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### Research Papers: Applications

J. Tribol. 2017;139(3):031101-031101-9. doi:10.1115/1.4034533.

This work deals with optimization of axially magnetized stack structured permanent magnet (PM) thrust bearing using generalized three-dimensional (3D) mathematical model having “n” number of ring pairs. The stack structured PM thrust bearing is optimized for the maximum axial force and stiffness in a given cylindrical volume. matlab codes are written to solve the developed equations for optimization of geometrical parameters (axial offset, number of ring pairs, air gap, and inner radius of inner and outer rings). Further, the results of proposed optimization method are validated using finite element analysis (FEA) and further, generalized by establishing the relationship between optimal design variables and air gap pertaining to cylindrical volume constraint of bearing's outer diameter. Effectiveness of the proposed method is demonstrated by optimizing PM thrust bearing in a given cylindrical volume. Mathematical model with optimized geometrical parameters dealt in the present work helps the designer in developing PM thrust bearings effectively and efficiently for variety of applications.

Commentary by Dr. Valentin Fuster
J. Tribol. 2017;139(3):031102-031102-10. doi:10.1115/1.4034532.

In the modeling of a uniformly distributed band heat flux region experiencing constant acceleration from rest over a half-space surface, it is found that the maximum surface temperature at the instantaneous speed and the corresponding Peclet number are already well approximated by the long-established steady-state constant-speed models very soon after the moment the flux region clears the overlap of its original footprint at the initiation of motion. During startup when the flux still overlaps its original footprint, maximum temperature at any instant given the level of flux is well approximated by a simple one-dimensional conduction problem with a correspondingly stationary heat flux initiating at time zero. The above acceleration behaviors are observed regardless of whether the uniform flux is constant or Coulombic (proportional to instantaneous speed as frictional heating), though during the initial startup the maximum temperature rise in the Coulombic case is only two-thirds that of the constant flux case. The case of constant deceleration was additionally modeled, where at the eventual instant of halt, the maximum temperature in the case of constant flux was found to be directly proportional to the rate of deceleration to the 1/4 power, whereas in the case of Coulombic flux it was found that maximum temperature was instead inversely proportional to the rate of deceleration.

Commentary by Dr. Valentin Fuster
J. Tribol. 2017;139(3):031103-031103-6. doi:10.1115/1.4034961.

In this paper, the driving force of a linear-guideway type recirculating ball bearing (linear bearing) is measured and explained as the first step toward an understanding of sticking, which is the significant increase in driving force required to move a linear bearing under back-and-forth operation with a short stroke length. First, the driving force required for operation of a test bearing (which is a linear-guideway type recirculating ball bearing with load balls) and acceleration of a moving body (which consists of a carriage of the test bearing, an arm, and weight) were measured. The measurements showed that the sticking occurred when the test bearing, under a relatively higher rolling moment load, was driven in an offset position for a certain period. Next, the driving force of a test bearing with alternating load balls and spacer balls was measured, and it was clear that the cause of the sticking was the sliding friction between rolling balls. Finally, the ball locations in the load zone of the test bearing with load balls were observed in operation, and the occurrence process of the sticking is explained.

Commentary by Dr. Valentin Fuster

### Research Papers: Coatings and Solid Lubricants

J. Tribol. 2016;139(3):031301-031301-6. doi:10.1115/1.4034077.

Titanium alloys are widely used in the field of artificial joints, but their poor wear resistance limits their clinical application. Therefore, in this paper, the diamondlike carbon (DLC) film deposited on Ti6Al4V alloy surface by unbalanced magnetron sputtering technology to improve its wear resistance. Swinging tests are conducted on a self-refit multifreedom degree friction tester, and their coefficient of friction, wear loss, and wear morphology were analyzed. Results show that there are no evident scratches on the socket surface with small axial load and angular displacement. The worst wear scratches appear under the largest load and swing angular displacement. A spot of scratches with different depths are found on the edge of the socket, which reveals the characteristic of swinging friction. The friction coefficient increases from 0.134 to 0.206 as the axial load increases, and increases from 0.11 to 0.186 as the swing angular displacement increases. Therefore, the swing angular displacement has greater influence on the wear degree. The wear mechanisms of DLC film involved a combination of fatigue, adhesive, and abrasive wear.

Commentary by Dr. Valentin Fuster
J. Tribol. 2016;139(3):031302-031302-12. doi:10.1115/1.4034331.

