Influence of internal excitation and boxbody flexibility on the vibration of high-speed train gearboxes

YU Hongda; LIU Jiahui; HUANG Zhihui; TIAN Mingjie

doi:10.13890/j.issn.1000-128X.2024.01.140

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Influence of internal excitation and boxbody flexibility on the vibration of high-speed train gearboxes

Railway Rolling Stock | Updated：2024-08-01

- Influence of internal excitation and boxbody flexibility on the vibration of high-speed train gearboxes
- role： First author , 第一作者 ,
  
  Affiliation：
  State Key Laboratory of Rail Transit Vehicle System, Southwest Jiaotong University, Chengdu, Sichuan 610031, China
  
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  No information about the author is available
  YU Hongda
  ,
  role：
  
  Affiliation：
  State Key Laboratory of Rail Transit Vehicle System, Southwest Jiaotong University, Chengdu, Sichuan 610031, China
  
  Email：
  
  No information about the author is available
  LIU Jiahui
  ,
  role： Corresponding author , 通讯作者 ,
  
  Affiliation：
  State Key Laboratory of Rail Transit Vehicle System, Southwest Jiaotong University, Chengdu, Sichuan 610031, China
  
  Email： hzh_95@163.com
  
  Introduction：黄志辉，男，工学博士，研究员，硕士生导师，主要从事车辆系统动力学、结构强度分析、机械产品结构设计方面的研究；E-mail: hzh_95@163.com
  
  No information about the author is available
  HUANG Zhihui
  ,
  role：
  
  Affiliation：
  State Key Laboratory of Rail Transit Vehicle System, Southwest Jiaotong University, Chengdu, Sichuan 610031, China
  
  Email：
  
  No information about the author is available
  TIAN Mingjie
  ,
- Electric Drive for Locomotives Issue 3, Pages: 45-52(2024)
- Affiliations：
  
  State Key Laboratory of Rail Transit Vehicle System, Southwest Jiaotong University, Chengdu, Sichuan 610031, China
- Author bio：
- Funds：
- DOI：10.13890/j.issn.1000-128X.2024.01.140
  CLC： U292.91⁺4;U264.4
- Published：10 May 2024，
  
  Received：21 August 2023，
  
  Revised：12 December 2023，
- Accepted：
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于宏达, 刘加蕙, 黄志辉, 等. 高速动车齿轮箱内部激励及箱体柔性对其振动的影响[J]. 机车电传动, 2024(3): 45-52.

YU Hongda, LIU Jiahui, HUANG Zhihui, et al. Influence of internal exand boxbody flexibility on the vibration of high-speed train gearboxes[J]. Electric drive for locomotives,2024(3): 45-52.
于宏达, 刘加蕙, 黄志辉, 等. 高速动车齿轮箱内部激励及箱体柔性对其振动的影响[J]. 机车电传动, 2024(3): 45-52. DOI：10.13890/j.issn.1000-128X.2024.01.140.

YU Hongda, LIU Jiahui, HUANG Zhihui, et al. Influence of internal exand boxbody flexibility on the vibration of high-speed train gearboxes[J]. Electric drive for locomotives,2024(3): 45-52. DOI：10.13890/j.issn.1000-128X.2024.01.140.

Abstract

During the operation of high-speed trains, the loads on the gearbox are very complex, and cracks often occur in the boxbody. To ensure the service safety of the gearbox body, a dynamic model of high-speed trains with a gear transmission system was established based on SIMPACK. Comparative analysis of the vibration response of the gearbox rigid body at speeds of 200 km/h, 250 km/h, 300 km/h and 350 km/h was conducted, considering only track excitation and both gears internal excitation and track excitation. In addition, a rigid-flexible coupling dynamic model of a high-speed train considering a flexible gearbox body was established to analyze its impact on the vibration calculation results of the gearbox body. The results indicate that the internal excitation of the gearbox has a little impact on the lateral vibration acceleration of the gearbox body, but at the rotational frequency of the driving gear and the engagement frequency of the gears, the vertical vibration acceleration of the gearbox body will exhibit a peak value, which significantly increases its root mean square value, with an average increment of 4.8 m/s². At a speed of 200 km/h, the resonance is caused by the similarity between the rotational frequency of the driving gear and the modal frequency of the gearbox pitching, resulting in a very significant increase in the root mean square value of the vertical vibration acceleration of the gearbox body. Therefore, when analyzing the vibration of the gearbox body, the internal excitation of the gearbox cannot be ignored. The flexibility of the gearbox body has a little impact on the lateral vibration acceleration of the gearbox body when considering the internal excitation, but it will reduce the root mean square value of the vertical vibration acceleration to some extent. The average reduction after the speed reaches 300 km/h is large, reaching 2.72 m/s².

