The rotor profiles of twin screw compressors have a significant influence on the compressor performance. Three different rotor profile design methods are derived mathematically and their limitations are addressed. This dissertation presents the complete theory and algorithm of the deviation function (DF) method for the twin screw compressor design. This method is based on conjugate pair design and generates new twin screw compressor profiles from generating curves derived by the deviation functions. The deviation functions used in this research are composed of the Bezier curves. The partially overlapped three-segment third-order Bezier curve-based deviation function is proposed to achieve the goal of minimizing the blowhole area along with shorter interlobe sealing line length. The complication of combining curves as the generating curves and determining values of parameters of those curves are problems for the rotor profile designs of twin screw compressors in industry. Thanks to the adoption of Bezier curves for the deviation functions, these problems can be avoided when the rotor pro-files of twin screw compressors are designed in this study. In addition, it helps discover a more diverse range of designs and thus leads to the more universal optimal results. Those advantages are emphasized by showing a variety of design examples and the improvement for the industry applications. Moreover, the effects of the lead non-uniformity of the twin screw compressor are investigated and the results are compared to the twin screw compressor with constant lead in this research. It is found that the twin screw compressor with increasing lead tends to reduce the leakage, and thus, the volumetric efficiency of this kind is improved, especially in the practical operating conditions when the working gas has a significant tendency to leak out of the compression chamber of the compressor.

Conventional rotary engine designs are based on an epitrochoidal housing bore that is found by the path of the point at the rotor profile's apex. To seal the engine, the rotor apexes are replaced by spring-loaded apex seals that slide along the housing bore during rotation. The conventional designs are limited to the point-based epitrochoid housing profiles and cannot incorporate the profile of the apex seal. This dissertation presents the complete theory and algorithm of the deviation function (DF) method of rotary engine design. This method is based on conjugate pair design and generates new engine profiles from generating curves. The DF method of rotary engine design by apex seal profile is introduced and developed for generating new profile designs in which the housing profile conforms to the apex seal profile, for better sealing. The DF method of design by geometric parameters is developed to select profiles using the standard rotary engine geometry. Maximum theoretical compression ratio and swept area are two criteria that have a range of possible DF-designed profile solutions. For the apex seal design and selection process, a sealing index is defined and a multi-apex-sealing grid is developed to further improve apex sealing. The DF method of rotary engine design is extended to noncircular pitch curves, for generating more new profiles that incorporate a variable speed ratio between the rotor and main shaft.

By using the DF method, a larger variety of engine profiles is available to meet multiple design criteria and allow more flexibility in the design process. Some example deviation functions are provided for process illustration and design development. Engine profile designs and methods using circular pitch curves are developed using both arc-based and nonarc-based apex seal profiles. Engine profile designs with noncircular pitch curves are developed using the arc-based seal profile.