CHAPTER 3

Angular & TaperMeasurement*

Angular MeasurementAn Angle is the opening between two lines meeting at a point1 Circle = 360 Degrees ( 360 ), 1 Degree ( 1 ) = 1/360th of a Circle1 Degree ( 1) = 60 Minutes ( 60' ), 1 Minute ( 1' ) = 1/60th of a Degree1 Minute ( 1') = 60 Seconds ( 60" ), 1 Second ( 1" ) = 1/60th of a MinuteAnother method of defining an Angle is based on the relation between the Radius & Arc of a circle. It is called as Radian2 radians = 360 1 radian = 57.2958

*

Angular Measurement

The unit of degree can also be divided into either decimal or fractional parts and is referred to as decimal degrees or fractional degrees respectively.

1 Degree = 1.5 Degree ( 1.5)

87 Degrees = 87.25 Degrees ( 87.25 )*

Angular MeasurementMinutes and seconds can each be expressed as decimal or fractional degrees.

1 Minute ( 1' ) = 1/60th of a Degree = 0.01667

1 Second ( 1" ) = 1/60th of a Minute = 0.01667'*

Angular MeasurementChange 525' to decimal degrees*Divide the minutes by 60 Add 0.4167 to 5 = 5.4167525' = 5.416725 divided by 60 = 0.4167

Angular MeasurementChange 2752'35" to decimal degrees*Divide the seconds by 60, add to minutesDivide the minutes by 60, add to degrees2752'35" = 27.876435 divided by 60 = 0.5833Added to the 52 minutes, it becomes 52.5833'52.5833 divided by 60 = .8764Added to the 27 degrees, it becomes 27.8764

Angular MeasurementChange 47.75 to degrees, minutes, and seconds*Multiply the decimal portion by 60This decimal .75 becomes 45 minutes. Add this to the degrees.47.75 = 4745'75 x 60 = 45Since there isn't any decimal portion after the 45, no further work is necessary.

Angular MeasurementChange 82.3752 to Degrees, minutes, and seconds*Multiply the decimal portion by 60Multiply the decimal minutes by 6082.3752 = 8222'30.72"0.3752 x 60 = 22.512 (the 22 becomes the minutes) Now add this to the degrees0.512 x 60 = 30.72 Now add this to the degrees and minutes to become seconds.82.3752 = 8222.512'

Angular Measurement instrumentsSimple ProtractorVernier bevel protractorOptical bevel protractorSine barSine plateAngle gaugesClinometerAngle dekkorAuto collimator*

Protractor*

Protractor*Whole degree increments

Protractor*Built-in Spirit Level

Protractor*Angular Measure with Protractor Head

Universal Bevel ProtractorPrecision angles to within 5' (0.083)Consist of baseVernier scaleProtractor dialSliding bladeDial clamp nut*

Vernier bevel Protractor JUNE 13,NOV11*

*Base plate stock

Used to measure obtuse angle (90-180)Acute-angle attachment is fastened to protractor to measure angles less than 90Main scale is divided into two arcs of 180Blade is 150-300 mm long, 13 mm wide & 2 mm thick.Least count = (Minimun dimension on mail scale)/( total number of division on vernier scale that occupy 23 )= 1/12=60/12 = 5 minutes

*

*

*Reading a Vernier Protractor51 9 x 5'= 45' Reading = 51 45'

Reading a Vernier Protractor*50 4 x 5'= 20' Reading = 50 20'

Reading a Vernier Protractor*28 3 x 5'= 15' Reading = 28 15'

*

Various use*

Optical bevel Protractor*Reading upto 2 with the help of small microscope eye piece provided

Sine Bars JUNE 11,MAY12, OCT12*Used when accuracy of angle must be checked to less than 5 minutes.Made of tool hardened steelConsists of steel bar with two cylinders of equal diameter fastened near ends

Centers of cylinders exactly 90 to edgeDistance between centers usually 5 or 10 inches and 100 /200/300 mmHave surface finish of 0.2m RaHoles are made to make Sine bar lighter & easy handling.

*

Principle of sine bar*

Accuracy requirementsRollers axes must be parallel to each other.Rollers centre distance(L) must be known through which size of the bar is specifiedTop surface must be flat & parallel to the plane of rollers axes.Rollers must be of identical diameters & round within a close tolerance*

Use of Sine barSame as discussed in Principle of Sine bar*1 ) LOCATING ANY WORK TO A GIVEN ANGLE

*2 ) CHECKING OR MEASURING UNKNOWN ANGLES DEC12 :

{I} When component is of small size

*2 ) CHECKING OR MEASURING UNKNOWN ANGLES :

{II} When component is of Large size

*2 ) CHECKING OR MEASURING UNKNOWN ANGLES :

{II.I} Other method When component is of Large size

*Advantages of Sine barPrecise & accurate angle measuring deviceSimple in design & construction

Sources of Errors in Sine barFairly reliable for angles less than 15 Becomes inaccurate gradually as the angle increasesImpractical to use for angles above 45 DUE TO :Physically difficult to hold in positionLong gauge stacks are not nearly as accurate as shorter gauge blocks.Slight error in it will cause large angular errorsLimited sized w/p can be inspectedA difference in deformation occurs at the point of roller contact supporting the surface and to the gauge blocks, because at higher angles, the load is shifted more towards the fulcrum roller.

*

Limitations of Sine barERROR IN :Rollers centre distanceSlip gauges combination usedParallelism between gauging surface & plane of roller axesEquality of Rollers size & cylindrical accuracyParallelism of roller axes with each otherFlatness of the upper surface of the bar.

*

Sine cenrte JUNE10*

*

*

*

*Sine table

Angle gauges*The angle gauges are hardened steel blocks of 75 mm length and 16 mm wide which has lapped surfaces lying at a very precise angle.

*

*

*

Sine Bars*

Sine Plate*

ClinometersIt is a special case of application of Spirit level.It is used for measuring angle relative to the horizontal planeUsed to check angular faces of large cutting tools & milling cutter insertsVarious types:Vernier clinometerMicrometer clinometerDial clinometerOptical clinometer*

Vernier ClinometersConsists a Housing having perpendicular facesOne face forms the base of the instrument.One rotary member carries the spirit levelThis rotary member is pivoted & can be locked at any position on the circular scale for angle measurement

*

*Base is placed on w/p as shownThen rotary member is adjusted till zero reading of the bubble is obtainedThen reading is taken as in Vernier bevel protractor.

*Micrometer Clinometers

Auto collimator*f

*

*

*

*Angle Dekkor

*http://mechanical14.blogspot.in/2012/06/notes.html

*

*

Angle checking of one sided tapered workpiece*

Angle checking of tapered hole*

* ******