The working surface of the grinding wheel is formed by the rotation of the plane profile on the shaft section around the axis of the grinding wheel. The tooth surface of the workpiece is formed by a spiral motion of the plane tooth shape on the end section around the axis (the spur gear is translational). Therefore, to reduce the amount of calculation, the numerical simulation envelope calculation can be performed in the calculation plane. When calculating the tooth profile of the workpiece, select one end section of the workpiece as the calculation plane. When calculating the sand profile, select the grinding wheel axis section as the calculation plane and its spatial position. In the figure, Op2xpypzp is the workpiece coordinate system, Opzp is the workpiece axis, and Ow2xwywzw is the grinding wheel coordinate system. Owxw is the axis of the grinding wheel.
Firstly, according to the relative positional relationship between the grinding wheel coordinates and the workpiece coordinates and the rotary motion relationship between the grinding wheel and the workpiece, the known workpiece tooth profile is converted into the grinding wheel calculation plane, and then the converted tooth profile is used to calculate the value in the grinding wheel plane. Simulate the envelope calculation to get the desired sand profile. The numerical simulation calculates the model, which consists of a series of line segments that are radially evenly arranged in the calculation plane. The workpiece tooth profile converted to the calculation plane intersects with the line segment in the model to find the intersection point, leaving only the portion within the intersection point.
The computational process envelope algorithm consists of triple nested loops. The outermost loop 1 is the relative motion cycle between the grinding wheel and the workpiece. The grinding wheel performs a transformation with respect to each micro-step movement of the workpiece, and transforms the tooth profile of the workpiece into a calculation plane of the grinding wheel to form a curve. The middle layer loop 2 is a data point loop, and the converted curve is represented by a point coordinate sequence on the calculation plane, and the line segments between the points are sequentially processed. The inner loop 3 is a calculation model cut loop, which in turn determines whether each line segment intersects the profile.
Since the sand profile is a point coordinate list curve, if the general profile is used to gradually approach the desired profile along the profile equidistance curve, the gap between the data points will be outwardly offset and a gap will appear in the middle, resulting in complicated calculation. Moreover, with this trimming strategy, the desired shape and thickness cannot be restored when the wheel needs to be rebuilt after wear.
The process of dressing the dressing wheel is the machining process of the three-axis linkage of the CNC machine tool. The two translation coordinate axes are linked to form the profile trajectory curve, and the rotary shaft drives the dresser to swing the diamond pen to adapt to the slope change of the profile curve. Since the sand profile is not a continuous curve, but a polyline consisting of line segments between data points, the profile normal slope will mutate at the turning point during the trimming process.
Conclusion The results of grinding experiments show that the proposed method for numerical simulation of sand contour shape of disc internal grinding gear grinding technology is correct. The calculation accuracy of profile calculation processing software meets the requirements of use. The machining method is feasible and provides for improving gear mold precision. An effective way.
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