Development of Nonlinear Coupled Mode Bushing Model Based on the Bouc-Wen Hysteretic Model

In this paper, a coupled bushing model for vehicle dynamics analysis based on the Bouc-Wen hysteretic model is proposed. Bushing components of a vehicle suspension system are tested to capture the nonlinear and behavior of the typical rubber bushing elements using MTS machine. Test results are used to define the parameters of the Bouc-Wen bushing model. The Bouc-Wen model is employed to represent the hysteretic characteristics of the bushing. A coupled relation for radial mode and torsional mode are suggested. Model parameters are obtained by using the genetic algorithm, and sensitivity indices of parameters are also extracted from the sensitivity analyses. ADAMS program is used for the identification process and VisualDOC program is employed to find the optimal parameters of the proposed model. A half-car simulation is carried out to validate the proposed bushing model.

Modeling Expected Wear in Revolute Joints With Clearance in Multibody Mechanical Systems

The main goal of this work is to develop a methodology for studying and quantifying the wear phenomenon in revolute clearance joints. In the process, a simple model for a revolute joint in the framework of multibody systems formulation is presented. The evaluation of the contact forces developed is based on a continuous contact force model that accounts for the geometrical and materials properties of the colliding bodies. The friction effects due to the contact in the joints are also represented. Then, these contact-impact forces are used to compute the pressure field at the contact zone, which ultimately is employed to quantify the wear developed and caused by the relative sliding motion. In this work, the Archard’s wear model is used. A simple planar multibody mechanical system is used to perform numerical simulations, in order to discuss the assumptions and procedures adopted throughout this work. Different results are presented and discussed throughout this research work. From the main results obtained, it can be drawn that the wear phenomenon is not uniformly distributed around the joint surface, owing to the fact that the contact between the joint elements is wider and more frequent is some specific regions.

Modeling and Simulation of Woven Fabrics and Woven Fiber-Reinforced Composites Based on a Nonlinear Fiber Model

A three-dimensional nonlinear thread formulation developed by the first two authors [1] has been extended in this paper for modeling and simulation of woven fabrics and fiber-reinforced composites of various configurations under arbitrary large deformation. The resultant model accounts for extensibility of the woven fibers in the composite, geometry nonlinearity, tension variation along the fiber, and other nonlinear effects due to the woven composition and large deformation. The new modeling effort includes the development of a contact model for simulating the contact between fibers, which can be used to predict high-fidelity behavior of woven fibers in the composite and their interactions. Matrix model is also added into the composite for studying the coupling between woven fibers and matrix material such as resin. The incremental form of original nonlinear equation is discretized using a finite element method with an iteration scheme. Two numerical examples are given to demonstrate the effectiveness of the proposed modeling technique.

Discrete Mechanics and Optimal Control for Constrained Multibody Dynamics

This paper formulates the dynamical equations of mechanics subject to holonomic constraints in terms of the states and controls using a constrained version of the Lagrange-d’Alembert principle. Based on a discrete version of this principle, a structure preserving time-stepping scheme is derived. It is shown that this respect for the mechanical structure (such as a reliable computation of the energy and momentum budget, without numerical dissipation) is retained when the system is reduced to its minimal dimension by the discrete null space method. Together with initial and final conditions on the configuration and conjugate momentum, the reduced time-stepping equations serve as nonlinear equality constraints for the minimisation of a given cost functional. The algorithm yields a sequence of discrete configurations together with a sequence of actuating forces, optimally guiding the system from the initial to the desired final state. The resulting discrete optimal control algorithm is shown to have excellent energy and momentum properties, which are illustrated by two specific examples, namely reorientation and repositioning of a rigid body subject to external forces and the reorientation of a rigid body with internal momentum wheels.

Nonlinear Formulation for Flexible Multibody System Applied With Thermal Load

In this paper, temperature variation and dynamic performance of flexible multibody system applied with thermal load are investigated. Considering thermal strain and geometric nonlinear terms, heat conduction equations and dynamic equations for a flexible beam are derived, and then the system heat conduction equations and dynamic equations of flexible multibody system are assembled, and temperature, kinematic and driving constraint equations are used to obtain Lagrange’s equations of the first kind with Lagrange multipliers. Simulation of a rotating hub-beam system with simply-supported boundary condition is carried out to show the softening effect of the beam with temperature increase. Finally, thermal bending of flexible beam system applied with heat flux at upper surface is investigated. Coupling between rotational motion and transverse deformation as well as sudden change of constraint forces and axial stresses are shown to reveal the characteristics of thermal shock.

