LuGre Friction Research Articles

Electromechanical Simulation and Analysis of Displacement Failure of Input Shaft for Harmonic Drives

Axial displacement of the input shaft is one of the faults of harmonic drives in industrial robots. Aiming at finding a monitoring method of this kind of failure in this paper, the simulation of axial displacement failure is performed by establishing the electromechanical system model of the harmonic drive. The exponential LuGre friction model is used in the developed harmonic drive model, and an additional friction torque model caused by the axial displacement failure was established. The nominal load is input into the harmonic drive, and the simulation experiment was implemented with different degrees of input shaft axial displacement failure. The simulation result shows that the input shaft axial displacement failure of the harmonic drive affects the state (the internal current) of the drive motor. In the future, one can detect the axial displacement failure of the harmonic drives based on this finding.

A Novel Methodology for Comprehensive Modeling of the Kinetic Behavior of Steerable Catheters

This paper presents a novel methodology for building a kinetic model for steerable catheters by capturing the nonlinearity of the steerable catheter, the flexibility of the pathway, and the contact and friction between the pathway and the moving catheter. The planar catheter system was used to illustrate the methodology. An experiment was conducted to validate the model along with the friction model. The experimental result and model-predicted result have a good agreement in both displacement and force of the distal tip of the catheter along with the input force. The experiment also shows that the LuGre friction model is most accurate. The methodology is thus applicable to modeling specific catheter-pathway systems. The kinetic model of the steerable catheter is useful to 1) design and for evaluation of new steerable catheters and 2) planning of catheter-based operations. Furthermore, the methodology has a generalized implication to other systems such as colonoscopy systems.

Comparative Investigation of Phenomenological Modeling for Hysteresis Responses of Magnetorheological Elastomer Devices.

Magnetorheological elastomer (MRE) is a type of magnetic soft material consisting of ferromagnetic particles embedded in a polymeric matrix. MRE-based devices have characteristics of adjustable stiffness and damping properties, and highly nonlinear and hysteretic force–displacement responses that are dependent on external excitations and applied magnetic fields. To effectively implement the devices in mitigating the hazard vibrations of structures, numerically traceable and computationally efficient models should be firstly developed to accurately present the unique behaviors of MREs, including the typical Payne effect and strain stiffening of rubbers etc. In this study, the up-to-date phenomenological models for describing hysteresis response of MRE devices are experimentally investigated. A prototype of MRE isolator is dynamically tested using a shaking table in the laboratory, and the tests are conducted based on displacement control using harmonic inputs with various loading frequencies, amplitudes and applied current levels. Then, the test results are used to identify the parameters of different phenomenological models for model performance evaluation. The procedure of model identification can be considered as solving a global minimization optimization problem, in which the fitness function is the root mean square error between the experimental data and the model prediction. The genetic algorithm (GA) is employed to solve the optimization problem for optimal model parameters due to its advantages of easy coding and fast convergence. Finally, several evaluation indices are adopted to compare the performances of different models, and the result shows that the improved LuGre friction model outperforms other models and has optimal accuracy in predicting the hysteresis response of the MRE device.

온도에 따른 시선 안정화 시스템의 마찰 변수 추정

The objective of this study was to address the parameter estimation of the line-of-sight stabilization system on temperature variation, which is a significant element in regulating the control performance of mobile platform with visual targeting system. To this end, the LuGre friction model in this study was used both to represent the characteristic of the friction behavior and to design a control algorithm for the friction compensation. Results from both simulation and experimental tests helps to identify the friction parameters on LuGre friction model. Based on LuGre with parameter estimation, PI-LEAD control algorithm is designed to compensate nonlinear characteristic of the line-of-sight stabilization system on the variation of temperature. Finally, through simulation, the good control performance of line-of-sight stabilization system was evaluated according to the temperature variation.

Effect of friction on the dynamic analysis of slider-crank mechanism with clearance joint

In this paper, we are interested in the effect of friction on dynamic behavior of a crank-slider mechanism with clearance joint. Due to the clearance existence in the revolute joint, it is important to choose an appropriate contact force model to analyze the dynamic response, the dynamic equations are established by combining Lagrange’s equation of the first kind with modified contact force model and LuGre friction model, the Baumgarte stabilization approach was used to improve the numerical stability. Simulation and experimental tests were carried out to verify this model. The system dynamic response hysteresis, and the more energy consumption when friction is considered in the mechanism. The influence of friction coefficient on the nonlinear dynamic characteristics of the mechanism with clearance joint is analyzed. The dynamic performance of the mechanism considering friction presents significant differences at the accelerations level. Friction plays a positive role in the stability of the system.

