# Development of Piezoelectric Inertial Rotary Motor for Free-Space Optical Communication Systems
## 4 Experimental Investigation of Motor
At the highest applied voltage of 180 V\({}_{\text{p-p}}\), the motor achieved a maximum stall torque of 13.1 N\(\cdot\)mm, which corresponds to a torque-per-voltage ratio of 72.7 mN\(\cdot\)mm/V\({}_{\text{p-p}}\). This value represents the maximum torque capacity, indicating its ability to handle significant loads before stalling. In contrast, at the lowest excitation voltage of 40 V\({}_{\text{p-p}}\), the stall torque was measured at 0.38 N\(\cdot\)mm, or 9.5 mN\(\cdot\)mm/V\({}_{\text{p-p}}\). This lower stall torque reflects the expected reduction in torque output with decreased voltage amplitude, demonstrating the sensitivity to changes in the driving signal. Overall, considering the stall torque-excitation signal amplitude relationship, it can be stated that the motor can provide stable characteristics that are suitable for FSO systems. Finally, to simulate the thermal environment that a small satellite could encounter in low Earth orbit (LEO), the impedance and phase characteristics were measured under varying temperature conditions, from \(-20\)\({}^{\circ}\)C to \(+40\)\({}^{\circ}\)C. These temperatures represent the thermal fluctuations experienced by satellites in orbit as they pass through sunlight and shadow. The experiment was carried out in a RUMED XTS-T500 Ex cold-heat cabinet, and measurements, conducted using the SinePhase 16,777 k impedance analyzer (SinPhase, Modling, Austria), are presented in Figure 15.1  
As shown in the Figure 20a impedance, frequency characteristics have a dependence on temperature. At lower temperatures, particularly \(-20\)\({}^{\circ}\)C and \(-10\)\({}^{\circ}\)C, the motor exhibits higher impedance values, with a range of 4000-4300 \(\Omega\). This behavior can be attributed to increased electrical resistance and material stiffness at colder temperatures. As the temperature increases, the impedance decreases, with the lowest values observed at 30 \({}^{\circ}\)C and 40 \({}^{\circ}\)C, where the impedance ranges from 3000-3500 \(\Omega\). Figure 15.2 Stall torque characteristics of motor under different excitation signal amplitudes. Furthermore, the impedance behavior is strongly frequency-dependent, with noticeable resonant peaks occurring between 12 kHz and 12.3 kHz across all temperatures. Peak impedance values decrease as temperature rises, and the resonance frequency changes slightly, suggesting that the resonance characteristics are influenced by the thermal environment. This behavior is critical in space applications, where the motor's electrical and mechanical performance must remain consistent despite rapid thermal fluctuations. The phase-frequency response further complements the impedance findings, showing phase shifts around the resonant frequency. At \(-20\)\({}^{\circ}\)C, the phase angle remains close to \(-85\)\({}^{\circ}\) for most of the frequency range, indicating that the motor operates predominantly in a reactive state with minimal energy dissipation. As the temperature increases, the phase angle becomes less negative, with a peak phase shift around \(-70\) at \(20\)\({}^{\circ}\)C and \(-75\)\({}^{\circ}\) at \(40\)\({}^{\circ}\)C.  
Figure 15.3 Impedance– and phase–frequency characteristics of the motor under different temperature conditions: (**a**)—impedance–frequency characteristics of the motor; (**b**)—phase–frequency characteristics of the actuator. This shift means that as the motor heats up, the real component of the impedance increases, suggesting that more energy is being transferred to mechanical work or dissipated as heat. Notably, the phase deviation near resonance broadens as the temperature increases. At \(-20\)\({}^{\circ}\)C, the phase shift occurs sharply around 12.2 kHz, while at 40 \({}^{\circ}\)C, the deviation begins at lower frequencies (around 11.9 kHz) and persists over a broader range. This behavior indicates that the motor resonance response becomes more diffuse at higher temperatures, likely due to changes in material properties affecting both the electrical and mechanical energy storage components.