## 3 Results and Discussion  
### Uncontrolled Welding Process and Validation of Clamping Concept  
Figure 7 shows the top view of an uncontrolled weld with unhindered gap formation. Sheet 2 was able to move freely within the y-direction since the actuators and the load cells were not connected to it. The weld started in zero gap but was interrupted after approximately 205 mm due to the increasing gap size with longer process duration. It should be noted that the gap formation changes over time and the gap may close after the welding process during cooling [15]. A detailed view of the gap size occurring time-dependent due to the unhindered sheet displacement is shown in Figure 8a. The gap that occurred was time-delayed in comparison to the process start at time zero corresponding to the initial keyhole penetration. It was assumed that there is no significant effect on gap formation by conduction-mode welding at the start of the process, as the keyhole is formed in times of less than 1 ms [32]. The gap started to increase for the first probe IP1 close to the sheet edge at process start while probe IP2 and IP3 follow its order along the weld seam. The gap size increased until the weld reached the corresponding measuring point in the x-direction, or the weld has been discontinued because of a too excessive gap size. A gap size of more than 0.5 mm was reached at probe IP3 when the process was interrupted. The intended clamping situation could be achieved with the developed clamping device, i.e., the position of sheet 1 is almost constant over time while sheet 2 can move freely in the y-direction (see Figure 8b). Sheet 2 remained almost unchanged in the z-direction while Figure 8a showed an unhindered gap opening. This suggests that the gap of 0.1 mm between clamping jaw 6 and sheet 2 (see Section 2.1) was sufficiently dimensioned to allow for a free movement in the y-direction. Figure 6: Realized control cabinet for sensor and actuator integration and control in testing mode. Figure 7: Top view of an uncontrolled weld with unhindered gap formation (v\({}_{\mathrm{w}}\) = 1 m/min, P\({}_{\mathrm{L}}\) = 0.4 kW). A rigid clamping was considered in addition for the uncontrolled process to provide information on occurring forces during welding (see Figure 9). The tensile forces have a positive sign, the compressive forces have a negative sign. Load cell LC 1 was located at the start of the sheet and load cell LC 2 was located at the end of the sheet as described in Section 2.1. Load cell LC 1 showed a short period under compressive forces directly after process start. The load cell LC 2 at the end of the sheet did not record any change in load at this point. The tensile forces caused by the cooling process and shrinkage of the weld seam started to predominate over the further course of the process for load cell LC 1. The force at load cell LC 2 increased shortly after the weld started to form and then continued to decrease until the resulting tensile force became predominant due to the cooling process from approximately 15 s onwards. The experiment was carried out several times to obtain the acting compressive forces whereby an average value of \(-\)95.6 N \(\pm\) 6.9 N was reached (\(n=3\)). It should be noted that the forces follow the description of resulting residual stresses during welding when it comes to changes from compressive stresses to tensile stresses over time [33]. Figure 8: Unhindered gap formation (\(\mathrm{v_{w}}=1\) m/min, \(\mathrm{P_{L}}=0.4\) kW): (a) Gap measurement via inductive probes; (b) High-speed recording of sheet edges at the end of the specimen at different times. Figure 9: Force measurement of a rigid clamping for an uncontrolled process (\(\mathrm{v_{w}}=1\) m/min, \(\mathrm{P_{L}}=0.4\) kW). It can be stated that tensile and compressive forces and gap formation behave differently along the weld seam, i.e., they are dependent on time and position. If the process is to be controlled, action must be taken accordingly at different times and at different positions.