Research Papers: Applications

J. Tribol. 2017;140(1):011101-011101-12. doi:10.1115/1.4036451.

Cage motions in ball bearings are investigated using a dynamic analysis program. Increases in the cage friction coefficient induce unstable motions of the cage. The instability is more likely to occur under high load and low‐speed conditions due to less ball-race sliding. A simple theory of cage instability is developed, and a critical cage friction coefficient formula is proposed, which is a function of the cage mass, ball-race traction, ball-cage contact stiffness, cage rotational speed, and number of balls. The prediction of this formula agrees with the results of the dynamic analysis. With a nonuniform separation between the balls, a high-speed whirl is superimposed on the normal whirl with the ball group speed. The direction of the high-speed whirl is the same as the cage rotational direction in inner race rotation (IR), but they are opposite in outer race rotation (OR). These results agree with some experimental results in the literature and validate the dynamic analysis.

Commentary by Dr. Valentin Fuster
J. Tribol. 2017;140(1):011102-011102-9. doi:10.1115/1.4036835.

The transient simulation of the journal bearing temperature in the internal gear pumps is hard due to the complicated shaft motion caused by the complicated loads. In this paper, a thermohydrodynamic analysis method, based on dynamic mesh techniques, is presented with the application of the general computational fluid dynamics (CFD) code fluent. This method can simulate the complex whirling orbit induced temperature variation in internal gear pumps and has taken into account the conduction in the rotating and orbiting rotor of a hydrodynamic bearing. A test rig has been built according to the structure of an internal gear pump to carry out the validation. The results show that the model is reliable. The relationship between bearing temperature, leakage, and axial clearance in the internal gear pump has been studied. It is found that the bearing temperature will decrease slightly, while the leakage increases heavily with larger axial clearance. A thermohydrodynamic analysis of the self-lubricating bearing in the internal gear pump has been done based on this method. The results show that the pressure profile changes regularly with the whirling motion of the journal, while the whirling motion has little effect on the distribution of the temperature. Besides, the increase of the whirling radius will result in the decrease of the pressure profile and the increase of the temperature profile.

Commentary by Dr. Valentin Fuster
J. Tribol. 2017;140(1):011103-011103-9. doi:10.1115/1.4037066.

Movement analyses of bearings with regard to stable and unstable motion behavior typically investigate the cage whirl. However, some experimental and simulation-based studies exist that analyze the movements of the rolling elements. The majority of these investigations focus on lower shaft speeds. This paper presents an image-based approach for investigating the rolling element motions under high-speed operation condition. A new evaluation algorithm is presented and its suitability is verified first by generic images and afterward by experiments on cylindrical roller bearings.

Commentary by Dr. Valentin Fuster

Research Papers: Coatings and Solid Lubricants

J. Tribol. 2017;140(1):011301-011301-9. doi:10.1115/1.4036628.

Ternary iron–tungsten–phosphorus (Fe–W–P) coatings were electrodeposited with different sodium tungstate (NaWO4·2H2O) concentration on stainless steel 316 L substrate. These coatings were characterized by energy dispersive X-ray spectrometer (EDX), scanning electron microscope (SEM), and X-ray diffraction (XRD). The friction and wear behavior of these coatings were investigated using ball-on-disk tribometer under dry conditions. This study reveals a nanocrystalline and nodular structure with nanometric grain size of the deposited alloy. The maximum level of incorporation of tungsten (W) is about 29.54 at %. It was obtained with 0.5 M of sodium tungstate concentration, and it increases the microhardness of the coatings. Moreover, it was found that Fe–W–P coatings had significantly improved the tribological properties of the substrate due to their higher wear resistance and lower friction coefficient.

Commentary by Dr. Valentin Fuster
J. Tribol. 2017;140(1):011302-011302-7. doi:10.1115/1.4037213.

Aluminum alloy metal matrix composites (Al-MMCs) have been considered as promising materials for aerospace and automotive industries due to their excellent balance of physical, mechanical, and tribological properties. In the present work, the Al–Fe–V–Si alloy matrix composites with 0–20 wt. % copper-coated graphite were fabricated by hot-pressed sintering. The dry sliding tests were carried out at various temperatures ranging from room temperature (RT) to 350 °C. The microstructure, phase, hardness, and worn surface of the sintered composites were examined in detail. The effect of copper-coated graphite amount on the properties of the composite was also investigated. The results show that the Al–Fe–V–Si–graphite composites mainly consist of α-Al, Al8Fe2Si intermetallic, and graphite phases. The addition of Cu-coated graphite can decrease the friction coefficient and wear rate from RT to 350 °C. The Al–Fe–V–Si–graphite composite containing 10 wt. % copper-coated graphite exhibits better wear properties than other composites. The favorable lubricating properties were attributed to the tribolayer with graphite lubricating film formed on the worn surface.

