Special Issue in Elastohydrodynamics: Remembering Ramsey Gohar

A special issue of Lubricants (ISSN 2075-4442).

Deadline for manuscript submissions: closed (30 June 2022) | Viewed by 34378

Special Issue Editors

Mechanical Engineering Department, North Dakota State University, Fargo, ND 58102, USA
Interests: elastohydrodynamic lubrication; computational mechanics; biomechanics; constitutive relations
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

It is with great sadness that we note the passing of Dr. Ramsey Gohar of Imperial College London on 12th March 2021. Ramsey was one of the pioneering contributors to the fields of contact mechanics and elastohydrodynamic lubrication (EHL). He furthered the fundamental understanding of EHL through the development of state-of-the-art experimental methods and numerical analysis techniques. His innovative works were published in Nature [1], Proceedings of the Royal Society of London [2] and New Scientist [3], as well as in other renowned scientific journals, for example [4–9].

Ramsey’s key research interests encompassed all aspects of EHL and its many applications, including mechanics of concentrated contacts, impact dynamics, ball and rolling element bearings, cam–follower pairs, and journal, thrust, and externally pressurised bearings, to name but a few. His contributions to the fundamentals of EHL and its theoretical formulation, as well as to microscale contact mechanics, were particularly outstanding [1,2,5–11]. In addition, he authored highly regarded books [12,13] for a broad range of audience: from undergraduates, postgraduates and practising engineers to highly accomplished researchers.

With his development of optical interferometric study of EHL [1,14] and use of ultra-thin film micro-miniature transducers under both contacting [15–17] and impacting [18] EHL conditions, Ramsey carved a special place for himself in the history of EHL and bearings.

He was an approachable, helpful, unassuming educator who aided the career of many professionals in both academia and industry, and whose many papers and books will continue to do so well into the future.

As two of his ex-researchers, we invite contributions to this special issue commemorating the many works of an outstanding scientist, Dr. Ramsey Gohar.

Submissions (in the form of original papers, technical notes, and reviews of specific aspects of EHL and contact mechanics) in the following fields are welcome:

- Fundamentals of elastohydrodynamic lubrication (EHL): theoretical developments, measurement techniques including interferometry, spectrometry, thin film technology and its applications in tribology;

- Contact mechanics of semi-infinite and bonded layered elastic solids with particular application to bearings;

- Shaft and bearing systems: rotor dynamics, tribodynamics.

References:

[1] Gohar, R. and Cameron, A., “Optical measurement of oil film thickness under elasto-hydrodynamic lubrication”, Nature, 1963, 200(4905), pp. 458–459.

[2] Cameron, A. and Gohar, R., “Theoretical and experimental studies of the oil film in lubricated point contact”, Proceedings of the Royal Society of London, Series A: Mathematical and Physical Sciences, 1966, 291(1427), pp. 520–536.

[3] Gohar, R. and Thorp, N., “Keeping the bearings rolling (ball and roller bearing fabrication and performance)”, New Scientist, 1977, 74, pp. 124–126.

[4] Gohar, R. and Cameron, A., “The mapping of elastohydrodynamic contacts”, ASLE Transactions, 1967, 10(3), pp. 215–225.

[5] Thorp, N. and Gohar, R., “Oil film thickness and shape for a ball sliding in a grooved raceway”, Trans. ASME, Journal of Tribology, 1972, 94, pp. 199–208

[6] Jalali-Vahid, D., Rahnejat, H., Gohar, R. and Jin, Z.M., “Comparison between experiments and numerical solutions for isothermal elastohydrodynamic point contacts”, Journal of Physics, D: Applied Physics, 1998, 31(20):2725.

[7] Mostofi, A. and Gohar, R., “Oil film thickness and pressure distribution in elastohydrodynamic point contacts”, Proceedings of the Institution of Mechanical Engineers, Journal of Mechanical Engineering Science, 1982, 24(4), pp. 173–182.

[8] Mostofi, A. and Gohar, R., "Elastohydrodynamic lubrication of finite line contacts", Trans. ASME, Journal of Lubrication Technology, 1983, 105(4), pp. 598–604.

