Case Study on the Determination of the Local Fatigue Limit of a Mechanical Component

The described task is tackled here with reference to the fatigue limit of gears, con­sidering bending fatigue at the tooth root.

The cyclic load is applied by a pair of twin punches, as shown in Fig. 7.46. The load trend is basically a pulsating one, even if a non-zero minimum load is applied to ensure the correct positioning of the gear with respect to the horizontal surfaces of the punches throughout the test. As a consequence, the load ratio is not exactly zero, but is increased to 0.1.

The tests are performed on a resonant testing machine, operating at a frequency of approximately 110 Hz. The fatigue limit is initially determined in terms of the maximum load (Fmax) applied by the pair of punches. Afterwards, a simple linear relationship, determined by Finite Element Modeling (FEM), will be introduced to provide the conversion of loads into stresses.

The first step, like in the examples concerned with explosives, consists in the estimation of the most likelihood value for the fatigue limit. In the present case, this value is estimated, based on the material data (high strength steel), on the heating and surface treatments (quenching, carburizing, shot-peening and super-finishing) and on the literature [55, 57, 60-67]. The resulting value, in terms of Fmax, is 12 kN. Afterwards, an important issue consists in the most proper choice of the load step. This is not an easy choice, as in [54] it is specified that the most suitable value should range between 0.5 and 2 a, where a stands for the standard deviation affecting the fatigue limit. It is clear that problems arise from the occurrence that the value of the standard deviation can be retrieved only at the end of the campaign. The only available option lies in a reasonable estimation of the standard deviation and therefore of the step value, with a final check of it being within the aforementioned interval. Moreover, it is interesting to observe that the optimal value for the load step is the result of a compromise. A low value would lead to a refined estimation of the fatigue limit; however, it would require many tests, especially considering the many like responses that could be obtained at the beginning of the series.

For instance, if the initial load value is too high, we could have many failure responses before a not-failure occurs.

Conversely, if it is too low, many subsequent tests would lead to not-failure, before having a failure outcome. On the other hand, a higher value is likely to lead to a coarse estimation of the fatigue limit with a fewer number of trials.

In [54] a distinction is made between the overall number of fatigue tests and that of the so-called nominal tests. This number, usually regarded as N, can be defined as the total amount of tests (N’), reduced by one less than the number of like responses at the beginning of the series. The response of a fatigue test may be failure or not — failure, when the test is stopped upon run-out (corresponding to the number of cycles at the fatigue limit in the Wohler curve). When considering specimens in steel, this number usually lies between 106 and 5 ■ 106, to be incremented up to 107 for the sake of safety. For aluminium alloy samples, higher run-out values must be set, usually between 107 and 108.

The Dixon method [54] makes it possible to roughly estimate the fatigue limit, based on the results of even just two nominal tests. However, the recommended amount for the nominal tests is at least 6, to obtain a sufficiently reliable result. The uncertainty decreases, as the number of tests increases and becomes generally quite low for 10 nominal tests (or more). The proposed formulation for the processing of the experimental data and for fatigue limit computation depends on the number of nominal tests. Two cases are possible: N between 2 and 6, or N beyond this amount.

Updated: 5 сентября, 2015 — 12:10 пп