Abstract:
This thesis presents the numerical solutions for the stresses and the displacements of spur
gear teeth considering them as two-dimensional mixed boundary-value problems.
However, the analysis used here covers allmost all arbitrarily bounded "plane stress" and
"plane strain" bodies.
This work is an extension of the recent studies of the two-dimensional elastic problems of
rectangular bodies based on the finite-difference solutions of a displacement potential
function. It covers all the practical problems of irregular shaped bodies and thus removes
the limitations of rectangular boundaries. The bi-harmonic equation of the potential
function and its derivatives associated with the four possible boundary conditions in
terms of normal and tangential components of stresses and displacements of boundary
points are discretized using finite difference equations. These formulae are appropriately
applied to the domain of discretized rectangular mesh points at which the solutions are
sought. A computer program is developed which is generalized for solution of all types
of two-dimensional problems with all possible mixed boundary conditions. The program
solves the problems by finding the solution for a single discretized variable from a system
of linear algebraic equations resulting from the discretization of the domain concerned.
The solutions of a number of different involute spur gear teeth in terms of relevant stress
and displacement components are presented in the form of graphs and also in the forms
of contours. The critical stress concentration regions are dealt with as a separate problem
with fine meshing. The results are compared with available solutions in the literature. The
results arc found to be reasonable and rational and thus establish the reliability and
suitability of the present methodology in solving the clastic problems of arbitrarily
bounded bodies, subjected to all possible mixed boundary conditions.
