Sliding Friction Coefficient Research Articles

Calibration and Experimental Verification of Finite Element Parameters for Alfalfa Conditioning Model

Conditioning is an important step in harvesting alfalfa hay, as squeezing and bending alfalfa stems can break down the stem fibers and accelerate the drying rate of alfalfa. The quality of alfalfa hay is directly affected by the conditioning effect. The finite element method (FEM) can quantitatively analyze the interaction relationship between alfalfa and conditioning rollers, which is of great significance for improving conditioning effects and optimizing conditioning systems. The accuracy of material engineering parameters directly affects the simulation results. Due to the small diameter and thin stem wall of alfalfa, some of its material parameters are difficult to measure or have low measurement accuracy. Based on this background, this study proposed a method for calibrating the finite element parameters of thin-walled plant stems. By conducting radial tensile, shear, bending, and radial compression tests on alfalfa stems and combining with the constitutive relationship of the material, the range of engineering parameters for the stems was preliminarily obtained. By conducting a Plackett–Burman experiment, the parameters that affect the maximum shearing force of stems were determined, including Poisson’s ratio in the isotropic plane, radial elastic modulus, and the sliding friction coefficient between the alfalfa stem and steel plate. By conducting the steepest ascent experiment and Box–Behnken experiment, the optimal values of Poisson’s ratio, radial elastic modulus, and sliding friction coefficient were obtained to be 0.42, 28.66 MPa, and 0.60, respectively. Finally, the double-shear experiment, radial compression experiment, and conditioning experiment were used to evaluate the accuracy of the parameters. The results showed that the average relative error between the maximum shear and the measured value was 0.88%, and the average relative error between the maximum radial contact force and the measured value was 2.13%. In the conditioning experiment, the load curve showed the same trend as the measured curve, and the simulation results could demonstrate the stress process and failure mode of alfalfa stems. The modeling and calibration method can effectively predict the stress and failure of alfalfa during conditioning.

Study of the Sliding Friction Coefficient of Different-Size Elements in Discrete Element Method Based on an Experimental Method

The materials involved in geotechnical engineering are objects of concern in granular mechanics. In order to study the influence of the sliding friction coefficient corresponding to different-sized elements in the discrete element method (DEM) on the simulation results, we establish a two-dimensional DEM model based on the experimental method to analyze a slope example. The correctness of the DEM model is verified by comparing the sliding surface of a finite element method (FEM) model and the DEM slope model. A sliding friction coefficient algorithm based on the experimental method is embedded into the DEM slope model and compared with the original model. The comparison results show that embedding the DEM model into the sliding friction coefficient algorithm leads to an increase in displacement. The reason for this is that the contact information between elements of different sizes has changed, but the displacement trend is the same. Different sliding friction coefficients should be set based on different-sized elements in the DEM, as they can improve simulation accuracy.

Calibration of Discrete Element Method Parameters for a High-Fidelity Lunar Regolith Simulant Considering the Effects of Realistic Particle Shape

The Discrete Element Method (DEM) is an important tool for investigating the geotechnical properties of lunar regolith. The accuracy of DEM simulations largely depends on precise particle modeling and the appropriate selection of mesoscopic parameters. To enhance the reliability and accuracy of the DEM in lunar regolith studies, this paper utilized the high-fidelity IRSM-1 lunar regolith simulant to construct a DEM model with realistic particle shapes and conducted an angle of repose (AoR) simulation test. The optimal DEM parameters were calibrated using a combination of the Plackett–Burman test, steepest ascent test, and Box–Behnken design. The results indicate that the sliding friction coefficient, rolling friction coefficient, and surface energy significantly influence the simulation AoR. By optimizing against the measured AoR using a second-order regression model, the optimal parameter values were determined to be 0.633, 0.401, and 0.2, respectively. Under these optimal parameters, the error between the simulation and experimental AoR was 2.1%. Finally, the calibrated mesoscopic parameters were validated through a lifting cylinder test, showing an error of 6.3% between the simulation and experimental results. The high similarity in the shape of the AoR further confirms the accuracy and reliability of the parameter calibration method. This study provides a valuable reference for future DEM-based research on the mechanical and engineering properties of lunar regolith.

