Dynamic simulation of a parallel robot: Coulomb friction and stick–slip in robot joints

Robotica ◽  
2009 ◽  
Vol 28 (1) ◽  
pp. 35-45 ◽  
Author(s):  
Nidal Farhat ◽  
Vicente Mata ◽  
Álvaro Page ◽  
Miguel Díaz-Rodríguez
Keyword(s):  
Dynamic Simulation ◽  
Coulomb Friction ◽  
Parallel Robot ◽  
Friction Model ◽  
Robotic Systems ◽  
Stick Slip ◽  
Integration Interval ◽  
Simulation Process ◽  
Coulomb Friction Model ◽  
And Control

SUMMARYDynamic simulation in robotic systems can be considered as a useful tool not only for the design of both mechanical and control systems, but also for planning the tasks of robotic systems. Usually, the dynamic model suffers from discontinuities in some parts of it, such as the use of Coulomb friction model and the contact problem. These discontinuities could lead to stiff differential equations in the simulation process. In this paper, we present an algorithm that solves the discontinuity problem of the Coulomb friction model without applying any normalization. It consists of the application of an external switch that divides the integration interval into subintervals, the calculation of the friction force in the stick phase, and further improvements that enhance its stability. This algorithm can be implemented directly in the available commercial integration routines with event-detecting capability. Results are shown by a simulation process of a simple 1-DoF oscillator and a 3-DoF parallel robot prototype considering Coulomb friction in its joints. Both simulations show that the stiffness problem has been solved. This algorithm is presented in the form of a flowchart that can be extended to solve other types of discontinuity.

Asperity Spring Friction Model With Application to Belt-Drives

2003 ◽  
Author(s):  
Tamer M. Wasfy
Keyword(s):  
Finite Element ◽  
Coulomb Friction ◽  
Friction Model ◽  
Belt Drive ◽  
Finite Element Code ◽  
Time Step ◽  
Stick Slip ◽  
Normal Contact ◽  
Belt Drives ◽  
Coulomb Friction Model

An asperity spring friction model that uses a variable anchor point spring along with a velocity dependent force is presented. The model is incorporated in an explicit timeintegration finite element code. The friction model is used along with a penalty-based normal contact model to simulate the dynamic response of a two-pulley belt-drive system. It is shown that the present friction model accurately captures the stick-slip behavior between the belt and the pulleys using a much larger time-step than a pure velocity-dependent approximate Coulomb friction model.

Studies of Stick-Slip Friction, Presliding Displacement, and Hunting

2000 ◽  
Vol 124 (1) ◽  
pp. 111-117 ◽  
Author(s):  
Ruh-Hua Wu ◽  
Pi-Cheng Tung
Keyword(s):  
Coulomb Friction ◽  
High Speed ◽  
Experimental Studies ◽  
Friction Model ◽  
Smooth Transition ◽  
Stick Slip ◽  
Modified Model ◽  
Cyclic Motion ◽  
Coulomb Friction Model ◽  
The Stability

This paper presents the studies of stick-slip friction, presliding displacement and its influence on hunting. Experimental studies reveal that presliding displacement could affect the stability of hunting. A modified Coulomb friction model integrating presliding displacement in the microsliding regime is proposed to demonstrate such effect. Finally, step responses obtained from experiments and from the modified model are compared. These comparisons yield the conclusion that the transition of friction between the sticking state and the sliding state is smooth and continuous, not abrupt. Such a smooth transition of friction is critical to the studies of systems performing high-speed cyclic motion.

