# SIST ISO 4156:2000

(Main)## Straight cylindrical involute splines -- Metric module, side fit -- Generalities, dimensions and inspection

## 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

### RELATIONS

### Standards Content (sample)

SLOVENSKI STANDARD

SIST ISO 4156:2000

01-januar-2000

5DYQLXWRUL]HYROYHQWQLPLERNLQDYDOMLK0HWUVNLPRGXOERþQRSULOHJDQMH

6SORãQRPHUHLQNRQWUROD

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

and inspectionCannelures cylindriques droites à flancs en développante -- Module métrique, à centrage

sur flancs -- Généralités, dimensions et vérificationTa 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

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

vérificationFirst 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

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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

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

...................... 86 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 tolerancesTables

30° pressure angle

38-65

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

- flat root66-93

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

94-12137,5O 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,

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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, PbThe 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,.

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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 spllinesDimensions 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

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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 diameteri = 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 ofthickness 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 angle8.1 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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