Abstract
A new method, comprising Navier–Stokes equations, Rayleigh–Plesset volume fraction equation, an analytical control-volume thermal-mixed approach and asperity interactions, is reported. The method is employed for prediction of lubricant flow and assessment of friction in the compression ring–cylinder liner conjunction. The results are compared with Reynolds-based laminar flow with Elrod cavitation algorithm. Good conformance is observed for medium load intensity part of the engine cycle. At lighter loads and higher sliding velocity, the new method shows more complex fluid flow, possessing layered flow characteristics on the account of pressure and temperature gradient into the depth of the lubricant film, which leads to a cavitation region with vapour content at varied volume fractions. Predictions also conform well to experimental measurements reported by other authors.
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Abbreviations
- A :
-
Apparent contact area
- A a :
-
Asperity contact area
- b :
-
Ring axial face width
- C p :
-
Lubricant specific heat
- d :
-
Ring thickness
- E 1 :
-
Young’s modulus of elasticity of the ring
- E 2 :
-
Young’s modulus of elasticity of the liner
- E′:
-
Equivalent (reduced) modulus of elasticity
- f b :
-
Boundary friction
- f t :
-
Total friction
- f v :
-
Viscous friction
- F T :
-
Ring tension force
- F G :
-
Combustion gas force
- \(F_{2} ,\,F_{5/2}\) :
-
Statistical functions
- g :
-
Ring end gap
- g s :
-
Switch function
- H :
-
Enthalpy
- h :
-
Elastic film shape
- h m :
-
Minimum film thickness
- h s :
-
Ring axial profile
- h t :
-
Heat transfer coefficient of boundary layer
- I :
-
Ring cross-sectional second area moment of inertia
- k :
-
Lubricant thermal conductivity
- k s1 :
-
Thermal conductivity of the bore/liner
- k s2 :
-
Thermal conductivity of the ring
- l :
-
Connecting rod length
- L :
-
Ring peripheral length
- p atm :
-
Atmospheric pressure
- p c :
-
Cavitation/lubricant vaporisation pressure
- p h :
-
Hydrodynamic pressure
- p gb :
-
Gas pressure acting behind the ring
- \(\dot{Q}_{1}\) :
-
Conductive heat flow rate through the liner
- \(\dot{Q}_{2}\) :
-
Conductive heat flow rate through the ring
- \(\dot{Q}_{cv}\) :
-
Convective heat flow rate
- \(r\) :
-
Crank-pin radius
- \(r_{0}\) :
-
Nominal bore radius
- R l :
-
Conductive thermal resistance for the lubricant layer
- R v :
-
Convective thermal resistance of the boundary layer (between film and surface)
- Re :
-
Reynolds number
- t :
-
Time
- U :
-
Ring sliding velocity
- U 1, U 2 :
-
Surface velocities of contacting bodies
- \(\vec{V}\) :
-
Velocity vector
- W :
-
Contact load
- W a :
-
Load share of asperities
- W h :
-
Load carried by the lubricant film
- x c :
-
Oil film rupture point
- Z :
-
Pressure–viscosity index
- \(\alpha_{0}\) :
-
Pressure/temperature–viscosity coefficient
- \(\beta\) :
-
Lubricant bulk modulus
- \(\varphi\) :
-
Crank angle
- \(\zeta\) :
-
Number of asperity peaks per unit contact area
- \(\eta\) :
-
Lubricant dynamic viscosity
- \(\eta_{0}\) :
-
Lubricant dynamic viscosity at atmospheric pressure
- \(\kappa\) :
-
Average asperity tip radius
- \(\lambda\) :
-
Stribeck’s oil film parameter
- \(\mu\) :
-
Pressure coefficient for boundary shear strength of asperities
- \(\nu_{1}\) :
-
Poisson’s ratio of the ring material
- \(\nu_{2}\) :
-
Poisson’s ratio of the liner material
- \(\rho\) :
-
Lubricant density
- \(\rho_{0}\) :
-
Lubricant density at atmospheric pressure
- \(\sigma_{r}\) :
-
Liner surface roughness
- \(\sigma_{l}\) :
-
Ring surface roughness
- \(\tau\) :
-
Shear stress
- \(\tau_{0}\) :
-
Eyring shear stress
- \(\Upgamma\) :
-
Diffusion coefficient
- θ :
-
Temperature
- θ e :
-
Average (effective) lubricant temperature
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Acknowledgments
The authors would like to express their gratitude to the Lloyd’s Register Educational Foundation (LREF) for the financial support extended to this research. Thanks are also due to the Engineering and Physical Sciences Research Council (EPSRC) for the Encyclopaedic Program Grant, some of research findings of which are used in this paper.
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Shahmohamadi, H., Rahmani, R., Rahnejat, H. et al. Thermo-Mixed Hydrodynamics of Piston Compression Ring Conjunction. Tribol Lett 51, 323–340 (2013). https://doi.org/10.1007/s11249-013-0163-5
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DOI: https://doi.org/10.1007/s11249-013-0163-5