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Review Article: Review Articles

J. Tribol. 2018;140(4):040801-040801-20. doi:10.1115/1.4039226.

Partial slip texture surfaces have proven to be effective to improve load capacity and reduce coefficient of friction in slider and journal bearings. By controlling the partial slip surface texture properties, bearing with desired performance can be designed. It is of consequent interest to study the lubrication of slider and journal bearing systems taking into consideration design of partial slip texture surfaces. This paper aims at covering several investigation works related to slider and journal bearing lubricated with Newtonian fluids focusing on partial slip texture influence on bearing performance characteristics.

Commentary by Dr. Valentin Fuster

Research Papers: Applications

J. Tribol. 2018;140(4):041101-041101-13. doi:10.1115/1.4038953.

This paper reports a new three-dimensional model for heat conduction in a half-space containing inhomogeneities, applicable to frictional heat transfer, together with a novel combined algorithm of the equivalent inclusion method (EIM) and the imaging inclusion approach for building this model. The influence coefficients (ICs) for temperature and heat flux are obtained via converting the frequency response function (FRF) and integrating Green's function. The model solution is based on the discrete convolution and fast Fourier transform (DC-FFT) algorithm using the ICs, convenient for solving problems involving multiple elliptical inhomogeneities with arbitrary orientations. A group of parametric studies are conducted for understanding the thermal fields in the inhomogeneous half-space due to surface frictional heating, influenced by the properties of the inhomogeneity, its depth, and orientation.

Commentary by Dr. Valentin Fuster
J. Tribol. 2018;140(4):041102-041102-9. doi:10.1115/1.4039164.

Contact fatigue is a main fatigue mode of gears such as those used in wind turbines, due to heavy duties occurring in engineering practice. The understanding of the gear contact fatigue should be based on the interaction between the local material strength and the stress state. Under the rolling–sliding motion, the multi-axial stress state makes the gear contact fatigue problem more complicated. A numerical contact model is proposed to evaluate the contact fatigue life of an intermediate parallel gear stage of a megawatt level wind turbine gearbox. The gear meshing theory is applied to calculate the geometry kinematics parameters of the gear pair. The gear contact is assumed as a plane strain contact problem without the consideration of the influence of the helical angle. The quasi-static tooth surface load distribution is assumed along the line of action. The elastic mechanics theory is used to calculate the elastic stress field generated by surface tractions. The discrete convolute, fast Fourier transformation method is applied to estimate the subsurface stresses distributions. In order to describe the time-varying multi-axial stress states during contact, the Matake, Findley, and Dang Van multi-axial fatigue criteria are used to calculate the critical planes and equivalent stresses. Both the statistic and the deterministic fatigue life models are applied by choosing the Lundberg–Palmgren (LP), Zaretsky models, respectively. The effect of the residual stress distribution on the contact fatigue initiation lives is discussed. In addition, the crack propagation lives are estimated by using the Paris theory.

Commentary by Dr. Valentin Fuster

Research Papers: Coatings and Solid Lubricants

J. Tribol. 2018;140(4):041301-041301-9. doi:10.1115/1.4039135.

TiAlN and TiSiN coatings were deposited on YT15 cemented carbide using a cathodic arc ion plating (CAIP). The surface-cross section morphologies, chemical elements, surface roughness, phases, and chemical valences of as-obtained coatings were analyzed using a scanning electron microscopy (SEM), energy dispersive spectroscopy, atomic force microscopy (AFM), X-ray diffractometer (XRD), and X-ray photoelectron spectroscopy (XPS), respectively, and the bonding strength, hardness and Young's modulus of TiAlN and TiSiN coatings were measured using a scratch tester and nano-indentation, respectively, and the wear mechanism at high temperatures was also discussed. The results show that the surface roughness of TiAlN and TiSiN coatings is 69.1 and 58.0 nm, respectively, and the corresponding average particle size is 998.8 and 817.2 nm, respectively. The TiAlN coating is composed of TiAlN and AlN, while the TiSiN coating is composed of TiN and Si3N4. The bonding strength of TiAlN and TiSiN coatings is 84.3 and 72.6 N, respectively, the hardness and Young's modulus of TiAlN coating is 23.67 and 415.80 GPa, respectively, while that of TiSiN coating is 20.46 and 350.40 GPa, respectively. The average coefficients of friction (COFs) of TiAlN and TiSiN coatings are 0.4516 and 0.4807, respectively; the corresponding wear rate is 589.7 × 10−6 and 4142.2 × 10−6 mm3 N−1 s−1, respectively; the wear mechanism of TiAlN and TiSiN coatings is oxidation wear and abrasive wear.

