Das Digitale Beukenmodell mit nichtkonstanten Koeffizienten — eine Matrixmethode zur Lösung nichtlinearer Ausgleichsvorgänge

Zusammenfassung Mit Hilfe des Digitalen Beukenmodells mit nichtkonstanten Koeffizienten lassen sich ein- und mehrdimensionale Ausgleichsvorgänge berechnen. Besonders einfach ist das Verfahren, wenn nur die Wärmeleitfähigkeit von der Temperatur oder der Diffusionskoeffizient von der Konzentration abhängig ist. Der Hauptvorteil des Digitalen Beukenmodells liegt in der einfachen Handhabung. Für viele praktische Fälle kann die Rechenzeit gegenüber dem herkömmlichen reinen Differenzenverfahren entscheidend verkürzt werden. Das Digitale Beukenmodell mit nichtkonstanten Koeffizienten ist die genaueste Rechenmethode für nichtlineare Ausgleichsvorgänge.

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The digital Beuken-Model with non-constant coefficients — a matrix method for the solution of non-linear diffusion processes

By the help of the digital Beuken-Model with nonconstant coefficients it is possible to compute one- or multidimensional diffusion processes. Especially simple is that method, if only the thermal conductivity depends on the temperature or if the diffusion coefficient depends on the concentration. The main advantage of the digital Beuken-Model is its simple handling. In many practical cases the computing time can be shortened decisively to the traditional difference methods. The digital Beuken-Model with non-constant coefficients is the most exact computing-method for the solution of nonlinear diffusion processes.

     

Experimental visualization of bubble formation from an orifice in microgravity in the presence of electric fields

 The formation of air bubbles injected into a stagnant, isothermal liquid in microgravity through an orifice was studied. The bubbles grew very large in microgravity. They attained a nearly spherical shape and showed pronounced affinity towards coalescence in the absence of electric fields and other perturbations. Under the influence of electric fields, periodic detachment was observed, with bubble sizes larger than in terrestrial conditions. The bubble shape was elongated. After detachment, the bubbles moved away from the electrode at which they formed without coalescing with other bubbles. Experimental data on bubble shape and size at detachment showed good agreement with models. Received: 26 March 2001 / Accepted: 16 August 2001     

Zur analytischen Behandlung des nichtlinearen aeroelastischen Galloping-Problems

Übersicht Es wird ein graphisch-numerisches Verfahren zur Lösung der nichtlinearen Galloping-Differential- gleichung dargelegt. Die Einzelheiten des Lösungsverfahrens werden beschrieben und an Hand eines typischen Beispiels näher erläutert.

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Summary A graphical-numerical method for the solution of the non-linear Galloping differential equation is presented. The details of the analytical procedure are discussed and explained by means of a typical example.

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Diese Arbeit entstand im Rahmen eines einjährigen Stipendiums der Alexander von Humboldt-Stiftung. Der Stipendiat Dr.-Ing. V. Manea ist Mitarbeiter im Institut de Mecanica Fluidelor si Constructii Aerospatiale, Bukarest.     

Ein Beitrag zum dynamischen Verhalten der Kurvengetriebe mit Schwinghebel

Übersicht Die Abtriebsglieder in Kurvengetrieben werden bei dynamischen Untersuchungen zum größten Teil als starr angenommen. In der vorliegenden Arbeit werden speziell Kurvengetriebe mit Schwinghebel untersucht. Dabei wird die Schwinge selbst als ein dünner, elastischer Stab betrachtet, wobei alle anderen Glieder als starr angesehen werden. Nach Aufstellung der Differentialgleichung der Querschwingungen der Schwinge in der Getriebeebene, die eine partielle Differentialgleichung vierter Ordnung mit zeit- und ortsabhängigen Koeffizienten ist, werden diese Schwingungen nach Reduzierung der Differentialgleichung in ein Hillsches Differentialgleichungssystem auf Stabilität untersucht. Danach wird mit Hilfe einer Näherungslösung des erhaltenen Systems der Einfluß verschiedener Parameter auf den Kraftschluß zwischen der Kurve und der Abtriebsrolle untersucht. Insgesamt kommt man zu der Feststellung, daß die Berücksichtigung der Schwingenelastizität, verglichen mit dem Falle einer starren Schwinge, unterschiedliche Ergebnisse liefert und daher diese Eigenschaft möglichst in Betracht gezogen werden sollte.

