Involute Spline Calculation Formulas in Metric Units

Transferred torque

where:

	P	transferred power [Kw]
	n	speed [min -1 ]

Pressure on groove supporting surface

1. shaft inside diameter d _h > 0

a)

b) if d _min ≤d _h -> d _min = 1.1 d _h [mm]

c) if d _min ≤ 1.5 d _h -> d _min = 1.5 d _h [mm]

2. shaft inside diameter d _h = 0

where:

	d min	minimal shaft diameter [mm]
	d h	shaft inside diameter [mm]
	T	torque [Nm]
	K a	application factor
	K f	fatigue-life factor
	S v	desired safety
	τ Al	Allowable Shear Stress

Minimum splines length to transfer the torque

1. Fixed connection:
2. Flexible connection:
where:

	T	torque [Nm]
	K a	application factor
	K f	wear-life factor
	K w	application factor
	K m	load distribution factor
	S v	desired safety
	d s	middle diameter = (D + d) / 2 [mm]
	D	outside diameter of groove section [mm]
	d	inside diameter of groove section [mm]
	N	number of grooves [-]
	h	height of groove = (D - d) / 2 [mm]
	s	chamfer [mm]
	h st	connection height h st = h - 2 s [mm]
	p Dmin	allowable pressure on supporting surface of shaft or groove [MPa]

Allowable pressure

1. Fixed connection:
2. Flexible connection:
where:

	T	torque [Nm]
	K a	application factor
	K f	wear-life factor
	K w	application factor
	K m	load distribution factor
	S v	desired safety
	d s	middle diameter = (D + d) / 2 [mm]
	D	outside diameter of groove section [mm]
	d	inside diameter of groove section [mm]
	N	number of grooves [-]
	h	height of groove = (D - d) / 2 [mm]
	s	chamfer [mm]
	h st	connection height h st = h - 2 s [mm]
	l f	active key length [mm]

Strength Check

p _min ≤ p _ds

p _min ≤ p _dh

where:

	p min	minimal calculated h/2 pressure [MPa]
	p ds	allowable pressure in shaft [MPa]
	p dh	allowable pressure in hub [MPa]

Metric calculation according to CSN 01 4950

Bending stress

where:

s sf	shaft chordal tooth dedendum thickness	s sf = 2.17m
h	shaft tooth height	h = 1.1m - 0.05	centering to tooth sides, flat groove bottom
		h = 1.28m - 0.05	centering to tooth sides, round groove bottom
		h = 1.2 m	outside centering

Pressure on groove supporting groove surface

where:

h n

load bearing spline height

h n = 0.9 m - 0.05

Minimum splines length

L _min = max {L ₁ , L ₂ } [mm]

where:

Recommended values: L = (0.8 - 1.6) D

Splines check

p ≤ p _d and σ≤σ _d

where:

	P	transferred power [kW]
	n	speed [min -1 ]
	z	tooth number [-]
	p D	allowable pressure on contact surfaces of teeth [MPa]
	σ D	allowable bending stress [MPa]
	L	active spline length [mm]
	D	nominal spline diameter [mm]
	ϕ	factor of tooth side contact