Im Zuge der kontinuierlichen Weiterentwicklung von Verarbeitungs- und Verpackungsmaschinen werden immer höhere Anforderungen an die für den Gütertransfer eingesetzte Fördertechnik gestellt. Neben der erhöhten Förderleistung sind zudem ein schmiermittelfreier Betrieb sowie eine hundertprozentige Verfügbarkeit gefordert. Durch die zunehmende Leistungssteigerung kommt es zu hohen Beanspruchungen, die bei falscher Auslegung zu mechanischem oder thermischem Versagen der Kunststoff-Bauteile im Fördersystem führen können. Während das mechanische Versagen mit den aktuellen Dimensionierungen vermieden werden kann, gibt es bezüglich des thermischen Versagens keine hinreichend genaue Auslegungsvorschrift. Die vorliegende Arbeit befasst sich mit der thermischen Analyse von Gleitketten-Fördersystemen sowie den darin eingesetzten thermoplastischen Kunststoff-Kunststoff-Gleitpaarungen. Diesbezüglich werden die Gleitkontakte eines Gleitkettenförderers und deren Belastungen analysiert. Durch Abstraktion des Kette–Schiene-Systems wird ein semi-analytisches Berechnungsmodell zur Abschätzung der Reibtemperatur entwickelt, welches mittels experimenteller Untersuchungen auf einem Tribo-Prüfstand und an einem Fördersystem verifiziert wird. Aus den Untersuchungsergebnissen konnte ein thermisches Auslegungskriterium für Kunststoff-Kunststoff-Gleitpaarungen abgeleitet werden, welches sowohl auf Gleitketten-Förderer als auch perspektivisch auf ähnliche tribologische Systeme übertragen werden kann. / In the course of the continuous enhancements of processing and packaging machines, higher demands are set on conveying technology used for transferring goods. In addition to an increased delivery rate, a lubricant-free operation as well as a hundred percent availability are claimed. Increasing performance leads to high stresses that can result to mechanical or thermal failure of plastic components in the conveying system, if incorrectly designed. While mechanical failure can be avoided with up to date dimensioning, there is no sufficiently precise dimensioning criterion in regard to thermal failure. The present thesis is concerning with the thermal analysis of sliding chain conveyor systems as well as the thermoplastic plastic-plastic sliding pairs used therein. In this regard, the sliding contacts of a sliding chain conveyor and their loads are analyzed. By abstraction of the chain–rail system, a semi-analytical model for estimating the frictional temperature is developed, which is verified by experimental studies on a tribo test bench and a conveyor system. From the study results, a thermal dimensioning criterion for plastic plastic pairings could be derived, which can be applied to sliding chain conveyor as well as perspectivly similar tribological systems.

<p>Анализиран је судар два тела као и дисипација енергије укључена кроз механизам сувог трења моделираног неглатком вишевредносном функцијом и кроз деформацију вискоеластичног штапа чији модел укључује фракционе изводе. Проблем судара два тела је приказан у форми Кошијевог проблема који припада класи неглатких вишевредносних диференцијалних једначина произвољног реалног<br />реда. Кошијев проблем је решен нумеричким поступком заснованим на Тарнеровом алгоритму. Испитано је кретање система и дисипација енергије за разне вредности улазних параметара. Показано је да се уведене методе могу применити и на проблем судара три тела.</p> / <p>Analiziran je sudar dva tela kao i disipacija energije uključena kroz mehanizam suvog trenja modeliranog neglatkom viševrednosnom funkcijom i kroz deformaciju viskoelastičnog štapa čiji model uključuje frakcione izvode. Problem sudara dva tela je prikazan u formi Košijevog problema koji pripada klasi neglatkih viševrednosnih diferencijalnih jednačina proizvoljnog realnog<br />reda. Košijev problem je rešen numeričkim postupkom zasnovanim na Tarnerovom algoritmu. Ispitano je kretanje sistema i disipacija energije za razne vrednosti ulaznih parametara. Pokazano je da se uvedene metode mogu primeniti i na problem sudara tri tela.</p> / <p> Impact of two bodies was analyzed as well as energy dissipation, which was<br /> included through dry friction phenomena modelled by a set-valued function,<br /> and through deformation of a viscoelastic rod modelled by fractional<br /> derivatives. The impact problem was presented in the form of the Cauchy<br /> problem that belongs to a class of set-valued fractional differential equations.<br /> The Cauchy problem was solved by the numerical procedure based on<br /> Turner&rsquo;s algorithm. Behaviour and energy dissipation of the system was<br /> investigated for different values of input parameters. It was shown that<br /> suggested procedure can be applied on the problem of impact of three<br /> bodies.</p>

No description available.

