Transient TriboDynamics of ThermoElastic Compliant HighPerformance Piston Skirts
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Abstract
Advanced piston technology for motorsport applications is driven through development of lightweight pistons with preferentially compliant short partial skirts. The preferential compliance is achieved through structural stiffening, such that a greater entrainment wedge is achieved at the skirt’s bottom edge through thermoelastic deformation, whilst better conforming contact geometry at the top of the skirt. In practice, the combination of some of these conditions is intended to improve the loadcarrying capacity and reduce friction. The approach is fundamental to the underlying ethos of race and highperformance engine technology. Contact loads of the order of 5 kN and contact kinematics in the range 0–35 m/s result in harsh transient tribological conditions. Therefore, piston design requires detailed transient analysis, which integrates piston dynamics, thermoelastic distortion and transient elastohydrodynamics. The paper provides such a detailed analysis as well as verification of the same using noninvasive ultrasonicassisted lubricant film thickness measurement from a fired engine under normal operating conditions, an approach not hitherto reported in literature. Good agreement is noted between measured film thickness and predictions.
Keywords
Highperformance IC engines Compliant piston skirt Thermoelastic distortion Ultrasonic film thickness measurement Transient thermoelastohydrodynamicsList of symbols
 a
In Reynolds’ discretisation—contact halflength (m)
Elsewhere—distance from gudgeon pin axis to piston crown (m)
 b
In Reynolds’ discretisation—contact halfwidth (m)
Distance from piston’s centre of mass to piston crown (m)
 c
Nominal clearance (m)
 C_{c}
Crankshaft offset (m)
 C_{g}
Centre of gravity offset (m)
 C_{pb}
Gudgeon pin offset (m)
 C_{p}
Combined gudgeon pin and crankshaft offset (C _{p} = C _{pb} + C _{c}) (m)
 e_{b}
Clearance between bottom end of piston skirt and cylinder liner (m)
 e_{t}
Clearance between top end of piston skirt and cylinder liner (m)
 E′
Reduced Young’s modulus
 f_{con}
Connecting rod force (N)
 f_{g}
Gas force (N)
 f_{gg}
Inertial force of gudgeon due to primary motion (N)
 f_{gp}
Inertial force of piston due to primary motion (N)
 f_{ig}
Inertial force of gudgeon due to secondary motion (N)
 f_{ip}
Inertial force of piston due to secondary motion (N)
 f_{r1}
Reaction force at skirt’s antithrust side (N)
 f_{r2}
Reaction force at skirt’s thrust side (N)
 f_{s}
Side load due to connecting rod (N)
 h
Oil film thickness (m)
 i
Nodal location on skirt—axial direction (m)
 j
Nodal location on skirt—circumferential direction (m)
 I_{p}
Inertia of piston (kg m^{2})
 l
Connecting rod length (m)
 L
Skirt height (m)
 m_{g}
Mass of gudgeon pin (kg)
 m_{p}
Mass of piston (kg)
 M_{con}
Moment due to crankshaft offset (Nm)
 M_{fr1}
Moment due to antithrust’s reaction force (Nm)
 M_{fr2}
Moment due to thrust’s reaction force (Nm)
 M_{s}
Moment due to assembly’s offsets (Nm)
 nxx
Number of nodes along discretised skirt along the xdirection
 nyy
Number of nodes along discretised skirt along the ydirection
 p
Hydrodynamic pressure (Pa)
 p_{1}
Hydrodynamic pressure on antithrust side (Pa)
 p_{2}
Hydrodynamic pressure on thrust side (Pa)
 P
Cylinder pressure (bar)
 P_{b}
Pressure resulting from asperity interactions (Pa)
 P_{h}
Nondimensionalisation reference pressure (Pa)
 P_{ref}
Reference pressure (Pa)
 P_{v}
Viscous/hydrodynamic pressure (Pa)
 r
Crankshaft radius (m)
 r_{p}
Piston radius (m)
 R_{x}
Equivalent radius of curvature (m)
 t
Time (s)
 u
Speed of entraining motion (ms^{−1})
 u_{av}
Average speed used for nondimensionalisation (ms^{−1})
 v_{l}
Side leakage (ms^{−1})