[9] Kushwaha, M., Rahnejat, H. and Gohar, R., “Aligned and misaligned contacts of rollers to races in elastohydrodynamic finite line conjunctions”, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 2002, 216(11), pp. 1051–1070.

[10] Johns, P.M. and Gohar, R., “Roller bearings under radial and eccentric loads”, Tribology International, 14(3), pp.131–136.

[11] Teodorescu, M., Rahnejat, H., Gohar, R. and Dowson, D., “Harmonic decomposition analysis of contact mechanics of bonded layered elastic solids”, Applied Mathematical Modelling, 2009, 33(1), pp. 467–485.

[12] Gohar, R., “Elastohydrodynamics”, 2nd Edition, World Scientific, Singapore, 2001

[13] Gohar, R. and Rahnejat, H., “Fundamentals of Tribology”, 3rd Edition, World Scientific, London, 2018.

[14] Bahadoran, H. and Gohar, R., “Research note: end closure in elastohydrodynamic line contact”, Proceedings of Institution of Mechanical Engineers, Journal of Mechanical Engineering Science. 1974, 16(4), pp. 276–278.

[15] Johns‐Rahnejat, P.M. and Gohar, R., “Measuring contact pressure distributions under elastohydrodynamic point contacts”, Tribotest, 1994, 1(1), pp. 33–53.

[16] Gohar, R. and Safa, M.M.A., “Measurement of contact pressure under elastohydrodynamic lubrication conditions”, In Tribology and Dynamics of Engine and Powertrain, Woodhead Publishing, 2010, pp. 222–245.

[17] Mohammadpour, M., Johns-Rahnejat, P.M., Rahnejat, H. and Gohar, R., “Boundary conditions for elastohydrodynamics of circular point contacts”, Tribology Letters, 2014, 53(1), pp. 107–118.

[18] Safa, M. M. A. and Gohar, R., "Pressure distribution under a ball impacting a thin lubricant layer", Trans. ASME, Journal of Tribology, 1986, 108(3), pp. 372–376.

Dr. Patricia Johns-Rahnejat
Prof. Dr. Ghodrat Karami
Guest Editors

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Keywords

  • elastohydrodynamics
  • interferometry and thin film tribotronics
  • contact mechanics and contact fatigue
  • elastostatics
  • tribodynamics
  • bearings
  • gears

Published Papers (12 papers)

