are used for:

(i) Direct precise measurement, where the accuracy of the work piece demands it.

(ii) For checking accuracy of venire calipers, micro metes, and such other measuring instruments.

(iii) Setting up a comparator to specific dimension. (iv) For measuring angle of work piece and also for angular setting in

conjunction with a sine bar. (v) The distances of plugs, spigots, etc. on fixture are often best measured

with the slip gauges or end bars for large dimensions. (vi) To check gap between parallel locations such as in gap gauges or

between two mating parts.

There are many measurements which can be made with slip gauges either alone or in conjunction with other simple apparatus such as straight edges, rollers, balls sine bars etc. Wringing of Slip Gauges

The success of precision measurement by slip gauges on the phenomenon of wringing. The slip gauges are wrung together by hand through a combined sliding and twisting motion. The gap between two wrung slips is only of the order of 0.00635

microns (0.63510-3mm) which is negligible. Procedure for Wringing

(i) Before using, the slip gauges are cleaned by using a lint free cloth, a chamois leather or a cleansing tissue.

(ii) One slip gauge is then oscillated slightly over the other gauge with a light pressure.

(iii) One gauge is then placed at 900 to other by using light pressure and then it is rotated until the blocks one brought in one line.

In this way is air is expelled out from between the gauge faces causing the gauge

blocks to adhere. The adhesion is caused partly by molecular attraction and partly by atmospheric pressure. When two gauges are wrung in this manner is exactly the sum of their individual dimensions. The wrung gauge can be handled as a unit

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without the need for clamping all the pieces together.

Indian Standard on Slip Gauges

According to IS: 2984-1966, the size of the slip gauges is defined as the distance l between two plane measuring faces, are being constituted by the surface of an auxiliary body with which one of the slip gauge faces is wrung and the other by the exposed face to the slip gauge faces is wrung and the other by the exposed face to the slip gauge. Generally the slip gauges are made from high grade steel with

coefficient of thermal expansion (11.5+1.5) 10-6 per degree Celsius between 10C to 300C. The slip gauges are hardened more than 800 HV to make them wear resistant. IS:2984 ‗ slip gauges‘ gives recommendations covering the manufacture of gauge blocks upto 90mm in length in five grades of accuracy. Grade II. Grade II gauge blocks are workshop grade for rough checks. They are used for preliminary setting up of components where production tolerances are relatively wide; for positioning milling cutters and checking mechanical widths. Grade I. Grade I gauge blocks are used fro more precise work such as setting up since bars, checking gap gauges and setting dial test indicators to zero. Grade 0. These are inspection grade gauge blocks, used in tool room and inspection department for high accuracy work. Grade OO. These gauges are placed in the standard room and used for highest precision work. Such as checking Grade I and Grade II slip gauges. Calibration Grade. This is a special grade, with the actual size of the slips calibrated on a special chart supplied with a set. The chart must be referred while making up dimension. The following two sets of slip gauges are in general use: Normal set (M-45)

Range (mm), Step (mm)

Pieces

1.01 to 1.009 1.01 to 1.09 1.1 to 1.9

1 to 9 10 to 90

0.001 0.01 0.1 1 10

9 9 9 9 9

Total 45 Pieces

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Special set (M-87)

Range (mm) Step (mm) Pieces

1.001 to 1.009 1.01 to 1.09

0.5 to 0.5 10 to 90 1.005

0.001 0.01 0.5 10 -

9 49 19 9 1

Total 87 Pieces

The other sets available in metric units are: M112,M105,M50,M33 and M27. The sets M112 and M33 are as follows.

Set M112

Range (mm) Step (mm) Pieces

1.001 to 1.00 1.01 to 1.49 0.5 to 24.50 25 to 100

1.005

0.001 0.01 0.05 25 -

9 49 49 4 1

Total 112 Pieces

Set M33/2(2mm based set

Range (mm) Step (mm) Pieces

2.005 2.01 to 2.09 2.10 to 2.90

1 to 9 10.30

60 100

- 0.01 0.1 1 10 - -

1 9 9 9 3 1 1

Total 33 Pieces

different types of limit gauges: Limit Gauges: Limit gauges are very widely used in industries. As there are two permissible limits of the dimension of a part, high and low, two gauges are needed to check each dimension of the part, one corresponding the low limit of size and other to the high limit of size of that dimension. These are known as GO and NO-GO gauges.

The differences between the sizes of these two gauges is equal to the tolerance on the work piece. GO gauges check the Maximum Metal Limit (MML) and NO-GO gauge checks the minimum metal limit (LML). In the case of hole, maximum metal limit is when the hole is as small as possible, that is, it is the low limit of size. In case of hole, therefore, GO gauge corresponds to the low limit of size, while NO- GO gauge corresponds to high limit of size. For a shaft, the maximum metal limit is when the shaft is on the high limit of size. Thus, in case of a shift GO gauge corresponds

27

to the high limit of size and NO-GO gauge corresponds to the low limit size.

While checking, each of these two gauges is offered in turn to the work. A part is considered to be good, if the GO gauge passes through or over the work and NO-GO gauge fails to pass under the action of the part ;is within the specified tolerance. If both the gauges fail to pass, it indicates that hole is under size or shaft is over size. If both the gauges pass, it means that the hole is over size or the shaft is under size.

Limit Plug Gauges

Gauges used for checking the holes are called ―Plug gauges‖. The ‗GO‘ plug gauge is the size of the low limit of the hole while ‗NO-GO‘ plug gauge is the size of the high limit of hole. Types of Plug Gauges

1. Solid type. For sizes up to 10mm. (Refer Fig. 9.17)

2. Renewable type (Taper inserted type). For sizes over 10mm and up to 30mm.

(Refer Fig. 9.18)

3. Fastened type:

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(a) Double – ended: For sizes over 30mm and up to 63mm (b) Single-ended: For sizes over 63mm and up to 100mm (Refer Fig.

9.20).

4. Flat type. For sizes over 100mm and up to 250mm. (Refer Fig. 9.22).

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5. Progressive type. For relatively short through hole. It has both the ends on one side of the gauge as shown in Fig. 9.21.

6. Pilot Plug gauge. To avoid jamming of the plug gauge inside of the hole pilot groove type gauge (Fig. 9.25) may be used. In pilot plug gauge there is first a small chamber, then a narrow ring or pilot-its diameter being equal to that of

30

the body of the gauge, the pilot is of the nature of an ellipse in respect to the hole. It touches at two points across the major axis which is the diameter of the plug on entering the hole. If the pilot enters the hole it is sufficiently large for the rest of the gauge to enter. The chamber behind the pilot lifts the gauge into link, making jamming impossible. The advantages of such a gauge are that the operator can work even with less care and there is saving in time.

Pilot Plug Gauge

7. Combined dual purpose limit gauge. Combined plug gauge combines both the GO and NO-GO dimensions in a single member. Thus a single gauge may be used to check both the upper and lower limits. It consist of a spherical end A of the diameter equal to the lower limit. A spherical projection B of the outer edge of the spherical member (Refer Fig. 9.26) is arranged so that the spherical surface B and the diametrically opposite part on the spherical surface is equal to the maximum limit.

For checking the hole by combined limit gauge, for ‗GO‘ limit the gauge is inserted

into the hole with the handle parallel to the axis of the hole. For checking the hole the ‗NO- GO‘ limit, the gauge is tilted so that the spherical projection B is normal to the hole. The gauge in this position should not enter the hole.

The plug gauges are marked with the following on their handles for their identification:

(i) Nominal size, (ii) Class of tolerance (iii) The word Go on the Go side

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(iv) The words NOGO (or Not- Go) on the Not-Go side (v) The actual value of the tolerance (vi) Manufacturer‘s trade mark. (vii) A red colour band near the Not-Go end to distinguish in from the Go-end.

Snap, Gap or Ring Gauges

Snap gauges, Gap gauges or Ring gauges are used for checking the shafts or male components. Snap gauges can be used for both cylindrical as well as non-cylindrical work or compared to ring gauges which are conventionally used only for cylindrical work. To Go snap gauge is the size corresponding to the high limit of the shaft, while the ‗NO GO‘ gauge corresponds to the low limit. Double – ended snap gauges can be conveniently used for checking sizes from 3 mm to 100mm and single- ended progressive type snap gauges are suitable for sizes from 100mm to 250mm. The gauging surfaces of the snap gauges are hardened up to 750 HV and are suitably stabilized, ground, and lapped. Ring gauges are available in two designs, ‗GO‘ and ‗NO-GO‘. These are designated by ‗GO‘ and ‗NO-GO‘ as may be applicable, the nominal size, the tolerance of the work piece to be gauged, and the number of the standard allowed.

Adjustable Type Gap Gauges

In case of fixed gap gauges, no change can be made in the size, range, whereas in adjustable gauges the gauging anvils are adjustable endwise in the horse-shoe frame. Thus, a small change within about 0.002mm can be made in the size range. For example, suppose gauge is used to check a 50mm for shaft. If for some reason the tolerance is changed to, say, a tolerance grade of f8 or f6, the same gauge can be used after adjustment. Also the anvils of such gauges can be reset with the help of slip gauges, by means of independent and finely threaded screws provided at the back end. After resetting they can be finally locked in position by means of clamping screw. Fixed gauges are less expensive initially, but they do not permit adjustment to

32

compensate for wear and can also be used over a small range of different setting.

Fig9.29 Fig9.30 Fig.9.31

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Fig.9.32 Taylor‟s Principle of Gauge Design:

It state that (1) GO gauges should be designed to check the maximum material limit, while the NO-GO gauges should be designed to check the minimum material limit.

Now, the plug gauges are used to check the hole, therefore the size of the GO plug gauge should correspond to the low limit of hole, while that of NO-GO plug gauge corresponds to the high limit of hole.

Similarly, the ‗GO Snap gauge‘ on the other hand corresponds to the high limit of shaft, while ‗NO-GO Snap‘ gauge corresponds to the low limit of shaft.

The difference in size between the GO and NOGO plug gauges, as well as the difference in size between GO and NO-GO Snap gauges is approximately equal to the tolerance of the tested hole or shaft in case of standard gauges.

(2) ‗GO‘ gauges should check all the related dimensions (roundness, size, location etc). Simultaneously whereas ‗NO-GO‘ gauge should check only one element of the dimension at a time.

According to this rule, GO plus gauge should have a full circular section and be of full length of the hole it has to check. This ensures that any lack of straightness, or

34

roundness of the hole will prevent the entry of full length GO-plug gauge. If this condition is not fulfilled, the inspection of the part with the gauge may give wrong give wrong results.

For example, suppose the bush to be inspected has a curved axis and a short ‗GO‘ plug gauge is used to check it. The short plug gauge will pass through all the curves of the bent bushing. This will lead to a wrong result that the work pieces (hole) are within the prescribed limits. Actually, such a bushing with a curved hole will not mute properly with its mating part and thus defective. A GO plug gauge with adequate length will not pass through a curved bushing and the error will be detected. A long plug gauge will thus check the cylindrical surface not in one direction, but in a number of sections simultaneously. The length of the ‗GO‘ plug gauge should not be less than 1.5 times the diameter of the hole to be checked.

Fig. 9.34

Now suppose the hole to be checked has an oval shape While checking it with the cylindrical ‗NOT GO‘ gauge the hole under inspection will over lap (hatched portion) the plug and thus will not enter the hole. This will again lead to wrong conclusion that the part is within the prescribed limits. It will be therefore more appropriate to make the ‗NOT GO‘ gauge in the form of a pin as shown in Fig. 9.35. The Johansson Mikrokator This instrument was first devised by m/s C.F. Johansson and hence the name. It uses a twisted strip to convert small linear movement of a plunger into a large circular movement of a pointer. It is therefore, also called as twisted strip comparator. It uses the simplest method for obtaining the mechanical magnification designed by H.Abramson which is known as ‗Abramson, movement‘. A twisted thin metal strip carries at the centre of its length a very light pointer made of thin glass. One end of the strip is fixed to the adjustable cantilever strip and the other end is anchored to the spring elbow, one arm of which is carried on measuring plunger. The spring elbow acts as a bell crank lever. The construction of such a comparator is shown in Fig.5.2.

