## 7 Conclusions  
In this study, by considering the HPGT actual structure characteristics, manufacturing eccentric errors of components (i.e., each gear, and carrier), tooth profile errors of gears, gear tooth time-varying meshing stiffness and bearing deflections, different from the two-dimensional model, a novel and generalized three-dimensional lumped-parameter dynamic model of herringbone planetary gears has been given for studying the dynamic feature of the HPGT system in the presence of arbitrary number of planets and different types of manufacturing errors. The effects of manufacturing errors such as the planet eccentricity on the HPGT dynamic features were investigated. The main conclusions are given below. 1. Manufacturing errors such as the planet eccentricity prominently affect the HPGT dynamic features, and the manufacturing error excitations significantly increase the fluctuations of the  
Figure 12: Variations of the vibration accelerations of the main members from the model in the absence of error excitations with gear mesh time. (**a**,**d**,**g**,**j**) the carrier accelerations in \(x\)-\(y\)-, \(z\)-, and \(u\)-directions, expressed as \(\mathrm{a_{c}}\), \(\mathrm{a_{c}}\), \(\mathrm{a_{c}}\), and \(\mathrm{a_{c}}\), respectively; (**b**,**e**,**h**,**k**) the sun accelerations in \(x\)-\(y\)-, \(z\)-, and \(u\)-directions, expressed as \(\mathrm{a_{sx}}\), \(\mathrm{a_{sy}}\), \(\mathrm{a_{sz}}\), and \(\mathrm{a_{su}}\), respectively; (**c**,**f**,**i**,**l**) the planet accelerations in \(x\)-, \(y\)-, \(z\)-, and \(u\)-directions, expressed as \(\mathrm{a_{p1x}}\), \(\mathrm{a_{p1y}}\), \(\mathrm{a_{p1z}}\), and \(\mathrm{a_{p1u}}\), respectively. dynamic meshing forces, dynamic bearing forces, and vibrations of components of herringbone planetary gears. 2. The fluctuations of the dynamic meshing forces and dynamic bearing forces for the model in the existence of the planet eccentricity excitation are evidently greater than those in the absence of error excitations. The amplitudes of vibration accelerations in each DOF direction of HPGT members for the model in the presence of the planet eccentricity excitation are also significantly larger than those in the absence of error excitations. 3. Manufacturing error excitations such as the planet eccentricity distinctly impact the axial vibrations of the carrier, sun, and planet of HPGT. Manufacturing error excitations are the axial vibration source in the HPGT system. For the model in the absence of error excitations, the axial forces and vibrations of the HPGT disappear, similar to spur PGT. This investigation provides the new effective idea and methodology for the prediction and analysis of the dynamic feature of complex herringbone planetary gear systems with other type of error faults, and also offers the theoretical foundation for the error fault diagnosis and dynamic optimization of herringbone planetary gears in the next step. Our ongoing investigation will focus on the studies of the effects of system stiffness on herringbone planetary gear dynamic response. [PERSON] presented the HPGT system dynamic model, analyzed the results, and wrote this paper; [PERSON] analyzed some simulation results and reviewed the manuscript; [PERSON] modified the first draft of the manuscript and guided the contribution; [PERSON] revised the manuscript and gave some helpful and valuable suggestions; [PERSON] analyzed some simulation results. All authors have read and agreed to the published version of the manuscript. This research was funded by the Science and Technology Research Project of Henan Province (Grant Nos. 202102210085, 172102210056), the Open Funding of Henan Key Laboratory of Intelligent Manufacturing of Mechanical Equipment (Grant No. IM201912), and the Doctoral Science Research Foundation of Zhengzhou University of Light Industry (Grant No. 2015 BSJ[030]).