1 metrology-and-measurements

8/2/2019 1 Metrology-And-Measurements

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Standards of Measurements

The different types of standards of length are

1. Material Standards

(a)Line Standard When length is measured as the distancebetween centers of two engraved lines.

(b)End Standard When length is measured as the distancebetween to flat parallel faces.

2. Wavelength StandardThe wavelength of a selected orange radiation of Krtypton-86isotope was measured and used as the basic unit of length.

International Prototype Meter

International Prototype meter is defined as the straight linedistance, at 0c between the engraved lines of a platinum irridiumalloy of 1020 mm of total length and having a tresca cross-sectionas shown in the figure. The graduations are on the upper surface ofthe web, which coincides with the neutral axis of the section. Thesectional shape gives better rigidity for the amount of metalinvolved and is therefore economic in use for an expensive metal.

Line and End Standards and differentiate between them.

Line Standards When length is measured as the distancebetween centers of two engraved lines, it is called Line Standards.Both material Standards, yard and metre are line standards

E.g. Scale, Rulers, Imperial Standard Yard.

Characteristics of Line Standards :

(i) Scale can be accurately emblemed, but the engraved linesposses thickness and it is not possible to accurately measure

(ii) Scale is used over a wide range(iii) Scale markings are subjected to wear. However the ends are

subjected to wear and this leads to undersize measurements(iv) Scale does not posses built in datum. Therefore it is not

possible to align the scale with the axis of measurement(v) Scales are subjected to parallax errors

(vi) Assistance of magnifying glass or microscope is required.


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End Standards When length is expressed as the distancebetween centers of two flat parallel faces, it is called EndStandards. Slip Gauges, End Bars, Ends of micrometer Anvils.

Characteristics of End Standards

(i) Highly accurate and used for measurement of closedtolerances in precision engineering as well as standardlaboratories, tool rooms, inspection departments.

(ii) They require more time for measurement and measure onlyone dimension.

(iii) They wear at their measuring faces(iv) They are not subjected to parallax error.

Differentiate between Line and End Standards

Sl no Characteristics Line Standard End Standard

1. Principle Length is expressedas distancebetween 2 lines

Length is expressed

as distance between 2ends

2. Accuracy Ltd. To 0.2mm.

Highly accurate ofclosed tolerances to

0.001mm

3. Ease Quick and easy Time consuming andrequires skill

4.Effect of wear Wear at only the

ends

wear at measuring

surfaces

5. Allignment Cannot be easilyaligned

easily aligned

6. Cost low cost high cost

7. Parallax Effect Subjected toparallax effect

not subjected toparallax effect

Slip Gauges

Slip Gauges are universally accepted end standards of Length inindustry. Also known as Johnson gauges. Slip gauges arerectangular blocks of high grade steel with close tolerances. Theyare hardened throughout to ensure maximum resistance to wear.For successful use of slip gauges their working faces are truly flatand parallel. Most slip gauges are made from constant alloy which isextremely hard and wear resistance.


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Wringing of slip gauges

Wringing :Success of precision elements which can be made withslip gauges either by using it alone or in conjunction with othersample apparatus such as rollers, sine centers, sine bars, etc,

depends on the phenomenon of wringing. The slip gauges arewrung together by hand by a combined sliding and twisting motionas shown.

The gap between two wrung slip gauges is only of the order of0.0065 microns, which is negligible.

Procedure :

(i) Before using, the slip gauges are cleaned

(ii) One slip gauge is then oscillated slightly over the other slipgauge with a light pressure.(iii) One gauge is then raised at 90 degrees, to the other, andby using light pressure it is rotated until the blocks are in line.

Principle of Interchangeability and selective assemblyInterchangeability - It occurs when one part in an assembly can besubstituted for a similar part which has been made to the samedrawing. Interchangeability is possible only when certain standards

are strictly followed. In universal interchangeability the mating partsare drawn from two different manufacturing sources. This isdesirable. When all parts to be assembled are made in the samemanufacturing unit, then local standards may be followed which isknown as local interchangeability.

Selective assembly - In selective assembly the parts are gradedaccording to the size and only the matched grades of mating partsare assembled. The technique is most suitable where a close fit oftwo component assemblies is required. It results in complete

protection against non-conforming assemblies and reducesmachining costs since close tolerances are maintained.

Different types of fits.

When two parts are to be assembled, the relationship resulting fromthe difference between their sizes before assembly is called a fit.

Clearance fit : In this type of fit, the largest permitted shaft

diameter is smaller than the diameter of the smallest hole, so that


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the shaft can rotate or slide through the different degrees offreedom according to the purpose of mating parts.

Interference fit : It is defined as the fit established when a negativeclearance exist between the sizes of the holes and the shaft. In this

type of fit, the minimum permitted diameter of the shaft is largerthan the maximum allowable diameter of the hole. In this case thehole members are intended to be attached permanently and used asa solid component Example : Bearing Bushes

Transitional Fit : The diameter os the largest allowable hole isgreater than that of the smallest shaft, but the smallest hole issmaller than the largest shaft and the hole. Example : CouplingRings

Wavelength standards and its advantages

A major drawback wit the material standards, that their lengthchanges with time. Secondly, considerable difficulty is expressedwhile comparing the sizes of the gauges by using materialstandards.

Jacques Babinet suggested that wave length of a monochromaticlight can be used as a natural and invariable unit of length. 7th

general Conference of Weights and Measures approved in 1927,

approved the definition of standard of length relative to meter.

Orange radiation of isotope Krypton-86 was chosen for the newdefinition of length in 1960, by the 11th General Conference ofWeigths and Measures. The committee recommended Krypton-86and that it should be used in hot cathode discharge lamp,maintained at a temperature of 63K.

According to this standard metre was defined as equal to 165763.73wavelengths of the red-orange radiation of Krypton-86 isotope.

A standard can now be produced to an accuracy of about 1 part of10^9.

Advantages :

(a)Not a material standard and hence it is not influeced by effects ofvariation of environmental conditions like temperature, pressure

(b)It need not be preserved or stored under security and thus thereis not fear of being destroyed.

(c)It is subjected to destruction by wear and tear.


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(d)It gives the unit of length which can be produced consistently atall times.

(e)The standard facility can be easily available in all standardlaboratories and industries

(f) Can be used for making comparative measurements of very high

accuracy.


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CHAPTER 2

SYSYTEM OF LIMITS, FITS, TOLERANCES AND GAUGING

Definitions:

Tolerance: Tolerance is defined as the magnitude of permissible variation of

dimension from the specified value. They constitute an engineering legality fordeviation from ideal value. Primary purpose of tolerances is to permit variation in

dimensions without degradation of the performance beyond the limits establishedby the specification of the design.

The tolerance is specified because it is impossible to have actual dimensions dueto:

Variations in the properties of the material being machined, introduce

errors.

The production machines have some inherence problems and limitations. Human effect, operator may do imperfect settings.

Tolerance may be unilateral or bilateral.

Ex.:

Unilateral: 25.000mm, 25.002mm (dia. of hole)

24.999mm, 24.997mm (die of shaft)

OR

25.000 + 0.002 0.000mm (dia. of hole)

25.000 0.001 0.003mm (dia. of shaft)

Bilateral 25.000 mm

Basic size: The basic size is the standard size for the part and is the same for

both the hole and its shaft. Ex. 50mm diameter hole and shaft.

Nominal size: the normal size of a dimension of part is the size by which it is

referred to as a matter of convenience (used for purposes of generalidentification). Often, basic and nominal sizes of a part of dimensions are usedwish the same sense.

Actual size: It is the measured size of part.

Zero line: It is the line, which represents the base size so that the deviation fromthe basic size is zero.

Hole above basic size.

Hole of basic size.


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Holebelow

basicsize.

Fig.2.1

Limits: These are the maximum and minimum permissible size of the part.

Go Limit: It refers to upper limit of the shaft and upper limit of a hole.Corresponds to minimum material condition.

No Go Limit: It refers to the lower limit of the shaft and upper limit of the hole.

Corresponds to min. material condition.

Tolerance: The difference between the maximum and minimum limit of size.

Grades of tolerance: It is indication of degree of accuracy of manufacture and isdesignated by IT followed by a number.

Ex. IT01, IT0, IT1, IT16


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Fig.2. 2

Allowances: An intentional difference between the hole dimension and shaftdimension for any type of fit is called allowance.

