Machinery's Handbook, 31st Edition
708 Out Of Roundness—Lobing Using a V-block (even of appropriate angle) for parts with odd numbers of lobes will give exaggerated readings when the distance R – r (Fig. 7) is used as the measure of the amount of out-of-roundness. The accompanying table shows the appropriate V-block angles for various odd numbers of lobes and the factors (1 + csc α) by which the readings are increased over the actual out-of-roundness values. Table of Lobes, V-Block Angles and Exaggeration Factors in Measuring Out-of-Round Conditions in Shafts Number of Lobes Included Angle of V-Block (deg) Exaggeration Factor (1 + csc α) 3 60 3.00 5 108 2.24 7 128.57 2.11 9 140 2.06 Measurement of a complete circumference requires special equipment, often incorporat ing a precision spindle running true within two millionths (0.000002) inch. A stylus attached to the spindle is caused to traverse the internal or external cylinder being inspected, and its divergences are processed electronically to produce a polar chart similar to the wavy outline in Fig. 6e. Electronic circuits provide for the variations due to surface effects to be separated from those of lobing and other departures from the “true” cylinder traced out by the spindle. Coordinates for Hole Circles Type “A” Hole Circles.— Type “A” hole circles can be identified by hole number 1 at the top of the hole circle, as shown in Fig. 1a and Fig. 1b. The x , y coordinates for hole circles of from 3 to 33 holes corresponding to the geometry of Fig. 1a are given in Table 1a, and cor responding to the geometry of Fig. 1b in Table 1b. Holes are numbered in a counterclock wise direction as shown. Coordinates given are based upon a hole circle of (1) unit diameter. For other diameters, multiply the x and y coordinates from the table by the hole circle diam- eter. For example, for a 3-inch or 3-centimeter hole circle diameter, multiply table values by 3. Coordinates are valid in any unit system.
X
Ref
1
1
Y
5
2
– Y
Ref
2
5
– X
+ X
3
4
+ Y
4
3
Fig. 1a. Type “A” Circle Fig. 1b. Type “A” Circle The origin of the coordinate system in Fig. 1a, marked “Ref”, is at the center of the hole circle at position x = 0, y = 0. The equations for calculating hole coordinates for type “A” circles with the coordinate system origin at the center of the hole circle are as follows: (1a) where n = number of holes in circle; D = diameter of hole circle; q = angle between adjacent holes in circle; H = number (from 1 to n ) of the current hole; x H = x coordinate at position of hole number H ; and, y H = y coordinate at position of hole number H . Example 1(a): Calculate the hole coordinates for the 5-hole circle shown in Fig. 1a when circle diameter = 1. Compare the results to the data tabulated in Table 1a. sin cos n n x D H y D H 360 2 2 1 2 1 H i r i i = = =− − = − − ^^ ^^ h h h h H
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