Investigation on effect of joint clearance on dynamics of four-bar mechanism

As a result of design, manufacturing and assembly processes or a wear effect, clearances are inevitable at the joints of mechanisms. In this study, dynamic response of mechanism having revolute joints with clearance is investigated. A four-bar mechanism having two joints with clearance is considered as a model mechanism. A neural network was used to model several characteristics of joint clearance. Kinematic and dynamic analyses were achieved using continuous contact mode between journal and bearing. A genetic algorithm was also used to determine the appropriate values of design variables for reducing the additional vibration effect due primarily to the joint clearance. The results show that the optimal adjusting of suitable design variables gives a certain decrease in shaking forces and their moments on the mechanism frame.     

多体系统动力学中关节效应模型的研究进展

在一般的多体系统动力学研究中认为运动关节是理想运动副. 然而,实际中的运动关节不仅含有间隙与摩擦,还有间隙引起的关节元素之间的接触碰撞、局部变形和磨损. 多体系统动力学中的关节效应不仅引起了系统的振动和噪声,减小了系统的可靠性和寿命,而且损失了系统的精度和稳定性. 为此,对近十几年多体系统动力学中关节效应的研究进行了详细分析,总结了关节效应中间隙运动学模型、接触力模型与磨损模型在多体系统动力学中的建模过程. 其中,着重分析了多体系统动力学中关节磨损效应的研究进展,并对常用的Reye'shypothesis 和Archard 磨损模型进行了比较,详细地分析了Archard 磨损模型的演变形式以及主要磨损参数(接触应力,接触面积和滑移距离),特别分析了关键磨损参数接触应力的建模方法,解释了基于Winkler 弹性基础理论在求解接触应力时遇到的困难. 另外,介绍了4 种间隙运动副(转动副、移动副、圆柱副和球面副) 的运动学模型. 分析了考虑关节磨损多体系统动力学模型的一般建模方法,并以平面五杆机构为例说明了其建模过程.最后,简要地展望了多体系统动力学中关节效应模型的发展趋势以及应用前景.      

Modeling 3D revolute joint with clearance and contact stiffness

The clearances in the kinematic joints are due to deformations, wear, and manufacturing errors; the accurate modeling of these effects in multibody analysis is a complex issue but in many practical applications, it is mandatory to take into them into account in order to understand the actual behavior of mechanical systems. In this paper, the authors present a general computer-aided model of a 3D revolute joint with clearance suitable for implementation in multibody dynamic solvers. While a perfect revolute joint imposes kinematic constraints, the proposed revolute joint with clearance leads to a force constraint. The revolute joint has been modeled by introducing a nonlinear equivalent force system, which takes into account the contact elastic deformations. The model depends on the structural and geometrical properties of materials in contact that have been investigated using finite element models. The purpose is to give a general approach to study the influence of actual joints on kinematic, dynamic, and structural behavior of mechanisms. The proposed model has been applied in dynamic simulations of a spatial slider-crank mechanism.     

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.     

Dynamic analysis of planar rigid-body mechanical systems with two-clearance revolute joints

In this paper, the behavior of planar rigid-body mechanical systems due to the dynamic interaction of multiple revolute clearance joints is numerically studied. One revolute clearance joint in a multibody mechanical system is characterized by three motions which are: the continuous contact, the free-flight, and the impact motion modes. Therefore, a mechanical system with n-number of revolute clearance joints will be characterized by 3 ⁿ motions. A slider-crank mechanism is used as a demonstrative example to study the nine simultaneous motion modes at two revolute clearance joints together with their effects on the dynamic performance of the system. The normal and the frictional forces in the revolute clearance joints are respectively modeled using the Lankarani–Nikravesh contact-force and LuGre friction models. The developed computational algorithm is implemented as a MATLAB code and is found to capture the dynamic behavior of the mechanism due to the motions in the revolute clearance joints. This study has shown that clearance joints in a multibody mechanical system have a strong dynamic interaction. The motion mode in one revolute clearance joint will determine the motion mode in the other clearance joints, and this will consequently affect the dynamic behavior of the system. Therefore, in order to capture accurately the dynamic behavior of a multi-body system, all the joints in it should be modeled as clearance joints.     

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?Ccrank 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.     

Fractional Order Control of a Hexapod Robot

This paper studies the performance of integer and fractional order controllers in a hexapod robot with joints at the legs having viscous friction and flexibility. For that objective the robot prescribed motion is characterized in terms of several locomotion variables. The walking performance is analysed through the Nyquist stability criterion and several indices that reflect the system dynamical properties. A set of model-based experiments reveals the influence of the different controller implementations upon the proposed metrics.     

