A differential approach for modeling revolute clearance joints in planar rigid multibody systems

A non-penetration approach of frictional contact analysis is presented for modeling revolute clearance joints of planar rigid multibody systems. In the revolute clearance joint, the motion modes of the journal are divided into three categories, namely, the free motion, collision, and permanent contact modes. The switch between different contact modes is identified by the state of the journal and bearing, including the gap and the normal relative velocity. When impact in the revolute clearance joint is detected, the collision process is simulated by the impulse-based differential approach, where Stronge’s improved model for restitution is employed to determine the relative velocity after impact. Instead of algebraic equations, the impact process is described by a set of ordinary differential equations (ODEs), which avoids solving complementarity problems. Moreover, in the permanent contact mode, the constraint-based approach and modified Coulomb’s friction law are adopted. The permanent contact mode maintains for most of the time and the governing ODEs are non-stiff. There is general agreement that the constraint-based approach is more efficient than the force-based method. A slider–crank mechanism with a revolute clearance joint is considered as a demonstrative application example where the comparison with the continuous contact force model is investigated.     

Computed torque control of fully-actuated nondeterministic multibody systems

In this paper we are interested in the dynamic behavior of a slider-crank mechanism with single and two revolute clearance joints. Due to the clearance existence in the revolute joints, it is important to choose an appropriate contact force model in analyzing the dynamic response of a slider-crank mechanism with clearances. The dynamic equations are established by combining the Newton–Euler equations with modified contact force model and improved Coulomb friction force model, and the Baumgarte stabilization approach is used to improve the numerical stability. According to numerical and experimental results, the method of continuous contact can be verified to be reasonable. Comparing dynamic the response between one clearance joint and two clearance joints in a crank-slider mechanism, it is easy to find a significant mutual coupling region due to the presence of two clearance joints by simply contact figures. The dynamic response in a mechanism with two clearance joints is not a simple superposition of that in mechanism with one clearance joint. Therefore, all the joints in a multibody system should be modeled as clearance joints.     

Recursive formulations for multibody systems with frictional joints based on the interaction between bodies

In practice, the clearances of joints in a great number of mechanical systems are well under control. In these cases, some of the existing methods become unpractical because of the little differences in the order of magnitude between relative movements and computational errors. Assuming that the effects of impacts are negligible, we proved that both locations and forces of contacts in joints can be fully determined by parts of joint reaction forces. Based on this fact, a method particularly suited for multibody systems possessing frictional joints with tiny clearances is presented. In order to improve the efficiency of computation, recursive formulations are proposed based on the interactions between bodies. The proposed recursive formulations can improve the computation of joint reaction forces. With the methodology presented in this paper, not only the motion of bodies in a multibody system but also the details about the contacts in joints, such as forces of contacts and locations of contact points, can be obtained. Even with the assumption of impact free, the instants of possible impacts can be detected without relying upon any ambiguous parameters, as indicated by numerical examples in this paper.     

Dynamics of spatial flexible multibody systems with clearance and lubricated spherical joints

A computational methodology for analysis of spatial flexible multibody systems, considering the effects of the clearances and lubrication in the system spherical joints, is presented. The dry contact forces are evaluated through a Hertzian-based contact law, which includes a damping term representing the energy dissipation. The frictional forces are evaluated using a modified Coulomb’s friction law. In the case of lubricated joints, the resulting lubricant forces are derived from the corresponding Reynolds’ equation. An absolute nodal formulation is utilized in flexible body formulation. The generalized-α method is used to solve the resulting equations of motion. The effectiveness of the methodology is demonstrated by two numerical examples.     

Dynamic analysis of planar multi-body systems with LuGre friction at differently located revolute clearance joints

In this paper, the dynamic response of a planar rigid multi-body system with stick?Cslip friction in revolute clearance joints is studied. LuGre friction law is proposed to model the stick?Cslip friction at the revolute clearance joints. This is because using this law, one can capture the variation of the friction force with slip velocity, thus making it suitable for studies involving stick?Cslip motions. The effective coefficient of friction is represented as a function of the relative tangential velocity of the contacting bodies, that is, the journal and the bearing, and an internal state. In LuGre friction model, the internal state is considered to be the average bristle deflection of the contacting bodies. By applying the LuGre friction law on a typical slider?Ccrank mechanism, the friction force in the revolute joint having clearance is seen not to have a discontinuity at zero slip velocity throughout the simulation unlike in static friction models. In addition, LuGre model was observed to capture the Stribeck effect which is a phenomenon associated directly with stick?Cslip friction. The friction forces are seen to increase with increase in input speed. The effect of stick?Cslip friction on the overall dynamic behavior of a mechanical system at different speeds was seen to vary from one clearance joint to another.     

An approach for modelling a clearance revolute joint with a constantly updating wear profile in a multibody system: simulation and experiment

Multibody System Dynamics - An approach for modelling a clearance revolute joint with a constantly updating wear profile in a multibody system is proposed. Before the contact analysis, the...     

An approach for dynamic analysis of planar multibody systems with revolute clearance joints

Engineering with Computers - Clearance is inevitable for manufacture and assembly in the revolute joints of multibody systems. Excessive value of joint clearance will lead to the poor dynamic...     

