Coulomb Friction Coefficient Research Articles

The dynamics of a disk on a rough inclined plane when there is an uneven normal stress distribution

The motion of a uniform circular disk of non-zero height on a fixed rough inclined plane is considered on the assumption that the disk moves without losing contact, resting on the plane with its own base. The friction forces and moment are calculated using a model of the contact stress distribution, including three independent parameters. During the translational motion of the disk, the normal pressure distribution corresponds to the normal stress distribution on the base of a punch with a flat base and, for zero height of the disk, agrees with Galin's law. A qualitative analysis of the dynamics of the disk in the case when the slope of the plane is less than the Coulomb friction coefficient is given.

Influence of Load Application Methodology in the Performance of Ring Compression Tests

The main objective of this work is to determine the differences found in friction calibration maps when applying different methodologies of load-lubricant application during the implementation of ring compression tests. To accomplish this aim, friction calibration maps have been obtained by conducting ring compression tests to flat rings of Al-7075 aluminum alloy under lubrication. The compression tests were conducted using two different methodologies, incremental and continuous. Simultaneously, in order to determine the particular values of the Coulomb friction coefficient, the same problem was simulated using the finite element code ABAQUS. Calibration curves from experiments and simulation are drawn to compare the friction coefficients obtained for each load methodology. This study allows to quantify the differences found when using both types of load methodology in the determination of friction coefficients by the ring compression test, giving some guidelines about the use of these maps depending on the actual process conditions.

An Estimation Method of Ski Friction Coefficients in Ski Running on Actual Snow Fields by Sensor System

This paper proposes an estimation method of ski friction coefficients in ski running by using sensor system. It is important for development of skies, ski waxes to obtain ski friction coefficient in ski running on actual snow filed. The ski friction coefficients are assumed as the sum of the Coulomb friction coefficient and the viscous friction coefficient of a ski. The ski friction coefficients are estimated using the Kalman filter by the information of reaction force from snow surface and gliding velocity in ski's coordinate. The reaction force from snow surface was measured by 6-axis force sensor installed to between ski and binding, and the direction and vertical components of reaction force from snow surface are used for estimation of ski friction coefficient. The gliding velocity was estimated by the 3D posture and the acceleration of ski boot, and the 3D position. The 3D posture was estimated by using the sensor fusion from the angular velocity of gyro sensor and the acceleration of accelerometer attaching the ski boot. The 3D position was obtained by GPS receiver attaching to top of head. We used the estimation method of ski friction coefficients to measurement information obtained by the skier conducting carving turns on an actual snow field, and we obtained the ski friction coefficients varying from moment to moment on an actual snow field. The estimation results of ski friction coefficients fitted for the previous reference. Therefore, the proposed method can use to evaluation of skies, ski waxes.

Friction effect of surface treated tools used for warm forming of Mg alloy sheets

Sheet forming of Mg alloy is usually performed at moderately high temperature since the formability of these alloys is very low at room temperature. However, it is difficult to use lubricant especially in a multi-stage sheet forming at moderately high temperatures. Therefore, tool coating is a better than lubricant application for Mg alloy sheet warm forming. In this study, some tool coating methods were investigated to reduce friction and prevent adhesion between the tool and sheet. Tools with three different non-metallic coating layers, namely, TiBCN, DLC, and TAC, were compared with a no-coated tool for friction effects by a pin-on-disc friction test. The friction coefficients for the different coating layers were measured at room temperature, 170 and 250°C. AISI H-13 and AZ31 were used as pin and disc materials, respectively. Two of the tool coatings, namely, TiBCN and DLC, were not good enough to prevent sticking between the tool and AZ31 sheet. The coulomb friction coefficient in the case of these coatings was 0.4 in ambient air. On the other hand, the friction coefficient of the TAC coating layer was lower(< 0.2~0.3) than the coefficients of these two coatings before the adhesion of the Mg alloy with the tool.

Inertia and Friction Estimation of a Velocity-Controlled Servo Using Position Measurements

This paper proposes a method that estimates the parameters of a velocity-controlled servo. A proportional-integral controller, which uses only position measurements, closes the loop. The proposed approach uses the steady-state response produced by steps and sine-wave signals; they do not produce high levels of vibration on the servo compared with random signals commonly used with the least squares algorithm; moreover, it relies on simple numerical calculations. The method, which is called in the sequel as the steady-state response method (SSRM), consists of two steps. The first step uses three constant reference inputs in order to identify a constant disturbance and the viscous and Coulomb friction coefficients of the servo. In the second step, the SSRM estimates the servo inertia using a sine wave plus a constant signal as a velocity reference input and employs the estimate of the viscous friction coefficient obtained in the first step. Experiments on a testbed employing a brushless servomotor allow comparing the results obtained using the SSRM and those produced by a standard recursive least squares method (RLSM).

