Date of Graduation


Document Type


Degree Type



Statler College of Engineering and Mineral Resources


Mechanical and Aerospace Engineering

Committee Chair

Gregory Thompson

Committee Member

Nigel Clark

Committee Member

Derek Johnson

Committee Member

Terence Musho

Committee Member

Parviz Famouri


In power/energy systems, free-piston linear machines are referred to as a mechanism where the constrained crank motion is eliminated and replaced with free reciprocating piston motion. Depending on the application, the piston motion can be converted into other types of energy and includes compressed air/fluid, electricity, and high temperature/pressure gas. A research group at West Virginia University developed a free-piston linear engine alternator (LEA) in 1998 and have achieved significant accomplishment in the performance enhancement of the LEAs to date. The present LEA design incorporates flexure springs as energy restoration components and as bearing supports. The advantages of using flexure springs are threefold and include: (1) it increases the LEA’s stiffness and resonant frequency, and hence the power density; (2) it eliminates the need for rotary or linear bearings and lubrication system; and (3) it reduces the overall frictional contact area in the translator assembly which improves the durability.

The current research focuses on the design and optimization of the flexure springs as the system’s resonant dominating component for a 1 kW free-piston LEA. First, the flexure springs were characterized according to the LEA’s target outputs and dimensional limitations. The finite element method (FEM) was used to analyze the stress/strain, different modes of deformation, and fatigue life of a range of flexure spring designs under dynamic loadings. Primary geometric design variables included the number of arms, inside and outside diameter, thickness, and arm’s length. To find the near-optimum designs, a machine learning algorithm incorporating the FEM results was used in order to find the sensitivity of the target outputs to the geometrical parameters. From the results, design charts were extracted as a guideline to flexure spring selection for a range of operations. Then, methods were introduced, investigated, and analyzed to improve the overall energy conversion performance and service life of the flexure springs and the overall LEA system.

These included: a transient FE tool used for fatigue analysis to quantify the life and factors of safety of the flexure springs as well as the spring’s hysteresis; a fluid/structure interaction model used to quantify the energy loss due to drag force applied on the flexures’ side surfaces; packaging of multiple flexures to increase the overall stiffness and to reduce the vibration-induced stresses on flexure arms due to higher harmonics; a model to investigate the two-way interactions of the flexures’ dynamics with the alternator and engine components to find an optimum selection of the LEA’s assembly; a non-linear friction analysis to identify/quantify the energy losses due to the friction of the sliding surfaces of the flexures and spacers; and a series of static and transient experiment to determine the non-linearity of flexures’ stiffness and comparison to FEM results and for validation of the energy audit results from numerical and analytical calculations.

With over 6000 flexure designs evaluated using artificial intelligent methods, the maximum achievable resonant frequency of a single flexure spring for a 1 kW LEA was found to be around 150 Hz. From the FEM results, it was found that under dynamic conditions the stress levels to be as high as twice the maximum stress under static (or very low speed) conditions. Modifications of the arm’s end shape and implementation of a shape factor were found as effective methods to reduce the maximum stress by 20%. The modal analysis showed that the most damaging modes of deformations of a flexure spring were the second to fourth modes, depending on the number of arms and symmetry of the design. Experiment and FEM results showed that using bolted packaging of the springs can damp a portion of the vibration and improve the performance. The drag force loss was found to account for 10-15% of the mechanical losses in a 100 Wnet LEA prototype. From the manufacturing perspective, use of water jet was found the most economical method for manufacturing the flexures which could make the commercial production of the LEAs feasible; however, for high-efficiency, high-durability machines, additional material treatments, and alternative manufacturing methods are essential.