# 05.2020.260.271 ## Numerical Method for Finding the Balancing and Unbalancing Forces of Single Piston Engine

Author(s):
Muslim Ali†, Iqbal Alshalal‡*, Arshad Abdula Rashed‡†, Z. C. Feng‡‡

Affiliation(s):
†Power Mechanics, Al-Furat Al-Awsat Technical University, Babylon Technical Institute

‡ Training and Workshops Center, University of Technology, Baghdad, Iraq

‡† Ministry of Oil, Baghdad, Iraq.

‡‡ Mechanical and Aerospace engineering, University of Missouri, USA.

Corresponding author Email: 11110@uotechnology.edu.iq

This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Mathematical equations are derived in this research with the use of a binomial theorem for finding balancing forces acting on a single piston engine. This method does not reflect the exact mathematical model because of its approximate solution. In order to achieve high accuracy of calculations, the Newton-Raphson method has been employed to calculate the response of the system. The moment exerted on the crank is found out in two cases, the effect of gas pressure and without gas pressure on the piston. Results revealed similar behavior generated in the two theorems of the resultant of all external forces in x-direction, y-direction, and the moment exerted on the crank in case of without gas pressure effect. The obtained results of the response, with the help of MATLAB code, confirm the applicability of the Newton-Raphson method to give more accurate results than the binomial theorem. The results improvement of the moment values without pressure effect is 5% and with pressure is 2.9%. The improvement of all external forces in x-direction values is 10% without pressure and 9.8% with pressure effect, however for the external forces in y-direction values is 9.98% where is no pressure effect.