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

 Page 1


Springs 
Spring provide a flexible joint between two parts or bodies. Spring may be used to 
absorb the energy and control the motion of two mating bodies.
Basic Functions of Spring
• Cushioning, absorbing, or controlling of energy due to shock and vibration. 
E.g. Car
• Springs or railway buffers
• To control energy, springs-supports and vibration dampers.
• Control of motion, and maintaining contact between two elements (cam and 
its follower)
• Creation of the necessary pressure in a friction device (a brake or a clutch)
• Restoration of a machine part to its normal position when the applied force is 
withdrawn (a governor or valve). A typical example is a governor for turbine 
speed control. A governor system uses a spring controlled valve to regulate 
flow of fluid through the turbine, thereby controlling the turbine speed.
• Measuring forces, spring balances, gages
• Storing of energy, in clocks or starters, the clock has spiral type of spring 
which is wound to coil and then the stored energy helps gradual recoil of the 
spring when in operation.
Materials Used for Spring: One of the important considerations in spring design is 
the choice of the spring material. Some of the common spring materials are given 
below. •
• Hard-drawn wire: This is cold drawn, cheapest spring steel. Normally used for 
low stress and static load. The material is not suitable at subzero
Page 2


Springs 
Spring provide a flexible joint between two parts or bodies. Spring may be used to 
absorb the energy and control the motion of two mating bodies.
Basic Functions of Spring
• Cushioning, absorbing, or controlling of energy due to shock and vibration. 
E.g. Car
• Springs or railway buffers
• To control energy, springs-supports and vibration dampers.
• Control of motion, and maintaining contact between two elements (cam and 
its follower)
• Creation of the necessary pressure in a friction device (a brake or a clutch)
• Restoration of a machine part to its normal position when the applied force is 
withdrawn (a governor or valve). A typical example is a governor for turbine 
speed control. A governor system uses a spring controlled valve to regulate 
flow of fluid through the turbine, thereby controlling the turbine speed.
• Measuring forces, spring balances, gages
• Storing of energy, in clocks or starters, the clock has spiral type of spring 
which is wound to coil and then the stored energy helps gradual recoil of the 
spring when in operation.
Materials Used for Spring: One of the important considerations in spring design is 
the choice of the spring material. Some of the common spring materials are given 
below. •
• Hard-drawn wire: This is cold drawn, cheapest spring steel. Normally used for 
low stress and static load. The material is not suitable at subzero
temperatures or at temperatures above 120°C.
• Oil-tempered wire: It is a cold drawn, quenched, tempered, and general 
purpose spring steel. However, it is not suitable for fatigue or sudden loads, at 
subzero temperatures and at temperatures above 180°C. When we go for 
highly stressed conditions then alloy steels are useful.
• Chrome Vanadium: This alloy spring steel is used for high stress conditions 
and at high temperature up to 220°C. It is good for fatigue resistance and long 
endurance for shock and impact loads.
• Chrome Silicon: This material can be used for highly stressed springs. It 
offers excellent service for long life, shock loading and for temperature up to 
250°C.
• Music wire: This spring material is most widely used for small springs. It is 
the toughest and has highest tensile strength and can withstand repeated 
loading at high stresses. However, it cannot be used at subzero temperatures 
or at temperatures above 120°C. Normally when we talk about springs we will 
find that the music wire is a common choice for springs.
• Stainless steel: Widely used alloy spring materials.
• Phosphor Bronze / Spring Brass: It has good corrosion resistance and 
electrical conductivity. That’s the reason it is commonly used for contacts in 
electrical switches. Spring brass can be used at subzero temperatures.
Helical spring
• The figures below show the schematic representation of a helical spring acted 
upon by a tensile load F and compressive load F . The circles denote the cross 
section of the spring wire. The cut section, i.e. from the entire coil somewhere 
we make a cut, is indicated as a circle with shade.
Solid Length
• The axial length of the spring under the loaded condition when the coils of 
the spring touch each other is known as solid length of the spring as shown in 
below figure.
Free Length
Page 3


Springs 
Spring provide a flexible joint between two parts or bodies. Spring may be used to 
absorb the energy and control the motion of two mating bodies.
Basic Functions of Spring
• Cushioning, absorbing, or controlling of energy due to shock and vibration. 
E.g. Car
• Springs or railway buffers
• To control energy, springs-supports and vibration dampers.
• Control of motion, and maintaining contact between two elements (cam and 
its follower)
• Creation of the necessary pressure in a friction device (a brake or a clutch)
• Restoration of a machine part to its normal position when the applied force is 
withdrawn (a governor or valve). A typical example is a governor for turbine 
speed control. A governor system uses a spring controlled valve to regulate 
flow of fluid through the turbine, thereby controlling the turbine speed.
• Measuring forces, spring balances, gages
• Storing of energy, in clocks or starters, the clock has spiral type of spring 
which is wound to coil and then the stored energy helps gradual recoil of the 
spring when in operation.
Materials Used for Spring: One of the important considerations in spring design is 
the choice of the spring material. Some of the common spring materials are given 
below. •
• Hard-drawn wire: This is cold drawn, cheapest spring steel. Normally used for 
low stress and static load. The material is not suitable at subzero
temperatures or at temperatures above 120°C.
• Oil-tempered wire: It is a cold drawn, quenched, tempered, and general 
purpose spring steel. However, it is not suitable for fatigue or sudden loads, at 
subzero temperatures and at temperatures above 180°C. When we go for 
highly stressed conditions then alloy steels are useful.
• Chrome Vanadium: This alloy spring steel is used for high stress conditions 
and at high temperature up to 220°C. It is good for fatigue resistance and long 
endurance for shock and impact loads.
• Chrome Silicon: This material can be used for highly stressed springs. It 
offers excellent service for long life, shock loading and for temperature up to 
250°C.
• Music wire: This spring material is most widely used for small springs. It is 
the toughest and has highest tensile strength and can withstand repeated 
loading at high stresses. However, it cannot be used at subzero temperatures 
or at temperatures above 120°C. Normally when we talk about springs we will 
find that the music wire is a common choice for springs.
• Stainless steel: Widely used alloy spring materials.
• Phosphor Bronze / Spring Brass: It has good corrosion resistance and 
electrical conductivity. That’s the reason it is commonly used for contacts in 
electrical switches. Spring brass can be used at subzero temperatures.
Helical spring
• The figures below show the schematic representation of a helical spring acted 
upon by a tensile load F and compressive load F . The circles denote the cross 
section of the spring wire. The cut section, i.e. from the entire coil somewhere 
we make a cut, is indicated as a circle with shade.
Solid Length
• The axial length of the spring under the loaded condition when the coils of 
the spring touch each other is known as solid length of the spring as shown in 
below figure.
Free Length
• The axial length of the spring under no loading condition is known as solid 
length of the spring as shown in below figure,
Compressed Length
• The compressed length is defined as the axial length of the spring, that is 
subjected to maximum compressive force.
Free
Length
?
Compressed Length = Free Length - Maximum deflection 
= Ntd+(Nt-l) x gap between adjacent coils
Spring Index
• Spring index is defined as the ratio of the mean coil diameter to the 
wire diameter of the spring and denoted as "C".
C = D/d = Mean coil diameter / Wire diameter
• The spring index indicates the relative sharpness of curvature of the coil. 
Spring Rate
• Spring rate may be defined as the force per unit deflection of the spring, it is 
also known as stiffness constant.
Types of Stresses Produced In The Wire of the Closed Coiled Helical Spring:
• In addition to the torsional shear stress ( t - i ) induced in the wire,
8JV.D
The following stresses also act on the wire:
1. Direct shear stress due to the load W , and
2. Stress due to the curvature of wire.
load
T, =----------------------------------------
cross-sectional area of thewire 
rr 4rr
4
The Resultant Shear Stress
Page 4


Springs 
Spring provide a flexible joint between two parts or bodies. Spring may be used to 
absorb the energy and control the motion of two mating bodies.
Basic Functions of Spring
• Cushioning, absorbing, or controlling of energy due to shock and vibration. 
E.g. Car
• Springs or railway buffers
• To control energy, springs-supports and vibration dampers.
• Control of motion, and maintaining contact between two elements (cam and 
its follower)
• Creation of the necessary pressure in a friction device (a brake or a clutch)
• Restoration of a machine part to its normal position when the applied force is 
withdrawn (a governor or valve). A typical example is a governor for turbine 
speed control. A governor system uses a spring controlled valve to regulate 
flow of fluid through the turbine, thereby controlling the turbine speed.
• Measuring forces, spring balances, gages
• Storing of energy, in clocks or starters, the clock has spiral type of spring 
which is wound to coil and then the stored energy helps gradual recoil of the 
spring when in operation.
