Influence of load spectrum on contact fatigue damage of a case carburized wind turbine gear
Introduction
One of the most concerning issues in advanced geared machines is the contact fatigue, which significantly undermines the service lives and reliabilities of the associated gear systems. With the view to reveal the mechanism of the gear rolling contact fatigue (RCF), extensive investigations have been conducted considering multifarious factors, such as the lubrication state [1], hardness gradient [2] and residual stress distribution [3]. The RCF of gears can manifest itself in various types including micro-pitting [4], pitting [5] and tooth flank fracture (TFF) [6].
Fig. 1 shows the main factors affecting gear RCF and resultant contact fatigue failures. Aiming to estimate the contact fatigue performance, diverse multiaxial fatigue criteria have been developed to evaluate RCF life or failure risk. Among them, the Dang Van criterion [7], combining the historical characteristics of maximum shear stress and hydrostatic stress histories, is widely adopted in RCF studies. Desimone et al. [8] modified the fatigue failure locus of Dang Van criterion according to the test results. Results suggest that the proposed method is likely to constitute a more suitable RCF limit than the traditional method. Cerullo [9] applied the Dang Van criterion to study the effect of residual stress and hardness gradients on the RCF performance of wind turbine bearings. They found that RCF was most likely to initiate within the material a bit beneath surface, which was consistent well with that in the literatures. In addition, the Basquin equation is well accepted in the high-cycle fatigue life evaluations [10]. Reis et al. [11] combined the Dang Van criterion and the Basquin equation to estimate the plastic strain accumulation on rails for heavy-haul transportation and the impacts on the fatigue lives. Zhao et al. [12] applied the Basquin equation in fatigue assessment under service loadings of a torsion beam rear axle. The fatigue tests demonstrated the accuracy of the life prediction, which could be dramatically improved by considering the strengthening and damaging effects of loadings below fatigue limits.
To improve the gear RCF resistances, diverse techniques have been implemented in engineering practice, such as the case carburizing [13], coating [14] and tooth modification [15]. Despite the continuous improvements on the theoretical and experimental studies, and industrial techniques, the gear RCF is inevitable. Large amounts of specific investigations are yet to be further launched.
As revealed by the experimental observations [16], the fatigue crack nucleation of carburized gears is more possible to initiate within the contact regime, where the material mechanical properties varies sharply from the gear case to the core [17]. The residual stress distributions induced by the machining, heat or surface treatments processes can significantly influence the contact fatigue performance [18]. Mackaldener and Olsson [19] investigated the tooth interior fatigue fracture of case-hardening gears based on the critical plane criterion developed by Findley [20], addressing the obvious impact of residual stress distribution. Boiadjiev et al. [21] studied the mechanism of TFF in carburized gears. Results indicate that the compressive residual stress makes the transition area between the case and the core more vulnerable to the TFF than the tooth surface or subsurface initiated failures. Katsumi and Masana [22] established an experimental equation to estimate the bending strength of a group of case carburized gears. This equation shows that the increases of surface hardness value and residual stress amplitude are beneficial for improving the fatigue strength. Wang et al. [23] evaluated the contact fatigue failure of a wind turbine gear pair considering the hardness and residual stress distributions. Results indicate that the plastic strain accumulation within the substrate is dramatically affected by the initial residual stress state under heavy loading condition.
The damage accumulation during the service stage can be estimated based upon the load spectrum when suffering the stochastic loadings. The Palmgren-Miner rule is widely applied in the evaluation of the damage accumulation under variable loading conditions, making the fatigue life design more applicable to the engineering practice [24]. Qiao [10] calculated the fatigue failure risk and cumulative damage of a gear pair during cycling contact, enabling the comparison among several classic multiaxial fatigue criteria. Raje et al. [25] established a damage theory based fatigue model to simulate the initiation of pitting at subsurface. This model included the gradual material degradation due to cyclic contact through an empirical damage evolution equation. Niesłony [26] proposed a damage-time function for predicting the position of crack nucleation. Results imply that a shortened service loading history possess the same frequency characteristic as the whole operation history, which is beneficial for preparing the fatigue experiments during early stage design. Höhn et al. [27] conducted a gear test to evaluate the relative pitting resistances of various lubricants. In their work, two different test procedures were presented, one with a load spectrum and the other a constant loading.
However, the above studies hardly evaluate the contact fatigue life or the damage accumulation under the load spectrum together with the lubrication state and mechanical gradients. In this work, a wind turbine gear contact fatigue model with the EHL effect, residual stress and hardness gradients, was established. The load spectrum was programmed through the obtained wind loading histories via rain-flow algorithm. The Dang Van multiaxial criterion and the Basquin equation were used to predict the fatigue life, where the influence of the mean stress was considered. The Palmgren-Miner rule was employed to evaluate the fatigue damage accumulation for analyzing the impact of the load spectrum on gear contact fatigue behaviors.
Section snippets
Simulation methodology
The stress and strain components was calculated under the EHL condition when studying gear RCF. The effects of the residual stress and the hardness gradients were also incorporated. The evaluations of the RCF life and the damage accumulation were proceeded after obtaining the load spectrum. Fig. 2 depicts the overall technical route of this work.
Life estimation with constant load amplitude
According to the modified Basquin equation, the predicted fatigue life would decrease with the increase of the Dang Van equivalent stress , or with the decreasing magnitude of the mean of the compressive normal stress . These stress results displayed in Fig. 10 were calculated under the reference working condition during a complete loading cycle. The maximum is 0.28 GPa, which appears at the depth of around 0.31 mm. Besides, the maximum magnitude of is 1.09 GPa, which
Conclusions
In this work, a numerical EHL model was developed for a carburized wind turbine gear pair to investigate the contact fatigue behavior. The Dang Van multiaxial criterion and the Basquin equation were employed to predict the fatigue life. The damage accumulation under the measured load spectrum was evaluated by the linear Palmgren-Miner rule. The effect of each loading stage within the load spectrum on the fatigue damage accumulation was discussed. Main conclusions can be mainly summarized:
- 1)
As the
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
The work is supported by the National Natural Science Foundation of China (Grant Nos.: U1864210, 51775060).
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