Coulomb Friction Coefficient Research Articles

Practical Approach of Modeling and Parameters Estimation for Omnidirectional Mobile Robots

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> This paper presents a nonlinear modeling approach for omnidirectional mobile robots. Three experimental methods of estimation of the parameters related to dynamic equations of the robot's model are developed. The estimation methods are based on least-squares methods to obtain the viscous friction coefficients, the coulomb friction coefficients, and the moment of inertia of the robot. Simulation results and real results of navigation are provided to demonstrate the performance of the proposed modeling approach. </para>

An identification method for static and coulomb friction coefficients

This paper deals with the identification of static and Coulomb friction coefficients. An approach based on limit cycles properties once the mechanical system is brought to oscillations is proposed. This leads to an explicit formulation in the regulator parameters on one part, and the oscillation amplitude and period on the other part. The method is validated by a simulation example and an experimental benchmark.

A new adaptive backstepping Coulomb friction compensator for servo control systems

AbstractA new Coulomb friction compensator is proposed for servo control systems in this paper. The novelty of the new approach lies in its capability of assigning the eigenvalues of the resulting closed loop system while attacking the problem. First, based on the standard backstepping methodology, an implicit Lyapunov function, with part of the components being only symbolically constructed at the very beginning, is utilized. To increase the robustness of the system against disturbance and model inaccuracy, an integral term is employed in the design. Using part of the variable gradient method, we are able to turn the implicit Lyapunov function into an explicit one, which is positive definite, and whose time‐derivative is negative definite. Second, it will be shown that the resulting closed loop error system is a switched linear system with two possible active modes that share the same set of eigenvalues, which is at our disposal. Unlike the common adaptive control design methods, such as the Control Lyapunov Function approach, in which the gains are typically positive but otherwise arbitrary, and are hence difficult to choose and have a lack of connection with the system's performance, our new scheme imposes two further constraints on the gains. It turns out that we can then match these gains with the coefficients of the desired characteristic equation of the closed loop system. In this respect, the gains are linked to the system's overall performance, which is a new and very appealing feature for such a scheme. Finally, a procedure of constructing a common Lyapunov function is provided to prove exponential stability of the aforementioned switched linear system. In addition, using the invariance principle, we will show the convergence of the estimated Coulomb friction coefficient to its real value. Numerical simulations are given to validate the effectiveness of the design and its robustness against friction time‐variations. Compared to existing results, the proposed scheme is much simpler, hence, much more advantageous computationally. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society

Analysis of interface temperature, forward slip and lubricant influence on friction and wear in cold rolling

To improve cold rolling processes, it is necessary to understand and to optimise contact at roll–strip interface. Thus a simulation test has been developed in our laboratory. The upsetting rolling test (URT) enables to study friction and iron fines pollution by the reproduction of the main industrial contact conditions such as plastic strain, normal and tangential stresses and forward slip. On the basis of the URT, a new experimental protocol has been developed to reproduce industrial lubrication regime. Moreover, a new heating system has been designed to simulate interface temperature which has a decisive effect on lubricant behaviour. These optimisations permit to analyse contact temperature, forward slip and lubricant influence on friction, iron fine pollution and surface aspects. A great influence of temperature and lubricant on friction and wear has been put forward. Actually an increase of the Coulomb friction coefficient associated with a decrease of the iron fines quantity have been shown with an increase of temperature. These results seem to indicate more adhesive wear when temperature increases.

Precision radial turning of AISI D2 steel

This paper compares finite element model (FEM) simulations with experimental and analytical findings concerning precision radial turning of AISI D2 steel. FEM machining simulation employs a Lagrangian finite element-based machining model applied to predict cutting and thrust forces, cutting temperature and plastic strain distribution. The results show that the difference between the experimental and simulated cutting force is near 20%, irrespectively of the friction coefficient used in the simulation work (approximately 19.8% for a friction of 0.25% and 18.4% for the Coulomb approach). Concerning the thrust force, differences of about 22.4% when using a friction coefficient of μ = 0.25 and about 56.9% when using the Coulomb friction coefficient (μ = 0.378) were found. The maximum cutting temperature obtained using the analytical model is 494.07°C and the difference between experimentation and simulation methods is 15.2% when using a friction coefficient of 0.25 and when using the Coulomb friction only 3.1%. Regarding the plastic strain, the differences between analytical calculations and FEM simulations (for the presented friction values) suggest that the finite element method is capable of predictions with reasonable precision.

