Tiêu chuẩn iso 04156 1 2005

INTERNATIONAL
STANDARD

ISO
4156-1
First edition
2005-10-01

Straight cylindrical involute splines —
Metric module, side fit —
Part 1:
Generalities
Cannelures cylindriques droites à flancs en développante — Module
métrique, à centrage sur flancs —
Partie 1: Généralités
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Reference number
ISO 4156-1:2005(E)

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ISO 4156-1:2005(E)

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ISO 4156-1:2005(E)

Contents

Page

Foreword............................................................................................................................................................ iv
Introduction ........................................................................................................................................................ v
1

Scope ......................................................................................................................................................1

2

Normative references ............................................................................................................................1

3

Terms and definitions ...........................................................................................................................1

4
4.1
4.2
4.3

Symbols, subscripts and abbreviated terms ......................................................................................7
General symbols ....................................................................................................................................7

Subscripts ..............................................................................................................................................9
Formulae for dimensions and tolerances for all fit classes..............................................................9

5

Concept of side fit splines ..................................................................................................................12

6

Effective fit concept.............................................................................................................................14

7

Basic rack profiles for spline..............................................................................................................22

8

Spline fit classes..................................................................................................................................24

9
9.1
9.2
9.3
9.4
9.5
9.6
9.7
9.8

Space width and tooth thickness tolerances....................................................................................26

Total tolerance T + λ ............................................................................................................................26
Deviation allowance, λ ........................................................................................................................27
Total pitch deviation, Fp ......................................................................................................................27
Total profile deviation, Fα ...................................................................................................................28
Total helix deviation, Fβ ......................................................................................................................29
Machining tolerance, T ........................................................................................................................29
Effective clearance tolerance, Tv........................................................................................................30
Use of effective and actual dimensions for space width and tooth thickness .............................30

10
10.1
10.2

Minor and major diameters.................................................................................................................31
Tolerances ............................................................................................................................................31
Adjustment to minor diameters (Die), form diameters (DFe) and major diameters (Dee) of
external splines....................................................................................................................................32

11
11.1
11.2
11.3

Manufacturing and design considerations .......................................................................................32
Radii ......................................................................................................................................................32
Profile shifts .........................................................................................................................................32
Eccentricity and misalignment...........................................................................................................33

12
12.1

12.2
12.3
12.4

Spline data............................................................................................................................................34
Basic dimensions ................................................................................................................................34
Combination of types ..........................................................................................................................34
Designation ..........................................................................................................................................34
Drawing data ........................................................................................................................................35

Annex A (informative) Drawing data example calculations ..........................................................................40
Bibliography ......................................................................................................................................................59

iii

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ISO 4156-1:2005(E)

Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies

(ISO member bodies). The work of preparing International Standards is normally carried out through ISO
technical committees. Each member body interested in a subject for which a technical committee has been
established 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. ISO collaborates closely with the
International Electrotechnical Commission (IEC) on all matters of electrotechnical standardization.
International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2.

Attention is drawn to the possibility that some of the elements of this document may be the subject of patent
rights. ISO shall not be held responsible for identifying any or all such patent rights.
ISO 4156-1 was prepared by Technical Committee ISO/TC 14, Shafts for machinery and accessories.
This first edition of ISO 4156-1, together with ISO 4156-2 and ISO 4156-3, cancels and replaces
ISO 4156:1981 and ISO 4156:1981/Amd 1:1992, of which it constitutes a technical revision. The values and
tables are the same as in ISO 4156:1981; however, some explanations and definitions have been clarified.
ISO 4156 consists of the following parts, under the general title Straight cylindrical involute splines — Metric
module, side fit:


Part 1: Generalities



Part 2: Dimensions



Part 3: Inspection

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The main task of technical committees is to prepare International Standards. Draft International Standards
adopted by the technical committees are circulated to the member bodies for voting. Publication as an
International Standard requires approval by at least 75 % of the member bodies casting a vote.