Dynamic Analysis of Planar Mechanical Systems With Clearance Joint Based on LuGre Friction Model

2018 ◽  
Vol 13 (6) ◽  
Author(s):  
Xiao Tan ◽  
Guoping Chen ◽  
Dongyang Sun ◽  
Yan Chen
Keyword(s):  
Contact Force ◽  
Coulomb Friction ◽  
Friction Model ◽  
Stick Slip ◽  
Stribeck Effect ◽  
Revolute Clearance Joint ◽  
Lugre Friction Model ◽  
Clearance Joint ◽  
Lugre Friction ◽  
Coulomb Friction Model

A computational methodology to model and analyze planar rigid mechanical system with stick–slip friction in revolute clearance joint is presented. In this work, the LuGre friction model, which captures the Stribeck effect and spring-like characteristics for stiction, is employed to estimate the stick–slip friction in revolute clearance joint. A hybrid contact force model, combining Lankarani–Nikravesh model, and improved elastic foundation model, is used to establish contact model. The generalized-α method, which can dissipate the spurious high-frequency responses caused by the strongly nonlinear contact force and friction in numerical simulation, is adopted to solve the equations of motion and make the result closer to the physics of the problem. A slider-crank mechanism with revolute clearance joint based on LuGre friction model and modified coulomb friction model are simulated, respectively, and utilized to discuss the influences of the Stribeck effect and stiction on dynamic behavior of the mechanism. Different test scenarios are considered to investigate the effects of the clearance size and friction coefficient on the dynamic response of the mechanism. The results show that the mechanism based on LuGre friction model has better energy dissipation characteristics, while there are stiction phenomena of the contacting surfaces in many cases. When the relative velocity is zero or close to zero, the contact force of mechanism based on the LuGre friction model is significantly lower than that based on the modified coulomb friction model. Clearance size and friction coefficient obviously affect dynamic behavior of the mechanism.

Analysis, Design, and Modeling of a Rotary Vane Engine (RVE)

2004 ◽  
Vol 126 (4) ◽  
pp. 711-720 ◽  
Author(s):  
B. V. Librovich ◽  
A. F. Nowakowski
Keyword(s):  
Coulomb Friction ◽  
Simple Structure ◽  
Dynamical Behavior ◽  
Friction Model ◽  
Reciprocating Engine ◽  
Torque Transmission ◽  
Analysis Design ◽  
Work Units ◽  
Coulomb Friction Model ◽  
Moving Parts

This paper introduces a mathematical model to analyze the dynamic behavior of a novel rotary vane engine (RVE). The RVE can be considered to have a number of advantages when compared to a majority of other reciprocating engine types. The advantages are found in the simple structure and the small number of moving parts. In this paper the geometrical structure and dynamical behavior of engines with a different number of work units is considered in detail. This has been examined through a study of torque transmission with a particular reference to how this is affected by the noncircular geometry of gear pitch curves. Using the Coulomb friction model, consideration has been given to the mechanical power loss due to friction in different parts of the engine, which must be taken into account. The study also proposes a possible method for balancing of asymmetric cogwheels. The analysis concludes that by using an appropriate design and arrangement of cogwheels and all moving parts, vibration can be attenuated due to impulsive gas torque.

Control for Robots With Braking Actuators in a Uniform Force Field

2015 ◽  
Author(s):  
Erlend Framstad ◽  
Mark D. Bedillion
Keyword(s):  
Force Field ◽  
Control Strategy ◽  
Coulomb Friction ◽  
Energy Equation ◽  
High Accuracy ◽  
Friction Model ◽  
Second Law ◽  
Inclined Plane ◽  
Position And Orientation ◽  
Coulomb Friction Model

This paper concerns the control strategy of a robot with controllable brakes placed in a uniform force field. Without loss of generality this force field is assumed to be gravity, and the robot to be an object resting on an inclined plane. The controller’s objective is then to use the brakes to lead the robot into a desired position and orientation. The system’s dynamics were derived from Newton’s second law with a Coulomb friction model. The controller was derived from geometric properties and the energy equation. The controller was then tested using Matlab and Simulink on the dynamics that were derived. The results of the simulation shows high accuracy even with some disturbances, and uncalibrated parameters.

scholarly journals Recent Developments and Trends in the Friction Testing for Conventional Sheet Metal Forming and Incremental Sheet Forming

Metals ◽  
2019 ◽  
Vol 10 (1) ◽  
pp. 47 ◽  
Author(s):  
Tomasz Trzepiecinski ◽  
Hirpa G. Lemu
Keyword(s):  
Sheet Metal ◽  
Sheet Metal Forming ◽  
Metal Forming ◽  
Coulomb Friction ◽  
Sheet Forming ◽  
Friction Model ◽  
Friction Resistance ◽  
Friction Testing ◽  
Coulomb Friction Model

