In order to verify the feasibility and working performance of the proposed walking type piezoelectric actuator with flexible mechanism vertical installation, the prototype was manufactured as shown in Fig. 5, with the volume of 90×70×40mm. The experimental system consists of a function signal generator (R332 RIGOL), a signal amplifier (E-481 PICA PI), a prototype, a laser displacement sensor (LK-H080 KEYENCE), a laser displacement sensor controller (LK-HD500 KEYENCE) and a PC. In the experiment process, the signal generator generates two sawtooth signals, which are amplified by the signal amplifier and respectively applied to both ends of the two piezoelectric stacks to achieve the effect of walking. With a resolution of 10 nm and a sampling period of 200µs, the laser displacement sensor can test the performance of the vertically-mounted flexible mechanism walking type piezoelectric actuator proposed in this study at different voltages and driving frequencies.

The theoretical optimal phase difference of walking type piezoelectric actuator is 180°, but the contact force between the two driving feet and the slider tends to be unequal due to factors such as the error in the preload force during piezoelectric stack mounting and the error of the preload force during the flexible mechanism installation. Therefore, the relationship between the phase difference of the two driving feet and the stepping displacement in the walking type actuator is studied to find the best phase angle. According to Fig 6, when moving forward, when the phase angle rises from 0° to 20°, the stepping displacement rises to 10.754µm; when the phase angle rises from 20° to 140°, the stepping displacement gradually decreases to 9.687µm; when the phase angle rises from 140° to 160°, the stepping displacement rises to 12.467µm. When the phase angle rises from 160° to 360°, the stepping displacement gradually decreases by 8.062µm. When moving in reverse, when the phase angle rises from 0° to 20°, the stepping displacement rises to 7.988µm, when the phase angle rises from 20° to 280°, the stepping displacement is relatively stable, when the phase angle is 180°, the stepping displacement reaches the maximum value of 7.913µm, when the phase angle rises from 280° to 320°, The stepping displacement increases to 8.603µm, and when the phase angle rises from 320° to 360°, the stepping displacement decreases by 4.436µm. Combined with the relationship between the forward and reverse motion phase difference and the stepping displacement and the phase angle commonly used in the experiment, the phase of walking type piezoelectric actuator was selected to be 160°.

After obtaining the optimal phase angle of the walking type piezoelectric actuator, the frequency, load force and horizontal resistance experiments are carried out for the single driving foot piezoelectric actuator.

Fig. 7 shows the relationship between the input frequency *f* and the speed *v* of the single driving foot piezoelectric actuator at *U*=120V. From the figure, it can be seen that when moving in forward direction, the piezoelectric actuator speed reaches 140.72µm/s for the case where the input frequency rises from 1 to 100Hz, the speed of the actuator decreases to 97.33µm/s when the input frequency rises from 100 to 150Hz, and the speed of the actuator continues to increase to 403.11 when the input frequency rises from 150 to 200Hz µm/s, as the input frequency increases from 200 to 350Hz the actuator speed decreases to 149.65µm/s, as the input frequency increases from 350 to 400Hz the speed increases to 327.1µm/s, then as the frequency increases the speed decreases rapidly until the frequency increases to 500Hz and the speed decreases to 0. So, the maximum speed for forward motion of the single driving foot piezoelectric actuator is 403.11µm/s and the actuator is unstable when the frequency is greater than 500Hz. When moving in reverse motion, the piezoelectric actuator speed reaches 515.26µm/s with the input frequency increasing from 1 to 300Hz, the piezoelectric actuator speed decreases to 333.5µm/s with the input frequency increasing from 300 to 350Hz, and the speed of the actuator continues to increase to 927.55µm/s with the input frequency increasing from 350 to 650Hz. The actuator speed continues to rise to 927.55µm/s, and then the speed decreases rapidly as the frequency increases until the frequency increases to 700Hz and the speed drops to 0. As a result, the maximum speed at which the single driving foot piezoelectric actuator moving in reverse motion is 927.55µm/s, and the actuator is unstable when the frequency is greater than 700Hz.

