Effect of non-Coulomb dry friction on the stability of automatic systems

2005 ◽  
Vol 50 (3) ◽  
pp. 151-153
Author(s):  
V. N. Shamberov
Keyword(s):  
Dry Friction ◽  
The Stability ◽  
Coulomb Dry Friction ◽  
Automatic Systems

Two-Frequency Oscillation With Combined Coulomb and Viscous Frictions

2002 ◽  
Vol 124 (4) ◽  
pp. 537-544 ◽  
Author(s):  
Gong Cheng ◽  
Jean W. Zu
Keyword(s):  
Steady State ◽  
Dry Friction ◽  
Single Frequency ◽  
Friction Oscillator ◽  
One Stop ◽  
Frequency Excitation ◽  
Stop Motion ◽  
The One ◽  
Coulomb Dry Friction ◽  
Mass Spring

In this paper, a mass-spring-friction oscillator subjected to two harmonic disturbing forces with different frequencies is studied for the first time. The friction in the system has combined Coulomb dry friction and viscous damping. Two kinds of steady-state vibrations of the system—non-stop and one-stop motions—are considered. The existence conditions for each steady-state motion are provided. Using analytical analysis, the steady-state responses are derived for the two-frequency oscillating system undergoing both the non-stop and one-stop motions. The focus of the paper is to study the influence of the Coulomb dry friction in combination with the two frequency excitations on the dynamic behavior of the system. From the numerical simulations, it is found that near the resonance, the dynamic response due to the two-frequency excitation demonstrates characteristics significantly different from those due to a single frequency excitation. Furthermore, the one-stop motion demonstrates peculiar characteristics, different from those in the non-stop motion.

scholarly journals On the inclusion of a velocity-dependent basal drag in avalanche models

1998 ◽  
Vol 26 ◽  
pp. 277-280 ◽  
Author(s):  
J.M.N.T. Gray ◽  
Y.C. Tai
Keyword(s):  
Stress State ◽  
Constant Coefficient ◽  
Dry Friction ◽  
Earth Pressure ◽  
Asymptotic Model ◽  
Drag Coefficients ◽  
Finite Velocity ◽  
Large Thickness ◽  
Coulomb Dry Friction ◽  
Avalanche Models

The Savage-Hutter model is generalized by including a velocity-dependent drag in addition to the usual Coulomb dry friction at the base of the avalanche. Both linear and quadratic velocity dependencies are considered, with either constant or asymptotically constant drag coefficients for large thickness h. The singular nature of the constant coefficient model for small h is demonstrated and it is shown that the asymptotic model allows the tail of the avalanche to move at a finite velocity. The inclusion of velocity drag changes the stress state in the avalanche and new earth-pressure relations are derived and investigated.

Synthesis of a High-Precision Missile Homing System with an Permissible Stability Margin of the Normal Acceleration Stabilization System

2021 ◽  
Vol 22 (7) ◽  
pp. 365-373
Author(s):  
Quang Thong Do
Keyword(s):  
High Precision ◽  
Parametric Optimization ◽  
Stability Margin ◽  
Optimization Method ◽  
Synthesis Process ◽  
Stabilization System ◽  
Gain Margin ◽  
The Stability ◽  
Automatic Systems ◽  
Normal Acceleration

The proportional guidance method-based missile homing systems (MHS) have been widely used the real-world environments. In these systems, in order to destroy the targets at different altitudes, a normal acceleration stabilization system (NASS) is often utilized. Therefore, the MHS are complex and the synthesis of these systems are a complex task. However, it is necessary to synthesize NASS during the synthesis of the MHS. To simplify the synthesis process, a linear model of the NASS is used. In addition, we make use of the available commands in Control System Toolbox in MATLAB. Because the Toolbox has the commands to describe the transfer function, determine the stability gain margin, and the values of the transient respond of the linear automatic systems. Thus, this article presents two methods for synthesizing the missile homing systems, including (i) a method for synthesizing the MHS while ensuring the permissible stability gain margin of the NASS, and (ii) a method for synthesizing the MHS while ensuring the permissible stability margin of the NASS by overshoot. These techniques are very easy to implement using MATLAB commands. The synthesis of the proposed MHS is carried out by the parametric optimization method. To validate the performance of the proposed techniques, we compare them withthe MHS synthesized by ensuring the stability margin of the NASS bythe oscillation index. The results show that, two our proposed methods and the existing method provide the same results in terms of high-precision. Nevertheless, the proposed methods are simple and faster than the conventional method. The article also investigates the effect of gravity, longitudinal acceleration of the rocket, andblinding of the homing head on the accuracy of the synthesized MHS. The results illustrate that they have a little effect on its accuracy.