Discrete element parameter calibration during cottonseed crushing process

In order to address the current deficit in research on discrete elements within the context of the cotton seed pressing process, a combination of physical tests and simulation experiments were conducted on Xinluzao 84 cottonseed. The Plackett-Burman experimental design was employed to identify the parameters that had a significant impact on the accumulation angle. Subsequently, the Box-Behnken design was employed to establish a second-order regression model for the accumulation angle and the significant parameters. This resulted in the optimal parameter combination for the maximum friction coefficient, minimum sliding friction coefficient and critical shear stress being 0.207, 0.388, and 5×10⁶ Pa, respectively. In order to calibrate the cottonseed bonding parameters, a Box-Behnken test was designed based on the results of the cottonseed particle crushing test. The optimal parameter combinations of normal stiffness, tangential stiffness, and bond radius were obtained as 1.25×10⁹ N/m², 7.57×10⁸ N/m², and 0.727 mm, respectively. The obtained parameters were verified by the simulation of stacking angle and the crushing test simulation. The relative error was 0.84% and 0.46%, respectively. This serves to validate the cottonseed bonding model and simulation parameters, thereby providing a foundation for optimising the core structural parameters of the cottonseed shelling machine.

ANALYTICAL STUDY OF DURABILITY AND CONTACT CHARACTERISTICS OF METAL-POLYMER COMPOSITE SLIDING BEARINGS FOR MEANS OF TRANSPORT

The field of application of metal-polymer bearings is vast: transport of various types, processing industry equipment, medical equipment, various types of maintenance equipment, etc. With the use of the developed generalized author's analytical method of metal-polymer plain bearings on the basis of which it is laid the author's research methodology of materials wear kinetics at sliding friction (dry, lubricated), calculation of their durability is carried out. Contact parameters are also determined. Metal-polymer bearings with a bushing made of PA6, PA66 polyamide and PA6 based composites filled with glass (PA6 + 30GF) and carbon (PA6 + 30CF) dispersed fibres, molybdenum disulphide (PA6 + MoS2) and oil filled cast polyamide (PA6 + oil) are considered. These polyamides (unfilled and filled), as self-lubricating materials, are widely used in this type of dry friction sliding bearings. The predictive estimation of durability of investigated bearings depending on loading, polymer materials Young's modulus, their wear resistance and sliding friction coefficient is executed. Regularities of change from the specified factors of bearing's durability and the maximum contact pressures are established. Experimental indicators, diagrams, and wear resistance characteristics of the specified polymeric materials are presented. The results of researches of sliding friction coefficient and modulus of elasticity for carbon steel (0.45%C) – polyamides tribocouples are presented.

Parameters of a robotic loading device for selection seeder

In cassette-type selection seeders, a cassette loading device sequentially conveys cassettes filled with seed material to the planting mechanism of the seeder. (Research purpose) The research aims to calculate the geometric parameters and identify the cassette material in the development of a robotic cassette loading device for the selection seeder. (Materials and methods) The geometric parameters of the cassettes are determined based on the existing cassette loading device of the model SSS-2-6 selection seeder and the selection sowing specifi cations. Fourier transform infrared spectroscopy with the wavenumber range of 400-4000 cm–1 is used to identify a polymer material suitable for manufacturing cassettes and a guide plate for a selection seeder. (Results and discussion) The geometric parameters of cassettes, cells, cassette blocks, and guide plates are determined by using various design solutions employed in previous cassettes for the loading device. The objectives of the study also encompass the selection of polymer material for the manufacture of the cassette using 3D modeling techniques. To accomplish this, it was necessary to identify the specific polymer material of the plastic cassette and guide plate samples currently used in the loading device of the SSSe-6 selection seeder. The qualitative composition of these samples is determined by infrared spectroscopy using a Simex FT-801 Infrared Fourier spectrometer. (Conclusions) The geometric parameters essential for modeling, manufacturing and further development of a robotic cassette loading device are calculated. It has been established that the device is made of a copolymer consisting of acrylonitrile, polybutadiene and styrene (known as ABS plastic), which has a sliding friction coefficient approximately 0.47-0.54. In order to decrease the coefficient of cassette friction when driving along the guide plates, additives like ceramide can be introduced into ABS during their production enhancing its sliding properties.

