We were discussing theÂ power
transmitted by a circular shaft,Â derivation of
strain energy due to torsionÂ and alsoÂ derivation of
torsional equationÂ 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.Â spring in
strength of material.

###
**Spring deflection**

Deflection in
spring is basically defined as the distance moved by spring under the action of
load.Â Deflection will be indicated by Î´ and its unit will be mm.Â

Numerically, we can
write spring deflection as the ratio of applied load to the spring stiffness.

Î´ = W/k

Deflection in
spring could also be calculated by using the following formulas mentioned here

Î´ = 8WD

_{m}^{3Â }n/ (Gd^{4})
Where,

W is the applied
load and k is the spring stiffness

D

_{m}Â = 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/ Î´

###
**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

###
**
Wahlâ€™s correction factor**

Wahlâ€™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 â€“ wire
diameter

D

_{m}Â = D â€“ d
Where,

D

_{m}Â 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 = L

_{F}Â / (n-1)
Where,

P is the pitch of
spring

L

_{F}Â 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 L

_{S}Â and its unit will be mm.Â
Solid length of
spring could be determined as mentioned here

L

_{S}Â = 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 L

_{F}Â and its unit will be mm.
Free length of
spring could be determined as mentioned here

L

_{F}Â = L_{SÂ }+ Î´Â_{Max}Â + 0.15 x Î´Â_{Max}
Where,

L

_{S}Â is the Solid length of the spring
Î´Â

_{Max}Â 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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