Optimization Design of Low Sensitivity Tooth Surface of Aviation Spiral Bevel Gear
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摘要: 为了降低弧齿锥齿轮的齿面接触印痕关于安装距偏差（又称安装误差）的敏感度，需要开展某航空弧齿锥齿轮的低敏感度齿面优化设计。在轮齿承载接触分析（Loaded tooth contact analysis，LTCA）技术中，引入齿轮副的安装误差，形成了计及安装误差的轮齿接触分析（Error loaded tooth contact analysis，ELTCA）方法，基于ELTCA建立了齿面接触印痕与安装误差间的内在关系；借助接触印痕的量化描述，获得了齿面接触印痕关于安装误差的敏感度矩阵；基于局部综合法建立敏感度关于齿面接触参数的优化设计目标函数，形成弧齿锥齿轮的低敏感度齿面优化设计模型；采用神经网络与遗传算法进行求解，获得了低敏感度齿面的切齿参数；算例结果表明，优化后的齿面接触印痕关于安装误差的敏感度较优化前降低了78.87%。Abstract: In order to reduce the sensitivity of contact marks of an aviation spiral bevel gear to installation distance deviation (also called installation error), it is necessary to carry out its low sensitivity tooth surface optimization design. By introducing the installation error into the loaded tooth contact analysis (LTCA) technology, the error loaded tooth contact analysis (ELTCA) method that considers the installation error is proposed. Based on the ELTCA method, the internal relationship between tooth contact mark and installation error is established. With the help of the quantitative description of the contact mark, the sensitivity matrix of the tooth contact mark with respect to the installation error is obtained. Based on the local synthesis method, the objective function of sensitivity with respect to tooth contact parameters is established, and the low sensitivity tooth surface optimization design model of the spiral bevel gear is established. Using the neural network and the genetic algorithm to solve this optimization problem, the cutting parameters of low sensitivity tooth surface are obtained. The results show that the sensitivity of the optimized tooth contact mark to installation error is reduced by 78.87%.
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Key words:
- spiral bevel gears /
- tooth surface design /
- sensitivity /
- installation errors /
- tooth surface marks
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表 1 弧齿锥齿轮轮齿基本参数
参数名称 参数数值 小轮齿数 36 大轮齿数 45 压力角/（°） 20 大端模数/mm 1.500 中点螺旋角/（°） 20 轴交角/（°） 100 齿轮宽度/mm 8 齿顶高系数 0.85 顶隙系数 0.18800 径向变位系数 0.1737 切向变位系数 0 最大侧隙/mm 0.28 最小侧隙/mm 0.2 大轮旋向（1为右旋，2为左旋） 2 
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表 2 动力与安装误差参数
小轮扭矩/Nm 大轮扭矩/Nm 啮合力/N 最大错位量 9.0265 11.3 233.4139 Hp/mm −0.05 Hg/mm 0.05 V/mm 0.078 ∆Σ/rad −0.00045
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表 3 优化前后2阶接触参数
工况 接触迹线与
根锥的夹角β/（°）传动比1阶
导数η接触椭圆的长轴
与齿宽之比δ第一组参数 75 −0.01 0.23 第二组参数 45 −0.01 0.23 优化后 60.5133 0.0047 0.1601
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