Dynamics modeling and sliding mode control of tractor-trailer wheeled mobile robots subject to wheels slip

Wheeled mobile robots have vast applications in various areas of technology, and hence improving their autonomy has been the subject of extensive research. To enhance the payload carrying capacity of single-platform wheeled robots, an additional wheeled platform (called trailer) is connected to the active platform (called tractor) and the whole system is called the Tractor-Trailer Wheeled Mobile Robot (TTWMR). In the present study, a novel control rule is presented for trajectory tracking control of such robotic systems. To this end, the dynamics model of such nonholonomic systems is for the first time derived such that lateral and longitudinal slip in the wheels are taken into account. To model the interaction between the wheels and the ground, the LuGre friction model has been utilized. Then, the obtained dynamics model has been verified using ADAMS multibody simulation software. In the next step, to track the desired trajectories, a novel controller, based on sliding mode robust approach, is suggested in which slipping is modeled as a set of unknown but finite disturbances in the robot model. Validity and accuracy of the proposed controller have been examined via computer simulations.

Wpływ zjawiska tarcia na poziom dyskomfortu pracy operatora żurawia leśnego

A mathematical model of a forest crane that is suitable for dynamics analysis of its operation cycle is presented in this paper. The flexibility of the operator’s seat, drives and supports is taken into account. Joint coordinates are applied to describe the motion of the links together with the homogeneous transformations technique. Lagrange equations of the second order are used when deriving the equations of motions. Joint forces and torques are determined based on recursive Newton-Euler algorithms. These joint forces are then used in the LuGre friction model, which allows to calculate the friction coefficients and friction forces. Numerical analyses performed here show the influence of various friction forces on the vibration level as perceived by the operator of the crane. The level of discomfort is discussed based on standards commonly used in the vehicle and transportation industry for evaluations of vibration comfort

High-Precision XY Stage Motion Control of Industrial Microscope

This paper presents an economic way to implement a high-precision (micrometer level) XY stage motion control for the industrial microscope using dc motors. Other than the prevailing design of using stepper motors where the stage is always locked under the motorized mode, the proposed design allows users to manually move the stage by introducing the friction engagement in between. The nonlinearity from the friction is then fully compensated by the sliding mode control so that the stage can strictly follow the predefined motion profile. Possible chattering suppression methods are discussed and the accuracy loss is analyzed using the LuGre friction model. A fine-tuning algorithm is then proposed to limit the position error within $\pm$ 2 $\mu$ m. Compared to the other micrometer-level industrial microscopes using stepper motors, the proposed solution achieves comparable performance with much lower costs.

Study on dynamic characteristics and compensation of wire rope tension based on oil pressure sensor

The oil pressure sensors are installed on the hydraulic connection device to monitor the tension of wire ropes. The change of acceleration during the operation process of hoist causes the tension change of each wire rope. It leads to impact on the cylinder of hydraulic connection device, enlarges the pressure loss, and makes the non-linear friction become more complex which affects the monitoring accuracy. In this article, the mathematical model of hydraulic connection device is established. To analyze the dynamic characteristics of the hydraulic connection system, the model of single hydraulic cylinder and hydraulic connection device is established and simulated by AMESim software. Then, the friction and pressure compensation in the working process of hydraulic connecting device are obtained by LuGre friction model and corresponding formulas of pressure loss. Finally, the monitoring system is designed and real-time compensation test is carried out. The results show that the compensation improves the accuracy of the real-time measurement system of wire rope tension.

Design and Analysis of a Long-Stroke Planar Switched Reluctance Motor for Positioning Applications

This paper presents the design, control, and experimental performance evaluation of a long-stroke planar switched reluctance motor (PSRM) for positioning applications. Based on comprehensive consideration of the electromagnetic and mechanical characteristics of the PSRM, a motor design is first developed to reduce the force ripple and deformation. A control scheme with LuGre friction compensation is then proposed to improve the positioning accuracy of the PSRM. Furthermore, this control scheme is proven to ensure the stable motion of the PSRM system. Additionally, the response speed and steady-state error of the PSRM system with this control scheme are theoretically analyzed. Finally, the experimental results are presented and analyzed. The effectiveness of the precision long-stroke motion of the PSRM and its promise for use in precision positioning applications are verified experimentally.

A method for dynamic modeling and simulation of the translational joint with clearance and LuGre friction

The main purpose of this paper is to present a method for dynamic modeling and simulation of the translational joint with friction and clearance. The sizes of the clearances and the impacts between the slider and the guide in the translational joint can be neglected when the clearance sizes are very small. The geometric constraints of the translational joint are treated as bilateral constraints. The contact forces acting on the slider are reduced to the forces on the slider corners. The LuGre friction model is used to describe friction between slider and guide, because it can capture the variation of the friction force with slip velocity and the slider motion with stick–slip phenomenon. The problem of computing the normal forces on the slider is formulated and solved as a horizontal linear complementarity problem (HLCP), which is embedded in the event-driven method. Finally, a numerical example is considered and numerical results are presented to show the feasibility and the effectiveness of the method.

