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Spline Transmitted Torque and Pressure Analysis Formula and Calculator

Gear Design and Engineering Data

Spline Transmitted Torque and Pressure Analysis Formula and Calculator

Splines are keys which are made integral with the shaft. They are used when there is a relative axial motion between the shaft and the hub. The gear shifting mechanism in automobile gearboxes requires such type of construction. Splines are cut on the shaft by milling and on the hub by broaching. A splined connection, with straight splines, is shown in Fig. 1.0. The following notations are used:

Preview Spline Transmitted Torque and Pressure Calculator

D = major diameter of splines (mm)
d = minor diameter of splines (mm)
l = length of hub (mm)
n = number of splines

The torque transmitting capacity of splines is given by,

Eq. 1.0
M_t = p_m · A · R_m

Where:
M_t = transmitted torque (N-mm)
p_m = permissible pressure on spline (N/mm²)
A = total area of splines (mm²)
R_m = mean radius of splines (mm)

The area A is given by,

Eq. 2.0,
A = .5 ( D - d ) · l · n

Eq. 3.0,
R_m = ( D + d ) / 4

Substituting the above values in Eq. (1.0),

Eq. 4.0
M_t = ( 1 / 8 ) · p_m · l · n · ( D² - d² )

Manipulated for Length of Hub
Eq. 5.0
l = ( 8 · M_t ) / [ p_m · n · ( D² - d² ) ]

Reference:

Design of Machine Elements, Third Edition
V. B Bhandari
Professor and Head Department of Mechanical Engineering
Vishwakarma Institute of Technology,
Pune, India

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