Commentary by Dr. Valentin Fuster
J. Tribol. 2018;140(4):041302-041302-6. doi:10.1115/1.4039227.

To enhance the friction property of Al–Si alloy cylinder liner in running-in period, MoS2 coatings were electrodeposited on the chemical-etched surface of cylinder liner. The friction coefficient decreased by 15% comparing with the original honed surface, indicating the better friction property. This is because the synergistic action between solid lubricant and etched surface. MoS2 coatings prevent the direct contact between silicon particles and piston ring during friction. At top dead center, the oil film was thinnest and even was broken during the reciprocate friction. When oil film was invalidated, MoS2 coatings undertook lubrication. Then, MoS2 coatings were depleted, and advantage of etched surface became apparent.

Commentary by Dr. Valentin Fuster

Research Papers: Contact Mechanics

J. Tribol. 2018;140(4):041401-041401-11. doi:10.1115/1.4038984.

This work presents a finite element study of a two-dimensional (2D) plane strain fretting model of a half cylinder in contact with a flat block under oscillatory tangential loading. The two bodies are deformable and are set to the same material properties (specifically steel), however, because the results are normalized, they can characterize a range of contact scales (micro to macro), and are applicable for ductile material pairs that behave in an elastic-perfectly plastic manner. Different coefficients of friction (COFs) are used in the interface. This work finds that the edges of the contacting areas experience large von Mises stresses along with significant residual plastic strains, while pileup could also appear there when the COFs are sufficiently large. In addition, junction growth is investigated, showing a magnitude that increases with the COF, while the rate of growth stabilization decreases with the COF. The fretting loop (caused by the tangential force during the fretting motion) for the initial few cycles of loading is generated, and it compares well with reported experimental results. The effects of boundary conditions are also discussed where a prestressed compressed block is found to improve (i.e., reduce) the magnitude of the plastic strain compared to an unstressed block.

Commentary by Dr. Valentin Fuster
J. Tribol. 2018;140(4):041402-041402-8. doi:10.1115/1.4039231.

Greenwood and Tripp (GT model) have proposed that the contact analysis of two rough surfaces (two-rough-surface contact model) could be considered as an equivalent rough surface in contact with a rigid flat (single-rough-surface contact model). In this paper, by virtue of finite element method, the normal contact analysis was performed with two-rough-surface contact model and its equivalent single-rough-surface contact model, and it was verified that the resultant normal contact forces are in good agreement with each other for these two models, meanwhile the equivalent stress is a little bit lower for two-rough-surface model due to shoulder-to-shoulder contact. In contrast, the sliding contact analysis was also performed with these two models, respectively, and the results show a great disparity with each other in all contact parameters due to the strong plowing effects in two-rough-surface model. Therefore, this equivalence approach proposed by Greenwood and Tripp is only valid for normal contact of rough surfaces and not valid for sliding contact.

Commentary by Dr. Valentin Fuster

Research Papers: Elastohydrodynamic Lubrication

J. Tribol. 2018;140(4):041501-041501-7. doi:10.1115/1.4038985.

An “inverse” formulation is described for general problems of unsteady elastohydrodynamic lubrication (EHL). Spatial discretization gives an explicit initial-value ordinary differential equation (ODE) problem with (interior) nodal film thicknesses as state variables. Numerical results are compared with published experimental results for normal approach of a spherical surface to an elastic foundation.

Commentary by Dr. Valentin Fuster
J. Tribol. 2018;140(4):041502-041502-8. doi:10.1115/1.4039161.

Soft elastohydrodynamic lubrication (soft-EHL) is an important mechanism in biotribological systems. The soft-EHL has some distinct differences from the traditional hard-EHL, and a systematic analysis factoring in key features of the “softness” appears to be lacking. In this paper, a complete soft-EHL line-contact model is developed. In the model, the half-space approximation is replaced by the finite thickness analysis; the geometrical and material nonlinearity due to finite deformation is factored in; the surface velocities altered by the curvature effect are considered, and the load balance equation is formulated based on the deformed configuration. Solutions are obtained using a finite element method (FEM). The film thickness, pressure distributions, and material deformation are analyzed and discussed under various entraining velocities, elastic modulus, and material thickness of the soft layer. Comparisons are made between soft-EHL and hard-EHL modeling assumptions. The analyses show that the classical EHL modeling is not suitable for soft materials with high loads. The results show that the finite deformation (Green strain) should be considered in soft-EHL analysis. In the contact region, the hard EHL solver overestimates the pressure distribution and underestimates the film thickness and deformation.

