Dynamics of windscreen wiper blades: Squeal noise,reversal noise and chattering

The motion of a windshield wiper blade is modelled by a mass-spring-damper system on a moving frictional surface. The system dynamics is time-varying, since three different regimes of motion, characterized by different degrees of freedom, are possible. Indeed the system, which schematizes a blade cross-section, can experience stick and slip motions when it is in contact with the glass surface, and free-flight motion when it is detached. The contact between the system and the surface is governed by Stribeck׳s friction law and Poisson׳s impact law, which make the dynamics non-smooth. The model is numerically implemented in an event-driven code, and simulations are performed which reproduce the three basic classes of undesired oscillations observed in the motion of real windscreen wipers, i.e., squeal, reversal and chattering noises. Attention is focused on the causes of these vibrations, and remedies for reducing or avoiding them are proposed.     

Rheological characteristics of human joints with particular reference to the knee

Summary Stiffness is an important subjective phenomenon diagnostically and therapeutically in rheumatic diseases such as rheumatoid arthritis and osteoarthrosis. A quantitative and qualitative assessment of these phenomena have been made by arthrographs which impose a sinusoidal motion on the metacarpo-phalangeal and knee joints respectively and record the torque in relation to the displacement. The reproducibility with the joint in situ and moved is satisfactory. A hysteresis torque/ displacement plot is obtained with both joints. Reflex muscle activity may be measured at the joint, as in myotonia congenita and Parkinsonism. In patients without neuromuscular disorders electromyographic studies have shown that the muscles are electrically silent during sinusoidal motion and that active contraction distorts the tracing. The latter fact may be useful in the evaluation of patients with psychological factors producing muscle tension, which may be decreased with diazepam. Using the cat's wrist joint it has been shown that the passive stretching of muscles accounts for 41 per cent of the stiffness recorded at the joint and the capsule 47 per cent, a finding in keeping with work on the distal interphalangeal joint of the human finger.Stiffness increases with advancing age and decreased temperature. Conversely, warming the joint reduces its stiffness. Articular gelling in patients with osteoarthrosis may be demonstrated after periods of rest and the results suggest that such changes are due to alterations in the periarticular and muscle tissues. The rapid diminution in torque after rest in one position was not detected in normal joints even after longer periods of immobilisation.

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Zusammenfassung Steifheit ist ein Problem, das dem Kliniker bekannt ist. Steifheit am Morgen ist ein Hauptgesichtspunkt für die Diagnose von rheumatischer Arthritis und ist ein äußerst wichtiges Merkmal für die Diagnose von Wirbelsäulenversteifungs (pocker back). Diese ist ein wichtiges Merkmal in Fällen von Patienten mit Osteoarthrosis, die unter Gelenkschwellung leiden, und die Gelenke daher nach einer Ruheperiode viel steifer sind. Therapeutisch hat sie Bedeutung für das Symptomenbild des Patienten und sie ist ein Maßstab für die Wirksamkeit der Behandlung von rheumatischer Arthritis.Arthrographen wurden angefertigt, um die Steifheit des Metacarpophalangealgelenks des Fingers und des Kniegelenkes zu messen. Tierexperimente haben gezeigt, daß 50% der Gelenksteifheit von passiver Muskelstrek-kung und 50% von Geweben im Gelenk selbst und außerhalb herrühren. Reflexbedingte Muskelaktivität spielt keine Rolle, mit Ausnahme von Fällen mit neuro-muskulären Erkrankungen wieParkinsonismus und Myotonia Congenita. Um ein charakteristisches Spannungs-Dehnungsdiagramm zu erhalten, wird das Gelenk in eine sinusartige Bewegung gebracht. Untersuchungen der Spannungsrelaxation haben einige Hinweise auf die Komponenten der physischen Steifheit gegeben.Zunehmende Steifheit ist physiologisch altersbedingt. Eine Temperaturerhöhung auf 45 °C vermindert die Steifheit um etwa 25%, und eine Temperaturerniedrigung erhöht, im Gegensatz dazu, die Steifheit um etwa denselben Betrag. Erhöhte Steifheit ist pathologisch in Fällen mit rheumatischer Arthritis, Systemsklerose und Osteoarthrose. Das Auftreten von Gelenkschwellungen bei Osteoarthrose ist, wie die Analyse von Überlagerungsdiagrammen andeutet, mehr eine Erscheinung, die von Veränderungen der umhüllenden Gewebe herrührt, als von Veränderungen zwischen den Gelenkflächen. Mit diesem Gerät wurden einige künstliche Schmiermittel geprüft.

