Establishment of dynamic equation of sealed rotor system with spur gear

According to the equivalent dynamic model shown in the figure, the dynamic differential equation of the system can be deduced as follows:


XZ, YZ — radial vibration displacement of rotor;

XM, YM — radial vibration displacement of seal;

T — input torque of sealed rotor system;

RZ radius of rotor;

Iz — moment of inertia of rotor;

UZ — Torsional line displacement of rotor;

FX, FY — represents the radial force on the rotor.

The equations are transformed dimensionless

The parameters c and ω are the bearing radial clearance and rotor angular velocity respectively. The bearing radial clearance is taken as 0.1 mm, and the angular velocity can be calculated according to the rotor speed. Therefore, the dimensionless equation of the system can be obtained as follows:

In order to facilitate the subsequent calculation, the left side of the equation is homogenized into the system state equation with only quadratic term

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