A Model Of Spur Gears Supported By
Ball Bearings
Author(s)
F. Viadero, A. Fernandez del Rincon, R. Sancibrian,
P. Garcia Fernandez & A. de Juan
Abstract
In this work a model of a 2D spur gear transmission is described for analysis of
tooth contact forces and deformations. Assuming the position of each wheel is
known, the contact points between gears are obtained taking into account the
geometric description of the tooth profiles including profile errors and relief
modifications. Then the deformation in each contact point is separated into a
global and a local term combining a finite element model and an analytical
formulation originating from Hertzian contact theory. The proposed procedure
does not need new element meshing for each angular position thus obtaining an
important computational advantage. Afterwards, a non-linear system of
equations is obtained and solved for each gear position in order to calculate the
meshing contact forces. The model can include the possibility of bidirectional
single-flank or double-flank action as well as friction forces in the out-of-action
line. Once the contact forces are known, it is possible to use the procedure in the
calculation of loaded transmission error and meshing stiffness. Furthermore,
each gear is supported by ball bearings that are included in the model taking into
account their clearance and their variable stiffness due to the change in the
number of balls supporting the load. This variable bearing compliance modifies
the gear centre distance and as a consequence the transmission error during a
turn. Using this methodology a numerical example is presented where the static
behaviour of a spur gear transmission is described and analysed. Special
attention is focused on the influence of load level on the final loaded
transmission error.
Keywords: gear, transmission error, bearings, tooth contact, load ratio.
Keywords
gear, transmission error, bearings, tooth contact, load ratio.
Related Book
Other papers in this volume
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