Dynamic friction modelling and parameter identification for electromagnetic valve actuator

A new modified LuGre friction model is presented for electromagnetic valve actuator system. The modification to the traditional LuGre friction model is made by adding an acceleration-dependent part and a nonlinear continuous switch function. The proposed new friction model solves the implementation problems with the traditional LuGre model at high speeds. An improved artificial fish swarm algorithm (IAFSA) method which combines the chaotic search and Gauss mutation operator into traditional artificial fish swarm algorithm is used to identify the parameters in the proposed modified LuGre friction model. The steady state response experiments and dynamic friction experiments are implemented to validate the effectiveness of IAFSA algorithm. The comparisons between the measured dynamic friction forces and the ones simulated with the established mathematic friction model at different frequencies and magnitudes demonstrate that the proposed modified LuGre friction model can give accurate simulation about the dynamic friction characteristics existing in the electromagnetic valve actuator system. The presented modelling and parameter identification methods are applicable for many other high-speed mechanical systems with friction.

Robust Adaptive Tracking Control Based on State Feedback Controller With Integrator Terms for Elastic Joint Robots With Uncertain Parameters

This brief addresses a robust adaptive control scheme based on a cascaded structure with a full state feedback controller with integrator terms as inner control loop and computed torque as outer control loop for flexible joint robots. Together with integrator effect, the adaptive control law can enhance position accuracy under uncertainties of the robot model, especially, the high friction caused by harmonic drive with high gear ratio. In this brief, the adaptive friction compensation is designed based on the LuGre friction model, which exhibits some advantages compared with the static friction model (e.g., no chattering effect at zero motor velocity). Furthermore, structural oscillations of the link side can be effectively damped by using joint torque feedback in the state feedback controller. Therefore, the proposed adaptive control approach can simultaneously provide high control performance both in terms of the dynamic behavior and the position accuracy. Global asymptotic tracking is achieved for the complete controlled system. The system stability is derived using Lyapunov approaches and Barbalat’s lemma. Experimental results validate the practical efficiency of the approach.

Numerical analysis of the friction-induced oscillator of Duffing's type with modified LuGre friction model

This paper focuses on analysis of a friction-induced mechanical oscillator with cubic nonlinearity and an applied dynamical model of dry friction. The studied model is based on the classical LuGre approach to friction force modelling. Lyapunov exponents spectrum of the frictional oscillator is calculated by means of a recently implemented method of their estimation for non-smooth systems. Results of the numerical research, observations of the nature of the oscillator's response and interaction of the applied dynamic friction model with the oscillator are reported.

Dynamic analysis of planar mechanical systems considering stick-slip and Stribeck effect in revolute clearance joints

The phenomena of friction in clearance joints have time- dependent nonlinear characteristics, which could lead to undesirable and unstable dynamic behavior of mechanical systems. Various mathematical models have been proposed to describe friction force in clearance joints. However, most of the previous models have different limitations, such as discontinuity at zero velocity or disability of detecting stick-slip motion. In this paper, a hybrid friction model is presented to analyze the dynamics of planar mechanical systems, considering sliding, sticking and Stribeck effect in revolute clearance joints. According to the kinematic analysis, the relative tangential motion between the journal and the bearing is categorized as sticking state, sliding state and transitional state. In the sticking state, an assumed acceleration constraint for the contact points is proposed to estimate the static friction force. This method not only eliminates the calculation of the implicit external force, but also accurately reflects the sticking process in accordance with the friction physics. Furthermore, the Stribeck effect is introduced in the description of the friction force in the sliding state, revealing the influence of the sliding velocity on the friction force. The stick-slip motion could also be accurately described by the Stribeck effect, which guarantees the continuity of the friction force during the transition process. Finally, a space robot manipulator is taken as an example to demonstrate the hybrid friction model. Dynamics of the space robot manipulator with Coulomb friction model, LuGre friction model, Wojewoda friction model and the hybrid friction model are compared, respectively. And the effects of clearance size, static friction coefficient and sliding friction coefficient on the dynamics of the manipulator are also analyzed.

