## 7 Conclusions  
This paper focuses on the study of the mechanical structure contact mechanism considering modified tangential stiffness with friction's interaction. A tangential contact stiffness model considering friction's interaction is constructed. The derivation process of this model begins with [PERSON]'s elastic deformation theory along the \(x\), \(y\) and \(z\)-axis, whose construction contains the potential function along with their own direction respectively. The generalized Hertz contact theory is used to calculate the forces needed in this model. With the help of the symmetrical characteristics in the contact area, the derivation process is simplified, and the tangential contact stiffness model considering independent variables, which are \begin{table}
\begin{tabular}{c c c} \hline \hline
**Index** & **Equipment Element** & **Error Band** \\ \hline
1 & Kistler 9317C Force Sensor & \(\left[-0.01,0.01\right]\) (N) \\
2 & Kistler 8776A Accelerometer & \(\left[0.0833,0.1127\right]\) (m/s\({}^{2}\)) \\
3 & Fixture (with contact measuring unite) & \(\left[-0.001,0.0011\right]\) (m) \\
4 & Replaceable contact unites & \(\left[-0.001,0.001\right]\) (m) \\
5 & Plate workpiece & \(\left[-0.001,0.001\right]\) (m) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: The error band of each element in the modified experiment’s platform. the contact force along the \(x,y\) and \(z\)-axis and the friction coefficient of the contact area, is eventually carried out; these variables are barely considered simultaneously in the model construction of the tangential contact stiffness in previous research. To verify this model, a tangential stiffness measuring platform is constructed by putting two spherical objects into contact with each other to measure the tangential contact stiffness. The relative displacement and the contact force of the contact area are calculated with the data collected by a force sensor and accelerometer connected to the PC Dewesoft client. With a deeper analysis of the effect of the model's parameter, an experimental scheme based on single-parameter control (material mechanical character and contact radius) containing eight groups is carried out. The relative errors of the tangential contact stiffness model are all less than 10% for each data group in the experiment. A comparison with an existing model is carried out. The evaluation indicator of the comparison is the relative error of the tangential stiffness, along with the directions of the \(x\) and \(y\)-axis, respectively. The results show that the model deduced in this research has a much better performance than the original one. Along the direction of the \(x\)-axis, the relative error of the original model over 50% occupies more than half of the 30 data sets in each of these 8 groups, and only 1/4 of these groups' relative error is below 30% in half of the data sets; along the direction of the \(y\)-axis, the original model's relative error exceeded 50% captures in more than 3/4 of the 30 data sets in each of these 8 groups, and only 1/4 of these groups' relative error below 30% in half of the data sets. While the relative errors of the modified model are all less than 10% on the foundation of the same data sets. This could show the advantage of the modified contact tangential model proposed in this paper. In summary, the correctness of the modified tangential contact stiffness model is verified by the experiment, and that means the mechanical structure contact mechanism analysis considering modified tangential stiffness with friction's effect is effective. This improved tangential contact stiffness model, the first key step in establishing a systematic dynamic model, would be an effective improvement for the fixture-workpiece system dynamic analysis, which is eventually an inevitable foundation of vibration reduction for aerospace blade manufacturing. [PERSON]: first author, constructed the model, interpreted the data, drafting, performed the numerical calculation and milled the experiments.