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Keywords

high-speed train; gear transmission system; gearbox; vibration response; resonance

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0 引言

齿轮箱作为动车牵引传动系统的重要组成部分，其振动情况直接影响着齿轮箱箱体及其内部齿轮、轴承等部件的使用寿命。在动车运行过程中，齿轮箱不仅受到轨道不平顺、轮轨冲击等外部激励的作用，还受到齿轮时变啮合刚度、齿轮啮合冲击等内部激励的作用。随着动车组运行速度的提高，齿轮箱所受的内外激励也在不断增大，箱体出现裂纹的情况时有发生。

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为保证动车齿轮箱服役安全，近年来，许多学者对动车齿轮箱箱体振动响应开展研究。文献[

1]对齿轮箱开展线路跟踪服役试验，分析了测试系统在齿轮箱箱体多路线工况下采集的数据，对齿轮箱箱体在实际运营线路中的振动特性进行了研究。文献[2]建立了包含齿轮传动系统的某高速动车组动力学模型，研究了传动系统所受载荷对车辆主要部件振动的影响。文献[3]计算了齿轮箱箱体仅在轨道不平顺激励下的动应力，对其进行动应力评估。文献[4]建立高速动车模型，以车轮多边形为外部激励对齿轮箱箱体的动应力分布形式进行了探析。文献[5]基于高速动车传动系统动力学模型，结合实际工况对齿轮箱箱体的动态特性进行了分析，发现车轮多边形磨损对齿轮箱箱体振动具有明显影响。

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上述文献通过线路跟踪试验或仿真计算对齿轮箱振动特性已经有了较为深入的研究，但关于齿轮箱内部激励对齿轮箱箱体振动影响的研究较少。文献[

6]建立了高速动车齿轮箱传动系统刚柔耦合仿真模型，对齿轮箱内部激励下的高速动车齿轮箱振动响应进行评估，但没有考虑齿轮箱在运行过程中所受的外部激励。此外，在分析齿轮箱箱体振动响应的大部分研究中齿轮箱箱体都已考虑成柔性体^{[Reference 7-9

7-9]}，但齿轮箱箱体柔性对其箱体振动的影响鲜有人研究，考虑齿轮箱柔性在一定程度上能更准确地反映齿轮箱的振动情况，但同时会增加计算成本，因此有必要研究齿轮箱箱体柔性对箱体振动的影响。为此，本文将建立包含齿轮传动系统的某动车动力学模型，考虑高速动车组运行过程中齿轮箱所受外部激励，研究齿轮箱内部激励及箱体柔性对其振动的影响。

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1 考虑齿轮箱内部激励的某动车动力学模型

1.1 齿轮箱内部激励

齿轮箱内部激励来源于齿轮动态啮合力。在齿轮啮合过程中，其啮合力动态变化，动态啮合力通过主动齿轮传递到齿轮箱箱体，进而引起整个齿轮箱振动，以下将对齿轮动态啮合力产生机理进行分析。齿轮啮合示意图如图1所示，x轴、y轴、z轴分别对应轨道的纵向、横向、垂向3个方向，坐标原点在主动齿轮中心处。

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图1 齿轮啮合示意图

Fig. 1 Schematic diagram of gear engagement

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主动齿轮1与从动齿轮2的自由度如表1所示，系统广义位移列阵为{δ}，具体如下：

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\{δ\} = {\{\begin{matrix} x_{1} & y_{1} & z_{1} & \begin{matrix} θ_{1} & x_{2} & y_{2} & \begin{matrix} z_{2} & θ_{2} \end{matrix} \end{matrix} \end{matrix}\}}^{T}

（1）

表1 齿轮自由度

Table 1 Gear degree of freedom

刚体	自由度
刚体	沿x轴平动	沿y轴平动	沿z轴平动	绕y轴转动
主动齿轮1	x₁	y₁	z₁	θ₁
从动齿轮2	x₂	y₂	z₂	θ₂

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主动齿轮1与从动齿轮2在啮合点处的位移与系统广义位移的关系为^[