Validation on fly ash DEM microparameters based on coarse-grained method

The computational efficiency of the discrete element simulation process is often a limiting factor. However, the use of the coarse-grained method, which employs dimensional analysis to amplify particles, significantly improves computational efficiency. This research utilizes the coarse-grained method to amplify particles and examines the impact of linear models on the mechanical of fly ash. By examining parameters such as magnification, stiffness, sliding friction coefficient, and rolling friction coefficient, we establish the relationship between fly ash cohesion, internal friction angle, and microscopic parameters in discrete element method (DEM) simulation. The simulation results demonstrate that the shear strength of fly ash increases as magnification, stiffness, and sliding friction coefficient increase. The rolling friction coefficient, on the other hand, has minimal effect on shear strength. The elastic potential energy of the system is unaffected by magnification, with stiffness inversely proportional to adaptable potential power. However, sliding and rolling friction coefficients positively impact adaptable potential power. Furthermore, this study proposes a practical simplification method for amplification of materials with small particle sizes. The comparison between numerical simulation and experimental data yields consistent results. As a result, this study provides a foundation for the application of large-scale fly ash transportation, storage, and other engineering purposes.

A methodology for the selection of low friction/anti-seize coating in applying bolted joints of ITER blanket modules

The application of bolted joints with the Spiralock®/Selflock® technology for remote handling system in fusion machines leads to develop a methodology for selection a low friction/anti-seize coating in applying sliding surfaces of high-loaded threaded fasteners. This study discusses the analytical engineering method for calculation the maximum/minimum allowable friction coefficients in the thread and on the bearing surface during the tightening/untightening procedure. Calculations were made to determine the maximum/minimum allowable coefficient of friction in threaded pairs used for the ITER Blanket Module Connections and enhanced flux First Wall Panel fasteners (bolts with a regular metric thread/nuts with a self-locking thread, Spiralock®/Selflock® technology) of the ITER fusion experimental reactor under maximum torque conditions of the robot manipulator (remote handling system) and tensile load (preload) generated in the bolt during the tightening/untightening procedure. Design features of the Spiralock® technology were derived for calculation the working ranges of thread friction coefficient in the threaded pairs of the Blanket Module Connection and enhanced Heat Flux First Wall Panels fasteners at different coefficient of thread proportionality values (ζ=0.45–1.00). The lowest thread friction coefficients were obtained by the coefficient of thread proportionality ζ=1.00: 0.022≤μth≤0.171 for the M24 × 3 SB Electrical strap central bolts, 0.013≤μth≤0.047 for the М52 × 4 Outboard Flexible Cartridge central bolts, 0.010≤μth≤0.055 for the M64 × 4 Inboard Flexible Cartridge central bolts. The new method of determining the total tightening torque of the M24 × 3, M52 × 4, M64 × 4 bolted joints fastened to the Spiralock® female thread under conditions of elastoplastic, plastic deformation was applied to assess the suitability the solid lubricating coating MoS2 (VNIINP-212) under preload force Fa=10–1200 kN. The performed design verification indicated the significant differences in the calculated tightening torque obtained according to the standard and proposed method for the Spiralock® female thread by the plastic deformation of the tip of bolt thread and change of sliding friction coefficient depending on the contact pressure.

Insight into the tribological performances of coconut shells as a potential natural water lubrication material

To better understand the tribological performance of coconut shell and to demonstrate its potential as a wear-resistant material for use in a water-lubricated environment, the microstructure of coconut shell was hereby characterized, and its hardness and water absorption properties were correspondingly measured. The tribological characteristics of coconut shells rubbing against a ZrO2 ceramic ball in dry and wet environments were studied, and the wear mechanism was revealed. The measurement characterization and experimental results indicate that the long axis of coconut shell ellipsoid cells grows along the direction of the long axis pointing towards the coconut shell ellipsoid, but this directionality has a relatively small impact on the tribological properties. The average sliding friction coefficient of coconut shell rubbing against ZrO2 ceramic balls is about 0.52 and 0.095, respectively under dry and wet friction conditions. Under dry friction conditions, the wear of coconut shells is mainly because of cell tearing, detachment and abrasive wear caused by alternating friction forces. Mainly considering the combined effects of the high hardness, high strength and good water absorption of coconut shells, as well as the water film at the friction interface, the friction force significantly reduces and makes it difficult to damage the cell structure, leading to a wear rate decrease by more than 100 times under wet friction conditions, much lower than that of lignum vitae. Overall, this study indicates the potential of coconut shell as a water lubricated friction pair material featuring excellent performance.

