9. Geometric Features.pdf

Roundness is a condition where all the points in a

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Roundness is a condition where all the points in a plane are equidistant from a centre. Roundness error Radial deviation between two concentric circles which enclose the actual part. e + Part

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19 Diametral Method Never commit this mistake! 0.999 95, 0.999 85, 0.999 80, 0.999 90 and 0.999 95 Roundness = ½ (max – min) = ½ (0.999 95 – 0.99980) = 0.000 075 Not detected 3 lobe
20 V-Block and Dial Indicator V-block Surface plate Dial indicator

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21 Detected Not detected (a) Diametrical method (b) Chordal method Detected Not detected Oval 3 lobe Intrinsic Datum Method
22 Extrinsic Datum Method The reference datum is not formed by the points on the object, but is a separate precision bearing or other external datum E.g. § Precision spindle instruments (Form tester) § Co-ordinate Measuring Machine (CMM) Form tester Typical spindle run-out: 0.05 - 0.025 µ m CMM Typical repeatability: 5 – 0.5 μ m

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23 Form Tester Workpiece Turntable Ref. spindle Worktable Pick-up Form testers generate polar data Only deviation from a reference feature is measured and hence there is a size (radius) suppression. Plotting is done on a polar chart with suitable radial magnification. These instruments are used to get data from axi- symmetrical components like bearings, spindles etc. Part profile Profile on a polar chart
Co-ordinate Measuring Machine (CMM) Measurement of circular feature (Size and deviations) Y X P( x i , y i ) Probe X y z

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25 Sample Point Strategies
26 Reference Circles 1. Least-Squares Circle 2. Minimum Circumscribing (MC) Circle 3. Maximum Inscribing (MI) Circle 4. Minimum Zone (MZ) Circle - based on ISO

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27 Least - Squares Circle Actual (Measured) Profile Least Squares Circle Roundness error Circle is fitted to the data points such that the sum of the squares of the deviations of the actual profile from the fitted circle is minimum. This is the most straight forward in the sense that all the data of the profile is used to establish the centre. Fast, easy for implementation and gives unique solution.
Example DIFFERENCE IN RADII 25.3 mm Magnification x 250 Least squares centre. Calculation of roundness error Difference in radii, Δ r = r max r min = 14.73 Roundness error = Δ r Magnification x1000 = 58.95 microns Radius (mm) 52.82 2 2x63.5 10.58 12 2 2x67.5 11.25 12 i i X X n Y Y n = = = = = = Center Coordinates Drawback : Does not conform to standards and generally overestimates the error. As a result, good parts may be rejected during inspection.

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29 Min. Circumscribed Circle (MCC) MC Circle Roundness error Corresponds to ring gauge.
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• Winter '15
• Subbu
• Geometry, Euclidean geometry, Line segment

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