Damping Mechanisms in Cable-Harnessed Structures for Space Applications: Analytical Modeling

Recent developments in the aerospace industry have driven focus toward accurately modeling the effects of the cables and electronic cords on space structures. In the past, researchers have modeled the mass and stiffness effects of these cables but primarily overlooked their damping effects through careful analytical model developments. The objective of the current work is to present analytical models for cable-harnessed structures that also include the damping effects in their vibration response. Obtaining simple, low-order and high-fidelity models are highly advantageous in designing robust vibration real-time control algorithms for structures. Additionally, the analytical models are useful tools in providing insight into and better understanding of the dynamics of space structures as they are often difficult to be tested prior to launch due to their large size and at best only a few components may be tested. Motivated by the space applications, this work considers beam structures wrapped with cables which are modeled using beam and string theory assumptions. Two different damping models namely Kelvin–Voigt and hysteretic damping are considered. The homogenization approach is used as a starting point for structures of periodic wrapping patterns. Using the variational principle, the governing partial differential equation for the transverse coordinate of vibrations is found for three cable patterns and the results are compared to those from the distributed transfer function method (DTFM). Finally, the effects of several structural parameters are studied on the overall system damping.

Effects of Varying Dynamics of Flexible Workpieces in Milling Operations

In this study, surface error calculations and stability conditions are presented for milling operations in case of slender parts. The dynamic behavior of the flexible beam-type workpiece is modeled by means of finite element method (FEM), while the varying dynamical properties related to the feed motion as well as the material removal process are incorporated in the model. The FEM-generated direct frequency response function is verified through a closed-form solution based on the distributed transfer function method. Relative errors and convergence of the FEM are investigated based on the analytical solutions of the continuum model, from which appropriate element size and mode number can be selected for modal coordinate transformations. The pattern in the variation of the natural frequencies is explored using the analytical model in case of high radial depth of cut relative to the original cross section of the beam-like workpiece. Both the stability conditions and the resulted surface errors are predicted as a function of the tool position. The presented approach and the results are validated by laboratory tests.

Optimal Vibration Reduction of Flexible Rotor Systems by the Virtual Bearing Method

This paper presents a new approach to optimal bearing placement that minimizes the vibration amplitude of a flexible rotor system with a minimum number of bearings. The thrust of the effort is the introduction of a virtual bearing method (VBM), by which a minimum number of bearings can be automatically determined in a rotor design without trial and error. This unique method is useful in dealing with the issue of undetermined number of bearings. In the development, the VBM and a distributed transfer function method (DTFM) for closed-form analytical solutions are integrated to formulate an optimization problem of mixed continuous-and-integer type, in which bearing locations and bearing index numbers (BINs) (specially defined integer variables representing the sizes and properties of all available bearings) are selected as design variables. Solution of the optimization problem by a real-coded genetic algorithm yields an optimal design that satisfies all the rotor design requirements with a minimum number of bearings. Filling a technical gap in the literature, the proposed optimal bearing placement approach is applicable to either redesign of an existing rotor system for improvement of system performance or preliminary design of a new rotor system with the number of bearings to be installed being unforeknown.

A Virtual Bearing Method for Optimal Bearing Placement of Flexible Rotor Systems

Flexible multistage rotor systems have a variety of engineering applications. Vibration optimization is important to the improvement of performance and reliability for this type of rotor systems. Filling a technical gap in the literature, this paper presents a virtual bearing method for optimal bearing placement that minimizes the vibration amplitude of a flexible rotor system with a minimum number of bearings. In the development, a distributed transfer function formulation is used to define the optimization problem. Solution of the optimization problem by a real-coded genetic algorithm yields the locations and dynamic coefficients of bearings, by which the prescribed operational requirements for the rotor system are satisfied. A numerical example shows that the proposed optimization method is efficient and accurate, and is useful in preliminary design of a new rotor system with the number of bearings unforeknown.

A Discrete-Continuous Method of Mechanical System Modelling

The paper describes a discrete-continuous method of dynamic system modelling. The presented approach is hybrid in its nature, as it combines the advantages of spatial discretization methods with those of continuous system modelling methods. In the proposed method, a three-dimensional system is discretised in two directions only, with the third direction remaining continuous. The thus obtained discrete-continuous model is described by a set of coupled partial differential equations, derived using the rigid finite element method (RFEM). For this purpose, firstly the general differential equations are written. Then these equations are converted into difference equations. The derived equations, expressed in matrix form, allow to create a global matrix for the whole system. They are solved using the distributed transfer function method. The proposed approach is illustrated with the examples of a simple beam fixed at both ends and a simply supported plate.

Vibrations of Flexible Multistage Rotor Systems Supported by Water-Lubricated Rubber Bearings

Flexible multistage rotor systems that are supported by water-lubricated rubber bearings (WLRBs) are seen in various engineering applications. Vibration analysis is important to design and performance of such dynamic systems. In the past, due to the lack of reliable models of WLRBs, vibration analysis of this type of rotor systems has not been well addressed. In this paper, a method for modeling and analysis of WLRB-supported multistage rotor systems is proposed. In the development, a new model of WLRBs is integrated with a distributed transfer function formulation, which eventually yields accurate results on the eigensolutions, critical speeds, and steady-state responses of WLRB-supported rotor systems. The proposed method is illustrated in a numerical study on a three-stage rotor system. It is shown that the proposed method provides a useful tool for optimal design of flexible multistage rotor systems with WLRBs.