| 摘要: |
| 针对刀倾法加工的螺旋锥齿轮采用常用的样条拟合方法重构误差不均布,而影响齿面接触仿真分析的精度问题,提出根据齿面控制顶点权重系数实现自适应齿面分区重构的方法。由Newton-Raphson方法确定齿面理论控制顶点而实现齿面分区,基于双二次NURBS曲面权重系数的计算方法,得出齿面控制顶点的权重分布,根据控制顶点权重系数确定各区域最优插值节点数而实现齿面的重构。以刀倾法加工的螺旋锥齿轮小轮齿面为例,比较基于权重控制的齿面重构方与基于CATIA的样条线重构以及基于Spline的插值法重构,研究表明:通过CATIA重构的齿面,其齿面误差呈现随机性,齿面误差均值为2.62μm,齿长方向的误差敏感度更大,导致接触仿真分析存在斑点歧义;通过Spline插值重构方法,其齿面局部区域出现“过拟合”现象,齿高方向的误差敏感度更大,齿面误差均值为1.9μm,导致局部区域接触斑点异常;而采用控制顶点权重自适应分配插值节点数进行曲面拟合这一方法,整体上齿面误差分布均匀,齿面误差均值为0.79μm,且瞬时接触斑点具有唯一性,为齿轮接触区域修正提供了可靠的保证。 |
| 关键词: 虚拟加工 权重系数 齿面重构 齿面误差 有限元分析 |
| DOI： |
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| Tooth Surface Reconstruction Techniques Based on Weight Control and Finite Element Analysis |
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ZHANG Kaijie, YUE Kunming, XUE Hao
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School of Mechanical Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China
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| Abstract: |
| Aiming at the problem of uneven distribution of the commonly used spline fitting method for the spiral bevel gear processed by the knife pouring method, which affects the accuracy of the tooth surface contact simulation analysis, the method of realizing adaptive tooth surface partition reconstruction was proposed according to the vertex weight coefficient of the tooth surface control. The tooth surface partition was realized by the Newton-Raphson method to determine the tooth face theory control vertex. Based on the calculation method of the double quadratic NURBS surface weight coefficient, the weight distribution of the tooth surface control vertex was obtained, and the reconstruction of the tooth surface was realized by determining the optimal number of interpolation nodes in each region according to the control vertex weight coefficient. Taking the tooth surface of spiral bevel gear small gear machined by knife pouring method as an example, the tooth surface reconstruction side based on weight control was compared with the CATIA-based spline reconstruction and the Splinebased interpolation method reconstruction. The results showed that the tooth surface error of the tooth surface reconstructed by CATIA was random, the average error of the tooth surface was 2. 62 μm, and the error sensitivity of the tooth length direction was greater, resulting in spot ambiguity in the contact simulation analysis. By using the method of Spline interpolation reconstruction, the local area of the tooth surface appeared "overfitting", the error sensitivity of the tooth height direction was greater, and the average error of the tooth surface was 1. 94 μm, resulting in abnormal contact spots in the local area. By using the method of surface fitting with the adaptive distribution of the number of interpolation nodes with controlled vertex weights, the overall tooth surface error was uniformly distributed with a mean value of 0. 79 μm and the instantaneous contact spots were unique, providing a reliable guarantee for the correction of the gear contact area. |
| Key words: virtual processing weight coefficient tooth surface reconstruction tooth surface error finite element analysis |
