Rigid-flexible Coupling System Research Articles

Dynamical analysis of the flexible beam-cam oblique-impact system

A mechanical system is often modeled as a multi-body system with non-smoothness. Typical examples are the noises and vibrations produced in railway brakes, impact print hammers, or chattering of machine tools. These effects are due to the non-smooth characteristics such as clearance, impact, intermittent contact, dry friction, or a combination of these effects. In a non-smooth system, neither of the time evolutions of the displacements and the velocities are requested to be smooth. Beam-cam device is an important kind of impacting system which has a wide range of applications. The rotation of the cam at some constant speed provides a force to operate the beam. The most common example is the valve trains of internal combustion engines, where the rotation of the cam imparts the proper motion to the engine valves through the follower while a spring provides a restoring force necessary to maintain contact between the components. The impact on beam-cam is a typical oblique-impact. It has been observed that under variations of the cam rotational speed and other parameters, the follower can exhibit a complex behavior including bifurcations and chaos. We study a rigid flexible coupling system, which moves in the horizontal plane, and is composed of the hub, the flexible beam and a cam with constant rotating speed. Considering the second-order coupling of axial displacement which is caused by the transverse deformation of the beam, the kinetic energy and the potential energy of the whole system are calculated. The governing equations of the flexible beam-cam oblique-impact system are derived from Hamilton theory, when taking into account the second-order coupling quantity of axial displacement caused by the transverse displacement of the beam. Hertz contact theory and nonlinear damping theories are used to establish the contact model. By the equivalent conversion method in structural mechanics, the deflection curve of flexible beam is calculated. The acceleration at the contact point of beam and cam is used to judge whether they are separate, or contacted, or impacting. Due to the flexibility of beam, the impact point of beam-cam always changes with time and speed. We propose a method, which is a trial calculation method, to determine the impact point of flexible beam-cam. Simulation results show that there is transverse vibration at the free end of flexible beam. There is inter-coupling among the flexible of beam, the large range of motion, and the impact. After the impact, the rotation angle of the flexible beam changes with time and the angle amplitude mainly decreases with the increase of the time, but the regularity is poor.

Dynamic Modeling and Response of a Rotating Cantilever Beam with a Concentrated Mass

The rigid-flexible coupling system with a hub and concentrated mass is studied in this paper. Considering the second-order coupling of axial displacement which is caused by transverse deformation of the beam, the dynamic equations of the system are established using the second Lagrange equation and the assumed mode method. The simulation results show that the concentrated mass mainly suppresses the vibration and exhibits damping characteristics. When the nondimensional mass position parameterβ>0.67, the first natural frequency is reduced as the concentrated mass increases. Whenβ<0.67, the first natural frequency is increased as the concentrated mass increases. We also find the maximum first natural frequency nondimensional position for the concentrated mass.

Satellite antenna dynamics and control with thermal effect

Purpose – The purpose of this paper is to analyze the effect of the space thermal effect on satellite antenna. Design/methodology/approach – In this paper, according to the geometric characteristics of parabolic reflector, the transient temperature field of an element along its thickness direction is built for shell structures using finite element discretization and the quadratic function interpolation, and heat conduction equations are derived based on the theory of the thermo-elastic dynamics. The modeling theory of rigid–flexible coupling system considering thermal effect is extended to the satellite antenna system. Then, the coupling dynamic equations are established including coupling stiffness matrix and thermal loaded undergoing a large overall motion. Finally, an adaptive controller is proposed and the adaptive update laws are designed under the parameter uncertainty. Findings – The results of dynamic characteristic analysis show that the dynamic thermal loaded coupled with structure deformation i...

Key Technologies of Rigid-Flexible Coupling System Modeling and Simulation

We studied key technologies of the rigid-flexible coupling systems modeling and simulation based on the theory of multi-body dynamics and virtual prototyping technology. The study proposed concrete measures to ensure the accuracy of the simulation to short the simulation time and improve simulation speed. It greatly improved the reliability and interoperability of research used three software UG, Ansys and Adams on rigid-flexible coupling system and found the existing issue of key parts of the design department, provided a strong quantitative basis for optimizing the loader working device.