Finite-element analysis of layered rolling contacts

A fundamental, two-dimensional finite-element analysis (FEA) of coated surfaces in rolling contact is presented with detailed listing of all modelling steps. A large number of basic results from a parametric study has been derived, focusing on the stress analysis and the effect of coatings on the life expectancy of coated surfaces, without actually getting into the ambiguities of fatigue life evaluation. Parameters included in the study are the metallic coating thickness (from zero to 50 μm) and elastic modulus (from 180 to 240 GPa), the Coulomb friction coefficient (0, 0.05, and 0.10) and the endurance limit of the coated substrate. A generalization involves the application of traction to simulate driving or driven wheels. The effect of that traction on the stress results is thoroughly examined. The set of results, summarized in a figure with nine diagrams, assists the quick selection of the optimum parameter values for maximizing coating performance and minimizing the risk of contact fatigue within the design limits used in the study. The model is realistic in that it does not use idealized load distributions in the rolling contact but actual geometrical solids in contact under normal operating conditions, letting the FEA software resolve the loads and stresses, which are subsequently validated.

Identifying dynamic model parameters of a BLDC motor

An off-line identification method founded on the least-squares approximation technique and a closed-loop disturbance observer is applied for identifying the parameters of a BLDC motor model. No special configuration of the motor is required besides the availability of experimental data for back-EMF, phase currents, rotor position, and rotor speed. This method is used to identify the back-EMF harmonics and mechanical parameters, where the mechanical parameters refer to cogging-torque, viscous friction coefficient, and Coulomb friction coefficient. The proposed identification method is theoretically investigated, and the method’s effectiveness is proved by experimental results performed on a low-power BLDC motor.

Viscoelastic and elastic–plastic behaviors of amorphous polymeric surfaces during scratch

In this study, we propose an analysis of the residual groove after contact between a spherical indenter and an amorphous polymeric surface (polymethylmethacrylate, PMMA) in scratch experiments. The geometrical shape of the residual groove was mathematically described using an exponential decay law. Finite element modeling (FEM) of scratch tests was compared to the corresponding experimental results. Assuming a two-segment simplified constitutive law with linear elastic behavior followed by linear strain hardening, the friction at the interface between the indenter and the material was modeled with a Coulomb's friction coefficient varying from 0 to 0.4, for computed ratios a/ R between 0.1 and 0.4. The FEM results for elastic–plastic contact indicate that the shape of the residual groove is directly related to the plastic strain field in the deformation beneath the indenter during scratching. It is shown that the dimensions of the plastically deformed volume and the plastic strain gradient both depend on the ratio a/ R and also on the friction coefficient.

Simulation of interface temperature and control of lubrication in the study of friction and wear in cold rolling

A prototype testing device called upsetting rolling test (URT) was developed a few years ago and was recently optimised in our laboratory to simulate mechanical and thermal contact conditions in cold rolling. Moreover a new experimental protocol has been designed to reproduce the industrial quasi-boundary lubrication regime. Numerous experiments have been then carried out to study the influence of contact temperature and forward slip on friction, iron fines residues and microscopic surface aspects. A great influence of temperature on friction and wear has been put forward. An increase of the Coulomb friction coefficient associated with a decrease of the iron fines quantities has been shown when temperature increases which seems to indicate more adhesive wear.

Experimental and finite-element analysis of scratches on amorphous polymeric surfaces

The scratch behaviour of two amorphous polymers is investigated to understand how the materials characteristics affect the scratch resistance. A thermosetting resin (CR39) and a thermoplastic polymer polymethylmethacrylate (PMMA) are studied using both an experimental set-up allowing in situ observations of the contact area during indentation or scratching with spherical tips, and a finite-element modelling (FEM). The rheological properties of CR39 and PMMA surfaces are modelled assuming a linear elastic behaviour and a plastic law with high strain hardening, described by G'sell Jonas equation. A description of the plastic strain field, beneath the indenter during scratch is proposed. The main parameter of the description is the level of the deformation imposed on the samples, related in first approximation to the ratio a/ R set between 0.1 and 0.4, a being the contact radius, and R the tip radius. The true friction μloc at the interface between the indenter and the material was modelled with a Coulomb's friction coefficient varying between 0 and 0.4, for each computed ratio a/ R. The two polymers display the same scratching behaviour for low levels of deformation, whereas at high strain, PMMA shows a more pronounced plastic behaviour, with high level of average plastic strain, especially for higher friction coefficient. This results obtained by FEM are in good correlation with experimental observations and show that the plastic strain gradient beneath the indenter depends clearly on the ratio a/ R, on the true friction coefficient and also the rheological parameters of tested material.

Identification of the Mechanical Subsystem of the NEES-UCSD Shake Table by a Least-Squares Approach

A least-squares method is used to determine the fundamental parameters of a simple mathematical model for the mechanical subsystem of the NEES-UCSD large high performance outdoor shaking table. The parameters identified include the effective horizontal mass, the effective horizontal stiffness, and the coefficient of the classical Coulomb friction and viscous damping elements representing the various dissipative forces in the system. The values obtained for these parameters are validated by comparisons with previous results based on an alternative identification method applicable only to periodic tests and by comparisons with experimental data obtained during earthquake simulation tests and harmonic steady-state tests. The proposed identification approach works well for periodic sinusoidal and triangular tests, earthquake simulation tests, and white noise tests with table root mean square above 10% of gravity.

