Wind turbine main bearings have come under increased research scrutiny of late, due to higher-than-expected failure rates and failure mechanisms which are yet to be fully understood . Integral to main-bearing function and performance is the fact that it is a rolling bearing, tasked with allowing low-friction, free rotation of the shaft while also supporting the turbine rotor. Lubrication of the main bearing is therefore necessary to prevent rapid wear and damage propagation from taking place. As such, the lubricant and lubrication mechanisms acting within this component must be accounted for as part of any attempt to fully characterise and understand main-bearing internal operational conditions, failure mechanisms and reliability. This two-part study seeks to begin this process.

Lubrication, and elastohydrodynamic lubrication (EHL) in particular, is a complex, nuanced and rapidly evolving field. While simplified film thickness formulas have been developed, their application should be accompanied by careful consideration of their validity and possible limitations in any given case. Furthermore, additional effects may be present where operational conditions vary rapidly or where grease lubrication is used. For the benefit of non-EHL-specialists, it is therefore argued that there is considerable value in an introductory review of this field which presents the reader with a comprehensive overview of EHL theory, including fundamental equations and the problem formulation, the approximations being applied, numerical solution methods, general characteristics of EHL contacts, simplified film thickness equations and their validity, and an overview of additional effects caused by time-varying conditions, starvation, surface roughness and grease behaviour. While a number of excellent review papers are available in this field , some are older now, and for others a prior familiarity with topic fundamentals is ideally required. In the case of review papers which cover specific topics within EHL , a much higher level of familiarity is necessary. This paper, “Part 1” of the main-bearing lubrication study, therefore presents an introductory

This being the case, the aim is to provide an accessible and representative overview of EHL theory, as opposed to an exhaustive review of the entire field.

Fluid film lubrication exists when two machine surfaces are completely separated by a layer of lubricant. In such circumstances, forces are carried via pressures generated within the lubricant, and frictional/wear conditions are greatly improved. The presence of an adequate lubricant film is therefore critical to the reliability and longevity of machine components. In the context of wind energy, one normally encounters non-conformal contacts (roller bearings, gear teeth, etc.) operating in the elastohydrodynamic regime

Although a novel (conformal) journal bearing design in this space is being developed .

For completely smooth surfaces a lubricant film would always be present, even if vanishingly small. However, in reality material surfaces are not perfectly smooth and exhibit roughness and geometrical variations, on the order of 0.01–10 µm . It transpires that typical lubricating film thicknesses also sit somewhere within this range, meaning film thickness needs to be considered relative to surface roughness in order to determine whether a separation of surfaces has been achieved. The appropriate relative quantity is the film parameter, 1Λ=hmσ, which relates the minimum film thickness, hm, to the combined (root-mean-square) roughness of contacting surfaces I and II, σ=σI2+σII2 . While delineations between lubrication regimes are difficult to make exactly, the following rough estimates indicate film parameter values associated with each :

hydrodynamic lubrication, 5<Λ<100;

Lubricated conjunctions can support applied loads as a result of pressure distributions generated through fluid film interactions. The differential equation governing these interactions is known as the Reynolds equation. While derivations and applications of this equation are commonplace, a proper discussion of nuances occurring in the current problem requires a more detailed understanding of the equation's origin and underlying terms. As such, key elements from the derivation based on the laws of viscous flow and mass conservation will be presented; for more detailed considerations see and . The full EHL problem is then defined. Note a table of symbols is provided in Appendix . The derivation of the Reynolds equation begins by considering the rectangular control volume shown in Fig.  of height h, width Δx and length (into the page) Δy. The mass of lubricant contained within this control volume at any point in time is ρhΔxΔy, where ρ is the lubricant density. The rate at which this mass changes over time is determined by the difference between mass flowing into and out of the control volume. From Fig. , mass-flow differences in the x and y directions are given by 2-∂ρqx′∂xΔxΔyand-∂ρqy′∂yΔyΔx, where 3qx′=∫ohudzandqy′=∫ohvdz are volume flow rates per unit length and width. Conservation of mass requires that the rate at which mass is accumulated in the control volume equals the total difference between mass flowing into and out of the volume. Thus, 4-∂ρqx′∂xΔxΔy-∂ρqy′∂yΔyΔx=∂∂t(ρhΔxΔy), from which Δ terms cancel such that 5-∂ρqx′∂x-∂ρqy′∂y=∂∂t(ρh). Applying zero-slip boundary conditions at lubricant–solid interfaces, and performing a number of integrations

