Differential equation of motion for vibration performance system of centrifugal casting mold

The rotor and foundation of centrifugal casting were analyzed separately, and the differential equations of motion were obtained.

The rotor is analyzed by transfer matrix method. Firstly, the continuous casting rotor is discretized into n rigid disks and elastic shaft segments by lumped parameter method, as shown in Figure 1. The thickness of the disk is neglected, and the mass and moment of inertia are MLI respectively

And JLI (I = 1,2,…, n is the number of disc shaft segment combination), and the mass of shaft segment is not taken into account. As shown in Fig. 2, the force balance equation of the i-th disk is obtained as follows:

Where, peix and meix are the external excitation force and moment of the rotor respectively, and FCI is the force between the rotor and the foundation.

The value of FCI is 0 at the non support position.

The transfer relationship between the two ends of the disc is as follows:

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