# Leaf Springs In Mechanical Systems

There are various types of springs available in the design world. Leaf springs are one of these types of springs. Here, you can find out the general explanation of leaf springs and technical calculations about them.

## What Is Leaf Spring?

Leaf springs are also known as laminated springs in general mechanics. Leaf spring systems are generally used in heavy-duty mechanisms such as trucks, trains, busses, etc.

Leaf springs are mechanical structures multiple numbers of thin and long plates are clamped on each other to carry loads. Because of the deflection of the plates which is bending, a damping effect is obtained.

In general, leaf springs are produced in three types; elliptical, semi-elliptical, and cantilever. In general types of machinery, the most used type of leaf-spring is the semi-elliptical one.

### General Mechanics Of Springs

To understand the mechanics and design characteristics of leaf springs, you need to know some terminology and information about general spring classes.

In the spring systems in mechanisms, designers are utilizing the elastic deformation capacity of the springs. Spring is actually, specially designed mechanical elements to carry the dynamic or static loads more effectively than bulk shapes.

In general application, spring must carry the static or dynamic load in elastic limits. We do not want to see plastic deformation in the spring in the working conditions. So, there must be a load value that spring can carry in elastic limits, which is called as proof load. And corresponding stress is calculated by using this proof load value called proof stress.

Sometimes, engineers are using the term proof resilience which is the maximum strain energy that a spring can carry. The modulus of resilience is calculated as the maximum strain energy for unit volume.

The stiffness of a spring is another important value. This can be defined as the minimum stress value that can cause unit deformation of that spring.

The required deflection of a spring must be linear because we are using the spring in the elastic region. After the elastic region, the plastic region starts in which the deformation and stress behavior of the spring is non-linear.

## Explanation Of Leaf Springs In Technical Basis

The structure of leaf spring mechanisms is very easy. The first layer of the system is the longest plate, which is curved from both ends. These curves are hinged to the axles. Other plates are placed below the first plate, which is in the same thickness as the first plate.

This first plate is also called the master leaf, which other leaves are shorter than this. But the second and third leaves can be produced in the same length as the master leaf, to obtain a more rigid structure.

All these leaves are clamped from the center of the leaves. This clamp also carries the load and transmits the load to the leaves.

Between the load and axles, leaves are acting as springs for damping of the dynamic loads and carrying the static loads.

### Bending Stress Calculation Of The Leaf Springs

To calculate the deflection of a semi-elliptical leaf system, we need to know some symbolic and geometric variables about the leaf system; Illustration of a semi-elliptical leaf spring system(Image Source:D. K. Singh – Strength of Materials-Springer, 2020, pg.370).

As you see in the representation of a leaf spring system above, the span of the biggest leaf is denoted as ‘l’.
As we stated above that the thicknesses of each plate are the same and it is denoted as ‘t’.
The number of plates that are used in the leaf spring system is ‘n’.
The bending stress occurrence on the leaf spring system is ‘σ’.
Deflection of the master plate is denoted with ‘θ’.
Again, we stated that the curvature of each plate in the leaf spring system is the same. The radius of the curvature of the leaf spring system is denoted as ‘r’.
Each plate in the leaf spring system has the same width. This width value can be denoted with ‘w’.
The load acting on the leaf spring system is denoted with the ‘W’.

By knowing the all of these values related to a leaf spring system, you can calculate the total bending stress on the spring system with this calculator;

#### Bending Stress Calculator For Leaf Springs

The use of the calculator above is very simple. Just enter the required values inside the brackets. Then click on the ‘Calculate!’ button to calculate the bending stress. If you want to do another calculation, just click on the ‘Reset’ button then re-enter the whole values again.

Required unit sets are given in the parentheses. You can use them. If you need to convert your units into correct unit sets, you can use the MB-Unit Converter tool.

### Deflection Calculation For The Leaf Springs

Also, the total deflection of the leaf spring system can be easily calculated. Just like above, use the calculator below to calculate the total deflection of your leaf spring system;

#### Deflection Calculator For Leaf Springs

There is an additional variable in this calculator is the elasticity modulus of the spring material.

### Strain Energy Calculation For The Leaf Springs

Sometimes, stored strain energy can be a very important parameter for engineers. You can calculate the total stored strain energy in leaf spring systems by using the calculator below;

## Conclusion

The general expression of the leaf spring systems could be like that, both verbal and technical.

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