Fractional Order Control of a Hexapod Robot

This paper studies the performance of integer and fractional order controllers in a hexapod robot with joints at the legs having viscous friction and flexibility. For that objective the robot prescribed motion is characterized in terms of several locomotion variables. The walking performance is analysed through the Nyquist stability criterion and several indices that reflect the system dynamical properties. A set of model-based experiments reveals the influence of the different controller implementations upon the proposed metrics.     

Trajectory optimization of a walking mechanism having revolute joints with clearance using ANFIS approach

Clearance as a real joint characteristic leads to deviation from desired trajectory in articulated mechanisms. This phenomenon makes the kinematic and dynamic performances of the mechanism worse. In this study, kinematic analysis of a Jansen’s mechanism used in a walking machine is performed. The model mechanism having two revolute joints with clearance is investigated for the trajectory analysis of the output link. It is clear that the mechanism’s trajectory is very sensitive to the clearance joint characteristics even if the clearance size is small. The adaptive network-based fuzzy inference system (ANFIS) is used to model the characteristics of joints with clearance. By using the suitable design variables and constraints, minimization of the trajectory errors arising from clearance is considered as an optimization problem. Optimization techniques are used to solve this problem for adjusting the optimum values of design variables. The obtained link dimensions show the success of the proposed modeling and optimization approach.     

Modeling of joints with clearance in flexible multibody systems

This paper is concerned with the modeling of joints with clearance within the framework of finite element based dynamic analysis of nonlinear, flexible multibody systems. For actual joints, clearance, lubrication and friction phenomena can significantly affect the dynamic response of the system. In this work, the effects of clearance and lubrication are studied for revolute and spherical joints. The formulation is developed within the framework of energy preserving and decaying time integration schemes that provide unconditional stability for nonlinear, flexible multibody systems. Numerical examples are presented that demonstrate the efficiency and accuracy of the proposed approach. The importance of modeling structural damping and limited driving power are discussed.     

An approach for calculating the dynamic load of deep groove ball bearing joints in planar multibody systems

This study is focused on dynamic modeling of planar multibody systems with multiple deep groove ball bearing joints, in which the radial clearance, contact deformation, and bearing kinematics are included. By using the approach presented, the variation of the joint reaction force and the dynamic load on each ball element in bearings can be simulated. The deep groove ball bearing joints are modeled by introducing a nonlinear force system, which takes into account the contact elastic deformations between the ball elements and the raceways. The contact force is calculated by the Hertzian contact deformation theory that accounts for the geometrical and material properties of the contacting bodies. A planar slider-crank mechanism with two deep groove ball bearing joints is chosen as an example to demonstrate the application of the methodologies presented in this paper. In this model, one bearing locates at the joint between the ground and crank, while the other one locates at the joint between the crank and connecting rod. By numerical calculation, the dynamic load distribution characteristics of bearings under real mechanism movement conditions are simulated. From the results, it can be concluded that the dynamic load on each rolling element varies differently and belongs to a variable load with the change of mechanism configuration. Load characteristic analysis is the foundation of developing research on the fatigue life and reliability of bearings. This study will provide a key mechanical support for the performance evaluation, dynamic design, and geometrical parameter optimization of the joint rolling element bearings.     

Interaction solutions for a reduced extended $$\mathbf{(3}\varvec{+}{} \mathbf{1)}$$ ( 3 + 1 ) -dimensional Jimbo–Miwa equation

Heavy-duty industrial robots have great advantages in the manufacturing industry. Considering the heavy process load and low stiffness of the robot, an accurate and efficient dynamic model plays an important role in the behavior analysis and performance improvement in the robot. This paper presents a novel methodology for the inverse dynamic analysis of the heavy-duty industrial robot with elastic joints. In particular, high-order kinematics and dynamics are concisely deduced using Lie group to deal with elastic joints for the robot inverse dynamic analysis. Meanwhile, position errors of the end-effector due to elastic joints are evaluated through the inverse dynamic analysis when the robot is in heavy-duty applications. Compared with previous approaches, the advantage of proposed method is that new formulas for inverse dynamic analysis are shown to be more concise and computationally efficient using Lie group. Moreover, the position error evaluation method considering dynamic forces is proved to be more accurate than the traditional method when the robot is in the high-speed application. Because of the high computational efficiency and accurate evaluation results, the proposed approach is applicable to trajectory optimization and position error compensation, especially for the robot in heavy-load and high-speed applications.     