ISO 4156-1:2005(E)

Introduction
ISO 4156 provides the data and indications necessary for the design, manufacture and inspection of straight
(non-helical) side-fitting cylindrical involute splines.
Straight cylindrical involute splines manufactured in accordance with ISO 4156 are used for clearance, sliding
and interference connections of shafts and hubs. They contain all the necessary characteristics for the
assembly, transmission of torque, and economic production.
The nominal pressure angles are 30°, 37,5° and 45°. For electronic data processing purposes, the form of
expression 37,5° has been adopted instead of 37°30’. ISO 4156 establishes a specification based on the
following modules:


for pressure angles of 30° and 37,5° the module increments are
0,5; 0,75; 1; 1,25; 1,5; 1,75; 2; 2,5; 3; 4; 5; 6; 8; 10



for pressure angle of 45° the module increments are
0,25; 0,5; 0,75; 1; 1,25; 1,5; 1,75; 2; 2,5

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INTERNATIONAL STANDARD

ISO 4156-1:2005(E)

Straight cylindrical involute splines — Metric module, side fit —

1

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Part 1:
Generalities

Scope

This part of ISO 4156 provides the data and indications necessary for the design and manufacture of straight
(non-helical) side-fitting cylindrical involute splines.
Limiting dimensions, tolerances, manufacturing errors and their effects on the fit between connecting coaxial
spline elements are defined in the equations and given in the tables. Unless otherwise specified, linear
dimensions are expressed in millimetres and angular dimensions in degrees.

2

Normative references

The following referenced documents are indispensable for the application of this document. For dated
references, only the edition cited applies. For undated references, the latest edition of the referenced
document (including any amendments) applies.
ISO 286-1, ISO system of limits and fits — Part 1: Bases of tolerances, deviations and fits
ISO 1101, Geometrical Product Specifications (GPS) — Geometrical tolerancing — Tolerances of form,
orientation, location and run-out
ISO 4156-2, Straight cylindrical involute splines — Metric module, side fit — Part 2: Dimensions
ISO 4156-3:2005, Straight cylindrical involute splines — Metric module, side fit — Part 3: Inspection

3

Terms and definitions

For the purposes of this document, the following terms and definitions apply.
3.1
spline joint
connecting, coaxial elements that transmit torque through the simultaneous engagement of equally spaced
teeth situated around the periphery of a cylindrical external member with similar spaced mating spaces
situated around the inner surface of the related cylindrical internal member
3.2
involute spline
member of spline joint having teeth or spaces that have involute flank profiles
3.3
internal spline
spline formed on the inner surface of a cylinder

1

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ISO 4156-1:2005(E)

3.4
external spline
spline formed on the outer surface of a cylinder
3.5
fillet
concave surface of the tooth or space connecting the involute flank and the root circle.
NOTE

This curved surface as generated varies and cannot be properly specified by a radius of any given value.

3.6
fillet root spline
spline having a tooth or space profile in which the opposing involute flanks are connected to the root circle (Dei
or Die diameter) by a single fillet.
3.7
flat root spline
spline having a tooth or space profile in which each of the opposing involute flanks are connected to the root
circle (Dei or Die diameter) by a fillet
3.8
module
m
ratio of the circular pitch, expressed in millimetres, to the number π (or the ratio of the pitch diameter
expressed in millimetres, to the number of teeth)
3.9
pitch circle
reference circle from which all normal spline dimensions are derived, and the circle on which the specified
pressure angle has its nominal value
3.10
pitch diameter
D

diameter of the pitch circle, in millimetres, equal to the number of teeth multiplied by the module
3.11
pitch point
intersection of the spline tooth profile with the pitch circle
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3.12
circular pitch
p
length of arc of the pitch circle between two consecutive pitch points of left- (or right-) hand flanks, which has a
value of the number π multiplied by the module
3.13
pressure angle

α

acute angle between a radial line passing through any point on a tooth flank and the tangent plane to the flank
at that point
3.14
standard pressure angle

