Friction Models

In this paper hybrid theory has been applied to design a state-feedback control law of an electrical drive with friction. The drive is modeled as a piecewise affine (PWA) system and a finite time optimal control problem is formulated for such a hybrid system. Three most often used friction models are considered and compared based on their suitability for the PWA description. It is shown that a reset-integrator friction model gives a PWA model of smaller complexity than LuGre and Karnopp friction
models. A state-feedback optimal control law in a form of a look-up table is then derived via dynamic programming. The control system behavior is tested by computer simulations. The results indicate that
the proposed control strategy is a valuable alternative to the currently used control strategies.

An analytical ploughing model is used to compute the forces on a rigid, elliptical, i.e. ellipsoid and elliptic-paraboloid shaped, asperity sliding through a rigid-plastic substrate as a function of its axes size, ellipticity ratio and sliding orientation. The normal force due to the plastic deformation of the substrate and the tangential force due to the shearing of the asperity-substrate interface are calculated from the surface normal vector and the tangent vector along the direction of plastic flow. The elemental forces are integrated over the boundaries of the asperity-substrate contact to obtain the individual force components. In this way, an analytical model to study the effect of asperity geometry on ploughing forces has been developed and compared with the available theories .

Contemporary archaeology recognises the modern landscape as a material resource. This resource has the ability to challenge assumptions regarding the 20th and 21st centuries based in historiography and memory. In this way it engages with a chronology of historical and prehistoric archaeologies, revealing a continuum which extends into the present day. The 20th century is characterised by its superfluity in the contemporary landscape. The utility of contemporary archaeology lies in its ability to articulate detail from this morass of data. The recent past has the potential to illustrate the complex relationship materiality shares with social constructs of verbal meaning and social action. The architecture of The New Brutalism came to dominate architecture in Britain and Australia for a brief period of time in the late-20th century. As such it is well represented today. Its formal register is one of the most recognisable in its use of raw untreated concrete and lack of ornament, and for this reason it is also one of the most controversial. This thesis aims to address Brutalism as a diagnostic formal type in the modern built landscape. Through the application of material non-correspondence theory, Brutalism is shown to have archaeological validity. The principles of dissonance and inertia and highlighted in the Brutalist case study, and illustrate the direct utility of archaeology in shallow temporal contexts.

Friction is a system property, which indicates that it depends on multiple factors, such as the material properties, contact parameters and the environment.
Friction is one of the themes in tribology, an engineering technology which is the science and technology of interacting surfaces in relative motion and of the practices related thereto.
Friction of a textile material against itself and that of a textile material against another surface has been the subject of numerous investigations during the past four decades.
Most of these investigations have been devoted to understanding of fiber and yarn friction.
Relatively little work has been done devoted to understanding fabric frictional properties measurement.

Hazen-Williams equation is used widely by irrigation systems’ designers due to its simplicity.However, Darcy-Weisbach equation is more accurate and reliable. The accuracy of the latter is due to its friction coefficient, which depends on both flow characteristics and pipe surface state. On the other hand, Hazen-Williams’ coefficient (C) depends only on pipe substance and age. A comparative analysis of both models was performed through a simple iterative model. The analysis was based on the real state design procedure of drip laterals. More accurate values of coefficient C were suggested to be used in designing drip laterals. A straightforward equation was developed to compute C depending on emitter flowrate, emitter flow exponent, and pipe diameter.The results reveal that C ranges from 132 to 138 for drip laterals, while it was proved that using C=150 is reasonable for manifolds design.

Cuff tear arthropathy (CTA) is a shoulder pathology characterized by a massive and irreparable rotator cuff tear and an abnormal contact between the humeral head and the acromion. CTA is often associated with shoulder pseudo-paralysis. However, the fact that some patients still maintain a functional shoulder remains unexplained. The goal of the present work was to numerically assess the biomechanical parameters that influence the function of the shoulder with CTA. The specific objectives were to show the influence of: (1) a variation of the medial offset of the proximal humerus on the destabilizing forces at the intact (healthy) shoulder; (2) the elevation plane and the friction coefficient on the “mechanics of CTA” and; (3) the geometrical parameters of the humeral head on the “mechanics of CTA” in the context of an hemiarthroplasty.

