渐开线花键美国标准 ANSI B92.1-1970 SAE花键标准1.pdf

外文版渐开线花键标准（美标）INVOLUTE SPLINES2129
 Form Circle is the circle which defines the deepest points of involute form control of the
tooth profile. This circle along with the tooth tip circle (or start of chamfer circle) deter-
mines the limits of tooth profile requiring control. It is located near the major circle on the
internal spline and near the minor circle on the external spline.
 Form Clearance (cF) is the radial depth of involute profile beyond the depth of engage-
ment with the mating part. It allows for looseness between mating splines and for eccen-
tricities between the minor circle (internal), the major circle (external), and their respective
pitch circles.
 Form Diameter (DFe, DFi
) the diameter of the form circle.
 Internal Spline is a spline formed on the inner surface of a cylinder.
 Involute Spline is one having teeth with involute profiles.
 Lead Variation is the variation of the direction of the spline tooth from its intended direc-
tion parallel to the reference axis, also including parallelism and alignment variations (see
Fig. 1a). Note: Straight (nonhelical) splines have an infinite lead.
 Length of Engagement (Lq) is the axial length of contact between mating splines.
 Machining Tolerance (m) is the permissible variation in actual space width or actual
tooth thickness.
 Major Circle is the circle formed by the outermost surface of the spline. It is the outside
circle (tooth tip circle) of the external spline or the root circle of the internal spline.
 Major Diameter (Do, Dri
) is the diameter of the major circle.
 Minor Circle is the circle formed by the innermost surface of the spline. It is the root cir-
cle of the external spline or the inside circle (tooth tip circle) of the internal spline.
 Minor Diameter (Dre, Di
) is the diameter of the minor circle.
 Nominal Clearance is the actual space width of an internal spline minus the actual tooth
thickness of the mating external spline. It does not define the fit between mating members,
because of the effect of variations.
 Out of Roundness is the variation of the spline from a true circular configuration.
 Parallelism Variation is the variation of parallelism of a single spline tooth with respect
to any other single spline tooth (see Fig. 1b).
 Pitch (P/Ps) is a combination number of a one-to-two ratio indicating the spline propor-
tions; the upper or first number is the diametral pitch, the lower or second number is the
stub pitch and denotes, as that fractional part of an inch, the basic radial length of engage-
ment, both above and below the pitch circle.
 Pitch Circle is the reference circle from which all transverse spline tooth dimensions are
constructed.
 Pitch Diameter (D) is the diameter of the pitch circle.
 Pitch Point is the intersection of the spline tooth profile with the pitch circle.
 Pressure Angle (φ) is the angle between a line tangent to an involute and a radial line
through the point of tangency. Unless otherwise specified, it is the standard pressure angle.
 Profile Variation is any variation from the specified tooth profile normal to the flank.
 Spline is a machine element consisting of integral keys (spline teeth) or keyways
(spaces) equally spaced around a circle or portion thereof.
 Standard (Main) Pressure Angle (φD) is the pressure angle at the specified pitch diame-
ter.
 Stub Pitch (Ps) is a number used to denote the radial distance from the pitch circle to the
major circle of the external spline and from the pitch circle to the minor circleof the internal
spline. The stub pitch for splines in this standard is twice the diametral pitch.
 Total Index Variation is the greatest difference in any two teeth (adjacent or otherwise)
between the actual and the perfect spacing of the tooth profiles.
 Total Tolerance (m + λ) is the machining tolerance plus the variation allowance.
 Variation Allowance (λ) is the permissible effective variation.2130INVOLUTE SPLINES
Tooth Proportions.—There are 17 pitches: 2.5⁄5, 3⁄6, 4⁄8,5⁄10, 6⁄12, 8⁄16, 10⁄20,
12⁄24, 16⁄32, 20⁄40, 24⁄48, 32⁄64, 40⁄80, 48⁄96, 64⁄128, 80⁄160, and 128⁄256. The
numerator in this fractional designation is known as the diametral pitch and controls the
pitch diameter; the denominator, which is always double the numerator, is known as the
stub pitch and controls the tooth depth. For convenience in calculation, only the numerator
is used in the formulas given and is designated as P. Diametral pitch, as in gears, means the
number of teeth per inch of pitch diameter.
Table 1 shows the symbols and Table 2 the formulas for basic tooth dimensions of invo-
lute spline teeth of various pitches. Basic dimensions are given in Table 3.
Table 1. American National Standard Involute Spline Symbols
 ANSI B92.1-1970, R1993
cv effective clearance Mi
measurement between pins, internal
cF form clearancespline
D pitch diameter N number of teeth
Db base diameter P diametral pitch
Dci
pin contact diameter, internal Ps stub pitch
spline p circular pitch
Dce pin contact diameter, external rf
fillet radius
spline s actual space width, circular
DFe form diameter, external spline sv effective space width, circular
DFi
form diameter, internal spline sc allowable compressive stress, psi
Di
minor diameter, internal spline ss allowable shear stress, psi
Do major diameter, external spline t actual tooth thickness, circular
Dre minor diameter, external spline tv effective tooth thickness, circular
(root) λ variation allowance
Dri
major diameter, internal spline ∈ involute roll angle
(root) φ pressure angle
de diameter of measuring pin for external φD standard pressure angle
spline φci
pressure angle at pin contact diameter,
di
diameter of measuring pin for internalinternal spline
spline φce pressure angle at pin contact diameter,
Ke change factor for external splineexternal spline
Ki
change factor for internal spline φi
pressure angle at pin center, internal
L spline lengthspline
La active spline length φe pressure angle at pin center, external
Lg length of engagementspline
m machining tolerance φF pressure angle at form diameter
Me measurement over pins, external
splineINVOLUTE SPLINES2131
Table 2. Formulas for Basic Dimensions   ANSI B92.1-1970, R1993
TermSymbol
Formula
30 deg φD 37.5 deg φD 45 deg φD
Flat Root Side FitFlat Root Major Dia FitFillet Root Side FitFillet Root Side FitFillet Root Side Fit
2.5⁄5–32⁄64 Pitch3⁄6–16⁄32 Pitch2.5⁄5–48⁄96 Pitch2.5⁄5–48⁄96 Pitch10⁄20–128⁄256 Pitch
Stub Pitch Ps 2P 2P 2P 2P 2P
Pitch Diameter D
Base Diameter Db D cos φD D cos φD D cos φD D cos φD D cos φD
Circular Pitch p
Minimum Effective
Space Width sv
Major Diameter,
Internal Dri
Major Diameter,
External Do
Minor Diameter,
Internal Di
N
P
--- -
N
P
--- -
N
P
--- -
N
P
--- -
N
P
--- -
π
P
---
π
P
---
π
P
---
π
P
---
π
P
---
π
2P
------ -
π
2P
------ -
π
2P
------ -
0.5π 0.1 +
P
------------------------ -
0.5π 0.2 +
P
------------------------ -
N 1.35 +
P
--------------------
N 1 +
P
------------ -
N 1.8 +
P
-----------------
N 1.6 +
P
-----------------
N 1.4 +
P
-----------------
N 1 +
P
------------ -
N 1 +
P
------------ -
N 1 +
P
------------ -
N 1 +
P
------------ -
N 1 +
P
------------ -
N 1 –
P
------------ -
N 1 –
P
------------ -
N 1 –
P
------------ -
N 0.8 –
P
-----------------
N 0.6 –
P
-----------------INVOLUTE SPLINES 2132
π = 3.1415927
Note: All spline specification table dimensions in the standard are derived from these basic formulas by application of tolerances.
Minor
Dia.
Ext.
