## 1 Introduction
[22] detailed the Finite Element Analysis (FEA) models for calculating the torsional stiffness and tooth load sharing ratio of the gears in mesh, considering spalling and crack damage. However, it is important to note that this method can be computationally intensive and sensitive to both the mesh element type and the density of the mesh used. (b) Analytic method. [PERSON] et al. [23] simulated the tooth tip chipping and crack faults, utilized the smoothed pseudo-Wigner-Ville distribution to analyze the residual vibration signal, and summed up the evolutionary process of fault on the spur gear. [PERSON] [24] and [PERSON] et al. [25] processed the vibration response of fault gear systems to detect the fault type. [PERSON] et al. [26] derived the analytical equations for the rotating system of spur gears whilst considering tooth tip chipping. The more severe the tooth tip chip is, the greater the reduction in TVMS. [PERSON] et al. [27] established a lumped parameter dynamic model of planetary gear with tooth tip chipping and derived the analytical equation of tooth tip chipping on composite planetary gears. [PERSON] et al. [28] and [PERSON] et al. [29] combined the analytical geometry method with the potential energy method to analyze the effects of varying degrees of tooth tip chipping. However, it is challenging to analyze the fault of the gears. (c) Semi-analytic method. [PERSON] et al. [30] calculated the TVMS and transmission errors by LTCA considering angular contact and tooth fracture faults. [PERSON] et al. [31] proposed a mesh characteristics model of SBG that considered spalling fault based on LTCA and verified the accuracy using the finite element method. However, they only discussed the TVMS of the spalling fault and did not consider other gear faults and assembly errors. The LTCA method offers the advantages of both the FEM and the Analytic method and can obtain the results with high accuracy. However, the utilization of LTCA remains an area ripe for further exploration by researchers. (d) Experimental method. [PERSON] et al. [32] analyzed three types of gear faults by experiment and confirmed the experimental results using simulations. [PERSON] et al. [33] developed a method of detecting gear faults which combines wavelet and time domain averaging and uses it to detect tooth tip chipping. Although this method yields accuracy, simulating large devices is challenging, and analyzing errors becomes difficult. When unloaded, SBGs have a local point contact. However, when loaded, they transition to elliptical contact. This leads to numerous challenges in modeling and analysis, particularly when considering assembly errors and tooth tip chipping. Undesirable assembly errors can result in the movement of the contact area from the center of the tooth surface to the tooth tip which will cause edge contact. An increase in edge contact may worsen the mesh characteristics of SBGs, and even lead to tooth tip chipping. Hence, conducting research on SBG considering assembly errors and tooth tip chipping is deemed highly essential. Despite the existence of research focusing on assembly errors, there remains a scarcity of scholars who have explored the combined effects of assembly errors and tooth tip chipping, notably in SBG. Hence, this paper primarily focuses on two aspects: (1) proposing an enhanced method for analyzing mesh characteristics that can incorporate assembly errors and tooth tip chipping; and (2) investigating the impact of assembly errors and tooth tip chipping on the SBG pairs. The structure of this paper is outlined as follows: Section 2 develops an enhanced method which is based on LTCA and incorporates considerations for assembly errors and tooth tip chipping. Section 3 validates the proposed method with publications, and analyzes the effects of assembly errors and tooth tip chipping. Finally, Section 4 provides a summary of the findings presented in this paper.