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Contents
Shafts 509
C
H
A
P
T
E
R 14
Shafts
1. Introduction.
2. Material Used for Shafts.
3. Manufacturing of Shafts.
4. Types of Shafts.
5. Standard Sizes of
Transmission Shafts.
6. Stresses in Shafts.
7. Maximum Permissible
Working Stresses for
Transmission Shafts.
8. Design of Shafts.
9. Shafts Subjected to Twisting
Moment Only.
10. Shafts Subjected to Bending
Moment Only.
11. Shafts Subjected to
Combined Twisting Moment
and Bending Moment.
12. Shafts Subjected to 14.1 Introduction
Fluctuating Loads.
A shaft is a rotating machine element which is used
13. Shafts Subjected to Axial
Load in addition to
to transmit power from one place to another. The power is
Combined Torsion and delivered to the shaft by some tangential force and the
Bending Loads. resultant torque (or twisting moment) set up within the shaft
14. Design of Shafts on the Basis permits the power to be transferred to various machines
of Rigidity. linked up to the shaft. In order to transfer the power from
one shaft to another, the various members such as pulleys,
gears etc., are mounted on it. These members along with
the forces exerted upon them causes the shaft to bending.
In other words, we may say that a shaft is used for the
transmission of torque and bending moment. The various
members are mounted on the shaft by means of keys or
splines.
Notes: 1. The shafts are usually cylindrical, but may be square or
cross-shaped in section. They are solid in cross-section but
sometimes hollow shafts are also used.
509
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Contents
510 A Textbook of Machine Design
2. An axle, though similar in shape to the shaft, is a stationary machine element and is used for the
transmission of bending moment only. It simply acts as a support for some rotating body such as hoisting drum,
a car wheel or a rope sheave.
3. A spindle is a short shaft that imparts motion either to a cutting tool (e.g. drill press spindles) or to a
work piece (e.g. lathe spindles).
14.2 Material Used for Shafts
The material used for shafts should have the following properties :
1. It should have high strength.
2. It should have good machinability.
3. It should have low notch sensitivity factor.
4. It should have good heat treatment properties.
5. It should have high wear resistant properties.
The material used for ordinary shafts is carbon steel of grades 40 C 8, 45 C 8, 50 C 4 and 50 C 12.
The mechanical properties of these grades of carbon steel are given in the following table.
Table 14.1. Mechanical properties of steels used for shafts.
Indian standard designation Ultimate tensile strength, MPa Yield strength, MPa
40 C 8 560 - 670 320
45 C 8 610 - 700 350
50 C 4 640 - 760 370
50 C 12 700 Min. 390
When a shaft of high strength is required, then an alloy steel such as nickel, nickel-chromium or
chrome-vanadium steel is used.
14.3 Manufacturing of Shafts
Shafts are generally manufactured by hot rolling and finished to size by cold drawing or turning
and grinding. The cold rolled shafts are stronger than hot rolled shafts but with higher residual stresses.
The residual stresses may cause distortion of the shaft when it is machined, especially when slots or
keyways are cut. Shafts of larger diameter are usually forged and turned to size in a lathe.
14.4 Types of Shafts
The following two types of shafts are important from the subject point of view :
1. Transmission shafts. These shafts transmit power between the source and the machines
absorbing power. The counter shafts, line shafts, over head shafts and all factory shafts are transmission
shafts. Since these shafts carry machine parts such as pulleys, gears etc., therefore they are subjected
to bending in addition to twisting.
2. Machine shafts. These shafts form an integral part of the machine itself. The crank shaft is
an example of machine shaft.
14.5 Standard Sizes of Transmission Shafts
The standard sizes of transmission shafts are :
25 mm to 60 mm with 5 mm steps; 60 mm to 110 mm with 10 mm steps ; 110 mm to 140 mm
with 15 mm steps ; and 140 mm to 500 mm with 20 mm steps.
The standard length of the shafts are 5 m, 6 m and 7 m.
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Shafts 511
14.6 Stresses in Shafts
The following stresses are induced in the shafts :
1. Shear stresses due to the transmission of torque (i.e. due to torsional load).
2. Bending stresses (tensile or compressive) due to the forces acting upon machine elements
like gears, pulleys etc. as well as due to the weight of the shaft itself.
