A combined analytical-experimental investigation of friction in cylinder liner inserts under mixed and boundary regimes of lubrication

It is necessary to develop an analytical solution in order to combine predictions with measured tribolog- ical parameters and fundamentally understand the mechanism of lubrication in a typical region of engine cycle, using tribometric studies. This paper deals with the development of such a representative approach. An analytical, rather than a numerical approach is expounded, as it is shown to suf ﬁ ce for the purpose of precise time-ef ﬁ cient predictions, which conform well to the measurements. The effect of surface topography, material and operating conditions are ascertained for the representative case of top compression ring — cylinder liner contact at the top dead centre reversal in transition from the compression to power stroke. Stainless steel uncoated surface used as press ﬁ t cylinder liners for niche original equipment manufacturer applications are compared with those furnished with a Nickel-Silicon Carbide wear-resistant coating of choice in high performance motorsport. © 2017 The Authors Lubrication Science Published by John Wiley & Sons Ltd.

δ localised Hertzian deformation ξ number of asperity peaks per unit area κ average asperity tip radius σ composite standard deviation of surface roughness λ Stribeck lubricant film ratio λ c critical film ratio ε error of convergence for load balance φ* standard height distribution ψ numerical damping factor η lubricant dynamic viscosity υ Poisson's ratio τ 0 Eyring shear stress τ v viscous shear ς coefficient of boundary shear strength of asperities

