Machinery's Handbook, 31st Edition
HELICAL GEARING 2287 Change-Gears for Helical Gear Hobbing.— If a gear-hobbing machine is not equipped with a differential, there is a fixed relation between the index and feed gears and it is necessary to compensate for even slight errors in the index gear ratio, to avoid excessive lead errors. This may be done readily (as shown by the example to follow) by modifying the ratio of the feed gears slightly, thus offsetting the index gear error and making very accurate leads possible. Machine Without Differential: The formulas which follow may be applied in computing the index gear ratio. R = index-gear ratio L = lead of gear, inches F = feed per gear revolution, inch K = machine constant
T = number of threads on hob N = number of teeth on gear P n = normal diametral pitch P nc = normal circular pitch A = helix angle, relative to axis M = feed gear constant
Driven gear sizes Driving gear sizes
R L F L F ' ! ' =
N KT
L F L
N KT
=
=
(1) Use minus ( − ) sign in Formulas (1) and (2) when gear and hob are the same “hand” and plus (+) sign when they are of opposite hand; when climb hobbing is to be used, reverse this rule. 1 # ! # ^ h
sin N P A F KT n ! # #
sin N P A F KT ! #
=
=
R
(2) (3) (4)
π
nc
F M F Ratio of feed gears = L NR KT FNR lead obtained with available index and feed gears = − = ^ h NR L NR KT = − ^ h
Note: If gear and hob are of opposite hand, then in Formulas (3) and (4) change ( NR − KT ) to ( KT − NR ). This change is also made if gear and hob are of same hand but climb hobbing is used. Example: A right-hand helical gear with 48 teeth of 10 normal diametral pitch, has a lead of 44.0894 inches. The feed is to be 0.035 inch, with whatever slight adjustment may be necessary to compensate for the error in available index gears. K = 30 and M = 0.075. A single-thread right-hand hob is to be used. . . . . R 44 0894 0 035 440894 48 30 1 0 62549654 # # = − = Using the method of Conjugate Fractions beginning on page 5 , several suitable ratios close to 0.62549654 were found. One of these, (34 × 53)/(43 × 67) = 0.625477264839, will be used as the index ratio. Other usable ratios and their decimal values were found to be as follows:
Copyright 2020, Industrial Press, Inc.
ebooks.industrialpress.com
Made with FlippingBook - Share PDF online