Jerzy T. Sawicki

Nonlinear Vibrations of Fractionally Damped Systems

This paper deals with the harmonic oscillations of periodically excited nonlinear systems where hysteresis is simulated via fractional operator representations. Employing a diophantine version of the fractional operational powers, the energy constrained Lindstedt–Poincaré perturbation procedure is utilized to establish the harmonic solution. The constrained perturbation procedure was employed since it allows for the handling of strong damping and exciting forces over the full span of the driving frequency range. Based on the approach taken, the long time behavior of the fractionally damped Duffings equation is studied in detail. Of special interest is the determination of the influence of fractional order on the frequency amplitude response behavior.

Condition monitoring of rotor using active magnetic actuator

It has been widely recognized that the changes in the dynamic response of a rotor could be utilized for general fault detection and monitoring. Current methods rely on the monitoring of synchronous response of the machine during its transient or normal operation. Very little progress has been made in developing robust techniques to detect subtle changes in machine condition caused by rotor cracks. It has been demonstrated that the crack-induced changes in the rotor dynamic behavior produce unique vibration signatures. When the harmonic excitation force is applied to the cracked rotor system, nonlinear resonances occur due to the nonlinear parametric excitation characteristics of the crack. These resonances are the result of the coexistence of a parametric excitation term and different frequencies present in the system, namely critical speed, the synchronous frequency, and excitation frequency from the externally applied perturbation signals. This paper presents the application of this approach on an experimental test rig. The simulation and experimental study for the given rig configuration, along with the application of active magnetic bearings as a force actuator, are presented.

Finite Element Analysis of Coupled Lateral and Torsional Vibrations of a Rotor With Multiple Cracks

The coupling between lateral and torsional vibrations has been investigated for a rotor dynamic system with breathing crack model. The stiffness matrix has been developed for the shaft element which accounts for the effect of the crack and all six degrees of freedom per node. Since the off-diagonal terms of the stiffness matrix represent the coupling of the respective modes, the special attention has been paid on accurate determination of their values. Based on the concepts of fracture mechanics, the variation of the stiffness matrix over the full shaft revolution is represented by the truncated cosine series where the fitting coefficient matrices are extracted from the stiffness matrices of the cracked shaft for a number of its different angular positions. The variation of the system eigenfrequencies and dynamic response of the rotor with two cracks have been studied for various shaft geometries, crack axial locations, and relative phase of cracks.Copyright

Experimental and Theoretical Rotordynamic Characteristics of a Hybrid Journal Bearing

This paper describes an experimental and theoretical investigation of a four-pocket, oil-fed, orifice-compensated hydrostatic bearing including the hybrid effects of journal rotation. The test apparatus incorporates a double-spool-shaft spindle which permits independent control over the journal spin speed and the frequency of an adjustable-magnitude circular orbit, for both forward and backward whirling. This configuration yields data that enables determination of the full linear anisotropic rotordynamic model. The dynamic force measurements were made simultaneously with two independent systems, one with piezoelectric load cells and the other with strain gage load cells. Theoretical predictions are made for the same configuration and operating conditions as the test matrix using a finite-difference solver of Reynolds lubrication equation. The computational results agree well with test results, theoretical predictions of stiffness and damping coefficients are typically within thirty percent of the experimental results.

Auxiliary State Variables for Rotor Crack Detection

In the present study, a new model-based method for rotor crack detection and crack location is proposed. The finite-element model of the rotor-bearing system accounts for the breathing mechanism of the crack. The model of the rotor system is augmented with an auxiliary single-degree-of-freedom oscillator. The observer is designed and the estimates of its two auxiliary state variables are proposed as crack indicators. The crack location along the shaft is determined by designing a set of observers, which calculate the values of these indicators for different possible crack locations along the shaft. The proposed method is validated numerically and the results prove its capability to detect and locate the crack. Further study will include experimental and numerical investigations to make the approach more robust.

