11. Angle Measurement 2

8/3/2019 11. Angle Measurement 2

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DBIT Pvt. circulationNotes by Prof.S.P.Sabnis

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Angle may be defined as the opening between two lines which meet at apoint. An angle is generated by simply moving a line in an arc arround apoint. By this method a complete circle can be made. From such a circleunits of angular measurement have been derived.

A circle divided into 360 parts, by lines passing through its centre, eachpart is called a degree of arc. The angle between the two lines passingthrough the centre of circle for one degree arc is an angle of 1 degree (o).

Each degree can be divided into sixty parts called minutes and eachminute is further divided into 60 seconds. So angle can be generated veryeasily, requiring no absolute standard. It is the precision with which thecircle can be divided to get the correct measure of an angle. The

calibration of angular subdivision is a self checking process. Angular measurements are so common and so essential in themanufacture of interchangeable parts, jigs, dies, and fixtures that a basicknowledge of angles and their measurement is indispensable tosuccessful manufacturing.

Among the tools most commonly used for industrial angular measurementare the bevel (vernier) protractor, universal angle gage blocks, sine bar,squares, and levels.

Vernier and Optical Bevel Protractor

Angle Measurement

Bevel protractor is the simplest instrumentfor measuring the angle between two facesof component.

It consists of a base plate attached to themain body, and an adjustable blade whichis attached to a circular plate containingvernier scale. The adjustable blade iscapable of rotating freely about the centre ofthe main scale engraved on the body of theinstrument and can be locked in anyposition.

An acute angle attachment is provided atthe top, as shown in the fig.

It is capable of measuring from 0 to 360. The vernier scale has 24 divisionscoinciding with 23 main scale divisions. Thus the least count of theinstrument is 5. This instrument is most commonly used in workshops forangular measurements till more precision is required.


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A recent development of the vernier bevel protractor is optical bevel protractIn this instrument, a glass circle divided at 10 intervals throughout the whole360is Fitted inside the main body. A small microscope is fitted through whicthe circle graduations can be viewed. The adjustable blade is clamped to arotating member which carries this microscope. With the aid of microscope itpossible to read by estimation to about 2.

Optical Bevel Protractor.

Universal Bevel Protractor.

It is used for measuring and laying out of angles accurately and precisely

within 5 minutes. The protractor dial is slotted to hold a blade which can be

rotated with the dial to the required angle and also independently adjusted toany desired length. The blade can be locked in any position.

Measuring Acute Angles Measuring Obtuse Angles

Using a bevel protractor with

General Description of Various Components ofBevel Protractors Body

It is designed in such a way that its back is flat and there are no

Projections beyond its back so that when the bevel protractor is placed on its

back on a surface plate there shall be no gap between the two. The flatness

the working edge of the stock and body is tested by checking the square-nes

of blade with respect to stock when blade is set at 90.

Stock. The working edge of the stock is about 90 mm in length and 7 mm

thick. It is very essential that the working edge of the stock be perfectly straig

and if at all departure is there, it should be in the form of concavity and of the

order of 0.01 mm maximum over the whole span.

Blade. It can be moved along the turret throughout its length and can also be

reversed. It is about 150 or 300 mm long, 3 mm wide and 2 mm thick and en

bevelled at angles of 45and 60within the accuracy of 5 minutes of arc. Its

working edge should be straight upto 0.02 mm and parallel upto 0.03 mm ov

the entire length of 300 mm. It can be clamped in any position.

Acute angle attachment.

It can be readily fitted into body and clamped in any position. Its working edg

should be flat to within 0.005 mm and parallel to the working edge of the stoc

within 0.015 mm over the entire length of attachment.

The bevel protractors are tested for flatness, square-ness, parallelism,

straightness and angular intervals by suitable methods.


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Using bevel protractor for checkingthe inside bevelled face of a groundsurface.

Use of bevel protractorfor checking of vee block.

Any angle can be measured withthe vernier bevel protractor, butyou have to be careful to notewhich part of a full circle you aremeasuring.

For every position of the bevelprotractor, four angles are formedsee Fig.

Two of the angles can be readdirectly on the main scale and thevernier scale while the other twoare supplemental angles. Keeptrack of the obtuse and acuteangles and try to read from zerowhenever possible.

There is no general rule for use,just keep in mind that you areadding to 90 degrees to make upthe angle being measured.


