Accurate modeling of equal-distance spiral bevel gear and the trial production by metal powder injection molding process
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摘要: 等距螺旋锥齿轮作为一种新型锥齿轮，其螺旋齿面具有法向等距的特点，适用于金属粉末注射成型工艺批量化生产。根据坐标变换理论推导出球面渐开线和等距圆锥螺旋线的参数方程，再基于齿面形成原理建立齿面数学模型；在MATLAB中对齿面数学模型编程计算出齿面离散点坐标，并通过UG逆向工程完成等距螺旋锥齿轮的精确建模；利用ANSYS仿真分析等距螺旋锥齿轮的啮合接触，得出齿轮的传动性能；最后通过金属粉末注射成型工艺完成等距螺旋锥齿轮的试制。研究结果表明，齿面数学模型结合离散点逆向建模可确保模型的精度，金属粉末注射成型工艺可用于等距螺旋锥齿轮的批量化生产。Abstract: As a new type of bevel gear, the equal-distance spiral bevel gear is suitable for the mass production by metal powder injection molding (MIM) due to the characteristic as the normal equal-distance of spiral tooth surface. According to the coordinate transformation theory, the parametric equations of spherical involute and equal-distance conical spiral curves were derived. The mathematical model of tooth surface was established by the formation principle of tooth surface. The mathematical model of tooth surface was programmed by MATLAB to calculate the coordinates of discrete points on tooth surface, and the accurate modeling of equal-distance spiral bevel gear was completed by reverse engineering of UG. The meshing contact of equal-distance spiral bevel gear was simulated to obtain the transmission performance in ANSYS. Finally, the trial production of equal-distance spiral bevel gear was completed base on the MIM process. In the results, the mathematical model of tooth surface combined with the inverse modeling of discrete points can ensure the accuracy of 3D model, and MIM process can be used to produce the equal-distance spiral bevel gears for mass production.
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图 4 等距螺旋锥齿轮齿面模型（单位：mm）
Figure 4. Tooth surface mode of the equal-distance spiral bevel gear (unit: mm)
图 10 齿面接触区等效应力仿真模拟
Figure 10. Equivalent stress simulation of the tooth surface in contact area
表 1 等距螺旋锥齿轮设计参数
Table 1. Design parameters of the equal-distance spiral bevel gear
名称 旋向 齿数, N 轴交角, Σ / (o) 节锥角, δ / (o) 模数, m / mm 中点螺旋角, β / (o) 齿宽, b / mm 压力角, α / (o) 小轮 左 16 90 34.824 0.905 30 5 20 大轮 右 23 90 55.176 0.905 30 5 20 
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表 2 Fe8Ni材料属性
Table 2. Material properties of Fe8Ni
材料 密度 / (kg·m−3) 弹性模量 / GPa 泊松比 Fe8Ni 7600 190 0.28
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