## 1 Introduction
To study the joint interfaces in mechanical structures under dynamic loading, the tangential damping and its dissipation factor models of joint interfaces were developed by [PERSON] [19], and the dimensionless total tangential stiffness is proportional to the dimensionless total tangential damping so that the calculation of tangential stiffness is a key step. Faying surface directly influences overall machine performance, and its tangential and normal contact stiffness in a steady-state represents almost half of a machine's stiffness, and with this background, [PERSON] [20] carried out the tangential contact stiffness of cylindrical asperities, and its influencing factors were discussed. Considering stationary interfaces between different substructures of an engineered structure are always full of compliance and damping, [PERSON] [21] launched the research of spherical contacts' load-dependent nonlinearities in tangential stiffness with the help of a scanning electron microscope (SEM). [PERSON] [22] developed a micro-slip friction model with the classical Iwan model on the cylindrical contact surface to improve the simulation of the frictional contact of blade platforms/dampers. [PERSON] [23] constructed a systematic finite element model to calculate the fixture unit stiffness between its substructures' contact surfaces. He also designed a new experimental way to identify the normal and tangential contact stiffness with static and dynamic forms, respectively [24]. [PERSON] [25] accomplished the dynamics character of jointed structures with the reduced-order modeling method, and in this method, the tangential contact stiffness is one of the key factors of the interfacial representations. In summary, the tangential contact stiffness plays a vital role in various trades and professions. While, in consideration of their performance and the effect they have, although these studies are full of excellent innovation points, there are still some aspects left that are indispensable factors for interface modeling:  
1. The slip's interaction effect has not been fully taken into consideration. In most cases, the geometric shape of the contact areas is treated as a circle. However, this is a simplification based on the assumption that the contact sphere is only under normal contact load without any slip, which is apparently a special case for the machine system's subunits interaction. 2. The radius of the contact sphere is directly set as a parameter of the contact model. For most of the existed contact stiffness models, it is prevalent to set the contact surface's radius, or the long axis and short axis, as an independent parameter to the calculation, but the contact radius is not easy to measure, so a theoretical expression for this is necessary. This research modifies a purely theoretical tangential contact model by considering friction's interaction, and a manufacturing experiment to validate this model is taken by measuring the tangential contact stiffness between mechanical structures. A modified tangential contact stiffness model according to [PERSON]'s elastic deformation theory and generalized Hertz contact theory is proposed, with the effectiveness of friction, the normal force and the radius of curvature about each of the contact unites which eventually influences the model's structure considered. An experiment platform to measure the tangential contact stiffness between mechanical structures is designed, and with its help, the accuracy of the modified model is validated. The rest of the paper is organized as follows. Section 2 presents the mathematical derivation process of the tangential contact stiffness model considering friction's effect. Section 3 displays the experiment's validation procedure to measure the tangential contact stiffness. Section 4 shows the data analysis process of Section 3, mainly focusing on the relative error of tangential stiffness and the difference between the model calculation and the measured value.