Study #1 assessed the influence of a minimum (0 mm), average (7 mm) and maximum (14 mm) medial offset on the destabilizing glenohumeral forces (transverse to the glenoid) at the intact (healthy) shoulder. Study #2 assessed the influence of the elevation plane (frontal, scapular, sagittal) and the contact friction (coefficient of 0.15, 0.3 and 0.6) on the “mechanics of CTA” (i.e. deltoid length and force; contact forces (glenoid and acromion)). Study #3 assessed the influence of a large medial offset (17 mm) associated with an oversized humeral head hemiprosthesis (120 %) on the same “mechanics of CTA” as in study #2.

Study #1 showed that the maximum medial offset (14 mm) greatly decreases the destabilizing action of the deltoid without affecting the stabilizing action of the rotator cuff. The CTA model of study #2 showed that the elevation plane influences the mechanics of CTA, but that the contact condition (friction) combined with the poor mechanics of the deltoid is more likely to lead to a poor function. Study #3 showed that the combination of a large medial offset with an oversized humeral head hemiprosthesis decreases the acromio-humeral contact force and increases the range of motion more significantly compared to a simple oversized prosthetic head.

The present work highlights the potential of the AnyBody software to study the sensitivity of the human musculoskeletal system (intact and injured) to morphological parameters. This work also brings new lines of thoughts regarding biomechanical parameters that influence the function of the shoulder with CTA. Finally, this work proposes an oversized humeral hemiprosthesis with a large medial offset as an alternative CTA treatment for young patients with poor function, thus leaving more room for revision surgery.

В настоящей статье рассмотрены примеры достаточно простых задач, иллюстрирующие взаимосвязь приближенных моделей описывающих силы, действующие при качении деформируемого колеса. Основные причины, побудившие автора представить настоящий материал, состоят в следующем. Во-первых, вопросы теории качения деформируемого колеса как правило не находят отражения в курсах теоретической механики. В этих курсах обсуждаются упрощенные сигнатурные модели контактных сил, но при этом не поясняется, от знака какой именно величины зависят силы в контакте колеса с дорогой. Во-вторых, в настоящее время широкое распространение получила теория поликомпонентного сухого трения [4], результаты которой на первый взгляд не согласуются с известными моделями качения деформируемого колеса. В тоже время подход к моделированию контактных сил c использованием модели cухого трения для деформируемого колеса известен давно и изложен, например, в книге [1]. Различные приближения построенных моделей  используются при описании таких явлений как, например, увод колеса, шимми управляемых колес автомобиля и самолета и т.д.  Недостатком этого изложения следует считать отсутствие аккуратного обоснования для пренебрежения «моментом трения верчения». Наконец, в русскоязычной литературе, обсуждающей особенности современных моделей качения деформируемых колёс, подобные вопросы обсуждаются крайне редко.

Thesis at the Western Michigan University by Ravishankar Thangavelu, 2004
111 pages
Not about Wankel rotary engines (dealing with the Hopkins rotor engine), but, the subject "friction" is pretty important ...

