Disc Springs: Calculation Examples | Tokai Spring industries, Inc.

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Disc
Springs

Shown here are the calculation examples of load and stress when the disc springs shown in Table 2 are set at 199.8 mm and are compressed by 5.5 mm.

Coefficients Used for Calculation

Table 2. Disc Spring Specifications

Symbol	Unit	Value
D	mm	50
d	mm	25.4
t	mm	3
H0	mm	4.1
h0	mm	1.1
E	N/mm²	2.06 × 10⁵
n	piece	2
m	layer	30
R	mm	0.3

Calculation of Load

The free height (L0) when the disc springs are stacked is as follows.

The defections when mounted and at its maximum (δmin and δmax) are as follows.

As there are two springs stacked in parallel, the combined load is 6,911 × 2 = 13,822 N.
Similarly, when δ max. = 0.623 mm, the single load is P max. = 9,576 N, and the combined load is 9,576 × 2 = 19,152 N.

Calculation of Stress

When δ min. = 0.44 mm, the stress of each part is as per the following formula.

Similarly, the stress of each part when δ max. = 0.623 mm is as follows:
σI max ＝-1658 N/mm²
σII max ＝1030 N/mm²
σIII max ＝882 N/mm²
From the results above, the load characteristics of these disc springs are shown in Table 3.

Table 3.

Load(N)	Height(mm)	Deflection(mm)	Stress(N/mm)²
Load(N)	Height(mm)	Deflection(mm)	σI	σII	σIII
0	213.0	0	–	–	–
13822	199.8	13.2	-1196	702	639
19152	194.3	18.7	-1658	1030	882

Service Life Estimation

Next, the service life is estimated. The following figure shows the plotting and applying of stresses at angles II and III in Table 3 corresponding to the tensile load. As the line immediately above the plotted points is a line of 2 million cycles, the service life estimation of this spring is 2 million cycles.