We were discussing the  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.

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 = 8WDmn/ (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 = LF / (n-1)
Where,
P is the pitch of spring
LF 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 LS and its unit will be mm.

Solid length of spring could be determined as mentioned here
LS = 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.

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 LF and its unit will be mm.
Free length of spring could be determined as mentioned here
LF = L+ δ Max + 0.15 x δ Max
Where,
LS 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