Y.H. Wijnant

Validation of EHL Contact Predictions under Time Varying Load

Abstract In this paper, it is investigated how accurately current models predict the response of an elasto-hydrodynamically lubricated contact to time varying load conditions. For two patterns of time varying load, under conditions of pure rolling, the results obtained experimentally on a ball on disk interferometry apparatus by Sakamoto et al. (Behaviour of point contact EHL films under pulsating loads. Proceedings of the 30th Leeds-Lyon Symposium on Tribology, Elseviers Tribology Series, Vol. 43, pp. 391-399) are compared with the results of numerical simulations using the dynamic contact model of Wijnant (Contact dynamics in the field of elastohydro-dynamic lubrication. PhD Thesis, University of Twente, Enschede, The Netherlands, 1998 ISBN 90-36512239), Wijnant and Venner (Contact dynamics in starved elastohydrodynamic lubrication. Proceedings of the 25th Leeds-Lyon Symposium on Tribology, Elsevier Tribology Series, Vol. 36, pp. 705-716). The observed film changes are explained and related to the piezoviscous behaviour of the lubricant. Results for two different viscosity pressure relations are presented. It is shown that the details of the viscosity pressure relation have little effect on the local phenomena observed. The agreement between experimental and theoretical results is excellent in terms of the location and width of induced film thickness changes. The accuracy of the amplitude of the predicted changes is less. A amore accurate amplitude prediction requires more precise knowledge of the dynamic parameters, which describe the load system used in the experiments.

Analysis of an EHL circular contact incorporating rolling element vibration

The dynamics of rolling bearings is governed by both the dynamics of its structural components, and the elastohydrodynamic lubricated (EHL) contacts connecting these structural elements. In this paper, as an initial stage in quantifying the influence of the lubricant on the vibrations in rolling bearings, the influence of the lubricant on the vibration of one rolling element is investigated. For that purpose, inertia forces of the rolling element are incorporated into the analysis of an EHL circular contact. The model thus obtained includes both squeeze and entraining motion and hence it is time-dependent. It is shown that, to incorporate inertia forces, only one additional dimensionless parameter, the natural frequency, is needed. First, a Hertzian dry contact is investigated, as its solution will serve as an asymptote for the lubricated case. Subsequently, for a given load condition and different values of the natural frequency parameter, numerical solutions are presented showing both the influence of the lubricant on the vibration of the rolling element, as well as the influence of the vibration on film thickness and pressure.

Contact Dynamics in Starved Elastohydrodynamic Lubrication

In this paper, the, transient, pressure, film thickness and lubricant profile of a starved EHL contact, operating under sinusoidally varying loads, is presented. In a theoretical section, the dimensionless, quasi-static, dry contact solution is discussed. Subsequently, the equations for lubricated contacts will be stated, as well as the Jakobsson-Floberg-Olsson (JFO) relation for time-dependent, two-dimensional contacts. Numerical solutions are presented, which were obtained by a transient version of Elrods algorithm. Apart from a brief discussion of the steady state results, the paper focuses on the transient solution. It is shown that the induced oscillatory motion of the rolling element, leads to film thickness modulations, which are similar to the modulations observed for free vibrations reported in [10]. These modulations propagate at the dimensionless speed of unity and their (dimensionless) wavelength will be shown to equal 2π/Ωe, where Ωe is the dimensionless excitation frequency. Furthermore, it is shown that lubricant layer modulations are induced in the wake. Initially, these modulations, deposited as a result of the squeeze motion, are concentric with the Hertzian contact region and, like the film thickness modulations, propagate at the dimensionless speed of unity. At later times, the film thickness modulations which have propagated through the contact, interfere with the lubricant layer modulations, giving rise to a particular lubricant profile in the wake. It is shown that the phenomena, as described by the JFO relation, indeed show in the numerical solution.

An efficient finite element model for viscothermal acoustics

Standard isentropic acoustic models do not include the dissipative effects of viscous friction and heat conduction. These viscothermal effects can be important, for example in models of small acoustic transducers. Viscothermal acoustics can be modeled in arbitrary geometries with models that contain four or five coupled fields. Therefore, these fully coupled models are computationally costly. On the other hand, efficient approximate viscothermal acoustic models exist, but these are only applicable to certain simplified geometries. A new approximate model is presented which fills the gap between these two extremes. This new model can be used for arbitrary geometries and has a computational efficiency which is higher than the full model and lower than the models with geometrical constraints. The new model is derived and demonstrated on several problems, including acoustic-structure interaction problems

A one-dimensional heat transfer model for parallel-plate thermoacoustic heat exchangers

A one-dimensional (1D) laminar oscillating flow heat transfer model is derived and applied to parallel-plate thermoacoustic heat exchangers. The model can be used to estimate the heat transfer from the solid wall to the acoustic medium, which is required for the heat input/output of thermoacoustic systems. The model is implementable in existing (quasi-)1D thermoacoustic codes, such as DeltaEC. Examples of generated results show good agreement with literature results. The model allows for arbitrary wave phasing; however, it is shown that the wave phasing does not significantly influence the heat transfer.