Dynamic modeling and simulation for the rigid flexible coupling system with a non-tip payload in non-inertial coordinate system

The rigid flexible coupling system with a payload at non-tip position of the flexible beam is studied in this paper. Using the theory about mechanics problems in a non-inertial coordinate system and the subsystem modeling principle, the dynamic equations of the rigid flexible coupling system with dynamic stiffening are established via material mechanics and the angular momentum principle. This paper elucidates that dynamic stiffening is produced by the coupling effect of the centrifugal inertial load distributed on the beam and the transverse vibration deformation of the beam. First, the payload at non-tip position is incorporated into the continuous dynamic equations of the system by means of the Dirac function and the Heaviside function. Then, the constrained modes of the flexible beam are analyzed. According to the boundary conditions of the constrained modes, a reasonable position interval of the payload is proposed. It corrects the inaccurate understandings in some papers. Finally, based on the conclusions of orthogonalization about the normal constrained modes, the finite dimensional state space model suitable for controller design is obtained. In addition, in order to make the finite dimensional dynamic model established more practical, based on the common constrained modes, the dimensionless variables and parameters are introduced, and the dimensionless finite dimensional dynamic model of the system is derived. The numerical simulation results show that: dynamic stiffening is included in the first-order dynamic model established in this paper, therefore, it can indicate the dynamic responses of the rigid flexible coupling system with large overall motion accurately; the payload has a softening effect on the dynamic behaviors of the flexible beam, and the effect would be more obvious when the payload has a larger rotary inertia or a larger mass, or lies closer to the tip of the beam.

Nonlinear analysis and vibration suppression control for a rigid–flexible coupling satellite antenna system composed of laminated shell reflector

In this paper, a nonlinear dynamic modeling method for a rigid–flexible coupling satellite antenna system composed of laminated shell reflector is proposed undergoing a large overall motion. For the study of the characteristics of the reflector using laminated shell structure, the displacement field description of a point in a 3-noded shell element is acquired in conjunction with the length stretch, lateral bending and torsional deformation. Hence, a nonlinear dynamic model of the satellite antenna system is deduced based on Lagrange's equations. The complete expressions of nonlinear terms of elastic deformation and coupling terms between rigid motion and large deflection are considered in the dynamic equations, and the dynamic behavior of the rigid–flexible coupling system is analyzed using linear model and nonlinear model, respectively. In order to eliminate the system vibration, the PD with vibration force feedback control strategy is used to achieve its desired angles and velocity in a much shorter duration, and can further accomplish reduction of residual vibration. Then, the asymptotic stability of the system is proved based on the Lyapunov method. Through numerical computation, the results show that the linear model cannot capture the motion-induced coupling terms and geometric nonlinearity variations. However, the nonlinear model is suitable for dealing with large deformation rigid–flexible problem undergoing large overall motions. Hence, the satellite antenna pointing accuracy would be predicted based on the nonlinear model. Furthermore, the results also show that the proposed control strategy can suppress system vibration quickly. The above conclusions would have important academic significance and engineering value.

Dynamics Simulation Analysis of Centrifuge Facility-Vibration Shaker System Virtual Mocking Based on Flexible Centrifuge Arm

In order to study the dynamic characteristics of centrifuge facility-vibration shaker system, In the establishment of centrifuge facility-vibration shaker system multi-body dynamic model based on virtual mocking technology, the virtual dynamic model of the entire centrifuge facility-vibration shaker system more close to reality is built up by the transmission of finite element of flexible centrifuge arm. This paper describes how to build the 3-D virtual prototype of centrifuge facility-vibration shaker system by using Pro/e and ADAMS software, and how to create the modal neutral file of the centrifuge arm by using ANSYS software. Considering the system as a rigid-flexible coupling system, the dynamical simulation is carried out, and the results are benefit for the further research of its kinetic behavior, dynamic and variable characteristics basis and the design of such system.

Dynamics Simulation of Multi-Mechanism Operation Parameterization Bridge Crane Modeling Based on Rigid-Flexible Coupling System

The rigid-flexible coupled system modeling of parameterization bridge crane is conducted based on Pro/E, Multi-body systems dynamics simulation & Finite element analysis software, simulation of multi-mechanism operation process is performed as well. The results of dynamic simulation were analyzed and summarized, which is essential to complete crane fatigue strength calculation.

Accurate shape description of flexible beam undergoing oblique impact based on space probe-cone docking mechanism

The purpose of this paper is to do some researches on the accurate shape description of flexible beam undergoing oblique impact based on space probe-cone docking mechanism. The docking dynamics model is built based on Lagrange analytical method. Accurate modal equations of rigid–flexible coupling system, which include modified modal equations and modal frequencies, are derived. The MSC.Patran/Dytran is introduced to be the simulation tool. Third models with different parameters are built by both theoretical method and finite element method to verify the correctness of the new modal equations of rigid–flexible coupling system.

