Contact-impact Events Research Articles

An enhanced contact force model with accurate evaluation of the energy dissipation during contact-impact events in dynamical systems

The accurate calculation of energy dissipation during impact plays a decisive role in the prediction of the motion status after impact and the maximum contact force. However, how to precisely depict the energy loss and simplify the contact evaluation process meanwhile is an intractable issue. This investigation aims at analyzing the capacity of accurately evaluating the dissipated energy during impact based on the viscous damping factor contingent on frequency dependency and developing a new viscous damping factor by integrating the relative impact velocity from the linearized underdamped vibration system associated with the energy conservation during impact. Two pivotal dissipative coefficients are introduced into the damping force terms in the elastoplastic and plastic contact phases for the sake of compensating the derivation error of the new viscous damping factor. A new contact model with a viscous damper is proposed based on the Hertz contact theory and dimension analysis approach in conjunction with the linearized elastoplastic stiffness from the ML model. A comparative analysis between the novel contact model and the available contact models with viscous damping factors is conducted using an external impact scenario involving two spheres, which proves that the proposed contact model is the most precise viscous contact model in calculating the loss energy during impact. Finally, the slider-crank mechanism with clearance and horizontal granular chain are considered as the numerical example to illustrate the correctness of the new viscous contact model.

Multibody dynamics in robotics with focus on contact events

Abstract Multibody dynamics methodologies have been fundamental tools utilized to model and simulate robotic systems that experience contact conditions with the surrounding environment, such as in the case of feet and ground interactions. In addressing such problems, it is of paramount importance to accurately and efficiently handle the large body displacement associated with locomotion of robots, as well as the dynamic response related to contact-impact events. Thus, a generic computational approach, based on the Newton–Euler formulation, to represent the gross motion of robotic systems, is revisited in this work. The main kinematic and dynamic features, necessary to obtain the equations of motion, are discussed. A numerical procedure suitable to solve the equations of motion is also presented. The problem of modeling contacts in dynamical systems involves two main tasks, namely, the contact detection and the contact resolution, which take into account for the kinematics and dynamics of the contacting bodies, constituting the general framework for the process of modeling and simulating complex contact scenarios. In order to properly model the contact interactions, the contact kinematic properties are established based on the geometry of contacting bodies, which allow to perform the contact detection task. The contact dynamics is represented by continuous contact force models, both in terms of normal and tangential contact directions. Finally, the presented formulations are demonstrated by the application to several robotics systems that involve contact and impact events with surrounding environment. Special emphasis is put on the systems’ dynamic behavior, in terms of performance and stability.

Contact-impact events with friction in multibody dynamics: Back to basics

Multibody dynamics deals with the study of mechanical systems composed of multiple bodies, whose motion interactions are governed by the presence of kinematic constraints and by the application of external forces. Frictional contact-impact events are among the most complex and important phenomena that can be modeled under the umbrella of multibody systems, since their behavior depend on critical factors, including geometry of the contacting surfaces, material properties of the colliding bodies, and constitutive laws utilized to mimic the contact response. This paper is aimed to present a comprehensive description of the most relevant aspects and the state-of-the-art techniques concerning the modeling collisions in multibody dynamics. For that purpose, the contact geometry, contact detection and contact resolution procedures are subjected to a critical analysis. Particular attention is given to the regularized or continuous models to treat frictional contacts in dynamical systems. Moreover, relevant numerical ingredients associated with contact-impact events in multibody systems are examined with the intent to discuss the computational accuracy and efficiency. Application examples are provided whose results allow to highlight the key features related to the modeling process of frictional contacts and impacts in multibody systems.

Colliding solids interactions of earthquake-induced nonlinear structural pounding under stochastic excitation

A simplified analysis model of structural pounding, used in the study of the effects of earthquakes subjected to Gaussian white noise of relatively high intensity, filtered through a Kanai-Tajimi filter is proposed in this investigation. The required distance to avoid pounding is important in structural engineering. 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. Buildings without enough separation often create structural pounding under seismic events. Other effects associated with friction in mechanical systems are the vibration and noise propagation of the system components, nonlinear systems behavior and wear. In this paper, we prove that because of the inherent stochastic nature of the applied earthquake loads or the uncertainty arising from randomness (non-smooth behavior), stochastic p-bifurcations occur at law noise intensities and disappear when increasing noise intensities. Because of the presence of both impact-friction events, p-bifurcations should be observed at weak noise intensities. P-bifurcation occurs and created instability that will increase pounding effects. Some relationship between impact-friction events appears: small noise intensity occurs when the time of friction (continuous) is greater than the impacting events, hence high probability density function (PDF). But if the noise intensity increases, the impact events are great (small friction) with weak PDF. But successive jump effects can create noisy system and great impact. The models stochastic processes of stationary probability density function (PDF) of the earthquake ground motion are set up. The demonstrative application examples which include friction in systems involving contact-impact events are illustrated in Central Africa, a part of Congo Stable Block.

