T.S. Sankar

Dynamic Response of Rotors Using Modal Reduction Techniques

A modal reduction technique is discussed and proposed for solving rotor-dynamic problems. The component mode method is used to model a rotor shaft, and the resulting system matrices are reduced in size by considering only the contribution of the more important lower modes. The final system response including the bearing and disk is obtained using complex modal analysis. Since the higher modes do not contribute significantly to the system response, this method is found to be computationally economical. Unbalance response analyses of a simple Jeffcott rotor obtained by experiments are compared with those obtained by the modal reduction technique and show strong agreement.

Response of Rotors Subjected to Random Support Excitations

Response of rotor systems subjected to random support excitations is studied. Support excitations may occur for rotating machines installed either on the ground due to earthquake motion, or on board moving systems such as ships. These excitations in general are random in nature and hence the response of the machine can be obtained following a statistical analysis. In this paper, the amplitude power spectral densities (PSD) due to random support excitations are obtained for rotor systems, using modal analysis methods. The excitations are assumed to be stationary and Gaussian with a white noise type of PSD. Excitations through different supports are assumed to be statistically independent so that their cross correlations are zero. Results for rotors with various parametric combinations are presented.

Optimum Journal Bearing Parameters for Minimum Rotor Unbalance Response in Synchronous Whirl

Optimization techniques are employed to design hydrodynamic bearings for minimum unbalance response of rotors in synchronous whirl. The analysis for the unbalance response considers the effects of direct and cross coupled coefficients of stiffness and damping in the bearings. A parametric study of the unbalance response is carried out to show the influence of bearing parameters on the response and to demonstrate the merits of applying optimization techniques in bearing design. The bearing parameters optimized are the diameter, clearance, and the oil viscosity. In addition to setting upper and lower limits on the foregoing design variables, the Sommerfeld number is also constrained to be within a certain range for the operational speeds of the rotor. The quantity minimized is the maximum unbalance response of the rotor in the operational speed range. Plain cylindrical, grooved, elliptical, and four shoe tilting pad type bearings are considered in the optimal design of the rotor bearing system. The results indicate that an optimal design of hydrodynamic bearings can reduce the unbalance response of rotors.

Vibration and shock isolation performance of a pressure-limited hydraulic damper

Abstract A pressure-limited hydraulic damper is proposed to achieve variable damping within a vibration isolation system. The variation in damping parameters is achieved passively by limiting the pressure differential across the damper piston, using pressure relief valves. The pressure-limited hydraulic damper is modeled as a non-linear dynamical system incorporating control valve dynamics. The significance of the pressure differential across the damper piston is discussed in view of vibration isolation, and a methodology for estimation of a suitable value of the limiting pressure is proposed. The vibration and shock isolation characteristics of the passive pressure-limited damper are investigated through computer simulation. The vibration and shock isolation performance of the proposed damper is compared to those of passive and semi-active “on-off” vibration isolators. A comparison of the simulation results reveals that the vibration and shock isolation performance of the pressure-limited damper is superior to that of a conventional passive damper, and is comparable to that of a semi-active “on-off” damper. The proposed pressure-limited damper can be realised passively and does not require the sophisticated control devices and feedback instrumentation essential for a semi-active “on-off” vibration isolation system.

Analysis of deceleration phenomenon of high speed rotor systems

Abstract The problem of decelerating a rotor from a high speed through its critical speeds has received very little attention in technical literature although transient processes occurring during coastdown of machinery usually provide a lot of information about their tribodynamics. The problem of deceleration is critically examined and the governing equations for a mechanical system are derived using Lagrangian dynamics. The governing non-linear equations have been solved under quasi-static conditions. The results confirm the relationship between dynamic unbalance, damping and the deceleration during coastdown.

On friction and motion accuracy in jewel bearing

In this paper, modeling of the rotor motion in a jewel bearing is presented. Due to the presence of dry friction forces between the steel tip of the rotor and the cup sapphire surface, the rotor motion no longer consists only of pure rotation. The secondary motion based on the deviation from pure rotation, as well as the driving torque variations (sensitivity threshold) are determined and three basic cases are studied, i.e., the arbitrary position and initial driving torque at the time of motion initiation, the asymptotic position and driving torque which supports pure rotation, and the self-centering process, i.e., the transition from the rest state to pure rotation

Random response analysis of a non-linear vehicle suspension with tunable shock absorbers

Abstract Dynamic analysis of a non-linear vehicle model, employing tunable shock absorbers, is presented for random road excitations. A generalised discrete harmonic linearisation technique, based upon a processed energy function, is developed to characterise non-linear restoring and damping forces by an array of equivalent linear stiffness and damping coefficients. An array of locally linear systems is thus formulated to determine the random ride response of the non-linear vehicle model. The simulation results show that the vehicle ride performance can be improved considerably in the frequency range to which the human body is most sensitive, via the tunable shock absorbers.

The Steady-State Dynamics of Jewel Bearing with a Free Ball

A type of jewel bearing employing two sapphire cup surfaces (one fiwed and the other movable) which were in contact with a free steel ball were analyzed. This arrangement reduced wear substantially as compared to conventional jewel bearings and had more degrees of freedom. The analysis of the ordinary jewel bearing was extended to the present case in order to determine the bearing steady-state motion reaches asymptotically from an arbitrary starting state

Rotational Stiffness and Damping Coefficients of Fluid Film in a Finite Cylindrical Bearing

The dynamic behavior of flexible rotors supported on fluid-film bearings are studied including the rotational stiffness and damping coefficients of the oil film. The rotational stiffness and damping coefficients have been evaluated for a finite cylindrical fluid-film bearing by solving the appropriate Reynolds equation for the oil film, using finite difference method. The resulting critical speeds and the unbalance response for a single-disk flexible-rotor system modelled by finite element method are compared with those which were obtained using a short bearing approximation. Presented at the 40th Annual Meeting in Las Vegas, Nevada May 6–9, 1985

Analytical Methods for Rotors Supported on Hydrodynamic Journal Bearings

Large rotor systems are commonly supported on hydrodynamic journal bearings and the dynamic behavior of such rotors is significantly influenced by the bearing characteristics. The major factors in the design and operation of such rotor systems are critical speeds, response due to residual unbalance and stability against self-excited vibration. In this paper a study of the various design criteria is made. Results are presented for unbalance response, dissipation coefficient, maximum transmitted force, stress amplitudes and fatigue life in the case of an industrial electric motor rotor supported on partial journal bearings using the transfer matrix method