Modeling and simulation of the nonsmooth planar rigid multibody systems with frictional translational joints

The main purpose of this paper is to present a modeling and simulation method for the rigid multibody system with frictional translational joints. The small clearance between a slider and guide is considered. The geometric constraints of the translational joints are treated as bilateral constraints and the impacts between sliders and guides are neglected when the clearance sizes of the translational joints are very small. The contact situations of the normal forces acting on the sliders are described by inequalities and complementarity conditions, while the frictional contacts are characterized by a set-valued force law of the type of Coulomb’s law for dry friction. The dynamic equations of the multibody systems with normal and tangential contact forces are written on the acceleration-force level using the Lagrange multiplier technique. The problem of the transitions of the contact situation of the normal forces acting on sliders and the transitions of the stick-slip of the sliders in the system is formulated as a horizontal linear complementarity problem (HLCP), which is solved by event-driven method. Baumgarte’s stabilization method is used to decrease the constraint drift. Finally, two typical mechanisms are considered as demonstrative application examples. The numerical results obtained show some dynamical behaviors of the systems with frictional translational joints and constraint stabilization effect.     

Investigation of joint clearance effects on the dynamic performance of a planar 2-DOF pick-and-place parallel manipulator

In this study, the effects of joint clearance on the dynamic performance of a planar 2-DOF pick-and-place parallel manipulator are investigated. The parallel manipulator is modeled by multi-body system dynamics. The contact effect in revolute joints with clearance is established by using a continuous analysis approach that is combined with a contact force model considering hysteretic damping. The evaluation of the contact force is based on Hertzian contact theory that accounts for the geometrical and material properties of the contacting bodies. Furthermore, the incorporation of the friction effect in clearance joints is performed using a modified Coulomb friction model. By numerical simulation, variations of the clearance joint's eccentric trajectory, the joint reaction force, the input torque, the acceleration, and trajectory of the end-effector are used to illustrate the dynamic behavior of the mechanism when multiple clearance revolute joints are considered. The results indicate that the clearance joints present two obvious separation leaps in a complete pick-and-place working cycle of the parallel manipulator, following a collision. The impact induces system vibration and thus reduces the dynamic stability of the system. The joint clearances affect the amplitudes of the joint reaction force, the input torque, and the end-effector's acceleration, additionally the joint clearances degrade the kinematic and dynamic accuracy of the manipulator's end-effector. Finally, this study proposes related approaches to decrease the effect of joint clearances on the system's dynamic properties for such parallel manipulator and prevent “separation-leap-impact” events in clearance joints.     

Modeling planar slider-crank mechanisms with clearance joints in RecurDyn

Revolute joints in applications always show clearance between pin and bushing due to manufacturing tolerances, the need of relative motion or progressing wear. Many researchers developed and investigated methodologies to calculate the dynamic behavior of mechanisms with such imperfect joints. Very often they use a simple slider-crank mechanism to test or demonstrate the capability of their approaches. In this paper, a methodology for simulating a slider-crank mechanism with an imperfect revolute joint in RecurDyn, a commercial multibody simulation tool, is presented. Therefore, a thorough investigation of existing contact, damping and friction force models as well as different ways of modeling revolute joints in RecurDyn was conducted. For the investigation of the damping models, a special program for calculating the model parameters for a given coefficient of restitution was developed. Only one damping model was capable of reproducing the experimental results, which were found in literature. Some characteristic results of the slider-crank mechanism are presented in a way that they can be compared to results in other papers. Thereby. a good correlation was achieved, demonstrating the capabilities of the methodology.     

含铰链间隙的刚-柔机械臂动力学模型

根据Hertz接触定律和Coulomb摩擦定律,建立了含间隙平面旋转铰的力学模型;采用几何变形约束法和模态缩聚技术描述柔性机械臂的非线性变形;同时考虑两个旋转铰的间隙特性和柔性臂的弹性变形,最终采用Kane方程建立了含铰链间隙的刚-柔机械臂系统的动力学模型．     

Improved bushing models for general multibody systems and vehicle dynamics

The development and computational implementation, on a multibody dynamics environment, of a constitutive relation to model bushing elements associated with mechanical joints used in the models of road and rail vehicles is presented here. These elements are used to eliminate vibrations in vehicles, due to road irregularities, to allow small misalignment of axes, to reduce noise from the transmission, or to decrease wear of the mechanical joints. Bushings are made of a special rubber, used generally in energy dissipation, which presents a nonlinear viscoelastic relationship between the forces and moments and their corresponding displacements and rotations. In the methodology proposed here a finite element model of the bushing is developed in the framework of the finite element code ABAQUS to obtain the constitutive relations of displacement/rotation versus force/moment for different loading cases. The bushing is modeled in a multibody code as a nonlinear restrain that relates the relative displacements between the bodies connected with the joint reaction forces, and it is represented by a matrix constitutive relation. The basic ingredients of the multibody model are the same vectors and points relations used to define kinematic constraints in any multibody formulation. One particular, and relevant, characteristic of the formulation now presented is its ability to represent standard kinematic joints, clearance, and bushing joints just by defining appropriate constitutive relations. Spherical, revolution, cylindrical, and translational bushing joints are modeled, implemented, and demonstrated through the simulation of two multibody models of a road vehicle, one with perfect kinematic joints for the suspension sub-systems, and other with bushing joints. The tests conducted include an obstacle avoidance maneuver and a vehicle riding over bumps. It is shown that the bushing models for vehicle multibody models proposed here are accurate and computationally efficient so that they can be included in the vehicle models leading reliable simulations.     

