Christiansen, Jens

Hyun-Hwang, Jong

Klit, Peder

Vølund, Anders

In 1966 Jorgen W. Lund published an approach to find the dynamic coefficients of a journal bearing by a first order perturbation of the Reynold's equation. These coefficients made it possible to perform a rotor-bearing stability analysis for a statically loaded bearing. In the mid seventies Jorgen W. Lund pointed out in lecture notes that the dynamic damping coefficients of the bearing could be used to find the shaft orbit for dynamically loaded bearings. In the present paper this method is further developed and utilized to determine the dynamic behavior of a piston ring in a combustion engine. The basic idea is to use the fluid film damping coefficients to estimate the film thickness variation for a piston ring under cyclic varying load. Reynolds Equation is solved for a piston ring and the oil film thickness is determined. In this analysis hydrodynamic lubrication is assumed and the effect of the squeeze motion is considered

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Downloaded from orbit.dtu.dk on: Dec 17, 2017Calculation of Oil Film Thickness from Damping Coefficients for a Piston Ring in anInternal Combustion EngineChristiansen, Jens; Klit, Peder; Vølund, Anders; Hyun-Hwang, JongPublished in:BaltTrib'2007Publication date:2007Document VersionPeer reviewed versionLink back to DTU OrbitCitation (APA):Christiansen, J., Klit, P., Vølund, A., & Hyun-Hwang, J. (2007). Calculation of Oil Film Thickness from DampingCoefficients for a Piston Ring in an Internal Combustion Engine. In BaltTrib'2007 (pp. 162-167). Kaunas,Lithuania: Lithuanian University of Agriculture.Proceedings of the International Conference BALTTRIB’2007Calculation of Oil Film Thickness from DampingCoefficients for a Piston Ring in an InternalCombustion EngineJens Christiansen∗, Peder Klit∗, Anders Volund∗∗ and Jong-Hyun Hwang∗∗∗∗ Department of Mechanical Engineering, Technical University of Denmark, Denmark∗∗ MAN Diesel A/S, Denmark∗∗∗ Hyundai Heavy Industries CO. LTD., KoreaAbstract: In 1966 Jorgen W. Lund [1] published an approach to find the dynamic coefficientsof a journal bearing by a first order perturbation of the Reynold’s equation. These coefficientsmade it possible to perform a rotor-bearing stability analysis for a statically loaded bearing.In the mid seventies Jorgen W. Lund pointed out in lecture notes that the dynamic dampingcoefficients of the bearing could be used to find the shaft orbit for dynamically loaded bearings.In the present paper this method is further developed and utilized to determine the dynamicbehavior of a piston ring in a combustion engine. The basic idea is to use the fluid film dampingcoefficients to estimate the film thickness variation for a piston ring under cyclic varying load.Reynolds Equation is solved for a piston ring and the oil film thickness is determined. In thisanalysis hydrodynamic lubrication is assumed and the effect of the squeeze motion is consid-ered. Cavitation zones are taken into account and the piston ring is assumed to be fully flooded.Governing equations and numerical schemes are presented. Numerical computations show goodcorrelation with analytical results.Keywords: Piston Rings, Cavitation, Prediction of oil film thickness, Engine lubrication.1 IntroductionInternal combustion engines are used for many purposes, e. g. ship propulsion. The classicmethod to analyze the interface between the piston ring and cylinder liner is to solve ReynoldsEquation by integration and calculate e. g. oil film thickness. This is shown by [2]. In [1]is presented a method to determine the dynamic coefficients for a journal bearing. Volund [3]developed from Lund a method to calculate the orbit of the cross head in an internal combustionengine. This paper describes how this method is implemented for a piston ring.2 Reynolds EquationIn this analysis endflow is neglected because b ¿ l. Reynolds Equation for a one dimensionalflow is shown in equation (1).