Volume 4,Issue 3
非赫兹接触下Kalker理论的非线性修正模型
轮轮轨接触建模的准确性直接影响轨道车辆动力学仿真可靠性。传统Kalker线性理论在中高蠕滑率条件下存在切应力分布描述失真及力饱和效应缺失的问题，导致预测偏差。为此，本文提出一种融合非赫兹接触几何与非线性修正机制的切向接触模型：基于Kalker线性理论推导非椭圆接触斑的切向力表达式，引入椭圆牵引边界划分黏着区与滑动区，结合Vermeulen-Johnson模型与Shen-Hedrick-Elkins理论构建蠕滑力非线性折减机制。仿真结果表明：在横移量-6mm～6mm、摇头角-0.03～0.03rad工况下，模型计算的纵向切向力相对误差＜15%、横向误差＜10%，较Kalker变分法模型（KVM）效率提升28.7%，实现了中高蠕滑率工况下“高精度预测”与“高效计算”的工程需求，为多体动力学仿真提供了可靠的理论支撑，适用于轨道车辆多体动力学中的高效切向接触建模。
[1] Hertz R H. On the contact of elastic solids[J]. J Reine AngewMath,1882, 92:156-171.
[2] Kalker J J. On the rolling contact of two elastic bodies in the presence of dry fraction [D]. Delft University of Technology, 1967.
[3] Sun Y, Shi F, Zhang S, et al. Improving the robustness of non-Hertzian wheel-rail contact model for railway vehicle dynamics simulation[J]. Multibody Syst Dyn,2023,59:193-237.
[4] Sun, Y, Ling, L. An optimal tangential contact model for wheel-rail non-Hertzian contact analysis and its application in railway vehicle dynamics simulation[J]. Veh Syst Dyn, 2022，60(9): 3240-3268.
[5] VERMEULEN P J, JOHNSON K L. Contact of Nonspherical Elastic Bodies Transmitting Tangential Forces[J]. Journal of Applied Mechanics, 1964, 31(2):338-340.
[6] KALKER J. On the Rolling Contact of Two Elastic Bodies in the Presence of Dry Friction [J]. Delft University of Technology, Netherland, 1967.
[7] SHEN Z Y, HEDRICK J K, ELKINS J A. A Comparison of Alternative Creep Force Models for Rail Vehicle Dynamic Analysis[J]. Vehicle System Dynamics, 1983, 12:79- 83.
[8] 李粮余, 田春香, 周佳仪等. 一种应用于轮轨滚动接触的非赫兹型简化计算模型[J]. 高速铁路技术,2021,12(3):6-13.
[9] 安博洋. 轮轨滚动接触行为的数值研究[D]. 西南交通大学,2020,10:27414.
[10] Sichani M, Enblom R, Berg M. A fast wheel-rail contact model for application to damage analysis in vehicle dynamics simulation[J]. Wear, 2016, 366-367:123-130.
[11] 周佳仪. 几种非赫兹轮轨滚动接触模型的对比研究[D]. 西南交通大学,2021,000548.
[12] Li G, Yang F, Fu J, et al. A modified Hertzian-based wheel-rail contact model for vehicle system dynamics simulation[J]. Vehicle System Dynamics, 2024,1–18.
[13] Zhai W. Vehicle-Track Coupled Dynamics Theory and Applications[M]. Singapore Springer, 2020.
[14] Sun Y, Zhai W, Ye Y, et al. A simplified model for solving wheel-rail non-Hertzian normal contact problem under the influence of yaw wangle[J]. International Journal of Mechanical ences, 2020, 174:105554.
[15] An B, Wang P. A wheel–rail normal contact model using the combination of virtual penetration method and strip-like Boussinesq’s integral[J]. Vehicle System Dynamics, 2022, 61(6):1583–1601.
[16] Yang Y, Wang R, Wang J, et al. Comparison of wheel/rail contact modelling in prediction of wheel tread wear under changeable friction conditions[J]. Vehicle System Dynamics, 2024, 1–30.
[17] Liu B, Bruni S. Comparison of wheel–rail contact models in the context of multibody system simulation: Hertzian versus non-Hertzian[J]. Vehicle System Dynamics, 2020, 60(3): 1076–1096.
[18] Vollebregt E. A, H. Detailed wheel/rail geometry processing using the planar contact approach[J]. Vehicle System Dynamics, 2020,60(4):1253–1291.
[19] Pascal J, P Sany, J R. Dynamics of an isolated railway wheelset with conformal wheel–rail interactions[J]. Vehicle System Dynamics, 2019, 57(12):1947–1969.
[20] Yang Y, Guo X, Sun Y, et al. Non-Hertzian contact analysis of heavy-haul locomotive wheel/rail dynamic interactions under changeable friction conditions[J]. Vehicle System Dynamics, 2021, 60(6):2167–2189.
[21]Gómez-Bosch J, Giner Navarro J, Carballeira J, Baeza González LM. A direct method for the extension of Fast Sim under non-Hertzian contact conditions[J]. Vehicle System Dynamics, 2023,61(10):2551-2569.
[22] Sun Y, Zhai W, Guo Y. A robust non-Hertzian contact method for wheel-rail normal contact analysis[J]. Veh Syst Dyn, 2018,56(12):1899-1921.