> Hopkins rotor engine with 4 interacting oval rotors

> Content ...
> Acknowledgments  4
> Title  5
> Table of contents  6
> List of tables  10
> List of figures  11
> Chapter 1 - Introduction  12
  » Prologue  12
  » Why non-conventional engines ?  13
  » Need for predictive models  15
  » Nature + scope of the work  15
  » Organization of work  17
> Chapter 2 - Literature survey  19
  » Introduction  19
  » Engine friction  20
  » Friction model  21
  » Liquid lubrication  21
  » Rotary engine seals  21
> Chapter 3 - Theory + concepts of friction  23
  » Friction in engines  23
  » Piston + ring friction  24
  » Crank shaft + connecting rod bearing friction  25
  » Valve train friction  26
  » Pumping friction  26
  » Accessory friction  26
  » Hydrodynamic friction theory  27
  » Dynamic viscosity of the oil film  29
> Chapter 4 - Rotary engine description  31
  » Rotary engine  31  (Hopkins rotor engine)
  » Rotor geometry  34
  » Rotor radius  34
  » Rotor length  39
  » Rotor seals  40
> Chapter 5 - Rotary engine friction  44
  » Components of rotary engine friction  44
  » Rotor seal friction  44
  » Bearing friction  48
  » Mechanical efficiency  49
  » Wear  51
> Chapter 6 - Friction parameters  52
  » Friction parameters  52
  » Seal material  53
  » Velocity gradient  53
  » RPM  54
  » Angle of contact  54
  » Clearance between the rotors  54
> Chapter 7 - Detailed methodology  55
  » Introduction  55
  » Instantaneous contact radius  55
  » Method for calculating instantaneous contact radius  57
  » Wear cycle approximation  61
  » Rotor + seal material  62
> Chapter 8 - Results from the friction model  63
  » Introduction  63
  » Mechanical efficiency  65
  » Indicated power  66
> Chapter 9 - Conclusion  69
  » Introduction  69
  » Surface velocity constrain  69
  » User friendly nature of the model  70
  » Seal type  71
> Bibliography  72
> Appendix - A - Maple program
> Appendix - B - LabView program

This paper presents the dynamics modeling and dynamic identification of a dual-blade wafer handling robot. An explicit form dynamic model for this 8-link parallel robot is proposed. The dynamic model is transformed into a decoupled form to enable dynamic parameters identification with least-square regression. A well conditioned trajectory is chosen for identification experiment. Both viscous friction and Coulomb friction are considered to make the model more reliable. Model has been validated by experiments.

This paper proposes an iterative method that can simulate mechanical systems featuring a large number of contacts and joints between rigid bodies. The numerical method behaves as a contractive mapping that converges to the solution of a cone complementarity problem by means of iterated fixed-point steps with separable projections onto convex manifolds. Since computational speed and robustness are important issues when dealing with a large number of frictional contacts, we have performed special algorithmic optimizations in order to translate the numerical scheme into a matrix-free algorithm with O(n) space complexity and easy implementation. A modified version, that can run on parallel computers is discussed. A multithreaded version of the method has been used to simulate systems with more than a million contacts with friction.

Results from an experimental and numerical study of skin friction levels obtained when hydrogen is injected into turbulent boundary layers are presented. Measurements are reported from experiments in the T4 free-piston reflected shock tunnel. Hydrogen was injected from a 3 mm high slot into the boundary layer on the flat surface of one of the walls of a duct 100 mm wide, 60 mm high, and 1745 mm long. The experiments were conducted at Mach numbers ranging from 4.2 to 4.7, flow stagnation enthalpies of 4.8 MJ/kg to 9.5 MJ/kg, static pressures of 59 kPa to 86 kPa, and Reynolds numbers of 8.9  106 m-1 to 17.2  106 m-1. Hydrogen fuel was injected 245 mm downstream of the inlet through a 3 mm slot. Mass flow rates of 0 kg/s/m and 0.36 kg/s/m, at a nozzle area ratio of 1.7, were used for test flows of air. Combustion occurred at all flow conditions with results indicating a maximum reduction in skin friction coefficient, of approximately 80% of the level measured with no injection. Skin friction reductions of approximately 60% were obtained at two other test flows. Measured heat transfer levels were found to be comparable with levels obtained without injection, for most of the experimental conditions. Hydrogen injection into a test flow of nitrogen was also trialed at all flow conditions to compare with the results obtained when fuel was injected into an air flow, in order to identify the effects of combustion. In general, the results showed that reductions in local skin friction coefficient were greater when combustion occurred than when fuel was injected and did not burn.  This paper is unpublished.

