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The modified Reynolds equation for non-Newtonian lubricant is derived using the viscous adsorption theory for thin-film elastohydrodynamic lubrication (TFEHL) of circular contacts. The proposed model can reasonably calculate the phenomenon in the thin-film lubrication (TFL) unexplained by the conventional EHL model. The differences between classical EHL and TFEHL with the non-Newtonian lubricants are discussed.

The power-law lubricating film between the elastic surfaces is modeled in the form of three layers: two adsorption layers on each surface and one middle layer. The modified Reynolds equation with power-law fluid is derived for TFEHL of circular contacts using the viscous adsorption theory. The finite difference method and the Gauss–Seidel iteration method are used to solve the modified Reynolds equation, elasticity deformation, lubricant rheology equations and load balance equations simultaneously.

The simulation results reveal that the present model can reasonably calculate the pressure distribution, the film thickness, the velocity distribution and the average viscosity in TFL with non-Newtonian lubricants. The thickness and viscosity of the adsorption layer and the flow index significantly influence the lubrication characteristics of the contact conjunction.

The present model can reasonably predict the average viscosity, the turning point and the derivation (log film thickness vs log speed) phenomena in the TFEHL under constant load conditions.

The purpose of this paper is to deal with the qualitative analysis of hydrodynamic lubrication of asymmetric rollers with non-Newtonian incompressible power law lubricants including Newtonian.

The fluid flow governing equations such as equation of motion along with continuity and thermal equations are solved first analytically and investigated numerically by the Runge-Kutta Fehlberg method.

As a result of this work, it is found that there is a significant change in temperature, pressure, load and traction with Newtonian and non-Newtonian fluids.

The authors considered incompressible hydrodynamic lubrication of two rigid asymmetric rollers, one of them is assumed to be adiabatic. The convection term of the heat flow equation is taken in its average form.

It is a theoretical problem of two heavily loaded rigid cylindrical rollers with cavitations, where the consistency of the power law lubricant is assumed to vary with pressure and the mean film temperature. It has not appeared in the literature.

The purpose of this paper is to provide more information for fluid‐film bearing selection and designing. The present paper is mainly concerned with the dynamic characteristics of a wide composite slider bearing lubricated with non‐Newtonian couple stress fluids.

Taking into account the non‐Newtonian couple stress effects resulting from a Newtonian lubricant blended with additives, the non‐Newtonian dynamic coefficients are obtained for composite slider bearings.

Comparing with the non‐Newtonian inclined‐plane bearing, the non‐Newtonian composite bearing provides an improvement in the dynamic stiffness and damping coefficients; better bearing characteristics are achieved for the non‐Newtonian composite bearing under specific length‐ratio parameters.

The paper includes a numerical example to provide guidance for non‐Newtonian composite slider bearings.

The paper focuses on the solution of a numerical model to explore the sliding and non‐Newtonian fluid behaviour in soft elastohydrodynamic nip contacts. The solution required the coupling of the fluid and elastomer regimes, with the non‐Newtonian fluid properties being described using a power law relationship. The analysis showed that the fluid characteristics as defined by the power law relationship led to large differences in the film thickness and flow rate with a movement of the peak pressure within the nip contact. The viscosity coefficient, power law index and sliding ratio were shown to affect the nip performance in a non‐linear manner in terms of flow rate and film thickness. This was found to be controlled principally by the level of viscosity defined by the power law equation. The use of a speed differential to control nip pumping capacity was also explored and this was found to be most sensitive at lower entrainment speeds.

On the ground of the Hopf bifurcation theory derived by Hassard et al., the purpose of this paper is to investigate the weakly nonlinear dynamics of transverse rough‐surface short journal bearings.

By application of the stochastic model of rough surfaces, developed by Christensen and Tonder, the roughness effects of transverse surface patterns on the bifurcation behaviors close to the Hopf bifurcation point are investigated.

It is found that the dynamic behavior of transverse rough‐surface short journal bearings can display Hopf bifurcation phenomena. Comparing with the case of isotropic rough‐surface bearing by Lin, under the same parameters, the effects of transverse surface roughness provide a reduced sub‐critical Hopf bifurcation region as well as an increased super‐critical Hopf bifurcation region. In addition, the effects of transverse surface roughness result in a lower stability‐threshold critical speed for both the sub‐critical bifurcation profile and the super‐critical bifurcation profile.

The present study, associated with the results of Hopf bifurcation regions and periodic orbits, can provide useful information for engineers when the transverse surface roughness effects and the bifurcation behavior are considered in a journal bearing system.

This paper aims to carry out tribological experiments to explore the applications of femtosecond laser surface texturing technology on rock bit sliding bearing to enhance the lifetime and working performance of rock bit sliding bearing under high temperature and heavy load conditions.

Surface textures on beryllium bronze specimen were fabricated by femtosecond laser ablation (800 nm wavelength, 40 fs pulse duration, 1 kHz pulse repetition frequency), and then the tribological behaviors of pin-on-disc configuration of rock bit bearing were performed with 20CrNiMo/beryllium bronze tribo-pairs under non-Newtonian lubrication of rock bit grease.

