The machining coordinate system of cylindrical gear grinding with form grinding wheel is established, as shown in Figure 1. In Figure 1: the coordinate system o1-x1y1z1 is fixedly connected with the cylindrical gear, the axis Z1 coincides with the axis of the cylindrical gear, and the axis X1 passes through the initial meshing point of the contact line; the coordinate system o2-x2y2z2 is fixedly connected with the grinding wheel, the axis Z2 coincides with the axis of the grinding wheel, and the direction of axis x2 and axis X1 is opposite; the included angle between the axis of the grinding wheel and the axis of the cylindrical gear workpiece is σ, and the distance between the axes is a.
According to the generating rules of cylindrical gear tooth surface, the axial section profile of forming grinding wheel for grinding cylindrical gear is designed. When the revolving surface of the forming grinding wheel is used to process the tooth surface of the cylindrical gear, the grinding wheel and the workpiece of the cylindrical gear make relative spiral motion, so as to realize the grinding of the tooth surface. At any moment of relative spiral motion, there is such a meshing point on the contact line of the cylindrical gear. On the normal plane of the point, there is a contact arc curve between the axial section profile of the formed grinding wheel and the tooth section profile of the cylindrical gear. The relative position of the axial section of the grinding wheel and the tooth section on the normal plane of the meshing point is shown in Figure 2. Taking the arc curve as the generatrix, the corresponding cylindrical gear tooth surface can be enveloped by spiral motion. In the grinding process, the position of the circular arc curve of the contact between the rotary surface of the grinding wheel and the tooth surface of the cylindrical gear in space is fixed; Therefore, as long as the axial section of the grinding wheel coincides with the tooth section on the normal plane of the initial meshing point of the contact line of the cylindrical linear gear and remains unchanged, and the cylindrical linear gear workpiece makes a spiral motion around the axis of the cylindrical linear gear, the grinding of the tooth surface of the cylindrical linear gear can be realized.
Based on the formula of the parameter equation of the tooth profile of the cylindrical gear on the normal plane at the initial meshing point om of the contact line in the coordinate system om xmymzm, and the coordinate transformation matrix M2M from the coordinate system om xmymzm to the coordinate system o2-x2y2z2, the parameter equation of the axial section profile of the grinding wheel in the grinding wheel coordinate system o2-x2y2z2 can be obtained
Where: A is the distance between the axis of the grinding wheel and the axis of the cylindrical gear; X2, Y2 and Z2 are the coordinate values of the axial section profile of the grinding wheel in the coordinate system o2-x2y2z2.