## 1 Introduction
conducted a detailed analysis on the membrane stress of the high-power laminated membrane coupling, pointed out the stress distribution characteristics of the elastic element and calculated its torsional stiffness [14]. [PERSON] proposed a four-hole joint bearing coupling structure to improve the angular displacement compensation ability of the laminated membrane coupling between two shafts. Then they analyzed the maximum stress position and non-centering compensation ability of three different coupling sizes through mechanical experiments and finite element simulation methods [15]. [PERSON] et al. studied the strength and stiffness of the diaphragm assembly in direct contact with plates in the diaphragm assembly, and analyzed the influence of the number of layers of the diaphragm assembly and the preload value of the diaphragm assembly gasket on the strength and stiffness of the diaphragm assembly [16]. [PERSON] applied the finite element method and established a model for the multi-layer contact coupling. He demonstrated that results obtained from the stress calculation can more accurately show the stress characteristics of elastic elements when the comparison is made with the conventional single-chip model [17]. [PERSON] et al. established the stiffness model for the diaphragm of the joint type laminated membrane coupling based on the relevant mathematical expressions and classical mechanics. They showed that the compensation ability of the joint laminated membrane coupling for radial and angular displacements is far better than that of the ordinary laminated membrane coupling [18; 19]. [PERSON] proposed a mathematical model for the contact stiffness of the lamination group and showed the accuracy and superiority of the lamination group for calculating the stiffness of the lamination coupling [20]. Recently, [PERSON] applied the finite element simulation method to analyze the correlation between structural parameters and the torsional stiffness of the laminated membrane coupling, and found that the laminated thickness, the diameter and total number of boltshave a certain impact on the torsional stiffness of the coupling [21]. More recently, [PERSON] et al. analyzed the influence of the bolt-predicted force and the friction coefficient on the stress and stiffness of laminated membrane coupling. They utilized the finite element method and studied the correlation between the misalignment slip and nonlinear characteristics of the coupling [22]. Reviewing the literature indicates that in the majority of performed numerical simulations for investigating laminated membrane couplings, the surface shear and extrusion caused by small relative motions between laminations are ignored. Moreover, it is assumed that the external load is evenly distributed in each lamination. Based on these assumptions, only the single lamination was analyzed. However, the contact stiffness is produced in laminated contact. This is especially more pronounced for extreme deformations and heavy loads. In these cases, the shear, radial and torsional stresses and angular deformations caused by the contact cannot be ignored. In real applications, the internal contact between laminations and the contact between laminations and the gasket affect the lamination state. Therefore, calculate the overall stiffness of the lamination coupling, which is not in line with the actual working condition. In other words, it is necessary to consider the elastic deformation and the contact deformation of the lamination surface, and study the lamination coupling as a whole. In the present study, it is intended to establish a finite element model of the waist type laminated membrane coupling. To this end, contacts between 16 pieces of laminations are considered. Moreover, an appropriate mesh is utilized and boundary conditions are set. Four stiffness characteristics of the coupling, including the torsional, axial, radial and angular stiffness are analyzed, and the torsional stiffness is verified through the static torsional test.