I. R. Praveen Krishna

Dynamic Analysis of Rotors Supported on Journal Bearings by Solving Reynolds Equation Using Pseudospectral Method

In the dynamic analysis of rotors supported on journal bearings, Reynolds equation is solved at each time step. In the present work, Reynolds equation is solved using pseudospectral method to estimate fluid film forces. Fluid pressure is approximated by a finite number of Chebyshev polynomials along the bearing length and Fourier series along the bearing circumference. Fluid domain is reduced to a finite set of algebraic equations with pressure at specific grid points as variables using collocation method. Unlike in finite element method (FEM), spectral method uses higher order global basis functions which guarantee high accuracy and lower computational time. A comparison study of fluid film forces for a bearing geometry with an L/D ratio of 0.25 with short bearing theory, solution of Reynolds equation using FEM and pseudospectral method (PSM) is presented. Two different elements are studied in FEM: 3 node triangular element and 9 node quadrilateral element. Computational time taken for one time pressure calculation is also compared. Pseudospectral method is found to be efficient than FEM for a converged solution.

Experimental and numerical investigations on rotor–stator rub:

The focus of the current study is on the dynamics of rubbing between the rotor and stator parts in a rotating machine. Rub is a malfunction associated with the physical contact of rotating and stationary parts, which are otherwise not in contact. Because of the nonlinear nature of the problem the simulation time is significant even for small size systems. The rubbing is localized in space, either at the seal locations or at the interface between the rotor blade and stator. Since the nonlinearity is localized, reduced models can be developed for efficient computation. The objective of the present study is to develop a computationally efficient methodology for analyzing the rotor stator rub, by applying model reduction techniques using component mode synthesis, solving the reduced problem using harmonic balance method and time variational method. A hypersphere-based continuation algorithm is used for tracing the unstable branches and a backward differentiation formula based predictor is used for the Newton–Raphson update. The numerical results are validated by performing experiments.

A Modified Model Reduction Technique for the Dynamic Analysis of Rotor-Stator Rub

This paper discusses a modified model reduction technique for the nonlinear rubbing analysis of a rotor disk with its stator. The rotor system consisting of a rigid disk, shaft and bearings is modeled using finite elements, incorporating the effects of rotary inertia and gyroscopic moments of both shaft and disk. The stator is modeled as an added stiffness to the rotor system without considering the stator dynamics and dry friction effect at the contact. The nonlinearities are localized at the rub location which permits the use of model reduction techniques, making the finite element model more compact. Component Mode Synthesis with a Craig-Bampton type sub-structuring is an efficient technique for model reduction. But, this method has some limitations due to the presence of nonlinearities in the system. In this paper, a modified Component Mode Synthesis method with dynamic sub-structuring is developed for the reduction of complete finite element model into a smaller model containing nonlinear degrees of freedom (DOF) only. This method has an advantage over existing methods is that it can be used for systems with non-symmetric element matrices. The reduced model is solved using Harmonic Balance Method (HBM) coupled with a hypersphere based continuation algorithm.

Coupled Simulation of Rotor Systems Supported by Journal Bearings

Oil whirl and whip phenomena are fundamental to rotor systems supported by journal bearings. Published studies opt for a reduced formulation of the Reynolds equation of lubrication in order to aid the computations. In the current study, the complete Reynolds equation is solved using Pseudo Spectral Methods (PSM) and results compared with reduced solutions. The possibility of certain trends being missed in reduced model simulations is also brought out using a simple example. Rotor shaft and journal bearing systems are numerically modelled and coupled simulations have been carried out for test rotors inspired from literature. A semi analytical derivative estimation method is demonstrated to be superior to conventional finite difference methods in terms of processor load. This will be a useful addition for iterative solvers applied on rotors with more complicated geometry. Time transient analysis is carried out for two test rotors in order to bring out the oil whirl and whip phenomena, where the second one, with an added nonlinear node, shows a whirl along a branch which went undetected in the published reference. In the light of the above trends, the importance of full model numerical simulation is further emphasized.