Marc Carpino

Damage-Mitigating Control of Mechanical Systems: Part I—Conceptual Development and Model Formulation

A major goal in the control of complex mechanical systems such as advanced aircraft, spacecraft, and power plants is to achieve high performance with increased reliability, availability, component durability, and maintainability. The current state-of-the-art in control systems synthesis focuses on improving performance and diagnostic capabilities under constraints that often do not adequately represent the dynamic properties of the materials. The reason is that the traditional design is based upon the assumption of conventional materials with invariant characteristics. In view of high performance requirements and availability of improved materials, the lack of appropriate knowledge about the properties of these materials will lead to either less than achievable performance due to overly conservative design, or over-straining of the structure leading to unexpected failures and drastic reduction of the service life. The key idea of the research reported in this paper is that a significant improvement in service life could be achieved by a small reduction in the system dynamic performance. The concept of damage mitigation is introduced and a continuous-time model of fatigue damage dynamics is formulated in this paper which is the first part of a two-part paper. The second part which is a companion paper presents synthesis of an open loop control policy and the results of simulation experiments for transient operations of a reusable rocket engine.

Coulomb Friction Damping Effects in Elastically Supported Gas Foil Bearings

A theoretical model is developed to investigated the effect of Coulomb damping in the sub-foil structure of a foil bearing. Equivalent viscous damping is found for the Coulomb friction. The foil is treated as a continuous perfectly surface on an elastic foundation. The fluid is modeled with compressible Reynolds equation. A perturbation approach is used to determine the bearing stiffness and damping coefficients from the coupled fluid-structural model. Results are presented for foil bearing with an elastic foundation constructed of a corrugated foil

Prediction of Rotor Dynamic Coefficients in Gas Lubricated Foil Journal Bearings with Corrugated Sub-Foils

A finite element foil bearing model that incorporates radial and circumferential deflections of a corrugated sub-foil into the prediction of rotor dynamic coefficients is presented. The corrugated sub-foil is treated as a continuous structure that supports the top-foil. Radial and circumferential deflections are coupled in the sub-foil model. The Coulomb friction between the top-foil, sub-foil, and the bearing shell is modeled as an equivalent viscous friction. The foil deflections, the film thickness, and gas pressure are then perturbed to calculate the rotor dynamic coefficients. The results are presented demonstrating the effects of frequency, orbit size, and friction coefficient on the rotor dynamic coefficients and the energy dissipation rate.

A fully coupled finite element formulation for elastically supported foil journal bearings

Foil gas journal bearings consist of a compliant metal shell structure that supports a rigid journal by means of a gas film. The prediction of steady operating characteristics such as minimum film thickness, load capacity, and drag require the coupled solution of the shell structure and the gas flow. A general fully coupled finite element approach is presented. A single four noded finite element that incorporates the elastically supported shell structure of the foil and the gas film modeled by a compressible Reynolds equation is developed. The resulting system of nonlinear finite elements is solved by the Newton Raphson method. Presented at the 58th Annual Meeting in New York City April 28–May 1, 2003

Misalignment In A Complete Shell Gas Foil Journal Bearing

The effect of misalignment on the performance of a complete shell gas foil bearing is discussed. An iterative theoretical model based on the finite element method is used. The model includes membrane and elastic foundation effects in the structural model. An isothermal perfect gas is used as the lubricant fluid. Results are presented demonstrating the effect of misalignment on load capacity, minimum clearance, and moments acting normal to the journal.

Damage-Mitigating Control of Mechanical Systems: Part II—Formulation of an Optimal Policy and Simulation

The objective of damage-mitigating control introduced in the first part of this two-part paper is to achieve high performance without overstraining the mechanical structures. The major benefit is an increase in the functional life of critical plant components along with enhanced safety, operational reliability, and availability. Specifically, a methodology for modeling fatigue damage has been developed as an augmentation to control and diagnostics of complex dynamic processes such as advanced aircraft, spacecraft, and power plants. In this paper which is the second part, an optimal control policy is formulated via nonlinear programming under specified constraints of the damage rate and accumulated damage. The results of simulation experiments for upthrust transient operations of a reusable rocket engine are presented to demonstrate efficacy of the damage-mitigating control concept.

