## 5 Discussion  
The acting force in the seatbelt buckle cable is divided into \"n\" forces that act on the balls, kept equidistant through a special cage, all around the tube generator, as shown in Figure 5. The present analysis considers the force in the cable equally distributed on the number of balls. The acting time of the force in the cable differs depending on tests, considering the degree of compression of the spring, but we can say that it is approximately 10 ms, as shown in Figures 9-11. The deformation produced in the pretensioner tube is two-fold, under the action of both normal and tangential forces, a fact that is established due to the geometry of the component parts and the acting force in the cable. The indentation left by a ball in the tube takes the form of a drop. The marks left by the balls on the tube generator were compared, and deviations of up to 10% of the measured diameters were found. For the proposed mathematical model, during the action of the force, it is considered that only the tube deforms plastically. The accuracy of the obtained results can be influenced by the characteristics of the materials in contact. Figure 9: Area of interests for force acting on buckle cable, sample test 11. Thus, elastic deformation in the spherical indenter can cause prediction errors of up to 12%, as shown in [50]. [PERSON] [51] has suggested that the yield strength of a spherical indenter should equal 2.5 times that of the flat indenter to prevent the plastic deformation of the indenter. For the steel ball, \(S_{y}\) is approximately 650 MPa, and for the tube material, it reaches 350 MPa [52]. Therefore, elastic deformations that produce errors on the size of marks may occur. Eleven experimental tests were performed, with various action forces in the shutter cable. In the case of test no. 4, shown in Figure 10, the values cannot be used because of the displacement/movement of the tube while the force was acting in the cable. The pretensioning tube did not remain firmly fixed; thus, the force shows two humps, unlike the other cases, as shown in Figure 11.  
The values of the forces measured and the dimensions of the marks are given in Table 2.  
Figure 11: Cable force variation for all tests. Figure 10: Cable force sample for test 4. After performing the tensile tests, in the first step, the dimensions of the spherical indentations obtained through the virtual CAD-3D model were compared with those obtained after the experiments. In Figure 12, the values of the diameters that define the elliptical shape of the indention on the curved surface, together with their two trendlines, are represented. In Figure 13 we have a sample of shape and diameter measured using the microscope. Following the experiments, the shape of the indentations marks in the tube was predominantly close to the diameter \"\(d_{2}\)\" of the indentation, their size fitting in the corridor defined by the two trendline curves. From the microscopic analysis, it was not possible to highlight the elliptical shape of the deformation, most probably due to the deformation process under the action of a normal force, as well as of the tangential one. Thus, a good correlation is observed. The ratio between theoretical and experimental, as a percentage between 95.7% and 101%, observed probably due to the measurement errors of the indentation diametsprompted us to proceed to the stage of determining the forces. The values of the indentation depth were determined, according to Figure 3, by a calculation with relations (8) and (9), or with the CAD-3D model presented in Section 3.4. Figure 12: Values of diameter indentation for 3D model and experimental data. Figure 13: Sample of diameter measure based on experimental data. In the next stage, the normal forces with which the balls act on the cylinder were compared by using three methods:  
* The mathematical model proposed in this study;
* The \"Hardness\" model;
* The Komvopoulos-Ye model, described in [27; 38; 39].