Abstract The influence of the mechanical performance of a workpiece material and the shape of the contact surface of a deformation region on the change in the yield point along the arc of roll contact under cold bar rolling is considered. The error in calculating the equivalent yield point during the replacement of a hardening curve with a linear and an exponential dependence is estimated. A hardening curve approximation is suggested the parameters of which depend on power n of the hardening curve, the initial deformation degree, and the equivalent yield point. This approximation is used to derive the analytical solutions of the von Karman equation for replacing the arc of roll contact and define the contact stresses and the roll effort. We compare the already known and new solutions by analysis. In particular, it is established that the replacement of an arc of roll with a chord at n = 1 weakens the design roll effort by 20% and greater.

中文翻译：

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在定义强化材料板的接触应力和冷轧力时考虑变形区域的形状

摘要 考虑了冷轧下工件材料的力学性能和变形区接触面形状对屈服点沿辊接触圆弧变化的影响。估计在用线性和指数相关性替换硬化曲线期间计算等效屈服点的误差。提出了一种硬化曲线近似，其参数取决于硬化曲线的幂n、初始变形程度和等效屈服点。该近似值用于推导出 von Karman 方程的解析解，用于替换滚动接触弧并定义接触应力和滚动作用力。我们通过分析比较已知和新的解决方案。特别是，