Coulomb Friction Torque Research Articles

Adaptive PI Controller for Speed Control of Electric Drives Based on Model Reference Adaptive Identification

In this paper, to achieve auto-setting of PI controller gains when mechanical parameters are unknown, two adaptive PI controllers for speed control of electric drives are developed based on model reference adaptive identification. The adaptive linear neuron (ADALINE) neural network is used to interpret the proposed adaptive PI controller. The effect of the low-pass filter used for the feedback speed and the Coulomb friction torque on parameter identification is analysed, and a new motion equation using filtered speed is given. Additionally, a parameter identification method based on unipolar speed reference is provided. The two proposed adaptive PI controllers and the conventional PI controller are compared based on the high-precision digital simulation using MATLAB/Simulink (version R2023a). The simulation results show that both of the two proposed adaptive PI controllers are able to identify mechanical parameters, but the adaptive PI-1 controller outperforms the adaptive PI-2 controller due to its better noise attenuation performance.

Research and Analysis of Coulomb Friction in Landing Gear Shimmy

Aircraft are subject to small disturbances during taxiing, many of which are accidental and difficult to explain. Although nonlinear factors are considered in traditional analysis, Coulomb friction is generally ignored, and the interaction and common effects of nonlinear factors are mostly not discussed. In this paper, the dynamic model of shimmy is established, and the influence of Coulomb friction on shimmy is studied by using bifurcation theory and the structural mechanics analysis method. The results show that the system with Coulomb friction has subcritical Hopf bifurcation and that the system with square damping has supercritical Hopf bifurcation. Although the two do not change the stability of the system, their cooperation can improve the stability of the system. The Coulomb friction torque of the system has a complex piecewise functional relationship with the stability distance, rake angle, and acceleration. Some combinations will lead to very low Coulomb friction and deteriorate the anti-interference ability of the landing gear. This paper provides theoretical basis and support for the rational design of structural parameter collocation, enhancing the antidisturbance ability of the system during constant-speed or variable-speed taxis and explaining the shimmy phenomenon in the process of variable-speed taxis of some aircraft.

The influence of temperature rise on the friction torque of ball screw during low speed operation

This study used innovative testing methods to investigate the effect of physical temperature rise on low-speed friction torque of double nut ball screws. 72 experiments were conducted using two samples and three protocols. Found the inflection point temperature and inflection point velocity. Below the inflection point temperature, the frictional torque increases with the increase of speed; Above this temperature, the frictional torque first decreases and then increases. Below this inflection point speed, the frictional torque first decreases and then increases; Above the inflection point velocity, the friction torque decreases with increasing temperature. Based on the Strebeck theory, the variation of friction coefficient with temperature was studied; When it is below the inflection point speed, it fluctuates greatly with the increase of temperature, but when it is above the inflection point speed, the fluctuation is small and steadily decreases with the increase of temperature. In addition, based on the theoretical models of Coulomb friction torque and viscous friction torque, the results of this model are in good agreement with the measurement results above the inflection point speed, indicating the correctness of the theory and providing good theoretical guidance for engineering designers.

Theoretical and experimental analysis of the temperature rise of a ball screw

The temperature rise of a ball screw is the main factor affecting machining accuracy. The traditional methods of calculation and analysis carry out coefficient fitting of known experimental data or using the formula for a friction heat source in bearing theory. However, the screw raceway parameters are ignored in the model. The variation in friction torque with temperature is not considered in the model, so it cannot be effectively applied to engineering. In this paper, the friction heat equation of the ball screw is established theoretically with the screw raceway parameter, and the friction torque is considered with the effect of temperature. A mathematical model of steady temperature and stable time is established for the effective heat source stroke section of the screw, and the temperature rise curve of the screw is fitted. The friction is divided into Coulomb friction torque and viscous friction torque. The viscosity affects viscous friction torque at low temperatures, so the variation in friction torque should be considered when calculating the temperature rise. When a specific temperature is reached, the viscous friction torque has little effect on the overall friction torque; then the ratio of temperature rises at different rotational speeds has an exponential relationship with the ratio of those speeds. The screw stability time decreases with increasing rotational speed. Twelve groups of tests are conducted to verify the theoretical analysis using two samples, two lubricating media, and three speeds. The experimental results agree well with the theory. This proves that the approach can be applied to engineering practice.

