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Compression spring design and general considerations

Author : Chris Petts is Managing Director at Lee Spring UK

21 December 2016

Let’s first consider stress, set and weight as important considerations in establishing a custom spring design which need to be understood at the outset.

The dimensions, along with the load and deflection requirements, determine the stresses in the spring. When a compression spring is loaded, the coiled wire is stressed in torsion. The stress is greatest at the surface of the wire; as the spring is deflected, the load varies, producing a range of operating stress. 

In designing compression springs the space allotted governs the dimensional limits of a spring with regard to allowable solid height and outside and inside diameters. These dimensional limits, together with the load and deflection requirements, determine the stress level. It is important to consider carefully the space allotted to insure that the spring will function properly to begin with, thereby avoiding costly design changes. 

Compression spring set

When a compression spring is compressed and released, it is supposed to return to its original height and, on further compressions, the load at any given point should remain constant at least within the load limits specified. When a spring is made and then compressed the first time, if the stress in the wire is high enough, the spring will not return to its original height. This is referred to as "taking a set", or "setting". When a custom spring is supplied longer than specified to compensate for length loss, this is referred to as “Allow for Set”. This is usually recommended for large quantity orders to reduce cost. 

Compression spring weight

For cost and manufacturing purposes, it is useful to calculate the weight of springs to determine raw material use and shipping requirements. For manufacturing purposes, it is easier to work with a unit quantity of 1,000 springs, so the weight per 1,000 springs is the standard ratio to figure.

Let’s look at general considerations where the following design procedure (and associated formulas) should be used for all compression spring designs. 

1. Select the appropriate material for the spring design. Take note of the shear modulus (G) and tensile strength (TS), as these numbers will be used in future calculations.

2. Calculate the mean diameter (Dm) and inside diameter (ID) of the spring using the outside diameter (OD) and wire diameter (d). Compare the ID of the spring to any work over rod requirements. Remember to incorporate the low side of the OD (or ID) tolerance when examining the work over rod requirements.

D_m (in)=OD-d
ID (in) = OD - 2d

3. The diameter of a compression spring will increase when compressed. This increase is a function of the pitch (p). Calculate the OD expansion and compare this to any work in hole requirements. Remember to incorporate the high side of the OD tolerance when examining the work in hole requirements.

4. Calculate the pitch (and therefore coils per inch) and the spring index. Verify that the pitch of the spring is not greater than the OD, as this will result in coiling difficulties. Also, take note of the spring index. 

5. Once the spring rate (R) and number of active coils (NA) has been established, calculate the number of total coils (NT). (This does not apply to designs that are based on physical dimensions.)

Formula for NT based on End Type

6. Calculate the solid height (SH) and verify that any customer requirements are satisfied and that any load heights are above solid height. Allow a 5 percent variation to the nominal solid height value to calculate the maximum solid height.

Formula for SH based on End Type

7. If the design has load requirements, the stress at these load heights must be calculated and compared against the tensile strength of the material. If the percent stress at any load height is greater than 40 percent, then a set operation or allow for set should be considered. If the percent stress is greater than 60 percent, a set operation would be inadequate and a re-design must be considered. 

8. Unless the working range is specifically known, the stress at solid height must be examined. If the percent stress at solid height is greater than 40 percent, then a set operation or allow for set should be considered. If the percent stress is greater than 60 percent, a re-design must be considered. (See for details.)

9. Tolerances should be assigned to all required design criteria. Commercial tolerances should be used whenever possible to reduce cost. Tighter tolerances could be possible; however, should be compared against the calculated process capability (CPC) for manufacturability.

Diameter tolerances - OD commercial tolerances chart:

 .025” to  .039” O.D. ± .002”
  .851” to 1.125” O.D. ± .020”
 .040” to  .118” O.D. ± .003”
1.126” to 1.218” O.D. ± .025”
 .119” to  .250” O.D. +.003”/-.005”
1.219” to 1.460” O.D. ± .030”
 .251” to  .299” O.D. ± .005”
1.461” to 1.687” O.D. ± .040”
 .300” to  .500” O.D. ± .008”
1.688” to 2.000” O.D. ± .055”
 .501” to  .850” O.D. ± .015”

CPC values:

OD_CPC=(2/ 3)OD Tol_c

Free length tolerances, Rate tolerances and Load tolerances should all be calculated according to formulae to be found at

Squareness - a tolerance of 3° maximum is standard. For any requirements that call for tighter squareness requirements, particular attention must be given to costs associated with coiling and grinding setup.

Number of coils - generally speaking, the number of coils is not a dimension that will have a tolerance placed on it for manufacturing purposes. 

Designing a custom spring is a well-known and understood process for manufacturers who are engaged in it every day, so Lee Spring would recommend that time spent in discussion with a manufacturer’s spring engineer would be very worthwhile prior to committing to a particular specification.

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