The Nonlinear Oil-film Forces Model Analysis And Application Of Journal Bearings Considering Thermohydrodynamic Effects

It is common knowledge that there exists no the closed form of the bearing forces unless full short bearing model is assumed. For the pad bearing mostly used in industry, in order to obtain the instantaneous values of the nonlinear oil-film forces, the unsteady Reynolds equation has to be solved numerically by the methods such as finite differential method and finite element method. These discrete methods with enough accuracy, however, usually involve considerable computing time and, therefore, may be of limited use to analyze the dynamic instability of nonlinear unbalance responses of the rotor. It is desired, for the practical bearings, to investigate a fast computing method of the oil-film forces so that the nonlinear dynamic behaviors of a rotor-bearing system can be easily studied. At the same time, with today's need for the design of high-speed and light-structure rotating machinery, the problem of the heat conduction in the bearing is considerable significant and the classical assumption of constant temperature theory are becoming increasingly unacceptable in the design of hydrodynamic bearings. The isothermal lubrication theory is unable to describe accurately the bearing's hydrodynamic behavior. So it is necessary to take into account the thermal phenomena and to predict their effects on the bearing behaviors.Because of taking into account temperature variation, it is necessary to solve the generalized Reynolds equation which includes the variation properties of the lubricant temperature. The isothermal theory can not give the bearing temperatures. Such the generalized Reynolds equation numerical solutions, however, usually take more computing time. In this paper, the variational approach, which is used to solve the Reynolds equation based on the assumption of constant temperature, is extended to the generalized Reynolds equation calculation and the direct solution method of the generalized Reynolds equation is presented.A simplified one-dimensional thermohydrodynamic effects model is built on the basis of the original two-dimensional thermohydrodynamic effects model. The model not only concerns the thermohydrodynamic effects of the lubricating film, but also offers a direct and rapid numerical algorithm for solving lubricating film temperature field. The numerical results of the temperature distributions for the one model are in good agreement with experiment and the less computing time is needed and the one-dimensional thermohydrodynamic effects model can be applied to the engineering thermohydrodynamic effects of the lubricating film analysis.The direct solution method of the generalized Reynolds equation and the one-dimensional thermohydrodynamic effects model are the major creative meanings of this paper and some creative notes are as follows:1 One-dimensional instantaneous finite journal bearing model which is definedby analysis formula in the axial direction and distributed by finite element in the circumferential pressure direction is built. Based upon the variational approach, variational inequality and complementary problem, which are equivalent to the generalized Reynolds equation under Reynolds boundary condition, the film pressure distribution in the axial direction can be solved analytically and the two-dimensional variational inequality reduces to one-dimensional form by partitioning the film pressure function and minimizing the variational approach.2 The direct solution method of one-dimensional problem is developed which efficiently solves the one-dimensional model for the nonlinear oil-film forces of journal bearings. The cavitation zone boundary of the film can be directly determined without iterating. The one-dimensional nonlinear instantaneous oil-film forces model still obeys the general formula of instantaneous oil-film forces. The initial location of oil-film pressure calculation is determined by the arithmetic symbol of the journal bearing's inlet. By means of this method, all pads of the bearing can be calculated totally. The oil-film pressure and dynamic coefficients are calculated within the nonnegative domain without needing to form the total coefficient matrix, therefore less CPU time is needed. Furthermore, the Newton method is used to find the equilibrium position of the bearing at a given static load because of its high convergence rate and the computing time spent on the solution of the Jacobian matrices is very small compared with the solution of the film forces.3 It is the first time to apply the iterative method for the discrete problem to the generalized Reynolds equation successfully. The three-dimensional and two-dimensional thermohydrodynamic governing equations are solved using finite element method. It is found that the temperature variation in the axial direction is negligible and the temperature field in the oil-film is described by the midsection temperature field of the bearing. This assumption can be employed to build the two-dimensional and one-dimensional thermohydrodynamic models.4 The one-dimensional steady state thermohydrodynamic analysis model is built. The oil-film temperature governing equation and the generalized Reynolds equation are uncoupled by assuming that the Poiseuille component of the circumferential velocity can be neglected compared to the Couette term. It is assumed that the temperature variation across the film can be represented by a polynomial, the simplified form of one-dimensional mean film temperature governing equation is derived by integrating across the film thickness. The journal surface is imposed a uniform circumferential temperature and the one-dimensional temperature analysis model takes into account the adiabatic boundary conditions at the oil-bush and the oil-shaft interfaces or the flux continuity conditions at the interface between the film and the bush. Such simple boundary conditions result in significant computational savings for excluding heat transfer between the bush and the shaft.5 One-dimensional thermohydrodynamic liquid-lubricated analysis for two partial arcs journal bearing is presented and compared with experimental data. The results show that for good comparison and tendency between measured and predictedtemperature variation of the oil-bush interface. It is also found that excellent agreement with experimental findings by imposing the flux continuity condition at the interface between the film and the bush and the adiabatic boundary condition on the shaft surface. As an application, the thermohydrodynamic analysis for the three partial arcs journal bearing is examined.6 It is the first time to extend the Newton iterative method to the thermohydrodynamic effects of the lubricating film analysis at a give static load successfully. The computer program also produces the linearised dynamic coefficients which are needed for rotordynamic response and stability calculations. The convention adopted in the program is that the displacement coefficients and the velocity coefficients were being calculated the temperature in the film was maintained at their steady-state values. This was considered a reasonable approach since temperature transients in the film due to rapid vibrations would be small. The method is well suited for the Jacobian matrices calculation when the journal is located at a random position.