Particle action behavior on the tooth surface of straight cylindrical gears by spindle finishing
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摘要: 为探究主轴式滚磨光整加工中齿轮与颗粒接触界面处的作用行为，基于离散元法(discrete element method, DEM)对主轴式滚磨光整加工进行模拟仿真。首先阐述齿轮附近及齿面接触颗粒的运动形式，然后探究齿轮埋入深度、齿轮和滚筒的转速对齿面接触颗粒相对运动速度及齿面接触力的影响，最后通过实验进行验证。结果表明：主轴式滚磨光整加工对齿轮齿面的作用具有周期性；齿轮上下齿面受力不均匀，上齿面所受接触力是下齿面的1.5～1.8倍。增加齿轮埋入深度主要影响颗粒与齿面的接触力，埋入深度增大75%，齿面接触力增大76%；提升齿轮与滚筒转速则主要影响颗粒与齿面的相对运动速度，齿轮与滚筒转速增大150%，齿面接触颗粒相对运动速度增大148%。且增加齿轮埋入深度可减小齿轮齿面沿轴向的加工差异性，埋入深度由80 mm增大到140 mm后，上下齿面沿轴向的粗糙度下降率由17%和36%变为62%和55%，而改变转速和埋入深度对沿齿廓方向的加工差异性改变不明显。Abstract: The objective of this study is to explore the mechanism of action at the contact interface between gears and particles in spindle barrel finishing, using the Discrete Element Method (DEM) for simulation. The motion of the particles in the vicinity of the gear and the contact particles on the tooth surface is first described. Then the effects of gear embedment depth, gear and roller speed on relative particle motion velocity and tooth contact force are investigated. Finally, the simulation results are verified by experiments. The results show that the action of spindle barrel finishing on the gear tooth face is cyclical in nature. Contact force on the upper and lower tooth surfaces of the gear is not uniform, and the contact force on the upper tooth surface is 1.5 to 1.8 times that on the lower tooth surface. Increasing the gear embedment depth mainly affects the contact force between the particles and the tooth surface. A 75% increase in embedment depth leads to a 76% rise in tooth surface contact force. Similarly, increasing the gear and drum speed mainly affects the relative movement speed between particles and the tooth surface. A 150% increase in gear and drum speed results in a 148% increase in the relative movement speed of particles in contact with the tooth surface. Increasing the embedment depth of the gear can reduce the processing variability of the gear tooth surface along the axial direction. After increasing the embedment depth from 80 mm to 140 mm, the roughness of the upper and lower tooth surfaces along the axial direction decreases from 17% and 36% to 62% and 55%, respectively. However, the processing variability along the tooth profile direction does not change significantly by changing the speed and embedment depth.
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Key words:
- gear /
- barrel finishing /
- discrete element simulation /
- particle flow field /
- stress testing
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图 7 1周期内齿面接触颗粒相对速度矢量图
Figure 7. Relative velocity vector diagram of of particles in contact with the tooth surface in one cycle
图 10 不同转速和深度齿面接触力变化云图
Figure 10. Cloud diagram of the variation of tooth contact forces at different speeds and depths
图 11 不同转速与埋入深度颗粒平均相对速度变化图
Figure 11. Chart of the mean relative velocity of particles at different speeds versus burial depth
图 14 应力和法向接触力随深度与转速变化图
Figure 14. Chart of stress and normal contact force as a function of depth and speed
图 15 不同深度与转速下粗糙度变化图
Figure 15. Roughness variation chart at different depths and speeds
图 16 不同深度下齿面粗糙度变化图
Figure 16. Tooth roughness variation diagram of at different depths
表 1 材料本征参数[4]
Table 1. Material parameters of the model
材料参数 密度 $\rho $ / (kg·m−3) 泊松比 $\varepsilon $ 剪切模量 E / MPa 滚筒（钢） 7 850 0.300 7 940 颗粒
（棕刚玉）2 675 0.360 1 260 齿轮（40 Cr） 7 870 0.277 8 080 
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相互作用 碰撞恢复
系数 μ1静摩擦
系数 μ2滚动摩擦
系数 μ3颗粒-滚筒 0.50 0.35 0.10 颗粒-齿轮 0.43 0.36 0.10 颗粒-颗粒 0.46 0.39 0.10
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表 3 滚磨光整加工离散元模拟设计
Table 3. Discrete element simulation design for barrel finishing
齿轮埋入深度 $ {h}_{1} $ / mm 滚筒转速 $ {n}_{1} $ / (r·min−1) 80，110，140 12，21，30
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