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Paper presented to the British Society of Rheology Conference on Rheology in Medicine and Pharmacy, London, April 14–15, 1970.     

Bifurcation phenomena of the reversal behavior of an automobile wiper blade

Reducing the noise generated by windshield wipers during reversal is desirable. As a fundamental first step in exploring the cause of this noise, the present study attempts to theoretically and experimentally clarify the dynamics of the behavior of the wiper blade near the reversal point. First, an experiment is conducted to observe the reversal behavior using the cross sectional model of the blade rubber. In order to theoretically explain the experimentally observed phenomena, an analytical link model of the wiper blade is introduced. The reversal behavior of a blade is theoretically investigated through the bifurcation analysis by considering Coulomb??s friction during reversal. Then we show the continuous variation of the angle of blade rubber, and predict a rapid variation of the normal force, which can cause reversal noise, acting to the blade rubber.     

Bases for predicting gas-particle flows with particular reference to turbomachinery

Advances in the understanding of particle dynamics and their trajectories and the resultant erosion of solid surfaces are reviewed. Particular attention is given to the calculation procedures used in the analysis of gas-particle flows, always with the intention of application to turbo-machines. One, two and three-dimensional analyses are considered and the limitations of each are discussed. As in the analysis of a real fluid flows, resort is made to empirical correlations of many phenomena and, even then, the predictions of particle trajectories are restricted. The correlation and restrictions are discussed where appropriate.     

Numerical solution of the flow of thin viscous sheets under gravity and the inverse windscreen sagging problem

The slumping of a thin sheet of very viscous liquid glass is used in the manufacture of windscreens in the automotive industry. The governing equations for an asymptotically thin sheet with variable viscosity are derived in which the vertical coordinate forms the centre‐line of the sheet. The time‐dependant equations have been solved numerically using the backward Euler method to give results in both two and three dimensions. The flow of an initially flat sheet falls freely under gravity until it becomes curved and the flow becomes very slow in the ‘slumped’ phase. Finally the sheet freefalls as the thickness becomes small at the boundaries. The inverse problem in which the viscosity profile is to be determined for a given shape can be solved as an embedding problem in which a search is made amongst the forward solutions. Possible shapes in the two‐dimensional problem are very restrictive and are shown to be related to the sheet thickness. In three dimensions the range of shapes is much greater. Copyright © 2002 John Wiley & Sons, Ltd.     

Bound vortex boundary layer control with application to V/STOL airplanes

Effectiveness of the bound vortex boundary layer control is assessed with reference to airfoils modified with a leading edge rotating cylinder. Results of the test program and the numerical models suggest the following:

• The surface singularity method in conjunction with the boundary layer correction scheme is capable of predicting useful information concerning bound vortex boundary layer control. The predicted pressure distributions are in good agreement with experiment almost up to the point of complete separation from the the airfoil surface except near the trailing edge where more accurate results of the flow field would require the modelling of the separated flow region using the full Navier-Stokes equations.

• The concept of bound vortex boundary layer control appears to be quite promising. With cylinder rotation. the flow never separated completely from the upper surface. The higher rates of rotation promoted reattachment of the partially separated flow giving a significant improvement in the maximum lift and stall characteristics.     

