## 6 Conclusions  
To the best of our knowledge, no current study addresses the possibility of determining the forces in asaetbelt by analyzing the deformations in the pretensioning tube system. On-board sensors may provide information about the travel regime of a vehicle and may determine whether active or passive occupant protection systems are triggered. However, there is no on-board device to measure or estimate forces in the seatbelt. Specialized equipment used to determine these forces is only found in research laboratories where accidents can be reproduced, obviously at a highcost.  
The method used to analyze the deformations in the tube of the PBP or PLP pretensioning system provides information on the value of the force in the buckle cable, and implicitly the force in the safety belt, by inspecting these systems at a relatively low cost.  
We believe that amodel based on hardness measurement is not feasible for this type of analysis.  
The method herein proposedcan provide information for the analysis and reconstruction of traffic accidents by establishing the force with which the passenger's body acts on the seatbelt buckle at the time of impact. These data can help to further determine the intensity of the frontal impact and the forces on the occupant's torso, especially at the level of the ribcage. The determination of the forces with which the spherical indenter acts on the tube of the pretensioning system was carried out by using three models.  
The proposed mathematical and the elastic-plastic model show close results for normal forces that deform the tube, with the difference between the two models not exceeding 7.8%.  
The values of the two normal forces resulting from the two methods are considered to be equal for calculations. With this assumed approximation, and using the proposed mathematical model, starting from the normal deformation force, the value of the force in the cable may be determined.  
The maximum force in the cable, experimentally determined, varies between 2146 and 7858 N, depending on the precompression of the spring. The diameter of the impressions varies between 0.81 and 1.245 mm, and the depths of the impression are 0.0557 and 0.135 mm. Since the dimensionless factor was in all cases in the range of \(21<Q\leq 400\), the contact occurs in the elastic-plastic medium deformation.  
A polynomial regression function, with a coefficient of determination (R\({}^{2}\)) = 0.92, based on the results of experimental tests, has been proposed to establish the traction force in the seatbelt buckle cable, depending on the deformations in the tube of the PBP pretensioning system.  
Future research can be extended to other elements of the belt retractor component in order to determine the strength of the seatbelt webbing.  
We also aimto improve the proposed mathematical model by taking into account the dynamic aspect of the phenomena, as well as the properties of the materials.  
This research received no external funding.  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** Data is contained within the article.  
**Conflicts of Interest:** The authors declare no conflicts of interest.