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Squares : One of the very important ability of a machine shop is tomachine surfaces square to each other and the ability to check them forsquareness. There are many useful tools that can be used to preciselymeasure or check for squareness.The most common is the solid square. The wide portion is referred to asthe beam and the slender upright portion is called the blade. The solidsquare is usually used to check squareness of surfaces or to square upparts on a surface plate prior to inspection.Combination squares find frequent use where it is necessary to check fo

squareness, check lengths and heights, or for layout work.Several methods are available to determine squareness. After holding thesquare up to the feature to be checked, the simplest method is to just look

with the naked eye. For closer work you might use a magnifying glass or astrong beam of light as an aid to see any opening that might be there. Evea white sheet of paper to reflect light might be useful. These methods willtell if the feature is out of square but not by how much. The deviation fromsquareness can be determined by using feeler stock, paper, or other itemsof known thickness.

solid square

Combination squares

Squares

Combination sets

Sine Bar The sine principle uses the ratio of the length of two sides of a right

triangle in deriving a given angle. It may, be noted that devices operatingon sine principle are capable of self generation. The measurement isusually limited to 45from loss of accuracy point of view.

The accuracy with which the sine principle can be put to use is dependenton form of linear measurement. The sine bar in itself is not a completemeasuring instrument. Another datum such as a surface plate is needed,as well as other auxiliary equipment, viz. slip gauges, and indicatingdevice are required to make measurements.

Sine bars used in conjunction with slip gauges constitute a very gooddevice for the precise measurement of angles. Sine bars are used eitherto measure angles very accurately or for locating any work to a givenangle within very close limits.

Sine bars are made from high carbon, high chromium, corrosion resistantsteel, hardened, ground and stabilised. Two cylinders of equal diameterare attached at the ends. The axes of these two cylinders are mutuallyparallel to each other and also parallel to and at equal distance from theupper surface of the sine bar. The distance between the axes of the twocylinders is exactly 5 inches or 10 inches in British system, and 100, 200and 300 mm in metric system.

Depending upon the accuracy of the centre distance, sine bars are gradedas of A grade or B grade. B grade of sine bars are guaranteed accurateupto 0.02 mm/m of length and A grade sine bars are more accurate andguaranteed upto 0.01mm/m of length.

Sine Bar

Although there are several forms of sine bars, the one shown above ismost commonly used. Some holes are drilled in the body of the bar toreduce the weight and to facilitate handling.

The various parts are hardened and stabilised before grindingand lapping. All the working surfaces and the cylindrical surfaces of therollers are finished to surface finish of 0.2 m Ra value or better.

following accuracy requirements and tolerances are specified by I.S.53591969 for 100 mm sine bar

Characteristics Permissible Tolerance Flatness of upper and lowersurfaces 0.001 mm

Parallelism of upper and lower surfaces w.r.t. datumsurface whenresting on it 0.001 mm

Flatness of side faces 0.005 mm

Squareness of side faces to upper surface 0.003/25 mm

Parallelism of side faces to the axes of rollers 0.01/25 mm

Flatness of end faces 0.003 mm

Squareness of end faces to the upper surface 0.003/25 mm

Parallelism of end faces to the axes of the rollers 0.01/25 mm

Straightness of individual rollers and freedom from lobing anduniformity in diameter 0.002 mm

Mean diameter of rollers 0.002 mm

Distance between the roller axes 0.003 mm

Roller axes:

(i) In a common plane over the length of either roller 0.003 mm(ii) Parallel to and equidistant from the upper surface over thelength of either roller 0.003 mm

Flatness of the bearing surface of the setting foot 0 003 mm


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The accuracy of sine bar depends on its constructional features and onmaintaining these features.

These important features of sine bar are :

(i) The two rollers must have equal diameter and be true cylinders.(ii) The rollers must be set parallel to each other and to the upper face.(iii) The precise centre distance between the rollers must be known.(iv) The upper face must have a high degree of flatness. The variouscharacteristic tolerances have already been indicated above.

Use of Sine Bar.

(1) Measuring known angles or locating any work to a given angle.

For this purpose the surface plate is assumed to be having a perfectly flat

surface, so that its surface could be treated as horizontal. One of thecylinders or rollers of sine bar is placed on the surface plate and otherroller is placed on the slip gauges of height h. Let the sine bar be set at anangle .

Then sin = h / l

where I is the distance between the center of the rollers. Thus knowingangle h can be found out and any work could be set at this angle as thetop face of sine bar is inclined at angle to the surface plate.

The use of angle plates and clamps could also be made in case of heavycomponents.

