# Analysis of a Novel Automatic Control Approach for the Free Forging Hammer
## 4 Control Schemes for Free Forging Hammer  
### Blow Energy Model  
For a servo free forging hammer, the forging energy carried by the hammerhead each time the forging hammer descends to strike the forging is determined by the thrust and the descend speed of the piston rod. Therefore, the output energy of the hammerhead (\(E_{Output}\)) in a working stroke can be expressed as,  
\[E_{Output}=\int_{t_{1}}^{t_{2}}F_{r}\dot{h}dt \tag{1}\]  
where \(t_{1}\) and \(t_{2}\) are the start time and the end time of the downward strike, respectively; \(F_{r}\) is the thrust of the piston rod; and \(h\) is the position of the piston rod in the vertical direction. Since the hydraulic cylinder driving the hammerhead is connected in a differential connection, its thrust and descending speed (\(\
u_{M}\)) can be described by,  
\[F_{r}=p_{1}(A_{1}-A_{2})\eta_{cm} \tag{2}\]  
\[v_{M}=\dot{h}=\frac{q_{m}\eta_{cm}}{A_{1}-A_{2}} \tag{3}\]  
where \(p_{1}\) is the pressure inside the upper chamber of the main cylinder; \(A_{1}\) and \(A_{2}\) are the ram areas of the two chambers; \(q_{m}\) is the flow rate supplied to the upper chamber; and \(\eta_{cm}\) and \(\eta_{cm}\) are the mechanical efficiency and volumetric efficiency of the main cylinder, respectively. Therefore, the output energy can be rewritten as follows,  
\[E_{Output}=\int_{t_{1}}^{t_{2}}p_{1}q_{m}\eta_{cm}\eta_{cm}dt \tag{4}\]  
When the upper chamber feeds, the flow rate from the main control valve into the main cylinder that controls the movement of the forging hammer can be obtained as follows according to fluid mechanics:  
\[q_{m}=C_{d}\omega x_{m}\sqrt{1/\rho(p_{s}-p_{1})} \tag{5}\]  
where \(C_{d}\) and \(\omega\) are the discharge coefficient and spool area gradient, respectively; \(\rho\) is the oil density; \(x_{m}\) is the spool displacement; and \(p_{s}\) is the supply pressure. The working principle of the main control valve is basically the same as that of the electromagnetic valve, which is based on adjusting the spool displacement to change the output flow and output pressure of the main control valve. The only difference is that the power source for the spool is different. In this system, a servo cylinder is adopted to drive the main control valve, and the servo cylinder and the main control valve are rigidly connected, so the displacement of the servo cylinder is the  
Figure 10: Response characteristics of the electrohydraulic servo all-hydraulic forging hammer. displacement of the main control valve spool. According to the mechanics, the servo cylinder force balance equation can be described by  
\[A_{3}p_{3}-A_{4}p_{4}=m\ddot{x_{m}}+B\dot{x_{m}}+F_{l} \tag{6}\]  
where \(A_{3}\) and \(A_{4}\) are the ram areas of the two chambers; \(p_{3}\) and \(p_{4}\) are the pressure inside the two chambers; \(m\) is the mass of the main control valve spool; \(B\) represents the viscous friction coefficient; and \(F_{l}\) denotes deformation resistance. Then, the speed of the spool can be written as  
\[\dot{x_{m}}=\frac{q_{s}}{A_{3}} \tag{7}\]  
where \(q_{s}\) is the flowrate supplied to the rodless cavity and can be expressed as follows,  
\[q_{s}=k_{q}x_{s}\sqrt{p_{in}-p_{3}} \tag{8}\]  
where \(p_{in}\) is the supplied pressure of the servo valve; \(k_{q}\) is the flowrate gain coefficient of the servo valve; and \(x_{s}=k_{d}u\), where \(k_{d}\) is a positive constant and \(u\) is the control input. Therefore, Equation (8) can be rewritten as,  
\[q_{s}=k_{q}k_{d}u\sqrt{p_{in}-p_{3}} \tag{9}\]  
Therefore, the striking energy of the hammerhead can be controlled automatically and obtained as,  
\[F_{r}=p_{1}(A_{1}-A_{2})\eta_{cm} \tag{2}\]0  
By adjusting the input signal \(u\), motion state control of the servo cylinder and the main cylinder can be realized, thereby realizing control of the striking energy of the forging hammer. Unlike die forging, since there are many variable forging shapes and the randomness of the production process is too large, the energy switching between different steps is frequent during the free forging process.