Results from an experimental and numerical study of skin friction levels obtained when hydrogen is injected into turbulent boundary layers are presented. Measurements are reported from experiments in the T4 free-piston reflected shock tunnel. Hydrogen was injected from a 3 mm high slot into the boundary layer on the flat surface of one of the walls of a duct 100 mm wide, 60 mm high, and 1745 mm long. The experiments were conducted at Mach numbers ranging from 4.0 to 4.5, flow stagnation enthalpies of 4.8 MJ/kg to 9.5 MJ/kg, static pressures of 75 kPa to 110 kPa, and fuel equivalence ratios of 0.3 and 0 for test flows of air. Combustion occurred at all flow conditions with results indicating a maximum reduction in skin friction coefficient, of approximately 77% of the level measured with no injection. Skin friction reductions of approximately 60% were obtained at two other test flows. Measured heat transfer levels were found to be comparable with levels obtained without injection, for most of the experimental conditions. Hydrogen injection into a test flow of nitrogen was also trialed at all flow conditions to compare with the results obtained when fuel was injected into an air flow in order to identify the effects of combustion.

This work deals with the hydraulic gradient estimation in real-time of a transport pipeline computational model by considering a slightly compressible fluid and slightly deformable conduit walls. Since the hydraulic gradient (J(Q)) caused by the friction phenomenon in a pipeline plays an important role in the system's behavior, and this function is affected by fluid properties' deviations, environmental disturbances and conduit deteriorations, it is proposed that the on-line estimation of J(Q) could be part of a monitoring system. The proposition can be applied to obtain computational models of a line with a junction and assumes only measurements of pressure and flow rate at the ends of the conduit and the junction outflow. The generic form of the gradient function J(Q) is a second-order polynomial with coefficients that involve indirectly pipe roughness, the transversal area of the conduit, fluid viscosity and elements connected to the line. The extended Kalman filter (EKF) is applied to estimate the coefficients of the function J(Q). As a test apparatus, a 163 m long hydraulic pipeline is used. Diverse experiments show the usefulness of the on-line estimation of J(Q) for monitoring and simulation tasks where computational models are necessary.

The paper presents direct measurement of in-cylinder friction from a single cylinder motocross race engine under motored conditions and compares the same with a new analytical predictive method. These conditions are encountered in piston-cylinder system with the application of cylinder deactivation (CDA) technology, which is a growing trend. The analytical method takes into account the various regions within instantaneous contact of compression ring-cylinder liner, including lubricant film rupture, cavitation zone and the subsequent lubricant film reformation. The analysis also includes the effect of boundary friction and lubricant rheology. The predictions and direct measurements of cyclic friction show good agreement and indicate dominance of viscous friction under the investigated engine running conditions. In particular, it is shown that the compression ring contribution to in-cycle friction is most pronounced in the region of high cylinder pressures because of combined Poiseuille friction and some boundary solid interactions. The combined experimental-analytical approach has not hitherto been reported in literature.

A coating layer is often present on engineering surfaces. An example is a zinc coating on steel sheet, this being a
soft metallic coating on a hard substrate. To characterize the tribological behaviour of these engineered surfaces,
it is necessary to understand the mechanical behaviour of the coating during ploughing. The material point
method (MPM)-based ploughing model has been used to compute friction and the ploughed profile when an
asperity is ploughing through a coated surface. An analytical ploughing model has also been used to study the
effect of the thickness and hardness of the coating relative to the substrate on coefficient of friction using rigidplastic
material behaviour and its results have been compared with the MPM-model results. The MPM-based
ploughing model has been experimentally validated and is shown to agree well with the ploughing experiments
using rigid spherical indenters sliding through lubricated-zinc coated steel, uncoated steel and bulk zinc
over a range of applied loads.

