Purpose -The purpose of this paper is to present, for the first time, a mathematical model for a piston skirt in mixed lubrication with respect to applying a smart fluid in lubrication. In this way, the smart fluid, as a lubricant with controlled variable viscosity, is proposed and applied to minimize the power loss in the interaction between liner and skirt. Design/methodology/approach -Based on signal processing, the relationships between viscosity of lubricant and the friction loss, the hydrodynamic and contact friction force consequently are found, as part of an effective approach to acquire the function of variable viscosity. Findings -It is shown that hydrodynamics and contact friction forces can be controlled and minimized by using the variable viscosity signal with the optimized viscosity signal technique. Originality/value -In this paper, a mathematical model for a piston skirt in mixed lubrication with respect to applying a smart fluid in lubrication is presented for the first time.Nomenclature a ¼ vertical distance from the top of the skirt to the wrist pin (m) b ¼ vertical distance from the top of the skirt to the piston center of gravity (m) C ¼ clearance (m) c g ¼ horizontal distance between piston center of mass and wrist pin (m) c p ¼ wrist-pin offset (m) e b , e t ¼ distance between the center at the bottom and top of the skirt and the cylinder axis, respectively, (m) e c ¼ eccentricity of center of piston skirt (m) e r ¼ angle of piston rotation (rad) F ¼ connecting rod force (N) F f ¼ total friction acting on the skirt (N) F G ¼ combustion gas force acting on the top of piston (N) F IC ¼ lateral inertia force due to piston skirt mass (N) F IC ¼ axial inertia force due to piston skirt mass (N) F IP ¼ lateral inertia force due to wrist pin mass (N) F IP ¼ axial inertia force due to wrist pin mass (N) hðu; y; tÞ ¼ mean oil-film thickness (m) I pis ¼ piston momentum of inertia (kg · m 2 ) L ¼ piston skirt length (m)M ¼ total moment about wrist-pin due to all the normal forces (N · m) M c ¼ moment about wrist-pin due to solid-tosolid contact pressure (N · m) M f ¼ moment about wrist-pin due to all the friction forces (N · m) M fc ¼ moment about wrist-pin due to contact friction (N · m) M fh ¼ moment about wrist-pin due to hydrodynamic friction (N · m) M h ¼ moment about wrist-pin due to hydrodynamic pressure (N · m) M IC ¼ inertia moment of piston (N · m) U ¼ piston sliding velocity (m/s) m pin ¼ wrist-pin mass (kg) m pis ¼ piston mass (kg)¼ hydrodynamic shear stress (Pa) F x , F y ¼ pressure flow factors F s ¼ shear stress flow factor F f , F fp , F fs ¼ shear stress flow factors f ¼ angle of connecting road (rad) c ¼ crank angle (rad) v ¼ crankshaft rotational speed (rad/s)The current issue and full text archive of this journal is available at