Deviation: Algebraic difference between a size and corresponding basic size.

fig.2.3

Upper deviation: Maximum limit of size basic size. It is positive whenmaximum limit of size > basic size and vice versa.

(ES for hole, es for shaft)

Lower deviation: Minimum limit size basic size positive when minimum limit ofsize > basic size and vice versa (EI for hole ei for shaft)

Fundamental deviation: this is the deviation either the upper or the lowerdeviation, which the nearest one to the zero line (for both hole or a shaft).

Fits: When two parts are to assemble, the relation resulting from the differencebetween the size before assembling is called fit.

Basic size of a fit: It is that basic size which is common to the two parts of a fit.

Variation of a fit: This is arithmetical sum of tolerances of the two mating parts

of fit.

Clearance: This is the difference between the size of the hole and shaft, beforeassembly, when the difference is positive (i.e. shaft smaller than the hole).

Interference: This is the arithmetic difference between the sizes of the hole and

the shaft before assembly, when the difference is negative.

Type of fit:

Depending upon the actual limits of the hole or shaft, fits may be classified intothe following 3 categories.


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Clearance fit

Interference fit

Transition fit

Fig.2. 4

Clearance fit: In this type of fit, the largest permitted shaft diameter is smaller

than the diameter of the smallest hole, so that the shaft can rotate or slidethrough the difference degrees according to purpose of mating members Ex.

Bearing and shaft.

Interference fit: In this type of fit, the minimum permitted diameter of the shaftis larger than the maximum allowable diameter of the hole. In this case the shaftand the hole members are intended to be attached permanent and used as a solidcomponent but according to the application of this combination, this type of fitcan be varied. Ex. Bearing bushes, which are in interference fit in their housing

Ex. The small end of the connecting rod in an engine.

Transition fit: In this type of fit, the diameter of the largest allowable hole is

greater than that of the smallest shaft, but the smallest hole is smaller than thelargest shaft, so that small positive or negative clearance between the shaft andhole members employable. Location fits Ex. Spigot in mating holes, coupling ringsand recesses are the examples of transition fit.

Note: Minimum clearance: In the clearance fit it is the difference between theminimum size of the hole and the maximum size of the shaft.

Maximum clearance: In a clearance or transition fit it is the difference betweenthe maximum size of hole of the minimum size of the shaft.

Minimum interference: It is the difference between maximum size of hole andthe minimum size of shaft in an interference fit prior to assembly.


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Fig 2. 5

Maximum interference: In an interference fir or a transition fit it is thedifference between the minimum size of hole and the maximum size of shaft priorassembly.

Hole based system: This is one which the limits one the hole or kept constantand the variations necessary to obtain the classes of fit are arranged by varying

those on the shaft (Pl. note: Hole is kept constant)

Ex. Assume a hole of dimensions

1. Shaft (S1) of 28 mm Clearance fit

2. Shaft (S2) of 28 mm Transition fit

fig.2. 6

Shaft (S3) of 28 mm Interference fit

Shaft based system: This is one which the limits on the shaft are kept constant

and the variation necessary to obtain the classes of fit are arranged by varyingthe limits on the holes.


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fig.2.2.7

Note: (1) From manufacturing point of view it is preferable to use hole-based

system. Because holes are produced with standard tooling (reamers, drills) thosesize not adjustable and shaft sizes are readily variable. Thus hole based systemresults in considerable reduction in reamers and other previsions tools ascompared to a shaft based system.

(2) Basic shaft: A shaft whose upper deviations is zero.

(I.e. Max. lt. of size = Basic size)

(3) Basic hole: A hole whose lower deviation is zero.

(I.e. Min. lt. of size = Basic size)

Principles of inter-changeability: Today mass production techniques are

adopted for economic production. This approach led to breaking up of a completeprocess into several smaller activities, which in term are specialized. As a resultnone of the manufacturing activity is self reliant with respect to components.

Various mating components would undergo production on several machines.Hence it is absolutely essential to have a precise control over the dimensions of

portions, which have to match with other part. "Any one component selected atrandom should assemble correctly with any other mating component, that tooselected at random." When a system of this kind is ensured it is known asinterchangeable system.

Advantages or characteristics

An operator can easily specialize since he is concerned with only a limited portionof work. (Improves quality)


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Interchangeability ensures increased output with reduced production cost.

Assembly time is reduced considerably.

Decentralized production depending on the resources available can be achieved.(i.e. factories may be located suiting to availability of men, machine andmaterials).

Note: Interchangeability is followed only when certain standards are strictly

followed. When universal interchangeability is desired, the common standards areto be followed by all and all standards used by various manufacturing units should

be traceable to single i.e. international standards.

Universal or full interchangeability: This indicates that any component willmatch with other mating component without classifying manufacturedcomponents in sub group or without carrying out any minor alterations for matingpurpose. This type of interchangeability is not a must for interchangeable

production and many times not feasible also as it requires machine capable ofmaintaining high process capability and very high accuracy and also very closesupervision on production from time to time ( 3 -> process capability is to be

observed.)

For full interchangeability only such machine, whose process capability is equal to

an or less than the manufacturing tolerance allowed for that part should beselected.

2.2.18 Selective assembly: In this kind of production (assembly), the parts aremanufactured to rather wide tolerances and function as though they were slowlymanufactured in a precision laboratory to very close tolerance. In selective

assembly the components products by machined are classified into several groupsaccording to size.

This is done both for hole and shaft and then the corresponding groups will match

properly. Ex. If some parts are to assembled are manufactured to nominaltolerances of 0.01mm an automatic gauge can segregate them into ten differentgroups with 0.001mm limit for selective assembly.

Characteristics:

The parts obtained can be served with both high quality and low cost usingselective assembly.

The two component parts to be assembled must be kept with in the normaldistribution i.e. mean value should be at desired calculated value and processcapability of two machines producing shafts and holes must be identical otherwisefor some components the mating components will not be available.

Best and cheapest method of assembly of widely used in industries. Ex. Aircraft,automobile, ball bedding industries.

This concept overcomes the drawback of scraping the bad components afterinspection, thus reducing the loss.

Limit gauge: gauge are inspection tools of rigid design, without a scale, whichserve to check the dimension of manufactured parts, Gauges do not indicate the


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actual value of the inspected dimension on the work. They can only be used fordetermining as to whether the inspected parts are made with the specified limits.

Go No go gauges: These are two gauges having basic size corresponding tothe two limits of size for the component of used to check the dimensions of acomponent.

The go gauge checks the maximum metal condition.

The No-go gauge checks the minimum metal condition.

Note: In case of hole the maximum metal condition is when the hole is as smallas possible.

In case of shafts the maximum metal condition is when the shaft is on the high

limit of size.

The difference between the basic sizes of the two gauges is equal to thetolerances on the component. If the size of the component is within the

prescribed limits, the gauge made to the maximum metal limit will assemble withit, whereas the other will not. It for this reason the gauge made to the maximummetal limit is called the Go gauge and that made to the minimum metal limit iscalled the No Go gauge.

Note: closer attention must be paid to Go gauges than is necessary with No Go

gauges because a component might be accepted even though the No-Go gaugeassembles, under no circumstances should a component be accepted when the

Go gauge fails to assemble.


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Taylors principle: Taylor postulated some rules for designing the form ofgauges. When gauging a plain cylindrical plug gauges, the diameter of one, the

Go confirming to the maximum metal limit of the hole and the diameter of theother the No-Go confirming to the minimum metal limit. If the go gauge enterswhile the no go fails to enter the hole is considered to be with in the specifiedlimits.

Taylors principles may be stated as follows:

The Go gauge should be as far as possible be the geometrical equivalent of themating part and [(i.e. it should be able to check all the possible dimensions at atime (roundness, size, location etc)]

Separate No-Go gauges should check the minimum metal condition of thedimensions of the component. No-Go gauge should check only one element of the

dimension at a time.

This is because a No-Go gauge designed to check more than one dimension wouldfail to detect any dimension out side the minimum metal limit if one of the

dimensions is being checked within the minimum metal limit as illustrated below.

Fig.2.2.9

According to Taylor it is not adequate to use simple Go gauge on outerdimensions only but the shape is an important factor i.e. Go gauge should be full

form gauge and it should be constructed with reference to the geometrical formof the part being checked in addition to its size. In other words go gauge should

check all the dimensions of a work piece in the maximum metal condition.

