Short Notes: Shafts | Short Notes for Mechanical Engineering PDF Download

 Page 1


Shafts
Shaft is a common machine element which is used to transmit rotary motion or 
torque.Shafts are supported on the bearings and transmit torque with the help of 
gears, belts and pulleys etc. Shafts are generally subjected to bending moment, 
torsion and axial force or a combination of these three.
Axle
• A stationary member used as support for rotating elements such as wheels, 
idler gears, etc.
Spindle
• A short shaft or axle (e.g., the headstock spindle of a lathe).
Stub shaft
• A shaft that is integral with a motor, engine or prime mover and is of a size, 
shape, and projection as to permit easy connection to other shafts.
Line shaft
• A shaft connected to a prime mover and used to transmit power to one or 
several machines.
Jackshaft
• A short shaft that connects a prime mover with a line shaft or a machine.
Flexible shaft
Page 2


Shafts
Shaft is a common machine element which is used to transmit rotary motion or 
torque.Shafts are supported on the bearings and transmit torque with the help of 
gears, belts and pulleys etc. Shafts are generally subjected to bending moment, 
torsion and axial force or a combination of these three.
Axle
• A stationary member used as support for rotating elements such as wheels, 
idler gears, etc.
Spindle
• A short shaft or axle (e.g., the headstock spindle of a lathe).
Stub shaft
• A shaft that is integral with a motor, engine or prime mover and is of a size, 
shape, and projection as to permit easy connection to other shafts.
Line shaft
• A shaft connected to a prime mover and used to transmit power to one or 
several machines.
Jackshaft
• A short shaft that connects a prime mover with a line shaft or a machine.
Flexible shaft
• A connector which permits transmission of motion between two members 
whose axes are at an angle with each other.
Shapes
• Most shafts are round but they can come in many different shapes including 
square and octagonal. Keys and notches can also result in some unique 
shapes.
Hollow Shafts Vs Solid Shafts
• Hollow shafts are lighter than solid shafts of comparable strength but are 
more expensive to manufacture.
• Thusly hollow shafts are primarily only used when weight is critical.
• For example, the propeller shafts on rear wheel drive cars require lightweight 
shafts in order to handle speeds within the operating range of the vehicle.
Shaft Design
Shafts are primarily designed on the basis of strength or rigidity or both.
• Based on Strength: To ensure that stress at any location of the shaft does not 
exceed the material yield stress.
• Based on Rigidity: To ensure that maximum deflection (because of bending) 
and maximum twist (due to torsion) of the shaft is within the allowable limits.
Note: Rigidity consideration is also very important in some cases for example 
position of a gear mounted on the shaft will change if the shaft gets deflected and 
if this value is more than some allowable limit, it may lead to high dynamic loads 
and noise in the gears.
General Principles
• Keep shafts short, with bearings close to the applied loads. This will reduce 
deflections and bending moments, and increases critical speeds.
• Place necessary stress raisers away from highly stressed shaft regions if 
possible. If unavoidable, use generous radii and good surface finishes. 
Consider local surface-strengthening processes (shot-peening or cold-rolling).
• Use inexpensive steels for deflection-critical shafts because all steels have 
essentially the same modulus of elasticity.
• Early in the design of any given shaft, an estimate is usually made of whether 
strength or deflection will be the critical factor. A preliminary design is based 
on that criterion; then, the remaining factor is checked.
Shaft Equations: All of the following equations are general equations; you may 
need to use modifying factors such as: loading factors, pulsating power source 
factors, safety factors, and stress concentration factors.
Basic equations in torsion:
• Solid round shaft:
16 - J 
r = ----- r
n D'
Page 3


