Mathematical modeling of dynamic behavior of a piston during expansion stroke for an internal combustion engine using boundary value method

In the present study a simplified internal combustion engine is simulated. To contribute engine kinematics and its geometry, simple relations are derived for constrained motions. The equation of motion for the piston forms a singular boundary value problem. Solution of the boundary value problem with other governing equations was done in an iterative algorithm. The numerical method has shown very fast convergence. With this simulation the gas expansion process is related to the piston movement. Simulating an engine working at constant torque and polytropic expansions has shown that under certain conditions the expansion stroke can generate piston vibrations at high frequencies.

Keywords:

boundary value problem , Green's function , internal combustion engine , polytropic expansion