Dynamic modelling and properties analysis of 3RSR parallel mechanism considering spherical joint clearance and wear

The collision and wear caused by inevitable clearance in kinematic pair have an effect on the dynamic characteristics of the mechanism.Therefore,we established the dynamic model of a 3RSR(R is the revolute joint and S is the spherical joint)parallel mechanism with spherical joint clearance based on the modified Flores contact force model and the modified Coulomb friction model using Newton-Euler method.The standard quaternion was introduced in the constraint equation,and the four-order Runge-Kutta method was adopted to solve the 3RSR dynamic model.The simulation results were compared and analyzed with the numerical results.The geometrical parameters of the worn ball socket were solved based on the Archard wear model,and the geometrical reconstruction of the worn surface was carried out.The geometric reconstruction parameters were substituted into the dynamic model,which was to analyze the dynamic response of the 3RSR parallel mechanism with wear and spherical joint clearance.The simulation results show that the irregular wear occurs in the spherical joint with clearance under the presence of the impact and friction force.The long-term wear will increase the fluctuation of the contact force,thereby decreasing the movement stability of the mechanism.

Dynamic Analysis of Four-Bar Beating-up Mechanism with Joint Clearance

For the four-bar beating-up mechanism of air-jet loom,the plain bearing of linkage is the bearing with dynamic load,and is immersed in the lubricant-box.If the joint clearance is considered,the research on linkage movement could be very complicated.In this paper,the kinematic characteristics of four-bar beating-up mechanism with joint clearance were studied by analyzing the trace of journal center and the balance of radial,tangential forces,and bearing load.The region of principal vibration and its forming causes were discussed.And the results could interpret the measuring curves of four-bar beating-up mechanism completely.

Analysis of Robot Accuracy Assessed via its Joint Clearance by Virtual Prototyping Method

This paper discusses how joint clearance influences robot end effectorpositioning accuracy and a robot accuracy analysis approach based on a virtual prototype isproposed. First, a 5-DOF(Degree of freedom) neurosurgery robot was introduced. Then we built itsvirtual prototype, made movement planning and measured the manipulator tip accuracy, through whichthis robot accuracy portrait was obtained. Finally, in order to validate the robot accuracyanalysis approach which is based on a virtual prototype, the result was compared with that from amodel built by robot forward kinematics and robot differential kinematics. The robot accuracyanalysis approach presented in this paper gives a new way to enhance robot design quality , and helpto optimize the control and programming of the robot.

Forward-Kinematics-Based Approaches for Pose Accuracy of Docking Mechanism with Joint Clearance

Joint clearance,as an important stochastic factor,can significantly deteriorate positioning and repeatability accuracies and lower assembly quality of a 6-DOF docking mechanism.Considering pose accuracy with traditional error model that possesses inherent imprecision,both probabilistic and deterministic approaches based on forward kinematics are presented to analyze comprehensive pose error(CPE)in simulation.Results indicate an identical trend emerges for each CPE with both approaches,and both CPEs perform opposite variations as the moving platform upgrades.The findings provide theoretical reference for refinement of assembly quality evaluation of this mechanism.

Experimental Study of the Motion Modes of a Planar Mechanical System with Multi-Clearance Revolute Joints

Clearances in joints of a mechanical multibody system can induce impulsive forces, leading to vibrations that compromise the system’s reliability, stability, and lifespan. Through dynamic analysis, designers can investigate the effects of the clearances on the dynamics of the multibody system. A revolute joint with clearance exhibits three motions which are;free-flight, impact and continuous contact motion modes. Therefore, a multibody system with n-number of revolute clearance joints will exhibit 3n motion modes which are a combination of the three motions in each joint. This study investigates experimentally the nine motion modes in a mechanical system with two revolute clearance joints. A slider crank mechanism has been used as the demonstrative example. We observed that the experimental curve exhibits a greater impact compared to the simulation curve. In conclusion, this experimental investigation offers valuable insights into the dynamics of planar mechanical systems with multiple clearance revolute joints. Utilizing a slider-crank mechanism for data acquisition, the study successfully confirmed seven out of nine motion modes previously identified in numerical research. The missing modes are attributed to inherent complexities in real-world systems, such as journal-bearing misalignment.

