On the Effect of Contact Compliance on Vibrational Smoothing of Dry Friction

High-frequency vibrations may be utilized in order to smooth the characteristics of dry friction at low sliding velocities and, consequently, quench undesired friction induced phenomena. Many studies have been published so far, most of them using classical Coulomb friction models and yielding compact results. Unfortunately, the agreement with related experimental results is insufficient. As the Coulomb model overestimates the smoothing effect, improved modelling seems to be necessary. Based on Dahl's friction model, the effect of longitudinal and transverse high-frequency vibrations on a 1-DoF-friction oscillator is investigated here. Accounting for contact compliance, a reduction of the smoothing effect is observed. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the Influence of High-Frequency Excitation on Systems with Dynamic Friction

By imposing high-frequency vibrations to a system, the characteristics of dry friction for low sliding velocities can be smoothed and, consequently, undesired friction induced phenomena such as stick-slip motion can be quenched. Many studies have been published so far, most of them focussing on the reduction of friction between metal surfaces and using classical Coulomb friction models. Within this contribution the effect of high-frequency excitation on dry friction taking into account dynamic friction models will be discussed. To this end, the friction law suggested by Dahl is used and the resulting friction characteristics are compared to those obtained for the classical Coulomb friction model. Using Dahl's friction model, a reduction of the smoothing effect is observed. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Free vibration analysis of a rigidly fixed viscothermoelastic hollow sphere

In this paper an exact analysis of homogenous rigidly fixed vibrations of viscothermoelastic hollow sphere is presented. The basic governing partial differential equations have been reduced to ordinary differential equations by using Helmholtz decomposition equations. The uncoupled equation is taken for first class vibrations and remains independent of temperature variations, while coupled system of equations are taken for second class vibrations. Matrix Fröbenious method of extended power series has been applied in the coupled system of differential equations to get displacements and temperature. Numerical results have been presented, giving lowest frequency, dissipation factor, displacements and temperature change.     

On the influence of vibrations on macroscopic frictional contacts

Ultrasonic vibrations in the micrometer amplitude range have been proven to be capable to influence frictional contacts with respect to decreasing friction coefficients in experiments on small test set-ups solely loaded by their small weight [1]. In this paper experimental results on applying this effect to large objects are presented. To get large vibration amplitudes and velocities detailed pre-investigation on the excitation of the structures in contact have been performed. These structures are investigated in a roller rig designed for these purposes. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Simulation of friction phenomena between randomly rough elastic surfaces

Friction induced vibrations are a widely studied field in which the friction coefficient is one of the most important parameters. Measurements show that the friction coefficient underlies stochastic fluctuations. To gain more knowledge about the friction coefficient a finite element study is carried out in order to simulate the friction forces. The Bowden-Tabor model is implemented which calculates the friction force as the force which is needed to shear apart contact areas hold together by welding or adhesion. The dependency of the friction value on sliding velocity and normal pressure can be determined with this model. Different realization are studied and the stochastic properties of the friction value such as mean value, standard deviation, amplitude spectrum and correlation coefficient can be calculated depending on the roughness of the surface. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Effect of high-frequency excitation in regenerative turning of metals and brittle materials

We have analyzed vibrations generated in an orthogonal cutting process. Using a simple single degree of freedom model with friction we have observed the chatter vibrations. In the limit of a high rotational velocity the rough cutting surface combined with a friction phenomenon caused effective damping in the system. For simplicity, we used a harmonic function to describe the profile of the initial surface.     

Bifurcation analysis of a stochastic non-smooth friction model

Non-smooth friction systems such as systems with dry friction show several bifurcation phenomena. The discontinuity of these so called slip-stick vibrations makes these systems interesting and there has been a lot of research in this field, see for example Hinrichs [1]. Due to the non-smooth friction force even the deterministic system shows a rich bifurcation behavior. Measurements indicate that the friction coefficient which plays a large role in the system behavior is not deterministic but can be described as a friction characteristic with added white noise. Therefore, the stochastic characteristic is introduced into the non-smooth system and the change of the bifurcation behavior is studied. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Evolution of the resonance vibrations of an oscillator with dry friction

We study the problem of free and forced vibrations of a mechanical system modeling the functioning of seismic isolation systems of “kinematic foundation” type in the case when the sliding friction damper is not centrally located. We determine the damping characteristics in the case of free vibrations and the critical values of the damping parameter for the case of forced vibrations. For the case of resonance vibrations with one degree of freedom we establish the relation of the increase in the amplitude of the vibrations to time at subcritical values of the friction. Translated fromDinamicheskie Sistemy, Vol. 11, 1992.     