αD

pressure angle at the specified pitch point

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ISO 4156-1:2005(E)

3.15
base circle
circle from which Involute spline tooth profiles are generated
3.16
base diameter
Db
diameter of the base circle
3.17
base pitch
pb
arc length of the base circle between two consecutive corresponding flanks
3.18
major circle
outermost (largest) circle of the external or internal spline
3.19
major diameter
Dee, Dei
diameter of the major circle
3.20
minor circle
innermost (smallest) circle of the external or internal spline
3.21
minor diameter, Die, Dii

diameter of the minor circle
3.22
form circle
circle used to define the depth of involute profile control
NOTE
In the case of an external spline it is located near and above the minor diameter, and on an internal spline
near and below the major diameter

3.23
form diameter
DFe, DFi
diameter of the form circle
3.24
depth of engagement
radial distance from the minor circle of the internal spline to the major circle of the external spline, minus
corner clearance and/or chamfer depth
3.25
basic (circular) space width or tooth thickness at the pitch diameter
E or S
for 30°, 37,5° and 45° pressure angle splines, half the circular pitch.
3.26
actual space width
practically measured circular space width, on the pitch circle, of any single space width within the limit values
Emax and Emin

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ISO 4156-1:2005(E)

3.27
effective space width
Ev
space width where an imaginary perfect external spline would fit without clearance or interference, given by
the size of the tooth thickness of this external spline, considering engagement of the entire axial length of the
splined assembly
NOTE
The minimum effective space width (Ev min, always equal to E) of the internal spline is always basic, as shown
in Table 3.

3.28
actual tooth thickness
practically measured circular tooth thickness, on the pitch circle, of any single tooth within the limit values Smax
and Smin
3.29
effective tooth thickness
Sv
tooth thickness where an imaginary perfect internal spline would fit without clearance or interference, given by
the size of the space width of this internal spline, considering engagement of the entire axial length of the
splined assembly

3.30
effective clearance
cv
〈looseness or interference〉 effective space width of the internal spline minus the effective tooth thickness of
the external spline
NOTE

For looseness, cv is positive; for interference, cv is negative.

3.31
theoretical clearance
c
〈looseness or interference〉 actual space width of the internal spline minus the actual tooth thickness of the
external spline
NOTE

It does not define the effective fit between internal and external spline, because of the effect of deviations.

3.32
form clearance
cF
radial clearance between the form diameter of the internal spline and the major diameter of the external
spline, or between the minor diameter of the internal spline and the form diameter of the external spline
NOTE

It allows eccentricity of their respective pitch circles.

3.33
total pitch deviation
Fp

absolute value of the difference between the greatest positive and negative deviations from the theoretical
spacing
3.34
total profile deviation
Fα
absolute value of the difference between the greatest positive and negative deviations from the theoretical
tooth profile, measured normal to the flanks

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ISO 4156-1:2005(E)

3.35
total helix deviation
Fβ
absolute value of the difference between the two extreme deviations from the theoretical direction parallel to
the reference axis
NOTE

This includes parallelism and alignment deviations, see Figure 1.

a)

Helix deviation

b) Parallelism deviation

c)
a

Alignment deviation

Reference axis.

b

Centreline of teeth.

c

Effective spline axis.

Figure 1 — Helix deviations
3.36
parallelism deviation
deviation of parallelism of a single spline tooth to any other single spline tooth
See Figure 1 b).
3.37
alignment deviation

deviation of the effective spline axis with respect to the reference axis
See Figure 1 c).
3.38
out-of-roundness
deviation of the spline from a true circular configuration
3.39
effective deviation
accumulated effect of the spline deviations on the fit with the mating part

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ISO 4156-1:2005(E)