2.5⁄5 thru
12⁄24 pitch
Dre
…
16⁄32 pitch
and finer
10⁄20 16⁄32
pitch
and finer
…
Form Diameter,
Internal DFi
Form Diameter,
External DFe
Form Clearance
(Radial)
cF 0.001 D, with max of 0.010, min of 0.002
Table 2. (Continued) Formulas for Basic Dimensions  ANSI B92.1-1970, R1993
TermSymbol
Formula
30 deg φD 37.5 deg φD 45 deg φD
Flat Root Side FitFlat Root Major Dia FitFillet Root Side FitFillet Root Side FitFillet Root Side Fit
2.5⁄5–32⁄64 Pitch3⁄6–16⁄32 Pitch2.5⁄5–48⁄96 Pitch2.5⁄5–48⁄96 Pitch10⁄20–128⁄256 Pitch
N 1.35 –
P
--------------------
N 1.8 –
P
-----------------
N 1.3 –
P
-----------------
N 2 –
P
------------ -
N 1 –
P
------------ -
N 1 +
P
------------ -2cF +
N 0.8 +
P
-----------------0.004 –2cF +
N 1 +
P
------------ -2cF +
N 1 +
P
------------ -2cF +
N 1 +
P
------------ -2cF +
N 1 –
P
------------ -2cF –
N 1 –
P
------------ -2cF –
N 1 –
P
------------ -2cF –
N 0.8 –
P
-----------------2cF –
N 0.6 –
P
-----------------2cF –INVOLUTE SPLINES 2133
Table 3. Basic Dimensions for Involute Splines   ANSI B92.1-1970, R1993
Tooth Numbers.—The American National Standard covers involute splines having tooth
numbers ranging from 6 to 60 with a 30- or 37.5-degree pressure angle and from 6 to 100
with a 45-degree pressure angle. In selecting the number of teeth for a given spline applica-
tion, it is well to keep in mind that there are no advantages to be gained by using odd num-
bers of teeth and that the diameters of splines with odd tooth numbers, particularly internal
splines, are troublesome to measure with pins since no two tooth spaces are diametrically
opposite each other.
Types and Classes of Involute Spline Fits.—Two types of fits are covered by the Amer-
ican National Standard for involute splines, the side fit, and the major diameter fit. Dimen-
sional data for flat root side fit, flat root major diameter fit, and fillet root side fit splines are
tabulated in this standard for 30-degree pressure angle splines; but for only the fillet root
side fit for 37.5- and 45-degree pressure angle splines.
 Side Fit: In the side fit, the mating members contact only on the sides of the teeth; major
and minor diameters are clearance dimensions. The tooth sides act as drivers and centralize
the mating splines.
 Major Diameter Fit: Mating parts for this fit contact at the major diameter for centraliz-
ing. The sides of the teeth act as drivers. The minor diameters are clearance dimensions.
The major diameter fit provides a minimum effective clearance that will allow for con-
tact and location at the major diameter with a minimum amount of location or centralizing
effect by the sides of the teeth. The major diameter fit has only one space width and tooth
thickness tolerance which is the same as side fit Class 5.
A fillet root may be specified for an external spline, even though it is otherwise designed
to the flat root side fit or major diameter fit standard. An internal spline with a fillet root can
be used only for the side fit.
Classes of Tolerances.—This standard includes four classes of tolerances on space width
and tooth thickness. This has been done to provide a range of tolerances for selection to suit
a design need. The classes are variations of the former single tolerance which is now Class
5 and are based on the formulas shown in the footnote of Table 4. All tolerance classes have
the same minimum effective space width and maximum effective tooth thickness limits so
that a mix of classes between mating parts is possible.
Pitch,
P/Ps
Circular
Pitch,
p
Min Effective Space Width
(BASIC),
Sv min
Pitch,
P/Ps
Circular
Pitch,
p
Min Effective Space Width
(BASIC),
Sv min
30 deg φ 37.5 deg φ 45 deg φ 30 deg φ 37.5 deg φ 45 deg φ
2.5⁄5 1.2566 0.6283 0.6683 … 20⁄40 0.1571 0.0785 0.0835 0.0885
3⁄6 1.0472 0.5236 0.5569 … 24⁄48 0.1309 0.0654 0.0696 0.0738
4⁄8 0.7854 0.3927 0.4177 … 32⁄64 0.0982 0.0491 0.0522 0.0553
5⁄10 0.6283 0.3142 0.3342 … 40⁄80 0.0785 0.0393 0.0418 0.0443
6⁄12 0.5236 0.2618 0.2785 … 48⁄96 0.0654 0.0327 0.0348 0.0369
8⁄16 0.3927 0.1963 0.2088 … 64⁄128 0.0491 … … 0.0277
10⁄20 0.3142 0.1571 0.1671 0.1771 80⁄160 0.0393 … … 0.0221
12⁄24 0.2618 0.1309 0.1392 0.1476 128⁄256 0.0246 … … 0.0138
16⁄32 0.1963 0.0982 0.1044 0.1107 … … … … …2134INVOLUTE SPLINES
Table 4. Maximum Tolerances for Space Width and Tooth Thickness of Tolerance
Class 5 Splines  ANSI B92.1-1970, R1993
(Values shown in ten thousandths; 20 = 0.0020)
For other tolerance classes: Class 4 = 0.71 × Tabulated value
Class 5 = As tabulated in table
Class 6 = 1.40 × Tabulated value
Class 7 = 2.00 × Tabulated value
No.
of
Teeth
Pitch, P/Ps
2.5⁄5
and
3⁄6
4⁄8
and
5⁄10
6⁄12
and
8⁄16
10⁄20
and
12⁄24
16⁄32
and
20⁄40
24⁄48
thru
48⁄96
64⁄128
and
80⁄160
128⁄256
N Machining Tolerance, m
1015.814.512.512.011.711.79.69.5
2017.616.014.013.012.412.410.210.0
3018.417.515.514.013.113.110.810.5
4021.819.017.015.013.813.811.4—
5023.020.518.516.014.514.5——
6024.822.020.017.015.215.2——
70———18.015.915.9——
80———19.016.616.6——
90———20.017.317.3——
100———21.018.018.0——
N Variation Allowance, λ
1023.520.317.015.714.212.211.09.8
2027.022.619.017.415.413.412.010.6
3030.524.921.019.116.614.613.011.4
4034.027.223.021.617.815.814.0—
5037.529.525.022.519.017.0——
6041.031.827.024.220.218.2——
70———25.921.419.4——
80———27.622.620.6——
90———29.323.821.8——
100———31.025.023.0——
N Total Index Variation
102017151514121110
202420181715131211
302822201916151413
4032252220181615—
50362725221917——
60403027242018——
70———262120——
80———282221——
90———292423——
100———312524——
N Profile Variation
All
+7 +6 +5 +4 +3 +2 +2 +2
−10 −8 −7 −6 −5 −4 −4 −4
Lead Variation
Lg, in.0.30.512345678910
Variation2345678910111213INVOLUTE SPLINES2135
Fillets and Chamfers.—Spline teeth may have either a flat root or a rounded fillet root.
Flat Root Splines: are suitable for most applications. The fillet that joins the sides to the
bottom of the tooth space, if generated, has a varying radius of curvature. Specification of
this fillet is usually not required. It is controlled by the form diameter, which is the diameter
at the deepest point of the desired true involute form (sometimes designated as TIF).
When flat root splines are used for heavily loaded couplings that are not suitable for fillet
root spline application, it may be desirable to minimize the stress concentration in the flat
root type by specifying an approximate radius for the fillet.
Because internal splines are stronger than external splines due to their broad bases and
high pressure angles at the major diameter, broaches for flat root internal splines are nor-
mally made with the involute profile extending to the major diameter.
Fillet Root Splines: are recommended for heavy loads because the larger fillets provided
reduce the stress concentrations. The curvature along any generated fillet varies and can-
not be specified by a radius of any given value.
External splines may be produced by generating with a pinion-type shaper cutter or with
a hob, or by cutting with no generating motion using a tool formed to the contour of a tooth
space. External splines are also made by cold forming and are usually of the fillet root
design. Internal splines are usually produced by broaching, by form cutting, or by generat-
ing with a shaper cutter. Even when full-tip radius tools are used, each of these cutting
methods produces a fillet contour with individual characteristics. Generated spline fillets
are curves related to the prolate epicycloid for external splines and the prolate hypocycloid
for internal splines. These fillets have a minimum radius of curvature at the point where the
fillet is tangent to the external spline minor diameter circle or the internal spline major
diameter circle and a rapidly increasing radius of curvature up to the point where the fillet
comes tangent to the involute profile.