 W
Nondimensionalisation reference load (N)
 x
In Reynolds’ equation—direction of entraining motion (m)
In piston kinematics—primary piston displacement (m)
 \({\ddot{x}}_{\text{ref}}\)
Reference acceleration (ms^{−2})
 y
In Reynolds’ equation—direction of side leakage (m)
 α
Pressureviscosity index (Pa^{−1})
 β
Piston’s rigid tilt angle (rad)
 β′
Thermal expansion coefficient of lubricant (K^{−1})
 ɛ_{p}
Pressure convergence criteria (−)
 η
Viscosity (Pa s)
 θ
Crankshaft torsional displacement (rad)
 ρ
Density (kg m^{−3})
 ϕ
Connecting rod angle
 φ_{j}
Circumferential location along the skirt (rad)
 ω
Crankshaft angular velocity (rad s^{−1})
 Ω
Pressure relaxation parameter (−)
Subscripts
 o
Denotes at ambient temperature and pressure
 p
Integrator time step number in linear acceleration method (−)
 q
Iteration step in linear acceleration method (−)
Superscripts
 \(\cdot\)
First time derivative (s^{−1})
 \(\cdot \cdot\)
Second time derivative (s^{−2})
1 Introduction
Frictional losses in the piston skirtcylinder liner conjunction account for approximately 3 % of the input fuel energy, whereas piston ring pack losses account for a further 4 % [11]. These losses are primarily due to viscous shear of the lubricant film and asperity interactions of contiguous surfaces. However, for most of the piston cycle, the regime of lubrication in the skirtcylinder liner conjunction is dominated by hydrodynamic or soft elastohydrodynamic (isoviscous elastic) regimes of lubrication [2, 16]. Therefore, aside from piston reversals at top and bottom dead centres, where mixed regime of lubrication can ensue, friction is usually generated through viscous shear of a lubricant film. Consequently, it has generally been surmised that reducing the lubricant viscosity would improve engine efficiency. However, the limiting factor is the lubricant loadcarrying capacity in conjunctions with relatively high load intensity, such as the camfollower contact [17]. Alternatively, a smaller piston skirt area would decrease friction as any boundary interaction is a function of the contact area. Through increased contact pressures, one may encourage piezoviscous action of the lubricant, leading to elastohydrodynamic conditions, which would yield the lowest friction [12, 35].
Lightweight aluminium pistons are seen more frequently in highperformance race engines as opposed to the OEM engines. They generally exhibit a more flexible contact area between the skirt and the liner. This is, however, usually at the expense of their operational life expectancy, because of the large distortions seen and the potential of ensuing fatigue. The growing emphasis on the reduction in the reciprocating mass and the increased demands brought by downsizing (with the resulting increase in the break mean effective pressure—BMEP) have a significant effect on the loads that the piston skirt needs to support. This has affected the deformed operating profile of contiguous solids, and therefore the contact conditions. Realistic prediction of these effects upon the mechanism of lubrication is the key to the ongoing developments for highperformance piston systems. In order to combine the effect of the aforementioned parameters throughout an engine cycle, a transient tribodynamic analysis is required. There is a dearth of reported research in this area with regard to the compliant race engine technology.
Li et al. [18] reported a transient hydrodynamic analysis of piston skirt. In particular, they studied the effects of lubricant viscosity and gudgeon pin offset on the overall friction. Knoll and Peeken [15] produced a similar study for the effects of piston offset on the generated tilting moments and maximum generated pressures. These works were confined to a rigid hydrodynamic analysis.
