# Multi-Physics Analysis of a Magnetorheological Valve Train with Experimental Validation
## 3 Magnetic and Thermal Studies
To determine the maximum possible temperature, steady-state analysis was performed in this multiphysics simulation. First, the thicknesses of the MR layer and the partition plate were optimized. The resistance offered by the MR fluid layer is inversely proportional to its thickness. However, if the MR fluid layer is too thin, the MR fluid cannot pass, and the plates come into direct contact with each other. This creates excessive resistance, thereby preventing plate movement. Therefore, the thickness of the MR fluid layer was set to 1 mm. Similarly, the resistance force is inversely proportional to the separator thickness. However, the separator plates should have a certain minimum thickness to prevent their deformation. Therefore, the separator plate thickness was set to 3 mm. To increase the resistance offered by the valve, a large number of layers are needed. However, the cylinder head limits the available space for the number of layers, and it depends on the thickness of the MR layer and the partition plate. Finally, in the existing limited volume, six MR layers and five partition plates with the best possible thicknesses were used in the proposed design, as illustrated in Figure 3.  
Second, the maximum possible input current was estimated. Magnetic materials reach saturation at the maximum possible input supply. This affects the magnetic field and, eventually, the resistance force. The input supply is the product of the applied current and number of turns. For the selected coil wire, the maximum supply was 2 A. Therefore, it was important to identify the number of coil turns (T) that would achieve the maximum torque. Figure 4 shows the resistance force and MR layer temperature corresponding to different numbers of ampere-turns (ATs). The multiphysics simulation results were more accurate than those of the conventional magnetic field simulations because the multiphysics simulation considered the effects of working temperature on coil resistivity. Especially at higher input ATs, the multiphysics simulation yielded more accurate results, as depicted in Figure 4a. The maximum force was reached when the magnetic flux channel was magnetically saturated. For this reason, after 1500 AT, the resistance force did not increase. Figure 2:0 Design factors of magnetic plate block. Moreover, the slope of the temperature rise in Figure 4b increases after 2000 AT. This is because the heat generated by the coil was considerably higher than the heat transferred to the surrounding. Therefore, 1500 AT--750 coil turns--is appropriate for this device. Third, the magnetic core channel material was selected. It was decided that this material must have high magnetic permeability and favorable thermal conductivity. In this study, steel alloys, including AISI1010 containing 0.1% carbon, AISI 1008 containing 0.08% carbon, and AISI 1018 containing 0.18% carbon, as well as SS400 containing 0.15-0.2% carbon, were used. By considering the magnetic permeability properties depicted in Figure 5a, temperature conditions depicted in Figure 5b, and suggestions from various manufacturers, SS400 was finally selected as the study material. Then, the optimal magnetic core area (\(A\)) was estimated. This area must be less than the available space for the valve train in the engine, that is, 900 mm\({}^{2}\). Figure 6 shows an analysis of the effects of the channel area on the output force and temperature of the device. According to Figure 6a, the smaller the area, the lower the resistance force. However, for areas exceeding 625 mm\({}^{2}\), this relationship was found to be weak; for example, the force generated with the channel area of 625 mm\({}^{2}\) was 99.28% of the force with the channel area of 900 mm\({}^{2}\). By contrast, as illustrated in Figure 6b the temperature of the MR fluid was lower when the area was larger, which facilitated more heat transfer. However, this drop  
Figure 2:1 Effects of the input current on the (**a**) resistance force and (**b**) MR fluid temperature.