Machinery's Handbook, 31st Edition
2354
Metric Module Involute Splines Table 13. Formulas for Dimensions and Tolerances for All Fit Classes— Metric Module Involute Splines
Formula
30-Degree Flat Root 0.5 to 10 module
30-Degree Fillet Root 0.5 to 10 module
37.5-Degree Fillet Root 0.5 to 10 module
45-Degree Fillet Root 0.25 to 2.5 module
Term
Symbol
Pitch Diameter Base Diameter Circular Pitch
D mZ
DB mZ cos α D
p
π m
Base Pitch
π m cos α D
p b es
Tooth Thick Mod Min Maj. Diam. Int
According to selected fit class, H/h, H/f, H/e, or H/d (see Table 14 )
DEI min
m ( Z + 1.5)
m ( Z + 1.8)
m ( Z + 1.4)
m ( Z + 1.2)
Max Maj Diam. Int. DEI max DEI min + ( T + λ )/tan α D (see Footnote a ) Form Diam, Int. DFI m ( Z + 1) + 2 c F m ( Z + 1) + 2 c F
m ( Z + 0.9) + 2 c F
m ( Z + 0.8) + 2 c F
Min Minor Diam, Int DII min DFE + 2 c F (see Footnote b ) Max Minor Diam, Int DII max DII min + (0.2 m 0.667 − 0.01 m − 0.5 ) (see Footnote c ) Cir Space Width, Basic E bsc 0.5 π m Min Effective EV min 0.5 π m Max Actual
E max EV min + ( T + λ ) for classes 4, 5, 6, and 7 (see Table 15 for T + λ )
Min Actual Max Effective Max Major Diam, Ext d Min Major Diam. Ext
E min EV min + λ (see text on page 2355 for λ ) EV max E max − λ (see text on page 2355 for λ )
m ( Z +1) − es /tan α D
m ( Z +0.9) − es /tan α D
m ( Z +0.8) − es /tan α D
m ( Z +1) − es /tan α D
DEE max DEE min
DEE max − (0.2 m 0.667 − 0.01 m − 0.5 ) (see Footnote c )
[
]
2
tan
. 05
h
es
⁄
+
α
^
h
Form Diam, External
DFE
s
D
2
. 05
. 05
sin
2
DB
D
h
^
+
α
−
#
sin
D
α
D
Max Minor Diam, Ext d
m ( Z − 1.5) − es /tan α D
m ( Z − 1.8) − es /tan α D
m ( Z − 1.4) − es /tan α D
m ( Z − 1.2) − es /tan α D
DIE max
Min Minor Diam, Ext DIE min DIE max − ( T + λ )/tan α D (see Footnote a ) Cir Tooth Thick, Basic S bsc 0.5 π m Max Effective SV max S bsc − es Min Actual
S min SV max − ( T + λ ) for classes 4, 5, 6, and 7 (see Table 15 for T + λ )
Max Actual Min Effective
S max SV max − λ (see text on page 2355 for λ ) SV min S min + λ (see text on page 2355 for λ )
Total Tolerance on Circular Space Width or Tooth Thickness Machining Tolerance on Circular Space Width or Tooth Thickness Effective Variation Allowed on Circular Space Width or Tooth Thickness Form Clearance Rack Dimension
( T + λ ) See formulas in Table 15
T T = ( T + λ ) from Table 15; λ from text on page 2355 .
See text on page 2355 .
λ
0.1 m
c F h s
0.6 m (see Fig. 6a ) 0.6 m (see Fig. 6b ) 0.55 m (see Fig. 6c ) 0.5 m (see Fig. 6d )
a Use ( T + λ ) for class 7 from Table 15 b For all types of fit, always use the DFE value corresponding to the H/h fit.
c Values of (0.2 m 0.667 - 0.01 m - 0.5 ) are as follows: for 10 module, 0.93; for 8 module, 0.80; for 6 module, 0.66; for 5 module, 0.58; for 4 module, 0.50; for 3 module, 0.41; for 2.5 module, 0.36; for 2 module, 0.31; for 1.75 module, 0.28; for 1.5 module, 0.25; for 1.25 module, 0.22; for 1 module, 0.19; for 0.75 module, 0.15; for 0.5 module, 0.11; and for 0.25 module, 0.06. d See Table 17 for values of es /tan α D .
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