## 1 Introduction  
Owing to the characteristics of power split flow, compactness, and high torque-to-weight ratio, planetary gear train (PGT) is extensively employed in various industrial applications, such as in aerospace, automobiles, wind turbines, and nuclear power plants. In contrast to spur or helical gears, herringbone gears possess many benefits, including smoother transmission, lower axial force, and greater transmission torque. Consequently, the herringbone planetary gear system has also been used in the power train of heavy machinery such as aerospace engines, and long-wall shearers. The existence of inevitable processing errors in the manufacturing process of a drive train can significantly affect the reliability and durability of herringbone planetary gears. Nevertheless, there have been few related reports on the manufacturing error impacts on the dynamic properties of herringbone planetary gears. For the sake of achieving reliable and quiet operation, it is vital and necessary to formulate a dynamic model of herringbone planetary gears for the analysis of manufacturing error effects on dynamic properties.  
There have been several investigations into the PGT dynamic properties. [PERSON] and [PERSON] constructed a spur PGT dynamic model to examine the modal characteristics [1,2]. [PERSON] established an analytical model of spur PGTs with bearing backlash nonlinearity and tooth wedging [3]. [PERSON] and [PERSON] proposed a nonlinear torsional model of multi-stage spur PGTs applied to a wind turbine gearbox for the analysis of nonlinear vibration characteristics [4]. [PERSON] presented an analytical model for a stage of helical PGT for the study of its dynamic behavior [5]. Based on the lumped-parameter and finite element theories, [PERSON] et al. constructed a three-dimensional analytical model of helical planetary geared rotor sets by considering gyroscopic effects to investigate the dynamic behavior [6]. [PERSON] incorporated journal bearings to a dynamic model of herringbone planetary gears to study their modal properties [7]. [PERSON] and [PERSON] investigated the free and forced vibration characteristics of double-helical planetary gears [8]. [PERSON] considered the eccentric and profile errors and examined the manufacturing error impacts on the spur PGT dynamic properties [9]. [PERSON] studied the influences of pin error and stiffness in wind turbine gearbox on the PGT load distribution performance [10]. [PERSON] et al. conducted a study of the manufacturing error effects on dynamic performance and load distribution properties for HPGT [11; 12; 13; 14]. [PERSON] et al. explored the impact of meshing-frequency and run-out errors on dynamic load distribution among different planets for encased differential gear sets [15].  
However, there has been no research on the impact of manufacturing errors such as the planet-gear eccentricity on the dynamic properties for herringbone planetary gears. In this paper, by considering the actual structural features of herringbone gears, a novel transverse-axial-torsional coupling dynamic analytical model for herringbone planetary gears involving manufacturing errors is formulated by applying the lumped-parameter method. The dynamic features of a HPGT system are then numerically studied, and the impacts of manufacturing errors such as the planet-gear eccentricity on the dynamic performance are examined.