35

Fig.5.2.Johansson Mikrokator F.g.5.3 Twisted strip of Mikrokator

A slight upward movement of plunger will make the bell crank lever to rotate. Due to this a tension will be applied to the twisted strip in the direction of the

arrow. This causes the strip to untwist resulting in the movement of the point. The spring will ensure that the plunger returns when the contact pressure between the bottom tip of the plunger and the workpiece is not there, that is, when the workpiece is removed from underneath the plunger.

The length of the cantilever can be varied to adjust the magnification. In order

to prevent excessive stress on the central portion, the strip is perforated along the centre line by per formation as shown in Fig.5.3. The magnification of the instrument is approximately equal to the ratio of rate of change of pointer movement to rate of

change in length of the strip, i.e., dQ

dL. It can be shown that the magnification of the

instrument 2

,dQ L

dL n

Where, Q = twist of mid point of strip with respect to the end L = length of twisted strip measured along its

neutral axis

= width of twisted strip and, n = number of turns

It is thus obvious that in order to increase the magnification of the instrument a very thin rectangular strip must be used. Reed Type Mechanical Comparator In reed type mechanical comparator, the gauging head is usually a sensitive, high quality, dial indicator. The dial indicator is mounted on a base supported by a sturdy column. Fig.5.4 shows a read type mechanical comparator.

36

The read mechanism is frictionless device for magnifying small motions of the spindle. It consists of a fixed block. A which is rigidly fastened to the gauge head case, and floating block B, which carries the gauging spindle and is connected horizontally to the fixed block by read C.

A vertical reeds are indicated by D. Beyond this joint extends a pointer. A linear motion of the spindle moves the free block vertically causing the vertical reed on the floating block to slide past the vertical reed on the fixed block. However, as the vertical reeds are joined at the upper end, instead of slipping, the movement causes both reeds swing through an arc. The scale may be calibrated by means of gauge block to indicate any deviation from an initial setting. The mechanical amplification is usually less than 100 but it is multiplied by the optical lens system. It is available in amplification ranging from 500 to 1000. Sigma comparator This is a mechanical comparator providing magnification in the range of 300 to 5000. It consists of a plunger mounted on two flat steel strings

Fig.5.5 Sigma of comparator

37

This is a mechanical comparator providing manificaton in the range of 300 to

5000. it consists of a plunger mounted on two flat steel string (diaphragms) this provides a frictionless linear movement for the plunger. The plunger carries a knife edge, which bears upon the face of the mounting block of a cross-strip hinge. The cross strip hinge is formed by pieces of flat steel springs arranged at right angle and is a very efficient pivot for smaller angular movements. The moving block carries a might metal Y-forked arms. A thin phosphor bronze ribbon is fastened to the ends of the forked arms and wrapped around a small drum, mounted on a spindle carrying the pointer. Any vertical displacement of the measuring plunger and hence that of the knife edge makes the moving block of the cross strip liver to pivot. This causes the rotation of the Y-arms. The metallic band attached to the arms makes the driving drum and hence the pointer to rotate.

The ratio of the effective length (L) of the arm and the distance (a) of the knife edge from the pivot gives the first stage magnification and the ratio of the pointer length (l) and radius ( r ) of the driving drum gives second stage magnification of the

instrument. Total magnification of the instrument is thus L l

a r

. The magnification

of the instrument can be varied by changing the distance (a) of Knife edge of tightening or slackening of the adjusting screws: The range of instruments available provides magnifications of x 300 to X 5000, the most sensitive models allowing scale estimation of the order of 0,0001 mm to be made. Some important features (advantages) of the sigma comparator are:

1. Safety: As the knife edge moves away from the moving member of the hinge and is followed by it, therefore, if too robust movement of plunger is made due to shock load, that will not be transmitted through the movement.

2. Dead beat Readings: By mounting a nonferrous disc on the pointer spindle and making it move in field of a permanent magnet, dead beat reading can be obtained.

3. Parallax: The error due to Parallax is avoided by having a reflective strip on the scale.

4. Constant pressures: The constant measuring pressure over the range of the instrument is obtained by the use of magnet plunger. On the frame

5. Fine adjustments are possible

Disadvantages: 1. Due to motion of the parts there is a wear in the moving parts. 2. It is not sensible as optical comparator due to friction of the moving parts.

Fig.5.6 cross strip liver used in sigma comparator.

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Advantages of Mechanical comparators

1. Cheaper, Mechanical comparators are less costly as compared to other amplifying devices.

2. No need of external agency. These instruments do not require any external agency such as electricity or air and as such the variations in outside supply do not affect the accuracy.

3. Linear Scale. Usually the mechanical comparators have linear scale. 4. Robust and compact: These instruments are robust and compact in design

and easy to handle. 5. Portable: For ordinary workshop conditions, these instruments are very

suitable and being portable can be issued from the stores. Disadvantages of Mechanical Comparators

1. Less accuracy (a) Due to more moving parts, the friction is more which reduces the accuracy.

2. Sensitive to vibrations: The mechanisms in mechanical comparators have more inertia and this may cause them to be sensitive to vibrations.

3. Faults magnified: Any wear backlash or dimensional faults in the mechanical devices used will also be magnified.

4. Limited range: The range of the instrument is limited as the pointer moves over a fixed scale.

5. Parallax error: Error due to Parallax are more likely with these instruments as the pointer moves over a fixed scale.

Electrical Comparators: Principle: These comparators depend on their operation on an A.C. Whetstone bridge circuit incorporating a galvanometer. In these comparators, the movement of the measuring contact is converted into an electrical signal. This electrical signal is recorded by an instrument which can be calibrated in terms of plunger movement.

Fig.5.11 Principle of electrical comparator

The principle of an electrical comparator is shown in Fig.5.11. An armature supported on thin steel strips is suspended between two coils A and B. When the

39

distance of the armature surface from the two coils is equal, the Whetstone bridge is balanced and no current flows through its galvanometer. Sight movement of the measuring plunger unbalances the bridge resulting in the flow of current through the galvanometer. The scale of the galvanometer is calibrated to give the movement of the plunger. Electrical comparators have minimum moving parts and therefore give a high degree of reliability. Magnification of the order of X30,000 are possible with these comparators. Visual Gauging Heads The purpose of the visual gauging heads is to give visual inspection using small coloured signal lamps, of the acceptability of an engineering component with regard to the dimension under test. Clearly an electrical principle is involved, which may be simply described, as follows, with reference to Fig.5.12. Vertical displacement of an interchangeable plunger causes movement of the rod C either to the left or right, as shown in the figure A and B are electrical contacts, capable of precise adjustment in the direction of the arrows, a micrometer device is available. In the position shown, that is to say with the rod in mid position between the contacts A and B, the dimension under test is within the limits. If the dimension is oversize, the rod C moves to the right and makes contact with B. Immediately the top red lamp is illuminated. Likewise if the dimension is undersize the rod moves to left, making contact with A and illuminating the yellow lamp. It may, however, be noted that the actual magnifying device is not shown in the figure; levers and thin steel strips, together with knife-edge seatings, are employed.

With various detachable plungers, there is practically no limit to the

application of this instrument. Fig.5.12 illustrates the visual gauging of a single dimension, but the same principle can be applied in measuring the several dimensions simultaneously.

Fig.5.12. Visual gauging head

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Advantages of electrical comparators:

1. Few number of moving parts: The electric and electronic comparators have few number of moving parts, and there is less friction and wear.

2. High magnification: It has a wide range of magnification. 3. Not sensitive to vibrations: The mechanism carrying the pointer is very light

and not sensitive to vibrations. 4. Easy to set up and operate. 5. Less error due to sliding friction: operation of the instrument on AC supply

reduces sliding friction errors. 6. The instrument is small and compact. 7. The indicating instrument need not be placed close to the measuring unit.

(ii) Disadvantages:

1. Fluctuation in the voltage or frequency of the electric supply may affect the results.

2. Heating of coils in the measuring unit may cause zero drift and alter the calibration.

3. When measuring unit is remote from the indicating unit, reliability is lower. 4. Cost is generally more than mechanical comparator. 5. If only a fixed scale is used with a moving pointer than with high magnification

a very small range is obtained. Solex pneumatic Gauges This instrument was commercially introduced by solex Air Gauges Ltd. It is generally designed for internal measurement, but with suitable measuring head it can be used for external gauging also.

Fig.5.15 Solex Pneumatic Gauge It uses a water manometer for the indication of back pressure. It consist of a vertical metal cylinder filled with water upto a certain level and a dip tube immersed into it upto a depth corresponding to the air pressure required. A calibrated manometer tube is connected between the cylinder and control artifice as shown in Fig.5.15. If the pressure of the air supplied is higher than the desired pressure, some air will bubble out from the bottom of the dip tube and air moving to the control volume will be at the desired constant pressure. The constant pressure air then

41

passes through the control orifice and escape from the measuring jets when there is no restriction to the escape of air, the level of water in the manometer tube will coincide with that in the cylinder. But, if there is a restriction to the escape of air through the jets, a back pressure will be induced in the circuit and level of water in the manometer tube will fall. The restriction to the escape of air depends upon the variations in the dimensions to be measured. Thus the variation in the dimension to be measured are converted into corresponding pressure variations, which can be read from the calibrated scale provided with the manometer. To find concentricity (roundness of any job at any section).the workpiece may be revolved around measuring gauge. If no change in reading is there, then it is perfectly round hole. Similarly the diameter can be noted down at several places along the length of bore and thus tapering of hole is determined. This is method is therefore, best suited for measuring roundness and taper ness of cylinder bases and gun barrel bores. Differential Comparator It is the balanced circuit type of air gauge. Fig.5.16 shows a differential comparator. Compressed air from a suitable source, after passing through air-drier and filter is regulated for constant pressure by a pressure regulator. The air flows into two channels each of which has control orifice O1 and O2. From the control artifice O1, air flows to the measuring head where it meets further restriction of workpiece or the master setting. The restriction of the workpiece builds up back pressure. At the same time, other half of the air is flowing through the other control orifice O2 to the reference jet on. By closing or opening the valve of reference jet Om, the pressure in the space between O2 and Om is regulated codjusted to match the back pressure from the measuring jets, which is sensed by the pressure indicating device fitted across the two channels as shown. At this adjustment of the reference jet, the preference indicator would indicate equal pressure in the two channels and hence read zero on the scale. The zero setting (adjusting of reference jet Om) is done with master workpiece whose dimension is exact nominal size.

Fig. 5.16 Differential circuit.

Now, the variation of the dimension at the measuring head will cause change

42

of back pressure in channel A. This pressure will be different from the mean pressure which has been already set in the channel B (by reference jet. Now the difference of pressure of the two channels will be indicated device which can be directly calibrated in terms of variation of dimension from the mean dimensions. The instrument is thus based on the measurement of differential pressure and is called as differential comparator. Advantages of pneumatic Comparators

1. It is possible to obtain high degree of magnification (30,000 : 1) or more coupled with good stability and readability.

2. The gauging member does not come in contract with the part to be measured and hence practically no wear takes place on gauging member.

3. It has few number of moving parts and in some cases none. Thus the accuracy obtainable is more due to absence of friction and less inertia.

4. Measuring pressure is very small and the jet of air helps in cleaning the dust, if any, from the part to be measures.

5. The indicating instrument can be remote from the measuring unit. 6. It is very suitable for measuring diameter of holes whose the diameter is small

compared with the length. 7. It is probably the best method to determine the loyalty and taperness of

circular holes. Disadvantages:

1. Limited range of measurement is available with these comparators. 2. It gives low speed of response compared with electrical magnification system. 3. It requires elaborate auxiliary equipment such as accurate pressure regulator. 4. The scale is generally not uniform. 5. When indicating device is the glass tube, then high magnification is necessary

in order to avoid the meniscus errors. 6. The apparatus is not easily portable. 7. Different gauging heads are required for different dimensions.