∂∂x(h312ηdpdx) =u2∂h∂x+∂h∂t(1)Figure 1: Shape of piston ring3 Equilibrium of ForcesEquilibrium of forces is found by Newtons 2. Law. The forces from the mass of the pistonring is neglected, because this is considered to be small compared to the film forces. The forcesacting on the piston ring are the external load and the film forces from the oil. This gives theequilibrium in force seen in equation (2).F ′ext −W ′ = 0 (2)4 Geometry of Piston RingA piston ring in an engine is worn over time, and the initial shape of the ring changes to beroughly approximated by a circle or parabola. The piston ring shape used in the present paperis set to be parabolic. The piston ring shape are seen in figure 1.5 Solution from damping coefficientsSolutions to equation 2 in time are found by perturbation approach. This can be done byintroducing a perturbation in the velocity.The piston ring is given a small perturbation in velocity ∆h˙. This leads to a perturbation inthe pressure ∆p. The perturbed pressure and velocity are given by equation (3).h˙ = h˙+∆h˙p = p0 + ph˙∆h˙ (3)The perturbation pressure and perturbation velocity are introduced in Reynolds Equation. Thisis seen in equation (4).∂∂x(h312η∂∂x(p0 + ph˙∆h˙) = u˜∂h∂x+ h˙ (4)This equation is divided into two equations (5) and (6).∂∂x(h312η∂p0∂x) = u˜∂h∂x+ h˙ (5)∂∂x(h312η∂ph˙∂x) = 1 (6)Equations (5) and (6) are solved by the Finite Difference Method. The pressure distribution isfound by applying the Modified Reynolds Cavitation criteria seen in (7).p = p1 at x = x1 anddpdx= 0 at x = x∗ (7)Here the damping is calculated from the perturbation pressures in equation (8).c′ =∫ph˙dx (8)The load carrying capacity is calculated from the pressure distribution, p0 in equation (9).W ′ =∫ l0p0dx (9)A new value of the perturbation velocity is calculated from an equilibrium in forces seen inequation (10).F ′ext =W′ + c′∆h˙i ⇔ ∆h˙i = F′ext −W ′c′(10)The new h0 is calculated by equation (11).˙hi+1 = h˙i +∆h˙i (11)When convergence between film forces and outer forces is obtained, the new position of thepiston ring is calculated by assuming that the velocity and damping are constant over a timestep. This is done by Eulers algorithm.6 Performance ParametersThe flow is given by equation (12).q′x = −h312η∂p∂x+ hu˜ (12)The shear stresses are seen in equation (13).τliner = −h2∂p∂x− η(uring − uliner)hand τring = −h2∂p∂x+η(uring − uliner)h(13)The friction forces are then found by integrating the shear stresses. These are shown in equation(14).F ′a =∫τlinerdx and F′b =∫τringdx (14)The power loss is calculated from the friction force. This is seen in equation (15).h′p,liner = −F ′lineruliner and h′p,ring = −F ′buring (15)The coefficient of friction at is calculated from equation (16).µliner =F ′linerW ′and µring =F ′ringW ′(16)The center of the pressure distribution is calculated by equation (17). This is the position wherethe resulting force is acting.xcp =∫pxdxW ′(17)Description Size/Number/Typel 9, 5mmsh 9, 5µmη 0, 01PasTable 1: Piston ring geometry7 Results from simulationData from MAN Diesels research engine, T50mx are used simulate the top ring in the piston.The data, shown in figure 2 contains information about the boundary pressure and velocityof the ring. Parameters to describe the piston ring shape and lubrication oil, type SAE 50 ispresented in table 1.pi/2 pi 3pi/2 2pi pi/2051015Angle [rad]Pressure [MPa]  Combustion chamberScavenge air ports(a) Boundary pressurepi/2 pi 3pi/2 2pi pi/2−8−6−4−202468Angle [rad]Rel. vel. [m/s](b) Relative velocityFigure 2: Input parametersThe simulation is started in the midpoint between TDC and BDC where the velocity has reachedmaximum and the boundary pressures are relatively small.Stroke from pi/2 to piThe velocity is decreasing which gives smaller load carrying capacity. At first the OFT is de-creasing until the ring passes the scavenge air ports, where the pressure drops. The pressuredrop leads to a smaller load behind the ring, which gives an increase in OFT. The steady de-creasing velocity provides decreasing load carrying which makes the OFT decrease again. Thefluctuations in OFT