Metrology lecture-2: Angular

Measurement

IE 441: Metrology and Instrumentations

Dr. Belal Gharaibeh

Fall 2011

UOJ

October 27, 2011

1

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

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

3

• Minutes 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'

Examples for decimal conversion

Change 6°25' to decimal degrees

4

Divide the minutes by 60

Add 0.4167 to 6 = 6.4167°

Final answer:

6°25' = 6.4167°

25 /60 = 0.4167

Conversion to decimal degrees

Change 27°52'35" to decimal degrees:

5

1. Divide the seconds by 60, add to minutes

2. Divide the minutes by 60, add to degrees

Final answer: 27°52'35" = 27.8764°

35 /60 = 0.5833

Add to the 52 minutes, it becomes 52.5833'

52.5833 / 60 = .8764

Add to the 27 degrees, it becomes 27.8764°

Conversion from decimal to degree, minutes and seconds

Change 47.75° to degrees, minutes, and seconds

6

Multiply the decimal portion by 60

This decimal .75 becomes 45 minutes.

Add this to the degrees.

Final answer: 47.75° = 47°45'

75 x 60 = 45

Since there isn't any decimal left after the

45, no further conversion is needed.

Conversion from decimal to degrees, example 2

Change 82.3752° to Degrees, minutes, and seconds

7

Multiply the decimal portion by 60

Multiply the decimal minutes by 60

Final answer 82.3752° = 82°22'30.72“

Note: no more conversion is necessary after the

seconds are obtained

0.3752 x 60 = 22.512 (the 22 becomes

the minutes) Now add this to the degrees

0.512 x 60 = 30.72 Now add this to the

degrees and minutes to become seconds.

82.3752° = 82°22.512'

Angular Measurement

• Most common tools

– Simple Protractor

– Gage blocks

– Sine bar

– Sine plate

8

Protractor

9

Protractor

10

Whole degree increments

Multi-Use Gage

11

Pre-set positions for

45 and 90 degrees,

59 degree drill point

angle, and whole

degree increments.

Multi-Use Gage

12 Pre-set position for 90 degrees.

Multi-Use Gage

13

Pre-set position for 45 degrees.

Multi-Use Gage

14

Measuring 59 degree drill point angle.

15

Combination Set Protractor

16

Whole degree increments

Protractor Head

17

Whole

degree

increments

Protractor

18

Angular

Measure

with

Protract

or Head

Transfer-type Protractors

19

Universal Bevel Protractor

• Precision angles to within 5' (0.083º)

• Consist of base

– Vernier scale

– Protractor dial

– Sliding blade

– Dial clamp nut

20

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

Reading a Vernier Protractor • Note number of whole degrees between zero on main scale and

zero on vernier scale

22

• 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'

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:

23

15

This surface is inclined with 15 degrees

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

24

Added block

Block angle inclined to the right

Added block is in opposite

direction to previous block, to

the left

"'0 133712

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)sin( 1

l

h

l

h

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

27

][degree/mm hinput

outputysensitivit

Applications of sine bar

28

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)

1091.25

)95.24sin()sin(

95.24

95.060

57 :angle decimal to

5724: '0

hh

l

h

angle

convert

angle

Gage blocks

Scanning direction