为了获得粗糙表面点接触的力学特性
提高接触元件的承载能力
采用Weierstrass-Mandelbrot函数生成了三维粗糙球形表面
建立了粗糙球形表面与一刚性平面接触的分形力学模型
推导出不同接触区域上各个频率指数的微凸体的截断面积密度分布函数
获得了真实接触面积与总接触载荷的解析表达式
得到了接触半宽上的接触压力分布。计算结果表明:微凸体的频率指数范围直接影响粗糙球形表面的接触力学性质;当最小频率指数n
min
与临界弹性频率指数n
ec
满足n
min
+5≤n
ec
时
粗糙球形表面在整个接触过程中呈现弹性变形性质
当最小频率指数n
min
与临界弹塑性频率指数n
epc
满足n
min
>n
epc
时
粗糙球形表面在整个接触过程中呈现非弹性变形性质;粗糙球形表面的接触半宽主要由基圆确定
对于相同比例的下压量
接触压力峰值与最小频率指数成正比;在弹性变形与弹塑性变形阶段
接触压力在接触区域中心达到最大
向接触区域边缘方向递减
在完全塑性变形阶段
接触压力在整个接触区域近似均匀分布。
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