Nonlinear friction in tendon-sheath mechanism (TSM) introduces difficulties in predicting the end-effector force inside the human body during surgical procedures. This brings a critical challenge for surgical robots that need high fidelity in haptic devices. This paper presents a new friction model for a TSM in surgical robots. The model considers the TSM as an element
disregarding the tendon sheath curvature and permits an arbitrary configuration of sheath. It allows for the accurate modelling of friction force at both sliding and presliding regimes. Unlike existing approaches in the literature, the model employs not only velocity but also acceleration information. It is also able to capture separate hysteresis branches in the large displacement using a unique differential equation. Transition between the two regimes is smooth. To validate
the approach, an experimental setup is developed to measure the tensions at both ends of the TSM. The model parameters are identified and experimentally validated using an optimization method and different types of input signals. It assures an accurate prediction of nonlinear hysteresis behavior of TSM, especially at near zero velocities. This model can be used to provide an estimate of the friction force in a haptic feedback device to the surgeons.

Purpose – The purpose of the paper was to find a simple structure of motion controller for permanent magnet direct drive. Application of sliding mode controller theory and equivalent disturbance estimator creates proper non-linear characteristics, which ensures controller robustness against friction.
Design/methodology/approach – The position and speed controller is based on robust design methodology introduced by a sliding mode technique. The paper proposes a combination of sliding mode controller and Proportional Integral PI  equivalent disturbance estimator. The friction model is Coulomb friction with a large static friction effect. The double boundary layer is used to compensate the effect of stiction. The synthesis is performed using simulation techniques and subsequently the behaviour of a laboratory speed control system is validated in the experimental setup. The control algorithms of the system are performed by a microprocessor floating point DSP control system.
Findings – The proposed sliding mode controller structure with equivalent disturbance estimator guarantees expected robustness against friction. Experimental results show that the control approach can decrease the tracking error, enhance the system's robustness and attenuate high-frequency chattering in the control signal.
Research limitations/implications – The proposed controller was tested on a single machine under well-defined conditions. Further investigations are required before any industrial applications.
Practical implications – The proposed controller synthesis and its results may be very helpful in robotic systems where non-linear friction is a characteristic for many industrial robots and manipulators.
Originality/value – The method of sliding mode controller synthesis was proposed and validated by simulation and experimental investigations.

Keywords – robust control, motion control, direct drive, sliding mode controller, friction

We study the dynamics of an incommensurate chain sliding on a periodic lattice, modeled by the
Frenkel-Kontorova Hamiltonian with initial kinetic energy, without damping and driving terms. We show
that the onset of friction is due to a novel type of dissipative parametric resonances, involving several
resonant phonons which are driven by the (dissipationless) coupling of the center of mass motion to the
phonons with the wave vector related to the modulating potential. We establish quantitative estimates
for their existence in finite systems and point out the analogy with the induction phenomenon in Fermi-
Ulam-Pasta lattices.

The consequence of highway accidents in terms of injuries, loss of lives, and road closures is a major strain on any economy. It has therefore become necessary to look into the causes of such accidents from a road condition view point with the aim of limiting their frequency of
occurrence.
This paper summarizes previous research works that have been carried out on the significant factors of skid resistance and texture over time, models that have been created for predicting texture and skid resistance under traffic, and different methods of measuring skid resistance and
texture.