Sine bar 1. Locating any work to a given angle: To set the given angle, the surface plate is assumed to be perfectly flat, so that the surface can be treated as horizontal. One roller of the sine bar is placed on the surface plate and a combination of slip gauges is inserted under the second roller. Let, h be the height of slip gauge combination

and the sine is to be set at an angle .

Then sin = h/l, where l is the distance between the centre of the rollers.

Thus knowing , h can be found out and any work could be set at this angle, as the

top face of the sine bar is inclined at angle to the surface plate. For better results, both the rollers could also be placed on slip gauges of height h1 and h2 respectively,

2 1sinh h

l

43

Fig.6.9 SINE BAR

Checking or measuring unknown angle: (a) When component is of small size. For measuring unknown angle it is necessary to first find the angle approximately with the help of a bevel protractor. The sine bar is then set up at that nominal (approximate) angle on a surface plate by suitable combination of slip gauges. The component to be checked is placed over the surface of the sine bar (if necessary the component may be clamped with the angle plate). The dial gauge is then set at one end of the work and moved along the upper surface of the component. If there is a variation in parallelism of the upper surface of the component and the surface plate, it is indicated by the dial gauge. The combination of the slip gauges is so adjusted that the upper surface of the component is truly parallel with the surface plate.

Fig.6.10

The angle of the component is then calculated by the relation 1sinh

L

The perfect adjustment of slip gauge combination requires too much time, so the variation in the parallelism of the upper surface of the component and the surface plate indicated by the dial gauge is converted into corresponding angular variation. If ‗dx‘ is the variation in parallelism over a distance ‗x‘ the corresponding variation in

angle 1sinh

L

b. When the component is of large size/heavy. In such cases, the component is placed over a surface plate. The sine bar is placed over the component as shown in Fig.6.11. The height over the rollers can then be measured by a vernier height gauge; using a dial test gauge mounted on the anvil of height gauge to ensure constant measuring pressure.

44

The anvil of height gauge is adjusted with probe of dial test gauge showing same reading for the topmost position of rollers of sine bar. The height gauge is thus used to obtain two readings for either of the rollers of sine bar. If ‗h‘ is the difference in the heights and T distance between the roller centres of the sine bar, then

1sinh

L

.

Another method of determining angle of large size part is shown Fig.6.12. The component is placed over a surface plate and the sine bar is set up at approximate angle on the component so that its surface is nearly parallel to the surface plate. A dial gauge is moved along the top surface of the sine bar to note the variation in parallelism. If ‗h‘ is height of the combination of the slip gauge and ‗dh‘ the variation in parallelism over distance ‗L‘ then,

1sinh

L

Fig.6.12 Iimitations of Sine Bars (i) Sine bar is fairly reliable for angles less than 15o, and becomes increasingly

inaccurate as the angle increases. It is impractical to use sine bars for angle above 45o.

(ii) It is physically clumsy to hold in position. (iii) Slight errors of the sine bar cause larger angular errors. (iv) A difference of deformation occurs at the point of roller contact with the surface

plate and to the gauge blocks. (v) The size of parts which can be inspected by since bar is limited. Sources of Error in Sine Bars The difference sources of errors in angular measurement by a sine bar are:

1. Error in distance between roller centres.

45

2. Error in slip gauge combination used for angle setting. 3. Error in parallelism between gauging surface and plane of roller axes. 4. Error in equality of size of rollers and cylindrical accuracy in the form of the

rollers. 5. Error is parallelism of roller axes with each other. 6. Error in flatness of the upper surface of the bar.

Modifications of sine bar: Sine Centre: Due to difficulty of mounting conical work easily on a conventional sine bar, sine centres are used. Two blocks as shown in Fig.6.13 are mounted on the top of sine bar. These blocks accommodate centres and can be clamped at any position on the sine bar. The centres can also be adjusted depending on the length of the conical work-piece, to be held between centres. Sine centres are extremely useful for the testing of conical work, since the centres ensure correct alignment of the work-piece. The procedure for its setting is the same as that for sine bar.

Fig.6.13 Sine Table: The sine table is the most convenient and accurate design for heavy work-piece. The equipment consist of a self-contained sine bar, hinged at one roller and mounted on its datum surface. The table is quite rigid one and the weight of unit and work-piece is given fuller and safer support. The table may be safety swing to any angle from 0 to 900 by pivoting it about it hinged end. Due to the work being held axially between centres, the angle of inclination will be half the included angle of the work. The use of since centres and sine table provides a convenient method of measuring the angle of a taper plug gauge.

46

Angle Dekkor. This is a type of auto-collimator. It consists of microscope, objective (collimating) lens and two scales engraved on a glass screen which is placed in the focal plane of the objective lens. One of the scales, called datum scale, is horizontal and fixed. It is engraved across the centre of the screen and is always visible in the microscope eye-piece. Another scale is an illuminated vertical scale fixed across the centre of the screen and the reflected image of the illuminated scale is received at right angles to this fixed scale, and the two scales, in the position intersect each other. Thus the reading on illuminated scale measures angular deviations from one axis at 90o to the optical axis, and the reading on the fixed datum scale measures the deviation about an axis mutually perpendicular to the other two.

Figure. Angle dekkor

Thus, the changes in angular position of the reflector in two planes are indicated by changes in the point of intersection of the two scales. Readings from scale are read direct to 1‘ without the use of a micrometer.

47

Uses of angle dekkor in combination with angle gauges:- (i) Measuring angle of a component:- It may be made clear that angle dekkor is capable of measuring small variations in angular setting, i.e. determining angular tilt. In operation the measuring principle is that of measurement by comparison; the angle dekkor is set to give a fixed reading form a known angle (i.e. using known angular standards to obtain a zero reading). (Refer Figure) Thus first the angle gauge combination is set up to the nearest known angle of the component and the angle dekkor is set, (using special attachment and link), such that zero reading is obtained on the illuminated scale. The angle-gauge build up is then removed and replaced by the component under test, a straight-edge being used to ensure that there is no change in lateral positions. The new position of the reflected scale with respect to the fixed scale gives the angular tilt of the component from the set angle (Refer Figure).

Figure. Measuring angle of a component.

48

(ii) To obtain precise angular setting for machining operations.

We will consider an example of milling a slot at a precise angle to a previously machined datum face. A parallel bar is used as a datum face, the component being securely clamped when in close contact with it parallel bar is positioned on the table of milling machine with the aid of angle dekkor. The setting-up technique is illustrated in Figure. Wit the aid of this surface as reference, the angle dekkor is set up such that zero reading is obtained; in other words, the axis of the optical beam is truly at 90o to the table feed. Then build up the combination of angle gauges to the exact

value , i.e. the inclination of the slot to the milled on the component. The angle gauges along with the parallel bar are placed on the table and adjusted in position such that the angle dekkor shows zero reading when viewing the flat surface of the angle gauge combination. It means that the angular inclination between the datum

face of the parallel bar and the feed direction of the table is now o. The parallel bar is firmly clamped in this position, a check being made to ensure that no movement has taken place during clamping; a few gentle taps will soon allows a zero reading on the angle dekkor to be regained. Finally, now the workpiece can be clamped on milling machine table, in closed contact with this pre-set parallel bar. (iii) Checking the sloping angle of a V-block:- The set up for checking the sloping angle of V-block is illustrated in Figure. The principle consists of comparing the reading obtained from the polished slip gauge in close contact with the work-surface, and a zero reading obtained from the angle-gauge build-up.

Figure

49

(iv) To measure the angle of cone or taper gauge:- A simple set-up for this purpose is shown in Figure. The instrument is first set for the nominal angle of cone on a combination of angle gauges or on a sine bar set to the nominal angle. The cone is then placed in position with its base resting on the surface plate. A slip gauge or other parallel reflector is held against the conical surface as no reflection can be obtained fro ma curved surface. Any deviation from the set angle will be noted by the angle dekkor in its eye-piece and indicated by the shifting of image of illuminated scale, whose reading while setting with angle gauge is noted down before hand. Vernier Bevel Protractor:- Vernier bevel protractor is the simplest angle measuring instrument. It consists of

1. Main body 2. Base plate stock 3. Adjustable blade 4. Circular plate containing Vernier scale 5. Acute angle attachment

Figure shows a Vernier bevel protractor with acute angle attachment. The body of the Vernier Bevel protractor is designed in such a way that its back is flat and there are no projections beyond its back. The flatness of the body is tested by checking the squareness of blade with respect to base plate when the blade is set at 90o.

Figure. Vernier Bevel Protractor The base plate is attached to the main body, and an adjustable blade is attached to a circular plate containing Vernier scale. The main scale graduated in degrees is provided on the main body. The adjustable blade is capable of rotating freely about the centre of the main scale engraved on the body of the instrument can be locked in any position. An acute angle attachment is provided at the top as shown in the figure for measuring acute angles. The base of the base of the base plate is made flat so that it could be laid flat upon the work and any type of angle measured. The blade can be moved along throughout its length and can also be reversed. It is about 150 or 300 m long, 13 mm wide and 2 mm thick. Its ends are

50

beveled at angles of 45o and 60o. The acute angle attachment can be readily fitted into the body and clamped in any position. The bevel protractors are tested for flatness, squareness, parallelism, straightness, etc.

Figure. The principle of the vernier protractor As shown in Figure the main scale is graduated in degrees of arc. The Vernier scale has 12 divisions each side of the centre zero. These are marked 0-60 minutes of arc, so that each division equals 1/12 of 60, that is 5 minutes of arc. These 12 divisions occupy the same space as 23 degrees on the main scale. Therefore, each

division of the Vernier is equal to : 1

12 of 23o or

111

12.

Since two divisions on the main scale equals 2 degrees of arc, the difference between two divisions on the main scale equals 2 degrees of arc, the difference between two divisions on the main scale and one division on the vernier scale is 2o -

111

12 =

1

12

o or 5 minutes of arc.

Uses of the Vernier Bevel Protractor Figure shows the various uses of bevel protractors.

Figure (a) Use of bevel protractor for checking inside beveled face of a ground

surface.

51

Figure(b)Use of bevel protractor for checking „V‟ block (c) Use of Vernier protractor for measuring acute angle

Taper Measurement Use of Precisions Balls and Rollers:- Precision balls and rollers are used to determine both linear and angular dimensions in conjunction with gauge blocks. These are made of good quality steel and are hardened and tapered. The length for the roller is equal to the diameter. The balls and rollers are available in sizes ranging from 1 to 25 mm diameter. The use of precision balls and rollers for determining both linear and angular dimensions is explained with the held of following examples: 1. Angle of the right – tapered piece can be measured by using two rollers of different sizes, slip gauges and a dial indicator. The two rollers whose diameters are known and slip gauges are placed on a surface plate as shown in Figure. The rollers (discs) may be clamped in position against an angle plate by c- clamps. The work is then placed on top of rollers and clamped against the angle plate by C-clamp. If the angle of the piece is all right, then the top edge will be parallel to surface plate and the dial indicator will show no variation when traversed along its surface.

Figure

With reference to Figure from triangle O1 A O2

52

tan /2 =

2 1

1

1 22

2 2

12 2

d dO A

d dAO

i.e., tan /2 = 2 1

1 22

d d

l d d

…(i)

Where l = length of slip gauge pile and d1 and d2 are diameters of rollers. From equation (i) the slip gauge length

L =

2 1

1 22

tan / 2 2

d dd d

…(ii)

Thus, initially the length of the slip gauges is calculated by the above equation and the rollers are placed just in contact with the slip gauges. Checking the angle of taper using rollers, micrometer and slip gauges.