<p>A time-discrete formulation of the variational principle of mechanics is used to provide a consistent theoretical framework for the construction and analysis of low order integration methods. These are applied to mechanical systems subject to mixed constraints and dry frictional contacts and impacts---machines. The framework includes physics motivated constraint regularization and stabilization schemes. This is done by adding potential energy and Rayleigh dissipation terms in the Lagrangian formulation used throughout. These terms explicitly depend on the value of the Lagrange multipliers enforcing constraints. Having finite energy, the multipliers are thus massless ghost particles. The main numerical stepping method produced with the framework is called SPOOK.</p><p>Variational integrators preserve physical invariants globally, exactly in some cases, approximately but within fixed global bounds for others. This allows to product realistic physical trajectories even with the low order methods. These are needed in the solution of nonsmooth problems such as dry frictional contacts and in addition, they are computationally inexpensive. The combination of strong stability, low order, and the global preservation of invariants allows for large integration time steps, but without loosing accuracy on the important and visible physical quantities. SPOOK is thus well-suited for interactive simulations, such as those commonly used in virtual environment applications, because it is fast, stable, and faithful to the physics.</p><p>New results include a stable discretization of highly oscillatory terms of constraint regularization; a linearly stable constraint stabilization scheme based on ghost potential and Rayleigh dissipation terms; a single-step, strictly dissipative, approximate impact model; a quasi-linear complementarity formulation of dry friction that is isotropic and solvable for any nonnegative value of friction coefficients; an analysis of a splitting scheme to solve frictional contact complementarity problems; a stable, quaternion-based rigid body stepping scheme and a stable linear approximation thereof. SPOOK includes all these elements. It is linearly implicit and linearly stable, it requires the solution of either one linear system of equations of one mixed linear complementarity problem per regular time step, and two of the same when an impact condition is detected. The changes in energy caused by constraints, impacts, and dry friction, are all shown to be strictly dissipative in comparison with the free system. Since all regularization and stabilization parameters are introduced in the physics, they map directly onto physical properties and thus allow modeling of a variety of phenomena, such as constraint compliance, for instance.</p><p>Tutorial material is included for continuous and discrete-time analytic mechanics, quaternion algebra, complementarity problems, rigid body dynamics, constraint kinematics, and special topics in numerical linear algebra needed in the solution of the stepping equations of SPOOK.</p><p>The qualitative and quantitative aspects of SPOOK are demonstrated by comparison with a variety of standard techniques on well known test cases which are analyzed in details. SPOOK compares favorably for all these examples. In particular, it handles ill-posed and degenerate problems seamlessly and systematically. An implementation suitable for large scale performance and accuracy testing is left for future work.</p>

A time-discrete formulation of the variational principle of mechanics is used to provide a consistent theoretical framework for the construction and analysis of low order integration methods. These are applied to mechanical systems subject to mixed constraints and dry frictional contacts and impacts---machines. The framework includes physics motivated constraint regularization and stabilization schemes. This is done by adding potential energy and Rayleigh dissipation terms in the Lagrangian formulation used throughout. These terms explicitly depend on the value of the Lagrange multipliers enforcing constraints. Having finite energy, the multipliers are thus massless ghost particles. The main numerical stepping method produced with the framework is called SPOOK. Variational integrators preserve physical invariants globally, exactly in some cases, approximately but within fixed global bounds for others. This allows to product realistic physical trajectories even with the low order methods. These are needed in the solution of nonsmooth problems such as dry frictional contacts and in addition, they are computationally inexpensive. The combination of strong stability, low order, and the global preservation of invariants allows for large integration time steps, but without loosing accuracy on the important and visible physical quantities. SPOOK is thus well-suited for interactive simulations, such as those commonly used in virtual environment applications, because it is fast, stable, and faithful to the physics. New results include a stable discretization of highly oscillatory terms of constraint regularization; a linearly stable constraint stabilization scheme based on ghost potential and Rayleigh dissipation terms; a single-step, strictly dissipative, approximate impact model; a quasi-linear complementarity formulation of dry friction that is isotropic and solvable for any nonnegative value of friction coefficients; an analysis of a splitting scheme to solve frictional contact complementarity problems; a stable, quaternion-based rigid body stepping scheme and a stable linear approximation thereof. SPOOK includes all these elements. It is linearly implicit and linearly stable, it requires the solution of either one linear system of equations of one mixed linear complementarity problem per regular time step, and two of the same when an impact condition is detected. The changes in energy caused by constraints, impacts, and dry friction, are all shown to be strictly dissipative in comparison with the free system. Since all regularization and stabilization parameters are introduced in the physics, they map directly onto physical properties and thus allow modeling of a variety of phenomena, such as constraint compliance, for instance. Tutorial material is included for continuous and discrete-time analytic mechanics, quaternion algebra, complementarity problems, rigid body dynamics, constraint kinematics, and special topics in numerical linear algebra needed in the solution of the stepping equations of SPOOK. The qualitative and quantitative aspects of SPOOK are demonstrated by comparison with a variety of standard techniques on well known test cases which are analyzed in details. SPOOK compares favorably for all these examples. In particular, it handles ill-posed and degenerate problems seamlessly and systematically. An implementation suitable for large scale performance and accuracy testing is left for future work.

