基于有效扭矩的冲击成形金属板的热弹性模型
摘要
制造业中常用的 shaping 金属面板的技术是冲击成形。硬钢球与较软金属板之间的碰撞会导致局部塑性变形，用于改善材料表面的疲劳性能。冲击还会施加残余应力分布，从而导致板材弯曲，表明存在与之相关的扭矩。本文将冲击成形建模为将空间分布扭矩应用于 Kirchhoff 板，并采用热弹性语言来引入这些扭矩分布。首先，我们推导热弹性薄板模型的支配方程，证明仅存在于温度分布的扭矩型结果才会出现在弯曲方程中。接下来，为校准从冲击成形操作中获得的用于热弹性模型的经验性有效扭矩参数，设计了一个简单且非侵入的测试方法。该测试仅依赖于测量均匀冲击成形的板的最大位移，而非特征化残余应力分布。After discussing how to handle the unconventional fully-free boundary conditions germane for peened plates, we introduce an approach to solving the inverse problem whereby the peening distribution required to obtain a specified plate contour can be obtained. Given the non-unique relationship between peening distributions and the displacement at discrete points, we explore a regularization of the inverse problem which gives rise to shot peen distributions that match the capabilities of equipment in the factory. In order to validate our proposed model, an experiment with quantified uncertainty is designed and carried out which investigates the agreement between the predictions of the calibrated model and real shot peen forming operations.
引用
@article{arxiv.2505.05236,
title = {A thermoelastic plate model for shot peen forming metal panels based on effective torque},
author = {Conor Rowan},
journal= {arXiv preprint arXiv:2505.05236},
year = {2025}
}