Figure Figure shows the method of checking the angle of a taper plug gauge using rollers, micrometer and slip gauges. Taper plug is placed on a surface plate. First two rollers of equal diameters are placed toughing on the opposite sides of the lower surface of the plug on the slip gauge combinations of equal heights (H1). The distance (M1) between the ends of the roller is measured with a micrometer. Then the rollers are placed on slip gauge combinations of height (H2) touching on the opposite sides of the top portion of the plug. The distance (M2) between the ends of the roller in this new position is again measured by means of micrometer. The half the taper angle of the plug is then calculated as follows: If d = diameter of roller, then

53

2 1

2 1

2 1

2 1

2 2tan

2/ 2

2

,

M tan /2=

2

M d M d

dH d H

thus

M

H H

To check the angle of a taper hole. Figure shows the arrangement for checking the internal taper of a taper ring gauge using two precision balls of different sizes. The taper ring gauge is placed on a surface plate and a small ball of radius ‗r1‘ is inserted in the ole close to the small end of the taper. Two piles of slip gauges of equal heights are then placed on the surface plate on either sides of tapered ring gauge. A depth micrometer is then used to determine the distance from the top face of the gauge blocks to the surface of the precision ball. Then, a bigger ball of radius r2 is placed in the hole near the big end of taper, and the distance from the top face of the gauge blocks to the surface of the bigger precision ball is determined with the depth micrometer. From Figure.

Figure

O2O1S = /2

Where = angle of tapered hole

2

1 2

0sin / 2

0 0

S

54

2 2

1 2

2 1 2 1

2 2 1 1 2 1 2 1

distance of balls (0 0 )

r r

centre

r r r r

h r h r h h r r

Measuring of included angle of an internal dovetail Dovetail slides are widely used in machine tool construction. The sloping sides of dovetail slide act as guide and prevent the lifting of the female mating part during sliding operation. This angle can be measured by using two rollers of equal size, slip gauges and a micrometer. The two rollers of equal diameters are placed, one each at the two corners and distance l1 is measured across the rollers with a micrometer. Then the rollers are placed on two sets of equal size slip gauge blocks and the distance l2 is measured. It should be noted that the rollers do not extend above the top surface of dovetail. Let the height of slip gauges be h, then

tan 2 1

2

l l

h

.

Measuring External Dovetail Slide

Figure shows an external dovetail slide with angle of dovetail . To check the

width of opening as shown in figure, two rollers of equal diameter d are placed one each in the two corners. Then the length l is obtained by trail and error with the help

of slip gauges or end bars if l I greater than 250 mm. Then the width ‗‘ can be calculated by the relation:

= l + d + d cot /2

Figure

55

use of sine bar for measurement of taper plug gauge:

Figure

Figure illustrates the use of sine bar for measurement of angle of a taper plug gauge. The sine bar is set up on a surface plate to the nominal angle of the taper plug gauge and clamped to an angle plate. Taper plug gauge is placed on the sine bar and prevented from slogging down by a stop plate. The axis of the taper plug gauge is aligned with the bar axis. A dial gauge, supported in a stand is set at one end of the plug gauge and moved to the other end, and the difference in the readings is noted. Let ‗dx‘ be the difference in the readings of the dial gauge over a distance ‗x‘. Let ‗h‘ be the height of the combination of the slip gauges used and ‗L‘, distance between the roller centres.

Then, nominal angle = sin-1 h

L

and variation in the angle,

1sindx

dx

Therefore, actual angle of the taper plug gauge,

= d = sin h

L

1indx

sx

56

UNIT – III-ADVANCES IN METROLOGY

Errors in threads : In the case of plain shafts and holes, there is only one dimension which has to be considered (i.e diameter) and errors on this dimension if exceed the permissible tolerance, will justify the rejection of part. While in the case of screw threads there are at least five important elements which require consideration and error in any one of these can cause rejection of the thread. In routine production all of these five elements (major diameter, minor diameter, effective diameter, pitch and angle of the thread form) must be checked and methods of gauging must be able to cover all these elements.

Errors on the major and minor diameters will cause interference with the mating thread. Due to errors in these elements, the root section and wall thickness will be less, also the flank contact will be reduced and ultimately the component will be weak in strength. Errors on the effective diameter will also result in weakening of the assembly due to interference between the blanks.

Similarly pitch and angle errors are also not desirable as they cause a progressive lightening and interference or assembly. These two errors have a special significance as they can be precisely related to the effective diameter. Now will consider come errors in detail and define some terms. Drunken Thread : This is the one having erratic pitch, in which the advance of the helix is irregular in one complete revolution of the thread.

Thread drunkenness is a particular case of a periodic pitch error recurring at

intervals of one pitch. In such a thread, the pitch measured parallel to the thread is not but to a true helix. If the screw thread be regarded as an inclined plane wound around a cylinder and if the thread be on wound from the cylinder. (i.e development of the thread are taken) then the drunkness can be visualized. The helix will be a curve in the case of drunken thread and not a bright line as shown in fig. True Thread Drunken Thread Helix angle II x Mean Dia

It is very difficult to determine such errors and moreover they do not have any great effect on the working unless the thread is of very large size.

Pitch Errors in Screw Threads : Generally the threads are generated by a point

Pitch

57

cutting tool. In this case, for pitch to be correct, the ratio of the linear velocity of tool and angular velocity of the work must be correct and this ratio must be maintained constant, otherwise pitch errors will occur. If there is some error in pitch, then the total length of thread engaged will be either too great or too small, the total pitch error in overall length of the thread being called the cumulative pitch error. Various pitch errors can be classified as, 1. Progressive pitch Error : This error occurs when the tool work velocity ratios incorrect though it may be constant. It can also be due to pitch errors in the lead screw of the lathe or other generating machine.

The other possibility is by using an incorrect gear or an approximate gear train between work and lead screw e.g while metric threads are cut with an inch pitch lead screw and a translatory gear is not available. A graph between the cumulative pitch error and the length thread is generally a straight line in case of progressive pitch error.

2. periodic Pitch Error : this repeats itself at regular intervals along the thread. In this case, successive portions of the thread are either longer or shorter than the mean. This type of error occurs when the tool work velocity ratio is not constant. This type of error also results when a thread is cut from a lead screw which lacks squareness in the abutment causing the lead screw to move backward and forward once in each revolution. Thus the errors due to these cases are pitch increases to a maximum, then reduces and through normal value to minimum and so on. The graph between the cumulative pitch error and length of thread for this error will, therefore be of sinusoidal form.

3. Irregular Errors : These arise from distributes in the machining setup variations in the cutting properties of material etc. thus they have no specifics causes and correspondingly no specific characteristics also.. these errors could be summarized as follows.

58

Erratic Pitch : This is the irregular error in pitch and varies irregularly in magnitude over different lengths of thread. Progressive Error : When the pitch of a screw is uniform, but is shorter or longer than its nominal value, it is said to have progressive errors. Periodic Error : If the errors vary in magnitude and recur at regular intervals, when measured from thread to thread along the screw are referred to as periodic errors. Effect of pitch errors :

An error in pitch virtually increases the effective diameter of a bolt or screw and

decreases the effective diameter of a nut. The meaning of the virtual change in effective diameter is that if any screw is perfect except for pitch error. It will not screw easily into a perfect ring gauge of same nominal size until its effective diameter is reduced.

For White worth thread, if sp is the error in pitch then the virtual increase (decrease) in the effective diameter of the thread in case of bolt (nut) is given by the relation.

Virtual change in effective diameter = 1.921 X ςp. Similarly errors in flank angles also require a corresponding reduction in the effective diameter if the screw is to fit a perfect ring gauge of the same nominal size.

It ςθ1 and ςθ2 are the errors flank angles in degrees (regardless of sign), the corresponding virtual change (increase or decrease) in effective diameter of the thread in case of a bolt or nut is given by (for Withworth thread) ςE=0.0105 X p (ςθ1+ ςθ2), where p is the normal pitch. It is assumed that the maximum pitch error over the length of engagement is equally disturbed at each end of engagement. Increase in effective diameter will obviously be the vertical movement of flanks necessary to produce coincidence.

It may be mentioned here that effect, of long or short pitch will be same, i.e increase of the interference between the mating threads, so each will lead to increase in effective diameter nut. In ∆ABC ABC = θ = half the angle of thread Cot θ = BC / AC = (ςEd/2)/( θ p/2), or ςEd = ςp cot θ Increase in effective diameter = ςp X cot θ.

Since cot 55/2 = 1.921 (for Whitworth), its effect is nearly doubled when the equivalent increase in effective diameter is calculated. Similarly the effect of pitch error will be reduce the effective diameter of the screw. Angle Errors : Angle errors on threads may be either due to errors on one or both flanks. Any error in angle of thread results in interface between the bolt and nut and

59

to accommodate it, the effective diameter of nut has to be increased. Thus like pitch errors, the angle errors also increase the virtual effective diameter of a bolt and decrease that of a nut. Assuming that one of the pairs is correct, it is possible to satisfactorily assemble the thread pairs by modifying the effective diameter. The effective diameter of an incorrect bolt must be decreased to permit a correct mating thread to make and similarly the effective diameter of an incorrect nut must be increased. If (ςθ1+ ςθ2) be equivalent to the errors in the adjoining flank angles of any thread, then the corresponding correction = Cp((ςθ1+ ςθ2 ) Where C = 0.0100 for unified thread = 0.0105 for Whitworth thread = 0.0091 for British associated threads = 0.0115 for ISO metric thread p = basic pitch of thread, (ςθ1+ ςθ2 ) = sum of errors in adjacent flank angles in degrees (regardless of signs of the errors) Diameter Errors : Errors of major, minor and pitch diameter and their mutual non-concentricity give rise to interference and strain in the joint. More forces is required for fitting. Measurement of Various elements of thread : The methods discussed here are from the point of view of measurement of gauges, but they can obviously be applied to precise work, threading tools, taps and hobs etc. we will be dealing with the measurement of most important six elements i.e major, minor and effective diameters, pitch angle and form of thread. Measurement of diameter in screw threads : for the measurements of major diameter of external threads, a good quality hand micrometer is quite suitable. In taking readings, a light pressure must be used as the anvils make contact with the gauge at points only and otherwise the errors due to compression can be introduced. It is however, also desirable to check the micrometer reading on a cylindrical standard of approximately the same size, so that the zero error etc, might not come into picture.

For greater accuracy and convenience, the major diameter is measured by bench micrometer. This instrument was designed by N.P.L to estimate some deficiencies inherent in the normal hand micrometer. It uses constant measuring pressure and with this machine the error due to pitch error in the micrometer threads avoided. In order to that all measurements be made at the same pressure, a fiducial indicator is used in place of the all measurements machine there is no provision for mounting the work piece between the centers and it is to be held in hand. This is so because, generally the centers of the work piece are not true with its diameter. This machine is used as a comparator in order to avoid any pitch errors of micrometers, zero error setting etc. a calibrated setting cylinder is used as the setting standard.

The advantage of using cylinder as setting standard and not slip gauges etc. is that it gives greater similarity of contact at the anvils. The diameter of the setting cylinder must be nearly same as the major diameter. The cylinder is held and the reading of the micrometer is noted down. This is then replaced by threaded work piece and again micrometer reading is noted for the same reading of fiducial

60

indicator. Thus, if the size cylinder is approaching that of major or diameter, then for a given reading the micrometer thread is used over a short length of travel and any pitch errors it contains are virtually eliminated. If D1 =diameter of setting cylinder

R1 =reading of micrometer on setting cylinder R2 =Micrometer reading on thread, then major diameter = D1 +(R – R1)

In order to determine the amount of taper, the readings should be taken at various positions along the thread and to detect the ovality, two or three readings must be taken at one plane in angular positions. Major diameter of internal threads: The measurement of the elements of an internal threads is more cumbersome. Since it is difficult to approach the elements of internal thread, an indirect approach is followed by making a cast of the thread. The main art thus lies in obtaining a perfect cast, because once good cast is available the various elements can be measured as for external threads.

Cast may be made by plaster of paris, dental wax, or sulphur. The part whose internal thread is to be measured is first cleaned and brushed with a fine oil. The part is then mounted between two wooden blocks whose upper surface lie about half way up the ring. Cast materials is then poured to depth less than the radius of part to permit easy removal of cast without screwing it out. After the plaster is set, it should be taken out without rotating, but by pulling up the middle portion of the cast. It may be mentioned that taking out of sulphur cast is easier than the plaster. Oiling is not necessary in case of sulphur cast. Measurement of Minor diameter : This is also measured by a comparative process using small Vee-pieces which make contact with root of the thread. The Vee pieces are available in several sizes having suitable radii at the edges. The included angle of the root of the thread. To measure the minor diameter by Vee pieces is suitable for only Whitworth and B.A threads which have a definite radius at the root of the thread. For other threads, the minor diameter is measured by the projector or microscope.