Im Zuge der kontinuierlichen Weiterentwicklung von Verarbeitungs- und Verpackungsmaschinen werden immer höhere Anforderungen an die für den Gütertransfer eingesetzte Fördertechnik gestellt. Neben der erhöhten Förderleistung sind zudem ein schmiermittelfreier Betrieb sowie eine hundertprozentige Verfügbarkeit gefordert. Durch die zunehmende Leistungssteigerung kommt es zu hohen Beanspruchungen, die bei falscher Auslegung zu mechanischem oder thermischem Versagen der Kunststoff-Bauteile im Fördersystem führen können. Während das mechanische Versagen mit den aktuellen Dimensionierungen vermieden werden kann, gibt es bezüglich des thermischen Versagens keine hinreichend genaue Auslegungsvorschrift. Die vorliegende Arbeit befasst sich mit der thermischen Analyse von Gleitketten-Fördersystemen sowie den darin eingesetzten thermoplastischen Kunststoff-Kunststoff-Gleitpaarungen. Diesbezüglich werden die Gleitkontakte eines Gleitkettenförderers und deren Belastungen analysiert. Durch Abstraktion des Kette–Schiene-Systems wird ein semi-analytisches Berechnungsmodell zur Abschätzung der Reibtemperatur entwickelt, welches mittels experimenteller Untersuchungen auf einem Tribo-Prüfstand und an einem Fördersystem verifiziert wird. Aus den Untersuchungsergebnissen konnte ein thermisches Auslegungskriterium für Kunststoff-Kunststoff-Gleitpaarungen abgeleitet werden, welches sowohl auf Gleitketten-Förderer als auch perspektivisch auf ähnliche tribologische Systeme übertragen werden kann. / In the course of the continuous enhancements of processing and packaging machines, higher demands are set on conveying technology used for transferring goods. In addition to an increased delivery rate, a lubricant-free operation as well as a hundred percent availability are claimed. Increasing performance leads to high stresses that can result to mechanical or thermal failure of plastic components in the conveying system, if incorrectly designed. While mechanical failure can be avoided with up to date dimensioning, there is no sufficiently precise dimensioning criterion in regard to thermal failure. The present thesis is concerning with the thermal analysis of sliding chain conveyor systems as well as the thermoplastic plastic-plastic sliding pairs used therein. In this regard, the sliding contacts of a sliding chain conveyor and their loads are analyzed. By abstraction of the chain–rail system, a semi-analytical model for estimating the frictional temperature is developed, which is verified by experimental studies on a tribo test bench and a conveyor system. From the study results, a thermal dimensioning criterion for plastic plastic pairings could be derived, which can be applied to sliding chain conveyor as well as perspectivly similar tribological systems.