Commentary by Dr. Valentin Fuster
J. Tribol. 2018;140(4):041503-041503-12. doi:10.1115/1.4039228.

This study investigates the effects of the microdimple texture on the friction and surface temperature performances of a ball-on-disk contact, operating under the speed and load ranges that cover typical gearing applications. Circular-shaped microdimple arrays with different dimple center distances and dimple depths are implemented on the ball surface to quantify the impacts of these two parameters on the friction coefficient and the maximum ball surface temperature. In addition, the contacts of three surface texture combinations, namely microdimpled and polished ball surface versus polished disk surface, polished ball surface versus polished disk surface, and ground ball surface versus ground disk surface, are compared to demonstrate any beneficial or detrimental effect of microdimples in heavily loaded high-speed applications. This study adopts a thermal mixed EHL point contact model, whose capability and accuracy have been well demonstrated by comparing to the experimental measurements, to quantify the deterministic tribological behavior within the contact, allowing the exploration of the underlying mechanism that governs the role of microdimples in the elastohydrodynamic lubrication (EHL).

Commentary by Dr. Valentin Fuster
J. Tribol. 2018;140(4):041504-041504-14. doi:10.1115/1.4039371.

In this study, a numerical model is developed for the analysis of elastohydrodynamic lubrication (EHL) at transient conditions during startup and shutdown processes. The time-dependent solutions are derived from an iterative algorithm with surface roughness involved, and the initial value is specified as the solution of the dry contact for the startup or steady-state solution of the lubrication contact at the starting velocity for the shutdown. The technique of discrete convolution and fast Fourier transform (DC-FFT) is employed to improve the computational efficiency. Solutions for smooth surfaces are compared with those obtained numerically and experimentally, and good consistency can be found. Profiles of pressure and film thickness and contours of subsurface stresses are analyzed to reveal the effects of acceleration/deceleration on the lubrication evolution. An isotropic roughness is then taken into account for the analysis. It is concluded that the coupling effects of the lubricant cavitation and oriented roughness would result in complex profiles of pressure and film thickness due to their disturbances to the lubrication film. A machined rough surface is presented to demonstrate the generality of the model. The analysis may potentially provide guidance to estimate the behavior of mechanical elements.

Commentary by Dr. Valentin Fuster

Research Papers: Friction and Wear

J. Tribol. 2018;140(4):041601-041601-7. doi:10.1115/1.4039029.

The present study includes the investigation on the frictional dynamics of hard and soft solid interface using low velocity linear tribometer. The effects of gelatin concentration, nanoparticles concentration, normal stress, and sliding velocity on the static and dynamic frictional shear stresses acting on the sliding gel block are studied using response surface methodology (RSM). The shear sliding experiments are conducted in steady sliding regime, well above the critical velocity. L31 orthogonal array consisting of five levels for each factor is selected for the experimentation and second-order quadratic model has been generated for both the responses. The mathematic models are validated with the available trends mentioned in the literature.

Commentary by Dr. Valentin Fuster

Research Papers: Hydrodynamic Lubrication

J. Tribol. 2018;140(4):041701-041701-10. doi:10.1115/1.4038864.

Spiral groove is one of the most common types of structures on gas mechanical seals. Numerical research demonstrated that the grooves designed for improving gas film lift or film stiffness often lead to the leakage increase. Hence, a multi-objective optimization approach specially for conflicting objectives is utilized to optimize the spiral grooves for a specific sample in this study. First, the objectives and independent variables in multi-objective optimization are determined by single objective analysis. Then, a set of optimal parameters, i.e., Pareto-optimal set, is obtained. Each solution in this set can get the highest dimensionless gas film lift under a specific requirement of the dimensionless leakage rate. Finally, the collinearity diagnostics is performed to evaluate the importance of different independent variables in the optimization.

