## 1 Introduction  
Gear transmission is widely used in aerospace [1; 2], vehicles [3], wind turbines [4; 5], etc. The mesh stiffness of gear pairs is an important excitation when a dynamic analysis is executed, and its accuracy has a significant effect on the results of the dynamic response [6; 7]. Many researchers have studied the methods for computing mesh stiffness. The methods can be summed up as the experimental method, finite element method, and analytical method. Generally, the experimental method is considered as conforming to reality. [PERSON] obtained the mesh stiffness by the experimental method over a range of tooth loads [8]. [PERSON] acquired the stress factor and calculated the mesh stiffness [9; 10]. [PERSON] designed a special test rig to measure the stiffness of an involute spur gear [11]. However, special facilities with a high cost are required to conduct experiments. Therefore, the finite element method is adopted by many researchers. Based on a Siemens NX and ANSYS Workbench, [PERSON] developed a technique to obtain the mesh stiffness [12]. [PERSON] obtained the mesh stiffness of a cylindrical gear by considering the fillet-foundation as a rigid body or flexible body [13]. By using the finite element method, [PERSON] studied the torsional stiffness [14]. [PERSON] analyzed the mesh stiffness with profile modification by the finite element method [15]. Nevertheless, many hours are required when the finite element method is used because this method deeply depends on the computer configuration. The analytical method has also been adopted to obtain the mesh stiffness with the goal of reducing the cost of experiments and the computing time required by the finite element method. [PERSON] first obtained the mesh stiffness with the assumption that the total potential energy can be sorted into three parts: bending, radial compressive and Hertzian contact energy [16]. On this basis, [PERSON] added the shear energy into the model [17; 18]. Additionally, [PERSON] fitted a formula to calculate the deformation of the fillet-foundation [19]. [PERSON] established a general combined model to obtain the mesh stiffness [20]. [PERSON]'s formula only applied the single-tooth engagement region. [PERSON] proposed a correction factor to eliminate this deficiency [21]. [PERSON] derived the formula to calculate the stiffness of the fillet-foundation when two tooth pairs of a spur gear are engaged simultaneously [22]. [PERSON] first considered the influence of axial force on the mesh stiffness of helical gears [23]. [PERSON] extracted the mesh stiffness of a helical gear by using the slice method and then extended the equation to a helical planetary gear train [24]. [PERSON] established the relationship between the loading and deflection, and then analyzed the static behavior of helical gears [25]. [PERSON] studied the influence of addendum modification on the mesh stiffness of spur gears [26]. [PERSON] et al. carried out a study on the mesh stiffness of gears with microcracks [27]. In the above literatures, the helical gear is considered as many independent spur gears, and the effect of the relationship between neighboring sliced gears and the influence of the axial mesh force on the comprehensive mesh stiffness have not been considered simultaneously. Obviously, the literature is incomplete. In order to reduce the cost of the experimental method and the calculating time of finite element method, and make up for the shortcomings of the traditional analytical method, this paper focuses on establishing a comprehensive analytical model for evaluating the mesh stiffness of the helical gear. Firstly, the helical gear is divided into independent sliced gears along the direction of gear width by using slice theory. Considering the effect of the relationship between neighboring sliced gears, the comprehensive mesh stiffness of the helical gear can be acquired.