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DESIGN OF SOLID TRANSMISSION SHAFT
ByANIMESH BHATTACHARYA
CLASS ROLL: Dx- 03 EXAM. ROLL: 111210003Semester: 6th Dept.: Mechanical Engineering
What is a Transmission Shaft?- It refers to a rotating machine element,
circular in cross-section, which supports transmission elements like gears, pulleys and sprockets and transmits power.
- In the industries, usually ‘stepped shaft’ is used.
DESIGN OF SOLID TRANSMISSION SHAFT
DESIGN OF SOLID TRANSMISSION SHAFT
Stepped Shaft:
Characteristics of Stepped Shaft:A shaft is always stepped with maximum
diameter in the middle and minimum diameter at the two ends, where bearings are mounted.
The steps on the shaft provide shoulders for positioning transmission elements like gears, pulleys and bearings.
DESIGN OF SOLID TRANSMISSION SHAFT
Characteristics of Stepped Shaft:The rounded-off portion between two cross-
sections of different diameters is called fillet. The fillet radius is provided to reduce the effect of stress-concentration due to abrupt change in the cross-section.
DESIGN OF SOLID TRANSMISSION SHAFT
Material of Shaft :Ordinary transmission shafts are made of
medium carbon steels with a carbon content from 0.15 to 0.40% such as 30C8 or 40C8. These steels are commonly called machinery steels.
For the requirement of higher strength, high carbon steels such as 45C8 or 50C8 or alloy steels are employed.
DESIGN OF SOLID TRANSMISSION SHAFT
Material of Shaft:Common grades of alloy steels used for
making transmission shafts are 16Mn5Cr4, 40Cr4Mo2, 16Ni5Cr2, 35Ni5Cr2 etc.
Commercial shafts are made of low carbon steels. They are produced by hot-rolling and finished to size either by cold-drawing or by turning and grinding.
DESIGN OF SOLID TRANSMISSION SHAFT
Shaft Design on Strength Basis:When the shaft is subjected to axial tensile
force, the tensile stress is given by, ; or, = …………….(1)When the shaft is subjected to pure bending
moment, the bending stress is given by, ; or, …..(2)
DESIGN OF SOLID TRANSMISSION SHAFT
Shaft Design on Strength Basis:When the shaft is subjected to pure
torsional moment, the torsional shear stress is given by, or, ……(3)
When the shaft is subjected to combination of loads, the principal stress and principal shear stress are obtained by constructing Mohr’s circle.
DESIGN OF SOLID TRANSMISSION SHAFT
Shaft Design on Strength Basis:Mohr’s Circle diagram –
DESIGN OF SOLID TRANSMISSION SHAFT
Shaft Design on Strength Basis: Let the normal stress be while the shear
stress is denoted by . So when both are there, from Mohr’s circle
principal stress is given by, + ……….(4) The maximum shear stress is given by, ……………..(5)
DESIGN OF SOLID TRANSMISSION SHAFT
Shaft Design on Strength Basis:Equations (1) to (5) are fundamental
equations for design of shafts.A shaft can be designed on the basis of
maximum principal stress theory or maximum shear stress theory. We shall apply these theories to transmission shafts subjected to combined bending and torsional moments.
DESIGN OF SOLID TRANSMISSION SHAFT
Maximum Principal Stress Theory:The theory states that the failure of the
mechanical component subjected to bi-axial or tri-axial stresses occurs when the maximum principal stress reaches the yield or ultimate strength of the material. This is called ‘Rankine’s Criterion’.
The maximum principal stress is . We have, ;
DESIGN OF SOLID TRANSMISSION SHAFT
Maximum Principal Stress Theory:Now from equation (4), we get the
following, +;Or, = ………... (6)The permissible value of maximum principal
stress is given by, ………………... (7) fs= factor of safety; = yield strength.
DESIGN OF SOLID TRANSMISSION SHAFT
Equations (6) and (7) are used to determine the shaft diameter on the basis of principal stress theory.
Experimental investigations suggest that maximum principal stress theory gives good predictions for brittle materials, but shafts are made of ductile material like steel and hence, this theory is not applicable to shaft design. We better use maximum shear stress theory.
