## 3 Experimental Research and Discussion
### Static Characteristic
#### 3.3.1 Influence of Different Diaphragm Displacements  
The experimental conditions of different diaphragm displacements were that the displacement of the CD started from 0 to 1.2 mm and increased by 0.1 mm for each group. The coil actuator displacement of the VCM was controlled by PID. The VCM moved from \(-1\) mm to 6 mm and back to \(-1\) mm in 1 mm intervals.  
In the static experiments of different RD displacements, when the set displacement of the CD was unchanged, there were 13 set displacements of the CD, in a range from 0 to 1.2 mm, as shown in Figure 16. When the displacement of the RD is 6 mm, and the displacement of the CD is 0, the maximum force of the RD is 17.6 N, and the maximum force of the CD is 44.1 N.  
Figure 15: Experimental system physical diagram. **(a)** Static characteristics experimental system; **(b)** friction force measurement experimental system; and **(c)** dynamic characteristics experimental system.  
Figure 16: Experiments of different RD displacements. (**a**) RD mechanical characteristics of area 1; (**b**) CD mechanical characteristics of area 1; (**c**) RD mechanical characteristics of area 2; (**d**) CD mechanical characteristics of area 2; (**e**) RD mechanical characteristics of area 3; (**f**) CD mechanical characteristics of area 3; (**g**) RD mechanical characteristics of area 4; and (**h**) CD mechanical characteristics of area 4.  
When the CD does not reach the set displacement, the force of the CD is basically zero. When the CD reaches the set displacement, the forces of the diaphragms increase with the increase in the RD displacement. When the set displacement range of the is CD from 0 to 0.8 mm, after least squares polynomial fittings, the average slope of the is RD 2.7581 N/mm, the maximum root mean square error is 0.5528, and the maximum slope deviation is 9.17%. The average slope of the CD is 6.8453 N/mm, the maximum root mean square error is 2.038, and the maximum slope deviation is 10.44%. When the set displacement of the CD was from 0.9 mm to 1.2 mm, the experimental points were not discussed, because there were too few experimental points, and there was no reference value.  
There is hysteresis in the axial reciprocating motion of the diaphragm, and the hysteresis decreases with the increase in the CD displacement. The hysteresis of the RD is reduced from 2.13 N to 1.5 N, and that of the CD is reduced from 6.28 N to 3.38 N. Hysteresis exists because there are friction forces between the shafts and the linear bearings during the diaphragm movements. Additionally, there is hysteresis in the diaphragm deformation. The larger the deformation of the diaphragm, the larger the hysteresis.  
In the static experiments of different CD displacements, when the set displacement of the RD was unchanged, there were 7 set displacements of the RD in a range from 0 to 6 mm, as shown in Figure 17.  
Figure 17: Experiments of different CD displacements. **(a)** RD mechanical characteristics. **(b)** CD mechanical characteristics.  
When the RD reaches the set displacement, the forces of the diaphragms decrease with the increase in the CD displacement. When the set displacement range of the RD is from 2 to 6 mm, after least squares polynomial fittings, the average slope of the RD is \(-5.1174\) N/mm, the maximum root mean square error is 0.5168, and the maximum slope deviation is 12.26%. When the average slope of the CD is \(-25.102\) N/mm, the maximum root mean square error is 2.279, and the maximum slope deviation is 15.36%. When the set displacement of the RD was 0 and 1 mm, the experimental points were not discussed, because there were too few experimental points, and there was no reference value.