The selection and simplification of physical models for simulation of abrasive flow machining uniformity
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摘要: 新能源汽车齿轮磨齿加工后的精密抛光对于改善其噪声、振动和声振粗糙度性能至关重要，磨料流加工是最适用于复杂齿面高效抛光的关键技术之一，而夹具设计是实现工艺目标（减小波纹度及粗糙度，同时尽量不破坏齿面精度）的关键。结合仿真方法设计磨料流加工夹具优势突出，但物理模型的选择与仿真结果的准确性和计算成本之间存在着矛盾。采用不同黏度介质、黏度模型和流动模型进行仿真试验，分析体现加工均匀性的流体压力分布、速度矢量、壁面剪切力和流线分布云图，探究狭缝模型中磨料流稳态仿真结果，发现不同物理模型的仿真结果具有相似的分布趋势，能够实现加工区域流线的一致，证明了用简化的物理模型替代复杂的物理模型进行夹具优化仿真的可行性，而复杂模型有望用于深入分析磨料流体流动行为及材料去除机理。基于简化模型，采用最简单的牛顿流体──水作为介质，以加工区域流线分布均匀化作为优化目标，进行齿轮轴磨料流夹具设计优化，成功实现了去除齿轮鬼阶的目标。Abstract: Objectives: With the rapid development of electric vehicles (EVs), the maximum rotational speed of EV motors has reached up to 20 000 r/min. Precision polishing of gear surfaces after grinding has become a promising method for improving the noise, vibration, and harshness (NVH) performance of EVs. Abrasive Flow Machining (AFM) is one of the key technologies for efficiently polishing complex gear tooth surfaces. Fixture design plays a critical role in achieving process objectives, reducing surface ripple and roughness, and minimizing damage to the tooth surface accuracy. This article addresses the trade-off between selecting physical models and balancing the accuracy and computational cost of simulation results. It analyzes the impact of different simulation models on the results, providing guidance for AFM fixture design and offering practical experience for fixture optimization in AFM gear processing. Methods: Simulations are conducted using media with different viscosities, viscosity models, and flow models, within the simplest and most typical slit model. Fluid pressure distribution, velocity vectors, wall shear, and streamline distribution cloud mapsare analyzed to reflect machining uniformity. Based on the conclusions drawn from slit model simulations, the simplest Newtonian fluid—water—is selected as the medium for AFM gear shaft processing simulations. The focus is on the uniformity of streamline distribution in the machining area to optimize fixture design. Results: The analysis of slit model simulation results reveals that different physical models have varying impacts on the outcomes: (1) The selection of viscosity models decisively affects the pressure distribution of low-viscosity media. The type of viscosity and turbulence models has little impact on pressure distribution, but it significantly affects the velocity vector, wall shear, and streamline distribution within the abrasive cylinder. (2) For low-viscosity media: implementing a non-Newtonian fluid model has a significant impact on the pressure distribution. Different flow models show marked differences only in wall shear force distributions. Various viscosity models yield different cloud map distributions, but they produce numerically similar values. (3) For high-viscosity media: simulations with non-Newtonian and Newtonian fluid models show consistent results. However, different flow models greatly influence the results, while various viscosity models lead to changes in all simulation results, except for pressure distribution and streamlines within the slit. Despite these variations, the streamline distribution in the processing area remains largely unchanged. Based on the consistency of streamline distribution, fixture design optimization for the AFM gear shaft is carried out, successfully achieving the goal of eliminating gear "ghost frequencies". Conclusions: Despite variations in the physical models, the simulation results exhibit similar trends in distribution, enabling consistent streamline distribution in the processing area. For low-viscosity media, a non-Newtonian fluid viscosity model with laminar flow simulation can be used, and the selection of viscosity models can be simplified based on the rheological characteristics of the actual abrasive flow medium. For high-viscosity media, setting appropriate viscosity values and using laminar flow simulation with a Newtonian fluid model yields consistent pressure and streamline distribution in the processing area, similar to adding viscosity and turbulence models. The slit model simulation results and AFM gear shaft processing tests both demonstrate that streamline information derived from simple physical models can significantly assist in AFM fixture design. In cases where the physical properties of the abrasive flow medium are uncertain—especially in complex flow paths prone to divergence—using the simplest Newtonian fluid, such as water, with laminar flow simulation can provide a reasonable streamline distribution in the processing area. This approach aids in the analysis of processing uniformity, significantly reduces simulation difficulty and costs, and accelerates the fixture design cycle, ultimately enhancing optimization efficiency.
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图 3 不同黏度牛顿流体层流仿真结果
Figure 3. Newtonian fluids simulation results with different viscosities
图 4 低黏介质不同非牛顿流体黏度模型层流仿真结果
Figure 4. Laminar flow simulation results of different non-Newtonian fluid viscosity models in low viscosity media
图 5 高黏介质不同非牛顿流体黏度模型层流仿真结果
Figure 5. Laminar flow simulation results of different non-Newtonian fluid viscosity models in high viscosity media
图 6 低黏介质牛顿流体湍流仿真结果
Figure 6. Low viscosity media simulation results of Newtonian fluid with different turbulence models
图 7 高黏介质牛顿流体湍流仿真结果
Figure 7. High viscosity media simulation results of Newtonian fluid with different turbulence models
图 8 低黏介质非牛顿流体Carreau模型湍流仿真结果
Figure 8. Low viscosity media simulation results of non-Newtonian Carreau model with different turbulence models
图 9 高黏介质非牛顿流体Power-Law模型湍流仿真结果
Figure 9. High viscosity media simulation results of non-Newtonian Power-Law model with different turbulence models
表 1 因素水平表
Table 1. Factor level table
试验因素 各因素试验条件（水平） 黏度介质 V V1=水 V2=低黏 V3=高黏 黏度模型 N N1=Power-Law N2=Carreau N3=Cross 流动模型 T 层流模型 T0=Laminar 湍流模型 T1=Spalart-Allmaras T2=Standard k-ε T3=SST k-omega T4=Reynolds Stress T5=LES 
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表 2 流体介质参数
Table 2. Fluid medium parameters
流体介质 密度 ρ / (kg·m−3) 黏度 η / (Pa·s) 雷诺数 Re 湍流强度 I / % 牛顿流体参数 水 998.2 0.001 286 673.597 3.326 低黏 2 865.5 1.33 232.201 5 8.098 高黏 1308.16 412.11 0.001 165 7 37.220 非牛顿流体
黏度模型参数K / (Pa·sn) n η0 / (Pa·s) η∞ / (Pa·s) λ / s 最小黏度 / (kg·m−1s−1) 最大黏度 / (kg·m−1s−1) Power-Law 低黏 33.29 0.488 高黏 7295.23 0.358 0 196 438.41 Carreau 低黏 0.36 347.3 0 60 高黏 0.41 196438.41 0 138.04 Cross 低黏 0.221 514.63 50.91 高黏 1.813 236934.77 70.85
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