PSI - Issue 46

A. Wetzel et al. / Procedia Structural Integrity 46 (2023) 10–16 Anna Wetzel et al. / Structural Integrity Procedia 00 (2019) 000–000

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the application of a wire rope as a connecting element between the seat-belt buckle and the car body is focused. Fig. 2. depicts a seat-belt buckle and the connecting wire rope.

Fig. 1. Wire rope used as link between seat-belt buckle and car body.

This application involves a reversed bending of the wire rope due to the usage of the seat-belt buckle by the car passengers. It is required that the wire rope fulfills its function as long as the vehicle is in operation. Therefore, the fracture force should not be reduced significantly by the fluctuating bending. Hence, a numerical fatigue analysis of the wire rope can help to determine the lifetime and to find the best combination of wire material and wire design. The observed load scenario deals with the fatigue behavior of wire ropes with an outer diameter of less than 10 mm. This represents a significant difference to the fatigue research of wire ropes for ropeways, building structures, and working machines. Another difference is the loading by a combination of bending and torsion. The degradation mechanism of such wire ropes is presented in Mouradi et al. (2016). Within this reference, the phenomena of fatigue will be addressed. Currently, empirical lifetime models are used c.f. Feyrer (2006), Jikal et al. (2020), and Onur et al. (2017), whereas the nominal stress of the wire rope is used as reference value. Hence, the stresses of the single wires are smeared into one nominal value for the whole rope. Weis (2015) states that a fatigue analysis based on empirical approaches does not enable an analysis of the inner stresses. Thus, the influence of different wire rope constructions or dimensioning parameters can only be considered by extensive testing procedures. Hence, a prediction of the lifetime of new materials or rope designs is not possible. Therefore, Weis (2015) presents a finite element model of a wire rope considering every single wire. Cao and Wu (2018), Kastratović et al. (2014), Erdonmez and Imrak (2011), and Wenzheng et al. (2017) present similar models. All these models use an analytical approach to describe the helical structure of each wire. Thus, only the geometry of the wire rope, not the stranding process itself, is considered. Judge et al. (2012) remark that careful consideration is necessary if statements about the resulting stresses in a wire rope are to be made, without taking the stranding process into account. They create the geometry of the wire rope, like Korhunov et al. (2020), by starting with all outer wires parallel and in contact with the central wire, then twisting all wires, including the central wire. This research aims to represent the strand as accurately as possible for future fatigue analyses. For this reason, the stranding process should be modeled as realistic as possible. Therefore, the modeling of the stranding of seven wires into a strand will be described. Additionally, a validation of the results with experimental data from tensile, bending, and torsion tests will be presented, as well as a comparison to a geometrical model. Fig. 2. shows a simplified scheme of a technical stranding process. In this example, seven wires are stranded to a single strand whereas the wire ① represents the central wire. The wires ② to ⑦ are forced into a helical shape around the central wire by the rotating stranding disk Ⓓ . The rotational speed n of this disk and the pull-out speed v of the strand determine the lay length of the strand. The point where the wires eventually encounter is called the stranding point Ⓟ . In the technical process, the wires are additionally supported at this point with a guidance, which simultaneously applies the lubricant to the wires. Each wire is spooled on a coil, which itself is integrated into the rotating body of the stranding machine. The tension force F at the end of each wire indicates the braking force of the wire coils in order to tighten the wires. One challenge of simulating this process is to figure out the process parameters. They vary from one rope to another, because they strongly depend on the machine, the wire material, and the rope design. Therefore, the parameters are rarely published and it is necessary to estimate most of them.