Materials Used for Spring: One of the important considerations in spring design is 
the choice of the spring material. Some of the common spring materials are given 
below. •
• Hard-drawn wire: This is cold drawn, cheapest spring steel. Normally used for 
low stress and static load. The material is not suitable at subzero
temperatures or at temperatures above 120°C.
• Oil-tempered wire: It is a cold drawn, quenched, tempered, and general 
purpose spring steel. However, it is not suitable for fatigue or sudden loads, at 
subzero temperatures and at temperatures above 180°C. When we go for 
highly stressed conditions then alloy steels are useful.
• Chrome Vanadium: This alloy spring steel is used for high stress conditions 
and at high temperature up to 220°C. It is good for fatigue resistance and long 
endurance for shock and impact loads.
• Chrome Silicon: This material can be used for highly stressed springs. It 
offers excellent service for long life, shock loading and for temperature up to 
250°C.
• Music wire: This spring material is most widely used for small springs. It is 
the toughest and has highest tensile strength and can withstand repeated 
loading at high stresses. However, it cannot be used at subzero temperatures 
or at temperatures above 120°C. Normally when we talk about springs we will 
find that the music wire is a common choice for springs.
• Stainless steel: Widely used alloy spring materials.
• Phosphor Bronze / Spring Brass: It has good corrosion resistance and 
electrical conductivity. That’s the reason it is commonly used for contacts in 
electrical switches. Spring brass can be used at subzero temperatures.
Helical spring
• The figures below show the schematic representation of a helical spring acted 
upon by a tensile load F and compressive load F . The circles denote the cross 
section of the spring wire. The cut section, i.e. from the entire coil somewhere 
we make a cut, is indicated as a circle with shade.
Solid Length
• The axial length of the spring under the loaded condition when the coils of 
the spring touch each other is known as solid length of the spring as shown in 
below figure.
Free Length
• The axial length of the spring under no loading condition is known as solid 
length of the spring as shown in below figure,
Compressed Length
• The compressed length is defined as the axial length of the spring, that is 
subjected to maximum compressive force.
Free
Length
?
Compressed Length = Free Length - Maximum deflection 
= Ntd+(Nt-l) x gap between adjacent coils
Spring Index
• Spring index is defined as the ratio of the mean coil diameter to the 
wire diameter of the spring and denoted as "C".
C = D/d = Mean coil diameter / Wire diameter
• The spring index indicates the relative sharpness of curvature of the coil. 
Spring Rate
• Spring rate may be defined as the force per unit deflection of the spring, it is 
also known as stiffness constant.
Types of Stresses Produced In The Wire of the Closed Coiled Helical Spring:
• In addition to the torsional shear stress ( t - i ) induced in the wire,
8JV.D
The following stresses also act on the wire:
1. Direct shear stress due to the load W , and
2. Stress due to the curvature of wire.
load
T, =----------------------------------------
cross-sectional area of thewire 
rr 4rr
4
The Resultant Shear Stress
8 W D 4TT
71 7 ' 77 d * " TTd1
• The positive sign is used for the inner edge of the wire and negative sign is 
used for the outer edge of the wire. Since the stress is maximum at the inner 
edge of the wire, therefore
Maximum shear stress induced in the wire = Torsional shear stress + Direct shear 
stress.
8 JV D 4JV 8 rr_ D
1+ d
77dl
8 W D
TTd2 
[1 + . 1
X
< o
ii
2D 
8rV.D
TTd3 . 2cJ TTd3
Where Ks is Shear stress factor. 
Distribution of Stresses
• Torsional shear stress diagram:
i
(<i) T orsional shear stress diagram
• Direct shear stress diagram:
i
i
0 ) D ir rr t shear stress diagram .
• Resultant torsional shear and direct shear stress diagram
i i
(< ) Resultant to rsio n a l shear and d ire rl 
shear stress diagram
Page 5


Springs 
Spring provide a flexible joint between two parts or bodies. Spring may be used to 
absorb the energy and control the motion of two mating bodies.
Basic Functions of Spring
• Cushioning, absorbing, or controlling of energy due to shock and vibration. 
E.g. Car
• Springs or railway buffers
• To control energy, springs-supports and vibration dampers.
• Control of motion, and maintaining contact between two elements (cam and 
its follower)
• Creation of the necessary pressure in a friction device (a brake or a clutch)
• Restoration of a machine part to its normal position when the applied force is 
withdrawn (a governor or valve). A typical example is a governor for turbine 
speed control. A governor system uses a spring controlled valve to regulate 
flow of fluid through the turbine, thereby controlling the turbine speed.
