# FEM Modelling Approaches of Bolt Connections for the Dynamic Analyses of an Automotive Engine
## 1 Introduction
Particularly, one work compared a time-domain modelling of a whole joint and a frequency-domain node-to-node approach [11], whereas another compared multiple approaches (from detailed models to more simplified ones) to represent the behavior of single solid bolts under static and dynamic tension loading [12]. Bolt modelling approaches were also compared in [13], where a simplified modelling through 2D plates and bar elements (representing the bolts) and a fully nonlinear 3D modelling were presented. The effects of element mesh refinements on the nut and bolt contact surfaces, and types of contacts were analyzed and discussed. In [14], an improved modeling approach was developed that led to a good correlation with the experimental results and a good understanding of the underlying nonlinear mechanisms at the flange interface. The work in [15] investigated and compared four kinds of FEM modelling: a solid bolt model, a coupled bolt model, a spider bolt model and a no-bolt model. All the proposed models took into account of pretension effects and contacts between flanges to join and, among all these models. The solid bolt model (a 3D bolt with contact elements between head/nut and the flange interfaces) provided the most accurate responses compared with the experimental results. However, joining components through 3D models of bolts can be very expensive from the computational standpoint, especially for large structures, thus the coupled bolt model (a coupling between dofs of head/nut and flange), was reported as the best compromise between effectiveness and usefulness on accuracy and runtimes. For the sake of clarity, it is worth reporting that the case study was based on a large marine diesel engine, consisting of several parts connected by long stay bolts. Analytical models of bolted joint structures undergoing transient excitation were presented in [16]. A FEM based structural modelling of composite bolted joints was described in [17; 18]. In [19], four kinds of FEM bolt models were suggested for a structure with a bolted joint and, through a comparison with simple static experiment and modal test results, the effectiveness and usefulness of the bolt models were confirmed. Based on the Levenberg-Marquardt optimization algorithms, a more accurate calculation model of bolt head connection stiffness is proposed in [20], providing a universal assessment model for calculating the bolt head connection stiffness of various parameters. Similar to [15], the focus of this work is related to the industrial issue of modelling complex and large structures from the dynamic standpoint, with particular reference to an internal combustion engine (ICE) for the automotive industry. However, the presented investigation can be straightforwardly extended to further engineering areas. ICE dynamics are explored especially in the low frequency range and at low engine speeds, where the direct vibration transmission at the engine mounts represents a critical excitation mechanism [21]. Within this framework, this work presents three approaches for the modelling of bolts interconnecting the mechanical components of an ICE, already used in [7]. The ICE under analysis is a four-cylinder, four-stroke, with 1200 cc engine displacement and manual transmission, originally modelled with all its sub-components, i.e., exhaust system, brackets, mounts, alternator, intake manifold, etc. It is worth noting that such ICE model comprised more than 100 sub-components, all of them interconnected by means of several bolts with different sizes, tightening torques, pretension loads, etc. Therefore, the proper modelling of such connections not only has to be as accurate as possible, but also computationally affordable, of general validity and not prone to user error implementation. The rest of this paper is structured as it follows. Firstly, a description of the FEM model of the ICE is provided, highlighting the model simplifications (some components were discarded) adopted to speed up the analyses.