Commentary by Dr. Valentin Fuster
J. Tribol. 2018;140(4):041702-041702-10. doi:10.1115/1.4038960.

The status of the lubricating oil transport in the piston skirt-cylinder liner has important influence on the lubrication of piston assembly frictional pair, the consumption of lubricating oil, the emission, and the performance degradation of lubrication oil. In this paper, based on the model of piston secondary motion, fluid lubrication and lubricating oil flow, the status of the lubricating oil transport between the piston skirt and the cylinder liner on different engine operating condition is calculated, and the quantity of lubricating oil retained on the surface of cylinder liner is mainly analyzed when the piston skirt moves from the top dead center to the bottom dead center. The results show that the variation of the quantity of retained lubricating oil is almost same in the corresponding stroke on different engine operating condition; the quantity of retained lubricating oil is dissimilar at different moment and is equal in principle at the piston top and bottom dead center. The quantity of lubricating oil retention is dissimilar at different moment in the intake stroke or expansion stroke, but the quantity of lubricating oil retention is equal in principle at the top and bottom dead center on different engine operating condition. When the engine is on the same load condition, as the engine rotational speed increasing, the quantity of retained lubricating oil is decreased in the whole intake stroke and the middle and later parts of expansion stroke, but the quantity of retained lubricating oil is increased in the front part of expansion stroke. When the engine is on the same rotational speed condition, the quantity of retained lubricating oil increases with the increasing engine load in the front part of expansion stroke, it does not vary with the engine load in principle in the middle and later part of expansion stroke, the variation that the quantity of retained lubricating oil varies with the engine load is dissimilar in the intake stroke on different engine rotational speed condition.

Commentary by Dr. Valentin Fuster
J. Tribol. 2018;140(4):041703-041703-8. doi:10.1115/1.4038958.

Biotribology and biomechanics are evolving fields that draw from many disciplines. A natural relationship particularly exists between tribology and biology because many biological systems rely on tribophysics for adhesion, lubrication, and locomotion. This leads to many biomimetic inspirations and applications. The current study looks to mimic the function of articular cartilage in purely mechanical systems. To accomplish this goal, a novel coupling of phenomena is utilized. A flexible, porous, viscoelastic material is paired with a hydrodynamic load to assess the feasibility and benefit of a biomimetic thrust bearing. This study presents the dynamic properties of the coupled system, as determined from transient to steady operating states. The results indicate that bio-inspired bearings may have application in certain tribological systems, including biomechanical joint replacements, dampers, flexible rotordynamic bearings, and seals.

Commentary by Dr. Valentin Fuster
J. Tribol. 2018;140(4):041704-041704-14. doi:10.1115/1.4039143.

The high-temperature gas-cooled reactor pebble-bed modular (HTR-PM) has been proposed by the Institute of Nuclear and New Energy Technology of Tsinghua University, in which the active magnetic bearings (AMBs) are equipped to support the high-speed rotor in the helium circulator system. In the case of AMB failures, emergencies, or overload conditions, the auxiliary bearing is applied as the backup protector to provide temporary mechanical support and displacement constraint for the dropping rotor. A detailed dynamic model is established to reveal the behavior of the dropping rotor. This model is able to describe the rotor displacement and inclination around each axis. The left and right rotor orbits are revealed. Dropping experiments are also carried out to reveal the actual behavior of the dropping rotor in helium. The predicted and experimental results will benefit further study, design, and application of the auxiliary bearing in HTR-PM helium circulator.

Topics: Bearings , Rotors , Helium
Commentary by Dr. Valentin Fuster
J. Tribol. 2018;140(4):041705-041705-11. doi:10.1115/1.4039134.

The development of new machines capable of running at high loads and speeds is an important industrial requirement, which demands that the performance envelope of the support systems for these machines be extended. Conventional full cylindrical fluid film bearings may present instability problems at higher speeds and loads, which has been countered by the use of different bearing bore shapes. In this paper, the performance characteristics of a novel fluid film bearing, comprising of a number of adjustable bearing elements is presented. Experiments have been performed to measure the static characteristics of the novel bearing with different radial and tilt adjustments of the bearing elements. The test bearing has an L/D ratio of 0.53 and was run at 2000, 5000, and 7000 rpm. The load on the bearing was varied from 0 to 600 N. Eccentricity, attitude angle, temperature of oil; power absorbed; and stability are measured. Experimental results are compared with those for a conventional axial groove plain cylindrical bearing having the same L/D ratio and run under similar conditions. Test results indicate that the novel bearing is very stable at zero loads and at 8800 rpm. Typical results obtained are presented. A few of the attributes and features of the novel bearing are also presented.