Chamfers and Corner Clearance: In major diameter fits, it is always necessary to pro-
vide corner clearance at the major diameter of the spline coupling. This clearance is usually
effected by providing a chamfer on the top corners of the external member. This method
may not be possible or feasible because of the following:
A) If the external member is roll formed by plastic deformation, a chamfer cannot be pro-
vided by the process.
B) A semitopping cutter may not be available.
C) When cutting external splines with small numbers of teeth, a semitopping cutter may
reduce the width of the top land to a prohibitive point.
In such conditions, the corner clearance can be provided on the internal spline, as shown
in Fig. 2.
When this option is used, the form diameter may fall in the protuberance area.
Fig. 2. Internal corner clearance.
Spline Variations.—The maximum allowable variations for involute splines are listed in
Table 4.
0.120
P min
          
              0.200
P max2136INVOLUTE SPLINES
Profile Variation: The reference profile, from which variations occur, passes through the
point used to determine the actual space width or tooth thickness. This is either the pitch
point or the contact point of the standard measuring pins.
Profile variation is positive in the direction of the space and negative in the direction of
the tooth. Profile variations may occur at any point on the profile for establishing effective
fits and are shown in Table 4.
Lead Variations: The lead tolerance for the total spline length applies also to any portion
thereof unless otherwise specified.
Out of Roundness: This condition may appear merely as a result of index and profile
variations given in Table 4 and requires no further allowance. However, heat treatment and
deflection of thin sections may cause out of roundness, which increases index and profile
variations. Tolerances for such conditions depend on many variables and are therefore not
tabulated. Additional tooth and/or space width tolerance must allow for such conditions.
Eccentricity: Eccentricity of major and minor diameters in relation to the effective diam-
eter of side fit splines should not cause contact beyond the form diameters of the mating
splines, even under conditions of maximum effective clearance. This standard does not
establish specific tolerances.
Eccentricity of major diameters in relation to the effective diameters of major diameter
fit splines should be absorbed within the maximum material limits established by the toler-
ances on major diameter and effective space width or effective tooth thickness.
If the alignment of mating splines is affected by eccentricity of locating surfaces relative
to each other and/or the splines, it may be necessary to decrease the effective and actual
tooth thickness of the external splines in order to maintain the desired fit condition. This
standard does not include allowances for eccentric location.
Effect of Spline Variations.—Spline variations can be classified as index variations, pro-
file variations, or lead variations.
Index Variations: These variations cause the clearance to vary from one set of mating
tooth sides to another. Because the fit depends on the areas with minimum clearance, index
variations reduce the effective clearance.
Profile Variations: Positive profile variations affect the fit by reducing effective clear-
ance. Negative profile variations do not affect the fit but reduce the contact area.
Lead Variations: These variations will cause clearance variations and therefore reduce
the effective clearance.
Variation Allowance: The effect of individual spline variations on the fit (effective vari-
ation) is less than their total, because areas of more than minimum clearance can be altered
without changing the fit. The variation allowance is 60 percent of the sum of twice the pos-
itive profile variation, the total index variation and the lead variation for the length of
engagement. The variation allowances in Table 4 are based on a lead variation for an
assumed length of engagement equal to one-half the pitch diameter. Adjustment may be
required for a greater length of engagement.
Effective and Actual Dimensions.—Although each space of an internal spline may have
the same width as each tooth of a perfect mating external spline, the two may not fit
because of variations of index and profile in the internal spline. To allow the perfect exter-
nal spline to fit in any position, all spaces of the internal spline must then be widened by the
amount of interference. The resulting width of these tooth spaces is the actual space width
of the internal spline. The effective space width is the tooth thickness of the perfect mating
external spline. The same reasoning applied to an external spline that has variations of
index and profile when mated with a perfect internal spline leads to the concept of effective
tooth thickness, which exceeds the actual tooth thickness by the amount of the effective
variation.INVOLUTE SPLINES2137
The effective space width of the internal spline minus the effective tooth thickness of the
external spline is the effective clearance and defines the fit of the mating parts. (This state-
ment is strictly true only if high points of mating parts come into contact.) Positive effec-
tive clearance represents looseness or backlash. Negative effective clearance represents
tightness or interference.
Space Width and Tooth Thickness Limits.—The variation of actual space width and
actual tooth thickness within the machining tolerance causes corresponding variations of
effective dimensions, so that there are four limit dimensions for each component part.
These variations are shown diagrammatically in Table 5.
Table 5. Specification Guide for Space Width and Tooth Thickness
 ANSI B92.1-1970, R1993
The minimum effective space width is always basic. The maximum effective tooth thick-
ness is the same as the minimum effective space width except for the major diameter fit.
The major diameter fit maximum effective tooth thickness is less than the minimum effec-
tive space width by an amount that allows for eccentricity between the effective spline and
the major diameter. The permissible variation of the effective clearance is divided between
the internal and external splines to arrive at the maximum effective space width and the
minimum effective tooth thickness. Limits for the actual space width and actual tooth
thickness are constructed from suitable variation allowances.
Use of Effective and Actual Dimensions.—Each of the four dimensions for space width
and tooth thickness shown in Table 5 has a definite function.
Minimum Effective Space Width and Maximum Effective Tooth Thickness: These
dimensions control the minimum effective clearance, and must always be specified.
Minimum Actual Space Width and Maximum Actual Tooth Thickness: These dimen-
sions cannot be used for acceptance or rejection of parts. If the actual space width is less
than the minimum without causing the effective space width to be undersized, or if the
actual tooth thickness is more than the maximum without causing the effective tooth thick-
ness to be oversized, the effective variation is less than anticipated; such parts are desirable
and not defective. The specification of these dimensions as processing reference dimen-
sions is optional. They are also used to analyze undersize effective space width or oversize
effective tooth thickness conditions to determine whether or not these conditions are
caused by excessive effective variation.
Maximum Actual Space Width and Minimum Actual Tooth Thickness: These dimen-
sions control machining tolerance and limit the effective variation. The spread between
these dimensions, reduced by the effective variation of the internal and external spline, is2138INVOLUTE SPLINES
the maximum effective clearance. Where the effective variation obtained in machining is
appreciably less than the variation allowance, these dimensions must be adjusted in order
to maintain the desired fit.
Maximum Effective Space Width and Minimum Effective Tooth Thickness: These
dimensions define the maximum effective clearance but they do not limit the effective
variation. They may be used, in addition to the maximum actual space width and minimum
actual tooth thickness, to prevent the increase of maximum effective clearance due to
reduction of effective variations. The notation “inspection optional” may be added where
maximum effective clearance is an assembly requirement, but does not need absolute con-
trol. It will indicate, without necessarily adding inspection time and equipment, that the
actual space width of the internal spline must be held below the maximum, or the actual
tooth thickness of the external spline above the minimum, if machining methods result in
less than the allowable variations. Where effective variation needs no control or is con-
trolled by laboratory inspection, these limits may be substituted for maximum actual space
width and minimum actual tooth thickness.
Combinations of Involute Spline Types.—Flat root side fit internal splines may be used
with fillet root external splines where the larger radius is desired on the external spline for
control of stress concentrations. This combination of fits may also be permitted as a design
option by specifying for the minimum root diameter of the external, the value of the mini-
mum root diameter of the fillet root external spline and noting this as “optional root.”
A design option may also be permitted to provide either flat root internal or fillet root
internal by specifying for the maximum major diameter, the value of the maximum major
diameter of the fillet root internal spline and noting this as “optional root.”
Interchangeability.—Splines made to this standard may interchange with splines made
to older standards. Exceptions are listed below.
External Splines: These external splines will mate with older internal splines as follows:
Internal Splines: These will mate with older external splines as follows:
Year
Major Dia.
 Fit
Flat Root
Side Fit
Fillet Root
Side Fit
1946Yes No (A)a
a
For exceptions A, B, C, see the paragraph on Exceptions that follows.
No (A)
1950b
b
Full dedendum.
Yes (B)Yes (B)Yes (C)
1950c
c
Short dedendum.
Yes (B)No (A)Yes (C)
1957 SAEYesNo (A)Yes (C)
1960YesNo (A)Yes (C)
Year
Major Dia.
Fit
Flat Root
Side Fit
Fillet Root
Side Fit
1946 No (D)a
a
For exceptions C, D, E, F, G, see the paragraph on Exceptions that follows.
