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

2003 ◽  
Vol 70 (6) ◽  
pp. 871-884 ◽  
Author(s):  
G. Cheng ◽  
J. W. Zu
Keyword(s):  
Dry Friction ◽  
Excitation Frequency ◽  
Solution Procedure ◽  
Friction Torque ◽  
Drive System ◽  
Belt Drive ◽  
Stick Slip ◽  
Harmonic Excitations ◽  
Rotational Vibration ◽  
The Impact

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.

Stick–slip oscillations of an engine front-end accessory drive system with a mechanical tensioner

2020 ◽  
pp. 095440702095058
Author(s):  
H Zhu ◽  
WD Zhu ◽  
W Fan
Keyword(s):  
Dry Friction ◽  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Friction Torque ◽  
Drive System ◽  
Balance Method ◽  
Stick Slip ◽  
Front End ◽  
Rotational Vibration ◽  
Calculation Results

This article is aimed to investigate the stick–slip oscillations of an engine front-end accessory drive system with a mechanical tensioner. Based on several assumptions, a generic dynamic model of rotational vibrations of an engine front-end accessory drive system with arbitrary number of accessory pulleys and one mechanical tensioner is established. In this model, the tensioner dry-friction torque is approximated by a hyperbolic tangent function with a scaling factor to control the sticking zone. An improved multiple harmonic balance method is used to solve the governing equations of rotations of the engine front-end accessory drive system and obtain the periodic rotational vibrations of the system accessory components. The calculation results obtained from the improved multiple harmonic balance method are verified by the results obtained from the Runge–Kutta integration method. Amplitude–frequency responses of rotational vibrations of the accessory components in the engine front-end accessory drive system are calculated using the arc-length technique based on the improved multiple harmonic balance method. Stick–slip oscillations of the tensioner arm with different values of the tensioner dry-friction torque are calculated and influences of the tensioner dry-friction on system rotational vibration amplitudes are analyzed. Variations of system vibration energies dissipated by the tensioner dry-friction at different crankshaft speeds with increases of the maximum tensioner dry-friction torque are calculated, and an optimum design of the tensioner dry-friction damping is given according to the results.

Influence of Tensioner Dry Friction on the Vibration of Belt Drives With Belt Bending Stiffness

2007 ◽  
Vol 130 (1) ◽  
Author(s):  
Farong Zhu ◽  
Robert G. Parker
Keyword(s):  
Dry Friction ◽  
Harmonic Balance ◽  
Excitation Frequency ◽  
Harmonic Balance Method ◽  
Friction Torque ◽  
Stick Slip ◽  
Pulley System ◽  
Coulomb Damping ◽  
Belt Drives ◽  
Linear Subsystem

A model of dry friction tensioner in a belt-pulley system considering transverse belt vibration is developed, and the influence of the dry friction on the system dynamics is examined. The discretized formulation is divided into a linear subsystem including linear coordinates and a nonlinear subsystem addressing tensioner arm vibration, which reduces the dimension of the iteration matrices when employing the harmonic balance method. The Coulomb damping at the tensioner arm pivot mitigates the tensioner arm vibration but not necessarily the vibrations of other system components. The extent of the mitigation varies for different excitation frequency ranges. The critical amplitude of the dry friction torque beyond which the system operates with a locked arm is determined analytically. Superharmonic resonances are observed in the responses of the generalized span coordinates, but their amplitudes are small. The energy dissipation at the tensioner arm hub is discussed, and the stick-slip phenomena of the arm are reflected in the velocity reversals near the arm extreme location. Dependence of the span tension fluctuations on Coulomb torque is explored.