Commentary by Dr. Valentin Fuster

Research Papers: Contact Mechanics

J. Tribol. 2017;140(1):011401-011401-9. doi:10.1115/1.4036720.

This work is devoted to investigate the effects of thermal buckling on the tribological characteristics of a Cu-based wet clutch by artificially modifying friction pairs into different contact ratios. A thermal lubrication model is provided, and corresponding experiments are conducted on the wet clutch comprehensive test bench. The friction results from measurements and simulations for such modified friction pairs are analyzed. The results show that, as the contact ratio reduces, surface temperature rises obviously, and friction coefficient increases dramatically, so that local friction torque and total output torque grow significantly. In addition, the vibration of the output torque becomes more severe as the contact ratio reduces. Therefore, the nonuniform contact after thermal buckling exacerbates the friction characteristics of friction pairs severely and accelerates the failure of wet clutches.

Commentary by Dr. Valentin Fuster
J. Tribol. 2017;140(1):011402-011402-6. doi:10.1115/1.4036915.

Recently, generalizing the solution of the adhesiveless random rough contact proposed by Xu, Jackson, and Marghitu (XJM model), the first author has obtained a model for adhesive contact near full contact, under the Johnson, Kendall, and Roberts (JKR) assumptions, which leads to quite strong effect of the fractal dimension. We extend here the results with closed-form equations, including both loading and unloading which were not previously discussed, showing that the conclusions are confirmed. A large effect of hysteresis is found, as was expected. The solution is therefore competitive with Persson's JKR solution, at least in the range of nearly full contact, with an enormous advantage in terms of simplicity. Two examples of real surfaces are discussed.

Commentary by Dr. Valentin Fuster
J. Tribol. 2017;140(1):011403-011403-6. doi:10.1115/1.4036917.

We show that the full multiscale Persson's theory for rubber friction due to viscoelastic losses can be approximated extremely closely to simpler models, like that suggested by Persson in 1998 and similarly by Popov in his 2010 book (but notice that we do not make any use of the so-called “Method of Dimensionality Reduction” (MDR)), so it is essentially a single scale model at the so-called large wavevector cutoff. The dependence on the entire spectrum of roughness is therefore only confusing, at least for range of fractal dimensions of interest D2.2, and we confirm this with actual exact calculations and reference to recent data of Lorenz et al. Moreover, we discuss the critical assumption of the choice of the “free parameter” best fit truncation cutoff.

Commentary by Dr. Valentin Fuster
J. Tribol. 2017;140(1):011404-011404-11. doi:10.1115/1.4036920.

In this study, the concept of the fracture mechanics is used to solve the: (i) frictionless purely normal contact and (ii) the similar material contact under the mutual actions of the normal and tangential load. Considering the contact region is simply connected, the out-of-contact regions can be treated as periodic collinear cracks. Through evaluating the stress intensity factor (SIF), we are able to obtain the size and location of the contact/out-of-contact region. Then, the normal traction, shear traction and interfacial gap can be directly determined by the Green's function of the periodic collinear crack. In the case of frictionless purely normal contact, the new approach is applied to two classic problems, namely, the Westergaard problem (sinusoidal waviness punch) and the periodic flat-end punch problem. Then, the sinusoidal waviness contact pair in the full stick and the partial slip conditions under the mutual actions of the normal and tangential loads are solved by the newly developed approach.

Commentary by Dr. Valentin Fuster
J. Tribol. 2017;140(1):011405-011405-10. doi:10.1115/1.4037067.

