MEGR 6181 ENGINEERING METROLOGY

ANGULAR MEASUREMENTS

RAJESH PATEL

1. INTRODUCTION: The angle is the arithmetic difference between two directions. The term angle is used to refer the angular separation of intersecting lines, or to the angular spacing of points on the circumference of a circle. It is also refer as a deviation from a reference line or plane or other datum, or to the twist of a shaft subjected to torque. Angular spacing is frequently applied in engineering to specify conditions, which result from the division of circle. Frequently the features which have to be located lie on the concentric circles so that the dual parameters of radial distance and spacing angles. These different interpretations of angle imply different geometrical situations, which will govern the method of measurement, both regards to the reference datum and choice of instrument. Angular measurement requires no absolute reference standard since the 360 circle may be accurately subdivided by testing the equality of subdivisions. Any unit of angle is thus a geometrical concept and is not derived from material concept. Certain angle standards are required for practical applications. 2.UNITS: Radian is the basic unit of angle and is derived from geometrical consideration. Radian is defined as the angle subtended at the center of a circle by an arc equal in length to the radius. The round angle is there fore 2 π radian. The radian unit is actually unsuited to metrological, since 2 π is not a rational number, and therefore any whole number divisor of a full circle will necessarily also not be rational. For technical purposes, the 360 th division of the full circle is used instead, which bears the unit degree ( ° ). There is no primary artifact standard for the angle: it is defined in terms of the full circle. Angle metrology therefore is reduced to the quest of dividing the round angle as equally as possible. . There are two alternative systems are used for angular measurement; (a) Sexagesimal system and (b) Centesimal system. In Sexagesimal system the right is divided into 90 degrees and the each degree is further subdivided into 60 minutes and each minute into 60 seconds. Where as in Centesimal the right angle is divided into 100 grades with a further subdivision of the grade into 100 minutes and the minute into 100 seconds. Other than these two systems some trigonometric functions such as tangent, sine or cosine are used to define angular magnitude. 3.ANGLE MEASURING TECHNIQUES: 3.1.FIXED TAPER GAGES: Fixed taper gages are the direct checking tools. In this method the part are rubbed with gages for displaying the condition of compliance or deviation. This method does not provide any numerical information regarding the angular deviation between the part and the master gage.

3.2. ANGLE GAGE BLOCKS:

Fig.1 Angle gage Block source : Geneva Gage .Inc.

A reference angle of specific angular dimension can be created by combining appropriate individual members. The purpose of the gage block is to create a positive linear distance represented by stack’s two end faces. Angle gage blocks are assemble to produce a specific angular separation between two free faces. Angle blocks are usually supplied in sets. In set each individual member has particular angle and by combining different members it is possible to produce different angle. A small number of blocks set can produce a large variety of different angles. With use of different free edge of the each block it is possible to create two different angles. ( as shown in fig.2 )Angle gage blocks are come in different accuracy. + 5 - 5 + 45 50 + 45 40 Fig. 2 a. Addition & b. Subtraction of combination of gages. Normally gage blocks are made of hardened and ground steel. They are lightly magnetized for better holding. Applications of angle gage block.

a. Checking the circular dividing accuracy of the rotary table and dividing heads. b. Setting a revolving work holding table or a magnetic chuck into required tilt position c. Inspecting and refining the setting accuracy of tilt table d. Providing a reference angle for inspecting features on work piece.

3.3. ADJUSTABLE ANGULAR BODIES: In order to make an angle adjustable, one of its bounding elements must be movable. To qualify an angle as a reference body, the movement of the boundary element must be precisely

controlled, further more, any selected mutual position of the boundary element must result in an angular separation which is positive and of accurately known magnitude. 3.3.1.SINE BAR: These conditions are satisfied by the Sine bar, when it is used in conjunction with flat plate and gage block. Sine bar works on basic principle of trigonometry. The sine bar consists of a hardened and ground bar to which two rollers are attached. To function satisfactorily the sine bar requires to be made accurate. Important features of the sine bar are the parallelism of the top face with two rollers, the spacing of the rollers, the equality of diameter of the rollers, and the roundness of the rollers.

