Nonlinear Friction Model Research Articles

State Observation for Elastoplastic Friction Models in Positioning Systems by Utilizing Leunberger Observers

In this study, state observation in positioning systems is discussed. A dynamical friction model, also called an elastoplastic model, describing basic friction phenomena such as stick-slip dynamics, presiding motion, the Stribeck effect, etc., is included in the positioning system model. A Luenberger-type state observer is presented and developed for motion control systems with the non-linear elastoplastic friction model in order to overcome difficulties in measuring internal states physically. Since the parameters of the elastoplastic friction model are required in the experimental studies, a combined parameter identification method is also outlined in three different levels. Simulation and experimental results are presented to illustrate benefits of the method by observing both velocity and friction states. The proposed method is tested successfully on an electromechanical positioning system.

PRECISE MODELING OF ROLLING FRICTION IN BALL SCREW-DRIVEN TABLE POSITIONING SYSTEM

This paper presents a precise modeling methodology for fast-response andhighprecision positioning systems, where a ball screw-driven table positioning device is mathematically identified as a combination of a linear mechanical model with vibration modes and a nonlinear model with friction characteristics. In the nonlinear friction modeling, a nonlinear elastic behavior in the mechanisms, e.g. ball screw and rolling ball guide, is precisely modeled as a dynamic friction characteristic due to the rolling friction, as well as a well-known static friction modeling by Stiction, Coulomb, and viscous frictions. The proposed system modeling has been verified by comparative studies using a prototype for industrial positioning devices, especially paying attention to the precise simulation of positioning response around the settling position.

Friction identification of ball-screw driven servomechanisms through the limit cycle analysis

Friction degrades the positioning accuracy of servomechanisms. Friction compensators are required to fabricate high-performance servomechanisms. In order to compensate for the friction in the servomechanism accurately, identification of the friction is required first. This paper proposes a friction identification method of a ball-screw driven servomechanism in the frequency domain. A nonlinear friction model including static, Coulomb, and viscous friction as well as Stribeck effect is formulated by using describing functions. Friction elements are estimated through the limit cycle analysis in a velocity control loop. In order to increase the accuracy of the friction identification process, a Butterworth filter is incorporated into the velocity feedback loop. Validity of the proposed method is confirmed through the numerical simulation and experiment in a ball-screw driven servomechanism. In addition, a model-based friction compensator is applied as a feedforward controller to compensate for the nonlinear characteristics of the servomechanism and to verify the effectiveness of the proposed identification method.

Nonlinear friction compensation in mechatronic servo systems

Friction, especially its nonlinear component, may degrade the tracking performance of robots. Based on Kang’s method, a novel compensation method for nonlinear friction is presented in this paper, which modified Southward’s traditional compensation method for nonlinear friction. The stability of the systems which adopt the novel compensation method is proved with Layapunov’s stability theorem, and is enhanced further. Having estimated the nonlinear friction model using an identification method, the effect caused by its nonlinear component can be compensated, and enhanced tracking performance is verified under the SCARA robot experimental platform using Windows NT and VenturCom’s real-time extension module (RTX) environment.

Modelling of a hydraulic power steering system

Consideration is given to the modelling of a commercial hydraulic power steering system. The modelling philosophy with a comprehensive understanding of the control edge geometry is essential to an optimal system and the steady-state characteristics of a non-faceted valve and a two-facet valve are compared to understand the steering feeling. A test-rig is designed which incorporates the power steering assembly with a pneumatic loading system. The dynamics of the control valve and cylinder, pneumatic loading system, a non-linear friction model and the pump characteristics are then considered for dynamic performance and simulation results are compared with experimental results. The friction model contributes to the understanding of the pressure peak at the beginning of steering and the existence of a final steering angle error in practice.

QFT Robust Control Design for 3-Axis Flight Table Servo System with Large Friction

The 3-axis flight table is an important device and a typical high performance position and speed servo system used in the hardware in the loop simulation of flight control system. Friction force and uncertainty are the main characteristics in the 3-axis flight table servo system. Based on the description of dynamic and static model of a nonlinear Stribeck friction model, and taking account of the practical uncertainties of 3-axis flight table servo system, the QFT controller is designed. Simulation and real-time results are presented.

Glaciers and laws of friction and sliding

Glaciers slide at their base. A deeper understanding of the frictional behaviour and sliding between an ice mass and a rock bed is an important problem in glacier physics. In this study we investigate two approaches to the problem of glacier sliding. The first approach models friction forces between the ice and the bed. The second approach considers various proposals of a sliding velocity. Anisotropy of rock bed topographies is a source of anisotropic tribological phenomena. Therefore, anisotropic and inhomogeneous friction and anisotropic sliding are discussed in detail. Various types of friction anisotropy are distinguished with the aid of linear and nonlinear friction models. Next, anisotropic friction and sliding rules are derived using an elasto-plastic analogy. A sliding law proposed by Hindmarsh is applied in the analysis of anisotropic sliding. Extended forms of the sliding law are given with the aid of anisotropic friction models. Furthermore, stick-slip motions are identified as important in the dynamics of glacier sliding.

