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浙江大学学报(工学版)
浙江大学学报(工学版)  2022, Vol. 56 Issue (5): 879-889    DOI: 10.3785/j.issn.1008-973X.2022.05.005
机械工程     
弧齿锥齿轮全工序法及机床误差敏感性分析
杨羽1,2(),毛世民3,王迪1,曹伟1,2,*(),李宣秋2,刘存波2
1. 长安大学 道路施工技术与装备教育部重点实验室，陕西 西安 710064
2. 山推工程机械股份有限公司，山东 济宁 272073
3. 西安交通大学 机械制造系统工程国家重点实验室，陕西 西安 710049
Completing process method for spiral bevel gear and sensitivity analysis of machine tool motion error
Yu YANG1,2(),Shi-min MAO3,Di WANG1,Wei CAO1,2,*(),Xuan-qiu LI2,Cun-bo LIU2
1. Key Laboratory of Road Construction Technology and Equipment, Ministry of Education, Chang’an University, Xi’an 710064, China
2. Shantui Construction Machinery Limited Company, Jining 272073, China
3. State Key Laboratory for Manufacturing Systems Engineering, Xi’an Jiaotong University, Xi’an 710049, China
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摘要：

为了在全工序法中利用Free-form机床的灵活性与自由度，提出直接面向Free-form机床的弧齿锥齿轮全工序法，并分析小轮齿面的机床误差敏感性. 已知大轮齿面，对小轮齿面微观形式进行主动设计. 建立直接面向Free-form式机床的四轴联动全工序法小轮切齿数学模型，根据小轮目标齿面参数，求解刀盘和被加工小轮的相对运动关系，得到机床各轴的运动5次多项式，以及剩余待定的小轮刀盘廓形参数. 分析机床各轴运动误差对小轮齿面拓扑形状的影响规律. 算例表明：直接面向Free-form式机床的四轴联动全工序法可以保证小轮正车面接触迹线每个离散点的参数，和倒车面参考点的参数；机床各轴的运动误差可以引起小轮齿面的螺旋角误差、对角误差和压力角误差；Y轴对小轮齿面的影响最小.
关键词： 弧齿锥齿轮;  全工序法;  Free-form机床;  误差敏感性;  齿面修形    
Abstract:

A completing process method for spiral bevel gears directly facing the Free-form machine tool was proposed in order to use the flexibility and freedom of the Free-form machine tool, and the sensitivity of the pinion tooth surface to the motion error of the machine tool was analyzed. Firstly, given the wheel tooth surface, the active design of the microgeometry of the pinion tooth surface was conducted. Secondly, the pinion cutting model by the completing process method was established directly based on a four-axis linkage Free-form machine tool. Then, according to the target parameters of the pinion tooth surface, the relative motion between the cutter and the machined pinion was solved, and the fifth-degree motion polynomial of each axis of the machine tool and the remaining undetermined profile parameters of the pinion cutter were obtained. Finally, the influence of the motion error of each axis of the machine tool on the topological shape of the pinion tooth surface was analyzed. Numerical results show that the parameters of each discrete point of the contact path of the drive tooth surface of the pinion and the parameters of the reference point of the coast tooth surface of the pinion can be ensured by this method. In addition, the motion error of each axis of the machine tool can cause the spiral angle error, the diagonal error and the pressure angle error of the pinion tooth surface, and the Y-axis has the least influence on the pinion tooth surface.
Key words: spiral bevel gear    completing process method    Free-form machine tool    error sensitivity    tooth surface modification
收稿日期: 2021-06-08 出版日期: 2022-05-31
CLC:  TH 132.4  
基金资助: 国家自然科学基金资助项目（51805405）；中央高校基本科研业务费专项资金资助项目（300102251102）
通讯作者: 曹伟     E-mail: yyangu123@126.com;cw334926@163.com
作者简介: 杨羽（1988—），女，工程师，博士，从事齿轮传动研究. orcid.org/0000-0002-9212-2130. E-mail: yyangu123@126.com
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杨羽
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刘存波

引用本文:

杨羽,毛世民,王迪,曹伟,李宣秋,刘存波. 弧齿锥齿轮全工序法及机床误差敏感性分析[J]. 浙江大学学报(工学版), 2022, 56(5): 879-889.

Yu YANG,Shi-min MAO,Di WANG,Wei CAO,Xuan-qiu LI,Cun-bo LIU. Completing process method for spiral bevel gear and sensitivity analysis of machine tool motion error. Journal of ZheJiang University (Engineering Science), 2022, 56(5): 879-889.

链接本文:

https://www.zjujournals.com/eng/CN/10.3785/j.issn.1008-973X.2022.05.005    或    https://www.zjujournals.com/eng/CN/Y2022/V56/I5/879

图 1  小轮修形齿面的控制参数
图 2  加工小轮的机床、刀具及基于Free-form机床的小轮切齿原理图
图 3  基于Free-form机床的全工序法小轮切齿参数计算流程图
项 z ${\mathit{\Sigma}}$/(°) $ a $/mm 旋向 ${\;\beta _{\text{m} } }$/(°) $ {d_{\text{e}}} $/mm $ \delta $/(°) $ {\delta _{\text{a}}} $/(°) $ {\delta _{\text{f}}} $/(°)
小轮 15 90 0 左旋 31 93.333 18.435 22.086 16.915
大轮 45 90 0 右旋 31 280.000 71.565 73.085 67.914
表 1  弧齿锥齿轮副齿坯参数
坐标轴 0次项
系数 		1次项
系数 		2次项
系数 		3次项
系数 		4次项
系数 		5次项
系数
X ?84.931 926 24.121 703 4.239 980 ?0.248 903 ?0.263 390 ?0.156 503
Y ?0.188 649 ?0.094 379 ?0.010 120 ?0.321 459 ?0.825 279 ?0.734 557
Z ?75.172 414 ?25.245 899 2.797 448 0.748 208 0.108 400 0.109 390
A 17 0 0 0 0 0
表 2  加工小轮的各轴运动多项式系数
图 4  正车面齿面接触分析及小轮凹面虚拟测量
图 5  倒车面齿面接触分析及小轮凸面虚拟测量
图 6  四轴联动Free-form机床加工小轮时各轴运动曲线及一阶导数
图 7  四轴联动Free-form机床加工小轮时各轴多项式0阶、1阶系数变化引起的小轮齿面法向偏差
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