leads to oscillations in center of pressure and cavitation boundaries.Stroke from pi to 3pi/2In this part of the stroke the velocity is increasing. At first the boundary pressures are constant,which provides an increase in oil film thickness. Then the pressure increases because the com-bustion chamber volume gets smaller, which leads to decreasing oil film thickness.Stroke from 3pi/2 to 2piThe velocity gets smaller contemporary with a pressure increase. In TDC the pressure reachesmaximum and the velocity minimum over the cycle. This combination results in a steady de-creasing oil film thickness and the minimum oil film thickness is observed in TDC. The powerloss gets larger very fast.Stroke from 0 to pi/2The velocity increases and the overall pressure drops. An oscillation in combustion chamberpressure results in an oil film thickness peak of the concurrent increasing oil film. The peak canalso be observed in the squeeze velocity and cavitation boundary.8 ConclusionFrom dynamic coefficients have the oil film thickness and other performance parameters beenpredicted for a diesel engine. The results shows that the minimum oil film thickness arises whenthe piston is in the TDC.9 AcknowledgementsThe authors would like to thank The Internal Combustion Engine Section at The Department ofMechanical Engineering at Technical University of Denmark, Korean Government (MOEHRD)(KRF-2006-612-D00009) and MAN Diesel A/S for funding this research project.The test apparatus at hand is part of the EU - Sixth Framework Program. Contract no.TIP3-CT-2003-506676. The I.P. HERCULES (Integrated Project: High Efficiency R&D onCombustion with Ultra Low Emissions for Ships) is a large scale cooperative R&D projectsupported by the European Commission and the Swiss Federal Government (BBW & BFE).References[1] J. W. Lund and K. K. Thomsen. A calculation method and data for the dynamic coeffi-cients of oil lubricated journal bearings. Topics in Fluid Film Bearing and Rotor BearingSystem Design and Optimisation, pages pp.1–28, April 17-20 1978. The Design EngineeringConference, Chicago, Illinois.[2] D. Dowson M. Priest, R. I. Taylor and C. M. Taylor. Boundary conditions for reynoldsequation with particular reference to piston ring lubrication. Tribology series; 31, pages pp.441–452, 1996.[3] Anders Volund and Peder Klit. Guide bearing charateristics. 9 th Nordic Symposium onTribology, Nordtrib, 2000.Author for contacts:Peder KlitDepartment of Mechanical Engineering, Technical University of Denmark, Building 404, room009, 2800 Lyngby, Denmark.Phone: +45 45256267, Fax: +45 45931577, E - mail: klit@mek.dtu.dk.pi/2 pi 3pi/2 2pi pi/205101520253035404550time [s]OFT [µm](a) Oil film thicknesspi/2 pi 3pi/2 2pi pi/2−4000−200002000400060008000time [s]Squeeze velocity [µm/s](b) Squeeze velocitypi/2 pi 3pi/2 2pi pi/2010002000300040005000600070008000900010000time [s]Film position [µm]  CavitationStarvation(c) Cavitation boundariespi/2 pi 3pi/2 2pi pi/220002500300035004000450050005500time [s]Center of pressure [µm](d) Center of pressurepi/2 pi 3pi/2 2pi pi/2−3−2−101234x 10−4time [s]Flow [m2 /s]  Lead. EdgeTrail. Edge(e) Flowpi/2 pi 3pi/2 2pi pi/2−100−50050100150time [s]Friction Force [N/m]  LinerRing(f) Friction forcepi/2 pi 3pi/2 2pi pi/200.050.10.150.20.25time [s]Coeff. of friction  LinerRing(g) coeff. of frictionpi/2 pi 3pi/2 2pi pi/2−1000100200300400500600700800time [s]Power loss [W/m]  LinerRing(h) Power lossFigure 3: Resultsc′ Damping, Ns/mF ′ext Load per unit width, N/mP Oil pressure, Paq′ Volumetric flow rate per unit width, m2/ssh Shoulder height, mu˜ Mean surface velocity in x - direction, m/sW’ Load carrying capacity per unit width, N/mη Absolute viscosity, Pasρ Density, kg/m3Table 2: Nomenclature

Calculation of Oil Film Thickness from Damping Coefficients for a Piston Ring in an Internal Combustion Engine

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Calculation of Oil Film Thickness from Damping Coefficients for a Piston Ring in an Internal Combustion Engine

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