This work presents a finite-element model-based study of elastic cylindrical contact. The aim is to evaluate the transition between the plane stress and plane strain-based Hertz solutions when each assumption is most applicable. To accomplish this, a range of curvatures, widths, Poisson’s ratios, and friction coefficients are considered. The finite-element model results for the elastic cylindrical contact cases are compared with the Hertz contact model when assuming plane stress or plane strain. Perhaps, surprisingly, the finite-element model predictions show little dependence on Poisson’s ratio and friction coefficient. The finite-element model predictions of force as a function of deflection agree relatively well with the plane stress Hertz prediction for all cases considered. The finite-element model predictions of contact width as a function of force actually fall below all the analytical Hertz predictions. Therefore, an adapted version of the Hertz equations is provided, which shows better agreement with the cases considered in this work.

这项工作提出了基于弹性圆柱接触的有限元模型的研究。目的是评估每个假设最适用时平面应力和基于平面应变的赫兹解决方案之间的过渡。为此，要考虑一定范围的曲率，宽度，泊松比和摩擦系数。在假定平面应力或平面应变时，将弹性圆柱接触盒的有限元模型结果与赫兹接触模型进行比较。令人惊讶的是，也许有限元模型的预测几乎不依赖于泊松比和摩擦系数。对于所有考虑的情况，力作为挠度函数的有限元模型预测与平面应力赫兹预测相对较好。接触宽度作为力的函数的有限元模型预测实际上低于所有解析赫兹预测。因此，提供了Hertz方程的改编版本，该版本与本文中考虑的情况具有更好的一致性。