Multiresolution Wavelet Analysis of the Dynamics of a Cracked Rotor

We examine the dynamics of a healthy rotor and a rotor with a transverse crack, which opens and closes due to its self weight. Using discrete wavelet transform, we perform a multiresolution analysis of the measured vibration signal from each of these rotors. In particular, the measured vibration signal is decomposed into eight frequency bands, and the rms amplitude values of the healthy and cracked rotors are compared in the three lowest-frequency bands. The results indicate that the rms vibration amplitudes for the cracked rotor are larger than those of the healthy rotor in each of these three frequency bands. In the case of externally applied harmonic force excitation to the rotor, the rms values of the vibration amplitude of the cracked rotor are also found to be larger than those of a healthy rotor in the three lowest-frequency bands. Furthermore, the difference in the rms values between the healthy and cracked rotors in each of the three lowest-frequency bands is more pronounced in the presence of external excitation than that with no excitation. The obtained results suggest that the present multiresolution approach can be used effectively to detect the presence of a crack in a rotor.

Stability Characteristics of Herringbone Grooved Journal Bearings Incorporating Cavitation Effects

Stability characteristics of the herringbone grooved journal bearings (HGJBs) are analyzed taking into account cavitation of the fluid flow. The perturbed values of pressure and film thickness from a given equilibrium position are substituted into the Eirods universal equation, which considers mass conservation in the complete bearing geometry. In order to analyze the herringbone groove configuration, the governing equations under steady and perturbed states are transformed to a rectangular domain using the grid transformation techniques. It is assumed that under perturbed conditions, the cavitation extent in the bearing remains unchanged and the pressure gradients are computed in the full film region. The linearized stiffness and damping coefficients are evaluated in the complete bearing geometry from the predicted values of pressure gradients. The threshold speed parameter and whirl frequency ratio are computed using the linearized stability analysis. Results are generated for various eccentricity ratios and groove angles. The results of this study validate the use of HGJBs at the very higher operating speeds (at concentric journal operation) in rotating machinery.

Modeling and Performance Evaluation of Machining Spindle with Active Magnetic Bearings

Active magnetic bearings (AMBs) are increasingly employed in the machine tool industry to exploit their advantages over classical bearings such as high speed capability, rotation accuracy, high stiffness, and accurate displacement tracking capability. Furthermore, the possibility of on-line monitoring of the machining process (e.g., cutting force measurement, tool wear) makes AMB spindles very appealing to the High-Speed Machining (HSM) industry. Despite significant progress already reached in HSM technology, there remain numerous open challenges in modeling and control of magnetic bearings as applied to machining spindles. These include optimum control given AMB magnetic saturation levels, management of nonlinear effects, reduction of chatter, and rotor properties. This paper describes a five-degree-of-freedom, high-speed machining spindle supported on AMBs. The rotordynamic modeling and experimentally extracted transfer functions are presented and analyzed. The experimentally measured tool tip compliance is used to compare PID and mu-synthesis control schemes. The primary finding is that the achieved tool tip stiffness is substantially higher with the μ-synthesized controllers than with the best PID we were able to design.

Analytical solution of piston ring lubrication using mass conserving cavitation algorithm

A novel analytical approach for piston ring lubrication solution is presented by taking proper account of mass conservation in the cavitated region (JFO boundary conditions). A system of five nonlinear equations is employed to calculate such parameters as oil film thickness, frictional force, power loss, and oil flow rate. For an enclosed cavitation pattern in piston-ring assembly it was found, that JFO boundary conditions give much better accounting of the estimation of friction force, power loss and flow rate. To show the effectiveness of the undertaken approach, the widely accepted Jengs approach (Jeng, 1992a) was selected, in which the pressure contribution from the cavitated and the second full film regions, as well as the trailing edge pressure, are ignored. Presented as a Society of Tribologists and Lubrication Engineers Paper at the STLE/ASME Tribology Conference in Orlando, Florida, October 11–13, 1999

Cracked rotor detection by recurrence plots

Recurrence plots (RPs) analysis has been used to distinguish cracked and healthy rotor responses. It has been shown that the recurrence criteria of the dynamical systems defined by the RPs can indicate the damages of the rotating shaft using relatively short time series.