No (E)No (D)
1950Yes (F)YesYes (C)
1957 SAEYes (G)YesYes
1960Yes (G)YesYesINVOLUTE SPLINES2139
Table 6. Spline Terms, Symbols, and Drawing Data, 30-Degree Pressure Angle, Flat
Root Side Fit  ANSI B92.1-1970, R1993
The above drawing data are required for the spline specifications. The standard system is shown;
for alternate systems, see Table 5. Number of x's indicates number of decimal places normally used.
The fit shown is used in restricted areas (as with tubular parts with wall thickness too small to permit use of fillet roots, and to
allow hobbing closer to shoulders, etc.) and for economy (when hobbing, shaping, etc., and using shorter broaches for the internal
member).
Press fits are not tabulated because their design depends on the degree of tightness desired and must allow for such factors as the
shape of the blank, wall thickness, materila, hardness, thermal expansion, etc. Close tolerances or selective size grouping may be
required to limit fit variations.
Drawing Data
Internal Involute Spline DataExternal Involute Spline Data
Flat Root Side FitFlat Root Side Fit
Number of TeethxxNumber of Teethxx
Pitchxx/xxPitchxx/xx
Pressure Angle30° Pressure Angle30°
Base Diameterx.xxxxxx RefBase Diameterx.xxxxxx Ref
Pitch Diameterx.xxxxxx RefPitch Diameterx.xxxxxx Ref
Major Diameterx.xxx maxMajor Diameterx.xxx/x.xxx
Form Diameterx.xxxForm Diameterx.xxx
Minor Diameterx.xxx/x.xxxMinor Diameterx.xxx min
Circular Space WidthCircular Tooth Thickness
MaxActualx.xxxxMaxEffectivex.xxxx
MinEffectivex.xxxxMinActualx.xxxx
The following information may be added as required:The following information may be added as required:
Max Measurement Between Pinsx.xxx RefMin Measurement Over Pinsx.xxxx Ref
Pin Diameterx.xxxxPin Diameterx.xxxx
Optional
External
Spline
Internal
Spline
30-Deg Pressure Angle
Circular Pitch P
Space Width (Circular)
s = Actual
sv = Effective
Tooth Thickness (Circular)
t = Actual
tv = Effective
Pitch
Dia.
D
Ref
Fillet
Form Clearance CF
CF
Major Dia.
Major Dia.
Major Dia.
Dri
Dre
DFi
Do
Di
DFe2140INVOLUTE SPLINES
Exceptions:
A) The external major diameter, unless chamfered or reduced, may interfere with the
internal form diameter on flat root side fit splines. Internal splines made to the 1957 and
1960 standards had the same dimensions as shown for the major diameter fit splines in this
standard.
B) For 15 teeth or less, the minor diameter of the internal spline, unless chamfered, will
interfere with the form diameter of the external spline.
C) For 9 teeth or less, the minor diameter of the internal spline, unless chamfered, will
interfere with form diameter of the external spline.
D) The internal minor diameter, unless chamfered, will interfere with the external form
diameter.
E) The internal minor diameter, unless chamfered, will interfere with the external form
diameter.
F) For 10 teeth or less, the minimum chamfer on the major diameter of the external spline
may not clear the internal form diameter.
G) Depending upon the pitch of the spline, the minimum chamfer on the major diameter
may not clear the internal form diameter.
Drawing Data.—It is important that uniform specifications be used to show complete
information on detail drawings of splines. Much misunderstanding will be avoided by fol-
lowing the suggested arrangement of dimensions and data as given in Table 6. The number
of x's indicates the number of decimal places normally used. With this tabulated type of
spline specifications, it is usually not necessary to show a graphic illustration of the spline
teeth.
Spline Data and Reference Dimensions.—Spline data are used for engineering and
manufacturing purposes. Pitch and pressure angle are not subject to individual inspection.
As used in this standard, reference is an added notation or modifier to a dimension, spec-
ification, or note when that dimension, specification, or note is:
1) Repeated for drawing clarification.
2) Needed to define a nonfeature datum or basis from which a form or feature is gener-
ated.
3) Needed to define a nonfeature dimension from which other specifications or dimen-
sions are developed.
4) Needed to define a nonfeature dimension at which toleranced sizes of a feature are
specified.
5) Needed to define a nonfeature dimension from which control tolerances or sizes are
developed or added as useful information.
Any dimension, specification, or note that is noted “REF” should not be used as a crite-
rion for part acceptance or rejection.
Estimating Key and Spline Sizes and Lengths.—Fig. 1 may be used to estimate the size
of American Standard involute splines required to transmit a given torque. It also may be
used to find the outside diameter of shafts used with single keys. After the size of the shaft
is found, the proportions of the key can be determined from Table 1 on page 2342.
Curve A is for flexible splines with teeth hardened to Rockwell C 55–65. For these
splines, lengths are generally made equal to or somewhat greater than the pitch diameter
for diameters below 11⁄
4 inches; on larger diameters, the length is generally one-third to
two-thirds the pitch diameter. Curve A also applies for a single key used as a fixed cou-
pling, the length of the key being one to one and one-quarter times the shaft diameter. The
stress in the shaft, neglecting stress concentration at the keyway, is about 7500 pounds per
square inch. See also Effect of Keyways on Shaft Strength starting on page 283.
Curve B represents high-capacity single keys used as fixed couplings for stresses of 9500
pounds per square inch, neglecting stress concentration. Key-length is one to one and one-
quarter times shaft diameter and both shaft and key are of moderately hard heat-treatedINVOLUTE SPLINES2141
steel. This type of connection is commonly used to key commercial flexible couplings to
motor or generator shafts.
Curve C is for multiple-key fixed splines with lengths of three-quarters to one and one-
quarter times pitch diameter and shaft hardness of 200–300 BHN.
Curve D is for high-capacity splines with lengths one-half to one times the pitch diame-
ter. Hardnesses up to Rockwell C 58 are common and in aircraft applications the shaft is
generally hollow to reduce weight.
Curve E represents a solid shaft with 65,000 pounds per square inch shear stress. For hol-
low shafts with inside diameter equal to three-quarters of the outside diameter the shear
stress would be 95,000 pounds per square inch.
Length of Splines: Fixed splines with lengths of one-third the pitch diameter will have
the same shear strength as the shaft, assuming uniform loading of the teeth; however,
errors in spacing of teeth result in only half the teeth being fully loaded. Therefore, for bal-
anced strength of teeth and shaft the length should be two-thirds the pitch diameter. If
weight is not important, however, this may be increased to equal the pitch diameter. In the
case of flexible splines, long lengths do not contribute to load carrying capacity when there
is misalignment to be accommodated. Maximum effective length for flexible splines may
be approximated from Fig. 2.
Formulas for Torque Capacity of Involute Splines.—The formulas for torque capacity
of 30-degree involute splines given in the following paragraphs are derived largely from an
article “When Splines Need Stress Control” by D. W. Dudley, Product Engineering, Dec.
23, 1957.
In the formulas that follow the symbols used are as defined on page 2130 with the follow-
ing additions: Dh = inside diameter of hollow shaft, inches; Ka = application factor from
Table 1; Km = load distribution factor from Table 2; Kf
 = fatigue life factor from Table 3; Kw
= wear life factor from Table 4; Le = maximum effective length from Fig. 2, to be used in
stress formulas even though the actual length may be greater; T = transmitted torque,
pound-inches. For fixed splines without helix modification, the effective length Le should
never exceed 5000 D3.5 ÷ T.
Table 1. Spline Application Factors, Ka
Power Source
Type of Load
Uniform
(Generator-
Fan)
Light
Shock
(Oscillating
Pumps, etc.)
Intermittent
Shock
(Actuating
Pumps, etc.)
Heavy
Shock
(Punches,
Shears, etc.)
Application Factor, Ka
Uniform (Turbine, Motor)1.01.21.51.8
Light Shock (Hydraulic
Motor)
1.21.31.82.1
Medium Shock (Internal
Combustion, Engine)
2.02.22.42.82142INVOLUTE SPLINES
Table 2. Load Distribution Factors, Km, for Misalignment of Flexible Splines
For fixed splines, Km = 1.
