Analytical describing function of LuGre friction model

2022 ◽  
Author(s):  
Ahmad Mashayekhi ◽  
Saeed Behbahani ◽  
Ali Nahvi ◽  
Mehdi Keshmiri ◽  
Mehdi Shakeri
Keyword(s):  
Friction Model ◽  
Describing Function ◽  
Lugre Friction Model ◽  
Lugre Friction

scholarly journals Asymmetric and chaotic responses of dry friction oscillators with different static and kinetic coefficients of friction

Meccanica ◽  
2021 ◽  
Author(s):  
Gábor Csernák ◽  
Gábor Licskó
Keyword(s):  
Dry Friction ◽  
Continuation Method ◽  
Friction Model ◽  
Lugre Friction Model ◽  
Kinetic Coefficients ◽  
Friction Oscillator ◽  
Lugre Friction ◽  
Friction Parameters ◽  
Two Parameter ◽  
Parameter Bifurcation

AbstractThe responses of a simple harmonically excited dry friction oscillator are analysed in the case when the coefficients of static and kinetic coefficients of friction are different. One- and two-parameter bifurcation curves are determined at suitable parameters by continuation method and the largest Lyapunov exponents of the obtained solutions are estimated. It is shown that chaotic solutions can occur in broad parameter domains—even at realistic friction parameters—that are tightly enclosed by well-defined two-parameter bifurcation curves. The performed analysis also reveals that chaotic trajectories are bifurcating from special asymmetric solutions. To check the robustness of the qualitative results, characteristic bifurcation branches of two slightly modified oscillators are also determined: one with a higher harmonic in the excitation, and another one where Coulomb friction is exchanged by a corresponding LuGre friction model. The qualitative agreement of the diagrams supports the validity of the results.

Wheel independent-drive control based on dynamic tire LuGre friction model

2008 ◽  
Author(s):  
Ruan Jiuhong ◽  
Yang Fuguang ◽  
Qiu Xuyun ◽  
Li Yibin
Keyword(s):  
Friction Model ◽  
Lugre Friction Model ◽  
Drive Control ◽  
Lugre Friction

Modeling and Analysis of Spatial Flexible Mechanical Systems With a Spherical Clearance Joint Based on the LuGre Friction Model

2019 ◽  
Vol 15 (1) ◽  
Author(s):  
Xiao Tan ◽  
Guoping Chen ◽  
Hanbo Shao
Keyword(s):  
Mechanical Systems ◽  
Beam Element ◽  
Friction Model ◽  
Lugre Friction Model ◽  
Clearance Joint ◽  
Lugre Friction ◽  
Computational Methodology ◽  
Crank Mechanism ◽  
Flexible Components

Abstract A computational methodology for modeling spatial flexible mechanical systems with stick-slip friction in a spherical clearance joint is presented. A modified three-dimensional (3D) absolute nodal coordinate formulation based shear deformable beam element with two nodes is proposed and employed to discretize the flexible components. To avoid locking problems, we employed an enhanced continuum mechanics approach to evaluate the beam element elastic forces. The strain components εyz, εyy, and εzz are approximated using linear interpolation to improve the computational efficiency while the loss of accuracy is acceptable. The contact and friction forces in a spherical clearance joint were evaluated by the hybrid contact and LuGre friction models, respectively. Three numerical examples are presented and discussed. A simple pendulum was utilized to prove the correctness of the modified beam element. A classical slider–crank mechanism was employed to validate the computational methodology. A spatial rigid–flexible slider–crank mechanism with a spherical clearance joint was used to investigate the effect of link flexibility and joint clearance on the dynamic behavior of mechanical systems. Using the LuGre friction model, we reproduced the Stribeck effect as it is expected in real world settings. The components with appropriate stiffness play the role of suspension for spatial mechanical systems with imperfect joints. The vibrations of the flexible components play an active role of intensifying the collision in kinematic joint with clearance.

scholarly journals Study on the Low Velocity Stability of a Prostate Seed Implantation Robot’s Rotatory Joint

Electronics ◽  
2020 ◽  
Vol 9 (2) ◽  
pp. 284 ◽  
Author(s):  
Bing Li ◽  
Yongde Zhang ◽  
Lipeng Yuan ◽  
Xiaolin Xi
Keyword(s):  
Prostate Cancer ◽  
Parameter Identification ◽  
Control Method ◽  
Friction Model ◽  
Friction Torque ◽  
Low Velocity ◽  
Seed Implantation ◽  
Compensation Control ◽  
Lugre Friction Model ◽  
Lugre Friction

Prostate cancer has one of the highest incidences of male malignant tumors worldwide. Its treatment involves the robotic implantation of radioactive seeds in the perineum, a safe and effective procedure for early, low-risk prostate cancer. In order to ensure precise positioning, the seed implantation needle is set at low terminal velocity. In this paper, the motion output position instability caused by the friction torque of the robot’s motor and rotating joint during low velocity motion was analyzed and studied. This paper also presents a compensation control method based on the LuGre friction model, which offers piecewise parameter identification with GA-PSO. First, based on an analysis of its structure and working principle, the friction torque model of the robotic system and the torque model of the driving motor are established, and the influence of friction torque on motion stability analyzed. Then, based on experimental data of the relationship between velocity and friction torque for no-friction compensation, the velocity point of the minimum torque of the rotating joint and the critical Stribeck velocity point were used for segmental parameter identification; cubic spline interpolation was used for segmental fitting. Furthermore, on the basis of the LuGre model identification method, parameter identification of the genetic algorithm-particle swarm optimization, and compensation control of the LuGre friction model, a control method is analysed and set forth. Malab2017a/Simulink simulation software was used to simulate and analyze the control method, and verify its feasibility. Finally, the cantilever prostate seed implantation robot system was tested to verify the effectiveness of the segmented identification method and the compensation control strategy. The results reveal that motion output position stability at low velocity meets the requirements of the cantilever prostate seed implantation robot, thus providing a vital reference for further research.

Study of Dynamic Characteristics of Friction: A Comparative Analysis of the Velocity Dependent and the LuGre Friction Model

2005 ◽  
Author(s):  
Firoz Ali Jafri ◽  
David F. Thompson
Keyword(s):  
Hopf Bifurcation ◽  
Friction Model ◽  
Continuation Methods ◽  
Bifurcation Parameter ◽  
Lugre Model ◽  
Lugre Friction Model ◽  
Subcritical Hopf Bifurcation ◽  
Fold Bifurcation ◽  
Dependent Model ◽  
Lugre Friction

In this paper, we conduct numerical analysis to study the effects of friction on the dynamic response of a single degree of freedom mechanical system. Two different friction models, the velocity dependent friction model and the LuGre friction model, have been used to model the friction interface. Bifurcation analysis has been conducted using equilibrium and limit cycle continuation methods. With system viscous damping as the bifurcation parameter, a reverse subcritical Hopf bifurcation is observed in the case of velocity dependent model. In the case of the LuGre model for the same bifurcation parameter, a reverse supercritical Hopf bifurcation is observed at lower velocities but at higher velocities it changes to a reverse subcritical Hopf bifurcation. A fold bifurcation of the limit cycles is also seen at higher velocities for the LuGre model.

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