The measurement is carried out on a floating carriage diameter measuring machine in which the threaded work piece is mounted between centers and a bench micrometer is constrained to move at right angles to the axis of the center by a Vee

61

ball side. The method of the application of vee pieces in the machine is shown diagrammatically in fig. the dimension of vee piece play no important function as they are interposed between the micrometer faces and the cylindrical standard reading is taken.

It is important while taking readings, to ensure that the micrometer be located at right angles to the axis of the screw being measured. The selected vee are placed head is then advanced until the pointer of the indicator is opposite the zero marl, and note being made of the reading of the micrometer is taken.

If reading on setting cylinder with Vee pieces in position = R1 and reading on thread = R2 and diameter of setting cylinder = D1 then minor diameter = D1 +(R2 – R1). Readings may be taken at various positions in order to determine the taper ovality.

Before proceedings to the measurement of effective diameter, the screw diameter measuring machine is first described in brief here. The machine is shown. Also refer this figure. For schematic sketch. If consists of three main units. A base casting carries a pair of centers, on which the threaded work piece is mounted. Another carriage is mounted on it and is exactly at 90 to it.. On this is provided another carriage capable of moving towards the centers. On this carriage one head having a large thimble enabling reading upto 0.002mm is provided. Just opposite to it is affixed anvil which is spring loaded and its zero position is indicated by a fiducial indicator. Thus the micrometer elements are exactly perpendicular to the axes of the centers as the two carriages are located perpendicular to each other. On the fixed carriage the centers are supported in two brackets fitted on either end. The distance between the two centers the second carriage is adjusted depending upon the length of the thread job. After job is fitted between the centers the second carriage is adjusted in correct position to take measurements and is located in position. The third carriage is then moved till the fiducial indicator is against the set point. The readings are noted from the thimble head. It is now obvious that the axes of the indicator is specially designed for this class of this work and has only one index line. Against which the pointer is always to be set. This ensures constant measuring pressure for all readings. Sufficient friction is provided by the conical pegs to restrain the movement of carriage along the line of centers. The upper carriage is free to float on balls and enables micrometer readings to be taken on a diameter without restraint. Square ness of the micrometer to the line centers can be adjusted by rotating the pegs in the first carriage which is made eccentric in its mounting.

Above the micrometer carriage, two supports are provided for supporting the wires and vee pieces for measurement of effective diameter etc.

62

Minor diameter of internal threads : minor diameter of internal threads can be measured conveniently by the following methods. i) Using taper parallels : The taper parallels are pairs of wedges having radiuses and parallel outer edges. The diameter across their outer edges can be changes by sliding them over each other shown in fig. the taper parallels are inserted inside the thread and adjusted until firm contact is established with the minor diameter. The diameter over the outer edges is measured with a micrometer. This method is suitable for smaller diameter threads. ii) Using rollers : For threads bigger than 10mm diameter, precision rollers are inserted inside the thread and proper slip gauge inserted between the rollers as shown in fig.

So that firm contact is obtained. The minor diameter is then the length of slip gauges plus twice the diameter of rollers. effective diameter measurement in screw threads by micrometer. The effective diameter or the pitch diameter can be measured by any of the following methods. i) Micrometer method ii) One wire, two wire or three wire (or rod) method.

Thread micrometer method : the thread micrometer resembles the ordinary micrometer, but it has special contacts to suit the end screw thread form that is to be checked. In this micrometer, the end of the spindle is pointed to the Vee thread form with a corresponding vee recess in the fixed anvil. When measuring threads only, the angle of the point and the side of vee-anvil i.e the flanks of the threads should come into contact with the screw thread.

63

If correctly adjusted, this micrometer gives the pitch diameter.

This value should agree with that obtained by measurement by outside diameter and pitch from the following relation. Pitch dia = D-0.6403p (in case of Whitworth thread) where 0.6403p = depth of thread, D = outside dia p = pitch. Limitations of thread micrometer : The micrometer must be set to a standard thread plug. If not done so in the first instance, there will be error due to helix angle of the thread being measured. When setting the instrument to a standard plug gauge it will be observed that the reading is not exactly zero, as previously inferred, when the spindle and anvil are brought together.

For correct results it is necessary to use a separate thread micrometer for every size of screw thread to be gauged, otherwise there will be a small amount of error inherent in thread micrometer.

A big advantage of thread micrometer is that is the only method which shows the variation for the drunken thread. measuring effective diameter of screw threads: One wire method : In this method, one wire is placed between two threads at one side and on the other side anvil of the measuring micrometer contacts the crests as shown in fig. First the micrometer reading is noted on a standard gauge whose dimension is nearly same as to be obtained by this method. Actual measurement over wire on one side and threads on other side = size of gauge ± difference in two micrometer readings. This method is used for measuring effective diameter of counter pitch threads, and during manufacture of threads.

64

The difficulty with his method is that the micrometer axis may not remain exactly at right angles to the thread axis. Two wire method : The effective diameter of a screw thread may be ascertained by placing two wires or rods of identical diameter between the flanks of the thread, as shown in fig. and measuring the distance over the outside of these wires. The effective diameter E is then calculated as E = T + P, where T = Dimension under the wires = M -2d

M =Dimension over the wires, d = diameter of each wire

The wires used are made of hardened steel to sustain the wear and tear in use. These are given a high degree of accuracy and finish by lapping to suit different pitches.

Dimension T can also we determined by placing wires over a standard cylinder of diameter greater that the diameter under the wires and noting the reading R1 and then taking reading with wires over the gauge, say R2 then = S-(R1-R2) P = It is a value which depends upon the dia of wire and pitch of the thread. If P = pitch of the thread, then P = 0.9605p – 1.1657d (for whitworth thread) P = 0.866p-d (for metric thread)

Actually p is a constant value which has to be added to the diameter under the wires to give the effective diameter. The expression for the value P in terms of P (pitch), d (diameter of wire) and x (thread angle) can be derived as follows. Since BC lies on the effective diameter line,

Two wire method can be carried out only on the diameter measuring machine described for measuring the minor diameter, because alignment is not possible by 2

12

1

2

cosecx/2

2

(cosecx/2-1)

2

cot / 2 cot / 24

cotx/2 (cosecx/2-1)

4 2

is half the value of P

pP value =2AQ= cot cos 1

2 2 2

BC pitch p

dOP

dPA

PPQ QC x x

p dAQ PQ AP

AQ

x xd ec

65

wires and can be provided only by the floating carriage machine. In the case of three wore method, 2 wires on one side help in aligning the micrometer square to the thread while the third placed on the readings.

A simplified diagram of this measuring machine is shown in fig. as already pointed out the machine ensures that the axis of the micrometer is maintained at 90 to the axis of the screw under test. The lower slide (wrongly indicated as lower side ) is capable of movement parallel with the axis of thread while the top slide moves at 90 to thread axis.

Three wire method : This method of measuring the effective diameter is an accurate method, in this three wires or rods of known diameter are used one on one side and two on the other side. This method ensures the alignment of micrometer anvil faced parallel to the thread axis. This wires may be either held in hand or hung from a stand so as to ensure freedom to the wires to adjust themselves under micrometer pressure.

M = distance over wires, E=effective diameter, r=radius of the wires, d=diameter of wires, h=height of the center of the wire rod from the effective diameter, x=angle of thread. From fig. AD = AB cosec x/2 = r cosec x/2 CD = H/2 cotx/2 = cotx/2 h=AD-CD

66

r=cosecx/2 – p/4 cotx/2 distance over wires = M=E+2h+2r =E+2(r cosec x/2 – p/4 cot x/2) + 2r =E+2(1+ cosec x/2 – p/2 cot x/2) M=E+d(r cosec x/2 – p/ cot x/2 i) In case of Whitworth thread :

x=55, depth of thread =0.64p, so that, E=D-0.64p and cosecx/2=2.1657, cotx/2=1.921

M=E+d(1+cosecx/2)-p/2cotx/2=D-0.64p+d(1+2.1657)-p/2(1.921) = D+3.1657d – 1.605p

M=D+3.1657d-1.6p, where D=outside dia ii) In case of metric thread: depth of thread = 0.6495p so, E=D-0.6495p, x=60, cosec x/2=2; cotx/2 = 1.732 M=D-0.6495p+d(1+2)-p/2(1.732)=D+3d-(0.6495+0.866)p=D+3d-1.5155p

We can measure the value of M practically and then compare with the theoretical values with help of formula derived above. After finding correct value of M and knowing d, E can be found out.

If the theoretical and practical values of M(i.e measured over wires) differ, then this error is due to one or more of the quantities appearing in the formulas.

Effect of lead angle on measurement by 3 wire method. If the lead angle is large (as with warms; quick traversing lead screw, etc) then error in measurement is about 0.0125mm when lead angle is 4.5 for 60 single thread series. For lead angles above 4.5 compensation for rake and compression must also be considered. There is no recommendation for B.S.W threads. Rake correction in U.S Standard. Where x/2 = half the included angle of threads, E = effective diameter, M=actually measured diameter over wires, n=number of threads/inch, d=diameter of wire, s=tangent of the helix angle in thread. Best size wire: The wire is of such diameter that it makes contact with the flanks of the thread on the effective diameter or pitch line. Actually effective diameter can be measured with any diameter wire which makes contact on the true flank of the

2cot / 21 cos cos cot

2 2 2 2 2

x x S x xE m x ec

n

67

thread. Bu the values so obtains will differ from those obtained with best size wires if there is any error in angle or form of thread. It is recommended that for this condition the wire touches the flank at mean diameter line within ± 1/5 of flank length (refer solved problem) with best size wire, any error on the measured value of simple effective diameter due to error in thread form or angle is minimized. It can be shown that size of best wire diameter With best size wire, P value = d (cosecx/2+1)cotx/2 Measurement of effective diameter of tapered threads: The measurement of the effective diameter of taper threads is not made perpendicular to the axis, but at an angle depending on the taper. The measurement is made at a given point or distance from the end of the thread, and in the three wire method, the single wire is placed at this point. The other two wires are placed in two opposite grooves and care must be taken to ensure that the micrometer or measuring anvils make contact with each of the three wires. The formula for the effective diameter of the taper thread is : Where E=effective diameter, M=measurement over the wires, d=diameter of the wires, h=half the angle of taper, x/2=half the included angle of the thread form, n=number of threads per inch. Thread comparator : In this case a pair of a ball tips engage the flanks of the threads in the work and measure the effective diameter only. The ball tip on the right is fixed at the end of a measuring jaw attached to a floating head in the sliding brackets (B). the floating head has extension in contact with the spindle of the dial indicator and the movement of floating head towards the indicator is constrained by a spring. (The set up in fig does not show the ball tips) The instrument is set to a reference standard, with the dial pointer a zero. To use the gauge, the floating head is retracted to insert the ball tips in the internal threads of the work, and released to allow the tips to engage the flanks of the thread under the pressure of the spring. The dial indicator then shows the deviation from the nominal size to which the gauge is set. The instrument may be used on work in the machine, or on the working bench. The fixed head (A) carrying the left hand ball tip is adjusted by a fine screw to set gauge to the reference standard. The reference standard is built up from slip gauges as shown in fig. the two end pieces have V-jaws of an angle of vee corresponding to the thread i.e 60 degree or 55 degree.

2cos / 2

pd

x

21 sin / 2 cos / 2 1 sin / 2(1 sin / 2) .

sin / 2 2 cos / 2

x x p xd d x

x x

cot / 2( )sec cos / 2

2

xE M d h d ecx

n

68

The dimension J1 are marked on the pieces, and are the depths from the face to the apex points of the vees. Assuming the effective diameter and pitch of the thread to be known, the distance S is found from the formula. S = X + y - Z Where, X = mean effective diameter Y = Depth of the thread from apex to the apex of the V form The value of y depends on the V-form, angle of the thread, and is equal to 0.9605p for 55 threads and 0.866p for 60 threads. Z = J1 + J2 i.e, constants for the end gauge pieces. The assembled slips are set in a holder with a slip equal to half the pitch, bench one end piece to compensate for the helix angle.