Improving the robustness of the control volume finite element method with application to multiphase porous media flow

Control volume finite element methods (CVFEMs) have been proposed to simulate flow in heterogeneous porous media because they are better able to capture complex geometries using unstructured meshes. However, producing good quality meshes in such models is nontrivial and may sometimes be impossible, especially when all or parts of the domains have very large aspect ratio. A novel CVFEM is proposed here that uses a control volume representation for pressure and yields significant improvements in the quality of the pressure matrix. The method is initially evaluated and then applied to a series of test cases using unstructured (triangular/tetrahedral) meshes, and numerical results are in good agreement with semianalytically obtained solutions. The convergence of the pressure matrix is then studied using complex, heterogeneous example problems. The results demonstrate that the new formulation yields a pressure matrix than can be solved efficiently even on highly distorted, tetrahedral meshes in models of heterogeneous porous media with large permeability contrasts. The new approach allows effective application of CVFEM in such models.     

Nonlinear dynamics and control of a variable order oscillator with application to the van der Pol equation

We investigate the dynamics and control of a nonlinear oscillator that is described mathematically by a Variable Order Differential Equation (VODE). The dynamic problem in question arises from the dynamical analysis of a variable viscoelasticity oscillator. The dynamics of the model and the behavior of the variable order differintegrals are shown in variable phase space for different parameters. Two different controllers are developed for the VODEs under study in order to track an arbitrary reference function. A generalization of the van der Pol equation using the VODE formulation is analyzed under the light of the methods introduced in this work.     

Factors influencing heat transfer to the pressure surfaces of gas turbine blades

It is suggested that heat transfer through the laminar boundary layer flowing over the concave pressure surface of a turbine blade is strongly influenced by the presence of Taylor-Goertler vortices, as well as by mainstream turbulence. Transition occurs when these factors in concert outweigh the tendency of the boundary layer to remain laminar in the favourable pressure gradients characteristic of flow over pressure surfaces.     

Oscillations of a wedge in a free stream with particular reference to parachutes

The phenomenon of coupled breathing and longitudinal oscillations of a wedge-mass system in a free stream is examined. As a first step the unsteady pressure distribution on the surface of the oscillating wedge is calculated. For dynamic equilibrium of the wedge-mass system, the moment about the apex of the wedge must be zero. This condition establishes the amplitude and phase relation between breathing and longitudinal oscillations. As a final step the equation of motion of the store is used to calculate the frequency of the breathing oscillations. This frequency is shown to be dependent on four parameters. These parameters include the Froude number, the rigging line length to wedge breadth ratio and the rigging line stiffness and damping. Current results are compared with Hume and Stevens [1] experimental results.     

An investigation of electrostatic phenomena associated with flowing wet steam with particular reference to the wet steam turbine

A wet steam tunnel was constructed to simulate the ineteraction of liquid and vapour in order to investigate the nature and origin of static electrification phenomena which occur within wet steam turbines. The tunnel was operated at 0·17 bar pressure with steam velocity up to 290 m/s.The mechanisms likely to cause charging were investigated in turn. The major charging mechanism is ‘separation charging’ which occurs when a mass of water is torn rapidly from a solid surface. The rate of charging depends on the speed of separation, the geometry, and the surface contamination of the solid.     

Bifurcation analysis for T system with delayed feedback and its application to control of chaos

In this paper, a three-dimensional autonomous nonlinear system called the T system which has potential application in secure communications is considered. Regarding the delay as parameter, we investigate the effect of delay on the dynamics of T system with delayed feedback. Firstly, by employing the polynomial theorem to analyze the distribution of the roots to the associated characteristic equation, the conditions of ensuring the existence of Hopf bifurcation are given. Secondly, by using the normal form theory and center manifold argument, we derive the explicit formulas determining the stability, direction and other properties of bifurcating periodic solutions. Finally, we give several numerical simulations, which indicate that when the delay passes through certain critical values, chaotic oscillation is converted into a stable steady state or a periodic orbit.     

Vaccination control of an epidemic model with time delay and its application to COVID-19

Nonlinear Dynamics - This paper studies an SEIR-type epidemic model with time delay and vaccination control. The vaccination control is applied when the basic reproduction number $$R_0>1$$ ....     

