Friction-induced vibration considering multiple types of nonlinearities (original) (raw)
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Nonlinear Friction-Induced Vibration of a Slider–Belt System
Journal of Vibration and Acoustics, 2016
A mass–spring–damper slider excited into vibration in a plane by a moving rigid belt through friction is a major paradigm of friction-induced vibration. This paradigm has two aspects that can be improved: (1) the contact stiffness at the slider–belt interface is often assumed to be linear and (2) this contact is usually assumed to be maintained during vibration (even when the vibration becomes unbounded at certain conditions). In this paper, a cubic contact spring is included; loss of contact (separation) at the slider–belt interface is allowed and importantly reattachment of the slider to the belt after separation is also considered. These two features make a more realistic model of friction-induced vibration and are shown to lead to very rich dynamic behavior even though a simple Coulomb friction law is used. Both complex eigenvalue analyses of the linearized system and transient analysis of the full nonlinear system are conducted. Eigenvalue analysis indicates that the nonlinear ...
Analytical Approaches for Friction Induced Vibration and Stability Analysis
2011
The traditional mass on a moving belt model without external force excitation is considered. The displacement and velocity amplitudes and the period of the friction induced vibrations can be predicted using a friction force modelled by the mean of friction characteristics. A more precise look at the non-smooth transition points of the trajectories reveals that an extended friction model is looked-for. In present job, two so-called polynomial and exponential friction functions are investigated. Both of these friction laws describe a friction force that first drops off and then raises with relative interface velocity. An analytical approximation is applied in order to derive relations for the vibration amplitudes and base frequency and in parallel a stability analysis is performed. Moreover, results and phase plots are illustrated for both analytical and numerical approaches.
Accepted Manuscript Friction-induced vibration in a two-mass damped system
A two degree of freedom mass-spring-damper model on a moving lubricated belt is considered in this paper. The motions of the two masses are coupled through spring and damper and each mass interacts with a moving lubricated belt. The friction model includes the boundary, mixed and hydrodynamic regimes of lubrication contact regimes. Friction coefficient is presented as a function of sliding velocity at each mass interface that includes a combination of linear, exponential and cubic functions to account for relatively large coefficient at low sliding speed, followed by Stribeck effect at low to moderate speed ranges and finally a full hydrodynamic lubrication regime. A set of dimensionless parameters is introduced and system's dynamic response behavior as well as stability are studied for various combination of parameters.
Experimental investigation is performed on a test setup representing a single-degree-of-freedom friction-induced system. The experimental setup consists of a rigid mass (oscillator) connected to a fixed support through a spring and the mass in frictional contact with a moving belt. The major objectives of the experiments are to characterize (i) the nature of friction-induced oscillations, (ii) the nature of bifurcation associated with frictional instability in the system, and (iii) the nature of friction force that is responsible for the oscillations observed from the experiment. The phase portrait of the system shows significant overshoot of the oscillator velocity above the belt velocity indicating the existence of hys-teretic loop around zero relative velocity (pre-sliding regime). The bifurcation diagram clearly demonstrates the subcriticality of the Hopf bifurcation associated with the system negating all empirical friction models which yield supercritical Hopf bifurcation. The friction force-relative velocity curve shows significant hysteretic behavior, both in the pre-sliding as well as in the pure sliding domains. This observation hints towards a dynamic or an acceleration-dependent friction model as an appropriate choice for representing the friction force obtained from our experimental setup .
Numerical Modeling of Friction-Induced Vibrations and Dynamic Instabilities
Applied Mechanics Reviews, 1994
A numerical study of dynamic instabilities and vibrations of mechanical systems with friction is presented. Of particular interest are friction-induced vibrations, self-excited oscillations and stick-slip motion. A typical pin-on-disk apparatus is modeled as the assembly of rigid bodies with elastic connections. An extended version of the Oden-Martins friction model is used to represent properties of the interface. The mechanical model of the frictional system is the basis for numerical analysis of dynamic instabilities caused by friction and of self-excited oscillations. Coupling between rotational and normal modes is the primary mechanism of resulting self-excited oscillations. These oscillations combine with high-frequency stick-slip motion to produce a significant reduction of the apparent kinetic coefficient of friction. As a particular study model, a pin-on-disk experimental setup has been selected. A good qualitative and quantitative correlation of numerical and experimental ...
