Development of novel general equation for multistage epicyclic gearset with corrected teeth: non-constrained approach

A large number of commercial systems for condition monitoring of most common planetary gearboxes used in wind turbines and mining machinery have been developed for years. However nowadays, multistage constructions are encountered in industries. These are not necessarily planetary, but generally epicyclic. Current state of the art, according to the authors knowledge, does not give general equations for a case where multistage systems are considered, where some of the gears consist all moving parts. Hence, currently available CMS systems are not suitable for condition monitoring of these kinds of systems. The paper presents a new general equation, which allows calculating the characteristic frequencies of any kind of multistage gear sets, as a result of theoretical investigation. Illustrated solution does not assume a fixed speed of any element. Moreover, presented equation takes into account corrected teeth, making developed equations most general from all available in tribology science. Presented scientific development is currently implemented in a modern European CMS.