Friction is the main phenomenon that has a huge influence on the flow behavior of deformed material in sheet metal forming operations. Sheet metal forming methods are one of the most popular processes of obtaining finished products, especially in aerospace, automobile, and defense industries. Methods of sheet forming are carried out at different temperatures. So, it requires tribological tests that suitably represent the contact phenomena related to the temperature. The knowledge of the friction properties of the sheet is required for the proper design of the conditions of manufacturing processes and tools. This paper summarizes the methods used to describe friction conditions in conventional sheet metal forming and incremental sheet forming that have been developed over a period of time. The following databases have been searched: WebofKowledge, Scopus, Baztool, Bielefield Academic Search Engine, DOAJ Directory of Open Access Journals, eLibrary.ru, FreeFullPdf, GoogleScholar, INGENTA, Polish Scientific Journals Database, ScienceDirect, Springer, WorldCat, WorldWideScience. The English language is selected as the main source of review. However, in a limited scope, databases in Polish and Russian languages are also used. Many methods of friction testing for tribological studies are selected and presented. Some of the methods are observed to have a huge potential in characterizing frictional resistance. The application of these methods and main results have also been provided. Parameters affecting the frictional phenomena and the role of friction have also been explained. The main disadvantages and limitations of the methods of modeling the friction phenomena in specific areas of material to be formed have been discussed. The main findings are as follows—The tribological tests can be classified into direct and indirect measurement tests of the coefficient of friction (COF). In indirect methods of determination, the COF is determined based on measuring other physical quantities. The disadvantage of this type of methods is that they allow the determination of the average COF values, but they do not allow measuring and determining the real friction resistance. In metal forming operations, there exist high local pressures that intensify the effects of adhesion and plowing in the friction resistance. In such conditions, due to the plastic deformation of the material tested, the usage of the formula for the determination of the COF based on the Coulomb friction model is limited. The applicability of the Coulomb friction model to determine the COF is also very limited in the description of contact phenomena in hot SMF due to the high shear of adhesion in total contact resistance.

Modelling of the Steel Pushing V-Belt Continuously Variable Transmission

1994 ◽  
Vol 208 (1) ◽  
pp. 13-27 ◽  
Author(s):  
J D Micklem ◽  
D K Longmore ◽  
C R Burrows
Keyword(s):  
Mathematical Model ◽  
Coulomb Friction ◽  
Continuously Variable Transmission ◽  
Friction Model ◽  
Full Potential ◽  
Shear Connection ◽  
System A ◽  
Variable Transmission ◽  
Coulomb Friction Model ◽  
Good Agreement

The steel pushing V-belt continuously variable transmission (CVT) is now commercially available in the automobiles of a number of manufacturers but to date it has not led to a significant reduction in fuel consumption. To develop its full potential it is necessary to have a good mathematical model of the system. A number of models have been described in recent years but all make use of a Coulomb friction model for the shear connection between the belt and the pulleys. This paper proposes a friction model based on elastohydrodynamic theory. It is shown that there is good agreement between measured and calculated slip values for the transmission which justifies use of the model.

scholarly journals Dynamic Modeling and Experimental Verification of A Cable-Driven Continuum Manipulator With Cable-Constrained Synchronous Rotating Mechanisms

2021 ◽  
Author(s):  
Xudong Zheng ◽  
Taiwei Yang ◽  
Xianjin Zhu ◽  
Zhang Chen ◽  
Xueqian Wang ◽  
...  
Keyword(s):  
Dynamic Modeling ◽  
Friction Model ◽  
Modeling Method ◽  
Stick Slip ◽  
Dynamical Behaviors ◽  
Ale Formulation ◽  
Two Factors ◽  
New Type ◽  
Continuum Manipulator ◽  
Coulomb Friction Model

