Global linearization of non-linear state equations

2004 ◽  
Vol 19 (1-4) ◽  
pp. 637-642 ◽  
Author(s):  
Andrzej J. Jordan ◽  
Jerzy P. Nowacki
Author(s):  
Romain Farge`re ◽  
Philippe Velex

This article deals with the static and dynamic interactions between journal bearings and gears in mechanical transmissions. The proposed approach combines classic lumped parameter and shaft elements, a specific wide-faced spur or helical gear model and external bearing forces. Bearing reactions are determined based on the linearized and non-linear solution to the Reynolds equation for short bearings. The corresponding parametrically excited non-linear state equations are solved by inserting a Newton-Raphson’s method and a unilateral normal contact algorithm into a Newmark’s time-step integration schema. Finally, the influence of bearing non-linearity, external and internal forcing terms is analyzed on several single stage reduction units with spur and helical gears.


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