3.40
deviation allowance

λ

permissible deviation between minimum actual and minimum effective space width or maximum effective and

maximum actual tooth thickness
3.41
machining tolerance
T
permissible deviation between maximum actual and minimum actual space width or tooth thickness
3.42
effective clearance tolerance
Tv
permissible deviation between maximum effective and minimum effective space width or tooth thickness
3.43
total tolerance
T+λ
machining tolerance plus the deviation allowance
3.43.1
total tolerance
〈internal spline〉 difference between the minimum effective space width and the maximum actual space width
3.43.2
total tolerance
〈external spline〉 difference between the maximum effective tooth thickness and the minimum actual tooth
thickness
3.44
basic dimension
numerical value to describe the theoretically exact size, shape or location of a feature
NOTE

It is the basis from which permissible deviations are established by tolerances.

3.45
auxiliary dimension
dimension, without tolerance, given for information purposes only, for the determination of the useful

production and control dimensions.

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ISO 4156-1:2005(E)

4

Symbols, subscripts and abbreviated terms

4.1

General symbols

The general symbols used to designate the various spline terms and dimensions are given below.
D

Pitch diameter

mm

DFe

Form diameter, external spline

mm

DFe max

Maximum form diameter, external spline

mm

DFi

Form diameter, internal spline

mm

DFi min

Minimum form diameter, internal spline

mm

DRe

Diameter of measuring ball or pin for external spline

mm

DRi

Diameter of measuring ball or pin for internal spline

mm

Db

Base diameter

mm

Dee

Major diameter, external spline

mm

Dee max

Maximum major diameter, external spline

mm

Dee min

Minimum major diameter, external spline

mm

Dei

Major diameter, internal spline

mm

Dei max

Maximum major diameter, internal spline

mm

Dei min

Minimum major diameter, internal spline

mm

Die

Minor diameter, external spline

mm

Die max

Maximum minor diameter, external spline

mm

Die min

Minimum minor diameter, external spline

mm

Dii

Minor diameter, internal spline

mm

Dii max

Maximum minor diameter, internal spline

mm

Dii min

Minimum minor diameter, internal spline

mm

E

Basic space width, circular

mm

Emax

Maximum actual space width

mm

Emin

Minimum actual space width

mm

Ev

Effective space width, circular

mm

Ev max

Maximum effective space width

mm

Ev min

Minimum effective space width

mm

Fp

Total cumulative pitch deviation

µm

Fα

Total profile deviation

µm

Fβ

Total helix deviation

µm

Ke

Approximation factor for external spline

—

Ki

Approximation factor for internal spline

—

MRe

Measurement over two balls or pins, external splines

mm

MRi

Measurement between two balls or pins, internal

mm

S

Basic tooth thickness, circular

mm

7

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ISO 4156-1:2005(E)

Maximum actual tooth thickness

mm

Smin

Minimum actual tooth thickness

mm

Sv

Effective tooth thickness, circular

mm

Sv max

Maximum effective tooth thickness

mm

Sv min

Minimum effective tooth thickness

mm

T

Machining tolerance

µm

Tv

Effective clearance tolerance

µm

W

Measurement over k teeth, external spline

mm

b

Spline length

mm

cF

Form clearance

mm

cv

Effective clearance (looseness or interference)

µm

cv max

Maximum effective clearance

µm

cv min

Minimum effective clearance

µm

dce

Ball or pin contact diameter, external spline

mm

dci

Ball or pin contact diameter, internal spline

mm

esv

Fundamental deviation, external

µm

Form tooth height

mm

inv α

Involute α (= tanα − π ⋅ α /180° )

—

k

Number of measured teeth

—

m

Module

mm

p

Circular pitch

mm

pb

Base pitch

mm

z

Number of teeth

—

α

Pressure angle

°

αFe

Pressure angle at form diameter, external spline

°

αFi

Pressure angle at form diameter, internal spline

°

αce

Pressure angle at ball or pin diameter, external spline

°

αci

Pressure angle at ball or pin diameter, internal spline

°

αD

Standard pressure angle at pitch diameter

°

αe

Pressure angle at ball or pin centre, external spline

°

αi

Pressure angle at ball or pin centre, internal spline

°

λ

Deviation allowance

µm

ρFa

Fillet radius of the basic rack, external spline

mm

ρFi

Fillet radius of the basic rack, internal spline

mm

k; js; h; f; e; d

Fundamental deviation of the external spline

µm

hs

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Smax

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ISO 4156-1:2005(E)