In general, there is no available tool which can help engineers and researchers to choose optimal materials for friction pairs. This article proposes a dual approach for the choice of materials and coatings. First, in order to select the initial materials, a selection matrix helps to rank a reduced number of solutions to a tribological problem with the aim of building the most credible and viable experimental campaign. Then, this experimental phase is necessary for final selection taking into account tribological properties. The final step involves experimental validation on a prototype and on the real device. This methodology was applied on the complex geometry of an air compressor under severe friction conditions. Technical specifications are defined by a functional analysis of the tribological system. Then, the selection matrix is created on the basis of empirical rules and bibliographic data, including predetermined material/coating properties, process considerations, and tribological features, in accordance with the functional analysis. As an example, four potential solutions were tested: diamondlike carbon (DLC) and polytetrafluoroethylene (PTFE) coatings on 15-5PH stainless steel and two composites, reinforced PTFE and polyetheretherketone (PEEK). Experimental results were then compared to expected values from the specifications. The performance of each solution was highlighted by a graphic radar representation. The selection matrix gave the DLC coatings as one of the best solutions, and experimental tests confirmed this choice while allowing to refine the preselected solutions. This result shows that the selection matrix gives a reliable choice of optimal solutions.

Commentary by Dr. Valentin Fuster
J. Tribol. 2016;139(3):031303-031303-5. doi:10.1115/1.4034424.

In this study, the effect of flow velocity (4–7.5 m s−1) and impact angle (30–90 deg) on erosion–corrosion behavior of chromium carbide coating was investigated under impingement by silica containing NaCl solution. Chromium carbide coating was deposited on low carbon steel by thermal reactive deposition/diffusion method at 1050 °C for 12 h in a molten salt bath. Mass loss measurement and potentiodynamic polarization tests were employed in order to determine coating performance under impingement. Polarization curves showed that the coated samples had less corrosion current density and high chemical stability. High mass loss at low impact angle indicated ductile behavior for the uncoated sample, while the mass loss for the coated sample changes less than 30% with impact angle up to 60 deg. Furthermore, the erosion–corrosion behavior of the coated sample was slightly dependent on flow velocity. Scanning electron micrographs showed that at lower impact angle, the Cr7C3 coating eroded with flake fragmentation mechanism, while at high impact angle, fatigue fracture is the main degradation mechanism.

Commentary by Dr. Valentin Fuster

### Research Papers: Contact Mechanics

J. Tribol. 2016;139(3):031401-031401-12. doi:10.1115/1.4034211.

A liquid film can flow between two solid surfaces in close proximity due to capillary effects. Such flow occurs in natural processes such as the wetting of soils, drainage through rocks, water rise in plants and trees, as well as in engineering applications such as liquid flow in nanofluidic systems and the development of liquid bridges within small-scale devices. In this work, a numerical model is formulated to describe the radial capillary-driven flow between two contacting, elastic, annular rough surfaces. A mixed lubrication equation with capillary-pressure boundary conditions is solved for the pressure within the liquid film and both macro- and micro-contact models are employed to account for solid–solid contact pressures and interfacial deformation. Measurements of interfacial spreading rate are performed for liquids of varying viscosity flowing between an optical flat and a metallic counter surface. Good agreement is found between modeling and experiment. A semi-analytical relation is developed for the capillary flow between the two contacting surfaces.

Commentary by Dr. Valentin Fuster
J. Tribol. 2016;139(3):031402-031402-10. doi:10.1115/1.4034215.

This paper attempts to demonstrate a systematic spectral approach for the characterization of the topographic nature of rough surfaces. Multiscale roughness characterization reveals a panoramic structure of microgeometric features of engineering surfaces, and this is of practical importance in order to include length scale consideration in real contact problems. Surfaces with different levels of root mean square (rms) roughness values were prepared using mechanical finishing processes for this study. Both optical and stylus profilometry data were recorded and analyzed to plot autocorrelation and power spectral density functions (PSDFs) at five different cutoff bandwidths (BWs). Correlation distances were estimated by choosing normalized autocorrelation declination to 1/e as well as to 0.1. In most of the cases, these distances were found to be less than 10% of the corresponding cutoff lengths. Nature of power spectrum has been analyzed and discussion extended to the estimation of bandwidth limited fractal characteristics based on specific spectral information. Power spectral densities (PSD) and their higher moments were extensively used to compute roughness parameters of functional significance such as asperity curvature, asperity density, etc. Evolution of asperity sharpness and asperity density during finishing processes was demonstrated at par with their physical significances. The intrinsic bandwidth parameter as per Nayak's definition was estimated closely to be a value of two for all cases.

