Permissible Stresses
Permissible Stresses Under Static or Infrequently Changing Loads
Nelle molle a tazza realizzate con acciaio per molle, la tensione σOM in condizione piatta non dovrebbe essere molto superiore al limite di snervamento. Con tensioni superiori, la stabilità della molla a tazza non è più garantita ed il rilassamento sarà superiore rispetto ai valori indicati in paragrafo 8.3.
Per sollecitazione statica si intende un uso pratico con un basso numero di cicli (fino a circa 5000).
Permissible Stresses Under Cyclic (Dynamic) Loads
Minimum pre-load
During the pre-stressing ope ration, the yield poi nt of the material is exceeded at the Cross- Section Point I, resulting in residual tensile stresses in the disc spring. In use, the changes which result in the tensile stresses may lead to stress fracturing of the parts. The effects of the tensile stresses may be effectively counter- balanced to some extent by mea ns of pre- loadi ng the disc spring. The minimum pre-load should be approximately 15% to 20% of the disc spring's available travel. The pre-load deflection necessary may be greater or lesser depending on the general level of stress in the disc spring.
Stresses in the Working Range
The disc spring's performance is dependant upon the oscillations which occur in the tensile stresses on the bottom surface of the spring. The expected number of load changes which can be achieved before failure is determined by the magnitude of the change in the stresses between the lower stress point limit σu associated with the minimum disc spring deflection and the upper stress point limit σ0 associated with the maximum disc spring travel. Depending upon the disc spring's dimensions, either the cross-section point 11 or point lll will be determined to be the critical stress point. Which of the two points (II or III) is the critical stress point may be determined from the following chart.
In the indeterminate area, it is necessary to calculate the lower stress value σu as well as the upper stress value σ0, for both critical points (II and III) of the disc spring.
Figure 19:
Critical Cross-Sectional Points Dependant Upon delta = De/Di e ho/t and K4 · (h'o/t').
Graphs of Fatigue Resistance and Life Expectancy
The following graphs illustrate the expected life cycles of the disc spring, relative to su and σU e σO
Figure 20
Fatigue Resistance and Life Expectancy for Disc
Springs with t<1.25 mm
Figure 21:
Fatigue Resistance and Life Expectancy for Disc Springs with t = > 1.25 mm to t = < 6.00 mm
Figure 22:
Fatigue Resistance and Life Expectancy for Disc Springs with t = > 6.00 mm to t = <: 14.00 mm.
The graphs have been based upon laboratory test results, and indicate a survival probability in the 99 percentile range. The tests were conducted on individual disc springs as well as fully assembled disc spring stacks consisting of ten (10) disc springs arranged in single series orientation. The load was applied sinusoidally and the tolerances between the guide elements and the disc springs were exactly as recommended in Chapter 7.
All testing was accomplished at normal, ambient room temperature without the influence of any chemical contaminants. All tested parts were proven to be defect free prior to the onset of testing.
When deviating from these test conditions, either because of impact loading, increased disc spring stack lengths or by arrangement of disc spring components in parallel, it will be necessary to add a margin of safety to the predicted fatigue strength.
In disc spring stacks consisting of individual disc springs with strongly regressive load characteristics curve (for example, those disc springs listed in Series C), there are variations of the load/deflection characteristics from spring to spring and as a consequence there is uneven compression of the individual springs. This phenomenon is strongly increased by frictional influences. In such cases the fatigue lives will be less than those predicted by the graphs.
Figure 23:
Deformation Distribution in the Disc Spring Stack Consisting of Disc Springs 34.00 x 12.30 x 1.00 l0 = 2.25 mm, with 10, 20 and also 30 Disc Springs per Stack Arranged in Single Series. (Graph data derived from K.H. Hertzer)
Note: In each instance, a pre-load was applied which resulted in a pre-load deflection equal to 0.10 mm and a movement of 0.50 mm per spring.
Pre-Stressing of Disc Springs
Disc Springs are always pre-stressed after heat- treatment. During the pre-stressing procedure, the disc springs lose a portion of their original unloaded height as a direct result of the residual tensile stresses and, consequently, the final, finished l0 dimension is achieved.
The pre-stressing procedures must be done in such a fashion that, after loading the disc spring with double the normal calculated load for disc spring deflection of s = 0.75 ho', the allowable disc spring load variation does not exceed the values shown in Chapter 11.
While the pre-stressing procedures take place in a relatively short period of time, under long term load conditions, additional permanent set occurs. A continuous, constant loading of the disc spring will, over time, result in a gradual reduction of the disc spring load (relaxation).
Basic values for the degree of relaxation in disc springs at various points under various circumstances are reproduced in the graph below.
Beginning with the original spring load (F), each loss of load value ΔF was calculated as a function of the stress σOM and expressed as a percentage.
Figure 24:
Acceptable Relaxation for Disc Springs in Standard Carbon Steels
Figure 25:
Acceptable Relaxation for Disc Springs in Chrome and Chrome-Vanadium Alloy Spring Steel (DIN 17221 and DIN 17222 Listed Spring Steels)
Shet-Peening
Shot-peening improves the life expectancy of the disc spring in dynamic mode applications. This is accomplished by physically changing the surface of the disc spring, by inducing compressive stresses and thus countering of the deleterious effects of the critical tensile stresses.
Shot-peening does not always produce positive results. Therefore, we recommend that you contact our Technical Department for guidance prior to specifying shot-peening for all disc spring applications.