A Modified Jacking Force Model to Predict Sliding Friction Coefficient Considering Partially Developed Arching Effect in Highly Weathered Rocks

A Modified Jacking Force Model to Predict Sliding Friction Coefficient Considering Partially Developed Arching Effect in Highly Weathered Rocks

Low friction coefficient bioinspired copper/graphene nanolaminates with high content graphene

Graphene is widely used in metal matrix composites (MMC) to improve the tribological properties of metal due to its special lamellar structure and excellent tribological properties. However, because the aggregation of graphene, it is difficult to increase the content of graphene in metal materials, which seriously hinders the further optimization of friction coefficient. In this paper, we report a bioinspired strategy to fabricate nacre-like copper/graphene nanolaminates through chemical intercalation of copper precursor into the interlayer space of expandable graphite and subsequent reduction. The regular parallel arrangement of graphene can greatly improve the agglomeration phenomenon and the aspect ratio of graphene, which harden the copper matrix by effectively restricting the motion of dislocation and also form continuous lubricating film on the surface. A low dry sliding friction coefficient 0.13 is thus obtained among copper-based composites without severely deteriorating the electrical properties, providing new prospect in sliding electrical contact applications.

Effects of pellet-sinter interaction parameters on component segregation and bed porosity considering flow velocity and mixture composition: A DEM study

Bed permeability is a crucial factor in blast furnace performance which depends on the material distribution achieved through charging. Since a homogeneous bed of pellet and sinter is recommended, it is crucial to understand whether segregation of the pellet-sinter mixture occurs during charging. The Discrete Element Method is useful in this regard; however, simulations of pellet-sinter mixture charging currently lack credibility since pellet-sinter interaction parameters have not yet been calibrated and validated. Determining pellet-sinter interaction parameters will require significant efforts, so it is useful to know whether mixture segregation and the resulting bed permeability are sensitive to these parameters. In this work, we investigate to what extent the restitution coefficient, sliding friction coefficient and rolling friction coefficient between pellet and sinter affect segregation during bed formation and the resulting permeability in terms of porosity using a simplified charging setup. The investigation is done for different mixture compositions and flow velocities, and analysis settings including sample size and sampling directions. We conclude that all parameters affect segregation and porosity, regardless of the composition and velocity. Hence, all mixture parameters including the interaction parameters between the components must be carefully calibrated when developing a model for predicting permeability.

Study on friction characteristics between cotton stalk-residual film-external contact materials

Friction affects the crushing effect of materials. It is of great significance to explore the friction characteristics between cotton stalk-residual film-external contact materials for the analysis of the crushing mechanism of residual film. In view of this, the influence characteristics of inter residual films, residual films/external contact materials friction characteristics were explored. The inter-films static sliding friction coefficient fs and dynamic sliding friction coefficient fk are 0.425 and 0.372, the film/40Cr mean fs is 0.439. Meanwhile, the stalk/materials friction characteristics was analyzed. The response model of fs and static rolling stability Angle μe was constructed (Model coefficient p < 0.01, coefficient of determination R2 >0.93, calibration determination coefficient R2adj >0.86, coefficient of variation C.V >2.9%). The effects of different moisture content, sampling sites and external contact materials on the friction characteristics of inter-stalks and stalk/materials were explained.

Experimental observation of near-wall effects during the puncture of soft solids.

Performing conventional mechanical characterization techniques on soft materials can be challenging due to issues such as limited sample volumes and clamping difficulties. Deep indentation and puncture is a promising alternative as it is an information-rich measurement with the potential to be performed in a high-throughput manner. Despite its promise, the method lacks standardized protocols, and open questions remain about its possible limitations. Addressing these shortcomings is vital to ensure consistent methodology, measurements, and interpretation across samples and labs. To fill this gap, we examine the role of finite sample dimensions (and by extension, volume) on measured forces to determine the sample geometry needed to perform and unambiguously interpret puncture tests. Through measurements of puncture on a well-characterized elastomer using systematically varied sample dimensions, we show that the apparent mechanical response of a material is in fact sensitive to near-wall effects, and that additional properties, such as the sliding friction coefficient, can only be extracted in the larger dimension case where such effects are negligible.

