## 2 Design and Prototype of Linear Oscillating Load System  
### Voice Coil Motor (VCM)  
The VCM can be constructed as two parts, identified as the mover and the stator. The mover consists of copper coils and coil frame, as well as the stator is composed of irons and magnets. According to the features of large length to ratio of the mover with the large working stroke, axially magnetized magnets are chosen as the source of the main magnet field in the stator. Irons, i.e., cover irons and back iron, are designed as the flux-conducting paths, aiming at reducing magnet resistance and flux leakages. Due to the radial flux density in the air gap, axial thrust force can be generated in the coils of electric excitation. To improve usage rate of flux and increase axial thrust force, two parts of copper coils are install in the air gap. As a conclusion, the sketch structure of the VCM can be designed as shown in Figure 2.  
According to the sketch structure and material features of the VCM, the open-circuit flux paths are depicted in Figure 3 for detailed description. The flux produced by the end axial magnets passes through cover iron, back iron, air gap and inner iron as well as that by the middle axial magnet passes through inner iron, air gap and back iron. So the flux passes through a complete magnetic circuit, which reduces the magnet resistance as well as the flux leakage efficiently.  
Figure 2: Sketch structure of the voice coil motor (VCM).  
Furthermore, mechanical structures of mover coils and magnetic array are of necessity for support and fixation. A PEEK (polyether-ether-ketone) tube with no ferromagnetism and no electrical conductivity is wound by the mover coils, which fixes the mover coils and reduces eddy current effect and mover mass effectively. A core rod of no ferromagnetism, made up of stainless steel, is installed in the inner iron rings and magnets with screw joints at the ends of the rod to fix the magnets and irons firmly. As a result, the 3D object of the VCM is draw as depicted in Figure 4.  
Based on the structure design above, the prototype of the linear VCM is established as shown in Figure 5. The mover consists of coils and tube frame as well the stator is composed of magnetic array, cover irons and back iron. The model number of magnets is NdFe35 SH and the diameter of the coil copper wire is 1 mm.  
Figure 4: Three-dimensional (3D) structure of the VCM.  
Figure 5: Detailed structure of the VCM.  
Figure 3: Open-circuit flux lines of the VCM.  
Moreover, the comparison of the output force density between experimental results and simulation results is depicted in Figure 6, showing perfect consistency between theoretical results and experimental results and proving the validity of the proposed design. Furthermore, the fluctuation around the average force density is about 4.33%, to ensure the symmetry of load force within stroke. Meanwhile, the relationships between current and output thrust force at three locations of the mover, i.e., 0 mm, \(-5\) mm and 5 mm, are depicted in Figure 7, demonstrating the nearly proportional relationship between thrust force and current. Because of excellent symmetry and linearity of the VCM output thrust force, the VCM can be utilized as the load motor for the LOLS, having the advantages of accurate position and force control performance.