## 5 Discussion
From the experimental tests, we have the force in cable \"\(F_{\mathit{cable}}\)\" and also the diameter \"\(d\)\" of the indentation in the tube. In the mathematical model from Section 3.1., by using relation (1) to (5), we introduce as an input the experimentally obtained \"\(F_{\mathit{cable}}\)\" force, and thus we can determine the normal force \"\(N_{1}\)\" and \"\(N_{2}\)\". The ball acts with normal force \"\(N_{1}\)\" to produce these deformations in the tube; in this way, we were able to find correlation between \"\(F_{\mathit{cable}}\)\",\"\(N_{1}\)\", and \"\(d\)\". In the models described in Sections 3.2 and 3.3, we have as an input from the experimental data the diameter \"\(d\)\" of the impressions, and with the given materials' properties, we determine the normal forces \"\(N\)\" that produce deformations. So, we have another two set of points named \"Hardness\" and \"Komv.-Ye\". For these datasets, we determined some linear regressions, as shown in Figure 14.  
The force in the cable, obtained experimentally, was calculated as the average of the values over its range of action (see Table 2). These values cover the 1000-2400 N range, mostly up to the limit in which the effort limiter in the seatbelt retractor would come into operation. The normal force with which the ball acts on the tube is determined in the proposed mathematical model, starting from the force value measured in the belt buckle cable. The force values are lower than those determined by the \"hardness\" method. There is a good grouping of the values along a trend line (blue line). The coefficient of determination (R\({}^{2}\)) is 0.977, as shown in Figure 14.  
In the model described in [27], the value of the normal force that produces the indentation has more grouped values compared to the trend line (red line); in this case, the  
Figure 9:0 Normal forces resulted from hardness, elastic–plastic model, and experimental data, depending on indentation diameter. coefficient of determination (R\({}^{2}\)) is 0.996, shown in Figure 9:1 The values of the forces are the lowest, by comparison with the other models wherein they were determined. The dimensionless factor \(Q\) previously described is within the range of \(21<Q\leq 400\), so the contact occurs in the elastic-plastic medium deformation. Considering the proposed model and the one in [27], the ratio between the normal forces that deform the tube is between 0.99 and 1.134. Comparing the two trendlines, it is found that they are theoretically parallel, showing the same tendency, with the difference between the values of the forces slightly increasing towards the small values of the indentation diameter and decreasing towards the larger diameters. The average deviation between the two trendline curves is 7.8%, so it is considered that the proposed model is valid and the force in the cable can be determined depending on the normal force that deformed the tube. The normal strength values, obtained through the \"hardness\" method, are the highest, with variations of 32-40% compared to those resulting from the Komvopoulos-Ye method. Moreover, this is considered to be outdated in contact mechanics for the purpose of determining the plastic deformations of materials [27] and, therefore, we do not consider this method to be useful for the present case. The technical or judicial expert in traffic accidents can have easy access to the safety belt pretensioning system. In the case of a PBP or PLP type system, data can be obtained about the size of the indentations that the balls of the anti-return system carry out in the tube. Based on a regression curve, the dependence between the force in the cable and the size of the mark can be determined.