Friction-induced oscillations of a slider: Parametric study of some system parameters
Journal of Sound and Vibration, 2007
A typical frictionally excited pin on disk system is modeled as a basis for vibration control. The model is based on chosen experimental setup parameters. The analysis incorporates normal, tangential and torsional degrees of freedom. The effect of varying both the normal force and the pin stiffness on the response of the pin subsystem in all directions is investigated numerically. A detailed parametric study shows that the operating condition namely the normal force and the rotational speed have a remarkable influence on the response. A correlation between measured and calculated system response is presented, that supports the validity of the presented model. The dynamic characteristics of the system, namely stiffness of the pin in both normal and torsional direction, have no significant effect on its response, while its tangential stiffness has a minor effect. r coefficient of friction. Earles and Badi and Earles and Chambers used pin on disk systems in which two pins were acting on the disk to investigate and quantify the sprag-slip mechanism for squeal. The investigations performed consisted of examining how the damping influenced squeal. In these works, a linear stability analysis was performed on lumped parameter models of pin-disk systems in order to find the flutter boundaries in parameter space. After the constraints had been incorporated, these models were generally linear three-or five-degree-of-freedom systems. They found that damping in the pin assembly (corresponding to damping of the brake pad assembly in a disk brake) could enlarge the unstable regions under certain circumstances, while disk damping always reduced these regions.
A Non-Linear Friction Model for Self-Excited Vibrations
Journal of Sound and Vibration, 1997
The motivation behind this work is to develop a dynamical systems understanding of the phenomenon of squeal. Squeal is a form of self-excited vibration; vibrations are induced in a structure such as a wheel or violin string by the action of a frictional driving force. The nature of this force is rather difficult to define; however, a phenomenological model is proposed which combines the concepts of static and dynamic friction, which seems intuitively reasonable and for which there is documented evidence. In the case presented here, the vibrating structure is simplified to that of a block resting on a moving conveyor belt, restrained by a simple spring and dashpot to a rigid wall. The non-linear system dynamics predicted by using the new friction model are unusual in that the conditions giving rise to squeal include not only the belt speed, but also the initial conditions of the structure. It is thought that this information may be useful in the control of the onset of squeal.
Volume 4: 8th International Conference on Multibody Systems, Nonlinear Dynamics, and Control, Parts A and B, 2011
The principal aim of this paper is to deal with frictioninduced self-excited vibrations in the context of Stribeck law for friction coefficient. More precisely, the theoretical dynamic system under study consists of a single-degree-of-freedom massspring-damper oscillator subjected to a velocity-dependent frictional force as it slides on a conveyor belt, following a Stribeck law. We have analyzed the local stability of the static equilibrium and described the created periodic cycle using the averaging method. Numerical continuation with Matcont software is also used for qualitative analysis of this non linear system. In order to validate the theoretical analysis, an original experimental device, the named Lug test rig developed in our laboratory, was employed. For a glass/elastomer contact lubricated with water, friction force and dynamic displacement have been measured. The appearance of the instabilities is explained in relation to the friction measurements.
2017
Influence of frequency of excitation on chaotic dynamics of a 2-DoF mechanical system with dry friction is investigated. The analysed system consists of a block vibrating on a transmission belt driven by an electric motor. Stick-slip friction in a contact between the block and the belt introduce significant variability of load affecting operation of the driving system. In the naturally coupled systems, a resultant unsteady rotational velocity of the DC motor acts as a time varying high frequency disturbance of velocity of motion of the base. Bifurcational behaviour of the 2-DoF block-on-belt system with dry friction and its response to an irregular excitation caused by the disturbed velocity of motion of the base is analysed using bifurcation diagrams. Mathematical model of the block-on-belt system with a normal force intensification mechanism and the electric motor based driving system has been developed and numerically solved. Changes in the assumed stiffness parameter of bifurcat...
Friction-Induced Vibration Suppression via the Tuned Mass Damper: Optimal Tuning Strategy
Lubricants
Friction-induced vibrations are a significant problem in various engineering applications, while dynamic vibration absorbers are an economical and effective tool for suppressing various kinds of vibrations. In this study, the archetypal mass-on-moving-belt model with an attached dynamic vibration absorber was considered. By adopting an analytical procedure, the optimal tuning of the absorber’s parameters was defined. Furthermore, the bifurcations occurring at the loss of stability were analytically investigated; this analysis illustrated that a properly chosen nonlinearity in the absorber’s stiffness permits controlling the supercritical or subcritical character of the bifurcation. However, a numerical analysis of the system’s dynamics, despite confirming the analytical results, also illustrated that the system’s global behavior is only slightly affected by the bifurcation character. Indeed, a dynamic vibration absorber possessing a perfectly linear restoring force function seems to...