L θ H Fig.3 Sine bar

Source : Geneva Gages.Inc.

Sin θ = H / L

L = spacing between centers of two rollers H = height of flat plate Sensitivity of sine bar is known as the ability to produce a very small increase in angle by increasing the height H by a certain small amount. The sensitivity decreases as the angle increases from 1 to 90. Applications: The sine bar is an instrument for measuring how much a vertical surface is off from plumb. It can also be used for setting surfaces to be exactly plumb such as saws, anvils, line bars, face plates, press rolls. The sine bar is also used to measure small angles of plumb. Sine bar is used to set up angles on a layout or in a milling machine vice. The accuracy of the Sine bar is governed by

a. The straightness of the base generator. b. The sensitivity and accuracy of the dial gage c. The magnitude of the angle being measured d. The degree of alignment of the test piece with longitude axis of sine bar.

3.3.2 SINE BLOCKS:

Fig. 4 Sine Blocks Source : Taft- Peirce Inc.

In measuring process, the sloping platform of the sine block surface is used to support the tapered part whose vertex-actual or virtual-must point toward the elevated end of the sine plate, in position where the parts axis is contained in a plate precisely to the hinge of the block. 3.3.2.1 SINE BLOCK TAPER TESTING FIXTURES ( 9122 series ): These fixtures are designed specially for precise inspection of taper parts machined on centers. Tapered work is mounted between the centers, the sine block base elevated by gage blocks is one half the included angle, and the work then indicated at both ends to determine the accuracy of taper. Taper testing fixtures combine a special 20” sine block with a pair of identical center heads that may be positioned anywhere along a T slot running the length of the block and locked in place or removed entirely to free the Sine Block for general purpose angle checking. Used in the horizontal plane, a taper Testing Fixture becomes an extremely accurate Bench centers. 3.3.2.2 SINE BLOCK : ( 9118 series ): They are heavy-duty fixtures for holding work that must be set to precise angles for layout, light machining or inspection. Each block is equipped with a precision ground end plate that acts a work positioning stop, and tapped holes in the top surface and sides are provided to allow a wide variety of work clamping set ups. Sine blocks are made of high quality alloy steel, scientifically heat treated for maximum stability and wear resiatance, and precision ground on all working surfaces. Sine rolls are manufactured of tool steel ground and lapped alike for diameter, roundness and straightness and are mounted parallel to each other at their nominal distance within the specified limit. 3.4. SPIRIT LEVEL: Precisely calibrated and graduated spirit levels are used to measure the angular tilt. They are widely used because they are easy to understand, simple to use and reliable. The sensitivity of spirit level is defined as the angle of tilt, which causes the bubble in the vial to move through one scale division. Spirit level contains a glass tube of arcuate form almost completely filled with low viscous fluid such as alcohol or benzol, except for small portion to create an air bubble. When the spirit level is placed on a perfectly flat surface the air bubble will occupy the highest point in

middle of tube due to fluid’s greater specific mass. When the spirit level is placed on a tilted surface the bubble will moves through a distance along the arc depending upon the tilt constancy of radius R is essential to ensure equality of correspondence of the indicated value l to the angle of inclination θ of the level over the length of scale. The value I = R* θ

Fig. 5 Spirit Levels

Source : Wyler Products. Inc.

The following sensitivities are available in the precision levels:

Sensitivity in mm/m Sensitivity in Arcsec Range of Measurement in Arcsec

0.020 4.13 +/- 12.4 0.040 8.25 +/- 24.8 0.050 10.31 +/- 30.9 0.100 20.62 +/- 63.9 0.200 41.25 +/- 123.8 0.300

