Blog - How do I calculate the spring rate of a compression spring?

In this piece we explane how to calculate a spring constant of compression springs and how to design a compression spring on the springrate. This piece is an extension of the standard calculation of a spring constant. This piece is about standard compression/constant pitch coil springs.

The function of a compression spring is to withstand a certain pressure perpendicular to that spring. Compression springs consist of open coils (Pitch). The Pitch ensures that windings do not touch each other and thus give room to be pressed. The basic calculation to calculate a spring constant is C = F/u, see the standard calculation of a spring constant. In this piece we will go into the details of a compression spring design and the calculation of the spring constant in this way.

Technical drawing compression spring

Formula spring rate compression springs

The spring constant of compression springs is given in Newtons per mm (N/mm) compression. This depends on a number of parameters in the calculation. First of all, the Slip Modulus in Mpa is needed (G). This depends on the material used, request this from the spring specialist. Furthermore, the wire thickness (d) and the diameter of the spring center to center (Dm) in millimeters (mm) are required and finally the number of active turns (Nw) is required.

Formule veerconstante drukveren

C = Spring constant in N/mm
G = Slip Modulus (Mpa)
d = Wire thickness (mm)
Dm = Diameter spring center to center (mm)
Nw = Number of working windings

By playing with the d, Dm and Nw the spring can be made more or less strong. A larger wire gauge makes the spring stronger, the opposite for a thinner wire gauge. A larger diameter makes the spring weaker, a smaller wire diameter makes the spring stronger. More turns makes the spring weaker while fewer turns makes the spring stronger. To further look at how this works theoretically, two examples have been worked out:

  1. Example one: The weight is 85 kilograms (850N) and you want the spring to collapse a maximum of 5cm (50mm). Then a spring is needed with a spring constant of C = 850/50 = 17 N/mm.
  2. Example two: The weight is 65 kilograms (650N) and you want the spring to collapse a maximum of 5cm (50mm). Then a spring is needed with a spring constant of C = 650/50 = 13 N/mm.

With the previous two examples we can fill in the formula to arrive at a design. The result of the formula is given. Now the question is, which d, Dm and Nw belong to this? (or what options do I have)

Parameter Meaning Format Example 1 Example 2
C Spring rate Newton per milimeter (N/mm) 17 N/mm 13 N/mm
G Slip Modulus Megapascal (Mpa) an value of pressure. Specified in the material. 7900 7900
d Wire Thickness In Milimeter (mm) ? ?
Dm Center to center diameter In Milimeter (mm) ? ?
Nw Active turns In number ? ?

 

How do I get from a spring constant of compression springs to a compression spring design?

The data to be found is:

  1. Compression spring with a spring rate of 17 N/mm.
  2. Compression spring with a spring rate of 13 N/mm.

First, we recommend to find standard compression springs within the parameters. In order to make a custom compression spring design, we continue with the calculation of the wire thickness (d), Center to Center diameter of the spring (Dm) and the number of working turns (Nw). Below are some options for designing the spring. The options of the parameters of the compression spring can be calculated infinitely without implementing limitations.

Example 1 Option 1 Option 2 Option 3 Option 4
G 79000 79000 79000 79000
d 0.102453 1 5 0.4
Dm 0.4 4.011 30 1.43
Nw 1 9 13.5 5
C 17.00 17.00 16.93 17.29

 

Example 2 Option 1 Option 2 Option 3 Option 4
G 79000 79000 79000 79000
d 0.102453 1 5 0.4
Dm 0.435 4.011 33.2 1.57
Nw 1 11.5 13 5
C 13.21 13.3 12.97 13.06

To reproduce this formula in Excel, you can copy the following or similar formula:
=(C2*(C3^4))/(8*(C4^3)*C5)

In these examples you can see that option 1 has been played with the Dm. In option two, the number of active turns has changed, etc. Try it out yourself with the wire diameter (d).

Check on the found compression spring designs.

A spring constant of the desired spring has been found, it is now possible to proceed to design a spring. The following parameters have been set: The wire thickness, the center-to-center diameter and the number of active turns. The following parameters can be calculated with these parameters:

  • The minimum untensioned length of the spring.
    • The Ln (maximum compressed length of the spring)
    • The Lc (fully compressed length of the spring)
  • The maximum axle size for the spring.
  • The minimum bushing size for the spring.

First there is an explanation of what the parameters are and how the parameters are created, then we will look at the previous examples.

To calculate the minimum untensioned length of the compression spring:

To go back to the beginning, we want this spring to travel at least 50 mm downwards. The compression spring must therefore have at least a spring travel of 50 mm. A compression spring, cannot compress to the ground, because the turns of a compression spring are compressed on top of each other (to avoid this problem, conical compression springs are a solution). To calculate the minimum required length of the spring, we will need the length of the fully compressed spring. 

The parameter a fully compressed compression spring is then called the Lc. To arrive at the Lc we use the following calculation:

  • Lc mm = ( d * ( Nw + 2 ) ) *1,0064

Here is the rule. When we fully compress a spring, it is the wire gauge times the number of active turns along with two inoperative turns (Nt), this times a factor of 1.0064. The two inoperative turns are standard for ground/applied springs.

