Enhancing energy efficiency in fluid machinery: Analytical modeling of conjugate profiles for energy-losses aware design

This paper introduces a novel methodology for deriving closed-form expressions of conjugate curves to enhance the energy efficiency of fluid machinery via geometric optimization. Conjugate curves not only enable the definition of new rotor profiles mitigating internal losses in rotary positive displacement machines, but also support the design of tribological contacts to reduce external losses. Traditional methods for deriving conjugate profiles face significant challenges due to the non-linearity of equations based on envelope theory and often lack general applicability. This research introduces a systematic methodology for designing conjugate profiles, proposing a novel generalized approach for calculating closed-form expressions of conjugate curves by leveraging the properties of instant centers of rotation. This approach provides a general framework applicable across a wide range of systems. The proposed methodology was applied to design a new rotor with hyperbolic lobes, improving area efficiency of a roots type positive displacement machine to 47.33% (compared to 45.18% achieved using traditional circular-lobe rotors). Additionally, a new mechanical Variable Valve Actuation (VVA) system for motorcycle engines was developed, with kinematic analysis confirming a variable maximum valve lift from 10.7 mm to 0.5 mm. Frictional power dissipation within the VVA system was also evaluated, peaking at 1.7 $kW$ (average 0.228 $kW$) at 9500 $rpm$, with 88.65% of losses attributed to the cam–auxiliary rocker arm interface. To mitigate these losses, the auxiliary rocker arm was re-engineered to integrate a roller cam follower mechanism. Through this improvement, the average frictional power dissipation dropped from 0.228 $kW$ to about 0.017 $kW$. Furthermore, results revealed that the re-designed VVA system demonstrated a reduction in frictional losses of approximately 0.072 $kW$ compared to a conventional valvetrain. Overall, this approach provides a broadly applicable framework for improving energy efficiency in fluid machinery by systematically refining geometric parameters.