Table 3. Fatigue-Life Factors, Kf
, for Splines
Table 4. Wear Life Factors, Kw, for Flexible Splines
Wear life factors, unlike fatigue life factors given in Table 3, are based on the total number of rev-
olutions of the spline, since each revolution of a flexible spline results in a complete cycle of rocking
motion which contributes to spline wear.
Definitions: A fixed spline is one which is either shrink fitted or loosely fitted but piloted
with rings at each end to prevent rocking of the spline which results in small axial move-
ments that cause wear. A  flexible spline permits some rocking motion such as occurs when
the shafts are not perfectly aligned. This flexing or rocking motion causes axial movement
and consequently wear of the teeth. Straight-toothed flexible splines can accommodate
only small angular misalignments (less than 1 deg.) before wear becomes a serious prob-
lem. For greater amounts of misalignment (up to about 5 deg.), crowned splines are prefer-
able to reduce wear and end-loading of the teeth.
Misalignment,
inches per inch
Load Distribution Factor, Km
a
a
For fixed splines, Km=1.
1⁄
2-in. Face
Width
1-in. Face
Width
2-in. Face
Width
4-in. Face
Width
0.001111 1
1⁄
2
0.00211 1
1⁄
2
2
0.0041 1
1⁄
2
2 2
1⁄
2
0.008 1
1⁄
2
2 2
1⁄
2
3
No. of Torque
Cyclesa
a
A torque cycle consists of one start and one stop, not the number of revolutions.
Fatigue-Life Factor, Kf
UnidirectionalFully-reversed
1,0001.81.8
10,0001.01.0
100,0000.50.4
1,000,0000.40.3
10,000,0000.30.2
Number of
Revolutions
of Spline
Life Factor,
Kw
Number of
Revolutions
of Spline
Life Factor,
Kw
10,0004.0100,000,0001.0
100,0002.81,000,000,0000.7
1,000,0002.010,000,000,0000.5
10,000,0001.4 ……INVOLUTE SPLINES2143
Fig. 1. Chart for Estimating Involute Spline Size Based on Diameter-Torque Relationships
Fig. 2. Maximum Effective Length for Fixed and Flexible Splines
30
25
20
15
10
7.0
5.0
3.0
2.0
1.5
1.0
0.7
0.5
0.3
Pitch Diameter of Splines or OD of Keyed Shaft, inches
1001,00010,000
Torque, lb-inches
100,0001,000,000
D
E
Aircraft fixed
Limit of spline design
(65,000-psi solid shaft)
A
B
Aircraft flexible or single-key commercial
Single-key, high-capacity
CHigh-capacity fixed
10
9
8
7
6
5
4
3
2
1
Pitch Diameter inches
012
Maximum Effective Length Le, inches
345678
For maximum misalignment
For moderate misalignment
For flexible splines
For fixed splines with helix modification2144INVOLUTE SPLINES
Shear Stress Under Roots of External Teeth: For a transmitted torque T, the torsional
shear stress induced in the shaft under the root diameter of an external spline is:
(1)
(2)
The computed stress should not exceed the values in Table 5.
Table 5. Allowable Shear Stresses for Splines
Shear Stress at the Pitch Diameter of Teeth: The shear stress at the pitch line of the teeth
for a transmitted torque T is:
(3)
The factor of 4 in (3) assumes that only half the teeth will carry the load because of spac-
ing errors. For poor manufacturing accuracies, change the factor to 6.
The computed stress should not exceed the values in Table 5.
Compressive Stresses on Sides of Spline Teeth: Allowable compressive stresses on
splines are very much lower than for gear teeth since non-uniform load distribution and
misalignment result in unequal load sharing and end loading of the teeth.
(4)
(5)
In these formulas, h is the depth of engagement of the teeth, which for flat root splines is
0.9/P and for fillet root splines is 1/P, approximately.
The stresses computed from Formulas (4) and (5) should not exceed the values in Table
6.
Material
HardnessMax. Allowable
Shear Stress,
psi BrinellRockwell C
Steel160–200—20,000
Steel230–260—30,000
Steel302–35133–3840,000
Surface-hardened Steel—48–5340,000
Case-hardened Steel—58–6350,000
Through-hardened Steel
(Aircraft Quality)
—42–4645,000
Ss
16TKa
πDre
3 Kf
------------------ =for a solid shaft
Ss
16TDreKa
π Dre
4 Dh
4 – ()Kf
------------------------------------ =for a hollow shaft
Ss
4TKaKm
DNLetKf
---------------------- - =
For flexible splines,  Sc
2TKmKa
DNLehKw
------------------------- - =
For fixed splines,  Sc
2TKmKa
9DNLehKf
--------------------------- =INVOLUTE SPLINES2145
Table 6. Allowable Compressive Stresses for Splines
Bursting Stresses on Splines: Internal splines may burst due to three kinds of tensile
stress: 1) tensile stress due to the radial component of the transmitted load;  2) centrifugal
tensile stress;  and  3) tensile stress due to the tangential force at the pitch line causing
bending of the teeth.
(6)
where  tw = wall thickness of internal spline = outside diameter of spline sleeve minus spline
major diameter, all divided by 2. L = full length of spline.
(7)
where Doi
 = outside diameter of spline sleeve.
(8)
In this equation, Y is the Lewis form factor obtained from a tooth layout. For internal
splines of 30-deg. pressure angle a value of Y = 1.5 is a satisfactory estimate. The factor 4
in (8) assumes that only half the teeth are carrying the load.
The total tensile stress tending to burst the rim of the external member is:
St
 = [KaKm (S1 + S3) + S2]/Kf
; and should be less than those in Table 7.
Table 7. Allowable Tensile Stresses for Splines
Crowned Splines for Large Misalignments.—As mentioned on page 2142, crowned
splines can accommodate misalignments of up to about 5 degrees. Crowned splineshave
Material
Hardness
Max. Allowable
Compressive Stress,
psi
BrinellRockwell CStraightCrowned
Steel160–200—1,5006,000
Steel230–260—2,0008,000
Steel302–35133–383,00012,000
Surface-hardened
Steel
—48–534,00016,000
Case-hardened Steel—58–635,00020,000
Material
Hardness Max. Allowable Stress,
psi BrinellRockwell C
Steel160–200—22,000
Steel230–260—32,000
Steel302–35133–3845,000
Surface-hardened
Steel
—48–5345,000
Case-hardened Steel—58−6355,000
Through-hardened
Steel
—42–4650,000
Radial load tensile stress,  S1
T φ tan
πDt
wL
---------------- - =
Centrifugal tensile stress,  S2
1.656rpm ()2 × Doi
2 0.212Dri
2 + ()
1000000 ,,
------------------------------------------------------------------------------- =
Beam loading tensile stress,  S3
4T
D2LeY
---------------- =2146INVOLUTE SPLINES
considerably less capacity than straight splines of the same size if both are operating with
precise alignment. However, when large misalignments exist, the crowned spline has
greater capacity.
American Standard tooth forms may be used for crowned external members so that they
may be mated with straight internal members of Standard form.
The accompanying diagram of a crowned spline shows the radius of the crown r1; the
radius of curvature of the crowned tooth, r2; the pitch diameter of the spline, D; the face
width, F; and the relief or crown height A  at the ends of the teeth. The crown height A
should always be made somewhat greater than one-half the face width multiplied by the
tangent of the misalignment angle. For a crown height A, the approximate radius of curva-
ture r2 is F2 ÷ 8A, and r1 = r2 tan φ, where φ is the pressure angle of the spline.
For a torque T, the compressive stress on the teeth is:
and should be less than the value in Table 6.
Fretting Damage to Splines and Other Machine Elements.—Fretting is wear that
occurs when cyclic loading, such as vibration, causes two surfaces in intimate contact to
undergo small oscillatory motions with respect to each other. During fretting, high points
or asperities of the mating surfaces adhere to each other and small particles are pulled out,
leaving minute, shallow pits and a powdery debris. In steel parts exposed to air, the metal-
lic debris oxidizes rapidly and forms a red, rustlike powder or sludge; hence, the coined
designation “fretting corrosion.”
