## 6 Numerical Simulations
### Vibration Accelerations of the Components  
Figure 11 illustrates the variations of the accelerations in \(x\)-, \(y\)-, \(z\)-, and \(u\)-directions for some main components of HPGT (i.e., the carrier, sun and planet) with gear mesh time (denoted as a\({}_{\rm ix}\), a\({}_{\rm iy}\), a\({}_{\rm iz}\), a\({}_{\rm iu}\) (i = c, s, p1), respectively), which reflect the vibrations of main system components involving the carrier, sun, and planet in the corresponding directions, respectively, for the case of the planet eccentricity \(E_{\rm p1}\) = 100 \(\mu\)m, while Figure 12 shows the results for the case of without error excitations. For the model with the planet-gear eccentric error excitation, the time-domain vibration accelerations  
Figure 10: Variation of the dynamic bearing forces of main components ((**a**,**d**) carrier, (**b**,**e**) sun, and (**c**,**f**) planet) with gear mesh time, which are represented as F\({}_{\rm c}\), F\({}_{\rm s}\), and F\({}_{\rm p1}\), respectively. (**a**–**c**) the model with the planet–gear eccentric error excitation \(E_{\rm p1}\) = 100 \(\mu\)m; while (**d**–**f**) the model without error excitations. at each degree of freedom of system components behave the fluctuation up and down around the horizontal zero axis; the component vibration accelerations in the \(z\)-direction (i.e., axial direction) are pronouncedly smaller than in the lateral directions (i.e., \(x\), \(y\)-direction), induced by the symmetrical tooth structure of herringbone gear, making the axial forces of each component smaller. The carrier vibration accelerations in the horizontal, vertical, axial, and torsional directions are smaller than those in the corresponding directions of the sun and planet, possibly owing to the larger carrier inertia as given in Table 1. The vibration accelerations in \(x\)-, and \(y\)-directions of the planet-gear are larger than those in the corresponding directions of other components such as the carrier and sun gear, particularly the vibration acceleration in the \(y\)-direction (i.e., tangential direction) of the planet-gear is the greatest, due to the larger force transmitting power in the planet tangential direction. In the vibration accelerations in the torsional direction of each component, the sun acceleration is greater, with the maximal amplitude of 300 m\(\cdot\)s\({}^{-1}\), and that of the planet-gear is also relatively large, with great amplitude of 275 m\(\cdot\)s\({}^{-1}\). Figure 12 exhibits the variations of the accelerations for some main components of HPGT (i.e., the carrier, sun and planet) with gear mesh time (denoted as \(\mathrm{a_{iv}}\), \(\mathrm{a_{iv}}\), \(\mathrm{a_{iz}}\), \(\mathrm{a_{iu}}\) (i = c, s, p1), respectively), which reflect the vibrations of main system components containing the carrier, sun, and planet in the corresponding directions, respectively, for the case of the absence of manufacturing error excitations. A comparison of Figure 11a-c with Figure 12a-c indicates that in HPGT system, the vibration acceleration amplitudes in the \(x\)-direction of each component for the model without errors become evidently smaller than those for the model with the planet-gear eccentric error excitation, particularly the amplitude variation of vibration accelerations in the \(x\)-direction of the planet-gear is the most distinct in the two models with and without error excitations, on account of the planet eccentricity excitations. In the meantime, it is also seen that the vibration acceleration amplitudes in the \(y\)-direction of each member in the absence of error excitations displayed in Figure 12 are also noticeably smaller than those in the presence of the planet eccentricity excitation displayed in Figure 11, probably because of the planet-gear eccentricity excitation. The same tendency is also found for the vibration acceleration  
Figure 11: Variations of the vibration accelerations of the main components from the model in the presence of the planet–gear eccentric error excitation \(E_{\mathrm{p1}}=100\) μm with gear mesh time.