Zhu et al. [42, 43] presented a twopart analysis. In the first part, they developed transient hydrodynamics of rigid bodies in contact. The second part extended the approach to include gross piston distortions. They overcame the computation burden of the repeated timedependent calculations for piston skirt deflection through use of an influence coefficient matrix, derived from their own FEA model [43]. Common to both their contributions was the use of low relaxation Newton–Raphson iterative solution for system dynamics. McFadden and Turnbull [22] presented a model of secondary piston motions and used it for cases of differing skirt profiles. They calculated the piston’s primary motion dynamically using a reduced, coupled, spring and damper system. They illustrated the effect of incycle variable crank speed in a singlecylinder engine, though the analysis was limited to very low combustion pressures and, as such, relatively low side loads. Zhang et al. [41] demonstrated the effect of system inertia (including the connecting rod contribution) on the generated side forces. The dynamics of the system were solved using a fifthorder Runge–Kutta algorithm. Another solution with realistic combustion forces was presented by Perera et al. [28] who also included the effect of crank offset, using a flexible multibody dynamics’ approach in their transient analysis with GearStiff integration algorithm. However, although the effect of temperature on the lubricant film thickness was taken into account with realistic side forces, the tribological contacts of the skirtliner and piston ring pack were considered as rigid hydrodynamic. Offner and Priebsch [27] also used a flexible multibody model to simulate the lubricated impact and frequency response of the pistoncylinder bore. They showed, parametrically, the effects of varying the lubricant grade and the nominal clearance on the maximum generated hydrodynamic pressures. Balakrishnan and Rahnejat [2] undertook a transient dynamics analysis at high loads and speeds, but with only localised contact deflection in their skirtliner elastohydrodynamic analysis.
D’Agostino et al. [5] developed a transient elastohydrodynamic model, employing a multigrid approach for the solution of Reynolds equation with finite element analysis for piston skirt deflection. This approach can be computationally inefficient, as it employs a large influence coefficient matrix for a set of linear equations. However, the use of multithread synchronised calculations for the two opposing skirt sides yielded a significant gain in terms of computational efficiency.
McClure [21] and McClure and Tian [20] developed a thermoelastic transient routine, capturing the effect of moment contributions generated by the piston skirt conjunctional friction. They also included a simple model for pinbore interactions. They employed a compliance matrix in a similar manner to that of Littlefair et al. [19]. The work of McClure was developed further by Bai [1] to include a more accurate description of contact surface, using the average flow solution of Reynolds equation with limited oil availability. Partial verification was shown qualitatively using the laserinduced fluorescence (LIF) technique. Ning et al. [26] followed an approach similar to that of Li et al. [18], but included the effect of flexibility and friction moments in a transient analysis. The compliance array generated for the skirt was based on a linear system and applied in a similar way to that of Bai [1] and McClure [21], but somewhat oversimplifying the loading condition in the piston FEA model.
Overall, the importance of piston skirt shape is well understood, and the features are “optimised” to account for the differential thermal expansion, whilst still offering adequate entraining geometries. The inservice shape is much harder to control as this emerges as a result of various mechanical distortions. Recently, Hoshikawa et al. [13] showed, through experimental techniques, the effect of stiffness variations and compared it with the analysis on frictional changes using a floating liner setup. Qualitative observations from a visual liner were also made. Bai [1] also showed the effect of modifying the structural stiffness of the skirt using techniques detailed earlier by McClure [21]. The effects of varying the piston’s structural stiffness on contact conditions, film shape and generated pressures were discussed. Partial verification was reported through laserinduced fluorescence (LIF) observations of the contact, which gave a rough qualitative comparison in terms of clearance and film shape. A quantitative comparison was made by DwyerJoyce et al. [9] using a single ultrasonic sensor, which showed good agreement between the measured film thickness and the predictive transient analysis, although a full 2D film thickness measurement and validation was not conducted.