10]：

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\begin{array}{l} \bar{x_{1}} = x_{1} - \bar{z_{1}} \cdot t a n α_{t} = x_{1} - (z_{1} + R_{1} \cdot θ_{1}) \cdot t a n α_{t} \\ \bar{y_{1}} = y_{1} + \bar{z_{1}} \cdot t a n β = y_{1} + (z_{1} + R_{1} \cdot θ_{1}) \cdot t a n β \\ \bar{z_{1}} = z_{1} + R_{1} \cdot θ_{1} \\ \bar{x_{2}} = x_{2} + \bar{z_{2}} \cdot t a n α_{t} = x_{2} + (z_{2} - R_{2} \cdot θ_{2}) \cdot t a n α_{t} \\ \bar{y_{2}} = y_{2} + \bar{z_{2}} \cdot t a n β = y_{2} + (z_{2} - R_{2} \cdot θ_{2}) \cdot t a n β \\ \bar{z_{2}} = z_{2} - R_{2} \cdot θ_{2} \end{array}\}

（2）

式中： $\bar{x_{i}}$ 、 $\bar{y_{i}}$ 、 $\bar{z_{i}}$ (i=1, 2）为齿轮啮合点三向位移；R_i(i=1, 2)为齿轮节圆半径；α_t为齿轮端面压力角；β为斜齿轮螺旋角。

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齿轮相对传递误差为：

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\begin{array}{l} x_{e} = \bar{x_{1}} - \bar{x_{2}} \\ y_{e} = \bar{y_{1}} - \bar{y_{2}} \\ z_{e} = \bar{z_{1}} - \bar{z_{2}} \end{array}\}

（3）

齿轮啮合过程中单齿啮合与双齿啮合周期性交替，导致齿轮啮合刚度周期变化，齿轮时变啮合刚度可用Fourier 级数表示如下：

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k_{h} (t) = k_{m} + \sum_{n = 1}^{N} [a_{n} c o s (n ω_{0} t) + b_{n} s i n (n ω_{0} t)]

（4）

式中：k_m为齿轮副平均啮合刚度；ω₀为齿轮啮合基频；a_n，b_n ( n = 1，2，…，N) 为 Fourier级数展开系数。

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齿轮啮合阻尼可由下式计算：

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c_{m} = 2 ξ_{g} \sqrt[]{\frac{k_{m} m_{1} m_{2}}{m_{1} + m_{2}}}

（5）

式中： $ξ_{g}$ 为阻尼比，一般取0.03~0.17；m_i(i=1，2)为齿轮质量。

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齿轮啮合的过程中存在齿侧间隙，可表示为如下非线性函数：

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f (x) = \{\begin{array}{l} x - b, \\ 0, \\ x + b, \end{array}

\begin{array}{l} x > b \\ - b < x < b \\ x < - b \end{array}

（6）

式中：b为1/2齿侧间隙。

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齿轮三向动态啮合力计算公式为：

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\begin{array}{l} F_{x} = c_{m} \cdot x_{e}^{'} + k_{h} (t) \cdot f (x_{e}) \\ F_{y} = c_{m} \cdot y_{e}^{'} + k_{h} (t) \cdot f (y_{e}) \\ F_{z} = c_{m} \cdot z_{e}^{'} + k_{h} (t) \cdot f (z_{e}) \end{array}\}

（7）

从式(7)可以看出，由于时变啮合刚度与齿侧间隙存在，齿轮三向啮合力随时间动态变化，从而引起齿轮箱振动。因此，在建立考虑齿轮箱内部激励的动车动力学模型时，齿轮时变啮合刚度与齿侧间隙是仿真的关键。

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1.2 考虑齿轮传动系统的整车动力学模型

基于多体动力学理论^[

11]，采用SIMPACK建立包含齿轮传动系统的某动车动力学模型。动车转向架模型考虑牵引电机、C型吊架、齿轮箱箱体、联轴节、主/从动齿轮等结构。牵引电机与电机吊架固定连接，建模时将其考虑成一个刚体，电机吊架与转向架构架弹性连接。齿轮啮合采用225号力元，该力元能够模拟多种类型齿轮啮合过程，在计算时能够考虑齿轮副的时变啮合刚度、齿侧间隙和啮合阻尼等因素，齿轮设计参数见表2^{[Reference 12

Baidu Scholar

12]}。齿轮时变啮合刚度参考德国标准DIN 3990，由SIMPACK根据所给定的齿轮设计参数计算得出。动车200 km/h运行时齿轮啮合刚度的计算结果如图2所示，总体呈现周期时变特性，总体变化趋势与文献[7]相符；齿轮平均啮合刚度为1.45 GN/m，与文献[7]中齿轮平均啮合刚度值1.42 GN/m相近。

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表2 齿轮设计参数

Table 2 Gear design parameters

名称	主动齿轮	从动齿轮
压力角/(°)	20
螺旋角/(°)	18
泊松比	0.3
弹性模量/(N·m^-2)	2.1e11
齿轮中心距/mm	380
齿根高系数	0.35
齿顶高系数	1
齿数	35	85
变位系数	0.225	0.024
齿轮宽度/mm	66	65

