# Enhanced Adhesion--Efficient Demolding Integration DLP 3D Printing Device
## 3 Overall Scheme Design
### DLP Projection System
#### 3.1.2 Z-Axis Motion Mechanism  
First, the screw is selected. The calculation method of the helical pitch \(\mathrm{P_{h}}\) is shown in Equation (1):  
\[\mathrm{P_{h}}=\frac{\mathrm{V_{max}}}{\mathrm{n_{max}}} \tag{1}\]  
where \(\mathrm{V_{max}}\) is the maximum moving speed of the screw pair (mm/min), and \(\mathrm{n_{max}}\) is the maximum speed of the motor (r/min).  
The calculation method of the Dynamic Load Rating is shown in Equation (2):  
\[\mathrm{C_{am}}=\sqrt[3]{60\mathrm{n_{m}}\mathrm{L_{h}}}\times\frac{\mathrm{ F_{m}}\mathrm{f_{w}}}{100\mathrm{f_{a}}} \tag{2}\]  
where \(\mathrm{n_{m}}\) is the equivalent speed (r/min), \(\mathrm{L_{h}}\) stands for the expected working time (h), \(\mathrm{F_{m}}\) is the equivalent load (N), \(\mathrm{f_{w}}\) is the load coefficient and \(\mathrm{f_{a}}\) is the precision class.  
Screw installation is fixed at both ends, so the calculation method of the bottom diameter of thread \(\mathrm{d_{2}}\) is shown in Equation (3):  
\[\mathrm{d_{2}}\geq 0.039\sqrt{\frac{\mathrm{F_{0}}\mathrm{L}}{1000\mathrm{g_{m }}}} \tag{3}\]  
where \(\mathrm{F_{0}}\) is the static friction force of the guide rail (N), \(\mathrm{L}\) is the maximum distance between the two fixed supports (mm) and \(\mathrm{g_{m}}\) is the maximum allowable axial deformation (mm).  
According to Equations (1)-(3), it can be calculated that the helical pitch \(\mathrm{P_{h}}\) is 0.48 mm, the dynamic load rating \(\mathrm{C_{am}}\) is 31.241 N and the bottom diameter of thread \(\mathrm{d_{2}}\) is equal to or greater than 1.112 mm. Therefore, the specification code 0802-3 for the type of screw is selected. Its helical pitch \(\mathrm{P_{h}}\) is 2 mm, dynamic load rating \(\mathrm{C_{am}}\) is 1438 N, bottom diameter of thread \(\mathrm{d_{2}}\) is 7.1 mm, nominal diameter \(\mathrm{d_{1}}\) is 8 mm and all selections meet the transmission requirements. According to the printing size requirements, the stroke of the ball screw is 200 mm, and the stroke of the limit switch is 95 mm.  
In order to ensure the accuracy requirements of the experimental printing model, the pre-selected motor model is the 42 CM06 stepping motor (Dongguan Stepping motor Co., Ltd., Dongguan, China) its stepping angle is 1.8\({}^{\circ}\) and its rated torque is 0.6 N\(\cdot\)m. The  
Figure 4: Structure diagram of the porous printing platform for easy demolding. (**a**) The overall structure diagram of the printing platform; (**b**) Structure diagram of the demolding device.  
calculation methods of maximum acceleration torque at no load Teq1 and the maximum working load torque Teq2 of the stepping motor are shown in Equations (4) and (5):  
\[\text{T}_{\text{eq1}}=\frac{2\pi\text{J}_{\text{eq}}\text{n}_{\text{m}}}{60\text {t}_{\text{a}}\text{n}} \tag{4}\]  
\[\text{T}_{\text{eq2}}=\frac{\text{FP}_{\text{h}}}{2\pi\text{mi}} \tag{5}\]  
where Jeq denotes the total moment of inertia of the stepping motor (kg.m2), Nm is rotational speed (r/min), Ta is acceleration time of stepping motor (s), F is the maximum working load on the workbench (N), Ph is the stroke of the screw (m), \(\eta\) is transmission efficiency and i is total transmission ratio.  
According to the above calculations, the maximum load torque Teq on the loading stepping motor shaft should be:  
\[\text{T}_{\text{eq}}=\text{T}_{\text{eq1}}+\text{T}_{\text{eq2}} \tag{6}\]  
According to the mechanical structure, the total moment of inertia of loading on the stepping motor shaft is 1.54 \(\times\) 10\({}^{-5}\) kg.m2. When the stepping motor speed reaches 120 r/min, its acceleration time is 0.2 s, transmission efficiency is 0.85 and helical pitch is 2 mm. The maximum working load of the stepping motor is 4.06 N. According to Equations (4) and (5), Teq1 is 0.0010 N\(\cdot\)m, and Teq2 is 0.0015 N\(\cdot\)m, and according to Equation (6), Teq is 0.0025 N\(\cdot\)m. It can be known that the maximum load torque on the shaft of the loading stepping motor is within the torque range of the 42 CM06 stepping motor. Figure 5 shows the selected ball screw slide module.