A generalized Reynolds equation based on non-Newtonian flow is derived in this paper.This equation is suitable for a number of non-Newtonian flow models and can be solved numerically to obtain pressure fields in therm...A generalized Reynolds equation based on non-Newtonian flow is derived in this paper.This equation is suitable for a number of non-Newtonian flow models and can be solved numerically to obtain pressure fields in thermalhydrodynamically or elastohydrodynamically lubricated fluid films.A mathematical ap- proach is given for solving simultaneously the shearing stress,shearing rate,velocity and equivalent viscosity.To show the application of this equation,two rheological models which have been widely used in lubrication mechnaics are incorporated into this equation to obtain numerical solutions to the line contact thermal elastohydrodynamic lubrication problem.展开更多
The development work focuses on the numerical simulations of free body movement in viscous fluid. The aim is to make the simulation of very slow motion of the small body in viscous fluid. We developed bodies’ immerse...The development work focuses on the numerical simulations of free body movement in viscous fluid. The aim is to make the simulation of very slow motion of the small body in viscous fluid. We developed bodies’ immersed dynamics simulations in viscous fluid by seeking numerical solutions for appropriate field variables. We developed the methods for vertically and spherically cylindrical objects’ motions, the forces on bodies close to a plane stationary wall are computed from the velocity and pressure fields using the Stokes equation through COMSOL Multiphysics finite element software. The Navier-Stokes equation is reduced to Stokes equation there is independence of time which means object will have an effect only on the motion and the slightly compressible flow assumption is made in order to obtain smooth solution numerically. The forces on an object in slightly compressible Stokes flow have been exerted on the falling objects. The resulting forces have compared with analytical results from the Reynolds Lubrication Theory, and achieved significant results from the development method in Matlab and achieved significant numerical simulations in COMSOL. In addition, an investigation has been made to an object swimming at low Reynolds number. At low Reynolds number moving is possible when object scale is small and flow pattern is slow and sticky. We have developed a system for a thin two-dimensional (2D) worm-like object wiggle that is passing a wave along its centreline and its motion has simulated by the Ordinary Differential Equations (ODE) system and by the Arbitrary Lagrangian-Eulerian (ALE) moving mesh technology. The development method result shows that it is possible for the small object to have a motion from one position to another through small amplitudes and wavelengths in viscous fluid.展开更多
By an iteration method, the influence of oil film inertia on piston skirt lubrication in a high speed engine is investigated. By alternately solving the Navier-Stocks equations and the Reynolds equation, the new itera...By an iteration method, the influence of oil film inertia on piston skirt lubrication in a high speed engine is investigated. By alternately solving the Navier-Stocks equations and the Reynolds equation, the new iteration method can trace the variations of velocity field and pressure field with time. Based on this, the mixed-lubrication model suitable for the piston skirt of high engines is proposed. By introducing the inertia coefficient, the new lubrication model includes the inertia term in oil film. The model can be also used to solve for the lubrication performances of a piston skirt in low or medium speed engines and for lubrication problem in general excluding the inertia term of oil film , when the inertia coefficient is put equal to zero. The calculation results show that the influence of oil film inertia on the friction force increases with the ratio of the piston skirt's length to its diameter, the inertia coefficient and the eccentricities of the lower and the upper piston skirt, with other conditions kept constant, while the influence of it on the load capacity of oil film is small.展开更多
Elastohydrodynamic lubrication(EHL)is a type of fluid-film lubrication where hydrodynamic behaviors at contact surfaces are affected by both elastic deformation of surfaces and lubricant viscosity.Modelling of contact...Elastohydrodynamic lubrication(EHL)is a type of fluid-film lubrication where hydrodynamic behaviors at contact surfaces are affected by both elastic deformation of surfaces and lubricant viscosity.Modelling of contact interfaces under EHL is challenging due to high nonlinearity,complexity,and the multi-disciplinary nature.This paper aims to understand the state of the art of computational modelling of EHL by(1)examining the literature on modeling of contact surfaces under boundary and mixed lubricated conditions,(2)emphasizing the methods on the friction prediction occurring to contact surfaces,and(3)exploring the feasibility of using commercially available software tools(especially,Simulia/Abaqus)to predict the friction and wear at contact surfaces of objects with relative reciprocating motions.展开更多
Limitation and deficiency of main thcoogical models at present are descrital and analyzed, and seteralgeneral rheological models are discussed and compared with each other, and basic demands for a general model aresum...Limitation and deficiency of main thcoogical models at present are descrital and analyzed, and seteralgeneral rheological models are discussed and compared with each other, and basic demands for a general model aresummarized. The constitutive eqUation is proposetl for a new general theobocal model. The general medel feaaressimple structure and wide coverage, and can take the Place of many edsting thcofogical ed. The whel has suc-cessfully been used for Elastohydrodynamic lubrication calculation.展开更多
