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A NONSMOOTH APPROACH for the MODELLING of a MECHANICAL ROTARY DRILLING SYSTEM with FRICTION Samir Adly, Daniel Goeleven
A NONSMOOTH APPROACH FOR THE MODELLING OF A MECHANICAL ROTARY DRILLING SYSTEM WITH FRICTION Samir Adly, Daniel Goeleven To cite this version: Samir Adly, Daniel Goeleven. A NONSMOOTH APPROACH FOR THE MODELLING OF A ME- CHANICAL ROTARY DRILLING SYSTEM WITH FRICTION. Evolution Equations and Control Theory, AIMS, In press, X, 10.3934/xx.xx.xx.xx. hal-02433100 HAL Id: hal-02433100 https://hal.archives-ouvertes.fr/hal-02433100 Submitted on 8 Jan 2020 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Manuscript submitted to doi:10.3934/xx.xx.xx.xx AIMS’ Journals Volume X, Number 0X, XX 200X pp. X–XX A NONSMOOTH APPROACH FOR THE MODELLING OF A MECHANICAL ROTARY DRILLING SYSTEM WITH FRICTION SAMIR ADLY∗ Laboratoire XLIM, Universite´ de Limoges 87060 Limoges, France. DANIEL GOELEVEN Laboratoire PIMENT, Universite´ de La Reunion´ 97400 Saint-Denis, France Dedicated to 70th birthday of Professor Meir Shillor. ABSTRACT. In this paper, we show how the approach of nonsmooth dynamical systems can be used to develop a suitable method for the modelling of a rotary oil drilling system with friction. We study different kinds of frictions and analyse the mathematical properties of the involved dynamical systems. -
Thermal Properties and the Prospects of Thermal Energy Storage of Mg–25%Cu–15%Zn Eutectic Alloy As Phasechange Material
materials Article Thermal Properties and the Prospects of Thermal Energy Storage of Mg–25%Cu–15%Zn Eutectic Alloy as Phase Change Material Zheng Sun , Linfeng Li, Xiaomin Cheng *, Jiaoqun Zhu, Yuanyuan Li and Weibing Zhou School of Materials Science and Engineering, Wuhan University of Technology, Wuhan 430070, China; [email protected] (Z.S.); [email protected] (L.L.); [email protected] (J.Z.); [email protected] (Y.L.); [email protected] (W.Z.) * Correspondence: [email protected]; Tel.: +86-13507117513 Abstract: This study focuses on the characterization of eutectic alloy, Mg–25%Cu–15%Zn with a phase change temperature of 452.6 ◦C, as a phase change material (PCM) for thermal energy storage (TES). The phase composition, microstructure, phase change temperature and enthalpy of the alloy were investigated after 100, 200, 400 and 500 thermal cycles. The results indicate that no considerable phase transformation and structural change occurred, and only a small decrease in phase transition temperature and enthalpy appeared in the alloy after 500 thermal cycles, which implied that the Mg–25%Cu–15%Zn eutectic alloy had thermal reliability with respect to repeated thermal cycling, which can provide a theoretical basis for industrial application. Thermal expansion and thermal Citation: Sun, Z.; Li, L.; Cheng, X.; conductivity of the alloy between room temperature and melting temperature were also determined. Zhu, J.; Li, Y.; Zhou, W. Thermal The thermophysical properties demonstrated that the Mg–25%Cu–15%Zn eutectic alloy can be Properties and the Prospects of considered a potential PCM for TES. -
Leonardo Da Vinci's Contributions to Tribology
© 2016. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ Published as Wear 360-361 (2016) 51-66 http://dx.doi.org/10.1016/j.wear.2016.04.019 Leonardo da Vinci’s studies of friction Ian M. Hutchings University of Cambridge, Department of Engineering, Institute for Manufacturing, 17 Charles Babbage Road, Cambridge CB3 0FS, UK email: [email protected] Abstract Based on a detailed study of Leonardo da Vinci’s notebooks, this review examines the development of his understanding of the laws of friction and their application. His work on friction originated in studies of the rotational resistance of axles and the mechanics of screw threads. He pursued the topic for more than 20 years, incorporating his empirical knowledge of friction into models for several mechanical systems. Diagrams which have been assumed to represent his experimental apparatus are misleading, but his work was undoubtedly based on experimental measurements and probably largely involved lubricated contacts. Although his work had no influence on the development of the subject over the succeeding centuries, Leonardo da Vinci holds a unique position as a pioneer in tribology. Keywords: sliding friction; rolling friction; history of tribology; Leonardo da Vinci 1. Introduction Although the word ‘tribology’ was first coined almost 450 years after the death of Leonardo da Vinci (1452 – 1519), it is clear that Leonardo was fully familiar with the basic tribological concepts of friction, lubrication and wear. He has been widely credited with the first quantitative investigations of friction, and with the definition of the two fundamental ‘laws’ of friction some two hundred years before they were enunciated (in 1699) by Guillaume Amontons, with whose name they are now usually associated. -
Temperature & Thermal Expansion
