Metrology lecture-2: Angular Measurement. IE 441: Metrology and Instrumentations Dr. Belal Gharaibeh Fall 2011 UOJ October 27, 2011

Transcription

1 Metrology lecture-2: Angular Measurement IE 441: Metrology and Instrumentations Dr. Belal Gharaibeh Fall 2011 UOJ October 27,

2 Angles, minutes and seconds Circles are divided into 360 equal parts, each being a degree. Each of these degrees can be evenly divided into 60 equal parts. These parts are called minutes. These minutes can be evenly divided into 60 equal parts. These parts are called minutes. 2

3 Relations for degree conversion 1 Circle = 360 Degrees ( 360 ) 1 Degree ( 1 ) = 1/360th of a Circle 1 Degree ( 1 ) = 60 Minutes ( 60' ) 1 Minute ( 1' ) = 1/60th of a Degree 1 Minute ( 1') = 60 Seconds ( 60" ) 1 Second ( 1" ) = 1/60th of a Minute Minutes and seconds can each be expressed as decimal or fractional degrees. 1 Minute ( 1' ) = 1/60th of a Degree = Second ( 1" ) = 1/60th of a Minute = ' 3

4 Examples for decimal conversion Change 6 25' to decimal degrees Divide the minutes by /60 = Add to 6 = Final answer: 6 25' =

5 Conversion to decimal degrees Change 27 52'35" to decimal degrees: 1. Divide the seconds by 60, add to minutes 35 /60 = Add to the 52 minutes, it becomes ' 2. Divide the minutes by 60, add to degrees / 60 =.8764 Add to the 27 degrees, it becomes Final answer: 27 52'35" =

6 Conversion from decimal to degree, minutes and seconds Change to degrees, minutes, and seconds Multiply the decimal portion by x 60 = 45 This decimal.75 becomes 45 minutes. Add this to the degrees. Since there isn't any decimal left after the 45, no further conversion is needed. Final answer: = 47 45' 6

7 Conversion from decimal to degrees, example 2 Change to Degrees, minutes, and seconds Multiply the decimal portion by x 60 = (the 22 becomes the minutes) Now add this to the degrees = ' Multiply the decimal minutes by x 60 = Now add this to the degrees and minutes to become seconds. Final answer = 82 22'30.72 Note: no more conversion is necessary after the seconds are obtained 7

8 Angular Measurement Most common tools Simple Protractor Gage blocks Sine bar Sine plate 8

9 Protractor 9

10 Protractor Whole degree increments 10

11 Multi-Use Gage Pre-set positions for 45 and 90 degrees, 59 degree drill point angle, and whole degree increments. 11

12 Multi-Use Gage Pre-set position for 90 degrees. 12

13 Multi-Use Gage Pre-set position for 45 degrees. 13

14 Multi-Use Gage Measuring 59 degree drill point angle. 14

15 15

16 Combination Set Protractor Whole degree increments 16

17 Protractor Head Whole degree increments 17

18 Protractor Angular Measure with Protract or Head 18

19 Transfer-type Protractors 19

20 Universal Bevel Protractor Precision angles to within 5' (0.083º) Consist of base Vernier scale Protractor dial Sliding blade Dial clamp nut 20

21 Vernier Protractor Acute-angle attachment fastened to protractor to measure angles less than 90º Main scale divided into two arcs of 180º Scale divided into 12 spaces on each side of 0 If zero on vernier scale coincides with line on main: reading in degrees 21

22 Reading a Vernier Protractor Note number of whole degrees between zero on main scale and zero on vernier scale Proceeding in same direction, note which vernier line coincides with main scale line Multiply number by 5' and add to degrees on protractor dial 4 x 5'= 20' Reading = 50º 20' 22

23 Angular gage blocks Similar to linear gage blocks but for setting a needed angle. The upper surface of the gage block has the desired angle, example: Gage block with 15 degrees looks like this: 15 This surface is inclined with 15 degrees 23

24 Example of angular gage blocks The added blocks (+ sign indicated) means we are placing the blocks in the opposite direction of the previous block such that the final surface is adjusted to the desired dimension 12 0 ' " 3713 Added block Added block is in opposite direction to previous block, to the left Block angle inclined to the right 24

25 Sine Bars Used when accuracy of angle must be checked to less than 5 minutes Consists of steel bar with two cylinders of equal diameter fastened near ends Centers of cylinders exactly 90º to edge Distance between centers usually 5 or 10 inches and 100 or 200 millimeters. Made of stabilized tool hardened steel When gage blocks are placed under one end, the sine bar will tilt to a specific angle 25

26 sin( ) h l sin 1 h ( ) l 26

27 Sine Bars Used on surface plates and any angle by raising one end of bar with gage blocks Sensitivity of a sine bar is defined by the ratio of change in angle to the change in gage block height sensitivity output input [degree/mm ] h 27

28 Applications of sine bar The tapered part is machined to an angle of 24 degree and 57 minutes. Design a method to measure the accuracy of this angle after machining by using a 5 inch sine bar and 81 set of gage blocks Method: 1. calculate the elevation needed to construct and desired angle: 2. Choose the correct gage blocks to make the elevation (h=2.1091) 3. Install the gage blocks under one of the sine bar cylindrical wheels 4. Install the part on top of the sine bar surface 5. Use a stylus with dial gage, shown in figure, and pass it on the part top surface 6. take measurement from the dial 7. If the dial reading is positive it means the part is less tapered (less than desired angle value) 8. If the dial reading is negative it means the part is more tapped (more than desired angle value) angle : 24 convert to decimal angle sin( ) 0 h l 57 ' angle sin(24.95) 57 : h h Scanning direction Gage blocks 28