Only pressing a compression spring completely until the turns lie on top of each other gives the spring a minimum lifespan, the steel wil be placed under a lot of stress and the turns are rubbing against each other. To avoid that, the maximum pressed length is the parameter, this is the Ln.

The Ln calculation is:

  • Ln mm = Lc (mm) * 1,15

We do not recommend using a compression spring to the point of the Ln, but with the Ln you can use the Goodman Chart to calculate the lifetime of the spring.

To calculate the minimum untensioned length:

  • Minimum untensioned length = Ln (mm) + Spring travel (mm)

The minimum untensioned length is then the minimum design length that must be adhered to for this spring. This can be used to check within the application.

Suppose that the spring has to be pressed 50 millimeters in a space of 60 millimeters. Only the design of the spring shows that the minimum untensioned length of the calculated spring is already 65 millimeters, then the design cannot be applied. If the available space is 70 millimeters, this spring can be used with an untensioned length of 70 millimeters, making a compression spring longer has no effect on the spring rate.

Calculate maximum ax-size of the compression spring

The ax/shaft size is the parameter of the shaft attached to the inside of the compression spring. We are talking about a maximum shaft size, when it is larger than the max. the shaft will rub against the compression spring and the spring will have a low durability.

The calculation of the maximum ax-size:

  • Ax = Dm – (d*2)

Here we take the center to center diameter of the spring. From that we take the outside of the wire plus another safety correction of the spring. The safety correction is important because the turns of the compression spring may contain a margin of error (tolerance).

Calculating the minimum bushing size of the compression spring

The sleeve size is the parameter of the sleeve that is attached to the outside of the compression spring. We are talking about a minimum sleeve size, if it is smaller than the minimum, the sleeve will rub against the compression spring and the spring will have a low durability.

The calculation of the minimum bus size:

  • bus = Dm + (d*2)

Here we take the center to center diameter of the spring. To that we add the outside of the wire plus another safety correction of the spring. The safety correction is important because the turns of the compression spring may contain a margin of error (tolerance).

Check on design of compression springs examples:

There is one more parameter that has not been explained but has appeared in the design of the compression springs, the Goodman chart. This indicates whether the spring is working at all. Request the Goodman chart from the spring specialist with the designs of the springs.

Example 1 Option 1 Option 2 Option 3 Option 4
G 79000 79000 79000 79000
d (mm) 0.102453 1 5 0.4
Dm (mm) 0.4 4.011 30 1.43
Nw 1 9 13.5 5
C (N/mm) 17.00 17.00 16.93 17.29
Design Control factors
Spring travel (mm) 50.00 50.00 50.00 50.00
Lc (mm)
(=d*(Nw+2)*1.0064
2.12 11.07 69.94 4.03
Ln (mm)
(=Lc * 1.15)
2.43 12.73 80.44 4.63

Minimum untensioned length
(=Ln+ spring travel)

52.12 61.07 119.94 54.03
Max ax size
(=Dm-(d*2)
0.2 2.01 20.00 0.63

Min Bus size
(=Dm+(d*2)

0.6 6.01 40.00 2.23

Do the same with example 2:

Example 2 Option 1 Option 2 Option 3 Option 4
G 79000 79000 79000 79000
d (mm) 0.102453 1 5 0.4
Dm (mm) 0.435 4.011 33.2 1.57
Nw 1 11.5 13 5
C (N/mm) 13.21 13.3 12.97 13.06
Design Control factors
Spring travel (mm) 50.00 50.00 50.00 50.00
Lc (mm)
(=d*(Nw+2)*1.0064
0.31 13.59 75.48 2.82
Ln (mm)
(=Lc * 1.15)
0.36 15.62 86.80 3.24

Minimum untensioned length
(=Ln+ spring travel)

50.31 63.59 125.48 52.82
Max ax size
(=Dm-(d*2)
0.23 2.01 23.20 0.77

Min Bus size
(=Dm+(d*2)

0.64 6.01 43.20 2.37

 

Thus, four designs of springs come out of the specified force (countless more designs, but we'll stick to four per example). There are still a number of parameters by which the spring is limited.

  • Spring Index
    • Center to center (dm) / wire gauge (d)

The spring index indicates how difficult the spring is to produce. Rules of thumb here are 0 - 3.99 ratio can not be produced. 4 – 5 ratio is difficult to produce (read, high production costs). 6 – 12 perfect ratio. 13 – 15 good ratio. 15 – 25 ratio is difficult to produce. Above 25 extremely difficult to produce, often accompanied by high tolerances.

  • Buckling Index
    • L0 / center to center (dm)

The buckling index indicates whether the compression spring will buckle. When this ratio exceeds four, the spring will buckle. To prevent this, we recommend placing compression springs around an axle, it is also possible to place the springs in a bush.

Order compression springs

In the design of a compression spring, the dimensions are crucial for the spring properties. But compression spring designs are limited by the application where compression springs are placed. It is more convenient to adjust the design so that four or five types of springs can serve as replacements.

The division for ideal compression spring design is: one ideal spring that fits perfectly, two stronger and two weaker alternatives. So there is always room for maneuver. You can order the compression springs via our webshop, have compression springs made to measure via our online form or by mail to sales@tevema.com

Compression springs Custom compression springs

Posted on 2 February 2022