Improvement of the numerical modeling in orthogonal dry cutting of an AISI 316L stainless steel by the introduction of a new friction model

A better understanding of friction modeling is required to lead to more realistic finite element models (FEMs) of machining process. This work proposes to evaluate the performance of a new friction model depending on the local sliding velocity, compared to a standard approach considering a constant Coulomb friction coefficient. A finite element model, based on the Arbitrary Lagrangian–Eulerian (ALE) approach, was developed for orthogonal machining. This model has been applied to the investigation of an AISI 316L stainless steel in dry cutting. It has been shown that the material removal is very sensitive to the friction model. The flow of the workmaterial along the interfaces tool–workpiece–chip is very much disturbed by a variation of the friction model. The new friction model, previously published and introduced in this model, has shown its higher efficiency to reach reasonable data about the material removal phenomena.

A new approach for the friction identification during machining through the use of finite element modeling

Finite Element Modeling (FEM) of chip formation has proved great sensitivity to tool/chip friction coefficient. This parameter cannot be adequately identified through conventional tests, because thermal and mechanical loadings during these tests are far from those encountered during machining. In this study, the inadequacy of using constant Coulomb's friction coefficient in FEM is showed. Although a good agreement is found for cutting force and chip thickness variables, significant differences can be found for feed force and tool–chip contact length. Differences of more than 50% are observed in some cases for those variables when FEM results are compared with experimental ones. A new approach to identify a friction model after experimental tests will be detailed. This new approach involves application of a variable friction coefficient at the tool–chip interface, which allows obtaining a better agreement between numerical results (differences close to 10%) regarding the feed force.

A spinning-tube device for dynamic friction coefficient measurement of granular fertiliser particles

This paper describes the development of a device capable of measuring the dynamic friction coefficient of particles accelerated in a tube spinning in a horizontal plane. The dynamic friction coefficient is not the classical Coulomb friction coefficient, but a lumped parameter influenced by the Coulomb friction coefficient between particle and tube, aerodynamic effects, bouncing effects, as well as particle size, shape and texture. The principle consists of measuring the time interval associated with particles travelling through a known distance along a tube section. This time interval served as an input for a model that infers the dynamic friction coefficient. The results for plastic spheres showed that (1) the mean dynamic friction coefficient was higher than expected (0.25), and (2) there was significant variability in the data (standard deviation (SD) 0.03) even though the particles were inserted using a precise and reproducible method. The variability in dynamic friction coefficient was inversely proportional to the rotational velocity of the tube. This led to the conjecture that owing to the higher Coriolis forces, the particles more closely follow a straight trajectory along the inner sidewall of the tube. Owing to the lower variability, the dynamic friction coefficient measured at the highest rotational velocity (800 min −1 ) was assumed most reliable. The mean dynamic friction coefficient of irregularly shaped potassium chloride fertiliser was measured as 0.44, SD 0.05, and for the quasi-spherical ammonium nitrate fertiliser a mean value of 0.31, with an SD of 0.03 was obtained.

Identification for Sucker-Rod Pumping System’s Damping Coefficients Based on Chain Code Method of Pattern Recognition

In this paper, a method for identifying the damping coefficients of a directional well sucker-rod pumping system is put forward by means of the chain code method of pattern recognition. The 24-directional chain code is provided to encode the dynamometer card curve. The parametric equation of the dynamometer card curve is transformed into Fourier series whose coefficients can be computed according to the curve’s chain codes. By means of these coefficients, shape characteristics of the curve are extracted. The Euclidean distance is introduced as the measurement of similar degree between the shape characteristics of measured dynamometer card and that of simulated dynamometer card. Changing the value of viscous damping coefficient and Coulomb friction coefficient in the simulation program, different simulated dynamometer cards are obtained. Substituting their shape characteristics to the Euclidean distance, respectively, a series of distances are acquired. When the distance is less than the given error, the corresponding values of the damping coefficients in the simulation program are regarded as real damping coefficients of the sucker-rod pumping system of directional well. In the end, an example is provided to show the correctness and effectiveness of the presented method.

Measurements of dense snow avalanche basal shear to normal stress ratios (S/N)

We investigate frictional processes at the basal shear layer of snow flows. A chute is instrumented with basal force plates, velocity and flow height sensors to perform experiments with dry and wet snow. We find that a Mohr‐Coulomb relation of the form S = c + bN accurately describes the relation between normal (N) and shear stress (S). The Coulomb friction coefficient b ranges between 0.22 and 0.55. Several wet snow avalanches exhibited significant cohesion c ≈ 500 Pa. These quantitative measurements of stress, velocity and flow height allow us to probe the relation between basal work, internal dissipation and gravitational potential energy. We find that basal shearing is the primary frictional mechanism retarding snow flows. This mechanism shows no velocity dependence, contrary to many postulated constitutive relations for basal shearing in snow avalanches.