Fretting is mechanical in origin and has been observed in most materials, including those
that do not oxidize, such as gold, platinum, and nonmetallics; hence, the corrosion accom-
panying fretting of steel parts is a secondary factor.
Fretting can occur in the operation of machinery subject to motion or vibration or both. It
can destroy close fits; the debris may clog moving parts; and fatigue failure may be accel-
erated because stress levels to initiate fatigue in fretted parts are much lower than for
undamaged material. Sites for fretting damage include interference fits; splined, bolted,
keyed, pinned, and riveted joints; between wires in wire rope; flexible shafts and tubes;
between leaves in leaf springs; friction clamps; small amplitude-of-oscillation bearings;
and electrical contacts.
Vibration or cyclic loadings are the main causes of fretting. If these factors cannot be
eliminated, greater clamping force may reduce movement but, if not effective, may actu-
ally worsen the damage. Lubrication may delay the onset of damage; hard plating or sur-
face hardening methods may be effective, not by reducing fretting, but by increasing the
fatigue strength of the material. Plating soft materials having inherent lubricity onto con-
tacting surfaces is effective until the plating wears through.
Involute Spline Inspection Methods.—Spline gages are used for routine inspection of
production parts.
Sc 22902TDNhr2 ÷ ; =INVOLUTE SPLINES2147
Analytical inspection, which is the measurement of individual dimensions and varia-
tions, may be required:
A) To supplement inspection by gages, for example, where NOT GO composite gages
are used in place of NOT GO sector gages and variations must be controlled.
B) To evaluate parts rejected by gages.
C) For prototype parts or short runs where spline gages are not used.
D) To supplement inspection by gages where each individual variation must be
restrained from assuming too great a portion of the tolerance between the minimum mate-
rial actual and the maximum material effective dimensions.
Inspection with Gages.—A variety of gages is used in the inspection of involute splines.
Types of Gages: A composite spline gage has a full complement of teeth. A sector spline
gage has two diametrically opposite groups of teeth. A sector plug gage with only two teeth
per sector is also known as a “paddle gage.” A sector ring gage with only two teeth per sec-
tor is also known as a “snap ring gage.” A progressive gage is a gage consisting of two or
more adjacent sections with different inspection functions. Progressive GO gages are
physical combinations of GO gage members that check consecutively first one feature or
one group of features, then their relationship to other features. GO and NOT GO gages may
also be combined physically to form a progressive gage.
Fig. 3. Space width and tooth-thickness inspection.
GO and NOT GO Gages: GO gages are used to inspect maximum material conditions
(maximum external, minimum internal dimensions). They may be used to inspect an indi-
vidual dimension or the relationship between two or more functional dimensions. They
control the minimum looseness or maximum interference.
NOT GO gages are used to inspect minimum material conditions (minimum external,
maximum internal dimensions), thereby controlling the maximum looseness or minimum
interference. Unless otherwise agreed upon, a product is acceptable only if the NOT GO
gage does not enter or go on the part. A NOT GO gage can be used to inspect only one
dimension. An attempt at simultaneous NOT GO inspection of more than one dimension
could result in failure of such a gage to enter or go on (acceptance of part), even though all
but one of the dimensions were outside product limits. In the event all dimensions are out-
side the limits, their relationship could be such as to allow acceptance.
Effective and Actual Dimensions: The effective space width and tooth thickness are
inspected by means of an accurate mating member in the form of a composite spline gage.
The actual space width and tooth thickness are inspected with sector plug and ring gages,
or by measurements with pins.
Measurements with Pins.—The actual space width of internal splines, and the actual
tooth thickness of external splines, may be measured with pins. These measurements do
not determine the fit between mating parts, but may be used as part of the analytic inspec-
tion of splines to evaluate the effective space width or effective tooth thickness by approx-
imation.21, 48METRIC MODULE INVOLUTE SPLINES
Formulas for 2-Pin Measurement: For measurement between pins of internal splines
using the symbols given on page 2130:
1) Find involute of pressure angle at pin center:
2) Find the value of φi
, in degrees, in the involute function tables beginning on page 98.
Find sec φi
 = 1/cosine φi
 in the trig tables, pages 94 through 96, using interpolation to obtain
higher accuracy.
3) Compute measurement, Mi
, between pins:
For even numbers of teeth: Mi
 = Db sec φi
 − di
For odd numbers of teeth: Mi
 = (Db cos 90°/N) sec φi
 − di
where: di
=1.7280/P for 30° and 37.5° standard pressure angle (φD) splines
di
=1.9200/P for 45° pressure angle splines
For measurement over pins of external splines:
1) Find involute of pressure angle at pin center:
2) Find the value of φe and sec φe from the involute function tables beginning on page 98.
3) Compute measurement, Me, over pins:
For even numbers of teeth: Me = Db sec φe + de
For odd numbers of teeth: Mi
 = (Db cos 90°/N) sec φe − de
where  de =1.9200/P for all external splines
Example:Find the measurement between pins for maximum actual space width of an
internal spline of 30° pressure angle, tolerance class 4,
3⁄
6 diametral pitch, and 20 teeth.
The maximum actual space width to be substituted for s in Step 1 above is obtained as
follows: In Table 5, page 2137, the maximum actual space width is the sum of the mini-
mum effective space width (second column) and λ + m (third column). The minimum
effective space width sv from Table 2, page 2131, is π/2P = π/(2 × 3). The values of λ and
m from Table 4, page 2134, are, for a class 4 fit, 3⁄6 diametral pitch, 20-tooth spline: λ =
0.0027 × 0.71 = 0.00192; and m = 0.00176 × 0.71 = 0.00125, so that s = 0.52360 + 0.00192
+ 0.00125 = 0.52677.
Other values required for Step 1 are:
D=N/P = 20⁄3 = 6.66666
inv  φD = inv 30° = 0.053751 from a calculator
di
=1.7280⁄3 = 0.57600
Db =D cos φD = 6.66666 × 0.86603 = 5.77353
The computation is made as follows:
1) inv φi
 = 0.52677⁄6.66666 + 0.053751 − 0.57600⁄5.77353 = 0.03300
2) From a calculator, φi
 = 25°46.18′ and sec φi
 = 1.11044
3) Mi
 = 5.77353 × 1.11044 − 0.57600 = 5.8352 inches
American National Standard Metric Module Splines.—ANSI B92.2M-1980 (R1989)
is the American National Standards Institute version of the International Standards Orga-
nization involute spline standard. It is not a “soft metric” conversion of any previous, inch-
based, standard,
* and splines made to this hard metric version are not intended for use with
components made to the B92.1 or other, previous standards. The ISO 4156 Standard from
*
A “soft” conversion is one in which dimensions in inches, when multiplied by 25.4 will, after being
appropriately rounded off, provide equivalent dimensions in millimeters. In a “hard” system the tools
of production, such as hobs, do not bear a usable relation to the tools in another system; i.e., a 10 diame-
tral pitch hob calculates to be equal to a 2.54 module hob in the metric module system, a hob that does
not exist in the metric standard.
φi
inv  sD ⁄φd inv  di
Db ⁄ – + =
φe inv  tD ⁄φD inv  de Db ⁄π N ⁄ – ++ =METRIC MODULE INVOLUTE SPLINES2149
which this one is derived is the result of a cooperative effort between the ANSI B92 com-
mittee and other members of the ISO/TC 14-2 involute spline committee.
Many of the features of the previous standard, ANSI B92.1-1970 (R1993), have been
retained such as: 30-, 37.5-, and 45-degree pressure angles; flat root and fillet root side fits;
the four tolerance classes 4, 5, 6, and 7; tables for a single class of fit; and the effective fit
concept.
Among the major differences are: use of modules of from 0.25 through 10 mm in place of
diametral pitch; dimensions in millimeters instead of inches; the “basic rack”; removal of
the major diameter fit; and use of ISO symbols in place of those used previously. Also, pro-
vision is made for calculating three defined clearance fits.