A study of the frictional characteristics of metal and ceramic counterfaces against electro-deposited coatings for use on automotive seat rails

An investigation was conducted on the friction coefficient changes when ceramic balls oscillate against a series of epoxy-based cathodic electro-deposited coatings that could be used for automotive components. Reciprocating sliding tests were conducted using ball-on-plate apparatus; balls were made of silicon nitride, zirconia, and AISI 52100 (also known as GB GCr15, DIN 100Cr6, and JIS SUJ2) steel. Plates used for coating substrates were made of cold-reduced high strength steels. The Coulomb friction coefficient was measured under room temperature and ambient humidity. The endurance lives of cathodic electro-deposited coatings against various ball materials are directly compared using a plot of friction coefficient evolution. Using the basis of friction coefficient evolution, electro-deposited coatings maintained higher durability against zirconia than against Si3N4 and AISI 52100 balls. In addition, the frictional behavior is analyzed using a form of Kachanov-type damage law. It is concluded that the growth rate of the friction coefficient can be represented by the damage parameters in the law.

Finite–element analysis as a tool for the investigation of the mechanics of wire drawing

Wistreich's classical experiments where friction in Cu wire–drawing was determined from a combined measurement of were reproduced in a FE–analysis. There was good correspondence between Wistreich's experimental data and the m–computed results when friction was modelled as Coulomb friction. The dependence of the contact stresses transferred from the wire to the die, and the coefficient of friction, on different drawing parameters was analysed. It seems as if the friction between the die and the wire depends on the geometry of the wire inside the drawing cone, through its A–parameter, i.e. the height–to–length ratio of the wire inside this cone. The mean die pressure was found to increase linearly with increasing A–parameter. The mean shear stress transferred from the wire to the die was also found to increase linearly with this parameter. As a consequence of this the Coulomb coefficient of friction would increase in a parabolic manner with the A–parameter.

Ring Compression Test for High‐Temperature Glass Using the Generalized Navier Law

Glass‐forming processes such as high viscosity extrusion and Precision Glass Molding take place at temperatures where slip between the glass and mold/die surfaces is known to occur. Characterization of the frictional forces that accompany interface slip are essential in computational simulations of these processes for prediction of pressing time or force, distortion of the part and possible wear of expensive mold surfaces. In this study, the generalized Navier law, where the interface shear stress, τ, is related to the relative sliding speed of the glass on the mold surface, vs, by τ = kvse, is used in simulations of the ring compression test to produce friction calibration curves. Contrary to the nonlinear form of the Navier law, the linear form, just like the Coulomb friction model, leads to calibration curves that are loading rate and material behavior independent. This independence is achieved by normalizing the Navier friction coefficient with the viscosity. Friction calibration curves for the normalized coefficient are characterized for the full range of interface conditions from no‐slip to no friction. The results showed an approximate one‐to‐one correspondence between the normalized Navier coefficient and the Coulomb friction coefficient for the full range of axial deformation in the ring compression test.

Direct Evaluation of Coulomb Friction Coefficient from Sheet Strip Stretch Test on a Cylinder Surface

Knowing the flow curve of a sheet metal, strain distribution on a sheet strip may be used to roughly but quickly evaluate the Coulomb friction coefficient. Strain distribution on the strip being stretched on a cylindrical surface of interest may be measured by an optical strain measurement system. This could be used to estimate the stresses on the specimen. The capstan equation is then used to roughly evaluate the coefficient of friction acting between the sheet strip and the cylindrical surface. Validation of the approach is done using the simulation of the process. The corresponding experiments can be performed easily on a sheet metal testing device equipped with an optical strain measurement system, which is commonly used for the experimental evaluation of FLCs.