Study of Dynamic Modes of Current Stabilization Systems of Powerful Electromagnets with Pulse-Width Modulation

2021 ◽  
Vol 22 (6) ◽  
pp. 313-320
Author(s):  
M. S. Lur’e ◽  
O. M. Lur’e ◽  
A. S. Frolov
Keyword(s):  
Pulse Width ◽  
Pulse Width Modulation ◽  
Functional Differential Equations ◽  
Original System ◽  
Nyquist Stability ◽  
Detailed Assessment ◽  
Functional Differential ◽  
The Stability ◽  
Automatic Systems ◽  
A Current

This study is devoted to the consideration of a method for assessing the stability of systems with pulse-width modulation, based on the linearization of its equivalent system with pulse-width modulation. An approximate study of the dynamic modes of operation of systems with pulse-width modulation, taking into account the stability for the system of automatic control of the supply current of electromagnets under the conditions of external and internal interference, is carried out. Variants of execution of schemes of pulse-width regulators for the power supply of an electromagnet based on a unipolar and bipolar element with pulse-width modulation are presented. The possibility of linearization of systems with pulse-width modulation for the subsequent detailed assessment of the stability of such systems is shown. The prospects of using functional differential equations for stability analysis of automatic systems with pulse-width modulation are shown. The frequency characteristics of an equivalent pulse system are analyzed using the example of a current stabilization system of high-power electromagnets with a pulse-width regulator, taking into account the replacement of the latitude modulation by the amplitude one. Based on the analysis of the resulting transfer function, which is a stable linearized equivalent open system, the ways of evaluating the stability of the original system with pulse-width modulation using the Nyquist stability criterion are proposed. The conclusion is made about the advantage of a system with PWM, in relation to a system with AIM, in terms of stability, and recommendations are given for the use of the obtained data in the analysis oftransients in such systems.

scholarly journals On the Stability of Digital Position Control with Viscous Damping and Coulomb Friction

2017 ◽  
Vol 61 (4) ◽  
pp. 266 ◽  
Author(s):  
Csaba Budai ◽  
László Kovács L.
Keyword(s):  
Discrete Time ◽  
Dry Friction ◽  
Coulomb Friction ◽  
Control Parameter ◽  
Position Control ◽  
Viscous Damping ◽  
Sampled Data ◽  
Stable Domain ◽  
The Stability ◽  
Parameter Values

In this paper, we investigate the combined effect of viscous damping and Coulomb friction on sampled-data mechanical systems. In these systems, instability can occur due the sampling of the applied discrete-time controller which is compensated by the two different physical dissipation effects. In order to investigate the interplay between these, we focus on how the stable domain of operation is extended by the dry friction compared to viscous damping. We also show that dry friction causes concave envelope vibrations in this extended region. The analytical results, presented in the form of stability charts, are verified by a detailed set of simulations at different representative control parameter values.