The Standard recognizes that proper assembly between mating splines is dependent only
on the spline being within effective specifications from the tip of the tooth to the form
diameter. Therefore, the internal spline major diameter is shown as a maximum dimension
and the external spline minor diameter is shown as a minimum dimension. The minimum
internal major diameter and the maximum external minor diameter must clear the speci-
fied form diameter and thus require no additional control. All dimensions are for the fin-
ished part; any compensation that must be made for operations that take place during
processing, such as heat treatment, must be considered when selecting the tolerance level
for manufacturing.
The Standard provides the same internal minimum effective space width and external
maximum effective tooth thickness for all tolerance classes. This basic concept makes pos-
sible interchangeable assembly between mating splines regardless of the tolerance class of
the individual members, and permits a tolerance class “mix” of mating members. This
arrangement is often an advantage when one member is considerably less difficult to pro-
duce than its mate, and the “average” tolerance applied to the two units is such that it satis-
fies the design need. For example, by specifying Class 5 tolerance for one member and
Class 7 for its mate, an assembly tolerance in the Class 6 range is provided.
If a fit given in this Standard does not satisfy a particular design need, and a specific
clearance or press fit is desired, the change shall be made only to the external spline by a
reduction of, or an increase in, the effective tooth thickness and a like change in the actual
tooth thickness. The minimum effective space width is always basic and this basic width
should always be retained when special designs are derived from the concept of this Stan-
dard.
Spline Terms and Definitions: The spline terms and definitions given for American
National Standard ANSI B92.1-1970 (R1993) described in the preceding section, may be
used in regard to ANSI B92.2M-1980 (R1989). The 1980 Standard utilizes ISO symbols in
place of those used in the 1970 Standard; these differences are shown in Table 1.2150METRIC MODULE INVOLUTE SPLINES
Table 1. Comparison of Symbols Used in  ANSI B92.2M-1980 (R1989)
and Those in ANSI B92.1-1970, R1993
Dimensions and Tolerances: Dimensions and tolerances of splines made to the 1980
Standard may be calculated using the formulas given in Table 2. These formulas are for
metric module splines in the range of from 0.25 to 10 mm metric module of side-fit design
and having pressure angles of 30-, 37.5-, and 45-degrees. The standard modules in the sys-
tem are: 0.25; 0.5; 0.75; 1; 1.25; 1.5; 1.75; 2; 2.5; 3; 4; 5; 6; 8; and 10. The range of from 0.5
to 10 module applies to all splines except 45-degree fillet root splines; for these, the range
of from 0.25 to 2.5 module applies.
Symbol
Meaning of Symbol
Symbol
Meaning of Symbol B92.2MB92.1B92.2MB92.1
c … theoretical clearance m … module
cv cv effective clearance … P diametral pitch
cF cF form clearance … Ps stub pitch = 2P
DD pitch diameter Pb … base pitch
DBDb base diameter pp circular pitch
dce Dce pin contact diameter, external
spline
ππ 3.141592654
dci
Dci
pin contact diameter, internal
spline
rferf
fillet rad., ext. spline
DEEDo major diam., ext. spline rfirf
fillet rad., int. spline
DEIDri
major diam., int. spline Ebsc sv minbasic circular space width
DFEDFe form diam., ext. spline Emax s max. actual circular space width
DFIDFi
form diam., int. spline Emin s min. actual circular space width
DIEDre minor diam., ext. spline EVsv effective circular space width
DIIDi
minor diam., int. spline Sbsc tv maxbasic circular tooth thickness
DREde pin diam., ext. spline Smax t max. actual circular tooth thick.
DRIdi
pin diam., int. spline Smin t min. actual circular tooth thick.
hs … see Figs. 1a,  1b,  1c, and  1d SVtv effective circular tooth thick.
λλ effective variation αφ pressure angle
INV α… involute α=tan α − arc ααD φD standard pressure angle
KEKe change factor, ext. spline αci
φci
press. angle at pin contact diame-
ter, internal spline
KIKi
change factor, int. spline αce φce press. angle at pin contact diame-
ter, external spline
gL spline length αi
φi
press. angle at pin center, internal
spline
gw … active spline length αe φe press. angle at pin center, external
spline
gγ… length of engagement αFe φF press. angle at form diameter,
external spline
Tm machining tolerance αFi
φF press. angle at form diameter,
internal spline
MREMe meas. over 2 pins, ext. spline es … ext. spline cir. tooth thick.modifi-
cation for required fit
class=cv min (Table 3)
MRIMi
meas. bet. 2 pins, int. splineh, f, e,
or d
… tooth thick, size modifiers (called
fundamental deviation in ISO
R286), Table 3
ZN number of teethH … space width size modifier (called
fundamental deviation in ISO
R286), Table 3METRIC MODULE INVOLUTE SPLINES2151
Table 2. Formulas for Dimensions and Tolerances for All Fit Classes—Metric Module Involute Splines
TermSymbol
Formula
30-Degree Flat Root30-Degree Fillet Root37.5-Degree Fillet Root45-Degree Fillet Root
0.5 to 10 module0.5 to 10 module0.5 to 10 module0.25 to 2.5 module
Pitch Diameter DmZ
Base Diameter DBmZ cos αD
Circular Pitch p πm
Base Pitch pb πm cos αD
Tooth Thick Mod es According to selected fit class, H/h, H/f, H/e, or H/d (see Table 3)
Min Maj. Diam. Int DEI min m(Z + 1.5) m(Z + 1.8) m(Z + 1.4) m(Z + 1.2)
Max Maj Diam. Int. DEI max DEI min + (T + λ)/tan αD (see Note 1)
Form Diam, Int. DFIm(Z + 1) + 2cF m(Z + 1) + 2cF m(Z + 0.9) + 2cF m(Z + 0.8) + 2cF
Min Minor Diam, Int DII min DFE + 2cF (see Note 2)
Max Minor Diam, Int DII max DII min + (0.2m0.667 − 0.01m−0.5)a
Cir Space Width,
Basic Ebsc 0.5πm
Min Effective EV min0.5πm
Max Actual E max
EV min + (T + λ) for classes 4, 5, 6, and 7 (see Table 4 for T + λ)
Min Actual E min EV min + λ (see text on page 2153 for λ)
Max Effective EV max E max − λ (see text on page 2153 for λ)
Max Major Diam, Ext DEE max m(Z + 1) − es/tan αD
b m(Z + 1) − es/tan αD
b m(Z + 0.9) − es/tan αD
b m(Z + 0.8) − es/tan αD
b
Min Major Diam. Ext DEE min DEE max − (0.2m0.667 − 0.01m−0.5)a
Form Diam, External DFE
Max Minor Diam, Ext DIE max m(Z − 1.5) − es/tan αD
b m(Z − 1.8) − es/tan αD
b m(Z − 1.4) − es/tan αD
b m(Z − 1.2) − es/tan αD
b
20.5DB ()2 0.5D α sin D
hs
0.5es
α tan D
---------------

 +
α sin D
-------------------------------- –
2
+ ×METRIC MODULE INVOLUTE SPLINES 2152
Note 1: Use (T + λ) for class 7 from Table 4.
Note 2: For all types of fit, always use the DFE value corresponding to the H/h fit.
Fit Classes: Four classes of side fit splines are provided: spline fit class H/h having a minimum effective clearance, cv = es = 0; classes H/f, H/e, and
H/d having tooth thickness modifications, es, of f, e, and d, respectively, to provide progressively greater effective clearance cv, The tooth thickness
modifications h, f, e, and d in Table 3 are fundamental deviations selected from ISO R286, “ISO System of Limits and Fits.” They are applied to the
Min Minor Diam, Ext DIE min DIE max − (T + λ)/tan αD (see Note 1)
Cir Tooth Thick,
Basic Sbsc 0.5πm
Max Effective SV max Sbsc − es
Min Actual S min SV max − (T + λ) for classes 4, 5, 6, and 7 (see Table 4 for T + λ)
Max Actual S max SV max − λ (see text on page 2153 for λ)
Min Effective SV min S min + λ (see text on page 2153 for λ)
Total Tolerance on Circular Space
Width or Tooth Thickness
(T + λ)See formulas in Table 4
Machining Tolerance on Circular Space
Width or Tooth Thickness
TT = (T + λ) from Table 4 − λ from text on page 2153.
Effective Variation Allowed on Circular
Space Width or Tooth Thickness
λ See text on page 2153.
