﻿ 基于轮轨接触特征的转辙器区钢轨廓形设计
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 同济大学学报(自然科学版)  2019, Vol. 47 Issue (9): 1341-1349.  DOI: 10.11908/j.issn.0253-374x.2019.09.015 0

### 引用本文

CHEN Dilai, SHEN Gang, MAO Xin. Design of Rail Profile in Switch Area Based on Wheel / Rail Contact Characteristics[J]. Journal of Tongji University (Natural Science), 2019, 47(9): 1341-1349. DOI: 10.11908/j.issn.0253-374x.2019.09.015

### 文章历史

Design of Rail Profile in Switch Area Based on Wheel / Rail Contact Characteristics
CHEN Dilai , SHEN Gang , MAO Xin
Institute of Rail Transit, Tongji University, Shanghai 201804, China
Abstract: In view of existing serious failures and short service life of rails in the switch area of railway turnouts, based on the wheel-rail contact theory, the method employs the rolling radius difference function and the uniform distribution of the wheel-rail contact points for the primary design objectives. Using the position of the wheel-rail contact points as a boundary condition, the Euler method was adopted to solve the differential equation and obtained the target profile of rail grinding. A computer program based on this method was developed and is validated by way of examples. After the optimization, rail and wheel profiles are better matched, which improves the dynamic performance of rail vehicles crossing turnouts and reduces the wheel-rail contact stress. As a result, the distributions of contact points and wear are more uniform, leading to a prolonged rail service life.
Key words: switch rail    profile optimization    rolling radius difference function    contact stress    dynamic

RRD函数是描述轮对和钢轨接触的最主要特征之一，它对机车车辆的稳定性、曲线通过性以及轮轨磨耗有着重要的影响，也决定了轮对的动态性能[5].本文以RRD函数为主要目标函数，以轮轨接触点的位置为边界条件，提出以优化轮轨动力学性能为核心的道岔转辙器区的钢轨打磨廓形的设计方法，利用欧拉积分方法，依据钢轨上的横坐标直接反推设计钢轨纵坐标，从而获得钢轨的打磨廓形.利用该方法优化设计CN60-350-1:12普速单开道岔(曲线半径350 m，辙叉角为1:12)，并同时考虑直向过岔和侧向过岔2种工况，比较优化前后的轮轨接触几何以及车辆过岔时的动态相互作用.

1 转辙器区钢轨的优化设计 1.1 优化算法的描述

 图 1 道岔区钢轨优化设计的流程 Fig.1 Optimization design flow chart of rail in turnouts

(1) 车轮与钢轨均为刚性，不考虑轮轨间的弹性压缩量，这样能避免一个横移量下出现多个轮径差数值，保证设计的结果的唯一性.

(2) 设计的钢轨外形为凸曲线，即各点切线的斜率单调变化.

(3) 设计的钢轨区段的横坐标尽量保持单调.

(4) 设计的钢轨打磨廓形不应该超过原始廓形.

 图 2 刚性轮轨单点接触示意 Fig.2 Schematic of single point contact between the rigid wheel and rail

 $\left( \begin{matrix} {{y}_{\text{rl}\left( \text{r} \right)\text{(s/b)}}} \\ {{z}_{\text{rl}\left( \text{r} \right)\text{(s/b)}}} \\ \end{matrix} \right)\text{=}\left[ \begin{matrix} \cos {{\varphi }_{\text{w}}} & -\sin {{\varphi }_{\text{w}}} \\ \sin {{\varphi }_{\text{w}}} & \cos {{\varphi }_{\text{w}}} \\ \end{matrix} \right]\cdot \left( \begin{matrix} {{y}_{\text{wl(r)}}} \\ {{z}_{\text{wl(r)}}} \\ \end{matrix} \right)+\left( \begin{matrix} {{y}_{\text{w0}}} \\ {{z}_{\text{w}0}} \\ \end{matrix} \right)$ (1)

 $\operatorname{arctg} \frac{\mathrm{d} z_{\mathrm{wl(r)}}}{\mathrm{d} y_{\mathrm{wl}(\mathrm{r})}}=\operatorname{arctg} \frac{\mathrm{d} z_{\mathrm{rl}(\rm r)(\mathrm{s}/ \mathrm{b})}}{\left.\mathrm{d} y_{\mathrm{rr}(\mathrm{r}) (\mathrm{s} / \mathrm{b}}\right)}-\varphi_{\mathrm{w}}$ (2)

 $\tan \varphi_{\mathrm{w}}=\frac{z_{\mathrm{wl}}-z_{\mathrm{wr}}-\frac{z_{\mathrm{rl}({\rm s} / \mathrm{b})}-z_{\mathrm{rr} ({\rm s}/ \mathrm{b})}}{\cos \varphi_{\mathrm{w}}}}{\left|y_{\mathrm{wr}}\right|+\left|y_{\mathrm{wl}}\right|}$ (3)

