Analysis of the Effect of Structural Flexibility on Dynamic Characteristics of Power Tri-branching Reducers
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摘要: 为研究箱体、轴和花键联轴器的结构柔性对齿轮啮合刚度和传动系统动力学响应的影响, 对比不同建模方式之间的差异, 文中以功率三分支减速器为研究对象, 建立了全柔体耦合动力学模型以及将不同部件考虑为刚性的动力学模型, 采用时域和频域分析方法, 研究了结构柔性对齿轮啮合刚度和传动系统动力学响应的影响规律。研究结果表明: 部件柔性对齿轮啮合刚度的影响可以忽略; 箱体柔性对系统振动特性影响较大, 尤其当箱体模态与啮频重合或接近时, 共振会使系统振动响应幅值显著增大; 忽略轴的柔性可能导致部分啮频谱线丢失; 花键联轴器柔性仅影响其连接轴的振动特性, 对系统其他部分的振动响应影响较小。因此根据分析目的的不同, 需要采用不同的分析模型。分析啮合刚度时, 仅需要建立刚体模型; 而分析系统振动特性时, 则需要使用全柔体模型。Abstract: To investigate the effect of structural flexibility of the housing, shaft, and spline coupling on the meshing stiffness of the gear and dynamic response of the powertrain system and compare the differences between different modeling methods, a power tri-branching reducer was taken as the object, and a fully flexible coupled dynamics model was established, as well as dynamic models considering different components as rigid. The influence of structural flexibility on meshing stiffness of the gear and dynamic response of the powertrain system was studied using time domain and frequency domain analysis. The results show that the effect of structural flexibility on meshing stiffness of the gear can be ignored; the flexibility of the housing has a significant impact on the vibration characteristics of the system, especially when the housing mode coincides or approaches the mesh frequency; the resonance makes the vibration response amplitude of the system significantly increase; ignoring the flexibility of the shaft may result in the loss of spectral lines at certain mesh frequencies; the flexibility of a spline coupling only affects the vibration characteristics of its connecting shaft and has a small impact on the vibration responses of other components of the system. Therefore, different analysis models need to be used for different analysis purposes. When analyzing meshing stiffness, only a rigid body model needs to be established. When analyzing the vibration characteristics of the system, it is necessary to use a fully flexible model.
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表 1 齿轮参数表
Table 1. Parameters of gears
齿轮 模数/mm 齿数 螺旋角/(°) 齿宽/mm 变位系数 z1 2.5 15 16 33 0 z2-1 2.5 18 16 33 0.440 z2-2 2.5 50 16 33 0.144 z3i 2.5 62 16 33 0 z4i 3.0 25 16 40 0.300 z5 3.0 67 16 40 0 
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表 2 传动系统模型类型
Table 2. Types of transmission system models
模型序号 箱体柔性 轴柔性 花键联轴器柔性 模型I √ √ √ 模型II ○ √ √ 模型III ○ ○ √ 模型IV ○ √ ○
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表 3 减速器各部件材料属性
Table 3. Material properties of reducer components
组件 材料 密度
/(kg/m3)弹性模量
/MPa泊松比 箱体 20Cr13 7 750 200 0.32 轴 18Cr2Ni4WA 7 910 210 0.30 花键轴 18Cr2Ni4WA 7 910 210 0.30
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表 4 额定工况下啮合频率
Table 4. Mesh frequencies under rated working condition
传动级 啮合齿轮副 符号 啮频/Hz 输入级 z1-z2-1 f1 3 230 分流级 z2-2-z3A、z2-2-z3B、z2-2-z3C f2 8 010 汇流级 z4A- z5、z4B- z5、z4C- z5 f3 12 500
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