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图2 齿轮时变啮合刚度

Fig. 2 Time-varying engagement stiffness of gears

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整车模型包含1个车体、2个构架、4个轮对、8个轴箱、2个电机吊架、4个齿轮箱箱体、4个主动齿轮、4个从动齿轮。整车模型自由度见表3，动车转向架动力学模型如图3所示。动车运行过程中阻力按式(8)计算^[

13]，轨道激励采用京津高速轨道谱，加速度传感器设置在齿轮箱箱体的主动齿轮中心位置处。

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W = 7.75 + 0.062367 v + 0.00113 v^{2}

（8）

式中：W为动车运行基本阻力，N/kN；v为动车运行速度，km/h。

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表3 整车动力学模型自由度

Table 3 Degree of freedom of vehicle dynamics model

结构	伸缩	横移	浮沉	侧滚	点头	摇头
车体	√	√	√	√	√	√
构架	√	√	√	√	√	√
轮对	√	√	√	√	√	√
轴箱	-	-	-	-	√	-
电机吊架	√	√	√	√	√	√
齿轮箱箱体	-	-	-	-	√	-
主动齿	-	-	-	-	√	-
从动齿	-	-	-	-	√	-

注：其中轮对侧滚与浮沉为非独立自由度^[

14]。

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图3 动车转向架动力学模型

Fig. 3 Dynamic model of high-speed train bogie

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2 齿轮箱内部激励对其箱体振动加速度的影响

考虑轨道激励与考虑齿轮内部和轨道双激励时，分别计算200 km/h、250 km/h、300 km/h和350 km/h速度下的齿轮箱箱体振动加速度方均根值，计算结果如图4所示。从计算结果可以看出，齿轮箱内部激励会显著增加箱体垂向振动加速度方均根值（平均增量为4.8 m/s²），对其横向振动加速度方均根值影响不大（最大变化量仅为0.36 m/s²）。因此，重点分析齿轮箱内部激励对箱体垂向振动加速度的影响。

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（a）垂向

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（b）横向

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图4 各速度下齿轮箱箱体振动加速度方均根值计算结果

Fig. 4 Calculation results of root mean square value of vibration acceleration of gearbox box at various speeds

考虑齿轮箱内部激励后箱体垂向振动加速度会在主动齿轮转频与齿轮啮合频率处产生峰值，主动齿轮转频与齿轮啮合频率计算公式如式(9)所示，计算结果见表4。

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\begin{array}{l} f_{1} = f_{2} \cdot i = \frac{v}{3.6 π D} \cdot \frac{z_{2}}{z_{1}} \\ f_{m} = f_{1} \cdot z_{1} = f_{2} \cdot z_{2} \end{array}\}

（9）

式中：f₁为主动齿转频，Hz；f₂为被动齿转频，Hz；z₁为主动齿齿数；z₂为从动齿齿数；f_m为齿轮啮合频率，Hz；v为动车运行速度，km/h。

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表4 各速度下齿轮的特征频率

Table 4 Characteristic frequencies of gears at various speeds Hz

频率	运行速度/(km·h^-1)
频率	200	250	300	350
主动齿转频f₁	46.7	58.4	70.1	81.7
齿轮啮合频率f_m	1 633.8	2 042.3	2 450.8	2 859.2

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对4种速度下齿轮箱垂向振动加速度响应进行频域分析，计算结果如图5所示。从图5可看出，齿轮箱内部激励会使箱体垂向振动加速度幅值在100~1 100 Hz范围内有所增加，速度达到300 km/h后振幅明显增大。

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（a） 200 km/h速度

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（b） 250 km/h速度

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（c） 300 km/h速度

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（d） 350 km/h速度

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图5 4种速度下齿轮箱箱体垂向振动加速度频谱

Fig. 5 Vertical vibration acceleration spectrum of gearbox body at four different speeds

由图5(a)可知，动车运行速度为200 km/h时，齿轮箱内部激励会使主动齿轮转频处齿轮箱体垂向振动加速度的峰值显著增大（相对于不考虑齿轮箱内部激励时增量为6.57 m/s²），这是由于200 km/h时主动齿转频与齿轮箱箱体点头模态的固有频率相近引发共振。为验证此结论，改变齿轮箱悬挂的垂向刚度以改变齿轮箱点头模态频率，观察箱体振动加速度的变化，计算结果如6所示。齿轮箱悬挂垂向刚度变化范围在初始值6.5 MN/m的基础上上下波动50%，由图6可知，随着齿轮箱悬挂垂向刚度的减小，齿轮箱点头模态固有频率逐渐远离主动齿轮转频，箱体垂向振动加速度方均根值也随之减小。对比齿轮箱悬挂垂向刚度为3.25 MN/m与6.50 MN/m时的箱体振动加速度频域响应，计算结果如图7所示，相较于齿轮箱悬挂垂向刚度初始值6.50 MN/m，在其最小值3.25 MN/m时箱体垂向振动加速度在主动齿轮转频f₁处的振幅已大幅减小(减小量为4.16 m/s²）。

