Study on Relationship Between Three-dimensional Height Parameters and Maximum Mises Stress of Surface
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摘要: 为研究粗糙表面微观形貌特征参数与接触应力的关联性，选取粗糙度参数标准ISO25178中与接触变形密切相关的三维高度参数为研究对象。通过BP神经网络构建高度参数与最大Mises应力的关系模型，并分别采用Sobol和MIV敏感性分析法，基于220组实测超声磨削加工表面数据分析了高度参数对最大Mises应力的影响程度并筛选出了主要影响参数。利用统计学相关性原理和多项式回归分析方法，建立了主要影响参数和最大Mises应力的非线性回归模型。结果表明：1）7个高度参数对最大Mises应力的重要性由大到小为：算数平均高度Sa、均方根高度Sq、偏斜度Ssk、最大高度Sz、最大峰高Sp、最大谷深Sv和峭度Sku；2）以90% 的总影响度为基准，筛选出主要影响参数为：Sa、Sq和Ssk；3）回归模型相对于椭球微凸体接触算法，相对误差在10%以内，且计算效率更高，具有一定工程实用价值。Abstract: In order to study the relationship between the micro morphology characteristic parameters and the contact stress of rough surface, based on the definition standard ISO25178 of micro topography roughness parameters, the three-dimensional height parameters which are related to contact deformation were selected as the objects to build the relationship model with maximum Mises stress based on 220 sets of measured ultrasonic grinding surface by back propagation (BP) neural network. Then, the influence of the different height parameters on the maximum Mises stress was analyzed and the main parameters affecting maximum Mises stress were selected by Sobol and mean impact value (MIV) sensitivity analysis methods. Finally, the nonlinear regression model for height parameters selected above and the maximum Mises stress was established through statistical correlation principle and polynomial regression analysis method. The results show that: 1) The importance of all 7 height parameters to maximum Mises stress from large to small is as follows: arithmetic average height Sa , root mean square height Sq , skewness Ssk , maximum height Sz , maximum peak height Sp , maximum pit height Sv and kurtosis Sku ; 2) Based on 90% of total influence degree, the selected height parameters that play a major role in maximum Mises stress are: Sa, Sq and Ssk ; 3) Comparing with the ellipsoid contact algorithm, the relative error of regression model is less than 10%, and the calculation efficiency is greatly improved. These show that the model has a practical value.
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Key words:
- rough surface /
- height parameters /
- contact stress /
- relationship study /
- nonlinear regression
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表 1 超声磨削实验条件
加工参数 参数水平 砂轮 类型 CBN砂轮 半径 100 mm 目数 120 转速 1500 r/min 切削速度 200 mm/min 切削深度 5~25 μm 超声振动 频率 20 kHz 振幅 0~10 μm 
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表 2 Sa、Sq、Ssk和最大Mises应力之间相关系数
Sa Sq Ssk 最大Mises应力 Sa 1 0.979 0.191 0.814 Sq 0.979 1 0.097 0.792 Ssk 0.191 0.097 1 0.223 最大Mises应力 0.814 0.792 0.223 1
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