Quantification of Windage and Vibrational Losses in Flexure Springs of a One kW Two-Stroke Free Piston Linear Engine Alternator

Methods to quantify the energy losses within linear motion devices that included flexural springs as the main suspension component were investigated. The methods were applied to a two-stroke free-piston linear engine alternator (LEA) as a case study that incorporated flexure springs to add stiffness to the mass-spring system. Use of flexure springs is an enabling mechanism for improving the efficiency and lifespan in linear applications e.g. linear engines and generators, cryocoolers, and linear Stirling engines. The energy loss due to vibrations and windage effects of flexure springs in a free piston LEA was investigated to quantify possible energy losses. A transient finite element solver was used to determine the effects of higher modes of vibration frequencies of the flexure arms at an operational frequency of 65 Hz. Also, a computational fluid dynamics (CFD) solver was used to determine the effects of drag force on the moving surfaces of flexures at high frequencies. A parametric study was performed to understand the effects of geometrical and operational parameters including the diameter of flexures, gap width between flexure arms, stroke length, and frequency of oscillation on the drag force coefficient on the flexure surfaces. The numerical results were compared to experimental results obtained from damping tests and steady-state tests in a vacuum chamber. Modeled results were in good agreement with experiments and showed between 30 to 40 Watts of mechanical energy loss at 65 Hz in the 1 kW LEA design including windage and vibrational losses. It was also found that windage losses contributed to between 10-15% of the total mechanical losses. Also, damping tests in a vacuum chamber showed that in the absence of windage and acoustic losses between 30-35% of total input energy was lost due to structural and frictional damping. Measuring the amplitude of damped vibrations the damping ratio was calculated to be ζ=0.003.