Temperature & Thermal Expansion Temperature Zeroth Law of Thermodynamics Temperature Measurement Thermal Expansion Homework Temperature & Thermal Equilibrium Temperature – Fundamental physical quantity – Measure of average kinetic energy of molecular motion Thermal equilibrium – Two objects in thermal contact cease to have an exchange of energy The Zeroth Law of Thermodynamics If objects A and B are separately in thermal equilibrium with a third object C (the thermometer), the A and B are in thermal equilibrium with each other. Temperature Measurement In principle, any system whose physical properties change with tempera- ture can be used as a thermometer Some physical properties commonly used are – The volume of a liquid – The length of a solid – The electrical resistance of a conductor – The pressure of a gas held at constant volume – The volume of a gas held at constant pressure The Glass-Bulb Thermometer Common thermometer in everyday use Physical property that changes is the volume of a liquid - usually mercury or alcohol Since the cross-sectional area of the capillary tube is constant, the change in volume varies linearly with its length along the tube Calibrating the Thermometer The thermometer can be calibrated by putting it in thermal equilibrium with environments at known temperatures and marking the end of the liquid column Commonly used environments are – Ice-water mixture in equilibrium at the freezing point of water – Water-steam mixture in equilibrium at the boiling point of water Once the ends of the liquid column have -
Thermal Expansion
Protection from Protect Your Thermal Expansion Water Heater from Protection from thermal expansion is provided in a For further plumbing system by the installation of a thermal expansion tank and a temperature and information Thermal pressure relief valve (T & P Valve) at the top of the tank. contact your Expansion The thermal expansion tank controls the increased local water pressure generated within the normal operating temperature range of the water heater. The small purveyor, tank with a sealed compressible air cushion Without a functioning provides a space to store and hold the additional expanded water volume. City or County Temperature & building The T & P Valve is the primary safety feature for the water heater. The temperature portion of the Pressure Relief Valve T & P Valve is designed to open and vent water department, to the atmosphere whenever the water your water heater can temperature within the tank reaches approxi- licensed plumber º º mately 210 F (99 C). Venting allows cold water to enter the tank. or the The pressure portion of a T & P Valve is designed PNWS/AWWA to open and vent to the atmosphere whenever water pressure within the tank exceeds the Cross-Connection pressure setting on the valve. The T & P Valve is normally pre-set at 125 psi or 150 psi. Control Committee through the Water heaters installed in compliance with the current plumbing code will have the required T & P PNWS office at Valve and thermal expansion tank. For public health protection, the water purveyor may require (877) 767-2992 the installation of a check valve or backflow preventer downstream of the water meter. -
Physics/9803005
UWThPh-1997-52 27. Oktober 1997 History and outlook of statistical physics 1 Dieter Flamm Institut f¨ur Theoretische Physik der Universit¨at Wien, Boltzmanngasse 5, 1090 Vienna, Austria Email: [email protected] Abstract This paper gives a short review of the history of statistical physics starting from D. Bernoulli’s kinetic theory of gases in the 18th century until the recent new developments in nonequilibrium kinetic theory in the last decades of this century. The most important contributions of the great physicists Clausius, Maxwell and Boltzmann are sketched. It is shown how the reversibility and the recurrence paradox are resolved within Boltzmann’s statistical interpretation of the second law of thermodynamics. An approach to classical and quantum statistical mechanics is outlined. Finally the progress in nonequilibrium kinetic theory in the second half of this century is sketched starting from the work of N.N. Bogolyubov in 1946 up to the progress made recently in understanding the diffusion processes in dense fluids using computer simulations and analytical methods. arXiv:physics/9803005v1 [physics.hist-ph] 4 Mar 1998 1Paper presented at the Conference on Creativity in Physics Education, on August 23, 1997, in Sopron, Hungary. 1 In the 17th century the physical nature of the air surrounding the earth was es- tablished. This was a necessary prerequisite for the formulation of the gas laws. The invention of the mercuri barometer by Evangelista Torricelli (1608–47) and the fact that Robert Boyle (1627–91) introduced the pressure P as a new physical variable where im- portant steps. Then Boyle–Mariotte’s law PV = const. -
Transitions Still to Be Made Philip Ball