Commentary by Dr. Valentin Fuster
J. Tribol. 2016;139(3):031403-031403-9. doi:10.1115/1.4034529.

The accuracy and efficiency are hardly acquired together in most wear analysis methods. Especially, the effect of contact stiffness is rarely considered in the wear analysis process. Therefore, a wear analysis method of clearance joint considering the effect of contact stiffness is presented. Massless link and spring damping (MLSD) model is used to conduct dynamic analysis of clearance joint system considering the effect of contact stiffness. The nonsymmetric Winkler surface model is taken to compute the contact pressure distribution. The Archard wear theory is adopted to calculate the wear amount of contact surface. The surface contour changes with the wear calculation results over time. Then, the dynamic wear trend of clearance joint is acquired. The analysis results reveal that when the contact stiffness coefficients are small, the effect on wear results of clearance joint becomes obvious and turns to a different change trend with the change of rotation speed. The effect of different contact stiffness is fully considered and the wear analysis results are obtained with a high calculation accuracy and efficiency. The paper's work can provide guidance for the design of same type mechanisms, and have great theoretical significance and application value to the lifetime prediction of clearance joint system.

Commentary by Dr. Valentin Fuster
J. Tribol. 2016;139(3):031404-031404-5. doi:10.1115/1.4034530.

Pastewka and Robbins (2014, “Contact Between Rough Surfaces and a Criterion for Macroscopic Adhesion,” Proc. Natl. Acad. Sci., 111(9), pp. 3298–3303) recently have proposed a criterion to distinguish when two surfaces will stick together or not and suggested that it shows quantitative and qualitative large conflicts with asperity theories. However, a comparison with asperity theories is not really attempted, except in pull-off data which show finite pull-off values in cases where both their own criterion and an asperity based one seem to suggest nonstickiness, and the results are in these respects inconclusive. Here, we find that their criterion corresponds very closely to an asperity model one (provided we use their very simplified form of the Derjaguin–Muller–Toporov (DMT) adhesion regime which introduces a dependence on the range of attractive forces) when bandwidth α is small, but otherwise involves a root-mean-square (RMS) amplitude of roughness reduced by a factor $α$. Therefore, it implies that the stickiness of any rough surface is the same as that of the surface where practically all the wavelength components of roughness are removed except the very fine ones.

Commentary by Dr. Valentin Fuster

### Research Papers: Elastohydrodynamic Lubrication

J. Tribol. 2016;139(3):031501-031501-11. doi:10.1115/1.4034248.

Elastohydrodynamic lubrication (EHL) analysis in finite line contacts is usually modeled by a finite-length roller contacting with a half-space, which ignores effect of the two free boundaries existing in many applications such as gears or roller bearings. This paper presents a semi-analytical method, involving the overlapping method and matrix formation, for EHL analysis in the finite line contact problem to consider the effect of two free end surfaces. Three half-spaces with mirrored loads to be solved are overlapped to cancel out the stresses at expected surfaces, and three matrices can be obtained and reused for the same finite-length space. The isothermal Reynolds equation is solved to obtain the pressure distribution and the fast Fourier transform (FFT) is used to speed up the elastic deformation and stress related calculation. Different line contact situations, including straight rollers, tapered rollers, and Lundberg profile rollers, are discussed to explore the effect of free end surfaces.

Commentary by Dr. Valentin Fuster
J. Tribol. 2016;139(3):031502-031502-9. doi:10.1115/1.4034764.

The behavior of roughness features under rolling–sliding inside highly loaded elastohydrodynamically lubricated (EHL) contacts is studied in detail for many years now. In particular, the roughness deformation was subject to different theoretical analyses as well as experiments. A recent experimental work developed by Šperka et al. (2016, “Experimental Study of Roughness Effects in a Rolling–Sliding EHL Contact—Part I: Roughness Deformation,” Tribol. Trans., 59(2), pp. 267–276) studied the effect of kinematic operating conditions (mean velocity and slide to roll ratio) on the deformed profile of a ridge. The current paper presents results of full numerical simulations and their direct comparison to experiments in order to study the dependency of roughness deformation on the operating conditions. The assumption of non-Newtonian lubricant behavior seems to have a significant influence on the results as well. Results indicate that, in agreement with experiments, the variation of mean velocity causes changes in the deformed profiles of roughness while, on the other hand, the magnitude of slide to roll ratio (for sliding larger than ±50%) does not have influence on the size of the deformation.

