Straight cylindrical involute splines -- Metric module, side fit -- Generalities, dimensions and inspection

Provides data and guidance for the design, manufacture and inspection of the involute splines. Limiting dimensions, tolerances and manufacturing errors are defined and tabulated. Linear and angular dimensions are expressed in mm and degrees, respectively.

Cannelures cylindriques droites à flancs en développante -- Module métrique, à centrage sur flancs -- Généralités, dimensions et vérification

Ravni utori z evolventnimi boki na valjih - Metrski modul, bočno prileganje - Splošno, mere in kontrola

General Information

Status
Withdrawn
Publication Date
31-Dec-1999
Withdrawal Date
30-Jun-2006
Technical Committee
Current Stage
9900 - Withdrawal (Adopted Project)
Start Date
01-Jul-2006
Due Date
01-Jul-2006
Completion Date
01-Jul-2006

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SLOVENSKI STANDARD
SIST ISO 4156:2000
01-januar-2000
5DYQLXWRUL]HYROYHQWQLPLERNLQDYDOMLK0HWUVNLPRGXOERþQRSULOHJDQMH
6SORãQRPHUHLQNRQWUROD

Straight cylindrical involute splines -- Metric module, side fit -- Generalities, dimensions

and inspection

Cannelures cylindriques droites à flancs en développante -- Module métrique, à centrage

sur flancs -- Généralités, dimensions et vérification
Ta slovenski standard je istoveten z: ISO 4156:1981
ICS:
21.120.30 Mozniki, utori za moznike, Keys and keyways, splines
razcepke
SIST ISO 4156:2000 en

2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

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SIST ISO 4156:2000
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SIST ISO 4156:2000
International Standard

INTERNATIONAL ORGANIZATION FOR STANDARDIZATION.MEIK,4YHAPO~HAR OPl-AHM3Al.&lR fl0 CTAH~APTM3ALWWORGANISATION INTERNATIONALE DE NORMALISATION

Straight cylindrical involute splines - Metric module,
side fit - Generalities, dimensions and inspection

Cannelures cylindriques droites à flancs en développante - Module métrique, à centrage sur flancs - Généralités, dimensions et

vérification
First edition - 1981-05-01
U DC 621 n 24.44 Ref. No. ISO4156-1981 (E)

dimensions, dimensional tolerances, limits, definitions, symbols, formulae (mathemathics), design.

Descriptors : splines,
Price based on 138 pages
---------------------- Page: 3 ----------------------
SIST ISO 4156:2000
Foreword

ISO (the International Organization for Standardization) is a worldwide federation of

national standards institutes IISO member bodies). The work of developing Inter-
national Standards is carried out through ISO technical committees. Every member

body interested in a subject for which a technical committee has been set up has the

right to be represented on that committee. International organizations, governmental

and non-governmental, in liaison with ISO, also take part in the work.

Draft International Standards adopted by the technical committees are circulated to

the member bodies for approval before their acceptance as International Standards by

the ISO Council.
International Standard ISO 4156 was developed by Technical Committee ISO/TC 32,
Splines and serrations, and was circulated to the member bodies in October 1978.
It has been approved by the member bodies of the following countries :
Australia India Sweden
Austria
Italy Turkey
Belgium Japan United Kingdom
Chile Korea, Rep. of USA
Finland South Africa, Rep. of Y ugoslavia
France Spain

The member bodies of the fol lowing countries expressed disapproval of the document

on technical grounds :
Czechoslovakia
Germany, F. R.
0 International Organization for Standardization, 1981
Printed in Switzerland
---------------------- Page: 4 ----------------------
SIST ISO 4156:2000
Contents
Page
Section one : Generalities
.........................................................
1 Scope and field of application
............................................
2 Terms and definitions relating to splines

3 Symbols ....................................................................................

4 Pressure angle (standard) ..............................................................

Type of fit ..................................................................................

...................... 8
6 Space width and tooth thickness, total tolerance (T + A.)
...........................................................
7 Basic rack profiles for spline
.................................................
8 Machining tolerances and variations
...............................................................
9 Effect of spline variations
.........................................
10 Effective and actual dimensions for splines
Il Use of effective and actual dimensions for space width and tooth

thickness ...................................................................................