For example, this includes integrations: ∂∂zη∂u∂z→∂u∂z→u→∫u.

The current section deals with instances of dry contact. When an elastic solid is acted on by a load, deformation will occur. Cases of two contacting and loaded solids result in the formation of a contact patch, with the geometry of contacting solids determining the shape of the contact patch. Components which initially contact along a line (e.g. a cylindrical roller contacting a raceway), referred to as line contacts, lead to a rectangular contact patch with a semi-cylindrical surface normal-stress distribution which remains identical along its length

Ignoring end effects and roller crowning.

The first complete solution to an EHL problem was presented by Dowson and Higginson in 1959 for four line contact cases. All calculations were carried out by hand, using mathematical tables and mechanical calculators . Much important work followed this initial breakthrough, but it was not until almost 2 decades later that computing power became sufficient to allow EHL solutions in the point contact case to be obtained . Since then, a plethora of significant advances have followed regarding numerical solvers for EHL problems, including development of advanced multilevel multigrid solvers ; full coupling of elastic and hydrodynamic equations – the differential deflection method – which enhances algorithmic efficiency and stability; and computational fluid dynamics implementations. These listed solvers apply the elastic half-space approximation for evaluation of deflections. A full system approach has also been developed which incorporates full-body elasticity using finite element methods . Implementation of EHL in multibody dynamics software modelling has also been considered . For an overview of recent developments in numerical EHL modelling, see . Accurate EHL solutions are now generated routinely and fairly easily even for complex cases such as those involving time-varying loads and speed, moving surface roughness or mixed lubrication conditions. However, it should be noted that this only holds where solver code and relevant expertise are available, since setting up such solvers is highly non-trivial.

Simplified formulations of the EHL problem have also been developed which allow for analytical and semi-analytical solutions to be obtained . Such formulations, while approximate, are highly efficient and provide important insights into EHL behaviour and conditions, even proving useful when implementing full numerical solvers (e.g. they can help with the identification of appropriate mesh dimensions, as well as supporting interpretation and sense-checking of results).

Figure  details characteristic features which tend to be present in EHL contacts

More specifically, Fig.  shows a “slice” through the contact in the direction of rolling, x.

When modelling a physical system via a set of equations, such as for EHL, it is possible to re-express the problem in an equivalent dimensionless form which generally depends on a reduced number of, also dimensionless, parameters. These dimensionless parameters are constructed as appropriate products, powers and ratios of dimensional quantities appearing in the original set of equations. In reduced and dimensionless form the problem is simplified and generalised, with effects of interacting physical phenomena elucidated. To illustrate this last point, consider a system for which solutions depends on parameters q1 and q2 with physical units in common. It may be the case that system response (e.g. flow rate, wave height, etc.) is proportionately increased by q1, but decreased by q2. In such a scenario, ultimate response is driven by the dimensionless quantity q1/q2, rather than each value independently. The relevant number of parameters to characterise response is therefore reduced, and the interaction between effects associated with q1 and q2 is made clear. Dimensional analysis or similarity analysis are the names given to the study and application of such ideas and associated methods.

In EHL, the following parameters comprise the most common set of dimensionless groupings used to describe lubrication conditions in line contact conjunctions . 19Wl=wlE′Rx(load)20U=η0ũE′Rx(speed)21G=α*E′(material) Recall that wl is load per unit length. α* is the lubricant's inverse asymptotic isoviscous pressure coefficient, 1/α*=∫0∞η0ηdp, a quantity which can be directly determined for a given lubricant using high-pressure viscometer measurements.