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图6 齿轮箱箱体垂向振动加速度方均根值与固有频率随刚度变化曲线

Fig. 6 Root mean square value of vertical vibration acceleration and natural frequency of gearbox body changing with stiffness

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图7 两种刚度下齿轮箱箱体振动加速度频谱

Fig. 7 Vibration acceleration spectrum of gearbox bodies with two stiffness levels

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因此，在分析齿轮箱箱体振动时有必要考虑齿轮箱内部激励，由于存在主动齿转频导致箱体共振的情况，在设计动车齿轮传动系统时应使其固有模态频率尽量避开动车运行速度范围内的主动齿转频。

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3 齿轮箱箱体柔性对其振动的影响

3.1 考虑齿轮箱箱体柔性的动车刚柔耦合动力学模型

将齿轮箱箱体模型导入Hyhermesh中进行前处理，设置材料密度为2.7 kg/cm³，弹性模量为70 GPa，泊松比为0.33，采用Solid185单元对模型进行网格划分^[

15]，齿轮箱箱体有限元模型如图8所示。将前处理后的模型导入ABAQUS进行模态分析进而生成子结构，模态分析结果见表5。齿轮箱箱体子结构导入SIMPACK中生成柔性体文件，调用箱体柔性模型替换刚体模型，如图9所示，建立考虑齿轮箱箱体柔性的某动车动力学模型。

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图8 齿轮箱箱体有限元模型

Fig. 8 Finite element model of gearbox body

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表5 齿轮箱箱体前6阶模态频率

Table 5 The first 6-order modal frequencies of gearbox body

阶次	模态频率/Hz	阶次	模态频率/Hz
1	583.3	4	904.0
2	713.0	5	970.8
3	848.2	6	1 011.0

Download: CSV

Download: Table Images

图9 动力学模型中的柔性齿轮箱箱体

Fig. 9 Flexible gearbox body in dynamic model

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3.2 齿轮箱箱体柔性对其振动影响的仿真计算

考虑齿轮箱内部激励，分别计算4种速度下齿轮箱刚性与柔性箱体振动加速度方均根值，结果如图10所示。由计算结果可得，考虑齿轮箱箱体柔性后，箱体横向振动加速度方均根值有小幅增加（最大增量仅为0.6 m/s²），垂向振动加速度方均根值有所减小，尤其是当动车运行速度达到300 km/h后，其方均根值明显减小（平均减小量为2.72 m/s²）。因此，重点分析动车运行速度为300 km/h和350 km/h时齿轮箱箱体柔性对其垂向振动加速度的影响。

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（a）垂向

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（b）横向

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图10 齿轮箱箱体振动加速度方均根值计算结果

Fig. 10 Calculation results of the root mean square value of the vibration acceleration of the gearbox body

对上述两种速度下齿轮箱箱体刚性与柔性时的垂向振动加速度进行频域分析，计算结果如图11所示。由计算结果可知，考虑齿轮箱箱体柔性后其垂向振动加速度振幅在100~1 100 Hz范围内相较于刚性箱体大幅减小，但齿轮啮合频率f_m处的振动幅值有所增加，总体上使得箱体垂向振动加速度方均根值有所减小。在这2种速度下，考虑齿轮箱内部激励时刚性箱体垂向振动加速度在100~1 100 Hz范围内的振幅较大，考虑柔性箱体后其方均根值减小更为明显。

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（a） 300 km/h速度

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（b） 350 km/h速度

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图11 2种速度下齿轮箱刚性箱体与柔性箱体振动加速度频谱

Fig. 11 Vibration acceleration spectrum of rigid and flexible gearbox bodies at two different speeds

由仿真计算结果可知，动车运行速度到达300 km/h以上时，齿轮箱柔性箱体对箱体垂向振动加速度计算结果影响较大。目前，动车的运行速度在不断地提高，运营速度为400 km/h的动车组即将下线，在分析此类运行速度大于300 km/h的高速动车齿轮箱箱体振动时，建议将箱体考虑为柔性。

