Finite Element Simulation (FEA) is an engineering analysis technique used to study and predict the behavior of physical systems through numerical simulation and computation. It is based on the finite element method, in which a complex real physical system is partitioned into many small elements (finite elements), which are then analyzed using mathematical methods. These elements can represent a variety of structures, materials and physical phenomena, such as solids, liquids, gases, heat, electricity, magnetism, and so on. By numerically calculating the interactions and boundary conditions between these elements, finite element simulation is able to model the behavior and performance of real systems.

Finite element simulation is commonly used in engineering, science, and design fields to solve various problems such as structural analysis, heat transfer, fluid flow, and electromagnetic field analysis. It helps engineers and scientists to evaluate different design alternatives on computers, optimize product performance, reduce the need for prototyping and testing, lower development costs, improve reliability, and reduce potential risks. This technique has a wide range of applications in modern engineering and scientific research.

Finite element simulation methods are widely used in the design and calibration of fastened connection structures. The engineering value of finite element simulation of bolted connection structures lies in the fact that it allows engineers to evaluate connection performance through numerical simulation, reduce actual testing costs, improve design reliability, optimize bolt size, material and structure, reduce manufacturing costs, ensure the safety and durability of the connection, drive the efficiency and quality of engineering projects, and significantly reduce the number of major engineering accidents due to inadequate performance of the connection structure.

Finite element simulation requires a high level of meshing, and a good finite element mesh should conform to and have the following characteristics:

1) The unit shape is simple and the unit characteristic equations are easy to solve;

2) The mesh model should be as accurately as possible the same as the original defined domain;

3) Under the premise of guaranteeing accuracy, the number of units is reduced as much as possible to ensure the efficiency of solving.

However, due to the complex contour of the bolt, its difficulty in finite element modeling is much higher than that of general mechanical structures, so the bolt has to be simplified in simulation analysis. With the development of modeling and simulation technology, the finite element analysis model of threaded components has undergone many evolutions in recent decades:

1) Beam unit bolt model: The use of beam unit to simulate bolts is more applicable in many cases because of the simplicity of the model, the simple definition of the contact, and the ease of convergence. The beam unit simulation bolt cannot simulate the tightening process of threaded fastening connection and the rotational loosening behavior under external load.

2) Unthreaded Cylinder Model: The bolt and nut are modeled as "I" shaped entities with simple structure, easy and fast modeling and meshing. The unthreaded cylinder model is also unable to simulate the tightening process and loosening behavior.

3) Axisymmetric mesh model (2D model): Used to calculate the stress concentration at the bottom of threaded teeth, axial distribution of bolts, etc., but cannot simulate the tightening process and loosening behavior, and cannot present the contact behavior of threaded meshing surface.

4) Axisymmetric mesh model (3D model): The 3D bolt and nut model without rising angles is meshed and easily processed into regular hexahedral cells. The three-dimensional finite element model of a threaded component without a helical rise angle can be used to calculate the non-rotational loosening behavior of a bolted joint structure. However, the model has no helical rise angle and no helix, and is actually multiple turns of parallel tooth bodies that are not true threads.

5) Tetrahedral mesh model: The tetrahedral mesh model of threaded parts can be divided automatically in the finite element software, but it is difficult to control the mesh density in different areas, and the number of cells is larger, which leads to a larger amount of calculation. Using tetrahedral mesh to divide the threaded part model, it is difficult to ensure the mesh quality at the bottom of the threaded teeth and the precise contour of the threaded teeth. Most importantly, the tetrahedral mesh model will have the problem of difficult convergence, and the calculation accuracy is not high.

6) Bound modeling (threaded tooth and substrate bound modeling): The threaded tooth mesh is formed by scanning a 2D screw thread mesh along a helix. The threaded teeth and the substrate are meshed separately and bound together. However, the threads and the substrate of this model are partially processed by binding, and the force and displacement are not well transferred between the nodes at the interface.

