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Detailed Modeling of Threaded Connections

December 13, 2016 By: Peter Barrett

Threaded connections come in many forms, from screws to bolts to fitted pipes.  More than 300 billion fasteners are used in the US every year. Threaded joints are often the controlling design connection where failures may occur due to corrosion, fatigue, or excessive shear or pull out force. Standard screws and bolts are typically designed using vendor-prescribed force data without the need for detailed simulation. However, when accurate data is needed, engineering analysts must evaluate the trade-off of increased levels of complexity against increased simulation accuracy. This post provides comparisons of three connection modeling techniques to provide guidance in selecting the most efficient and accurate method needed for your analysis: 

1. No threads included, where bonded contact is used to model the thread connection.

2. Virtual threads modeled via modified contact normals with straight sided bolt-connector interface geometry.

3. Explicit modeling of the threads with surface-to-surface frictional contact.

No Threads Included

The simplest and most common method for modeling threaded connections is to ignore the threads. A straight circular shaft modeled with beam or continuum elements is the simplest and fastest model to solve. The connection surfaces can be modeled either using bonded contact or a flow through mesh. Significant computational efficiency is gained using a coarse bolt mesh and linear connection assumptions, since nonlinearities at the threads are ignored. Bolt pre-load can be included and stresses in the bolt head, shaft and flange can often be accurately obtained.

Virtual Threads

Virtual bolt threads can be used to increase the accuracy of the threaded connection simulation without the need of modeling the threads explicitly. With virtual bolt threads, contact and corresponding target elements are modified from pure radial contact to being aligned with the corresponding thread profile. Figure 1 illustrates the straight-forward user input required to implement this methodology in ANSYS Workbench. Contact and target element normals associated with the bolt/screw male and female threads are reoriented based on bolt thread pitch and spacing. This method can be used for both 3D and 2D axisymmetric models, including the effects of frictional contact. The added accuracy of this method can be seen by way of a better prediction of forces and stresses in the bolt, along with induced hoop stresses in the nut or other mating threaded component.  However, this approximation is only applicable for standard straight threads and small strains where the threaded connection does not undergo large deformations.

Figure 1: Virtual Thread Input used on Straight Radial Surface-to-Surface Contact


Explicit Thread Modeling

The most accurate, but also by far the most computationally expensive method, is to model the threads explicitly. Although 3D thread modeling is possible, in most practical problems, explicit thread modeling is limited to axisymmetric 2D models where the helix in the threads is typically ignored. A very fine mesh with fillets at the thread base are needed to capture accurate stresses and strains in the threads. Plasticity should also be included in the model since local yielding is common in the first few engaged threads.  The only limitation of this method is computational efficiency.

3D Comparison of Explicit vs. Virtual Threads

A comparison of explicit vs. virtual threads as part of a 3D pre-loaded connection is illustrated in Figure 2. For this example, similar peak stresses in the bolt is predicted between the virtual and explicit modeling methods. Even with a reasonably fine mesh in the thread region, as required using the virtual bolt section method, this method still yields similar bolt stresses in 1/10 the analysis time!

Figure 2: Stress Comparison Between Explicit & Virtual Thread Modeling


Bolt Pull-Out Modeling Comparison

The second example illustrates a limit load bolt pull-out simulation, where the three modeling methods (bonded contact, virtual and real threads) are compared. Figure 3 illustrates the three models used in a 2D axisymmetric bolted connection, along with a comparison of the final contact status along the interface. After the pre-load step, a displacement based axial loading on the flange is used to compute the pull-out response. For computational efficiency, all the nodes are coupled (see green line in Figure 3) and pulled to compute the limit loading force vs. deflection resistance of the threaded connection.

Figure 3: Comparison of Thread Models and Contact Status along Interface at Max Pullout Force


Figure 4 compares the force vs. deflection response for the three modeling techniques.

  • The fixed constraint model provides a reasonable estimate of the force vs. deflection response, but slightly overestimates the bolt force, and cannot capture local thread slippage and subsequent thread separation.
  • The virtual threads provide a very accurate representation of the bolt pull-out force prior to thread slipping, but cannot capture the separation and loss of strength.
  • The explicit thread modeling captures the thread stripping response and separation, but is much more computationally expensive, requiring a much more detailed model, combined with many load steps to overcome convergence challenges as the threads begin to slip when the limit force is approached. The termination of the blue curve in Figure 4 indicates where separation has occurred.


Figure 4: Comparison of Force vs. Deflection of Axisymmetric Bolt Pull-Out Simulation


All three methods illustrated provide value in modeling threaded connectors. I always recommend starting with a simple model and only adding complexity, such as explicit thread modeling, if warranted.