As regarding no go gauges, Taylor stated that it need not be of full form and each

feature being dealt should be checked with a specific no go gauges. In otherwords no go gauge shall check only one dimension of the piece at the time for theminimum metal conditions.


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Thus according to it, a hole should completely assemble with a go cylindrical pluggauge made to the length of engagement of the hole and shaft. In addition, the

hole is measured or gauged to check that its maximum diameter is not largerthan the no go limit.

The Taylor principle interprets the limit of size for gauging holes and shafts asfollows:

For holes: The diameter of the largest perfect imaginary cylinder, which can beinscribed within the hole so that it just contacts the highest points of the surface.

The diameter of the cylinder should not be less than the go limit of size furtherthe maximum diameter at any position in the hole should not exceed the no go

limit.

For shaft: The diameter of the smallest perfect imaginary cylindrical which canbe circumscribed around the shaft so that it contacts the highest points of thesurface. The diameter of cylinder should not be larger than go limit of size.Further the minimum diameter

At any position on the shaft should not be less than "No Go limit of size.

Note: According the Taylors principle the Go limit gauge should be a plug ringgauge with exactly Go diameter and length equal to the engagement length ofthe fit to be made and this gauge must perfectly assemble with the work pieceinspected.

The No Go gauge should contact the work piece surface only at two diametricallyopposite points and have exactly No Go diameter at these two points. The gauge

should not be able to pass over in the work piece in any consecutive position in

the various diametric directions on the work piece length.

Variations from Taylors principle.

In many applications Taylors principle cannot be blindly followed. Some of thedeviations are allowed which basically do not deviate from the principles as such.

For Go limit: it is not advisable to use full form and full length gauges which arebulky when the manufacturing process assures that the error of straightness willnot affect the character to fit.

Only segmental cylindrical bar could be used when gauge happens to be too

heavy and when manufacturing process assures that the error in roundness willnot have any effect on the character of fit.

For shafts (heavy) full form ring gauge need not be used. The manufacturingprocess should takecare of the error ofroundness(especially lobbing)

and error of straightness in such

cases only gapgauges could be

sufficient.


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Fig.2.10

For No Go limit: only two point contact should be there according to Taylor but itis not feasible because these devices are subjected to rapid wear etc. Hencethese can be safely replaced by small planes / cylindrical surfaces / spherical

surfaces. For

Gauging very small holes and in cases where work pieces may be deformed to anoral by a two point mechanical contact device, the No Go gauge of full form, may

have to be used.

Material for gauges: The material for gauges should fulfill most of the followingrequirements:

Hardness to resist wearing.

Stability to preserve size of form.

Corrosion resistance.

Merchantability for obtaining the required degree of accuracy

Low co-efficient of linear expansion to avoid temperature effect.

Ex. High carbon steel, case hardened mild steel, invar steel.


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Wear Allowance: The measuring surfaces of Go gauges, which frequentlyassemble with work, rubs constantly against the surfaces of the work. This result

in wearing of the surfaces of the gauges of a result this loses initial dimensions.Thus due to wear Go plug gauges size is reduced. Hence a wear allowance isadded to the Go gauge in a direction opposite toe wear. Thus for a Go plug gaugethe wear allowance will be added while in a ring or gap gauge the allowance is

subtracted.


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Gauge tolerance or Gauge makers tolerance: Gauges like any other job,require a manufacturing tolerance, to compensate for imperfections in workman

ship. This is known as gauge makers tolerance.

There are 3 methods giving tolerances on gauges

First system: (For workshop and inspection gauges) in this method, workshopand inspection gauges one made separately and their tolerance zones are

different.

According to this system the tolerances on the workshop gauge are arranged to

fall inside the work tolerances, while the inspection any tolerances fall outside thework tolerances. In workshop gauges Go gauge should eat away 10% of worktolerance and similarly No Go gauges tolerance is 1/10th of work tolerance. Inrespection gauges, the gauges are kept beyond work tolerance by 10% of itsvalue.

Fig.2.12

Disadvantages:

The components may be rejected by workshop gauges by inspection gauges mayaccept them.

The workshops of inspection gauges have to be made separately as theirtolerances are different

Second system: (revised gauge limits) Under this system reducing the tolerance

zone of inspection gauge reduces the disadvantages of inspection gauges and theworkshop gauge tolerance remains the same.

In this system 110 of the range of work tolerance is covered instead of 120 th as inthe first system for inspection gauges.


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Fig.2. 13

Third system: (Present British System) In this system following principles are

followed along with Taylors principle.

Tolerance should be as wide as is consistent with satisfactory functioningeconomical production and inspection.

No work should be accepted which lies outside the drawing specified limits.


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This system gives same tolerance limits on workshop and inspection gauges andthe same gauge can be used for both purposes. The tolerance zone for the Go

gauges should be placed inside the work limits and the tolerance for the No Gogauges outside the work limits. Provision for wear of Go gauges is made by theintroduction of a margin between the tolerance zone for the gauge and maximummetal limit of the work.

Fig.2.14

Fig.2.15

Types of limit gauges:

Limit gauges for internal diameters of holes


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Full form cylindrical plug gauge: A small circumferential groove is cut near theleading end of the gauge and the remaining part of the cylinder is slightly reduced

in order to act as a pilot.

Fig 2. 16

Full form spherical plug or disc gauge:

Segmental cylindrical bar gauge:

Fig.2.17

Gauges for tapers: A taper is tested by using taper plug a or ring gauge. Theimportant thing in testing a tapered job is to check the diameter at bigger endand the change of diameter per unit length.


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FIG:2.18


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CHAPTER - 3

Comparators

Laboratory standards: comparators are used as laboratory standards fromwhich

Working or inspection gauges are set and co-related.

Working gauges: they are also used as working gauges to prevent work

spoilage

and to maintain required tolerance at all-important stages of manufacture.

Types of Comparators:

The comparators differ principally in the method used for amplifying andrecording the variation measured. Most commonly available comparators are ofthe following types:

Mechanical comparators

Optical comparators

Electric and electronic comparator machines

Pneumatic comparators

Fluid displacement comparator machines

Projection comparators

Multi-check comparator Automatic gauging

Application of Comparators:

Used as laboratory standards from which working or inspections gauges

are set and correlated.

Used, as working gauges to prevent work spoilage and to maintain

required tolerance at all-important stages of manufacture.

Used as final inspection gauges where selective assembly of production

parts is necessary.

Used as receiving inspection gauges for checking parts received from

outside sources.

Advantages:

Not much skill is required on the part of operation.

The calibration of instrument over full range is not required since

comparison is done with a standard end length.

Zero error existing in comparator also does not lead to any problem.

High magnification resulting into great accuracy is possible.

Mechanical Comparator:


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Mechanical comparators use mechanical methods of amplifying the movement ofthe contact plunger and their manufacture requires high degree of accuracy.

Usual magnification of the mechanisms ranges from about 250 to 1,000.

Mechanical Comparator: Sigma comparator is the most widely used for higherprecision work. Magnification ranges from 300 to 5000. Figure shows the detailsof the magnifying system of the comparator. Plunger mounted on a pair of slitdiaphragms obtains the frictionless linear motion. A knife-edge is mounted on itand bears upon the face of the moving member of a cross strip hinge. This hingeconsists of the moving component and a fixed member, which are connected bythin flexible strips alternately at right angles to each other. A Y arm is attached

to the moving member which has an effective I. If the distance of the hinge fromthe knife-edge be a then the magnification of the first stages is I/a. A phosphor bronze strip is attached to the two extremities of the Y arm and is passed round

a radius r attached to the pointer spindle. The second stage magnification is R/rwhere R is the length of pointer. Then total magnification is I/a x R/r. The

magnification can be altered by tightening one end slackening the other screwattaching the knife-edge to the plunger and thus adjusting the distance a.

Some features of this instrument:

The shock will not be transmitted since the knife-edge moves away from

the moving member of the hinge.

A non-ferrous disc is mounted on the pointer spindle and it is made tomove in field of a permanent magnet to obtain deadbeat reading.

Parallax error is avoided by having a reflective strip on the scale.

A magnet plunger on the flame and keeper bar on the top of the plunger is

used to have the constant pressure over the range of the instrument.


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Electrical Comparators: Electrical and electronic comparators depend on wheatstone bridge circuit for their operations. We know that for the bridge is to balance

electrically the ratio of the resistances in each pair must be equal.

