# Dynamics Analysis of a Double-Plunger-Type Turbine Overspeed Protection Mechanism
## 6 Dynamic Simulation and Validation
### Simulation of the Trip Process  
Validation experiments using turbine units are too expensive and time-consuming to compete. In this study, simulation experiments are chosen to verify the correctness of the theoretical analysis [16]. Furthermore, we use the dynamics module in ADAMS to simulate the whole process of the overspeed protection system. Similar to the common process of using ADAMS for mechanism motion simulation [17], we set up constraints, loads, and motion subsets for the imported physical model in ADAMS, and we set up sensors to obtain motion parameters.  
Figure 12 shows the model of the overspeed protection system in ADAMS.  
Because the eccentricities of each part of the inner and outer springs are different during the motion of the plunger, the magnitude of the centrifugal force is also different. The resulting inhomogeneous deformation changes the spring's mass distribution, and the centrifugal force changes with the change in mass distribution. Therefore, although the reaction force that varies linearly with the displacement of the constrained end can be achieved by setting a spring-damper force in ADAMS, to accurately simulate the actual spring force in the rotating system, the spring needs to be imported into the simulation model and defined as a flexible body. In this study, the modal neutral file is generated using the Ansys workbench, and the.mnf file is used to generate the modal neutral file and provide the mesh and stress information in ADAMS to realize the flexibility of the spring. In the multibody system dynamics simulation environment, the pre-compression condition of the spring cannot be set, and the spring force used to hold the plunger in place is simulated by defining the force acting directly on the plunger after the inner and outer springs are pre-compressed.  
The spindle is driven with uniform acceleration, and the displacement of the outer plunger along the Z-axis direction of the spindle is used as the condition for the simulation process to stop. Specifically, the simulation process stops when the outer plunger flies outward by more than 1 mm. According to the acceleration value and the spindle acceleration time consumption, the final speed of the spindle can be obtained when the outer plunger hits the leveraging mechanism.  
Figure 13a shows the speed-displacement curve of the inner and outer plungers along the radial direction of the main shaft.  
Figure 12: Model in ADAMS.  
The horizontal coordinate of Figure 13a is the rotational speed of the spindle, and the vertical coordinate is the displacement of the inner or outer plungers along the radial direction of the spindle relative to the initial position. The motion process is divided into the following four stages:  
1. The spindle speed is low, and the inner and outer plungers are not displaced.
2. The spindle speed is gradually approaching the inner plunger trip speed, and the inner and outer plungers show an unstable state, resulting in a small displacement (less than 0.1 mm).
3. The inner plunger overcomes the spring resistance with the driving of centrifugal force and starts accelerated motion, and the outer plunger does not move in this process.
4. The inner plunger moves to the end and comes into contact with the top of the inner wall of the outer plunger, and then both inner and outer plungers fly outward together.  
As shown in Figure 13b, the final tripping speed of the plunger increases with acceleration, and the trend is consistent with the results of the theoretical model.  
As shown in Figure 14, trip speed grows with spring stiffness, and the inner plunger trips at a higher speed over a shorter eccentric distance.  
In summary, the simulation of the plunger motion is consistent with the theoretical analysis.