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A Numerical Study on Influence of Temperature on Lubricant Film energies Article A Numerical Study on Influence of Temperature on Lubricant Film Characteristics of the Piston/Cylinder Interface in Axial Piston Pumps Yueheng Song 1, Jiming Ma 2 and Shengkui Zeng 1,3,* ID 1 School of Reliability and System Engineering, Beihang University, Beijing 100191, China; [email protected] 2 Sino-French Engineering School, Beihang University, Beijing 100191, China; [email protected] 3 Science and Technology on Reliability and Environmental Engineering Laboratory, Beihang University, Beijing 100191, China * Correspondence: [email protected]; Tel.: +86-108-231-6369 Received: 13 June 2018; Accepted: 12 July 2018; Published: 13 July 2018 Abstract: The loss of kinetic energy of moving parts due to viscous friction of lubricant causes the reduction of piston pump efficiency. The viscosity of lubricant film is mainly affected by the thermal effect. In order to improve energy efficiency of piston pump, this research presents a numerical method to analyze the lubricant film characteristics in axial piston pumps, considering the thermal effect by the coupled multi-disciplinary model, which includes the fluid flow field expressed by Reynolds equation, temperature field expressed by energy equation and heat transfer equation, kinematics expressed by the motion equation. The velocity and temperature distributions of the gap flow of piston/cylinder interface in steady state are firstly numerically computed. Then the distributions are validated by the experiment. Finally, by changing the thermal boundary condition, the influence of thermal effect on the lubricant film, the eccentricity and the contact time between the piston and cylinder are analyzed. Results show that with the increase of temperature, the contact time increases in the form of a hyperbolic tangent function, which will reduce the efficiency of the axial piston pump. There is a critical temperature beyond which the contact time will increase rapidly, thus this temperature is the considered as a key point for the temperature design. Keywords: thermodynamic; numerical simulation; thermal effect; axial piston pumps 1. Introduction As sliding pairs of axial piston pump move, both the metal parts and lubricants heat up, which causes temperature to increase significantly, decreases oil viscosity, reduces the bearing capacity of the oil, and intensifies the radial movement of the parts simultaneously [1]. The shape of the oil film changes, as does the lubrication mode, and the trajectory of piston could vary with the changing of oil film. The temperature impacts on oil film characteristics are important for analysis of the efficiency of the sliding pair. Practical experience also indicates that the medium temperature significantly affects life. Cai et al. [2] tested the life of steel materials with a lubricating medium in the range of 23–175 ◦C and verified that the wear degree was directly related to the temperature. Specifically, the life of steel materials was closely related to the oil temperature distribution in the gap, and the distribution condition had a distinct influence on the oil characteristics. Unfortunately, the general test method could take temperature as the only variables; thus the results obtained by this way could only indicate the existence of a fuzzy relationship between temperature and life. Energies 2018, 11, 1842; doi:10.3390/en11071842 www.mdpi.com/journal/energies Energies 2018, 11, x FOR PEER REVIEW 2 of 16 Energies 2018, 11, 1842 2 of 16 To indicate the relationship between the temperature and life more precisely, the behavior of lubricantTo indicate film between the relationship the moving between pair need thes temperatureto be studied. and Because life more the moving precisely, process the behavior is affected of lubricantby fluid, filmsolid, between and thermal the moving conditions pair needs together, to be it studied. is a typical Because multiple the moving-domain process coupled is affected problem. by fluid,Many solid,researchers and thermal have conditionsstudied this together, problem it isaround a typical the multiple-domain bearing. McCallion coupled et al. problem. [3] solved Many the researchersReynolds and have e studiednergy equations this problem separately around the and bearing. neglected McCallion the effects et al. [ 3]of solved pressures the Reynolds during andthe energycalculation equations of temperature separately distribution and neglected. Ferron the effects et al. of[4] pressures thoroughly during studied the calculationthe thermohydrodynamic of temperature distribution.