## 6 Discussion  
From the experimental results of both computer simulation and physical machining of our proposed method, the following notes can be made. (1) Due to the unique structure of an aero-engine casing, i.e., it is axisymmetric, the fixture elements are arranged in an axisymmetric manner, and the interactions among fixtures are simple. If complex fixtures are used, mutual coupling between the fixtures should be considered. (2) The proposed method may cause a certain amount of clamping distortion to the part before machining. In order to prevent the support force from affecting the subsequent machining, the maximum support force should be calculated based on the machining allowance and the equivalent flexibility. However, not all of these clamping deformations are harmful. Part of the clamping deformation will be eventually offset by the part machining deformation, which is actually beneficial to improving the machining accuracy of the part. Harmful clamping deformations are mostly due to prediction errors. The confidence level selected can be adjusted according to the machining accuracy during the actual machining process. (3) The model training data in this work are obtained from simulation. Naturally, there is always a gap between a simulation environment and the real physical machining  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{ \begin{tabular}{c} **Clamping** \\ **Points** \\ \end{tabular}  } & \multirow{2}{*}{ \begin{tabular}{c} **Deformation** \\ **Force (N)** \\ \end{tabular}  } & \multicolumn{1}{c}{ \begin{tabular}{c} **Calculated** \\ **Deformation** \\ **(mm)** \\ \end{tabular}  } & \multicolumn{1}{c}{\ \begin{tabular}{c} **Measured** \\ **Deformation** \\ **(mm)** \\ \end{tabular}  } & \multicolumn{1}{c}{ \begin{tabular}{c} **Prediction Error** \\ **(mm)** \\ \end{tabular}  } \\ \hline
1 & \(-\)71.466 & \(-\)0.017 & \(-\)0.014 & 0.003 \\
2 & \(-\)53.301 & \(-\)0.013 & \(-\)0.012 & 0.001 \\
3 & \(-\)37.275 & \(-\)0.009 & \(-\)0.014 & 0.005 \\
4 & \(-\)34.744 & \(-\)0.008 & \(-\)0.006 & 0.003 environment due to errors in the estimation of various physical data, such as the cutting force, cutting heat, residual stress, and intrinsic model errors. The gap is reduced in our model by using the Kalman filter via fusing the predicted and measured data. In our future work, more practical data will be accumulated, which will improve the accuracy of the model predictions and the contrast of the predicted distribution. (4) The proposed method requires a special fixture to accurately exert the support force. Nevertheless, the current fixture used in the experiments is not sophisticated enough to accurately control the support force; thus, further improvements on the design of the fixture are needed. (5) The accuracy of measurement of the deformation force is limited to a large extent by that of the clamping force measuring device. The device will be further improved to reduce the effects of machining vibration, cutting force and cutting fluid, so to enhance the measurement accuracy of the clamping force. (6) The existing deformation monitoring methods are usually only applicable to locators or clampers but not auxiliary supports. However, for thin-walled aerospace parts, it is very difficult to perform finish-machining using only positioning and clamping elements without any auxiliary support. In other words, they are insufficient in actual parts processing. The proposed deformation force monitoring method based on adaptive adjustment provides a good example for monitoring the deformation force due to auxiliary bracing. It can also be extended to other types of auxiliary support. (7) Most existing methods based on applying clamping forces and monitoring the deformation force are not stable, due to the lack of residual stress data and deformation force training data. We are currently conducting another study on how to estimate the residual stress distribution of an area-engine casing blank based on the deformation force.