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Research

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17 pages, 5573 KiB  
Article
The Applicability of the Hertzian Formulas to Point Contacts of Spheres and Spherical Caps
Lubricants 2022, 10(10), 233; https://doi.org/10.3390/lubricants10100233 - 23 Sep 2022
Cited by 4 | Viewed by 3035
Abstract
Hertzian formulas are commonly used for the evaluation of deformation and pressure distribution of non-conformal and slightly conformal mechanical pairs to estimate component stiffness and durability. For the sake of simplicity, their use is extended even to those cases in which Hertz’s hypotheses [...] Read more.
Hertzian formulas are commonly used for the evaluation of deformation and pressure distribution of non-conformal and slightly conformal mechanical pairs to estimate component stiffness and durability. For the sake of simplicity, their use is extended even to those cases in which Hertz’s hypotheses do not hold. This paper summarizes Hertz’s theory and compares the results obtained with theoretical and finite element analysis of the point contact of non-conformal and conformal pairs made of spheres, caps, and spherical seats. This study was motivated by the non-Hertzian behavior of a tilting pad bearing ball-and-socket pivot conforming contact observed by the authors in previous experiments. In particular, the displacement and force relation were investigated by varying the geometrical parameters, the materials, the boundary conditions, and the friction coefficient. In the case of non-conformal contact, the parameter variations had negligible effect in agreement with Hertz’s theory while for conformal contact, the cap and seat height and width and the relative clearance were the most influential parameters on the non-Hertzian behavior. These novel results indicate that in conformal pairs, such as for tilting pad bearing ball-and-socket pivots, whenever Hertz’s hypotheses are not satisfied and the assessment of contact stiffness is crucial, Hertzian formulas should not be applied as done in common practice, instead more accurate numerical or experimental evaluation should be made. Full article
(This article belongs to the Special Issue Special Issue in Elastohydrodynamics: Remembering Ramsey Gohar)
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10 pages, 391 KiB  
Article
Lubricated Impact Dynamics and Pressure Spike Generation: Expanding on Contributions of Dr. R. Gohar
Lubricants 2022, 10(8), 186; https://doi.org/10.3390/lubricants10080186 - 16 Aug 2022
Viewed by 963
Abstract
The current paper focuses on the research of Dr. R. Gohar and in particular on his impacting ball and pressure spike measurement work. Its scope then expands to discuss contributions from other researchers concerning these two fields. The authors combined the two themes [...] Read more.
The current paper focuses on the research of Dr. R. Gohar and in particular on his impacting ball and pressure spike measurement work. Its scope then expands to discuss contributions from other researchers concerning these two fields. The authors combined the two themes in a numerical study of an impacting contact. This study shows the detailed position of the pressure spike as a function of time. Then, the pressure spike position velocity is derived, and it is demonstrated that this velocity varies with time. As such, the paper concludes that the pressure spike shape itself must vary with time. Full article
(This article belongs to the Special Issue Special Issue in Elastohydrodynamics: Remembering Ramsey Gohar)
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21 pages, 3831 KiB  
Article
Non-Newtonian Thermo-Elastohydrodynamics and Sub-Surface Stress Field of High-Performance Racing Spur Gears
Lubricants 2022, 10(7), 146; https://doi.org/10.3390/lubricants10070146 - 08 Jul 2022
Cited by 9 | Viewed by 1474
Abstract
Meshing teeth pairs of involute spur gears often form the final drive of high-performance motorsport transmissions. They are subject to high normal and shear loading. Under transient conditions pertaining to a meshing cycle, the contact conditions alter from the onset of teeth pair [...] Read more.
Meshing teeth pairs of involute spur gears often form the final drive of high-performance motorsport transmissions. They are subject to high normal and shear loading. Under transient conditions pertaining to a meshing cycle, the contact conditions alter from the onset of teeth pair engagement through to maximum normal loading, followed by contact separation. Sliding motion only ceases instantaneously at the pitch point. The regime of lubrication remains mostly in non-Newtonian thermo-elastohydrodynamic conditions. The results show that a starved inlet boundary is attained throughout most of the meshing cycle which leads to the diminution of the pressure spike at the exit from the contact conjunction. The reversing sub-surface shear stresses are the main source of the onset of any inelastic deformation, which is dominated by the primary pressure peak in compliance with the Hertzian maximum pressure. The shear stress field is supplemented by an induced field due to the presence of the pressure spike. Under starved conditions this secondary stress field is diminished. The combined solution of elastohydrodynamics with a thermal network model, non-Newtonian lubricant traction, and sub-surface stress evaluation provides for a comprehensive solution not hitherto reported in the literature. Full article
(This article belongs to the Special Issue Special Issue in Elastohydrodynamics: Remembering Ramsey Gohar)