The reference gauge thus assembled is ready for setting the comparator. Ball tips

must be of suitable size for the thread. The size is not critical provided the ball point first the thread so as to bear o the flack near the mean pitch line.

For threads from 4 to 7 t.p.i a ball of 0.095 inch dia is used, from 7 to 12 t.p.i 0.060 inch diameter and from 12 to 20 t.p.i. 0.035 inch diameter balls are used. A pair of

V-jaws, 55 or 60 covers all pitches from 4 to 20 t.p.i. The method of calculating the value of S from the effective diameter excluded the radius OY at the creset and root of the thread, as the form is considered to extend to the apex of the vee. In some cases it may be necessary to accept the major diameter as it may be the basic

69

dimension of the thread, and the form at the root of the thread must then be taken into account. P r For metric threads, S=D+0.2165p-Z; for whitworth threads, S=D+0.3202p-Z.

Layman‘s method of finding the effective diameter (internal thread) is by taking the impression of threads with the help of wax or any other material, say sulphur. Sulphur is mostly used because it can be used many times. Checking the “Thread form “ and “Angle by optical projection of thread”. This method is applicable only to external threads because internal threads cannot be projected.

The standard type of projector is used, consisting of a projector lamp, a condenser lens or collimator, the projection lens and the screen.

The screw thread to be examined is placed in the parallel beam of light between the condenser lens and the projector lens. The modern projectors are quipped with work holding pictures, the projection lamp and the lenses situated on top of the cabinet, and the screen at the front. The light rays from the lens are directed downwards into the cabinet, and hence to the screen by a system of prisms and mirrors, bringing every thing within the reach of the operator. The enlarged image of the thread form appears on the ground –glass screen on which is mounted the template or drawing of the form made to scale equal to the magnification of the lens. This way the two forms (i.e ideal and projected) are compared.

One of the difficult I projecting screw thread is the fact that form is specified on an

70

axial plane. So we must consider the correction for it. Referring to fig. the normal pitch p is less than the axial pitch P and is given by the relation; p = P cosθ; where θ is the helix angle. Referring to fig. IfA = half the included angle of thread on the axial plane.

X = half the included angle of the thread on normal plane B = full depth of thread to apex and Or we say tan X = tan A cosθ Values of A and θ are known 2X is the included angle 2X and then compare it to the theoretically calculated value 2X=2tan-1 (tan A cos θ ) The included angle can be determined by two ball method. measurement of pitch of screw threads: Measurement of pitch : The accuracy of pitch in any form of thread is very important. Therefore it is very important to able to measure this element of thread to high degree of accuracy, at least double that of the effective diameter measurement. The measurement must be made in such a way that other features or dimensions e.g diameter and thread angle do not influence the result. External Threads : 1. For less accurate methods, the zees pitch or lead measuring instrument may be used. It utilizes contact members having two ball points which are applied to the effective surface of the thread. These points are aligned parallel to the thread axis either by a thread pin at the back or a special back rest having a plane face parallel to the thread axis. The instrument is adjusted to zero before making a measurement, with the aid of a special micrometer gauge supplied for the purpose, or buying a standard plug gauge. Upon applying the instrument to the thread it registers the pitch deviation from the standard measurement. The scale of the indicator has a range of ± 0.1mm and each division reads to 0.01mm. The measuring accuracy of the indicator is ± 0.003mm. 2. The pitch of external threads can be measured by using screw pitch or profile gauge. Such a gauge consists of series of thread forms with varying pitch. The one which coincides perfectly with the thread under test gives the pitch. The accuracy of measurement depends on the method of sighting used to judge the perfect ness. 3. A more accurate method is the microscope method. Screw threads can be inspected and their profile angles and linear pitches checked with the aid of a goniometric microscope. The parts to be gauged are usually held between centers

0.5 0.5 cos 0.5tan ; tan tan

P P pA X or X

B B B

71

and illuminated from below, their silhouettes appearing in the field of the viewing eyepiece. Effective pitch diameters can also be measured by this method.

The method of measuring pitch is shown in fig. the microscope has two reticules that can be oriented to the slopes of the thread and the point of intersection of these is used as the measuring reference. The movement of the longitudinal carriage is read off the linear scale, the micrometer microscope being employed for this purpose. The linear measuring accuracy is within 0.001mm and for angles, it is 10 sec of arc.

A comparatively simple, method of testing the pitch of a screw thread with the cooke tool room microscope fitted with its projection screen is as follows.

The screw to be checked is mounted in a cradle under the microscope objective

and the necessary adjustments made to project the sharp enlarged image of the thread on the screen. The appropriate thread form on the microscope thread template is then brought into coincocide with the projected image, as shown in fig. and a reading of the lon-gitudinal table micrometer screw taken; this can be done to an accuracy of 0.0025mm. The table is then moved by means of the micrometer screw until the image of the next thread on the screen under inspection fills the template profile and the reading of the micrometer again taken. The difference between the readings gives the measured pitch of the screw. The procedure is repeated for each in individual thread in order to find the separate pitch error, if any. Finally, the difference between the initial and last readings of the micrometer when divided by the number of threads that have been measured enables the ―mean pitch‖ of the screw to be estimated.

72

For still more accurate purpose it is necessary to employ a special screw pitch measuring machine by which the actual pitch error of individual threads can be measured. The Pitter and Matrix are typical examples of pitch measuring machines.

The Pitter screw measuring machine employs various stylus points to suit screw threads that are to be checked. The screw under measurement is held stationary between centers on the machine. The indicator unit, carrying the stylus which bears on the flanks of each thread successively, is carried on a slide which is mounted on balls. The slide is actuated by means of a micrometer. The act of rotating the micrometer spindle causes the slide to move in relation to the fixed centers. i.e causes the indicator to move in relation to the work being measured. The stylus which is mounted on a leaf spring, falls in and out of each thread; the pointer of the indicator reads zero (it is adjusted to read zero in the first groove) when this stylus is in a central position in each successive thread. The micrometer reading is taken each time the indicator reads zero; these readings then shown the pitch error of each thread of the screw ordinary pitches whilst special can be provided for.

It may be mentioned that is small hand wheel below the micrometer actuates screw for the purpose of moving the indicator in relation to the slide so as to bring the stylus opposite to the screw to be tested in any position between the centers. The total travel of the micrometer is 25mm.

As the pitch of the micrometer screw is checked accurately when the machine is inspected and a curve of errors is provided, it is possible to attain a high standard of precision in measuring screws. The pitch errors are extremely small, being of the order of 0.002mm for a thread. A test screw is also supplied with the machine and a chart of itch error for this screw.

The metric pitch measuring machine operates on a similar principle to the pitter machine. It is robust in construction and sensitive in measurement, revealing pitch accuracies of 0.0025mm for all thread forms. In this machine refer fig. a micrometer head is provided on the headstock which is fixed on the base. The rotation of micrometer head produces movement of the longitudinal carriage along the bed of the base.

73

Another carriage carrying the indicating and amplifying units comprising a

radiuses stylus and visual scale allowing a zero reading to be taken, and also capable of moving at 90 longitudinally and locked in any position. A weight ensures a unidirectional thrust at all times. The micrometer screw of 40 t.p.i has a 50 mm traverse and also has a compensator for any small residual pitch errors. In operation, the screw thread to be checked is placed between centers and the correct stylus mounted in the indicating head.

When the test screw is in position between the centers, and the correct stylus chosen i.e the one which makes contact at or near the diameter, the carriage carrying the indicating unit is traversed until the stylus is located in the first thread of the test screw and the indicator of coincident with the fiducial line; the second carriage is then locked. The stylus, by virtue of an ingenious mounting device, is capable of free movement riding up and down the thread flanks on linear movement of the screw thread by rotation of micrometer head. The stylus is now traversed along the thread, pitch by pitch, reading being taken each time the indicator is set to zero. The micrometer can be fitted with a series of graduated dials that can be changes quickly. With the proper dial for the pitch that is to be measure the readings of the error obtained from the displacement of the lines on the disc which is graduated in (0.002 mm) divisions. It is after making this test, to the turn to first thread and repeat the readings, and the micrometer should read zero again.

74

Additional description of pitch measuring machines: To correct any error pitch of the micrometer screw a compensator bar is provided.

The instrument is checked periodically with a master reference screw which is placed between centers and measured for the pitch over full range of micrometer. In this case variation in the reading is taken to indicate errors in the micrometer screw, and the compensator bar modified accordingly.

The micrometer screw has 40 t.p.i and with a graduated dial of 250 divisions

numbered every 10 divisions, the instrument is read as on ordinary micrometer calibrated to 0.0001inch. the micrometer dial may be replaced by any one of the five alternative dials to simplify the measurement of the threads of certain pitches. Each of the dials is marked with a number of divisions to suit a range of pitches as follows.

Dial No.of div

For measurement

A 6 9

6,12,24,48,15,30,60 t.p.i 4,5,9,18,36 t.p.i

B 7 11

7,14,28,56,5,10,20,40, t.p.i 11,2 t.p.i

C 8 4,8,16,32t.p.i

D 13 19

13,26 t.p.i 19 t.p.i

E 25 20

(Each 0.002mm numbered every fifth division pitch multiples of 0.025mm)

Dial C is for British association, metric or non-standard pitches. Dial E is for metric

machines only. The provision of a dial marked to suit a particular pitch simplifies pitch measuring, a division on the dial is opposite the zero mark for nominal pitch each thread. Any variation of the division from the zero may then be read directly to 0.0001‖ on either side of the zero line.

Stylus points are available to suit any particular thread. Care should be taken to

make the stylus point touch the thread at or near the pitch line. The stylus holder is pivoted to allow the stylus point to follow in and out of the threads, as the carriage is moved along, and is adjustable for pressure. expression for the best size wire:

The best size wire is one, in which case the wire makes contact with the thread flank. i.e the contact points of the wires should be, on the pitch line or effective diameter. In other words, OP is perpendicular to the flank position of the thread. Let half the included angle of thread be x.

75

Then in ∆OAP, sin POA Since AP = r, and wire diameter = 2r=2AP sec x As AP lies on the pitch line, AP=p/4 (where p = pitch of the thread) Problem 1: Derive an expression from first principles for the limits of diameter for ‗best size‘ wires for measuring threads of BA form in terms of pitch

Best wire size is d

Refer fig please note that point B could not be shown in fig. Actually B lies on line OF such that AB ┴OF. Point C lies on inter section of line AD and OF).

BF = CE + BC + EF = CE + 2BC

AP, or sin (90 -x)=

OP

secsin(90 ) cos

APSinPOA

OP

AP APOP AP x

x x

2sec sec

4 2p

p pd x x

sec2 2

here x=included angle of the thread

p 47 30 1= sec 0.5465

2 2 2 0.9150

1( ) upper limit/lower limit:

5

1

5

p xd

pp

a

flank length BF

76

BC = (OA sin x/2) tan x/2 = [(0.1808p + 0.2682p). sin 23 45] X tan 23 45 = 0.0378p Hence upper limit for best wire size = 0.5465p + 0.0378p = 0.5843p and lower limit for best wire size = 0.5465p – 0.0378p = 0.5087p.

corrections applied in the measurement of effective diameter by the method of wires: The two corrections applied are : i) Rake correction, and ii) Compression correction. i) Rake Correction : The rake correction becomes necessary because in the determination of formula for effective diameter by three wires method, a plane axial section of the thread had been considered and it is assumed that the wore touches each flank of the thread in this plane. This assumption is true for angular grooves with zero helix angle, but not for screw threads which have a helix; and in the later case wire lies on parallel to the helix at the radius of the point of contact. The points of contact on opposite flanks will lie on opposite sides of the mean axial plane. As a result of this, the wire lies slightly father from the thread axis than what has been assumed and a correction has to be applied to the effective diameter as measured and calculate. This correction is different effective diameters being measured. A general formula for calculating rake correction is Where C = Rake correction, X/2 = Half the included angle of thread, l=Lead of thread, D = diameter of wire A= Constant Where T = Diameter under the wires. This correction is always subtracted from the measured diameter. ii) Compression Correction : As the micrometer exerts some force on the wires while measuring the effective diameter of threads, some degree of comparison takes place and as a result the diameter observed is less. This correction, is therefore added to the value of diameter obtained. This correction is more pronounced on fine threads and those whose included angle is small e.g B,A threads, for measuring forces upto about 350gm. The correction is within 0.0025mm for thread diameter down to about 3.5mm and only 0.005mm at 1 mm diameter for larger threads, for the some measuring force, the compression is less and can be ignored. Formula for determining compression correction is

22 2 2

2

cosx/2cotx/2 lC= (1 sin / 2 sin / 2)

2 dA A x A X

dConstant

T+d

2/3

1/3

E =0.001 .