RRD为

 $\Delta R={{z}_{\text{wl}}}-{{z}_{\text{w}r}}$ (4)

 $\begin{array}{l}{f=\min \left\{\frac{\int_{-y_{\mathrm{w} \max }}^{y_{\mathrm{w} \max }}\left(\left|\Delta R_{\mathrm{real}}\left(y_{\mathrm{w}}\right)-\Delta R_{\mathrm{opt}}\left(y_{\mathrm{w}}\right)\right|\right) \mathrm{d} y_{\mathrm{w}}}{\int_{-y_{\mathrm{w} \max} }^{y_{\mathrm{w} \max }} \Delta R_{\mathrm{opt}}\left(y_{\mathrm{w}}\right) \mathrm{d} y_{\mathrm{w}}} \times\right.} \\ \qquad {100 \%\}}\end{array}$ (5)

 ${{z}_{\text{wl}}}\left( {{y}_{\text{w}}} \right)-{{z}_{\text{wr}}}\left( {{y}_{\text{w}}} \right)=\min \left\{ {{z}_{\text{wl}}}\left( {{y}_{\text{w}}} \right)-{{z}_{\text{wr}}}{{\left( {{y}_{\text{w}}} \right)}|_{\text{y=yw}}} \right\}$ (6)
 $\left\{ \begin{array}{*{35}{l}} \text{sign}\left( \frac{\text{d}{{z}_{\text{wl}}}}{\text{d}{{y}_{\text{wl}}}} \right)=\text{sign}\left( \frac{\text{d}{{z}_{\text{rl(s/b)}}}}{\text{d}{{y}_{\text{rl(s/b)}}}} \right)\equiv 1 \\ \text{sign}\left( \frac{\text{d}{{z}_{\text{wr}}}}{\text{d}{{y}_{\text{wr}}}} \right)=\text{sign}\left( \frac{\text{d}{{z}_{\text{rr(s/b)}}}}{\text{d}{{y}_{\text{rr(s/b)}}}} \right)\equiv 1 \\ \end{array} \right.$ (7)

 $\text{sign}\left( \frac{{{\text{d}}^{2}}{{z}_{\text{rl(s/b)}}}}{\text{d}y_{\text{rl(s/b)}}^{2}} \right)=\operatorname{sign}\left( \frac{{{\text{d}}^{2}}{{z}_{\text{rr}(\text{s}/\text{b})}}}{\text{d}y_{\text{rr}\left( \text{s}/\text{b} \right)}^{2}} \right)\equiv 1$ (8)

 $\left\{\begin{array}{l}{y_{k+1}=y_{k}+h \cdot f\left(x_{k}, y_{k}\right)} \\ {y_{0}=y\left(x_{0}\right)}\end{array}\right.$ (9)

1.2 优化方案

 图 3 道岔结构 Fig.3 Switch structure diagram

 图 4 道岔转辙器区的优化方案 Fig.4 Optimization plan of rail profiles in switch panel
2 优化实例 2.1 直向过岔

 图 5 原始轮轨接触点的分布 Fig.5 Wheel-rail contact before optimization for a straight turnout
 图 6 滚动圆半径差曲线 Fig.6 RRD curves for a straight turnout

 图 7 优化前后廓形对比 Fig.7 Rail profiles before and after the optimization for a straight turnout

 图 8 优化后轮轨接触点的分布 Fig.8 Wheel-rail contact after optimization for a straight turnout

 图 9 目标与优化后滚动圆半径差的误差 Fig.9 Error between of object and optimized RRD for a straight turnout
2.2 侧向过岔

 图 10 原始轮轨接触点的分布 Fig.10 Wheel-rail contact before optimization for a curved turnout
 图 11 滚动圆半径差曲线 Fig.11 RRD curves for a curved turnout

 图 12 优化前后廓形对比 Fig.12 Rail profiles before and after the optimization for a curved turnout

 图 13 优化后轮轨接触点的分布 Fig.13 Wheel-rail contact after optimization for a curved turnout
 图 14 目标与优化后滚动圆半径差的误差 Fig.14 Error between of object and optimized RRD for a curved turnout
2.3 道岔区的组合廓形

 图 15 直向过岔时优化前后右侧廓形对比 Fig.15 Right rail profiles before and after the optimization for a straight turnout

 图 16 直向过岔时优化前后的轮轨接触应力 Fig.16 Wheel-rail contact stress before and after the optimization for a straight turnout

 图 17 侧向过岔时优化前后左侧廓形对比 Fig.17 Left rail profiles before and after the optimization for a curved turnout
 图 18 侧向过岔时优化前后的轮轨接触应力 Fig.18 Wheel-rail contact stress before and after the optimization for a curved turnout