Commentary by Dr. Valentin Fuster
J. Tribol. 2017;139(3):031503-031503-13. doi:10.1115/1.4035028.

A thermal elastohydrodynamic lubrication (TEHL) model is developed for a coated spur gear pair to investigate the effect of soft coatings and hard coatings on the tribological behavior of such a gear pair during meshing. The coating properties, i.e., the ratio of the Young's modulus between the coating and the substrate, and the coating thickness, are represented in the calculation of the elastic deformation. Discrete convolution, fast Fourier transform (DC-FFT) is utilized for the fast calculation of the surface deformation. The variation of the radius of curvature, the rolling speed, the slide-to-roll ratio, and the tooth load along the line of action (LOA) during meshing is taken into account and the transient squeeze effect is considered in the Reynolds equation. Energy equations of the solids and the oil film are derived. The temperature field and the pressure field are solved iteratively. The tribological behavior is evaluated in terms of the minimum film thickness, the maximum pressure, the temperature rise, the coefficient of friction, and the frictional power loss of the tooth contact during meshing. The results show discrepancies between the soft coating results and hard coating results.

Commentary by Dr. Valentin Fuster

### Research Papers: Friction and Wear

J. Tribol. 2016;139(3):031601-031601-10. doi:10.1115/1.4034022.

The dispenser ejects the ceramic filler and phosphor-containing liquid for making various products. When the particle-containing liquid is ejected under high-velocity conditions, however, the ejection reliability decreases because of the wear of the contact surface between the rod and nozzle even though these components are made of hard materials. It is therefore necessary to characterize the friction and wear properties of the hard materials, tungsten carbide (WC) and zirconium (Zr), with the high-viscosity liquid-containing nitride or yttrium aluminum garnet (YAG) particles under reciprocating conditions. Particle contents of 15 wt.% and 30 wt.% are added to the liquid. A reciprocating test was implemented to this end, and WC and Zr specimens were used. The liquid used in the experiment contains nitride and YAG. The experimental results show that the particles inside the liquid are worn out, leading to particle lubrication and the decrease in the coefficient of friction. Also, it is confirmed that the more the particles are, the less the coefficient of friction is due to particle lubrication. For each experimental condition, the coefficient of friction is measured and compared. Moreover, the contact surface of the specimen is analyzed using an electron microscope, and a profilometer is used to measure the surface roughness of the specimen before and after the test. The reciprocation friction and wear characteristics of WC and Zr with phosphor-containing liquid are evaluated by analyzing the experimental results.

Commentary by Dr. Valentin Fuster
J. Tribol. 2016;139(3):031602-031602-13. doi:10.1115/1.4034246.

The torsional fretting wear behaviors of artificial cervical disk were studied under different loads (50, 100, and 150 N) and angular displacement amplitudes (±2 deg, ±5 deg, and ±7 deg). The cervical prosthesis was simplified and designed as a ball-on-socket contact with the material configuration of ultrahigh molecular weight polyethylene (UHMWPE) and thermally oxidized titanium alloy. The fretting running regime changed from mixed regime (MR) to slip regime (SR) when the angular displacement increased from 2 deg to 7 deg. The frictional torque became larger with an increasing load at all of the angular displacement amplitudes. Larger load and angular displacement amplitude also led to more severe wear for UHMWPE ball. The damage patterns for titanium socket were only slight scratches and polished tracks on the raised oxide scales. However, the dominant wear mechanism was abrasive and adhesive wear as well as deformation for UHMWPE ball. Hence, titanium socket revealed less severe damage than UHMWPE ball due to the protection of oxide film. Arc-shaped wear scars and scratches appeared in both the central and edge zones of the ball and socket component, which were rather different with that of ball-on-flat. In addition, a new damage pattern, annular stress concentration damage, occurred on the edge of UHMWPE ball characterized by severe abrasive and adhesive wear.

Commentary by Dr. Valentin Fuster
J. Tribol. 2016;139(3):031603-031603-10. doi:10.1115/1.4034528.