61.86 +/-185.6

3.5 THE ELECTRONIC LEVELS: The electronic levels uses electronics to sense and display the angular values. A Pendulum is freely suspended into the body of the instrument whose base simulates true horizontality corresponding to the zero central position of the pendulum. The slight tilt of the base can cause an electrical inequality between pendulum and body, which can be measured and interpreted in form of angular measurement. 3.5.1 NIVELTRONIC INCLINOMETERS: The Nileltronic inclinometers are available with the built in display system. The basic elements of the instrument are the extremely sensitive pendulum system, the analogue pointer and a sturdy housing of cast iron. The measuring principle is based on the mechanical pendulum which is friction free suspended and has therefore tendency to swing back the vertical position and at the lower end of the pendulum a ferrite core is fastened which is penetrating a double winded coil fed by alternative current (Principle of an inductive probe). The vibration of the pendulum will be dampened by means of a magnetic brake. The position of the ferrite core influencing the inductance in the coil, which is responsible for the changing of the voltage produced by the inclination. This voltage will be treated and displayed by the galvanometer. The system is friction free and sensitive to the slightest change of inclination. The instrument is well liked for measurement of machine tool geometry. The analogue display allows the recognition of measuring trends. When setting of large machine bed is to be done the excellent zero point stability is highly appreciated. A disadvantage is the possible interference of the other magnetic fields and the sensitivity to mechanical shocks. Specifications: Traveling distance between two lines corresponds to 10 to 50 micro m /m Measuring range :+/- 0.150 to 0.750 mm/m Analogue output : 0.24 V Cast iron scraped prismatic bases. 3.5.2 LEVELMATIC INCLINOMETER: Due to the use of high precise sensors this instrument is used for high precision measurements. Principle: The pendulum suspended by the Archimedes helical spring, is mounted between two electrodes. Depending upon the inclined position of the system, the pendulum will swing out of the zero position and by that, changing the capacity between the pendulum and the two electrodes. These capacities will be transformed into different frequencies through the RC-oscillator. The ratio of the two frequencies available will be used as the primary signal for determining the required angle. Specifications: Measuring range : 2 mm/m to 20 mm/m Sensitivity : 0.001 mm/m Limits of errors: max. 1% of measured value

Inclination signal;2000 mV Excitation: +/- 5 V dc 3.6 OPTICAL INSTRUMENTS: Optical instruments are used for precise angular measurements. These instruments work on the principle of the collimation of light. 3.6.1 AUTOCOLLIMATOR: An autocollimator is an optical instrument that is used to measure small angles with very high sensitivity. As such, they have a wide variety of applications including precision alignment, detection of angular movement, verification of angle standards and angular monitoring over long periods. Principles of operation : As the name suggests, the autocollimator projects a beam of collimated light. As external reflector returns all or part of the beam back into insrument, where the beam is focused and detected by a photo detector. Essentially the autocollimator measure the deviation between the beam and the return beam. Because the autocollimator uses light to measure angles, it never comes into contact with the test surface. Also because the autocollimator projects a collimated beam, the working distance is limited only by the power of the light source. X Vertical deviation between two reflected beams δ Angular deflection of the mirror

Fig. 6 Autocollimator The relation between vertical deviation and angular deflection can be given by

X = 2* f*δ

Where f= focal length of the lens.

δ

x

3.6.1.1 VISUAL AUTOCOLLIMATORS : Visual autocollimators rely on the operator’s eye as the photodetector. Visual autocollimators use pinholes as the “light source”. The operator views the pinhole image through an eyepiece or on a video monitor. Because the human eye acts as the photodetector, resolution will vary by user. Typically, people can resolve from 3 to 5 seconds. Because the human eye is able to discern multiple images simultaneously, visual autocollimator can accommodate several return images (i.e. They can look at several reflective surfaces simultsneously). This makes them ideal alignment instruments in applications like alignment laser rod ends. Also, visual autocollimator are typically focused on infinity, makig them equally useful for short or long distance measurements. Visual pinhole autocollimators are designed for aligning multiple surfaces. Ideal applications include:

• Easy to operate go /no-go gauge for surface alignment. • Detecting non-parallelism in windows, laser rod ends, and optical wedges. • Checking square ness of outside corners. • Angle comparisons of reflecting surfaces. • Verifying right angle prisms for angular and pyramid errors. • Field use as a compact, lightweight, and robust autocollimator. • Estimating angular measurements to 3 seconds.

