基于Matlab计算滚动轴承滚滑接触内部应力分布

Calculation of Stress Field in Rolling-Slip Contact of Rolling Bearings Based on Matlab

滚动轴承服役过程中,因滚滑现象和残余应力的存在,使赫兹接触应力不能反映材料真实的受力状态,应力分布与实验现象存在一定的偏差,因此滚滑接触下材料的内部应力计算显得尤为重要。研究一种快速、简单的材料滚滑接触内部应力的计算方法,以替代耗时长的有限元法。以现有公式为基础,通过Matlab编程计算滚滑接触下材料内部的应力场;对比不同摩擦因数下2D、3D滚滑接触内部应力场的差别。结果表明:摩擦因数越大,最大剪切应力越大,位置越接近表面,与滚动方向的夹角越小;切向摩擦力使接触点两侧最大正交切应力大小及位置发生变化;随着摩擦因数增大,一侧应力值上升,位置靠近表面,另一侧反之。提出的计算方法简单、方便,其结果为解析解,便于与残余应力或其他应力结合求出真实应力场。通过实例分析发现,真实应力场能够更好地解释实验现象,对于轴承材料组织演变的研究有重要意义。

During the service of rolling bearings,the rolling-slip phenomenon occurs and residual stress is generated within the material,which makes the Hertz contact stress can not reflect the real stress state,and causes the Hertz contact stress distribution to deviate from experimental results.It is necessary to calculate the internal stress under rolling-slip contact for obtaining the real stress field.A fast and simple calculation method of the internal stress under rolling-slip contact was presented to replace the the time-consuming finite element method.Based on the existing formulas,the stress field in the material under rolling-slip contact was calculated by Matlab programming.The variation was compared of the internal stress field in two-dimensional and three-dimensional rolling-slip contact under different friction coefficients.The results show that with the increasing of friction coefficient,the maximum principal shear stress becomes larger,the position is closer to the surface and the angle with rolling direction is smaller.The tangential friction force changes the magnitude and position of the maximum orthogonal shear stress on both sides of the contact point.As friction coefficient increases,the maximum orthogaonal shear stress on one side of the contact point becomes larger and the position becomes closer to the surface,while on the other side,the change shows an opposite trend.The method of internal stress calculation presented is convenient,the calculation results are analytical solutions,which is convenient to combine with other stress fields to obtain the real stress field inside the material.Through case analysis,it is revealed that the real stress field can explain the experimental phenomena better,which is significant to the study of microstructural evolution in bearing materials.