Topics: Bearings , Stress , Stability
Commentary by Dr. Valentin Fuster
J. Tribol. 2018;140(4):041706-041706-9. doi:10.1115/1.4039163.

The influence of donut-shaped bump texture on the hydrodynamic lubrication performance for parallel surfaces is presented in this paper. A mathematical equation has been applied to express the shape of three-dimensional donut-shaped bump texture. Numerical simulation of the pressure distribution of lubricant between a textured slider and a smooth, moving slider has been performed to analyze the geometrical parameters' influence on the hydrodynamic performance for textured surfaces. The numerical results show that the convex of the donut-shaped bump provides a microstep slider, which can form a convergent wedge and build up hydrodynamic pressure. Optimum values of horizontal spacing and bump height are obtained to maximize the hydrodynamic pressure. It is also noted that the average pressure increases monotonically with the increase of bump radius, but decreases with the increase of vertical spacing and dimple depth, respectively.

Commentary by Dr. Valentin Fuster
J. Tribol. 2018;140(4):041707-041707-9. doi:10.1115/1.4039409.

During ultrasonic vibration honing (UVH), a thin hydrodynamic oil film formed can seriously affect the cavitation effect in the grinding fluid, but the mechanism is still unclear now. Based on the hydrodynamics theory, a revised cavitation bubble model with oil film pressure is developed, and it has been calculated by the four-order Runge–Kutta method. The calculation results show that the oil film pressure under UVH is a positive–negative alternant pulse pressure, and it can induce the secondary expansion of the bubble, leading to double microjets during the process of the bubble collapsing. The effects of ultrasonic amplitude, ultrasonic frequency, oil film height, and reciprocation speed of the honing stone on the bubble dynamics are discussed. With the increase of ultrasonic amplitude, the amplitude of the bubble expansion is increased, and the oscillation interval is extended. As increasing normalized oil film height, the variation of the bubble first expansion is slight, while the amplitude of the bubble secondary expansion is reduced and the oscillation interval is also shortened. The main effect of ultrasonic frequency and reciprocation speed of the honing stone on the bubble dynamics is connected with the secondary bubble expansion. The bubble secondary expansion is decreased with the increasing reciprocation speed of the honing stone, ultrasonic frequency, and oil film height. The results of the simulations are consistent with the surface roughness measurements well, which provides a theoretical prediction method of cavitation bubbles control.

Commentary by Dr. Valentin Fuster
J. Tribol. 2018;140(4):041708-041708-15. doi:10.1115/1.4039370.

The bulk-flow theory for the rotordynamic (RD) fluid force has been investigated for many years. These conventional bulk-flow analyses were performed under the assumption and restriction that the whirl amplitude was very small compared to the seal clearance while actual turbomachinery often causes the large amplitude vibration, and these conventional analyses may not estimate its RD fluid force accurately. In this paper, the perturbation analysis of the bulk-flow theory is extended to investigate the RD fluid force in the case of concentric circular whirl with relatively large amplitude. A set of perturbation solutions through third-order perturbations are derived explicitly. It relaxes the restriction of conventional bulk flow analysis, and it enables to investigate the RD fluid force for the whirl amplitude up to about a half of the clearance. Using derived equations, the nonlinear analytical solutions of the flow rates and pressure are deduced, and the characteristics of the RD fluid force are investigated in both radial and tangential directions. The influence of the whirl amplitude on the RD fluid force is explained and validated by comparing with computational fluid dynamics (CFD) analysis. These results are useful for the analysis and prediction of frequency response of the vibration of the rotating shaft system considering the RD fluid forces.

