# Development of a Magnetorheological Damper with Self-Powered Ability for Washing Machines
## 6 Conclusions
**Nomenclatures**  
\(A_{c}\) & Sectional area of the inducing coil  
\(A_{gm}\) & Cylindrical surface area of the air gap  
\(A_{m}\) & Sectional area of the magnet  
\(A_{r}\) & Projected area of the seal  
\(B\) & Applied magnetic density  
\(B_{rem}\) & Magnet remanent flux density  
\(c\) & Damping coefficient  
\(d_{w}\) & Diameter of the copper wire  
\(E\) & Induced voltage in the inducing coil  
\(E_{i}\) & Induced voltages in the \(i\) active coil  
\(EH\) & Energy-harvesting  
\(F_{0}\) & Zero-field friction force  
\(F_{d}\) & Damping force  
\(F_{\sigma\sigma}\) & Coulomb friction force between the shaft and the O-ring  
\(F_{r}\) & Required damping force for the MR damping part  
\(F_{u}\) & Exciting force due to an unbalanced mass in the \(u\) direction  
\(F_{u0}\) & Magnitude of the exciting force  
\(f_{c}\) & Friction per unit length caused by the compression of the O-ring  
\(f_{h}\) & Friction force caused by the fluid pressure on a unit projected area of the O-ring  
\(H_{\omega e}\) & Magnetic coercivity of the magnet  
\(h_{c}\) & Height of the exciting coil  
\(h_{d\omega}\), \(w_{\sigma h}\) & Chamfer dimensions of the exciting coil  
\(h_{cm}\) & Height of the inducing coil  
\(I\) & Applied current  
\(k\) & Stiffness of each spring  
\(L\) & Length of the MR fluid gap  
\(L_{e}\) & Effective length of the active MR fluid in the gap \begin{tabular}{l l} \(L_{r}\) & Length of the seal rubbing surface \\ \(L_{s}\) & Length of the shaft end \\ \(l_{m}\) & Length of the magnet \\ \(l_{p}\) & Length of the pole of the MR damping part \\ \(MRF\) & Magnetorheological fluid \\ \(m\) & Mass of the suspended tub assembly \\ \(m_{u}\) & Unbalanced mass \\ \(N\) & Number of winding turns of each inducing coil \\ \(P\) & Power of four active coils \\ \(P_{1}\), \(P_{2}\) & Powers of coil 1 and coil 2 \\ \(p_{c}\) & Pitch of the coil slot of the EH part \\ \(p_{m}\) & Pitch of the pole pair of the EH part \\ \(R\) & Outer radius of the self-powered MR damper \\ \(R_{c}\) & Resistance of each inducing coil \\ \(R_{s}\) & Radius of the shaft \\ \(R_{u}\) & Radius from the rotation axis of the unbalanced mass \\ \(r_{i}\) & Inner radius of the magnet \\ \(r_{o}\) & Outer radius of the magnet \\ \(r_{s}\) & Radius of the shaft \\ \(r_{\omega}\) & Frequency ratio \\ \(T_{f}\) & Force transmissibility from the tub assembly to the cabinet \\ \(t\) & Time \\ \(t_{g}\) & Thickness of the MR fluid gap \\ \(t_{gm}\) & Thickness of the air gap \\ \(t_{o}\) & Thickness of the outer housing of the MR damping part \\ \(t_{om}\) & Thickness of the housing of the EH part \\ \(t_{w}\) & Thickness of the thin wall of the MR damping part \\ \(t_{wm}\) & Thickness of the thin wall of the EH part \\ \(v\) & Velocity of the shaft \\ \(w_{c}\) & Width of the exciting coil \\ \(w_{cm}\) & Width of the inducing coil \\ \(X\) & Amplitude of the tub vibration \\ \(x\) & Displacement of the shaft \\ \(Y\) & MR fluid rheological property such as postyield viscosity or yield stress \\ \(\alpha_{1}\), \(\alpha_{2}\) & Angle between the spring and the \(y\)-axis \\ \(\alpha_{SY}\) & Saturation moment of the \(Y\) property \\ \(\beta_{1}\), \(\beta_{2}\) & Angle between the damper and the \(y\)-axis \\ \(\Delta u\) & Displacement of the center of the tube assembly in the \(u\) direction \\ \(\eta\) & Postyield viscosity of the active MR fluid in the gap \\ \(\lambda\) & Efficiency of the magnetic flux considering leakage effect \\ \(\mu_{0}\) & Relative magnetic permeability \\ \(\xi\) & Damping ratio \\ \(\tau_{y}\) & Field-dependent yield stress of the active MR fluid in the gap \\ \(\Phi_{g}\) & Magnetic flux of the air gap between the magnets and the stator core \\ \(\varphi\) & Angle of the \(u\) direction \\ \(\varphi_{0}\) & Initial phase angle of the inducing coil \\ \(\omega_{d}\) & Damped frequency \\ \(\omega_{n}\) & Natural frequency \\ \end{tabular}