﻿ 复杂运营条件下重载货车车轮磨耗发展的数值预测
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 同济大学学报(自然科学版)  2019, Vol. 47 Issue (1): 71-78.  DOI: 10.11908/j.issn.0253-374x.2019.01.009 0

### 引用本文

WANG Pu, WANG Shuguo. Numerical Prediction of Wheel Wear Development of Heavy-haul Freight Car Under Complex Operation Conditions[J]. Journal of Tongji University (Natural Science), 2019, 47(1): 71-78. DOI: 10.11908/j.issn.0253-374x.2019.01.009

### 文章历史

Numerical Prediction of Wheel Wear Development of Heavy-haul Freight Car Under Complex Operation Conditions
WANG Pu , WANG Shuguo
Railway Engineering Research Institute, China Academy of Railway Sciences Corporation Limited, Beijing 100081, China
Abstract: A numerical prediction model was established for wheel wear development of heavy-haul vehicle under complex operating conditions, and the corresponding calculating program was written. According to Archard's material wear theory, the wear distributions were calculated based on the vehicle-track dynamics simulation and wheel-rail rolling contact analysis. Simulations were made respectively for every possible case and weight factors were introduced, in order to model the complex operating conditions. An adaptive step algorithm was adopted to update the wheel profile, which could improve the stability and reliability of numerical model. The wheel wear developing processes of heavy haul vehicle of Da-Qin railway under actual operating conditions were predicted based on the established model. The results show that the wear grows continuously with running distance increasing for every wheel, but the wear development shows a slowdown trend. The wear is mainly distributed in the contact area near nominal rolling circle, and the distribution range is wider for guiding wheel. The wear develops faster near the flange, which is more obvious for guiding wheel. The calculated results verified the rationality of the established model.
Key words: heavy haul railway    wheel-rail wear    vehicle-track coupling dynamics    wheel-rail contact    numerical iteration

1 重载车辆轨道耦合动力学模型

 图 1 心盘车辆接触摩擦作用 Fig.1 Center plate-vehicle contact friction interaction
 图 2 三大件式转向架力学模型 Fig.2 Mechanical model of three-piece bogie

 图 3 轮轨接触点变化过程 Fig.3 Changing process of wheel-rail contact point

 图 4 轨道力学模型 Fig.4 Mechanical model of track

 图 5 轮轨接触斑离散化 Fig.5 Discretization of wheel-rail contact patch
 $\left\{ \begin{gathered} {\text{d}}x\left( y \right) = 2a\sqrt {1-{{\left( {y/b} \right)}^2}} /{n_x} \hfill \\ {\text{d}}y = 2b/{n_y} \hfill \\ \end{gathered} \right.$ (1)

2 车轮磨耗计算模型

 图 6 轮轨接触斑磨耗深度分布计算模型 Fig.6 Calculation model of wear distribution in wheel-rail contact patch
 $\begin{gathered} \Delta {V_{\text{w}}}\left( {x, y} \right) = {k_{\text{w}}}\left( {x, y} \right) \hfill \\ \;\;\;\;\;\;\;\;\;\;\;\;\;\;\frac{{p\left( {x, y} \right) \cdot {\text{d}}x\left( y \right) \cdot {\text{d}}y \cdot \Delta s\left( {x, y} \right)}}{H} \hfill \\ \end{gathered}$ (2)

 图 7 磨耗系数取值 Fig.7 Value of wear coefficient
 $p\left( {x, y} \right) = \frac{{3N}}{{2\pi ab}}\sqrt {1-{{\left( {\frac{x}{a}} \right)}^2}-{{\left( {\frac{y}{b}} \right)}^2}}$ (3)

 $\Delta s\left( {x, y} \right) = \frac{{\left\| {\mathit{\boldsymbol{v}}\left( {x, y} \right)} \right\| \cdot {\text{d}}x\left( y \right)}}{{{V_0}}}$ (4)

 $\begin{gathered} \mathit{\boldsymbol{v}}\left( {x, y} \right) = {\mathit{\boldsymbol{v}}_{\text{r}}}\left( {x, y} \right)- {\mathit{\boldsymbol{v}}_{\text{e}}}\left( {x, y} \right) = \hfill \\ \;\;\;\;\;\;\;\;\;\;\;\;\;\;\left[\begin{gathered} {\xi _x}-\varphi y \hfill \\ {\xi _y} + \varphi x \hfill \\ \end{gathered} \right] \cdot {V_0} - \left[\begin{gathered} \partial {u_x}\left( {x, y} \right)/\partial x \hfill \\ \partial {u_y}\left( {x, y} \right)/\partial x \hfill \\ \end{gathered} \right] \cdot {V_0} \hfill \\ \end{gathered}$ (5)

 $\Delta {D_{\text{w}}}\left( {x, y} \right) = \frac{{\Delta {V_{\text{w}}}\left( {x, y} \right)}}{{{\text{d}}x\left( y \right) \cdot {\text{d}}y}}$ (6)

 图 8 车轮磨耗速率 Fig.8 Wheel wear rate
3 重载铁路复杂运营条件的模拟

 $\left\{ \begin{gathered} {c_{{\text{w}}, k, {\text{l}}}}\left( {{y_{\text{w}}}} \right) = \sum\limits_j^m {{\beta _{{\text{w}}, j}}} \sum\limits_i^{{n_j}} {{\alpha _{{\text{w}}, ij}}{c_{{\text{w}}, k, {\text{l}}, ij}}\left( {{y_{\text{w}}}} \right)} \hfill \\ {c_{{\text{w}}, k, {\text{r}}}}\left( {{y_{\text{w}}}} \right) = \sum\limits_j^m {{\beta _{{\text{w}}, j}}} \sum\limits_i^{{n_j}} {{\alpha _{{\text{w}}, ij}}{c_{{\text{w}}, k, {\text{r}}, ij}}\left( {{y_{\text{w}}}} \right)} \hfill \\ \end{gathered} \right.$ (7)