Traction between a thin tensioned tape and a grooved roller could be significantly affected by lubrication effects that stem from the air entrainment into the tape–roller interface. An experimental and theoretical investigation was carried out to investigate the tape contact with a grooved roller. The tape-to-roller spacing was measured in a modified tape drive at various operational speed and tension values. The experiments showed that increasing tape tension and tape speed causes the tape-to-land spacing to increase. This unusual result is shown to be due to the tape bending laterally into the grooves. The effects of air entrainment on tape deflection and contact with a land is modeled by using shell theory, air lubrication, and contact mechanics. A relatively wide range of design parameters (groove width, land width) and device parameters (velocity and tension) were simulated to characterize the traction of a thin tape over a grooved roller. It was shown that air lubrication effects reduce the contact force; however, the underlying effects of tape mechanics are not entirely eliminated. This work shows that in order to characterize the mechanics of thin tape over grooved rollers, the tape deflection in the lateral direction should be included in the analysis.

Commentary by Dr. Valentin Fuster
J. Tribol. 2017;140(1):011406-011406-13. doi:10.1115/1.4037212.

In multiparticle simulations of industrial granular systems such as hoppers, tumblers, and mixers, the particle energy dissipation is governed by an important input parameter called the coefficient of restitution (COR). Oftentimes, the wall thickness in these systems is on the order of a particles diameter or less. However, the COR value implemented in event-driven simulations is either constant or a monotonically decreasing function of the impact velocity. The present work experimentally investigates the effect of wall thickness on the COR through sphere–thin plate elastoplastic impacts and elucidates the underlying impact phenomena. Experiments were performed on 0.635 cm and 0.476 cm diameter (d) spheres of various materials impacting aluminum 6061 plates of different thicknesses (t) with the low impact velocities up to 3.1 m/s. Besides COR, indentation measurements and numerical simulations are performed to gain a detailed understanding of the contact process and energy dissipation mechanism. As the “t/d” ratio decreases, a considerable amount of energy is dissipated into flexural vibrations leading to a significantly lower COR value. Based on the results, it can be concluded that using a constant COR input value in particle simulations may not always be an appropriate choice, especially, in the case of thin plates. However, these new COR results validate that when the wall thickness is more than twice the sphere diameter (i.e., t/d > 2), a constant COR value obtained for an impact with semi-infinite plate can be reasonably used.

Commentary by Dr. Valentin Fuster

Research Papers: Elastohydrodynamic Lubrication

J. Tribol. 2017;140(1):011501-011501-9. doi:10.1115/1.4037135.

Under repeated overrollings, the elastohydrodynamic lubrication (EHL) film thickness can be much less than the fully flooded value due to the ejection of the lubricant from the track. The ejection of the lubricant is caused by the pressure flow in the inlet, and under conditions of negligible reflow, the reduction rate is predicted by the numerical analysis with a uniform inlet film thickness. However, the degree of starvation is determined by the balance of the ejection and reflow. In the previous papers for circular contacts, the reflow is taken into account using a nonuniform inlet film thickness obtained based on the Coyne–Elrod boundary condition. In this paper, the model for circular contacts is extended to elliptical contacts, which are of more practical importance in rolling bearings. The model is verified for the inlet distance and the film thickness using a roller on disk optical test device. Numerical results are fitted to an inlet distance formula, which is a function of the initial film thickness, the fully flooded central film thickness, the capillary number, and the ellipticity ratio. The inlet distance formula can be applied to the Hamrock–Dowson formulas for the starved film thickness.

Commentary by Dr. Valentin Fuster

Research Papers: Friction and Wear

J. Tribol. 2017;140(1):011601-011601-7. doi:10.1115/1.4036912.

The dynamic evolutionary law and tribological behavior of tribopair AISI 52100-AISI 1045 were studied via the multifractal method. Friction experiment was performed on a ring-on-disk tribometer under lubrication, and the multifractal detrended fluctuation analysis (MF-DFA) method was adapted to characterize the multifractality of the friction coefficient. The multifractal spectra first exhibited a left-hook, then right-hook, and left-hook, respectively, during the friction stages. The multifractal spectrum width W decreases in running-in friction process, maintains at small values in steady friction process, and increases rapidly in increasing friction process. Corresponding shuffled series was analyzed to distinguish that the multifractality of friction coefficient is due to the long-range correlation of the fluctuations. The results inform quantitative interpretations of friction system's tribological behavior and friction process identification.

Commentary by Dr. Valentin Fuster
J. Tribol. 2017;140(1):011602-011602-6. doi:10.1115/1.4036721.

