| Mechanical Engineering |
|
| | Engineering Subjects |
|
| | GATE preparation tips |
|
| | More Engineering Links |
|
|
|
Design of Helical Springs
|
|
By Prof S S Chauhan, IEC College of Engineering & Technology, Greater Noida
|
Design of Helical Springs
A helical spring is a spiral wound wire with a constant coil diameter and uniform pitch. The most common form of helical spring is the
compression spring but tension springs are also widely used. Helical springs are generally made from round wire. It is comparatively rare
for springs to be made from square or rectangular sections. The strength of the steel used is one of the most important criteria to consider in
designing springs. Most helical springs are mass produced by specialist’s organizations. It is not recommended that springs are made specifically
for applications if off-the-shelf springs can be obtained to the job.
The design of a new spring involves the following considerations:
 Space into which the spring must fit and operate.
Values of working forces and deflections
Accuracy and reliability needed.
Tolerances and permissible variations in specifications.
Environmental conditions such as temperature, presence of a corrosive atmosphere.
Cost and qualities needed.
The designers use these factors to select a material and specify suitable values for the wire size, the number of turns, the coil diameter
and the free length, type of ends and the spring rate needed to satisfy working force deflection requirements. The primary design constraints
are that the wire size should be commercially available and that the stress at the solid length be no longer greater than the tensional yield
strength. Further functioning of the spring should be stable.
Stability of the spring (Buckling)
Buckling of column is a familiar phenomenon. Buckling of column is a familiar phenomenon. We have noted earlier that a slender member or column
subjected to compressive loading will buckle when the load exceeds a critical value. Similarly compression coil springs will buckle when the
free length of the spring is larger and the end conditions are not proper to evenly distribute the load all along the circumference of the coil.
The coil compression springs will have a tendency to buckle when the deflection (for a given free length) becomes too large. Buckling can be
prevented by limiting the deflection of the spring or the free length of the spring.
The behavior can be characterized by using two dimensionless parameters, critical length and critical deflection. Critical deflection can be
defined as the ratio of deflection (y) to the free length (Lf) of the spring. The critical length is the ratio of free length (Lf) to mean
coil diameter (D) The critical deflection is a function of critical length and has to be below a certain limit. As could be noticed from the
figure absolute stability can be ensured if the critical length can be limited below a limit.
Similarly compression coil springs will buckle when the deflection (for a given free length) becomes too large. The condition for
absolute stability can be given as:
For steels this can be simplified as:
Where a is a constant related to the nature of support of the ends simply referred as end constant
Spring Surge and Critical Frequency
If one end of a compression spring is held against a flat surface and the other end is disturbed, a compression wave is created that
travels back and forth from one end to the other exactly like the swimming pool wave. Under certain conditions, a resonance may occur
resulting in a very violent motion, with the spring actually jumping out of contact with the end plates, often resulting in damaging
stresses. This is quite true if the internal damping of the spring material is quite low. This phenomenon is called spring surge or
merely surging. When helical springs are used in applications requiring a rapid reciprocating motion, the designer must be certain that
the physical dimensions of the spring are not such as to create a natural vibratory frequency close to the frequency of the applied force.
The final equation for the natural frequency, derived from the governing equation of the wave motion, for a spring placed between two flat
parallel plates is given by:
For steels this can be simplified as:
The fundamental critical frequency should be from 15 to 20 times the frequency of the force or motion of the spring in order to avoid resonance
with harmonics. If the natural frequency is not high enough, the spring should be redesigned to increase k or decrease the weight W.
Fatigue Loading
The springs have to sustain millions of cycles of operation without failure, so it must be designed for infinite life. Helical springs are
never used as both compression and extension springs. They are usually assembled with a preload so that the working load is additional. Thus,
their stress-time diagram is of fluctuating nature. Now, for design we define,
Certain applications like the valve spring of an automotive engine, the springs have to sustain millions of cycles of operation without failure,
so it must be designed for infinite life. Unlike other elements like shafts, helical springs are never used as both compression and extension
springs. In fact they are usually assembled with a preload so that the working load is additional. Thus, their stress-time diagram is of
fluctuating nature. Now, for design we define, then the stress amplitude and mean stress values are given by: if we employ the Goodman
criterion, then The best data on tensional endurance limits of spring steels are those reported by Zimmerli. He discovered the surprising
fact that the size, material and tensile strength have no effect on the endurance limits (infinite life only) of spring steels in sizes
under 10mm(3/8 inches). For all the spring steels in table the corrected values of tensional endurance limit can be taken as: = 310 Mpa for
unpeened springs= 465 Mpa for peened springs. The stress amplitude and mean stress values are given by:
If we employ the Goodman criterion, then
The design or resulting factor of safety will depend on the spring material selected and their endurance strength. In the absence of data on the endurance limit, the best data on torsional endurance limits of spring steels are those reported by Zimmerli. He discovered the surprising fact that the size, material and tensile strength have no effect on the endurance limits (infinite life only) of spring steels in sizes under 10mm(3/8 inches). For all the spring steels the corrected values of torsional endurance limit can be taken as:
= 310 MPa for unpeened springs = 465 MPa for peened springs.
|
|
|
