The number of teeth of circular gear is the total number of teeth on the whole circumference of circular gear, and the number of teeth of non-circular gear is the total number of teeth on the circumference of pitch curve of non-circular gear. The number of teeth of the first-order non-circular gear used is 43, so as to prevent more or less measurement of gear teeth during detection. As shown in Fig. 5, the coordinate system is established, and the tooth above the positive direction of x-axis is taken as the first Number the remaining teeth in a counter clockwise direction.
The tooth profile deviation is the normal distance between two designed tooth profiles which contain the actual working part of the tooth profile and the distance is the smallest. The total tooth profile deviation of the first order elliptic gear measured by CMM, articulated arm scanner and 3D scanner is expressed by F α 1, f α 2 and f α 3 respectively.
In non-circular gears, the difference between the arc length of the non-circular gear’s pitch curve intersecting with the theoretical tooth profile of any tooth and the actual tooth profile is defined as the tooth thickness deviation of the non-circular gear. The total tooth profile deviation of the first-order elliptic gear measured by CMM, articulated arm scanner and 3D scanner is expressed by esn1, esn2 and esn3 respectively.