钢轨砂带磨削温度场建模与有限元仿真

王海鹏; 李建勇; 赵超越; 刘月明

doi:10.13394/j.cnki.jgszz.2024.0050

钢轨砂带磨削温度场建模与有限元仿真

doi: 10.13394/j.cnki.jgszz.2024.0050

王海鹏^{1, 2},
李建勇¹,
赵超越^1, ,,
刘月明¹

1.
北京交通大学机械与电子控制工程学院, 北京 100044
2.
国能铁路装备有限责任公司, 北京 100089

基金项目: 自然科学横向项目（KML21172530）。

详细信息

通讯作者:
赵超越，男，1996年生，工学博士、中级实验师。主要研究方向：开式砂带钢轨磨削。E-mail：10124@bjtu.edu.cn

中图分类号: TG58; TG74; TH16
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出版历程
- 收稿日期: 2024-03-16
- 修回日期: 2024-08-02
- 录用日期: 2024-08-12
- 刊出日期: 2025-06-30

Modeling and finite element simulation of temperature field in rail abrasive belt grinding

1.
School of Mechanical, Electronic and Control Engineering, Beijing Jiaotong University, Beijing, 100044, China
2.
China Energy Railway Equipment Co., Ltd., Beijing 100089, China

摘要

摘要: 使用砂带磨削钢轨表层材料可去除钢轨病害、延长钢轨服役寿命，但磨削过程中砂带与钢轨的接触区域内会产生高温，磨削后钢轨表面的热塑性变形使钢轨表层和内部分别产生残余拉应力和残余压应力，加快钢轨损伤，准确掌握钢轨磨削过程中磨削参数对磨削温度的影响规律，可进一步提高钢轨磨削质量并延长钢轨服役寿命。为此，基于弹性接触理论和内凹接触轮驱动的钢轨砂带磨削过程，建立钢轨表面接触压力分布区域模型；根据磨削热产生和传导原理构建钢轨砂带磨削表面温度分布模型，且采用仿真分析法，分析磨削温度在磨削功率、进给速度、砂带速度和钢轨磨削深度影响下的变化规律，并对钢轨亚表层的磨削温度分布进行研究，验证温度场模型的正确性。结果表明：磨削区最高温度与磨削功率和砂带速度呈正相关，与进给速度和钢轨磨削深度呈负相关，且进给速度对温度的影响最显著。
- 接触压力 /
- 磨削热 /
- 温升模型 /
- 磨削温度场
Abstract: Objectives Rail is an important component of rail transit, carrying train loads and guiding vehicle direction in service. Due to worn-outs and shocks during service, rails can cause various defects such as corrugation, spalling and squat, which seriously threaten the safety of train running, reduce the stability of train running and produce huge running noise. The use of sand belt grinding to remove the surface material of steel rails can remove surface defects and achieve the goal of extending the service life of steel rails. However, during the grinding process, a large amount of grinding heat will be generated in the grinding area between the sand belt and the rail, causing the temperature of the rail to rise. Due to differences in temperature distribution and cooling rates, residual stress will be generated on the surface of the rail, and martensitic burns may occur in severe cases, reducing the service life of the rail and accelerating the rate of rail damage. Therefore, it is necessary to accurately control the grinding temperature during rail grinding, and accurately grasp the influence law of rail grinding parameters on the grinding temperature, so as to further improve the grinding quality of rails and extend their service life. Methods Based on elastic contact theory and the grinding process of an abrasive belt rail driven by a concave contact wheel, a contact pressure distribution region model of the rail surface is established. According to the principles of grinding heat generation and conduction, a grinding surface temperature distribution model of the abrasive belt rail is established, and the accuracy of the model is verified by simulation analysis. At the same time, the variation rule of grinding temperature under the influence of grinding power, grinding speed and sand belt speed is analyzed, and the distribution of grinding temperature in the rail subsurface is studied. Results Firstly, based on the theory of elastic contact and the abrasive belt rail grinding process driven by a concave contact wheel, the actual contact situation between the rail and the abrasive belt is further simplified to make the contact problem more universal and regular. The contact model of rail abrasive belt grinding is solved based on Hertz contact theory, and the distribution shape of the contact area is obtained. And based on the contact model, the maximum stress model of the area is solved, and the relationship between the concentrated grinding positive pressure during the grinding process and the distribution of grinding pressure in the contact area is established, obtaining the grinding pressure distribution model. Secondly, based on the grinding pressure distribution model, the total energy of the grinding area is obtained, and the form of conversion from grinding energy to grinding heat is analyzed. The thermal flow rate in the grinding area is analyzed and integrated, and the discrete point heat source set generated by multi-abrasive grinding is transformed into a continuous surface heat source. The total heat in the grinding zone is calculated based on the grinding power and grinding contact area. The relevant theory of ultimate chip energy is applied to solve the heat flow into the chip. Based on the energy distribution model of a single abrasive grain rubbing on the workpiece surface and the heat distribution ratio between the rail and the belt, the heat flow into the rail is calculated. Based on the transient point heat transfer model in heat conduction theory, the multiple discrete moving point heat source set is transformed into a moving surface heat source model according to the generation and conduction mechanism of grinding heat. The dynamic temperature distribution model and the maximum temperature solution model for the rail grinding surface are constructed. Finally, the simulation model of the temperature field in the grinding area is established based on the heat transfer model of the rail abrasive belt, the grinding pressure distribution model, and the general thermal conductivity differential equation derived from the variational principle of heat transfer and the Gaussian formula. The mathematical model is validated using simulation analysis. At the same time, the influence mechanism of the grinding power, grinding speed, and abrasive belt speed on grinding temperature and the variation law of grinding temperature are analyzed, and the grinding temperature distribution of the rail subsurface is studied. Conclusions The highest temperature in the grinding zone is positively correlated with the grinding power and the abrasive belt speed, and negatively correlated with the grinding speed. Moreover, the influence of grinding speed on temperature is the most significant. Therefore, in the process of rail abrasive belt grinding, a higher grinding speed should be used as much as possible to reduce the grinding temperature. At the same time, the increase in abrasive belt speed has a significant effect on temperature rise, so the grinding power should be increased first and then the abrasive belt speed should be increased when the grinding efficiency is increased.
- contact stress /
- grinding heat /
- temperature rise model /
- grinding temperature field

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图 1 钢轨砂带磨削过程示意图

Figure 1. Schematic diagram of abrasive belt grinding process for steel rail

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图 2 钢轨接触模型及接触区域俯视图

Figure 2. Rail contact model and top view of contact area

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图 3 钢轨横切面示意图

Figure 3. Rail cross section schematic diagram

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图 4 接触区域长度示意图

Figure 4. Schematic diagram of contact area length

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图 5 接触区域的压力分布

Figure 5. Stress distribution in contact zone

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图 6 三维传热模型

Figure 6. Three-dimensional heat transfer model

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图 7 磨削热流作用模型

Figure 7. Model of grinding heat flow effect

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图 8 有限元三维模型的网格划分

Figure 8. Mesh partitioning of finite element three-dimensional models

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图 9 温度仿真云图

Figure 9. Simulated thermal nephogram of temperature

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图 10 不同磨削功率下最高温度的理论和仿真值对比

Figure 10. Comparison of theoretical and simulated values of maximum temperature under different grinding powers

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图 11 磨削功率对最高温度理论和仿真值相对误差的影响

Figure 11. Influence of grinding power on relative error between theoretical and simulated values of maximum temperature

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图 12 砂带速度对最高温度理论和仿真值的影响

Figure 12. Influences of abrasive belt speeds on theoretical and simulated values of maximum temperature

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图 13 砂带速度对最高温度理论与仿真值相对误差的影响

Figure 13. Influences of abrasive belt speeds on relative error between theoretical and simulated values of maximum temperature

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图 14 不同进给速度下的最高温度理论和仿真值

Figure 14. Theoretical and simulation values of maximum tempera-ture at different feed rates

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图 15 进给速度对最高温度理论与仿真值相对误差的影响

Figure 15. Influences of feed rates on relative error between theore-tical and simulated maximum temperature values

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图 16 不同深度下的温度变化曲线

Figure 16. Temperature variation curves at different depths

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图 17 钢轨磨削实验现场

Figure 17. Rail grinding experiment site

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图 18 T440型热像仪温度测量结果

Figure 18. Temperature measurement results of T440 thermal imager

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图 19 理论温度与实验温度对比

Figure 19. Comparison between theoretical temperature and experimental temperature

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图 20 砂带速度对理论温度与实验温度相对误差的影响

Figure 20. Influences of abrasive belt velocities on relative errors of theoretical and experimental temperature

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表 1 温度仿真参数

Table 1. Temperature simulation parameters

参数	取值
密度 ρ_w / (kg·m⁻³)	7 850
泊松比 ε	0.32
弹性模量 E / GPa	208
导热系数 K_IC / （W·m⁻¹·K⁻¹）	51
比热容 c / （J·kg⁻¹·K⁻¹）	460
热辐射系数 C_T	0.8
热对流系数 h / (W·m⁻²·K⁻¹)	5
接触轮内凹面半径 R₀ / mm	200

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表 2 磨削功率对最高温度的影响

Table 2. Effect of grinding power on maximum temperature

参数	取值
磨削功率 P / kW	0.72, 0.78, 0.84, 0.90, 0.96
最高温度理论值 θ_max1 / ℃	502.1, 522.6, 542.3, 561.4, 579.8
最高温度仿真值 θ_max2 / ℃	505.4, 518.5, 530.9, 542.8, 554.1

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表 3 砂带速度对最高温度的影响

Table 3. Influences of abrasive belt velocities on maximum temperature

参数	取值
砂带速度 v_s / （m·s⁻¹）	20, 22, 24, 26, 28
最高温度理论值 θ_max1 / ℃	495.1, 519.2, 542.3, 564.5, 585.8
最高温度仿真值 θ_max2 / ℃	472.7, 502.3, 530.9, 558.8, 586.1

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表 4 进给速度对最高温度的影响

Table 4. Influences of feed speeds on maximum temperature

参数	取值
进给速度 v_w / （m·s⁻¹）	0.15, 0.20, 0.25, 0.30, 0.35
最高温度理论值 θ_max1 / ℃	700.1, 606.3, 542.3, 495.1, 458.3
最高温度仿真值 θ_max2 / ℃	685.0, 593.3, 530.6, 484.6, 449.0

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