## 3 Effects of Process Parameters on Surface Straightness
### Design and Analysis of Orthogonal Experiment  
In this paper, straightness tolerance is used to reflect the straightness of variable-section conical spun parts. The calculation method is illustrated in Figure 7 and Equations (2)-(4). A total of 20 sampling points are selected along the axial equal distance of the cone after spinning, and these points are on the axisymmetric plane of the part. The smaller the \(\Delta Y\) is, the better the straightness is.  
\[\Delta Y_{k}=|y_{k}-y| \tag{2}\]  
\[\Delta Y_{a}=\Delta Y_{k}\cdot\sin\theta \tag{3}\]  
\[\Delta Y=\max\Delta Y_{a}-\min\Delta Y_{a} \tag{4}\]  
where \(y_{k}\) is the actual coordinate value of the \(Y\)-axis of sampling point, \(k=1\)\(\sim\)20; \(y\) is theoretical coordinate value of the sampling point; \(\Delta Y_{k}\) is the position deviation of the sampling point in a \(Y\)-axis direction; \(\theta\) is the angle between the theoretical contour of the cone and the horizontal plane; \(\Delta Y_{a}\) is the vertical distance from the sampling point to the theoretical contour of the cone; \(\Delta Y\) is straightness tolerance.  
An orthogonal experimental design is an experimental design method to study multi-factor and multi-level features. It has the advantages of high efficiency, rapidity and low costs. In the spinning process, numerous process parameters affect the forming quality. The main process parameters studied in this orthogonal experiment are spinning temperature \(T_{c}\), roller nose radius \(r\), mandrel rotation rate \(n\), and roller feed ratio \(f\). In this paper, a four-factor and four-level orthogonal experiment was designed by finite element simulation with straightness tolerance as the response variable. To avoid repeated experiments, an empty column was set in the table. The orthogonal experiment scheme and experiment results are listed in Table 5.  
A variance analysis on the straightness tolerance was carried out in Table 5 to get the range analysis table of straightness, as listed in Table 6. R is the range, and the larger the R value is, the greater the effect of this factor on the test index is, and the more substantial it is. Therefore, the effect order of various factors on the straightness of cone surface is ABCD, that is, spinning temperature has the greatest influence on the straightness, followed by  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**No**} & \multicolumn{2}{c}{**Spinning**} & \multirow{2}{*}{**Roller Nose**} & \multirow{2}{*}{**Mandrel Rotation**} & \multirow{2}{*}{**Roller Feed**} & \multirow{2}{*}{**Null**} & \multirow{2}{*}{**Straightness**} \\  & **Temperature \(T_{c}\)** & & & & & \\  & **Radius \(R\) (mm)** & & & & &  
the roller nose radius, then the mandrel rotation rate. The roller feed ratio has the least influence on the straightness. The optimal level of the factors can be judged by the size of T. The test index is the straightness tolerance of the outer surface of the cone. The smaller the T value, the higher the straightness of the outer surface of the cone. The best combination of A, B, C and D is A2B1C2D1. Under this process combination, the outer surface straightness of GH4169 superalloy conical spun parts are ideal. The optimal process parameters of this group are numbered as 17, and the simulation of the 17 th group was carried out. Its straightness tolerance was 0.155 mm. From the 16 groups of simulation results in Table 5, it can be inferred that in the orthogonal experiment plan, the maximum straightness tolerance of the cone outer surface was 1.723 mm, and the minimum was 0.225 mm, while in the 17 th optimal combination, the straightness tolerance of the cone outer surface did not exceed 70% of the minimum value in Table 5. The optimization result is satisfactory, and the optimal combination of process parameters has reference significance.