## 1 Introduction
[14] established the TSFT equations based on [PERSON]'s theory and calculated the tooth surface deformation caused by contact temperature; [PERSON] et al. [15] found that the TSFT changes the time-varying mesh stiffness, which leads to the change of cyclic kinematic characteristics of the gear rotor system. [PERSON] et al. [16] found that the thermal deformation of the tooth in a planetary gearest due to the equilibrium temperature of the system also changes the time-varying mesh stiffness and increases the vibration of the system. [PERSON] et al. [17] demonstrated that tooth modification can improve the surface thermal distribution and reduce the temperature and friction loss during gear rotation. [PERSON] et al. [18] derived calculation methods for instantaneous TSFT based on the Hertz contact theory and thermal shock model. They also analyzed the effect of the variable factor and tooth modification on flash temperature and demonstrated that a reasonable choice of variable coefficients and modification values can improve the gearest scuffing load capacity. [PERSON] et al. [19] investigated the mechanisms by which surface topography, rolling-slip contact stress, subsurface shear stress, and depth of spur gears under EHL conditions influence the formation of tooth pitting. [PERSON] et al. [20] proposed a new method based on the pressure-velocity-temperature (PVT) limit to assess the anti-scuffing of gears. Experimental results showed a maximum deviation of 6.6%, proving that the PVT limit evaluates gear anti-scuffing capacity effectively under different conditions. [PERSON] et al. [21] employed the finite element method to simulate the effects of friction in the contact zone during the worm-gear meshing on heat transfer on the gear tooth. The tooth modification of gears can improve certain problems encountered during meshing to reduce failure rates and increase equipment reliability. [PERSON] et al. [22] investigated the solution for meshing stiffness, taking into account tooth modifications, misalignment, and machining errors, as well as the tooth surface optimization method based on that stiffness model. Using a statistical model, [PERSON] et al. [23] studied the effects of tooth modification on the distribution of contact stress and flash temperature in order to predict the risk of scuffing in vehicle transmissions and discussed the sensitivity of the tooth modification to scuffing temperature. In conclusion, a substantial body of research has been conducted on the flash temperature of gear surfaces in transmission systems. These studies are typically conducted in accordance with the calculation method of scuffing load-carrying capacity and/or through the scuffing test method. The calculation method employs equations from international standards, and the gear surface load calculation generally uses average line load without considering factors such as system deformation that may lead to edge contact and uneven load distribution. This results in an inaccurate calculation of the TSFT distribution on the gear surface. The aim of this study is to investigate the influence of geometric parameters on the flash temperature and scuffing load-carrying capacity of gears. This paper puts forward a dense teeth design method and evaluates its potential to reduce the flash temperature and enhance the load-carrying capacity. The effects of changing the pressure angle and helix angle on the flash temperature are investigated. The gears studied in this paper take into account the system misalignment and have made a micro-modification on the tooth surface to improve the distribution of tooth surface loads. Consequently, the paper assesses the influence of three geometric parameters of gears on the contact ratio, specific sliding, surface load distribution, flash temperature distribution, and scuffing safety factor.