## 3 Results
### Gear Pair Dynamic Tests  
Following the static identification of the NES restoring torque, the device was attached to the gear pair output shaft as described in the beginning of this section. The NES-gear assembly was then tested at different input pinion speeds between 700 rpm and 1000 rpm. The first order of the pinion shaft speed was used to excite gear vibrations across all tests.  
First, the data were analysed to verify the restoring torque dynamically. The recorded NES speed was differentiated to compute the NES angular acceleration, and, knowing the NES inertia, the non-conservative restoring torque was computed. Figure 10 shows the  
Figure 8: Sketch of the apparatus used to measure the static torque profile of the NES.  
Figure 9: Theoretical torque curve computed with Equation (6) compared with statically identified torque profile given by Equation (6).  
torque of the NES for four pinion speeds against the fluctuating part of the instantaneous angular position. The theoretical torque following the Taylor expansion up to the fifth order, shown in Equation (6), is also plotted to compare the experimental results.  
A significant deviation of these results from the predicted (and statically identified) torque is observed. This mismatch persists across the examined speed range, where the NES was activated and consequently forced to oscillate with relatively higher torques (700 rpm and 800 rpm), and in the range beyond its expected activation, where the NES oscillates with low angular amplitudes (900 rpm and 1000 rpm). Additionally, a weak linear component is also observed, particularly in the deactivated state. Upon examination of the device following the tests, the clamps holding the beam shims were found to rigidly keep the beams ends in place. The tests were repeated, and similar behaviour was observed. In order to investigate this unexpected response, damping was eliminated from the experimentally calculated restoring torque, leading to the stiffness torques plotted in Figure 10b. Note that the viscous linear damping was retained in the identification procedure to maintain its accuracy, but it was then analytically removed. The stiffness curves are plotted together with the nonlinear torque model \(T_{NL}\) given by Equation (6) and a hypothetical scenario in which only one of the shims is in contact with its rollers, thus reducing the effective stiffness of the NES to half (\(T_{NL}\)/2). This reveals that the NES stiffness agrees remarkably well with the one-shim scenario when it attains high oscillation amplitudes, as Figure 10b shows for the case of 800 rpm. This observation possibly indicates that imperfections in the  
Figure 10: (**a**) Identification of the NES restoring torque computed from the experimental results for pinion speeds of 700, 800, 900 and 1000 rpm and comparison against the model results \(T_{NL}\) given by Equation (6); (**b**) elimination of damping from the restoring torque and comparison with NES model torque with two working shims (\(T_{NL}\)) and only one working shim (\(T_{NL}\)/2).  
design realisation are aggravated by the intensive NES vibrations, leading to undesired malfunction of one of the shims.