Multi-objective Optimization of Counterweights: A Substitute for the Balance Shaft or Mass Unbalancing in Three-Cylinder Engines

摘要

Three-cylinder engines were launched, given the increasing demand for improved fuel economy and efficiency along with reduced friction and weight. Unlike four-cylinder engines, these engines are not naturally balanced. So, in order to compete with four-cylinder engines, some methods to solve this inherent weakness, such as balance shaft, mass unbalancing of flywheel and crankshaft pulley, or counterweights configuration (angular orientation and correction amount), have been used. Considering the undesirable characteristics of the balance shaft, such as cost, weight, friction, and noise, as well as dynamically inappropriate mass unbalancing method, this research proposes multi-objective optimization of counterweights to reduce vibrations. In this regard, after modeling a three-cylinder engine in constant speed and without the gas force effects, counterweights are optimized by non-dominated sorting genetic algorithm (NSGAII) method, to reduce shaking force, pitch and yaw moments, and bearing loads. Then possibility of removing the balance shaft and mass unbalancing, as the main purpose, with the help of counterweights is shown. Finally, a simple formula aimed at determining counterweights configuration to prevent the implementation of a long-term optimization process for each three-cylinder engine with a new specification is introduced. Due to the 92% reduction in pitching vibration for two similar engines, one with optimized counterweights and the other with mass unbalancing but more bearing loads, optimization is a more appropriate method. Also, with a reduction of about 80% of pitching vibration for two similar engines, one with optimized counterweights and the other with a balance shaft, along with the undesirable characteristics of the shaft, optimization is a good substitute for it.