基于弹性赫兹接触的钢轨砂带打磨材料去除建模研究

Research on Modeling Method of Material Removal for Rail Grinding by Abrasive Belt Based on Elastic Hertzian Contact

为揭示钢轨砂带打磨材料去除机理,针对接触轮-钢轨曲面接触和砂带表面磨粒尺寸、位置随机特点,基于弹性赫兹接触理论,分析接触轮-钢轨宏观接触区域状态,获得接触面积和名义接触压力分布;结合砂带表面磨粒出刃高度分布统计学模型与单颗磨粒微观受力分析,获得单位面积打磨压力与磨粒最大切入深度关系;综合考虑磨粒出刃高度、磨粒外形、磨粒密度、砂带旋转速度、行车作业速度、打磨压力、接触轮硬度以及接触轮与钢轨之间的相对主曲率等多项参数,最终建立钢轨砂带打磨材料去除深度数学模型和材料去除量数学模型.试验结果表明,材料去除深度与材料去除量预测值同试验结果的最大偏差分别为3.6％和11.95％,验证了上述模型的正确性和有效性.

To investigate the material removal mechanism in rail grinding by abrasive belt, the contact situation is analyzed initially based on elastic Hertzian contact theory, the curved face touch between contact wheel and rail surface is considered. Meanwhile, the contact area as well as the contact pressure distribution is calculated. Then the relationship between grinding pressure and maximum cut depth is introduced based on statistic model of grains’ protrusion height and force bearing analysis on the single grit to deal with the irregularity and randomness of grains’ shape and distribution. Finally, the mathematical model of material removal depth and material removal amount are derived, involved with grains’ protrusion height, grains’ shape, grains’ density, abrasive belt velocity, driving speed, grinding normal force, contact wheel hardness, relative principal curvature and so on. The maximum deviation between the predicted values and the experimental results for material removal depth and material removal amount are 3.6% and 11.95%, respectively, which verifies correctness and validity of the above mentioned models.