impacts Transitions still to be made Philip Ball A collection of many particles all interacting according to simple, local rules can show behaviour that is anything but simple or predictable. Yet such systems constitute most of the tangible Universe, and the theories that describe them continue to represent one of the most useful contributions of physics. hysics in the twentieth century will That such a versatile discipline as statisti- probably be remembered for quantum cal physics should have remained so well hid- Pmechanics, relativity and the Standard den that only aficionados recognize its Model of particle physics. Yet the conceptual importance is a puzzle for science historians framework within which most physicists to ponder. (The topic has, for example, in operate is not necessarily defined by the first one way or another furnished 16 Nobel of these and makes reference only rarely to the prizes in physics and chemistry.) Perhaps it second two. The advances that have taken says something about the discipline’s place in cosmology, high-energy physics and humble beginnings, stemming from the quantum theory are distinguished in being work of Rudolf Clausius, James Clerk important not only scientifically but also Maxwell and Ludwig Boltzmann on the philosophically, and surely that is why they kinetic theory of gases. In attempting to have impinged so forcefully on the derive the gas laws of Robert Boyle and consciousness of our culture. Joseph Louis Gay-Lussac from an analysis of But the central scaffold of modern the energy and motion of individual physics is a less familiar construction — one particles, Clausius was putting thermody- that does not bear directly on the grand ques- namics on a microscopic basis. -
Kinetic Theory of Gases and Thermodynamics
Kinetic Theory of Gases Thermodynamics State Variables Kinetic Theory of Gases and Thermodynamics Zeroth law of thermodynamics Reversible and Irreversible processes Bedanga Mohanty First law of Thermodynamics Second law of Thermodynamics School of Physical Sciences Entropy NISER, Jatni, Orissa Thermodynamic Potential Course on Kinetic Theory of Gasses and Thermodynamics - P101 Third Law of Thermodynamics Phase diagram 1/112 Principles of thermodynamics, thermodynamic state, extensive/intensive variables. internal energy, Heat, work First law of thermodynamics, heat engines Second law of thermodynamics, entropy Thermodynamic potentials References: Thermodynamics, kinetic theory and statistical thermodynamics by Francis W. Sears, Gerhard L. Salinger Thermodynamics and introduction to thermostatistics, Herbert B. Callen Heat and Thermodynamics: an intermediate textbook by Mark W. Zemansky and Richard H. Dittman About 5-7 Tutorials One Quiz (10 Marks) and 2 Assignments (5 Marks) End Semester Exam (40 Marks) Course Content Suppose to be 12 lectures. Kinetic Theory of Gases Kinetic Theory of Gases Thermodynamics State Variables Zeroth law of thermodynamics Reversible and Irreversible processes First law of Thermodynamics Second law of Thermodynamics Entropy Thermodynamic Potential Third Law of Thermodynamics Phase diagram 2/112 internal energy, Heat, work First law of thermodynamics, heat engines Second law of thermodynamics, entropy Thermodynamic potentials References: Thermodynamics, kinetic theory and statistical thermodynamics by Francis W. Sears, Gerhard L. Salinger Thermodynamics and introduction to thermostatistics, Herbert B. Callen Heat and Thermodynamics: an intermediate textbook by Mark W. Zemansky and Richard H. Dittman About 5-7 Tutorials One Quiz (10 Marks) and 2 Assignments (5 Marks) End Semester Exam (40 Marks) Course Content Suppose to be 12 lectures. -
2. Classical Gases
2. Classical Gases Our goal in this section is to use the techniques of statistical mechanics to describe the dynamics of the simplest system: a gas. This means a bunch of particles, flying around in a box. Although much of the last section was formulated in the language of quantum mechanics, here we will revert back to classical mechanics. Nonetheless, a recurrent theme will be that the quantum world is never far behind: we’ll see several puzzles, both theoretical and experimental, which can only truly be resolved by turning on ~. 2.1 The Classical Partition Function For most of this section we will work in the canonical ensemble. We start by reformu- lating the idea of a partition function in classical mechanics. We’ll consider a simple system – a single particle of mass m moving in three dimensions in a potential V (~q ). The classical Hamiltonian of the system3 is the sum of kinetic and potential energy, p~ 2 H = + V (~q ) 2m We earlier defined the partition function (1.21) to be the sum over all quantum states of the system. Here we want to do something similar. In classical mechanics, the state of a system is determined by a point in phase space.Wemustspecifyboththeposition and momentum of each of the particles — only then do we have enough information to figure out what the system will do for all times in the future. This motivates the definition of the partition function for a single classical particle as the integration over phase space, 1 3 3 βH(p,q) Z = d qd pe− (2.1) 1 h3 Z The only slightly odd thing is the factor of 1/h3 that sits out front. -
Lecture 15 November 7, 2019 1 / 26 Counting