INTRODUCTION
Reciprocating sliding contacts, such as the piston-cylinder system are often subject to a broad range of regimes of lubrication, from boundary to hydrodynamics. Under boundary and mixed regimes of lubrication, frictional losses of piston and ring-pack conjunctions can account for a significant proportion of the overall frictional losses from an IC engine. 1 Of the components in this system, the share of frictional losses of the top compression ring is one of the largest, 2 because of its close adherence to the cylinder liner surface to seal the combustion chamber from the bottom end of the engine. Considering its usual small contact area (circa 300 mm 2 ), it contributes up to 3% of total fuel energy consumption in a typical automotive engine. 3,4 Therefore, understanding and subsequent palliation of these losses has attracted considerable attention. The transient nature of the compression ring-cylinder liner contact and the broad range of cyclic regimes of lubrication make the nature of analysis quite complex. 5 There are a host of influential parameters, often interacting in a non-linear fashion. These include the effect of ring contact face geometry and topography, [6][7][8] which are also subject to wear. [9][10][11] Owing to the variations in the applied gas pressure, the ring is subject to elastic modal behaviour both in its radial plane as well as out of plane motion in twist and bending. 12,13 Additionally, the heat generated due to combustion as well as shear of the lubricant film and any direct boundary interaction also affects the tribological conditions. [14][15][16] The complexity of the problem is exacerbated by ring-bore conformability 17,18 and particularly with realistic out-of-roundness of the bore taken into account. 19 Furthermore, the lubricant flow into the contact conjunction is far more complex than an assumed flooded inlet on the account of reverse and recirculating flow, starvation, 20 cavitation and lubricant film reformation at the contact exit. [20][21][22] Therefore, complex boundary conditions exist in practice, 23 which are often not taken into account in predictive analyses.
As a result of the complexities of the multi-variate and interactive nature of the problem, tribometric studies have received much attention in recent years in order to gain a fundamental understanding of the effect of some of the aforementioned parameters in isolation from the others. The sliding tribometers have been extensively used. Dearlove and Cheng 24 and Ting 25 designed a slider test rig by converting a conventional piston-cylinder system to study the tribology of ring-bore friction under motored conditions. The former measured both friction and film thickness; whilst the latter only measured the contact friction. Dearlove and Cheng 24 measured friction using a load cell which was mounted onto a floating liner sample. The film thickness was measured using the laser-induced florescence technique. Akalin and Newaz 26 and Bolander et al 27 also developed slider rigs based on motored engine cylinders, measuring friction under mixed regime of lubrication. The former used a strain gauge system to measure friction, whilst the latter measured film thickness, using fibre-optic displacement sensors, mounted onto a pivot arm. For measurement of friction, Furuhama and Sasaki 28 were amongst the first to propose the use of a floating liner. The technique was improved by Gore et al 29 using precision piezoelectric load cells intervening between the floating liner and the cylinder block, with gas pressure contained within the chamber using a labyrinth seal. In this manner, friction was measured directly under fired engine conditions in a single cylinder high performance engine.
With motored cylinder systems, described earlier, there is still a fair number of parametric interactions. To reduce these effects to basic study of surface materials (including coatings), topography and lubricant types and their combinations, reciprocating plates were used by Felter et al 30 and Johansson et al, 31 where the plate was made of cylinder liner material and a stationary loaded block, representing the counter face surface. They measured friction using a transducer mounted onto the block. Truhan et al 32 also studied the effect of lubrication conditions on the frictional and wear behaviour of ring-liner contact using a Cameron-Plint high frequency reciprocating test rig with different coated surfaces. Sliding tribometers have also been used to study the effect of surface texturing, 33 surface scuffing, 34 as well as observation of cavitation. 35 In the current study, a precision sliding tribometer is used to study frictional performance of a series of coated plates used as cylinder liner material, particularly for advanced high-performance engines.
Cylinder liners used in the IC engines are usually made of cast iron, steel or high grade aluminium for some high performance race engines. Progressively, use of hard wear-resistant coatings for cylinder liner, top compression ring contact face or both, particularly in niche original equipment manufacturer and racing applications has been adopted. Styles et al 11 described the use of plasma sprayed Ni-chromium nitride coating with inclusion of molybdenum to reduce the solid solubility of the coating with a standard cast iron liner. Plasma sprayed coating is porous, thus aiding retention of lubricant. Tung and Gao 36 studied friction and wear performance of thermal-sprayed chromium nitride and physical vapour deposited diamond-like carbon on nitrided stainless steel and chrome-plated stainless steel piston rings. Nickel silicon carbide (Ni-SiC) is the coating of choice for cylinder liners in motorsport applications. Howell-Smith et al 37 used a number of coated cylinder liners, including Ni-SiC as well as plasma-assisted physical vapour deposited diamond-like carbon coating. These were subjected to accelerated wear under fired engine condition, using a motocross motorbike engine. The Ni-SiC coating on a high grade aluminium liner was shown to perform best under severe simulated cross-country race conditions. Despite a significant number of reported investigations, the fundamental question still remains with respect to the choice of cylinder coating for a broad range of applications, and particularly for the dominant mixed and boundary regimes of lubrication at the top dead centre (TDC) reversal.
The current study benchmarks the use of Ni-SiC against an uncoated steel liner for motorsport applications. A combined analytical-experimental study, using a sliding tribometer, is presented. 296 M. GORE ET AL.