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19 pages, 3067 KiB  
Article
An Analytical Approach for Predicting EHL Friction: Usefulness and Limitations
Lubricants 2022, 10(7), 141; https://doi.org/10.3390/lubricants10070141 - 06 Jul 2022
Cited by 3 | Viewed by 1778
Abstract
The article studies the friction coefficient in elastohydrodynamic lubrication (EHL) by means of analytically obtained equations for different contact geometries. The introduction of some simplifications allows for the simultaneous consideration of piezoviscous, pseudoplastic and thermal phenomena, resulting in complete and realistic models, which [...] Read more.
The article studies the friction coefficient in elastohydrodynamic lubrication (EHL) by means of analytically obtained equations for different contact geometries. The introduction of some simplifications allows for the simultaneous consideration of piezoviscous, pseudoplastic and thermal phenomena, resulting in complete and realistic models, which provide results in a quick and easy manner. The predictive potential of this analytical approach is analyzed by comparing the estimates of friction with full-EHL simulations and experimental data under different operating conditions. The results obtained allow us to discuss the influence of some assumptions taken into account and the scope of applicability of the models, in order to determine their usefulness and limitations. Full article
(This article belongs to the Special Issue Special Issue in Elastohydrodynamics: Remembering Ramsey Gohar)
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16 pages, 4963 KiB  
Article
Electrical Field Strength in Rough Infinite Line Contact Elastohydrodynamic Conjunctions
Lubricants 2022, 10(5), 87; https://doi.org/10.3390/lubricants10050087 - 05 May 2022
Cited by 4 | Viewed by 2044
Abstract
Rolling element bearings are required to operate in a variety of use cases that determine voltage potentials will form between the rolling elements and races. When the electrical field strength causes the dielectric breakdown of the intermediary lubricant film electrical discharge can damage [...] Read more.
Rolling element bearings are required to operate in a variety of use cases that determine voltage potentials will form between the rolling elements and races. When the electrical field strength causes the dielectric breakdown of the intermediary lubricant film electrical discharge can damage the bearing surfaces. To reduce the prevalence and severity of electrical discharge machining an improved understanding of the coupled electrical and mechanical behavior is necessary. This paper aims to improve understanding of the problem through a combined elastohydrodynamic and electrostatic numerical study of charged elastohydrodynamic conjunctions. The results show the effect of amplitude reduction means that for typical surface topographies found in EHL conjunctions the maximum field strength is adequately predicted by the elastohydrodynamic minimum film thickness and potential difference. The paper also indicates the width of the elevated electrical field strength region is dependent on EHL parameters which could have important implications on the magnitude of current density during dielectric breakdown. Full article
(This article belongs to the Special Issue Special Issue in Elastohydrodynamics: Remembering Ramsey Gohar)
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29 pages, 7710 KiB  
Article
Effect of Preload on the Vibrations of EHL Angular Contact Ball Bearings: Theoretical and Experimental Results
Lubricants 2022, 10(3), 46; https://doi.org/10.3390/lubricants10030046 - 16 Mar 2022
Cited by 3 | Viewed by 3225
Abstract
The vibrations of a shaft in rotary mechanical systems supported by angular contact ball bearings are investigated theoretically and experimentally for various preloads in this paper. In the theoretical part of the study, a dynamic bearing model is presented, a rigid shaft supported [...] Read more.
The vibrations of a shaft in rotary mechanical systems supported by angular contact ball bearings are investigated theoretically and experimentally for various preloads in this paper. In the theoretical part of the study, a dynamic bearing model is presented, a rigid shaft supported by EHL angular contact bearing has been modelled as 5 DoF. Non-linear equations of motion are solved numerically by the Runge–Kutta method. In the second part of the study, an experimental setup that enables performing different operating cases has been designed to validate the theoretical results. Theoretical and experimental data are investigated and compared in both time and frequency domains and the results are compared. It is observed from both the theoretical and experimental studies that preload has a significant effect on the vibration behaviour. Results show that the increase in preload reduces the amplitude of the variable compliance frequencies of bearing, the natural frequency of system is shifted to a higher value, and using signal processing with an envelope spectrum gives better results in spectral analysis; small deviations occur between the theoretical and the experimental data due to modulation and noise from machine elements such as gear, motor, misalignment, waviness, etc. Therefore, the presented dynamic bearing model can be used with a reasonable accuracy to examine effect of preload on the vibration of shaft-bearing system. Full article
(This article belongs to the Special Issue Special Issue in Elastohydrodynamics: Remembering Ramsey Gohar)
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20 pages, 7516 KiB  