This paper investigates the wear characteristics of a novel squeeze-film hip implant design. Key features of the design are elastic elements attached to the cup which provide a mechanical means for ball separation during the swing phase of the gait loading cycle. An Archard-based wear formulation was implemented utilizing the ansys finite element analysis program which relates contact pressure and sliding distance to linear wear depth. It is found that low-modulus elastic elements with bonded high-modulus metal coatings offer significant predicted improvement in linear and volumetric wear rates when compared with conventional implant geometries for gait cycle loading and kinematic conditions found in practice.

Topics: Wear , Design , Cycles , Stress
Commentary by Dr. Valentin Fuster

### Research Papers: Hydrodynamic Lubrication

J. Tribol. 2016;139(3):031701-031701-11. doi:10.1115/1.4034247.

Effects of groove textures on the performances for gaseous bubbles in the lubricant used for a textured journal bearing is studied under the consideration of thermal effect of lubricant. The Reynolds, energy, and Rayleigh–Plesset (RP) equations are solved simultaneously for simulating the behavior of the bubble. Numerical results show that the gaseous bubble radius shows a nonlinearly oscillation in a full cycle period, and high bubble pressure and temperature appear when the bubble collapses. Moreover, appropriately choosing groove length, width, or interval can reduce the maximum radius, collapse pressure, and collapse temperature of the bubble. There exists a critical groove depth minimizing the bubble pressure and temperature.

Commentary by Dr. Valentin Fuster
J. Tribol. 2016;139(3):031702-031702-17. doi:10.1115/1.4033053.

Commentary by Dr. Valentin Fuster
J. Tribol. 2016;139(3):031703-031703-17. doi:10.1115/1.4034244.

In the current study, a modified fast converging, mass-conserving, and robust algorithm is proposed for calculation of the pressure distribution of a cavitated axially grooved journal bearing based on the finite volume discretization of the Adams/Elrod cavitation model. The solution of cavitation problem is shown to strongly depend on the specific values chosen for the lubricant bulk modulus. It is shown how the new proposed scheme is capable of handling the stiff discrete numerical system for any chosen value of the lubricant bulk modulus ($β$) and hence a significant improvement in the robustness is achieved compared to traditionally implemented schemes in the literature. Enhanced robustness is shown not to affect the accuracy of the obtained results, and the convergence speed is also shown to be considerably faster than the widely used techniques in the literature. Effects of bulk modulus, static load, and mesh size are studied on numerical stability of the system by means of eigenvalue analysis of the coefficient matrix of the discrete numerical system. It is shown that the impact of static load and mesh size is negligible on numerical stability compared to dominant significance of varying bulk modulus values. Common softening techniques of artificial bulk modulus reduction is found to be tolerable with maximum two order of magnitudes reduction of $β$ to avoid large errors of more than 3–40% in calculated results.

Commentary by Dr. Valentin Fuster
J. Tribol. 2016;139(3):031704-031704-11. doi:10.1115/1.4034423.

The traditional eight-coefficient bearing model only considers the translational motion of the bearings and neglects the tilting motion and coupling effects between them. In this paper, the dynamic characteristics of the spiral-grooved opposed-hemisphere gas bearing considering five degrees-of-freedom are studied, and 50 dynamic coefficients including the translational, tilting, and coupling components are completely calculated. The Reynolds equations and their perturbed equations are solved by the finite element method to obtain the dynamic stiffness and damping coefficients. The effects of the tilting motion on the dynamic coefficients and response are analyzed, respectively. The results show that the coupling coefficients between the translational and tilting motions, which have been neglected in most previous studies, are significant at large eccentricity ratio. But these coupling coefficients have little effect on the dynamic response. On the other hand, the influences of the tilting motion on the synchronous response and natural frequency are remarkable and will decrease the stability of the rotor bearing system.

Commentary by Dr. Valentin Fuster
J. Tribol. 2017;139(3):031705-031705-11. doi:10.1115/1.4034616.

Commentary by Dr. Valentin Fuster

### Research Papers: Tribochemistry and Tribofilms

J. Tribol. 2016;139(3):032301-032301-6. doi:10.1115/1.4034381.

In the present work, the image features of cavitation erosion surfaces at different temperatures are extracted using wavelet decomposition transform. The results obtained indicate that the extract parameters, wavelet energy, and entropy can characterize the cavitation intensity in a similar manner to that of the mass loss and average particle size at different temperatures. Based on the analysis of the eroded surface and particle morphologies for different temperatures, it was found that the predominant failure mode was fatigue.