A friction model for loading and reloading effects in deep drawing processes

Deep drawing is one of the most widely-used forming processes to manufacture automotive body parts from sheet metal. In order to simulate deep drawing processes, a finite element (FE) method was used to predict formability. The accuracy of the FE simulation depends on the material models, numerical techniques, and contact algorithms. Despite the fact that the contact conditions between the tool and sheet material influences the coefficient of friction in forming processes, the coefficient of friction is often treated as a constant Coulomb friction coefficient in FE simulations. However, a friction model based on local contact conditions and surface topography is required to improve forming predictability. There is growing interest in developing contact models to predict the nature of friction conditions for use in FE calculations. In deep drawing processes, the sliding contact predominantly occurs in the blank holder region between the tool and sheet material. The contact pressure in the blank holder is non-uniform due to bending and material compression which vary depending on tool geometry. The sheet metal surface is subjected to repeated contact during sliding, which in turn affects the local friction conditions. The objective of this paper is to develop a sliding friction model for mixed modes of surface deformation. The deterministic approach used in the current model includes the roughness of both the sheet material and the tool. The sheet material is subject to an asperity flattening process. Further, the tool surface indents into the sheet material under normal loading. The geometry of the asperities is characterized by an elliptical paraboloid shape to better calculate the load-dependence of friction. The model has been compared with data from experiments using a rotational friction tester under multiple loading conditions.

Influence of Contact Friction on the Experimental Determination of the Balanced Biaxial Strain-Ratio Using the Disc Compression Test

In the present work the disc compression test used to determine the balanced biaxial strain-ratio $r_b$ is analyzed in terms of the influence of contact friction using non-linear finite element analysis (FEA). The FEA results reveal an unexpectedly strong sensitivity of the $r_b$-value on contact friction, which is discussed in detail. The most important outcome of the present work is that the FEA can reproduce the $r_b$-value imposed by the utilized yield function very well, but only when the prescribed Coulomb friction coefficient has a very small value; for increasing friction coefficients a gradual deviation from the imposed $r_b$-value can be observed. This finding implies that in experiments contact friction must be eliminated to a larger extent than commonly expected, otherwise the determined $r_b$-value using disc compression testing will considerably deviate from the actual one, particularly when $r_b$ is far from one.

Identification of Friction Law to Model Orthogonal Cutting

A first approach of tool-chip interface behaviour for high-speed machining modelling has been carried out by Al Brocail and 2010 and an empirical friction law has been first determined. This law has been established for high temperatures (initial sample temperature equal to 750 K) and low sliding velocities (less than 0.5 m.s-1) and an extrapolation has been considered for higher velocities. This article intends to determine an empirical friction law for low temperatures (ambient) combined with high sliding velocities (up to 1.5m.s-1) by means of a tribometer developed by Meresse and Al. A new experimental device is designed to carry out several tests and simulate the friction behaviour at the tool-chip interface. The experimental results are compared with a numerical model and an iterative method is used to minimize the error between experimental and numerical simulations on normal and tangential forces. This method allows to recover a Coulomb friction coefficient which is associated to local pressure, temperature and sliding velocity. The completion of several tests provides an empirical friction law for high sliding velocities and low temperatures.

Improved passivity criterion in haptic rendering: influence of Coulomb and viscous friction

In this paper, a new criterion for passivity of haptic devices is obtained. This criterion creates a relationship between Coulomb friction coefficient, viscous friction coefficient, sampling rate, and the maximum simulated stiffness. The process of derivation of the passivity criterion is described in detail. This criterion is improved compared with other existing criteria and predicts passivity in haptic rendering more accurately. In particular, for speeds of less than 5 cm/s, the new passivity criterion should replace the previous criteria to avoid unwanted vibrations of stiff virtual walls. Analytical and numerical investigations are presented to validate the new criterion. A specific trajectory is designed and the movement of the haptic robot is investigated on this trajectory to validate and compare this passivity criterion with the previous criteria.

Effect of Friction on Tandem Cold Rolling Mills Chattering

Chatter phenomenon in the rolling mills is the undesired mechanical vibrations which reduces the productivity and quality of the products. Many studies have led to the point that friction is one of the most effective factors incurring chatter. In this paper, a chatter simulation model for the tandem cold rolling mills based on the well-known Coulomb and the Tresca friction models is proposed. By considering the effects of the material strain-hardening and the elastic deformation of the work roll, the model relaxes certain assumptions. The simulation results are verified by comparing to experimental data obtained from Mobarakeh Steel Company. In addition, a numerical method is developed to introduce a relationship between the Tresca friction factor and the Coulomb friction coefficient. A parametric study on the effects of friction coefficients of the two stand rolling mill on the chatter critical speed is conducted. The results show that an optimal setting of friction coefficients improves the process efficiency. Under the operating conditions stated in this paper, the friction coefficient of the second stand should be increased as much as possible in order to get closer to its optimum point. The optimum friction coefficient of the first stand depends on the friction coefficient of the second stand.

