# System Design and Monitoring Method of Robot Grinding for Friction Stir Weld Seam
## 2 Method
### Monitor Method of Grinding Process Based on PSO-SVM  
#### 2.3.1 Analysis of Weld Seam Grinding Process in Designed System  
The grinding process of the weld seam is complex and dynamic. The contact force of the grinding tool shows different dynamic characteristics during normal and excessive grinding. Meanwhile, these characteristics are also related to the characteristics of the weld seam. In this section, firstly, the control method of the grinding tool is explained. The position error of the weld seam occurs due to the system calibration error, robot positioning error, etc. Therefore, in the robot belt grinding, the force control method must be used, because the position control method is adopted, even a small position error will significantly affect the grinding effect. In this system, a Proportion - Integral - Derivative (PID) control method based on the force is conducted for the compensation part of the grinding. Incremental PID is an effective and widely used method in practice, in our method, there are:  
\[L_{k}=L_{k-1}+\Delta L_{k}, \tag{8}\]  
where \(L_{k}\) is the command position for the grinding tool, and  
\[\Delta L_{k}=K_{p}\left(\Delta F_{k}-\Delta F_{k-1}\right)+K_{i}\Delta F_{k}+K _{d}\left(\Delta F_{k}-2\Delta F_{k-1}+\Delta F_{k-2}\right), \tag{9}\]  
where  
\[\Delta F_{k}=F_{k}-F_{d}, \tag{10}\]  
\(F_{k}\) and \(F_{d}\) are actual force and desired force value, separately, \(K_{p}\), \(K_{i}\) and \(K_{d}\) are appropriate parameters of the controller. In this control mode, when the grinding wheel does not touch the weld seam or contact too deep due to the system position error, the tool can compensate for this error through moving the contact wheel according to the actual value \(\Delta F_{k}\). Considering the situation of the weld seam and the application of force control method mentioned above, when grinding, a dynamic contact process is inevitable. In general, the belt grinding process is divided into three parts: approach state, transition state, and steady state, as shown in Figure 4. Different from traditional belt grinding, weld seam grinding in this paper has two types due to the particularity of the weld seam. The first type is grinding of the uniform line weld seam, and the second type is the grinding of the uneven part, as shown in Figure 5.  
For the first type of weld seam, the grinding process goes through the above three contact stages. Robot holding the grinding tool moves and grinds along the direction of the weld seam. During the process, the grinding is basically in a steady state stage due to the uniform weld shape. For the second type of weld seam, the robot moves and grinds weld seam from top to bottom. There are two reasons for this way of grinding. One is that when grinding along the line, if there exists a uneven part, the contact state will change, that is, the grinding is easy to exit the steady stage and then affects the final effect of grinding. The other reason is that grinding this kind of weld seam needs more energy. Considering the wear and heat of the abrasive belt, when using this method, the tool can be lifted to dissipate heat after the grinding of the uneven part is completed. During the process, the grinding is basically in a transition state stage due to the uncertainty of trimming shape. Figure 4: Grinding Stages. Figure 5: Weld seam grinding type. Therefore, during the linear weld seam grinding of the first type of weld seam, the robot's reasonable processing speed and force strategy can almost ensure that the processing is not excessive, because it is basically in the steady-state stage. So the authors put forward a relatively simple monitoring method, that is, monitoring the displacement of the end compensation movement. If the change rate of displacement exceeds the threshold value, it is judged as excessive grinding. However, it needs to be emphasized that if the robot strategy is suitable, the excessive grinding rarely occurs. Therefore, this paper focuses on the second kind of weld seam grinding monitoring.