Dynamic Analysis for Planar Multibody Mechanical Systems with Lubricated Joints

The dynamic analysis of planar multibody systems with revolute clearance joints, including dry contact and lubrication effects is presented here. The clearances are always present in the kinematic joints. They are known to be the sources for impact forces, which ultimately result in wear and tear of the joints. A joint with clearance is included in the multibody system much like a revolute joint. If there is no lubricant in the joint, impacts occur in the system and the corresponding impulsive forces are transmitted throughout the multibody system. These impacts and the eventual continuous contact are described here by a force model that accounts for the geometric and material characteristics of the journal and bearing. In most of the machines and mechanisms, the joints are designed to operate with some lubricant fluid. The high pressures generated in the lubricant fluid act to keep the journal and the bearing surfaces apart. Moreover, the lubricant provides protection against wear and tear. The equations governing the dynamical behavior of the general mechanical systems incorporate the impact force due to the joint clearance without lubricant, as well as the hydrodynamic forces owing to the lubrication effect. A continuous contact model provides the intra-joint impact forces. The friction effects due to the contact in the joints are also represented. In addition, a general methodology for modeling lubricated revolute joints in multibody mechanical systems is also presented. Results for a slider-crank mechanism with a revolute clearance joint between the connecting rod and the slider are presented and used to discuss the assumptions and procedures adopted.     

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.     

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.     

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.     

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.     

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.     

Experimental investigation of joint clearance effects on the dynamics of a slider-crank mechanism

Clearance is inevitable for assembly and mobility in the kinematic joints of mechanisms. Excessive value of this clearance leads to poor operational characteristics, and these result in losses in kinematic and dynamic performances of mechanism. In this study, effects of joint clearances on vibration and noise characteristics of mechanism are investigated. An experimental test rig has been set up, and a planar slider-crank mechanism having two joints with clearance has been used as a model mechanism. Joint clearance is modeled as a massless virtual link and continuous contact mode between journal and bearing in joint connection is considered in theoretical analyses. Three accelerometers and two microphones have been located at different points to measure the vibrations and noises on system during the mechanism motion. The results obtained for the cases with and without joint clearance are evaluated for vibration and noise characteristics of mechanism.     

考虑含间隙与润滑平面机构的简化算法

为了更快速、高效地确定含润滑铰间间隙对机构动态特性的影响,文中建立了一种新的计算思路.首先,通过理想机构与含间隙机构的运动学模型求出间隙力,进一步把间隙力以主动力的形式带入动力学方程,得到机构的相应动态特性.然后,以含间隙与润滑的曲柄滑块机构为例,基于二状态接触模型与流体润滑模型,对比分析该模型与干摩擦模型,来进一步验证该方法的正确性与可行性.Simulink仿真数据表明,文中建立的模型能有效地抑制机构的振动,动态特性更接近于理想模型,符合实际情况.     

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.     

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.     

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．     

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.     

Numerical investigation of a flexible slider–crank mechanism with multijoints with clearance

This paper aims to study the dynamic behavior of a slider–crank mechanism with flexible components and a multijoint clearance. A numerical investigation was developed for this objective. The mechanism model used for the simulation tests has been performed under MSC ADAMS software using the contact force under the “Impact-function” library. The obtained results illustrate that the mechanism performance is more significantly influenced with multiple joints with clearance. Three contact modes are involved: (i) a continuous contact motion, (ii) a free motion, and (iii) an impact motion. Numerical outcomes prove that the clearance dimension and location have a determinant effect on the slider responses precision. The mechanism reliability decay and a random overall behavior govern the dynamic response along the free flight mode.     

An improved dynamic modeling of a multibody system with spherical joints

A dynamic modeling of multibody systems having spherical joints is reported in this work. In general, three intersecting orthogonal revolute joints are substituted for a spherical joint with vanishing lengths of intermediate links between the revolute joints. This procedure increases sizes of associated matrices in the equations of motion, thus increasing computational burden of an algorithm used for dynamic simulation and control. In the proposed methodology, Euler parameters, which are typically used for representation of a rigid-body orientation in three-dimensional Cartesian space, are employed to represent the orientation of a spherical joint that connects a link to its previous one providing three-degree-of-freedom motion capability. For the dynamic modeling, the concept of the Decoupled Natural Orthogonal Complement (DeNOC) matrices is utilized. It is shown in this work that the representation of spherical joints motion using Euler parameters avoids the unnecessary introduction of the intermediate links, thereby no increase in the sizes of the associated matrices with the dynamic equations of motion. To confirm the efficiency of the proposed representation, it is illustrated with the dynamic modeling of a spatial four-bar Revolute-Spherical–Spherical-Revolute (RSSR) mechanism, where the CPU time of the dynamic modeling based on proposed methodology is compared with that based on the revolute joints substitution. Finally, it is explained how a complex suspension and steering linkage can be modeled using the proposed concept of Euler parameters to represent a spherical joint.     

