CircularityRoundness

1
Circularity/Roundness
2
Measurement of Form
3
Geometric characteristic symbols
4
Circularity Tolerance applied to a cylindrical
feature
5
Circularity Tolerance applied to a sphere
6
Cylindrical Tolerance directed to either view
7
Characteristic irregularities of basically Round
forms - 1
8
Characteristic irregularities of basically Round
forms - 1
9
Characteristic irregularities of basically Round
forms - 2
10
Characteristic irregularities of basically Round
forms - 2
11
Application examples of Engineering parts with
functional need for roundness - 1
12
Application examples of Engineering parts with
functional need for roundness - 1
13
Circularity/Roundness

• Measurement Techniques
• Filtering and Reference circles
• Numerical Evaluation
• Error Correction

14
Measurement Techniques

• Intrinsic Datum Methods
• Use part surface as a datum
• Extrinsic Datum Methods
• External datum such as a precision spindle

15
Intrinsic Datum Methods

• Diametral measurement
• V block
• Bench center

16
Diametral Methods
Dowel pin three lobed characteristic
D1D2D3D4
Dowel pin with three lobes out-of-roundness
characteristic
Elliptical part
17
V Block Methods
18
Fixed and Adjustable V - blocks
108o V block
60o V block
Adjustable V block
128o 34 V block
19
Conversion Factors for Roundness Measurements
using V blocks
A180 - (360/n)
A included angle of the V block n number
of lobes
20
Bench Center
21
Extrinsic Datum Methods

• External datum Precision spindle
• Part on a precision spindle
• Probe on a precision spindle

22
Precision spindle instruments
23
Stylus Shape and Material
24
Sharp and Blunt Stylus
25
Effect of Stylus
26
Suppressed Zero
27
Magnification
28
Effect of imperfect centers
29
Effect of Combined Eccentricity and Zero
Suppression
30
Filters
31
Effect of filters
32
Polar profiles at various filter values
33
Reference criteria
Minimum Radial Separation
Least Squares Circle
Maximum Inscribed Circle
Minimum Circumscribed Circle
34
Eccentric Circle
35
Equation of Eccentric Circle
If E ltlt R, ignoring the higher order terms, we get
36
Equation (Contd.)
(Suppressed radius)
where
37
Limacon of Pascal
38
Determination of Least Squares Center and Circle
39
Determination of Least Squares Center and Circle
The distances a and b of the least squares center
from the center of the paper are calculated from
the following formula
Alternate Formula
The radius R of the least squares circle
40
A sample uncertainty Budget for the Measurement
of Roundness
41
Uncertainty Budget for the Measurement of Ball
Roundness at NIST
Using k2 we have U0.016 mm