Fig 3.2 Electrical Comparator

The principle of electrical comparator (electrical limit gauge) is explained withreference to the above figure. If alternating current is applied to the bridge, theinductance and capacitance of the arms must also be accounted for along withresistance. The pair of coils forms a pair of inductance. The movement of theplunger displaces an armature thus causing a variation in the inductance in thecoils. The amount of unbalance caused by movement of measuring plunger isamplified and shown on a linear scale magnifications of about 30,000 are possible

with this system. Zero setting arrangement is provided. The degree ofmagnification is adjustable and other examples of electrical comparators are

electricator, electric gage and sigma electronic comparator.

Advantages of Electrical Comparators:

Remote indication is possible

High magnification with smaller number of moving parts

Insensitive to vibration and mechanism carrying the pointer is high

The cyclic vibration reduces errors due to sliding friction on an AC supply

Smaller measuring unit and several magnifications is possible with same

instrument

Optical comparators:

All optical comparators involve some system of magnification, generally through

tilting of a mirror which provides an optical lever by reflecting a beam of light.The Cooke comparator works on this principle.


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Cookes Optical Comparator

Fig 3.3

A plunger working in a head consists of a mechanical lever carrying two pivots atits ends. On one end a plunger actuates it and the other end actuates a mirror. A

circular scale is provided. The mirror onto the scale accordingly reflects a beam oflight coming through an electric bulb.

Optical comparators are used in metrology labs and standard room, but not inroutine production checking.

The optical system offers the advantage of lightness & simplicity in its indicatingunit.

Pneumatic comparators:

A pneumatic gauge consists of 2 important Units:

An air controller to regulate the pressure and the amount of airflow from

the supply. The unit incorporates a manometer A gauging head designed for the work to be checked.

Air supply from the supply is fed into the instrument at pressure higher than the

constant pressure required in the manometer. Air enters the tube extendingdownwards into a tank of liquid. Initially the tube is filled with liquid to the same

level as that in the tank. Entry of air into the top of the tube exerts pressure onthe liquid to completely empty it. Any excess pressure than that necessary to

clear the tube will escape into the tank as air bubbles. The pressure between thevalve V and the control jet G is therefore always the same, irrespective of anyvariation in the air supply pressure.


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The air will now pass through the control jet at the full controlled pressure andwill reach the measuring jet S. If this jet S cannot pass the full volume of the air

from the control jet, then a pressure will tend to develop between them. The backpressure is instantly released through the opening into the manometer tubewhere it will change the height of the liquid, which indicates the amount of backpressure built up. The back pressure is the result of restriction at the measuring

jet due to the effect of variations in the dimension of the work being checked sothat the variations in the height of the liquid of the manometer are a measure of

the dimension variations.

Pneumatic Comparator

Fig 3.2.7.1

The pneumatic method is easily adaptable for the examination of bores, since themachining element can be housed inside the plug used for accommodating thecomponent. This method is very simple and minimum wear of working parts takesplace, but it requires a supply of air to provide the motive force.


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Angular measurements and Interferometer

Bevel protractors as per Indian standard practice.

The bevel protractors are of two types. They are

1. Mechanical bevel protractor, and2. Optical bevel protractor.

Mechanical Bevel Protractor

The mechanical bevel protractors are further classified into four types; A, B, C

and D. in types A and B, the Vernier is graduated to read to 5 minutes of arc

whereas in case of type C, the scale is graduated to read in degrees and the bevelprotractor is without Vernier or fine adjustment device or acute angle attachment.The difference between types A and B is that type A is provided with fineadjustment device or acute angle attachment whereas type B is not. The scales ofall types are graduated either as full circle marked 0-90-0-90 with one Vernier or

as a semicircle marked 0-90-0 with two Verniers 1800 apart. Type D is graduatedin degrees and is not provided with either Vernier or fine adjustment device or

acute angle attachment.

Fig 4.1

Optical bevel protractor:

In case of an optical bevel protractor, it is possible to take reading upto

approximately 2 minutes of arc. The provision is made for an internal circularscale, which is graduated in divisions of 10 minutes of arc. Readings are taken

against a fixed index line or Vernier by means of an optical magnifying system,which is integral with the instrument.


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Fig 4.2

Clinometers :

A Clinometer is a special case of application of spirit level. Here the spirit level ismounted on a rotary member carried in a housing. One face of the housing formsthe base of the instrument. On the housing, there is a circular scale. The circularscale can measure the angle of base. The Clinometer is mainly used to determine

the included angle of two adjacent faces of work piece. Thus for this purpose, theinstrument base is placed on one face & the rotary body adjusted till zero reading

of the bubble is obtained. The angle of rotation is then noted on the circular scaleagainst the index. A second reading is then taken in a similar manner on the

second face of the work piece. The included angle between the faces is thedifference between the two readings.

Clinometers are also used for checking angular faces, and relief angles on largecutting tools & milling cutter inserts. These can also be used for setting inclinabletable on jig boring machines & angular work on grinding machines etc.. The mostcommonly used Clinometer is of the Hilger & Watts type.

Precision Microptic Clinometer :

These are also used for measuring angular displacements of small parts & settingout angles. The special features of Precision Microptic Clinometer are directreading over the range 00-3600, optical reading system; totally enclosed glasscircles & easy to read scales ; main scale & micrometer scale visible

simultaneously in the eyepiece external scale for rapid coarse setting, slowmotion screw for fine setting, eye piece rotatable to most convenient viewingposition, & hardened ground steel base.

Precision Microptic Clinometer utilizes bubble unit with a prismatic coincidencereader, which presents both ends of the bubble as adjacent images in a split field

of view. As the vial is leveled, the two half images move into coincidence, makingit very easy to see when the bubble is exactly centered, without reference to anygraduation.

To determine the inclination of the Clinometer, the bubble unit is levelled & scaleis read. On looking through the reader eyepiece, the apertures can be seen. The

upper aperture contains two pairs of double lines & two single lines; to set themicrometer the knob is turned until the single lines are brought exactly central


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between the double lines. The scales can be read, the required angle being thesum of the readings of the main scale & the micrometer scale. The double lines

are imaged from one side of circle & the single ones from a point diametricallyopposite; by using the double lines as an index for the single line, any residualcentering error of the circle is cancelled out. An integral low voltage lampilluminates the scales. The bubble unit is day light illuminated, but is also

provided with a lamp for alternative illumination.

The reference for inclination is the bubble vial. In order to measure the inclination

of a surface, the vial to which the circle is attached is turned until it isapproximately level; then the slow motion screw is used for a final adjustment to

center the bubble. To measure the angle between two surfaces the Clinometer isplaced on each surface in turn & the difference in angle can be calculated. TheClinometer can be used as a precision setting tool to set a tool head or table at aspecific angle also.

Fig 4.3

Optical Instruments for Angular Measurement:

Autocollimator:

This is an optical instrument used for the measurement of small angular

differences. For small angular measurements, autocollimator provides a verysensitive & accurate approach. It is essentially an infinite telescope & a collimator

combined into one instrument.

4.2.5.2 Principle of auto collimator:

Auto collimator is an optical instrument of small angular differences. For smallangular measurement, auto collimator provides a very sensitive and accurateapproach. Auto collimator is actually a infinity telescope and a collimatorcombined into one instrument. The instrument is designed to measure small

angular defection and may be used in conjuncture with a plane mirror or otherreflecting device. If a scale is provided on the graticule the tilt of the reflecting


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surface, so that a direct two to one reading is obtained. The light rays thusreflected are linearly displaced from the target by a amount of 20f.

Fig4.4

Figure shows the diagrammatic representative principle of a autocollimator. The

gratitude GH is focused in the principal focal plane of the objective lens isilluminated from a suitable light rays parallel to the optic axis. If a reflectingmirror AA is situated at right angle to the optical axis, then the light rays will bereflected back on their original paths and the returned image of the object willcoincide with the object at G.

If the mirror is deflected about O through an angle to the position BB and

therefore to be at right angles to the optical axis, the graticule, an image of the

object, giving a displacement x from G. the distance x is a measure of angle 2

and which is twice the angle deflection of the mirror.

If

X distance traveled by the image from the initial position of the object.


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F focal length of the lens.

the angle of tilt of the reflecting mirror and considered to be small.

Then,

2 = x/f where x = 2f .

The points to be noted are:

1. The position of the final image does not depend upon the objective lens.

2. If the reflector is completely moved back i.e. if become gauge, thereflected rays will completely miss the lens and no image will be formed.

