Analysis and control of friction-induced oscillations in a continuous system (original) (raw)
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Delayed feedback for controlling the nature of bifurcations in friction-induced vibrations
Journal of Sound and Vibration, 2011
We analyse the control of friction-induced vibrations using time-delayed displacement feedback. We have used the exponential model for the drooping characteristics of the friction force for which the bifurcation is subcritical in nature. With an appropriate choice of the control parameters we have managed to change the nature of the bifurcation to supercritical along with increasing the stability boundaries. A nonlinear controller is required when the control force is applied in a direction parallel to the friction force. In contrast, a linear time-delayed displacement feedback applied in a direction normal to the friction force achieves our dual objective of controlling the nature of the bifurcation as well as quenching the vibrations. We also consider a dynamic friction model (the LuGre model) and observe that the qualitative change in the nature of the bifurcation is independent of the complexity considered in modeling the friction force.► We control the nature of bifurcation associated with friction-induced vibrations. ► Time-delayed feedback control has been used. ► Linear controller normal to the contact surface is found to be sufficient. ► Results are robust with respect to the friction model used for the study.
2013
We analyse the effect of time-delayed position feedback in controlling frictioninduced vibrations of a single degree-of-freedom spring-mass-damper system on a moving belt. The friction force is modeled by a dynamic (LuGre) friction model. The control force is applied in a direction normal to the friction force. Linear stability analysis shows that the stability of the steady-state changes via a Hopf bifurcation. Numerical analysis of the full nonlinear equations reveals the possibility of changing the nature of the bifurcation from subcritical to supercritical using the linear control force employed in our study. Detailed numerical studies using a continuation scheme shows an interesting range of control parameters for which the steady-state is stable for low and high belt velocities and unstable for the intermediate ones. Interestingly, this phenomena is observed only for those control parameters for which the bifurcation is supercritical in nature. In particular, there are combina...
International Journal of Non-Linear Mechanics, 2014
We investigate the control of friction-induced vibrations in a system with a dynamic friction model which accounts for hysteresis in the friction characteristics. Linear time-delayed position feedback applied in a direction normal to the contacting surfaces has been employed for the purpose. Analysis shows that the uncontrolled system loses stability via. a subcritical Hopf bifurcation making it prone to large amplitude vibrations near the stability boundary. Our results show that the controller achieves the dual objective of quenching the vibrations as well as changing the nature of the bifurcation from subcritical to supercritical. Consequently, the controlled system is globally stable in the linearly stable region and yields small amplitude vibrations if the stability boundary is crossed due to changes in operating conditions or system parameters. Criticality curve separating regions on the stability surface corresponding to subcritical and supercritical bifurcations is obtained analytically using the method of multiple scales (MMS). We have also identified a set of control parameters for which the system is stable for lower and higher relative velocities but vibrates for the intermediate ones. However, the bifurcation is always supercritical for these parameters resulting in low amplitude vibrations only.
A comparative study on the control of friction-driven oscillations by time-delayed feedback
Nonlinear Dynamics, 2010
We perform a detailed study of two linear time-delayed feedback laws for control of frictiondriven oscillations. Our comparative study also includes two different mathematical models for the nonlinear dependence of frictional forces on sliding speed. Linear analysis gives stability boundaries in the plane of control parameters. The equilibrium loses stability via a Hopf bifurcation. Dynamics near the bifurcation is studied using the method of multiple scales (MMS). The bifurcation is supercritical for one frictional force model and subcritical for the other, pointing to complications in the true nature of the bifurcation for frictiondriven oscillations. The MMS results match very well with numerical solutions. Our analysis suggests that one form of the control force outperforms the other by many reasonable measures of control effectiveness.
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 .
Friction-induced vibration considering multiple types of nonlinearities
Nonlinear Dynamics, 2020
The friction-induced vibration of a novel 5-DoF (degree-of-freedom) mass-on-oscillating-belt model considering multiple types of nonlinearities is studied. The first type of nonlinearity in the system is the nonlinear contact stiffness, the second is the non-smooth behaviour including stick, slip and separation, and the third is the geometrical nonlinearity brought about by the moving-load feature of the mass slider on the rigid belt. Both the linear stability of the system and the nonlinear steady-state responses are investigated, and rich dynamic behaviours of the system are revealed. The results of numerical study indicate the necessity of the transient dynamic analysis in the study of friction-induced-vibration problems as the linear stability analysis fails to detect the occurrence of self-excited vibration when two stable solutions coexist in the system. The bifurcation behaviour of the steady-state responses of the system versus some parameters is determined. Additionally, th...
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.
Applied Sciences
Friction-Induced Vibration and noisE (FIVE) is still a complex and nonlinear physical phenomenon which is characterized by the appearance of instabilities and self-sustained vibrations. This undesirable vibrational phenomenon is encountered in numerous industrial applications and can cause major failures for mechanical systems. One possibility to limit this vibration phenomenon due to the appearance of instabilities is to add a controller on the system. This study proposes to discuss the efficiency but also limitations of an active control design based on full linearization feedback. In order to achieve this goal, a complete study is performed on a phenomenological mechanical system subjected to mono or multi-instabilities in the presence of friction. Transient and self-excited vibrations of the uncontrolled and controlled systems are compared. More specifically, contributions of linear and nonlinear parts in the control vector for different values of friction coefficient are invest...
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 ...
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.