Model of stiff rotor with six degrees of freedom

This paper presents model of stiff rotor with six degrees of freedom. Generalized coordinates in a form of three translations of rotor's geometric center and three Euler's rotation angles were chosen. Configuration of Euler's angles was selected to prevent phenomenon of gimbal lock. It is assumed that rotation angle may be arbitrary, while angles of inclination of rotating surface are small. Rotor may have static and dynamic unbalance. To formulate motion equations Lagrange formalism is used. Rotor is affected by mass forces, dumping rotational and non-rotational forces, and two groups of forces: elastic and dumping from two parts of shaft, on which the rotor is mounted. Equations of motion of such a system have complicated form, coefficients dependent on position and are coupled both in elastic and inertial way. It is noted that explicit form of equations of motion is not necessary to determinate state coordinates - displacements and velocities. Matrix notation of equations is proposed to be easily solved with Simulink. Rotor model is closed in a form of Simulink block with one output (state coordinates) and four inputs. Two of them enable to introduce forces coming from elastic parts of the system. Next inputs are used to introduce forces acting on geometrical center and mass center of the rotor. Block modeling stiff rotor is the main part of developed Simulink library to investigate non-steady states in rotating systems consisting of rotors, shafts and bearings in arbitrary configuration.