在基于计算机视觉的齿轮检测中，首次运用极坐标变换算法对预处理后的齿廓采样数据进行变换，将圆周上的齿廓曲线变换到水平方向，并将得到的齿廓看作正弦曲线，再采用Matlab工具箱中傅里叶变换函数得到正弦曲线的拟合表达式，对齿廓采样数据的总数（即列数）与拟合函数的周期比值取整，得到所检测齿轮的齿数。在检测公法线长度变动时，首先求得齿顶圆半径、模数，从而得到基圆半径，可求得基圆与齿廓交点的中点与斜率，利用点斜式方程求得与基圆相切的切线方程，该切线与跨过k个齿的齿廓相交的长度即为公法线长度，根据其最大值与最小值之差得到公法线长度变动。文中提出的基于计算机视觉系统的检测齿轮的齿数以及公法线长度的检测方法，实现了齿轮精度非接触式检测，且其检测精度能够满足工程实践的需求。

Based on the computer vision system, the methods of measuring the teeth number and the length of common normal line of gear was put forward for the first time in gear detection. The polar coordinate transformation algorithm was first used to transform the preprocessed tooth profile sampling data. The tooth profile curve on the circumference was transformed into a horizontal state, and the obtained tooth profile regarded as a sinusoidal curve. The Fourier transform function in the Matlab toolbox was employed to get the fitting expression of the sine curve, and then the ratio of the total number of tooth profile sampling data (i.e., the number of columns) and the period of the fitting function was rounded to obtain the number of teeth of the detected gear. As for the dection of changes of common normal line length, first, the radius and modulus of the tooth tip circle were obtained to get the radius of the base circle, thereby obtaining midpoint and slope at the intersection of the base circle and the tooth profile. The tangent equation tangent to the base circle was obtained by using the point slope equation, and the length of the intersection of the tangent line and the tooth profile spanning k teeth was whose length of the common normal, the length variation whose was obtained according to the difference between the maximum value and the minimum value. By the methods proposed above, the non-contact accuracy detection of gear can be realized, whose accuracy can meet the needs of engineering practice.

TP391.4

国家自然科学基金（51765007，51675186，81960332）；广西自然科学基金（2016GXNSFAA380111）。