Spatial rigid-multibody systems with lubricated spherical clearance joints: modeling and simulation

The dynamic modeling and simulation of spatial rigid-multibody systems with lubricated spherical joints is the main purpose of the present work. This issue is of paramount importance in the analysis and design of realistic multibody mechanical systems undergoing spatial motion. When the spherical clearance joint is modeled as dry contact; i.e., when there is no lubricant between the mechanical elements which constitute the joint, a body-to-body (typically metal-to-metal) contact takes place. The joint reaction forces in this case are evaluated through a Hertzian-based contact law. A hysteretic damping factor is included in the dry contact force model to account for the energy dissipation during the contact process. The presence of a fluid lubricant avoids the direct metal-to-metal contact. In this situation, the squeeze film action, due to the relative approaching motion between the mechanical joint elements, is considered utilizing the lubrication theory associated with the spherical bearings. In both cases, the intra-joint reaction forces are evaluated as functions of the geometrical, kinematical, and physical characteristics of the spherical joint. These forces are then incorporated into a standard formulation of the system’s governing equations of motion as generalized external forces. A spatial four bar mechanism that includes a spherical clearance joint is considered here as an example. The computational simulations are carried out with and without the fluid lubricant, and the results are compared with those obtained when the system is modeled with perfect joints only. From the general results, it is observed that the system’s performance with lubricant effect presents fewer peaks in the kinematic and dynamic outputs, when compared with those from the dry contact joint model.     

Numerical and experimental investigation on multibody systems with revolute clearance joints

A comprehensive combined numerical and experimental study on the dynamic response of a slider-crank mechanism with revolute clearance joints is presented and discussed in this paper to provide an experimental verification and validation of the predictive capabilities of the multibody clearance joint models. This study is supported in an experimental work in a test rig, which consists of a slider-crank mechanism with an adjustable radial clearance at the revolute joint between the slider and the connecting rod. The motion of the slider is measured with a linear transducer and an accelerometer. Dynamic tests at different operating crank speeds and with several clearance sizes are performed. The maximum slider acceleration, associated with the impact acceleration, is used as a measure of the impact severity. The obtained results demonstrate the dynamical behavior of a multibody mechanical system with a clearance joint. Finally, the correlation between the numerical and experimental results is presented and discussed leading to validated models of clearance revolute joints.     

Modeling and analysis of sliding joints with clearances in flexible multibody systems

The modeling of the sliding joint with clearance between a flexible beam and a rigid hole is investigated in this paper. The flexible beam is discretized using the three-dimensional curved Euler–Bernoulli beam element of the Absolute Nodal Coordinate Formulation, while the motion of the rigid hole is described by the Cartesian coordinates. Moreover, the cross sections of both the flexible beam and the rigid hole are assumed to be circular. The existing joints with clearances are mainly rigid joints with small clearances, and the contact detection algorithm adopted can solve only one pair of potential contact points within one section. In order to model the contact problem in the sliding joint with clearance, a new contact detection method based on the intersection of the rigid hole’s cross section and the flexible beam is proposed, which yields a two-dimensional contact detection problem. Based on the common-normal concept, the ellipse–circle contact detection problem within the hole’s cross section can be solved. The potential contact point on the hole’s cross section will be determined, and the closest point projection on the beam’s neutral axis can be defined further. The proposed contact detection method can deal with the sliding joint with large clearance and the multiple-point contact problem within one section. In addition, the penalty method is adopted to model the frictionless contact between the flexible beam and the rigid hole. Finally, two numerical examples about sliding joints with clearances, one with an initially curved beam under gravity and the other with a straight beam under zero gravity, are presented to demonstrate the influence of the clearance of sliding joint on the dynamic performance of flexible multibody systems.     

A comprehensive model for 3D revolute joints with clearances in mechanical systems

Nonlinear Dynamics - A mechanical system with clearance joints is well known as a nonlinear dynamic system that may exhibit chaotic responses under certain conditions. In the previous literature,...     

