基于非特征分块插值技术的准双曲面齿轮数字化真实齿面建模方法
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摘要
针对含磨损情况的准双曲面齿轮真实齿面数字化模型构造问题,提出基于非特征分块插值技术的准双曲面齿轮数字化齿面构造方法。基于非特征的离散数据分块技术对三坐标测量仪测量获得的真实齿面离散数据进行分块,判断出的齿面磨损区域。再结合插值改进算法对齿面磨损区域进行局部插值。对传统离散数据点光顺算法进行改进,提高插值构造齿面的光顺性。通过实例比较,本方法不仅减少插值算法计算量,提高齿面插值数据点的精度,改善数字化齿面的光顺性。为含磨损情况的准双曲面齿轮动态性能预测打下基础。
A modeling approach of digital real tooth surfaces of hypoid gears based on non-geometric-feature segmentation and interpolation algorithm aiming at hypoid gears with wear of tooth surfaces is proposed. Above of all, the discrete data of real tooth surfaces, which are measured by 3D coordinate-measure-machine, is segmented by segmentation based non-geometric-feature. The wear areas of tooth surfaces are identified. In addition, a revised interpolation algorithm is applied to interpolation partial tooth surfaces. Finally, on the basis of traditional fairing algorithm for scattered point data, the revised fairing algorithm is proposed. By comparing the instance, this method not only reduces the amount of interpolation algorithm calculation, but also improves the accuracy of interpolation data points, and improved the smoothness of digital gear tooth surfaces. The digitization construction of real tooth surfaces of hypoid gears with wear lays the foundation for its dynamic performance prediction.
A modeling approach of digital real tooth surfaces of hypoid gears based on non-geometric-feature segmentation and interpolation algorithm aiming at hypoid gears with wear of tooth surfaces is proposed. Above of all, the discrete data of real tooth surfaces, which are measured by 3D coordinate-measure-machine, is segmented by segmentation based non-geometric-feature. The wear areas of tooth surfaces are identified. In addition, a revised interpolation algorithm is applied to interpolation partial tooth surfaces. Finally, on the basis of traditional fairing algorithm for scattered point data, the revised fairing algorithm is proposed. By comparing the instance, this method not only reduces the amount of interpolation algorithm calculation, but also improves the accuracy of interpolation data points, and improved the smoothness of digital gear tooth surfaces. The digitization construction of real tooth surfaces of hypoid gears with wear lays the foundation for its dynamic performance prediction.
引文
[1]KONNO K,TOKUYAMA Y,CHIYOKURA H.G1connection around complicated curve meshes using C1NURBS boundary gregory patches[J].Computer-Aided Design,2001,33(4):293-306.
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[11]张军辉,方宗德,王成,等.基于NURBS的弧齿锥齿轮真实齿面的数字化仿真[J].航空动力学报,2009,24(7):1672-1676.ZHANG Junhui,FANG Zongde,WANG Cheng,et al.Digital simulation of spiral bevel gears real tooth surfaces based on non-uniform rational B-spline[J].Journal of Aerospace Power,2009,24(7):1672-1676.
[12]WU Qingbiao,XIA Feihai.Shape modification of Bézier curves by constrained optimization[J].Journal of Zhejiang University Science,2005,6A(Suppl.1):124-127.
[13]TANG Kai,PANG A.Optimal connection of loops in laminated object manufacturing[J].Computer-Aided Design,2005,35(11):1011-1022.
[14]WOO H,KANG E,WANG S Y,el al.A new segmentation method for point cloud data[J].International Journal of Machine Tools&Manufacture,2002,42:167-178.
[15]汪中厚,周晓玲,小熊辰照,等.螺旋锥齿轮齿面扫描式测量法及其应用研究[J].仪器仪表学报,2007(2):11-13.WANG Zhonghou,ZHOU Xiaoling,OGUMA T,et al.Surface error measurement of spiral bevel gears using scanning measurement[J].Chinese Journal of Scientific Instrument,2007(2):11-13.
[2]蔺宏伟,王国瑾,董辰世.用迭代非均匀曲线(曲面)拟合给定点集[J].中国科学(E辑),2003,33(10):912-923.LIN Hongwei,WANG Guojin,DONG Chenshi.Interative NURBS curve(surface)fitting assigned points set[J].Science in China(Series E),2003,33(10):912-923.
