Angular measurement

Angular measurement

1. Angular Measurement
Instructor
Mr. GauravBharadwaj
AssistantProf.
DepartmentofME
GLAUniversity

2. Introduction
•Angularmeasurementsarefrequentlynecessaryforthemanufacture
ofinterchangeableparts.
•Theangleisdefinedastheopeningbetweentwolineswhichmeetat
apoint.
•Ifacircleisdividedinto360equalparts.Eachpartiscalledas
degree(0).Eachdegreeisdividedin60minutes(‘),andeachminuteis
dividedinto60seconds(“).
•Therearemanydevicesusedfortheangularmeasurementinthefield
ofengineeringapplications.

3. Protractor
•AsimpleProtractoristhebasicdeviceformeasuringangles.
•Atbest,itcanprovideleastcountofonedegreeforsmaller
protractorandhalfdegreeforlargeprotractors.
•Likeasteelrule,thesimpleprotractorhaslimitedusagein
engineeringmetrology.

4. VernierBevel Protractor
•Simpleprotractorhassomelimitationsi.e.itcannotmeasurein
minutesasitsleastcountis1degreeor0.5degree.
•But,afewadditionsandasimplemechanism,whichcanholda
mainscale,aVernierscaleandarotatableblade,canmakeitvery
versatile.
•Auniversalbevelprotractorisonesuchinstrument,whichhasa
mechanismthatenableseasymeasurement.

5. Parts of VernierBevel Protractor

6. Parts of VernierBevel Protractor
1.Stock:–Thisisoneofthecontactingsurfacesduringthe
measurementofanangle.Preferablyitshouldbekeptincontactwith
thedatumsurfacefromwhichtheangleismeasured.
2.Dial:–Thedialisanintegratedpartofthestock.Itiscircularin
shape,andtheedgeisgraduatedindegrees.
3.Blade:-Thisistheothersurfaceoftheinstrumentthatcontactsthe
workduringmeasurement.Itisfixedtothedialwiththehelpofthe
clampinglever.Aparallelgrooveisprovidedinthecentreoftheblade
toenableittobelongitudinallypositionedwhenevernecessary.
4.LockingScrews:-Twoknurledlockingscrewsareprovided,oneto
lockthedialtothedisc,andtheothertolockthebladetothedial.

7. Least count formula
Leastcount
•LeastCountreferstothesmallestdistancethatcanbemeasuredusingan
instrument.
•Least Count = Length of 2 MSD –Length of 1 VSD
WhereMSDisMainScaleDivisionandVSDisVernierScaleDivision
respectively
Generally,
12 divisions on Vernierscale = 23 divisions on main scale
1 VSD= 23/12 main scale divisions
Using the formula for Least Count, we get
LC = 2 MSD–1VSD
= 2 MSD–23/12MSD
= (24-23)/12 MSD
=1/12 MSDin degree
In min =60/12 = 5 min

8. Use of VernierBevel Protractor
Thevernierbevelprotractorisusedtomeasureacuteanglesand
obtuseangles.

9. Formula for Measurement
Although the least count may vary between different calipers.
The length formula for any caliper is as follows:
Length = MSR + (VSD * LC)
Where MSR = Main Scale Reading
VSD = VernierScale Divison
LC = Least Count.

10. Sine Bar
•The sine bar is used to measure angles based on the sine principle.
•Upper surface forms the hypotenuse of a right angled triangle.
•When one of the roller, is resting on a flat surface, the bar can be
set at any desired angle by simply raising the second roller.