4.2

Subscripts

The following subscripts are used as part of the above general symbols to designate relative conditions or
locations:
i

minor or internal (in the last case in the last position)

e

major or external (in the last case in the last position)

b

at the base

c

at contact point

d

tolerance based on pitch diameter (D)

E

tolerance based on space width (E) or tooth thickness (S)

F

pertaining to form diameter

v

effective

R

pertaining to gauges

D

standard

NOTE
In electronic data processing (EDP), it is not always possible to present symbols in their theoretically correct
form because of limitations of connected printing equipment. For this reason, some alternative symbols for EDP usage are
given in Table 1 (for example, the symbol for Db for base diameter may be printed as DB).

4.3

Formulae for dimensions and tolerances for all fit classes

The formulae for dimensions and tolerances for all fit classes are given in Table 1.

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ISO 4156-1:2005(E)

Table 1 — Formulae for dimensions and tolerances for all fit classes
Term

EDP
representation

Symbol

Formula

Pitch diameter

D

m⋅ z

D

Base diameter

Db

m ⋅ z ⋅ cosα D

DB

Circular pitch

p

m⋅π

P

Base pitch

pb

m ⋅ π ⋅ cos α D

PB

Fundamental deviation, external

esv

Resulting from fundamental deviation
k, js, h, f, e and d

ESV

30°, flat root

Dei min

m ⋅ ( z + 1,5)

DEIMIN

30°, fillet root

Dei min

m ⋅ (z + 1,8)

DEIMIN

37,5°, fillet root

Dei min

m ⋅ (z + 1,4)

DEIMIN

45°, fillet root

Dei min

m ⋅ (z + 1,2)

DEIMIN

Dei max

D ei min + (T + λ ) / tan α D (see Note 1)

DEIMAX

30° flat root and fillet root

DFi min

m ⋅ ( z + 1) + 2 ⋅ c F

DFIMIN

37,5° fillet root

DFi min

m ⋅ ( z + 0,9) + 2 ⋅ c F

DFIMIN

45° fillet root

DFi min

m ⋅ ( z + 0,8) + 2 ⋅ c F

DFIMIN

Dii min

DFe max + 2 ⋅ c F (see Note 2)

DIIMIN

m u 0,75

Dii max

D ii min + IT 10

DIIMAX

0,75 < m < 2

Dii max

D ii min + IT 11

DIIMAX

mW2

Dii max

D ii min + IT 12

DIIMAX

Maximum major diameter, internal
Minimum form diameter, internal:

Minimum minor diameter, internal
Maximum minor diameter, internal:

E

0,5 ⋅ π ⋅ m

E

Ev min

0,5 ⋅ π ⋅ m

EVMIN

class 4

Emax

E v min + (T + λ ) (see Note 3)

EMAX

class 5

Emax

E v min + (T + λ ) (see Note 3)

EMAX

class 6

Emax

E v min + (T + λ ) (see Note 3)

EMAX

class 7

Emax

E v min + (T + λ ) (see Note 3)

EMAX

Emin

E v min + λ

EMIN

Ev max

E v min + T v

EVMAX

30°, flat root and fillet root

Dee max

m ⋅ ( z + 1) + es v /tanα D (see Note 4)

DEEMAX

37,5°, fillet root

Dee max

m ⋅ ( z + 0,9) + es v /tanα D (see Note 4)

DEEMAX

45°, fillet root

Dee max

m ⋅ ( z + 0,8) + es v /tanα D (see Note 4)