Emm

77

Gear errors. Various possible types of error on spur, helical, bevel and worm gears are described below: (i) Adjacent pitch error Actual pitch – design pitch. (ii) Cumulative pitch error Actual length between corresponding flanks of teeth

not adjacent to each other-design length. (iii) Profile error The maximum distance of any point on the tooth

profile form and normal to the design profile when the two coincide at the reference circle.

(iv) The tooth to tooth The range of difference composite error – single flanks between the displacement

(Refer Fig. 15.13a) at the pitch circle of a gear and that of a master gear meshed with it at fixed centre when moved through a distance corresponding to one pitch with only the driving and driven flanks in contact.

(v) The total composite The range of difference errors – single flank between the displacement at the pitch circle of a gear and that of a master gear meshed with it at fixed centre distance when moved through one revolution with it at fixed centre distance when moved through one revolution with only the driving and driven banks in contact (Refer Fig.15.3a).

(vi) The tooth to tooth The range of variation in composite error – double the minimum centre flank distance between a gear and a master gear when rotated through a distance corresponding to the pitch of the teeth (Refer Fig. 15.13a)

(vii)The total composite The range of variation in error-double flank. The minimum centre distance between gear and a master gear when the gear is rotated through one revolution (Refer Fig.15.13b)

(viii) The tooth thickness error Actual tooth thickness measured along the surface of the reference cylinder – design tooth thickness.

(ix) Cyclic error An error occurring during each revolution of the element under consideration.

(x) Periodic error An error occurring at regular intervals not necessarily corresponding to one revolution of the component.

(xi) Run out It is the total range of reading of a fixed indicator with the contact point applied to a surface rotated, without axial movement about a fixed axis.

(xii) Radial run out It is the run – out measured along a perpendicular to the axis of ration.

(xiii) Eccentricity It is half the radial run-out. (xiv) Axial run-out (wobble) It is the run- out measured parallel to the axis of

rotation, at a specified distance from the axis. (xv) Undulation A periodical departure of the actual tooth surface

from the design surface (Refer Fig. 15.13b). (xvi) Undulation height The normal distance between two surface from the

78

design surface (Refer Fig. 15.13c) (xvii) Wave length of an The distance between two undulation adjacent

crests of an undulation (Refer Fig. 15.13c) (xviii) Tooth alignment error The distance of any point on a tooth trace from the

design tooth trace passing through a selected reference point on that tooth (Refer Fig.15.13c)

The presence of these errors caused interference in efficient Operation of gears. These result in non-smooth and noisy Operation which ultimately affect the working life. Gear Measurements: For proper inspection of gear, it is essential to pay attention to the raw material, each process in the production cycle, machining the blanks, heat treatment, the cutting and surface finish of the teeth. The gear blank should be tested for dimensional accuracy (face width, bore, hub, length, and outside diameter), and eccentricity As outside diameter forms the datum from where the tooth thickness is measured, it forms an important item to be controlled. Concentricity of the blanks is also essential and the side faces should be true to the bore. On very precise gears details like tip radius, shape of root provided and surface finish are also measured. Concentricity of teeth is an important item and should be checked to ensure that the set up and equipment is in good order. If teeth are not concentric then fluctuating velocity will be noticed on the pitch line while transmitting motion. This also leads to inaccuracy of parts when being used for indexing purposes. Tooth concentricity can be checked by (i) mounting the gear between the bench centres, placing a standard roller in each tooth space and then using a dial indicator, (ii) using a projector in which case the teeth are brought against a stop and each image of tooth on screen should coincide with a line on the screen (iii) using a gear testing fixture fitted with a spring loaded slide and dial indicator, in which case the spring exerts a constant pressure on the mating teeth and the movement of the dial indicator, in which case the spring exerts a constant pressure on the mating teeth and the movement of the dial indicator gives the measure of the eccentricity of teeth. Good alignment of each tooth on a gear is essential, as otherwise the load will not be distributed evenly over its face. If teeth of a gear be machined poorly, it is quite probable that the load may be carried by one edge only introducing high bearing stresses. Tooth alignment can be checked by placing a standard roller in the tooth space and checking for parallelism off a surface plat. In the other method, the teeth on one gear are lightly marked with Prussian blue and mounted in a testing machine having a master gear. The contacts made on the mating gear give good idea of tooth alignment. Hardness of gear tooth should be tested to ensure that heat treatment is proper and that the desired harness due to provision of adequate thickness and grain size have been attained.

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The method employed for measuring and testing of gears depends upon various factors, such as the precision of gears, method of manufacturing equipment available etc. The accuracy of any gear mainly depends upon the cutter accuracy and the setting of the machine. Thus for most of the gears, optical projection and rolling tests will suffice. But in manufacture of high precision gear, it is necessary to determine the accuracy of individual elements e.g., tooth thickness, pitch of teeth and form of teeth etc. Accuracy of measurement. While the accuracy of measuring of gear depends upon the measuring equipment available, it must be emphasized that there are some in-built limitations in the gear itself, such as the inability of a gear to define its own axis of rotation. Thus if the reference circle of gear is eccentric, it would be reflected in pitch error. Similarly the errors in tooth surface finish such as undulation would jeopardize the validity of a signal point measurement on a tooth flank. The inspection of gear is mainly of two types (a) Analytical, and (b) functional. By analytical inspection of gears we mean that all the individual elements of the gear teeth are checked. This method is slow and tedious and not of much use for industry. The discrete error values of pitch, tooth profile etc. cant give a true overall assessment of the accuracy of a gear. It is not easy to asses accurately how these elemental values combine in practice to give a prescribed performance under operational conditions. How ever this method is of great understanding of the subject to student. Nevertheless it may be stressed that all errors in pitch profile cause variations in the uniformity of rotary motion and the errors in tooth alignment or helix angle result in the concentration at small areas instead of being distributed uniformly. The analytical inspection of the gears consists in determination of the following teeth elements in which the errors are caused due to manufacturing errors. (A) Profile. (B) Spacing. (C) Pitch (D) Run out or eccentricity or concentricity. (E) Thickness of tooth (F) Lead. (G) Backlash. The functional type of inspection consists of carrying out the running test of gear with another gear which is more accurate and is known as control gear or master gear, to determine composite vibration, noise level, or variation in action. If a pair of gears work together at the designed speed and under load with little noise, they are considered satisfactory for many purposes. If drive is noisy, then individual elements have to be measured. However master gear has to be measured on elemental basis only. Rolling Tests This is the most commonly used test under production conditions. This consumes much less time and gives quite accurate results. In rolling test, the gear to be tested is actually compared with a hardened and ground master gear. This test is generally performed on a most commonly used machine Parson Gear Tester. This test reveals any errors in tooth form, pitch and concentricity if pitch line, When

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two gears are in mesh with each other, then any of the above errors will cause the variation of centre distance. This fact is utilized for testing the errors in gear by this machine. It essentially consists of a base. Two carriages, one fixed and the other movable are mounted on the base. The position of the fixed carriage can be adjusted in order to accommodate a wide range of diameters. While in use, this fixed carriage is locked in one position. The movable carriage is spring loaded towards the fixed carriage. Two spindles are mounted in a parallel plane on each carriage and these are made to suit the bore of the gears. The distance between the centre of two spindles is adjusted to be equal to the centre distance by slip gauges. A dial gauge is made to rest against the movable carriage and its reading is adjusted at zero at this time. The master gear is mounted on the spindle on fixed carriage and gear to be tested on the movable carriage. The gears when in mesh are then rotated by hand and the variations in the dial gauge readings are observed. If it falls outside the set limits, then gear is rejected. The variations might also be recorded by some electrical pick up in which the movement of carriage is first converted into electrical impulse which is magnified further and trace of variation obtained on a graph paper. The trace obtained will be depicting the compound errors i.e., all errors like eccentricity and tooth form errors etc., which occur together and the trace will be as shown in Fig.15.8.

The machine could also be used to carried out more complex tests by suitable modification in its operation, e.g., by locking the movable carriage at the running centre distance of the gears, and by fixing the master gear, the black flash can be determined by setting a dial gauge at the pitch line of the production gear. It is also possible to check the gears for smooth running at this setting and this is very essential for gears. This is judged by the noise produced. For these tests, if master gear is not available, then any two mating gears are mounted on the spindle and they are tested twice at relative angular positions of 1800 to each other so that any compensating errors in one angular position in gears are also revealed. measurement of tooth thickness by gear tooth Vernier method: Measurement of tooth thickness. The permissible error or the tolerance on thickness of tooth is the variation of actual thickness of tooth from its theoretical value. The tooth thickness is generally measured at pitch circle and is therefore, the pitch line thickness o tooth. It may be mentioned that the tooth thickness is defined

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as the length of an arc, which is difficult to measure directly. In most of the cases, it is sufficient to measure the chordal thickness i.e., the chord joining the intersection of the tooth profile with the pitch circle,. Also the difference between chordal tooth thickness and circular tooth thickness is very small for gear of small pitch. The thickness measurement is the most important measurement because most of the gears manufactured may not undergo checking of all other parameters, but thickness measurement is a must for all gears. There are various methods of measuring the gear tooth thickness. (i) Measurement of tooth thickness by gear tooth venire caliper. (ii) Constant chord method. (iii) Base tangent method. (iv) Measurement by dimension over pins. The tooth thickness can be very conveniently measured by a gear tooth venire. Since the gear tooth thickness varies from the tip of the base circle of the tooth, the instrument must be capable of measuring the tooth thickness at a specified position on the tooth. Further this is possible only when there is some arrangement to fix that position where the measurement is to be taken. The tooth thickness is generally measured at pitch circle and is, therefore, referred to as pitch-line thickness of tooth. The gear tooth vernier has two vernier scales and they are set for the width (w) of the tooth and the depth (d) from the top, at which w occurs. Considering one gear tooth, the theoretical of values of w and d can be found out which may be verified by the instrument. In Fig. 15.14, it may be noted that w is a chord ADB, but tooth thickness is specified as an arc distance AEB. Also the distance d adjusted on instrument is slightly greater than the addendum CE, w is therefore called chordal thickness and d is called the chordal addendum.

In Fig.15.14, w = AB = 2AD Now, AOD = = 3600/4N, where N is the number of teeth,

W = 2AD = 2xAO Sin = 2R Sin 360/4N (N = pitch circle radius)

Module m = . . 2 . .

,. 2

P C D R N mR

No of teeth N

360 90

2 . .2 4

Nmw Sin N m Sin

N N

---- (1)

Also from Fig 15.14, d = OC –OD But OC = OE + addendum = R + m = (Nm/2) + m

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and 90

2

NmOD RCos Cos

N

90 2 901

2 2 2

Nm Nm Nmd m Cos Cos

N N N

--- (2)

Any error in the outside diameter of the gear must be allowed for when measuring tooth thickness. In the case of helical gears, the above expressions have to be modified to take into account the change in curvature along the pitch line. The virtual number of teeth Nv for helical gear = N/cos3

Hence in Eqs. (1) and (2), N can be replaced by N/cos3

and m by mn (normal module).