12 Drawing data ..............................................................................

Section two : Dimensions

. . . . . . . . . . ..I..............................................................

13 Introduction.. . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

14 Dimensions and tolerances
Tables
30° pressure angle
38-65

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

- flat root
66-93

- fillet root . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...*.

94-121

37,5O pressure angle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122-139

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
45O pressure angle
Section three : Inspectiod)
1) In preparation : Will be the subject of an addendum.
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SIST ISO 4156:2000
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SIST ISO 4156:2000
ISO 4X56-1981 (E)
INTERNATIONAL STANDARD
lute splines - Metric module,
Straight cylindric
side fit - Generalities, dimensions and inspection
: Generalities
Section one
2.6 fillet root spline : A spline having a tooth or space pro-
1 Scope and field of application
file in which the opposing involute flanks are connected to the
root circle (Dei or Di, diameter) by a single fillet.
This International Standard provides data and guidance for the
design, manufacture and inspection of straight (non-helical)
cylindrical involute splines with side fit. It establishes a
2.7 flat root spline : A spline having a tooth or space profile
specification based on the module within the range 0,25 to 10
in which each of the opposing involute flanks are connected to
inclusive, relating to nominal pressure angles of 30°, 37,5O and
the root circle (Dei or Di, diameter) by a fillet.
45O. (For electronic data processing purposes, the form of ex-
“37,5”’ has been adopted instead of 37O 30’.)
pression
module, m : The ratio of the circular pitch, expressed in
2.8
millimetres, to the number n: (or the ratio of the pitch diameter,
Limiting dimensions, tolerances, manufacturing errors and
expressed in millimetres, to the number of teeth).
their effects on the fit between connecting co-axial spline
elements are defined and tabulated. Linear dimensions are ex-
2.9 pitch circle : The reference circle from which all normal
pressed in millimetres and angular dimensions in degrees.
spline dimensions are derived, and the circle on which the
specified pressure angle has its nominal value.
2 Terms and definitions relating to splines
2.10 pitch diameter, D : The diameter of the pitch circle, in
millimetres, equal to the number of teeth multiplied by the
module.
2.1 spline joint : Connecting, co-axial elements that
transmit torque through the simultaneous engagement of

equally spaced teeth situated around the periphery of a cylin- 2.11 pitch point : The intersection of the spline tooth profile

with the pitch circle.
drical external member with similar spaced mating spaces
situated around the inner surface of the related cylindrical inter-
nal member.
A length of arc of the pitch circle
2.12 circular pitch, p :
between two consecutive pitch points of left- (or right-) hand
flanks, which has a normal value of the number n: multiplied by
One member of spline joint having
2.2 involute spline :
the module.
teeth or spaces that have involute flank profiles.
The acute angle between a radial
2.13 pressure angle, a :
: A spline formed on the inner surface of
2.3 interna1 spline
line passing through any point on a tooth flank and the tangent
a cylinder.
plane to the flank at that point.
2.14 standard pressure angle, an : The pressure angle at
2.4 external spline : A spline formed on the outer surface of
the specified pitch point.
a cylinder.
2.15 base circle : The circle from which involute spline
2.5 fillet : The concave surface of the tooth or space con-
tooth profiles are generated.
necting the involute flank and the root circle. This curved sur-
face as generated varies and cannot be properly specified by a
: The diameter of the base circle.
radius of any given value. 2.16 base diameter, D,
---------------------- Page: 7 ----------------------
SIST ISO 4156:2000
ISO 4156-1981 (E)

: The arc length of the base circle be- 2.30 effective clearance, cv Hooseness or interference) :