An experimental assessment of friction effects in the split Hopkinson pressure bar using the ring compression test

The potential error due to friction in compression split Hopkinson pressure bar (SHPB) tests is assessed and conditions for minimising this error are investigated. Theoretical friction factors are inferred from ring compression tests. Experimental results are reported for mild steel, copper and aluminium ring specimens tested quasi-statically (∼10 −2 s −1), using a servo-hydraulic test machine, and at high strain rates (∼10 3 s −1) on a SHPB. Specimens were tested dry, or lubricated using a molybdenum disulphide grease. The influence of surface finish and strain rate on the friction effect is discussed. The inferred friction factors are in the range m=0.08–0.14 (equivalent to Coulomb friction coefficients between μ=0.05 and 0.08). These results imply that the friction error in routine compression SHPB tests of metals lies between 2% and 3%.

Ameliorative characteristic recognition method based on modified chain code and its application in damping coefficients identification for rod pumping system

Aimed at the shortcomings of the eight-directional Freeman chain code method, a new 24-directional chain code is put forward to encode the closed boundary curve of an image. The parametric equation of the closed boundary curve is transformed into Fourier series whose coefficients can be computed according to curve's chain codes. By means of these coefficients, shape characteristics of the boundary curve are extracted. The Euclidean distance based on shape characteristics is introduced as the measurement of similar degree between two different closed boundary curves. Changing the value of viscous damping coefficient and Coulomb friction coefficient in the simulation program, different simulated dynamometer cards are obtained. Substituting their shape characteristics to the Euclidean distance, respectively, a series of distances are acquired. When the distance is less than the given error, the corresponding values of the damping coefficients in the simulation program are regarded as real damping coefficients of the sucker-rod pumping system of directional well. In the end, an example is given to show the correctness and effectiveness of the presented method.

Consequence of contact local kinematics of sliding bodies on the surface temperatures generated

When studying contact with friction between two bodies, it is not possible to obtain data on real contact conditions on the basis of steady-state situations. Indeed, contacts with friction usually lead to dynamic instabilities generated at the contact interface. It is therefore necessary to take into account contact dynamics in order to better understand the phenomena involved during sliding with friction. The explicit dynamic finite element code PlastD in 2D is used to simulate the contact between two bodies. A constant Coulomb friction coefficient is imposed at the interface. The simulations carried out permitted identifying local contact conditions (kinematics, tribological state, stresses, etc.). They revealed that different instability regimes can be generated (stick–slip, slip–separation, stick–slip–separation, etc.). Local contact stresses and the sliding velocity oscillate through time when instabilities are generated and their maximum values can be much higher than those expected for steady-state conditions. The aim of this paper is to analyse the frictional instabilities and their consequences on the heat generated in the contact. First, the influence of the different instability regimes is studied on a simple contact. Then, an industrial mechanism is studied (wheel–rail contact) to investigate the influence of local contact conditions on the temperature of the rail surface.

Rebound characteristics for 50-μm particles impacting a powdery deposit

The formation of powdery deposits on the tubes in a waste heat boiler reduces the heat transfer coefficient by about 25%. Because of these fouling layers, the efficiency with which energy can be recovered from flue gases is reduced. The growth of the layers by the deposition of fly ash particles onto the tubes is strongly dependent on the interaction of the incident particle with the bed of particles. In this study the interaction is modelled as the outcome of a 2-body collision between an incident fly-ash particle and a second particle that represents a developing fouling layer. The mass of this second particle is dependent on the characteristics of the layer. The present paper focuses on the applicability of the 2-body collision model to predict the rebound characteristics of 50-μm particles impacting a powdery deposit. This is studied by impaction experiments of glass particles on different types of glass layers (powdery vs. glued), under various impaction angles (ranging from 0° to 30°) and with different incident velocities (ranging from 0.5 to 1 m/s). The experiments are carried out in a vacuumed column and, using a digital camera system, individual impacts are recorded. With this set-up the normal coefficient of restitution, the Coulomb friction coefficient and the proportionality factor are determined for particles in the 50-μm range. Besides, a 2-body collision model is developed to simulate the rebound characteristics. From a comparison between the experimental results and the model, it is shown that the 2-body approach to model the rebound characteristics of particles impacting a powdery layer is valid and that the proportionality factor is dependent on the binding between the particles in the layer and the relative particle size of the particles in the layer compared to the size of the incident particles.