 ${\beta _{{\text{w}}, j}} = \frac{{S\left( {{T_j}} \right)}}{{\sum\limits_j^m {S\left( {{T_j}} \right)} }}$ (8)

4 车轮磨耗发展的型面更新策略

 ${c_{{\text{w}}, \max }} = \mathop {\max }\limits_k \left\{ {\max \left\{ {\mathop {\max }\limits_{{y_{\text{w}}}} \left\{ {{c_{{\text{w}}, k, {\text{l}}}}\left( {{y_{\text{w}}}} \right)} \right\}, \mathop {\max }\limits_{{y_{\text{w}}}} \left\{ {{c_{{\text{w}}, k, {\text{r}}}}\left( {{y_{\text{w}}}} \right)} \right\}} \right\}} \right\}$ (9)

 $P = {\xi _{\text{w}}}/{c_{{\text{w}}, \max }}$ (10)

 $\left\{ \begin{gathered} {C_{{\text{w}}, k, {\text{l}}}}\left( {{y_{\text{w}}}} \right) = {c_{{\text{w}}, k, {\text{l}}}}\left( {{y_{\text{w}}}} \right)P \hfill \\ {C_{{\text{w}}, k, {\text{r}}}}\left( {{y_{\text{w}}}} \right) = {c_{{\text{w}}, k, {\text{r}}}}\left( {{y_{\text{w}}}} \right)P \hfill \\ \end{gathered} \right.$ (11)

 图 9 车轮磨耗发展数值预测的迭代计算流程 Fig.9 Iterative computation process for numerical prediction of wheel wear development
5 大秦铁路实际运营条件下重载列车车轮磨耗发展预测分析

 $\begin{gathered} {c_{{\text{w}}, k, {\text{l'}}, ij}}\left( {{y_{\text{w}}}} \right) = {c_{{\text{w}}, k, {\text{r'}}, ij}}\left( {{y_{\text{w}}}} \right) = \hfill \\ \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\frac{{{c_{{\text{w}}, k, {\text{l}}, ij}}\left( {{y_{\text{w}}}} \right) + {c_{{\text{w}}, k, {\text{r}}, ij}}\left( {{y_{\text{w}}}} \right)}}{2} \hfill \\ \end{gathered}$ (12)

 $\left\{ \begin{gathered} {c_{{\text{w}}, k, {\text{l'}}}}\left( {{y_{\text{w}}}} \right) = \sum\limits_j^m {{\beta _{{\text{w}}, j}}} \sum\limits_i^{{n_j}} {{\alpha _{{\text{w}}, ij}}{c_{{\text{w}}, k, {\text{l'}}, ij}}\left( {{y_{\text{w}}}} \right)} \hfill \\ {c_{{\text{w}}, k, {\text{r'}}}}\left( {{y_{\text{w}}}} \right) = \sum\limits_j^m {{\beta _{{\text{w}}, j}}} \sum\limits_i^{{n_j}} {{\alpha _{{\text{w}}, ij}}{c_{{\text{w}}, k, {\text{r'}}, ij}}\left( {{y_{\text{w}}}} \right)} \hfill \\ \end{gathered} \right.$ (13)

 图 10 车轮编号 Fig.10 Wheel number
 图 11 大秦铁路实际运营条件下车轮磨耗发展及型面变化 Fig.11 Wheel wear development and profile evolution under actual operation conditions of Da-Qin railway
 图 12 大秦铁路实际运营条件下车轮最大磨耗深度增长曲线 Fig.12 Increasing curves of maximal wheel wear depth under actual operation conditions of Da-Qin railway

1、2号车轮磨耗主要分布在[-35 mm, 40 mm]范围, 随着运行里程的增加, 最大磨耗深度均主要发生在[20 mm, 25 mm]范围内, 当运行里程达到35 000 km时, 最大磨耗深度达2.197 mm.

3、4号车轮磨耗主要分布在[-30 mm, 30 mm]范围, 随运行里程增加, 最大磨耗深度主要发生在[5 mm, 10 mm]范围, 当运行里程达到35 000 km时, 最大磨耗深度为2.138 mm.

5、6号车轮磨耗主要分布在[-35 mm, 40 mm]范围, 随运行里程的增加, 最大磨耗深度位置逐渐从10 mm位置向轮缘方向移动至20 mm位置附近, 运行里程达35 000 km时, 最大磨耗深度2.160 mm.

7、8号车轮磨耗主要分布在[-35 mm, 30 mm]范围, 随运行里程的增加, 最大磨耗深度发生位置在[5 mm, 15 mm]范围变动, 运行35 000 km后, 最大磨耗深度2.164 mm.

6 结论

(1) 随运行里程增加各车轮磨耗均不断增大, 但磨耗发展呈逐渐减缓趋势;

(2) 各车轮磨耗主要分布在名义滚动圆两侧走行区域, 起导向作用的车轮磨耗分布范围更宽;

(3) 各车轮在靠近轮缘侧磨耗发展均更快, 导向轮对车轮这一特征更为明显;

(4) 导向车轮最大磨耗位置更靠近轮缘而非导向车轮最大磨耗位置更靠近名义滚动圆.计算结果验证了模型的合理性.

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