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How are leaf springs designed?

ByAnthony
Table of Contents
1 Parts of a Leaf Spring
2 Leaf Spring History
3 How many types of leaf springs are there?
4 What do leaf springs do?
5 Are leaf springs better than coil springs?
6 Why leaf springs are not used in cars?
7 How leaf springs should look?
8 How do you calculate leaf spring forces?
8.1 Design a symmetrical semi-elliptic light truck spring with tapered leaf ends to meet the following specifications (rate, as tested with center clamp):
9 Frequently Asked Questions

A leaf spring is a basic type of spring often used for suspension in vehicles. Originally known as a laminated or carriage spring, and sometimes called a semi-elliptical spring, elliptical spring, or cart spring, leaf springs are one of the oldest forms of vehicle suspension. A Leaf spring consists of one or more narrow, curved, thin plates that are connected to the axle and chassis in a way that allows the spring to bend vertically in response to bumps or uneven road surfaces. The most common arrangement is lateral leaf springs, which run along the length of the vehicle and are mounted perpendicular to the wheel axle.

Rear leaf spring suspension on a 2022 Nissan Frontier
This 2022 Nissan Frontier’s rear suspension uses semi-elliptic leaf springs, a leaf spring design that supports the truck’s weight while damping road vibration through friction between the stacked leaves.

Leaf springs can perform several suspension functions, including supporting the vehicle’s weight, providing springiness, and to some extent, damping by using friction between the layers of the spring.

Just like any other component in a vehicle, leaf springs need to be replaced from time to time. There are multiple reasons why leaf springs might become defective, such as sagging, cracking, breaking, and leaning.

Parts of a Leaf Spring

A typical multi-leaf spring assembly is made up of a handful of standard components:

  • Main Leaf (Master Leaf) — the longest, topmost leaf in the stack, with an eye formed at each end that attaches the spring to the vehicle’s frame.
  • Graduated Leaves — the progressively shorter leaves stacked beneath the main leaf, which add stiffness and share the load as the spring deflects.
  • Spring Pack (Spring Assembly) — the complete stack of leaves, held together with a center bolt and alignment clips to keep the leaves from shifting sideways.
  • Shackle — a pivoting bracket at one end of the spring that lets the leaf spring lengthen and shorten slightly as it flexes, without binding against the frame.
  • U-Bolts and Center Bolt — the U-bolts clamp the spring pack to the axle, while the center bolt keeps the leaves centered and aligned within the pack.
  • Hangers and Bushings — the brackets and rubber or polyurethane bushings that mount the spring eyes and shackle to the vehicle’s frame.

Leaf Spring History

The Leaf spring is the oldest type of automotive spring. They have a long history, initially appearing on carriages in France in the mid-17th century and later spreading to England and Germany by around 1750. Dr. Richard Lovell Edgeworth’s demonstrations in 1768 highlighted the superiority of sprung carriages, leading to leaf springs becoming a regular feature in the late 18th-century carriage industry. The latter half of the 19th century saw developments in steel rolling processes and alloys, making leaf spring manufacture more consistent and cost-effective.

Diagram of an older solid rear axle suspension design
Older vehicles used a non-independent, solid-axle rear suspension paired with leaf springs, a layout many automakers phased out in favor of front-wheel drive and coil spring suspensions, though leaf spring design remains common on trucks and SUVs today.

While leaf springs were once common in automobiles, their use declined in the 1970s with the shift to front-wheel drive and coil spring-based suspension systems. However, they remain prevalent in heavy commercial vehicles, SUVs, and railway carriages due to their ability to spread loads widely over a chassis and simplify rear axle location without the need for additional components like trailing arms and Panhard rods.

How many types of leaf springs are there?

There are two types of leaf spring suspensions: mono and multi. Mono-leaf spring suspension is made up of a single piece of metal or leaf. while multi-leaf spring suspensions are made up of multiple leaves. The springs in a multi-leaf spring suspension can be oriented in either a symmetrical or unsymmetrical stack-up.

Diagram comparing symmetrical and unsymmetrical multi-leaf spring stack-ups
Multi-leaf spring suspensions can be built with a symmetrical or unsymmetrical leaf stack-up, a fundamental leaf spring design choice that shapes how the spring rate and load distribution behave under a vehicle’s weight.

