The Numerical Methods in Geometric Construction Mapping
A dynamic development of numerical methods enables even so complicated geometrical modelling as modelling of hypoidal teeth, and in particular of worm teeth. Building on the basis of the finite element method of this type of geometrical mathematical model enables observing and analysing physical phenomena taking place in the teeth, e.g. changes of pressure distribution along the contact lines depending on the phase of meshing for particular cooperating pairs of teeth. Due to limited technical possibilities and mathematical apparatus such analyses were carried out only on the basis of the theory of plates with constant thickness. An unquestionable advantage of such numerical modelling is a short time needed to obtain final results, which enables profound analysis of the transmitted load. The knowledge of course of pressure distribution along the contact lines of particular pairs of intermeshing teeth in worm gears already in the design phase enables taking into consideration in adequate correction or even modification of the working surface of teeth, with the aim to equalise the distribution of pressure.
H. G. Sabiniak and R. Cichowicz, "The Numerical Methods in Geometric Construction Mapping", Key Engineering Materials, Vol. 490, pp. 312-322, 2012