Spring Worksheet

Spring Worksheet S E_D
Machine Element I
1) A helical compression spring is made of hard-drawn spring steel wire 2 mm in

diameter and has an outside diameter of 22 mm. The ends are plain and ground,
and there are 8.5 total coils.
a) The spring is wound to a free length, which is the largest possible with a
solid-safe property.
b) Find this free length.
c) What is the pitch of this spring?
d) What force is needed to compress the spring to its solid length?
e) Estimate the spring rate.
f) Will the spring buckle in service?
2) Listed below are five springs described in SI units. Investigate these squared-
and-ground-ended helical compression springs to see if they are solid-safe. If
not, what is the largest free length to which they can be wound using ns = 1.2?
3) A static service music wire helical compression spring is needed to support a

load of 89 N after being compressed 51 mm. The solid height of the spring
cannot exceed 38 mm. The free length must not exceed 102 mm. The static
factor of safety must equal or exceed 1.2. For robust linearity use a fractional
overrun to closure ξ of 0.15. There are two springs to be designed.
a) The spring must operate over a 19 mm rod. A 1.27 mm diametric
clearance allowance should be adequate to avoid interference between the
rod and the spring due to out-of-round coils. Design the spring.
b) The spring must operate in a 25 diameter hole. A 1.27 mm diametric
clearance allowance should be adequate to avoid interference between the
spring and the hole due to swelling of the spring diameter as the spring is
compressed and out-of-round coils. Design the spring.
4) Not all springs are made in a conventional way. Consider the special steel
spring in the illustration
a) Find the pitch, solid height, and number of active turns
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b) Find the spring rate. Assume the material is A227 HD steel.
c) Find the force Fs required to close the spring solid.
d) Find the shear stress in the spring due to the force Fs.
5) A helical extension spring is required to exert a force of 30 N when the length

between attachment locations is 70 mm and a force of 20 N at a length of
60mm.The spring will be cycled through its load 100 times a day. ASTM A228
music wire steel has been proposed for the spring. The diameter of the spring
should not exceed .Determine suitable dimensions for the spring wire diameter,
number of coils and mean diameter.
6) A helical spring is required to exert a force of 160 N at a length of 170 mm and
200 N at a length of 150 mm. Specify a suitable spring for this application. The
maximum operating temperature is 50°C and the load varies slowly with time
and a total life of 200000 cycles is required.
7) Design an infinite-life helical coil extension spring with full end loops and
generous loop-bend radii for a minimum load of 40 N and a maximum load of
80 N, with an accompanying stretch of 6.5 mm. The spring is for food-service
equipment and must be stainless steel. The outside diameter of the coil cannot
exceed 25.5 mm, and the free length cannot exceed 64 mm. Using a fatigue
design factor of nf = 2, complete the design.
8) A helical extension spring is required to exert a force of 30 N when the length
between attachment locations is 70 mm and a force of 20 N at a length of 60
mm. The spring will be cycled through its load 100 times a day. ASTM A228
music wire steel has been proposed for the spring. The diameter of the spring
should not exceed 20 mm. Determine suitable dimensions for the spring wire
diameter, number of coils and mean diameter.
9) A helical compression spring is required to exert a force of 35 N when
compressed to a length of 60 mm. At a length of 48 mm the force must be 50 N.
The spring is to be installed in a hole with a diameter of 24mm.The application
involves slow cycling and a total life of 250000 cycles is required. The
maximum temperature of operation is 80°C.
10) The extension spring shown in the figure has full-twisted loop
ends. The material is AISI 1065 OQ&T wire. The spring has 84 coils and is
close-wound with a preload of 80 N.
(a) Find the closed length of the spring.
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(b) Find the torsional stress in the spring corresponding to the preload.
(c) Estimate the spring rate.
(d) What load would cause permanent deformation?
(e) What is the spring deflection corresponding to the load found in part d?
11) A helical compression spring, made of circular wire, is subjected to an axial

force, which varies from 2.5 kN to 3.5 kN. Over this range of force, the
deflection of the spring should be approximately 5 mm. The spring index can be
taken as 5. The spring has square and ground ends. The spring is made of
patented and cold-drawn steel wire with ultimate tensile strength of 1050
N/mm2 and modulus of rigidity of 81370 N/mm2. The permissible shear stress
for the spring wire should be taken as 50% of the ultimate tensile strength.
Design the spring and calculate
(i) wire diameter;
(ii) Mean coil diameter;
(iii) Number of active coils;
(iv) Total number of coils;
(v) Solid length of the spring;
(vi) Free length of the spring;
(vii) Required spring rate; and
(viii) Actual spring rate
12) A safety valve operated by a helical tension spring through the lever
mechanism is schematically illustrated in Fig1. The diameter of the valve is 50
mm. In normal operating conditions, the valve is closed and the pressure inside
the chamber is 0.5 N/mm2. The valve is opened when the pressure inside the
chamber increases to 0.6 N/mm2. The maximum lift of the valve is 5 mm. The
spring index can be taken as 8. The spring is made of patented and cold-drawn
steel wire with ultimate tensile strength of 1200 N/mm2 and modulus of rigidity
of 81 370 N/mm2. The permissible shear stress for the spring wire can be taken
as 30% of the ultimate tensile strength. Design the spring and calculate:
i. Wire diameter;
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ii. Mean coil diameter; and
iii. Number of active coils.
Fig1. Fig2.
13) Design a helical spring for a spring loaded safety valve (Ramsbottom safety
valve) for the following conditions fig 2: Diameter of valve seat = 65 mm;
Operating pressure = 0.7 N/mm2; Maximum pressure when the valve blows off
freely = 0.75 N/mm2; Maximum lift of the valve when the pressure rises from
0.7 to 0.75 N/mm2 = 3.5 mm; Maximum allowable stress = 550 MPa; Modulus
of rigidity = 84 kN/mm2; Spring index = 6. Draw a neat sketch of the free
spring showing the main dimensions.
14) A rail wagon of mass 20 tonnes is moving with a velocity of 2 m/s. It is
brought to rest by two buffers with springs of 300 mm diameter. The maximum
deflection of springs is 250 mm. The allowable shear stress in the spring
material is 600 MPa. Design the spring for the buffers.
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Spring Worksheet

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Spring Worksheet S E_D

1) A helical compression spring is made of hard-drawn spring steel wire 2 mm in

3) A static service music wire helical compression spring is needed to support a

5) A helical extension spring is required to exert a force of 30 N when the length

11) A helical compression spring, made of circular wire, is subjected to an axial

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