Nonlinear constitutive force model selection, update and uncertainty quantification for periodically sequential impact applications

Contact–impact events frequently occur between solid contact interfaces in complex dynamic mechanical systems and engineering applications. Impact force models are used to determine the responses of contacting solids. The selection of the impact force model strongly affects the predictions of the dynamic behavior of the contacting bodies, mainly in sequential repeated impacts. In this work, the strong nonlinear dynamic behavior of a cantilever steel beam, repeatedly impacting a steel rigid stop, is investigated applying experimental and numerical methodologies. The applicability of a nonlinear constitutive force model selection and model-updating framework at engineering problems where contact–impact phenomena happen in a sequential periodic manner is presented. At first, the dynamic behavior of the examined problem due to variation in impact parameters, excitation frequency and applied force model is examined. The general viscoelastic impact force law based on the Hertz contact theory, augmented with a damping term is integrated in the FE model. Experimental trials of the impacting cantilever beam under base excitation were carried out, and a model selection process between nine different expressions of the viscous term at a constant impact parameter is performed. Inadequacy of the updated selected model dictated a new model selection approach including the constant impact parameter. A new model selection and updating process is finally presented in order to tune and study in detail the effect of impact parameters and clearance gap between the contacting bodies in a specific sinusoidal excitation frequency of the impacting cantilever beam, validating the experimental results.

A Contact Force Model Considering Meshing and Collision States for Dynamic Analysis in Helical Gear System

The current research on gear system dynamics mainly utilizes linear spring damping model to calculate the contact force between gears. However, this linear model cannot correctly describe the energy transfer process of collision that often occurs in gear system. Focus on the contact-impact events, this paper proposes an improved gear contact force model for dynamic analysis in helical gear transmission system. In this model, a new factor associated with hysteresis damping is developed for contact-impact state, whereas the traditional linear damping factor is utilized for normal meshing state. For determining the selection strategy of these two damping factors, the fundamental contact mechanics of contact-impact event affected by supporting forces are analyzed. During this analysis, an effect factor is proposed for evaluating the influence of supporting forces on collision. Meanwhile, a new restitution of coefficient is deduced for calculating hysteresis damping factor, which suitable for both separation and non-separation states at the end of collision. In addition, the time-varying meshing stiffness (TVMS) is obtained based on the potential energy approach and the slice theory. Finally, a dynamic analysis of a helical gear system is carried out to better understand the contact force model proposed in this paper. The analysis results show that the contribution of supporting forces to the dynamic response of contact-impact event within gear pair is important. The supporting forces and dissipative energy are the main reasons for gear system to enter a steady contact state from repeated contact-impact state. This research proposes an improved contact force model which distinguishes meshing and collision states in gear system.

A dynamic model of polyethylene damage in dry total hip arthroplasties: wear and creep

The creep and wear of ultra-high-weight polyethylene hip prostheses under physiological conditions are studied in the present research work. A fully integrated contact-coupled dynamic model based upon multibody dynamics methodology is developed, allowing the evaluation of not only sliding distance, but also contact mechanics as well as cross-shear effects and both average pressure and in-service duration associated with the creep phenomenon. In vivo forces and motions of hip joint are used as input for the dynamic simulation, which result in more realistic contact point trajectory and contact pressure, and consequently wear and creep, compared to simplified inputs. The analysis also takes into account inertia forces due to hip motion, tribological properties of bearing bodies, and energy loss owing to contact-impact events. The principal molecular orientation (PMO) of the polyethylene cup is determined through an iterative algorithm and dynamic outcomes. Archard’s wear law is also integrated into the multibody dynamics model for wear prediction in hip implants. Creep, besides wear, is attributed to polyethylene damage, which is investigated by implementing a creep model extracted from experimental data. The model is validated using clinical data and numerical results available from previously published studies. It is shown that creep plays a significant role in hip damage along with wear, both of which can be influenced by hip parameters, e.g., hip and clearance sizes. Moreover, the creep mechanism according to creep experiment is discussed, and contributing factors to the wear phenomenon are analyzed throughout this study.

Comprehensive analyses of the elasto-plastic oblique contact-impact with vibration response

Contact-impact between different surfaces is a ubiquitous phenomenon especially in the mechanical systems. Previous work of authors indicated that the effect of longitudinal and/or transverse vibration response during the motion and dynamic modeling cannot be neglected for the elasto-plastic contact-impact events. In this study, further analyses were performed to characterize the contribution of longitudinal and transverse vibration responses during the elasto-plastic oblique contact-impact, and the formula to calculate the influence factor of vibration, ξ, was proposed based on the contact force with different vibrations during the impact. The momentum theorem and assumed mode method were used to develop the equations of motion of a flexible bar with a solid flat surface. Simulation results were compared with experimental results reported in the literature to verify the accuracy of the established model. The tangential and normal velocities of the contact point after the impact were compared with the simulations for different vibration cases, and the comparison between the simulations and the experimental results had yield encourage results. For different elasto-plastic materials, three critical initial impact angles had been found from the simulation to determine whether the flexible bar slides or sticks the flat surface. Although considering the effect of vibration response during the motion and dynamic modeling is very significant, increasing the number of shape functions did not effect the result significantly. The longitudinal and transverse vibration responses were found to effect the normal and tangential velocities of the contact point after the impact, respectively. Moreover, it had been shown that for the oblique contact-impact with sliding, considering the response of longitudinal and transverse vibration at the same time is more reasonable than other cases, which also reveals that, in this case, there is a good agreement between the simulation and experimental results. Besides, the mathematical expression on the influence factor of vibration depending on the initial velocity also had been obtained by a numerical analysis. This work can provide useful insights for dynamic modeling of complex multi-body systems during the contact-impact.