Commentary by Dr. Valentin Fuster

### Technical Brief

J. Tribol. 2016;139(3):034501-034501-5. doi:10.1115/1.4034206.

A starved lubrication experiment and analytical model have been developed to investigate the friction condition transition (FCT) at the interface between a piston ring and a cylinder liner with the piston ring reciprocating liner test rig. To obtain a solution for the friction condition transition, phase space trajectories are used to extract the transient features of the friction force. The trajectories have three typical patterns for starved lubrication conditions. The irregular friction force of different strokes is classified based on the trajectories. When the projection of the trajectories in the phase space enters into the third pattern variation, this indicates the onset and progression of scuffing. The autocorrelation analysis of the wear surface topography at the stroke end validates the characterization method.

Commentary by Dr. Valentin Fuster
J. Tribol. 2016;139(3):034502-034502-7. doi:10.1115/1.4034380.

In order to obtain the viscoelastic properties of friction linings and their effect on the tribological properties, three friction linings (K25, G30, and GM-3) are studied. Results show that higher creep and stress relaxation performances are favorable for promoting the friction coefficient. The friction coefficient of GM-3 is inversely proportional to the load. Meanwhile, the friction coefficients of K25 and G30 first increase to the peak under the load and later decrease. Under high load, GM-3 has the largest friction coefficient, whereas K25 has the smallest, with that of G30 being the median. The friction coefficient of GM-3 is inversely proportional to the loss factor, whereas those of K25 and G30 are directly proportional.

Commentary by Dr. Valentin Fuster
J. Tribol. 2016;139(3):034503-034503-5. doi:10.1115/1.4034457.

This study focuses on the thermohydrodynamic lubrication (THD) analysis of fluid film bearings with steps on the bearing surface, such as Rayleigh step. In general, the Reynolds equation does not satisfy the continuity of fluid velocity components at steps. This discontinuity results in the difficulty to solve the energy equation for the lubricants by finite differential method (FDM), because the energy equation needs the velocity components explicitly. The authors have solved this issue by introducing the equivalent clearance height and the equivalent gradient of the clearance height at steps. These parameters remove the discontinuity of velocity components, and the Reynolds equations can be solved for any bearing surfaces with step regions by FDM. Moreover, this method results in pseudocontinuous velocity components, which enables the energy equation to be solved as well. This paper describes this method with one-dimensional and equal grids model. The numerical results of pressure and temperature distributions by the proposed method for an infinite width Rayleigh step bearing agree well with the results obtained by solving full Navier–Stokes equations with semi-implicit method for pressure-linked equations revised (SIMPLER) method.

Commentary by Dr. Valentin Fuster
J. Tribol. 2017;139(3):034504-034504-4. doi:10.1115/1.4034534.

The wear characteristics of a hearing-aid battery assembly, which consist of an acrylonitrile-butadiene-styren (ABS) button cell compartment and a stainless steel bracket with the locking knob, have been studied in the current work to predict its lifespan in service. The main failure mechanism is the worn-out of the cell compartment by the locking knob when changing the battery. Its wear rate is determined by the relationship between knob geometry and corresponding pressure distribution on the worn surface. Due to the third-body entrapment, the wear rate is highly influenced by the presence of the debris, and fortunately, it can be reduced by applying microsurface texture onto the knob. Experiments are conducted here to validate the wear reduction mechanism.

Commentary by Dr. Valentin Fuster

### Discussion

J. Tribol. 2016;139(3):035501-035501-1. doi:10.1115/1.4034637.

Professor Sadeghi and his coworkers have been developing a method to estimate the rolling contact fatigue life of rolling bearings in recent years using a continuum damage mechanics (CDM) approach. Development of the method has involved progression from a defect-free and inclusion-free model to ones incorporating grain boundary cracks and inclusions.

Commentary by Dr. Valentin Fuster

### Closure

J. Tribol. 2016;139(3):036001-036001-2. doi:10.1115/1.4034638.

The premise of the continuum damage mechanics (CDM) model for rolling contact fatigue (RCF) is based on the hypothesis that the damage mechanisms for torsion fatigue and rolling contact fatigue are equivalent. Mr. Lewis commented that the verification of this hypothesis has not been carried out within the paper. However, the reasoning behind such hypothesis has been explained in many papers authored by Sadeghi et al. [16]. For the readers' benefit, the explanation is provided here in brief.

Commentary by Dr. Valentin Fuster