Differential model of friction based on bristle model and phase-transition theory

2021 ◽  
pp. 135065012110625
Author(s):  
Fan Wang ◽  
Lin-Xiang Wang
Keyword(s):  
Phase Transition ◽  
System Analysis ◽  
Hysteresis Loops ◽  
Potential Energy Function ◽  
Nonlinear Ordinary Differential Equation ◽  
Friction Model ◽  
Transition Theory ◽  
Motion Direction ◽  
Friction Mechanism ◽  
Differential Model

For high-precision position and angle control in robots, it is essential to compensate for the hysteretic behaviour caused by friction when the motion direction is reversed. An accurate friction model which is suitable for control system analysis and implementation is highly desirable. A differential model is proposed in the current paper for the modelling of hysteresis effects caused by friction phenomena. The model is constructed by employing a phenomenological phase-transition theory to mimic the friction mechanism. The bristle friction mechanism is adapted. The switching between static and dynamic friction is regarded as a reversible phase-transition phenomenon, which could be characterized by the local minima of a non-convex potential energy function. The Stribeck effect and the hysteretic relation between friction and velocity are modelled by a nonlinear ordinary differential equation. The comparison of the numerical simulation results and existing experimental friction data are presented. It is illustrated that the friction hysteresis loops are well captured, the capability of the proposed model is verified.

Dynamic Models for Magnetorheological Dampers and its Feedback Linearization

2009 ◽  
Vol 79-82 ◽  
pp. 1205-1208 ◽  
Author(s):  
Cheng Zhang ◽  
Lin Xiang Wang
Keyword(s):  
Differential Equation ◽  
Phase Transition ◽  
Ordinary Differential Equation ◽  
Feedback Linearization ◽  
Dynamic Models ◽  
Nonlinear Ordinary Differential Equation ◽  
Transition Theory ◽  
Magnetorheological Dampers ◽  
Differential Model ◽  
Mr Dampers

In the current paper, the hysteretic dynamics of magnetorheological dampers is modeled by a differential model. The differential model is constructed on the basis of a phenomenological phase transition theory. The model is expressed as a second order nonlinear ordinary differential equation with bifurcations embedded in. Due to the differential nature of the model, the hysteretic dynamics of the MR dampers can be linearized and controlled by introducing a feedback linearization strategy.

Analysis of Ultralong Friction Pile Based on Gradient Dependent Nonlocal Friction Model

2014 ◽  
Vol 638-640 ◽  
pp. 380-383
Author(s):  
Xiao Yan Luo ◽  
Wei Ping Liu
Keyword(s):  
Frictional Resistance ◽  
Friction Model ◽  
Gradient Theory ◽  
Friction Mechanism ◽  
New Model ◽  
Friction Law ◽  
Nonlocal Friction ◽  
Set Up ◽  
Friction Pile ◽  
Geotechnical Problems

Based on the gradient theory, the gradient dependent nonlocal friction model is established. It is a new model which can describe the nonlocal friction effect. Based on Mindlin’s solution of displacement, an elastic solution of the lateral frictional resistance for ultralong friction pile is derived. The ultralong friction pile is analyzed by using the gradient dependent nonlocal friction model. Compared with the solution to the local friction law, the results shows that nonlocal friction law is feasible and reliable. The study is helpful for understanding the friction mechanism in geotechnical problems. It is a good attempt to set up the more actual and more accurate friction model.

Some Comments on the Differential Model of Hysteresis

1998 ◽  
Author(s):  
Y. H. Liu ◽  
G. Tuan ◽  
G. C. Foliente ◽  
F. Ma
Keyword(s):  
Computational Mechanics ◽  
Hysteresis Loops ◽  
External Excitation ◽  
Differential Model ◽  
General Acceptance ◽  
Robust Model

Abstract The differential model of hysteresis has found general acceptance in computational mechanics. Shapes of hysteresis loops generated by the model depend on both the loop parameters and external excitation. In this paper, sensitivity of the differential model to various constituent parameters is studied. A more robust model of hysteresis can be constructed if sensitivity to loop parameters and excitation can be better understood.