Before a good estimate of friction in an engine cycle can be made, the regime of lubrication should be ascertained in a transient thermoelastohydrodynamic analysis, which takes into account salient practical features such as thermoelastic distortion of the piston skirt. The prerequisite step in this quest is accurate prediction of film thickness throughout the engine cycle and validation of the methodology against precise measurement of film thickness. This is the area where hitherto lack of research findings is the most poignant. This paper is an attempt to overcome this particular shortcoming through combined noninvasive ultrasonicassisted measurement of lubricant film thickness and transient thermoelastohydrodynamics of a thermoelastically distorted compliant piston skirtliner conjunction for a highperformance motocross race engine. The ultrasonic film thickness measurement technique used here is based on the same overall principles as that reported in DwyerJoyce et al. [9]. However, the measurement resolution is much enhanced by fabrication of an array of ultrasonic sensors of considerably smaller size. It is important to note that coarser sensor dimensions, such as that reported in DwyerJoyce et al. [9], provide only an average film thickness over their actual physical dimension. Furthermore, measurement with a single sensor provides a time history of the film thickness as the piston traverses past the sensor’s position. Hence, the film profile is not representative of a given instantaneous film shape and can lead to erroneous film shape determination by secondary motion of the piston. These shortcomings are overcome with the use of an array of fineresolution sensors, but with the drawback of much more complex data acquisition and data processing.
2 Experimental SetUp
A number of techniques have been developed and documented for measuring film thickness within IC engines. Laserinduced fluorescence (LIF) documented by Inagaki et al. has been used [14], inductance techniques by Taylor and Evans [38] and finally a capacitance approach by Söchting and Sherrington [36]. Each of these techniques needs to invasively modify (to varying degrees) the structural components for the installation of sensing elements. Thermal and loadgenerated deformation may then be affected, and differences in local tribological conditions may inadvertently be introduced.
By generating ultrasound on the exterior surface of the cylinder liner which is reflected back from the bore surface, the parent material of the liner remains unaltered. The conditions at the contact between bore and piston, however, affect the properties of the reflected wave. A brief overview of the ultrasonic technique used is provided here. However, the reader is directed to Mills et al. [23] for a more detailed account of the methodology.
Basic engine parameters
Bore  96 mm 
Stroke  62 mm 
Conrod length  107 mm 
Capacity  449 cc 
Nominal skirtliner clearance  1525 μm 
Operating speed range  3,000–10,000 rpm 
Maximum power  41 kW at 9,000 rpm 
Maximum torque  49.8 Nm at 7,000 rpm 
The piezoelectric elements used for this test were pulsed at their centre frequency of 10 MHz. The pulses were generated and received in pulseecho mode, using a PCmounted ultrasonic pulse receiver. Pulses were generated at a rate of 80 k pulse/s, and the local portion of the reflection was digitised at 100 M samples/s. The region of the signal corresponding to the first linerskirt reflection was windowed and stored to a hard disk drive with the corresponding crank angle position obtained from a crankmounted, 360count encoder. A remotely operated multiplexer was used to switch between the active elements. Each element was pulsed for a period of 2 s before switching to the next. A total of between 70 and 120 engine cycles were captured at each sensor position over the engine speeds tested. The presented results are therefore the mean lubricant film thickness obtained from multiple cycles.
Prior to measuring lubricant film thickness, a liner instrumented with 8 ktype thermocouples was used to provide an axial temperature distribution along the accessible region of the liner. The thermocouples were positioned 0.8 mm from the internal surface of the liner. During testing, it was found that the internal surface of the cylinder was typically 30 °C hotter than the exiting coolant temperature. The operational temperatures were used to obtain the acoustic properties of the lubricant during the test (the oil having been characterised using an oven prior to testing).
The spectral content of the reflected pulses was extracted using fast Fourier transform (FFT) and the reflection coefficient obtained by normalising the measured spectral content with that from a reference pulse. The term reference pulse refers to the condition of total internal reflection of the ultrasound pulse. This essentially occurred when a gas interface was present at the liner surface. The reference condition was obtained during periods when the position of the piston was away from the location of the sensors. By continually updating the reference reflection, temperatureinduced transducer drifts could be eliminated. The measured reflection coefficient was then used to calculate film thickness using Eq. (3).
3 Numerical Model
3.1 Dynamic and Kinematic Analysis
To adequately replicate the physics of motion of the pistonconnecting rodcrankshaft assembly, the inertial dynamics of the system must be addressed. It is necessary to derive the equations of motion of the system, comprising piston primary and secondary motions.