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On the dynamic behavior of cam mechanisms with followers

Summary The followers in cam mechanisms are usually regarded as rigid elements in a dynamical analysis. In this work, cam mechanisms with oscillating followers were investigated. The follower was considered as a thin elastic rod and the other members of the mechanism were taken as rigid. After setting up the equation of lateral motion of the oscillating follower in the plane of the mechanism — which is a partial differential equation of fourth order with time and space dependent coefficients — the lateral vibrations were investigated from a stability point of view by reducing the differential equation to a Hill system. Then, using an approximate solution of the system obtained above, the effect of various parameters on the contact between the cam and its roller were analyzed. It was found that the consideration of the elasticity of the follower gave different results as compared to the analysis where it was assumed to be rigid. Thus the elasticity of the follower is an important parameter to be considered.

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Ein Auszug aus der 1979 an der TU Istanbul genehmigten Dissertation mit dem Titel Elastokinetische Probleme bei Kurvengetrieben, die unter der Leitung meines verehrten Professors Dr.-Ing. Fuat Pasin entstand, dem an dieser Stelle noch einmal aufrichtig gedankt sei     

Deep field noise in holographic particle image velocimetry (HPIV): numerical and experimental particle image field modelling

 Holographic recording overcomes the limits in 2-D particle image velocimetry (PIV) to cover a 3-D flow field volume. Interrogation by focusing on single planes in a reconstructed particle field is disturbed by noise from out-of-focus particles. A numerical simulation models image reconstruction and shows how validation rates depend on aperture and volume depth. An experimental model environment of scattering particles in moveable plastic slices gives support to the numerical results. Simulations and tests are carried out for interrogation by autocorrelation and crosscorrelation techniques and furnish guidelines for system design. Received: 27 December 1996 / Accepted: 14 August 1997     

Constructing dynamical systems having homoclinic bifurcation points of codimension two

A procedure is derived which allows for a systematic construction of three-dimensional ordinary differential equations having homoclinic solutions. The equations are proved to exhibit codimension-two homoclinic bifurcation points. Examples include the non-orientable resonant bifurcation, the inclination-flip, and the orbit-flip. In addition, an equation is constructed which has a homoclinic orbit converging to a saddle-focus satisfying Shilnikov's condition. The vector fields are polynomial and non-stiff in that the eigenvalues are of moderate size.     

Beitrag zur Prüfung metallischer Werkstoffe im Torsionsversuch

Zusammenfassung Der Torsionsversuch eignet sich zur Untersuchung des plastischen Verhaltens von Metallen bei erhöhten Temperaturen, wenn die Fließspannung stark von der Umformgeschwindigkeit abhängt. Aus der gemessenen Drehmoment-Drehwinkel-Kurve wird die Fließkurvek _f () berechnet. Hierfür wird ein Fließkriterium benötigt, dessen Unsicherheit im allgemeinen größer ist als alle Meßfehler. Diese Unsicherheit geht aber nicht in die berechnete Dehngeschwindigkeitsempfindlichkeit ein, die somit als Hauptergebnis des Versuches anzusehen ist.Um die Bedingungen technischer Warmumformung zu simulieren, wird die Verwendung extrem kurzer Proben (flacher Scheiben) empfohlen, womit sehr hohe Umformgeschwindigkeiten erreicht werden können. Für die Auswertung derartiger Versuche ist die wirksame Länge der kurzen Proben — experimentell oder semiempirisch — zu bestimmen und die Kerbwirkung zu berücksichtigen. Im Gegensatz zur herkömmlichen Vorgehensweise wird empfohlen, die örtliche Spannung und Verzerrung nicht für die Mantelfläche der Probe zu berechnen, sondern für einen kritischen Radialabstand im Innern der Probe, für den die Schiebung von der Kerbwirkung unabhängig ist, so daß sich die zuverlässigsten Werte ergeben.