An Error Equivalent Model of Revolute Joints with Clearances for Antenna Pointing Mechanisms

Joint clearances in antenna pointing mechanisms lead to uncertainty in function deviation. Current studies mainly focus on radial clearance of revolute joints, while axial clearance has rarely been taken into consideration. In fact, own?ing to errors from machining and assembly, thermal deformation and so forth, practically, axial clearance is inevitable in the joint. In this study, an error equivalent model(EEM) of revolute joints is proposed with considering both radial and axial clearances. Compared to the planar model of revolute joints only considering radial clearance, the journal motion inside the bearing is more abundant and matches the reality better in the EEM. The model is also extended for analyzing the error distribution of a spatial dual?axis("X–Y" type) antenna pointing mechanism of Spot?beam antennas which especially demand a high pointing accuracy. Three case studies are performed which illustrates the internal relation between radial clearance and axial clearance. It is found that when the axial clearance is big enough, the physical journal can freely realize both translational motion and rotational motion. While if the axial clearance is limited, the motion of the physical journal will be restricted. Analysis results indicate that the consideration of both radial and axial clearances in the revolute joint describes the journal motion inside the bearing more precise. To further validate the proposed model, a model of the EEM is designed and fabricated. Some suggestions on the design of revolute joints are also provided.

Dynamic Modeling and Analysis of 4UPS-UPU Spatial Parallel Mechanism with Spherical Clearance Joint

Clearance between the moving joints is unavoidable in real working process. At present, many researches are mainly focused on dynamics of plane revolute joint in plane mechanism, but few on dynamics of spatial spherical joint clearance in spatial parallel mechanism. In this paper, a general method is proposed for establishing dynamic equations of spatial parallel mechanism with spatial spherical clearance by Lagrange multiplier method. The kinematic model and contact force model of the spherical joint clearance were established successively. Lagrange multiplier method was used to deduce the dynamics equation of 4 UPS-UPU mechanism with spherical clearance joint systematically. The influence of friction coefficient on dynamics response of 4 UPS-UPU mechanism with spherical clearance joint was analyzed. Non-linear characteristics of clearance joint and moving platform were analyzed by Poincare map, phase diagram, and bifurcation diagram. The results show that variation of friction coefficient and clearance value had little effect on stability of the mechanism, but the chaotic phenomenon was found at spherical clearance joint. The research has theoretical guiding significance for improving the dynamic performance and avoiding of chaos of parallel mechanisms including spherical joint clearance.

Comparison and analysis of two Coulomb friction models on the dynamic behavior of slider-crank mechanism with a revolute clearance joint

The objective of this study is to investigate the effects of the Coulomb dry friction model versus the modified Coulomb friction model on the dynamic behavior of the slider-crank mechanism with a revolute clearance joint. The normal and tangential forces acting on the contact points between the journal and the bearing are described by using a Hertzian-based contact force model and the Coulomb friction models, respectively.The dynamic equations of the mechanism are derived based on the Lagrange equations of the first kind and the Baumgarte stabilization method. The frictional force is solved via the linear complementarity problem(LCP) algorithm and the trial-and-error algorithm.Finally, three numerical examples are given to show the influence of the two Coulomb friction models on the dynamic behavior of the mechanism. Numerical results show that due to the stick friction, the slider-crank mechanism may exhibit stick-slip motion and can balance at some special positions, while the mechanism with ideal joints cannot.

