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

Zhou Peng-kang; Lu Yao-an; Zhou Qi-xuan; Wang Cheng-yong

doi:10.12052/gdutxb.230105

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

更新时间：2026-05-27

- B-spline Curve Fitting Method of the Formed Grinding Wheel Profile for Gears
- Vol. 40, Issue 6, Pages: 44-51(2023)
- 作者机构：
  
  1. 广东工业大学机电工程学院,广东,广州,510006
  2. 高性能工具全国重点实验室,广东,广州,510006
- 作者简介：
- 基金信息：
- DOI：10.12052/gdutxb.230105
  CLC： TH164
- Online First：25 November 2023，
  
  Published：2023
- 稿件说明：
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周鹏康, 卢耀安, 周启轩, 王成勇. B样条曲线拟合成形磨齿砂轮轮廓方法[J]. 广东工业大学学报, 2023, 40(6): 44-51.

Zhou Peng-kang, Lu Yao-an, Zhou Qi-xuan, et al. B-spline Curve Fitting Method of the Formed Grinding Wheel Profile for Gears[J]. 2023, 40(6): 44-51.
周鹏康, 卢耀安, 周启轩, 王成勇. B样条曲线拟合成形磨齿砂轮轮廓方法[J]. 广东工业大学学报, 2023, 40(6): 44-51. DOI： 10.12052/gdutxb.230105.

Zhou Peng-kang, Lu Yao-an, Zhou Qi-xuan, et al. B-spline Curve Fitting Method of the Formed Grinding Wheel Profile for Gears[J]. 2023, 40(6): 44-51. DOI： 10.12052/gdutxb.230105.

摘要

目前常用直线或圆弧逼近成形磨齿砂轮的轮廓，导致砂轮轮廓曲线容易出现不连续和波动现象，甚至会改变原来轮廓曲线的凹凸性，导致修整的成形砂轮加工出的齿轮精度有限，并且修整程序繁琐、数据量大。针对此问题，提出一种采用B样条曲线拟合成形磨齿砂轮轮廓的方法，方便磨齿机的数控系统使用样条插补功能修整成形砂轮。该方法首先计算渐开线斜齿轮成形磨削砂轮的轮廓，在砂轮轮廓数据点中提取特征点进行B样条曲线拟合，利用差分演化算法计算非特征点拟合误差，把最大拟合误差处的数据点添加到特征点集，然后反复迭代计算，最终生成一条满足拟合误差要求的B样条曲线，在满足指定误差要求下用较少的控制点拟合成形砂轮轮廓。仿真计算结果表明，该方法可以有效拟合成形磨齿砂轮轮廓，并且拟合误差满足指定要求。

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.

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references

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