Dynamic Response Of Multibody Systems Research Articles

Modeling and analysis of friction including rolling effects in multibody dynamics: a review

Friction exists in most mechanical systems, and it can have a major influence on their dynamic performance and operating conditions. As a consequence of frictional contact phenomena, energy is dissipated and the state of a system can change slowly and rapidly, depending on the nature of the contact, continuous or impact condition. Other effects associated with friction in mechanical systems are the vibration and noise propagation of the system components, nonlinear systems’ behavior and wear. Overall, the knowledge of the friction regimen, as well as the frictional forces developed at the interface of mechanical parts in contact with relative motion, is crucial for the dynamic analysis of mechanical systems, and has consequences in the design process. Thus, this work is a review of the modeling and analysis of frictional effects in multibody systems with the purpose of better understanding and obtaining accurate responses. In this process, pure dry sliding friction, stick–slip effect, viscous friction, Stribeck effect, and frictional lag are some of the main phenomena associated with friction, which are addressed in depth. Overall, the friction models can be divided into two main groups, namely the “static friction models” and the “dynamic friction models”. The static models describe the steady-state behavior of the relation friction-force/relative-velocity, while the dynamic models allow for the capturing of more physical responses and properties by using extra state variables. In a simpler manner, the static and dynamic friction models differ mostly in the modeled frictional effects, implementation complexity, and computational efficiency. Hence, this research is aimed at analyzing in detail the role of friction modeling in the dynamic response of multibody system, as well as addressing the importance of friction models selection for accurately describing the friction related phenomena. Demonstrative application examples, which include friction in ideal mechanical joints and systems involving contact–impact events, including an example of rolling contact will be considered and investigated to illustrate the main assumptions and procedures adopted in this work. The results from this study indicate that in most cases, a static friction model, which accounts for static friction and avoids the discontinuity at zero velocity, is a suitable choice. A more advanced dynamic friction model has to be developed to be utilized for systems containing high variations of normal load, namely with impact conditions.

Pin-slot clearance joints in multibody systems

The pin-slot joint is one of the most commonly used form of kinematic pairs, which with clearance will have a significant effect on the motion and dynamic response of multibody systems. In this study, the multibody system with a pin-slot clearance joint is modeled and the kinematic and dynamic effects are studied. Firstly, the generalized coordinate systems were established and the motion constraint equations of the pin-slot clearance joint were derived. Then, the theories of kinematics and dynamics were used to deduce equations of motion and dynamics. Finally, using slider-crank mechanism as the application example, the simulation study of the multibody system with a pin-slot clearance joint was carried out. The results show that there is an impact phenomenon in the moving process of the end slider, and with the increase of the slot angle, the impact phenomenon is earlier and the impact strength is weaker, however, with the increase of the slot value, the time when the impact phenomenon appearing doesn't change while the impact strength increasing. Furthermore, the maximum displacement of the end slider reduces with the increase of the slot value while the maximum value of driving torque doesn't change and the fluctuation of driving torque increased.

An enhanced formulation to model spatial revolute joints with radial and axial clearances

The primary objective of this work is to present a new formulation to model spatial revolute joints with radial and axial clearances. The methodology developed is based on the relative motion between the journal and bearing elements, which accounts for all the possible contact scenarios within a revolute clearance joint. In this process, normal and tangential contact force models are reexamined to evaluate their suitability to represent the contact-impact interactions between the mechanical parts connected by clearance joints. Also the equations of motion that govern the dynamic response of multibody systems and incorporate the intra-joint contact forces are presented. The Newton-Euler approach is applied here for these procedures. Finally, several numerical examples of the application are presented to discuss the main assumptions and procedures adopted in this work. The obtained results show that the clearance in mechanical joints can be quite significant in terms of the dynamic response of the system, and, consequently, plays a crucial role in the analysis, design and control of multibody systems.