3. For high sensitivities i.e. for large value of X for smaller angular deviation

a long focal length is required.

Autocollimator Applications :

i. The measurement of straightness & flatnessii. Precise angular indexing in conjunction with polygons

iii. Comparative measurement using master anglesiv. Assessment of square ness & parallelism of components

v. Measurement of small linear dimensions

Angle Dekkor:

This is also a type of an autocollimator. It contains a small illuminated scale in thefocal plane of the objective lens. This scale in normal position is outside the viewof the microscope eye piece as shown in the fig: The illuminated scale is

projected as a parallel beam by the collimating lens which after a striking thereflector below the instrument is re-focused by the lens in the field of view of the

eye piece. In the field of view of the microscope there is another datum scalefixed across the center of screen & the reflected image of the illuminated scale isreceived at right angle to this fixed scale & the two scales, in this positionintersect each other. Thus the reading on the illuminated scale measures angulardeviation from one axis at 900 to the optical axis & the reading on the fixeddatum scale measures the deviation about an axis mutually perpendicular to theother two. In other words, changes in angular position of the reflector in twoplanes 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. Thewhole of the optical system is enclosed in a tube, which is mounted on an

adjustable bracket. There is a lapped flat & reflective base on which all thesethings are placed. It is mostly used as a Comparator. The instrument measures by

comparing the readings obtained from a standard, a sine bar or combination ofangular gauges with that from the work under test. Though this is not a preciseinstrument in comparison to autocollimator, it has wide field of application forgeneral angular measurement, as angular variations are read direct without theoperation of a micrometer.


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Fig 4.5


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CHAPTER - 5

Screw Thread and Gear Measurement

Terminology:

Fig 5. 1

Screw thread: a screw thread is the helical ridge produced by forming acontinuous helical groove of uniform section on the external or internal surface of

a cylinder or a cone. A screw thread formed on a cylinder is known as straight orparallel screw thread, while the one formed on a cone is known as tapered

threads.

External thread: a thread formed on outside of a work piece is known asexternal thread. Example: on bolts or studs etc.

Internal thread: a thread formed on inside of a work piece is known as internalthread. Example: on a nut or female screw gauge.

Multiple-start screw thread: forming two produces this or more helical grooves

equally spaced and similarly formed in an axial section on a cylinder. This givesquick traverse without sacrificing core length.

Axis of a thread: this is imaginary line running longitudinally through the centerof the screw.

Hand (right or left hand thread): Suppose a screw is held such that theobserver is looking along the axis, if a point moves along the thread in clockwise

direction and thus moves away from the observer, the thread is right hand: and ifit moves towards the observer the thread is left hand.

Form of thread: this is the shape of the contour of one complete thread as seenin axial section.

Crest of thread: this is defined as the prominent part of thread, whether it isexternal or internal.


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Root of thread: this is defined as bottom of the groove between the two flanksof the thread, whether it is external or internal.

Flanks of thread: these are straight edges, which connect the crest with theroot.

Angle of thread (included angle): this is the angle between the flanks andslope

of the thread measured in an axial plane.

Flank angle: the flank angles are angles between individual flanks and theperpendicular to the axis of the thread which passes through the vertex of thefundamental angle. The flank angle of a symmetrical thread is commonly termedas the half angle of thread.

Pitch: the pitch of the thread is the distance, measured parallel to the axis of the

thread, between corresponding points on the adjacent forms in the same axialplane and on the same side of the axis. The basic pitch is equal to the lead

divided by the number of the thread starts. On drawings of thread sections, thepitch is shown as the distance from the center of one thread crest to the center of

next, and this representation is correct for single start as well as multi-startthreads.

Lead: lead is the axial distance moved by the threaded part when it is given onecomplete revolution about its axis with respect to fixed mating thread. theuniformity of pitch measurement does not necessarily assure uniformity of lead.variations in either or pitch cause the functional or virtual diameter of thread to

differ from the pitch diameter.

Thread per inch: this is the reciprocal of pitch in inches.

Lead angle: on straight threads, lead angle is the angle made by the helix of thethread at the pitch line with plane perpendicular to the axis. The angle ismeasured in actual plane.

Helix angle: on a straight thread, the helix angle is the angle made by the helixof the thread at the pitch line with the axis. the angle is measured in an axialplane.

Depth of thread: this is the distance from the crest or tip of the thread to the

root of the thread-measured perpendicular to the longitudinal axis. This couldalso be defined as the distance measured radially between the major and minorcylinders.

Axially thickness: this is the distance between the opposite faces of the samethread measured on the pitch cylinder in the direction parallel to the axis of thethread.

Truncation: a thread is sometimes truncated at the crest or at the root or at

both crest and root. Truncation at crest is the radial distance from the crest tonearest apex of the fundamental triangle. Similarly the truncation at the root isthe radial distance from the root to the nearest apex.


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Addendum: for an external thread, this is defined as the radial distance betweenthe major and pitch cylinders. For an internal thread this is the radial distance

between the minor and pitch cylinders.

Dedendum: this is radial distance between the pitch and minor cylinder for anexternal thread and for internal thread, this is radial distance between the majorand pitch cylinders.

Major diameter: in case of a straight thread, this is the diameter of the majorcylinder (imaginary cylinder, coaxial with the cylinder, which just touches the

roots of an internal thread). It is often referred to as root diameter or conediameter of external threads.

Effective diameter or pitch diameter: in case of straight thread, this is thediameter of the pitch cylinder (the imaginary cylinder which is coaxial with theaxis of the screw and intersects the flank of the threads in such a way as to makethe width of the threads and width of the spaces between the threads equal.). Ifthe pitch cylinder were imagined as generated by the straight line parallel to theaxis of the screw that straight line is referred to as pitch line. Along the pitch line

the widths of the threads and the widths of the spaces are equal on a perfectthread. This is the most important dimension as it decides the quality of the fit

between screw and nut.

Functional (virtual) diameter: for an external or internal thread, this is thepitch diameter of the enveloping thread of perfect pitch, lead and flank angleshaving full depth of engagement but clear at crest and root. This is defined over aspecified length of thread. This may be greater than the effective diameter by anamount due to errors in pitch and angle of thread. The virtual diameter being the

modified effective diameter by pitch and angle errors is the most important singledimension of a screw thread gauge. In case of a taper screw thread, the cone

angle of taper, for measurement of effective diameter and whether the pitch ismeasured along the axis or along the pitch code generator also needs to be

specified.

Errors in threads:

In case of plain shafts and holes, there is only one dimension, which has to beconsidered, and errors on this dimension if exceed the permissible tolerance, will

justify the rejection of the part. While in case of screw threads there are at leastfive important elements, which require consideration, and error in any one of

these can cause rejection of the thread. In routine production all of theseelements (major dia, minor dia, effective dia, pitch and angle of thread form)

must be checked and method of gauging must be able to cover all theseelements.

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

of the assembly due to interference between the flanks.

Similarly pitch and angle errors are also not desirable as they cause progressive

tightening and interference on assembly. These two errors have a special

significance as they can be precisely related to effective diameter.

Pitch errors in screw threads:


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A point cutting tool generates Generally screw threads. In this case, for pitch tobe correct, the ratio of linear velocity of tool and angular velocity of work must be

correct. This ratio must be maintained constant; otherwise pitch errors will occur.If there is any error in the pitch the total length of thread engaged would beeither too great or too small, the total pitch in overall length of the thread beingcalled the cumulative pitch error. Various pitch errors are:

Progressive pitch error

Periodic pitch error

Drunken error

Irregular errors

Drunken error: this is the one having erratic pitch, in which the advance of thehelix 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. Insuch a thread, the pitch measured parallel to the pitch measured parallel to the

thread axis will always be correct, the error being that the thread is not cut to thetrue helix. If the screw thread be regarded as an inclined plane wound around the

cylinder and if the thread be unwound from the cylinder, (that is development ofthe thread be taken) then the drunkenness can be visualized. The helix will be acurve in the case of drunken thread and not a straight line as shown in the figure.

Fig 5.2.

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

Progressive pitch error: this error occurs when the tool work velocity ratio isincorrect, though it may be constant. It can also be caused 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 trainbetween the work and lead screw. E.g. while metric threads are cut with an inchpitch lead screw and a translatory gear are not available. A graph between thecumulative pitch error and the length of thread is generally a straight line in case

of progressive error.