Modified models for revolute joints coupling flexibility of links in multibody systems

Multibody System Dynamics - This paper develops three different types of finite element models for revolute joints in flexible multibody systems, in which the dry clearance revolute joints have...     

Frictional contact analysis of spatial prismatic joints in multibody systems

The contact analysis of spatial prismatic joints remains a hard problem due to its complex nature. In this paper, a methodology for the frictional contact analysis of rigid multibody systems with spatial prismatic joints is presented, which is free of calculating the relative motion between the slider and guide, and is particularly suitable to the case of clearances being tiny. Under the assumption of the slider and guide being rigid, we prove that all types of contacts in the joint can be converted to point-to-point contacts. At each of the candidate points, two gap functions are introduced. However, in the proposed method, not the values of these gap functions but the relations between them are essential. In view of the non-colliding contacts being predominant when clearances of joints are tiny, we formulate the contact forces in terms of resultant frictional forces in the joint, resulting in a linear complementarity problem. By the proposed method, details about the contacts including the impact instants can be obtained, although impacts are not taken into consideration explicitly, as indicated by the numerical examples in this paper.     

Optimization of transmission angle for slider-crank mechanism with joint clearances

In this study, kinematic analysis of a planar slider-crank mechanism having revolute joints with clearances was presented. Joint clearance was modelled as a massless virtual link, and Multi-Layered Neural Network (MLNN) structure was used for approximating the motion of this link with respect to the position of input link. Training and testing data sets for the neural network were obtained from mechanism simulation using the ADAMS software. A genetic algorithm was also used to optimize the design parameters for minimizing the deviations due to clearances. When two joint clearances at crank-pin and piston-pin centers were considered, the effects of these clearances on the kinematic characteristics and transmission quality of the mechanism were investigated using continuous contact model between the journal and bearing at a joint.     

多体系统中典型铰的摩擦力计算模型

在铰内间隙很小的前提下,多体系统中铰仍具有运动学约束作用.但由于铰内接触形式与系统状态相关,铰内摩擦力与约束反力之间具有复杂的函数关系.本文在假设铰内接触为刚性接触的前提下,基于分布接触反力与点接触反力之间的等效关系,给出了几种典型铰内摩擦力的计算模型,并通过数值算例验证了所提模型的正确性.     

A Continuous Analysis Method for Planar Multibody Systems with Joint Clearance

Clearance from manufacturing tolerances or wear is likely to degrade the dynamic performance of connected machine parts. When joint clearance is introduced, the dynamic response of the mechanical system is substantially changed, seen as high acceleration and force peaks and dissipation of energy. Looking at contact models, the simpler ones, such as the linear Kelvin–Voigt or the nonlinear Hertz model, are characterized by a set of parameters. These include material parameters, coefficient of restitution and possibly a coefficient of friction. The analysis models can be divided into two groups – continuous and dis-continuous, related to whether integration is carried out through the period of contact, or stopped and restarted after the impact.Based on the equations of motion for a multibody system of rigid bodies, it is suggested that the continuous analysis approach is combined with a contact force model to describe joint clearance in rotational joints. Performing simulations with this methodology allows not only to quantify the overall mechanism behaviour, but also in-depth analysis of the impact mechanics in the clearance joint. Experimental data from a double pendulum impacting a rigid plate is used to verify the suggested continuous analysis method.     

Analysis of Joint Clearances in Multibody Systems

A methodology for the study of typical smooth joint clearances in multibody systems is presented. The proposed approach takes advantage of the analytical definition of the material surfaces defining the clearance, resulting in a formulation where the gap does not play a central role, as it happens in standard contact models. The contact forces are formulated in conserving form, such that the balance of total energy during the intermittent contact is exactly established in the discrete time integration scheme. Some numerical applications are presented, showing that the proposed methodology is very stable in long-term simulations with relatively large time step sizes. Therefore, it appears to be promising in terms of efficiency and robustness for the numerical analysis of real joints with clearances.     

An Efficient Method for Synthesis of Planar Multibody Systems Including Shape of Bodies as Design Variables

A point contact joint has been developed and implemented in a joint coordinate based planar multibody dynamics analysis program that also supports revolute and translational joints. Further, a segment library for the definition of the contours of the point contact joints has been integrated in the code and as a result any desired contour shape may be defined. The sensitivities of the basic physical variables of a multibody system, i.e., the positions, velocities, accelerations and reactions of the system with respect to the automatically identified independent design variables may be determined analytically, allowing design problems where the shape of the bodies are of interest to be handled in both a general and efficient way.