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The paper presents a mathematical rotordynamic model regarding excitation due to elliptical shaft journals in sleeve bearings of electrical motors also considering the gyroscopic effect. For this kind of excitation, a mathematical rotordynamic model was developed considering the influence of the oil film stiffness and damping of the sleeve bearings, the stiffness of the end-shields and bearing housings, the stiffness of the rotor, the electromagnetic stiffness in the air gap of the electrical motor and the mass moment of inertia of the rotor and therefore also considering the gyroscopic effect. The solution of the linear differential equation system leads to the mathematical description of the absolute orbits of the shaft centre, the shaft journals and the bearing housings and to the relative orbits between the shaft journals and the bearing housings. Additionally, the bearing housing velocities can also be derived with this mathematical rotordynamic model.