DEEMAX

m u 0,75

Dee min

D eemax − IT 10

DEEMIN

0,75 < m < 2

Dee min

D ee max − IT 11

DEEMIN

mW2

Dee min

D ee max − IT 12

DEEMIN

Basic space width
Minimum effective space width
Maximum actual space width:

Minimum actual space width
Maximum effective space width
Maximum major diameter, external:

Minimum major diameter, external:

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Minimum major diameter, internal:


ISO 4156-1:2005(E)
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Table 1 (continued)
Term

Maximum form diameter (see Note 5)

Symbol

DFe max

EDP
representation

Formula

0,5 × es v

hs −

tanα D
2

2 × ( 0,5D b ) +  0,5D × sinα D −

sinα D










2

DFEMAX

Maximum minor diameter, external:
30°, flat root

Die max

m ⋅ ( z − 1,5) + es v /tanα D

DIEMAX

30°, fillet root

Die max

m ⋅ ( z − 1,8) + es v /tanα D

DIEMAX

37,5°, fillet root

Die max

m ⋅ ( z − 1,4) + es v /tanα D

DIEMAX

45°, fillet root

Die max

m ⋅ ( z − 1,2) + es v /tanα D

DIEMAX

Die min

D ie max − (T + λ )/tanα D (see Note 1)

DIEMIN

S

0,5 ⋅ π ⋅ m

S

Sv max

S + es v

SVMAX

class 4

Smin

S v max − (T + λ ) (see Note 3)

SMIN

class 5

Smin

S v max − (T + λ ) (see Note 3)

SMIN

class 6

Smin

S v max − (T + λ ) (see Note 3)

SMIN

class 7

Smin

S v max − (T + λ ) (see Note 3)

SMIN

Maximum actual tooth thickness

Smax

S v max − λ

SMAX

Minimum effective tooth thickness

Sv min

S v max − T v

SVMIN

Total tolerance, space width or tooth
thickness

(T + λ )

(see Note 6)

TLAM

Maximum effective clearance

cv max

E v max − S v min

CVMAX

Minimum effective clearance

cv min

E v min − S v max

CVMIN

Form clearance

cF

see Note 5

CF

Form tooth height

hs

see Note 5

HS

Ball or pin diameter, internal spline

DRi

see Note 7

DRI

Ball or pin diameter, external spline

DRe

see Note 7

DRE

Measurement between balls or pins

Mri

see Note 7

MRI

Measurement over balls or pins

Mre

see Note 7

MRE

Change factor, internal

Ki

see Note 7

KI

Change factor, external

Ke

see Note 7

KE

Minimum minor diameter, external
Basic tooth thickness
Maximum effective tooth thickness
Minimum actual tooth thickness:

NOTE 1
NOTE 2

(T + λ) for class 7 — see 9.1.
For all classes of fit, always take the DFe max value corresponding to the H/h fit.

NOTE 3
NOTE 4

See Clause 8 and ISO 4156-2.
Take esv = 0 for fundamental deviation js and k.

NOTE 5

For hs, see Figure 15 et Table 2.

NOTE 6
NOTE 7

See 9.1.
See ISO 4156-3 concerning the choice of balls or pins.

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ISO 4156-1:2005(E)

5

Concept of side fit splines

This part of ISO 4156 defines side fit involute splines with pressure angles of 30°, 37,5° and 45°. The
transmission of torque is achieved by contact of the tooth flanks only. This is possible in the clockwise or
anticlockwise direction of rotation (see Figure 2). The opposite tooth flanks, major and minor diameters shall
have clearance.

Clockwise rotation

Anticlockwise rotation

Figure 2 — Side fit tooth flank contact

--`,,```,,,,````-`-`,,`,,`,`,,`---

The nature of the involute profile divides the torque into two directions resulting in a centring force (see
Figure 3). This centring force enables side fit involute splines to be centralized by the tooth flanks.

a

Centring force.

b

Rotation force.

c

Torque.

Figure 3 — Centring force

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ISO 4156-1:2005(E)

The sizes of space width and tooth thickness (see Figure 4) are defined as the length of the arc at the
theoretical pitch circle diameter.

