Issue 52

A. Ahmadi et alii, Frattura ed Integrità Strutturale, 52 (2020) 67-81; DOI: 10.3221/IGF-ESIS.52.06 68 as predicted, at low frequency loading, there is no major difference between the results of both methods. K EYWORDS . Body-In-White; Inertia relief; Modal dynamic; Spot weld; Structural stress method. I NTRODUCTION ue to the competitiveness of the automotive industry, the production of high-quality vehicles is a necessity to sustain the fast-growing auto market. One of the main considerations in vehicle design is the durability of the components and the joints which reflects the quality of the manufactured product. The vehicle body is considered the main load-bearing component in a vehicle and therefore the durability of its components and joints is important. A vehicle Body-In-White (BIW) is referred to a stage in the production line where the body sheets are joined together and the main structure of the vehicle is formed. The BIW does not include the closures i.e., doors, fenders, hood, and trunk lid. BIW sheets are mostly joined by spot welds and a typical BIW contains about 5000 spot welds. Failure of these joints due to fatigue phenomenon changes the vibro-acoustic behavior of the vehicle, leading to unwanted noise and vibrations felt by the passengers [1, 2]. Moreover, as it was demonstrated by Xiang et al. who analyzed a spot welded thin-walled component, failure of some spot welds degrades the crashworthiness behavior of the structure [3]. Therefore, knowledge of the BIW fatigue behavior is an important consideration for auto manufacturers. Because of the time consuming and costly nature of experiments (like using the full body fatigue test rigs [4]) and also lack of prototypes in the early stages of the vehicle design, Finite Element Method (FEM) is widely used for stress and fatigue analysis of vehicle components. There are two main methods for the numerical stress analysis of the BIW. The first is the quasi-static method that is mainly implemented using inertia relief approach. In brief, the inertia relief method uses the rigid body accelerations and the d’Alembert’s principle to analyze an unconstrained structure like the BIW. An example of this method is the research done by Wen and Du [5] who analyzed the fatigue behavior of a mini car body. A similar research was also done on a truck cab by Chen et al. [6]. There are also other studies on the vehicle body and its parts which used the quasi-static method [7-9]. Although this method of analysis is quite easier and faster than other methods [10], it has the big disadvantage of neglecting inertia effects. There are many parts attached to the BIW like the battery, some parts of the powertrain, the seats, the doors, etc. Since these parts are composed of highly concentrated masses, near their mounting locations, they may have very low natural frequencies which lie in the loading frequency spectrum and cause resonance [11]. To take the resonance and inertia effects into account, dynamic methods should be utilized in the analysis. Dynamic analysis of the linear systems with high degrees of freedom like the BIW is mainly done using mode-based dynamic solvers since other methods are not economical in such a case. In brief, the modal dynamic method uses the superposition of the structure’s mode shapes to calculate the response of the structure under loading. There are multiple examples in the literature that have applied this method for the analysis of vehicle components. For example, Farrahi and Khalaj used the modal dynamic technique (also known as modal superposition method) to analyze the durability of the rear spindle of the vehicle [12]. Wang [13] and Jordan [14] used this method for the analysis of the vehicle BIW from the fatigue point of view and Lu et al. [15] used the same method on a high-speed train bogie frame. Also, in a more thorough analysis [16], the vehicle body was analyzed using modal dynamic method and the regions having a high probability of fatigue failure were successfully modified to mitigate the stress intensity. In addition, there were other hybrid methods which utilized both static and dynamic analyses simultaneously [17, 18]. Based on the results published in a previous research by Anvari and Beigi [19], the use of quasi-static method for the stress analysis of the BIW is only allowed if the loading frequency is less than 10% of the first nonzero natural frequency of the structure. Although the loading applied in their research was fully reversed sinusoidal force at a specific node (not a real loading condition), it gave a good understanding that how much difference inertia effects can make in the results. In order to have a finer conclusion on the effect of incorporating inertia into the durability analysis of BIW, the present research is aimed at comparing inertia relief and modal dynamic analyses formulations and their results for the fatigue life of the vehicle body. To this end, the Multi-Body Dynamics (MBD) model of the full vehicle is driven on different roads that are standardized by the International Organization for Standardization (ISO) at three different speed regimes and the D