3. Stresses due to combined torsional and bending loads.
14.7 Maximum Permissible Working Stresses for Transmission Shafts
According to American Society of Mechanical Engineers (ASME) code for the design of
transmission shafts, the maximum permissible working stresses in tension or compression may be
taken as
(a) 112 MPa for shafts without allowance for keyways.
(b) 84 MPa for shafts with allowance for keyways.
For shafts purchased under definite physical specifications, the permissible tensile stress (σt)
may be taken as 60 per cent of the elastic limit in tension (σel), but not more than 36 per cent of the
ultimate tensile strength (σu). In other words, the permissible tensile stress,
σt = 0.6 σel or 0.36 σu, whichever is less.
The maximum permissible shear stress may be taken as
(a) 56 MPa for shafts without allowance for key ways.
(b) 42 MPa for shafts with allowance for keyways.
For shafts purchased under definite physical specifications, the permissible shear stress (τ) may
be taken as 30 per cent of the elastic limit in tension (σel) but not more than 18 per cent of the ultimate
tensile strength (σu). In other words, the permissible shear stress,
τ = 0.3 σel or 0.18 σu, whichever is less.
14.8 Design of Shafts
The shafts may be designed on the basis of
1. Strength, and 2. Rigidity and stiffness.
In designing shafts on the basis of strength, the following cases may be considered :
(a) Shafts subjected to twisting moment or torque only,
(b) Shafts subjected to bending moment only,
(c) Shafts subjected to combined twisting and bending moments, and
(d) Shafts subjected to axial loads in addition to combined torsional and bending loads.
We shall now discuss the above cases, in detail, in the following pages.
14.9 Shafts Subjected to Twisting Moment Only
When the shaft is subjected to a twisting moment (or torque) only, then the diameter of the shaft
may be obtained by using the torsion equation. We know that
T τ
= ...(i)
J r
where T = Twisting moment (or torque) acting upon the shaft,
J = Polar moment of inertia of the shaft about the axis of rotation,
τ = Torsional shear stress, and
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Contents
Shafts 509
C
H
A
P
T
E
R 14
Shafts
1. Introduction.
2. Material Used for Shafts.
3. Manufacturing of Shafts.
4. Types of Shafts.
5. Standard Sizes of
Transmission Shafts.
6. Stresses in Shafts.
7. Maximum Permissible
Working Stresses for
Transmission Shafts.
8. Design of Shafts.
9. Shafts Subjected to Twisting
Moment Only.
10. Shafts Subjected to Bending
Moment Only.
11. Shafts Subjected to
Combined Twisting Moment
and Bending Moment.
12. Shafts Subjected to 14.1 Introduction
Fluctuating Loads.
A shaft is a rotating machine element which is used
13. Shafts Subjected to Axial
Load in addition to
to transmit power from one place to another. The power is
Combined Torsion and delivered to the shaft by some tangential force and the
Bending Loads. resultant torque (or twisting moment) set up within the shaft
14. Design of Shafts on the Basis permits the power to be transferred to various machines
of Rigidity. linked up to the shaft. In order to transfer the power from
one shaft to another, the various members such as pulleys,
gears etc., are mounted on it. These members along with
the forces exerted upon them causes the shaft to bending.
In other words, we may say that a shaft is used for the
transmission of torque and bending moment. The various
members are mounted on the shaft by means of keys or
splines.
Notes: 1. The shafts are usually cylindrical, but may be square or
cross-shaped in section. They are solid in cross-section but
sometimes hollow shafts are also used.
509
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Contents
510 A Textbook of Machine Design
2. An axle, though similar in shape to the shaft, is a stationary machine element and is used for the
transmission of bending moment only. It simply acts as a support for some rotating body such as hoisting drum,
a car wheel or a rope sheave.
3. A spindle is a short shaft that imparts motion either to a cutting tool (e.g. drill press spindles) or to a
work piece (e.g. lathe spindles).
14.2 Material Used for Shafts
The material used for shafts should have the following properties :
1. It should have high strength.
2. It should have good machinability.
3. It should have low notch sensitivity factor.
4. It should have good heat treatment properties.
5. It should have high wear resistant properties.
The material used for ordinary shafts is carbon steel of grades 40 C 8, 45 C 8, 50 C 4 and 50 C 12.