2.17 base pitch, Pb
The effective space width of the interna1 spline minus the effec-
tween two consecutive corresponding flanks.
tive tooth thickness of the mating external spline.
2.18 major circle : The circle formed by the outermost sur-
2.31 theoretical clearance, c (looseness or interference) :
face of the spline. It is the outside circle (tooth tip circle) of the
The actual space width of an interna) spline minus the actual
external spline or the root circle of the interna) spline.
tooth thickness of the mating external spline. It does not define
the fit between mating members, because of the effect of varia-
2.19 major diameter, Dec, Dei : The diameter of the major
tions.
2.32 form clearance, CF : The radial depth of involute pro-
2.20 minor circle : The circle formed by the innermost sur-
file beyond the depth of engagement with the mating part. It
face of the spline. It is the root circle of the external spline or
allows eccentricity of the minor circle (internal), of the major
the inside circle (tooth tip circle) of the interna1 spline.
circle (external) and of their respective pitch circles.
Dii : The diameter of the minor
2.21 minor diameter, Di,,
2.33 total index variation : Amount of absolute values of
circle.
the two greatest actual (or practically measured) positive and
negative variations from the theoretical spacing.
2.22 form circle : The circle which establishes the deepest
points of involute form control of the tooth profile. This circle
2.34 total profile variation : Amount of absolute values of
along with the tooth tip circle (or start of chamfer circle) deter-
the two greatest positive and negative variations, from the
mines the limits of tooth profile requiring control. It is located
theoretical tooth profiles, measured normal to flanks.
near and below the major circle on the interna1 spline and near
and above the minor circle on the external spline.
2.35 total lead variation : Amount of absolute values of the
two greatest opposite direction variations, from the theoretical
2.23 form diameter, &,, DFi : The diameter of the form
direction (parallel to the datum axis), also including parallelism
circle.
and alignment variations (see figure IL
NOTE - Straight (non-helical) splines have an infinite lead.
: The radial distance from the
2.24 depth of engagement
minor circle of the interna1 spline to the major circle of the ex-
ternal spline, minus corner clearance and/or chamfer depth.
2.25 basic (circular) space width or tooth thickness at
the pitch diameter, E or S : For 30°, 37,5’ and 45O pressure
Datum axis
angle splines, half the circular pitch.
2.26 actual space width : The practically measured circular
space width, on the pitch circle, of any single space width
a) Lead variation
within the limit values E,,,, and E,i,..
Datum axis -
2.27 effective space width, EV : For an interna1 spline,
equal to the circular tooth thickness on the pitch circle of an im-
aginary Perfect external spline which would fit the interna1
spline without looseness or interference, considering engage-
ment of the entire axial length of the splined assembly. The
b) Parallelism variation
minimum effective space width (EV min., always equal to E) of
Effective spline
the interna1 spline is always basic, as shown in table 1. Fit varia-
tions may be obtained by adjusting the tooth thickness of the
Datum axis
external spline.
-YY
2.28 actual tooth thickness : The practically measured cir-
cular tooth thickness, on the pitch circle, of any single tooth
C) Alignment variation
within the limit values S,,,. and S,i,..
2.29 effective tooth thickness, S, : For an external spline,
equal to the circular space width on the pitch circle of an im-
Figure 1 - Lead variations
aginary Perfect interna1 spline which would fit the external
spline without looseness or interference, considering engage-
ment of the entire axial length of the splined assembly. Fit
variations are obtained by adjusting this value S,.
---------------------- Page: 8 ----------------------
SIST ISO 4156:2000
ISO 41!56-1981 (E)
parallelism variation : The variation of parallelism of a
2.36 Db [DB1 = base diameter
single spline tooth to any other single spline tooth (see
dei = pin contact diameter, interna1 spline
figure IL
d,, = pin contact diameter, external spline
DFe [DFEI = form diameter, external spline
2.37 alignment variation : The variation of the effective
spline , axis with respect to the reference axis (sec figure 1).
DFi [DFII = form diameter, interna1 spline
Dii [DII] = minor diameter, interna1 spline
2.38 out-of-roundness : The variation of the spline from a
Dec [DEEI = major diameter, external spline
true circular configuration.
Die [DIEI = minor diameter, external spline
2.39 effective variation : The accumulated effect of the
D,i [DEI1 = major diameter, interna1 spline
spline variations on the fit with the mating part.
DRe [DREI = diameter of measuring pin for external spline
D,i [DRI] = diameter of measuring pin for interna1 spline
2.40 variation allowance, A : The permissible effective
Â. = variation allowance
variation.
inv a = involute a ( = tan a - a)
2.41 machining tolerance, T : The permissible variation in
Ke [KEI = approximation factor for external spline
actual space width or actual tooth thickness.
Ki [KI] = approximation factor for interna1 spline
= spline length
2.42 total tolerance, (T + A) : The machining tolerance
plus the variation allowance. The total tolerance on an interna1
= active spline length
spline is the difference between the minimum effective space
= length of engagement
width and the maximum actual space width; on an external
T = machining tolerance
spline, it is the difference between the maximum effective tooth
thickness and the minimum actual tooth thickness.
IMRe [MRE] = measurement over two pins, external spline
h/lRi [MRI] = measurement between two pins, interna1 spline
2.43 length of engagement, g, : The axial length of con-
W = measurement over k teeth, external spline
tact between mating splines.
2 = number of teeth
2.44 active spline length, g, : The maximum axial spline m = module
length in contact (when working) with the mating spline. On
Pb = base pitch
sliding splines, the active length exceeds the length of engage-
p = circular pitch
ment.
@Fe = fillet radius of the basic rack, external spline
2.6 basic dimension : A numerical value to describe the
@Fi = fillet radius of the basic rack, interna1 spline
theoretically exact size, shape or location of a feature. It is the
E = basic space width, circular
basis from which permissible variations are established by
E = actual maximum space width, circular
max
tolerances.
= actual minimum space width, circular
min
2.46 auxiliary dimension : A dimension, without tolerance,
E,, EV1 = effective space width, circular
given for information purposes only, for the determination of
S= basic tooth thickness, circular
the useful production and control dimensions.
S = actual maximum tooth thickness, circular
max
S = actual minimum tooth thickness, circular
min
3 Symbols
= effective tooth thickness, circular
s, WI
a = pressure angle
3.1 General symbols
= standard pressure angle
The general symbols used to designate the various spline terms
a,i = pressure angle at pin contact diameter, interna) spline
and dimensions are given below (sec figures 10, 11, 12, 13, 14
a = pressure angle at pin contact diameter, external
and 15).
spline
NOTE - In electronic data processing (EDP), it is not always possible
ai = pressure angle at pin centre, interna1 spline
to present symbols in their theoretically correct form because of limita-
a, = pressure angle at pin centre, external spline
tions of connected printing equipment. For this reason, some alter-
native symbols for EDP usage are given in brackets below (for exam-
= pressure angle at form diameter, external spline
aFe
ple, the symbol Db for base diameter may be printed as DB).
aFi = pressure angle at form diameter, interna1 spline
c, = effective clearance (looseness or interference)
k-j,--h-f- e and d = fundamental deviation on the
cF = form clearance
external spline = c, min
D = pitch diameter H = fundamental deviation on the interna1 spline
---------------------- Page: 9 ----------------------
SIST ISO 4156:2000
ISO 41!56-1981 (El