Effects of restitution coefficient and material characteristics on dynamic response of planar multi-body systems with revolute clearance joint

To study the effects of restitution coefficient and material parameters on the dynamic characteristics of planar multi-body systems with revolute clearance joints, a comprehensive methodology for clearance revolute joints in a planar multibody system is presented and analyzed. A new nonlinear contact force model, which accounts for the axial length of bearing and has a wide suitable range of impact situation, is presented to evaluate the contact force between journal and bearing. Furthermore, a modified Coulomb friction force model also presented to consider the effect of friction in clearance joint. Then, a typical journal-bearing model and a planar slider-crank mechanism has revolute clearance joint are used as examples. From the main numerical results under the different restitution coefficient and material parameters, it can be concluded that coefficient of restitution has significant effects on dynamic response of multi-body systems with revolute clearance joint. Additionally, materials of journal and bearing with smaller Young’s modulus will cause obvious delay on dynamic response of multi-body systems.

Dynamic Response of Multibody Systems with Multiple Clearance Joints

A general methodology for the dynamic modeling and analysis of planar multibody systems with multiple clearance joints is presented. The inter-connecting bodies that constitute a real physical mechanical joint are modeled as colliding components, whose dynamic behavior is influenced by the geometric, physical and mechanical properties of the contacting surfaces. A continuous contact force model, based on the elastic Hertz theory, together with a dissipative term associated with the internal damping, is utilized to evaluate the intra-joint normal contact forces. The incorporation of the friction phenomenon, based on the classical Coulomb’s friction law, is also included in this study. The suitable contact force models are embedded into the dynamic equations of motion for the multibody systems. In the sequel of this process, the fundamental methods to deal with contact-impact events in mechanical systems are presented. Finally, two planar mechanisms with multiple revolute clearance joints are used to demonstrate the accuracy and efficiency of the presented approach and to discuss the main assumptions and procedures adopted. The effects of single versus multiple clearance revolute joints are discussed.

The effect of the lubricated revolute joint parameters and hydrodynamic force models on the dynamic response of planar multibody systems

In this work a comprehensive methodology for dynamic modeling and analysis of planar multibody systems with lubricated revolute joints is presented. In general, this type of mechanical systems includes journal-bearings in which the load varies in both magnitude and direction. The fundamental issues associated with the theory of lubrication for dynamically loaded journal-bearings are revisited that allow for the evaluation of the Reynolds equation for dynamic regime. This approach permits the derivation of the suitable hydrodynamic force laws that are embedded into the dynamics of multibody systems formulation. In this work, three different hydrodynamic force models are considered, namely the Pinkus and Sternlicht approach for long journal-bearings and the Frêne et al. models for both long and short journal-bearings. Results for a planar slider–crank mechanism with a lubricated revolute joint between the connecting-rod and slider are presented and utilized to discuss the assumptions and procedures adopted throughout the present study. Different test scenarios are taken into account with the purpose of performing a comparative study for quantifying the effect of the clearance size, lubricant viscosity, input crank speed and hydrodynamic force model on the dynamic response of multibody systems with lubricated revolute joints. From the global results obtained from computational simulations, it can be concluded that the clearance size, the lubricant viscosity and the operating conditions play a key role in predicting the dynamic behavior of multibody systems.

A parametric study on the dynamic response of planar multibody systems with multiple clearance joints

A general methodology for dynamic modeling and analysis of multibody systems with multiple clearance joints is presented and discussed in this paper. The joint components that constitute a real joint are modeled as colliding bodies, being their behavior influenced by geometric and physical properties of the contacting surfaces. A continuous contact force model, based on the elastic Hertz theory together with a dissipative term, is used to evaluate the intrajoint contact forces. Furthermore, the incorporation of the friction phenomenon, based on the classical Coulomb’s friction law, is also discussed. The suitable contact-impact force models are embedded into the dynamics of multibody systems methodologies. An elementary mechanical system is used to demonstrate the accuracy and efficiency of the presented approach, and to discuss the main assumptions and procedures adopted. Different test scenarios are considered with the purpose of performing a parametric study for quantifying the influence of the clearance size, input crank speed, and number of clearance joints on the dynamic response of multibody systems with multiple clearance joints. Additionally, the total computation time consumed in each simulation is evaluated in order to test the computational accuracy and efficiency of the presented approach. From the main results obtained in this study, it can be drawn that clearance size and the operating conditions play a crucial role in predicting accurately the dynamic responses of multibody systems.