The mechanical properties of these grades of carbon steel are given in the following table.
Table 14.1. Mechanical properties of steels used for shafts.
Indian standard designation Ultimate tensile strength, MPa Yield strength, MPa
40 C 8 560 - 670 320
45 C 8 610 - 700 350
50 C 4 640 - 760 370
50 C 12 700 Min. 390
When a shaft of high strength is required, then an alloy steel such as nickel, nickel-chromium or
chrome-vanadium steel is used.
14.3 Manufacturing of Shafts
Shafts are generally manufactured by hot rolling and finished to size by cold drawing or turning
and grinding. The cold rolled shafts are stronger than hot rolled shafts but with higher residual stresses.
The residual stresses may cause distortion of the shaft when it is machined, especially when slots or
keyways are cut. Shafts of larger diameter are usually forged and turned to size in a lathe.
14.4 Types of Shafts
The following two types of shafts are important from the subject point of view :
1. Transmission shafts. These shafts transmit power between the source and the machines
absorbing power. The counter shafts, line shafts, over head shafts and all factory shafts are transmission
shafts. Since these shafts carry machine parts such as pulleys, gears etc., therefore they are subjected
to bending in addition to twisting.
2. Machine shafts. These shafts form an integral part of the machine itself. The crank shaft is
an example of machine shaft.
14.5 Standard Sizes of Transmission Shafts
The standard sizes of transmission shafts are :
25 mm to 60 mm with 5 mm steps; 60 mm to 110 mm with 10 mm steps ; 110 mm to 140 mm
with 15 mm steps ; and 140 mm to 500 mm with 20 mm steps.
The standard length of the shafts are 5 m, 6 m and 7 m.
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Contents
Shafts 511
14.6 Stresses in Shafts
The following stresses are induced in the shafts :
1. Shear stresses due to the transmission of torque (i.e. due to torsional load).
2. Bending stresses (tensile or compressive) due to the forces acting upon machine elements
like gears, pulleys etc. as well as due to the weight of the shaft itself.
3. Stresses due to combined torsional and bending loads.
14.7 Maximum Permissible Working Stresses for Transmission Shafts
According to American Society of Mechanical Engineers (ASME) code for the design of
transmission shafts, the maximum permissible working stresses in tension or compression may be
taken as
(a) 112 MPa for shafts without allowance for keyways.
(b) 84 MPa for shafts with allowance for keyways.
For shafts purchased under definite physical specifications, the permissible tensile stress (σt)
may be taken as 60 per cent of the elastic limit in tension (σel), but not more than 36 per cent of the
ultimate tensile strength (σu). In other words, the permissible tensile stress,
σt = 0.6 σel or 0.36 σu, whichever is less.
The maximum permissible shear stress may be taken as
(a) 56 MPa for shafts without allowance for key ways.
(b) 42 MPa for shafts with allowance for keyways.
For shafts purchased under definite physical specifications, the permissible shear stress (τ) may
be taken as 30 per cent of the elastic limit in tension (σel) but not more than 18 per cent of the ultimate
tensile strength (σu). In other words, the permissible shear stress,
τ = 0.3 σel or 0.18 σu, whichever is less.
14.8 Design of Shafts
The shafts may be designed on the basis of
1. Strength, and 2. Rigidity and stiffness.
In designing shafts on the basis of strength, the following cases may be considered :
(a) Shafts subjected to twisting moment or torque only,
(b) Shafts subjected to bending moment only,
(c) Shafts subjected to combined twisting and bending moments, and
(d) Shafts subjected to axial loads in addition to combined torsional and bending loads.
We shall now discuss the above cases, in detail, in the following pages.
14.9 Shafts Subjected to Twisting Moment Only
When the shaft is subjected to a twisting moment (or torque) only, then the diameter of the shaft
may be obtained by using the torsion equation. We know that
T τ
= ...(i)
J r
where T = Twisting moment (or torque) acting upon the shaft,
J = Polar moment of inertia of the shaft about the axis of rotation,
τ = Torsional shear stress, and
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