Calculating the estimated fatigue life of a disc spring
Disc springs are extremely useful components in a wide range of applications, being able to be statically loaded either continuously or intermittently, or dynamically subjected to continuous load cycling. And they can be used singly or in multiples, stacked parallel, in series or in a combination thereof. But perhaps what makes them unique is that, based on standardised calculations, the deflection for a given load is predictable and the minimum life cycle can be determined. Here we look at how.
Disc Springs are conically-shaped, washer-type components designed to be axially loaded. Not to be confused with conical spring washers, disc springs offer a number of benefits in use compared with other types of springs. They offer a wide range of load/deflection characteristics, and high load capacity with small deflection. With consistent performance under design loads, they offer longer fatigue life, and inherent dampening especially with parallel stacking. Further, the high load to size ratio means they can offer significant space savings.
Disc springs may be used to apply either static or dynamic loads and are specified by DIN EN 16983 (formerly DIN 2093). Typically disc springs have a thinner cross section than conical spring washers. Some variation in size is permissible, but calculations only apply to spring steels and when the ratio of the outside diameter to thickness is between 16 and 40 and the ratio of OD to ID between 1.8 and 2.5.
Deflection of a disc spring at a given load is predictable making it possible to calculate force and stress levels in the disc. As the disc spring flexes, stress levels in the disc change; the greater the change, the faster the disc spring fatigues. Tensile stress at points II and III in are critical in determining fatigue life, as these locations are where fatigue cracks originate. Estimation of fatigue life requires evaluation of the maximum stress difference between preload and final load at locations II and III. The location with the highest stress differential is used to estimate fatigue life. Once it is determined which stress values will be used (from location II or III), the fatigue life charts in DIN EN 16983 can be used to estimate the fatigue life of the disc spring.
Let’s look at a couple of worked examples that explain how to interpret fatigue life graphs, looking first at the fatigue life of a given disc spring with a preload of 15% of its initial height and with a final position at 75% of its initial height. Referencing the DIN EN 16983 specification chart we see stress at point II at 15% is 128N/mm2 and stress at point III is 264N/mm2. Stress at point II at 75% is 923N/mm2 and stress at point III is 1,140N/mm2.
The difference in stress levels at each point are 795N/mm2 at point II and 876N/mm2 at point III. As the maximum differential in stress occurs at location III, we will use the stress values from this location and the fatigue life charts to estimate the fatigue life of the disc spring.
On the fatigue life graph, the intersection of a vertical line drawn on the X-axis representing the minimum stress at location III and a horizontal line drawn on the Y-axis representing the maximum stress at location III is the estimated fatigue life. In this example and using top graph, the line on the X-axis is drawn at 264N/mm2, and the line drawn on the Y-axis is drawn at 1,140N/mm2. The intersection is slightly above the 100,000 cycle line, representing an estimated fatigue life of slightly less than 100,000 cycles.
Now let’s consider the same spring but with a preload of 25% of its initial height with a final position at 50% of its initial height. The maximum differential in stress occurs again at location III. Referencing the lower fatigue life graph and plotting 430N/mm2 on the X-axis and 810N/mm2 on the Y-axis, the intersection of the lines is slightly below the 2 million cycle line; therefore the estimated fatigue life is over 2 million cycles.
We can see, then, how the deflection range deflection of the disc spring determines its fatigue life. Increasing final load increases stress in the disc spring resulting in lower fatigue life. Increasing preload reduces deflection resulting in increased fatigue life.
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