Adaptive Multi-Parameter Estimation of Inertial Stabilization Platform with Unknown Load

In order to improve the state monitoring and adaptive control capability of inertial stabilization platforms (ISPs) with unknown loads, it is necessary to estimate the dynamic parameters comprehensively online. However, most current online estimation methods regard the system as a linear dual-inertia model which neglects the backlash and nonlinear friction torque. It reduces the accuracy of the model and leads to incomplete and low accuracy of the estimated parameters. The purpose of this research is to achieve a comprehensive and accurate online estimation of multiple parameters of ISPs and lay a foundation for state monitoring and adaptive control of ISPs. First, a dual-inertia model containing backlash and nonlinear friction torque of the motor and load is established. Then, the auto-regressive moving average (ARMA) model of the motor and load is established by the forward Euler method, which clearly expresses the online identification formula of the parameters. On this basis, the adaptive identification method based on the recursive extended least squares (RELS) algorithm is used to realize the online estimation of multiple parameters. The simulation and experimental results show that the proposed adaptive multi-parameter estimation method can realize the simultaneous online identification of the moment of inertia of the load, the damping coefficient of motor and load, the transmission stiffness, the Coulomb friction torque of motor and load, and the backlash, and the steady-state error is less than 10%. Compared with the traditional linear dual-inertia model, the similarity between the model based on the proposed adaptive parameter estimation algorithm and the actual system is increased by 65.3%.

Online Parallel Estimation of Mechanical Parameters for PMSM Drives via a Network of Interconnected Extended Sliding-Mode Observers

The accurate estimation of mechanical parameters is essential for the control optimization and condition monitoring of permanent-magnet synchronous motor (PMSM) drives. In this article, an online parallel estimation scheme is proposed based on a network of three interconnected extended sliding-mode observers. With a two-step mechanism derived from the developed network, this scheme can simultaneously achieve the accurate real-time observation of three mechanical parameters, including the viscous friction coefficient, the moment of inertia, and the load torque. The first step utilizes the presented network to precisely acquire the Coulomb friction coefficient by offering only one speed. With aiding from this estimated coefficient, the second step attains the high-precision online identification of the three concerned parameters by compensating the Coulomb friction torque to counteract its adverse effect. These two steps are implemented utilizing the identical network, thus, furthest avoiding increasing the estimation complexity. Besides, any additional knowledge other than the rotor speed and electromagnetic torque is no longer required for guaranteeing the asymptotic convergence of the estimation errors. Sufficient evaluations from simulations and experiments confirm the validity of the proposed scheme.

Design and applications of steering angle tracking control with robust compensator for steer-by-wire system of intelligent vehicle

Abstract The steer-by-wire (SBW) system is a key component for an intelligent vehicle, which is related to the safety, comfort, and drivability of vehicle. Hence, it is supposed to ensure strong robustness and functional safety under various operating conditions, which is one of the main difficulties of SBW. In this paper, a linear quadratic regulator (LQR) with a novel robust compensator is designed for steering angle control of SBW to improve the tracking performance. The SBW actuator is regarded as a permanent magnet synchronous motor (PMSM) control system with parameter perturbation and external disturbance, including Coulomb friction and self-aligning torque. Theoretical analysis proves that the proposed method can ensure the system stability and make the tracking error converge to zero against multiple uncertainties. The main parameters are obtained by offline calculation and the online calculation burden is small, so the proposed method is suitable for vehicle applications. Both simulations and experiments show that the robust compensator is effective.

An Experimental Method for Estimating Combined Friction Torque in Vane Type Pneumatic Semi Rotary Actuators

In this paper, an experimental method is proposed for estimation of friction torque in vane type pneumatic semi rotary actuators. The friction is modelled in the form of fully combined Stribeck model since this combined friction model provides good solutions for precise control applications. The study aims estimating static friction torque, Coulomb friction torque, Stribeck speed and viscous friction&damping coefficient which is included in fully combined Stribeck model for both counterclockwise and clockwise directions of the rotary actuator since these unknown parameters show differences when direction of motion is altered. For that purpose, an experimental setup is designed which includes pressure sensors for measuring the chamber pressures of actuator, analogue potentiometer for reading angular position as well as speed of vane and Arduino microcontroller card for data acquisition. A proper MATLAB Simulink block diagram is prepared for the simultaneous estimation of processed data from experimental data. Nonlinear curve fitting operation is applied and the unknown friction parameters are estimated on the fitted curve easily.