Fig. 8 shows the relationship between the input frequency *f* and the speed *v* of the walking type piezoelectric actuator at *U*=120V and *φ*=160°. It can be seen from the figure that when moving forward, the speed of the piezoelectric actuator gradually increases to 2705.85µm/s when the input frequency rises from 1 to 400Hz, and then the speed gradually decreases with the increase of frequency. Therefore, the maximum forward moving speed of the walking type piezoelectric actuator is 2705.85µm/s, and when the frequency is greater than 700Hz, the actuator is unstable. When moving in reverse, the speed of the piezoelectric actuator reaches 970.77µm/s when the input frequency rises from 1 to 200Hz, and then the speed gradually decreases as the frequency increases. Therefore, the maximum speed of the walking type piezoelectric actuator moving in reverse is 970.77µm/s, and the actuator is unstable when the frequency is greater than 500Hz.

Fig. 9 shows the relationship between the stepping displacement and vertical load of the single-foot piezoelectric actuator under the conditions of *U*=120V and *f*=1Hz. It can be seen from the figure that when the load is moving forward, the stepping displacement gradually increases when the load is 0~600g, and gradually decreases when the load is 600~800g, the stepping displacement gradually increases again when the load is 800~1500 g, and the stepping displacement is unstable when the load is greater than 2000g. The stepping displacement is relatively stable in the range of 400g~1500g, so the preload of the forward motion of the single-foot piezoelectric actuator is 1600g. In the reverse motion, the stepping displacement decreases with the increase of the load, and the maximum load is about 1100g.

Fig. 10 shows the relationship between the stepping displacement and vertical load of the walking type piezoelectric actuator under the conditions of *U*=120 V, *f*=1Hz, *φ*=160°. It can be seen from the figure that when the load is moving forward, the stepping displacement gradually increases when the load is 0~2500g, while the stepping displacement gradually decreases when the load is 2500~3500g. When it is greater than 3500g, the stepping displacement tends to be stable. Because the flexible mechanism is installed vertically, the contact force between the platform and the driving foot will be increased continuously when loading the load on the surface of the platform, and the load capacity of the actuator will gradually increase within a certain range. Therefore, when the load is loaded to 10kg, the stepping displacement can still be stable at about 10μm. Because the load of the designed piezoelectric actuator platform is small in actual working conditions, it does not continue to load more than 10kg. In the reverse motion, when the load is 0~2500g, the stepping displacement gradually increases, when the load is 2500~4000g, the stepping displacement gradually decreases, when it is greater than 4000, the stepping displacement gradually stabilizes at about 5μm, and the loading experiment stops after 10kg.

In practical, the motion of the piezoelectric actuator slider is affected by the resistance from the guide roller and other additional resistance. Fig. 11 shows the driving effect of the single foot piezoelectric actuator under different horizontal resistance at *U*=120V, *f*=1 Hz. In forward motion and reverse motion, the stepping displacement decreases with the increase of horizontal resistance. After applying horizontal resistance greater than 0.3N, the stepping distances of reverse motion decreases faster, while the stepping displacement decreases slower. The maximum horizontal resistance of the forward motion is about 0.8N, and the maximum horizontal resistance of the reverse motion is about 0.5N. Fig. 12 shows the driving effect of the walking type piezoelectric actuator with different horizontal resistance under the condition of *U*=120V, *f*=1Hz. In forward motion and reverse motion, the stepping displacement piezoelectric actuator decreases with the increase of horizontal resistance. After the horizontal resistance greater than 1 N is applied, the stepping displacement of the reverse motion decreases faster, while the stepping displacement decreases slower. The maximum horizontal resistance of forward motion is about 4.5N, and the maximum horizontal resistance of reverse motion is about 1.6N. In summary, the ability of walking type piezoelectric actuator to overcome the horizontal resistance in the forward motion is 5 times that of the single foot actuator, and the ability of bipedal piezoelectric actuator to overcome the horizontal resistance in the reverse motion is 3 times that of the single foot actuator, which is much greater than the single foot piezoelectric actuator in both forward and reverse motion.