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...     

A novel transition model for lubricated revolute joints in planar multibody systems

The dynamic behavior and the life of machineries are greatly affected by lubricated clearance joints,which are inevitable in mechanical systems, whereas investigations on lubricated clearance joints are very limited due to the difficulty in coupling lubrication theory with dynamics. By analyzing the transition status and considering the hydrodynamic lubrication, elasto-hydrodynamic lubrication, and partial lubrication and contact a novel transition model for the lubricated clearance joint is proposed to tackle with the transition between the lubrication statuses and the contact status. With the novel transition model, we performed numerical dynamic simulations based on a slider crank mechanism with a lubricated clearance joint. Using the novel transition model and the existed transition model (Flores model) in numerical simulations, we obtained and compared dynamic results, which demonstrate that the novel transition model is more accurate, efficient, and feasible than the Flores model.     

Modeling and analysis of planar rigid multibody systems with translational clearance joints based on the non-smooth dynamics approach

The main purpose of this paper is to present and discuss a methodology for a dynamic modeling and analysis of rigid multibody systems with translational clearance joints. The methodology is based on the non-smooth dynamics approach, in which the interaction of the elements that constitute a translational clearance joint is modeled with multiple frictional unilateral constraints. In the following, the most fundamental issues of the non-smooth dynamics theory are revised. 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 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 a linear complementarity problem, which is embedded in the Moreau time-stepping method. Finally, the classical slider-crank mechanism is considered as a demonstrative application example and numerical results are presented. The results obtained show that the existence of clearance joints in the modeling of multibody systems influences their dynamics response.     

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...     

基于LuGre模型非光滑柱铰链平面多体系统动力学的建模和数值方法

以含非光滑柱铰链平面多刚体系统为研究对象,将间隙充分小的柱铰链视为双边约束,用LuGre摩擦模型描述柱铰链内的摩擦;由第一类Lagrange方程导出该系统的动力学方程(微分 代数方程).铰链处的摩擦使得其动力学方程是关于Lagrange乘子的非线性代数方程组,由于LuGre摩擦模型具有很好的连续性,可将非线性代数方程组与常微分方程组的数值算法(如拟牛顿法和龙格 库塔法)相结合求解其动力学方程.最后,通过数值仿真算例说明了该算法的可行性和有效性,既能很好地反映柱铰链摩擦对系统动力学特性的影响,又能避免Coulomb干摩擦给方程求解带来的困难.     

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.     

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.     

Dynamics analysis of planar multi-DOF mechanism with multiple revolute clearances and chaos identification of revolute clearance joints

Multibody System Dynamics - The clearance joint is one of the important factors which influence system performance and dynamic characteristics. Traditional studies are mainly focused on the planar...     

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.     

Determining power consumption using neural model in multibody systems with clearance and flexible joints

Multibody System Dynamics - Even if today’s manufacturing technology has great advances, clearance between joint parts in a multibody system is inevitable due to the assemblage and relative...     

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.     

Composite rigid body formalism for flexible multibody systems

The paper describes the extension of the composite rigid body formalism for the flexible multibody systems. The extension has been done in such a way that all advantages of the formalism with respect to the coordinates of large motion of rigid bodies are extended to the flexible degrees of freedom, e.g. the same recursive treatment of both coordinates and no appearance of O(n ³) computational complexity terms due to the flexibility. This extension has been derived for both open loop and closed loop systems of flexible bodies. The comparison of the computational complexity of this formalism with other known approaches has shown that the described formalism of composite rigid body and the residual algorithm based on it are more efficient formalisms for small number of bodies in the chains and deformation modes than the usual recursive formalism of articulated body inertia.     

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...     

Interface reduction methods for mechanical systems with elastohydrodynamic lubricated revolute joints

In this contribution, three different reduction methods for elastic structures with lubricated interfaces are presented and compared with each other. While for the first two methods, classical reduction strategies from component mode synthesis are applied, for the third method, a dual reduction basis is used, consisting of vibration modes of the free floating structure, attachment modes and residual modes. Within this new dual approach, it is shown how the residual modes can be obtained by applying pressure distributions of analytical solutions of the hydrodynamic equations. The described methods are compared for two classical simulation example—for a one-sided elastohydrodynamic lubricated joint of a slider–crank mechanism in a floating frame of reference formulation as well as for an elastic rotor in a flexible journal bearing.     

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.     

Nonlinear control of planar multibody systems in shape space

Modeling, reduction, and nonlinear control of planar multibody systems motivated by the classicalcat-fall problem and the practical problem of reorientation of free-floating multibody satellites with rotational joints using angular-momentum-preserving controls is studied. The system model considered is reduced by the first integral (the system angular momentum) resulting in a Hamiltonian system with a configuration space of relative joint angles (shape space). Reconstruction of dynamics is applied to modify the shape-space model and track the phase shift of the absolute angles. An important reachability result is then proved in the unreduced configuration space. Control synthesis can then be found in a feedback form, solving the reorientation problem completely. Surprisingly, the reachability result breaks down in the case of the planar coupled two-body system with zero angular momentum, proving that the cat-fall phenomenon is definitely nonplanar.     

A differential inclusion approach for modeling and analysis of dynamical systems under uncertainty

In this paper we deal with the application of differential inclusions to modeling nonlinear dynamical systems under uncertainty in parameters. In this case, differential inclusions seem to be better suited to modeling practical situations under uncertainty and imprecision than formulations by means of fuzzy differential equations. We develop a practical algorithm to approximate the reachable sets of a class of nonlinear differential inclusion, which eludes the computational problems of a previous set-valued version of the Heun’s method. Our algorithm is based on a complete discretization (time and state space) of the differential inclusion and it suits hardware features, handling the memory used by the method in a controlled fashion during all iterations. As a case of study, we formulate a differential inclusion to model an epidemic outbreak of dengue fever under Cuban conditions. The model takes into account interaction of human and mosquito populations as well as vertical transmission in the mosquito population. It is studied from the theoretical point of view to apply the Practical Algorithm. Also, we estimate the temporal evolution of the different human and mosquito populations given by the model in the Dengue 3 epidemic in Havana 2001, through the computation of the reachable sets using the Practical Algorithm.     

Impacts in multibody systems: modeling and experiments

This paper outlines a novel approach to the modeling and analysis of impact involving multibody systems. This approach is based on an analysis of energy absorption and restitution during impact, using a decomposition of the kinetic energy, which decouples the parts associated with the spaces of admissible and constrained motions of the underlying unilateral constraints. Such a decomposition turns out to be useful in the analysis of energy dissipation during impact, and leads to a generalized definition of the energetic coefficient of restitution, which targets particularly collisions in multibody systems. The applicability of the approach reported is investigated by conducting an experimental study on a robotic testbed. It is shown that impact between multibody systems is considerably affected not only by the local dynamics characteristics of the interacting bodies, but also the configuration of the whole multibody system. The results reported here show that our decomposition can offer a sound characterization of impact in several problems of multibody systems.