For better results, both the rollers could also be placed on slip gauges ofheight h1 and h2 respectively. Then sin = (h2 h1) / l


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(2) Checking of unknown angles.

Many a times, angle of a component to be checked is unknown. In suchcase, it is necessary to first find the angle approximately with the helpof a bevel protractor.

Let the angle be . Then the sine bar is set at an angle and clamped tan angle plate. Next, the work is placed on sine bar and clamped to angplate as shown in Fig. and a dial indicator is set at one end of the workand moved to the other, and deviation is noted.

Again slip gauges are so adjusted (according to this deviation) that dialindicator reads zero across work surface.

If deviation noted down by the dial indicator is h over a length l of work

then height of slip gauges by which it should be adjusted in equal to= h x l / I.

Where greater accuracy is required, the position of dial test gaugeprobe can be sensed by adjusting a pile of slip gauges till dial indicatorindicates same reading over roller of sine bar and the slip gauges.

Limitations of Sine Bars.

The establishment of angle by the sine principle is essentially a lengthmeasuring process. Thus the accuracy, in practice, is limited bymeasurement of centre distance of two precision rollers.

The geometrical condition involved in measuring the exact, effectivecentre distance existing between two rollers of the sine bar to acertainty of fraction of a m is an infinitely complex problem.

This fundamental limitation alone precludes the use of the sine bar as aprimary standard of angle.

(3)Checking of unknown angles of heavy component.

In such cases where components are heavy and cant be mounted on thesine bar, then sine bar is mounted on the component as shown in Fig.

The height over the rollers can then be measured by a vernier heightgauge ; using a dial test gauge mounted on the anvil of heightgauge as the fiducial indicator to ensure constant measuring pres-sure.

The anvil on height gauge is adjusted with probe of dial test gaugeshowing same reading for the top most position of rollers of sine bar. Fig.shows the use of height gauge for obtaining two readings for either of theroller of sine bar. The difference of the two readings of height gaugedivided by the centre distance of sine bar gives the sine of the angle of thecomponent to be measured.

Devices operating on the sine principle are fairly reliable at angles lessthan 15, but become increasingly inaccurate as the angle increases.Sine bars inherently become increasingly impractical and inaccurate asthe angle exceeds 45.

The major limitations of sine bar are

The sine bar is physically clumsy to hold in position. The body of the sine bar obstructs the gauge block stack, even ifrelieved. Slight errors of the sine bar cause large angular errors. Long gauge stacks are not nearly as accurate as shorter gaugeblocks. Temperature variation becomes more critical. A difference in deformation occurs at the point of roller contact to the

support surface and to the gauge blocks, because at higher angles, theweight load is shifted more toward the fulcrum roller. The size of gauges, instruments or parts that a sine bar can inspectis limited, since it is not designed to support large or heavy objects.

Sine Centre

Sine centre is basically a sine bar with block holding centres which canbe adjusted and rigidly clamped in any position. These are used forinspection of conical objects (having male and female centres.)between centres.

These are used upto inclination of 60. Rollers are clamped firmly to thebody without any play. This is a very useful device for testing theconical work centered at each end.


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Angle Gauges The first set of combination of angle gauges was devised by Dr.

Tomlinson of N.P.L.

With thirteen separate gauges used in conjunction with one square blockand one parallel straight-edge, it is possible to set up any angle to thenearest 3.

In the same way, as slip gauges are built up to give a linear dimension,the angle gauges can be build up to give a required angle.

Angle gauges are made of hardened steel and seasoned carefully toensure permanence of angular accuracy,and the measuring faces arelapped and polished to a high degree of accuracy and flatness like slipgauges. These gauges are about 3inch (76.2 mm) long, 5/8 inch (15.87mm) wide with their faces lapped to within 0.0002 mm and anglebetween the two ends to 2 seconds.

The thirteen gauges can be divided into three series ; degrees, minutesand fractions of a minute. The gauges available in first series are of angle1, 3, 9, 27and 41. Second series comprises 1, 3, 9 and 27 anglegauges and third series has 0.05 , 0.1, 0.3 and 0.5 (or 3, 6, 18 and30) angle gauges.

All these angle gauges in combination can be added or subtracted, thus,making a large number of combinations possible.


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Angle gauges can be used in addition and subtraction mode.

It is seen that any angle could be made up, but the block formed by thecombination of a number of these gauges is rather bulky and, therefore,cannot be always directly applied to the work.

Hence these gauges are used as reference and aid of other anglemeasuring devices is taken.