Nonlinear Numerical Prediction of Gas Foil Bearing Stability and Unbalanced Response

2008 ◽  
Vol 131 (1) ◽  
Author(s):  
Sébastien Le Lez ◽  
Mihaï Arghir ◽  
Jean Frêne
Keyword(s):  
Dry Friction ◽  
Stability Limit ◽  
Time Step ◽  
Structural Dynamic ◽  
Friction Forces ◽  
Foil Bearings ◽  
Mass Unbalance ◽  
Foil Bearing ◽  
Highly Nonlinear ◽  
The Stability

One of the main interests of gas foil bearings lies in their superior rotordynamic characteristics compared with conventional bearings. A numerical investigation on the stability limit and on the unbalanced response of foil bearings is presented in this paper. The main difficulty in modeling the dynamic behavior of such bearings comes from the dry friction that occurs within the foil structure. Indeed, dry friction is highly nonlinear and is strongly influenced by the dynamic amplitude of the pressure field. To deal with these nonlinearities, a structural dynamic model has been developed in a previous work. This model considers the entire corrugated foil and the interactions between the bumps by describing the foil bearing structure as a multiple degrees of freedom system. It allows the determination of the dynamic friction forces at the top and at the bottom of the bumps by simple integration of ordinary differential equations. The dynamic displacements of the entire corrugated sheet are then easily obtained at each time step. The coupling between this structural model and a gas bearing prediction code is presented in this paper and allows performing full nonlinear analyses of a complete foil bearing. The bearing stability is the first investigated problem. The results show that the structural deflection enhances the stability of compliant surface bearings compared with rigid ones. Moreover, when friction is introduced, a new level of stability is reached, revealing the importance of this dissipation mechanism. The second investigated problem is the unbalanced response of foil bearings. The shaft trajectories depict a nonlinear jump in the response of both rigid and foil bearings when the value of the unbalance increases. Again, it is evidenced that the foil bearing can support higher mass unbalance before this undesirable step occurs.

scholarly journals TWO MODELS OF NONSMOOTH DYNAMICAL SYSTEMS

2011 ◽  
Vol 21 (10) ◽  
pp. 2853-2860 ◽  
Author(s):  
MADELEINE PASCAL
Keyword(s):  
Dry Friction ◽  
Coupled Oscillators ◽  
Degrees Of Freedom ◽  
Analytical Form ◽  
Critical Value ◽  
Form Solution ◽  
Nonsmooth Systems ◽  
The Stability ◽  
Close Form ◽  
Nonsmooth Dynamical Systems

Two examples of nonsmooth systems are considered. The first one is a two degrees of freedom oscillator in the presence of a stop. A discontinuity appears when the system position reaches a critical value. The second example consists of coupled oscillators excited by dry friction. In this case, the discontinuity occurs when the system's velocities take a critical value. For both examples, the dynamical system can be partitioned into different configurations limited by a set of boundaries. Within each configuration, the dynamical model is linear and the close form solution is known. Periodic orbits, including several transitions between the various configurations of the system, are found in analytical form. The stability of these orbits is investigated by using the Poincaré map modeling.

scholarly journals Influence of Dry Friction on the Dynamics of Cantilevered Pipes Conveying Fluid

2022 ◽  
Vol 12 (2) ◽  
pp. 724
Author(s):  
Zilong Guo ◽  
Qiao Ni ◽  
Lin Wang ◽  
Kun Zhou ◽  
Xiangkai Meng
Keyword(s):  
Flow Velocity ◽  
Friction Force ◽  
Dry Friction ◽  
Critical Flow Velocity ◽  
Pipe System ◽  
Pipes Conveying Fluid ◽  
Cantilevered Pipe ◽  
The Stability ◽  
Friction Parameters ◽  
Conveying Fluid

A cantilevered pipe conveying fluid can lose stability via flutter when the flow velocity becomes sufficiently high. In this paper, a dry friction restraint is introduced for the first time, to evaluate the possibility of improving the stability of cantilevered pipes conveying fluid. First, a dynamical model of the cantilevered pipe system with dry friction is established based on the generalized Hamilton’s principle. Then the Galerkin method is utilized to discretize the model of the pipe and to obtain the nonlinear dynamic responses of the pipe. Finally, by changing the values of the friction force and the installation position of the dry friction restraint, the effect of dry friction parameters on the flutter instability of the pipe is evaluated. The results show that the critical flow velocity of the pipe increases with the increment of the friction force. Installing a dry friction restraint near the middle of the pipe can significantly improve the stability of the pipe system. The vibration of the pipe can also be suppressed to some extent by setting reasonable dry friction parameters.

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