DESIGN OF SOLID TRANSMISSION SHAFT
Maximum Shear Stress Theory:The theory states that the failure of a
mechanical component subjected to bi-axial or tri-axial stresses occurs when the maximum shear stress at any point in the component becomes equal to the maximum shear stress in the standard specimen of the tension test, when yielding starts. This is called ‘Tresca’s Criterion’.
The maximum shear stress is .
DESIGN OF SOLID TRANSMISSION SHAFT
Maximum Shear Stress Theory: In a similar way, as done in case of
maximum principal stress theory, here according to maximum shear stress theory, we have-
or, = …………. (8)
DESIGN OF SOLID TRANSMISSION SHAFT
According to maximum shear stress theory, and the permissible value of maximum shear stress is given by,
……………………… (9) Equations (8) and (9) are used to determine
the shaft diameter on the basis of maximum shear stress theory.
Finally we have the following two equations, =
=
DESIGN OF SOLID TRANSMISSION SHAFT
Equivalent Torsional Moment:The expression is called ‘equivalent
torsional moment’. It is defined as the torsional moment, which when acting alone, will produce the same torsional shear stress in the shaft as under the combined action of bending moment (and torsional moment ).
DESIGN OF SOLID TRANSMISSION SHAFT
Equivalent Bending Moment:The expression is called ‘equivalent
bending moment’. It is defined as the bending moment, which when acting alone, will produce the same bending stresses (tensile or compressive) in the shaft as under the combined action of bending moment (and torsional moment ).
DESIGN OF SOLID TRANSMISSION SHAFT
The concept of equivalent torsional moment is used in the design of shafts on the basis of maximum shear stress theory of failure.
The concept of equivalent bending moment is used in the design of shafts on the basis of maximum principal stress theory of failure.
DESIGN OF SOLID TRANSMISSION SHAFT
Shaft Design on Torsional Rigidity Basis: A transmission shaft is said to be rigid on the basis
of torsional rigidity, if it does not twist too much under the action of an external torque.
Similarly, the transmission shaft is said to be rigid on the basis of lateral rigidity, if it does not deflect too much under the action of external forces and bending moment.
In some applications, like machine tool spindles, it is necessary to design the shaft on the basis of torsional rigidity, i.e., on the basis of permissible angle of twist per metre length of shaft.
DESIGN OF SOLID TRANSMISSION SHAFT
Shaft Design on Torsional Rigidity Basis:The angle of twist (in radians) is given by, ; Converting from radians to degrees (θ), θ = x ;For solid circular shaft, , we’ve- θ = ……………….……. (10)
DESIGN OF SOLID TRANSMISSION SHAFT
Shaft Design on Torsional Rigidity Basis: Where, angle of twist (deg.) length of shaft subjected to twisting moment (mm) = torsional moment (N-mm)G = modulus of rigidity (N/ d = shaft diameter (mm) Equation (10) is used to design the shaft on the basis of
torsional rigidity. Permissible angle of twist for machine tool applications is per metre length. Modulus of rigidity for steel is 79,300 N/ or 80kN/(approx.).
DESIGN OF SOLID TRANSMISSION SHAFT
ASME Code for Shaft Design:According to this code, the permissible
shear stress for the shaft without keyways is taken as 30% of yield strength in tension or 18% of the ultimate strength of the material, whichever is minimum. Therefore,
, or, (whichever is minimum). If keyways are present, the above values
are to be reduced by 25%.
DESIGN OF SOLID TRANSMISSION SHAFT
ASME Code for Shaft Design:According to ASME code, the bending and
torsional moments are to be multiplied by factors and respectively, to account for shock and fatigue in operating condition.
= combined shock and fatigue factor applied to bending moment.= combined shock and fatigue factor applied to torsional moment.
DESIGN OF SOLID TRANSMISSION SHAFT
Table-1: Values of shock and fatigue factors
So, finally we have the following equations to determine the shaft diameter to design a solid transmission shaft,
= =
DESIGN OF SOLID TRANSMISSION SHAFT
Serial no.
Application
1. Load gradually applied 1.5 1.02. Load suddenly applied (minor shock) 1.5-2.0 1.0-1.53. Load suddenly applied (heavy shock) 2.0-3.0 1.5-3.0
DESIGN OF SOLID TRANSMISSION SHAFT