Discrete-Time Robust Control of Linear Periodically Time-Varying Systems

An approach for robust control of periodically time-varying systems is proposed. The approach combines the point-mapping formulation and a parameterization of the control vector to formulate an equivalent time-invariant discrete-time representation of the system. The discrete-time representation of the dynamic system allows for the application of known sampled-data control design methodologies. A perturbed, discrete-time dynamic model is formulated and plant parametric uncertainty are obtained using a truncated point-mapping algorithm. The error bounds due to point-mapping approximation are computed and a robustness analysis problem of the system due to parametric uncertainties is formulated using structured singular value theory. The proposed approach is illustrated by two design examples. Simulation studies show good performance robustness of the control system to parameter perturbations and system nonlinearities.

Design Sensitivity Analysis of Nonlinear Multidisciplinary Multibody Systems in the MIXEDMODELS Platform

Most state-of-the-art multibody systems are multidisciplinary and encompass a wide range of components from various domains such as electrical, mechanical, hydraulic, pneumatic, etc. The design considerations and design parameters of the system can come from any of these domains or from a combination of these domains. In order to perform analytical design sensitivity analysis on a multidisciplinary system (MDS), we first need a uniform modeling approach for this class of systems to obtain a unified mathematical model of the system. Based on this model, we can derive a unified formulation for design sensitivity analysis. In this paper, we present a modeling and design sensitivity formulation for MDS that has been successfully implemented in the MIXEDMODELS (Multidisciplinary Integrated eXtensible Engine for Driving Metamodeling, Optimization and DEsign of Large-scale Systems) platform. MIXEDMODELS is a unified analysis and design tool for MDS that is based on a procedural, symbolic-numeric architecture. This architecture allows any engineer to add components in his/her domain of expertise to the platform in a modular fashion. The symbolic engine in the MIXEDMODELS platform synthesizes the system governing equations as a unified set of non-linear differential-algebraic equations (DAE’s). These equations can then be differentiated with respect to design to obtain an additional set of DAE’s in the sensitivity coefficients of the system state variables with respect to the system’s design variables. This combined set of DAE’s can be solved numerically to obtain the solution for the state variables and state sensitivity coefficients of the system. Finally, knowing the system performance functions, we can calculate the design sensitivity coefficients of these performance functions by using the values of the state variables and state sensitivity coefficients obtained from the DAE’s. In this work we use the direct differentiation approach for sensitivity analysis, as opposed to the adjoint variable approach, for ease in error control and software implementation. The capabilities and performance of the proposed design sensitivity analysis formulation are demonstrated through a numerical example consisting of an AC rectified DC power supply driving a slider crank mechanism. In this case, the performance functions and design variables come from both electrical and mechanical domains. The results obtained were verified by perturbation analysis, and the method was shown to be very accurate and computationally viable.

Time Delay and Feedback Control of an Inverted Pendulum With Stick Slip Friction

We consider an experimental system consisting of a pendulum, which is free to rotate 360 degrees, attached to a cart which can move in one dimension. There is stick slip friction between the cart and the track on which it moves. Using two different models for this friction we design feedback controllers to stabilize the pendulum in the upright position. We show that controllers based on either friction model give better performance than one based on a simple viscous friction model. We then study the effect of time delay in this controller, by calculating the critical time delay where the system loses stability and comparing the calculated value with experimental data. Both models lead to controllers with similar robustness with respect to delay. Using numerical simulations, we show that the effective critical time delay of the experiment is much less than the calculated theoretical value because the basin of attraction of the stable equilibrium point is very small.

Dynamics of Multibody Systems: Generalized Mass Metric in Riemannian Velocity Space and Recursive Momentum Formulation

This paper describes two aspects of multibody system (MBS) dynamics on a generalized mass metric in Riemannian velocity space and recursive momentum formulation. Firstly, we present a detailed expression of the Riemannian metric and operator factorization of a generalized mass tensor for the dynamics of general-topology rigid MBS. The derived expression allows a clearly understanding the components of the generalized mass tensor, which also constitute a metric of the Riemannian velocity space. It is being the fact that there does exist a common metric in Lagrange and recursive Newton-Euler dynamic equation, we can determine, from the Riemannian geometric point of view, that there is the equivalent relationship between the two approaches to a given MBS. Next, from the generalized momentum definition in the derivation of the Riemannian velocity metrics, recursive momentum equations of MBS dynamics are developed for progressively more complex systems: serial chains, topological trees, and closed-loop systems. Through the principle of impulse and momentum, a new method is proposed for reorienting and locating the MBS form a given initial orientation and location to desired final ones without needing to solve the motion equations.

On Fractional Hamilton Formulation Within Caputo Derivatives

The fractional Lagrangian and Hamiltonian dynamics is an important issue in fractional calculus area. The classical dynamics can be reformulated in terms of fractional derivatives. The fractional variational principles produce fractional Euler-Lagrange equations and fractional Hamiltonian equations. The fractional dynamics strongly depends of the fractional integration by parts as well as the non-locality of the fractional derivatives. In this paper we present the fractional Hamilton formulation based on Caputo fractional derivatives. One example is treated in details to show the characteristics of the fractional dynamics.