## 3 Development of Test FPSE and Experimental Setup  
Figure 2 shows the test FPSE, designed and developed by the institute, and its test rig: (a) cross-sectional drawing of the test FPSE with sensors, (b) manufactured FPSE inside casing, and (c) the test rig with an electric heater and an external electric load. Table 1 lists the dimensions and specifications of the test FPSE. Figure 2: Test FPSE developed by the institute and its test rig: (**a**) cross-sectional drawing of the test FPSE with sensors, (**b**) manufactured FPSE inside casing, and (**c**) the test rig with an electric heater and an external electric load. Moving parts: The PP and DP are manufactured to have masses of 3.6 kg and 1.64 kg, respectively, with an identical diameter of 84 mm. The DP is connected to the DP spring across the PP with the DP rod. The PP is directly connected to the PP spring. Designed piston amplitudes are 12 mm. The PP and DP have gap clearances of 50 \(\upmu\)m and 150 \(\upmu\)m with cylinders, respectively. The clearance is set larger for DP than for PP considering thermal expansion at high temperatures. For parameter-varying experiments, the PP can have additional masses attached to the bottom. The DP and PP spring parts have a form of stack with multiple springs for stiffness variation. Each spring has a planar shape with multiple spirals and a stiffness of 42 kN/m. Both the PP and DP spring assemblies have a reference stiffness of 84 kN/m. Stationary parts: The heat exchangers and regenerator, which has an annular shape, are located between the casing and DP liner. The hot and cold heat exchangers are \"fin\" types, with identical dimensions. The regenerator is made of a laminated screen wire mesh with a wire diameter of 120 \(\upmu\)m and porosity of 87%. The bounce space volume is set to be large enough to neglect the gas spring effect. The linear alternator of a single-phase permanent magnet type has a stator composed of inner and outer cores and a winding coil, along with a mover for the permanent magnets on the PP. Test rig: A cartridge electric heater heats the upper engine head around the hot heat exchanger, while a cooling water jacket cools the lower engine head around the cold heat exchanger. An electric circuit with load resistances is formed outside the engine and connected to the linear alternator. The electric loads are applied to the engine by changing the load resistance of the external circuit, and also acts as an actuator during engine start using an AC power supply. A high-pressure compressor charges the engine casing with a working gas, which, in this study, is air. Five thermocouples measure the temperatures of the heater, expansion and compression spaces, and the inlet and outlet of cooling water. Two pressure sensors measure the pressures in the compression space and bounce space. Two accelerometers are used for measurement of piston displacements by converting acceleration via a transmitter. A flow meter measures the cooling flow rate. Experiments on dynamic behavior measurements were designed with experiment parameters of PP mass and PP spring stiffness were based on the factorial design. Each experiment parameter has three levels with \(\pm\)10% for mass and \(\pm\)50% for stiffness, and a total of five cases. Table 2 lists all the experimental cases with the reference of case 3 having a mass of 3.6 kg and stiffness of 84 kN/m.