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Straight Cylindrical Involute Splines


Important note:
The information on this page is not detailed and has been obtained by reference to the relevant BS and Machinerys handbook.    Detail design should be completed using the relevant standards or quality reference sources.

Introduction

The notes and tables below relate to straight cylindrical involute splines in accordance with BS ISO 4156:2005-1 Straight cylindrical involute splines. Metric module, side fit.
It is emphasised that the splines identified are side fit with the centering based on the sides of the splines

Involute splines are the predominant form bacause they are stronger than straight sided splines and are easier to cut and the fit.  The external spline can be formed either by hobbing or by a gear shaper.    Internal splines are formed by broaching or by a gear shaper.    To control tolerances , the minimum efffective space width and the minimum major diameter of the internal spline are held to basic dimensions .    The external spline is varied to obtain the desired fit.

The very simplest method of initially selecting of involute spline based on a shaft dia is to arrive at an initial Pitch circle dia (D) and a module (m).     eg. a spline for a 50mm OD spline with say a module of 2mm would have a PCD (D) of 50 - 2 = 48mm. The number of teeth = D/m and as an whole number of teeth is required a value of D = 48mm is easily selected with number of teeth z =24 teeth.    The detailed manufacturing requirements are obtained using the various notes and tables in the relevant standard / detailed technical publications.    The notes and tables below provide outline information.

The fit of the spline ( interference , close, loose etc ) is primariy specified based on the ISO system of limits and fits as detailed in BS EN 20286-1/2. Refer to webpage ISO limits..

Shafts connections based on involute splines are suitable for transfering of high, cyclical and shock torsional moments.    Involute splines are used for fixed and for sliding connections of shafts with hubs..

The splined profile is shaped as involute toothing in the cross section, with nominal pressure angles of the profile 30, 37.5 or 45.

It is centered to the outer diameter or sides of the teeth. Centering to the diameter is more accurate. Centering to sides is more economical and is used much more frequently in practice.(see figure below )

The groove bottom can be flat or rounded.

BS ISO 4156 is based on the following modules.

For pressure angles of 30 and 37,5 the modules 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


Male Involute Spline


Advantages of the involute splines compared with keyways:

Lower pressures than couplings with keys, higher loading capacity of the coupling
Lower wear of sliding couplings
Suitable also for cyclical torsional moments
Easy assembly and disassembly of the coupling

Advantages of involute compared to straight splines

Higher number of teeth resulting in lower pressures and higher loading capacity of the coupling
More uniform distribution of forces along the perimeter
Option of fine adjustment of the hub on the shaft)
Stronger shaft the shaft, lower notch coefficient
Economical lot production using a hobbing method
High accuracy of production similarly as with accurate gears

Disadvantages of the Involute Splines

More complicated to engineer
Higher production costs than couplings with keys
Higher notch coefficient than couplings with keys
Difficult execution of alignment and perpendicularity of the coupling
non-parallelism of sides of the teeth causes additional radial forces in the coupling; these forces then try to open the hub

Standards

BS ISO 4156:2005_1: Straight cylindrical involute splines. Metric module, side fit. Generalities
BS ISO 4156:2005_2: Straight cylindrical involute splines. Metric module, side fit. Dimensions
BS ISO 4156:2005_3: Straight cylindrical involute splines. Metric module, side fit. Inspection



Designation of involute splines

An example set of designations for a mating spline pair with 32 teeth, 2,5 module, with a 30pressure angle, a fillet root and a class 5 fit is...

