## 3 Results  
The airbearing
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The cross-coupled stiffness coefficient \(K_{tx,ty}\) is approximately 10 times smaller than the direct stiffness coefficient \(K_{tx,tx}\), and lies in the range of 6-15 kN\(\cdot\)m/rad (see Figure 5). It is highly sensitive to all parameters, except for \(i_{x}\). \(K_{tx,ty}\) increases with decreasing \(t_{x}\) and \(i_{y}\), and increasing \(t_{y}\) (see Figure 5a,b). Eccentricity \(\varepsilon_{x}\) can increase or decrease \(K_{tx,ty}\), depending on \(\varepsilon_{y}\) (see Figure 5c). Figure 4: Parameter sensitivity of the direct stiffness coefficient \(K_{tx,tx}\): (**a**) Effects of the tilting angle and tilting velocity in the x-direction; (**b**) Effects of the tilting angle and tilting velocity in the y-direction; (**c**) Effects of relative eccentricities. All unreferenced parameters have zero values. \(K_{ty,tx}\), which is another cross-coupled stiffness coefficient, is of the same order of magnitude; however, it is negative, and falls in the range of \(-18\)-\(0\)\(\mathrm{kN}\cdot\mathrm{m}/\mathrm{rad}\) (refer to Figure 6). It is not sensitive to \(t_{x}\), and the \(t_{y}\) effect on it is also negligible (see Figure 6a,b). The magnitude of \(K_{ty,tx}\) is higher at lower \(t_{x}\) and \(\epsilon_{y}\) and at higher \(t_{y}\) and \(\epsilon_{x}\). Figure 5: Parameter sensitivity of the cross-coupled stiffness coefficient \(K_{tx,y}\): (**a**) Effects of tilting angle and tilting velocity in the x-direction; (**b**) Effects of the tilting angle and tilting velocity in the y-direction; (**c**) Effects of relative eccentricities. All unreferenced parameters have zero values. The direct stiffness coefficient \(K_{ty,ty}\) is higher than that of \(K_{tx,tx}\). \(K_{ty,ty}\) falls in the range of 110-140 kN\(\cdot\)m/ rad (refer to Figure 7). This is triggered by the cut arc, which increases force and decreases the stiffness in the x-direction [27]. The y-tilting angle \(t_{y}\) exerts a strong nonlinear effect on \(K_{ty,ty}\). The stiffness coefficient \(K_{ty,ty}\) is almost constant for a low positive \(t_{y}\), and then increases with increasing \(t_{y}\). In contrast to \(K_{tx,tx}\), which is primarily sensitive to \"its own\" parameter \(t_{x}\) and significantly less sensitive to \(t_{y}\). \(K_{ty,ty}\) is equally sensitive to both \(t_{x}\) and \(t_{y}\). In addition, it is equally sensitive to both higher \(\varepsilon_{x}\) and \(\varepsilon_{y}\), with a negligible \(i_{y}\) effect, and no \(i_{x}\) effect. Furthermore, it is higher for lower \(t_{x}\) and higher \(t_{y}\), \(\varepsilon_{x}\), and \(\varepsilon_{y}\). Figure 6: Parameter sensitivity of the cross-coupled stiffness coefficient \(K_{ty,tx}\): (**a**) Effects of the tilting angle and tilting velocity in the x-direction; (**b**) Effects of the tilting angle and tilting velocity in the y-direction; (**c**) Effects of relative eccentricities. All unreferenced parameters have zero values. Because the simultaneous variation of tilting velocities was not studied, the effect of \(\dot{t}_{x}\) was solely studied for \(D_{tx,tx}\) and \(D_{ty,tx}\), while the effect of \(\dot{t}_{y}\) was solely studied for \(D_{tx,ty}\) and \(D_{ty,ty}\). Instead of the missing parameter, the coupling between \(t_{x}\) and \(t_{y}\) is comprehensively presented in Figures 8-11. The direct damping coefficient \(D_{tx,tx}\) is positive and falls in the range 0.2-2.2 kN\(\cdot\)m s/rad (refer to Figure 8). It is higher for lower \(t_{x}\), and higher \(t_{y}\) and higher \(\dot{t}_{x}\) (see Figure 8a,b). The effect of eccentricity is also substantial, nonlinear, and strongly coupled between \(\varepsilon_{x}\) and \(\varepsilon_{y}\) (see Figure 8c). Figure 7: Parameter sensitivity of the direct stiffness coefficient \(K_{ty,ty}\): (**a**) Effects of the tilting angle and tilting velocity in the x-direction; (**b**) Effects of the tilting angle and tilting velocity in the y-direction; (**c**) Effects of relative eccentricities. All unreferenced parameters have zero values.