This
article will discuss drive shaft design concepts and shaft design formulas for
shafts subjected to combined bending and torsion loading.
In a
previous article we have seen how to design a drive shaft only for
bending. But, for many practical shaft design problems you have to
consider bending as well as torsional load when designing the shaft. Such drive
shaft design problem can be solved in two ways:
○ By calculating the
equivalent bending moment and toque of bending and torsion.
○ By using the
principle stress concept.
In this
article we will limit our discussion to the equivalent bending moment and
torque method.
○ Equivalent bending
moment equation:
Meqv. = 0.5 [M + SQRT (M^2 + T^2)]……………..eqn.1.1
○ Equivalent torque
equation:
Teqv.
= SQRT (M^2 + T^2)………………………..eqn.1.2
○ Equation of bending
stress:
Tb =
(32*M/(pi*d^3)………………………………eqn.1.3
○ Equation for
torsional shear stress:
St =
(16*T)/(pi*d^3)………………………….eqn.1.4
Where,
Meqv. – Equivalent bending moment
M –
Bending moment
T – Torque
Tb –
Bending stress
St –
Shear stress
d –
Diameter of the circular shaft
Refer the
picture above, apart from the self weight (1000N) of the pulley a torque (1000
N-mm) due to belt tension is also applied on the shaft. Assuming the maximum
allowable stress in tension for the shaft material as 40 MPa, The following
steps need to be performed for obtaining the minimum diameter of the shaft as
per maximum principle stress theory:
○ Maximum bending
moment applied on the shaft = 1000 * 100 = 100000 N-mm
○ Applied torque is
given as 1000 N-mm.
○ Equivalent bending
moment (from eqn.1.1):
Meqv.= 1207 Mpa
○ Equivalent torque (
from eqn1.2):
Teqv.= 1414 N-mm
○ Maximum principle
stress (from eqn 1.3):
Sigma1
= Tb= (12301/d^3)
○ Now for getting
minimum shaft diameter as per maximum principle stress theory, we have to
equate Sigma1 with allowable stress, hence:
40 =
(12301/d^3)
Or, d
= 6.7 mm
Most of
the time you will come across a shaft design problem with the combination of
bending and torsional loading. Accurate use of the four shaft design formulae
will lead to the solution for most cases. You can get help from the FEA
tools as well.