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4 结论

通过建立包含齿轮传动系统的某动车刚柔耦合动力学模型，对齿轮箱内部激励及箱体柔性对其振动的影响进行了研究。得出以下结论：

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①齿轮箱内部激励对齿轮箱箱体横向振动加速度的影响较小，但会使箱体垂向振动加速度在主动齿轮转频与齿轮啮合频率处产生峰值，使其方均根值显著增加。在200 km/h速度时主动齿转频引发了齿轮箱箱体共振，因此在设计动车齿轮传动系统时应使齿轮箱固有模态频率尽量避开动车运行速度范围内的主动齿转频。

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②相较于刚性齿轮箱箱体，考虑箱体柔性后其横向振动加速度方均根值有小幅增加，垂向振动加速度振动幅值在100~1 100 Hz范围内大幅减小、在齿轮啮合频率处有所增加，4种速度下的箱体垂向振动加速度方均根值均有所减小，当动车运行速度达到300 km/h后减小量较大。动车运行速度较高时，齿轮箱柔性箱体对箱体垂向振动加速度计算结果影响较大，在分析运行速度大于300 km/h的高速动车齿轮箱箱体振动时，建议将箱体考虑为柔性。

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参考文献

朱海燕, 朱志和, 邬平波, 等. 服役工况下高速动车组齿轮箱箱体振动特性分析[J]. 噪声与振动控制, 2021, 41(2): 15-20. [Baidu Scholar]

ZHU Haiyan, ZHU Zhihe, WU Pingbo, et al. Vibration characteristics analysis of high-speed EMU gearbox housings under service conditions[J]. Noise and vibration control, 2021, 41(2): 15-20. [Baidu Scholar]

孙刚, 任尊松, 辛欣, 等. 高速动车组齿轮传动系统振动特性[J]. 机械工程学报, 2019, 55(18): 104-111. [Baidu Scholar]

SUN Gang, REN Zunsong, XIN Xin, et al. Vibration characteristics of the gear transmission system of high-speed multiple unit trains[J]. Journal of mechanical engineering, 2019, 55(18): 104-111. [Baidu Scholar]

张建超, 胡玉飞, 陈湛, 等. 外部激励下齿轮箱振动分析与动应力评估[J]. 机械设计与制造, 2023, 389(7): 116-124. [Baidu Scholar]

ZHANG Jianchao, HU Yufei, CHEN Zhan, et al. Vibration analysis and dynamic stress evaluation of gearbox under external excitation[J]. Machinery design & manufacture, 2023, 389(7): 116-124. [Baidu Scholar]

WU Hao, WU Pingbo, LI Fansong, et al. Fatigue analysis of the gearbox housing in high-speed trains under wheel polygonization using a multibody dynamics algorithm[J]. Engineering failure analysis, 2019, 100: 351-364. [Baidu Scholar]

WANG Zhiwei, ALLEN P, ZHANG Weihua, et al. Dynamic characteristics of a high-speed train gearbox in the vehicle-track coupled system excited by wheel defects[J]. Journal of rail and rapid transit, 2020, 234(10): 1210-1226. [Baidu Scholar]

胡玉飞, 张建超, 陈湛, 等. 内部激励下高速动车齿轮箱振动响应评估[J]. 北京交通大学学报, 2022, 46(4): 148-156. [Baidu Scholar]

HU Yufei, ZHANG Jianchao, CHEN Zhan, et al. Evaluation of gearbox vibration response in high-speed train under internal excitation[J]. Journal of Beijing jiaotong university, 2022, 46(4): 148-156. [Baidu Scholar]

邓晓宇, 张卫华. 基于刚柔耦合的高速列车齿轮传动系统动态特性研究[J]. 高速铁路技术, 2016, 7(4): 50-54. [Baidu Scholar]

DENG Xiaoyu, ZHANG Weihua. Research on the dynamic characteristics of gear transmission system of high-speed train based on the rigid-flexible coupling dynamics[J]. High speed railway technology, 2016, 7(4): 50-54. [Baidu Scholar]

黄冠华, 王兴宇, 梅桂明, 等. 内外激励下高速列车齿轮箱箱体动态响应分析[J]. 机械工程学报, 2015, 51(12): 95-100. [Baidu Scholar]

HUANG Guanhua, WANG Xingyu, MEI Guiming, et al. Dynamic response analysis of gearbox housing system subjected to internal and external excitation in high-speed train[J]. Journal of mechanical engineering, 2015, 51(12): 95-100. [Baidu Scholar]

朱海燕, 黎洁, 尹必超, 等. 牵引电机悬挂参数对高速列车牵引传动部件振动特性的影响[J]. 交通运输工程学报, 2023, 23(1): 156-169. [Baidu Scholar]