Article
High-Performance Ni-SiC Coatings Fabricated by Flash Heating
Lubricants 2022, 10(3), 42; https://doi.org/10.3390/lubricants10030042 - 14 Mar 2022
Cited by 4 | Viewed by 2071
Abstract
In this research, a novel flash heating coating application technique was utilized to create Ni-SiC coatings on carbon steel substrates with SiC contents much higher than is achievable using certain conventional coating techniques. Hardness profiles showed that the coatings improved the substrate by [...] Read more.
In this research, a novel flash heating coating application technique was utilized to create Ni-SiC coatings on carbon steel substrates with SiC contents much higher than is achievable using certain conventional coating techniques. Hardness profiles showed that the coatings improved the substrate by as much as 121%, without affecting the substrate. Tribotests showed that the wear performance was improved by as much as 4.7× in terms of the wear rate (mm3/N·m) for the same coating when using an Al2O3 counterpart. Pure SiC coatings as a reference were also fabricated. However, the SiC coatings experienced elemental diffusion of Fe from the carbon steel substrate into the coating during fabrication. This occurred due to the increased heat input required for pure SiC to fuse to the substrate compared to the Ni-SiC coatings and resulted in decreased tribological performance. Diffusion of Fe into the coating weakened the coating’s hardness and reduced the resistance to wear. It was concluded that ceramic–metallic composite coatings can successfully be fabricated utilizing this novel flash heating technique to improve the wear resistance of ceramic counterparts. Full article
(This article belongs to the Special Issue Special Issue in Elastohydrodynamics: Remembering Ramsey Gohar)
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18 pages, 2207 KiB  
Article
Modelling of Lubricated Electrical Contacts
Lubricants 2022, 10(3), 32; https://doi.org/10.3390/lubricants10030032 - 22 Feb 2022
Cited by 11 | Viewed by 3416
Abstract
Electrical contacts, although critically important for a wide range of applications, are susceptible to degradation due to fretting corrosion, especially when sliding and vibrations occur. To overcome fretting corrosion and sliding wear, lubricants are often used. However, the use of lubricants can cause [...] Read more.
Electrical contacts, although critically important for a wide range of applications, are susceptible to degradation due to fretting corrosion, especially when sliding and vibrations occur. To overcome fretting corrosion and sliding wear, lubricants are often used. However, the use of lubricants can cause other detrimental issues. Lubricants usually consist of non-conductive fluids such as hydrocarbons and fluorocarbons. Due to fluid dynamics, when sliding, vibration or other excitation occurs, these fluids can cause prolonged gaps between the conducting metal surfaces. Practically, this has been observed in data centers where vibrations due to technician maintenance or even earthquakes can occur. Depending on the viscosity and roughness of the surfaces, the time it takes these connector surfaces to return to solid conductive contact can be many seconds or longer. This work uses a novel theoretical model of the coupled fluid and solid mechanics between the rough metallic surfaces to evaluate these intermittent breaks in contact due to sliding. The influence of variation in lubricant properties, roughness, contact radius and contact force are considered by the model. Full article
(This article belongs to the Special Issue Special Issue in Elastohydrodynamics: Remembering Ramsey Gohar)
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17 pages, 5563 KiB  
Article
Remarks on Modeling the Oil Film Generation of Rod Seals
Lubricants 2021, 9(9), 95; https://doi.org/10.3390/lubricants9090095 - 16 Sep 2021
Cited by 4 | Viewed by 2594
Abstract
The oil film generation of a U-cup rod seal and the oil film thickness on the rod after outstroke were analyzed analytically, numerically, and experimentally. The analyzed sealing system consists of an unmodified, commercially available U-cup, a polished rod, and mineral oil. The [...] Read more.
The oil film generation of a U-cup rod seal and the oil film thickness on the rod after outstroke were analyzed analytically, numerically, and experimentally. The analyzed sealing system consists of an unmodified, commercially available U-cup, a polished rod, and mineral oil. The inverse theory of hydrodynamic lubrication (IHL) and an elastohydrodynamic lubrication (EHL) model—both based on the Reynolds equation for thin lubricating films—were utilized to simulate the oil film generation. In the EHL analysis, physical parameters and numerical EHL parameters were varied. Both the analytical and numerical results for the varied parameters show that the film thickness follows a square-root function (i.e., with a function exponent of 0.5) with respect to the product of dynamic viscosity and rod speed, also referred to as the duty parameter. In comparison to the analytical and numerical results, the film thickness obtained via ellipsometry measurements is a function of the duty parameter with an exponent of approximately 0.85. Possible causes for the discrepancy between theory and experiments are discussed. A potential remedy for the modeling gap is proposed. Full article
(This article belongs to the Special Issue Special Issue in Elastohydrodynamics: Remembering Ramsey Gohar)
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Review