Influence of Tensioner Dry Friction on the Vibration of Belt Drives With Belt Bending Stiffness

2007 ◽  
Author(s):  
Farong Zhu ◽  
Robert G. Parker
Keyword(s):  
Dry Friction ◽  
Harmonic Balance ◽  
Excitation Frequency ◽  
Harmonic Balance Method ◽  
Friction Torque ◽  
Stick Slip ◽  
Pulley System ◽  
Coulomb Damping ◽  
Belt Drives ◽  
Linear Subsystem

A model of dry friction tensioner in a belt-pulley system considering transverse belt vibration is developed, and the influence of the dry friction on the system dynamics is examined. The discretized formulation is divided into a linear subsystem including linear coordinates and a nonlinear subsystem addressing tensioner arm vibration, which reduces the dimension of the iteration matrices when employing the harmonic balance method. The Coulomb damping at the tensioner arm pivot mitigates the tensioner arm vibration but not necessarily the vibrations of other system components. The extent of the mitigation varies for different excitation frequency ranges. The critical amplitude of the dry friction torque beyond which the system operates with a locked arm is determined analytically. Superharmonic resonances are observed in the responses of the generalized span coordinates but their amplitudes are small. The energy dissipation at the tensioner arm hub is discussed, and the stick-slip phenomena of the arm are reflected in the velocity reversals near the arm extreme location. Dependence of the span tension fluctuations on Coulomb torque is explored.

Experimental Exploration of Schallamach Waves and Self-Excitation in a Belt-Drive System

2018 ◽  
Author(s):  
Yingdan Wu ◽  
Michael Varenberg ◽  
Michael J. Leamy
Keyword(s):  
Angular Velocity ◽  
Dynamic Behavior ◽  
Oscillation Amplitude ◽  
Operating Conditions ◽  
Drive System ◽  
Belt Drive ◽  
Stick Slip ◽  
Stick Slip Motion ◽  
System Inertia ◽  
Slip Motion

We study the dynamic behavior of a belt-drive system to explore the effect of operating conditions and system moment of inertia on the generation of waves of detachment (i.e., Schallamach waves) at the belt-pulley interface. A self-excitation phenomenon is reported in which frictional fluctuations serve as harmonic forcing of the pulley, leading to angular velocity oscillations which grow in time. This behavior depends strongly on operating conditions (torque transmitted and pulley speed) and system inertia, and differs between the driver and driven pulleys. A larger net torque applied to the pulley generally yields more remarkable stick-slip oscillations with higher amplitude and lower frequency. Higher driving speeds accelerate the occurrence of stick-slip motion, but have little influence on the oscillation amplitude. Contrary to our expectations, the introduction of flywheels to increase system inertia amplified the frictional disturbances, and hence the pulley oscillations. This does, however, suggest a way of facilitating their study, which may be useful in follow-on research.

Structural Stiffness, Dry-Friction Coefficient and Equivalent Viscous Damping in a Bump-Type Foil Gas Bearing

2005 ◽  
Author(s):  
Dario Rubio ◽  
Luis San Andre´s
Keyword(s):  
Friction Coefficient ◽  
Dry Friction ◽  
Structural Parameters ◽  
Excitation Frequency ◽  
Single Frequency ◽  
Viscous Damping ◽  
Periodic Load ◽  
Stick Slip ◽  
Equivalent Viscous Damping ◽  
Frequency Domain Methods

High performance oil-free turbomachinery implements gas foil bearings (FBs) to improve mechanical efficiency in compact units. FB design, however, is still largely empirical due to their mechanical complexity. The paper provides test results for the structural parameters in a bump-type foil bearing. The stiffness and damping (Coulomb or viscous type) coefficients characterize the bearing compliant structure. The test bearing, 38.1 mm in diameter and length, consists of a thin top foil supported on bump-foil strips. A prior investigation identified the stiffness due to static loads. Presently, the test FB is mounted on a non-rotating stiff shaft and a shaker exerts single frequency loads on the bearing. The dynamic tests are conducted at shaft surface temperatures from 25 °C to 75°C. Time and frequency domain methods are implemented to determine the FB parameters from the recorded periodic load and bearing motions. Both methods deliver identical parameters. The dry friction coefficient ranges from 0.05 to 0.20, increasing as the amplitude of load increases. The recorded motions evidence a resonance at the system natural frequency, i.e. null damping. The test derived equivalent viscous damping is inversely proportional to the motion amplitude and excitation frequency. The characteristic stick-slip of dry friction is dominant at small amplitude dynamic loads leading to a hardening effect (stiffening) of the FB structure. The operating temperature produces shaft growth generating a bearing preload. However, the temperature does not affect significantly the identified FB parameters, albeit the experimental range was too small considering the bearings intended use in industry.

