图1 齿轮啮合示意图
Published:10 May 2024,
Received:21 August 2023,
Revised:12 December 2023
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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.
high-speed train;
gear transmission system;
gearbox;
vibration response;
resonance
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。
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[
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[
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 齿轮啮合示意图
Fig. 1 Schematic diagram of gear engagement
主动齿轮1与从动齿轮2的自由度如
(1) |
刚体 | 自由度 | |||
---|---|---|---|---|
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 |
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[
(2) |
式中:
齿轮相对传递误差为:
(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:
(4) |
式中:km为齿轮副平均啮合刚度;ω0为齿轮啮合基频;an,bn ( n = 1,2,…,N) 为 Fourier级数展开系数。
齿轮啮合阻尼可由下式计算:
(5) |
式中:
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:
(6) |
式中:b为1/2齿侧间隙。
齿轮三向动态啮合力计算公式为:
(7) |
从
基于多体动力学理论[
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 |
图2 齿轮时变啮合刚度
Fig. 2 Time-varying engagement stiffness of gears
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
(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。
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[
图3 动车转向架动力学模型
Fig. 3 Dynamic model of high-speed train bogie
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
(a) 垂向
(b) 横向
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
(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;fm为齿轮啮合频率,Hz;v为动车运行速度,km/h。
频率 | 运行速度/(km·h-1) | |||
---|---|---|---|---|
200 | 250 | 300 | 350 | |
主动齿转频f1 | 46.7 | 58.4 | 70.1 | 81.7 |
齿轮啮合频率fm | 1 633.8 | 2 042.3 | 2 450.8 | 2 859.2 |
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
(a) 200 km/h速度
(b) 250 km/h速度
(c) 300 km/h速度
(d) 350 km/h速度
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
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
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。
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[
图8 齿轮箱箱体有限元模型
Fig. 8 Finite element model 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 |
图9 动力学模型中的柔性齿轮箱箱体
Fig. 9 Flexible gearbox body in dynamic model
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
(a) 垂向
(b) 横向
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
(a) 300 km/h速度
(b) 350 km/h速度
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。
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:
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。
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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