車輪・レール間の非Hertz接触計算手法の研究: 第2報，解析の対象領域の見積もりと車輪・レール間の接触問題への適用

摘要

In this paper, we present the result of a study made on an effective numerical method for evaluating the area, which has to be analyzed to find a contact area precisely. The contact area is found as an area where normal contact pressure is plus in the analyzed area when one solves a normal contact problem applying Kalker's "EXACT THEORY". Therefore, it is inferable that one can find a contact area and contact pressure finely within a limited amount of analyzed points if the analyzed area can be set slightly larger than the true contact area. It is allegeable in this paper that applying our proposed method one can find a better analyzing area minifying the former analyzed area in the process of an optimal calculation and can find a precise contact area, pressure distribution, etc. in the end of the calculation. First, the algorithm of reducing the analyzed area is stated and applied to the normal contact problem of two balls. Then, it is applied to contact problems of wheel and rail. The algorithm works satisfactorily, and the results revealed a good coincidence with the results calculated by the Kalker's original algorithm. The iteration counts of our method where the analyzed area is set approximately 10 to 100 times as large as the true contact area is less than two times that of Kalker's where the analyzed area is purposely set slightly larger than the true contact area.%鉄道車両の運動を考えるうえで，走行シミュレーションを行うような場合，車輪とレールの間の接触問題，特に，車輪とレールの接触蘭域でどのような弾性変形やそれに伴うクリープカが生じているのかという問題を精度よく高速に解けることが重要である. 本論文第1報［りでは，KalkerのEXACT THEORYについて，EXACT THEORYの内部で行う最適計算のアルゴリズムについて検討を行い，Kdkerによる計算手法，及び本研究で適用した主双対内点法による計算手法について記し，同一の接触問題に対して同等の解を得るにあたって主双対内点法による計算のほうがより高速に計算が可能であることを記した.