Paul E. Allaire

Stiffness and Damping Coefficients for the Five-Pad Tilting-Pad Bearing

Stiffness and damping coefficients are presented for the 5-pad tilt-pad bearing for various preloads, offsets, length to diameter ratios and pad loadings (on and between pad). Finite elements and the pad assembly method are used to calculate these coefficients and the effects of the unloaded pads are included. Design curves suitable for tilt-pad bearings in widespread industrial use are presented. Presented as an American Society of Lubrication Engineers paper at the ASLE/ASME Lubrication Conference in Kansas City, Missouri, October 3–5, 1977

Design, Construction, and Modeling of a Flexible Rotor Active Magnetic Bearing Test Rig

A successful industrial application of flexible rotors supported on active magnetic bearings (AMBs) requires careful attention not only to rotordynamic design aspects but also to electromagnetic and feedback control design aspects. Model-based control design provides the framework to ensure efficient, reliable, and safe operation of turbomachinery on AMBs. This paper describes in detail the design, construction, and modeling process for a high performance AMB test rig which typifies a small industrial super-critical centrifugal compressor. A unique aspect of the design are the two additional radial AMBs to allow the application of simulated destabilizing fluid or electromagnetic forces to the rotor. These forces are difficult to predict and can lead to rotordynamic instability of industrial machinery if not properly accounted for. This test rig provides a realistic platform to evaluate stabilizing control algorithms for high performance turbomachinery. A complete model of rotor, AMB actuators and accompanying electronics, is constructed from individually verified component models. Model validation is confirmed through the successful design and implementation of a μ-synthesis controller.

Magnetic Bearing Design for Reduced Power Consumption

Magnetic bearings have relatively low power consumption compared to fluid film and rolling element bearings. They are now candidates for supporting gas turbines and aeropropulsion engines. This paper describes the design and construction of permanent magnet biased, actively controlled magnetic bearings for a flexible rotor. The rotor was originally supported in fluid film bearings consuming as much as 3000 watts of power. For the magnetic bearing, both permanent magnets and electromagnets are used in a configuration which effectively provides the necessary fluxes in the appropriate air gaps to support the rotor. The theoretical development related to the bearing design is presented along with some experimental performance results. The results include measurements of power consumption, load capacity, bearing linearized coefficients, and the dynamic response of the rotor. The measured total power consumption, excluding shaft losses, was 210 watts in the permanent magnet biased bearing.

A pad perturbation method for the dynamic coefficients of tilting-pad journal bearings

A pad assembly method for analyzing tilting-pad bearings is presented. The method results in the complete coefficient matrix for a tilting-pad bearing; the matrix is independent of the pad inertia, the pitch frequency and the number of degrees of freedom of the pad. A pad assembly method is used because it allows the collection of more bearing data with less computer time than a brute force iterative procedure. The results given show the complete dynamical matrices for a five-pad tilting-pad bearing both including and ignoring the damping effects of the unloaded (top) pads. For a symmetrical tilting-pad bearing the reduced cross-coupling coefficients are zero when the moment of inertia of the pad is ignored.

Review: Rotor Balancing

This article reviews the literature concerning the balancing of rotors including the origins of various balancing techniques including ones that use influence coefficient, modal, unified, no phase, and no amplitude methods to balance. This survey covers the computational algorithms as well as the physical concepts involved in balancing rotating equipment.

Frequency Effects in Tilting-Pad Journal Bearing Dynamic Coefficients

This paper examines the effects of damped vibrational frequencies on the linear reduced dynamical stiffness and damping coefficients of tilting-pad journal bearings. The frequency ratio (damped frequency/running speed) can be used to judge the accuracy of employing synchronously reduced linear coefficients in rotordynamic stability analyses. The use of these coefficients can result in simpler formulations of the system dynamical equations of motion and solution techniques as well as reduced computational and analysis time. Results presented here indicate that synchronously reduced bearing dynamical coefficients are generally adequate for stability analyses with positively preloaded tilting-pad bearings. Plots of dynamic coefficients are included for a five-pad bearing. Presented at the 37th Annual Meeting in Cincinnati, Ohio, May 10–13, 1982

Integral sliding-mode control of a magnetically suspended balance beam: analysis, simulation, and experiment

This paper presents a sliding-mode controller with integral compensation for a magnetic suspension balance beam system. The control scheme comprises an integral controller which is designed for achieving zero steady-state error under step disturbances, and a sliding-mode controller which is designed for enhancing robustness under plant uncertainties. A procedure is developed for determining the coefficients of the switching plane such that the overall closed-loop system has stable eigenvalues. A proper continuous design signal is introduced to overcome the chattering problem. The performance of the balance beam control system is illustrated by simulation and experimental results showing that the proposed integral sliding-mode controller method is effective under external step disturbances and input channel parameter variations.

Pediatric circulatory support systems.

Ventricular assist devices (VADs) are a valid option for long-term circulatory support in pediatric patients with postoperative myocardial failure or debilitating heart defects. Most clinical experience to date has involved the short-term support of patients weighing 6 kg and larger. For cases of VAD implementation in pediatric patients, the assist device showed tremendous promise in reversing cardiac failure and providing adequate support as a bridge to cardiac transplantation. The Medos-HIA system, Berlin Heart, Medtronic Bio-Medicus Pump, Abiomed BVS 5000, Toyobo-Zeon pumps, and Hemopumps have proven successful for short-term circulatory support for the pediatric population. The Jarvik 2000 and Pierce-Donachy pediatric system further demonstrate the potential to be used for pediatric circulatory support. The clinical and experimental success of these support systems provide encouragement to believe that long-term support is possible.

Modeling, Estimation, and Control of Human Circulatory System With a Left Ventricular Assist Device

In this paper, a state-space model is developed through theoretical analysis and numerical solutions to approximate the response of the human circulatory system. This system model has one critical time-varying parameter: the resistance of peripheral blood vessels. A parameter estimation scheme is derived to estimate this parameter, and the parameter estimate is used to implement an adaptive observer to estimate the aortic pressure for physiological control. An optimal adaptive controller is proposed to control the estimated aortic pressure to track a reference signal updated by a nonlinear function of the pump head to meet the physiological need. A Matlab simulation program and an experimental mock human circulatory loop are employed as test environments for the human circulatory systems with a left ventricular assist device and their physiological controllers. Different physiological conditions, such as the variation of left ventricular failures, variation of activities, and collapse of the left ventricle, are evaluated to test the designed physiological control system. Simulation and experimental results consistently show that the aortic pressure estimation error is small, and that the abnormal hemodynamic variables of a congestive heart failure patient are restored back to the normal physiological range.

Digital control of active magnetic bearings

Theoretical relationships are developed to relate the characteristics of a controller transfer function to the stiffness and damping properties of an active magnetic bearing for machine rotors. Both proportional and derivative feedback are shown to be necessary for closed-loop system stability, and, for the ideal case, bearing stiffness and damping properties are shown to be simple linear functions of the proportional and derivative feedback gain constants, respectively. The flexibility of a digitally controlled magnetic bearing is demonstrated by the implementation of algorithms which include second-derivative and integral feedback. Second-derivative feedback is shown to be effective at extending the usable bandwidth of the digital controller, and integral feedback rejects rotor position error in the presence of static loads. The relationship between controller sampling rate and bearing performance is investigated, and it is shown that increased sampling rate and increased amounts of second-derivative feedback have similar effects on the bearing properties. >