Application of Mapping Theory to the Integral Equation for the Stress Analysis of Spur Gear. Boundary Integral Equation Method for Gear Tooth Analysis.

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  • 積分方程式への写像理論の応用および歯車解析　境界積分方程式法による平歯車解析
  • セキブン ホウテイシキ エ ノ シャゾウ リロン ノ オウヨウ オヨビ ハグル

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Abstract

In a previous work, a conformal mapping function was used to transform an integral equation into a system of linear equations which can be solved. This paper describes how the conformal mapping technique is applied for solving the boundary integral equation discussed in the previous work. In order to avoid constructing a mapping function, the boundary integral equation method is also employed for the numerical solution of a conformal mapping function that transforms a gear domain into a half-domain. Then, the obtained boundary values of mapping are used to solve the boundary integral equation formulated in the half-plane. A comparison with the old method has proved the highest accuracy of the new method proposed here.

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