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Periodic pitch error: this repeats itself at regular intervals along the thread. Inthis case, successive portions of the thread are either shorter or longer than the

mean. This type of error occurs when the tool work velocity ratio is not constant.This type of error also results when the thread is cut from a leads crew, whichlacks square ness in the abutment causing the leads crew to move back and forthin each revolution. Thus the errors due to these cases are cyclic in nature and so

the pitch increases to a maximum value, decreases to the mean and then to theminimum value and so on. The graph between the cumulative pitch error and

length of threads for this error will, therefore, be of sinusoidal form.

Irregular errors: these arise from the disturbances in the machining setup,

variations in the cutting properties of material etc. thus they have no specificcauses and correspondingly no specific characteristics also. These errors could besummarized as follows:

Erratic pitch: this is irregular error in pitch and varies irregularly in magnitudeover 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 error.

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 periodicerrors.

Screw threads measurements:

There are a large number of different standard forms of screw threads in common

use. A few important measuring types of screw thread elements are discussed

here. Here the nomenclature of the screw threads is not discussed here.

Full diameter: for measuring the full diameter of a screw, an ordinarymicrometer with anvils of a diameter sufficient to span two threads may be used.To eliminate the effect of errors in the micrometer screw and the measuringfaces, it is advisable first to check the instrument on a cylindrical standard ofabout the same diameter as the screw. For such purposes a plug gauge is useful.

Core diameter: the diameter over the root of a thread may be checked by

means of a special micrometer adapted with shaped anvils, or an ordinarymicrometer may be used in conjunction with a pair of vee pieces. The second

method is more universal in application, and a diagram showing the arrangement

is given in the figure. It is important that while making the test the micrometer ispositioned at right angles to the axis of the screw being measured.

The vee pieces used for this test are of hardened steel with an angle of about 450

finished with a radius less than that of the root of the thread. The back facesshould be finished flat, perpendicular with the axis of the vee and parallel with theedge of the radius.

Effective diameter: the only reliable means of inspecting the effective diameter

of a screw is to use some method, which enables a reading to taken from thestraight, sloping flanks of the threads.

This is accomplished in a simple manner by using small cylindrical test wires,which rest in the thread angle and make contact with the sloping sides. If means


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are available (e.g. a floating micrometer) for maintaining the micrometer at theright angles to the screw axis, two opposite wires may be used; or else three

wires are required to align the micrometer, and this method is the rule whenusing an ordinary micrometer. The wires should be hardened and polished andtheir surfaces should be round, straight, parallel, and uniform to a high degree ofaccuracy.


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Three-wire method: checking the effective diameter when a screw is measuredover wires is given below for general case. One side of the screw is shown in thefigure, where w= distance over the wires and D E the effective diameter. The wireis designated with radius r and diameter d.From this general formula we mayapply the special adaptation for common threads.

Fig 5.4


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Pitch:

An error in the pitch requires a compensating reduction in effective diameter ofapproximately twice the amount; pitch errors are to be reduced to absoluteminimum. A pitch-measuring device consists of a bed with centers at each end tosupport the screw, with alternative means for holding nuts and sleeves wheninternal threads are to be tested. Sliding along the bed and moved by an accuratemicrometer is head which carries a feeler piece or stylus shaped to fit in the veeof the thread provided with an indicator which shows when it is bedded home

centrally in the vee (i.e. in its lowest position). When making a test, the head ismoved along causing the stylus to seat itself successively in each of the threads

over the length being examined. Observation and analysis of the micrometerreading obtained then enables the pitch of the thread to be determined. Adiagrammatic sketch of the stylus is shown in the figure.

Fig 5.5

With a good projection measuring the image and dividing by the magnificationmay determine the pitch of the portion of the thread. Greater accuracy isobtained if, the measurement is made perpendicular to the thread flanks (insteadof measuring parallel to the screw axis), and the result divided by the cosine of

half of the thread angle. Thus in figure length AB is measured when pitchAC=AB/cosa .


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Measurement of gear teeth elements:

A few types of measuring gear teeth elements are discussed here. Thenomenclature of a toothed is a prerequisite for the following section.

The tooth Venire:

Fig 5.6

A gear tooth Vernier, figure is provided with two mutually perpendicular scales 1and 5; the first is used in adjusting for a chordal height and the second, to

measure the chordal tooth thickness. Before measurement, the adjustable tongue3 is set by means of Vernier 2 to the height at which the chordal thickness is tobe measured and locked in position. The measuring jaws are moved apart, andafter testing the instrument with the tongue on the tip circle of gear being

measured, the jaws are drawn closer together and brought into contact with thetooth flanks.

The values of the measured chordal thickness are directly read from Vernier 4.Measurement at the constantchord tooth thickness is preferable (the constantchord is the chord between the points of contact of the basic rack profile with thetooth flanks at a normal section). The nominal values of the constant chord heightand tooth thickness are selected from the corresponding tables compiled or are

calculated by the corresponding formulae.

For standard spur gears with a normal pressure angle of 20 0< the constant-chordheight h equal to

h=0.7476m.

And the constant chord tooth thickness is

S=1.387m.

Where m is module, mm.

Base pitch:


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The base pitch is the circular pitch of the teeth measures on the base circle. Thetooth span micrometer is used to check the mean value and variation in the base

tangent length. It varies from the standard micrometers only with respect to themeasuring anvils. Here disk type measuring anvils are used. The disk anvil framemay be partly cut away. These micrometers are often used to determine anunknown gear module. To this end the base tangent length is measured first over

n teeth then over n-1 teeth. The difference in measurement gives the base pitcht0 which is used for module by the formula m=t0/p cosf where f is the pressure

angle.


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Gear Measurements

The most commonly used forms of gear teeth are involute & cycloid. The involutetooth is derived from the trace of the point on a straight line, which rolls withoutslipping around a circle, which is the base circle, or it could be defined as a locusof a point on a piece of string which is unwounded from a stationary cylinder. Thecycloid tooth is derived from the curve, which is the locus of a point on a circle

rolling on the pitch circle of the gear. Here the addendum tooth is the trace of thepoint on a circle rolling outside of the pitch circle and this is an epicycloidal curve

whereas the dedendum portion of the tooth is the trace of the point on a circlerolling on the inside of the pitch circle of the gear and is hypocycloidal gear.

The various types of commonly used gears are:

Spur gear: it is a cycloid gear whose tooth traces is straight line.

Helical gear: it is a cylindrical gear whose tooth traces is straight helices.

Spiral gear: a gear whose tooth traces is curved line.

Straight bevel gear: a gear whose tooth traces is a straight-line generator of acone. It is conical in form in operating and intersecting axes usually at angles.

Worm gear pair: the worm and mating worm wheel have their axes non-paralleland non-intersecting.

Gear Terminologies


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FIG.5.7

PITCH CIRCLE

When two gears are meshed and running there are two circles which appear to

roll one on another. These two rolling circles are called pitch circles. Diameter ofthe gear is represented by diameter of the pitch circles and is denoted by "d".

ADDENDUM CIRCLE

It is a circle, which passes through the tip of the tooth.

DEDENDUM CIRCLE

It is a circle, which passes through the root of the tooth.

TOOTH THICKNESS

It is the thickness of the tooth measured along the pitch circle.

SPACE WIDTH

It is the distance between two adjacent teeth measured along the pitch circle.

CIRCULAR PITCH (P or Pc)

It is the distance from a point on one tooth to a similar point on the adjacenttooth measured along the pitch circle. It is also the ratio of the circumference ofthe pitch circle to the number of teeth.

Pc = d/t

Where t number of teeth

FACE WIDTH

It is the length of the tooth measured parallel to the axis of the gear.

ADDENDUM

It is the radial height of the tooth between the pitch circle and addendum circle.

DEDENDUM

It is the radial height of the tooth between the pitch circle and dedendum circle.

FACE

It is the working area of the tooth between addendum circle and pitch circle.

FLANK


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It is the working area of the tooth between pitch circle and dedendum circle.

MODULE (m)

It is the diameter measured per tooth of the gear. It is always represented in mmonly m= d/t

But Pc = d/t

Pc = m

DIAMETRAL PITCH (Pd)

It is a reciprocal of module of the number of teeth per mm of diameter.

PITCH POINT

It is the point of contact or tangency of two pitch circles.

