It is well known that springs will resonate if activated fast enough, which means they will be subject to dynamic stresses higher than expected from calculation. The calculated stresses apply under static conditions. Additional dynamic stresses are a factor that may help to explain why a spring has failed when all calculations show that it’s not at risk.
The natural frequency of a spring is the speed at which it will move if the constraints on that spring are suddenly removed — i.e. when a loaded spring is allowed to “go twang.” This speed depends upon a number of factors as shown in the formula for calculating natural frequency of compression springs.
Natural frequency (Fe) depends upon wire diameter (d), number of active coils (n), mean diameter (D), torsional modulus (G), and density (ρ). (Please note: In the U.S. the formula used for wire diameter is 3507.)
IST often undertakes tests to validate results obtained from calculation; one example of this is a new test jig that enables measurement of natural frequency. This jig has shown that the calculation is reasonably accurate, but the measured values are usually lower than the calculated ones by a few percentage points.
The difference in calculated and measured results lies with the true number of active coils. In other words, an active coil does not suddenly become completely inactive when it contacts the end tip. A comparison of the resonant wave, in which the detector on the jig is placed near an end coil and then by a central coil, is shown in figures 1 and 2. The calculated natural frequency for this spring was 343Hz, but the measured value in both figures 1 and 2 was 321Hz. Note that damping from the end coil does not change the natural frequency at all.
After actuation, the spring keeps vibrating, this means that near the end coil the stress profile seen in the middle coil will interfere with the wave reflected by the end coil, resulting in the more complicated waveform shown in figure 2. Sometimes the input and reflected wave will combine to create a higher stress range than elsewhere. This may explain why compression springs nearly always fail on fatigue tests near the end — often at 1.5 to 2 coils from the moving or static end.
The jig can be used with springs having more than one pitch, springs with various degrees of pre-load, conical springs and other configurations for which calculation of natural frequency is more difficult. An example is shown in figure 3.
In usual operational mode it is the axial natural frequency that is measured, as shown in each of the examples here. However, recent tests have shown that lateral natural frequency can also be measured, which is different from the axial result, as one might reasonably expect, and the jig works well in this mode also.
Mark Hayes is the senior metallurgist at the Institute of Spring Technology (IST): The International Independent Centre of Excellence for Spring Technology. He manages IST’s spring failure analysis service, and all metallurgical aspects of advice given by the Institute. He also designs and delivers the majority of the spring training courses that the IST offers globally. Readers are encouraged to contact him with comments about this cautionary tale, and with subjects that they would like to be addressed in future tales. Contact Hayes at (011) 44 114 252 7984, fax (011) 44 114 2527997, or e-mail Mark's Email.