Soft Sensor Simulation of Minimum Energy Consumption of Joint Manipulator Drive System Based on Improved BP Neural Network

The energy dissipation level of articulated mechanical arms directly affects the control stability of industrial robot systems. For a six-degree-of-freedom articulated robot driven by a DC servo motor and reduction gear, based on the Hamiltonian and Minimum theories, a model of the articulated manipulator drive system under load torque is established, and the expressions of optimal angular velocity and control current are obtained considering the viscous friction and coulomb factors. According to the analysis of actual parameter simulation experiments, it can be seen that the energy consumption of the joint manipulator drive system increases with the decrease of efficiency, the increase of the coulomb friction torque of the servo motor, and the increase of the load torque. Within the transit time, the total energy consumption of the drive system is smaller, so it is very important to obtain the transit time within the optimal area for the minimum energy consumption of the joint robotic arm drive system. At the same time, a soft neural network model based on the improved BP neural network built on the neural network toolbox for the energy consumption of the articulated mechanical arm is established. Finally, the experimental platform of servo motor drive system is built and used for the experiment of servo motor drive, and the purpose of closed-loop control is also achieved. Through experimental analysis, it can be seen that the proposed soft sensor model of joint minimum energy consumption based on improved BP neural network can more accurately realize the energy consumption prediction under unknown angular displacement and unknown load, and provide a theoretical basis for joint energy monitoring.

Simultaneous Identification of Multiple Mechanical Parameters in a Servo Drive System Using Only One Speed

In some servo applications, restricted by the measurement noise and the stiffness of the mechanical system, the bandwidth of the disturbance observer cannot be high enough to realize a good robust control to parameters uncertainties, it is essential to identify the mechanical parameters. In the existing mechanical parameter identification methods, the viscous and Coulomb friction torque coefficients are usually identified using two different constant speeds, and the moment of inertia can be identified with various methods. However, no one method can identify these three parameters at the same time using only one speed. The contribution of this article is to propose a method that can identify the three mechanical parameters simultaneously using only one speed. A low-pass filter is used to suppress the measurement noise in the speed feedback, thus parameters are identified with high precision. A unidirectional sine-wave speed is used to decouple the viscous friction torque and the Coulomb friction torque, two speeds with different amplitudes and the detection of the speed amplitude are no more required. Adaptive extended state observer (ESO) is designed based on the Lyapunov's stability theory, can be easily changed to the normal ESO used in active disturbance rejection control. The proposed method is easy to understand and implement. The effectiveness of the method is verified by both the simulation and experimental results.

Fault Tolerant Control of Electronic Throttles with Friction Changes

To enhance the reliability of the electronic throttle and consequently the vehicles driven by the internal combustion engines, a fault tolerant control strategy is developed in this paper. The proposed method employs a full-order terminal sliding mode control in conjunction with an adaptive radial basis function network to estimate change rate of the fault. Fault tolerant control to abrupt and incipient changes in the throttle viscous friction torque coefficient and the throttle coulomb friction torque coefficient is achieved. Whilst the throttle position is driven to track the reference signal, the post-fault dynamics are guaranteed to converge to the equilibrium point in finite time, and the control is smooth without chattering. A nonlinear Simulink model of an electronic throttle is developed with real physical parameters and is used for evaluation of the developed method. A significant change of the throttle friction torque is simulated, and the fault tolerant control system keeps system stability and tracking the reference signal in the presence of the fault.