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.

Analysis of geometric dispersion effect of impact-induced transient waves in composite rod using dynamic substructure method

Wave propagation in a composite rod is encountered in many contact-impact events. During the travelling of the impact-induced waves along the rod, geometric dispersion is possible when the diameter of the rod is of the same order as the wavelength. The aim of this paper is to develop an efficient method, namely dynamic substructure method to analyze the geometric dispersion of the waves in the problem of the finite-length composite rod coaxially struck by a moving rigid mass. For analyzing the geometric dispersion, a new rod element is presented through taking the lateral kinetic energy of the rod into account. The transient dynamic equation expressed by the reduced modal coordinates is derived by the Lagrange equation and the fixed-interface mode synthesis method. An adhesive contact model is used to account for contact constraint. The applications of the proposed method are demonstrated using 1) compress trapezoidal impulse and 2) impact-induced waves propagate in the large-diameter rod. In order to validate the feasibility of the proposed method, the comparison is also presented between the LS-DYNA3D solutions and the substructure solutions. It indicates that the proposed method is sufficiently accurate to compute the time history of contact force and to describe the geometric dispersion characteristics such as the attenuation of the amplitude of wavefront and the increasing of rise time. The error of the 2nd peak value of the contact force Fc2 is less than 5.0%, while the time cost of the proposed method are only 1.8% of those of the LS-DYNA3D program. Furthermore, numerical results show that the geometric dispersion results in “succession collisions” phenomenon become more complicated, and it experiences three times of the transitions from contact to separation.

A comparative study of the viscoelastic constitutive models for frictionless contact interfaces in solids

The nature of the constitutive contact force law utilized to describe contact–impact events in solid contact interfaces plays a key role in predicting the response of multibody mechanical systems and in the simulation of engineering applications. The goal of this work is to present a comparative study on the most relevant existing viscoelastic contact force models. In the sequel of this process, their fundamental characteristics are examined and their performances evaluated. Models developed based on the Hertz contact theory and augmented with a damping term to accommodate the dissipation of energy during the impact process, which typically is a function of the coefficient of restitution between the contacting solids, are considered in this study. In particular, the identified contact force models are compared in the present study for simple solid impact problems with the sole purpose of comparing the performance of the various models and examining the corresponding system behavior. The outcomes indicate that the prediction of the dynamic behavior of contacting solids strongly depends on the selection of the contact force model.

Application of the nonsmooth dynamics approach to model and analysis of the contact-impact events in cam-follower systems

The dynamic modeling and analysis of planar rigid multibody systems that experience contact-impact events is presented and discussed throughout this work. The methodology is based on the nonsmooth dynamics approach, in which the interaction of the colliding bodies is modeled with multiple frictional unilateral constraints. Rigid multibody systems are stated as an equality of measures, which are formulated at the velocity-impulse level. The equations of motion are complemented with constitutive laws for the forces and impulses in the normal and tangential directions. In this work, the unilateral constraints are described by a set-valued force law of the type of Signorini’s condition, while the frictional contacts are characterized by a set-valued force law of the type of Coulomb’s law for dry friction. The resulting contact-impact problem is formulated and solved as an augmented Lagrangian approach, which is embedded in the Moreau time-stepping method. The effectiveness of the methodologies presented in this work is demonstrated throughout the dynamic simulation of a cam-follower system of an industrial cutting file machine.

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.

63975 MODELING AND ANALYSIS OF CONTACT PHENOMENA IN MULTIBODY SYSTEMS USING A LINEAR COMPLEMENTARITY FORMULATION(Contact, Impact, and Friction)

The dynamic modeling and analysis of rigid multibody systems that experience contact-impact events is presented and discussed in this study. The methodology is based on the nonsmooth dynamics approach, in which the interaction of the colliding bodies is modeled with multiple frictional unilateral constraints. The generalized contact kinematics is formulated in terms of gap functions and normal and tangential relative velocities. The dynamics of rigid multibody systems are stated as an equality of measures, which are formulated at the velocity-impulse level. The equations of motion are complemented with constitutive laws for the normal and tangential directions. In the present work, the unilateral constraints are described by a set-valued force law of the type of Signorini's condition, while the frictional contacts are characterized by a set-valued force law of the type of Coulomb's law for dry friction. Then, the resulting contact-impact problem is formulated and solved as a linear complementarity problem, which is embedded in the Moreau's time-stepping method. This method is considered here mainly due to its simplicity and robustness. The effectiveness of the methodologies presented in this study is demonstrated throughout the dynamic simulation of a planar multibody system.