# Development of a Magnetorheological Damper with Self-Powered Ability for Washing Machines
## 3 Energy-Harvesting Part
### Optimal Design of the Energy-Harvesting Part  
As mentioned above, the generated power in Equation (10) should be as large as possible to maximize the efficiency of the EH part. In the design of the EH part, the height of coil \(h_{cm}\), the width of coil \(w_{cm}\), the pitch of coil \(p_{c}\), the pitch of pole pair \(p_{m}\), and the thickness of housing \(t_{om}\) are significant dimensions and thus set as design variables. Another problem that should be considered is the available assembly space in the washing machine. Since the total length of the damper in equilibrium is approximately 230 mm and the desired maximum damper stroke is established by 40 mm, the length of the shaft end carrying the pole pairs \(L_{s}\) is restricted to be smaller than 30 mm. From the aspects of compactness and low cost, it would not be ideal to improve the possibility of generating power by increasing the EH part size. Therefore, although the outer radius of the EH part has no restriction, it should not be so much larger than that of commercial passive dampers and conventional MR dampers. In this optimization, the value of 22 mm is chosen to be the upper limit of radius \(R\) of the EH part. The final concern is the possibility of machining and assembling the stator core without warping, for which the thickness of the housing \(t_{om}\) is set to be 2 mm or greater. In summary, the design optimization of the EH part can be expressed: Determine the optimal geometry of the proposed EH part that maximize the generated power, subjected to the outer radius \(R\) is smaller than 22 mm and the length of the shaft end \(L_{s}\) is smaller than 30 mm.  
In this work, the finite element model of the EH part is implemented using the 2D-axisymmetric couple element (plane 13) of ANSYS. It is noteworthy that the geometry of the EH part will continuously vary during the optimization process, so the meshing size is defined by the constant number of elements per line rather than the size of each element. Figure 4 shows the finite element model of the EH part. In order to obtain the optimal design of the EH part, the golden section algorithm combined with first-order method of the ANSYS optimization tool is utilized. The procedure in detail based on finite element analysis (FEA) has been presented in some researches [21,22].  
The optimal solution of the proposed EH part is specified in Table 1. It is noted that the thicknesses of the air gap \(t_{gm}\) and thin wall \(t_{um}\) should be as small as possible. In this study, both are set by 0.8 mm considering the manufacturing cost. Figure 5a,b shows the magnetic flux distribution and magnetic flux density of the optimized EH part, respectively. From Figure 5a, it is observed that the magnetic flux passes through the air gap between the magnets and the stator core. As a result, the induced voltages could be generated in the inducing coils of the EH part to power the exciting coils of the MR damping part. Besides, there is almost a saturation of magnetic flux toward the south poles of the magnets, which is marked in Figure 5b.