Investigation of joint clearance effects on welding robot manipulators

In this study, effects of joint clearance on a welding robot manipulator are investigated. Theoretical analysis is performed for different clearance sizes. By using the nonlinear spring-damper characteristic, contact model in revolute joint with clearance is established and the friction effect is performed using the Coulomb friction model. Then the simulation is carried out to investigate the kinematic and dynamic characteristics of the welding robot manipulator with joint clearance. For the case of two different clearance sizes, the results show that the joint clearance causes to degradation of kinematic and dynamic performance of the system. Even if the clearance size is small, it has a crucial role on amplitudes of the end-effector's accelerations and joint forces.     

A methodology for the generation of planar models for multibody chain drives

To overcome the difficulty on building manually complex models of chain drives, this work proposes a comprehensive methodology to build multibody models of any general chain drive automatically from a minimal set of data. The proposed procedure also evaluates the initial positions and velocities of all components of the drive that are consistent with the kinematic joints or with the contact pairs used in the model. In this methodology, all links and sprockets are represented by rigid bodies connected to each other either by ideal or by clearance revolute joints. The clearance revolute joint contact is further extended to handle the contact between the chain rollers and the sprocket teeth exact profiles. A suitable cylindrical continuous contact law is applied to describe the interaction on all contact pairs. One of the complexities of the computational study of roller chain drives is the large number of bodies in the system and the dynamics of the successive engagement and disengagement of the rollers with the sprockets. Each time a roller engages or disengages with a sprocket tooth, the number of rigid bodies in contact changes. The search for the contact pairs is recognized as one of the most time consuming task in contact analysis. This work proposes a procedure to specify the contact pairs and their update during the dynamic analysis optimizing the computational efficiency of the contact search. The methodologies adopted result in a general computer program that is applied and demonstrated in a generic chain drive that can be used in industrial machines, vehicle engines or any other type of mechanical system.     

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...     

Implementation of consequent stabilization method for simulation of multibodies described in absolute coordinates

In this article, we propose methods that increase numerical efficiency of dynamic simulation of spatial multibody systems described in absolute coordinates. The successive coordinate projection method efficiently stabilizes the system constraints in the case when a non-minimal set of orientation coordinates is used to describe the orientation of bodies in space. The new procedure of generation of Newton–Euler equations is shown in detail for systems with the most popular types of joints (prismatic joint, revolute joint, etc.). The proposed algorithms were tested with models of a governor mechanism and Yamaha YZF-R1 motorcycle engine. The simulation results show that the successive coordinate projection method is stable and can be implemented for complex mechanical systems.     

Analytical development of dynamic equations of motion for a three-dimensional flexible link manipulator with revolute and prismatic joints

In this paper, a mathematical model capable of handling a three-dimensional (3D) flexible n-degree of freedom manipulator having both revolute and prismatic joints is considered. This model is used to study the longitudinal, transversal, and torsional vibration characteristics of the robot manipulator and obtain kinematic and dynamic equations of motion. The presence of prismatic joints makes the mathematical derivation complex. In this paper, for the first time, prismatic joints as well as revolute joints have been considered in the structure of a 3D flexible n-degree of freedom manipulator. The kinematic and dynamic equations of motion representing longitudinal, transversal, and torsional vibration characteristics have been solved in parametric form with no discretization. In this investigation, in order to obtain an analytical solution of the vibrational equations, a novel approach is presented using the perturbation method. By solving the equations of motion, it is shown that mode shapes of the link with prismatic joints can be modeled as the equivalent clamped beam at each time instant. As an example, this method is applied to a three degrees of freedom robot with revolute and prismatic joints. The obtained equations are solved using the perturbation method and the results are used to simulate vibrational behavior of the manipulator.