Nonlinear friction phenomena in direct-drive robotic arms: an experimental set-up for rapid modelling and control prototyping

This paper considers the design and the experimental validation of digital control algorithms when both low and high velocity precision issues are important for the quality of the controlled equipment. At low velocities friction phenomena are dominant, while at high velocities the nonlinear coupled and configuration-dependent dynamics plays a major role. Since rapid control prototyping (RCP) requires “finely-tuned” models of the equipment under investigation, an accurate definition of the nonlinear friction model is of capital importance for assessing the qualification of the proposed algorithms. An experimental validation of the proposed models and control algorithms with friction compensation is presented and discussed for a two-arms planar manipulator with brushless directdrive actuators.

転がり案内における速度反転時の非線形摩擦挙動

This paper presents a new dynamic model of nonlinear friction in a ball guide way. This model includes Coulomb friction, viscous friction, Stribeck effect and nonlinear behavior of elastic deformation. By the proposed model contrary to the conventional one, the motion is not decelerated but accelerated by the elastic recovery force just after the direction is reversed This model is not symmetrical for the zero speed of motion. In our simulations the friction models of the proposed and conventional were tuned using Generic Algorithm and by applying these models the driving forces for the same reversed motion were also estimated. These simulations indicated the proposed model is much more accurate than the conventional one. The friction force compensation experiments considering the proposed model were carried out by using a linear slider for a motion in which the velocity was reversed. The tracking error was reduced to less than a half of that without compensation.

A simulation and control design environment for single-stage and dual-stage hard disk drives

We describe an integrated tool for the design and evaluation of the performance of different control algorithms and strategies, applied to hard disk drives (HDDs) with single-stage actuators and dual-stage actuators. The tool is composed of a set of procedures for the computer-aided design of servocontrollers and a HDD simulator. In order to perform realistic simulations, each part of the HDD is described with high level of detail. As for the mechanics, the usual inertia plus resonance model of the voice coil motor (VCM) has been enriched with nonlinear friction modeling and, in case of DSAs, with the dynamic coupling between primary and secondary actuator. The nonlinear friction model has been tuned on experimental data, using an experimental system presented in the paper. As for the electronics, the VCM driver model is included and quantizations in the position error signal measurement and computation are explicitly considered. Also, in order to evaluate the tracking performance of different servocontrollers, repetitive run outs and nonrepetitive run outs are included. Such disturbances have been obtained from commercial HDDs, with a procedure that is detailed in the paper. The simulator is then validated by comparing simulation and experimental results, both in open-loop and closed-loop conditions, thus, confirming the effectiveness of the developed tool.

Decomposition-based friction compensation of mechanical systems

In this paper, a linear parametric friction model is formulated by linearizing a nonlinear empirical friction model in parameters. A proposed decomposition-based control design framework is applied to synthesize the friction compensation scheme. A separate compensator is designed for each type of friction utilizing the most suitable control technique. The nominal friction is compensated by feed forward. An adaptive compensator is derived to compensate for parametric unmodeled friction with unknown but constant parameters, and a robust compensator is used to deal with friction model parameter variations, as well as non-parametric unmodeled friction. The combination of the compensators yields the overall compensation scheme. Adaptive and robust compensators complement each other in compensating the effects of model uncertainties. The analytical and simulation studies have confirmed the efficiency of the proposed friction compensation method.

Adaptive friction compensation using extended Kalman–Bucy filter friction estimation

An extended Kalman–Bucy filter (EKBF)-based friction compensation method is presented and validated. The method relies on an accurate model of system rigid-body dynamics and measured motion, rather than a structured nonlinear friction model, to estimate external friction torque. The estimate is used in a traditional friction compensator to cancel friction effects. The EKBF compensator is compared with other model-based and non-model-based friction compensation strategies through position tracking experiments. Results show that when motion is dominated by static and Stribeck friction, non-model-based friction estimation and compensation using the EKBF consistently provides equal or superior performance over model-based adaptive friction compensation methods.

Comparative study of tracking control for a mobile manipulator: Nonholonomic and dynamic cases

This paper gives an in-depth treatment of the modeling and control of a mobile manipulator which consists of a robotic manipulator mounted upon a mobile robot. By neglecting slip of the platform's tires, nonholonomic constraints are introduced into the equations of motion. By considering wheel slip, the assumption of nonholonomic motion is violated. Nonholonomic and dynamic models of a mobile manipulator are developed and compared using the Lagrange-d'Alembert formulation and the Newton-Euler method, respectively. The dynamic model which considers wheel slip incorporates a nonlinear tire friction model. The tracking problem is investigated by using imput-output linearization for the nonholonomic model. For the dynamic model, a robust control method based on a matching condition is developed to eliminate the harmful effects of wheel slip, which acts as a disturbance to the system. Then, the effect of wheel slip on the tracking of commanded motion is identified via simulation. The effectiveness of the proposed control algorithm is demonstrated through computer simulation.

