In fact, due to the influence of processing accuracy and other factors, the profile of roller and mold will produce In this case, the roller and the outer surface of the mold will not be the standard circle (as shown in Figure 1). The dotted line in the figure represents the ideal surface profile (circle with radius R), and the solid line represents the actual contour of the roller or mold. Establish the coordinate system; X’0’y ‘, the origin 0’ is located in the center of the ideal contour, at the azimuth angle θ, the point coordinates on the ideal contour are (x ‘, y’), and the point coordinates of the actual contour are (x, y), then the relationship between (x ‘, y’) and (x, y) is as follows:

Where △ R (θ) is the distance between the point on the actual contour at the azimuth angle θ and the point on the ideal contour. According to the formula, the actual surface profile equation of the roller and the mold in the coordinate system shown in Fig. 1 is deduced

In other words, as long as we know the function △ R (θ), which is used to represent the surface geometric error, we can determine the contour equation after considering the surface error.

As shown in Figure 2, when considering the geometric errors of the two rollers and the outer surface of the mold, the contour of the outer circle of the supporting roller and the mold at the initial time can be described by the following equation:

Left wheel:

Right wheel:

casting mold:

Assuming that the relative motion between the roller and the mold is pure rolling, the rotation angles of the left and right rollers are equal after time (i.e. ω 1t), and the rotation angle of the mold is ω T, where ω 1 and ω represent the rotation angular velocity of the roller and the mold respectively, and the rotation direction is shown in Fig. 2.

Left wheel:

Right wheel:

casting mold: