Machinery's Handbook, 31st Edition
Involute Splines 2351 2) Find the value of φ i in degrees, in the involute function tables beginning on page 112 . Find sec φ i = 1/cosine φ i in the trig tables, pages 108 through 110 , using interpolation to obtain higher accuracy. 3) Compute measurement, M i , between pins: For even numbers of teeth: M i = D b sec φ i − d i For odd numbers of teeth: M i = ( D b cos 90 ° / N ) sec φ i − d i where: d i = 1.7280/ P for 30 ° and 37.5 ° standard pressure angle ( φ D ) splines d i = 1.9200/ P for 45 ° pressure angle splines Example: Find the measurement between pins for maximum actual space width of an internal spline of 30 ° pressure angle, tolerance class 4, 3 ∕ 6 diametral pitch, and 20 teeth. Solution: The maximum actual space width to be substituted for s in Step 1 above is obtained as follows: In Table 5, page 2341 , the maximum actual space width is the sum of the minimum effective space width (second column) and λ + m (third column). The minimum effective space width s v from Table 2, page 2336 , is π /2 P = π /(2 × 3). The values of λ and m from Table 4, page 2338 , are, for a class 4 fit, 3 ∕ 6 diametral pitch, 20-tooth spline: λ = 0.0027 × 0.71 = 0.00192; and m = 0.00176 × 0.71 = 0.00125, so that s = 0.52360 + 0.00192 + 0.00125 = 0.52677. Other values required for Step 1 are: D = N ÷ P = 20 ÷ 3 = 6.66666 inv φ D = inv 30 ° = 0.053751 from a calculator d i = 1.7280 ∕ 3 = 0.57600 D b = D cos φ D = 6.66666 × 0.86603 = 5.77353 The computation is made as follows: 1) inv φ i = 0.52677 ∕ 6.66666 + 0.053751 − 0.57600 ∕ 5.77353 = 0.03300 2) From a calculator, φ i = 25 ° 46.18 ′ and sec φ i = 1.11044 3) M i = 5.77353 × 1.11044 − 0.57600 = 5.8352 inches Formulas for 2-Pin Measurement Over Pins: For measurement over pins of external splines: 1) Find involute of pressure angle at pin center: D t D d N inv inv e D b e φ φ π = + + − 2) Find the value of φ e and sec φ e from the involute function tables beginning on page 112 . 3) Compute measurement, M e , over pins: For even numbers of teeth: M e = D b sec φ e + d e For odd numbers of teeth: M e = ( D b cos 90 ° / N ) sec φ e + d e where: d e = 1.9200/ P for all external splines American National Standard Metric Module Splines.— ANSI B92.2M-1980 (R1989) is the American National Standards Institute version of the International Standards Orga nization involute spline standard. It is not a “soft metric” conversion of any previous, inch- based, standard, * and splines made to this hard metric version are not intended for use with components made to the B92.1 or other, previous standards. The ISO 4156 Standard * A “soft” conversion is one in which dimensions in inches, when multiplied by 25.4 will, after being ap- propriately rounded off, provide equivalent dimensions in millimeters. In a “hard” system the tools of production, such as hobs, do not bear a usable relation to the tools in another system; i.e., a 10 diametral pitch hob calculates to be equal to a 2.54 module hob in the metric module system, a hob that does not exist in the metric standard.
Copyright 2020, Industrial Press, Inc.
ebooks.industrialpress.com
Made with FlippingBook - Share PDF online