Dynamic Modeling for a Thin Plate with Large Deformation

In this paper, based on the nonlinear elastic theory, dynamic modeling for a thin plate with large deformation is proposed considering high-order deformation terms using hybrid-coordinate formulation. Through the calculation the potential energy and kinetic energy of the plate, rigid-flexible coupling dynamic equations is established. It is shown that the difference between the deformation results obtained by the present high-order dynamic model and those obtained by one-order approximate dynamic model is not significant in case of large deformation ,both them can calculation large deformation problem. However, the amplitude of vibration obtained by the present high-order dynamicmodel is smaller than that obtained by one-order approximate dynamic model. Furthermore, dynamic stiffening and softening effect of the rigid-flexible coupling system undergoing translational large overall motion is investigated. It is shown that with the reduce of the modulus of elasticity, the influence of the translational acceleration on the vibration frequency of the rigid-flexible coupling system is more significant.

Analysis of dynamic properties of a spatial flexible beam with large overall motion and nonlinear deformation in non-inertial reference frame

In this paper, the dynamic properties of a spatial flexible beam with large overall motion and nonlinear deformation in non-inertial reference frame are investigated. The dynamic response of the present model is compared with those of zero-order approximate model and one-order coupling model. Then changing of dynamic stiffening terms due to the new coupling terms is discussed according to different models. At the same time, the effect of initial static deformation on the tip is considered to study the vibrant deformation of flexible beam. In addition, when the overall motion is free, the rigid-flexible coupling dynamic theory is extended to spatial structure from planar structure. The difference among zero-order approximate model, one-order coupling model and the present exact model is revealed by the frequency spectrum analysis method and concludes that the speed of overall motion is a vital cause for the difference among different models. And the dynamic stiffening phenomenon still exists in a rigid-flexible coupling system while the overall motion is free.

Nonlinear dynamic analysis on rigid-flexible coupling system of an elastic beam

Previous work examined the effect of the attached stiffness matrix terms on stability of an elastic beam undergoing prescribed large overall motion. The aim of the present work is to extend the nonlinear formulations to an elastic beam with free large overall motion. Based on initial stress method, the nonlinear coupling equations of elastic beams are obtained with free large overall motion and the attached stiffness matrix is derived by solving sub-static formulation. The angular velocity and the tip deformation of the elastic pendulum are calculated. The analytical results show that the simulation results of the present model are tabled and coincide with the one-order approximate model. It is shown that the simulation results accord with energy conservation principle.

Geometric nonlinear dynamic analysis of curved beams using curved beam element

Instead of using the previous straight beam element to approximate the curved beam, in this paper, a curvilinear coordinate is employed to describe the deformations, and a new curved beam element is proposed to model the curved beam. Based on exact nonlinear strain-displacement relation, virtual work principle is used to derive dynamic equations for a rotating curved beam, with the effects of axial extensibility, shear deformation and rotary inertia taken into account. The constant matrices are solved numerically utilizing the Gauss quadrature integration method. Newmark and Newton-Raphson iteration methods are adopted to solve the differential equations of the rigid-flexible coupling system. The present results are compared with those obtained by commercial programs to validate the present finite method. In order to further illustrate the convergence and efficiency characteristics of the present modeling and computation formulation, comparison of the results of the present formulation with those of the ADAMS software are made. Furthermore, the present results obtained from linear formulation are compared with those from nonlinear formulation, and the special dynamic characteristics of the curved beam are concluded by comparison with those of the straight beam.

Kinematics Analysis of on-Off Pressure Mechanism with Flexible Link for Offset Press

In order to analyze the influence on the motion state of on-off pressure mechanism with flexible link of offset press, pneumatic on-off pressure was as the research object, the three-dimensional model of on-off pressure mechanism was established by using ADAMS, the kinematics simulations of the on-off pressure process was carried out, the curve of the angular velocity, angle acceleration and displacement between rollers of eccentric bushing in both rigid and the rigid-flexible coupled system was got, the significant basis of optimal design for on-off pressure mechanism was provided.

Simulation and Analysis of Dynamical Transmission Precision of 2K-V Cycloid pin Gear Reducer Based on Multi-Body System Dynamics

The dynamic model of multi-rigid-body system and rigid-flexible coupling system of 2K-V cycloid pin gear reducer are constructed with ADAMS, the output-angle error curves are obtained by multi-body system dynamic simulation, and the influence of elastic deformation come from planet gear, cycloid gear and pin gears on the transmission accuracy are analyzed. The work this paper introduced provides a useful approach for further study on the dynamic transmission accuracy of precision gear drive system, exploration of active control technology for the transmission accuracy and improvement of structural design for the gearing.