Mating: INT/EXT 32z 2,5m 30R 5H/5f ISO 4156
Internal spline: INT 32z 2,5m 30R 5H ISO 4156
External spline: EXT 32z 2,5m 30R 5f ISO 4156



Pressure Angle α degree (o)
Pressure Angle
At Pitch Diameter
αD degree (o)
Number of teeth z -
Module m D / z
Pitch (Circular) p m.π
Basic Tooth thickness
Circular
S p/2
Basic space width
Circular
E p/2
Effective space width
Circular (minimum)
EV min p/2
Pitch diameter D m.z
Base diameter Db m z cos α D
Base pitch pb m π cos α D
Fundamental deviation, external es v Tooth mod'n factor -Results from fit (h,f,e,d) see table below
Minimum major diameter, internal
30, flat root
30, fillet root
37,5, fillet root
45, fillet root
Dei min       
m (z + 1,5)
m (z + 1,8)
m. (z + 1,4)
m. (z + 1,2)
Maximum major diameter, internal Dei maxD ei min + (T + λ ) / tan α D
Minimum form diameter, internal
30, flat root &fillet
37,5, fillet root
45, fillet root
DFi min       
m (z +1)+2.cF
m (z +0,9)+2.cF
m (z +0,8)+2.cF)
Minimum minor diameter, internal Di i min DFe max + 2 cF
Maximum minor diameter, internal:
m =< 0,75
0,75 < m < 2
m > 2
Di i max
Dii min +  IT 10
Dii min +  IT 11
Dii min +  IT 12
Maximum actual Space width
class 4
class 5
class 6
class 7
Emax       
EV min + (T + λ)
EV min + (T + λ)
EV min + (T + λ)
EV min + (T + λ))
Minimum actual Space Width EminEv.min + λ
Maximum effective Space Width EV maxEv.min + TV
Maximum major dia external.
30, flat root & fillet
37,5, fillet root
45, fillet root
Dee max       
m (z +1)+ esv  /  (tan αD )
m (z + 0,9)+ esv  /  (tan αD )
m (z + 0,8)+ esv   /  (tan αD )
Minimum major diameter, external:
m =< 0,75
0,75 < m < 2
m = > 2
Dee min
Dee max - IT 10
Dee max - IT 11
Dee max - IT 12
Maximum form diameter DFe max
Maximum minor diameter, external
30, flat root
30, fillet root
37,5, fillet root
45, fillet root
Die max       
m (z - 1,5)+ esv  /  (tan αD)
m (z -1,8)+ esv /  (tan αD)
m. (z - 1,4) + esv   /  (tan αD)
m. (z -1,2 ) + esv   /  (tan αD)
Minimum minor, external Die minD ie max - (T + λ )  / tan α D
Maximum effective tooth thickness S V max S + esV
Minimum actual tooth thickness
class 4
class 5
class 6
class 7
Smin       
SV max - (T + λ)
SV max - (T + λ)
SV max - (T + λ)
SV max - (T + λ)
Maximum actual tooth thicknes S maxSv.max - λ
Minimum effective tooth thickness S V minSv.max - TV
Total tolerance,
Space width or tooth thickness
T + λSee table below
Maximum effective clearance C V maxEv max - S v min
Minimum effective clearance C V minEv min - S v max
Form tooth height h sSee sketch and table for basic rack profile below

Note: The Form circle is the circle used to define the depth of involute profile control.
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



Basic Rack Shape



ParameterPressure Angle
30o37,5o45o
Flat rootFillet root
Major Space height0,75.m 0,9.m 0,7.m 0,6. m
Major Tooth height0,5.m 0,5.m 0,45.m 0,4. m
Form tooth height (hs0,6.m 0,6.m 0,55.m 0,5. m
Minor tooth height0,75.m 0,9.m 0,7.m 0,6. m
Root radius (ρFi )0,2.m 0,4.m 0,3.m 0,25. m
Root radius (ρFe )0,2.m 0,4.m 0,3.m 0,25. m
Form radius (cF)0,1.m 0,1.m 0,1.m 0,1. m




Table showing tooth thickness modification (esv   ) of external splines relative to basic tooth thickness

Important Note: These values are all reductions and so they are negative (-ve) values.