LINE OF CONTACT

It is the line along which the points of contact between two pairs of teeth

proceed.

PRESSURE ANGLE

It is the angle between the line of contact and the common tangent at the pitchpoint.

CLEARANCE

It is the difference between the dedendum and addendum.

BACKLASH

It is the difference between the space width and tooth thickness.

LENGTH OF PATH OF CONTACT

It is the distance measured along the line of contact from the point of

engagement to the point of disengagement.

GEAR RATIO (G)

It is the ratio of the gear diameter to the pinion diameter or the ratio of the pinionspeed to the gear speed or ratio of number of teeth on gear to that on pinion.

G = D/d = n/N = T/t

Measurement of individual elements

Measurement of tooth thickness


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The permissible error or the tolerance on thickness of tooth is the variation ofactual thickness of tooth from its theoretical value the tooth thickness is generally

measured at pitch circle and is therefore, the pitch line thickness of the tooth. Itmay be mentioned that the tooth thickness is defined as the length of an arc,which is difficult to measure directly. In most of the cases, it is sufficient tomeasure the chordal thickness that is the cord joining the intersection of the

tooth profile with the pitch circle. Also the difference between chordal tooththickness and circular tooth thickness is very small for gear of small pitch. The

thickness measurement is the most important measurement because most of thegears manufactured may not undergo checking of all other parameters, but

thickness measurement is a must for all gears. There are various methods ofmeasuring the gear tooth thickness:

Measurement of tooth thickness by

Gear tooth vernier caliper.

Constant chord method.

Base tangent method.

Measurement by dimension over pins

The tooth thickness can be very conveniently measured by a gear tooth vernier.Since the tooth thickness varies from the tip of the base circle of the tooth, theinstrument must be capable of measuring the tooth thickness at a specifiedposition on the tooth. Further this is possible only when there is somearrangement to fix that position where the measurement is to be taken. The tooth

thickness is generally measured at pitch circle & is, therefore, referred to as pitch

line thickness of tooth. The gear tooth in the vernier has two vernier scales &they are set for the width w of the tooth & the depth d from the top, at which woccurs.

FIG- 5.8

Considering one gear tooth, the theoretical values of w & d can be found outwhich may be verified by the instrument. In the fig it may be noted that w is a


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chord ADB, but tooth thickness specified as an arc distance AEB. Also the distanced adjusted on instrument is slightly greater than the addendum CE, w is therefore

called chordal thickness & d is called the chordal addendum.

From the fig, w=AB=2AD,

Now angle AOD = = 3600/4N

Where N is the number of teeth,

w=2AD=2*AO*sin

= 2R sin (360/4N) (R=PITCH CIRCLE RADIUS)

Module, m= P.C.D/number of teeth = 2R/N

R=N*m/2

w=(N*m)*sin(360/4N)

Also from fig, d= OC-OD

OC = OE+ addendum = R+m

= (N*m/2)+m

OD = R * cos

= N*m/2 cos(90/N)

d = (N*m/2)+m-(N*m/2) cos(90/N)

Any error in the outside diameter of the gear must be allowed for when

measuring tooth thickness.

In case of helical gears the above expressions must have to be modified to takeinto account the change in curvature along the pitch line. These formulae applywhen backlash is ignored.

Gear tooth Caliper


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FIG-5.9

It is used to measure the thickness of gear teeth at the pitch line or chordalthickness of teeth & the distance from the top of a tooth to the chord. Anadjustable tongue, each of which is adjusted independently by adjusting thescrew on graduated bars, measures the thickness of the tooth at pitch line & the

addendum. The effect of zero errors should be taken into consideration.

This method is simple & inexpensive. However it needs different setting for a

variation in number of teeth for a given pitch & accuracy is limited by the leastcount of instrument. Since the wear during use is concentrated on the two jaws,caliper has to be calibrated at regular intervals to maintain the accuracy ofmeasurement.

Gear tooth Vernier

Most of the times a gear Vernier is used to measure the tooth thickness. As the

tooth thickness varies from top to the bottom, any instrument for measuring on asingle tooth must.

Fig 5.10

A gear tooth Vernier, figure is provided with two mutually perpendicular scales 1and 5; the first is used in adjusting for a chordal height and the second, to

measure the chordal tooth thickness. Before measurement, the adjustable tongue3 is set by means of Vernier 2 to the height at which the chordal thickness is tobe measured and locked in position. The measuring jaws are moved apart, andafter testing the instrument with the tongue on the tip circle of gear beingmeasured, the jaws are drawn closer together and brought into contact with thetooth flanks.

The values of the measured chordal thickness are directly read from Vernier 4.

Measurement at the constantchord tooth thickness is preferable (the constantchord is the chord between the points of contact of the basic rack profile with the


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tooth flanks at a normal section). The nominal values of the constant chord heightand tooth thickness are selected from the corresponding tables compiled or are

calculated by the corresponding formulae.

For standard spur gears with a normal pressure angle of 20 0< the constant-chordheight h equal to h=0.7476m.

And the constant chord tooth thickness is

S=1.387m.

Where m is module, mm.

Base pitch

The base pitch is the circular pitch of the teeth measures on the base circle. Thetooth span micrometer is used to check the mean value and variation in the base

tangent length. It varies from the standard micrometers only with respect to themeasuring anvils. Here disk type measuring anvils are used. The disk anvil framemay be partly cut away. These micrometers are often used to determine an

unknown gear module. To this end the base tangent length is measured first overn teeth then over n-1 teeth. The difference in measurement gives the base pitcht0 which is used for module by the formula m=t0/ cos where is the pressure

angle.

FIG:5.11


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GENERAL MEASUREMENT SYSTEM

1. Introduction

2. General Measurement System

3. Types of Input Quantities

4. Error Classification

5. Calibration

6. Experimental Test Plan

7. Measurements

1. Introduction

Measurements are important for quality assurance and process control, and to obtain

process information. Three aspects will be covered in the Experimental Engineering

class:

Sensors-- fundamentals of sensors for mechanical and thermal quantities.

Systems-- response and configuration.

Experimental methods-- planning, acquisition, and analysis.

Quantities of interest include displacement, strain, temperature, pressure, force,

torque, moment,velocity, acceleration, volumetric flow rate, mass flow rate,

frequency, time, heat flux, etc.

1.1 Definitions commonly used in Sensors and Instrument

Readability-- scales in analog instrument.

Least Count-- smallest difference between two indications. Static Sensitivity-- displacement versus input, e.g., scale in oscilloscope (cm/mV),

etc.

Hysteresis-- measured quantity which depends on the history to reach that particular

condition; generally it is a result of friction, elastic deformation, magnetic, or thermal

effects.

Accuracy-- deviation of a reading from a known input.

Precision-- related to reproducibility of measurement.


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Error-- deviation from a known input, a measure of accuracy.

Uncertainty-- data scatter, a measure of precision.

1.2. Calibration

Calibration involves a comparison of a particular instrument with respect to a known

Quantity provided from (1) a primary standard, (2) a secondary standard with a higher

accuracy

than the instrument to be calibrated, or (3) a known input source.

1.3. Standards

The National Institute of Standards and Technology (NIST) has the primary

responsibilityto maintain standards for such quantities as length, time, temperature, and electrical

quantities for the US.

Mass. International Bureau of Weights and Measurements (Sevres, France) maintains

several primary standards, e.g., the kilogram is defined by the mass of a particular

platinum iridium bar maintained at very specific conditions at the Bureau.

Time. One second has been defined as the time elapsed during 9,192,631,770 periods

of

the radiation emitted between two excitation levels of the fundamental state of

cesium-

The Bureau International del' Hueure (BIH) in Paris, France maintains the primary

standard for clock time. The standard for cyclical frequency is based on the time

standard, 1 Hz = 1 cycle/second, or 1 Hz = 2 radian/second.

Length. One meter is defined as the length traveled by light in 3.335641 x 10-9 second

(based on the speed of light in a vacuum).

Temperature. The absolute practical scale is defined by the basic SI unit of a Kelvin,

K.

The absolute temperature scale, Kelvin, is based on the polynomial interpolation

between th eequilibrium phase change points of a number of pure substances from the

triple point of th eequilibrium hydrogen (13.81 K) to the freezing point of gold

(1337.58 K). Above 1337.58 the 4 scale is based on Planck's law of radiant emissions.

The details of the temperature standard are governed by the International Temperature

Scale-1990.