This paper deals with the improvement in surface properties and microscratch resistance of graphites by means of an ultrasonic nanocrystalline surface modification (UNSM) technique. The surface roughness and surface hardness of the untreated and UNSM-treated graphites were investigated using an atomic force microscopy (AFM) and a microhardness tester, respectively. The scratch resistance was assessed using a microscratch tester at a progressive load. Moreover, a Raman spectroscopy was employed to characterize the microstructure of graphites before and after UNSM treatment. The scratch test results revealed that the resistance to scratch of both UNSM-treated graphites was found to be better in comparison with the untreated graphites. The increase in scratch resistance of both UNSM-treated graphites may be mainly attributed to the reduced surface roughness and increased surface hardness by UNSM treatment. The graphite produced by Poco exhibited a higher resistance to scratch compared to that of the graphite produced by Mersen. The objective of this study is to extend the service life of three-dimensional (3D) cover glass moldings made of graphite by the application of UNSM treatment through the understanding the effects of surface roughness and surface hardness on the scratch defect generation behavior during glass molding process.

Commentary by Dr. Valentin Fuster
J. Tribol. 2017;140(1):011603-011603-19. doi:10.1115/1.4036918.

Friction and wear properties of hypereutectic Al–25Si alloy were studied under dry and lubricated sliding conditions. Hypereutectic Al–25Si alloys were prepared by rapid solidification process (RSP) under the T6 condition. Experimental studies were conducted using a ball on disk type tribometer. The effect of the sliding distance and normal load on the friction and wear were investigated. The coefficient of friction (COF) remained stable with an increase in the sliding distance (250–1500 m) and decreased with an increase in the normal load (10–50 N), whereas the wear rate decreased with an increase in the sliding distance, and increased with the increase in the normal load up to 40 N and then attained a steady-state value under dry and lubricated sliding conditions. The improvements in COF and wear rate were mainly attributed to the morphology, size, and distribution of hypereutectic Si particles due to its fabrication process. Scanning electron microscopy (SEM), energy dispersive spectroscopy (EDS), optical microscopy, and three-dimensional (3D)-surface profilometer were used for characterization of the wear tracks. The dominant wear mechanisms for a hypereutectic Al–25Si alloy were adhesive wear, abrasive wear, and plastic deformation.

Commentary by Dr. Valentin Fuster
J. Tribol. 2017;140(1):011604-011604-21. doi:10.1115/1.4036922.

Fretting wear studies were conducted on AZ91 and AE42 magnesium alloys against steel ball. Average coefficient of friction (COF) remains steady with the increase in running time. However, average coefficient of friction decreases with the increase in normal load and frequency and marginally increases with the increase in amplitude. A constant average coefficient of friction of 0.06 was observed for both AZ91 and AE42 under dry sliding conditions at normal load of 50 N. Wear volume increases linearly with increasing running time. Wear volume first decreases sharply, attains minima, and then increases marginally with the increase in normal load. However, wear volume increases with increasing amplitude and frequency. Higher specific wear rate of 10.5 × 10−6 mm3 N−1·m−1 was observed for AE42, as compared to 4.5 × 10−6 mm3 N−1·m−1 for AZ91. The wear in magnesium alloy was caused by a combination of adhesion, abrasion, oxidation, delamination, and plastic deformation under different fretting conditions.

Commentary by Dr. Valentin Fuster
J. Tribol. 2017;140(1):011605-011605-6. doi:10.1115/1.4036935.

Tribological and mechanical properties of aramid fiber (AF), graphite (Gr), and hexagonal boron nitride (h-BN) hybrid polyimide composites were investigated under room and high temperature. Results show that, Gr in composite reinforced with AF and h-BN can reduce coefficient of friction (COF) and improve antiwear property of composites under room temperature. Gr can accelerate the formation of transfer film under high temperature without sacrificing the wear resistant of composites. Transfer film of composites reinforced with Gr and h-BN simultaneously present more smooth and uniform compared with that of composites reinforced with only AF and h-BN. However, under higher temperature, composite reinforced with pure Gr present higher COFs and wear rates (WRs) compared with composites filled with h-BN and Gr simultaneously. Comprehensively, composite filled with 10% AF, 3% h-BN, and 4% Gr is the optimum composition.

Commentary by Dr. Valentin Fuster
J. Tribol. 2017;140(1):011606-011606-11. doi:10.1115/1.4036924.