Shafts
Shaft is a common machine element which is used to transmit rotary motion or 
torque.Shafts are supported on the bearings and transmit torque with the help of 
gears, belts and pulleys etc. Shafts are generally subjected to bending moment, 
torsion and axial force or a combination of these three.
Axle
• A stationary member used as support for rotating elements such as wheels, 
idler gears, etc.
Spindle
• A short shaft or axle (e.g., the headstock spindle of a lathe).
Stub shaft
• A shaft that is integral with a motor, engine or prime mover and is of a size, 
shape, and projection as to permit easy connection to other shafts.
Line shaft
• A shaft connected to a prime mover and used to transmit power to one or 
several machines.
Jackshaft
• A short shaft that connects a prime mover with a line shaft or a machine.
Flexible shaft
• A connector which permits transmission of motion between two members 
whose axes are at an angle with each other.
Shapes
• Most shafts are round but they can come in many different shapes including 
square and octagonal. Keys and notches can also result in some unique 
shapes.
Hollow Shafts Vs Solid Shafts
• Hollow shafts are lighter than solid shafts of comparable strength but are 
more expensive to manufacture.
• Thusly hollow shafts are primarily only used when weight is critical.
• For example, the propeller shafts on rear wheel drive cars require lightweight 
shafts in order to handle speeds within the operating range of the vehicle.
Shaft Design
Shafts are primarily designed on the basis of strength or rigidity or both.
• Based on Strength: To ensure that stress at any location of the shaft does not 
exceed the material yield stress.
• Based on Rigidity: To ensure that maximum deflection (because of bending) 
and maximum twist (due to torsion) of the shaft is within the allowable limits.
Note: Rigidity consideration is also very important in some cases for example 
position of a gear mounted on the shaft will change if the shaft gets deflected and 
if this value is more than some allowable limit, it may lead to high dynamic loads 
and noise in the gears.
General Principles
• Keep shafts short, with bearings close to the applied loads. This will reduce 
deflections and bending moments, and increases critical speeds.
• Place necessary stress raisers away from highly stressed shaft regions if 
possible. If unavoidable, use generous radii and good surface finishes. 
Consider local surface-strengthening processes (shot-peening or cold-rolling).
• Use inexpensive steels for deflection-critical shafts because all steels have 
essentially the same modulus of elasticity.
• Early in the design of any given shaft, an estimate is usually made of whether 
strength or deflection will be the critical factor. A preliminary design is based 
on that criterion; then, the remaining factor is checked.
Shaft Equations: All of the following equations are general equations; you may 
need to use modifying factors such as: loading factors, pulsating power source 
factors, safety factors, and stress concentration factors.
Basic equations in torsion:
• Solid round shaft:
16 - J 
r = ----- r
n D'
Hollow round shaft:
16 T D0 
x -(D * -D * )
Basic equation In bending:
• Solid shaft:
32 M 
a = --------
n D '
• Hollow shaft:
3 2 M D .
a = ------- ------ ° —
n-(D 0 - D t )
• Max shear stress:
71 D'
• Von Mises stress
£ T ' = — M + F D ): + 48 r : 
71 D'
• Torsional deflection:
6 =
32 T L 
7 i G DJ
• Factors of Safety:
° Max sheer stress theory
° Distortion energy
n
Where
• T = torque (lb-in, N-m),
• F = axial load (lb, N),
• Sy = yield strength,
• n = factor of safety,
• t = sheer stress (psi, Pa),
• D = diameter of solid shaft (in, m),
• D0 = outside diameter of solid shaft (in, m),
• Dj = inside diameter of solid shaft (in, m),
• M = bending moment (lb-in, N-m),
• L = length of shaft (in, m),
• G = sheer modulus (psi, Pa)
A.S.M.E. Code for Shaft Design
Page 4


