滚动轴承的弹塑性静动力学响应

针对当前滚动轴承的弹塑性力学行为研究相对薄弱等问题,以深沟球轴承为例,建立了研究滚动轴承弹塑性静动力学特性的分析模型.该模型通过引入一个与应力球张量有关的混合硬化屈服准则,建立了各向同性材料的弹塑性增量型本构方程,基于Hertz接触理论确定了作用在内外套圈上荷载之间的关系,由对称性得到了正交曲线坐标系下1/4轴承外圈的平衡方程和相应的定解条件,并综合应用有限差分法和Newmark-β法对问题进行迭代求解.数值结果表明,荷载大小、轴承尺寸和材料的塑性性能均是轴承设计时应考虑的重要因素,传统的弹性模型会过高地估计轴承的刚度,而弹塑性模型能更加精准地描述滚动轴承的力学性能.

Elasto-Plastic Analysis for Static and Dynamic Performance of Rolling Element Bearings

Aiming at the status quo of research in the elasto-plastic mechanical behavior of rolling bearings, taking deep groove ball bearings as an example, a semi-analytical model was established to study the elasto-plastic mechanical behavior of rolling bearings. By introducing a mixed strain hardening yield criterion which is related to spherical stress tensor, the model established an elasto-plastic incremental constitutive equation for mixed hardening materials. The model used Hertz contact theory to determine the relationship between the load exerted on the inner and outer rings. And from the symmetry between the inner and outer rings, the equilibrium equations, as well as the corresponding deterministic conditions for a quarter of the outer ring of the bearings were obtained in the orthogonal curvilinear coordinate system. And then the finite difference method, as well as Newmark-β approach, was applied comprehensively to find an iterative solution of related problems. The numerical results show that the elasto-plastic model can more accurately describe the mechanical properties of rolling bearings; the traditional elastic model might overestimate the stiffness of bearings; the load weight, bearing dimensions and plastic properties of materials are all important factors that should be considered in the design of bearings.