An Algebraic Recursive Method for Parameter Identification of a Servo Model

This study proposes a two-step identification method for estimating the four parameters of a nonlinear model of a position-controlled servomechanism. In the first step, the proposed approach, called the algebraic recursive identification method (ARIM), uses a parametrization derived from the operational calculus currently employed in algebraic identification methods (AIM) recently proposed in the literature. The procedure for obtaining this parametrization eliminates the effect of constant disturbances affecting the servomechanism and filters out the high-frequency measurement noise. A recursive least squares algorithm uses the parametrization for estimating the linear part of the servomechanism model, and allows eliminating the singularity problems found in the AIM. The second step uses the parameters obtained in the first step for computing the Coulomb friction coefficient and the constant disturbance acting on the servomechanism. Experimental results on a laboratory prototype allow comparing the results obtained using the AIM and the ARIM.

Evaluation of the Coulomb Friction Coefficient by the Erichsen Test

In this study, the Erichsen test is used to identify the friction coefficient of the Coulomb friction model coupling experimental tests results with numerical ones. The evaluation of the Coulomb friction coefficient is based on the distance measured between the thinnest area of the specimen and the lateral surface of the blankholder. Two types of aluminium alloys, AA 2017 Al-Cu alloy and AA 5083 Al-Mg alloy, with thickness of 1.0 mm are selected as the experimental materials for Erichsen test. Specimens are tested in unlubricated condition as well as using two different lubricants, namely Grease LB4 and Mexmoly.

The dynamics of a homogeneous disc on an inclined plane with friction

The problem of the motion of a homogeneous circular cylinder along a fixed rough inclined plane is discussed. It is assumed that the cylinder is supported on the plane by its base and executes continuous motion. The frictional forces and moment are calculated within the limits of the dynamically consistent model proposed by Ivanov, for which the pressure distribution over the contact area is non-uniform. A qualitative analysis of the dynamics of the cylinder is given in the case when the slope of the plane is less then the Coulomb coefficient of friction.

Effects of shot peening on the nanoindentation response of Cu47.5Zr47.5Al5 metallic glass

Abstract The effects of shot peening (SP) on the nanoindentation response of Cu47.5Zr47.5Al5 metallic glass, both in the as-cast state and after thermally induced structural relaxation (i.e., after annealing close to the glass transition), are investigated. As expected, annealing causes an increase of hardness attributable to annihilation of free volume. Conversely, nanoindentation tests, carried out on a transverse section at different distances from the SP surface, reveal that SP induces mechanical softening. Both the hardness and the reduced Young’s modulus progressively decrease as the peened surface is approached. Finite-element simulations of the nanoindentation curves indicate that the cohesive stress and the Mohr–Coulomb friction coefficient also decrease after SP, an observation which is in line with the induced mechanical softening. Differential scanning calorimetry measurements reveal an increase of the relaxation enthalpy, particularly when SP is performed on the previously annealed metallic glass, consistent with deformation-induced creation of free volume.

Dynamic Parameters Estimation Based on Set Inversion and Interval Analysis Algorithm

In the paper, an approach, based on bounded-error estimation via interval analysis, is presented to identify viscous damping coefficient and Coulomb friction coefficient of such-rod pumping system of directional well. The approach assumes the error of colleted output data of suck-rod pumping system is bounded. Hence, the problem of parameter estimation can be viewed as that of set inversion, which will be effectively solved via interval analysis. The main advantage of the proposed method in comparison with the traditional estimation methods is that, as it is global, it bypasses the problem of initialization. Moreover, the method avoids amount error due to transformation of measurement output data. An identification example is given to show the correctness and efficiency of the proposed method.

Fretting corrosion damage of total hip prosthesis: Friction coefficient and damage rate constant approach

This paper analyzes friction coefficient evolution between materials related to total hip prosthesis. Fretting corrosion tests were conducted with stainless steel and poly(methyl methacrylate) interacting surfaces. In the course of fretting corrosion tests, the Coulomb friction coefficient is determined as a function of the number of cycles. It was found that the friction coefficient growth rate can be expressed as a power-law function. The influences of ionic strength, applied potential, pH, and albumin content on fretting corrosion were then investigated on the basis of the evolution of the friction coefficient. Finally, we identify the damage rate constant as being relevant for linking the mechanical and chemical parameters in the evolution of damage.