# Optimization Method of the Clamping Force for Large Cabin Parts
## 5 Experiment  
In order to further verify the feasibility of the clamping force's gradient flow optimization method and the above simulation's reliability, an experimental prototype of the ring pneumatic fixture is used to clamp an object. The normal clamping force of each clamping mechanism is measured by the force sensor measuring system and is compared with the corresponding simulation results. The prototypes of the ring pneumatic fixture and the force sensor measuring system are shown in Figure 12. The ring pneumatic fixture is set in a static state during the experimental process. The required sensor measuring system consists of four thin-film pressure sensors and a four-channel data acquisition card produced by Vaax Technology, which can simultaneously measure up to four channel pressure changes. Figure 12: Cont. Since four force sensors are used in this experiment and the ring pneumatic fixture has eight clamping mechanisms, the normal clamping force of the lower clamping mechanism is first measured, and then the normal clamping force of the upper clamping mechanism is measured. The contact model between the clamping mechanism and the object is the surface contact model and the measuring area of the force sensor is small. In this experiment, the center of the contact surface between the clamping mechanism and the object is taken as the measuring position of the force sensor and the value of the normal clamping force measured at this point is taken as the normal clamping force under the equivalent point contact model of the clamping mechanism. The measuring position of the force sensor on the contact surface between the clamping mechanism and the object is shown in Figure 13.  
The mass of the clamped object is 2 t. The radius of the clamped object is \(r=0.7\) m. The sequence number of each clamping mechanism is shown in Figure 7 above. Each clamping mechanism simultaneously clamps the object. The changes in the normal clamping force  
Figure 12: Experimental equipment: (**a**) Experimental prototype and its supporting device of the ring pneumatic fixture: 1. Experimental prototype, 2. Clamping mechanism 3. Auxiliary support bracket, 4. Roll support bracket. (**b**) Experimental force sensor. (**c**) Four-channel data acquisition card. (**d**) Force measuring system with the upper computer: 1. Experimental prototype, 2. Force sensor attached to the surface of the clamping mechanism, 3. Data acquisition card, 4. Upper computer. of each clamping mechanism measured via the clamping force experiments are shown in Figure 14.  
Figure 14: Change in the normal damping force obtained by the experiment: (**a**) The normal clamping force change of the upper clamping mechanism; (**b**) the normal clamping force change of the lower clamping mechanism. Figure 13: Measuring position of the force sensor. In order to compare with the corresponding simulation results of the clamping force, it is necessary to process the clamping force data of each clamping mechanism obtained from the experiment. Here, the average value of the normal clamping force obtained via the experiment is taken as the stable clamping force under the equivalent point contact model of each clamping mechanism. Then, the normal clamping force is combined into a vector \(\mathbf{F}_{\text{n}}=[f_{\text{n1}},f_{\text{n2}},\dots,f_{\text{n8}}]^{\text{T}}\). This vector can be regarded as the normal clamping force value of each clamping mechanism after a stable clamping, which can be expressed as follows:  
\[\mathbf{F}_{\text{n}}= \begin{bmatrix}1.324&2.893&1.224&3.091&1.013&2.894&1.645&2.8 73\end{bmatrix} ^{\text{T}} \tag{19}\]  
After the experiment and data processing, the corresponding clamping force optimization simulation is performed. The penalty function method is used for the initial value calculation of the 2 t object. The initial optimized value of the normal clamping force \(\mathbf{F}_{\text{ne}}\) calculated by the simulation is obtained as follows:  
\[\mathbf{F}_{\text{ne}}=