, Volume 4, Issue 4, pp 335–346 | Cite as

Design approach for optimization of a piston ring profile considering mixed lubrication

  • Zhinan Zhang
  • Jun Liu
  • Youbai Xie
Open Access
Research Article


To reduce the friction of a piston ring while maintaining a large oil film load-carrying capacity, an approach comprising of the inverse method and the sequential quadratic programming algorithm was proposed. The approach considers the variation of mixed lubrication and variable lubricant viscosity with temperature along the engine stroke, is developed to optimize the profile of a piston ring. A piston ring profile is represented by a polynomial function. A case study of the second piston ring shows that the proposed method can be applied for the optimization of a piston ring profile. In addition, this paper illustrates the effects of the degree of a polynomial function. The results show that the minimization of friction and maximization of oil film load-carrying capacity can be balanced simultaneously when the degree of the polynomial is 2 and 5.


piston ring profile inverse method tribology design mixed lubrication hydrodynamic lubrication 



Parameters in the Vogel equation


Outlet film thickness


Minimum film thickness


Shoulder length


Actual contact area


Intermediate variable


Asperity contact friction force


Piston ring elastic force


Gas force at inner side of piston ring


Load-carrying capacity of film


Total friction force


The viscous shearing force of film


Pressure on the ring


Pressure below the ring


The liner temperature at the bottom dead center (BDC)


The liner temperature at the mid-stroke point (MID)


The liner temperature at the top dead center (TDC)


Piston velocity


Asperity contact force


Normal gas pressure


Boundary friction coefficient


Viscosity invariant


Density of asperity


Constant of shear stress


Contact factor


Geometric stress factor


Pressure stress factor


Shear stress factors


Shear flow factor


Pressure flow factors


Area of nominal contact


Piston ring width


Film thickness


Crank speed


Lubricant viscosity


Composite roughness


Composite elastic modulus of the materials’ contact surface


The length of the piston stroke


Connecting rod length


Oil film pressure




The piston location downward from TDC


Fixed asperity radius of curvature


Crank angle


Angular speed of crankshaft



This study is supported by the National Natural Science Foundation of China (Nos. 51575340 and 51575342), Research Project of State Key Laboratory of Mechanical System and Vibration (No. MSVZD201104).


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Authors and Affiliations

  1. 1.State Key Laboratory of Mechanical System and VibrationShanghai Jiao Tong UniversityShanghaiChina
  2. 2.School of Mechanical EngineeringShanghai Jiao Tong UniversityShanghaiChina

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