Dynamics of luffing motion of a hydraulically driven shell manipulator with revolute clearance joints

In this study,a modeling method for investigating the dynamic characteristics of a hydraulically driven shell manipulator with revolute clearance joints is presented.This model accounts for the effect of the clearance,the flexibility of the rotating beam,and the coupled dynamic characteristics of the hydraulic cylinder.A modified contact force model was developed to simulate the physical properties of realistic revolute joints with small clearances,heavy loads,and variable contact stiffnesses and damping coefficients with variations of the indentations.Considering the strong coupling relationship between the hydraulic cylinder and the flexible beam,a system equation of motion combining the state variables of the hydraulic cylinder and mechanical system was established.The complex nonlinear friction force of the hydraulic cylinder motion was constructed using a modified Lu Gre model,and the parameters of the friction model were identified using intelligent identification algorithms.Moreover,a test system for the shell manipulator was established to achieve experimental validation.Finally,the effects of the clearance size and the stiffness of the cylinder support on the dynamic response were investigated.

The compliance contact model of cylindrical joints with clearances

This paper is concerned with the determination of the normal force-displacement （NFD） relation for the contact problem of cylindrical joints with clearance. A simple formulation for this contact problem is developed by modeling the pin as a rigid wedge and the elastic plate as a simple Winkler elastic foundation. The numerical results show that the normal displacement relation based on Hertz theory is only valid for the case of large clearance with a small normal load, and the NFD relation based on Persson theory is only effective in the case of very small clearance. The proposed approximate model in this paper gives better results than Hertz theory and Persson theory in a large range of clearances as seen from the comparison with the results of FEM.

A quantitative analysis method for contact force of mechanism with a clearance joint based on entropy weight and its application in a six-bar mechanism

Contact force in a clearance joint affects the dynamic characteristics and leads to nonlinear response of the mechanism.It is necessary to assess the nonlinearity of contact force quantitatively.Therefore,a new method named contact-force entropy weight is proposed in this paper.This method presents a comprehensive description of the judgment matrix in the X,Y,and Z directions.To assess the influence degrees of different clearances and angular velocities on the contact force,the method is applied to numerical calculation and simulation of a six-bar mechanism with a clearance joint to illustrate its application and investigate the influence degree of angular velocity and clearance on the contact force.By combining the simulation results and theoretical calculations,the influence degrees of different clearances and angular velocities on the contact-force entropy weight of the six-bar mechanism with a clearance joint are revealed.It is found that the angular velocity has a significant influence on the contact force entropy weight of the clearance joint,showing that the contact-force entropy weight is a feasible new method of assessing non-linearity of contact force quantitatively.The method gives a theoretical reference for quantitatively analyzing the nonlinear dynamics.

A comprehensive method for joint wear prediction in planar mechanical systems with clearances considering complex contact conditions

A comprehensive method to predict wear in planar mechanical systems with clearance joints is presented and discussed in this paper.This method consists of a system dynamic analysis and a joint wear prediction.As the size and shape of the clearance are dictated by wear and evolve with the dynamic response of the system,the contact between the journal and bearing could be conformal or non-conformal,which makes the contact conditions in clearance joints quite complicated.Therefore a modified contact force model is employed to evaluate the joint reaction force in this study.As the nonlinear stiffness coefficient is related to the physical and geometrical properties of contact bodies and varies with the deformation,this contact force model is applicable to different contact conditions between the journal and bearing.Furthermore,based on the Archard’s wear model,the amount of wear can be quantified in the joint.And the geometry is updated to reflect the evolving contact boundary.Then,the wear process and the contact force model are integrated into the motion equations of the system to perform coupled iterative analyses between system dynamic response and joint wear prediction.In addition,a slider-crank mechanism is simulated as an example to demonstrate efficiency of the proposed method and to carry out a parametric study on mechanical systems considering joint wear.The influence of clearance size and driving power are discussed and compared respectively.The index of concordance is introduced to quantify contributions of contact pressure and sliding distance to wear rate under different types of journal motion.This study could help to predict joint wear in mechanical systems with clearances and optimize mechanisms in design.