11. Principle of Sine Bar
•Thesinebarbyitselfisnotacompletemeasuringinstrument.
•Accessoriessuchasasurfaceplate,slipgauges,etcareneededto
accomplishthemeasurementprocess.
•Thesineoftheangle‘θ’formedbetweentheuppersurfaceofsinebar
andthesurfaceplate(datum)isgivenby:
Sin (θ) = h/L

12. Use of Sine Bar
•Tomeasuretheangleofgivenspecimen.
•Tolocateaworkpieceonagivenangle.

13. Measuring angle using sine bar

14. Locating a work piece to a given angle using sine bar

15. Locating a work piece to a given angle using sine bar
•Thetopsurfaceissettotheangle,usingslipgauges
•Adialgaugeisbroughtincontactwiththetopsurfaceofthework
partatoneendandsettozero.
•Thedialindicatorismovedtotheotherendoftheworkpartina
straightline.
•Azeroonthedialindicatorindicatesthattheworksurfaceisperfectly
horizontal/thesetangleistheright.
•Ifthedialindicatorshowsanydeviations,adjustmentsintheheight
ofslipgaugesisnecessarytoensurethattheworksurfaceishorizontal.

16. Requirements of a Sine bar
•AxesoftherollermustbeparallelandthecenterdistanceLmust
beknown.
•Topsurfaceofthebarmusthaveahighdegreeofflatness.
•Therollermustbeofidenticaldiameters.

17. Limitations of a Sine bar
•Sinebarisusedforanglemeasurementabove45°.
•Forbuildingtheslipgauges,thereisnoscientificapproach
available,itistobebuiltonthetrialanderrorbasisandtime-
consuming.
•Anyunknownprojectionspresentinthecomponentwillcauseto
induceerrorsintheanglemeasured.

18. Why sine bar is not used above 45̊?
•Theaccuracyoftheanglesetbyasinebardependsonthetheerrorsin
itsimportantdimensionssuchaserrorindistancebetweenrollercentres,
errorincombinationoftheslipgaugesusedforsetting,errorin
parallelismbetweengaugingsurfaceandplaneofrolleraxesetc.
•Theslipgaugecombination(h)requiredtosetangle(ϴ)isgivenby,
h = L sin ϴ
Theeffectoferrorinspacingofrollercentres(dL)orerrorsin
combinationofslipgauges(dh)onangularsettingaccuracycanbe
obtainedbypartialdifferentiationoftheaboveequation.
dh/dϴ = (sin ϴ) (dL/dϴ) + L cosϴ
dh = (sin ϴ) dL+ (L cosϴ) dϴ
dϴ = tan ϴ ((dh/h) -(dL/L))
Fromtheaboveequation,wecanseethat,theeffectoferrorinroller
spacingorslipgaugecombinationisafunctionofangleϴ.Astheangle
ϴincreases,theerror(dϴ)intheangularmeasurementincreasesand
above45

19. Angle Gauges
•Anglegauges,whicharemadeofhighgradewearresistantsteel
worksimilartoslipgauges.
•anglegaugescanbebuiltuptogivetherequiredangle.
•Thegaugescomeinastandardsetofangleblocksthatcouldbe
wrungtogetherinasuitablecombinationtobuildanangle.
•Angleblockshaveaspecialfeaturethatisimpossibleinslip
gauges—theformercanbesubtractedaswellasadded.

20. Angle Gauges
•Angleblockgaugesprovidearange0to90degree59minutes59
seconds.
•Thegaugesareavailableinsetsof6,11and16.
6gauges-1⁰,3⁰,5⁰,15⁰,30⁰,45⁰
11gauges-1⁰,3⁰,5⁰,15⁰,30⁰,45⁰and1’,3’,5’,20’and30’
16gauges-1⁰,3⁰,5⁰,15⁰,30⁰,45⁰and1’,3’,5’,20’and30’andalso
1’’,3’’,5’’,20’’and30’’

21. Example of using Angle Gauges
Ifa5°angleblockisusedalongwitha30°angleblock,asshown
inFig.(a),theresulting
angleis35°.
Ifthe5°angleblockisreversedandcombinedwiththe30°angle
block,asshowninFig.(b).

22. Use of Angle Gauges
•Anglegaugesareusedformeasurementandcalibrationpurposes
intoolrooms.
•Usedformeasuringtheangleofadieinsert.
•Inspectingcompoundanglesoftoolsanddies.
•Usedinmachineshopsforsettingupamachine.

23. Angle Gauges to be used