Research on analytical modeling of spline coupling based on three-dimensional contact friction unit
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摘要:
以柔性套齿结构为对象，首先利用三维接触有限元模型仿真了套齿受载过程中的变形特征和接触状态变化；其次，以仿真结果为指导，通过在各齿面啮合点处引入三维接触摩擦单元并利用受力平衡关系和数值迭代法，提出了一种套齿连接迟滞行为预测的解析模型；最后对所提模型进行验证，并利用该模型分析了套齿连接结构迟滞行为和接触特性。结果表明：所提出的模型能够充分考虑各齿面接触分离、黏滞滑移及其沿轴向分布特征，与有限元模型相比，所提模型在能准确预测结构迟滞特性的同时计算效率可提升3个数量级；剪力载荷作用下啮合齿面接触面积降低是导致结构刚度降低的原因，而啮合齿面滑移导致了套齿内阻尼，其中以轴向滑移的贡献最为显著；套齿连接迟滞特性对齿宽和扭矩变化较为敏感，受摩擦因数影响相对较小。
Abstract:Taking the flexible spline coupling as the object, a three-dimensional contact finite unit model was used to simulate the deformation characteristics and contact state changes of the spline. Guided by the simulation results, an analytical model for predicting the hysteresis behavior of tooth coupling was proposed by introducing three-dimensional contact friction unit at the meshing points of each tooth surface and using the force balance relationship and numerical iteration method. The proposed model was verified, and the hysteresis behavior and contact characteristics of the coupling structure were analyzed by using the proposed model. The results showed that the proposed model can fully consider the contact-separation, viscous-slip and their axial distribution characteristics. Compared with the finite element model, the proposed model can accurately predict the hysteresis characteristics of the structure and improve the computational efficiency by 3 orders of magnitude. The reduction of structural stiffness was attirbutable to the reduction of contact area of meshing tooth under shear load. And, the sliding of contact surface led to the internal damping, of which axial sliding had the most significant contribution. The hysteresis characteristic of spline coupling was more sensitive to the change of tooth width and torque, and was less affected by the friction coefficient.
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图 2 套齿连接三维接触有限元模型
Figure 2. Three-dimensional contact finite element model of spline coupling
图 3 不同剪力载荷下啮合齿接触状态
Figure 3. Contact state of meshing teeth under different shear loads
图 4 套齿连接横向变形示意图及线位移随剪力载荷变化规律
Figure 4. Schematic diagram of lateral deformation of spline coupling and the law of linear displacement changing with shear load
图 5 套齿连接扭转变形示意图及扭转角随剪力载荷变化规律
Figure 5. Schematic diagram of torsion deformation of spline coupling and the law of torsion angle changing with shear load
图 6 横向载荷作用下内轴偏转示意图
Figure 6. Schematic diagram of internal axis deflection under lateral load
图 8 内轴偏移和扭转时各齿侵入量变化示意图
Figure 8. Schematic diagram of the change of each tooth invasion when the inner shaft offsetting and twisting
图 9 三维接触摩擦单元示意图
Figure 9. Schematic diagram of three-dimensional contact friction unit
图 11 简谐载荷下套齿连接结构线位移曲线及对比
Figure 11. Linear displacement curve and comparison of the spline coupling structure under simple harmonic load
图 12 不同载荷幅值下套齿连接结构迟滞回线
Figure 12. Hysteresis loop of the spline coupling structure under different load amplitudes
图 13 循环载荷下套齿连接接触状态变化
Figure 13. Change of contact state of spline coupling under cyclic load
图 14 不同载荷步下的啮合齿接触状态（载荷幅值为20 kN）
Figure 14. Contact state of meshing teeth under different load steps （load amplitude of 20 kN）
图 15 载荷幅值为15 kN时啮合齿滑移状态
Figure 15. Sliding state of meshing teeth for load amplitude of 15 kN
图 16 载荷幅值为20 kN时啮合齿滑移状态
Figure 16. Sliding state of meshing teeth for load amplitude of 20 kN
图 17 不同结构力学参数对套齿连接迟滞特性的影响
Figure 17. Influence of different structural mechanical parameters on hysteresis characteristics of spline coupling
表 1 套齿连接结构参数
Table 1. Spline coupling structure parameters
参数 数值 涡轮轴 风扇轴 齿数 22 22 齿宽/mm 30 30 摩擦因数μ 0.15 0.15 模数/mm 3 3 弹性模量/GPa 210 210 泊松比 0.25 0.25 压力角/（°） 20 20 内轮廓半径r1/mm 21 外轮廓半径r2/mm 44 
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