In the case of point contacts, speed and material parameters remain unchanged, whereas dimensionless load becomes 22W=wE′Rx2, where w is the applied load. Point contact geometry is captured in dimensionless form by the ellipticity parameter, k, or equivalently by D=Ry/Rx. Equivalence follows from the fact that k can be expressed as a function of D only . Non-dimensional film thickness is given by H=h/Rx.

Dimensionless groupings are commonly identified using a combination of intuition, experience and trial and error. However, systematic processes exist by which a minimal, or “optimal”, set of dimensionless quantities can be identified that fully determine system behaviour as defined by governing equations . It should be emphasised that identification processes, and the resulting optimal dimensionless sets, depend on the governing equations and boundary conditions of a problem only. Note, also, that minimal sets of dimensionless quantities for a given problem tend not to be unique. While the number of elements in each minimal set will be the same, alternative choices for the groupings of dimensional variables are generally present. All alternative groupings which form a minimal set can be identified if required .

For the EHL problem (as defined by equations in Sect. ) in line and points contacts, optimal parameter analysis reduces the three parameters above (load, speed and material) to just two , a load parameter, 23Ml=wl12ũη0E′Rx1/2=Wl(2U)-1/2(linecontact),24M=w18ũ3η03E′Rx51/4=W(2U)-3/4(pointcontact), and viscosity parameter, 25L=α*2ũη0E′3Rx1/4=G(2U)1/4. The factors of 2 are present to coincide with , in which entrainment speed is taken to be the sum, rather than mean, of surface velocities. While this is the form generally used , the parameters are equally valid with the factors of 2 removed. Both forms have appeared in the literature ; hence, it is important to ascertain which has been applied if comparing operating conditions or applying related film thickness equations. Non-dimensional film thickness in the optimal parameter case takes the form H=(h/Rx)(2U)-1/2. The same analysis identifies D-1, introduced above, as the parameter representing contact patch geometry in the elliptical case . Additional parameters are required to fully capture more complex viscosity and density characteristics; for full details see . Despite the proven reduction in the number of parameters required to characterise EHL conditions, use of Wl (or W), U and G persists, although film thickness equations utilising reduced sets of parameters have been developed . The parameters Ml (or M) and L are, however, commonly used when plotting operating regions and results, since visualisation becomes clearer and easier with a reduced number of variables.

Having identified a set of dimensionless parameters (optimal or otherwise) which determine the response of the system defined by governing equations, it follows that features of interest (e.g. hm and hc) will also be determined by these same parameters. If such relationships can be sufficiently well approximated by analytical equations, fast evaluation and analysis of key features becomes possible without requiring complex numerical solvers to be implemented in every case. Film thickness formulas have therefore been developed by performing least-squares curve fits between outputs of full EHL solvers and analytical expressions containing dimensionless parameters. Equations () and () present two of the earlier equations identified this way for estimating minimum film thickness (hm) in line and point contacts, respectively, Line contacts 26hmRx=2.65U0.70G0.54Wl0.13 Point contacts 27hmRx=3.63U0.68G0.49W0.0731-e-0.68k Despite the early stage at which they were developed, these equations provide remarkably accurate estimates and are still used today . Equation () is based on Barus law viscosity modelling and Eq. () on Roelands equation viscosity modelling. The relative importance of speed, load, viscosity and material properties (as described at the end of Sect. ) may be seen to be reflected in the exponent values of the above equations. Quite a number of subsequent refinements have been undertaken using larger datasets generated by more advanced solvers . Some of the most extensive fitting was undertaken for line and point contacts in and , respectively, resulting in the following equations. Line contacts 28hmRx=1.652U0.716G0.695Wl0.077 Point contacts 29hmRx=1.637U0.711k-0.023G0.65k-0.045W0.09k-0.151-0.974e-0.676k Both of these equations are based on Roelands equation viscosity modelling. Unfortunately, the full range of dimensionless parameter values over which these formulas were fitted appears to have been misrepresented in the literature. In , and then reproduced in , parameter limits for the point contact hm equation are given (approximately) as 15≤M≤104 and 5≤L≤20. While these limits are those of the cases shown in the results tables of , it is explicitly stated that only a subset of the full analysis is reproduced there. Moreover, the full range of dimensionless parameter values used for curve fitting are also given. Taking the stated limiting values in , the domain across which these equations were fitted is in fact bounded by 2.82≤M≤1.49×105 and 2.97≤L≤28.20. The true domain of validity for these equations is therefore significantly larger than has been reported. For completeness, parameter limits for the line contact equation are also stated; limits in L match those of the point contact case and for Ml, 1.41≤Ml≤353.55. With respect to ellipticity, Eq. () was developed across the range 1≤k≤8. At k=8, film thickness predictions closely match those of the line contact formula (Eq. ) applied to an “equivalent line contact” representation of the conjunction (see Sect. ). It was therefore recommended that the equivalent line contact approach is taken for cases where k>8 .

