# Development of a Numerical Model of the Hot Air Staking Process Based on Experimental Data
## 2 Materials and Methods  
For the experimental investigations a hot air staking machine of the company bdtronic GmbH (Weikersheim, Germany) (type B2000-H) was used. Figure 2 shows the schematic illustration of the hot air staking process, consisting of four process steps. In step 1 the mating parts are inserted in the part mounting and the hot air pipe moves to its work position. In the work position the hot air pipe surrounds the rivet pin. In the following step 2 the hot air flows in the wall of the hollow cylinder down to the bottom, leaves the wall and flows upward in the middle of the hot air pipe. This fact leads to a heating of the rivet pin. After a sufficient heating time, the coaxial mounted forming tool forms the rivet heat by moving to the top of the upper mating part. Subsequently, the cooling starts by haven a cool air flow to the top of the forming tool (step 3). In step 4 the forming tool as well as the hot air pipe move back to their home position.  
Figure 2: Schematic illustration of the hot air staking process consisting of four process steps.  
The plastic material for all investigations was polypropylene (PP), type Moplen HP501 H (manufacturer Lyondell-Basell, Rotterdam, the Netherlands), which has excellent properties for structural analysis by microscopy to investigate the heating and forming behavior. The rivet pin has a diameter of 3.0 mm and a length of 10.8 mm. By using an upper mating part of steel X5 CrNi18-10 (1.4301) its properties are not changed by the staking process. The thickness of the mating part is 3.0 mm, which leads to a constant protruding length of the rivet pin of 7.8 mm. The rivet head had the common industrial design of a hemisphere with a diameter of 6.0 mm, and was adapted to the protruding volume of the rivet pin. In addition, the following (optimized) process parameters were used for the experimental analysis:  
* Air temperature T\({}_{\text{A}}\) = 300 \({}^{\circ}\)C
* Air flow rate Q\({}_{\text{A}}\) = 75 L/min
* Variation of the heating time t\({}_{\text{E}}\) = 1 s/2 s/3 s/5 s/8 s
* Joining force F\({}_{\text{J}}\) = 80 N
* Cooling time t\({}_{\text{C}}\) = 12 s  
To investigate the heating and forming behavior, transmitted-light microscopy was used. Therefore, the rivet pin and rivet joint were prepared as an extracted thin cut (thickness 10 \(\upmu\)m) in the center plane of the rivet pin. By using a polarization microscope (Olympus BX51, Olympus Corporation, Shinjuku City, Tokyo, Japan), the melted and recrystallized area was measured (software ImageJ, National Institutes of Health, Bethesda, Rockville, MD, USA) and characterized the melt formation during heating, and the materials structure after forming, respectively. In addition, the necessary thermal material parameters for thermal capacity were determined experimentally. To determine the temperature-dependent thermal capacity, DSC (differential scanning calorimetry) measurements were carried out in accordance with DIN EN ISO 11357-1 with a dynamic heat flow differential calorimeter of type Q2000 (TA Instruments, New Castle, PA, USA) in the temperature range from 10 to 320 \({}^{\circ}\)C. The temperature-dependent thermal conductivity was taken from the Moldex 3D (CoreTech System Co., Taiyuan St. Zhubei City, Taiwan) software material database.  
Furthermore, a numerical process simulation was used to increase process transparency. Therefore the software simufact.forming, (simufact engineering gmbh, part of Hexagon's Manufacturing Intelligence division, Hamburg, Germany), was used. With the help of the simulation, the material flow during staking was observed, depending on different heating times.