What do leaf springs do?

A Leaf spring is part of a vehicle’s suspension system and must support the entire weight of a vehicle. The automotive industry has been going away from leaf springs in recent years, however, they can still be found on the rear suspension system of many trucks or large SUVs. The main function of leaf springs is to provide comfort to the passengers by minimizing the vertical vibration caused by the nonuniformity of road geometry. Leaf springs also help to maintain the tire’s grip on the road and regulate the wheelbase lengths when it is speeding up or slowing down.

Close-up photo of leaf springs on a 2022 Nissan Frontier
A close-up of the semi-elliptic leaf spring pack on a 2022 Nissan Frontier’s rear axle, illustrating the stacked-leaf truck suspension design used to minimize vertical vibration and control axle wind-up.

Where the leaf spring sits on an axle, it should be as close to the center line of the axle as possible. As the spring seat moves further away from the center line of the axle, there is an increase in axle wind-up. This is because, as the fulcrum (the point on which a lever rests or is supported and on which it pivots.) lever gets longer, it makes twisting the axle easier.

Are leaf springs better than coil springs?

Leaf springs are much sturdier when compared to coil springs. As a result, they are capable of handling higher loads with less deflection. Leaf springs are also better at spreading out the load over a larger area, whereas coil springs transfer it to a single point. That is the reason why many trucks still use leaf springs for the rear suspension system. However, this increased load-carrying capacity comes at the expense of vehicle ride comfort. The reason for the decreased ride comfort is because of the inter-leaf friction between each leaf. However, this friction is not always well controlled, leading to stickiness and irregular movements in the suspension. To address this issue, some manufacturers use mono-leaf springs.

Why leaf springs are not used in cars?

The biggest reason leaf springs are not used in cars is that they do not offer as much flexibility as coil springs. As a result, a vehicle that uses leaf springs provides a much harder and bumpier ride quality. While off-roading, a leaf spring suspension system is not as accommodating to the uneven ground as compared to a coil system. Leaf springs are still used in large commercial vehicles such as vans, full-size trucks, and SUVs. Outside of the automotive industry, leaf springs are also used by locomotives.

How leaf springs should look?

Leaf springs are primarily used on the rear of a vehicle, virtually no vehicle today uses leaf springs at the front. From a size view leaf springs appear to look like long different sizes of bowed, narrow strips of steel stacked together, which are held together using U-bolts and a center clip. However, upon further examination, the ends of leaf springs can vary from squared-off leaf springs to diamond-pointed leaf springs.

Diagram of squared-off and diamond-pointed leaf spring end types
Leaf spring ends can be manufactured with a squared-off or diamond-pointed profile, a detail that matters especially when designing tapered leaf ends for a semi-elliptic truck spring.

How the leaf spring is attached to the vehicle body and chassis will also vary. Below are some examples of common attachment strategies used in leaf spring designs.

Diagram of common leaf spring attachment strategies to the vehicle chassis
Common leaf spring attachment strategies connect the spring eyes and shackles to the vehicle’s chassis, a design decision that affects how vertical and torsional loads are transferred through the truck suspension.

How do you calculate leaf spring forces?

Leaf springs are loaded not only by vertical forces but also by horizontal forces and torques in the longitudinal vertical and transverse vertical planes. Torque in the longitudinal vertical plane (windup) is usually produced by a longitudinal force applied above or below the spring seat. To calculate the number of leaf springs and the size of each leaf spring the following steps can be followed. These force calculations follow the same fundamentals covered in our guide to suspension system loads, and are closely related to the stiffness tuning discussed in our sway bar design guide:

  • Establish the total moment of inertia for the specified rate and length
  • to establish the maximum permissible leaf thickness within the specified maximum stress limit at the corresponding load.
  • calculate the spring stress.
  • estimate an approximate mass of steel for comparing optional designs from the preliminary calculation.
Diagram of spring windup in a symmetrical leaf spring under braking
Braking forces applied above or below the spring seat generate windup torque in a symmetrical leaf spring, an effect that leaf spring design calculations must account for in the longitudinal vertical plane.