The same studies which result in formulas for hm also use curve fitting to identify similar formulas for hc .

EHL behaviour and film thickness equations discussed above assume fully flooded conditions, in which an adequate supply of lubricant is available to the contact. Starvation is the term given to cases in which lubricant supply is insufficient. Figure  illustrates these different regimes. Under starved conditions, surface-to-surface filling of the inlet with lubricant only occurs close to the contact edge. This reduces the magnitude of developed hydrodynamic pressures, in turn reducing the load-carrying capacity relative to fully flooded conditions, and, hence, the film thickness at any given load is also reduced.

Starvation levels are commonly characterised by the dimensionless inlet meniscus distance, m̃=xm/b, where xm is shown in Fig. . In the case of line contacts, film thickness reduction formulas under starvation have been presented in the literature based on a semi-analytical analysis of the starved EHL problem and curve fitting to the results of numerical integration of simplified lubrication equations . Starvation was studied in these works by varying the inlet location in hydrodynamic pressure integrals. Note, the non-dimensional inlet distance used in these earlier works differs from m̃, and the viscosity–pressure relationship was characterised using a Barus law. More recently, undertook an extensive computational study of film thickness reductions under starvation, with surface roughness also present. Similar to earlier work, starvation is generated by moving the inlet of the solver domain towards the contact centre. A Roelands pressure–viscosity relationship was used. While in other work starvation levels are indicated by an appropriately non-dimensionalised inlet distance, Masjedi and Khonsari instead propose that starvation be linked to the mass-flow rate through the starved contact (m˙s) relative to fully flooded conditions (m˙ff). Their starvation degree is therefore defined as the fractional reduction in flow rate, 30ζ=1-m˙sm˙ff. ζ takes values between 0 and 1, with 0 indicating fully flooded conditions and 1 complete starvation. This definition has an intuitive appeal, since film thickness is fundamentally linked to the quantity of lubricant moving through the contact. The appropriateness of ζ in this context is evidenced by the quality of fits and simplicity of parametric equations obtained from curve fitting to model outputs. In the case of line contacts, hc reductions were found to be linear in ζ, with hm reductions similar but weakly nonlinear. The latter fit takes the form 31hm,shm=1-ζ1.08, for which the maximum reported error across the fitted points was less than 5 %. This analysis closely mirrored those authors' previous work in which Eqs. () and () were presented.