Angle gauge blocks seem to lack the requisites for use as primarystandards because errors are easily compounded when angle blocksare wrung in combination.

Further the absolute verification of angle blocks is usually dependent onsome other primary standard.

All gauges added. Total angle= 379 18 (Not to scale)

Angle set up = 27minus9 30 = 2650 30

Combination of 3 blocksof 9and one block of27so asto form parallel set of blocks.

Clinometer

A clinometer is a special case of the application of spirit level. Inclinometer, the spirit level is mounted on a rotary member carried in ahousing.

One face of the housing forms the base of the instrument. On the housing,there is a circular scale. The angle of inclination of the rotary membercarrying the level relative to its base can be measured by this circularscale.

The clinometer is mainly used to determine the included angle of twoadjacent faces of workpiece. Thus for this purpose, the instrument base isplaced on one face and the rotary body adjusted till zero reading of thebubble is obtained.

The angle of rotation is then noted on the circular scale against the index.A second reading is then taken in the similar manner on the second faceof work piece. The included angle between the faces is then the differencebetween the two readings.

Clinometers are also used for checking angular faces, and relief angles onlarge cutting tools and milling cutter inserts. These can also be used forsetting inclinable table on jig boring machines and angular work ongrinding machines etc.

Micro-optic clinometer

Fig. Principle of clinometer

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

angular differences. For small angular measurements, autocollimatorprovides a very sensitive and accurate approach.

Auto-collimator is essentially an infinity telescope and a collimatorcombined into one instrument. The principle on which this instrumentworks is given below.

O is a point source of light placed at the principal focus of a collimatinglens in Fig (a). The rays of light from O incident on the lens will now travas a parallel beam of light. If this beam now strikes a plane reflectorwhich is normal to the optical axis, it will be reflected back along its ownpath and focused at the same point O.

If the plane reflector be now tilted through a small angle , [Refer Fig. (bthen parallel beam will be deflected through twice this angle, and will bebrought to focus at O in the same plane at a distance x from O.

Therefore OO = x = 2.fwhere f is the focal length of the lens.The position of the final image does not depend upon the distance of

reflector from the lens, i.e. separation x is independent of the position ofreflector from the lens. But if reflector is moved too much back then reflectedrays will completely miss the lens and no image will be formed. Thus for fullrange of readings of instrument to be used, the maximum remoteness of thereflector is limited.

For high sensitivity, i.e. for large value of a; for a small angular deviation a long focal length is required

Principle of working of autocollimator


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A cross line target eyepiece graticule is positioned at the focal plane of atelescope objective system with the intersection of the cross line on theoptical axis, i.e. at the principal focus. When the target graticule isilluminated, rays of light diverging from the intersection point reach theobjective via a beam splitter and are projected from the objective asparallel pencils of light. In this mode, the optical system is operating as acollimator.

A flat reflector placed in front of the objective and exactly normal to theoptical axis reflects the parallel pencils of light back along their originalpaths. They are then brought to focus in the plane of the target graticuleand exactly coincident with its intersection.

A proportion of the returned light passes straight through the beam splitterand the return image of the target cross line is therefore visible throughthe eyepiece. In this mode, the optical system is operating as a telescopefocused at infinity.


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If the reflector is tilted through a small angle the reflected pencils of lighwill be deflected by twice the angle of tilt (principle of reflection) and willbrought to focus in the plane of the target graticule but linearly displacefrom the actual target cross lines by an amount 2 x f.

Linear displacement of the graticule image in the plane of the eyepiecedirectly proportional to reflector tilt and can be measured by an eyepiecgraticule, optical micrometer or electronic detector system.

The autocollimator is set permanently at infinity focus and no device forfocusing adjustment for distance is provided or desirable. It responds onto reflector tilt (not lateral displacement of the reflector). The deflection iindependent of separation between the reflector and the autocollimator.

The focal length determines basic sensitivity and angular measuring

range. The longer the focal length the larger is the linear displacement fa given reflector tilt, but the maximum reflector tilt which can beaccommodated is consequently reduced. Sensitivity is therefore tradedagainst measuring range.

The maximum separation between reflector and autocollimator, orworking distance, is governed by the effective aperture of theobjective, and the angular measuring range of the instrument becomesreduced at long working distances.