Rate and state friction has been extensively used to explain many features of the seismic cycle but the scaling of the experimentally derived parameters a, b and d c for real faults is problematic. The purpose of this paper is to present a micromechanical model for rate and state friction in which the contact between the two surfaces occur via plastic and elastic contacts. Shear deformation is accommodated in the bulk of cylindrical contacts rather than at the surface of the contact, as done classically. Assuming that the viscoplastic response is governed by the J 2 plastic flow theory, we retrieve the rate and state framework. Unlike previous works, we identify the state variable as representing the changes of plastic contact area. In our model, all macroscopic frictional parameters of the rate and state framework are related to the parameters of the elementary contacts. We provide a derivation of the aging evolution law for the state variable and propose a new evolution law that reconciles the aging, Linker-Dieterich and Nagata evolution laws. We discuss the scaling of the frictional parameters for active faults and landslides. The a and b parameters should have comparable value at fault scale since friction is mostly controlled by plastic contacts at large normal stress (typically hundreds of MPa). Our model predicts that the critical slip distance d c should be scale independent and controlled solely by the plastic contacts. Plain Language Summary The seismic cycle is controlled by the way friction evolves on active faults. We present here a micromechanical model, based on the idea that friction is accomodated by the plastic and elastic contacts on the fault interface. Our model allows the derivation of the rate and state friction laws, which have been widely used to model the seismic cycle. Our approach allows extrapolating laboratory results to the fault scale and suggests that laboratory experiments are suitable to describe fault dynamics. Our model presents an alternative to the reference Bowden and Tabor friction model, and allows, for the first time, the extrapolation of the frictional parameters derived in the laboratory to fault scale.

One of the ultimate goals in landslide hazard assessment is to predict maximum landslide extension and velocity. Despite much work, the physical processes governing energy dissipation during these natural granular flows remain uncertain. Field observations show that large landslides travel over unexpectedly long distances, suggesting low dissipation. Numerical simulations of landslides require a small friction coefficient to reproduce the extension of their deposits. Here, based on analytical and numerical solutions for granular flows constrained by remote-sensing observations, we develop a consistent method to estimate the effective friction coefficient of landslides. This method uses a constant basal friction coefficient that reproduces the first-order landslide properties. We show that friction decreases with increasing volume or, more fundamentally, with increasing sliding velocity. Inspired by frictional weakening mechanisms thought to operate during earthquakes, we propose an empirical velocity-weakening friction law under a unifying phenomenological framework applicable to small and large landslides observed on Earth and beyond.

We show that invariance properties of the Lagrangian of an incommensurate system, as described by the
Frenkel-Kontorova model, imply the existence of a generalized angular momentum that is an integral of
motion if the system remains floating. The behavior of this quantity can therefore monitor the character of the
system as floating ~when it is conserved! or locked ~when it is not!. We find that, during the dynamics, the
nonlinear couplings of our model cause parametric phonon excitations that lead to the appearance of Umklapp
terms and to a sudden deviation of the generalized momentum from a constant value, signaling a dynamical
transition from a floating to a pinned state. We point out that this transition is related but does not coincide with
the onset of sliding friction, which can take place when the system is still floating.

In this paper we analyze the influence of shear and normal stress changes on frictional properties. This problem is fundamental as, for instance, sudden stress changes are naturally induced on active faults by nearby earthquakes. As any stress changes can be seen as resulting from a succession of infinitesimal stress steps, the role of sudden stress changes is crucial to our understanding of fault dynamics. Laboratory experiments carried out by Linker and Dieterich (1992) and Nagata et al. (2012), considering steps in normal and shear stress, respectively, show an instantaneous response of the state variable (a proxy for the evolution of contact surface in our model) to a sudden stress change. We interpret this response as being due to an (instantaneous) elastic response of the plastic and elastic contacts. We assume that the anelastic response of the plastic contacts is frozen during sudden stress changes. The contacts, which were driven by plasticity before the stress change, are elastically accommodated during the sudden variation of the load. On the contrary, when the loading is slowly varying, elastic deformation of plastic contacts can be neglected. Our model is able to explain the evolution law for the state variable reported by Linker and Dieterich (1992). Plain Language Summary In this paper we analyze the influence of shear and normal stress changes on frictional properties. This problem is fundamental as, for instance, sudden stress changes are naturally induced on active faults by nearby earthquakes. Our model is able to retrieve the Linker and Dieterich evolution law, which is a reference one that describes the evolution of friction under variable normal stress. Our model assumption is that the plastic contacts that accommodate friction on a fault have an instantaneous elastic response to sudden changes in shear and normal stress. This allows the extrapolation of our frictional model to fault scale.

