# Research on High-Speed Vibration and Structure Optimization of Multiwire Sawing Machine
## 2 Materials and Methods
### Whole Machine Transient Dynamics Simulation
#### 2.2.2 Parameter and Boundary Condition Settings  
The materials and basic parameters used for each part of the machine are shown in Table 1.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Materials**} & **Density** & **Young’s** & **Poisson’s** & \multirow{2}{*}{**Name of Parts**} \\  & **/(kg\(\cdot\)m\({}^{-3}\))** & **Modulus** & & **Ratio** & \\ \hline QT-450-10 & 7300 & \(1.9\times 10^{5}\) & 0.27 & End caps, main frame. \\
38 CrMoAlA & 7830 & \(2.06\times 10^{5}\) & 0.29 & Spindle, \\ HT300 & 7300 & \(1.43\times 10^{5}\) & 0.27 & groove wheel steel core. \\ Polyurethane & 1200 & 896 & 0.41 & Bottom bracket, subframe, \\ \hline \hline \end{tabular}
\end{table}
Table 1: Material performance parameters.  
Figure 2: Simplification of the whole frame model.  
After analysis and calculation, the load on the whole machine of this multiline sawing machine mainly includes the following:  
1. A pre-load force of 58400 N for the long bolt on the outside of the swim end, where the torque of the long bolt is 250-280 N-m, taking the larger value of the upper boundary.
2. The wire tension of the diamond wire on the grooved wheel is 50 kN, the maximum tension of which is calculated according to the commonly used wire type and tension meter and rounded upwards.
3. Dual spindle motor speeds, where a slotted wheel diameter of 180 mm corresponds to different speeds for different alignment speeds.
4. Mass of the material feed platform section: 700 kg.
5. The take-up and payoff wheel mass is 70 kg.
6. The take-up and payoff motor mass is 206 kg.
7. Tension control motor with a mass of 46 kg.
8. The mass of the motor and screw parts of the discharge line is 33 kg.
9. The mass of the electrical components in the electric control cabinet is 300 kg.
10. The self-weight of the machine frame, etc.  
Mass point replacement is applied to the material feed platform, motor, and other parts above the main frame. The position and size of each center of mass are determined, and their corresponding actions on the frame are established. The MPC treatment was applied to the frame part, a fixed support treatment was applied to the bottom surface of the tab of the bottom bracket, and the contact was set according to the actual situation.  
Due to there being a large number of load types, the loads are applied in steps, and separate substeps are set for each load, and the substeps for different working conditions are reasonably tuned to reduce the number of dichotomies in the calculation process and accelerate the convergence speed in the calculation. Hybrid area meshing with advanced nodes is used for the whole frame, the mapping type is a hexahedron, and the free mesh type uses a hexahedron as the core. The spindle part is meshed separately, and its size is kept at 25 mm, The boundary conditions for finite element analysis are applied as shown in Figure 3. The arrows shown in Figure 3 represent the directions of the forces and torques applied as boundary conditions in the multi-wire sawing machine  
During the operation of the multi-wire sawing machine, the spindle motor moves in a certain cycle pattern, which makes the wire saw reciprocate and cut the material. Since the time variation is not considered in static devices for such complex conditions, although the dynamics calculation is tens or even hundreds of times more time-consuming than that for static devices, it is necessary to perform dynamic finite element simulations to understand the vibration characteristics more accurately.  
Figure 3: Finite element boundary condition.  
Since the transient dynamics simulation is time-consuming, the calculation time is simplified by taking one acceleration/deceleration cycle of the motor operating as a calculation time length, and the vibration characteristics of the machine tool at different linear speeds are simulated using dynamic finite element analysis.