Angle DekkorThis is also a type of an autocollimator.(Refer Fig.). It contains a small illuminatedscale in the focal plane of the objectivelens (collimating lens). This scale innormal position is outside theview of the microscope eyepiece asshown in Fig. (b). The illuminated scale isprojected as a parallel beam by thecollimating lens which after striking a

reflector below the instrument isrefocused by the lens in the field of viewof the eye-piece. In the field of view ofmicroscope there is another datum scale[Fig. (c)] fixed across the centre of screenand the reflected image of the illuminatedscale is received at right angle to thisfixed scale as shown in Fig. (a) and thetwo scales, in this position intersect eachother.

Thus the reading on the illuminated scale measures angular deviations

from one axis at 90to the optical axis and the reading on the fixed datum

scale measures the deviation about an axis mutually perpendicular to the

other two. In other words, changes in angular position of the reflector in

two planes are indicated by changes in the point of intersection of the two

scales. Readings from scale are read direct to 1 without the use of a

micrometer.

The whole of the optical system shown in the Fig. is enclosed in a tube

which is mounted on an adjustable bracket. There is a reflective base

which is lapped flat and on which all these things 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 of angle

gauges with that from the work under test. Though this is not a precise

instrument in comparison to autocollimator, it has wide field of application

for general angular measurement, as angular variations are read direct

without the operation of a micrometer.

Uses of angle dekkor in combination with angle gauges

( i) Measuring angle of a component. : Angle dekkor is capable of

measuring small variations in angular setting, i.e. determining angular tilt. In

operation the measuring principle is that of measurement by comparison; th

angle dekkor is set to give a fixed reading from a known angle (i.e. using

known angular standards to obtain a zero reading)

First the angle gauge combination is set up .to the nearest known

angle of the component and the angle dekkor isset, (using special attachme

and link), such that zero reading is obtained on the illuminated scale. The

angle-gauge build up is then removed and replaced by the component unde

test, a straight-edge being used to ensure that there is no change in lateral

positions.

The new position of the

reflected scale with respect to the

fixed scale gives the angular tilt ofthe component from the set angle.

(Refer Fig.below)

Zero-reading with anglegaugebuild-up Reading with component

in positionerror = 40 20= 20 divisions= 20 minutes


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(ii) To obtain precise angular setting for machining operationsconsider an example of milling a slot at a precise angle to a previouslymachined face. A parallel bar is used as a datum face, the component to millbeing securely clamped when in close contact with it. The parallel bar ispositioned on the table of milling machine with the aid of angle dekkor. Apolished reflector is firmly attached to the column of the milling machine. Withthe aid of this surface as reference, the angle dekkor is set up such that zeroreading is obtained ; hence, the axis of the optical beam is truly at 90oto the table feed. Then build up the combination of angle gauges to the exact

value , i.e. the inclination of the slot to be milled on the component. The anglegauges along with the parallel bar are placed on the table and adjusted inposition such that the angle dekkor shows zero reading when viewing the flatsurface of the angle gauge combination. The parallel bar is firmly clamped inthis position, a check being made to ensure that no movement has taken placeduring clamping. Finally, now the workpiece can be clamped on milling

machine table, in close contact with this pre-set parallel bar.

(ii) Checking the sloping angle of a V-block(iii) To measure the angle of cone or taper gauge

Fig. Set up for milling angular slot.


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Rotary tables are used for accurate circular indexing. These are

normally designed to rotate in one plane but in some cases tilting action is

also incorporated. Angular dimensions are either read from the common line

measurement at the periphery of the table or by optical display units or

digital readouts.

Dividing heads are used for angular and linear measurements and

for indexing. Clinometers, circular tables and dividing heads employ a

variety of mechanical, optical and electronic techniques to divide a circular

scale.

Dividing Heads and Circular Tables

Rotary Table Dividing Head

Optical dividing head : It mainly consists of a glass scale which is

mounted on the main spindle and the graduations of the scale are observed

through a microscope fitted with an eye-piece graticule and mounted in the

body of the instrument. It can measure directly upto 12 of arc. Fig show

arrangement of optical system.

Light passes through a system of lenses & illuminates the divided scale,

mounted on main spindle, projecting the readings on ground glass screen.

This instrument can be used in inspection shops or on machine tools as

it has a robust head and high standard of accuracy. This is very useful for

rotating a work piece through a given angle precisely.

Optical dividing head thus has a big advantage over mechanical

type i.e. the possible inaccuracies due to wear of the worm and worm wheel

mechanism are eliminated. As readings are taken at only one point on the

circle, the accurate centering of the glass circle with the axis of rotation is

very important. The effects of eccentricity of mounting glass circle are very

serious, though the glass is perfectly divided.


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11. Angle Measurement 2

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