Alın dişlilerin yığılı parametre ve sonlu elemenlar yöntemiyle modal davranışının incelenmesi

Dişli dinamiğinde, dişli dinamik kuvvetlerinin kesin olarak hesaplanması ve doğru modal davranış tahmini yüksek doğruluklu modelleme yöntemlerini gerektirmektedir. Bu çalışmada, bir alın dişli çiftinin doğrusal modal davranışı, belirlenmiş şartlar altında yığılı parametre ve sonlu elemanlar yöntemiyle incelenmektedir. Bu çalışmanın ana amacı yığılı parametre ve sonlu elemanlar yöntemiyle dişli çiftinin modal analiz sonuçlarını karşılaştırmaktır. Bunun için alın dişli çiftinin altı serbestlik dereceli dinamik modeli yığılı parametre yöntemiyle oluşturulmuştur. Bu yöntemde, dişli gövdeleri rijit kabul edilirken dişli temasları ve yatakları esnek kabul edilmiştir. Sonrasında, alın dişli çiftinin üç boyutlu katı modeli yüksek doğruluklu sayısal hesaplamalar için sonlu elemanlar yöntemiyle oluşturulmuştur. Sonlu elemanlar yönteminde, dişliler esnek üç boyutlu katı elemanlarla modellenmiştir. Bu modelde, dişli çifti temasında doğrusal olmama durumunun kaldırılması için temas rijit olarak basitleştirilmiştir. Doğal frekanslar ve mod şekilleri her iki yöntemde doğrusal modal analiz ile hesaplanmıştır. Her iki yöntemle elde edilen sonuçlar, yüksek frekanslarda görülen esnek dişli gövde modlarının sadece sonlu elemanlar yöntemiyle hesaplanabileceğini göstermektedir. Gövdenin hareket etmediği diş modları ise her iki yöntemle başarılı bir şekilde tespit edilebilmektedir.

Modal behaviour investigation of spur gears with lumped parameter and finite element methods

Computation of gear dynamic forces accurately and correct modal behaviour estimation require highly validated modelling techniques in gear dynamics. In this paper, linear modal behaviour of a spur gear pair under prescribed conditions is investigated with lumped parameter and finite element methods. The main aim of this study is to compare the modal analysis results of the spur gear pair with the lumped parameter and finite element methods. For this purpose, a six degrees of freedom dynamic model of a spur gear pair is created using the lumped parameter method. In this method, the gears are assumed to be rigid disks whereas the gear teeth contacts and bearings are considered as flexible, which are modelled with spring elements. Then, a 3D solid model of the spur gear pair is created using the finite element method for high fidelity numerical analyses. In the finite element method, the gears are modelled with flexible three-dimensional solid elements, which is one of the main differences between the two methods. To remove the nonlinearity in the gear pair system, the contact is simplified with a rigid bonding of nodes in the finite element model. The natural frequencies and mode shapes are calculated by linear modal analysis for both methods. The obtained results from the individual methods show that flexible gear body modes, which are seen at higher frequencies, can only be detected with the finite element method. The tooth modes in which the gear bodies acting as a rigid body can be detected successfully with the two methods.

Keywords:

Gear dynamics, spur gears, finite element method lumped parameter method, modal analysis,

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