Analysis of trochoidal-type machines with conjugate envelopes

John Bun Shung, Purdue University


Trochoidal-type machines belong to the category of planetary rotation machines and include pumps, blowers, compressors and engines. In general a trochoidal-type machine is simpler, quieter, lighter and smaller than a comparable reciprocating machine. This thesis focuses on two major aspects of trochoidal-type machines with conjugate envelopes: (i) the geometry and the characteristics of different types of trochoids and different types of conjugate envelopes; and (ii) methods to determine the contact forces and the contact stresses between the rotor and the chamber. The two types of trochoid are the peritrochoid and the hypotrochoid. For each type of trochoid, there are nine types of conjugate envelope. Conjugate envelopes provide, in general, the best geometry for sealing, high compression ratio and low contact forces and stresses. However, to date only two out of the nine types of conjugate envelope have been studied in any detail. General parametric equations of a conjugate envelope, in continuous form, are not available in the literature. In this thesis, unified and compact equations for the geometry and the geometric properties of trochoids are obtained. An additional type of conjugate envelope is discovered for each trochoid. Closed-form parametric equations for all nine types of conjugate envelopes, and the necessary and sufficient conditions for having a closed type 1 conjugate envelope are derived. A computer-aided design program, incorporating the equations, is developed. The characteristics and relationships of different types of trochoid and conjugate envelope are presented. Reducing the contact stresses in the trochoidal-type machine is very important because the machine can not be adjusted for wear. The main difficulty in calculating the contact forces and stresses is to determine the forces that are transmitted through each contact point. Since there are many contact points, the problem may be considered quasi-statically indeterminate. No satisfactory method of analyzing the contact forces and stresses in a trochoidal-type machine has been developed to date. Two methods to determine contact forces are developed in this thesis. One method is based on a versatile finite element model under quasi-static conditions. This model includes more detail such as the effects of contact friction and deformation, and provides contact forces and stresses everywhere. However, results need careful verification and interpretation. The other method is based on a simplified analytical model under the same conditions. This model provides physical insights to the problem and results to check the finite element model from different approaches. However, the accuracy and availability of the results is limited by additional assumptions. When the effects of contact friction and deformation are ignored, the results from both models are in good agreement. It is hoped that this thesis will prove valuable to the designer of all planetary rotation machines, especially for trochoidal-type machines with conjugate envelopes.




Pennock, Purdue University.

Subject Area

Mechanical engineering

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