ZHU Haiyan, LI Jie, YIN Bichao, et al. Influence of suspension parameters of traction motor on vibration characteristics of traction drive components of high-speed train[J]. Journal of traffic and transportation engineering, 2023, 23(1): 156-169. [Baidu Scholar]

李润方, 王建军. 齿轮系统动力学: 振动, 冲击, 噪声[M]. 北京: 科学出版社, 1997. [Baidu Scholar]

LI Runfang, WANG Jianjun. Gear system dynamics: vibration, impact, noise[M]. Beijing: Science Press, 1997. [Baidu Scholar]

翟婉明. 车辆-轨道耦合动力学[M]. 4版. 北京: 科学出版社, 2015. [Baidu Scholar]

ZHAI Wanming. Vehicle-track coupling dynamics[M]. 4th ed. Beijing: Science Press, 2015. [Baidu Scholar]

肖乾, 程玉琦, 许旭. 轨道不平顺影响下高速列车齿轮传动系统的振动特性分析[J]. 机械传动, 2021, 45(4): 135-141. [Baidu Scholar]

XIAO Qian, CHENG Yuqi, XU Xu. Vibration characteristic analysis of high-speed train gear transmission system under track irregularity[J]. Journal of mechanical transmission, 2021, 45(4): 135-141. [Baidu Scholar]

王伯铭. 高速动车组总体及转向架[M]. 成都: 西南交通大学出版社, 2008. [Baidu Scholar]

WANG Boming. High speed EMU overall and bogie[M]. Chengdu: Southwest Jiaotong University Press, 2008. [Baidu Scholar]

罗仁, 曾京, 戴焕云. 列车系统建模及运行平稳性分析[J]. 中国铁道科学, 2006, 27(1): 72-77. [Baidu Scholar]

LUO Ren, ZENG Jing, DAI Huanyun. Modeling and ride quality analysis of railway train system[J]. China railway science, 2006, 27(1): 72-77. [Baidu Scholar]

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ZHAO Xiangyan, MA Yu, YAN Shujun, et al. Research on modal analysis of gearbox box of EMU[J]. Measurement & control technology, 2022, 41(7): 81-86. [Baidu Scholar]

摘要

动车运行过程中齿轮箱受载情况十分复杂，箱体出现裂纹的情况时有发生。为保证齿轮箱箱体服役安全，文章在SIMPACK中建立了含有齿轮传动系统的某动车动力学模型，动车运行速度设为200 km/h、250 km/h、300 km/h和350 km/h，对比4种速度下只考虑轨道激励与考虑齿轮内部和轨道双激励时齿轮箱刚性箱体的振动响应，同时建立考虑齿轮箱箱体柔性的某动车刚柔耦合动力学模型，分析其对齿轮箱箱体振动计算结果的影响。结果表明：齿轮箱内部激励对箱体横向振动加速度影响不大，但在主动齿转频与齿轮啮合频率处箱体垂向振动加速度会产生峰值，使其方均根值显著增加，平均增量为4.8 m/s

。在200 km/h时主动齿转频与齿轮箱箱体点头模态频率相近引发共振，使得箱体垂向振动加速度方均根值增量异常显著，因此在分析齿轮箱箱体振动时齿轮箱内部激励不可忽略；齿轮箱箱体柔性对考虑齿轮箱内部激励时的箱体横向振动加速度影响不大，但会使垂向振动加速度方均根值有所减小，在速度达到300 km/h后减小量较大，平均减小量为2.72 m/s

。

Abstract

During the operation of high-speed trains

the loads on the gearbox are very complex

and cracks often occur in the boxbody. To ensure the service safety of the gearbox body

a dynamic model of high-speed trains with a gear transmission system was established based on SIMPACK. Comparative analysis of the vibration response of the gearbox rigid body at speeds of 200 km/h

250 km/h

300 km/h and 350 km/h was conducted

considering only track excitation and both gears internal excitation and track excitation. In addition

a rigid-flexible coupling dynamic model of a high-speed train considering a flexible gearbox body was established to analyze its impact on the vibration calculation results of the gearbox body. The results indicate that the

internal excitation of the gearbox has a little impact on the lateral vibration acceleration of the gearbox body

but at the rotational frequency of the driving gear and the engagement frequency of the gears

the vertical vibration acceleration of the gearbox body will exhibit a peak value

which significantly increases its root mean square value

with an average increment of 4.8 m/s

. At a speed of 200 km/h

the resonance is caused by the similarity between the rotational frequency of the driving gear and the modal frequency of the gearbox pitching

