改进边界元法及其在齿轮有源温度场中的应用

在齿轮本体温度场研究的基础之上，对齿轮有源温度场这一典型的位势问题从理论上进行了探讨．研究表明，在求解齿轮有源温度场问题时，采用二维Ｇｒｅｅｎ公式把区域积分变换成边界积分，不用建立内部单元，而仍只须离散问题的边界，避免了区域积分这个冗长的数值积分计算过程，使求解拉氏方程问题仅离散边界的主要优点得到充分发挥，因此，该方法是一种经济、实用的数值计算方法，此方法的引用使得齿轮有源温度场的实用研究成为可能．关键词

Improved BEM and its Application on theSource Temperature Field in Gears

On the basis of the research into the bulk temperature field in gears makes research theoretically on the source temperature field in gears, which is a typical geopotential problem.The result shows when the source temperature field in gears is solved, the region integral ischanged into the boundary integral by means of Green formula. This method avoids long numerical integral calculating process of region integral and only devides the boundary of theproblem instead of setting up inside unit, and thus the main advantage of deviding theboundary of the solving Laplace formula can be fully exerted. Therefore, this is a practicaland economic numerical computational method and makes it possible to research into thesource temperature field in gears practically.