Badanie wpływu wybranych kontrolowanych czynników na współczynnik tarcia ślizgowego za pomocą eksperymentalnych metod planowania

The article presents the use of mathematical statistics to determine controllable factors that influence the coefficient of friction in a dual-flow three-stage spur gear transmission of a newly designed sucker rod pumping unit. The load acting on the bearing units, the rotational speed of the main and auxiliary shafts, and the diametrical gap between the shaft and the bushing were assessed through tests. The tests were carried out in random order. The multivariate testing was used to determine the number of tests to be performed as well as the test conditions in order to achieve the required accuracy bushing. In the statistical analysis of the results, the Cochrane criterion was applied to verify the homogeneity of the variance values. Student's t-test was used to verify the significance of the coefficients included in the regression equation, Fisher’s F-test was used to determine the suitability of the adopted output function for describing the real object of study, i.e., the adequacy of the model, and sensitivity coefficients were used to assess the influence of the corresponding parameters on the optimization parameter. The analysis also considered the dispersion of optimization parameters, measurement repeatability, and errors in the model coefficients. Experimental values of the criteria, along with the dispersion of the adequacy and repeatability of the mathematical model, were evaluated to determine whether the model is fully suitable for the object of study. The impact of significant factors and their combinations, as well as their critical values, were assessed by comparing calculated values of the criteria. The significance or insignificance of the corresponding coefficients of the regression equation was determined. To investigate the impact of these controlled factors — load, rotational speed of the main and auxiliary shafts, and the diametrical gap between the auxiliary shaft and the bushing — on the sliding friction coefficient, a modernized device was developed. This device simulates the operating conditions of a double friction sliding bearing in a dual-flow, three-stage spur gearbox bushing. The experiments were conducted using I-40A industrial oil at room temperature. It has been determined that these factors significantly impact the coefficient of friction in a double friction bearing. Consequently, it is necessary to calculate their limit values to ensure the bearing assembly operates without failure during the required service life. Compared to other examined parameters, the optimization parameter, i.e., the coefficient of friction, is most significantly influenced by the diametrical gap between the auxiliary shaft and the bushing, and least affected by the magnitude of the load acting on the bearing assembly. The overall impact of controlled factors on the coefficient of friction is minimal. Employing the test planning method, a mathematical formula was derived, enabling the determination of the coefficient of friction in a double sliding friction bearing without additional tests within the range of limit bushing values of contact parameters.

Low friction under ultrahigh contact pressure enabled by self-assembled fluorinated azobenzene layers

Extensive efforts have been made to pursue a low-friction state with promising applications in many fields, such as mechanical and biomedical engineering. Among which, the load capacity of the low-friction state has been considered to be crucial for industrial applications. Here, we report a low friction under ultrahigh contact pressure by building a novel self-assembled fluorinated azobenzene layer on an atomically smooth highly-oriented pyrolytic graphite (HOPG) surface. Sliding friction coefficients could be as low as 0.0005 or even lower under a contact pressure of up to 4 GPa. It demonstrates that the low friction under ultrahigh contact pressure is attributed to molecular fluorination. The fluorination leads to effective and robust lubrication between the tip and the self-assembled layer and enhances tighter rigidity which can reduce the stress concentration in the substrate, which was verified by density functional theory (DFT) and molecular dynamics (MD) simulation. This work provides a new approach to avoid the failure of ultralow friction coefficient under relatively high contact pressure, which has promising potential application value in the future.

The role of rolling resistance in the rheology of wizarding quidditch ball suspensions

To elucidate the effect of particle shape on the rheology of a dense, viscous suspension of frictional, non-Brownian particles, experimental measurements are presented for suspensions of polystyrene particles with different shapes in the same solvent. The first suspension is made of spheres whereas the particles which compose the second suspension are globular but with flattened faces. We present results from steady shear and shear-reversal rheological experiments for the two suspensions over a wide range of stresses in the viscous regime. Notably, we show that the rheology of the two suspensions is characterised by a shear-thinning behaviour, which is stronger in the case of the suspension of globular particles. Since the shear-reversal experiments indicate an absence of adhesive particle interactions, we attribute the shear thinning to a sliding friction coefficient which varies with stress as has been observed previously for systems similar to the first suspension. We observe that the viscosity of the two suspensions is similar at high shear stress where small sliding friction facilitates particle relative motion due to sliding. At lower shear stress, however, the sliding friction is expected to increase and the particle relative motion would be associated with rolling. The globular particles attain a higher viscosity at low shear stress than the spherical particles. We attribute this difference to a shape-induced resistance to particle rolling that is enhanced by the flattened faces. Image analysis is employed to identify features of the particle geometry that contribute to the resistance to rolling. It is shown that the apparent rolling friction coefficients inferred from the rheology are intermediate between the apparent dynamic and static rolling friction coefficients predicted on the basis of the image analysis. All three rolling resistance estimates are larger for the globular particles with flat faces than for the spherical particles and we argue that this difference yields the stronger shear thinning of the globular particle suspension.