Modeling of thermoacoustic systems using the nonlinear frequency domain method

When modeling thermoacoustic (TA) devices at high amplitude, nonlinear effects such as time-average mass flows, and the generation of higher harmonics can no longer be neglected. Thus far, modeling these effects in TA devices required a generally computationally costly time integration of the nonlinear governing equations. In this paper, a fast one-dimensional nonlinear model for TA devices is presented, which omits this costly time integration by directly solving the periodic steady state. The model is defined in the frequency domain, which eases the implementation of phase delays due to viscous resistance and thermoacoustic heat exchange. As a demonstration, the model is used to solve an experimental standing wave thermoacoustic engine. The obtained results agree with experimental results, as well as with results from a nonlinear time domain model from the literature. The low computational cost of this model opens the possibility to do optimization studies using a nonlinear TA model.

The influence of the horn effect in tyre/road noise

The horn effect is known as an important amplification mechanism in tyre/road noise. The name is referring to the geometry between tyre and road surface which resembles an exponential horn. The horn effect is a common subject for both experimental and numerical research. Contrary to previous studies which considered point sources, this paper focusses on the horn effect by simulated tyre vibrations. The amplification of acoustic pressure, however, depends largely on the location of the observer. The sound power can be used as a measure for the horn effect which is independent on the point of observation. In this paper, the sound radiation problem is solved using the boundary element method (BEM). First, a case study considering equivalent point sources is used to validate the accuracy of the boundary element model and solver using experimental results. Next, the vibrations of tyres rolling on textured road surfaces are investigated numerically. The computed tyre vibrations are used to study the horn effect using different tyre designs. The amplification by horn effect is determined by the combined tyre/road geometry and the distribution of the noise. The current method may be used to systematically study the influence of the horn effect, for example, during tyre development.

Measuring oblique incidence sound absorption using a local plane wave assumption

In this paper a method for the measurement of the oblique incidence sound absorption coefficient is presented. It is based on a local field assumption, in which the acoustic field is locally approximated by one incident- and one specularly reflected plane wave. The amplitudes of these waves can be determined with an unidirectional sound intensity probe. The local active- and incident acoustic intensity are straightforwardly obtained. The area-averaged sound absorption coefficient is calculated after spatial integration of these quantities over the surface area of interest. Alternatively, one may use a three-dimensional intensity probe. In that case, the determination of the amplitudes of the plane waves can be formulated as a least-squares problem. Measurements performed for a sound absorbing foam demonstrate that accurate results can be obtained, even under non-ideal acoustic conditions. Measurements carried out for a periodic absorber show that the method is accurate below the cut-on frequency of scattering as long as the amplitude of the evanescent surface waves is significantly smaller than that of the specularly reflected wave.

A numerical study of a method for measuring the effective in situ sound absorption coefficient

The accuracy of a method [Wijnant et al., Proc. of ISMA 31, Leuven, Belgium (2010), Vol. 31] for measurement of the effective area-averaged in situ sound absorption coefficient is investigated. Based on a local plane wave assumption, this method can be applied to sound fields for which a model is not available. Investigations were carried out by means of finite element simulations for a typical case. The results show that the method is a promising method for determining the effective area-averaged in situ sound absorption coefficient in complex sound fields.

A contact solver suitable for tyre/road noise analysis

Road traffic noise is a major environmental problem in modern society. The interaction between tyre and road surface, the major noise source, is non‐linear and is best described in the time domain. The currently used contact models for acoustic analyses have problems with either accuracy or calculation speed. At the Structural Dynamics and Acoustics group of the University of Twente an alternative contact algorithm has been developed. The characteristic feature of this algorithm is that, while solving the set of equations, the contact condition, i.e. the condition stating that there is no overlap between the bodies, is satisfied exactly. Hence, there is no need for contact elements or contact parameters. The possibility to optimize and speed up the algorithm, using multigrid is the major advantage of the new approach. In this paper the contact algorithm is applied to a two‐dimensional finite element model. Coulomb friction is taken into account. Some test simulations illustrate the ease of the algorithm. ...