resulting in a very significant increase in the root mean square value of the vertical vibration acceleration of the gearbox body. Therefore

when analyzing the vibration of the gearbox body

the internal excitation of the gearbox cannot be ignored. The flexibility of the gearbox body has a little impact on the lateral vibration acceleration of the gearbox body when considering the internal excitation

but it will reduce the root mean square value of the vertical vibration acceleration to some extent. The average reduction after the speed reaches 300 km/h is large

reaching 2.72 m/s

关键词

高速动车组齿轮传动系统齿轮箱振动响应共振

Keywords

high-speed traingear transmission systemgearboxvibration responseresonance

references

朱海燕, 朱志和, 邬平波, 等. 服役工况下高速动车组齿轮箱箱体振动特性分析[J]. 噪声与振动控制, 2021, 41(2): 15-20.

ZHU Haiyan, ZHU Zhihe, WU Pingbo, et al. Vibration characteristics analysis of high-speed EMU gearbox housings under service conditions[J]. Noise and vibration control, 2021, 41(2): 15-20.

孙刚, 任尊松, 辛欣, 等. 高速动车组齿轮传动系统振动特性[J]. 机械工程学报, 2019, 55(18): 104-111.

SUN Gang, REN Zunsong, XIN Xin, et al. Vibration characteristics of the gear transmission system of high-speed multiple unit trains[J]. Journal of mechanical engineering, 2019, 55(18): 104-111.

张建超, 胡玉飞, 陈湛, 等. 外部激励下齿轮箱振动分析与动应力评估[J]. 机械设计与制造, 2023, 389(7): 116-124.

ZHANG Jianchao, HU Yufei, CHEN Zhan, et al. Vibration analysis and dynamic stress evaluation of gearbox under external excitation[J]. Machinery design & manufacture, 2023, 389(7): 116-124.

胡玉飞, 张建超, 陈湛, 等. 内部激励下高速动车齿轮箱振动响应评估[J]. 北京交通大学学报, 2022, 46(4): 148-156.

HU Yufei, ZHANG Jianchao, CHEN Zhan, et al. Evaluation of gearbox vibration response in high-speed train under internal excitation[J]. Journal of Beijing jiaotong university, 2022, 46(4): 148-156.

邓晓宇, 张卫华. 基于刚柔耦合的高速列车齿轮传动系统动态特性研究[J]. 高速铁路技术, 2016, 7(4): 50-54.

黄冠华, 王兴宇, 梅桂明, 等. 内外激励下高速列车齿轮箱箱体动态响应分析[J]. 机械工程学报, 2015, 51(12): 95-100.

朱海燕, 黎洁, 尹必超, 等. 牵引电机悬挂参数对高速列车牵引传动部件振动特性的影响[J]. 交通运输工程学报, 2023, 23(1): 156-169.

李润方, 王建军. 齿轮系统动力学: 振动, 冲击, 噪声[M]. 北京: 科学出版社, 1997.

LI Runfang, WANG Jianjun. Gear system dynamics: vibration, impact, noise[M]. Beijing: Science Press, 1997.

翟婉明. 车辆-轨道耦合动力学[M]. 4版. 北京: 科学出版社, 2015.

ZHAI Wanming. Vehicle-track coupling dynamics[M]. 4th ed. Beijing: Science Press, 2015.

肖乾, 程玉琦, 许旭. 轨道不平顺影响下高速列车齿轮传动系统的振动特性分析[J]. 机械传动, 2021, 45(4): 135-141.

XIAO Qian, CHENG Yuqi, XU Xu. Vibration characteristic analysis of high-speed train gear transmission system under track irregularity[J]. Journal of mechanical transmission, 2021, 45(4): 135-141.

王伯铭. 高速动车组总体及转向架[M]. 成都: 西南交通大学出版社, 2008.

WANG Boming. High speed EMU overall and bogie[M]. Chengdu: Southwest Jiaotong University Press, 2008.

罗仁, 曾京, 戴焕云. 列车系统建模及运行平稳性分析[J]. 中国铁道科学, 2006, 27(1): 72-77.

LUO Ren, ZENG Jing, DAI Huanyun. Modeling and ride quality analysis of railway train system[J]. China railway science, 2006, 27(1): 72-77.

赵翔彦, 马域, 闫树军, 等. 动车组齿轮箱箱体模态分析研究[J]. 测控技术, 2022, 41(7): 81-86.

ZHAO Xiangyan, MA Yu, YAN Shujun, et al. Research on modal analysis of gearbox box of EMU[J]. Measurement & control technology, 2022, 41(7): 81-86.

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