A Wave-Based Approach to Adaptively Control Self-Excited Vibrations in Drill-Strings

Due to their small diameter-to-length-ratio, drill-strings are vulnerable to torsional vibrations. Moreover, the string is exposed to unknown or uncertain time-variant and nonlinear loads (e.g. friction with falling friction characteristics, contact with the borehole, differential sticking), which can result in severe torsional vibrations and stick-slip. The control law for the boundary controller at the top drive of the string needs to adapt to those unknown loads in order to stabilize the vibrations. The torsional vibrations of a drill-string are governed by the wave equation. Analytical solutions and control laws are often based on a separation of the dynamics into a time- and a space-dependent part (modal representation). Here, we decompose the vibrations into two traveling waves according to the D'Alembert solution, using only few measurements along the string. The wave which travels up the string is then compensated by the actuator at the top drive. With this compensation, the upward-traveling wave is no longer reflected back into the string and vibration energy is absorbed, thus stabilizing the torsional vibrations. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On some regularities in dynamic response of cyclic periodic structures

The paper deals with cyclic periodic structures modelling bladed disk assemblies of blades with friction elements for vibration damping. These elements placed between adjacent blades reduce the vibration amplitudes by means of dry friction resulting from centrifugal forces acting on the elements and relative displacements of the blades. However, the application of these friction elements results in an additional dynamical coupling which together with mistuning of some system parameters (e.g., blade eigenfrequency or contact parameters) may cause localization of vibration. In the present paper a linear approximation of such a system is investigated. The structure composed of cyclic periodic cells modelled each as a clamped-free beam interacting with each other by means of viscoelastic elements of complex stiffness is applied for dynamic system analysis. In case of free vibrations as well as in case of steady-state dynamic response to a harmonic pressure field, a perfect periodic structure and the structures with periodically mistuned parameters (blade eigenfrequencies and contact parameters) are studied. Some regularities in the dynamic response of the systems with mistuning have been noticed. Despite the fact that only a linear approximation has been used, the results and conclusions can be applied for models which describe the blade interaction in a nonlinear way.     

The Vibrational Behavior of Bladed Disks in Consideration of Friction Damping and Contact Elasticity

Rotating turbine blading is subjected to fluctuating gas forces during operation that cause blade vibrations. One of the main tasks in the design of turbomachinery blading is the reduction of the vibration amplitudes of the blades to avoid high resonance stresses that could damage the blading. The vibration amplitudes of the blades can be reduced significantly to a reasonable amount by means of friction damping devices such as underplatform dampers. In the case of blade vibrations, relative displacements between the friction damping devices and the neighboring blades occur and friction forces are generated that provide additional damping to the structure due to the dry friction energy dissipation. In real turbomachinery applications, spatial blade vibrations caused by a complex blade geometry and distributed excitation forces acting on the airfoil accur. Therefore, a three dimensional model including an appropriate spatial contact model to predict the generalized contact forces is necessary to describe the vibrational behavior of the blading with sufficient accuracy, see [1] and [2]. In this paper the contact model presented in [2] is extended to include also local deformations in the contacts between underplatform dampers and the contact surfaces of the adjacent blades. The additional elasticity in the contact influences the resonance frequency of the coupled bladed disk assembly. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Influence of the hydraulic fluid pipe on the dynamic stability of a shift gearbox

