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浙江大学学报(工学版)
Journal of ZheJiang University (Engineering Science)  2022, Vol. 56 Issue (5): 879-889    DOI: 10.3785/j.issn.1008-973X.2022.05.005
    
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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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     
Received: 08 June 2021      Published: 31 May 2022
CLC:  TH 132.4  
Fund:  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）
Corresponding Authors: Wei CAO     E-mail: yyangu123@126.com;cw334926@163.com
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Yu YANG
Shi-min MAO
Di WANG
Wei CAO
Xuan-qiu LI
Cun-bo LIU
Cite this article:

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.

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


弧齿锥齿轮全工序法及机床误差敏感性分析

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 
Fig.1 Controlled parameters on modified tooth surface of pinion
Fig.2 Machine tool, cutter, and schematic diagram for machining pinion based on Free-form machine tool
Fig.3 Calculation flow chart of pinion cutting parameters by completing process method based on Free-form machine tool
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
Tab.1 Gear blank parameters of spiral bevel gear pair
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
Tab.2 Polynomial coefficients of each axis motion of machining pinion
Fig.4 Tooth contact analysis of drive side and virtual measurement of pinion concave tooth surface
Fig.5 Tooth contact analysis of coast side and virtual measurement of pinion convex tooth surface
Fig.6 Motion curve and first derivative of each axis for machining pinion on four-axis linkage Free-form machine tool
Fig.7 Normal deviation of pinion tooth surface caused by change of 0-order and 1-order coefficients of each axis polynomial for machining pinion by four-axis linkage Free-form machine tool
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