Development of Gear Tooth Stress Analysis System Based on Multi-Purpose CAE Software

用有限元方法分析齿轮啮合齿面接触问题是非常困难的。为了方便处理啮合齿面边界条件，考虑齿面修形和误差，提出了一种新的齿面膜单元。这是一个放置在齿侧的虚拟元件，可以评估啮合齿侧之间的接触压力分布。同时，全局局部有限元法（GLFEM）可以使齿面膜单元更加有效。该方法将解析域分为两部分：局部域仅用有限元解表示域，整体局部域用解析解与有限元解叠加表示域。本文采用矩形表面均布荷载作用下的半有限体的解析解。在此基础上，提出了一种将一些独立区域作为全局局部域的公式。不幸的是，我们还没有进行开发。同时，为了验证所开发的齿轮齿面分析系统的可靠性，设计了用测压膜测量静态啮合齿侧齿面接触压力分布的实验。然而，压力测量膜的力学性能与钢的力学性能不同。因此，测量结果应进行校正。提出了基于赫兹接触理论的修正方法。此外，我们的最终目标是分析整个系统，不仅包括齿轮，还包括轴，轴承和外壳。轴承的刚度可能是主要问题之一。因此，我们开始了评估轴承刚度的实验。

It is very difficult to apply Finite Element Method to analysis of a contact problem on meshing gear teeth. A new element, tooth flank film element, has been proposed to easily handle boundary conditions on meshing tooth flanks in consideration of tooth flank modification and any errors. This is a virtual element which is placed an a tooth flank, and enables distribution of contact pressure between meshing tooth flanks to be evaluated. Meanwhile, Global Local Finite Element Method(GLFEM) can make the tooth flank film element more effective. In this method, an analytical domain is divided two parts : in one part called local domain, fields are expressed by only finite element solutions, and in the other part called global local domain, they are expressed by superposing analytical solutions to finite element solutions. We use an analytical solution of semi-finite body subject to uniform distributed loads on rectangle area of its surface. Furthermore, we performed a formulation in which some independent area are taken as global local domains. Unfortunately, we have not done the development.Meanwhile, in order to confirm the reliability of the developing gear tooth analysis system, we planned experiments in which the distribution of tooth contact pressure between meshing tooth flanks in static is measured with a pressure measurement film. However, mechanical properties of the pressure measurement film are different from those of steel. Therefore, the measured results should be corrected. We have proposed the correcting method based on Hertzian contact theory.Furthermore, our ultimate objective is to analyze a whole system which includes not only gears but also shafts, bearings, and housing. The stiffness of bearing could be one of main issues. Therefore, we began the experiments of evaluating the bearing stiffness.