We were discussing the power
transmitted by a circular shaft, derivation of
strain energy due to torsion and also derivation of
torsional equation in
our previous posts.
Today we will start
here with the various terminologies used in design calculations of spring and
we will discuss here each basic definition in respect of springs.
Let us go ahead
step by step for easy understanding, however if there is any issue we can discuss
it in comment box which is provided below this post.
So, what is a spring?
Spring is basically
defined as the elastic element which is basically used for absorbing the energy
due to resilience and this absorbed energy may be released as and when required.
For detailed post about the concepts and types of springs, we may find our
recent post i.e. spring in
strength of material.
Spring deflection
Deflection in
spring is basically defined as the distance moved by spring under the action of
load. Deflection will be indicated by δ and its unit will be mm.Â
Numerically, we can
write spring deflection as the ratio of applied load to the spring stiffness.
δ = W/k
Deflection in
spring could also be calculated by using the following formulas mentioned here
δ = 8WDm3 n/ (Gd4)
Where,
W is the applied
load and k is the spring stiffness
Dm =
Mean coil diameter of spring
n = Number of turns
in spring
G = Modulus of
rigidity of material of spring
d = Wire diameter
of spring
Spring Stiffness
Spring stiffness is
basically defined as the applied load to the deflection of the spring.
Stiffness will be indicated by k and its unit will be N/mm.
k = W/ δ
Spring index
Spring index
provides a relation between mean diameter of spring and wire diameter of
spring. Spring index is basically defined as the ratio of mean diameter of
spring to the wire diameter of spring.
When mean diameter
of spring will be divided by the wire diameter of spring, we will have the
value of spring index.
Spring index will
be indicated by C and as spring index is basically one ratio, hence spring
index will be unit less.
C = D/d
Where,
D is the mean
diameter of spring and d is the wire diameter of spring. Spring index value
will be in the range of 4 to 10.
Shear stress correction factor
Shear stress factor
will be determined by the following formula as mentioned here
Ks = 1 + 0.5 x d/D
Ks = 1 + 0.5 / C
Where,
Ks is shear stress
correction factor
D is the mean
diameter of spring and d is the wire diameter of spring
C is the spring
index
Wahl’s correction factor
Wahl’s correction
factor will be determined by the following formula as mentioned here
Mean coil diameter of spring
Mean coil diameter
of spring could be determined by subtracting the wire diameter of spring from
outer diameter of spring
Mean coil diameter = Outer diameter – wire
diameter
Dm = D – d
Where,
Dm is
mean coil diameter
D is the mean
diameter of spring and d is the wire diameter of spring
Pitch of the spring
As displayed in
following figure, we have selected one point at center in one wire and same
point in adjacent wire and distance between these two points will be termed as
pitch of the spring.
Therefore, we can
define the pitch of the spring as the distance between center of one wire of
spring to the center of adjacent wire of spring.
Pitch of the spring
could be determined by using the following formula as mentioned here
P = LFÂ / (n-1)
Where,
P is the pitch of
spring
LFÂ is
the free length of spring
n is the number of
turns in spring
Solid length
Solid length of
spring could be defined as the length of spring in fully closed condition.
Under the sufficient load, each wire of spring will be in contact with adjacent
wire and there will be no gap between two adjacent wires of spring and that is
called as spring in fully closed condition.
The entire length
of spring in fully closed position will be termed as Solid length of spring.
Solid length of spring will be displayed by LSÂ and its unit
will be mm.Â
Solid length of
spring could be determined as mentioned here
LSÂ = n x d
Where,
n is the number of
turn in spring
d is the wire
diameter of spring
Free length
Free length of
spring could be defined as the length of spring in fully unloaded
condition.Â
In simple, we can
say that if a spring is not loaded or there is no load applied on spring then
in that situation the entire length of spring will be termed as free length of
spring.
Free length of
spring will be displayed by LFÂ and its unit will be mm.
Free length of
spring could be determined as mentioned here
LFÂ =
LS + δ Max + 0.15 x δ Max
Where,
LSÂ is
the Solid length of the spring
δ Max is
the maximum deflection of the spring
Active coils or active turns in spring
Active coils or
active turns are those which will take part in deflection under the action of
load. Bottom and top coil of spring will be fixed and they will not take part
in deflection under load.
We can use the following
formula in order to determine the number of active coils or active turns in a
spring.
Number of active coils = Total number of
coils - 2
Squared and ground ends
Let us consider we
have one helical spring as displayed in following figure, cross section of
spring coil or wire is circular and therefore spring could be misaligned under
action of load.
In order to avoid
the misalignment or shifting of spring under the action of load, we make top
and bottom coil of spring square and grind it.
Square and ground
end spring could be located precisely and accurately and buckling will also be
avoided due to any misalignment in spring under the action of load.
Do you have
suggestions? Please write in comment box.
We will now discuss
another topic i.e. Expression for bending stress developed in the plate of leaf spring, in the category of strength of material, in our next post.
Reference:
Strength of
material, By R. K. Bansal
Strength of
material, By Ekeeda academy
Image Courtesy:
Google
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