Application of rack method in generation of internally geared rotor profiles

This study explores the application of the rack method, traditionally used for generating rotor profiles in spur gears and twin screw compressors, to rotor profile generation of internally geared positive displacement machines. The necessary conditions for ensuring continuous contact in these profiles are examined. An analytical approach is proposed, where a rack profile based on trochoidal curves generates the inner rotor profile, from which the outer rotor profile is derived. Additionally, a numerical approach is introduced, demonstrating feasibility using a sine wave rack profile to generate the outer rotor, from which the inner rotor profile is derived. The methodology could be applied to rotor profiles with a non-zero minimum working chamber area, as found in gerotor pumps, and modified profiles with a zero minimum area, as required for internally geared screw machines. This work provides the first demonstration of general rack-generated rotor profiles for internally geared positive displacement machines. It establishes a foundation for refining the rack method and developing advanced numerical techniques for machine design and optimisation.