Dynamics of flexible mechanical systems with contact-impact and plastic deformations

A computer based formulation for the analysis of mechanical systems is investigated as a feasible method to predict the impact response of complex structural systems. A general methodology for the dynamic analysis of rigid-flexible multibody systems using a number of redundant Cartesian coordinates and the method of the Lagrange multipliers is presented. The component mode synthesis is then used to reduce the number of flexible degrees of freedom. In many impact situations, the individual structural members are overloaded giving rise to plastic deformations in highly localized regions, called plastic hinges. This concept is used by associating revolute nonlinear actuators with constitutive relations corresponding to the collapse behavior of the structural components. The contact of the system components is described using a continuous force model based on the Hertz contact law with hysteresis damping. The effect and importance of structural damping schemes in flexible bodies are also addressed here. Finally, the validity of this methodology is assessed by comparing the results of the proposed models with those obtained in different experimental tests where: a beam collides transversally with a rigid block; a torque box impacts a rigid barrier.     

Modeling and simulation for wear prediction in planar mechanical systems with multiple clearance joints

Nonlinear Dynamics - The main goal of this work is to develop a comprehensive methodology for predicting wear in planar mechanical systems with multiple clearance joints and investigating the...     

A nonlinear contact pressure distribution model for wear calculation of planar revolute joint with clearance

As various errors result from manufacture and assembly processes or wear effect, clearance joint widely exists in mechanical system as a base component. The coupling analysis of tribology and dynamics of clearance joint is important to the reliability of mechanical system. A nonlinear contact pressure distribution mode (NLCP) is proposed to combine dynamics analysis with wear calculation together in this paper. The discrete thought of Winkler model is adopted to deal with contact problem with a high conformal rate. The contact relationship in a local microcontact area can be regarded as the contact between cylinder and plane. And the local contact pressure is acquired based on Hertz contact theory. The NLCP model has not only described the nonlinear relationship between contact pressure and penetration depth, but also avoided the complexity in contact pressure computation. The performance of NLCP model is demonstrated in comparison with asymmetric Winkler model, revealing that NLCP model has enhanced the calculation accuracy with a good efficiency. A comprehensive experimental study on the wear calculation of a slider–crank mechanism with clearance joint is presented and discussed to provide an experimental verification for NLCP model. The paper’s work has solved the contact problem with a high conformal rate and has described the nonlinear relationship between contact pressure and penetration depth. It has great value to the wear analysis of clearance joint.     

A controller for 2-DOF underactuated mechanical systems with discontinuous friction

We propose a controller for a class of 2-DOF underactuated mechanical systems with discontinuous friction in the unactuated joint. The control objective is the regulation of the unactuated variable while the position and speed of the actuated joint remain bounded. The unactuated joint is considered as a mechanical system with discontinuous friction but continuous, artificial control input given by a term depending on the actuated positions and velocities. The proposed controller guarantees the convergence of the position error of the unactuated joint to zero, and it is robust with respect to some uncertainty in the discontinuous friction coefficients. We illustrate the technique with its application to two systems.     

平面棱柱铰内考虑摩擦效应的接触分析

研究了多体系统中平面棱柱铰内的摩擦接触分析。在忽略铰内的碰撞效应的前提下,根据接触力系与约束反力的等效关系,以及各个角点接触力自身满足的互补关系,得到了接触力系关于摩擦力的线性互补方程。结合库仑摩擦定律,确定了铰内角点处的接触反力以及摩擦合力;另外,由接触力曲线可以得到铰内的接触形式,以及各个接触形式发生改变的时刻。通过ADAMS算例验证,这些接触形式转换的时刻就是铰内发生碰撞的时刻,为高效率地研究铰内碰撞提供了可能。     

Dynamic analysis of a flexible slider–crank mechanism with clearance

In this paper we are interested in the study of the dynamic behavior of a planar flexible slider–crank mechanism with clearance. Simulation and experimental tests were carried out for this goal. For the simulation tests, we have built the model under the software ADAMS. We used a contact model based on the so called Impact-function. An experimental set-up was designed and built to achieve some experimental validations. The presented results show that, in the presence of clearance, the mechanism responses were greatly influenced. The motion is characterized by the occurrence of three phases: a free motion, a continuous contact motion and an impact motion. In this paper, both the case of the mechanism with rigid link and the case with flexible link were studied. It is shown that in the presence of clearance, the coupler flexibility has a role of suspension for the mechanism.     