The primary motion of the piston (in the xdirection in Fig. 3) is treated as kinematic, governed by the instantaneous rotational motion of the crankshaft. However, the secondary motion (in the zdirection in Fig. 3) of the piston is more complex dynamic problem, confined within its radial clearance (x–z plane). The inherent change in the connecting rod angle, combined with the effect of gudgeon pin and/or crankshaft offsets and the varying combustion pressure and rotational speed, induces transient secondary motions of the piston within the confine of its clearance (zdirection lateral excursion and the tilting motion β).
3.2 Lubrication Analysis
The short piston skirt has a heighttowidth ratio of around 1:1.8; thus, a twodimensional form of Reynolds equation is used. Given the transient nature of the problem, it is necessary to retain the squeeze film effect (i.e. the lubricant film history, dh/dt). However, an assumption of no side leakage of lubricant in the circumferential direction is reasonable to be made, thus v _{l} = 0.
Since, in the case presented here, the centroid of the piston lies on the central axis, there are no moments due to the effect of gudgeon pin or centre of gravity offset. Hence, M _{s} = 0.
For the case of the antithrust side, one must accommodate the distortion due to the reaction force f _{r1} and modify the signs of the corresponding \(\Updelta e_{\text{t}} \;{\text{and}}\;\Updelta e_{\text{b}}\) values.
3.3 Deformation Analysis
The methodology used for the estimation of the piston’s deflection is the same as that presented by Littlefair et al. [19]. However, for completeness, a brief summary is provided here. The overall deflection on the piston skirt is due to four main factors. These are: (1) mechanical distortion due to forces acting orthogonal to the skirt surface, (2) distortion due to the application of combustion pressure on the piston crown surface, (3) thermal distortion due to the temperature gradient and (4) inertialinduced piston distortion due to the primary accelerative motion.
Given the highly iterative nature of the transient analysis, a compliance matrix, [A], is created to reduce the computational time burden for the solution of Eq. (18).
A single unit load L _{u} is applied orthogonal to the skirt surface at each nodal position, and the corresponding deflection is recorded for the y and zdirections for all of the surface nodes. By repeating this process for each node location, in isolation and sequentially, a fivedimensional reduced array is formed: A(i, j, k, l, n), where i and j refer to the applied load location, k and l denote the skirt nodal deflection position, and n is either 1 or 2 for the y or zdirection in which the deflection occurs.
Using the same FEA model, the distortion due to combustion pressure can also be approximated. This is achieved by applying a single static case for a halfpiston model with symmetrical boundary conditions. The constraining reaction is provided by the pinbore axis with its XYZ directions constrained, replicating a stable vertical reaction from the gudgeon pinbore interface. Since a linear response is still retained, the direct proportionality between the incylinder pressure and the skirt deflection in the y–z plane is obtained.

There is no gudgeon pin offset, and the cylinder pressure acts evenly on the piston crown. This is the configuration for the engine under investigation.

The crown deflection has negligible effect on the direction of the application of pressure. At the maximum combustion pressure of 90 bar, the sense of application of pressure (surface normal) alters by a mere 0.1 degrees, which is quite insignificant. Therefore, the very small deflection of the piston crown at its edges does not set up an additional moment about the gudgeon pin.

The vertical component of the constraint on the gudgeon axis acts to oppose the application of pressure (i.e. transfers the force through the connecting rod). Therefore, any horizontal component generated by the connecting rod angle is opposed by the interaction between the liner and the piston skirt. This is insignificant in changing the application of the gudgeon pin constraint.
3.4 Method of Solution
The solution methodology is intrinsically iterative, accounting for a full numerical solution of Reynolds equation and a stepbystep numerical integration of equations of motion. The integration algorithm chosen is the linear acceleration method proposed by Timoshenko et al. [39], for the solution of nonlinear dynamic problems involving vibrationinduced impact and/or friction. It is based on Newmark’s algorithm [25], and previous experience has shown the effectiveness and accuracy of this method for contact dynamics problem (Rahnejat [32] and De la Cruz et al. [6]).
