Contact dynamic modelling and vibration response analysis of the spline pair between cylinder and shaft of a piston pump
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摘要:
柱塞泵缸体和主轴花键副的碰撞行为影响其运行可靠性，对花键副碰撞过程和缸体及主轴振动响应的研究具有重要意义。建立了柱塞泵缸体-主轴花键副碰撞动力学模型，并对碰撞过程和振动响应进行了分析。介绍了柱塞泵缸体-主轴花键碰撞动力学模型。分析了缸体的受力情况，获得了其激励。对不同出口压力工况下，花键副碰撞和缸体及主轴振动响应进行仿真分析。结果表明：柱塞泵缸体-主轴花键碰撞有限元模型可分析花键副碰撞过程和缸体及主轴振动响应；受到缸体内时变的液压力影响，柱塞泵缸体和主轴花键的齿面接触位置会随着转动角度的变化而发生变化；柱塞泵出口压力增大，花键副的齿面接触应力、缸体及主轴振动响应和主轴挠度增大；主轴花键处的挠度远大于其他位置的挠度，其挠度由花键处向两边递减。
Abstract:The contact of the spline pair between the cylinder and shaft of piston pumps affects their operation reliability. It is important to analyze the contact mechanism of the spline pair and the vibration responses of the cylinder and shaft. In this study, a finite element contact dynamic model of the cylinder and shaft was developed, and the vibration responses of the cylinder and shaft were analyzed. The finite element contact dynamic model was described. The forces acting on the cylinder were analyzed, and the excitation forces were obtained. The contact mechanism and the vibration responses at various outlet pressure conditions were simulated and analyzed. The results showed that: the contact dynamic model can simulate the contact mechanism of the spline pair and the vibration responses of the cylinder and shaft. Under the influence of time-varying piston chamber pressure, the tooth contact position of the spline changed with the varying rotational angle. The increase of the outlet pressure led to the increase in the tooth contact stress, vibration responses and shaft deflection. The deflection at the spline of the shaft was much larger than that at other positions, and the deflection decreased from the spline side to the two end sides.
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Key words:
- piston pump /
- spline pair /
- finite element method /
- contact analysis /
- vibration response
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图 1 柱塞泵缸体-主轴碰撞有限元动力学模型
Figure 1. Finite element contact dynamic model of the spline pair between the cylinder and shaft of the piston pump
图 2 柱塞泵缸体和主轴动力学模型
Figure 2. Dynamic model of the cylinder and shaft in the piston pump
图 5 不同压力下主轴和缸体各键齿接触应力云图（n=4 000 r/min）
Figure 5. Stress cloud of each tooth contact of the shaft and cylinder at different pressures （n=4 000 r/min）
图 6 不同压力下主轴和缸体各键齿最大接触应力
Figure 6. Maximum contact stress of each tooth of the shaft and cylinder at different pressures
图 7 不同压力下主轴和缸体键齿随时间变化的接触应力云图（n=4 000 r/min）
Figure 7. Contact stress cloud of the shaft and cylinder teeth with time at different pressures （n=4 000 r/min）
图 8 不同压力下主轴和缸体键齿随时间变化的最大接触应力
Figure 8. Maximum contact stress of the shaft and cylinder teeth with time at different pressures
图 9 不同压力下振动位移对比
Figure 9. Comparison of the vibration displacement at different pressures
图 10 不同压力下振动速度对比
Figure 10. Comparison of the vibration velocity at different pressures
图 11 不同压力下主轴各单元块沿y方向挠度
Figure 11. Deflection of each unit block of the shaft in y-direction at different pressures
图 12 不同压力下主轴各单元块沿z方向挠度
Figure 12. Deflection of each unit block of shaft in z-direction at different pressures
图 13 不同压力下主轴各单元块的空间挠度
Figure 13. Spatial deflection of each unit block of shaft at different pressures
表 1 渐开线花键副参数
Table 1. Parameters of involute spline sub
参数 外花键 内花键 齿数z 16 16 压力角α/（°） 30 30 齿顶圆直径Da/mm 12.75 11.36 齿厚H/mm 1.3 1.29 泊松比v 0.28 0.28 模数m/mm 0.75 0.75 齿槽宽E/mm 1.12 1.04 齿根圆直径Df/mm 10.88 13.13 弹性模量E/GPa 211 211 
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