Press hardening is employed in the automotive industry to produce advanced high-strength steel components for safety and structural applications. This hot forming process depends on friction as it controls the deformation of the sheet. However, friction is also associated with wear of the forming tools. Tool wear is a critical issue when it comes to the dimensional accuracy of the produced components and it reduces the service life of the tool. It is therefore desirable to enhance the durability of the tools by studying the influence of high contact pressures, cyclic thermal loading, and repetitive mechanical loading on tool wear. This is difficult to achieve in conventional tribological testing devices. Therefore, the tribological behavior of tool–workpiece material pairs at elevated temperatures was studied in a newly developed experimental setup simulating the conditions prevalent during interaction of the hot sheet with the tool surface. Uncoated 22MnB5 steel and aluminum–silicon (Al–Si)-coated 22MnB5 steel were tested at 750 °C and 920 °C, respectively. It was found that higher loads led to lower and more stable friction coefficients independent of sliding velocity or surface material. The influence of sliding velocity on the coefficient of friction was only marginal. In the case of Al–Si-coated 22MnB5, the friction coefficient was generally higher and unstable due to transfer of Al–Si coating material to the tool. Adhesion was the main wear mechanism in the case of uncoated 22MnB5.

Commentary by Dr. Valentin Fuster
J. Tribol. 2017;140(1):011607-011607-8. doi:10.1115/1.4037069.

In the present investigation, friction stir processing (FSP) was used to integrate Ni particles into the surface of copper in order to fabricate a surface composite. Determining an optimized percentage of Ni particles, different dimensions of grooves were machined into the Cu plates. Then, the specimens' grooves were filled by nickel reinforcement particles, and friction stir process was performed on the specimens with tool rotation speed of 800 rpm and traverse speed of 50 mm/min. Optical microscope (OM) and scanning electron microscope (SEM) were used to evaluate the microstructure. Pin-on-disk test was performed to evaluate wear properties using pins manufactured from the FSPed zone. Also, Micromet-Buehler Vickers hardness tester was used to test the FSPed surfaces' microhardness. The results show that the best properties are obtained when using 2 × 2 mm groove. In this situation, microhardness and wear properties were improved as 40% and 60% compared to the substrate, respectively.

Commentary by Dr. Valentin Fuster
J. Tribol. 2017;140(1):011608-011608-10. doi:10.1115/1.4037068.

SiC–TiB2 (10 wt. %) and SiC–TiB2 (10 wt. %)–TaC (5 wt. %) composites are consolidated using spark plasma sintering (SPS) technique at different sintering temperatures (2000 °C and 2100 °C) for 15 min soaking time under 35 MPa pressure. The effects of sintering temperature on densification and mechanical properties of composites have been investigated in detail. SiC–TiB2 and SiC–TiB2–TaC composites sintered at 2100 °C showed high Vickers hardness value, i.e., 27.20 ± 1.23 GPa and 26.40 ± 0.80 GPa, respectively, under 1 kgf (9.81 N) load. Poor fracture toughness {2.28 MPa(m)1/2 at 1 kgf (9.81 N) load} of monolithic silicon carbide (SiC) sintered at 2100 °C is improved with addition of titanium diboride (TiB2) and tantalum carbide (TaC) as secondary phases. Scratch resistance of SiC–TiB2 and SiC–TiB2–TaC composites show coefficient of friction value below 0.40 and 0.50 under 5 N and 10 N loads, respectively. SiC–TiB2 and SiC–TiB2–TaC composites show constant thermal conductivity response above 810 °C and 603 °C in the range of 48.70–47.15 W/m K and 60.35–60.41 W/m K, respectively.

Commentary by Dr. Valentin Fuster
J. Tribol. 2017;140(1):011609-011609-11. doi:10.1115/1.4037136.

This paper proposes a wear model for polymers based on so-called mechanistic processes comprising both low cycle fatigue and abrasive wear mechanisms, which are prominent in polymer–metal sliding interfaces. Repeated elastic contact causes localized fatigue, whereas abrasive part is an anticipatory outcome of plastic contacts by hard metal asperities on to soft polymer surface. Further, presuming adhesive interactions in elastic–plastic contacts, asperity contact theories with necessary modifications were analyzed to assess load and separation for their subsequent use in elementary wear correlations. Both Gaussian and Weibull distributions of asperity heights were considered to include statistics of surface microgeometry. Finally, volumetric wear was written in terms of roughness parameters, material properties, and sliding distance. Validation was conducted extensively, and reliability of the formulation was achieved to a large extent. Experimental part of this work included several pin-on-disk tests using polyether ether ketone (PEEK) pins and 316L stainless steel disks. Disks with different roughness characteristics generated by polishing, turning, and milling were tested. Experimental results agreed well with predictions for the polished surface and with some deviations for other two surfaces. Further, fatigue to abrasive wear ratio was identified as an analytical tool to predict prevailing wear mechanism for polymer-metal tribo-systems. After examining the considered cases, it was both interesting and physically intuitive to observe a complete changeover in wear mechanisms following simply an alteration of roughness characteristics.

