Machinery's Handbook, 31st Edition
Out Of Roundness—Lobing 707 sphere can be produced with a perfectly symmetrical round shape. Some of the conditions are diagrammed in Fig. 6, where Fig. 6a shows simple ovality and Fig. 6b shows ovality occurring in two directions. From the observation of such conditions have come the terms lobe and lobing. Fig. 6c shows the three-lobed shape common with centerless-ground components, and Fig. 6d is typical of multi-lobed shapes. In Fig. 6e are shown surface waviness, surface roughness, and out-of-roundness, which often are combined with lobing.
Ring Cage
Part
a
b
c
d
e
Fig. 6. In Fig. 6a through Fig. 6d, the cylinder (or hole) diameters are shown at full size, but the lobes are magnified some 10,000 times to make them visible. In precision parts, the deviation from the round condition is usually only in the range of millionths of an inch, although it occasionally can be 0.0001 inch, 0.0002 inch, or more. For instance, a 3-inch-diameter part may have a lobing condition amounting to an inaccuracy of only 30 millionths (0.000030 inch). Even if the distortion (ovality, waviness, roughness) is small, it may cause hum, vibration, heat buildup, and wear, possibly leading to eventual failure of the component or assembly. Plain elliptical out-of-roundness (two lobes), or any even number of lobes, can be detected by rotating the part on a surface plate under a dial indicator of adequate resolution, or by using an indicating caliper or snap gage. However, supporting such a part in a V-block during measurement will tend to conceal roundness errors. Ovality in a hole can be detected by a dial-type bore gage or internal measuring machine. Parts with odd numbers of lobes require an instrument that can measure the envelope or complete circumference. Plug and ring gages will tell whether a shaft can be assembled into a bearing but not whether there will be a good fit, as illustrated in Fig. 6e. A standard, 90-degree included-angle V-block can be used to detect and count the num ber of lobes, but to measure the exact amount of lobing indicated by R - r in Fig. 7 requires a V-block with an angle α, which is related to the number of lobes. This angle α can be cal culatedfromtheformula2α=180 ° – 360 ° / N , where N is the number of lobes. Thus, for a three- lobe form, α becomes 30 degrees, and the V-block used should have a 60-degree included angle. The distance M , which is obtained by rotating the part under the comparator plunger, is converted to a value for the radial variation in cylinder contour by the formula M = ( R – r ) (1 + csc α).
M
R
R
r
r
90°
Fig. 7.
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