## 4 Experimental Setup  
The experimental tests were performedon a test rig, as shown in Figure 8. A system with a spring was used to simulate the resistance of the human body and the force with which it acts on the safety belt strap with the body area (chest in particular). The PBP type pretensioning system was fixedly mounted, maintaining the angle that the pull cable of the closer has when mounted on the vehicle. The main geometric characteristics and properties of the materials are as follows:  
* The tube of the pretensioning system has an inner diameter of 18 mm;
* The ball of the anti-return system has a diameter of 3 mm;
* The material of the tube is carbon steel, ISO 3304-4 [45], with hardness HB 149;
* The ball is made of stainless steel X46 Cr13, ISO 3290-1 [46], with a hardness of 56 HRC. A HBM C9C--20 kN force transducer was mounted on the traction cable at a sampling frequency of 4800 Hz. In the first phase, the pyrotechnic system is triggered, which develops a pulling force on the seatbelt buckle cable. At this point, the displacement of the piston in the tube of the pretensioning system occurs. The second stage of the tests, in which the pretensioner is blocked and the marks left by the balls in the system tube appear, begins when the passenger's body (with the chest and pelvis area), due to the inertia and intensity of the impact, pulls the webbing; therefore, cable traction occurs with \"\(F_{cable}\)\" force. During the tests, the human body was replaced with a compressed spring. The energy accumulated is released upon decompression, and it subsequently acts on the pretensioning system, which, through the mounted anti-return balls, blocks the release (unwinding of the strap). In real accidents, this blocking is translated by preventing the passenger from moving from the vehicle towards the dashboard. The force in the spring can be adjusted by compressing its coils differently. The value of the maximum force that was developed by the spring in the seatbelt buckle cable during testing was between 2146 and 7858 N.  
The average values of these forces are given in Table 2. FMVSS208 [47] and FMVSS214 [48] regulations on frontal and side impacts of passenger cars indicate maximum limits for deceleration (60 g for frontal impact and 85 g side impact) at the level of the torso. Likewise, the ECE/96/27 regulation [49] indicates the force (2.5 kN) that occurs at the abdomen of the occupant of a motor vehicle. In reference [9], also, the values of  
Figure 7: Shape of indenters on both flat and cylindrical surfaces (**a**); image size increased on the penetration depth of the spherical indenter in the virtual model (**b**). the car body decelerations encountered in crashes of competition vehicles are indicated, mentioning values of over 20 g in many cases. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**No. Test**} & \multirow{2}{*}{**Force by [17]**} & \multirow{2}{*}{**Force by**} & \multirow{2}{*}{**Force by**} & \multirow{2}{*}{**Mathematical**} & \multirow{2}{*}{**Cable Force**} & \multirow{2}{*}{**Diameter**} & \multirow{2}{*}{**Depth from**} \\  & & & **Method** & **Model N1** & & **  
The force developed in this stage, \"\(F_{cable}\)\", acts on the occupant's chest and pelvis. If a certain value is exceeded, the seatbelt can trigger a limitation of the effort on the chest. The force values of the force limitation system (RLE) are set by the seatbelt manufacturer, depending on the vehicle manufacturer's requirements. The tension limiting force on the passenger's body, in most types of seatbelts used, can be constant, progressive, or degressive. The threshold value at which the RLE system is activated varies between 2 and 4 kN. In this way, less severe injuries may occur to the occupant's chest. After the traction test in the cable, the pretensioners were disassembled, and their tubes were sectioned in order to carry out a microscopic analysis on the impressions left by the balls.