Abstract The cable-driven segmented manipulator with cable-constrained synchronous rotating mechanisms (CCSRM) is a new type of continuum manipulator, which has large stiffness and less motors, and thus exhibits excellent comprehensive performance. This paper presents a dynamic modeling method for this type of manipulator to analyze the friction and deformation of the cables on the dynamical behaviors of the system. First, the driving cables are modeled based on the ALE formulation, the strategies for detecting stick-slip transitions are proposed by using a trial-and-error algorithm, and the stiff problems of the dynamic equations are released by a model smoothing method. Second, the dynamic modeling method for rigid links is presented by using quaternion parameters. Third, the connecting cables are modeled by torsional spring-dampers and the frictions between the connecting cables and the conduits are considered based on a modified Coulomb friction model. Finally, the numerical results are presented and verified by comparing with experiment results. The study shows that the friction and cable deformation play an important role in the dynamical behaviors of the manipulator. Due to these two factors, the constant curvature bending of the segments does not remain.

Experimental and Numerical Investigations on Frictional Behaviour under Consideration of Varying Tribological Conditions

2014 ◽  
Vol 966-967 ◽  
pp. 270-278 ◽  
Author(s):  
Marion Merklein ◽  
Fabian Zöller ◽  
Vera Sturm
Keyword(s):  
Coulomb Friction ◽  
Fe Simulation ◽  
Friction Model ◽  
Body Parts ◽  
Numerical Investigations ◽  
Drawing Test ◽  
Strip Drawing ◽  
Complex Test ◽  
Coulomb Friction Model ◽  
Frictional Behaviour

In present time the FE-simulation of body parts in sheet metal drawing processes has to be continuously improved to increase the prediction accuracy. The objective of this paper is to describe a methodology to improve the simulation by mapping the complex tribological conditions of the process in the simulation. This methodology focuses on the dependency of influencing parameters on the friction coefficient. The influence respectively the dependency of these factors has been investigated, both in an experiment of a plane strip drawing test and in a FE-simulation of this test. With the sensitivity analysis in the numerical simulation it is possible to compare the implemented Coulomb-friction-model against the experimental results. The results of the experimental and numerical investigation show the need of further investigations on a more geometrical complex test to prove if it is possible to transfer the knowledge and dependencies that has been found in the experiment with the strip drawing test to a more geometrical complex test.

Analysis of Actively Controlled Coulomb Damping for Rotating Machinery

1999 ◽  
Author(s):  
John M. Vance ◽  
Luis A. San Andrés
Keyword(s):  
Coulomb Friction ◽  
Critical Speed ◽  
Vibration Suppression ◽  
Friction Model ◽  
Rotating Machinery ◽  
Friction Damper ◽  
Control Laws ◽  
Coulomb Damping ◽  
Coulomb Type ◽  
Coulomb Friction Model

Attempts have been made in the past to use Coulomb damping for vibration suppression in rotating machinery. Typically, a dry friction damper is designed to operate on a flexible bearing support. These designs have usually been unsuccessful in practice, partly because the Coulomb coefficient changes with temperature, with ingress of dirt or lubricant, and with the surface wear conditions. It is known that purely Coulomb damping forces cannot restrain the peak rotor whirl amplitudes at a critical speed. The invention of a disk type of electroviscous damper, utilizing a fluid with electrorheological (ER) properties, has recently revived the interest in Coulomb type dampers. Several investigations have suggested that a Coulomb friction model was the best representation for an ER damper with voltage applied. This model was used to study the feasibility of developing actively controlled bearing dampers for aircraft engines. This paper analyzes the imbalance response of two different rotordynamic models with Coulomb friction damping and shows the benefit of adding active control. Control laws are derived to achieve minimum rotor vibration amplitudes while avoiding large bearing forces over a speed range that includes a critical speed. The control laws are derived for purely Coulomb type of damping and assuming a combination of Coulomb and viscous damping effects. It is shown that the most important feature of Coulomb damping for minimal rotordynamic amplitude response is the control of rotor support stiffness, i.e. leading to the relocation of critical speeds, rather than control of a damping coefficient.

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