# Study of Magnetorheological Grease's Thermomagnetic Coupling Rheology
## 4 Results and Discussion  
In Figure 4, the magnetic field scanning curves of the magnetorheological grease at different temperatures are depicted. From the graph, it can be observed that the shear stress of the magnetorheological grease decreased gradually as the temperature increased under zero field intensity. This phenomenon could be attributed to the reduction in the entanglement degree of the fibrous network structure formed by the base carrier fluid and the lubricating grease soap fibers, resulting in a decrease in the damping force during the  
Figure 3: Magnetorheological grease rate scanning scheme. Figure 2: Magnetorheological grease magnetic field scanning scheme. shearing process of the rotational rheometer. With an increase in magnetic field intensity, the shear stress of the magnetorheological grease gradually increased at each temperature [14]. However, when the magnetic field intensity reached 400 mT, the shear stress tended to stabilize and exhibited a slight decrease. This behavior could be explained by the alignment of magnetic particles in the magnetorheological grease along the magnetic field direction, forming chain-like structures with a certain yield strength. Consequently, the structural strength of the magnetorheological grease increased, leading to an increase in the damping force during the shearing process of the rotational rheometer. However, at 400 mT, the magnetic particles in the magnetorheological grease reached saturation magnetization, and the chain-like structures no longer strengthened. Furthermore, due to the continuous shear action, the degree of entanglement of grease soap fiber decreased, the phenomenon of shear thinning occurred, and the damping force in the shear process of the rotary rheometer decreased slightly. This was because, under the influence of an external magnetic field, the magnetic particles within the magnetorheological grease aligned themselves in chain-like structures along the direction of the magnetic field due to magnetic torque. With the increase in magnetic field intensity, the number of magnetic chains increased, and their structural strength was enhanced. The effect of these magnetic chains was similar to that of the soap fibers, leading to an increase in the apparent viscosity of the magnetorheological grease. Therefore, under high-temperature conditions, the application of an external magnetic field could mitigate the shear thinning phenomenon of magnetorheological grease. Viscosity served as a significant parameter for quantifying the frictional forces within magnetorheological grease. In the context of Newtonian fluids, the viscosity remained constant regardless of changes in shear rate. Conversely, non-Newtonian fluids exhibited varying viscosity with alterations in shear rate. Magnetorheological grease falls under the category of non-Newtonian fluids, and its viscosity is referred to as apparent viscosity. The formula for apparent viscosity was derived by referencing the viscosity formula applicable to Newtonian fluids [24; 25]. \[\eta=\frac{\tau}{\dot{\gamma}} \tag{1}\]  
where \(\eta\) is apparent viscosity, unit \(\mathrm{Pa}\cdot\mathrm{s}\); \(\tau\) is shear stress, unit \(\mathrm{Pa}\); and \(\dot{\gamma}\) is the shear rate, unit \(\mathrm{s}^{-1}\). Please refer to Equation (1). It was observed that the apparent viscosity of magnetorheological grease increased linearly with the increase in shear stress when a constant shear rate was applied. As shown in Figure 4, it can be inferred that at zero field intensity, the apparent viscosity of magnetorheological grease gradually decreased with increasing  
Figure 4: Magnetorheological grease magnetic field scanning curve. temperature. Furthermore, as the magnetic field intensity increased, the apparent viscosity of magnetorheological grease gradually increased at all temperatures. When the magnetic field intensity reached 400 mT, the apparent viscosity tended to stabilize and exhibited a slight decrease.