Wear analysis of revolute joints with clearance in multibody systems

In this work, the prediction of wear for revolute joint with clearance in multibody systems is investigated using a computational methodology. The contact model in clearance joint is established using a new hybrid nonlinear contact force model and the friction effect is considered by using a modified Coulomb friction model. The dynamics model of multibody system with clearance is established using dynamic segmentation modeling method and the computational process for wear analysis of clearance joint in multibody systems is presented. The main computational process for wear analysis of clearance joint includes two steps, which are dynamics analysis and wear analysis. The dynamics simulation of multibody system with revolute clearance joint is carried out and the contact forces are drawn and used to calculate the wear amount of revolute clearance joint based on the Archard's wear model. Finally, a four-bar multibody mechanical system with revolute clearance joint is used as numerical example application to perform the simulation and show the dynamics responses and wear characteristics of multibody systems with revolute clearance joint. The main results of this work indicate that the contact between the joint elements is wider and more frequent in some specific regions and the wear phenomenon is not regular around the joint surface, which causes the clearance size increase non-regularly after clearance joint wear. This work presents an effective method to predict wear of revolute joint with clearance in multibody systems.

An improved practical model for wear prediction of revolute clearance joints in crank slider mechanisms

A stationary clearance link algorithm(SCLA)for calculating the reaction-force of revolute clearance joints in crank slider mechanisms is proposed in this paper.The SCLA is more efficient than other algorithms of the same accuracy.Furthermore,based on the Winkler foundation model,an unsymmetrical Winkler foundation model and a double elastic layer Winkler model are proposed.By integrating a dynamic model and the unsymmetrical Winkler foundation model with Archard wear model,an improved integrated wear prediction model is also generated.A series of experiments have been performed to compare with the predicted analysis data,and the results showed a good agreement.As a real industry application,with the double elastic layer Winkler model,the integrated wear prediction model was successfully used to predict the wear depth of the joint bearing(bimetallic bearing)for the cantilever crane of a concrete pump truck of Sany Heavy Industry.

Parameter optimization for torsion spring of deployable solar array system with multiple clearance joints considering rigid–flexible coupling dynamics

In this paper,four novel evaluation indices and corresponding hierarchical optimization strategies are proposed for a deployable solar array system considering panel flexibility and joint clearance.The deployable solar array model consists of a rigid main-body,two panels and four key mechanisms,containing torsion spring mechanism,closed cable loop mechanism,latch mechanism and attitude adjustment mechanism.Rigid and flexible components are established by Nodal Coordinate Formulation and Absolute Nodal Coordinate Formulation,respectively.The clearance joint model is described by nonlinear contact force model and amendatory Coulomb friction model.The latch time,stabilization time,maximum contact force and impulse sum of the contact force of the solar array system are selected as the four novel evaluation indices to represent the complex dynamic responses of a deployable solar array with clearance joints instead of the lock torque widely used in conventional works.To eliminate the gross errors caused by the nonlinear and nonsmooth mechanical properties,a hierarchical optimization strategy based on an adaptive simulated annealing algorithm and a nondominated sorting genetic algorithm is adopted for the solar array system with clearance joints.Results indicate that the effects of panel flexibility on the evaluation index responses and design optimization of the solar array system cannot be neglected.Besides,increasing the weight factor of the stabilization time index of the rigid system may compensate for the differences in optimal results of the rigid–flexible coupling system.That may provide some references for optimization design of deployable space mechanisms considering clearance joints.

