Key takeaways
- Wire diameter has the strongest effect on rate because it enters the rate formula to the fourth power.
- Mean coil diameter and active coils both lower the rate as they rise, but they change stress differently.
- Free length sets the travel and the solid height, not the rate, when the coil count stays the same.
- State the load at a stated length on the drawing, not only the free length and the wire size.
The five variables that set the spring
A compression spring looks like a simple part: a wire coiled into a helix. Its behaviour is set by a small number of variables that interact. Change one and the rate, the stress, the travel or the solid height moves, often in a way that is not obvious from the drawing.
The five variables are the wire diameter, the mean coil diameter, the number of active coils, the free length and the end type. Material and finish sit behind them, because they set the allowable stress and the corrosion behaviour rather than the geometry.
Wire diameter
Wire diameter is the most powerful variable in the design. In the rate formula it appears to the fourth power, so a small change in wire size produces a large change in rate. An illustrative increase from 1.00 mm to 1.10 mm, with every other variable fixed, raises the rate by about 46 per cent.
The same variable also sets the stress. A larger wire carries more load at the same deflection, but it also has a larger section. At a fixed deflection, the stress rises with wire diameter because the force rises faster than the section does.
Wire diameter is controlled by the wire standard and its tolerance class. A drawing that gives a nominal diameter without a tolerance leaves the supplier to choose, and the rate will follow that choice. Specify the tolerance class as well as the nominal size.
Mean coil diameter and spring index
Mean coil diameter is the outside diameter minus one wire diameter, or the inside diameter plus one wire diameter. It is the diameter of the centreline of the wire, and it is the dimension that enters the rate and stress formulas. The drawing usually gives the outside or inside diameter, so the conversion has to be made before the calculation.
The ratio of mean coil diameter to wire diameter is the spring index. A high index means a slender spring with a low rate and low stress concentration. A low index means a stiff, tightly coiled spring where the curvature raises the stress on the inside of the coil. Spring index below about 4 is a design warning, not a manufacturing impossibility.
For a fixed wire and coil count, increasing the mean diameter lowers the rate, because the coil is less resistant to deflection. It also lowers the stress at a fixed deflection, so a spring that is too stiff can sometimes be corrected by opening the coil rather than changing the wire.
Active coils and end types
Active coils are the coils that deflect. Total coils include the active coils plus the end coils that sit against the seat. A closed and ground end has a dead coil at each end, so the active count is lower than the total. An open end has less dead coil, and a plain end has a different seating behaviour again.
The end type is not a cosmetic choice. It changes the number of active coils, the solid height, the squareness of the spring and the way the load is transferred into the seat. A spring with closed and ground ends stands square and seats well. A spring with open ends may be cheaper, but it can lean under load and it needs a seat that can accommodate the end.
Increasing the active coil count lowers the rate and lowers the stress at a fixed deflection, because the deflection is shared over more wire. It also raises the solid height for the same wire and diameter, which can remove travel from the envelope.
Free length, solid height and travel
Free length is the length of the spring with no load. It is not a rate variable when the coil count and diameter stay fixed, but it sets the installed length, the travel and the solid height. A longer free length gives more travel before the coils close, provided the envelope allows it.
Solid height is the length of the spring when all coils touch. It is roughly the total coil count multiplied by the wire diameter, with a correction for the end type. The gap between the working length and the solid height is the travel reserve. A spring that runs close to solid height will bind, and the load will rise sharply at the end of the stroke.
Design the spring around the installed length, not the free length. The load at the installed length and the load at the working length are the two numbers the assembly needs. The free length is a result of the geometry, and it should carry a tolerance that reflects the manufacturing process.
| Variable | Increase the variable | Effect on rate | Effect on stress | What else moves |
|---|---|---|---|---|
| Wire diameter | Thicker wire | Rises strongly | Rises | Solid height and weight |
| Mean coil diameter | Wider coil | Falls | Falls | Envelope and index |
| Active coils | More working coils | Falls | Falls | Solid height and travel |
| Free length | Longer spring | No change | No change | Travel and installed height |
| End type | Closed and ground | Sets active count | Sets active count | Squareness and seating |
Qualitative guide for a spring compared at a fixed deflection. Confirm the actual values with a rate calculation and a load test.
Rate, stress and the design check
The rate calculation gives the spring constant. The stress calculation gives the shear stress at the working load, corrected for the curvature of the coil. Both are needed. A spring can have the right rate and still fail because the stress at the working length is too high for the material and the cycle life.
Check the stress at the installed length and at the maximum working length, not only at one point. The range between them is the stress range that drives fatigue. A spring that is static may tolerate a stress that a cycling spring cannot.
Also check the buckling risk. A spring with a high free length to mean diameter ratio can buckle before it reaches solid height. A guided seat, a smaller free length or a larger mean diameter can remove the risk. The check is geometric and does not need a test to identify.
What to put on the drawing
A compression spring drawing should give the geometry, the material and the performance call in one place. The supplier needs enough information to make the part and enough freedom to use a standard setup where the function allows it.
- Wire diameter with its tolerance class
- Outside or inside diameter, and the mean diameter if it is critical
- Total coils and active coils, with the end type named
- Free length with a tolerance
- Load at the installed length and at the working length
- Material grade and temper
- Finish and any stress relief or peening requirement
- Direction of wind if the spring is used in a rotating assembly
Frequently asked questions
Which variable has the biggest effect on spring rate?
Wire diameter. Rate is proportional to the fourth power of the wire diameter, so a 10 per cent increase in wire size raises the rate by about 46 per cent if everything else stays the same. Mean coil diameter and active coils have a smaller proportional effect.
Does a longer free length change the rate?
Not if the wire diameter, mean diameter and active coil count stay the same. Free length changes the installed height, the travel and the solid height. It is a common mistake to lengthen a spring to reduce its rate without adding coils.
What is a good spring index?
A spring index between about 5 and 12 is comfortable for most compression springs. Below 4 the curvature raises the stress and the tooling gets difficult. Above 12 the spring becomes slender and may buckle or tangle.
Should the drawing give load or rate?
Give the load at a stated length, and give the rate if the assembly needs it. Load at length is easier to verify on a test fixture and it captures the combined effect of wire diameter, coil count and material. A rate alone can be met by a spring that does not fit the space.
Sources and further reading
- EN 13906-1, Cylindrical helical springs made from round wire and bar, compression springs
- EN 10270-1, Steel wire for mechanical springs, patented cold drawn unalloyed spring steel wire
- Qumek spring design and DFM notes for compression springs
Qumek Engineering Desk
Engineering team
The engineering team behind Qumek drawings, DFM notes, tolerances and inspection standards. Every guide is reviewed against the drawings and processes used on live programmes.
Check a compression spring before release
Send the wire size, the coil geometry and the load at the installed length. The engineering desk will check the rate, the stress and the travel reserve.
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