Tables 1 and 2 give the basic dimensions and fundamental formulae, a graphical presentation of which is given by figure 2.

Table 1 - Theoretical dimensions for spllines
Dimensions in millimetres
Basic space width or tooth thickness Base pitch
Circular
Tooth Module at pitch diameter E or S
pitch
-- -- --1
o!D 30” * m
&D 30” QD 37,5O o!D 45” &D 30” a!D 37,5O &D 45O
10 31,416 15,708 15,708 27,207 0 24,923 9
25,133 12,566 12,566 21,765 6 19,939 2
18,850 9,425 9,425 16,324 2 14,954 4
5 15,708 7,854 7,854 13,603 5 12,462 0
4 12,566 6,283 6,283 10,882 8 9,969 6
3 9,425 4,712 4,712 8,162 1 7,477 2
5,553 6
7,854 3,927 3,927 3,927 6,801 7 6,231 0
2,5
2 6,283 3,142 3,142 3,142 5,441 4 4,984 8 4,442 9
1,75 5,498 2,749 2,749 2,749 4,761 2 4,361 7 3,887 5
4,712 2,356 2,356 2,356 4,081 0 3,738 6 3,332 2
1,5
1,25 3,927 1,963 1,963 1,963 3,400 9 3,115 5 2,776 8
3,142 1,571 1,571 1,571 2,720 7 2,492 4 2,221 4
0,75 2,356
1,178 1 ,178 1 ,178 2,040 5 1,869 3 1,666 1
1,571 0,785 0,785 0,785 1,360 4 1,246 2 1,110 7
Or5
0,25 0,785 0,393 0,555 4