A novel reduced order dynamic model of axial piston motors with compression flow losses and Coulomb friction losses

Purpose The purpose of this paper is to identify the energy losses factors during the hydro-mechanical conversion process at high pressure via a novel reduced order dynamic model.Design/methodology/approach A novel reduced order dynamic model of the axial piston motor was proposed, which provides an explicit insight to the compression flow losses and the Coulomb friction losses. A fully coupled dynamic model of the piston motor was obtained based on the array bond graph method. And then, a reduced order model was obtained by the composition analysis of flow and torque of the axial piston motor. After that, the energy losses estimation model was presented to predict the energy loss of the piston motor under a wide range of working conditions. The model was verified by comparing the experimental and simulation results.Findings The simulation result indicates that the flow loss caused by oil compression accounts for 59 per cent of the total flow loss, and the Coulomb friction torque accounts for 40 per cent of the total torque loss under a specific working condition. The compression flow loss and Coulomb friction torque are the major factors that lead to the aggravation of energy loss under extreme working conditions of the piston motor.Originality/value At high-pressure condition, the compression flow losses due to fluid compressibility cannot be neglected, and the hydro-mechanical losses in varies friction pairs should involve Coulomb friction losses. Flow and torque loss analytical expression in the model involve the design and control parameters of the piston equipment, which can realize the parameter optimization of the piston equipment for the purpose of energy-saving.

Moment of Inertia and Friction Torque Coefficient Identification in a Servo Drive System

This paper proposes a new method to identify the mechanical parameters of a servo drive system, such as the moment of inertia and friction torque coefficients. Identification of the moment of inertia is essential for the design of a high-performance speed and position controller. Furthermore, the mechanical friction torque coefficients, such as the viscous and Coulomb friction torque coefficients, can be used to reduce the speed and position error without resorting to the use of a high gain for the speed controller. To simultaneously identify the moment of inertia and the friction torque coefficients, the proposed method uses the fact that the sinusoidal speed is in phase with the friction torque and out of phase with the torque for the moment of inertia. The proposed method is based on the speed control loop and the moment of inertia, and friction torque coefficients can be exactly obtained from a half-period integration of the torque reference of the low frequency sinusoidal speed control. Using computer simulations and experiments employing 600-W servo drive systems, the feasibility of the proposed method was verified.

Design, modeling and characterization of a novel meso-scale SMA-actuated torsion actuator

This paper presents our work on design, modeling, and characterization of a novel shape memory alloy (SMA)-actuated torsion actuator for meso-scale robots. Development of a miniature torsion actuator is challenging, but it can enhance the agility and enlarge the workspace of meso-scale robots. This torsion actuator comprises a pair of antagonistic SMA torsion springs, which bi-directionally actuate the actuator by Joule heating and natural cooling. First, the mechanical design of the torsion actuator is presented, followed by the fabrication of SMA torsion springs. Then, we present the constitutive model of the SMA torsion spring with an analysis of its strain change, and derive a quasi-static model with the Coulomb friction torque for this torsion actuator. Finally, a series of characterization experiments are conducted on the SMA torsion spring and the torsion actuator prototype to determine the values of all model parameters. This work shows that the properties of the SMA-actuated torsion actuator can be appropriately characterized by experiments and the actuator is feasible for robotics applications.

쿨롱마찰을 고려한 무인항공기용 영상 김발의 제어시스템 설계

One of the frequent problems in the stabilized gimbal system is the rejection of disturbances associated with moving components. Very often such disturbances have non-linear characteristics. In a typical gimbal system, each gimbal and platform are connected by a mutual bearing which induces inevitable friction. Particularly, the non-linear Coulomb friction causes position errors as well as slow responses that lead to unfavorable performance. In this paper, a modified PID controller that is augmented by Coulomb friction estimator is presented. Through constantly estimating the Coulomb friction torque, it is applied to the output of the existing PID controller. The effectiveness of the proposed controller is evaluated through a series of experiments.

Identification of Electro-mechanical Actuators within Limited Stroke

This paper presents a novel method for estimating the parameters of electro-mechanical systems, or known as actuators, within limited stroke. Identification of actuators with unlimited stroke is an ordinary problem in control applications. However, in identifying parameters of the actuator like the viscous damping coefficient, the Coulomb friction torque, and the equivalent moment of inertia reflected to the motor side, the mechanism with limited stroke is involved and the identification problem becomes more complicated. In this paper, a simple and straightforward method is developed to resolve this problem. A sequence of pulses with various levels is designed to estimate the viscous damping coefficient and the Coulomb friction torque within the limited stroke of the actuator. Then an optimal algorithm based on the interior-reflective Newton method is applied to search the moment of inertia of the overall system. It is demonstrated in the simulation examples that even when the velocity profile is calculated directly from the first difference of the sampled position and is corrupted by highly amplified noise, the proposed method can still find the moment of inertia with error less than 1%. Simulation and experimental results are both presented indicating the practical viability of the proposed approach.