Damage-mitigating control of a reusable rocket engine

The goal of damage mitigating control in reusable rocket engines is to achieve high performance with increased durability of mechanical structures such that functional lives of the critical components are increased. The major benefit is an increase in structural durability with no significant loss of performance. This report investigates the feasibility of damage mitigating control of reusable rocket engines. Phenomenological models of creep and thermo-mechanical fatigue damage have been formulated in the state-variable setting such that these models can be combined with the plant model of a reusable rocket engine, such as the Space Shuttle Main Engine (SSME), for synthesizing an optimal control policy. Specifically, a creep damage model of the main thrust chamber wall is analytically derived based on the theories of sandwich beam and viscoplasticity. This model characterizes progressive bulging-out and incremental thinning of the coolant channel ligament leading to its eventual failure by tensile rupture. The objective is to generate a closed form solution of the wall thin-out phenomenon in real time where the ligament geometry is continuously updated to account for the resulting deformation. The results are in agreement with those obtained from the finite element analyses and experimental observation for both Oxygen Free High Conductivity (OFHC) copper and a copper-zerconium-silver alloy called NARloy-Z. Due to its computational efficiency, this damage model is suitable for on-line applications of life prediction and damage mitigating control, and also permits parametric studies for off-line synthesis of damage mitigating control systems. The results are presented to demonstrate the potential of life extension of reusable rocket engines via damage mitigating control. The control system has also been simulated on a testbed to observe how the damage at different critical points can be traded off without any significant loss of engine performance. The research work reported here is built upon concepts derived from the disciplines of Controls, Thermo-fluids, Structures, and Materials. The concept of damage mitigation, as presented in this report, is not restricted to control of rocket engines. It can be applied to any system where structural durability is an important issue.

Effects of Membrane Stresses in the Prediction of Foil Bearing Performance

The effects of membrane stresses which result from both viscous drag and the three-dimensional structure of an incompressible journal foil bearing are discussed. The structural model includes combined bending, membrane, and elastic foundation effects. The pressure in the lubricant film is predicted using an incompressible Reynolds equation. Finite element methods are used to predict both the structural deflections and the pressures in the lubricant film. Results will demonstrate that membrane effects are significant in an elastically supported foil bearing where elastic foundation effects are normally considered to provide the primary resistance to deflection. The effects of viscous drag are small but not insignificant. Presented at the 48th Annual Meeting in Calgary, Alberta, Canada May 17–20, 1993

A Pseudospectral-Finite Difference Analysis of an Infinitely Wide Slider Bearing with Thermal and Inertial Effects

A pseudospectral-finite difference solution of the thermal hydraulic flow through an infinitely wide convergent slider bearing configuration is presented. The model includes both thermal and inertial effects. The approach combines a collocation technique with orthogonal polynomial representations of velocities, temperatures and prop erty variations through the thickness of the lubricant film with finite difference representations of derivatives in the stream wise direction. The technique is motivated by the need for general analyses of fluid film bearings which incorporate the before-mentioned effects. Results will be presented that separately demonstrate inertial and thermal effects in laminar flows.

Life-extending control of mechanical structures: experimental verification of the concept

The concept of life-extending control is built upon the two disciplines of Systems Science and Mechanics of Materials, and its goal is to achieve an optimized trade-off between dynamic performance and structural durability of the plant under control. Experimental and simulation results reported in recent publications show that a life extending control system can substantially reduce the structural damage accumulated in critical components with no significant loss of plant performance. This enhancement of structural durability is accomplished via nonlinear optimization to generate a sequence of open-loop commands that maneuver the plant from a known initial state, along a prescribed trajectory, close to the final desired-state subject to constraints on the damage rate and accumulation in critical components. This paper presents a methodology for analytical development of a robust feedforward-feedback control policy for life extension and high performance of mechanical structures. The concept of life-extending control is experimentally verified in a laboratory testbed which is a two-degree-of-freedom (2DOF) mechanical system excited by a computer-controlled shaker table. Test results demonstrate that the fatigue life of test specimens can be substantially extended with no appreciable degradation in the dynamic performance of the mechanical system.