鼓形蜗杆齿面误差检测原理与测量方法

Research on the Detection Principle and Measurement Method of Crown Worm Tooth Surface Errors

为对鼓形蜗杆齿面这一复杂螺旋面的误差进行检测,提出一种以鼓形齿面偏差作为综合判断平面包络鼓形蜗杆齿面加工误差的误差检测方法。基于齿轮啮合原理建立齿面数学模型,利用齿轮检测中心的轮廓扫描得到轴向齿形;为得到鼓形蜗杆齿面实际接触坐标值,依据鼓形蜗杆齿面方程和齿轮测量中心的特点,进行了测头半径补偿;为实现测量数据与鼓形蜗杆齿面的理想测头中心轨迹的比较,进行了坐标变换;应用最小二乘法原理对测量数据和理论数据进行匹配,得到评估函数,进而得到各测量点的齿面偏差值。对鼓形蜗杆样件齿面进行误差测量实验,验证了上述检测原理和测量方法的可行性。测量结果表明,该鼓形蜗杆样件的上侧齿面误差值为0.079mm,下侧齿面误差值为0.082 mm。研究内容能形成鼓形蜗杆齿面的误差检测评价体系,有利于内齿轮包络鼓形蜗杆传动的推广和应用。

To test complex helical cylindrical worm tooth surface error,a kind of error detection method is put forward and drum gear surface deviations are regarded as overall judgment of the tooth surface machining error for planar enveloping cylindrical worm. As for the crown worm tooth surface,the mathematical model of tooth surface is established,and the contour scan of test center gear is utilized to obtain axial tooth shape. In order to work out the position of the cylindrical worm tooth surface,the probe radius is compensated based on the cylindrical worm gear tooth surface equation and the characteristics of the gear measuring center. Coordinate transformation is performed to compare contour profile of worm gear tooth surface measured with the drum head center trajectory. LMS principle is adopted to optimize the model parameters and the tooth surface deviation is obtained. The crown worm prototype was used in experiment and the correctness and validity of this measurement method were proved. The results show that the tooth surface error of upside is equal to 0. 079 mm,as well as that of the underside is equal to 0. 082 mm. The error measurement and evaluation system are formed,and it is propitious to the promotion and application of internal gear enveloping crown worm drive.