Finite elements and sensitivity coefficients in flexible planar linkage analysis

Summary A Kineto-Elasto-Dynamic approach, which is based on the use of finite elements, is presented for 1 d.o.f. planar mechanisms. No requirements are needed for the reference rigid mechanism time-history, which is computed in a fully dynamic way.A simple test case shows the independence of the response from the chosen reference mechanism.The frequency content of the response matches the expected frequencies of the model.

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Sommario Viene presentato un approccio cineto-elasto-dinamico, basato su tecniche agli elementi finiti, per meccanismi piani ad 1 g.d.l. Nessuna ipotesi è richiesta per la legge del moto del meccanismo di riferimento a membri rigidi. Detta legge del moto è calcolata in maniera dinamica diretta. Un semplice caso di prova mostra l'indipendenza della risposta dalla scelta del meccanismo di riferimento. Il contenuto in frequenza della risposta corrisponde alle frequenze prevedibili per il modello.

     

Stability and oscillations in a slow-fast flexible joint system with transformation delay

Flexible joints are usually used to transfer velocities in robot systems and may lead to delays in motion transformation due to joint flexibility. In this paper, a linkrotor structure connected by a flexible joint or shaft is firstly modeled to be a slow-fast delayed system when moment of inertia of the lightweight link is far less than that of the heavy rotor. To analyze the stability and oscillations of the slowfast system, the geometric singular perturbation method is extended, with both slow and fast manifolds expressed analytically. The stability of the slow manifold is investigated and critical boundaries are obtained to divide the stable and the unstable regions. To study effects of the transformation delay on the stability and oscillations of the link, two quantitatively different driving forces derived from the negative feedback of the link are considered. The results show that one of these two typical driving forces may drive the link to exhibit a stable state and the other kind of driving force may induce a relaxation oscillation for a very small delay. However, the link loses stability and undergoes regular periodic and bursting oscillation when the transformation delay is large. Basically, a very small delay does not affect the stability of the slow manifold but a large delay affects substantially.     

Dynamic analysis of planar rigid-body mechanical systems with two-clearance revolute joints

In this paper, the behavior of planar rigid-body mechanical systems due to the dynamic interaction of multiple revolute clearance joints is numerically studied. One revolute clearance joint in a multibody mechanical system is characterized by three motions which are: the continuous contact, the free-flight, and the impact motion modes. Therefore, a mechanical system with n-number of revolute clearance joints will be characterized by 3 ⁿ motions. A slider-crank mechanism is used as a demonstrative example to study the nine simultaneous motion modes at two revolute clearance joints together with their effects on the dynamic performance of the system. The normal and the frictional forces in the revolute clearance joints are respectively modeled using the Lankarani–Nikravesh contact-force and LuGre friction models. The developed computational algorithm is implemented as a MATLAB code and is found to capture the dynamic behavior of the mechanism due to the motions in the revolute clearance joints. This study has shown that clearance joints in a multibody mechanical system have a strong dynamic interaction. The motion mode in one revolute clearance joint will determine the motion mode in the other clearance joints, and this will consequently affect the dynamic behavior of the system. Therefore, in order to capture accurately the dynamic behavior of a multi-body system, all the joints in it should be modeled as clearance joints.     

Experiment research and dynamic behavior analysis of multi-link mechanism with wearing clearance joint

Nonlinear Dynamics - Irregular wear is one of the main reasons leading to the failure of mechanical equipment and mechanical parts. The coupling between irregular wear and system dynamic behavior...     

