Principles of Dimensional Metrology
Balls of diameters 25 mm and 20 mm were used to measure a taper...

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Principles of Dimensional Metrology
Balls of diameters 25 mm and 20 mm were used to measure a taper ring gage.  The large ball protruded mm above the end face of ring gear while the distance of the end face from the top of the 20 mm diameter ball was 40 mm.
Determine:
Angle of taper and the large end diameter.
Assuming an error of up to 0.005 mm in measuring the distances and no errors in the ball diameter, determine the possible error in angle?
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2.
	
Document Preview: Principles of Dimensional MetrologyBalls of diameters 25 mm and 20 mm were used to measure a taper ring gage.  The large ball protruded mm above the end face of ring gear while the distance of the end face from the top of the 20 mm diameter ball was 40 mm.Determine:Angle of taper and the large end diameter.Assuming an error of up to 0.005 mm in measuring the distances and no errors in the ball diameter, determine the possible error in angle?------------------------------------------------------------------------------------------------------------------------------------------2.Figure above shows a method to measure taper of a cone with a 10 in sine bar as shown. If the height h of the slip blocks assembly is XXXXXXXXXXin, determine the taper of the cone.  A ½ in ball with a slip gage stack of s = XXXXXXXXXXin is assembled as shown such that the dial gage reading over the taper and the block are identical.Calculate the diameter of the smaller end of the cone.------------------------------------------------------------------------------------------------------------------------------------------3.  Given the following gages and their classify then in one of the eleven categories and justify your selectionGage DescriptionApplicationClassificationMahr/Federal XLI-22P=20 Portable Thickness GageVerify Flange thickness by an operator on assembly floorMahr Form MMQ 400-2Small lot of engine shafts to be measured for First ArticleNikon XC65d(-LS) Cross Scanner on a LK V XXXXXXXXXXMeasure Sheet metal profile in stamping inspection cellRenishaw EquatorIntroducing gage to replace multiple hand inspections for process controlZygo 7300 New ViewParts sent for measurement for a customer return.  Need improved data to complement production inspection from layoutStarrett 1-2” MicrometerSmall lot of engine shafts to be measured for First ArticleStarrett 0-2” MicrometerVerify Flange thickness by an operator on assembly floorHabco Model AF1000...

David · Accepted Answer

Principles of Dimensional Metrology  
1. Balls of diameters 25 mm and 20 mm were used to measure a taper ring gage.  The large ball protruded 5 mm above the end face of ring gage while the distance of the end face from the top of the 20 mm diameter ball was 40 mm. 
Determine 
A) Angle of taper and the large end diameter.
B) Assuming an error of up to 0.005 mm in measuring the distances and no errors in the ball diameter, determine the possible error in angle?
Answer  
Taper Angle = 3.372 degrees
Steps of Calculation: 
Let us consider the angle of taper as A
Sin (A/2) = (R2-R1)/(H1+H2+R1-R2)
Sin( A/2) = (12.5-10)/(5+40+10-12.5)
Sin( A/2)= 2.5/42.5
A=3.372*2 =6.744 degrees
As you know 
Cos A/2 = (Adjacent side /2)/Radius
Adjacent side/2 = 9.982
Adjaccent side =19.965
Sin A/2= Opposite side /Radius
0.0588*10=0.588=opposite side
Hence at a height of 50.588 the diameter is 19.965.
TanA= (Large end diameter-19.965)/50.588
Tan6.744*50.88=(large end diameter-19.965)
Large end diameter=25.981mm
Degree considering error =sin-1 (12.5-10)/(4.995+39.995+10-12.5)=3.373degrees
Total difference in degrees =0.002 degrees.

Principles of Dimensional Metrology Balls of diameters 25 mm and 20 mm were used to measure a taper ring gage. The large ball protruded mm above the end face of ring gear while the distance of the end...

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