In this paper,we propose a Static Condensation Reduced Basis Element(SCRBE)approach for the Reynolds Lubrication Equation(RLE).The SCRBEmethod is a computational tool that allows to efficiently analyze parametrized st...In this paper,we propose a Static Condensation Reduced Basis Element(SCRBE)approach for the Reynolds Lubrication Equation(RLE).The SCRBEmethod is a computational tool that allows to efficiently analyze parametrized structures which can be decomposed into a large number of similar components.Here,we extend the methodology to allow for a more general domain decomposition,a typical example being a checkerboard-pattern assembled from similar components.To this end,we extend the formulation and associated a posteriori error bound procedure.Our motivation comes from the analysis of the pressure distribution in plain journal bearings governed by the RLE.However,the SCRBE approach presented is not limited to bearings and the RLE,but directly extends to other component-based systems.We show numerical results for plain bearings to demonstrate the validity of the proposed approach.展开更多
To increase the hydrodynamic performance in different machine elements, as e.g. journal bearings and thrust bearings, during lubrication it is important to understand the influence of surface roughness. In this connec...To increase the hydrodynamic performance in different machine elements, as e.g. journal bearings and thrust bearings, during lubrication it is important to understand the influence of surface roughness. In this connection one encounters homogenization of the incompressible Reynolds equation, where the roughness of the lubricated surface is assumed to be periodic. This problem has recently been studied in more engineering- oriented papers by using the formal method of multiple scale expansion. In this paper, we rigorously prove both homogenization and corrector results by using two-scale convergence, which may be regarded as a justification of the formal multiple scale expansion method described above. Moreover, some numerical illustrations and results are presented.展开更多
The general discrete scheme of time-varying Reynolds equation loses the information of the previous step,which makes it unreasonable.A discretization formula of the Reynolds equation,which is based on the Crank-Nicols...The general discrete scheme of time-varying Reynolds equation loses the information of the previous step,which makes it unreasonable.A discretization formula of the Reynolds equation,which is based on the Crank-Nicolson method,is proposed considering the physical message of the previous step.Gauss-Seidel relaxation and distribution relaxation are adopted for the linear operators of pressure during the numerical solution procedure.In addition to the convergent criteria of pressure distribution and load,an estimation framework is developed to investigate the relative error of the most important term in the Reynolds equation.Smooth surface with frill contacts and mixed elastohydrodynamic lubrication is tested for validation.The asperity contact and sinusoidal wavy surface are examined by the proposed discrete scheme.Results show the precipitous decline in the boundary of the contact area.The relative error suggests that the pressure distribution is reliable and reflects the accuracy and effectiveness of the developed method.展开更多
文摘A generalized Reynolds equation based on non-Newtonian flow is derived in this paper.This equation is suitable for a number of non-Newtonian flow models and can be solved numerically to obtain pressure fields in thermalhydrodynamically or elastohydrodynamically lubricated fluid films.A mathematical ap- proach is given for solving simultaneously the shearing stress,shearing rate,velocity and equivalent viscosity.To show the application of this equation,two rheological models which have been widely used in lubrication mechnaics are incorporated into this equation to obtain numerical solutions to the line contact thermal elastohydrodynamic lubrication problem.
文摘The development work focuses on the numerical simulations of free body movement in viscous fluid. The aim is to make the simulation of very slow motion of the small body in viscous fluid. We developed bodies’ immersed dynamics simulations in viscous fluid by seeking numerical solutions for appropriate field variables. We developed the methods for vertically and spherically cylindrical objects’ motions, the forces on bodies close to a plane stationary wall are computed from the velocity and pressure fields using the Stokes equation through COMSOL Multiphysics finite element software. The Navier-Stokes equation is reduced to Stokes equation there is independence of time which means object will have an effect only on the motion and the slightly compressible flow assumption is made in order to obtain smooth solution numerically. The forces on an object in slightly compressible Stokes flow have been exerted on the falling objects. The resulting forces have compared with analytical results from the Reynolds Lubrication Theory, and achieved significant results from the development method in Matlab and achieved significant numerical simulations in COMSOL. In addition, an investigation has been made to an object swimming at low Reynolds number. At low Reynolds number moving is possible when object scale is small and flow pattern is slow and sticky. We have developed a system for a thin two-dimensional (2D) worm-like object wiggle that is passing a wave along its centreline and its motion has simulated by the Ordinary Differential Equations (ODE) system and by the Arbitrary Lagrangian-Eulerian (ALE) moving mesh technology. The development method result shows that it is possible for the small object to have a motion from one position to another through small amplitudes and wavelengths in viscous fluid.
