General representations
DYNAMICS R4 solves the rotor based on plain, or sleeve bearings dynamics problem for the rotor system as a whole. An integral part of the problem is the plain bearing static and dynamic characteristics analysis The DYNAMICS R4 software system implements algorithms for the following types of plain bearings.
Bearing design
The bearing static characteristics associated with the steady shaft axis under the external static forces action:
- Relative rotor eccentricity;
- The position and value of the minimal film clearance;
- Maximal specific pressure in the film;
- Friction power loss;
- Oil leakage from the bearing through the ends and a number of others;
Bearing Dynamic characteristics make base for the following performance calculation:
- Rotor stability limit, the moment of self-excited oscillations occurrence, oscillation frequency and form;
- Vibration level and resonant behavior of the rotor with residual imbalances.
DYNAMICS R4 software calculates the plain bearing dynamic characteristics with the [DynFB] module. The calculation algorithm is based on the numerical solution of two-dimensional Reynolds equation.
The Reynolds equation is solved by the finite difference method with boundary conditions partially specified by the user, for example, the number and position of axial grooves, pockets and segment grooves that change the working surface geometry, etc. During the bearing calculation various parameters are determined for a specific rotation speed. This includes static stiffness and damping coefficients that determine the rotor dynamics.
In general plain bearings are non-linear elements of the rotor system but their dynamic characteristics may be linearized within certain assumptions for small shaft journal deviations from its stationary position.
Stiffness and damping coefficients
The stiffness and damping coefficients are automatically transferred to the rotor model reference nodes, i.e. a quasi-linear model is formed. After that, the rotor model with sleeve bearings is completely ready for the dynamic characteristics calculation. Then the rotor system dynamics problem is solved either in a stationary formulation or in a non-stationary one.
Among the non-linear elements, the DYNAMICS R4 includes a non-linear cylindrical plain bearing module based on the Reynolds equation analytical solutions.