Dynamic analysis of planar mechanisms with revolute clearance joints based on two evaluation indices

Joint clearance is one of the most important factors that influence the dynamic performance of a mechanical system. In this study, a quantitative analysis method, which contains two clearance effect evaluation indices that can better evaluate influence of clearance joints on the dynamic performance of the mechanisms, is proposed. A dynamic modeling approach of planar mechanisms with clearance joints is introduced. A crank-slider mechanism with multiple clearance revolute joints is studied to support the proposed analysis methodology. Besides, different dynamic responses generated by different materials of the clearance joints are also investigated based on the clearance effect evaluation indices.     

A general method for impact dynamic analysis of a planar multi-body system with a rolling ball bearing joint

Impact affects the dynamic characteristics of mechanical multi-body systems and damages those rotating parts, such as the joint rolling element bearings, which are high-precision, defect intolerant components. Based on multi-body dynamic theory, Hertzian contact theory, and a continuous contact model, this study proposed a modelling method that can describe the dynamic behaviour of planar mechanical multi-body systems containing a rolling ball bearing joint under impact. In this method, the rigid bodies and bearing joint were connected according to their joint force constraints; the impact constraint between the multi-body system and the target rigid body was constructed using a continuous contact force model. Based on this method, the reflection relationship between the external impacts of the mechanical multi-body system and the variation law governing the dynamic load on the rolling bearing joint were revealed. Subsequently, an impact multi-body system, which was composed of a sliding–crank mechanism containing a rolling ball bearing joint and the target rigid body with an elastic support, was analysed to explore the dynamic response of such a complex discontinuous dynamic system andthe relevant relationship governing the dynamic load on the rolling bearing joint. In addition, a multi-body dynamic simulation software was used to build a virtual prototype of the impact slider–crank system. Compared with the theoretical model, the prototype had an additional deep groove ball bearing. That is to say, the prototype model took account of the specific geometric structural characteristics and the complex contact relationship of the inner and outer races, rolling balls, and bearing cage. Finally, the effectiveness of the theoretical method proposed in this study was verified by comparative analysis of the results. The results suggested that the external impact of a mechanical multi-body system was prone to induce sudden changes in the equivalent reaction force on its bearing joint and the dynamic load carried on its rolling balls. This study provided an effective method for exploring the distribution characteristics of dynamic loads on rolling ball bearing joints under working impact load conditions. Moreover, it offered support for the parameter optimisation of geometric structure, performance evaluation, and dynamic design of the rolling ball bearings.     

Chaotic characteristic analysis of spatial parallel mechanism with clearance in spherical joint

Nonlinear Dynamics - The spherical joint is one of the main motion pairs in spatial parallel mechanism, and the spherical clearance has a great effect on the nonlinear dynamic performance of...     

Dynamic buckling of a 2-DOF imperfect system with symmetric imperfections

Non-linear dynamic buckling of a two-degree-of freedom (2-DOF) imperfect planar system with symmetric imperfections under a step load of infinite duration (autonomous system) is thoroughly discussed using energy and geometric considerations. This system under the same load applied statically exhibits (prior to limit point) an unstable symmetric bifurcation lying on the non-linear primary equilibrium path. With the aid of the total energy-balance equation of the system and the particular geometry (due to symmetric imperfections) of the plane curve corresponding to the zero level total potential energy “surface” exact dynamic buckling loads are obtained without solving the non-linear initial-value problem. The efficiency and the reliability of the technique proposed herein is demonstrated with the aid of various dynamic buckling analyses which are compared with numerical simulation using the Verner-Runge-Kutta scheme, the accuracy of which is checked via the energy-balance equation.     

Dynamic modeling and analysis of multi-link mechanism considering lubrication clearance and flexible components

Nonlinear Dynamics - In mechanical system, lubricant is usually added into the clearance of moving pair to reduce friction, increase damping and prolong the service life of moving pair. Under the...