Daniele Vecchiato

Design and simulation of meshing of a cycloidal pump

Abstract Modification of the geometry of rotor profiles of a cycloidal pump is considered. The new geometry enables us to provide that only one pair of teeth is in mesh at every instant, and to avoid tooth interference and rapid wearing that occur in the case of a conventional pump whereas all the rotor teeth are in mesh at every instant. A Tooth Contact Analysis (TCA) computer program is developed. Such a program enables us to determine at every instant the virtual pair of contacting profiles, the backlash between the profiles that are not in mesh and the transmission errors that accompany the transformation of rotation. The meshing of rotor profiles is represented analytically and is illustrated conceptually. A numerical example is considered.

Geometry of a cycloidal pump

Abstract A cycloidal pump for transportation of liquid is considered. The rotor profiles are applied as circular arc and a conjugated epicycloidal curve. The contents of the paper cover: 1. Development of geometry of rotor conjugated profiles applying the theory of envelopes to a family of parametric curves and analysis of profile meshing. 2. Investigation of formation of an envelope by branches. 3. Determination of singularities and computerized design of pumps with rotor profiles free of singularities. Developed theory is illustrated with examples.

Computerized generation and simulation of meshing of modified spur and helical gears manufactured by shaving

Abstract Modification of geometry of spur and helical gears with parallel axes and helical gears with crossed axes is proposed. The finishing process of gear generation is shaving. The purposes of modification of gear geometry are: (i) localization and stabilization of bearing contact, and (ii) reduction of noise and vibration. The goals mentioned above are achieved as follows: 1. The pinion shaver tooth surface, in comparison with a conventional screw involute surface, is profile crowned. 2. Plunging during the process of pinion shaving is provided by variation of shortest distance E between the shaver and pinion axes. Variation of E is executed by application of a parabolic function. 3. The pinion tooth surface becomes double-crowned, in profile and longitudinal directions, due to profile crowning of pinion shaver and variation of plunging. The gear tooth surface is generated as a conventional involute gear. Tooth contact analysis (TCA) computer program for simulation of meshing and contact of shaved pinion-gear tooth surfaces is developed. The developed theory is illustrated with TCA results obtained for spur and helical gears.

Formation by branches of envelope to parametric families of surfaces and curves

The existence of envelope to family of surfaces (curves in planar gearing) is usually discussed as existence of envelope formed by one branch of a regular surface (curve in planar gearing). The authors consider cases of formation of envelopes formed by several branches. Existence of such envelopes is represented for the cases of cycloidal pumps and conventional worm gear drives. The formation of envelope by several branches is represented analytically, rules for discovery of different envelope branches are proposed, and the existence of branches is illustrated graphically. The obtained results are important for computerized design of generation of surfaces and curves and enable to separate real and false branches of envelope.

New developments in the design and generation of gear drives

Abstract Design, generation and simulation of the meshing and contact of gear drives with favourable bearing contact and reduced noise are considered. The proposed approach is based on replacement of the instantaneous line of contact of tooth surfaces by point contact and on application of a predesigned parabolic function of transmission errors that is able to absorb linear discontinuous functions of transmission errors caused by misalignment. Basic algorithms for analysis and synthesis of gear drives are presented. The developed theory is applied for design and generation of the following gear drives with modified geometry: (a) spur and helical gears, (b) a new version of Novikov-Wildhaber (N-W) helical gears, (c) asymmetric face gear drives with a spur pinion, (d) formate-cut spiral bevel gears. Generation of the tooth surface of a worm gear is presented as the formation of a two-branch envelope. The discussed topics are illustrated with examples.