* For illustration purposes : relative tooth sizes for various spline modules for pressure angle aiD = 30”.

---------------------- Page: 10 ----------------------
SIST ISO 4156:2000
ISO 4156-‘l981 (E)
Table 2 - ForanuBae for dimensions and tolerances for all fit classes
Formul a
Pitch diameter D mZ
Base diameter m z Cos O”D
Circular pitch Km
Base pitch x m Cos aiD
Effective Upper deviation, external
resulting from deviation allowance (fundamental)
k-j,--h-f-eandd
Minimum diameter, interna1
30°, flat root D
m(Z+ 1,5)
ei min
30”, fi I let root D
m(Z+ 1,8)
ei min
37,5 O, fillet root D m(Z+ 1,4)
ei min
45’, fillet root D
m(Z+ 1,2)
ei min
Maximum major diameter, interna1 D D
t (T t h)/tan aD (sec note 1 )
ei max ei min
Minimum form diameter, interna1
30°, flat root and fillet root m(zt 1) + 2cF
DFi min
37,5O, fi I let root m(z t o,g) t 2 cF
DFi min
45” , fi I let root dz + 0,8) + 2 CF
DFi min
Minimum diameter, interna1
DFe max f 2 CF (Set? Ilote 2)
Dii min
Maximum minor diameter, interna1
m < 0,75
+ tol. H 10
Dii max Dii min
0,75 < m < 2
+ tol. H 11
Dii max Dii min
m>2
+ toi. H 12
Dii max Dii min
Basic space width and E and
0,5x m
Minimum effective space width E
v min
Maximum actual space width
class 4 E E v min + (T + A) (sec note 3)
max
class 5 E E v min + (T + Al (sec note 3)
max
class 6 E E
v min + (T + h) (sec note 3)
max
class 7 E E
v min + (T + A) (sec note 3)
max
Minimum actual space width E E
v min + h (sec 8.2)
min
Maximum effective space width E E
max - h (see 8.2)
v max
Maximum major diameter, external
30°, flat root and fillet root D
m(z t 1) t esv/tan o!D (sec note 4)
ee max
37,5’, fillet root D
m(z t o,g) t es,/tan aD (sec note 4)
ee max
45”) fillet root
D m(Z + 0,8) + es,ltan QD (sec note 4)
ee max
Minimum major diameter, external
m < 0,75 D - tol. h 10
ee min ee max
0,75 < m < 2 D .
ee min
ma2 D
ee min
22)
Maximum form diameter, external
DFe max
Maximum minor diameter, external
(Sec note 6)
30”, flat root
m (z - 1 ,5) t es&n aD
Die max
30”, fillet root
m(Z- 1,8) + es,/tan &D
Die max
37,5’, fillet root
m (z - 1 $1 t esv/tan Q!D
Die max
45”, fil let root
m (z - 1 ,2) f es&an o!D
Die max
---------------------- Page: 11 ----------------------
SIST ISO 4156:2000
ISO 4156-1981 (E)
Table 2 - Formulae for dimensions and tolerances for all fit classes (conchded)
Basic tooth thickness
Maximum effective tooth thickness
Minimum actual tooth thickness
class 4 v max - (T + A) (sec note 3)
class 5
v max - (T f A) (sec note 3)
class 6 v max - (T + h) (sec note 3)
class 7 v max - (T + A) (sec note 3)
Maximum actual tooth thickness
Minimum effective tooth thickness
Total tolerance, space width or tooth thickness
Form clearance
Pin diameter, interna1 spline -
Pin diameter, external spline
Measurement between pins
Measurement over pins
Change factor, interna1 see section three, “1 nspection”
Change factor, external see section three, “Inspection”
NOTES
1 (T + h) for class 7 - see clause 6.
2 For all classes of fit, always take the &e max
value corresponding to the H/h fit.
3 See clause 6 and section two - tables of dimensions.
4 Take a null Upper deviation value for j, and k fundamental deviations.