Im Rahmen der Arbeit wurde ein semi-analytisches Berechnungsmodell für den Reibwert einzelner kugelförmiger Erhebungen erarbeitet, das die Berechnung der deformativen (μ_def) und adhäsiven (μ_adh) Reibanteile ermöglicht. Die Integration eines plastischen (Radius der Laufspur R_Spur) und eines viskosen (Rückstellwinkel ω) Verformungsanteils gestattet die Berechnung der realen Kontaktfläche während des Reibvorgangs. In Abhängigkeit des mittleren Kontaktdrucks kann damit der adhäsive Reibanteil μ_adh bestimmt werden. Die experimentelle Untersuchungen umfassten neben ungeschmierten Reibversuchen, die zur Ermittlung des gesamten Reibwertes (μ_ges) dienten, auch mit Silikonöl geschmierte Versuche aus denen sich μ_def ergibt. Anhand der Verifikationsversuche konnte einerseits gezeigt werden, dass beide Schmierungszustände zu gleichen Verformungen führen und andererseits wurde der Nachweis erbracht, dass der im Berechnungsmodell postulierte Zusammenhang zwischen dem Rückstellwinkel ω und μ_def Gültigkeit besitzt. Hierzu wurden Reibversuche mit segmentierten Kugeln durchgeführt, die eine gezielte Variation des Rückstellwinkels ω erlauben. Für beide untersuchten Reibpaarungen (Stahl | PE-UHMW und POM-C | PE-UHMW) kann abgeleitet werden, dass der deformative Reibanteil μ_def generell von untergeordneter Rolle ist (ca. 1/3 μ_ges) und der Einfluss des adhäsiven Reibanteils μ_adh überwiegt (ca. 2/3 μ_ges). Dabei sinkt μ_adh und folglich auch μ_ges mit zunehmendem Kontaktdruck p_(max,Ebene). Dieser wurde als verallgemeinerte Bezugsgröße eingeführt und beschreibt den maximalen Hertz´schen Kontaktdruck eines äquivalenten Kugel-Ebene-Kontaktes, der sich unter Eingabe des Kugelradius r_Kugel, der Normalkraft und der Verwendung der statischen E-Moduln beider Werkstoffe ergibt. Weiterhin zeigten die Untersuchungen, dass die oszillierende Bewegungsform im Vergleich zur rotierenden Bewegung immer einen erhöhten Reibwert μ_ges auszeichnet. Abschließend wurden noch Reibexperimente zu Mehrfachstrukturen aus POM-C mit je 6 Einzelerhebungen im Kontakt durchgeführt. Auch hier lag eine hohe Übereinstimmung zwischen Experiment und Modell vor. Es konnte gezeigt werden, dass Reibwerte für beide Bewegungsformen auf μ_ges ~ 0,13 gesenkt werden können. Bezogen auf den jeweiligen höchsten Reibwert (μ_(ges,rotierend) ~ 0,24, μ_(ges,oszillierend) ~ 0,34), welcher mit glatten Probekörpern ermittelt wurde, stellt dies eine erhebliche Reduktion dar. / In this thesis, a semi-analytical calculation model for the coefficient of friction (COF) of single spherical protrusions which allows the calculation of the deformative (μ_def) and adhesive (μ_adh) friction parts was developed. The integration of a plastic (radius of the running track R_Spur) and a viscous (rear angle ω) component of deformation allows the calculation of the real area of contact during the friction process. Depending on the mean contact pressure, the adhesive friction part μ_adh can be determined. The experimental studies included unlubricated friction tests, which served to determine the total COF (μ_ges), as well as tests being lubricated with silicone oil, from which μ_def is obtained. Based on the verification tests, it could be shown that both states of lubrication result in the same deformation and that the relationship between the rear angle ω and μ_def postulated in the calculation model is valid. Therefore, friction tests were carried out with segmented spheres, which allow a specific variation of the rear angle ω. For both friction pairings investigated (steel | PE-UHMW and POM-C | PE-UHMW), it can be concluded that the deformative friction part μ_def is generally of minor significance (approx. 1/3 μ_ges) and the influence of the adhesive friction part μ_adh predominates (approx. 2/3 μ_ges). Thereby μ_adh and consequently also μ_ges decreases with increasing contact pressure p_(max,Ebene). The latter was introduced as a generalised reference value and describes the maximum Hertzian contact pressure of an equivalent sphere-plane contact, which is obtained by entering the radius of the sphere r_Kugel, the normal force and using the static E-moduli of both materials. Furthermore, the investigations revealed that the oscillating form of motion always has an increased COF μ_ges compared to the rotating motion. Finally, friction experiments on multiple structures made of POM-C were carried out, each with 6 individual protrusions in contact. Also here, there was good agreement between the experiment and the model. It could be demonstrated that COF for both forms of motion can be reduced to μ_ges ~ 0.13. In comparison to the highest COF (μ_(ges,rotating) ~ 0.24, μ_(ges,oscillating) ~ 0.34), which were obtained with flat specimens, this is a significant reduction.