Commentary by Dr. Valentin Fuster

Research Papers: Lubricants

J. Tribol. 2018;140(4):041801-041801-10. doi:10.1115/1.4038957.

The present study is focused on the performance evaluation of MoS2, H3BO3, and multiwall carbon nanotubes (MWCNT) used as the potential oil additives in base oil for aluminum metal matrix composites (AMMC)–steel (EN31) tribocontact. Al–B4C composite is used for this purpose; based on a set of preliminary investigation under unlubricated and fresh oil lubrication, three different types of AMMCs (Al–SiC, Al–B4C, and Al–SiC–B4C) were used. A pin-on-disk tribometer is used for all the friction and wear tests under operating condition of load 9.8 N and sliding velocity of 0.5 m/s. From the particle-based wet tribology, it is clear that both the additives H3BO3 and MWCNT improve the friction as well as wear behavior for selected composite contacts. Multiwall carbon nanotubes emerged out as superior among all the additives, whereas MoS2 additives show marginal enhancement in frictional performance under given operating conditions. Fractography and morphological study of pin specimens are carried out to identify the underlying friction and wear mechanisms.

Commentary by Dr. Valentin Fuster

Research Papers: Other (Seals, Manufacturing)

J. Tribol. 2018;140(4):042201-042201-7. doi:10.1115/1.4038863.

The wear of dynamic sealing elements, i.e., elements that seal against a moving counter-surface, is highly complex. In dry-running reciprocating compressors, these sealing elements, commonly referred to as packing rings, have to seal the compressed gas against the environment along the reciprocating rod. Since the packing rings' seal effect arises from the differential pressure to be sealed, it is of paramount importance to take into account the gas pressure drop across the dynamic sealing surface. This paper presents a numerical model that allows us to calculate how the wear of such a packing ring evolves with time. An analytical solution is used to verify the numerical model.

Commentary by Dr. Valentin Fuster
J. Tribol. 2018;140(4):042202-042202-11. doi:10.1115/1.4038959.

Rubber O-rings are widely applied in the static and dynamic seals of machinery, energy, chemical, aviation, and other fields. Mechanical behavior and sealing performance of the O-ring were investigated in this paper. Effects of precompression amount, fluid pressure, friction coefficient on the static and dynamic sealing performances of the O-ring were studied. The results show that the maximum stress appears on the inside but not surface of the O-ring. The static sealing performance increases with the increasing of fluid pressure and compression amount. Reciprocating dynamic sealing performance of the rubber O-ring is different with its static sealing performance; the stress distribution and deformation are changing in reciprocating motion. Sealing performance in outward stroke is better than it in the inward stroke. Overturn of the O-ring occurs when the friction torque is greater than the torque that caused by fluid pressure in the inward stroke. Distortion, bitten, and fatigue failure are the main failure modes of the O-ring in the dynamic seal. Those results can be used in design, installation, and operation of rubber O-rings in static and dynamic seals.

Commentary by Dr. Valentin Fuster

Research Papers: Tribochemistry and Tribofilms

J. Tribol. 2018;140(4):042301-042301-10. doi:10.1115/1.4039162.

The nonprotective tribolayers of the titanium alloy were modified into additives-containing tribolayers through an artificial addition of multilayer graphene (MLG), Fe2O3 nanomaterials, or their mixtures with various proportions on the titanium alloy/steel sliding interface. The sustainability of the modified tribolayers under a high load was evaluated by the critical sliding distance for a mild-to-severe wear transition. The modified tribolayers were found to significantly improve or deteriorate tribological performance of the titanium alloy, which was decided by their ingredients. The pure MLG- or Fe2O3-containing tribolayers, because of their lacking load-bearing or lubricant capacity, presented poor sustainability and readily lost protection to cause high wear loss or frictional coefficient. However, for the addition of various mixtures of MLG and Fe2O3, the modified tribolayers possessed a double-layer structure consisting of friction-reducing MLG- and wear-resistant Fe2O3-predominated layers. They presented a sustainable protection, thus remarkably improving the tribological performance of the titanium alloy.

Commentary by Dr. Valentin Fuster

Technical Brief

J. Tribol. 2018;140(4):044501-044501-4. doi:10.1115/1.4038952.

The elastic approach of a w roller compressed by two flat plates is a basic building block in roller bearing design. According to the theory of contact mechanics, a finite element (FE) model was established in this paper to study the contact problem of a hollow roller. Research results show that deformation of the hollow roller due to contact has a strong relationship with roller's hollowness ratio. A new equation for calculating the contact deformation of a hollow roller is proposed. In addition, it is found that the accuracy of existing calculation method for bending deformation is also worth studying, and a new equation for calculating bending deformation of a hollow roller is established by data fitting. The experimental results are also presented to support the results of this work.

Commentary by Dr. Valentin Fuster

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