Research was conducted to determine the effect of lubricants on stress and strain in the contact of metal surfaces. Experiments were carried out on the introduction of a fixed and moving indenter in contact with a dry and lubricated surface.The steel spherical specimen was pressed into a lubricated and dry metal surface. The microstructures of the structure of the surface layer are studied under various conditions of deformation. The diagrams of the relative deformation of the surface layers are constructed. The mechanism of the formation and distribution of internal stresses for dry and greased contact is described. Experimental studies of the introduction of a moving steel indenter into a lubricated surface have been carried out. The relationship of the deformation mechanisms of lubricated surfaces with their wear resistance is determined. The results obtained are recommended for predicting the durability of lubricated friction units according to the criterion of contact strength.

The parasitic drag losses incurred by wet clutches, used in transmission systems, can significantly affect vehicular powertrain efficiency. This paper presents a novel implicit solution for hydrodynamic parasitic drag losses of disengaged clutches. These are generated by conjunctional friction, taking into account lubricant film separation during co-directional and counter-directional disc pair rotations. Lubricant film rupture is considered through application of incipient reverse flow boundary condition, which is representative of lubricant film separation. The results point to the operating conditions at which significant power losses occur. In particular, the time efficient model is able to represent the small losses incurred during co-directional rotation of disc pairs.

http://fluidsengineering.asmedigitalcollection.asme.org/article.aspx?articleid=2747813

The influence of isolator characteristics on the seismic response of multi-story base-isolated structure is investigated. The isolated building is modeled as a shear type structure with lateral degree-of-freedom at each floor. The isolators are modeled by using two different mathematical models depicted by bi-linear hysteretic and equivalent linear elastic–viscous behaviors. The coupled differential equations of motion for the isolated system

A material point method (MPM)-based numerical model has been used to study the effect of asperity size and orientation relative to sliding direction on the ploughing behaviour of a rigid, ellipsoidal asperity. Based on the simulated ploughing behaviour, an analytical model has been extended to calculate the ploughing depths over the wear track and compute the forces acting over the contacting surface of an ellipsoidal asperity sliding through a rigid-plastic substrate. The analytical model results have been compared with the MPM model results. The MPM model results are also validated to be in good agreement with the friction forces and ploughing depths measured from the ploughing experiments on lubricated steel sheets with ellipsoidal indenters up to certain sizes and orientations.

It is presented a method for numerical and experimental determination of the coefficient of rolling friction of the steel small ball (sphere). The sphere is hanged on a non-elastic and weightlessness thread. Such the formed pendulum oscillates in plane, which is inclined to the vertical. Moreover the sphere rolls without sliding over steel plate with microwaviness. By the experimental way the coefficient of rolling friction is determinate in dependence on the initial angle of deviation of the pendulum and the number of oscillations to the full attenuation. The exact non-linear differential equation of the vibration of the physical pendulum is deduced. The solving is carried out numerically by the software MATLAB. It was made a comparison of the experimental and numerical results

This work deals with the hydraulic gradient estimation in real-time of a transport pipeline computational model by considering a slightly compressible fluid and slightly deformable conduit walls. Since the hydraulic gradient (J(Q)) caused by the friction phenomenon in a pipeline plays an important role in the system's behavior, and this function is affected by fluid properties' deviations, environmental disturbances and conduit deteriorations, it is proposed that the on-line estimation of J(Q) could be part of a monitoring system. The proposition can be applied to obtain computational models of a line with a junction and assumes only measurements of pressure and flow rate at the ends of the conduit and the junction outflow. The generic form of the gradient function J(Q) is a second-order polynomial with coefficients that involve indirectly pipe roughness, the transversal area of the conduit, fluid viscosity and elements connected to the line. The extended Kalman filter (EKF)...