The stability and bifurcation of the unbalance response of a squeeze film dampermounted flexible rotor are investigated based on the assumption of an incompressible lubricant together with the short bearing approximation and the "it "film cavitation model. The unbalanced rotor response is determined by the trigonometric collocation method and the stability of these solutions is then investigated using the Floquet transition matrix method. Numerical examples are given for both concentric and eccentric damper operations. Jump phenomenon, subharmonic, and quasi-periodic vibrations are predicted for a range of bearing and unbalance parameters. The predicted jump phenomenon, subharmonic and quasi-periodic vibrations are further examined by using a numerical integration scheme to predict damper trajectories, calculate Poincare maps and power spectra. It is concluded that the introduction of unpressurized squeeze film dampers may promote undesirable nonsynchronous vibrations.

When a squeeze-film damper is operated eccentrically, the nonlinear damper forces are no longer radially symmetric and subharmonic and quasi-periodic vibrations may be excited by the rotor unbalance. In this study, the unbalance response of a rigid rotor, supported on an eccentric squeeze film damper, is first approximated by a harmonic series whose coefficients are determined by the collocation method, together with a nonlinear least-square regression. The stability of the resulting periodic solution is then examined using the Floquet transition matrix method. For sufficiently large values of the unbalance and the damper static radial misalignment, it is shown that the approximate harmonic motion loses its stability and bifurcates into a stable subharmonic motion and a quasi-periodic motion at speeds above twice the system critical speed. This analytical finding is verified by a numerical integration in forms of the Poincare´ map, the rotor trajectory, the bifurcation diagram, and the power spectrum. It is suggested that stability analysis and numerical integration should always be incorporated into an approximate analytical method to achieve an adequate approximation. The results of this study show that the introduction of squeeze-film dampers may give rise to the undesirable nonsynchronous vibrations, which limits the maximum speed at which dampers should be used.

Experiments are described in which a hardened steel wedge was indented vertically into the horizontal surface of an aluminium alloy specimen with subsequent horizontal movement of the specimen in a direction normal to the edge of the wedge with the vertical force held constant. Forces were recorded during a test and observations made of the plastic deformation of the specimen at the end of a test. Experimental results for a range of wedge angles and different lubricants are compared with results predicted from a slipline field analysis of asperity deformation in which the frictional force is considered to be the force needed to push waves of plastically deformed material ahead of wedge shaped asperities on the harder surface. Although the slipline field results are for an assumed non-hardening material, allowance is made in the calculations for the strain hardening of the actual test material by using average values of flow stress obtained from a stress-strain curve for the material.

A solution technique is developed whereby the problem of determining the synchronous unbalance response of general multi-degree of freedom rotor bearing systems is reduced to solving a set of as many simultaneous nonlinear equations in damper orbit eccentricities are there are dampers. It is shown how, in the case of a single damper, the resulting nonlinear equation may be solved directly to determine all possible orbit eccentricity solutions as a function of the rotor speed and bearing parameter, thereby ensuring completeness of solution, eliminating convergence problems and clearly indicating all multistable operation possibilities. Design maps portraying the effect of the relevant damper design parameters on system response may be conveniently obtained, allowing for optimal damper design. The technique is illustrated for the case of a simple squeeze film damped symmetric flexible rotor.

A technique is presented for investigating the stability of and the degree of damping in the circular synchronous orbit equilibrium solutions pertaining to radially symmetric multi-mass flexible rotor bearing systems. It involves the analysis of appropriate linearized perturbation equations about the equilibrium solutions and is applicable to systems with several squeeze film dampers. For a system with a single damper, stability threshold maps, independent of unbalance distribution, may be found in terms of the same damper parameters and operating conditions as the equilibrium solutions, thereby allowing for damper design and performance monitoring. The technique is illustrated for a simple symmetric four degree of freedom flexible rotor with an unpressurized damper. This example shows the utility of zero frequency stability maps for delineating multiple solution possibilities and that for low (in this case of the order of 0.06 or lower) bearing parameters, the introduction of an unpressurized squeeze film damper may promote instability in an otherwise stable system.