# A Haptic Feedback Actuator Suitable for the Soft Wearable Device
## 4 Results and Discussion  
### Output Performance of the Electro-Hydraulic Actuator  
Single electro-hydraulic actuator at different DC and AC voltages is characterized using the test bench described in Section 3.2. A high-voltage generator (Model 20/20C-HS, Trek, USA) was applied to output voltages from 1 kV to 12 kV. In Figure 4, DC voltage loading starts from 3 s, and displacement occurs in an instant and drops rapidly with time [26]. The maximum measured displacement of 1.1 mm is obtained from 3 to 4 s at 12 kV, and decreases to 0.4 mm at 30 s. The reason for the decrease in displacement is that the central film accumulates a large restoring force while the displacement is instantaneously obtained. The restoring force acts on the electrodes through the liquid, which increases the distance between the electrodes and reduces the Maxwell force. Figure 5a-c plots the displacement as a function of time with AC voltage with 10, 50, and 100 Hz. A smaller voltage frequency leads to a larger oscillation when the actuator outputs displacement. The voltage frequency has a significant influence on the oscillation of the displacement at low frequencies. Figure 5d plots the variance as a function of voltage frequencies from 1 to 100 Hz. The influence diminishes rapidly as the frequency increases and becomes smaller after the frequency reaches 20 Hz. The variance in the displacement value after a period of stability was used as a measure of displacement oscillation. Figure 4: The output displacement of the actuator under different DC voltages over time. Figure 6 explains the reason for obtaining different results with the two loading methods. Under DC (11 kV) voltage loading, the maximum measured displacement of 1.0 mm is obtained in 0.15 s, which makes the central film produce a larger restoring force. The large restoring force drives the liquid to flow back rapidly, which causes the displacement to decay rapidly under the action of the Maxwell force and restoring force. Under AC (11 kV) voltage loading, the maximum measured displacement of 1.0 mm is obtained in 1 s. Different from the DC voltage, in this process, the displacement reaches a maximum after several times of rising, and each time there is still enough Maxwell force to overcome the smaller restoring force of the central film, which prevents the liquid from flowing back and allows the actuator to continue to produce displacement. The enlarge image from 5 s to 10 s in Figure 6 describes the process before the displacement of the actuator rises to a steady state when the AC voltage is applied. The displacement reaches its maximum after several oscillations. The enlarge image from 10 s to 15 s in Figure 6 shows the actuator after the output displacement is stabilized at an AC voltage of 5 Hz. After the displacement is stabilized, each oscillation is arranged regularly. In total, 25 oscillations occurring within 5 s were recorded, and the obtained cycle was consistent with the applied AC voltage cycle, which confirms that each oscillation on the graph represents the combined effect of the central film restoring force and the Maxwell force. Compared with the DC voltage, the AC voltage was applied to overcome a smaller restoring force of the central film many times, which produced a better result. Figure 5: The oscillation of the output displacement of the actuator under the square wave voltage with the same amplitude of 12 kV and different frequencies of (**a**) 10 Hz, (**b**) 50 Hz, (**c**) 100 Hz, respectively. (**d**) The variance of the output displacement of the actuator under a square wave voltage (12 kV) with different frequencies (1–100 Hz). Based on the Maxwell force and hydraulic amplification principle, when DC voltage is applied, the displacement of the actuator will decrease, which is inevitable. The decrease in displacement with the DC voltage allows the user to obtain only a short feedback effect, while the AC voltage loading method can stably and continuously output displacement for the finger with different frequencies.