基于轮轨非Hertz接触的影响系数的有限元计算方法

Calculation of Influencing Number of WheelRail NonHertz Contact Using Finite Element Method

摘要:

采用非Hertz接触理论求解轮轨接触问题时，影响系数对轮轨接触应力与接触斑大小产生重要影响.由于当车轮轮缘与钢轨在轨距角处发生接触时，非Hertz接触理论中基于弹性半空间条件下的影响系数已不适用,所以利用有限元方法求解了全空间内轮轨非Hertz接触的影响系数，并对Kalker的非Hertz接触理论做了修正.在保证计算效率的前提下，以30 t轴重重载铁路CHN75钢轨和LM磨耗车轮踏面为例，采用修正的非Hertz理论及轮轨接触分区模型P_M（partition model）分别计算了轮对横移量为0~8 mm时的轮轨接触斑面积及接触斑应力.研究结果表明，用有限元法计算出的影响系数大于BossinisqeCerruti 公式求出的影响系数，并且在轨距角处的影响系数大于轨顶处.修正的非Hertz理论计算出的法向应力和接触斑面积始终要比P_M模型计算出的法向应力略大一些，且随轮对横移量的增加，两种轮轨法向接触模型计算出的法向应力和接触斑趋势一致.当横移量为0~4 mm时，最大接触斑面积可达173.75 mm2，轮轨型面较为匹配；当横移量持续增大时，由于车轮与钢轨轨距角接触，接触面积急剧降低，同时法向应力急剧增大.

Abstract:

When wheel/rail contact problems are solved using nonHertz contact theory, the influencing numbers have more important effect on wheel/rail contact stress and contact patch. When a contact between wheel flange and rail gauge angle occurs, the influencing number of nonHertz contact theory based on elastic half space hypothesis is not applicable. Based on elastic full space hypothesis, a finite element method was presented to calculate wheel/rail contact influence number of nonHertz contact theory, and the nonHertz contact model was innovatively revised. As an example of wheel/rail contact profile of the CHN75 standard rail and LM standard wheel in China, under the calculation of high efficiency, two wheel/rail contact models (revised nonHertz method and wheel/rail profile partition model P_M (Partition Model) were used to calculate the wheel/rail normal contact stress and contact patch area when lateral displacement of the wheelset ranged from 0 mm to 8 mm. The results show that the influencing number calculated by finite element method is larger than that obtained by using BossinisqeCerruti formula. And the result calculated by finite element method on the rail gauge corner is larger than that on the top of the rail. The normal stress calculated by revised nonHertz theory is larger than that calculated by the P_M model, and the change of the normal contact stress and contact patch area calculated by two wheel/rail contact model is almost the same with the increase of the lateral displacement of the wheelset. When the lateral displacement of the wheelset is 0 to 4 mm， the maximum of the wheel/rail contact patch area is 173.75 mm2 and the wheel/rail contact profile is best matched. With the increase of the lateral displacement of the wheelset, the contact between the wheel flange and rail gauge corner will be produced and the wheel/rail contact area decreases while the normal contact stress increases dramatically.