In the case of point contacts, perhaps the most important earlier work was that of Hamrock and Dowson , who studied the effects of starvation on elliptical contact conjunctions computationally. As above, this was achieved by adjusting the inlet distance of their solver domain and using a Roelands pressure–viscosity equation. Based on a parametric study and subsequent curve fitting, they proposed formulas for the reduction in central and minimum film thickness values under starvation, with the level of starvation indicated by m̃. For hm this takes the form 32hm,shm=m̃-1m*-10.25:ifm̃<m*(starved)1:ifm̃≥m*(fully-flooded), where 33m*=1+3.34Rxhmb20.56. m* represents the transition point to starved lubrication, this being the dimensionless inlet distance at which the minimum film thickness begins to change as m̃ is reduced further. hm is the fully flooded minimum film thickness, and hm,s the minimum film thickness under starvation. While a valuable contribution, important aspects of starved flow regimes in point contacts were not included, as will be outlined below.

Many EHL contacts operate under non-steady conditions in which load, speed and even contact curvature (the latter being the case during gear meshing) change with time. The critical timescale, tc, determining the impact of such variations is the time it takes for a particle of lubricant to pass through the contact . When the time taken for conditions to vary is large, compared to tc, non-steady effects become negligible, and a quasi-static analysis is sufficient for characterising film variations over time. For example, this is generally the case for roller bearings operating under constant load, in which each roller sees a continuous variation in applied force as it traverses the loaded zone. In the absence of additional effects, the film thickness variations are well captured by applying steady-state equations (Sect. ) at each time step. However, if variations occur rapidly, meaning over timescales similar to or shorter than tc, local surface deformations are induced at the inlet which then propagate through the contact. Non-steady EHL phenomena have been studied numerically, including via semi-analytical models, and experimentally . Steady-state formulae do not capture variations in film thickness and pressure within the contact resulting from rapid non-steady effects; their use in such cases therefore risks over-estimating minimum film thickness values . Piezoviscous behaviour plays an important role in non-steady EHL. Recall, as discussed in Sect. , that very high viscosities and Couette flow dominance hold in the central region of a loaded EHL contact. As the lubricant film passes into the central region, it therefore becomes very “stiff” and moves through the conjunction, at approximately ũ, as a shear flow that is independent (for the most part) of the contact inlet. In the case that entrainment speed is suddenly increased, increased film thicknesses occur at the contact inlet (via local surface deformations) which are then carried through the conjunction at the new entrainment speed . The new, increased film thickness values are only seen across the whole contact once the original values have passed out of the conjunction. While the increased entrainment speed (ũ) is seen simultaneously across the whole contact, a greater film thickness requires an increased volume of lubricant in the conjunction. For a shear-dominant flow, this can only happen through the advective process described above, irrespective of pressure changes at the inlet. This explains why film changes from rapid speed adjustments are not uniform across the contact. While in steady-state conditions film thickness sensitivity to load is known to be small, the effects of rapid load variations can be dramatic . As load increases, the width (b) of the contact also increases, meaning the contact edge is moving rapidly in the opposite direction to entrainment. The result is an augmented “effective” entrainment speed, 37ũeff=ũ+dbdt, for the inlet. Due to the stiff nature of the central film, this results in the formation of a dome-shaped entrapment of lubricant at the inlet which is then carried through the conjunction. Similarly, a rapid reduction in load results in negative values of db/dt and so a reduced effective entrainment speed at the inlet. In this case, a local drop in film thickness forms at the inlet and moves through the contact . A conceptual representation of the latter case is provided in Fig. . Somewhat counterintuitively, it is therefore the case that rapid increases in load can temporarily increase the minimum film thickness, while rapid load reductions can temporarily decrease the minimum film thickness. Periodic load variations have also been considered in the literature. Film height variations through the contact are accompanied by local variations in pressure and material stress . For time-varying loads, the rate of expansion or contraction, db/dt, relative to entrainment speed, ũ, has been proposed as a criterion for determining whether a quasi-static analysis may be used . Non-steady effects were found to become important where 38|db/dt|ũ(×100%)≥25%. While effective entrainment speed plays an important role in non-steady EHL, squeeze film effects (∂(ρh)/∂t in Eq. ) also strongly influence the resulting film thickness variations over time . Both effects must therefore be accounted for.