Analysis for Effect of Key Parts on Precision of High Precision Machine Center

Increasing the machining precision of machine tools has imposed higher demands for dynamic characteristics of the key components. Taking the MDH50 precision machining center as a example, this paper established the flexible body of five key components, bed, column, spindle boxes, slipway and worktable, and built the rigid-flexible coupling systems of whole machine, based on the basic theory of multi-body system dynamics. Then the cutting force reference to the actual constraints was applied to the system and the dynamics simulation was carried out. The effect of every component on machining precision was effectively identified. Dynamic stiffness testing of the machine is based of principles of testing the transmission components dynamic stiffness, and further analysis of the each component dynamic stiffness is conducted, which can verify the accuracy of flexible body analysis.

Modelling of Joint Interface of Turn-Milling Centre Based on Rigid-Flexible Coupling System

The mathematic models describing various joints of whole machine are founded to research dynamic performance of turn-milling center based on rigid-flexible coupling system. The various joint interfaces including the conical and cylinder contact, plane contact and fixed connection are regarded as flexible joints by using the spring and damping unit and the equivalent dynamic models of joint interfaces are built by finite element method based on different connection modes. Therefore, these mathematic models are used as references and foundations for research on dynamic performance of turn-milling center next stage.

Analysis and imitation of dynamic properties for rigid-flexible coupling systems of a planar flexible beam

The finite element method is used for the system discretization and the coupling dynamic equations of flexible beam are obtained by Lagranges equations. The second order coupling terms between rigid large overall motion, arc length stretch, lateral flexible deformation kinematics and torsional deformation terms are included in the present exact coupling model to expand the theory of one-order coupling model. The dynamic response of the present model is compared with that of zero-order approximate model and one-order coupling model. Then the changes of dynamic stiffening terms due to the new coupling terms are discussed according to different models. At the same time, the effect of initial static deformation in the tip is considered to study the vibrant deformation of flexible beam. The difference between zero-order approximate model, one-order coupling model and the present exact model is revealed by the frequency spectrum analysis method and it is concluded that the speed of overall motion is a vital cause for the difference between different models. And we found that the dynamic stiffening phenomenon still exists in rigid-flexible coupling system while the overall motion is free. But the effect of dynamic stiffening in the present exact model is not as severe as that in the one-order coupling model.

Research on Dynamic Behaviors for a Parallel Machine Tool Considering Elastic Component

In order to obtain dynamic behaviors of a spatial rigid-flexible coupling system of PMT(parallel machine tool) without the construction of mathematical model, a new method for dynamic behaviors simulation, which integrates CAD, CAE and visual technologies, was presented. The solid model of PMT was built in SolidWorks and transmitted to ADAMS, the modal neutral file of flexible body including driving limbs and spherical joints were generated in ANSYS, and introduced into ADAMS, then the rigid-flexible coupling model of PMT was build. Based on the rigid-flexible coupling model, the dynamic behaviors, which includes displacements error output response, dynamic stress of driving limbs and natural frequency, were realized. The simulation results show that the rigid-flexible coupling model established can indicate the dynamic behaviors of PMT. The flexibility of driving limbs and spherical joints are demonstrated to have significant impact on dynamics characteristics of PMT. This research can provide the important theoretical base of the optimization design of dynamic parameters for PMT.

Dynamic Properties of Hub-microbeam System

The dynamic properties of the micro-beam are obviously different from those of the traditional macro-beam due to the size effect of material on a micro scale. The dynamics of a rigid-flexible coupling system consisting of a rotating hub and a flexible micro-beam also known as hub-microbeam system, is studied. The coupling terms of the deformation motion, caused by transverse displacement are taken into account in the deformation displacements of micro-beam. The dynamic characteristic of a micro beam is analyzed theoretically by using couple stress theory (Cosserat theory). The governing equations of motion with the "dynamic stiffening" term and the size effect term for this system are derived by using the Hamilton principle. Based on the obtained dynamic equations, the dependence of the resonant frequency of a micro beam on its size is analyzed. For different rotating speeds, the vibration frequency of the zero order approximate model is compared with that of the coupling model and the suitable range of the zero order approximate model is determined, considering size effect on a micro scale. Finally, the influence of size effect and coupling terms of the deformation motion on the stiffness of micro beam is analyzed. The simulation demonstrates that the resonant frequency of micro-beam increases because of size effect. The influence of size effect is static and that of coupling terms of the deformation motion is related to the rotating speed.