# Finite Element Simulation of HELICOIL(r) Inserts
## 1 Introduction  
HELICOIL(r) inserts are a type of threaded insert, which are typically used to repair damaged threads or to increase the load-bearing capacity of a bolt connection for softer materials. The insert allows for a better stress distribution in the threads and, thus, an increase in the load-bearing capacity of the connection [1]. This system is suitable for connections which are often disassembled, and where the thread may be damaged by wear. The application range of threaded inserts is wide; however, in our case it is used in robotics, for the design of manipulator arms [2] (see Figure 1). Figure 1: The use of HELICOIL® inserts and the problem background. Experiments and simulations with HELICOIL(r) inserts have been described in a relatively small number of articles. In [2], tension experiments with different force-time dependences have been presented and, for the simulation Finite Element Analysis (FEA), the MSC Marc software [3] was used. HELICOIL(r) inserts are simulated using a so-called cohesive zone, interpreted as a part of the body that contains the threads and the threaded insert. The cohesive zone is modelled as a type of contact. In [4], experiments based on compression and torsion tests have been published. In addition to experiments (e.g., tightening tests, crash load tests, strength tests), the use of Finite Element Analysis (FEA; Abaqus, simplified with axisymmetry) has been presented in [5]. Another procedure to reduce the computational complexity has been presented in [6]. FEA is used for the simulation of one thread and, for the simulation, the entire screw connection is applied as an interface to simplify the thread hypotheses. The cohesive zone model was developed to simulate damage in composite laminates [7]. At present, this model can be used in various software (FEA), as a type of element. So-called interface elements are available, for example, in MSC Marc [3] and ANSYS [8]. These elements connect two different bodies; in this case, a specimen and a screw. Simplistically, we can imagine that a spring (normal and shear orientation) is defined between two elements (one for the specimen and one for the screw). The stiffness varies depending on the relative position of the two elements. The behaviour of the spring is non-linear and is defined by an equation. The software implementation may vary. The behaviour of the interface (cohesive zone) can be represented by a bilinear constitutive equation [3, 8], an exponential model, or a linear-exponential model. However, while models have been developed for the delamination of composite laminates [9], no similar theoretical model has been published for HELICOIL(r) inserts. Contact elements [3] allow us to define the behaviour of the cohesion zone using a multi-linear curve. We assume that a multi-linear curve can be described by a set of parameters. The interface model parameters in [2] were determined by hand, and the paper did not include a more detailed analysis. In this paper, we use the Finite Element Model Updating (FEMU) approach to identify the interface model parameters. In particular, the Finite Element Model Updating (FEMU) approach is used to identify material parameters through a FEA simulation; see [10]. This approach has been used in several areas; see, for example, [11] (indentation test) and [12] (composite materials). For the identification of parameters in an interface model, the extended Kalman filter (EKF) has been used in [13]. Experiments and simulations of the behaviour of screws (with threads) can be found more frequently in the literature. Experiments using elevated strain rates with results have been presented in [14], and experiments with 2D simulations have been presented in [15]. 3D thread simulations have been presented in [16, 17]; for shear behaviour, see [18]. Screws are also used in biomechanical areas; see [19]. The measured (Force-Displacement) curves in this case were very similar to those of HELICOIL(r) inserts; see, for example, [2, 15].