Calculation of contact point between roller and centrifugal casting mold

At any time t, the lower part of the mold contour always contacts with a point of the upper part of the left and right rollers at the same time

Superscripts 1 and 2 indicate that the left and right rollers are in contact with the mold. At this time, the equations of the upper half of the left and right rollers and the lower half of the mold can be written as Y1 = Y1 (x), y2 = Y2 (x) and Y3 = Y3 (x), where the expression of Y3 contains the unknowns A3 and B3, and the central coordinates of the mold (A3, B3) at the time of contact satisfy the following equation:

By solving the formula, the coordinates of the mold center (A3, B3) and Y3 = Y3 (x) can be obtained, and then the coordinates of the contact point can be obtained. Let Y1 = Y3, y2 = Y3, then xc1 and XC2 can be obtained by solving the two formulas, and Yc1 and YC2 can be obtained by substituting Y1 = Y1 (x) and y2 = Y2 (x) respectively.