3 动力学性能校验

 图 19 直向通过时的动力学响应 Fig.19 Dynamic response for a straight turnout
 图 20 侧向通过时的动力学响应 Fig.20 Dynamic response for a curved turnout
4 结语

 [1] 田常海. 我国高速铁路钢轨和道岔打磨技术应用与实践[J]. 中国铁路, 2017(11): 15 TIAN Changhai. Application and practice of grinding technique for rails and turnouts of china high-speed railway[J]. China Railway, 2017(11): 15 [2] 王军平. 个性化钢轨廓形打磨技术在高速铁路上的应用[J]. 铁道建筑, 2018, 58(5): 120 WANG Junping. Application of personalized rail profile grinding technology in high speed railway[J]. Railway Engineering, 2018, 58(5): 120 [3] SHEVTSOV I Y, MARKINE V L, ESVELD C. Optimal design of wheel profile for railway vehicles[J]. Wear, 2005, 258(7): 1022 [4] SHEN Gang, ZHONG Xiaobo. A design method for wheel profiles according to the rolling radius difference function[J]. Proceedings of the Institution of Mechanical Engineers, Part F, Journal of Rail & Rapid Transit, 2011, 225(5): 457 [5] 钟晓波, 沈钢. 高速列车车轮踏面外形优化设计[J]. 同济大学学报(自然科学版), 2011, 39(5): 710 ZHONG Xiaobo, SHEN Gang. Optimization for high-speed wheel profiles[J]. Journal of Tongji University(Natural Science), 2011, 39(5): 710 DOI:10.3969/j.issn.0253-374x.2011.05.015 [6] 毛鑫, 沈钢. 基于轮径差函数的曲线钢轨打磨廓形设计[J]. 同济大学学报(自然科学版), 2018, 46(2): 253 MAO Xin, SHEN Gang. Curved rail grinding profile design based on rolling radii difference function[J]. Journal of Tongji University(Natural Science), 2018, 46(2): 253 DOI:10.11908/j.issn.0253-374x.2018.02.017 [7] 张继恩. 钢轨廓形打磨技术在神朔线小半径曲线的应用研究[J]. 山西建筑, 2018, 44(15): 120 ZHANG Jien. Study on the application of rail profile polishing technology in shen-shuo-railway-line minor-radius curve[J]. Shanxi Architecture, 2018, 44(15): 120 [8] 吴仁义.钢轨接触应力分析与廓形优化[D].成都: 西南交通大学, 2014. WU Renyi. Rail contact stress analysis and optimization of rail profile shape[D]. Chengdu: Southwest Jiaotong University, 2014. http://cdmd.cnki.com.cn/Article/CDMD-10613-1014254620.htm [9] 赵向东. 基于轮轨法向间隙的道岔钢轨廓形优化方法[J]. 铁道建筑, 2018, 58(3): 83 ZHAO Xiangdong. Optimization method for turnout rail profile based on normal gap between wheel and rail[J]. Railway Engineering, 2018, 58(3): 83 DOI:10.3969/j.issn.1003-1995.2018.03.21 [10] 徐井芒, 王平, 徐浩, 等. 尖轨廓形对地铁道岔使用寿命的影响研究[J]. 铁道学报, 2014, 36(3): 75 XU Jingmang, WANG Ping, XU Hao, et al. Study on impact of switch rail profile on service life of subway switches[J]. Journal of the China Railway Society, 2014, 36(3): 75 DOI:10.3969/j.issn.1001-8360.2014.03.012 [11] WANG P, XU J M, WANG J, et al. Optimization of rail profiles to improve vehicle running stability in switch panel of high-speed railway turnouts[J]. Mathematical Problems in Engineering, 2017, 2017: 1 [12] PALSSON B. Design optimisation of switch rails in railway turnouts[J]. Vehicle System Dynamics, 2013, 51(10): 1619 DOI:10.1080/00423114.2013.807933 [13] 沈钢. 轨道车辆系统动力学[M]. 北京: 中国铁道出版社, 2015 SHEN Gang. Railway vehicle system dynamics[M]. Beijing: China Railway Press, 2015 [14] 任尊松. 轮轨多点接触及车辆道岔系统动态相互作用[M]. 北京: 科学出版社, 2014 REN Zunsong. Wheel/rail multi-point contacts and vehicle-turnout system dynamic interactions[M]. Beijing: Science Press, 2014 [15] 《常用道岔主要参数手册》编写组. 常用道岔主要参数手册[M]. 北京: 中国铁道出版社, 2007 The Committee of Routine Turnout Main Parameters Handbook. Routine turnout main parameters handbook[M]. Beijing: China Railway Press, 2007