Robust adaptive integral backstepping control for opto-electronic tracking system based on modified LuGre friction model

This paper presents a robust adaptive integral backstepping control strategy with friction compensation for realizing accurate and stable control of opto-electronic tracking system in the presence of nonlinear friction and external disturbance. With the help of integral control term to decrease the steady-state error of the system and combining robust adaptive control approach with the backstepping design method, a novel control method is constructed. Nonlinear modified LuGre observer is designed to estimate friction behavior. Robust adaptive integral backstepping control strategy is developed to compensate the changes in friction behavior and external disturbance of the servo system. The stability of the opto-electronic tracking system is proved by Lyapunov criterion. The performance of robust adaptive integral backstepping controller is verified by the opto-electronic tracking system with modified LuGre model in simulation and practical experiments. Compared to the adaptive integral backstepping sliding mode control method, the root mean square of angle error is reduced by 26.6% when the proposed control method is used. The experiment results demonstrate the effectiveness and robustness of the proposed strategy.

A Compact Impact Rotary Motor Based on a Piezoelectric Tube Actuator with Helical Interdigitated Electrodes.

This paper presents a novel impact rotary motor based on a piezoelectric tube actuator with helical interdigitated electrodes which has a compact structure and high resolution. The assembled prototype motor has a maximum diameter of 15 mm and a length of 65 mm and works under a saw-shaped driving voltage. The LuGre friction model is adopted to analyze the rotary motion process of the motor in the dynamic simulations. From the experimental tests, the first torsional resonant frequency of the piezoelectric tube is 59.289 kHz with a free boundary condition. A series of experiments about the stepping characteristics of different driving voltages, duty cycles, and working frequencies are carried out by a laser Doppler vibrometer based on a fabricated prototype motor. The experimental results show that the prototype rotary motor can produce a maximum torsional angle of about 0.03° using a driving voltage of 480 Vp-p (peak-to-peak driving voltage) with a duty ratio of 0% under a small friction force of about 0.1 N. The motor can produce a maximum average angle of about 2.55 rad/s and a stall torque of 0.4 mN∙m at 8 kHz using a driving voltage of 640 Vp-p with a duty ratio of 0% under a large friction force of about 3.6 N. The prototype can be driven in forward and backward motion and is working in stick-slip mode at low frequencies and slip-slip mode at high frequencies.

High-accuracy robust adaptive motion control of a torque-controlled motor servo system with friction compensation based on neural network

In this paper, a high-accuracy motion control of a torque-controlled motor servo system with nonlinear friction compensation is presented. Friction always exists in the servo system and reduces its tracking accuracy. Thus, it is necessary to compensate for the friction effect. In this paper, a novel controller that combines robust adaptive control with friction compensation based on neural network observer is proposed. An improved LuGre friction model is applied into the friction compensation as it is known as a good model to express the nonlinear friction. A single hidden-layer network is utilized to observe the immeasurable friction state. Then, the robust adaptive controller is used to handle the parametric uncertainty, the parametric estimation error, friction compensation error, and other uncertainties. Lyapunov theory is utilized to analyze the stability of the closed-loop system. The experimental results demonstrate the effectiveness of the proposed algorithm.

An improved cerebellar model articulation controller based on the compound algorithms of credit assignment and optimized smoothness for a three-axis inertially stabilized platform

An improved cerebellar model articulation controller (CMAC) based on the compound algorithms of credit assignment (CA) and optimized smoothness (OS) is proposed to improve the control performances of a three-axis inertially stabilized platform (ISP). On the basis of both advantages of CA and OS algorithms, the improved CMAC neural network controller can deal with the disadvantages of conventional CMAC in learning interference and output fluctuation. As a result, the main dynamic performances of the ISP control system are systematically promoted. To verify the method, the simulations and experiments are carried out respectively, in which the LuGre friction model is introduced to represent the main disturbances. The results show that the CA&OS-CMAC controller can efficiently restrain the nonlinear disturbances and obviously improve the ISP's pointing precision and output smoothness. Compared with the conventional CMAC controller, the root-mean-square (RMS) errors of tracking the angular position under the static base swinging and dynamic base leveling conditions are reduced by 17.17% and 30.55%, respectively.

Contour error pre-compensation for three-axis machine tools by using cross-coupled dynamic friction control

This paper focuses on improving the contouring performance for CNC machine tool by pre-compensated strategy. The predicted model of tracking error is established by utilizing the characteristic property of servo structure. Besides considering the frictional damping of transmission mechanism, a LuGre friction force compensated strategy is presented in the presence of both frictions and external disturbances. The contour error model based on the spatial relationship between the tracking error and contour error reduces the complex conventional iterative calculation and presents more flexibility. In order to acquire higher contouring accuracy, an adaptive cross-coupled pre-compensation controller is proposed to regulate the compensated values. Its central structure consists of a Fuzzy PID controller, and a modified particle swarm optimization is used to optimize the bottom parameters of membership functions. Compared with traditional cross-coupled control method, this new strategy has higher control accuracy and better robustness and universality. To validate the effectiveness, the proposed method is verified by several experiments, and the results show that the proposed method remarkably improves tracking performance and reduces contour error.