Machinery's Handbook, 31st Edition
2288
HELICAL GEARING . . . . . 23 57 20 41 0 62547674 # # # # # # = =
27 72 32 38 0 6255144 34 60 44 29 0 6254902 # # # # = =
42 37 27 42 0 62548263 96 42 26 97 0 62549603
= Index ratio error = 0.62549654 − 0.62547726 = 0.00001928. Now use Formula (3) to find slight change required in rate of feed. This change compen sates sufficiently for the error in available index gears. Change in Feed Rate: Insert in Formula (3) obtainable index ratio. . . . . . . . . . . F M F 48 0 62547726 44 0894 48 0 62547726 30 0 0336417 0075 0 0336417 0 448556 0 448556 1 651817 0348183 Modified feed gear ratio log logof reciprocal # # # = − = = = = = = ^ h To find close approximation to modified feed gear ratio, proceed as in finding suitable gears for index ratio, thus obtaining 71 106 75 112 # . Inverting, modified feed gear ratio = 106 71 112 75 # = 0.448534. Modified feed F = obtainable modified feed ratio × M = 0.448534 × 0.075 = 0.03364 inch. If the feed rate is not modified, even a small error in the index gear ratio may result in an excessive lead error. Checking Accuracy of Lead: The modified feed and obtainable index ratio are inserted in Formula (4). Desired lead = 44.0894 inches. Lead obtained = 44.087196 inches; hence the computed error = 44.0894 − 44.087196 = 0.002204 inch or about 0.00005 inch per inch of lead. Machine with Differential: If a machine is equipped with a differential, the lead gears are computed in order to obtain the required helix angle and lead. The instructions of the hobbing machine manufacturer should be followed in computing the lead gears, because the ratio formula is affected by the location of the differential gears. If these gears are ahead of the index gears, the lead gear ratio is not affected by a change in the number of teeth to be cut (see Formula (5)); hence, the same lead gears are used when, for example, a gear and pinion are cut on the same machine. In the formulas which follow, the notation is the same as previously given, with these exceptions: R d = lead gear ratio for machine with differential; P a = axial or linear pitch of helical gear = distance from center of one tooth to center of next tooth measured parallel to gear axis = total lead L ÷ number of teeth N . (5) The number of hob threads T is included in the formula because double-thread hobs are used sometimes, especially for roughing in order to reduce the hobbing time. Lead gears having a ratio sufficiently close to the required ratio may be determined by using the table of gear ratio logarithms as previously described in connection with the non-differential type of machine. When using a machine equipped with a differential, the effect of a lead- gear ratio error upon the lead of the gear is small in comparison with the effect of an index gear error when using a non-differential type of machine. The lead obtained with a given or obtainable lead gear ratio may be determined by the following formula: L = ( R d NK ) ÷ T . cosec R K P T N K L T P K A T Driving gear sizes Driven gear sizes d a n # # # # # # π = = = =
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