How The Stiffness Of Springs Are Calculated?

How The Stiffness Of Springs Are Calculated?

As you remember from the physical and mechanical applications, the stiffness factor of the springs is very important in calculations. There are lots of kinds of springs are available and all these springs have specific stiffness values. 

Here we show you how to calculate this stiffness value for springs. And we will explain all the parameters related to the stiffness of springs. 

Stiffness Of Springs

Illustration of the close coiled helical spring(Image Source: Mikell P. Groover; Fundamentals Of Modern Manufacturing, 4th edition, pg 382).

Helical springs are one of the most used spring types in most engineering applications. And in various applications, axial forces are acting on these helical springs. Stiffness values are defined according to these axial forces. And these stiffness values has the formula of; 

In this formula; 

  • ‘G’ is the modulus of rigidity of the spring material. 
  • ‘d’ is the diameter of the wire in which the helical spring is made. 
  • ‘R’ is the radius of the helical spring. 
  • ‘n’ is the number of turns of the total helical spring geometry. 

As you see above, the calculation of the spring stiffness coefficient is very simple, when the axial forces are present on helical springs. 

What Is The Angular Stiffness?

Close coiled helical springs can undergo angular twist action. In general, this property of helical springs is not utilized in general mechanical applications. But in some cases, this physical fact must be considered. 

With this twisting action, the ‘angular stiffness’ value must be defined to springs. This angular stiffness value is defined with the equation below;

At this new formula; 


As you see above, the logic of the stiffness of the springs is very simple. 

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