摘要
渐开线齿轮是机械装备中的关键零件,在齿轮测量或测绘过程中,基圆圆心需要通过测量点反求得到,其反求精度将直接影响齿轮测量或测绘的精度。在已知基圆半径的条件下,研究了基圆圆心反求方法,建立非线性最小二乘方程,并应用牛顿法进行求解得到基圆圆心坐标。给出了影响反求精度的主要因素:单条渐开线测量点数量、被测渐开线数量及位置分布、基圆圆心初值的选取范围,并设计了上述因素的精度影响分析试验。以模数3.5、齿数36的渐开线圆柱齿轮为例,对所提出的方法进行了试验验证并分析了主要因素对反求精度的影响,得到每条被测渐开线齿廓应选取至少100个测量点、在圆周均布方向选取四条渐开线齿廓进行基圆圆心反求效果较佳。研究为渐开线齿轮测量或测绘中的基圆圆心反求提供了依据,具有一定的指导意义和参考价值。
Involute gear is a key part of mechanical equipment. In the process of gear measurement or mapping, the base circle center needs to be obtained by inverse calculation of the measuring points, and the precision of inverse calculation will directly affect the accuracy of gear measurement or mapping. In this paper, under the condition of known radius of base circle, the method of establishing the non-linear least squares equation for inverse calculation of the center of base circle was studied and solved by Newton method, and the coordinates of the center of base circle were obtained. The main factors affecting the accuracy of inverse calculation were discussed: the number of measuring points of single involute, the number and position distribution of the measured involute, the selection range of the initial value of the center of base circle. The experimental design of the influence of the above factors on the accuracy was carried out. Taking the involute cylindrical gears with modulus 3.5 and tooth number 36 as an example, the method proposed in this paper was verified and the influence of main factors on the accuracy of reverse calculation was quantitatively analyzed. It is found that at least 100 measuring points should be selected for each measured involute profile, and four involute profiles should be selected in the circumferential uniform distribution direction for the reverse calculation of the base circle center. The research in this paper has certain guiding significance and reference value for the inversion of the base circle center in the measurement and mapping of involute gears.
作者
魏建杰
汤洁
石照耀
WEI Jianjie;TANG Jie;SHI Zhaoyao(Beijing Engineering Research Center of Precision Measurement Technology and Instruments,Beijing University of Technology,Beijing 100124,China)
出处
《航空制造技术》
2019年第20期70-76,共7页
Aeronautical Manufacturing Technology
基金
国家重点研发计划子课题(2017YFF0204804)
关键词
渐开线
反求方法
基圆圆心
齿廓
测量点
Involute
Reverse calculation
Base circle center
Profile
Measuring point