EHL contacts also experience non-steady conditions due to intermittent operation, i.e. starts and stops along with associated periods of acceleration/deceleration. Piezoviscous behaviour again plays an important role in such cases . Lubricant entrained into a contact at start-up initially forms a “front” which passes through the conjunction at constant height before characteristic features of the EHL contact (see Section ) are then established . Secondary fronts have also been found to occur in some cases , giving the initial film a stepped profile. Under cases of very high acceleration, oscillatory film thickness behaviour has been observed , which has been linked, in part, to dynamics of the overall mechanical system within which an EHL contact is operating . In instances of shutdown, halting of operation sees an EHL oil film begin to collapse, initially in a uniform manner . As the deceleration reduces the entrainment speed further, a local minimum forms at the contact inlet. Together with the minimum at the contact outlet, these features form an entrapment of lubricant within the contact. Subsequent reductions of the film thickness within the entrapment are slow; in some cases entrapped films remain almost unchanged for hours or days . The thickness of the initial entrapped lubricant film has been shown to increase with increasing values of the parameter, 39αη0×deceleration, indicating that both rheological and operational effects are important . Time variations in surface oil layer thickness distributions also occur within lubricated components. Such oil migration is driven by gravitational and surface tension effects after operation is halted and (additionally) by centrifugal forces while operating .

As discussed in Sect. , film thickness must be considered relative to surface roughness in order for the lubrication regime to be known. However, it is also the case that rough surface micro-geometry will interact with the lubricant flow and deform elastically, with both effects influencing surface separation and lubrication conditions. Much work has been undertaken over the years in what is now known as micro-EHL, leading to significant advances in understanding and modelling capabilities. An excellent overview is provided by . The presence of roughness results in part of the load being carried by surface asperities , as opposed to being carried purely hydrodynamically. Such interactions are important when considering micropitting of machine elements . With respect to conditions in the lubricated conjunction, roughness has been shown to result in both “mean” and “local effects”. Mean effects are overall modifications to surface separation and pressure, relative to an equivalent smooth contact. Local effects are in the form of local variations in film height and pressure which move through the contact and, hence, are non-steady in nature. The mean effect resulting from the presence of homogeneous surface roughness is an increase in film thickness, but, by an amount that is smaller than the change in surface σ . Therefore when roughness increases, hm increases, but Λ decreases. Note, more structured roughness can have a different effect . Film thickness equations presented in Sect.  are those for smooth surfaces. Additional multiplicative factors have been identified, also via curve fitting, which account for surface roughness effects. For the Masjedi and Khonsari line and point contact minimum film thickness equations these, respectively, take the form 40Φl=1+0.026sSDRx1.120V0.185Wl-0.312U-0.809G-0.977,41Φp=1+0.141sSDRx1.073V0.149W-0.044U-0.828G-0.954k-0.395, where sSD is the standard deviation of surface heights (assuming normally distributed roughness, sSD=σ), and V=vh/E′ is a dimensionless hardness number, with vh the surface Vickers hardness. From analysis across standard ranges of operating parameters, line and point contact results for dimensionless roughness levels, sSD/Rx, of around 1×10-6-5×10-6 or less have been shown to be well approximated by smooth surface results . Note, the above modification factors may be applied where Λ>0.5 but are no longer valid if the film parameter falls below this value .