The term \({\raise0.7ex\hbox{${\partial h}$} \!\mathord{\left/ {\vphantom {{\partial h} {\partial t}}}\right.\kern0pt} \!\lower0.7ex\hbox{${\partial t}$}}\) is the squeeze film velocity, which represents the history of film thickness variation with time during the simulation study. Therefore, instantaneous changes in contact kinematics and film thickness variation with time are retained in the tribological study. The inclusion of this term in Reynolds equation yields a transient analysis. When this is not retained as in some numerical analyses, a steadystate or quasistatic equilibrium in the conjunction is implied (i.e. the applied side force equates the contact reaction within a specified limit).
Equation (24) is then solved using the low relaxation effective influence Newton–Raphson (EIN) method with Gauss–Seidel iterations [15].
The overall algorithm describing the full solution can be summarised in the following four steps:
Step 1
Pressure p and displacements e _{t} and e _{b} are used to determine the deflections with the aid of the compliance matrix. The initial film shapes for thrust and antithrust sides are thus obtained.
Step 2
Step 3
Once a converged pressure distribution is achieved, the hydrodynamic reaction loads f _{r1} and f _{r2} and the corresponding moments m _{fr1} and m _{fr2}, acting on the piston skirt sides, are calculated.
It is important to note that given the transient nature of the problem, the standard load convergence usually found in quasistatic analyses is replaced by dynamic convergence of equations of motion based on acceleration. This takes into account inertial forces instantaneously applied to the piston and is the essence of a transient dynamic analysis [12].
Step 4
An inhouse piece of software was developed for this methodology in Fortran 95 (Linux environment), using the Intel ifort compiler, NAG libraries and OpenMP for parallel programming. The processor was a 2.9 GHz dual intel Xeon quad core chip. For a typical time step of 5 μs, at the nominal engine speed of 4,250 rpm and full throttle conditions, the computation time for one full engine cycle is around 8 h.
4 Results and Discussion
The Honda CRF 450 R engine was run for a number of speed/load combinations. The results for two specific conditions are reported here. These are at the engine speeds of 4,250 and 6,250 rpm, both with wide open throttle. Note that this is a relatively short stroke race engine, which idles smoothly at 4,000 rpm. Thus, the speed of 4,250 rpm represents a relatively low speed application. This together with high load (wide open throttle) represents relatively poor lubrication condition (low speed, high load). The higher speed of 6,250 rpm represents medium speed in highway driving.
The thermocouples installed on the liner (Sect. 2) show an average temperature of around 110 °C, once steadystate conditions are reached. Therefore, the temperature of entrant lubricant into the contact is assumed to remain the same.
The incylinder pressure is measured using a Kistler sparkplugtype pressure transducer, inserted into the combustion chamber. This enables calculation of the gas force f _{g} acting on the piston crown surface. Since there is no gudgeon pin offset, C _{pb} in this engine configuration, the gas force is assumed to be evenly distributed over the piston crown.
All the numerical results presented here correspond to an overall simulation run of 1,440° crank angle (i.e. two full engine cycles: Honda CRF 450 R is a 4stroke naturally aspirated engine). The reason behind this is to ascertain that any transient period of the numerical integrator has elapsed and a steadystate response has been reached. For plotting purposes, only the second cycle is presented, always starting from a crankshaft angle of −180°, corresponding to the beginning of the compression stroke. This is then followed by the power, exhaust and intake stokes, ending up at the crank angle of 540°.
Given the transient nature of the results obtained, it is worth starting the analysis with a description of the piston’s secondary motion. For all the cases shown, the piston’s minimum nominal clearance, c, with the liner subjected to uniform thermally distorted conditions is 18 μm. In reality, thermal distortion of the liner varies along its axial direction because of the axial temperature distribution. Additionally, the cylinder blocks; thus, the bore/liner undergoes dynamic thermoelastic deformation, which is not taken into account in the current analysis. The dynamic block thermal distortion is found to be insignificant for the current short interval of testing, but can become important in many engines as reported by Piao and Gulwadi [29]. This means that when the piston is perfectly aligned, the starting e _{t} and e _{b} values are 39 and 60 μm, respectively.