Calibration of Sliding Friction Coefficient in DEM between Different Particles by Experiment

Granular materials are widely prevalent in nature and industry, and the discrete element method (DEM) is the most effective method for the mechanical analysis of granular materials. Because of the difficulty inherent in friction coefficient determination, the friction behavior of granular geomaterials has always been a difficult problem in DEM. In order to study the variation rules of the sliding friction coefficients in DEM, an experiment designed to determine the sliding friction coefficient between particles with different shapes and different contact forms and an experiment designed to determine the sliding friction coefficient between particles and different boundaries were proposed, and the experimental results were fitted. In order to verify the reliability of the experiments, the fitting results were embedded into DEM software, and several packing experiments and simulation experiments were carried out and compared. The simulated results are detailed and discussed with reference to the experimental results as part of this paper. The results indicate that the simulation results are highly consistent with the experimental results, and the sliding friction coefficient obtained by the proposed experiment is in accordance with that determined theoretically. The sliding friction coefficient determined by fitting according to the experimental results can determine the sliding friction coefficient in DEM simulation and improve the accuracy of simulation results.

Structural transformations and their impact on the mechanical and antifriction properties in the process of alloying graphitized hypereutectoid steel with copper

The purpose of the work is to develop a cast antifriction material based on an iron-carbon alloy with a high copper content for use in large, heavy duty sliding friction units. Using the casting method in self-hardening liquid glass mixtures, two specimens of hypereutectoid graphitized steel with different copper contents (0.09 and 8.76 wt.%) were produced. To obtain graphite in the steel structure, modification with the silicocalcium (SiCa) was used. The microstructural examination was carried out using optical metallography, SEM and TEM methods. The impact of copper on the structure as well as the mechanical and antifriction properties of graphitized hypereutectoid steel was studied. It was found that adding 8.76 wt.% of copper to the steel composition leads to an increase in the Brinell hardness level of the material from 250 to 300 HB, ultimate tensile strength from 250 to 380 MPa and compressive strength from 1050 to 1200 MPa, which is associated with an increase in the microhardness of pearlite from 350 to 420 HV. To assess the impact of copper on the sliding friction coefficient of graphitized hypereutectoid steel, a curve of sliding friction coefficient vs applied load was plotted; the experiment was carried out according to the liner-on-disk scheme. The wear resistance of materials under sliding friction conditions was also assessed using this method. Copper alloying has a positive effect on the wear resistance of graphitized hypereutectoid steel by increasing the mechanical properties of the material and also by reducing the level of the sliding friction coefficient under boundary lubrication conditions.

Modelling the wall friction coefficient for a simple shear granular flow in view of the degradation mechanism

A steady granular flow experiment was performed in a confined annular shear cell to examine how the wall friction coefficient $\mu _w$ degrades from the intrinsic sliding friction coefficient $f$ between the grains and the container wall. Two existing models are invoked to examine the decay trend of $\mu _w/f$ in view of the ratio of shear velocity to the square root of granular temperature $\chi$ (Artoni &amp; Richard, Phys. Rev. Lett., vol. 115, 2015, 158001) and the ratio of grain angular and slip velocities $\varOmega$ (Yang &amp; Huang, Granul. Matt., vol. 18, issue 4, 2016, p. 77), respectively. As both models correlate $\mu _w/f$ to different flow properties, a hidden relation is speculated between $\chi$ and $\varOmega$ , or equivalently, between the granular temperature and the grain rotation speed. We used experiment data to confirm and reveal this hidden relation. From there, a unified $\mu _w/f-\chi$ model is proposed with physical meanings for the model coefficients and to show general agreement with the measured trend. Hence we may conclude that both the fluctuations in grain translations and their mean rotation are the crucial yet equivalent mechanisms to degrade $\mu _w/f$ .