Pitch Dia. D
(mm)
Selected fit class
defh
Thickness reduction (esv) (mm)
= < 3 0,020 0,14 0,006 0
3 to 6(inc) 0,030 0,020 0,010 0
6 to 10(inc) 0,04 0,025 0,013 0
10 to 18(inc) 0,05 0,032 0,016 0
18 to 30(inc) 0,065 0,040 0,020 0
30 to 50(inc) 0,080 0,050 0,025 0
50 to 80(inc) 0,10 0,060 0,030 0
80 to 120(inc) 0,12 0,072 0,036 0


Table showing total Tolerance (T + λ) for Space width and Tooth thickness

The Total Tolerance (T + λ) is the sum of the Machining Tolerance (T) and the Effective variation (λ)



Spline Tolerance class(T + λ)Formula for (T + λ) formula for i1 & i2
410i1 + 40i2 i 1 = 0,001[0,453.Sqrt (D) +0,001D ]
i 2 = 0,001[0,453.Sqrt (S +0,001 S ]
Note:    i 1 applies for D < 500mm
516i1 + 64i2
625i1 + 100i2
740i1 + 160i2

The effective variation is the combined effect of the total index variation (Fp ), the positive profile variation (ff ) and the tooth alignment variation ( F β ) . These combined effect i for convenience calculated using the following equation



Table showing equations for (Fp ), ( ff ) and ( F β )



Spline
Tolerance class
Fp ff F β
4 0,001.[ 2,5 Sqrt(M.z.β /2 ) + 6,3] 0,001 [1,6.m (1+0,012z) + 10] 0,01 [0,8.sqrt(g) + 4]
5 0,001.[ 3,55 Sqrt(M.z.β /2 ) + 9] 0,001 [2,5.m (1+0,012z) + 16] 0,01 [1,0.sqrt(g) + 5]
6 0,001.[ 5 Sqrt(M.z.β /2 ) + 12,5] 0,001 [4.m (1+0,012z) + 25] 0,01 [1,25.sqrt(g) + 6,3]
6 0,001.[ 7,1 Sqrt(M.z.β /2 ) + 18] 0,001 [6,3.m (1+0,012z) + 40] 0,01 [2,0.sqrt(g) + 10]


Table showing values for esv   / (tan αD ) for different Pressure angles and Fites



Pitch Dia.
D (mm)
α = 30α = 37,5α = 45 α = 30α = 37,5α = 45 α = 30α = 37,5α = 45 α = All
fit class = dfit class = efit class = f fit class = h
esv    / (tan αD ) - (mm)
=< 3 0,035 0,026 0,020 0,024 0,018 0,014 0,010 0,008 0,006 0
3 to 6 inc.0,035 0,039 0,030 0,035 0,026 0,020 0,017 0,013 0,010 0
6 to 10 inc. 0,052 0,052 0,040 0,043 0,033 0,025 0,023 0,017 0,013 0
10 to 18 inc. 0,069 0,065 0,050 0,055 0,042 0,032 0,028 0,021 0,016 0
18 to 30 inc. 0,087 0,085 0,065 0,069 0,052 0,040 0,035 0,026 0,020 0
30 to 50 inc. 0,113 0,104 0,080 0,087 0,065 0,050 0,043 0,033 0,025 0
50 to 80 inc. 0,139 0,130 0,100 0,104 0,078 0,060 0,052 0,039 0,030 0
80 to 120 inc. 0,173 0,156 0,120 0,125 0,094 0,072 0,062 0,047 0,036 0
180 to 250 inc. 0,208 0189 0,145 0,147 0,111 0,085 0,074 0,056 0,043 0
250 to 315 inc. 0,251 0,222 0,170 0,173 0,130 0,100 0,087 0,065 0,050 0
315 to 400 inc. 0,294 0,248 0,190 0,191 0,143 0,110 0,097 0,073 0,056 0



Sites Providing Relevant Information
  1. Mitcalc.com...Excel based programme allowing detailed design of shaft connection (19 Eur)
  2. Tasman industires...Supplier of keys
  3. Bonut Engineering...supplier of keys
  4. Technifast Ltd...Supplier of fasteners and keys.

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Last Updated 19/01/2013