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23 pages, 1179 KiB  
Review
Rough Surface Contact Modelling—A Review
Lubricants 2022, 10(5), 98; https://doi.org/10.3390/lubricants10050098 - 13 May 2022
Cited by 19 | Viewed by 6068
Abstract
It has been shown experimentally that boundary friction is proportional to load (commonly known as Amontons’ law) for more than 500 years, and the fact that it holds true over many scales (from microns to kilometres, and from nano-Newtons to Mega-Newtons) and for [...] Read more.
It has been shown experimentally that boundary friction is proportional to load (commonly known as Amontons’ law) for more than 500 years, and the fact that it holds true over many scales (from microns to kilometres, and from nano-Newtons to Mega-Newtons) and for materials which deform both elastically and plastically has been the subject of much research, in order to more fully understand its wide applicability (and also to find any deviations from the law). Attempts to explain and understand Amontons’ law recognise that real surfaces are rough; as such, many researchers have studied the contact of rough surfaces under both elastic and plastic deformation conditions. As the focus on energy efficiency is ever increasing, machines are now being used with lower-viscosity lubricants, operating at higher loads and temperatures, such that the oil films separating the moving surfaces are becoming thinner, and there is a greater chance of mixed/boundary lubrication occurring. Because mixed/boundary lubrication occurs when the two moving rough surfaces come into contact, it is thought timely to review this topic and the current state of the theoretical and experimental understanding of rough-surface contact for the prediction of friction in the mixed/boundary lubrication regime. Full article
(This article belongs to the Special Issue Special Issue in Elastohydrodynamics: Remembering Ramsey Gohar)
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18 pages, 1246 KiB  
Review
Increase Service Life for Rail Wheel Bearings—A Review of Grease Lubrication for This Application
Lubricants 2022, 10(3), 36; https://doi.org/10.3390/lubricants10030036 - 03 Mar 2022
Cited by 5 | Viewed by 3574
Abstract
Billions of rolling bearings (RB) are in use today in a broad and diverse range of applications. In the mobility sector, RB help to reduce friction losses and increase efficiency. In rail applications, the rail wheel rolling bearing is a critical component, which [...] Read more.
Billions of rolling bearings (RB) are in use today in a broad and diverse range of applications. In the mobility sector, RB help to reduce friction losses and increase efficiency. In rail applications, the rail wheel rolling bearing is a critical component, which requires a strict maintenance schedule. In this literature review, grease lubrication in RB is reviewed and potential ways to improve the service life of greases in RB are discussed with special emphasis on the application as rail wheel bearing. Understanding the discussed fundamental lubrication processes is the key to increase the service life of the rail wheel bearings and might provide a basis for future work that aims to make maintenance of these bearings condition-based (condition-based maintenance). This review is primarily intended for R&D professionals from rail (and related) industry and others being interested in a rather brief, but fundamental, overview of this subject. Full article
(This article belongs to the Special Issue Special Issue in Elastohydrodynamics: Remembering Ramsey Gohar)
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Other

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11 pages, 612 KiB  
Commentary
Fundamentals and Advances in Elastohydrodynamics: The Role of Ramsey Gohar
Lubricants 2021, 9(12), 120; https://doi.org/10.3390/lubricants9120120 - 08 Dec 2021
Cited by 3 | Viewed by 2449
Abstract
This paper commemorates Ramsey Gohar by acknowledging his contributions to the fields of contact mechanics and elastohydrodynamic lubrication (EHL) within the context of the developments of these subjects. A historical discourse is provided on elastohydrodynamics, from its inception in the 1940s to present. [...] Read more.
This paper commemorates Ramsey Gohar by acknowledging his contributions to the fields of contact mechanics and elastohydrodynamic lubrication (EHL) within the context of the developments of these subjects. A historical discourse is provided on elastohydrodynamics, from its inception in the 1940s to present. We demonstrate that Ramsey Gohar was not only a pioneer in the discoveries and fundamentals of the subject, but also led or contributed significantly to continual advances in the understanding of EHL and its diverse applications. Full article
(This article belongs to the Special Issue Special Issue in Elastohydrodynamics: Remembering Ramsey Gohar)
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