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工程设计学报
Chinese Journal of Engineering Design  2014, Vol. 21 Issue (3): 278-284    DOI: 10.3785/j.issn. 1006-754X.2014.03.013
    
NURBS design of spiral bevel gear with the spherical involute tooth profile
SUN Zhong-fei，ADAYI·Xieeryazidan，DING Han
School of Mechanical Engineering， Xinjiang University， Urumqi 830046， China
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Abstract  To avoid defects of traditional design and processing method for the spiral bevel gears with approximate spherical involute, a new design of spiral bevel gears is proposed. According to the precise composition and shape characteristics of tooth surface, the spherical involute theory was applied to derivate equation expressions of the basic curves of tooth surface which achieved the tooth surface parameterization. Then, discrete points on all areas of tooth surface were obtained respectively. In order to further improve the accuracy of the tooth surface, a unified precise fitting of NURBS curves and surfaces for tooth surfaces was processed. Examples showed that the relevant method was accuracy and useful which proposed new ideas and approaches for the digital design and manufacture of spiral bevel gears．

Key words： spherical involute      spiral bevel gear      NURBS      modeling for tooth surface      CAD/CAM     
Published: 28 June 2014
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Cite this article:

SUN Zhong-fei，ADAYI·Xieeryazidan，DING Han. NURBS design of spiral bevel gear with the spherical involute tooth profile. Chinese Journal of Engineering Design, 2014, 21(3): 278-284.

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https://www.zjujournals.com/gcsjxb/10.3785/j.issn. 1006-754X.2014.03.013     OR     https://www.zjujournals.com/gcsjxb/Y2014/V21/I3/278


球面渐开线齿形的螺旋锥齿轮NURBS设计

为避免传统设计和加工的近似球面渐开线齿形螺旋锥齿轮存在的缺陷，提出了一种新型螺旋锥齿轮设计方案．从齿面精确组成和形状特征出发，将球面渐开线理论应用于齿面基本曲线的方程表达式求导中，实现了齿面曲线的分段参数化．然后，对组成齿面的各区域分别求取齿面离散点数据，并采用三次均匀B样条曲面方法进行初步的拟合与拼接．为了进一步提高齿面精度，借助NURBS方法对拼接后的齿面进行了统一的NURBS精确拟合，并给出了齿面统一参数化的优化方法．最后的算例表明了相关方法的精确性和可行性，为螺旋锥齿轮的数字化设计与NURBS加工提供了新的思路与途径．

关键词： 球面渐开线,  螺旋锥齿轮,  NURBS,  齿面造型,  CAD/CAM 
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