System Identification for Boring Bar Chatter Control

The boring bar is used to provide smooth, accurate cuts in materials. However, when the length to diameter (L/D) ratio of the boring bar becomes large, low-frequency vibration, or chatter, results. Initial attempts to control this unwanted vibration with an active absorber have been successful, but in some configurations problems remain. In this paper, algorithms for flexible structure identification widely used in the aerospace industry are applied to a number of boring bar setups to identify the vibration characteristics of each system. Emphasis is placed on one class of methods which includes the Eigensystem Realization Algorithm (ERA), developed for identification of flexible space structures. The resulting identified characteristics are compared and contrasted. Results are also compared to finite element analysis predictions. From the current identification results, implications for chatter control are discussed, including the possibility of nonlinear modal interactions.

Design Optimization of Aircraft Engine-Mount Systems

Design optimization of aircraft engine-mount systems for vibration isolation is presented. The engine is modeled as a rigid body connected to a flexible base representing the nacelle. The base is modeled with mass and stiffness matrices and structural damping using finite element modeling. The mounts are modeled as three-dimensional springs with hysteresis damping. The objective is to select the stiffness coefficients and orientation angles of the individual mounts to minimize the transmitted forces from the engine to the base. Meanwhile, the mounts have to be stiff enough not allowing engine deflection to exceed its limits under static and low frequency loadings. It is shown that with an optimal system the transmitted forces may be reduced significantly particularly when mount orientation angles are also treated as design variables. The optimization problems are solved using a Constraint Variable Metric approach. The closed form derivatives of the engine vibrational amplitudes with respect to design variables are derived in order to achieve a more effective optimization search technique.

Transfer Function Analysis of Non-Uniformly Distributed Parameter Systems

This paper studies a transfer function formulation for general one-dimensional, non-uniformly distributed systems subject to arbitrary boundary conditions and external disturbances. The purpose is to provide an useful alternative for modeling and analysis of distributed parameter systems. In the development, the system equations of the non-uniform system are cast into a state space form in the Laplace transform domain. The system response and distributed transfer functions are derived in term of the fundamental matrix of the state space equation. Two approximate methods for evaluating the fundamental matrix are proposed. With the transfer function formulation, various dynamics and control problems for the non-uniformly distributed system can be conveniently addressed. The transfer function analysis is also applied to constrained/combined non-uniformly distributed systems.

An Application of Active Dynamic Absorber to the Milling Process and its Experimental Verification

In order to reach the inside surfaces of some workpieces, a prototype for milling extension is developed. The milling extension has a low static stiffness and is prone to machine tool chatter, therefore vibration control in this type of machining is of importance. The paper proposes the application of an active dynamic absorber to the milling process. A finite element model for the milling extension with consideration of the cutting dynamics is developed. An annular ring serving as the dynamic absorber mass is connected to the main system through active force generating systems which are piezoelectric translators functioning as actuators. The annular ring and the actuators are functioning as an active dynamic absorber in the theory to suppress the vibration of the milling system. Optimal control algorithms are used to calculate the Kalman feedback control for the equivalent lumped-mass milling structure model. Transient responses of the system are obtained. Oscillation of the milling extension equipped with the active dynamic absorber is attenuated appreciably, therefore the surface finish of a workpiece is improved. Harmonic responses are also obtained with and without the feedback control to show the superiority of the active control technique. A proof-of-concept experiment is designed and conducted to verify the theoretical prediction. Comparisons between the simulation and experimental results are made.

Modeling of Coupled Bending and Torsion in Elastic Structures

In this presentation we will report on joint efforts with D.J. Inman and his colleagues at MSL, SUNY at Buffalo, to develop viable models for the analysis and control of elastic structures exhibiting coupled torsional and flexural vibrations. A model for coupled torsion and bending is developed which incorporates Kelvin Voigt damping and warping. Approximation techniques are introduced and preliminary numerical results are discussed. Experimental data is presented and used to test our computational results.

Balancing of High Speed Flexible Overhung Rotor: A Case Study

This paper presents a case study of balancing a high speed overhung flexible rotor system. The system had several speeds, below the operating speed, where the amplitude of vibration was high. Mode shapes were obtained by measuring amplitude of 1X component and its phase at various locations & balancing was carried out by adding weights in a single plane.

A Brief Study of Passive Viscous Damping for the SPICE Bulkhead Structure

The SPICE Testbed at Phillips Laboratory is being used to evaluate the effects of structural vibration on line-of-sight error for this strut built structure. A design incorporating active control and passive damping techniques is suggested to reduce the optical path distortion created in the vibrating structure. The passive viscous damping applied to the structure serves to aid the active control system stability in the cross-over and spill-over frequency range by producing a specified magnitude of damping in specified critical modes. This magnitude of damping is to be achieved by replacing the standard filament wound undamped struts with optimally placed D-struts which contain series and parallel combinations of springs and viscous dampers and produce damped vibration response from in-line strut deflection. This D-strut must replace standard struts in a tear-down of the bulkhead. The present study proposes to provide the requisite damping by adding on viscous damping at diagonal nodal locations in the bulkhead, circumventing the need to disassemble the SPICE bulkhead. The study shows specific increase in loss factor and improved damping ratio provided by the diagonal dampers when compared to in-line D-struts for specific modes and frequencies.

Dynamic Interaction in a Slewing Motor-Beam System: Closed Loop Control

This paper considers the dynamic interaction between a DC motor and its slewing beam load. The system is described in terms of dimensionless parameters which generalize the results and define the tendency for interaction between the motor and beam. The study focuses on the performance and behavior of the system under closed-loop control. Motor-beam arrangements with differing amounts of dynamic interaction are defined by simple adjustments in gear ratio for a specified motor and beam. Each of these systems is controlled with full state feedback and various forms of output feedback. Controller performance is optimized in each case and the systems are compared to evaluate the effect of motor-beam interaction on the closed-loop system behavior. Systems with an appropriate amount of motor-beam interaction tend to be easier to control and require modest amounts of actuation effort. Systems with little motor-beam interaction are especially prone to beam vibrations and require feedback of beam motions for good closed-loop performance. Those systems with excessive interaction require stabilization efforts to obtain good transient performance and tend to consume increased levels of actuation energy.

A Discussion of Objective Functions in Structure-Control Simultaneous Optimum Design

The effect of the objective functions on the results of the structure-control simultaneous optimum design is discussed, comparing the optimum designs obtained by minimizing several different types of objective functions. These objective functions are defined as a linear combination of the structural and the control objective functions. One of the objective functions is a structural weight, another is a feedback gain norm and the others are transient characteristics values which are expressed as the quadratic form. A flexible cantilever beam is designed in the numerical example, and the results indicate that the usefulness of the structure-control simultaneous optimum design depends on the objective function for the example.

Active Vibration Control of the Axially Moving String by Wave Cancellation

Active vibration control of an axially moving string by wave cancellation is presented. The control problem is formulated in the frequency domain. An exact, closed-form expression for the transfer function of the closed-loop system, consisting of the flexible structure, a feedback control law and the dynamics of the sensing and actuation devices, is derived. It is shown that all vibration modes can be stabilized and that the controlled system has no resonance. Moreover, the designed controller is applicable to the control of the string transverse vibration under various kinds of loading and constraint conditions. Results for the response of the controlled string under different excitations are presented and discussed along with the wave propagation and cancellation characteristics.