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Electric Dimensions; volt (V), ampere (A), and ohm ( ) . One ampere absolute is

defined by 1.00165 times the current in a water-based solution of AuN2 that deposits

Au at an electrode at a rate of 1.118 x 10-5 kg/s. One ohm absolute is defined by

0.9995 times the resistance to current flow of a column of mercury that is 1.063 m inlength and has a mass of 0.0144521 kg at 273.15

K. The practical potential standard makes use of a standard cell consisting of a

saturated solution of cadmium sulfate. The potential difference of two conductors

connected across such a solution is set at 1.0183 V at 293 K.

Laboratory calibration is made with the aid of secondary standards, e.g. standard cells

for

Voltage sources and standard resistors, etc.

1.4. Dimensions and Units

Fundamental dimensions are: length, mass, time, temperature, and force. Basic SI

units

are: m, kg, s, A, K, cd (candela, luminous intensity), and supplemental units are rad

(radian, plane

angle) and sr (steradian, solid angle). There are many derived SI units, for example,

N, J, W, C (Coulomb = A s), V (W/A), (V/A), Hz, W/m2, N/m2 (Pa), Hz (1/s), etc.

Conversion factors between the SI and US engineering units are fixed, e.g. 1 in. =

0.02540005 m, 1 lbm

=0.45359237 kg., (oC) = (K) - 273.15, (oF) = (K) -459.67, etc.

2. General Measurement System

Most measurement systems can be divided into three parts:

Stage I -- A detector-transducer or sensor stage,

Stage II -- An intermediate stage (signal conditioning), and

Stage III-- A terminating or read-out stage ( sometimes with feedback signal for

control).

The dynamic response of a generalized measurement system can be analyzed by a

mechanical


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System. A schematic of the generalized measurement system is shown below.

INDICATOR

RECORDER

PROCESSOR

CONTROLLER

TRANSDUCER

SIGNAL

SENSOR CONDITIONER

CALIBRATION CONTROL STAGETO PROCESS

STAGE I STAGE II STAGE III

3. Types of Input Quantities

Time relationship

Static-- not a function of time.

Dynamic-- steady-state, periodic, a periodic, or transient (single pulse, continuing, or

random).

Analog or digital

Analog-- temperature, pressure, stress, strain, and fluid flow quantities usually are

analog

(continuous in time).

Digital-- quantities change in a stepwise manner between two distinct magnitudes,

e.g.,

TTL signals. The time relationship is important in selecting an instrument adequate

for the required time response, and proper but different signal conditioners are usually

needed depending on the inputsignal is digital or analog.

4. Error Classification

Three types of error can be identified: systematic, random and illegitimate errors.

Systematic errors are not susceptible to statistical analysis, and generally result from

calibration Errors, certain type of consistently recurring human error, errors of

technique, uncorrected loading errors, and limits of system resolution. Random or

accidental errors are distinguished by lack of

consistency. They involve errors stemming from environmental variations, certaintype of human


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errors, errors resulting from variations in definition, and errors derived from

insufficient definition of the measuring system. Illegitimate errors are those should

not exist-- blunders or mistakes, computational errors, and chaotic errors. Error

analysis is necessary for measurements.

5 . Calibration (Output versus Known Input)

Static Calibrations

Static independent of time

Only the magnitude of the known input is important in static calibrations.

D ynamic Calibrations

Time dependent variables are measured in dynamic calibrations.

C a libration Curve

Usually plotted in terms of output versus input of known values or standards.

6.Experimental Test Plan

A well thought-out experimental test plan includes

(1) An identification of pertinent process variables and parameters.

(2) A measurement pattern.

(3) A selection of a measurement technique and required equipment.

(4) A data analysis plan.

Random tests-- a random order set to the applied independent variables.

Replication-- an independent duplication of a set of measurements under similar

Controlled conditions.

Concomitant Methods-- two or more estimates for the result, each based on

adifferent method.

7. Measurement Overview

The overall planning of experiments should include

(1) Objective

(2) Plan -- to achieve the objectives

(3) Methodology

(4) Uncertainty Analysis

(5) Costs

(6) Calibration

(7) Data Acquisition

(8) Data Analysis


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UNCERTAINTY ANALYSIS

I. Statistical Analysis

I.1 Introduction

I.2 Statistical Properties of a Single Point Measurement

I.3 Test of Data Outliers

I.4 Chi-squared Test

I.5 Number of Measurements Required

I.6 Student's t distribution

I.7 Least Squares Fit

II. Uncertainty Analysis

II.1 Introduction

II.2 Measurement Errors

II.3 Error Sources

II.4 Bias and Precision Errors

II.5 Uncertainty Analysis : Error Propagation

II.6 Design-Stage Uncertainty Analysis

II.7 Multiple - Measurement Uncertainty Analysis

II.8 ASME/ANSI 1986 Procedure for Estimation of Overall Uncertainty

Statistical Analysis

I.1 Introduction

Variations are usually observed in engineering measurements repeatedly taken under

seemingly identical conditions. Source of the variation can be identified as follows:

M easurement System

Resolution and Repeatability

M easurement Procedure and Technique

Repeatability

M easured Variable

Temporal variation and spatial variation

Statistical analysis provides estimates of

(1) Single representative value that best characterizes the data set,

(2) Some representative value that provides the variation of the data,

1. Introduction


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Transducers - electromechanical devices that convert a change in a mechanical

quantity such as displacement or force into a change in electrical quantity. Many

sensors are used in transducer design, e.g., potentiometer, differential transformers,

strain gages, capacitor sensors, piezoelectric elements, piezoresistive crystals,

thermistors, etc.

2 . Metrology

The science of weights and measures, referring to the measurements of lengths,

angles,

and weights, including the establishment of a flat plane reference surface.

2.1 Linear Measurement

Line Standard are defined by the two marks on a dimensionally stable material.

End Standard the length of end standards is the distance between the flat parallel end

faces.

Gauge Block length standards for machining purposes.

Federal Accuracy Grade; combination of gauge blocks yields a range of length from

0.100to 12.000 in., in 0.001 in. increments.

Vernier Caliper

Micrometer

Tape Measure measuring tape up to 100 ft, uncertainty as low as 0.05%; hand

measuring tools are commonly used for length measurements.

3. Displacement Sensor

Potentiometer, Differential Transformer, Strain Gage, Capacitance, Eddy Current

3.1 Potentiometer

Displacement can be measured from the above equation. Different potentiometers are

available to measure linear as well as angular displacement. Potententiometers are

generally used to measure large displacements, e.g., > 10 mm of linear motion and >

15 degrees of angular motion. Some special potentiometers are designed with a

resolution of 0.001 mm.

Differential Transformer

LVDT (Linear Variable Differential Transformer) is a popular transducer which is

based on a variable-inductance principle for displacement measurements. The position

of the magnetic core controls the mutual inductance between the center of the primary

coil and the two outer of secondary coils. The imbalance in mutual inductance


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between the center location, and an output voltage develops. Frequency applied to the

primary coil can range from 50 to 25000 Hz. If the LVDT is used to measure dynamic

displacements, the carrier frequency should be 10 times greater than the highest

frequency component in the dynamic signal. In general, highest sensitivities are

attained at frequencies of 1 to 5 kHz. The input voltages range from 5 to 15 V.

Sensitivities usually vary from 0.02 to 0.2 V/mm of displacement per volt of

excitation applied to the primary coil. The actual sensitivity depends on the design of

each LVDT. The stroke varies in a range of +150 mm (low sensitivity). There are two

other commonly used differential transformers: DCDT--Direct Current Differential

Transformer and RVDT-- Rotary Variable Differential Transformer (range of linear

operation is 40 degrees). Consult Figs. 12.9 and 12.11 of Textbook for typical

schematic diagrams of LVDT and Fig. 12.12 for that of RVDT. LVDT and RVDT are

known for long lifetime of usage and no over travel damage.

3.2 Resistance-type stain gage

Lord Kelvin observed the strain sensitivity of metals (copper and iron) in 1856. The

effect can be explained in the following analysis.

R =L

A (uniform metal conduction)

Where R = resistance, = specific resistance, L = length of the conductor, A = cross

sectional area of the conductor dR

R =d+dL

L dA/A

Consider a rod under a uniaxial tensile stress state:

La =dL

L , t = -a = - dL

L

where a = axial strain, t = transverse strain, = Poisson ratiodf=

1 metrology-and-measurements

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