The use of perforated plates to control the flow emerging from a wide-angle diffuser,with application to electrostatic precipitator design

The flow through a wide-angle, pyramidal diffuser of area ratio 6.8, in which two perforated plates are used to control the emergent velocity distribution was investigated. (Wide-angle diffusers combined with perforated plates find application in electrostatic precipitator flow systems. The efficacy of these systems depends critically on the uniformity of the gas flow within the collection chamber downstream of the diffuser outlet plane.) The main results of the study are (i) the establishment of the main factor influencing the flow at the diffuser exit plane, (ii) the determination of plate characteristics which produce a uniform velocity profile in the collection chamber, and (iii) the establishment of the corresponding pressure drop characteristics of the plate—diffuser combinations. The results also extend the range of diffuser geometries for which two perforated plates provide uniform velocity profiles at exit.     

Measurements and treatment of LDA signals, comparison with hot-wire signals

 An experimental investigation was carried out in the wind tunnel F2 of the ONERA Fauga centre for the measurement of the characteristics of a turbulent wake behind a wing. As these measurements require the calculation of time and space correlations, two different types of acquisition means are used : a pair of crossed hot wires and a one-dimensional laser-Doppler anemometer. The non-intrusive characteristics of laser anemometry allow the measurement of fluid velocity upstream of a hot wire probe without disrupting the flow. It is well known that LDA generates individual realisations of randomly sampled velocity data because the random arrival of seeding particles in the measurement volume is nonperiodic. A detailed study of this random sampling quantifies the deviations from the theoretical lows, shows the limiting factors of this sampling, and gives a characterisation of the particles arrival law. The simultaneous acquisition of the two velocity signals at very close points allows a good comparison between the signals. A statistical analysis of the two signals enables us to precisely measure the error value of the velocity estimation made by the anemometer. The spectrum analysis of the laser signal coupled with one of the hot wire signals requires resampling the signal at constant steps. Two different methods of interpolation are analysed: the sample and hold interpolation method and the linear interpolation method. The influence of these interpolation methods on the spectrum of LDA signals is studied. Different estimators are then calculated to evaluate the convection velocities and the coherence length of the turbulence. Received: 9 December 1997/Accepted: 19 March 1999     

On the continuum modelling of porous media containing fluid: a molecular viewpoint with particular attention to scale

Mass conservation and linear momentum balance relations for a porous body and any fluid therein, valid at any given length scale in excess of nearest-neighbour molecular separations, are established in terms of local weighted averages of molecular quantities. The mass density field for the porous body at a given scale is used to identify its boundary at this scale, and a porosity field is defined for any pair of distinct length scales. Specific care is paid to the interpretation of the stress tensor associated with each of the body and fluid at macroscopic scales, and of the force per unit volume each exerts on the other. Consequences for the usual microscopic and macroscopic viewpoints are explored.Nomenclature material system; Section 2.1. - porous body (example of a material system); Sections 2.1, 3.1, 4.1 - fluid body (example of a material system); Sections 2.1, 3.1, 4.1 - weighting function; Sections 2.1, 2.3 - ,h weighting function corresponding to spherical averaging regions of radius and boundary mollifying layer of thicknessh; Section 3.2 - Euclidean space; Section 2.1 - V space of all displacements between pairs of points in; Section 2.1 - mass density field corresponding to; (2.3)₁ - ^P , ^f mass density fields for , ; (4.1) - P momentum density field corresponding to; (2.3)₂ - v velocity field corresponding to; (2.4) - S _r (X) interior of sphere of radiusr with centre at pointx; (3.3) - boundary ofany region - region in which ^p > 0 with = ,h; (3.1) - subset of whose points lie at least+h from boundary of ; (3.4) - abbreviated versions of ; Section 3.2, Remark 4 - strict interior of ; (3.7) - analogues of for fluid system ; Section 3.2 - general version of corresponding to any choice of weighting function; (4.6) - interfacial region at scale; (3.8) - ₀ scale of nearest-neighbour separations in ; Section 3.2. Remark 1 - porosity field at scales ( ₁; ₂); (3.9) - pore space at scales ( ₁; ₂); (3.12)