7) Parametric accurate modeling method: The core of this method is to analyze the thread geometry and obtain the thread profile segmentation function, so as to get the finite element model of the threaded part with accurate geometry and high-quality hexahedral mesh. The model is highly consistent with the actual thread profile, and can accurately simulate the tightening process of threaded parts, the evolution of the contact state of threaded meshing surfaces, and the loosening behavior of bolts, which is the most effective finite element model for the study of the failure mechanism of threaded fastening connection structures and the design checking at present.

VDI 2230 Part II divides the finite element models of bolted joints into four levels: Level 1 models model only the components and do not consider the body of the bolt; Level 2 models consider the bolt as a wire element, i.e., as a tensile member, a beam unit, or a spring unit; Level 3 models the bolt as an equivalent solid model, i.e., a bolt finite element model that does not consider the threads; and Level 4 models are the highest level and represent a detailed model of the bolt that includes threads and contact conditions in all contact surfaces and accurately represents every detail of the bolt. Level 4 models are the highest level and represent detailed modeling of the bolt, including threads and contact conditions in all contact surfaces, and accurately representing every detail of the bolt The models generated by Thread Designer software are fully compliant with the requirements of the VDI2230 guideline for Level 4 models.

VDI 2230 Part II states for the four-stage model that the calculated stresses of the four-stage model FEM meet the definition of nominal stresses required for the design concepts discussed in VDI 2230 and can be used to determine nominal loads. Furthermore, the local loads at each position of the thread can be determined and evaluated by means of the corresponding local verification concept. In addition, the minimum thread fit length is obtained by means of a four-level model taking into account elasto-plastic material properties.The evaluation of the accurate finite element model of bolts in VDI 2230 Part II can be summarized as a more accurate alternative to VDI 2230 for the design and verification of bolted joints.

The advantages of accurate finite element modeling of bolts for engineering applications are:

1) It can simulate the tightening process, study the influence of tightening method, tightening tools, bolt parameters, etc. on the tightening process, and obtain the best tightening strategy with high speed, high efficiency and low cost.

2) Simulate the loosening behavior to facilitate the study of bolt loosening mechanism and anti-loosening measures.

3) Calculate the stress concentration of the thread, determine whether the static strength, fatigue strength, etc. meets the standard, and reduce the risk of the project.

4) Supplement or replace VDI 2230 guidelines for bolted joint design and calibration.

The use of finite element models of threaded parts with highly consistent contours to simulate the failure behavior of threaded connections is an effective means to propose targeted anti-loosening measures and improve reliability. However, the parametric accurate modeling method of thread model still belongs to the frontier technology in the field of fastening connection research, and the mesh cannot be divided manually, which needs to be realized with the help of computer program. At present, the relevant domestic academic research is still concentrated in the Southwest Jiaotong University, Xi'an Jiaotong University, Beijing Institute of Technology, Dalian University of Technology and other individual research institutions, the algorithms of the institutions are strictly confidential, at the stage of technological monopoly, and the formation of a number of "technology islands". This has also led to the delay of academic research results can not be realized, should be widely used in the field of engineering and practical advanced technology for many years only exists in the top journal papers.

Localized accurate finite element model of MJ aerospace threads

Significance of accurate finite element simulation of bolted joints

The stress distribution and axial load carrying ratio distribution of bolted connection is one of the most important results in bolt finite element calculation. Through the calculation and evaluation of this parameter, we can analyze in detail the stress state of bolts under various loading conditions and different thread turns, determine the weak points of bolts, and look for ways to make the load carrying ratio more balanced, so as to optimize the threaded connection in a targeted way.

Equivalent force distribution on threaded surfaces under different loading forms

Through the friction dissipation energy of each ring of threaded teeth, contact state, stress distribution and bearing ratio, preload analysis of the comprehensive discussion, you can be the actual service conditions of the failure of the bolt failure analysis, locate the failure factors, determine the weak parts, so as to target the proposed improvement measures.