Figure 4 — Space width and tooth thickness

The major and minor diameters (see Figure 5) always have clearance and do not contact each other.
--`,,```,,,,````-`-`,,`,,`,`,,`---

Figure 5 — Diameters

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ISO 4156-1:2005(E)

6

Effective fit concept

To be able to machine the spaces of internal splines and the teeth of external splines, a machining tolerance
commonly referred to as the actual machining tolerance is necessary. Four classes of machining tolerance
(classes 4, 5, 6 and 7) are provided for the different needs of industrial use. The machining tolerance, T (see
Figure 6), is applied to the space width of internal splines and to the tooth thickness of external splines.
The upper machining tolerance limit is referred to as maximum actual and the lower one is referred to as
minimum actual.

The form deviations consist of three types: profile deviation, index deviation and helix deviation. The positive
material elements of these deviations result in a reduction of effective space width of an internal spline, or an
increase in the effective tooth thickness of an external spline, and hence a reduction in the effective clearance.
This effect can only be detected by the use of an imaginary perfect mating spline that fits without looseness or
interference.

a)

Internal spline

b) External spline
a

Largest space width.

d

Minimum actual tolerance.

b

Smallest space width.

e

Largest tooth thickness.

Maximum actual tolerance.

f

Smallest tooth thickness.

c

Figure 6 — Machining tolerance, T

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--`,,```,,,,````-`-`,,`,,`,`,,`---

Similar to cylindrical fits between hubs and shafts, form deviations of the geometry (see Figure 7) affect the
maximum material condition and hence the fit. The form deviation is the deviation compared to the perfect
cylinder. The form deviations of splines are much more complex and occur on each flank of every space or
tooth. These form deviations have an accumulative effect which is referred to as effective deviation.


--`,,```,,,,````-`-`,,`,,`,`,,`---

ISO 4156-1:2005(E)

a

Form deviation.

Figure 7 — Form deviations

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ISO 4156-1:2005(E)

The positive material elements of profile deviation (see Figure 8) will result in a smaller space or a larger tooth
thickness which has an effect on the fit with a mating part.

a

Internal spline.

b

External spline.

c

Space width, actual.

d

Tooth thickness, actual.

e

Space width, effective.

f

Tooth thickness, effective.

g

Mating part.
--`,,```,,,,````-`-`,,`,,`,`,,`---

Figure 8 — Profile deviation

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ISO 4156-1:2005(E)

The positive material elements of pitch deviation (see Figure 9) will also result in a smaller space width or a
larger tooth thickness which again affects the fit with a mating part.

--`,,```,,,,````-`-`,,`,,`,`,,`---

a

Internal spline.

b

External spline.

c

Space width, actual.

d

Tooth thickness, actual.

e

Space width, effective.

f

Tooth thickness, effective.

g

Mating part.

Figure 9 — Pitch deviation

17

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ISO 4156-1:2005(E)

--`,,```,,,,````-`-`,,`,,`,`,,`---

The positive material elements of helix deviation (see Figure 10) will also result in a smaller space width or a
larger tooth thickness which again affects the fit with a mating part.

a

Internal spline.

b

External spline.

c

Space width, actual.

d

Tooth thickness, actual.

e

Space width, effective.

f

Tooth thickness, effective.

g

Mating part.

Figure 10 — Helix deviation

The accumulated form deviations (see Figure 11) of each flank result in an effective size of space width or
tooth thickness.

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ISO 4156-1:2005(E)

--`,,```,,,,````-`-`,,`,,`,`,,`---

a

Profile deviation.

b

Pitch deviation.

c

Helix deviation.

d

Tooth.

e

Maximum at Tooth 1.

f

Maximum at Tooth 4.

g

Maximum at Tooth 6.

h

Maximum at Tooth 5.

i

Accumulation = effective deviation λ.

j

Theoretical maximum.

Figure 11 — Influence of form deviations

19

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