Numerical and experimental study on dynamics of the planar mechanical system considering two revolute clearance joints

Due to assembly,wear and manufacturing errors and clearance in the joints are inevitable.When the clearance is introduced into a mechanical system,the impact force in the clearance joint will cause undesirable vibration of the system.In this paper,the dynamic responses of the mechanical system with two revolute clearance joints are studied using computational and experimental methodology.The clearance joint is considered as force constraint.The normal contact force and tangential friction force between the journal and bearing in a clearance joint are modeled using a nonlinear contact force model considering energy loss and a modified Coulomb friction model considering a dynamic friction coefficient,respectively.A planar slider-crank mechanism with two revolute clearance joints is used to implement the study.The dynamic responses obtained from numerical simulation are compared with the experimental test.Numerical simulations and experimental tests for different clearance sizes and crank speeds are presented and discussed,respectively.The simulation results agree quite well with those of the experiment for different cases,which proves the accuracy and efficiency of the computational method for dynamics analysis of the mechanical system with two revolute clearance joints in this study.The investigation indicates that the clearances in revolute joints significantly affect the dynamic characteristics of mechanical systems,which must be considered in the precision analysis,design,and control of multibody systems,especially for high-speed machinery.

A review of friction models in interacting joints for durability design

This paper presents a comprehensive review of friction modelling to provide an understanding of design for durability within interacting systems.Friction is a complex phenomenon and occurs at the interface of two components in relative motion.Over the last several decades,the effects of friction and its modelling techniques have been of significant interests in terms of industrial applications.There is however a need to develop a unified mathematical model for friction to inform design for durability within the context of varying operational conditions.Classical dynamic mechanisms model for the design of control systems has not incorporated friction phenomena due to non-linearity behaviour.Therefore,the tribological performance concurrently with the joint dynamics of a manipulator joint applied in hazardous environments needs to be fully analysed.Previously the dynamics and impact models used in mechanical joints with clearance have also been examined.The inclusion of reliability and durability during the design phase is very important for manipulators which are deployed in harsh environmental and operational conditions.The revolute joint is susceptible to failures such as in heavy manipulators these revolute joints can be represented by lubricated conformal sliding surfaces.The presence of pollutants such as debris and corrosive constituents has the potential to alter the contacting surfaces,would in turn affect the performance of revolute joints,and puts both reliability and durability of the systems at greater risks of failure.Key literature is identified and a review on the latest developments of the science of friction modelling is presented here.This review is based on a large volume of knowledge.Gaps in the relevant field have been identified to capitalise on for future developments.Therefore,this review will bring significant benefits to researchers,academics and industry professionals.

Adhesion and surface forces in polymer tribology——A review

Polymer tribology is a fast growing area owing to increasing applications of polymers and polymer composites in industry, transportation, and many other areas of economy. Surface forces are very important for polymer contact, but the real origin of such forces has not been fully investigated. Strong adhesive interaction between polymers leads to an increase in the friction force, and hence, the asperities of the material may be removed to form wear particles or transfer layers on the counterface. The theory of polymer adhesion has not been completely elucidated yet and several models of adhesion have been proposed from the physical or chemical standpoints. This paper is focused on the research efforts on polymer adhesion with emphasis on adhesion mechanisms, which are very important in the analysis of polymer friction and wear.

Tribological behaviors of Ni-modified citric acid carbon quantum dot particles as a green additive in polyethylene glycol

A novel green lubricating oil additive(carbon quantum dot(CQD)particle‐doped nickel(Ni‐CQD))was synthesized from citric acid and nickel acetate.The effects of CQD and Ni‐CQD nanoparticles on the tribological behaviors of polyethylene glycol(PEG200)were investigated under different loads and reciprocation speeds.The results indicate that CQD and Ni‐CQD particles can both enhance the lubrication properties of PEG200.However,the Ni‐CQD nanoparticles enhanced the lubrication properties more than the plain CQD particles did.The average friction coefficient and wear rate of PEG200 containing 2 wt%Ni‐CQDs were reduced by 35.5%and 36.4%,respectively,compared to PEG200 containing pure CQDs under a load of 8 N and reciprocation speed of 25 mm/s over 60 min.The friction and wear mechanisms are attributed to the fact that friction induces the Ni‐CQDs to participate in the formation of a tribofilm,resulting in a low friction coefficient and wear rate.