scholarly journals Cluster synchronization of dry friction oscillators

2018 ◽  
Vol 148 ◽  
pp. 10004
Author(s):  
Michał Marszal ◽  
Andrzej Stefański
Keyword(s):  
Dry Friction ◽  
Numerical Study ◽  
Excitation Frequency ◽  
Friction Model ◽  
Cluster Synchronization ◽  
Stick Slip ◽  
Closed Ring ◽  
Mass Spring ◽  
Friction Oscillators ◽  
Two Parameter

Synchronization is a well known phenomenon in non-linear dynamics and is treated as correlation in time of at least two different processes. In scope of this article, we focus on complete and cluster synchronization in the systems of coupled dry friction oscillators, coupled by linear springs. The building block of the system is the classic stick-slip oscillator, which consists of mass, spring and belt-mass friction interface. The Stribeck friction itself is modelled using Stribeck friction model with exponential non-linearity. The oscillators in the systems are connected in nearest neighbour fashion, both in open and closed ring topology. We perform a numerical study of the properties of the dynamics of the systems in question, in two-parameter space (coupling coefficient vs. angular excitation frequency) and explore the possible configurations of cluster synchronization.

Modeling and Validation of Rotational Vibration Responses for Accessory Drive System—Part II: Simulations and Analyses

2013 ◽  
Vol 135 (3) ◽  
Author(s):  
Wen-Bin Shangguan ◽  
Xiang-Kun Zeng
Keyword(s):  
Excitation Frequency ◽  
General Purpose ◽  
Drive System ◽  
Dynamic Tension ◽  
Serpentine Belt ◽  
Rotational Vibration ◽  
Vibration Responses ◽  
System Part ◽  
Stiffness And Damping ◽  
General Purpose Software

This is the second part of the paper for modeling and validation of the rotational vibration responses for an accessory drive system. The unified formulas for modeling the rotational vibration of an accessory drive system are presented. In the modeling of an accessory drive system, the damping and stiffness of a belt are regarded as the function of the excitation frequency of an engine and the amplitude of belt stretching. Additionally, the creeping effect of a belt on the pulley wrap arc is included in the model. A general purpose software for calculating the rotational vibration of an accessory drive system is developed, based on the presented unified formulas. One accessory drive system with seven pulleys, a tensioner, and a serpentine belt is used as a studying example to demonstrate the unified formulas and the procedure for obtaining the rotational vibration. In the simulation of the accessory drive system, the stiffness and damping of the belt, the friction coefficient between the belt and pulley, and the excitation torques with multifrequency components from the crankshaft torsional vibration are obtained from the experiment in the first part of this paper. The static tension and steady-state tension of each belt span, along with the natural frequency of the accessory drive system, rotational vibrations of the driven pulley and tensioner arm, and the dynamic tension of the belt span are calculated and compared well with the experimental data, which validate the presented unified formulas and the developed general purpose software. The modeling method and the procedure described in this paper are instructive for designing an accessory drive system.

scholarly journals A New Efficient Adaptive Control of Torsional Vibrations Induced by Switched Nonlinear Disturbances

2019 ◽  
Vol 29 (2) ◽  
pp. 285-303 ◽  
Author(s):  
Maciej Wasilewski ◽  
Dominik Pisarski ◽  
Robert Konowrocki ◽  
Czesław I. Bajer
Keyword(s):  
Linear Quadratic Regulator ◽  
Drill String ◽  
Friction Torque ◽  
Nonlinear Behaviour ◽  
Torsional Vibrations ◽  
Linear Quadratic ◽  
Stick Slip ◽  
Direct Measurements ◽  
Excited Vibration ◽  
The Impact