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Summary The torsion test is often used for studying the plastic deformation of metals at elevated temperatures when stress depends strongly on the strain rate. From the measured torque-twisting angle curve, the stress-strain curvek _f () has to be calculated. For this purpose a yield criterion has to be used the uncertaintly of which normally exceeds all experimental errors. This uncertaintly, however, does not propagate into the calculated strain rate sensitivity which therefore may be considered as the main result of the torsion test.For simulating the conditions of technical hot forming processes, the use of extremely short test pieces (flat discs) by which very high strain rates can be obtained is recommended. For evaluating the test data the efficient lenght of short specimens has to be determined. In opposition to the conventional procedure of test evaluation, it is recommended not to calculate stress and strain for the surface of the specimen but for a critical radius for which strain is independent of the notch effect so that the most reliable values are obtained.

Mit 5 Abbildungen     

Heat generation at the tip of a moving crack

The high energy concentration at the tip of a moving crack causes irreversible deformations and produces heat as a consequence. The resulting temperatures were calculated by consideration of the crack tip as a moving heat-source of rectangular shape. In brittle materials with very small plastic zones and high crack velocities, these temperatures are predicted to be higher than 1000 K. For the experimental verification of these calculations, a very sensitive radiation thermometer was developed. It registers the intensity of the radiation at four wavelengths. By comparison of these intensities with that of black body radiation, the temperature was determined as 3200 K for glass and 4700 K for quartz.     

The background oriented schlieren technique: sensitivity, accuracy, resolution and application to a three-dimensional density field

Three-dimensional density information of a double free air jet was acquired using optical tomography. The projections of the density field were measured using the background oriented schlieren method (BOS). Preceding the free jet measurements, the sensitivity, accuracy and resolution of the BOS method were investigated. The sensitivity depends mostly on the focal length of the lens used, the relative position of the object between camera and background and the smallest detectable shift in the image plane. The accuracy was found to be sufficiently high to apply a tomographic reconstruction process. The resolution is determined by the transfer function of the BOS-method. It is not constant and depends on the size of the interrogation windows used for the cross-correlation-algorithm. The reconstruction of the free jet was computed, using filtered back projection. The reconstructed 3D density field shows with good resolution the typical diamond structure of the density distribution in under-expanded free jets.     

Plastic flow and dislocation structure at small strains in OFHC copper deformed in tension,torsion and combined tension-torsion

OFHC copper specimens of 39 μm grain size were deformed to small strains (up to 8%) in tension, torsion and combined tension-torsion at 300 K and the resulting dislocation structures, distributions and densities were determined using transmission electron microscopy. Employing the von Mises yield criterion and the plastic-work hypothesis good agreement was obtained for the three testing conditions for (i) equivalent stress $\text{}\text{?}$gs vs equivalent strain $\text{}\text{?}$g3^p curves, (ii) the dislocation structure, distribution and density ρ as a function of $\text{}\text{?}$g3^p, and (iii) $\text{}\text{?}$gs as a function of $\text{ρ}\text{1}\text{2}$. Furthermore, upon comparing the $\text{}\text{?}$gs vs $\text{ρ}\text{1}\text{2}$ curve for polycrystalline copper with the τ_RSS vs $\text{ρ}\text{1}\text{2}$ curve for single crystals, an average Taylor factor M= (σ/τ_RSS) of approximately 3.2 was obtained, which is in good accord with that predicted theoretically for FCC metals. Almost equally good correlations for the stressstrain curves and for the dislocation density were obtained on the basis of maximum shear stress τ_max and maximum shear strain γ^p_max as on the basis of $\text{}\text{?}$gs and $\text{}\text{?}$g3^P. Therefore, the present results do not permit a positive decision on the question whether the dislocation density correlates better with $\text{}\text{?}$gs and $\text{}\text{?}$g3^P or with τ_max and γ^P_max.A single test in which the direction of straining in torsion was reversed yielded a density and distribution of dislocations (and a corresponding value of $\text{}\text{?}$gs) equivalent to those that developed at a smaller strain in unidirectional straining.