TESTRIG SETUP AND EXPERIMENTAL PROCEDURE
The sliding tribometer The in-house designed and built sliding tribometer is shown in Figure 1. The sliding head is driven through an ultra-low backlash lead-screw by an electric motor, controlled through an interface to a laptop computer, using a National Instrument data logger. The rotational speed of the lead-screw is measured by an encoder (resolution of 10 000 pulses per revolution), also interfaced to the National Instrument data logger. Two Bruel and Kjaer torsional vibrometers are used to precisely measure the torsional, as well any tilting and lateral motions of the sliding head. A proportional-integralderivative controller for the motor speed is used to provide a reciprocal motion based on the encoder count. This arrangement is used to correct any potential errors in the measurements of the encoder or oscillatory motion caused by any backlash. A flat specimen (levelness of AE0.8μm) made of the same substrate material, coating and surface topography as that of a cylinder liner is mounted onto a base floating plate. This plate is mounted upon nominally frictionless bearings and is dragged by a sliding strip with the same contact face geometry as a compression ring, mounted into the loaded reciprocating head as shown in Figure 2. The strip is allowed to slightly sway; only fully constraining any rotation. This eliminates any problems associated with any waviness of the flat specimen. Loading is achieved by the application of precisely measured dead weights, which can be altered to represent loading conditions experienced by the top compression ring of a wide range of engines at the TDC reversal in transition from the compression to the power stroke (AE 10°crank-angle from the TDC), including for high-performance highly loaded engines (load per unit strip length of 400-850 N m À1 ). This is combined with the controlled sliding speed variation in the same region, also in a range representative of engine conditions (circa < AE0.5 m s À1 ). The tribometer is intended to replicate the conditions of the compression ring conjunction at the TDC reversal for a cold running engine, when worst tribological conditions under mixed and boundary regimes of lubrication are expected. In transition from the compression to the power stroke, a small quantity of lubricant would be expected on the free surface of the liner. Therefore, 1 mL of lubricant is applied onto the flat specimen surface and spread uniformly over it for a short period of reciprocation. This is prior to taking any measurement of friction.
The floating base plate and the mounted sample are dragged by the sliding strip through a combination of viscous friction of a formed lubricant film and any boundary interactions of the counter face opposing asperities. The surface topography of both the flat specimen sample and the sliding strip contact face are measured using infinite focus microscopy (Alicona, with measurement sensitivities of 1 nm in height; z and 0.18 μm in horizontal directions; x and y) prior and after testing. Two Honeywell FSG15N1A piezoelectric load cells ( Figure 2) with resolution of 0.24 mV/grf were used to measure the inertial force of the dragged arrangement, ma. The force causing the inertial motion is friction, f, thus Therefore, the tribometer forms the basis for understanding of the mechanisms of friction generation in reciprocating sliding contacts. It also provides a basis for validation of analytical/ numerical techniques, which are subsequently used for prediction of friction in real engine piston systems.

Preparation of samples
The strip and the flat specimen are lapped to a surface finish representing their counterparts in real engine applications. Figure 3 shows measurements taken from a sliding strip sample, representing a parabolic-type surface contact face-width profile. The slider strip is initially used in a set of preliminary tests to complete the 'running-in' process. Once the surface 'peakedness' was removed, the surface topography measurements showed that the strip profile, and its topography do not alter considerably during the friction tests. Since the running time for each friction test is very short (~2.5s), this also justifies the observed insignificant change in the measured topography of run-in strip profile after each test. In addition, to avoid the occurrence of edge contact, the lateral edges of the strip were chamfered.

Contact geometry
The profile of the sliding strip, representing that of a top compression ring in a motocross motorbike race engine with the origin of coordinate system located at the centre of face width can be described by a parabola (Figure 4): where, R is radius of curvature of the strip contact face-width. Therefore, the total gap between the ring sample and specimen flat plate becomes where, h 0 is the minimum film thickness (gap). The ring crown height and its contact face-width radius of curvature are related as in which, h rc and b are the ring crown height and strip face-width, respectively.

Hydrodynamic load carrying capacity
It should be noted that for the typical applied loads on the compression ring in the vicinity of TDC reversal, no localised deformation of the ring or liner face are noted 7,18 (see Appendix). The generated pressures are also insufficient to induce any piezo-viscous action of the lubricant (i.e. iso-viscous conditions). Assuming a sliding line contact for a parabolic profile, the hydrodynamic load carrying capacity per unit lateral width for an iso-viscous lubricant under isothermal conditions become 38 where, U is sliding velocity and η is lubricant dynamic viscosity. Equation 5 excludes the effect of squeeze film motion and assumes a fully flooded inlet with Reynolds exit boundary conditions: where, c is the location of lubricant film rupture; marking the start of the cavitation region, measured from geometrical centre of the strip. For the case of the sliding strip considered here, the inlet and outlet boundary pressures at its leading and trailing edges are the atmospheric pressure (equal to gauge pressure of zero).
Equation 5 can be extended to describe the total load carrying capacity of the contact; neglecting any side leakage of lubricant from its lateral edges: where, L is the length of the strip in the lateral direction.

