Global linearization of non-linear state equations

2004 ◽  
Vol 19 (1-4) ◽  
pp. 637-642 ◽  
Author(s):  
Andrzej J. Jordan ◽  
Jerzy P. Nowacki
Keyword(s):  
State Equations ◽  
Non Linear ◽  
Linear State ◽  
Global Linearization

Some Simulations of Gear–Journal Bearing Interactions

2011 ◽  
Author(s):  
Romain Farge`re ◽  
Philippe Velex
Keyword(s):  
State Equations ◽  
Time Step ◽  
Dynamic Interactions ◽  
Linear Solution ◽  
Normal Contact ◽  
Helical Gears ◽  
Contact Algorithm ◽  
Lumped Parameter ◽  
Non Linear ◽  
Linear State

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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