Commentary by Dr. Valentin Fuster

Research Papers: Hydrodynamic Lubrication

J. Tribol. 2017;140(1):011701-011701-19. doi:10.1115/1.4036770.

The form of the Reynolds-type equation which governs the macroscopic mechanics of hydrodynamic lubrication interfaces with a microscopic texture is well-accepted. The central role of the ratio of the mean film thickness to the texture period in determining the flow factor tensors that appear in this equation had been highlighted in a pioneering theoretical study through a rigorous two-scale derivation (Bayada and Chambat, 1988, “New Models in the Theory of the Hydrodynamic Lubrication of Rough Surfaces,” ASME J. Tribol., 110, pp. 402–407). However, the resulting homogenization theory still remains to be numerically investigated. For this purpose, after a comprehensive review of the literature, three microscopic regimes of lubrication will be outlined, and the transition between these three regimes for different texture types will be extensively demonstrated. In addition to conventional textures, representative re-entrant textures will also be addressed.

Commentary by Dr. Valentin Fuster
J. Tribol. 2017;140(1):011702-011702-13. doi:10.1115/1.4037134.

This paper studies the static and dynamic coefficients of an externally pressurized porous gas journal bearing. The finite difference method is used to solve the Reynolds equation of the bearing to obtain the static load capacity. The linear perturbation method is adopted to derive the perturbation equations considering four degrees-of-freedom (4DOF), namely, the translational movements in x and y directions and the rotational movements around x and y directions. The effects of various parameters on the dynamic behaviors of the journal bearing are studied. These parameters include the bearing number, the supply pressure, the feeding parameter, the length-to-diameter ratio, the porosity parameter, the eccentricity ratio, and tilting angles. Simulated results prove that the proposed method is valid in estimating the static and dynamic characteristics of a porous gas journal bearing with 4DOF.

Commentary by Dr. Valentin Fuster
J. Tribol. 2017;140(1):011703-011703-13. doi:10.1115/1.4037151.

Numerous previous numerical studies have investigated the effect of surface texturing upon the static characteristics of journal bearings, including their load-carrying capacity and friction torque. In general, the dynamic characteristics of journal bearings are also important, since they are essential factors in predicting the vibration behavior of actual rotors supported by journal bearings. However, the effects of surface texture upon these dynamic characteristics have not been investigated through either numerical or experimental analysis. Thus, in the present study, such analyses were conducted to investigate the dynamic characteristics of textured journal bearings, such as their dynamic coefficients of oil film and the stability-threshold shaft speed supported by the bearings. Numerical analysis was done using a model that included inertial effects and energy loss; this model agreed well with experimental results concerning static characteristics from our previous study. Dynamic testing based on a sinusoidal-excitation method was also performed using textured journal bearings with uniform square dimples to verify the numerical results, which agreed qualitatively with those of experiment, confirming the validity of the numerical analysis. These results suggest that under the same operating conditions, the main effect of texturing upon the dynamic coefficients is to yield the cross-coupled stiffness coefficients with lower absolute values than the conventional ones with a smooth surface. The linear stability-threshold shaft speed of the rotor supported by the textured journal bearings became higher than that of a smooth bearing, mainly due to the reduction of cross-coupled stiffness coefficients. This tendency became more pronounced for high Reynolds number operating conditions and textured bearings with a large number of dimples.

Commentary by Dr. Valentin Fuster


J. Tribol. 2017;140(1):017001-017001-1. doi:10.1115/1.4036925.

The values of λ for Fit A in Table 2 are incorrect as published; as correctly computed from Eq. (9), they are given below: Fit Aεξεηλ−0.8−0.50.689150.80.51.863690.8−0.51.863690.903.430460.9−0.22.978180.30.61.219610.980.143.98539

Commentary by Dr. Valentin Fuster

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