# Design of a 120 W Electromagnetic Shock Absorber for Motorcycle Applications
## 2 Concept and Analysis  
Based on the requirements of the design, the energy harvester is represented as a linear induction generator that incorporates shock absorber functions. The magnetic finite element method is then used to analyze the electromagnetic shock absorber. The energy harvester is represented as a linear induction generator with shock absorber functions based on the design requirements. Figure 1 schematically shows the geometry of conventional shock absorbers in motorcycles. The system transforms the kinetic energy of suspension vibration between the wheel and a sprung load into usable electrical power. The length and outer diameter of the shock absorber are in the range of 250-300 mm and 60-70 mm. To maximize the output power, the length and outer diameter chosen were 300 and 70 mm, respectively. The mechanical air gap chosen was 1 mm. To address concerns about practical application, because motorcycles are most often running on roads with relatively smooth surfaces during operation, the performance analysis considered was based on such conditions. The vibration frequency of 5 Hz was used to represent a relatively smooth road, while 2 Hz was used to indicate a rougher road surface [21]. The peak-to-peak stroke length was assumed to be 10 mm (as determined in [13]) for a vehicle moving at 70 km/h on a Type B road. Assuming the position of the vibration coil following the time \(t\) is:  
\[\mathrm{x}=\frac{St_{p}}{2}\sin(\omega t) \tag{1}\]  
and vibration speed can be calculated as:  
\[v=\frac{dx}{dt}=\frac{St_{p}}{2}\omega=v_{max}\cos(2\pi\mathrm{ft}) \tag{2}\]  
According to Equation (2), the relation between vibration speed, frequency, and stroke length can be determined as follows:  
\[v_{max}=\pi fSt_{p}(m/s) \tag{3}\]  
where \(St_{p}\) = 10 mm is the peak-to-peak stroke length and \(f\) = 5 Hz is the vibration frequency. These give the maximum vibration speed of 0.157 m/s. Figure 1: Conventional shock absorbers on a motorcycle. Table 1 provides a summary of the general specifications. The wire was chosen according to Korea Standard KS C 3107:2003. The diameter of the pure copper wire chosen was 0.6 mm, while the insulation thickness was 0.012 mm. This provided wires with a total diameter of 0.644 mm. The radial and axial PMs were made of rare-earth permanent magnets (PMs), NdFeB 40 SH and 50 SH, respectively, which were chosen due to their high magnetic density (1.26 T and 1.4 T), the relative permeability of r = 1.05 at room temperature and availability. The eight-slot wight-pole combination model was used to design an electromagnetic shock absorber for the motorcycles in this study. The one-to-one slot-pole ratio was found to produce the maximum output power and power density [19]. Furthermore, the hybrid permanent magnet construction, which is a combination of a classical Halbach array with iron spacers ([44,45]), was employed to improve the performance of the linear generator. The iron spacers were composed of magnetic material and were inserted into the Halbach array to increase the flux linkage on the winding, as well as to increase the flux density in the air gap. The magnetic flux density in the air gap can be significantly increased due to its high relative permeability. The iron core and spacers were made of magnetic carbon steel (S20C) and faced the coil slots directly in the initial alignment position to optimize power [20]. The radial PM assemblies employed a total of ten spacers (see Figure 2). The number of phases also has an important influence on the power output. Generally speaking, the more coil phases are used, the more power will be produced [16]. In rotating machines and linear (or one-directional motion) machines, the three-phase winding is commonly preferred due to its higher efficiency and better economy. However, in a short