Load carried by the asperities
The load carried by asperities is given by Greenwood and Tripp 39 as where, E 0 is the composite (equivalent) Young's modulus of elasticity: and ξ, κ and σ are the number of asperity peaks in unit area, the average asperity tip radius of curvature and composite surface roughness standard deviation. In addition, λ = h/σ is the Stribeck lubricant film where, λ c is the critical film ratio, indicating the point earlier which there would be no probability of direct asperity tip contact on the opposing surfaces.
In equation 8, A denotes the total (apparent) contact area, where the asperity tips may come into contact. Ignoring the curvature of the sliding strip face-width, the (projected) contact area may be stated as However, the ring face has a parabolic shape and the opposing asperities away from the centre of contact may never come into contact. Therefore, it is important to calculate the area of the ring face from which the film ratio falls below the critical film ratio. Considering the critical film ratio, the critical distance between the ring and plate surfaces becomes If the portion of the face-width whose gap with the plate surface falls below the critical film thickness is l c , then (Figure 4) Rearranging for l c : Therefore, the contact area in which there would be a chance of direct asperity interactions becomes It is important to note that since F 5/2 (λ) is calculated based on h 0 , not all of the asperities in the contact area would contribute to the contact load carrying capacity in the same way as the 302 M. GORE ET AL.
asperities located close to the contact centre would do. Consequently, the contact area should be corrected to take this issue into account. The correction should follow the variations of F 5/2 (λ) with λ as shown in Figure 5. Therefore, a more accurate representation of asperity load carrying capacity can be expressed as where, λ = h/σ, h 0 ≤ h ≤ h c , dA = 2Ldx and 0 ≤ x ≤ l c /2 ( Figure 4). The differentiation of the parabolic profile (equation 3) yields Therefore, dA in terms of dh becomes Consequently, the integral term in W a , can be recast as where, λ 0 = h 0 /σ and λ c = h c /σ = 2.2239 Performing the integration, the load carried by the asperities becomes where, M = À 1.449λ 3 + 22.099λ 2 À 146.421λ + 543.5892. Since in the mixed regime of lubrication the applied load is carried by the hydrodynamic reaction as well as asperity interactions, then The iterative procedure for the analytical study assumes an initial gap of h 0 . Then, the earlier components of total contact load are obtained.
At each time step during simulation, a quasi-static balance is sought as If the earlier convergence criterion is not met, then the assumed value of h o is corrected as where, ψ is found empirically and set as high as possible in order to achieve rapid convergence, whilst maintaining numerical stability. A typical value of ψ ≅ 0.075 is obtained. Once convergence is obtained the simulation is advanced to the next time step.

Friction
The total generated contact friction between the sliding strip and the flat specimen is as the result of viscous shear of a lubricant film as well as the interaction of opposing asperities on the contiguous surfaces: The viscous shear stress is given as This is the shear stress caused by Couette flow of the lubricant drawn into the conjunction by the relative sliding motion of the strip with respect to the flat specimen surface. In the current study, the Poiseuille component of shear, induced by the pressure gradient at the inlet conjunction, is ignored as the pressure gradient is deemed quite low for thin films and low pressure conjunctions, particularly under mixed and boundary regimes of lubrication.
Hence, viscous friction becomes However, due to the curvature of the ring face, the equation needs to be modified to and for the parabolic ring profile, it can be recast as The boundary friction is calculated using 11,41 where, τ 0 is the Eyring shear stress, ς stands for the pressure coefficient of boundary shear strength of the softer of the two interfaces. The value of this parameter is usually obtained using an atomic force microscope in lateral force mode. 11 The same procedure as in 11 is carried out, obtaining appropriate values for all of the specimens used in this study (Table I). A a represents the total contact area of the asperity tips on the opposing surfaces 39 : where, F 2 is a statistical function (with the generic form F n with n = 2 as described earlier) of the Stribeck lubricant film ratio, which is approximated by a fifth order polynomial 40 :  Figure 6 shows the variation of this function with the lubricant film ratio.