Shift gearboxes are used in vehicle drive trains in order to transmit the driving torque of the motor and to shift between different transmission ratios. Because of the occurrence of sliding friction forces and -torques during the shifting period, unwanted vibrations can arise. Several mechanisms which lead to a destabilization of the stationary state in shift gearboxes are conceivable: variable friction coefficient [1], wobbling clutch disc [2], or vibrations because of coupled DoFs due to the helical gearing [3]. The latter effect results in translational oscillations in axial and radial direction of the clutch disc. It was observed that damping forces influence the boundary of the region of stability in the parameter space - though it is not entirely clear where such forces originate from. For this reason, in this work the effect of the fluid of the hydraulic actuation of the clutch system is analyzed. The fluid pipe is situated in the center of the gear unit input shaft and forces the fluid to oscillate when the system becomes unstable. In return, the fluid implies shear stress and pressure on the adjacent mechanical parts (shaft, pressure plates). The analysis of the stationary state of the coupled system reveals a clear effect of fluid properties on the stability: both the mass density and the kinematic viscosity are able to change the location of the border between stable and instable regions in the parameter space. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Investigation of Damping of Vibrations in a System With Two‐Disc Inseparable Clutch

This paper presents the results of tests on free and forced harmonic torsional vibrations in a system with a two‐disc inseparable clutch, with structural friction taken into account. Nonlinear histeresis loop describing the frictional‐elastic properties of the system was introduced into the model. The mathematical model of the vibrating system containing two disks inseparable clutch was built. During free vibrations of the system, its damping characteristics were tested by a digital simulation method. The vibration damping decrement as a function of amplitude torsional displacement was determined. When vibrations were harmonically forced, the amplitude ‐ frequency characteristics of the system were determined numerically. The system was used as a nonlinear torsional vibration damper in a linear system with a harmonic force. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Effect of Holes on the Eigenmodes of Reinforced Shells of Rotation

The vibrational eigenmodes of reinforced shells of rotation with holes are examined. A solution is constructed on the basis of the linear theory of thin elastic shells using the Ritz method. Results are presented from numerical studies of the effect of holes and reinforcements on the eigenmodes and forms of the vibrations. The results are compared with experimental data.     

Efficient Calculation of Tread Block Vibrations

A model is presented that allows to calculate the dynamics of tyre tread blocks. The numerical efficiency is achieved by the combination of static and important modal ansatz functions, also known as Hurty/Craig/Bampton transformation. Nonlinear single point contacts provide the contact forces and consider the surface roughness. The non-smooth friction characteristic is approximated an arctan function and a parameter study of the slope parameter is conducted. Typical stickslip limit cycles of the tread block are shown. These phenomena can have a part in the tyre/road noise. Experimental results qualitatively agree with the modelled tread block vibrations. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Vibrations Action of the Trilling Machine MA750 on the Human Operator Hand

The Work includes identifying and analyzing vibrations produced by a trilling machine MA750 within space work. To identify vibration is used a special method, which has not been used so far in identifying vibrations, with the action on the human body. For obtaining a very good identification of the human body vibrations has been used the Moiré projection method. General conditions were applied to human hand operator during working hours on a trilling machine, with different speeds of main shaft. In the paper are presented successively two methods of measuring the vibrations: the Moiré projection method and conventional method of measuring the vibrometer. The results in the booth situation (classical measurements and Moiré projection method) were in the same order of the unit scale, and the optical method named Moiré projection method can be considered a valid method for the human vibrations measurements without touch of the surface. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Self-excited vibrations of deformable multibody systems due to friction: Explanation with the help of two point masses and a belt

The aim of this paper is to present the results of the investigations of the ability of self-excited vibrations due to friction in a planar simplified mechanical model, with a constant coefficient of friction. The Hurwitz criteria is used for the stability analysis and the determination of the critical value of the coefficent of friction. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Characterization of disk brake noise behavior via measurement of friction forces

Squealing of disk brakes is a major problem in the field of vehicle design. It is commonly acknowledged, that this squeal is initiated by instability due to friction forces between the pads and the disk, leading to self excited vibrations. This work addresses the mechanical work of these friction forces in order to draw conclusions for the investigation of the noise behavior of disk brakes. Therefore a multi degree of freedom model is used to compare its stability behavior with the frictional work at the pads. The results obtained are applied to experiments in which, on the one hand brake pads with integrated piezoceramic actuators cause a broad band excitation and, on the other hand, dynamic pad velocities/accelerations and friction forces are measured. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)