# Ground Simulation Tests in Two-Dimensional Dynamic Acceleration Environment
## 3 Simulation of Impact Overload Environment
### Clutch Engagement Process  
During the simulation analysis, the air cannon pushes the arm. The starting time is very short, the acceleration amplitude and loading time meet the simulation test requirements of the impact overload environment. The air cannon propulsion duration is about 120 ms, but the acceleration rise time is only 2 ms. The duration of the peak is too short. To maintain the impact state, the clutch needs to be engaged and the motor needs to be relayed to power the arm rotation. If the relay is completed at the peak of the acceleration, the acceleration of the arm can be achieved.  
The driving plate of the clutch is driven by the main control motor. The load on the driven plate includes the effective loads of the reducer, the rotating shaft, the arm, the vector distributor, and the unit being tested. The power transmission system of the centrifuge is shown in Figure 5.  
The dynamic equation of the clutch transmission can be written as  
\[\left\{\begin{array}{l}J_{c}\dot{\omega}_{c}=T_{c}-T_{f}\\ J_{d}\dot{\omega}_{d}=T_{f}-T_{d}\end{array}\right., \tag{5}\]  
where \(J_{c}\), \(\omega_{c}\), and \(T_{c}\) are the moment of inertia, revolution speed, and output torque of the main control motor, respectively, \(T_{f}\) is the friction torque transmitted by the clutch, and \(J_{d}\), \(\omega_{d}\) and \(T_{d}\) are the effective moment of inertia, revolution speed, equivalent resistance torque of the driven plate, respectively.  
When the clutch is completely disengaged, \(T_{f}=0\) Nm, and when the clutch is fully engaged, \(T_{f}=T_{c}=T_{d}\). The main operation process of the clutch in the test system varies from a fully engaged sliding  
Figure 4: Measured acceleration of the pulley and the tangential acceleration of the arm at the impact overload of 10 \(g\).  
Figure 5: Schematic diagram of the power transmission system of the centrifuge.  
friction state to a fully disengaged sliding friction state. The initial speed of the driven plate is zero rad/s. When the clutch is engaged, the speeds of the driven plate are shown in Figure 6.  
At the beginning, the driven plate keeps stationary, the clutch is disengaged, and the motor is idling. Therefore, \(T_{d}\), \(T_{f}\), and \(T_{c}\) are all zero Nm, and the motor's speed \(\omega_{c}\) is a constant. When the clutch is engaged, the difference in the speeds of revolution becomes large. \(T_{f}\) is gradually increased, the revolution speed (\(\omega_{d}\)) of the driven plate increases, and the output torque (\(T_{c}\)) of the motor also increases. Because \(T_{f}\) is less than \(T_{c}\), the motor accelerates. The difference in the speeds of revolution increases. \(T_{f}\) increases faster than \(T_{c}\), and the driven plate accelerates. When \(T_{f}\) > \(T_{c}\), the motor decelerates, the difference in the revolution speeds becomes increasingly small, and \(T_{f}\) gradually decreases. When \(T_{f}\) = \(T_{c}\), the clutch is fully engaged, the motor drives the load to accelerate and stabilize after attaining the set revolution speed.  
In the simulation tests, the arm is started by the air cannon. Ideally, the engagement process will be completed when the propelled acceleration reaches the maximum, and the tangential acceleration of the arm after launching will be equal to the set normal acceleration of the arm. Since the propulsion time is very short, \(\omega_{d}\) should be less than \(\omega_{c}\), and the arm always accelerates during the engagement process. If the timing is missed, the engagement occurs too late, the arm decelerates, the impact acceleration is less than zero \(g\), and the impact overload cannot be simulated. Therefore, it is necessary to select a suitable clutch and proper engagement timing. By controlling the pressures of the air cannon chambers and the revolution speed of the motor, the rapid transition between the impact overload and the continuous acceleration can be achieved.