基金National Natural Science Foundation of China (Grant No. 59990472)
文摘By an iteration method, the influence of oil film inertia on piston skirt lubrication in a high speed engine is investigated. By alternately solving the Navier-Stocks equations and the Reynolds equation, the new iteration method can trace the variations of velocity field and pressure field with time. Based on this, the mixed-lubrication model suitable for the piston skirt of high engines is proposed. By introducing the inertia coefficient, the new lubrication model includes the inertia term in oil film. The model can be also used to solve for the lubrication performances of a piston skirt in low or medium speed engines and for lubrication problem in general excluding the inertia term of oil film , when the inertia coefficient is put equal to zero. The calculation results show that the influence of oil film inertia on the friction force increases with the ratio of the piston skirt's length to its diameter, the inertia coefficient and the eccentricities of the lower and the upper piston skirt, with other conditions kept constant, while the influence of it on the load capacity of oil film is small.
基金The first author Zhuming Bi would like to acknowledge the sponsorship of Senior Summer Faculty Grant from Purdue University Fort Wayne (PFW) and the Faculty Collaborative Research Grant from Purdue University Fort Wayne (PFW).
文摘Elastohydrodynamic lubrication(EHL)is a type of fluid-film lubrication where hydrodynamic behaviors at contact surfaces are affected by both elastic deformation of surfaces and lubricant viscosity.Modelling of contact interfaces under EHL is challenging due to high nonlinearity,complexity,and the multi-disciplinary nature.This paper aims to understand the state of the art of computational modelling of EHL by(1)examining the literature on modeling of contact surfaces under boundary and mixed lubricated conditions,(2)emphasizing the methods on the friction prediction occurring to contact surfaces,and(3)exploring the feasibility of using commercially available software tools(especially,Simulia/Abaqus)to predict the friction and wear at contact surfaces of objects with relative reciprocating motions.
文摘Limitation and deficiency of main thcoogical models at present are descrital and analyzed, and seteralgeneral rheological models are discussed and compared with each other, and basic demands for a general model aresummarized. The constitutive eqUation is proposetl for a new general theobocal model. The general medel feaaressimple structure and wide coverage, and can take the Place of many edsting thcofogical ed. The whel has suc-cessfully been used for Elastohydrodynamic lubrication calculation.
基金We would like to thank Prof.A.T.Patera and Dr.J.Eftang for helpful discussions on the SCRBE method as well as Prof.G.Knoll and Dr.R.Schönen from ISTmbH for providing the specific application.This work was supported by the Excellence Initiative of the German federal and state governments and the German Research Foundation through Grant GSC 111.
文摘In this paper,we propose a Static Condensation Reduced Basis Element(SCRBE)approach for the Reynolds Lubrication Equation(RLE).The SCRBEmethod is a computational tool that allows to efficiently analyze parametrized structures which can be decomposed into a large number of similar components.Here,we extend the methodology to allow for a more general domain decomposition,a typical example being a checkerboard-pattern assembled from similar components.To this end,we extend the formulation and associated a posteriori error bound procedure.Our motivation comes from the analysis of the pressure distribution in plain journal bearings governed by the RLE.However,the SCRBE approach presented is not limited to bearings and the RLE,but directly extends to other component-based systems.We show numerical results for plain bearings to demonstrate the validity of the proposed approach.
文摘To increase the hydrodynamic performance in different machine elements, as e.g. journal bearings and thrust bearings, during lubrication it is important to understand the influence of surface roughness. In this connection one encounters homogenization of the incompressible Reynolds equation, where the roughness of the lubricated surface is assumed to be periodic. This problem has recently been studied in more engineering- oriented papers by using the formal method of multiple scale expansion. In this paper, we rigorously prove both homogenization and corrector results by using two-scale convergence, which may be regarded as a justification of the formal multiple scale expansion method described above. Moreover, some numerical illustrations and results are presented.
基金This study was financially supported by the National Natural Science Foundation of China(Grant No.U1637206)Shanghai Academy of Spaceflight Technology Projects(Grant Nos.SAST2017-079 and USCAST2019-25)the State Key Laboratory of Mechanical System and Vibration(Grant No.MSVZD201912).
文摘The general discrete scheme of time-varying Reynolds equation loses the information of the previous step,which makes it unreasonable.A discretization formula of the Reynolds equation,which is based on the Crank-Nicolson method,is proposed considering the physical message of the previous step.Gauss-Seidel relaxation and distribution relaxation are adopted for the linear operators of pressure during the numerical solution procedure.In addition to the convergent criteria of pressure distribution and load,an estimation framework is developed to investigate the relative error of the most important term in the Reynolds equation.Smooth surface with frill contacts and mixed elastohydrodynamic lubrication is tested for validation.The asperity contact and sinusoidal wavy surface are examined by the proposed discrete scheme.Results show the precipitous decline in the boundary of the contact area.The relative error suggests that the pressure distribution is reliable and reflects the accuracy and effectiveness of the developed method.
