Effect of the torsional vibration depending on the number of cylinders in reciprocating engines

This paper is aimed to explore the effect of increasing the number of pistons on the torsional vibration analysis of inline reciprocating machines with simplifications of equivalent masses to the connecting rod and crankshaft. A mathematical model of a mechanism of two degrees of dynamic freedom has been used to develop the equations of motion of the rotating and reciprocating parts of the single and multi-cylinder engine. Different configurations of single-cylinder and multi-cylinder engines are considered with the number of cylinders ranging from 1 to 6. The model of the crankshaft is established with the use of Lagrange's equations valid for a single and multi-pistons engine. This work shows the relation between the angular displacement of the crank angle and the twist angle of the crankshaft concerning three different damping coefficients. The maximum amplitude occurred with an engine of 2-cylinders while the minimum amplitude occurred with the single-cylinder engine. The twist angle does not depend upon the increasing number of the pistons. The torsional vibrations of the crankshaft by using 3 or more cylinders are significant in magnitude with values near to unity. Besides, the greatest amplitude of twist angle with odd cylinders and the reduction in the torsional vibration may be obtained for engine designs with even cylinders.