Reynolds Equation

(1)

Normalisation

x – axial direction

z- Circumferential direction

(2)

Film thickness profile (parabolic)

Solution procedure -

· Since film thickness dose not vary much at mid stroke position, therefore taking squeeze term for crank angle . And also taking initial guess for Minimum film thickness .for starting iteration.

· For a given crank angle minimum film thickness is updated according to following empirical relation-

,new ,old

Where under-relaxation factor (0.15-0.5)

k= crank angle position ( )

W= Load acting upon piston ring due to Ring tension and Gas pressure

DLoad = Hydrodynamic load calculated from Reynolds equation (Dimensional)

Empirical coefficient (0.1-0.2)

For crank angle (time) marching, a modified forward Euler method is used-

,estimate

For Load balancing –

Load acting due to combustion gas and tensioning of piston ring

And load balancing is done by