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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