Shafts
Shaft is a common machine element which is used to transmit rotary motion or 
torque.Shafts are supported on the bearings and transmit torque with the help of 
gears, belts and pulleys etc. Shafts are generally subjected to bending moment, 
torsion and axial force or a combination of these three.
Axle
• A stationary member used as support for rotating elements such as wheels, 
idler gears, etc.
Spindle
• A short shaft or axle (e.g., the headstock spindle of a lathe).
Stub shaft
• A shaft that is integral with a motor, engine or prime mover and is of a size, 
shape, and projection as to permit easy connection to other shafts.
Line shaft
• A shaft connected to a prime mover and used to transmit power to one or 
several machines.
Jackshaft
• A short shaft that connects a prime mover with a line shaft or a machine.
Flexible shaft
• A connector which permits transmission of motion between two members 
whose axes are at an angle with each other.
Shapes
• Most shafts are round but they can come in many different shapes including 
square and octagonal. Keys and notches can also result in some unique 
shapes.
Hollow Shafts Vs Solid Shafts
• Hollow shafts are lighter than solid shafts of comparable strength but are 
more expensive to manufacture.
• Thusly hollow shafts are primarily only used when weight is critical.
• For example, the propeller shafts on rear wheel drive cars require lightweight 
shafts in order to handle speeds within the operating range of the vehicle.
Shaft Design
Shafts are primarily designed on the basis of strength or rigidity or both.
• Based on Strength: To ensure that stress at any location of the shaft does not 
exceed the material yield stress.
• Based on Rigidity: To ensure that maximum deflection (because of bending) 
and maximum twist (due to torsion) of the shaft is within the allowable limits.
Note: Rigidity consideration is also very important in some cases for example 
position of a gear mounted on the shaft will change if the shaft gets deflected and 
if this value is more than some allowable limit, it may lead to high dynamic loads 
and noise in the gears.
General Principles
• Keep shafts short, with bearings close to the applied loads. This will reduce 
deflections and bending moments, and increases critical speeds.
• Place necessary stress raisers away from highly stressed shaft regions if 
possible. If unavoidable, use generous radii and good surface finishes. 
Consider local surface-strengthening processes (shot-peening or cold-rolling).
• Use inexpensive steels for deflection-critical shafts because all steels have 
essentially the same modulus of elasticity.
• Early in the design of any given shaft, an estimate is usually made of whether 
strength or deflection will be the critical factor. A preliminary design is based 
on that criterion; then, the remaining factor is checked.
Shaft Equations: All of the following equations are general equations; you may 
need to use modifying factors such as: loading factors, pulsating power source 
factors, safety factors, and stress concentration factors.
Basic equations in torsion:
• Solid round shaft:
16 - J 
r = ----- r
n D'
Hollow round shaft:
16 T D0 
x -(D * -D * )
Basic equation In bending:
• Solid shaft:
32 M 
a = --------
n D '
• Hollow shaft:
3 2 M D .
a = ------- ------ ° —
n-(D 0 - D t )
• Max shear stress:
71 D'
• Von Mises stress
£ T ' = — M + F D ): + 48 r : 
71 D'
• Torsional deflection:
6 =
32 T L 
7 i G DJ
• Factors of Safety:
° Max sheer stress theory
° Distortion energy
n
Where
• T = torque (lb-in, N-m),
• F = axial load (lb, N),
• Sy = yield strength,
• n = factor of safety,
• t = sheer stress (psi, Pa),
• D = diameter of solid shaft (in, m),
• D0 = outside diameter of solid shaft (in, m),
• Dj = inside diameter of solid shaft (in, m),
• M = bending moment (lb-in, N-m),
• L = length of shaft (in, m),
• G = sheer modulus (psi, Pa)
A.S.M.E. Code for Shaft Design
• According to A.S.M.E. code, the bending and twisting moment are to be 
multiplied by factors kb and kt respectively, to account for shock and fatigue 
in operating condition. Therefore, if the shaft is subjected to dynamic loading, 
equivalent torque and the equivalent bending moment will become:
and
r e = - f c t r a
Mg = [kbM - ^ k bM ^ -k tT2]
Values of kb and kt for different types of loading
kb kt
Gradually applied load 1.5 1.0
Suddenly applied load (minor shock) 1.5-2.0 1.0-1.5
Suddenly applied load 2.0-3.0 1.5-3.0