Interestingly, e _{t} undergoes a much smoother motion compared to e _{b}. The overall displacement variation along the full cycle is around 43 μm, as opposed to the 175 μm encountered in the 6,250 rpm case. The large changes in displacement observed at e _{t} at both investigated speed cases are as the result of the relatively low stiffness observed towards the bottom of the skirt (preferentially compliant skirt design). The purpose of this is twofold. It dampens the secondary motion, absorbing a portion of the kinetic energy. It also ensures in the downward sense of the piston the inlet wedge effect by altering the inlet geometry (radius). This enhances the thermoelastic deformation at the bottom of the skirt because of a lower structural stiffness there. This is important during the higher mechanical and thermal loading in the combustion stroke. Higher stiffness at the top of the piston skirt provides the necessary loadcarrying capacity. The effect of ensuring a suitable inlet wedge enhances lubricant entrainment into the contact and thus improves the mechanism of lubrication. This observation seems to be in line with the main design characteristics for this highperformance engine, a phenomenon also reported by Bai [1].
The reference positions for e _{t} and e _{b} are between the thermally deformed liner and the piston from their original starting positions when their axial alignments are set. In motion and with the combination of the various mechanical distortions, these values alter significantly. In some cases, where the distortions are significant enough, the values may become negative.
Referring back to Fig. 6, the highest measured combustion pressure is encountered at the engine speed of 6,250 rpm at 92 bar as opposed to 80 bar for the engine speed of 4,250 rpm. One may, therefore, surmise that higher hydrodynamic pressures and side loads would ensue at the higher engine speeds. However, this is to the contrary, because of the crankshaft offset and the connecting rod angle seen at the position of maximum pressure. Even though the combustion peak is higher at 6,250 rpm, it actually occurs 8° crank angle prior to that at 4,250 rpm in the power stroke as the ignition point is advanced as both the load and speed increase. Therefore, the effect of a higher gas force on the side load is diminished by a more vertical connecting rod orientation at the higher engine speed. The other reason for lower generated hydrodynamic pressures at the higher engine speed is related to the effect of higher speeds of entraining motion (given the assumption of fully flooded conditions). Higher speeds lead to thicker lubricant films. This means that for a similar loading condition the peak hydrodynamic pressure is reduced at a higher engine speed in the case of this type of engine.
5 Experimental Verification
It is important to present experimental verification of numerical predictions. With the arrangement described in the experimental section and, again, using the engine speed of 4,250 rpm, direct comparisons between numerically predicted film thickness and shape with those experimentally measured are presented.
Due to the intrinsic difficulties of the experimental measurement of film thickness under transient conditions, the data available are not necessarily for the crankshaft locations presented above. After exhaustive data processing, it was found that the largest amount of data successfully collected was at 38°, 43° and 53° crank angles. Therefore, validation work is conducted for these specific crank angle locations.
6 Concluding Remarks
A detailed methodology to predict piston skirtliner conjunctional performance is presented, which includes the effect of all major causes contributing to the thermoelastic deformation of the contiguous contacting solids under transient dynamic conditions. The elastohydrodynamics of the contact is also embedded within the transient dynamic analysis. The analysis shows that short piston skirts of light highperformance pistons with preferential skirt structural compliance promote good inlet wedge through most of the heavily loaded portion of the cycle. The predictions are verified by in situ noninvasive measurement of film thickness under transient conditions from a fired engine operating at various speedload combinations. Further work will account for additional cylinder liner distortions and experimental techniques to acquire the skirt’s instantaneous operating temperatures.
Notes
Acknowledgments
The authors wish to express their gratitude to the EPSRC for the financial support extended to the Encyclopaedic Program Grant, under which this research was carried out. Thanks are also due to the consortium of industrial partners of the Encyclopaedic project, particularly in this instance Capricorn Automotive.
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