Incorrect Contact of Screw Surfaces and its Consequences

The contribution deals with the analysis of the correct and incorrect contact of the screw surfaces which are represented with two-dimensional manifolds. One surface is defined by parametric equation and the conjugate surface is created in the direct envelope way according to the Distelli theorem. The solution which is presented in this contribution is founded on kinematical principles. The correct contact of both conjugate surfaces takes place in a contact line ch32, see Figure, for instantaneous time.

Correct line contact of conjugate screw surfaces σ

2

and σ

3

Temperature and force deformation bring about displacement of surfaces and the correct contact changes into the incorrect contact. Instead of the line contact of surfaces the contact at isolated points takes place. In this contribution the incorrect contact of surfaces is caused by a large parallel displacement of the axis of one of the surfaces. The inner deformation of screw surfaces is not involved into solution and likewise general position of rotor axes that arises by real deformation is not accepted. This simplification was necessary for the first step of the solution of this problem. The work is solved as three-dimensional problem. Theory of incorrect contact of screw surfaces is applied to the teeth of rotors of the screw machines.

One of the most important parts of screw machines, i.e. screw compressors or expanders, is a work space with its boundary surface which is produced by the screw surfaces of teeth and an inner cylinder surface of a machine box. In course of working process the work space has a complicated, non-stationary shape. The tooth screw surfaces, which consist of different coupled surfaces, create the most important part of the work space. The original line contact between surfaces changes into the contact in four points along a length of teeth of rotors. The rise of a technically undesirable gap between both conjugated surfaces and disturbance of gear ratio are consequences of this change. The arisen gaps caused the increase in inner loss of screw machines. Geometrical visualization of the conjugated teeth with the arisen gap is performed in instantaneous time.