Design a symmetrical semi-elliptic light truck spring with tapered leaf ends to meet the following specifications (rate, as tested with center clamp):

Table of design specifications for a symmetrical semi-elliptic leaf spring
The target design specifications for this symmetrical semi-elliptic light truck spring with tapered leaf ends, including the required spring rate as tested with a center clamp.
Diagram of leaf spring geometry used in the design calculation
The leaf spring geometry used in this design calculation, defining the dimensions needed to size a symmetrical semi-elliptic spring with tapered leaf ends to the target specifications.

Solution:

Worked solution for the leaf spring design calculation
The worked solution for this leaf spring design problem, walking through the calculations used to size a symmetrical semi-elliptic truck spring to the target rate and stress specifications.

Step 1: Find the required total moment of inertia

Calculation of the required total moment of inertia for the leaf spring
Step 1 of the leaf spring design calculation solves for the required total moment of inertia, the starting point for sizing the spring’s cross-section to the target spring rate.

Step 2: Find the maximum permissible leaf thickness

Calculation of the maximum permissible leaf spring thickness
Step 2 calculates a maximum permissible leaf thickness of 6.39 mm across four leaves, a constraint that narrows the leaf spring options considered in the design.

Leaf thickness should not exceed 6.39mm and limited to the total number of leaves 4

Step 3: 5 leaf springs were selected from the spring design manual SAE 1995

Table of five candidate leaf springs selected from the SAE 1995 design manual
Step 3 selects five candidate leaf springs from the SAE 1995 spring design manual for evaluation against the target rate and stress specifications.
Table comparing candidate leaf spring stress and stiffness values against design targets
Option 4 and 5 exceed 1000N max allowable stress. None of the K values (spring stiffness) are close enough to require 17.5N/mm (less than 5% difference)

Since having 4 common leaf springs would not meet design specifications, springs were mixed and matched to determine the best combination.

Table of mixed-and-matched leaf spring combinations evaluated against specifications
Since no single catalog leaf spring combination met the design specifications, leaves from different candidates were mixed and matched in search of a combination closer to the target spring rate.
Continued table of leaf spring combination results
Additional mixed leaf spring combinations evaluated against the target spring rate and stress limits, continuing the search for a design that satisfies the semi-elliptic truck spring specifications.
Additional leaf spring combination calculation results
Further calculations comparing mixed leaf spring combinations, narrowing the field before selecting the four options closest to the required spring rate.

Step 4: Select the top four combinations which are the closest to meeting design specifications:

Table of the top four leaf spring combinations closest to design specifications
Step 4 ranks the four leaf spring combinations closest to the design specifications, from which Option C is selected as the best combination based on mass and spring rate.
Summary table of the final selected leaf spring design
A summary of the final semi-elliptic leaf spring design selected for this light truck suspension, confirming Option C as the lowest-mass combination with a spring rate within 1% of the 17.5 N/mm target.

Option C is the best: it has the lowest mass and the K value is 1% of 17.5N/mm

Option C is 3 leaf springs size 6.3mm x 75mm and 1 leaf spring 6.3mm x 56mm.

Frequently Asked Questions

What are the parts of a leaf spring?
A typical multi-leaf spring assembly includes the main (master) leaf, graduated leaves, the spring pack held together by a center bolt, a shackle, U-bolts that clamp it to the axle, and the hangers and bushings that mount it to the frame.

What is a semi-elliptical leaf spring?
A semi-elliptical leaf spring is a leaf spring shaped like half of an ellipse, the most common leaf spring configuration used in vehicle suspensions, mounted horizontally between the vehicle’s frame and axle.

Are leaf springs still used in trucks?
Yes. While leaf springs have largely been replaced by coil springs in passenger cars, they remain common in the rear suspension of trucks, vans, and large SUVs due to their ability to support heavy loads and spread them widely across the chassis.

What’s the difference between a mono-leaf and multi-leaf spring?
A mono-leaf spring is made from a single piece of metal, while a multi-leaf spring stacks several leaves of progressively shorter length together, which can be arranged in a symmetrical or unsymmetrical stack-up.

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