Establishment of the coordinate system of mold geometry error and surface morphology in roller and centrifugal casting

Establish the coordinate system origin 0 as shown in Fig. 1, which coincides with the center of the left roller, X and Y represent the horizontal direction and vertical direction respectively, and the centers of the right roller and the mold are 02 and 03 respectively. In the ideal case, the outer surface of the supporting roller and the mold is cylindrical, the radius of the two supporting rollers is equal, R0, the radius of the mold is R0, the center of the two rollers O1 and O2 are on the same horizontal line, the distance is l, there is an angle β between o1o3 and O2O3.

In the coordinate system shown in the figure, the surface profile equations of the three circles are as follows:

Left wheel:

Right wheel:

casting mold:

Where (AI, BI) is the center coordinate, subscript i = 1,2,3 represents the left roller, right roller and mold respectively. The center coordinates of the three circles can be obtained from the geometric relationship

(a1,b1) = (0,0)

(a2,b2) = (L,0)

The coordinates of the contact points between the mold and the left and right rollers are as follows: