Dynamic Response and Nonlinear Characteristics of Spatial Parallel Mechanism With Spherical Clearance Joint

2019 ◽  
Vol 14 (4) ◽  
Author(s):  
Chen Xiulong ◽  
Li Yuewen ◽  
Jia Yonghao
Keyword(s):  
Dynamic Response ◽  
Contact Force ◽  
Dynamic Equation ◽  
Parallel Mechanism ◽  
Joint Clearance ◽  
Spherical Joint ◽  
Nonlinear Characteristics ◽  
Clearance Joint ◽  
Spatial Parallel Mechanism ◽  
Moving Platform

Spherical joint is a type of common kinematic pair in spatial parallel mechanism. The existence of spherical joint clearance has many adverse effects on the mechanism. A method of forecasting the dynamic behaviors of spatial parallel mechanism with spherical clearance joint is proposed. The 4-UPS-UPU spatial parallel mechanism with spherical clearance is taken as the research object, the dynamic response, and nonlinear characteristics of the mechanism are studied. The kinematic model and the contact force model of the spherical clearance are established. The dynamic equation of the spatial parallel mechanism with spherical joint clearance is derived by Newton–Euler method. The above-mentioned dynamic equation is solved by using the ODE113 function that is based on a variable order numerical differential algorithm in matlab. The dynamic responses of moving platform with different clearance values are analyzed. The contact force and the center trajectory of the sphere at the spherical joint are obtained. In addition, the phase trajectory, Poincare map, and bifurcation diagram are analyzed, and the nonlinear characteristics of the spherical clearance joint and the moving platform are obtained. By comparing the results, such as the acceleration of moving platform and the contact force, with virtual prototype simulation, the correctness of the dynamic equation of the spatial parallel mechanism with spherical clearance joint and the analysis results are verified. The researches show that the change of clearance value has a great influence on the motion state of spherical clearance joint, and chaos phenomena appears in the clearance joint with the increase in the clearance value. And the impact phenomenon appears between the spherical joint elements, which makes the mechanism generated vibration.

scholarly journals Dynamics Analysis of Spatial Parallel Mechanism with Irregular Spherical Joint Clearance

2019 ◽  
Vol 2019 ◽  
pp. 1-21
Author(s):  
Xiulong Chen ◽  
Yuewen Li
Keyword(s):  
Dynamic Response ◽  
Contact Force ◽  
Parallel Mechanism ◽  
Euler Method ◽  
Joint Clearance ◽  
Force Model ◽  
Wear Depth ◽  
Spherical Joint ◽  
Spatial Parallel Mechanism ◽  
Dynamic Wear

Clearances caused by machining accuracy and assembly requirements are regular, but they will be irregular due to the wear of the kinematic pairs. At present, there are few studies on wear of space kinematic pairs. In order to grasp the effect of irregular spherical joint clearance after wear on the dynamic response, a method for solving irregular clearance problems based on the Newton–Euler method is proposed, and the dynamic response of 4-UPS-UPU spatial parallel mechanism with irregular spherical joint clearance is investigated. The kinematic model and contact force model of the clearance of the spherical joint are derived. The dynamic model of the mechanism with spherical joint clearance is established by the Newton–Euler method. Based on the Archard model, the three-dimensional dynamic wear model for spherical joint with clearances is developed. The wear depth and wear position of the spherical joint are obtained by the numerical solution. The method of reconstructing the geometric morphology after wear is proposed based on the finite element thought. The solution of the irregular clearance problem is put forward, and the dynamic response of the mechanism after wear is also analyzed. The results show that the dynamic response curves of the mechanism fluctuate around the ideal curves whether before wear or after wear. Compared with the regular clearance before wear, the results of the irregular clearance after wear have a greater impact on acceleration and contact force, and the vibration of the acceleration and contact force curve become more intense than before. Moreover, the displacement, velocity, and acceleration curves of the irregular clearance show some hysteresis than that before wear. Therefore, it can be inferred that the irregular clearance has more adverse effects on the mechanism and aggravates the wear between the elements of the kinematic joint; in addition, the stability and the reliability of the mechanism can be reduced.

scholarly journals Dynamic response analysis for multi-degrees-of-freedom parallel mechanisms with various types of three-dimensional clearance joints

2021 ◽  
Vol 18 (3) ◽  
pp. 172988142110177
Author(s):  
Jia Yonghao ◽  
Chen Xiulong
Keyword(s):  
Dynamic Response ◽  
Multibody Systems ◽  
Parallel Mechanism ◽  
Three Dimensional ◽  
Response Analysis ◽  
Parallel Mechanisms ◽  
Dynamics Model ◽  
Clearance Joints ◽  
Clearance Joint ◽  
Spatial Parallel Mechanism

For spatial multibody systems, the dynamic equations of multibody systems with compound clearance joints have a high level of nonlinearity. The coupling between different types of clearance joints may lead to abundant dynamic behavior. At present, the dynamic response analysis of the spatial parallel mechanism considering the three-dimensional (3D) compound clearance joint has not been reported. This work proposes a modeling method to investigate the influence of the 3D compound clearance joint on the dynamics characteristics of the spatial parallel mechanism. For this purpose, 3D kinematic models of spherical clearance joint and revolute joint with radial and axial clearances are derived. Contact force is described as normal contact and tangential friction and later introduced into the nonlinear dynamics model, which is established by the Lagrange multiplier technique and Jacobian of constraint matrix. The influences of compound clearance joint and initial misalignment of bearing axes on the system are analyzed. Furthermore, validation of dynamics model is evaluated by ADAMS and Newton–Euler method. This work provides an essential theoretical basis for studying the influences of 3D clearance joints on dynamic responses and nonlinear behavior of parallel mechanisms.

The effect of joint clearance on the dynamic behavior of a needle driver mechanism in a typical sewing machine

2017 ◽  
Vol 29 (4) ◽  
pp. 578-593
Author(s):  
Esmaeil Salahshoor ◽  
Saeed Ebrahimi
Keyword(s):  
Dynamic Response ◽  
Dynamic Behavior ◽  
Contact Force ◽  
Reaction Force ◽  
Joint Clearance ◽  
Sewing Machine ◽  
Content Type ◽  
Needle Driver ◽  
Clearance Joint ◽  
Penetration Force

Purpose The purpose of this paper is to investigate the effect of joint clearance on the behavior of a needle driver mechanism (a slider-crank linkage) of a typical sewing machine with an imperfect joint between the coupler and the slider (including needle). Design/methodology/approach In order to model the clearance, the momentum exchange approach is used. The Lankarani and Nikravesh’s continuous contact force model is used to model the contact force, and the modified Coulomb’s friction law represents the friction between sliding members. The penetration force applied on the needle by fabric is chosen based on an experimental data in the literature. The dynamic response is validated for the existing properties in the literature without considering the penetration force. Findings It is shown that the clearance joint made considerable effect on the dynamic response of the system. The rough changes of the needle acceleration and jerk are obvious. The base reaction force changed roughly and did not vary as smooth as that of the mechanism with ideal joint. So, clearance joint in the mechanism could lead to an undesirable vibration in the system. Furthermore, the crank driver must provide a non-smooth moment on the crank to keep the crank rotational velocity constant. Moreover, reducing the clearance size sufficiently could make the dynamic response closer to that of the mechanism with ideal joint. In addition, smoother crank moment could be required if the clearance size is reduced sufficiently. Furthermore, the rough change of the base reaction force which can represent the vibration caused by the mechanism on the fixed frame could be reduced if the clearance size is small enough. Originality/value Lockstitch sewing machine is one of the most common apparel industrial machines. The needle driver mechanism of a sewing machine could have an important role for proper stitch forming. On the other hand, clearances are inevitable in assemblage of mechanisms to allow the relative motion between the members. This clearance is due to machining tolerances, wear, material deformations, and imperfections, and it can worsen mechanism performance such as precision, dynamic behavior and vibration. Unfortunately, despite the importance of the dynamic behavior of the needle driver mechanism from practical point of view, very little publications have focused especially on the investigation of the effect of clearance joint on the dynamic behavior of the sewing machine which could lead to undesired vibration of the system and shorter lifetime as a result. In this paper, the dynamic behavior of the system including, needle velocity and acceleration, crank moment and base reaction force was compared with that of the ideal mechanism. Finally, the effect of clearance size on the dynamic behavior of the system was investigated.

Dynamics Model of 4-SPS/CU Parallel Mechanism With Spherical Clearance Joint and Flexible Moving Platform

2017 ◽  
Vol 140 (2) ◽  
Author(s):  
Gengxiang Wang ◽  
Hongzhao Liu
Keyword(s):  
Parallel Mechanism ◽  
Dynamic Performance ◽  
Friction Model ◽  
Contact Forces ◽  
Flexible Body ◽  
Force Model ◽  
Spherical Joint ◽  
Dynamics Model ◽  
Clearance Joint ◽  
Moving Platform

Effects of flexible body and clearance spherical joint on the dynamic performance of 4-SPS/CU parallel mechanism are analyzed. The flexible moving platform is treated as thin plate based on absolute nodal coordinate formulation (ANCF). In order to formulate the parallel mechanism's constraint equations between the flexible body and the rigid body, the tangent frame is introduced to define the joint coordinate. One of the spherical joints between moving platform and kinematic chains is introduced into clearance. The normal and tangential contact forces are calculated based on Flores contact force model and modified Coulomb friction model. The dynamics model of parallel mechanism with clearance spherical joint and flexible moving platform is formulated based on equation of motion. Simulations show that the dynamic performance of parallel mechanism is not sensitive to the flexible body because of the inherent property of moving platform; however, when the clearance spherical joint is considered into the parallel mechanism with flexible body, the flexible moving platform exhibits cushioning effect to absorb the energy caused by clearance joint.

Three-Dimensional Wear Prediction of Four-Degrees-of-Freedom Parallel Mechanism With Clearance Spherical Joint and Flexible Moving Platform

2018 ◽  
Vol 140 (3) ◽  
Author(s):  
Gengxiang Wang ◽  
Hongzhao Liu
Keyword(s):  
Contact Force ◽  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Contact Forces ◽  
Force Model ◽  
Spherical Joint ◽  
Normal Contact ◽  
Tangential Contact ◽  
Moving Platform

Three-dimensional (3D) wear of the clearance spherical joint in four-degrees-of-freedom (DOF) parallel mechanism is predicted based on Archard's wear model. The flexible moving platform is treated as thin plate element based on absolute nodal coordinate formulation (ANCF). The tangent frame is introduced to formulate the constraint equation of universal joint. One of the spherical joints is treated as clearance joint. The normal and tangential contact forces are calculated based on Flores contact force model and modified Coulomb friction model. In order to predict 3D wear, the normal contact force, tangential contact velocity, and eccentricity vector are decomposed in the global coordinate system. Simulation results show that 3D wear occurred in three directions are not uniform each other.

Effects of Spherical Clearance Joint on Dynamics of Redundant Driving Spatial Parallel Mechanism

Robotica ◽  
2020 ◽  
pp. 1-17
Author(s):  
Xiulong Chen ◽  
Jingyao Guo
Keyword(s):  
Dynamic Characteristics ◽  
Parallel Mechanism ◽  
Dynamic Responses ◽  
Joint Clearance ◽  
Parallel Mechanisms ◽  
Spherical Joint ◽  
Ideal Situation ◽  
Spatial Parallel Mechanism ◽  
Redundant Drive ◽  
The Ideal

SUMMARY This paper proposes a dynamic modeling method of redundant drive spatial parallel mechanism, dynamics of 4-UPS-RPU redundant driving spatial parallel mechanism considering spherical joint clearance are analyzed. The dynamic equation of spherical joint clearance with Lagrange multiplier is built. The influences of single clearance and multiple clearances on dynamic responses of redundant drive spatial parallel mechanisms are analyzed under different clearance values. The results show that the dynamic characteristics of the mechanism with single clearance are basically consistent with the ideal situation, and the dynamic characteristics of the mechanism with multi-clearance are significantly different from the ideal situation.

A DOE- and Kriging-Based Model for Studying on the Dynamics of Multibody Mechanical Systems With Revolute Joint Clearance

2013 ◽  
Author(s):  
Zhenhua Zhang ◽  
Liang Xu ◽  
Paulo Flores ◽  
Hamid M. Lankarani
Keyword(s):  
Simulation Model ◽  
Mechanical System ◽  
Contact Force ◽  
Design Parameter ◽  
Joint Clearance ◽  
Design Parameters ◽  
Force Model ◽  
Revolute Joint ◽  
Clearance Joint ◽  
Contact Force Model

Over the last two decades, extensive work has been conducted on dynamic effect of joint clearances in multibody mechanical systems. In contrast, little work has been devoted to optimizing the performance of these systems. In this study, analysis of revolute joint clearance is formulated in term of a Hertzian-based contact force model. For illustration, the classical slider-crank mechanism with a revolute clearance joint at the piston pin is presented, and a simulation model is developed using the analysis/design code MSC.ADAMS. The clearance is modeled as a pin-in-a-hole surface-to-surface dry contact, with appropriate contact force model between the joint and bearing surfaces. Different simulations are performed to demonstrate the influence of the joint clearance size and the input crank speed on the dynamic behavior of the system with the clearance joint. An innovative design-of-experiment (DOE)-based method for optimizing the performance of a mechanical system with the revolute joint clearance for different ranges of design parameters is then proposed. Based on the simulation model results from sample points, which are selected by a Latin hypercube sampling (LHS) method, a polynomial function Kriging meta-model is established instead of the actual simulation model. The reason for development and use of the meta-model is to bypass computationally intensive simulations of a computer model for different design parameter values in place of a more efficient and cost-effective mathematical model. Finally, numerical results obtained from two application examples, considering the different design parameters, including the joint clearance size, crank speed, and contact stiffness, are presented for further analyzing the dynamics of the revolute clearance joint in a mechanical system. This allows for predicting the influence of design parameter changes, in order to minimize contact forces, accelerations, and power requirements due to the existence of joint clearance.

scholarly journals A Kriging Model for Dynamics of Mechanical Systems With Revolute Joint Clearances

2014 ◽  
Vol 9 (3) ◽  
Author(s):  
Zhenhua Zhang ◽  
Liang Xu ◽  
Paulo Flores ◽  
Hamid M. Lankarani
Keyword(s):  
Simulation Model ◽  
Contact Force ◽  
Design Parameter ◽  
Joint Clearance ◽  
Design Parameters ◽  
Force Model ◽  
Revolute Joint ◽  
Clearance Joint ◽  
Contact Force Model ◽  
Joint Clearances

Over the past two decades, extensive work has been conducted on the dynamic effect of joint clearances in multibody mechanical systems. In contrast, little work has been devoted to optimizing the performance of these systems. In this study, the analysis of revolute joint clearance is formulated in terms of a Hertzian-based contact force model. For illustration, the classical slider-crank mechanism with a revolute clearance joint at the piston pin is presented and a simulation model is developed using the analysis/design software MSC.ADAMS. The clearance is modeled as a pin-in-a-hole surface-to-surface dry contact, with an appropriate contact force model between the joint and bearing surfaces. Different simulations are performed to demonstrate the influence of the joint clearance size and the input crank speed on the dynamic behavior of the system with the joint clearance. In the modeling and simulation of the experimental setup and in the followed parametric study with a slightly revised system, both the Hertzian normal contact force model and a Coulomb-type friction force model were utilized. The kinetic coefficient of friction was chosen as constant throughout the study. An innovative design-of-experiment (DOE)-based method for optimizing the performance of a mechanical system with the revolute joint clearance for different ranges of design parameters is then proposed. Based on the simulation model results from sample points, which are selected by a Latin hypercube sampling (LHS) method, a polynomial function Kriging meta-model is established instead of the actual simulation model. The reason for the development and use of the meta-model is to bypass computationally intensive simulations of a computer model for different design parameter values in place of a more efficient and cost-effective mathematical model. Finally, numerical results obtained from two application examples with different design parameters, including the joint clearance size, crank speed, and contact stiffness, are presented for the further analysis of the dynamics of the revolute clearance joint in a mechanical system. This allows for predicting the influence of design parameter changes, in order to minimize contact forces, accelerations, and power requirements due to the existence of joint clearance.

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