3

3

33

3

90,

2 901

n

n

Nmw Sin Cos and

Cos N

Nm CosCos Cos

Cos N N

these formulae apply when backlash is ignores. On mating gears having equal tooth thickness and without addendum modifications, the circular tooth thickness equals half the circular pitch minus half the backlash. Gear Tooth Caliper. It is used to measure the thickness of gear teeth at the pitch line or chordal thickness of teeth and the distance from the top of a tooth to the chord. The thickness of a tooth at pitch line and the distance from the top of a tooth to the chord. The thickness of a tooth at pitch line and the addendum is measured by an adjustable tongue, each of which is adjusted independently by adjusting screw on graduated bars. The effect of zero errors should be taken into consideration.

This method is simple and inexpensive. However it needs different setting for a variation in number of teeth for a given pitch and accuracy is limited by the least

83

count of instrument. Since the wear during use is jaws, the caliper has to be calibrated at regular intervals to maintain the accuracy of measurement.

Constant Chord Method. In the above method, it is seen that both the chordal thickness and chodral addendum are dependent upon the number of teeth. Hence for measuring a large number of gears for se, each having different number of teeth would involve separate calculations. Thus the procedure becomes laborious and time – consuming one. The constant chord method does away with these difficulties. Constant chord of a gear is measured where the tooth flanks touch the flanks of the basic rack. Are straight and inclined to their centre line at the pressure angle as shown in Fig. 15.16.

Also to pitch line of the rack is tangential to the pitch circle of the gear and, by definition, the tooth thickness of the rack along this line is equal to the are tooth thickness of the gear round its pitch circle. Now, since the gear tooth and rack space are in contact in the symmetrical position at the points of contact of the flanks, the chord is constant at this position irrespective of the gear of the system in mesh with rack. This is the property utilized in the constant chord method of the gear measurement. The measurement of tooth thickness at constant chord simplified the problem for all number of teeth. If an involutes tooth is considered symmetrically in close mesh with a basic rack form, then it will be observed that regardless of the number of teeth for a given size of tooth (same module), the contact always occurs at two fixed point A and B. AB is known as constant chord. The constant chord is defined as the chord joining those points, on opposite faces of the tooth, which make contact with the mating teeth when the centre line of the tooth lie on the line of the gear centers. The value of AB and its depth from the tip, where it occurs can be calculated mathematically and then verified by an instrument, The advantage of the constant chord method is that for all number of teeth (of same module) value of constant for all gears of the meshing system. Secondly it readily lends itself to a form of comparator which is more sensitive than the gear tooth venire. In Fig 15.16, PD = PF = are PF = ¼ circular pitch =

11/ 4

4

P C Dm

N

Since line AP is the line of action, i.e.it is tangential to the base circle,

84

2

ÐCAP=Φ

in right angled ΔAPD,=PDcosΦ= π/4 mcosΦ

in triangle PAC,AC=APcosΦ= π/4 mcos Φ

2c=constant chord=2AC= π/2 mcos Φ

where is the pressure angle (from Fig.15.16)

For helical gear, constant chord = ( / 2 ) m cos 2 n

Where mn = normal module i.e. module of cutter used and n=normal pressure angle.

Now PC = m -

.......

n n n

π πmcosΦsinΦ=m 1- cosΦsinΦ 4

4 4

πFor helical gear,d=m 1- cosΦ sinΦ

4

Also height of AB above pitch line = PC= .........sin cos sin 2 54 8

m m

Base pitch.

This is defined as the circular pitch of the teeth measured on the base circle. In Fig.15.17,AB represents the portion of a gear base circle, CD and EF the sides of two teeth, FD being the base pitch. From the property of involutes if any line as GH is drawn to cut the involutes and tangential to the base circle, the GH=FD. Thus base pitch could also be defined as equal to the linear distance between a pair of involutes measured along a common generator.

Base circumference =2

2 /

B

B

R

Basepitch R N

If is the pressure angle, then

RB = P.C.R.

cos . . . / 2 cos

(2 ) / 2 cos

P C D

Basepitch N P C D

cosm

This is the distance between tangents to the curved portions of any two adjacent teeth and can be measured either with a height gauge or on an enlarged projected image of the teeth. This principle is utilized in ‗David Brown‘ tangent comparator and it is the most commonly used method.

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Base pitch measuring instrument.

This instrument has three tips. One is the fixed measuring tip, other one is the sensitive tip whose position can be adjusted by a screw and the further movement of it is transmitted through a leverage system to the dial indicator.; and the third tip is the supplementary adjustable stop which is meant for the stability of the instrument and its position can also be adjusted by a screw. The distance between the fixed and sensitive tip is set to the equivalent to the base pitch of the gear with the help of slip gauges. The properly set-up instrument is applied to the gear so that all the three tips contact the tooth profile. The reading on dial indicator is the error in the base pitch.

The Base Tangent Method.: (‗David Brown‘ tangent comparator). In this method, the span of a convenient number of teeth is measured with the help of the tangent comparator. This uses a single venires caliper and has, therefore the following advantages over gear tooth venires scales:

(i) The measurements do not depend on two venires readings, each being function of the other.

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(ii) The measurement is not made with an edge of the measuring jaw with the face.

Consider a straight generator (edge) ABC being rolled back and forth along a base circle (Fig.15.19). Its ends thus sweep out opposed involutes A2 AA1 and C2 CC1 respectively. Thus the measurements made across these opposed involutes by span gauging will be constant (i.e. AC = A1C1=A2 C2 = A0 C0) and equal to the are length of the base circle between the origins of involutes. Further the position of the measuring faces is unimportant as long as they are parallel and on an opposed pair of the true involutes. As the tooth from is most likely to conform to a true involutes at the pitch point of the gear, it is always preferable to choose a number of teeth such that the measurements is made approximately at the pitch circle of the gear. The value of the distance between two opposed involutes, or the dimension over parallel faces is equal to the distance round the base circle between the points where the corresponding tooth flanks cut i.e. ABC in fig.15.19. It can be derived mathematically as follows: The angle between the points A and C on the pitch circle where the flanks of the opposed involutes teeth of the gear cut this circle can be easily calculated. Let us say that the gear has got ‗N‘ Number of teeth and AC on pitch circle corresponds to ‗S‘ number of teeth. (Fig.15.20); Distance AC = (S – ½)pitches

Angle subtended by 1/ 2 2 /AC S N radians.

Angles of arcs BE and B D. In volute function of pressure angle tan

1 2

2 tan2

AngleofarcBD SN

BD = Angle of arc BD bR

1 22 tan cos cos

2

1 2cos tan

2 2 2

cos tan2

P b P

P

S R becauseR RN

mN mNS becauseR

N

SNm

N N

As already defined, length of arc BD = distance between two opposed involutes and thus it is.

cos tan2

SNm

N N

It may be noted that when backlash allowance is specified normal to the tooth flanks this must be simply subtracted from this derived value.

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Tables are also available which directly give this value for the given values of S,N and m. This distance is first calculated and then set in the ‗David Brown‘ tangent comparator (Fig.1521) with the help of slip gauges. The instrument essentially consists of a fixed anvil and a movable anvil. There is a micrometer on the moving anvil side and this has a very limited movement on either side of the setting. The distance is adjusted by setting the fixed anvil at desired place with the help of looking ring and setting tubes. Composite Method of Gear Checking. Composite testing of gears consists in measuring the variation in centre distance when a gear is rolled in tight mesh (double flank contact) with a specified or mast gear. In composite gear checking two types of checking‘s are made : (a) Total Composite Variation, (b) Tooth to Tooth Composite Variation.

Total composite variation is the centre distance variation in one complete revolution

of the gear being inspected; whereas tooth to tooth composite variation is the centre distance variation as the gear is rotated through any increment of 360º/N.A uniform tooth to tooth variation shows profile variation whereas a sudden jump indicates the pitch variations.

Composite type of checking takes care of all the errors in the gears. It is

specially very much suited for large gears as it also ensures control over the tooth spacing. The composite method of checking is very much suitable for checking worn gears.

Tolerance for Composite Errors. The following table gives the tolerance on total composite errors and tooth to tooth composite error.

Here factor 0.25F M D Master Gears. Master gears are made with sufficient accuracy capable of

being used as the basis for comparing the accuracy of other gears. These are mostly used in composite errors determination in which the master gears are rotated in close mesh (double flank) or in single contact with the gears under test. These can also be used for calibration of gear checking instruments used in shop-floor Master gears are generally of two types; i.e. Master gears type A used for checking precision gears of accuracy class up to 7and type B master gears used for checking gears from 8 to 12. Master gears are made from chromium –manganese tool steel or good quality gauge steel and are hardened to 62HRC These are properly stabilized to relieve internal stresses. The master gears should preferably have lower module values because with coarse pitches the master gear would have either a very few teeth or else it will be quite big making it difficult to handle besides high-production cost.

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Parkinson Gear Tester: The principle of this device is to mount a standard gear on a fixed vertical

spindle and the gear to be tested on another similar spindle mounted on a sliding carriage, maintaining the gears in mesh by spring pressure. Movement of the sliding carriage as the gears are rotated are indicated by a dial indicator, and these variations are a measure of any irregularities in the form of a waxed circular chart and records made of the gear variation in accuracy of mech.

Fig. shows a gear tester for testing spur gears. (Testers are available for bevel, helical and worm gears also)The gears are mounted on the two mandrels, so that they are free to rotate without measurable clearance. The left spindle can be moved along the table and clamped in any desired position. The right mandrel slide is free to move, running on steel balls, against sprint pressure and it has a limited movement. The two mandrels can be adjusted so that their axial distance is equal to the designed gear. Centre distance. The spring pressure can be regulated. There are also screws for limiting the movement of the sliding carriage. A scale is attached

Class or Grade of

Gear

Total Composite Error in Microns

Tooth or Tooth

Composite Errors in Microns

1 2 3 4 5 6 7 8 9

10 11 12

4+0.32F 6+0.30F 10+0.08F 16+1.25F 25+2.0 F 40+3.2 F 56+4.5 F 71+5.6 F 90+7.1 F 112+9.0F 140+11.2F 180+14.0F

2+0.16F 3+0.224F 4+0.32 F 6+0.45 F 9+0.56 F 12+0.90F 16+1.25F 22+1.8F 28+2.24F 36+2.8F 45+3.55F 56+4.50F

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to one carriage and a vernier to the other; this enables centre distances to be measured to within 0.025mm. The dial indicator on the right contacts the right end of the sliding carriage and therefore indicates any radial variations of the gear under test as the gears are rotated.

When the waxed paper recorder is fitted, the chart makes a revolution for

each one of the gears mounted on the sliding carriage. As the char moves or rotates, the line traced records the movements of the floating carriage, a circle is drawn at the same time as the record. The figures shown in Fig. 15.28 are reproduction of a few typical charts with a reduced scale and the radial errors magnified about 50 times. The gear shown by No.1 record is a fully satisfactory one, that at No.2 is a moderate gear at No.3 is an unsatisfactory one.

It may be noted that the method described above is dual flank method, i.e.,

both tooth flanks come in contact which is seldom the case in actual practice. The chart records obtained by this test do not give a clear indication of true cumulative pitch error. This test is an expedient test for accepting or rejecting a gear but not for finding out detailed causes for rejection. It is used mainly to detect poor tooth form caused by worn or inaccurate cutting tool, and pitch circle eccentricity arising from inaccurate centering of the gear blank prior to tooth cutting, etc.

Technically more correct method of mesh testing is single –flank method in

which, instead of measuring centre distance variation the angular variation is measured. The mesh tester is a complex system and more costly. The simplest machine of this type consist of two shafts each carrying a gear and a plain disc having diameter equal to the nominal pitch diameter of the gear. One shaft has a rotary joint between the gear and its associated pitch disc. An indicator is used to measure angular variation between the gear and disc on this shaft. In use, the two discs are brought into frictional contact so that one can drive the other without slip. This method is not popular because it requires these manufacture of two very accurate pitch discs for every gear pair of different size. Present day‘s single – flank mesh testers do not require different pitch discs. The two shafts carrying the gears are fitted with radial gratings having angular band of accurately spaced clear radial lines (one line for one minute of arc). When two such gratings (inclined at very small angle ) rotate in close proximity, interference bands known as Moire fringes are formed moving in radial direction which generate electric pulses. These pulse trains are continuously phase –compared to provide a detailed chart record of gear transmission errors.