# Investigation of Roller Press Surface and Stud Based on FEM Simulation
## 3 FEM Simulation
### Contact Analysis of Studded Rolls  
The studded rolls model is mainly simplified into three parts, the roller shaft, the studlining and the stud. In order to reduce the calculation time and improve the calculation efficiency, the chamfers and keyways of the roller shaft and the studlining are removed. Because there are too many studs in the studded rolls, the studs will affect the calculation process when recalculating. Therefore, the studded rolls are divided into two parts for simulation calculation. First, the simulation calculation is performed on the roller shaft and the studlining, as shown in Figure 4 below. Roller shaft and studlining simulation models. The other part is the simulation of studs and studlining. \begin{table}
\begin{tabular}{c c c c} \hline \hline \(\lambda\) & \(\mathbf{\alpha}\) & \(\mathbf{p(\alpha,\lambda)}\) & \(\mathbf{p_{1}(\alpha,\lambda)}\) \\ \hline \multirow{8}{*}{0} & \(-2\) & 3.177328295 & 4.32116648 \\  & \(-1\) & 45.82270455 & 62.3188781 \\  & 0 & 93.64323785 & 127.354803 \\  
Refer to the literature [28] and combine the material properties of the roller shaft and stud-lining on the studded rolls in the work, and set the material parameters of the roller shaft and the stud-lining according to the parameters in Table 2. By analyzing the stress distribution and contact pressure distribution of the roller shaft and the stud-lining, it is possible to predict where the studded rolls are most likely to fail, and provide theoretical data for later optimization. Because it is a simulation of the roller shaft and the stud-lining, the force model of the smooth rolls will be used. In order to make the stress situation more obvious, the pressure at the 0\({}^{\circ}\) position is used for simulation calculation. Static Analysis of Studded Rolls  
Through the contact pressure stress cloud diagram of the roller shaft and the stud-lining, it can be found that the contact pressure between the roller shaft and the stud-lining is mainly concentrated on both sides of the stud-lining, that is, the step where the stud-lining and the roller shaft contact. The contact pressure is greatest here. Using the formula below, calculate the maximum contact pressure \(p_{max}\) between the stud-lining and the roller shaft [28]. \[p_{max}=\sigma_{1}\left[\frac{1-(d/D)^{2}}{\sqrt{3+(d/D)^{4}}}\right] \tag{15}\]  
where \(\sigma_{1}\) is the yield strength of the stud-lining, \(\sigma_{1}\) = 835 MPa, \(d\) is the diameter of the roller shaft, and \(d\) = 1100 mm; \(D\) is the outer diameter of the stud-lining, and \(D\) = 1400 mm; \(p_{max}\)= 173.76 MPa was obtained. According to Figure 5a, the contact pressure between the stud-lining and the roller shaft is 280 MPa, which is more than the calculated maximum contact pressure. Therefore, the finite element model of studded rolls needs to be optimized. Through the contact pressure cloud diagram in Figure 5a, it can be found that the maximum value of the contact pressure appears at the outermost contact point between the roller shaft and the stud-lining. The distribution position of the contact pressure calculated by FEM is consistent with the model results of [PERSON] [28]. The contact pressure has a smaller value in the middle and a larger value on both sides, with a \"saddle\" distribution. This shows that the FEM of the roller shaft and stud-lining is consistent with the finite element models of other scholars. Figure 5b is the stress cloud diagram of the stud-lining. \begin{table}
\begin{tabular}{l l l l l} \hline \hline
**Part** & **Density** & **Elastic Modulus** & **Poisson’s Ratio** & **Yield Strength** \\  & **(kg/m\({}^{3}\))** & **(Pa)** & **\(\mu\)** & **(MPa)** \\ \hline Roller Shaft & 7850 & \(2.12\times 10^{11}\) & 0.280 & 930 \\ Stud-lining & 7850 & \(2.10\times 10^{11}\) & 0.275 & 835 \\ Stud & 10,000 & \(6.05\times 10^{11}\) & 0.275 & 600 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Material properties of studded rolls. Figure 4: Finite element model of studded rolls.