5 See section two : “Dimensions”, and section three : “Inspection”, concerning &oice of pins.

6 For h, see figures 3,4,5 and 6.
---------------------- Page: 12 ----------------------
SIST ISO 4156:2000
ISO 4156-1981 (E)
Piece
E effective
actual
max
(actual space width)
min -
vmax -
l- .
basic
v min
-0,5 n m-
(effective space width) z
basic :
a\1 max
(effective tooth thickness)
vmin -
max -
min
(actual tooth thickness)
Figure 2 - Graphical representation of tables 1 and 2
---------------------- Page: 13 ----------------------
SIST ISO 4156:2000
ISO 4156-1981 (El
3.2 Subscripts classes as follows :

The following subscripts (see also the note in 3.1) are used as Spline fit class Effective interfeaence

part of the above general symbols to designate relative con-
H/k cVmax = (T + A)
ditions or locations :
T+A
deviation allowance j, = -
MS CV max =
= minor or interna1 (in this last case, in the last position)
ilIl
c 2 )
= major or external (in this last case, in the last position)
CE1 Effective looseness
,[Bl = at base
H/h Cv min = deviation allowance h = zero
= at contact point
H/f CV min = deviation allowance f
= pertaining to form diameter
&FI
deviation allowance e
H/e Cv min =
= effective
“[VI
H/d Cv min = deviation allowance d
= active
The deviation allowances (fundamental) k - j, - h - f - e
pertaining to gauges
,Ml =
and d are the standard deviations selected from ISO/R 286 /SO
- of engagement System of limits and fits - Part 7 : General, tolerances and
deviations, which are applied to the external spline. A pre-
n = standard
scribed maximum effective interference or minimum effective
looseness is obtained, allowing the fitting by adjusting from the
zero line the maximum effective and minimum actual limit
values of tooth thickness by the amount of the deviation
4 Pressure angle (standard)
allowance (see 8.72). The spline dimensions in the spline
tables of this International Standard are given for spline fit class
Standard pressure angles included in this International Stan-
H/h, C, min = zero.
dard for involute splines are 30°, 37,5’ and 45’.
6 Space width and tooth thickness,
total tolerance (T + A)
5 Type of fit
Tolerance classes
This International Standard deals with only one type of fit, the
This International Standard includes four classes of total
side fit, for 30°, 37,5O and 45O pressure angle splines. Formulae
tolerance ( T + A) on space width and tooth thickness selected

for the dimensions and tolerances for these splines are shown from a combination of tolerance units (i) in ISO/R 286. The

in table 2.
tolerance classes are indicated below, with corresponding com-
bination of tolerance units (i). For the calculation of T and Â,
sec clause 8. The values of Â. are given in tables 3 to 6 of
5.1 Side fit
clause 8.
In this fit, the mating members contact on the sides of the teeth
Tolerance unit
Spline tolerance
only. Major and minor diameters are clearance dimensions. The
class (il
tooth sides act as drivers and centralize mating splines.
4 = (10 i* + 40 i”“)
5 = (16 i* + 64 i”“)
5.2 Spline fit classes
6 = (25 i* + 100 i”“)

This International Standard provides the side fit in six spline fit 7 = (40 i* + 160 i”“)

Tolerance based on pitch diameter
i = 0,45 $D + 0,001 D for-D Q 5OOmm
i = 0,004D + 2,l forD > 5OOmm
Tolerance based on space width or tooth thickness
i =
0,45 $?m + 0,001 E (or SI
where
D is the pitch diameter in millimetres;
E is the basic space width in millimetres;
S is the basic tooth thickness in millimetres.

the resultant ( T + A) in micrometres. For ( T + Â) in millimetres, multiply the result by 0,001.