EFFECT OF Z-PINS＇ DIAMETER, SPACING AND OVERLAP LENGTH ON CONNECTING PERFORMANCE OF CMC SINGLE LAP JOINT

The effect of through-thickness reinforcement by composite pins （Z-pins） on the static tensile strength and failure mechanisms of the joints made from ceramic matrix composite （CMC） is investigated. Overlap length of the single lap joint is 15 mm, 20 mm, 23 mm, 37 mm, and 60 mm, respectively. The experimental results indicate that the final failure modes of the joints can be divided into two groups, （a） the bond-line stops debonding until crack encounters Z-pins; and then the adherends break at the location of Z-pins, when overlap length is more than 20 mm; （b） the bond-line detaches entirely and Z-pins are drawn from adherends, when overlap length is equal to 15 mm. A simple efficient computational approach is presented for analyzing the benefit of through-thickness pins for restricting failure in the single lap joints. Here, the mechanics problem is simplified by representing the effect of the pins by tractions acting on the fracture surfaces of the cracked bond-line. The tractions are prescribed as functions of the crack displacement, which are available in simple forms that summarize the complex deformations to a reasonable accuracy. The resulting model can be used to track the evolution of complete failure mechanisms, for example, bond-line initial delamination and ultimate failure associated with Z-pin pullout, ultimate failure of the adherends. The paper simulates connecting performance of the single lap joints with different Z-pins＇ diameter, spacing and overlap length; the numerical results agree with the experimental results; the numerical results indicate enlarging diameter and decreasing spacing of Z-pins are in favor of improving the connecting performance of the joints. By numerical analysis method, the critical overlap length that lies between two final failure modes is between 18 mm and 19 mm, when Z-pins＇ diameter and spacing are 0.4 mm, 5 mm, respectively.     

EFFECT OF Z-PINS'' DIAMETER, SPACING AND OVERLAP LENGTH ON CONNECTING PERFORMANCE OF CMC SINGLE LAP JOINT

The effect of through-thickness reinforcement by composite pins (Z-pins) on the static tensile strength and failure mechanisms of the joints made from ceramic matrix composite (CMC) is investigated.Overlap length of the single lap joint is 15 mm,20 mm,23 mm,37 mm,and 60 mm,respectively.The experimcntal results indicate that the final failure modes of the joints can be divided into twó groups,(a) the bond-line stops debonding until crack encounters Z-pins;and then the adherends break at the location of Z-pins,when overlap length is more than 20 mm;(b) the bond-line detaches entirely and Z-pins are drawn from adherends,when overlap length is equal to 15 mm.A simple efficient computational approach is presented for analyzing the benefit of through-thickness pins for restricting failure in the single lap joints.Here,the mechanics problem is simplified by representing the effect of the pins by tractions acting on the fracture surfaces of the cracked bond-line.The tractions are prescribed as functions of the crack displacement,which are available in simple forms that summarize the complex deformations to a reasonable accuracy.The resulting model can be used to track the evolution of complete failure mechanisms,for example,bond-line initial delamination and ultimate failure associated with Z-pin pullout,ultimate failure of the adherends.The paper simulates connecting performance of the single lap joints with different Z-pins' diameter,spacing and overlap length;the numerical results agree with the experimental results;the numerical results indicate enlarging diameter and decreasing spacing of Z-pins are in favor of improving the connecting performance of the joints.By numerical analysis method,the critical overlap length that lies between two final failure modes is between 18 mm and 19 mm,when Z-pins' diameter and spacing are 0.4 ram,5 ram,respectively.     

Study of the effect of contact force model on the dynamic response of mechanical systems with dry clearance joints: computational and experimental approaches

The main objective of this work is to present a computational and experimental study on the contact forces developed in revolute clearance joints. For this purpose, a well-known slider-crank mechanism with a revolute clearance joint between the connecting rod and slider is utilized. The intra-joint contact forces that are generated at these clearance joints are computed by considering several different elastic and dissipative approaches, namely those based on the Hertz contact theory and the ESDU tribology-based cylindrical contacts, along with a hysteresis-type dissipative damping. The normal contact force is augmented with the dry Coulomb’s friction force. In addition, an experimental apparatus is used to obtained some experimental data in order to verify and validate the computational models. From the outcomes reported in this paper, it is concluded that the selection of the appropriate contact force model with proper dissipative damping plays a significant role in the dynamic response of mechanical systems involving contact events at low or moderate impact velocities.     

大型网架式可展开空间结构的非线性动力学与控制

我国航天工业迫切需要掌握可入轨后展开的大型网架式空间结构技术,以便研制口径十几米、乃至数十米的大型星载天线。该技术的主要科学基础是这类空间结构展开和服役过程的非线性动力学建模、分析和控制。本文综述了与上述科学基础相关的研究进展,提出应重点关注的三个科学问题：一是大型网架式空间结构展开过程的多柔体系统动力学,尤其是如何对微重力环境下索网的接触和缠绕、运动副内碰撞、结构展开与航天器本体间的耦合等导致的非线性动力学进行建模和分析;二是大型网架式空间结构展开锁定后服役的动力学分析,尤其是如何揭示结构柔性、众多运动副间隙、交变热载荷等因素引起的复杂非线性振动机理;三是大型网架式空间结构展开锁定后服役的动力学控制,尤其是如何在欠驱动、低能耗条件下对非线性振动和波动传播提出有效的控制方法。