[3]孙殿柱,李心成,李延瑞,等.G1连续三角Bézier曲面模型快速生成算法[J].机械工程学报,2010,46(15):125-129.SUN Dianzhu,LI Xincheng,LI Yanrui,et al.G1-continuous algorithms of triangular mesh surface[J].Journal of Mechanical Engineering,2010,46(15):125-129.
[4]贾明,吕震,李永青,等.基于B样条曲面裁剪计算的局部协调设计[J].机械工程学报,2003,39(2):74-78.JIA Ming,LüZhen,LI Yongqing,et al.Local coincided design based on trimmed B-spline surfaces[J].Chinese Journal of Mechanical Engineering,2003,39(2):74-78.
[5]汪中厚,久保愛三,浅野総一郎,等.ハイポイドギヤの性能経時劣化の追跡:第1報,実測歯面形状データの導入法[J].日本機械学会論文集,2000,66(647):2354-2362.WANG Zhonghou,KUBO A,ASANO S,et al.Simulation of deterioration of hypoid gears performance due to tooth flank wear(1st report,data processing of measured tooth flank form deviation for performance simulation)[J].JSME,2000,66(647):2354-2362.
[6]汪中厚.准双曲面齿轮动态性能仿真[M].北京:科学出版社,2013.WANG Zhonghou.Simulation of hypoid gears dynamic performance[M].Beijing:Science Press,2013.
[7]汪中厚,久保愛三,浅野総一郎,等.ハイポイドギヤの性能経時劣化の追跡:第2報,歯面形状劣化に伴う性能変化[J].日本機械学会論文集,2000,66(647):2363-2370.WANG Zhonghou,KUBO A,ASANO S,et al.Simulation of deterioration of hypoid gears performance due to tooth flank wear(2nd report,model for tooth flank wear and the change of gear performance resulted)[J].JSME,2000,66(647):2363-2370.
[8]汪中厚,久保愛三,浅野総一郎,等.ハイポイドギヤの性能経時劣化の追跡:第3報,初期歯面形状による経時劣化後の歯車性能の相異[J].日本機械学会論文集,2000,66(647):2371-2376.WANG Zhonghou,KUBO A,ASANO S,et al.Simulation of deterioration of hypoid gears performance due to tooth flank wear(3rd report,influence of initial tooth flank form on the deterioration of gear performance)[J].JSME,2000,66(647):2371-2376.
[9]孙殿柱,董学朱.描述真实齿面数字模型的研究[J].农业机械学报,2000,31(1):79-90.SUN Dianzhu,DONG Xuezhu.Research on the mathematical model describing real tooth surface[J].Transcations of the Chinese Society for Agricultural Machinery,2000,31(1):79-90.
[10]孙殿柱,董学朱.真实齿面对应点的求解算法[J].中国农业大学学报,1999,4(4):64-68.SUN Dianzhu,DONG Xuezhu.Solving algorithms of corresponding point of two real tooth surface[J].Journal of China Agricultural University,1999,4(4):64-68.
[11]张军辉,方宗德,王成,等.基于NURBS的弧齿锥齿轮真实齿面的数字化仿真[J].航空动力学报,2009,24(7):1672-1676.ZHANG Junhui,FANG Zongde,WANG Cheng,et al.Digital simulation of spiral bevel gears real tooth surfaces based on non-uniform rational B-spline[J].Journal of Aerospace Power,2009,24(7):1672-1676.
[12]WU Qingbiao,XIA Feihai.Shape modification of Bézier curves by constrained optimization[J].Journal of Zhejiang University Science,2005,6A(Suppl.1):124-127.
[13]TANG Kai,PANG A.Optimal connection of loops in laminated object manufacturing[J].Computer-Aided Design,2005,35(11):1011-1022.
[14]WOO H,KANG E,WANG S Y,el al.A new segmentation method for point cloud data[J].International Journal of Machine Tools&Manufacture,2002,42:167-178.
[15]汪中厚,周晓玲,小熊辰照,等.螺旋锥齿轮齿面扫描式测量法及其应用研究[J].仪器仪表学报,2007(2):11-13.WANG Zhonghou,ZHOU Xiaoling,OGUMA T,et al.Surface error measurement of spiral bevel gears using scanning measurement[J].Chinese Journal of Scientific Instrument,2007(2):11-13.