FRICTION IN CYLINDER LINER INSERTS UNDER MIXED REGIMES OF LUBRICATION
The total contact area is obtained as before, thus where, λ = h/σ, h 0 ≤ h ≤ h c , dA = 2Ldx and 0 ≤ x ≤ l c /2 ( Figure 4).  With a parabolic profile, the integral term in A a becomes where, λ 0 = h 0 /σ and λ c = h c /σ = 2.2239. Performing the integration, the asperity contact area can be recast as where, N = À 0.567λ 3 + 10.8185λ 2 À 85.536λ + 364.3794.
Consequently boundary friction becomes Finally, the total generated friction is obtained by substitution of f b in equation 26, thus

MEASURED INPUT DATA FOR THE ANALYSIS
Two specimens representing the material of choice for many cylinder liners are used. One specimen is an uncoated steel, often used as a thin press fit liner into niche original equipment manufacturer engines. The other is the same steel substrate material, coated with an approximately 20 μm of Ni-SiC. This is the coating of choice for most motorsport applications. Both flat test pieces were ground on a centre-less grinder and honed. Note that a rougher surface resulted by centre-less grinding of the Ni-SiC coated surface. This is because Ni-SiC is a hard, wear-resistant coating compared with the uncoated steel specimen, which is more ductile and malleable.  Table I, together with other required data as input for the analytical simulations. In order to ensure repeatability of testing conditions, a base lubricant without boundary active species is used. Formulated lubricants contain boundary active lubricant species such as friction modifiers, surfactants and other constituents, which may adsorb or chemically bond to the contacting surfaces, and are quite difficult to remove. As a result, repeatability of testing would be difficult. Therefore, the base oil, which underlies the usual lubricant SAE 10W40, is used. The rheological data is listed in Table I.

Experimental results
The speed of sliding is kept quite low, representative of TDC reversal. This also encourages mixed or boundary regimes of lubrication. The speed of the rotation of the reciprocating lead-screw is monitored by an encoder and converted to the sliding speed through pitch of the lead-screw. The variation is shown in Figure 9.
After an initial accelerative phase, the speed of sliding is kept constant as far as possible. The 'noise' resident on the measured signal is as the result of a combination of causes. One is the vibration of the driving motor, the other is the stick-slipping of the toothed belt drive system, another is some degree of backlash oscillations of the lead-screw at low speed operation, and finally there is some effect from contact stick-slip motion. Some of these are attenuated through application of belt tension control and use of a high ultra-precision lead-screw. Figure 10 shows the measured friction trace, corresponding to the sliding motion in Figure 9.
With an applied contact load of 11N, the variations in the coefficient of friction are shown in Figure 11. This shows an average value for coefficient of friction of μ = 0.225, indicating that a mixed to boundary regime of lubrication is prevalent. Note that for fluid film regime of lubrication, one would expect a value in the range 0.005-0.05.