The results showed that the surface texture on beryllium bronze specimens with specific geometrical features can be achieved by optimizing femtosecond laser processing via adjusting laser peak power and exposure time; more than 52 per cent of friction reduction was obtained from surface texture with a depth-to-diameter ratio of 0.165 and area ratio of 5 per cent at a shear rate of 1301 s−1 under the heavy load of 20 MPa and high temperature of 120°C, and the lubrication regime of rock bit bearing unit tribo-pairs was improved from boundary to mixed lubrication, which indicated that femtosecond laser ablation technique showed great potential in promoting service life and working performance of rock bit bearing.

Femtosecond laser-irradiated surface texture has the potential possibility for application in rock bit sliding bearing to improve the lubrication performance. Because proper micro dimples showed good lubrication and wear resistance performance for unit tribo-pairs of rock bit sliding bearing under high temperature, heavy load and non-Newtonian lubrication conditions, which is very important to improve the efficiency of breaking rock and accelerate the development of deep-water oil and gas resources.

In a harmonic drive during assembly of its components like strain wave generating (SWG) cam, flexspline (FS) and circular spline, a gap is formed between the cam’s outer surface and the FS cup inner surface due to mismatching. This gap, which is known as “Coning”, plays a vital role in the flow of lubricant at that interface. This paper aims to analyse the coning phenomenon and the lubrication mechanism.

In the present investigation, the geometry of the coning gap and its variation with the SWG cam rotation are established. Essentially, the deflection of FS cup and deformation of SWG cam (bearing outer race) are derived to find the gap due to coning. Next, the hydrodynamic lubrication equation is solved to get pressure profiles for this gap under suitable boundary conditions assuming non-Newtonian lubrication.

Methods of estimating the coning gap and lubrication pressure profiles are established. Effects of non-Newtonian terms (coupling number and non-dimentionalized characteristic length) and SWG length (finite, long and short) on pressure profiles are also shown. All analyses are done in non-dimensionalized form.

Establishing the geometry of coning and non-Newtonian hydrodynamic lubrication aspects in the coning in the FS cup and SWG cam interface are the originality of the present investigation.

The purpose of this paper is to examine the effect of surface roughness on the magneto-hydrodynamic (MHD) non-parallel squeeze film lubrication using non-Newtonian lubricant.

Based on the MHD thin film lubrication theory and the Stokes theory and homogenization method, the homogenized MHD Reynolds equation is derived considering the squeezing effect.

It is found that the obtained results indicate that the interaction among non-Newtonian, MHD and surface roughness influences is significant.

This study is original which compares the dimensionless load capacity and dimensionless response time among transverse, longitudinal and, for the first time, anisotropic surface roughness types under magneto-hydrodynamic non-Newtonian non-parallel squeeze film lubrication.

The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-02-2020-0071/

The purpose of this paper is to describe an inverse approach to estimate the pressure distribution, temperature distribution, and pressure‐viscosity index (z) in a thermal elastohydrodynamic lubrication (TEHL) line contact.

Once the film thickness is given, the pressure distribution can be calculated using the inverse approach. Subsequently, thermal expansivity and temperature‐viscosity coefficient of lubricant are given, and then the z is guessed initially. The Gauss‐Seidel iteration is employed to calculate the temperature distribution from the rheology, energy, and surface temperature equations. In order to increase the algorithm stability, the least‐squares method must be employed to calculate the optimum value of the z in the computational domain. Furthermore, the pressure‐viscosity index must be updated by the iteration method to calculate accurate temperature distribution and apparent viscosity until convergence.

This approach presents a smooth curve of the pressure and temperature distributions with the measurement error from the resolution in the film thickness measurement and z value. Furthermore, this approach still provides a superior solution in apparent viscosity, whereas the direct method provides a much larger error in apparent viscosity.

The paper describes an inverse approach to estimate the pressure distribution, temperature distribution, and pressure‐viscosity index in a TEHL line contact. This approach overcomes the problems of pressure and temperature rise fluctuations and generates accurate results of pressure and temperature distribution from a small number of measured points of film thickness, which also saves computing time. Furthermore, this approach still provides a superior solution in apparent viscosity.

This paper aims to present a numerical model to examine the finite magneto-hydrodynamic (MHD) journal bearings performances including both non-Newtonian couple stress and bearing deformation impacts.

Based upon the MHD and Stokes theories, a novel expression of modified Reynolds equation including bearing deformation is obtained. The bearing elastic deformation impact is predicted by means of the Winkler model. Using the numerical differentiation approach, the film pressure is iteratively solved. Different bearing characteristics are then numerically calculated. The validity of the proposed model was verified by comparing with some particular cases from literature.

From the numerical presented results, it is demonstrated that the conducting couple stress lubricant with an applied radial magnetic field results in an induced electric current density and thus significantly improves the performances of elastic journal bearings. Particularly, the load-carrying capacity is increased, whereas a reduction in friction factor is observed.

This numerical model is original, which combines both non-Newtonian couple stress and bearing deformation impacts on finite MHD journal bearings performances. It provides useful information in designing MHD journal bearings, given the lack of experimental studies.