Based on the generating principle, the profile error of gear teeth is measured on the machine, and the workpiece needs to rotate around its axis. Similarly, when using the spiral bevel gear measuring center equipped with one-dimensional probe to measure the profile error of spiral bevel gear, due to the restriction of the sensitive direction of the probe, the workpiece also needs to rotate around its axis. The rotation and positioning error of the workpiece will produce a certain measurement error. For the large wheel of spiral bevel gear pair, the pitch cone angle is greater than 45 °, and the spiral angle is not more than 35 °, and the change of tooth surface curvature is small. In addition, the on-machine measurement system constructed in this paper adopts a three-dimensional trigger probe, which can measure the tooth surface in any direction. Therefore, when using the on-line measuring mechanism to measure the profile error of gear teeth, the appropriate installation angle of machine tool should be selected δ M. After the positioning of the reference point of the measured tooth surface is completed by rotating the workpiece shaft, the whole tooth surface measurement can be completed without rotating the workpiece in the measurement process.
In order to realize the on-site measurement of the profile error of spiral bevel gear on the NC gear grinding machine, the ball center of the probe is made to approach the actual tooth surface along the normal direction of each discrete point of the theoretical tooth surface of the gear by controlling the movement of the three NC axes of the machine tool x, y and Z. When the measuring ball touches the actual tooth surface, the measuring head triggers and sends a signal to the NC system through the data line. The NC system records the reading of the NC axis of the machine tool and converts it into the spatial coordinate of the ball center in the machine tool coordinate system.
Set in the machine tool coordinate system SM, the readings of CNC axes x, y and Z at the initial position are XR, yr and Zr respectively, the coordinates of the ball center are XP, YP and ZP, and the radius of the ball is r. If the measuring ball of the probe contacts with each discrete point on the theoretical tooth surface of the large wheel and the probe is triggered, the readings of linear axis X, y and Z are (x’m (I, J), y’m (I, J), Z’m (I, J)), then:
When measuring the profile error of spiral bevel gear, the probe ball approaches the actual tooth surface along the normal vector direction of the theoretical tooth surface. Therefore, it is necessary to determine the starting point and ending point of the ball motion according to the spatial coordinates and normal vector parameters of each discrete point of the theoretical tooth surface. Assuming that the maximum estimated tooth profile error of the actual tooth surface relative to the theoretical tooth surface is l, the coordinates of the starting point of the ball motion are (x’m1 (I, J), y’m1 (I, J), z’m1 (I, J)), and the coordinates of the ending point of the ball motion are (x’m2 (I, J), y’m2 (I, J), z’m2 (I, J)), then: