The knowledge of tooth stiffness is fundamental in
the calculation of the load sharing between
meshing gear teeth, which can then lead to a
precise evaluation of the contact and bending
stresses.
Several analytical stiffness and stress models have
been presented in the past [I,2, 3, 4, 51 to solve
this problem, which is compounded by the
complexity of the tooth geometry. For spur and
helical gear teeth, where the tooth geometry
remains constant in the lengthwise direction,
reasonable agreement is obtained using analytical
models; for spiral-bevel and hypoid gear teeth,
where the tooth is curved and wound on a cone,
and tooth thickness and height varies along tooth
facewidth, so far only the Finite Element Method
(FEM) provides acceptable results.
This paper presents the Finite Strip Method (FSM),
an altemative to FEM and analytical formulations,
to obtain reliable results with reduced preparation
and solution time and that can be integrated to a
gear tooth geometry simulation software.
Cheung 161 and, independently, Powell and Ogden
[7], introduced the FSM which can be considered
as a special case of the FEM: the Finite Strip is a
2-D element for the analysis of plates, based on
simple polynomial functions in one direction and
continuously differentiable smooth series in the
other direction. Mawenya and Davies [8] included
the effect of transverse shear to make the FSM
applicable to thick, thin and sandwich plates. The
use of cubic B-splines, introduced by Cheung, Fan
and Wu [9], ensures C2- continuity and their local
characteristics allow different boundaw conditions.
FSM thin plates with variable thickness in the
longitudinal direction were treated by Uko and
Cusens [IO].
The analysis of gear teeth by the FSM, considered
as thick plates which may show either unidirectional
or bi-directional thickness variation and
constant or non-constant depth, is the focus of this
paper. To extend the application of the FSM from
thin to thick plates, Mindlin's theory is used in the
variant of the FSM presented in this paper [Il].
FEM deflection and stress results for the clampedfree
case are compared to those obtained by the
FSM and show good agreement.