For the calculation of tolerance units (i), only the above indicated formulae (notes *, **) are to be taken into consideration.

---------------------- Page: 14 ----------------------
SIST ISO 4156:2000
ISO 41564981 (El
volute spline of infinitely large diameter on a plane at right
It should to be noted that total values ( T + A) may always be

subtracted from the limit values of space width and tooth angles to the tooth surfaces, the profile of which is used as the

basis for defining the standard tooth dimensions of a system of
thickness given in section 2 and are usable even if the chosen
involute splines.
fit class is other than H/h.
NOTE - Below are listed the combinations of tolerance qualities IT
corresponding to the combinations of tolerance units (i) indicated
above. Those combinations of tolerance qualities IT are given only to
7.2 The reference line is a straight line crossing the profile of
indicate the conception principle of the tolerance system regarding its

eventual extension, and only to rediscover the corresponding com- the basic rack, with reference to which the tooth dimensions

binations of tolerance units (il.
are specif ied.
Spline tolerance Tolerance quality
class W-I
4 = (IT 6* + IT 9”“)
7.3 The profile of the basic rack for the standard pressure
angle splines is represented in the following figures :
5 = (IT 7* + IT 10”“)
6 = (IT 8* + IT II**)
figure 3 : 30° flat root spline, for modules 0,5 to 10;
7 = (IT 9* + IT 12”“)
figure 4 : 30° fillet root spline, for modules 0,5 to 10;
7 Basic rack profiles for spline
figure 5 : 37,5O fillet root spline, for modules 0,5 to 10;

7.1 The basic rack is a section of the tooth surface of an in- figure 6 : 45’ fillet root spline, for modules 0,25 to 2,5.

* Tolerance based on pitch diameter.
Tolerance based on space width and tooth thickness.
---------------------- Page: 15 ----------------------
SIST ISO 4156:2000
60 41564981 (El
0,5nm A 0,5n:m
=0,2m* /
I -Pl=i
I nternal spline
External spline \
i Reference line
Figure 3 - Profile of the basic rack for 30° flat root spline
External spline
Reference line
Figure 4 - Profile of the basic rack for 30’ fillet root spline
* and ** See next page.
---------------------- Page: 16 ----------------------
SIST ISO 4156:2000
ISO 4156-1981 0
= 0,3m”
PFi
Reference line
Figure 5 - Profile of the basic rack for 37,5’ fillet root spline
Interna1 spline
Figure 6 - Profile of the basic rack for 45O fillet root spline
NOTE concerning figures 3 to 6 :

For interna1 splines (hub), the form diameter, obtained by generating from the basic rack, is always greater than the form diameter shown in the

tables of dimensions (sec section two), which corresponds in all fit cases to the major maximum diameter of the shaft (with Upper deviation - es, -

zero) increased to diametral form clearance (2 c,-) equal to 0,2 module.

** For external splines (shafts), cF is obtained by generation from the basic rack @Fe maX

1 and for H/h fit (sec note 2 under table 2).

The size cF indicated is in fact a deviation permitting the form clearance cF given in table 2 to be obtained and is equal to 0,l m.

---------------------- Page: 17 ----------------------
SIST ISO 4156:2000
ISO 4156-1981 (E)

7.4 The minimum radial form clearance, CF, shown in the 8 Machining tolerances and variations

basic rack profiles is equal to 0,l m for all pressure angle
8.1 Variation allowance (il)
splines.
The variation allowance, being the addition of the total index
The form clearance is modified for fits other than H/h.
variation, total profile variation and total lead variation, has an
effect on the effective fit of an involute spline. The effect of
these individual spline variations on the fit is less than their
total, because areas of more than minimum clearance cari have
form, lead, or index errors without changing the fit. It is also
7.5 External splines may be produced by generating with a
unlikely that these errors would occur in their maximum
pinion-type shaper cutter or with a hob, or by cutting with no
amounts simultaneously on the same spline. For this reason,
generating motion using a tool formed to the contour of a tooth
total index variation, profile variation and total lead variation are
space. External splines are also made by cold f
...

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