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.

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.

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.

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.

scholarly journals Dual Time Stepping Algorithms With the High Order Harmonic Balance Method for Contact Interfaces With Fretting-Wear

2011 ◽  
Author(s):  
Loi¨c Salles ◽  
Laurent Blanc ◽  
Fabrice Thouverez ◽  
Alexander M. Gouskov ◽  
Pierrick Jean
Keyword(s):  
Frequency Domain ◽  
Dry Friction ◽  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Contact Forces ◽  
Balance Method ◽  
Fretting Wear ◽  
Rate Equations ◽  
Time Stepping ◽  
Dual Time Stepping

Contact interfaces with dry friction are frequently used in turbomachinery. Dry friction damping produced by the sliding surfaces of these interfaces reduces the amplitude of bladed-disk vibration. The relative displacements at these interfaces lead to fretting-wear which reduces the average life expectancy of the structure. Frequency response functions are calculated numerically by using the multi-Harmonic Balance Method (mHBM). The Dynamic Lagrangian Frequency-Time method is used to calculate contact forces in the frequency domain. A new strategy for solving non-linear systems based on dual time stepping is applied. This method is faster than using Newton solvers. It was used successfully for solving Nonlinear CFD equations in the frequency domain. This new approach allows identifying the steady state of worn systems by integrating wear rate equations a on dual time scale. The dual time equations are integrated by an implicit scheme. Of the different orders tested, the first order scheme provided the best results.

Forced Response Prediction of Blades With Loosely Assembled Dovetail Attachment by HBM

2009 ◽  
Author(s):  
Shangguan Bo ◽  
Zili Xu ◽  
Qilin Wu ◽  
XianDing Zhou ◽  
ShouHong Cao
Keyword(s):  
Friction Force ◽  
Centrifugal Force ◽  
Dry Friction ◽  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Forced Response ◽  
Balance Method ◽  
Force Model ◽  
Equivalent Stiffness ◽  
Equivalent Damping

To understand the mechanism of interfacial damping of axial loosely assembled dovetail to suppress blade vibration, a dry friction force model is presented by the Coulomb friction law and the macroslip model, and the mathematical expression of the friction force is derived. The nonlinear friction force is linearized as an equivalent stiffness and an equivalent damping through the one-term harmonic balance method. The effect of centrifugal force on the equivalent stiffness and the equivalent damping is studied. The forced response of one simplified blade with loosely assembled dovetail attachment is predicted by the harmonic balance method, in which the blade is described by the lumped mass and spring model, and the friction contact joints is simplified as a ideal friction damper. The results show that the equivalent stiffness of loosely assembled dovetail attachment increases with blade centrifugal force, gradually reaches a certain value, and there exists the maximum value for the equivalent stiffness. The equivalent damping increases at the beginning and then decreases with blade centrifugal force increasing, there exists a maximum too. The resonant frequency of blade rises with blade centrifugal force, but it no longer increases when the centrifugal force exceed a certain value. There exists a special centrifugal force on which the effect of dry friction damping is the best.

Multi-Harmonic Analysis of Dry Friction Damped Systems Using an Incremental Harmonic Balance Method

1985 ◽  
Vol 52 (4) ◽  
pp. 958-964 ◽  
Author(s):  
C. Pierre ◽  
A. A. Ferri ◽  
E. H. Dowell
Keyword(s):  
Time Domain ◽  
Dry Friction ◽  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Frequency Domain Analysis ◽  
Balance Method ◽  
Incremental Harmonic Balance Method ◽  
Incremental Harmonic Balance ◽  
The Time Domain ◽  
Damped Systems

A multi-harmonic, frequency domain analysis of dry friction damped systems is presented which uses an incremental harmonic balance method. When compared with time domain solution methods, it is found that the incremental harmonic balance method can yield very accurate results with some advantages over the time domain methods. Both one and two degree-of-freedom systems are studied.

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.

Nonlinear Dynamics of Shrouded Turbine Blade System with Impact and Friction

2014 ◽  
Vol 706 ◽  
pp. 81-92 ◽  
Author(s):  
B. Santhosh ◽  
S. Narayanan ◽  
C. Padmanabhan
Keyword(s):  
Frequency Response ◽  
Turbine Blade ◽  
Dry Friction ◽  
Normal Load ◽  
Harmonic Balance Method ◽  
Tangential Direction ◽  
Stick Slip ◽  
Variable Friction ◽  
Blade System ◽  
Constant Normal Load

Dry friction dampers are passive devices used to reduce the resonant vibration amplitudes in turbine bladed systems. In shrouded turbine blade systems, in addition to the stick- slip motion induced by dry friction during the contact state in the tangential direction, the interface also undergoes intermittent separation in the normal direction. The problem can thus be treated as a combination of impact and friction. In this work, the dynamics of dry friction damped oscillators which are representative models of dry friction damped bladed system is investigated. A one dimensional contact model which is capable of modeling the interface under constant and variable normal load is used. The steady state periodic solutions are obtained by multi - harmonic balance method (MHBM). Frequency response plots are generated for different values of normal load using the arc length continuation procedure. The MHBM solutions are validated using numerical integration. A single degree of freedom (dof) model under constant normal load with constant and variable friction coefficients, a dry friction damped two dof system under constant normal load and a two dof system under variable normal load are investigated. In the presence of variable normal load, the system shows multivalued frequency response and jump phenomenon. The optimal value of the normal load which gives minimum resonant response is also obtained.

Feasibility Research on Coupled Friction/Piezoelectric Dampers

2018 ◽  
Author(s):  
Lin Li ◽  
Yaguang Wu ◽  
Yu Fan
Keyword(s):  
Dry Friction ◽  
Harmonic Balance ◽  
Vibrational Mode ◽  
Piezoelectric Materials ◽  
Harmonic Balance Method ◽  
Forced Response ◽  
Friction Dampers ◽  
Feasibility Research ◽  
Aero Engines ◽  
Better Than

A new passive damper coupling the energy dissipative mechanisms of dry friction and piezoelectric shunting circuit is proposed. The idea is to embed the shunted piezoelectric materials to the dry friction dampers at appropriate positions, so that the elastic deformation of the dry friction dampers can be utilized to generate additional damping. Moreover, this provides a more practical way to install the piezoelectric dampers into realistic mechanical systems such as aero-engines. A five Degree-of-freedom (DOFs) lumped system model is introduced to demonstrate the feasibility of such an idea. The damping performance is revealed using the forced response results obtained by the Multi Harmonic Balance Method (MHBM). We show that the coupled damper significantly outperforms the standalone piezoelectric or dry friction dampers. The coupled damper is better than, at least equivalent to, the case where both piezoelectric and dry friction dampers are applied but in uncoupled manner. Eventually, the mechanism of the proposed damper is further explained from the perspective of vibrational mode and energy conversion.

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.

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