Journal of Guangdong University of Technology ›› 2023, Vol. 40 ›› Issue (06): 44-51.doi: 10.12052/gdutxb.230105

• Precision Manufacturing Technology and Equipment • Previous Articles     Next Articles

B-spline Curve Fitting Method of the Formed Grinding Wheel Profile for Gears

Zhou Peng-kang1,2, Lu Yao-an1,2, Zhou Qi-xuan1,2, Wang Cheng-yong1,2   

  1. 1. School of Electromechanical Engineering, Guangdong University of Technology, Guangzhou 510006, China;
    2. State Key Laboratory for High Performance Tools, Guangzhou 510006, China
  • Received:2023-08-12 Online:2023-11-25 Published:2023-11-08

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Abstract: Currently, straight lines or arcs are commonly used to approximate the profile of the formed grinding wheel for gears, resulting in discontinuity and fluctuations in the profile curve of the grinding wheel and even changing the concavity and convexity of the original profile curve, limiting the precision of the gears processed by the dressed formed grinding wheel. Besides, the dressing program is cumbersome and the amount of data is large. Aiming at this problem, a method of using B-spline curve to fit the profile of the formed grinding wheel is proposed, which is convenient for the numerical control system of the gear grinding machine to use the spline interpolation function to dress the formed grinding wheel. The method first calculates the profile of the involute helical gear formed grinding wheel. Feature points are then extracted from the data points of the grinding wheel profile and fitted with a B-spline curve. The fitting errors of the non-feature points are calculated using differential evolution algorithm. The data point with the maximum fitting error is added to the feature points. This process is iteratively repeated until the generated B-spline curve satisfies the fitting error requirement, fitting the profile of formed grinding wheel with fewer control points while meeting the specified error requirements. Simulation results show that the method can effectively fit the profile of the formed grinding wheel and the fitting error can meet the specified requirements.

Key words: gear grinding, formed grinding wheel dressing, B-spline curve, differential evolution algorithm

CLC Number: 

  • TH164
[1] 唐平. 普及型成形磨齿机砂轮修整技术研究与应用[D]. 重庆: 重庆大学, 2015.
[2] 张四弟, 左键民, 张兆祥, 等. 成形砂轮高精度修整技术研究[J]. 机床与液压, 2011, 39(17): 39-41.
ZHANG S D, ZUO J M, ZHANG Z X, et al. Research on the high-accuracy dressing technology of form grinding wheel [J]. Machine Tool & Hydraulics, 2011, 39(17): 39-41.
[3] 李先冲. 普及型数控成形磨齿机关键技术开发及应用[D]. 重庆: 重庆大学, 2015.
[4] YI J, JIN T, DEENG Z. The temperature field study on the three-dimensional surface moving heat source model in involute gear form grinding [J]. International Journal of Advanced Manufacturing Technology, 2019, 103(2): 3097-3108.
[5] 任小中, 李昊凯, 苏建新, 等. 修形内斜齿轮成形磨削砂轮廓形优化研究[J]. 机械设计与制造, 2021(8): 149-151.
REN X Z, LI H K, SU J X, et al. Profile optimization of grinding wheel for form-grinding modified inner helical gear [J]. Machinery Design & Manufacture, 2021(8): 149-151.
[6] DENG H, XU Z. Dressing methods of superabrasive grinding wheels: a review [J]. Journal of Manufacturing Processes, 2019, 45: 46-69.
[7] 任小中, 丁军鹏, 谢丰坤. 渐开线廓形砂轮数控修整实验系统的开发[J]. 实验室科学, 2011, 14(6): 107-109.
REN X Z, DING J P, XIE F K. Development of experimental system for CNC dressing involute grinding wheel [J]. Laboratory Science, 2011, 14(6): 107-109.
[8] 刘贵祥. 基于NUM Flexium的摆线轮成形磨削CAM系统开发[D]. 西安: 西安工业大学, 2018.
[9] 韩江, 江本赤, 夏链, 等. 基于轮廓关键点的B样条曲线拟合算法[J]. 应用数学和力学, 2015, 36(4): 423-431.
HAN J, JIANG B C, XIA L, et al. A B-spline curve fitting algorithm based on contour key points [J]. Applied Mathematics and Mechanics, 2015, 36(4): 423-431.
[10] PARK H, LEE J H. B-spline curve fitting based on adaptive curve refinement using dominant points [J]. Computer-aided Design, 2007, 39(6): 439-451.
[11] 陶浩, 何改云, 王太勇, 等. 一种基于插值拟合的复杂刀具轨迹在线平滑压缩算法[J]. 中国机械工程, 2018, 29(13): 1524-1530.
TAO H, HE G Y, WANG T Y, et al. An online complex tool path smooth compression algorithm based on interpolation curve fitting method [J]. China Mechanical Engineering, 2018, 29(13): 1524-1530.
[12] 张展. 渐开线圆柱齿轮传动[M]. 北京: 机械工业出版社, 2011: 103.
[13] 何文涛. 成形磨齿机运动轨迹规划及控制系统设计[D]. 重庆: 重庆大学, 2015.
[14] 吴序堂. 齿轮啮合原理[M]. 2版. 西安: 西安交通大学出版社, 2009: 98-99.
[15] LES P, WAYNE T. 非均匀有理B样条[M]. 赵罡, 穆国旺, 王拉柱, 译. 2版. 北京: 清华大学出版社, 2010: 256-257.
[16] 李钱宽. 连续微小线段NURBS曲线拟合及插补算法研究[D]. 镇江: 江苏科技大学, 2020.
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