Tracking control of mechanical systems in the presence of nonlinear dynamic friction effects

In this paper, we design an observer-based exact model knowledge position tracking controller for a second-order mechanical system with nonlinear load dynamics and a nonlinear dynamic friction model. Since the controller requires an estimate of the unmeasurable friction state, we demonstrate how the friction dynamics can be exploited to design three different observers which foster different transient response characteristics for the composite closed-loop system. We then present two adaptive controllers which utilize nonlinear observer/filter structures to provide for asymptotic position tracking while compensating for selected parametric uncertainty. Dynamic simulation and experimental results are utilized to illustrate control performance.

Disturbance Observer-Based Nonlinear Friction Compensation in Servo Drive System.

Solid friction in various machines is one of dominant nonlinearities limiting the control performance of servo drive systems. Nonlinear friction gives tracking errors and undesired stick-slip motion due to stiction (breakaway friction) and/or Stribeck effect. A wide variety of studies have been reported, which formulated nonlinear friction models, identified its parameters, and compensated for the friction. Those compensation schemes can significantly improve the conventional control performance, however, deterioration of the control accuracy is still the problems due to the inaccurate friction model and/or the restricted bandwidth of the compensation control loop.This paper presents the disturbance observer-based compensation for nonlinear friction in servo drive systems to improve the control performance. The proposed scheme uses a new disturbance observer which is designed on the basis of Coulomb friction characteristics. This scheme can realize the precise speed/position control without response delay which is caused by the restricted bandwidth in the conventional compensation scheme. Experimental results and analytical studies show the distinct performance improvement of the proposed scheme, comparing to the conventional compensation schemes.

Two-Dimensional Models of Boundary and Mixed Friction at a Line Contact

Two-dimensional dynamic friction models at a lubricated line contact, operating in boundary and mixed lubrication regimes, are developed. The friction coefficient is shown to be a function of the sliding velocity and the instantaneous separation of the sliding bodies, normal to the sliding direction. The models are based on unsteady friction experiments carried out under constant normal loads and under time-varying sliding velocities. The normal motions at the sliding contact were detected indirectly by contact resistance measurements. The contact resistance is related to the theoretical central film thickness for smooth surfaces. An advanced system identification technique (Minimum Model Error) is implemented to identify the most important terms in a number of nonlinear friction models. Two friction models are then nondimensionalized and parameterized. The validity and range of application of the models are then tested, by comparing them with experiments and with selected models proposed by other researchers.

Simulation and Optimization for Precise Centering Operations of Workpieces.

This paper proposes fundamental methodologies for automating centering operations which are now conducted by skilled workers. First, problems in automating centering operations are described. Then, the movement behavior of a workpiece when applying an impulse force with a hammer is observed using experimental equipment and the relationship between the applied force and displacement of the workpiece is measured. Next, frictional forces between a workpiece and a table are formulated as a nonlinear function of the velocity of the workpiece. To obtain the displacement behavior of the workpiece on a table numerically, the movement of the workpiece is simulated by the finite-element method (FEM) in which the nonlinear frictional force model is applied at the contact surface between the workpiece and the table. Finally, a method for determining the optimal impulse force for displacing a workpiece to a required position on a table with minimal positional error of the workpiece is constructed and numerical results are given to demonstrate the method.

Vibration Test of Plant Piping System Having Friction Support.

This report deals with the experimental study of seismic behavior of piping systems in the industrial facilities such as petro-chemical plants and nuclear power plants. Special attention is focussed on the nonlinear dynamic of piping systems due to frictional vibration appeared among piping and supporting devices. 3 dimensional mock-up piping model having 30 m Iength and 8 inches diameter is excited by large scale (15 m x 15 m) shaking table. Power spectra of the vibration and loading-response relations in the form of hysteresis loop under several excitation levels are calculated. Response reduction effect caused by frictional vibration is evaluated and demonstrated in terms of response reduction factor. Numerical simulation by use of nonlinear simplified friction model is also performed and calculated piping is compared with those from vibration tests.

WAVEFORMS IN FRETTING FATIGUE

Abstract— The magnitudes and directions of the frictional forces must be considered in any fracture mechanics analysis of crack growth under fretting fatigue conditions. A simple nonlinear friction model has been developed which relates the waveforms of the frictional forces to those of the applied forces when fretting occurs. It is shown that the waveforms are different in shape and that periods of dwell and phase shifts may occur in the frictional forces. These differences can significantly affect the rate of growth of cracks and hence life prediction.

Stick-slip stability by analogue simulation

An analogue simulation of stick-slip stability due to viscous damping effects has been undertaken. Upper and lower bound analytical theories have been validated for linearised friction models. Stability conditions have been examined based on realistic non-linear friction models from which three distinct stability situations have been defined. This suggests that stickslip stability can be achieved by viscous damping levels considerably less than those previously anticipated.