## 7 Case Validation and Analysis
### Deviation Transfer Model for MAP  
In order to ensure that the assembly deviation transfer mathematical model and the finite element simulation model are year-on-year, it is necessary to specify uniform KPC and KCC points for each part. The deviation of the KLCC point is determined by the fixture manufacturing process. The deviation of KLCC points is determined by processes such as fixture manufacturing, and the deviation of KCCC and KPC points is caused by the flexible deformation of the part. Based on the actual distribution characteristics of KC points on each part and fixture in the deviation source, the initial deviation values of KCCC points on parts Part1 to Part4 in the MAP are obtained, as shown in Table 1.  
Figure 14: Diagram of the rear fuselage frame structure of the aircraft. Figure 15: Diagram of the actual assembly production process. Similarly, the initial deviation values of the KLCC points in the MAP were obtained. Due to the flexible deformation of the weakly rigid parts Part1 and Part3 and the influence of the locating pins, the contact action in the contact fit area of each part has a significant non-linear contact phenomenon. In order to control the non-linear contact forces that may cause odd values, the position of the strongly rigid parts Part2 and Part4 is first temporarily adjusted to approximate the fit with Part1 and Part3, assuming an adjustment amount of h, after ensuring that all four contact pairs have been generated smoothly. Rigid displacement compensation is then applied according to the adjustment amount h to eliminate gaps and overfills. Under the part coordinate system shown in Figure 13, the nominal coordinate values of the KPC and KLCC points on the weakly rigid parts Part1 and Part3 and the strongly rigid parts Part2 and Part4 are determined from Table 2 before the assembly process begins. According to Tables 1 and 2, the spatial postures of parts Part1 to Part4 are determined, and the system matrices \(B\), \(E\), \(F\), \(G\) and \(L\) in the MAP are calculated to obtain the posture of each part under the coupling effect of its own flexible deformation and fixture positioning deviation. The coordinates of the KCCC points in the contact and fit area are obtained to reconstruct the contact state between the parts in the contact and fit area. The flush transformation matrix of parts Part1 to Part4 are calculated from the part coordinate system \(L_{\text{PC}}\) x (x = 1, 2, 3, 4) to \(L_{\text{gcc}}\), respectively, and MATLAB 9.10 software is used to implement the spatial triangle intersection detection algorithm and the spatial triangle penetration detection algorithm based on the deviation of the part measurement points to apply penalty force to the contact fit surface of each part to correct the contact gap or penetration. Finally, the mathematical modelling of the assembly deviation transfer model of each part in the \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Part Name**} & **KCCC Point Deviation (x-y-z)/mm** 1 \\ \cline{2-3}  & **Contact Fit Zone 1** & **Contact Fit Zone 2** \\ \hline Part 1 & (0, 0, 1.882) (0, 0, 1.882) & (0, 0, 2.503) (0, 0, 2.503) \\ Part 2 & (0, 0, 1.973) (0, 0, 1.972) & (0, 0, 2.556) (0, 0, 2.556) \\ Part 2 & (0, 0, 0) (0, 0, 0) & (0, 0, 0) (0, 0, 0) \\ Part 3 & (0, 0, 1.589) (0, 0, 1.588) & (0, 0, 0) (0, 0, 2.121) \\ Part 4 & (0, 0, 1.619) (0, 0, 1.618) & (0, 0, 0) (0, 0, 2.183) \\ Part 4 & (0, 0, 0) (0, 0, 0) & (0, 0, 0) (0, 0, 0) \\ \hline \hline \end{tabular} 1
[FOOTNOTE:1]Footnote 1: footnotetext: The data in Table 2 already existed when the flexible deformation of the parts was counted. 2
[FOOTNOTE:2]Footnote 2: footnotetext: Deviation values are counted in the part coordinate system. 3  
\end{table} 
Table 1: Deviation value of the KCCC point (flexible deformation already present).