# Study on the Position Deviation between the Iron Roughneck's Spin-Rollers and the Drilling Tool
## 2 Materials and Methods
### Analysis of Position Deviation between the Spin-Roller and the Drilling Tool
#### 2.2.3 Simulation Solution  
According to the relationship obtained from the above analysis, the Simulink module of MATLAB software can be used to solve it. Establish the model corresponding to the above mathematical relationship in Simulink software, as shown in Figure 3. By inputting the parameter values of each known mechanism into the model, the values of \(\delta_{1y}\), \(\delta_{2x}\), and \(\delta_{2y}\) corresponding to different deviations \(\delta\) can be obtained.  
The diameters of the driving rollers and the follow-up roller of the spinner mechanism are all 180 mm, and the diameters of the drilling tool are taken as 89 mm, 168 mm, and 311 mm. According to the geometric relationship, when the spinner mechanism holds different drilling tools, the corresponding angle \(\beta\)'s shown in Table 2.  
In the Simulink model, the deviation \(\delta\) is set as a variable gradually increasing within 0 to 10 mm, and the drilling tool diameters are set as 311 mm, 168 mm, and 89 mm. According to the angle \(\beta\) in Table 2, the value of \(\delta_{1y}\), \(\delta_{2x}\), and \(\delta_{2y}\) corresponding to different deviations \(\delta\) can be obtained, and the obtained data are draw into curves as shown in Figure 4.  
\begin{table}
\begin{tabular}{c c c c} \hline
**Drilling Tool Diameter (mm)** & **89** & **168** & **311** \\ \hline \(\beta\) (\({}^{\circ}\)) & 99.7 & 111.5 & 120.1 \\ \hline \end{tabular}
\end{table}
Table 2: Angle \(\beta\) corresponding to different diameters.  
According to the deviation relation curve, with the increase of the deviation \(\delta\) of the drilling tool, the deviation of the driving roller in the \(x\)-axis and \(y\)-axis direction \(\delta_{2x}\) and \(\delta_{2y}\) increases linearly, and the increase of \(\delta_{2y}\) is more obvious. With the increase of the drilling tool's diameter, the deviation also increases. When the drilling tool's diameter is 89 mm and the drilling tool deviation \(\delta\) is 10 mm, the deviation of the driving roller \(\delta_{2x}\) and \(\delta_{2y}\) is 3 mm and 17 mm, respectively. When the drilling tool's diameter is 168 mm, the corresponding \(\delta_{2x}\) and \(\delta_{2y}\) is 8 mm and 19 mm, respectively. When the drilling tool's diameter is 311 mm, the corresponding \(\delta_{2x}\) and \(\delta_{2y}\) reaches 12 mm and 20 mm, respectively. However, the deviations \(\delta_{1y}\) of the drilling tool in the \(y\) direction in the three cases are relatively small, indicating that the offset of the drilling tool mainly occurs in the \(x\)-axis direction under the restriction of the spin-roller. When the drilling tool is offset, the deviation of the driving roller \(\delta_{2y}\) is significantly greater than the drilling tool deviation \(\delta\). In practice, it often occurs that drilling tool's offset \(\delta\) is more than 10 mm, and its impact cannot be ignored. Excessive deviation will further aggravate the deflection amplitude of drilling tool and spin-rollers in the process of screwing, affect the contact between roller and drilling tool, the stability of action, and then affect the spinning efficiency. In addition, it is easy to aggravate the wear of spin-rollers and the damage of drilling tool's thread. Therefore, it is necessary to control the deviation of drilling tools and spin-rollers to ensure the stability and reliability of spinning action.