• Measuring forces, spring balances, gages
• Storing of energy, in clocks or starters, the clock has spiral type of spring 
which is wound to coil and then the stored energy helps gradual recoil of the 
spring when in operation.
Materials Used for Spring: One of the important considerations in spring design is 
the choice of the spring material. Some of the common spring materials are given 
below. •
• Hard-drawn wire: This is cold drawn, cheapest spring steel. Normally used for 
low stress and static load. The material is not suitable at subzero
temperatures or at temperatures above 120°C.
• Oil-tempered wire: It is a cold drawn, quenched, tempered, and general 
purpose spring steel. However, it is not suitable for fatigue or sudden loads, at 
subzero temperatures and at temperatures above 180°C. When we go for 
highly stressed conditions then alloy steels are useful.
• Chrome Vanadium: This alloy spring steel is used for high stress conditions 
and at high temperature up to 220°C. It is good for fatigue resistance and long 
endurance for shock and impact loads.
• Chrome Silicon: This material can be used for highly stressed springs. It 
offers excellent service for long life, shock loading and for temperature up to 
250°C.
• Music wire: This spring material is most widely used for small springs. It is 
the toughest and has highest tensile strength and can withstand repeated 
loading at high stresses. However, it cannot be used at subzero temperatures 
or at temperatures above 120°C. Normally when we talk about springs we will 
find that the music wire is a common choice for springs.
• Stainless steel: Widely used alloy spring materials.
• Phosphor Bronze / Spring Brass: It has good corrosion resistance and 
electrical conductivity. That’s the reason it is commonly used for contacts in 
electrical switches. Spring brass can be used at subzero temperatures.
Helical spring
• The figures below show the schematic representation of a helical spring acted 
upon by a tensile load F and compressive load F . The circles denote the cross 
section of the spring wire. The cut section, i.e. from the entire coil somewhere 
we make a cut, is indicated as a circle with shade.
Solid Length
• The axial length of the spring under the loaded condition when the coils of 
the spring touch each other is known as solid length of the spring as shown in 
below figure.
Free Length
• The axial length of the spring under no loading condition is known as solid 
length of the spring as shown in below figure,
Compressed Length
• The compressed length is defined as the axial length of the spring, that is 
subjected to maximum compressive force.
Free
Length
?
Compressed Length = Free Length - Maximum deflection 
= Ntd+(Nt-l) x gap between adjacent coils
Spring Index
• Spring index is defined as the ratio of the mean coil diameter to the 
wire diameter of the spring and denoted as "C".
C = D/d = Mean coil diameter / Wire diameter
• The spring index indicates the relative sharpness of curvature of the coil. 
Spring Rate
• Spring rate may be defined as the force per unit deflection of the spring, it is 
also known as stiffness constant.
Types of Stresses Produced In The Wire of the Closed Coiled Helical Spring:
• In addition to the torsional shear stress ( t - i ) induced in the wire,
8JV.D
The following stresses also act on the wire:
1. Direct shear stress due to the load W , and
2. Stress due to the curvature of wire.
load
T, =----------------------------------------
cross-sectional area of thewire 
rr 4rr
4
The Resultant Shear Stress
8 W D 4TT
71 7 ' 77 d * " TTd1
• The positive sign is used for the inner edge of the wire and negative sign is 
used for the outer edge of the wire. Since the stress is maximum at the inner 
edge of the wire, therefore
Maximum shear stress induced in the wire = Torsional shear stress + Direct shear 
stress.
8 JV D 4JV 8 rr_ D
1+ d
77dl
8 W D
TTd2 
[1 + . 1
X
< o
ii
2D 
8rV.D
TTd3 . 2cJ TTd3
Where Ks is Shear stress factor. 
Distribution of Stresses
• Torsional shear stress diagram:
i
(<i) T orsional shear stress diagram
• Direct shear stress diagram:
i
i
0 ) D ir rr t shear stress diagram .
• Resultant torsional shear and direct shear stress diagram
i i
(< ) Resultant to rsio n a l shear and d ire rl 
shear stress diagram
Resultant torsional shear, direct shear and curvature shear stress diagram
(</) Resultant to rsio n a l shrar. d im ! shear 
and curvature sh ra r stress diagram .
Here the "d" and "D" represents the wire diameter and mean coil diameter of the 
spring.