Numerical predictions and comparison with measurements
It is possible to use the measured sliding speed and the analytical method expounded earlier to show the variations in the minimum film thickness for the two cases of coated and uncoated plates. This is shown in Figure 12. It can be seen that a very thin film is predicted in both cases. Aside from the initial accelerative phase, a fairly consistent film is predicted with slightly higher thickness for the case of Ni-SiC coated substrate.
The regime of lubrication can be ascertained by plotting the predictions in the form of the Stribeck lubricant film parameter. This is shown in Figure 13. Note that the critical value of this parameter, λ c = 2.3, after which mixed or boundary regimes of lubrication are encountered. This critical value is also shown in Figure 13. Since the uncoated steel plate has a superior honed surface post centre-less grinding, it is clear that the Stribeck parameter remains above the indicated critical value. This means that a hydrodynamic regime of lubrication should be prevalent. For the case of Ni-SiC coating, the Stribeck parameter remains close to its critical value, thus; a mixed regime of lubrication is expected.  The predicted load carrying capacity should equate the applied load. If the predictions in Figure 13 were to be upheld, then the contributions to the load carrying capacity from boundary and viscous friction should show that in the case of steel plate the contribution is entirely due to hydrodynamic pressures. In the case of Ni-SiC coating, there must be a significant portion of predicted load carried by the asperities. Figures 14 and 15 below confirm this supposition.
In the case of the steel plate, the entire load is supported by the hydrodynamic reaction; whereas in the case of the Ni-SiC plate, a combination of hydrodynamic and boundary reactions support the carried load. Hence, a mixed regime of lubrication exists (see the asperity load shares in Figures 15). This is partly because of the rougher Ni-SiC surface, owing to the grinding process and the hard brittle nature of Ni-SiC, when compared with the uncoated steel substrate and partly because of the higher shear strength of the Ni-SiC. The repercussion is that even if nominally identical topographies could be achieved, under boundary regime of lubrication, there would be higher boundary friction with the Ni-SiC than steel. However, the wear resistance of the former is significantly superior.

FRICTION IN CYLINDER LINER INSERTS UNDER MIXED REGIMES OF LUBRICATION
Friction has not appreciably increased with the use of Ni-SiC with even rougher topographies than the parent steel substrate as demonstrated in Figure 16.
Referring to Figure 15, the analytical results indicate that the thin hydrodynamic film produced in the contact would be sufficient to keep the asperities of the smoother steel surfaces apart, whilst the same is not true for the case of the rougher Ni-Sic surface. This accounts for the observed prevalence of the mixed regime of lubrication. The relatively high coefficient of friction for the steel plate as shown in Figure 16 may indicate non-Newtonian shear of quite a thin film. An important aspect of this analysis is the validity of rather simple analytical method as opposed to the usual detailed and time consuming numerical analysis.
There are a number of implications for these findings. First, more defined topography with valleys and plateaus may be achieved with Ni-SiC than with the more ductile steel substrate. Surface modifications are usually carried out through cylindrical grinding/cross-hatch honing which is better suited to hard and brittle materials. With ductile materials, sharp features are difficult to produce and in many cases require further finishing operations in order to remove any excess ploughed residues. This means that for cross-hatch honed cylinder liners, Ni-SiC coating would be an advantage, which has been  shown by Howell-Smith. 42 Additionally, surface texturing of surfaces, particularly using laser ablation is being studied. Some preliminary work on this is reported either for partial dimpling of compression ring surface 43 or for chevron features on the cylinder liner surface in the vicinity of ring reversal 44 or on the surface of the piston skirt. 45 All these studies show some percentage gains in efficiency (reduced friction) due to hydrodynamic pressure perturbation of retained lubricant reservoirs. Again use of hard coatings lends itself to better controlled laser surface texturing. Second, with smoother surfaces, when boundary interactions occur, there would be a larger number of lower amplitude asperities, and as the boundary friction equation shows, this can be quite detrimental in terms of boundary friction.

CONCLUSIONS
The paper combines analytical and experimental investigation of sliding contact of a strip, with a representative profile to that of a piston top compression ring against a flat substrate with material choice, coating and topography, representative of a cylinder liner insert. The part of the 4-stroke engine cycle, at the TDC in transition from compression to the power stroke is investigated with representative of load intensity and sliding speed, using a precision fully instrumented designed sliding tribometer. The use of tribometer puts the focus of the investigation upon frictional performance of counter face geometry, topography and surface material. The approach eliminates the multi-variate multi-parameter nature of the problem, which occurs in situ in fired engines. The results clearly show the advantages and disadvantages of the highlighted parameters upon the regime of lubrication and the mechanisms underlying the generated friction.