The vast majority of rolling element bearings are grease lubricated, where “grease” may be defined as a dispersion of a thickening agent in a liquid lubricant . Lubricant base oil is held inside sponge-like structures of thickener fibres through a combination of Van der Waals and capillary forces. The resulting semi-solid consistency is beneficial due to its ease of use, good sealing action and corrosion resistance. However, this same consistency generally leads to starved lubrication conditions , since grease will not reflow (at a macroscopic level) back to the rolling track after being swept out by the passage of rolling elements. The total quantity of grease directly participating in the separation of contacting surfaces is therefore reduced. The initial phase of grease redistribution, the “churning phase”, occurs within the first ∼10 h of operation after a bearing has been freshly charged with grease . Once this initial grease flow has ceased, the bearing enters the “bleeding phase” in which swept grease reservoirs are generally only able to supply lubricant to the contacts by releasing (“bleeding”) oil through phase separation . Oil is also mechanically released from the thickener network by over-rolling, principally in the churning phase . The starved lubrication contribution of the bled-oil portion of a grease-lubricated contact may be treated as described in Sect.  . However, other effects can also be present, as will be outlined. Understanding, modelling and predicting grease lubrication is difficult. This is because thickener and base oil interactions result in nonlinear shear stress and shear rate behaviour, even at low shear rates and pressures. The apparent viscosity of grease also decreases continuously over time while being sheared, and then recovers once shearing stops (thixotropy) . Over longer timescales, grease properties change as the thickener structure deteriorates due to being mechanically worked . Oxidation also slowly degrades grease performance. Due to these complexities, there is as yet no complete theory which allows film thickness in grease-lubricated bearings to be accurately and consistently predicted in general. While a complete theory of grease lubrication is not yet established, significant advances have been made regarding the key mechanisms and interactions at work. A summary of pertinent results in this field will therefore be outlined.

The thickener contributes to film thickness at low speeds. At higher speeds the film thickness observed in fully flooded grease-lubricated contacts often coincides with that of oil lubrication using the grease base oil . However, this is not always the case since the bulk grease and bled oil can have significantly different rheological properties to the base oil, even at high speeds . Still, it is common at higher speeds for fully flooded grease lubrication to be strongly determined by the viscosity of the base oil. As speed is reduced, film thickness initially reduces in line with the behaviour predicted by standard film thickness equations (see Sect. ), but eventually a “transition speed” is reached after which further reductions in speed result in increasing film thickness values. The rate of increase in this region, as speed is decreased, can be similar to that seen for oil lubrication as speed is increased, meaning these low-speed grease effects are significant with respect to resulting film thicknesses. Speed versus film thickness plots for fully flooded grease lubrication therefore exhibit a characteristic “V” shape . The described behaviour at low speeds results from entrained thickener fibres becoming the dominant driver of surface separation, further evidenced by the fact that in this region the film thickness, for a given grease, is independent of base oil viscosity and temperature . As the grease is mechanically worked over time, the thickener structure degrades, and constituent particles become smaller. This reduces film thickness values seen in the low-speed region, whereas the higher-speed region is unaffected . The degradation process has been found to primarily occur within the first 100 h of operation. The transition from low-speed to higher-speed behaviour has been found to be dependent on film thickness . More specifically, experimental findings indicate that the described low-speed effects occur for film thicknesses h<cD, for some constant c and where D is the diameter of thickener fibres or possibly that of entangled fibre networks

This is our interpretation of results, summarising their findings and proposed mechanisms of grease film formation.

EHL theory has come an exceptionally long way since its inception around 1950. Incredibly complex elastohydrodynamic lubrication problems are now solved routinely, with experimental comparisons demonstrating the effectiveness of currently available models. However, important further work remains, much of which is centred around the need for more realistic modelling of lubricant rheological behaviour and the extension of results from single contacts to full bearings. Therefore, elastohydrodynamic lubrication is (and will likely remain) a complex and rapidly evolving field. The current review has attempted to ensure the details of these complexities are accessible to a more general engineering audience, in order to support cross-disciplinary understanding with respect to this field and future interdisciplinary work. It is again emphasised that when applying film thickness equations, or indeed any other output of lubrication modelling, the approximations, assumptions and overall validity of applied equations should be considered on a case-by-case basis, allowing predictions to be properly contextualised. Such considerations should also dictate which equations are used. The theory presented in this review is applied in “Part 2” of the study in order to consider lubrication in a wind turbine main-bearing.