Spring design calculations

Basic knowledge Construction

Springs are mechanical components that can store and deliver tension energy generated by the work used to tension, elongate or compress the spring in the form of deformation or tension energy. They are used in many applications and can be found in small electronic components as well as in large industrial machines. To ensure that a spring performs its function, it must be correctly designed. For this purpose, parameters such as the spring constant and the spring travel are calculated.

Types of springs

There are different types of springs that differ in function and appearance.

Springs are differentiated by load and shape. The most common types are:

Shapes of springs:

Coil springs: Coil springs have a helical shape. They can be tension springs, compression springs or torsion springs. They can have a constant spring force over a longer travel.
Leaf springs: Leaf springs consist of several metal strips that are connected to one another. They can absorb large loads over an extended period of time.
Disc springs: Disc springs consist of one or more concentric discs or plates. They absorb axial loads and are compressed.

Spring loads:

Compression springs: Compression springs are compressed by compressive loads (compressive force). They are cylindrical or conical.
Tension springs: Tension springs stretch under tensile load. They can for example be straight, conical or helical.
Torsion springs (also leg springs): Torsion springs twist when torque is exerted on them. They have a linear or nonlinear torsion spring constant.
Bending springs: Bending springs are capable of absorbing bending loads, which generates a spring effect.

You can learn more in our blog about Selecting tension springs and compression springs - overview / use / application examples.

Calculating springs

In order to calculate and design springs, parameters such as spring rate, spring constant and spring work should be determined or known in a first step. The spring force or the spring constant can for example be calculated.

Preliminary considerations for spring calculation and spring design

Before calculating or designing the spring, several important requirements and specifications should be established, such as:

Load requirements, e.g. maximum load, load type (compression, tension, torsion), frequency and duty cycle of the load type
Operating environment and operating conditions, e.g. temperature, corrosion risk, humidity and degree of contamination
Damping and vibration absorption, e.g. need for damping elements
Space and installation restrictions, e.g. for the dimensions of the spring, design of the coil geometry and ends

Cost-effective automation primarily makes use of tension springs and compression springs.

Parameters for calculating springs

The following parameters must be known first before calculating compression springs, tension springs, etc.:

For a tension spring as an example

What force (F) will be exerted on the spring? What free length (L₀) and spring travel (X) is available?
Should the spring be equipped with tension lugs or are additional tension lugs required? And what effect do additional tension lugs have on length?
Does the inner diameter (D) of the spring and/or a wire diameter (d) play a role?
Does the dead weight of the spring play a role in the application and what space is available for any necessary replacement of the spring
Do the lugs need to be arranged the same orientation or rotated by 90°?

Calculating the spring force using the spring force formula

The spring force, also called clamping force, is the force generated by a spring when it is stretched or compressed, based on its stiffness or spring constant. This force aims to return the spring to its original shape or position. The calculation is usually carried out using the spring force formula, also called Hookes' law. Hooke’s law describes the linear relationship between the force (F) exerted on an elastic body and the resulting elongation or compression (Δx) of that body in the elastic region of the material:

Where:

F = Spring force, measured in Newton (N)
k = Spring constant, the stiffness of the spring, in units such as N/m (Newton per meter)
Δx = Spring travel, the elongation (for tension springs) or compression (for compression springs) of the spring, measured in meters (m).

F = k \times \Delta x

What is the initial tension of a tension spring?

Initial tension (P_i), sometimes also called assembly preload, is defined as the tension (force in N) required to cause the spring to exhibit a change in length by deformation.

The spring constant and the spring travel (elongation or compression) can both be read from technical specifications and manufacturer data or are calculated as follows.

Calculating the spring constant using the spring force formula

The spring constant, often referred to as spring rate, is one of the basic parameters of a spring. It indicates how much force is required to deform the spring a certain distance.

k = \frac{F}{\Delta x}

The larger the spring constant, the stiffer the spring. A large spring constant means that a relatively high force is needed to deform the spring, while springs with a small spring constant are more easily deformed.

Calculating the total spring constant for multiple springs

In reality, only one spring is rarely installed. Instead, several springs are typically installed in succession or next to each other. How is the spring constant calculated in these cases? The total spring constant must be determined in all cases.

If several springs are connected in series (in-line configuration), the total spring constant is calculated as follows:

\frac{1}{k_{ges}} = \frac{1}{k_{1}} + \frac{1}{k_{2}} + ..

If several springs are installed side by side (parallel configuration), the total spring constant is calculated as follows:

k_{ges} = k_{1} + k_{2} + ..

Safety aspects

To prevent spring failure, the spring should not be loaded above its rated tension. The rated tension depends on the material of the spring. For example, for spring steel, the rated tension ranges from 550 MPa (megapascal) to 800 MPa, depending on the alloy and tempering. For stainless steel springs, the rated tension is between 500 MPa and 700 MPa.

Service life and fatigue

A spring can become fatigued over time, especially if it is frequently loaded and relieved. Therefore, it is important to consider the service life of the spring under the load conditions.

MISUMI Tension Springs - Load Range for Maximum Load Capacity by Series (Specified in N)

Version

Drawing

Material:
JIS-SWP-A

Material:
EN 1.4301 (WPB) Equiv.

Load Range - Maximum Load Capacity of the Series
(Material JIS-SWP-A)

Part number

Very low load

AWA

AUA

0.69

19.6

for low load capacity

AWY
BWY

AUY
BUY

1.86

78.45

Low/medium load

AWU
BWU

AUU
BUU

2.45

98.07

Medium load capacity

AWS
BWS

AUS
BUSS

3.53

225.55

Medium/heavy load

AWF

6.47

83.36

High-load capacity

AWT
BWT

AUT
BUT

8.8

430.51

Configurable

WFSP
BWFSP

UFSP
BUFSP

2.37
(at L = 50 mm)

156
(at L = 50 mm)

Long without eyelet

LWS

LUS

Note on heat resistance: (applies to spring wire material)	JIS-SWP-A:	Use between 0°C and 120°C
Note on heat resistance: (applies to spring wire material)	EN 1.4301 (WPB) Equiv.	Use between 0°C to 180°C
General note:	The data was obtained at room temperature. Permissible load and aging resistance may change depending on the different conditions at higher temperature.

Recommendations for MISUMI springs

MISUMI offers a wide range of springs, such as tension springs and round coil springs. Coil springs are designed to keep the maximum load constant at the same diameter. We recommend operating the springs within the allowable deflection to ensure functionality and shape and to achieve the expected service life. Springs are recommended at normal ambient temperatures (40°C or less). The load values decrease above 40°C. This temperature range is also assumed for MISUMI round coil springs.

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