The index of a spring is a key indicator of spring design. As we explained in a previous issue, the index is the mean diameter divided by the wire size. This ratio tells us how tightly the spring is coiled. For any given wire size, there is a diameter that is too small for the wire to be formed around without damaging the material.
For small wire sizes, most must be able to coil around themselves without showing any sign of breakage. For example, a 0.125″ material size will have an index of 2.0. This was done by taking the 0.125″ inside diameter (ID) and adding the wire size of 0.125″. This is 0.250″. Then divide the 0.250″ by 0.125″, and the result is 2.0.
This tells you that an index of 2.0 is when the ID and the wire size are the same. Incidentally, an index of 2.0 or less should never be expected from a spring of any kind. Although not impossible, it is highly impractical and demands capability beyond any standard coiling machine.
For larger wire sizes, a wrap test of 2.0 times the wire size is typical. If the wire size were 0.375″, the mean diameter would be 0.750″ plus 0.375″, or 1.125″. Dividing the 1.125″ by 0.375″ yields an index of 3.0.
This then shows that large wire sizes (usually greater than 0.200″) should not be coiled with an index smaller than 3.0.
Problems Caused by Small Indexes
High stresses. The stress at a given height can be calculated with a formula that uses the load, diameter and wire size of a spring. However, this formula does not consider the curvature of the material after it’s coiled. For that reason, this stress is called “uncorrected.”
To “correct” the stress, a multiplication factor is used. This factor is called “Wahl’s correction factor.” It is a formula that gets larger as the index gets smaller. For instance, an index of 6.0 has a correction factor of 1.252. This means if the uncorrected stress were 123,400 psi, you would need to multiply that number by 1.252 to get the corrected stress, which is 154,497 psi.
As you can see, this corrected stress is much higher than the uncorrected stress and indicates that the spring will, actually, have much shorter life. In other words, the corrected stress level is much more realistic than the uncorrected stress level.
As the index gets smaller, the correction factor becomes greater. Therefore, springs with smaller indexes tend to have shorter lives than those with larger indexes. This is important for spring designers to take into consideration when designing springs for long life. Compression springs used for engine valves and transmissions are good examples of springs that must move from one height to another millions and millions of times, without failure.
Next Problem: High Indexes
Non-uniform pitch, length and diameter. As indexes increase (around 20 or greater), the wire size gets smaller in comparison to the body diameter. This condition makes it difficult to coil springs and maintain a consistent pitch/coil spacing. This inconsistency in pitch creates varying free lengths, varying diameters and, therefore, varying rates and loads.
High-index springs demonstrate the opposite characteristics of small-index springs, whose pitches are very consistent but whose material curvature is too small.
Coiling difficulties. With large-index springs, the large material curvature creates springs that don’t “behave” well when coiled. This forces the spring maker to slow down the machine, reducing the piece-per-hour rate.
Another phenomenon with a large index is the “wobble” factor if the spring is very long. The spring maker is forced to use a guide to keep the long, wobbly spring from distorting and going wild in all directions as it’s coiled.
Typically, a spring with a small index will be easier and faster to coil than one with a large index. That said, the ideal spring index would be from 5.0 to 12.0. Anything less, or more, may result in any of the problems mentioned in this column.
By: Randy DeFord, Engineering Manager Mid-West Spring & Stamping