3.6.1.2 DIGITAL AUTOCOLLIMATORS: Digital autocollimators use an electronic photo detector to detect the reflected beam. The digital autocollimator uses an advanced silicon photo detector and the latest DSP technology to detect and process the reflected beam. This processing allows the instruments to compensate for the non-linearity of the detector and the objective lens as well as the stray/scattered light that would otherwise affect measurements. As a result the instrument s have a resolution capacity of 0.01 arc-second ( 0.0485 micro radian ), a linearity of 0.1% and a measurement rate as high as 1000 HZ. Digital autocollimators have the added benefit of direct readout of measurement data. The data can be acquired via the LCD to display the analog out put or the instruments have direct plug in compatibility with a computer or other electronic system. This makes high-speed data acquisition and transfer capability a characteristic of these instruments. Digital autocollimators are designed to measure angles in static and dynamic systems to a very high degree of resolution. As such, application vary widely, Past application includes :

• Remote monitoring of alignment in large mechanical systems. • Connection to servo system for creation of a stable platform in airborne system. • Verification of angle standards such as rotary table or angle blocks. • Measurement of carriage pitch and yaw along a rail. • Alignment and monitoring of robotic arms. • Operation in vacuumed chambers and space. • Angular measurements to 0.01 arc second, with very high linearity and repeatability.

3.6.1.3 LASER AUTOCOLLIMATORS:

An autocollimator that emits a laser beam has significant advantages over conventional autocollimator. For instance, the high intensity of the laser beam creates ultra-law noise measurements, increasing the accuracy and repeatability of the instrument. The high intensity of the beam also increases the autocollimator’s working distance ( to more than 15 meters with TL 160 Laser autocollimator) and permits angle measurements off of non-mirror quality surfaces. The use of a laser source also allows the TL40 Laser autocollimator to make precision angular measurements off of surfaces that are as small as 1 millimeter in diameter. Laser autocollimators represent the future of precision angle measurement technology. The superior beam intensity and collimation provided by laser light sources make them ideal for: Angle measurement of miniature angles, down to 1 mm diameter. Long range angle measurement and alignment monitoring, with distances to more than 15 meters. Measurement of non-mirror quality surfaces, including silicon wafers and bare metal. Ultra low noise measurements in metrology and calibration laboratories. An autocollimator is used to detect and measure small angular tilts of a reflecting surfaces placed in front of the objective lens of the autocollimator. Ideally, the area of the reflecting surface should be at least equal to the area of the objective lens. However, this is not generally the case when the autocollimator is used with conjunction with angle gauges or a polygon. Therefore, since the objective lenses fitted to most the autocollimator so that its optical axis passes through the center of the reflecting face of the angle gauge or polygon, reducing the effect of waveform errors to a minimum. An Autocollimator should ideally be used in an environment where air currents in the optical path between the autocollimator and the reflecting surface are minimal. Such air current, by introducing changes in density and therefore of refractive index, producing random movements of the observed image, impairing the accuracy of the autocollimator setting. For this reason, the distance between the objective lens and the reflecting surface should be kept to a minimum and, where practicable, the path should be shielded from the surrounding air. The autocollimator should be rotated about its optical axis, if such provision exists, until a movement of the reflected image perpendicular to the direction of measurement produces no change of reading. For photoelectric autocollimators, this condition should be achieved using photoelectric detector.

Fig 7. Visual Autocollimators , Source: Micro Radian Inc.

1. VISUAL AUTOCOLLIMATORS

MODEL 50 ALIGNMENT COLLIMATORS CCD –100 ALIGNMENT AUTOCOLLIMATORS

Specifications : o Resolution of 5 arc second. o 1-degree field of view. o Pinhole diameter of 100 microns. o Image diameter subtends 100 arc seconds. o Variable intensity incandescent light source. o Optional 2-axis adjustable reference mirror mounted

on front of body.