Form Clearance cF 0.1m
Rack Dimension hs 0.6m(see Fig. 1a)0.6m(see Fig. 1b)0.55m(see Fig. 1c)0.5m(see Fig. 1d)
a
Values of (0.2m0.667 − 0.01m−0.5) are as follows: for 10 module, 0.93; for 8 module, 0.80; for 6 module, 0.66; for 5 module, 0.58; for 4 module, 0.50; for 3 module, 0.41;
for 2.5 module, 0.36; for 2 module, 0.31; for 1.75 module, 0.28; for 1.5 module, 0.25; for 1.25 module, 0.22; for 1 module, 0.19; for 0.75 module, 0.15; for 0.5 module,
0.11; and for 0.25 module, 0.06.
b
See Table 6 for values of es/tan α D.
Table 2. Formulas for Dimensions and Tolerances for All Fit Classes—Metric Module Involute Splines
TermSymbol
Formula
30-Degree Flat Root30-Degree Fillet Root37.5-Degree Fillet Root45-Degree Fillet Root
0.5 to 10 module0.5 to 10 module0.5 to 10 module0.25 to 2.5 moduleMETRIC MODULE INVOLUTE SPLINES2153
external spline by shifting the tooth thickness total tolerance below the basic tooth thick-
ness by the amount of the tooth thickness modification to provide a prescribed minimum
effective clearance cv.
Table 3. Tooth Thickness Modification, es, for Selected Spline Fit Classes
Note: The values listed in this table are taken from ISO R286 and have been computed on the basis
of the geometrical mean of the size ranges shown. Values in boldface type do not comply with any
documented rule for rounding but are those used by ISO R286; they are used in this table to comply
with established international practice.
Basic Rack Profiles: The basic rack profile for the standard pressure angle splines are
shown in see Fig. 1a,  1b,  1c, and  1d. The dimensions shown are for maximum material
condition and for fit class H/h.
Spline Machining Tolerances and Variations.—The total tolerance (T + λ), Table 4, is
the sum of Effective Variation, λ, and a Machining Tolerance, T.
Table 4. Space Width and Tooth Thickness Total Tolerance, (T + λ), in Millimeters
Effective Variation: The effective variation, λ, is the combined effect that total index
variation, positive profile variation, and tooth alignment variation has on the effective fit of
mating involute splines. The effect of the individual variations is less than the sum of the
allowable variations because areas of more than minimum clearance can have profile,
tooth alignment, or index variations without changing the fit. It is also unlikely that these
variations would occur in their maximum amounts simultaneously on the same spline. For
this reason, total index variation, total profile variation, and tooth alignment variation are
used to calculate the combined effect by the following formula:
The above variation is based upon a length of engagement equal to one-half the pitch diam-
eter of the spline; adjustment of λ may be required for a greater length of engagement. For-
mulas for values of Fp,  ff
, and Fβ used in the above formula are given in Table 5.
Pitch
Diameter
in mm,
D
External Splinesa
a
Internal splines are fit class H and have space width modification from basic space width equal to
zero; thus, an H/h fit class has effective clearance cv = 0.
Pitch
Diameter
in mm,
D
External Splinesa
Selected Fit ClassSelected Fit Class
defhdefh
Tooth Thickness Modification (Reduc-
tion) Relative to Basic Tooth Thickness
at Pitch Diameter, es, in mm
Tooth Thickness Modification (Reduc-
tion) Relative to Basic Tooth Thickness
at Pitch Diameter, es, in mm
≤ 30.0200.0140.0060> 120 to 1800.1450.0850.0430
> 3 to 60.0300.0200.0100> 180 to 2500.1700.1000.0500
> 6 to 10 0.040 0.0250.0130> 250 to 3150.1900.1100.0560
> 10 to 180.0500.0320.0160> 315 to 4000.210 0.1250.062 0
> 18 to 300.0650.0400.0200> 400 to 5000.2300.135 0.068 0
> 30 to 500.0800.0500.0250> 500 to 6300.2600.145 0.076 0
> 50 to 800.1000.0600.0300> 630 to 8000.2900.160 0.080 0
> 80 to 1200.120 0.072 0.0360> 800 to 10000.320 0.1700.086 0
Spline
Toler-
ance
Class
Formula for
Total Toler-
ance,
(T + λ)
Spline
Toler-
ance
Class
Formula for
Total Toler-
ance,
(T + λ)
In these formulas, i* and i** are tolerance units
based upon pitch diameter and tooth thickness,
respectively:
410i* + 40i**625i* + 100i**
516i* + 64i**740i* + 160i**
i∗ 0.0010.45 D 3 0.001D + ()for D500 ≤ mm =
0.0010.004D 2.1 + () for D500mm > =
i**0.0010.45 Sbsc
3 0.001Sbsc + () =
λ 0.6 Fp ()2 f
f
()2 Fβ ()2 ++ millimeters =2154METRIC MODULE INVOLUTE SPLINES
Table 5. Formulas for Fp, ff
 , and Fβ used to calculate λ
g = length of spline in millimeters.
Table 6. Reduction, es/tan αD, of External Spline Major and Minor Diameters
Required for Selected Fit Classes
These values are used with the applicable formulas in Table 2.
Machining Tolerance: A value for machining tolerance may be obtained by subtracting
the effective variation, λ, from the total tolerance (T + λ). Design requirements or specific
processes used in spline manufacture may require a different amount of machining toler-
ance in relation to the total tolerance.
Spline
Toler-
ance
Class
Total Index
Variation, in mm,
Fp
Total Profile
Variation, in mm,
ff
Total Lead
Variation, in mm,
Fβ
40.001 [1.6m(1 + 0.0125Z) + 10]
50.001 [2.5m(1 + 0.0125Z) + 16]
60.001 [4m(1 + 0.0125Z) + 25]
70.001 [6.3m(1 + 0.0125Z) + 40]
Pitch
Diameter
D in mm
Standard Pressure Angle, in Degrees
3037.5453037.5453037.545All
Classes of Fit
defh
es/tan αD in millimeters
≤30.0350.0260.0200.0240.0180.0140.0100.0080.0060
>3 to 60.0520.0390.0300.0350.0260.0200.0170.0130.0100
> 6 to 100.0690.0520.0400.0430.0330.0250.0230.0170.0130
> 10 to 180.0870.0650.0500.0550.0420.0320.0280.0210.0160
> 18 to 300.1130.0850.0650.0690.0520.0400.0350.0260.0200
> 30 to 500.1390.1040.0800.0870.0650.0500.0430.0330.0250
> 50 to 800.1730.1300.1000.1040.0780.0600.0520.0390.0300
> 80 to 1200.2080.1560.1200.1250.0940.0720.0620.0470.0360
> 120 to 1800.2510.1890.1450.1470.1110.0850.0740.0560.0430
> 180 to 2500.2940.2220.1700.1730.1300.1000.0870.0650.0500
> 250 to 3150.3290.2480.1900.1910.1430.1100.0970.0730.0560
> 315 to 4000.3640.2740.2100.2170.1630.1250.1070.0810.0620
> 400 to 5000.3980.3000.2300.2340.1760.1350.1180.0890.0680
> 500 to 6300.4500.3390.2600.2510.1890.1450.1320.0990.0760
> 630 to 8000.5020.3780.2900.2770.2090.1600.1390.1040.0800
> 800 to 10000.5540.4170.3200.2940.2220.1700.1490.1120.0860
0.0012.5 mZπ 2 ⁄ 6.3 + () 0.0010.8 g 4 + ()
0.0013.55 mZπ 2 ⁄ 9 + () 0.0011.0 g 5 + ()
0.0015 mZπ 2 ⁄ 12.5 + () 0.0011.25 g 6.3 + ()
0.0017.1 mZπ 2 ⁄ 18 + () 0.0012 g 10 + ()METRIC MODULE INVOLUTE SPLINES2155
Fig. 1a. Profile of Basic Rack for 30° Flat Root Spline
Fig. 1b. Profile of Basic Rack for 30° Fillet Root Spline
Fig. 1c. Profile of Basic Rack for 37.5° Fillet Root Spline
Fig. 1d. Profile of Basic Rack for 45° Fillet Root Spline24280