Optimal Design of Gear Ratios and Offset for Energy Conservation of an Articulated Manipulator

It is important to minimize the energy dissipated by the reduction gears and motors in a three-jointed vertically articulated manipulator. This paper proposes an optimal design method for simultaneously determining eight design variables, which are three motor masses, three reduction gear ratios, a counterbalancer mass for the third link and an offset between the first and the second links. Using these design variables, the equation of motion and the dissipated energy can be expressed as functions of the moment of inertia and the Coulomb friction torque of the joints and the inertia matrix of the manipulator. Optimal design variables can be determined by minimizing the dissipated energy under the constraint conditions for the motors and the offset. The numbers of stages for the reduction gear trains are determined from the optimal gear ratios. Simulations show that the proposed design method can reduce the dissipated energy more effectively than the inertia matching method.

Nonstick and Stick-Slip Motion of a Coulomb-Damped Belt Drive System Subjected to Multifrequency Excitations

In this paper, the rotational vibration of a belt drive system with a dry friction tensioner subjected to multiple harmonic excitations is studied. The work is focused on the impact of the dry friction torque combined with the multiexcitation frequencies on dynamic characteristics of the system. An analytical solution procedure is developed for the first time to predict two kinds of periodic responses of the system, i.e., nonstop and one-stop motion characterized by the nonstick and stick-slip vibration of the tensioner arm in the system, respectively. Utilizing this method, parametric studies are carried out to obtain the frequency response of a prototypical belt drive system subjected to harmonic excitations from both the driving and driven pulleys. It is found that the tensioner Coulomb friction torque has a significant impact on the amplitude response of the system—it reduces the vibration amplitude of the tensioner arm, but for other components in the belt system it can either decrease or increase the amplitudes under different situations. Furthermore, if the excitation frequency from the driving pulley is larger than or equal to that from the driven pulley, the system vibration amplitudes are much larger than those under the opposite condition.

粘性摩擦，クーロン摩擦および一定外乱トルクの影響を除去したイナーシャ同定方式

This paper presents the inertia identification method in which the factors of viscous friction, Coulomb friction and constant disturbance torque are eliminated. It has a model of a velocity controller and rigid mechanical system integrating faur conditions described as follows. The first condition is that real velocity equals model velocity and is not zero. Under this condition, the inertia is calculated by taking the ratio of the integrated value of real torque reference in specified time range to the integrated value of the model torque. The second condition, elimination of viscous friction, is that the integrated value of velocity equals to zero in the specified time range. The third condition, elimination of Coulomb friction, is that the time range for velocity in positive direction equals the time range for velocity in negative direction. The last condition, elimination of constant disturbance torque requires selection of velocity references Vref1 which is satisfied with conditions 1 to 3 and Vref2 which is defined as inverting of Vref1. Then, the average inertia value under each velocity reference is computed. The experimentalresults using the one-axis stage verified the exact inertia identification.

Adaptive Velocity Control of DC Motors With Coulomb Friction Identification

A new dc motor control technique for the Coulomb friction compensation is proposed. The technique uses an adaptive velocity control scheme for a dc servo motor with on-line estimated parameters, including a Coulomb friction parameter, which is a combination of the Coulomb friction torque, motor time constant, moment of inertia of the motor, and sampling time of the discrete-time motor model. The estimation model used in the adaptive control process is validated off-line by a pseudo-linear regression algorithm for system parameters in a linear ARMAX model, and by adaptive Kalman filters for the Coulomb friction parameter described as pseudo-random binary sequences. The adaptive controller consists of a friction compensator and a PID controller, whose gains are adjusted adaptively in terms of estimated parameters. The proposed adaptive control law is implemented and tested on a microprocessor-based dc servo motor, and is applicable to many dc-motor-driven precision servo mechanisms. Experimental results are shown to be superior to those of conventional PID controls in terms of parameter fluctuation.