Specifications : o Resolution of 3 arc-seconds. o 1-degree field of view. o Pinhole diameter of 200 microns. o Image diameter subtends 200 arc seconds. o Variable intensity incandescent light source

2. Digital Autocollimators

Specifications : o Maximum range of +/- 1200 arc second, each

axis. o Maximum working distance of 3 meters. o Maximum resolution of 0.01 arc second. o Linearity of 0.2 %. o Light source : single ,visible red ultra bright LED. o Weight of 1.1 lbs.

Specifications : o Maximum range of +/-600 arc second, each

axis. o Maximum working distance of 5 meters. o Maximum resolution of 0.01 arc second. o Linearity of 0.2 %. o Light source : single, visible red ultra

bright LED. o Weight of 1.2 lbs.

T 160 Digital Autocollimator

T 100 Digital Autocollimator

Fig. 8 Digital Autocollimators Source : Micro Radian.Inc.

3.6.2 ANGLE DEKKOR : This is also a type of autocollimator. It contains a small illuminated scale in the collimating objective lens. In normal position this scale is outside of the view of the microscope eyepiece. The illuminated scale is projected as a parallel beam by the collimating lens. After reflected from the work piece it will refocus by the lens in field view of eyepiece. There is another datum scale is fixed across the center of screen and the reflected image of the illuminated scale is received at right angle to this fixed scale. Thus the reading on the illuminated scale measures angular deviations from one axis at 90 ° to the optical axis and the reading on the fixed datum scale measures the deviation about an axis mutually perpendicular to the other two.

TL 160 has a built in laser diode light source, which emits a 5 mm diameter beam. The use of a laser source gives the TL 160 a more powerful, better-collimated beam than is possible with other light sources. The superior beam quality results in ultra-low noise, low drift measurements. The intensity of the beam allows measurements to be taken off of surfaces that are not mirror quality and off of surfaces that are as far as 50 feet away. The compact, light weighty 160 is simple top operate and is ideal for use in remote monitoring applications or as a calibration standard with tractability to the NIST.

TL 160 Laser autocollimator

TL 40 laser autocollimator :

Specification :

o Maximum measuring range of +/- 600 arc-seconds in each axis

o Maximum resolution of 0.1 arc second. o Measurement linearity of 0.5 %. o Simultaneous two-axis measurement. o Maximum data bandwidth of 1000 Hz. o Diode laser light source, 670nm ,class II o Maximum working distance 15 meters.

Specifications : o Minimum target size of 1.0 mm diameter. o Maximum measuring range of +/- 3600 arc

seconds in each axis. o Maximum working distance is 1 meter. o Maximum resolution of 0.1 arc second. o Measurement linearity of 0.5 %. o Maximum bandwidth of 1000 HZ. o Diode laser source ,670 nm,classII

3.Laser Autocollimator

Fig.9 Laser Autocollimators Source : Micro Radian.Inc

Fig. 10 Angle Dekkor

The whole optical system is enclosed in a tube, which is mounted on an adjustable bracket. This instrument is mostly used as a comparator. It is not precise as an autocollimators. It has a wide range of application as angular variations are read directly without the operation of micrometer. 3.7 Angular Measurement using MR Technology : Philips Semiconductors, has launched the world’s first Silicon integrated sensor system for contact less angular measurement using Magneto resistive ( MR ) technology. Particularly relevant in automotive and industrial applications, where angle measurement is frequently required , the contact less MR approach provides a wear-free solution and removes the need for a discrete solution on a hybrid. It is highly accurate and insensitive to temperature effects, magnet ageing and displacement in a wide range. This new contact less angle measurement system consists of a magneto resistive sensor and sensor signal conditioning IC s. With the sensors and the signal conditioning electronics the system is robust against dirt, dust and liquid as well as high temperature and mechanical destruction. MR based systems tolerate variations in field strength caused by ageing to temperature-sensitivity of the magnet as well as mechanical tolerances. Automotive applications of the MR based system include chassis and seat positioning, throttle, variable ventile timing, suspension and positioning for drive wire.

Work piece

Collimating objective Lens

Microscope eye piece

Prism

Light Source

Glass screen

Illuminated scale engraved on glass screen

Datum scale