双圆弧刀具加工直齿锥齿轮的啮合性能分析及优化

doi:10.3969/j.issn.1004-132X.2025.08.004

摘要/Abstract

摘要：

提出了高效双圆弧刀具铣/磨直齿锥齿轮方法，以改善其啮合性能。采用双圆弧刀具模拟冠状产形轮，引入刀具修形系数、刀盘平均半径和刀刃角，建立考虑齿廓和齿向修形的直齿锥齿轮齿面模型。根据两啮合齿轮连续相切条件建立齿面接触分析模型，结合齿面间隙、法向柔度矩阵和数学规划建立轮齿承载接触分析模型。在此基础上，以几何传动误差对称性和承载传动误差波动量最小为目标，调整刀具修形原点位置和优化刀具参数，对比优化前后齿轮几何传动误差和承载传动误差。算例结果表明，刀具修形原点位置会影响几何传动误差的对称性，刀具修形系数越大，齿廓修形量越大，则几何传动误差幅值和承载传动误差幅值越大；随着刀盘平均半径的减小和刀刃角的增大，齿向修形量增大，则齿面印痕区域减小。优化后在工作载荷下，承载传动误差波动量减小56.54%，有效降低了齿轮副的振动激励。

关键词: 双圆弧刀具, 直齿锥齿轮, 齿面修形, 啮合仿真, 遗传算法

Abstract:

A method for milling/grinding straight-toothed bevel gears using high-efficiency double-arc cutting tools was proposed to improve their meshing performance. A double arc tool was used to simulate a crown-producing wheel， and tool trimming coefficients， the average radius of the cutter disk and the cutting edge angle were introduced to establish a straight bevel gear tooth face model that considered tooth profile and tooth direction trimming. According to the conditions of continuous tangency of two meshing gears， a tooth contact analysis model was established， and combined with tooth clearance， normal flexibility matrix and mathematical planning， a wheel tooth bearing contact analysis model was established. Then with the goal of achieving symmetry in geometric transmission errors and minimising fluctuations in load transmission errors， the tool profiling origin positions was adjusted and tool parameters were optimised. The geometric transmission errors and load transmission errors of the gear were compared before and after optimization. The example results show that the position of the tool reshaping origin affects the symmetry of the geometric transmission errors； the larger the tool reshaping coefficient is， the larger the amount of tooth profile reshaping is， the amplitude of the geometric transmission errors and the amplitude of the load bearing transmission errors will increase； with the decrease of the average radius of the knife holder and the increase of the blade angle， the amount of tooth profile reshaping is increased， and then the area of the tooth surface mark will be reduced. After optimization， the amount of bearing transmission error fluctuation is reduced by 56.54% under the working load， which may effectively reduce the vibration excitation of the gear pairs.

Key words: dual interlocking circular cutter, straight bevel gear, tooth surface modification, meshing simulation, genetic optimization

中图分类号:

TH132

苏进展, 冯要克, 刘镔, 曹新龙, 孙霖霖. 双圆弧刀具加工直齿锥齿轮的啮合性能分析及优化[J]. 中国机械工程, 2025, 36(8): 1683-1690.

Jinzhan SU, Yaoke FENG, Bin LIU, Xinlong CAO, Linlin SUN. Analysis and Optimization of Meshing Performance of Straight Bevel Gears Machined by Dual Interlocking Circular Cutters[J]. China Mechanical Engineering, 2025, 36(8): 1683-1690.

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链接本文: https://www.cmemo.org.cn/CN/10.3969/j.issn.1004-132X.2025.08.004

https://www.cmemo.org.cn/CN/Y2025/V36/I8/1683

图/表 16

图1 刀具坐标系

Fig.1 Tool coordinate system

图2 冠状产形轮和双圆弧刀具相对位置

Fig.2 Relative position of the crown generating wheel and the double arc cutter

图3 刀刃角δ

Fig. 3 Blade angle δ

图4 直齿锥齿轮的展成坐标系

Fig.4 Expanded coordinate system for straight bevel gears

图5 啮合坐标变换

Fig.5 Transformation of meshing coordinates

图6 优化流程

Fig.6 Optimize processes

表1 齿轮副基本参数

Tab.1 Basic gear parameters

参数	小轮	大轮
齿数N_i	25.0	36.0
模数m/mm	5.0
压力角α/（°）	25.0
轴交角∑/（°）	90.0
齿宽F_w/mm	29.2
齿顶高系数h_a	1.0
齿根高系数h_f	1.25

表2 刀具参数

Tab.2 Tool parameters

参数	小轮	大轮
刀盘平均半径ρ_m/mm	80.0/160.0/200.0	200.0
刀顶圆角半径ρ_f/mm	0.8	0.8
刀刃角δ/（°）	1.5/2.0/2.5	2.0
修形系数a_t	0.0001/0.0002/0.0003	0.0

图7 不同刀盘平均半径TCA和LTCA结果

Fig.7 TCA and LTCA results for different blade mean radii

图8 不同刀刃角TCA和LTCA结果

Fig.8 TCA and LTCA results for different knife edge angles

图9 不同修形系数TCA和LTCA结果

Fig.9 TCA and LTCA results with different trimming coefficients

表3 优化参数的边界

Tab.3 Optimizing the boundaries of the parameters

	a_t	δ/（°）	ρ_m/ mm
上界	0.0	0.0	100.0
下界	0.0008	2.5	300.0

表4 参数优化结果

Tab.4 Parameter optimization results

a_t1	δ₁/（°）	ρ_m1/ mm
0.000 56	1.7832	181.6523

图10 TCA和LTCA结果

Fig.10 TCA and LTCA results

图11 齿面偏差

Fig.11 Tooth surface deviation

图12 不同载荷承载传动误差幅值对比

Fig.12 Comparison of transmission error amplitude for different loads

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