(THD) performance Ferron etof al.a plain [4] thoroughly journal bearing studied and the determined thermohydrodynamic its thermal (THD)characteristics. performance Rohde of et a plainal. [5] journal studied bearing the elastic and determinedand thermal its deformations thermal characteristics. in a slider Rohdebearing, et al.noted [5] studiedthat the the variations elastic and in thermalfluid viscosity deformations with temperature in a slider bearing, were much noted more that influential the variations than in solid fluid deformation viscosity with due temperature to thermal wereand elastic much moreeffects. influential Researchers than ar solide still deformation interested in due the to journal thermal bearing and elastic where effects. oil or Researchers gas is used are as stilllubricants interested [6,7]. in Lu the et journal al. [8] conducted bearing where a thermal oil or- gasfluid is coupling used as lubricants study on characteristics [6,7]. Lu et al. [of8] air conducted–oil two aphase thermal-fluid flow and coupling heat transfer study onin a characteristics micro unmanned of air–oil aerial two vehicle phase flow(UAV and) bearing heat transfer chamber. in a microSome unmannedresearchers aerial took vehiclethe cavitation (UAV) bearinginto account chamber. [9] and Some others researchers develop tooked an the efficient cavitation numerical into account method [9] and[10].others developed an efficient numerical method [10]. Axial piston piston pumps pumps with with constant constant pressure pressure are arethe main the main type typeof engine of engine-driven-driven pumps pumps(EDP), (EDP),whose whoselifetime lifetime is affected is affected by three by three sliding sliding pairs, pairs, specifically specifically the the swash swash plate/slipper pair, cylinder/valvecylinder/valve plate plate pair, pair, and piston/cylinder pair, pair, as as shown shown in in Figure Figure 11.. Figure 1.1. Sliding pairs in axial piston pump.pump. Several Elasto Hydrodynamic Lubrication ( (EHL)EHL) researches have focused on the piston pump. Gels etet al.al. developed a simulation tool based on thethe ReynoldsReynolds equation,equation, which allowed to vary thethe geometry of the slidingsliding parts. With the help of thisthis tool,tool, GelsGels havehave foundfound an optimaloptimal compromise of piston/cylinderpiston/cylinder interface which reduces the losses ofof energy [[11].11]. MaMa etet al. presented a method onon thethe basis ofof thethe EHL EHL model model to to analyze analyze the the behavior behavior of of the the swash swash plate/slipper plate/slipper pair pair [12 [12].]. Olems Olems presented presented an analyticalan analytical model model that integratesthat integrates the multiphysics the multiphysics characteristic characteristic equations equations including including Reynolds Reynolds Equation andEquati energyon and equation energy [ 13equation]. Given [13]. inlet Given medium inlet temperature medium temperature and operating and conditions, operating the conditions, temperature the distributiontemperature indistribution the clearance in ofthe piston/cylinder clearance of piston/cylinder interface wasdetermined interface was using determined the model. using A series the ofmodel. studies A ofseries MAHA of studies research of centerMAHA were research carried center out based were oncarried Olem’s out results. based Ivantysynovaon Olem’s results. et al. establishedIvatysynova a et complete al. established model ofa complete main sliding model pairs of main for thermal sliding analysis pairs for of thermal oil film analysis gap [14]. of Kazama oil film establishedgap [14]. Kazama a non-isothermal established model a non- ofisothermal slipper/swash model plate of slipper/swash pair based on plate thermos-hydraulic pair based on thermos dynamic- theoryhydraulic [15 ].dynamic Pelosi, Ivantysynova theory [15]. Pe [16losi,], and Ivatysynova Zecchi [17 ][16], built and an EHLZecchi model [17] built for the an piston/cylinder EHL model for pair the andpiston/cylinder the swash plate/slipper pair and the pair.swash However, plate/slipper as shown pair. in However, all these studies,as shown few in studies all these have studies, modelled few thestudies interaction have modelled relationship the among interaction elastic, relationship thermal and among hydraulic elastic, behaviors thermal only and use hydraulic numerical be methodhaviors withoutonly use establishing numerical method the computer-aided without establishing design (CAD) the computer model or-aided using design commercial (CAD software.) model or using commercialThis study software. was designed to investigate the temperature distribution for the further accurate analysisThis on study the thermal was designed effect on to the investigate piston/cylinder the temperature interface. distribution The flow velocity for the distribution further accurate in the piston/cylinderanalysis on the thermal interface effect at a steady on the operating piston/cylinder state of interface.
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