...Thermodynamics Positive specific heats and compressibility Negative elastic moduli and auxetic materials Clausius Clapeyron Relation for Phase boundary \Phase" defined by discontinuities in state variables Gibbs-Helmholtz equation to calculate G Lecture 15 November 7, 2019 1 / 26 Counting There are five laws of Thermodynamics. 5,4,3,2 ... ? Laws of Thermodynamics 2, 1, 0, 3, and ? Lecture 15 November 7, 2019 2 / 26 Third Law What is the entropy at absolute zero? Z T dQ S = + S0 0 T Unless S = 0 defined, ratios of entropies S1=S2 are meaningless. Lecture 15 November 7, 2019 3 / 26 The Nernst Heat Theorem (1926) Consider a system undergoing a pro- cess between initial and final equilibrium states as a result of external influences, such as pressure. The system experiences a change in entropy, and the change tends to zero as the temperature char- acterising the process tends to zero. Lecture 15 November 7, 2019 4 / 26 Nernst Heat Theorem: based on Experimental observation For any exothermic isothermal chemical process. ∆H increases with T, ∆G decreases with T. He postulated that at T=0, ∆G = ∆H ∆G = Gf − Gi = ∆H − ∆(TS) = Hf − Hi − T (Sf − Si ) = ∆H − T ∆S So from Nernst's observation d (∆H − ∆G) ! 0 =) ∆S ! 0 As T ! 0, observed that dT ∆G ! ∆H asymptotically Lecture 15 November 7, 2019 5 / 26 ITMA Planck statement of the Third Law: The entropy of all perfect crystals is the same at absolute zero, and may be taken to be zero. Lecture 15 November 7, 2019 6 / 26 Planck Third Law All perfect crystals have the same entropy at T = 0. -
The Coefficient of Thermal Expansion and Your Heating System By: Admin - May 06, 2021
The Coefficient of Thermal Expansion and your Heating System By: Admin - May 06, 2021 We’ve all been there. The lid on pickle jar is impossibly tight, but when you run hot water over the jar you can easily unscrew the lid. The metal lid expands more than the glass jar, which is a simple illustration of how materials, when heated, expand at different rates. The relationship of how materials expand or contract through temperature change is driven by the coefficient of thermal expansion or CTE of those materials and is a critical factor when designing a heater. Determining the appropriate materials for the heater is not as simple as running warm water over a metal lid. The coefficient of thermal expansion is a critical factor when pairing dissimilar materials in a system. With the help of Watlow representatives, you can make sure your system is designed for success, efficiency and a long lifespan. What is the coefficient of thermal expansion? To understand the science behind the coefficient of thermal expansion (CTE), one must first understand the basics of thermal expansion. Physical property changes, such as shape, area, volume and density, occur during thermal expansion. Every material or metal/metal alloy will have a slightly different expansion rate. CTE, then, is the relative expansion or contraction of materials driven by a change in temperature. Metals, ceramics and other materials have unique coefficients of thermal expansion and do not expand and contract at equal rates. For example, if the volume of a section of aluminum and a section of ceramic are equal and are heated from X to Y degrees, the aluminum could increase in dimension by a factor of four compared to the ceramic. -
1 Classical Theory and Atomistics
1 1 Classical Theory and Atomistics Many research workers have pursued the friction law. Behind the fruitful achievements, we found enormous amounts of efforts by workers in every kind of research field. Friction research has crossed more than 500 years from its beginning to establish the law of friction, and the long story of the scientific historyoffrictionresearchisintroducedhere. 1.1 Law of Friction Coulomb’s friction law1 was established at the end of the eighteenth century [1]. Before that, from the end of the seventeenth century to the middle of the eigh- teenth century, the basis or groundwork for research had already been done by Guillaume Amontons2 [2]. The very first results in the science of friction were found in the notes and experimental sketches of Leonardo da Vinci.3 In his exper- imental notes in 1508 [3], da Vinci evaluated the effects of surface roughness on the friction force for stone and wood, and, for the first time, presented the concept of a coefficient of friction. Coulomb’s friction law is simple and sensible, and we can readily obtain it through modern experimentation. This law is easily verified with current exper- imental techniques, but during the Renaissance era in Italy, it was not easy to carry out experiments with sufficient accuracy to clearly demonstrate the uni- versality of the friction law. For that reason, 300 years of history passed after the beginning of the Italian Renaissance in the fifteenth century before the friction law was established as Coulomb’s law. The progress of industrialization in England between 1750 and 1850, which was later called the Industrial Revolution, brought about a major change in the production activities of human beings in Western society and later on a global scale.