Abstract Torsional vibrations induced in drilling systems are detrimental to the condition of the machine and to the effectiveness of the engineering process. The cause of vibrations is a nonlinear and unknown friction between a drill string and the environment, containing jumps in its characteristics. Nonlinear behaviour of the friction coefficient results in self-excited vibration and causes undesirable stick-slip oscillations. The aim of this paper is to present a novel adaptive technique of controlling vibrating systems. The scheme is based on the linear quadratic regulator and uses direct measurements of the friction torque to synthesize its linear dynamic approximation. This approach allows generating a control law that takes into account the impact of the friction on the system dynamics and optimally steers the system to the desired trajectory. The controller’s performance is examined via numerical simulations of the stabilization of the drilling system. The proposed solution outperforms the comparative LQG regulator in terms of the minimization of the assumed cost functional and the overall stability of the control system under the nonlinear disturbance.

Structural Stiffness, Dry Friction Coefficient, and Equivalent Viscous Damping in a Bump-Type Foil Gas Bearing

2006 ◽  
Vol 129 (2) ◽  
pp. 494-502 ◽  
Author(s):  
Dario Rubio ◽  
Luis San Andres
Keyword(s):  
Friction Coefficient ◽  
Dry Friction ◽  
Structural Parameters ◽  
Excitation Frequency ◽  
Single Frequency ◽  
Viscous Damping ◽  
Periodic Load ◽  
Stick Slip ◽  
Equivalent Viscous Damping ◽  
Frequency Domain Methods

High performance oil-free turbomachinery implements gas foil bearings (FBs) to improve mechanical efficiency in compact units. FB design, however, is still largely empirical due to its mechanical complexity. The paper provides test results for the structural parameters in a bump-type foil bearing. The stiffness and damping (Coulomb or viscous type) coefficients characterize the bearing compliant structure. The test bearing, 38.1mm in diameter and length, consists of a thin top foil supported on bump-foil strips. A prior investigation identified the stiffness due to static loads. Presently, the test FB is mounted on a non-rotating stiff shaft and a shaker exerts single frequency loads on the bearing. The dynamic tests are conducted at shaft surface temperatures from 25to75°C. Time and frequency domain methods are implemented to determine the FB parameters from the recorded periodic load and bearing motions. Both methods deliver identical parameters. The dry friction coefficient ranges from 0.05 to 0.20, increasing as the amplitude of load increases. The recorded motions evidence a resonance at the system natural frequency, i.e., null damping. The test derived equivalent viscous damping is inversely proportional to the motion amplitude and excitation frequency. The characteristic stick-slip of dry friction is dominant at small amplitude dynamic loads leading to a hardening effect (stiffening) of the FB structure. The operating temperature produces shaft growth generating a bearing preload. However, the temperature does not significantly affect the identified FB parameters, albeit the experimental range was too small considering the bearings intended use in industry.

scholarly journals The Stick-Slip Vibration and Bifurcation of a Vibro-Impact System with Dry Friction

2014 ◽  
Vol 8 (1) ◽  
pp. 308-313 ◽  
Author(s):  
Quanfu Gao ◽  
Xingxiao Cao
Keyword(s):  
Periodic Motion ◽  
Dry Friction ◽  
Low Frequency ◽  
Period Doubling ◽  
Periodic Motions ◽  
Vibratory System ◽  
Stick Slip ◽  
The Impact ◽  
Two Degree Of Freedom ◽  
Impact Motion

In this paper, the periodic motion, bifurcation and chatter of two-degree-of-freedom vibratory system with dry friction and clearance were studied. Slip-stick motion and the impact of system motions were analyzed and numerical simulations were also carried out. The results showed that the system possesses rich dynamics characterized by periodic motion, stick-slip-impact motion, quasi-periodic motion and chaotic attractors, and the routs from periodic motions to chaos observed via Hof bifurcation or period-doubling bifurcation. Furthermore, it was found that there exists the chatter phenomena induced by dry friction in low frequency, and the windows of chaotic motion are broadened in the area of higher excitation frequencies as the dry friction increases.

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