Dynamics of a Dual-Clutch Gearbox System: Analysis and Experimental Validation

2013 ◽  
Vol 58 (1) ◽  
pp. 17-28 ◽  
Author(s):  
David G. Lewicki ◽  
Hans DeSmidt ◽  
Edward C. Smith ◽  
Steven W. Bauman
Keyword(s):  
Experimental Validation ◽  
System Analysis ◽  
Friction Model ◽  
Test Facility ◽  
Motor Speed ◽  
Dynamic Simulations ◽  
Stick Slip ◽  
Dry Clutch ◽  
Six Degree Of Freedom ◽  
Validation Tests

Dynamic simulations and experimental validation tests were performed on a two-stage, two-speed gearbox. The gearbox was driven by two electromagnetic motors and had two electromagnetic, multidisk clutches to control output speed. A dynamic model of the system was created, which included a DC electric motor with proportional–integral–derivative speed control, a two-speed gearbox with dual electromagnetically actuated clutches, and an eddy current dynamometer. A six-degree-of-freedom model of the gearbox accounted for the system torsional dynamics and included gear, clutch, shaft, and load inertias as well as shaft flexibilities and a dry clutch stick-slip friction model. Experimental validation tests were performed on the gearbox in the NASA Glenn gear noise test facility. Gearbox output speed and torque as well as drive motor speed and current were compared to those from the analytical predictions. The experiments correlate very well with the predictions, thus validating the dynamic simulation methodologies.

scholarly journals Annealing Effect on Martensitic Transformation and Magneto-Structural Properties of Ni-Mn-In Melt Spun Ribbons

2009 ◽  
Vol 635 ◽  
pp. 81-87 ◽  
Author(s):  
T. Sánchez ◽  
José Luis Sánchez Llamazares ◽  
B. Hernando ◽  
J.D. Santos ◽  
M.L. Sánchez ◽  
...  
Keyword(s):  
Phase Transition ◽  
Structural Properties ◽  
Magnetic Transition ◽  
Structural Phase ◽  
Hysteresis Loops ◽  
Transition Temperatures ◽  
Average Chemical Composition ◽  
Saturation Field ◽  
Existence Region ◽  
Phase Transition Temperatures

We report the effect of a short-time vacuum annealing (1073 K during 10 minutes) on structural phase transition temperatures and magneto-structural properties of as-quenched ribbons of the Heusler alloy Ni50.6Mn34.5In14.9. This alloy crystallizes in a single phase cubic B2-type austenite with a Curie point of TCA=284 K that with the lowering in temperature transforms into a martensite with TCM185 K. The direct and reverse martensitic phase transition temperatures were MS=257 K, Mf = 221 K, AS = 239 K, and Af = 266 K. After annealing austenite shows the highly ordered L21-type structure while the average chemical composition as well as the structural and magnetic transition temperatures were shifted to Ni50.2Mn34.3In15.5 and MS = 253 K, Mf = 238 K, AS = 257 K, Af = 265 K, ΔT = 13 K, TCA = 299 K and TCM207 K. In the annealed samples the magnetization changes associated to the magnetic and structural transitions are more abrupt and magnetization isotherms in both the austenitic and martensitic existence region show higher initial magnetic susceptibility and faster approach to saturation. Field-cooled hysteresis loops at 10 K were shifted along the negative H-axis for both samples, but a significant anomaly was evident on the left side of the hysteresis loop for as-quenched ribbons.

scholarly journals Analytical solutions of mushy layer equations describing directional solidification in the presence of nucleation

2018 ◽  
Vol 376 (2113) ◽  
pp. 20170217 ◽  
Author(s):  
Dmitri V. Alexandrov ◽  
Alexander A. Ivanov ◽  
Irina V. Alexandrova
Keyword(s):  
Phase Transition ◽  
Supercooled Liquid ◽  
Crystal Nucleation ◽  
Supersaturated Solution ◽  
Pure Liquid ◽  
Particle Nucleation ◽  
Nucleation Kinetics ◽  
Differential Model ◽  
Phase Transition Interface ◽  
Phase Transition Boundary

The processes of particle nucleation and their evolution in a moving metastable layer of phase transition (supercooled liquid or supersaturated solution) are studied analytically. The transient integro-differential model for the density distribution function and metastability level is solved for the kinetic and diffusionally controlled regimes of crystal growth. The Weber–Volmer–Frenkel–Zel’dovich and Meirs mechanisms for nucleation kinetics are used. We demonstrate that the phase transition boundary lying between the mushy and pure liquid layers evolves with time according to the following power dynamic law: , where Z 1 ( t )= βt 7/2 and Z 1 ( t )= βt 2 in cases of kinetic and diffusionally controlled scenarios. The growth rate parameters α , β and ε are determined analytically. We show that the phase transition interface in the presence of crystal nucleation and evolution propagates slower than in the absence of their nucleation. This article is part of the theme issue ‘From atomistic interfaces to dendritic patterns’.

Coil-bridge transition in a single polymer chain as an unconventional phase transition: Theory and simulation

2014 ◽  
Vol 140 (20) ◽  
pp. 204908 ◽  
Author(s):  
Leonid I. Klushin ◽  
Alexander M. Skvortsov ◽  
Alexey A. Polotsky ◽  
Hsiao-Ping Hsu ◽  
Kurt Binder
Keyword(s):  
Phase Transition ◽  
Polymer Chain ◽  
Transition Theory ◽  
Single Polymer Chain
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