Influence of the contact—impact force model on the dynamic response of multi-body systems

This work deals with contact—impact force models for both spherical and cylindrical contact surfaces. The incorporation of the friction phenomenon, based on the Coulomb friction law, is also discussed together with an effective computational strategy, which includes the automatic step size selection procedure. Impacts within a revolute clearance joint in a basic slider—crank mechanism are used as an example to compare the different contact force models. The collision is a prominent phenomenon in many multi-body systems such as mechanisms with intermittent motion, kinematic discontinuities, and clearance joints. As a result of an impact, the values of the system state variables change very fast, eventually looking like discontinuities in the system velocities and accelerations. The impact is characterized by large forces that are applied and removed in a short time period. The knowledge of the peak forces developed in the impact process is very important for the dynamic analysis of multi-body systems and it has consequences in the design process. The model for the contact—impact force must consider the material and geometric properties of the colliding surfaces, consider information on the impact velocity, contribute to an efficient integration, and account for some level of energy dissipation. These characteristics are ensured with a continuous contact force model, in which the deformation and contact forces are considered as continuous functions.

Modelling of clearances and joint flexibility effects in multibody systems dynamics

An effective method for modelling the dynamic response of multibody systems with flexible joints is presented. The method combines the use of finite element method with Kane's equations to present an algorithm strictly in terms of the generalized coordinates of the system. The procedures developed outline the automatic incorporation of the joint flexibility in the equations of motion, hence a more accurate mathematical model is developed. One other advantage to the method presented lies in the explicit forms of the coefficients needed in the analysis where they are readily expressed in a form suited for computer implementation. A discussion on possible applications is also presented.

Effect of using composites on the dynamic response of multi-body systems

A finite element scheme is presented for studying the dynamic response of multi-body systems with components manufactured from orthotropic materials. The formulation presented is exemplified by using fiber-reinforced cornposite laminates. The multi-body system considered in this investigation consists of interconnected rigid and flexible components, each undergoing large angular rotations. The configuration of the elastic components is identified by using two sets of generalized co-ordinates, reference and elastic co-ordinates. Reference co-ordinates describe the location and orientation of a selected body reference while elastic co-ordinates describe the deformation with respect to the body reference. Component modes of elastic components in the system are used to reduce the number of generalized co-ordinates. The system differential equations of motion and the algebraic constraint equations describing mechanical joints in the system are written in terms of mixed sets of reference and modal co-ordinates. Two numerical examples, for a slider crank mechanism and a Peaucellier mechanism, are presented in order to demonstrate the effect of the use of the composites on the dynamic response of multi-body systems. Numerical results showed that the use of composites represents an effective passive control strategy.

Viscoelastic analysis of multi-body systems using the finite element method

A study of the effect of viscoelastic material damping on the dynamic response of multibody systems, consisting of interconnected rigid, elastic and viscoelastic components, is presented. The motion of each elastic or viscoelastic body is identified by using three sets of modes: rigid body, reference and normal modes. Rigid body modes describe translation and large angular rotation of a body reference. Reference modes are the result of imposing the body-axis conditions. Normal modes define the deformation of the body relative to the body reference. Constraints between different components are formulated by using a set of non-linear algebraic equations that can be introduced to the dynamic formulation by using a Lagrange multiplier technique or can be utilized to eliminate dependent co-ordinates by partitioning the constraint Jacobian matrix. In developing the system equations of motion of the viscoelastic component, an assumption of a linear viscoelastic model is made. A Kelvin-Voigt model is employed, wherein the stress is assumed to be proportional to the strain and its time derivative. The formulation yields a constant damping matrix and the damping forces depend only on the local deformation; thus, no additional coupling between the reference and elastic co-ordinates appears in the formulation when considering the viscoelastic effects. It is demonstrated, by a numerical example, that the viscoelastic material damping can have a significant effect on the dynamic response of multibody systems.