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Accurate Modeling of Threaded Fastener Joints

Threaded fastener joints such as bolted joints, screw joints and stud joints are widely used in engineering practice. In these joints, it is important to correctly preload the fastener. When the joint is designed with the proper balance of joint and fastener stiffness, correct preloading reduces load fluctuation in the fastener and thereby increases fatigue life. In addition, correct preloading ensures there is no separation or relative motion between the clamped parts that could lead to leakage or fretting fatigue, respectively.

One difficulty is that the fastener is tightened by specifying the torque. If the parts are flat, the torque/preload response is linear and the analytical bolt equation applies. However, if the parts are bent or warped, as is often the case after welding, the torque/preload response is nonlinear and no analytical solution exists for this response. Another major problem with threaded fastener joints is self-loosening.

In this Tech Brief, we show how Hitachi Construction Machinery uses ADINA to determine the torque/preload response and the self-loosening characteristics of a bolted joint*.

In the first analysis, the torque/preload response is computed for the M12 bolted joint shown in Figure 1. Frictional contact is assumed between all contacting surfaces with a friction coefficient of 0.15. A rotation is prescribed to the bolt head and the corresponding preload is measured.





Figure 1  Schematic of M12 bolted joint problem


Figure 2 shows the mesh used for the nut and bolt. A fine mesh is required for the threads to minimize the discretization error. The ADINA mesh glue feature is used to transition from the fine to the coarse mesh.



Figure 2  Mesh used for the bolt and nut


Figure 3 shows the torque/preload response for the flat plate problem. The ADINA results correlate closely with the analytical solution, where the stair-step behavior is due to the contact force needed to overcome the discretization error of the threaded mesh as the bolt rotates. The finer the mesh, the smaller the stair-steps observed in the results.

The flat plate torque/preload problem shown in Figure 1 was used to validate the bolt model. Once validated, ADINA can be used to perform a thermo-mechanically coupled analysis to determine the bolt torque/preload response for a warped assembly.





Figure 3  Torque/preload response of an M12 bolt between two flat plates

In the second analysis, ADINA is used to determine the self-loosening characteristics of a bolted joint. In this model, the bolt is first preloaded, and then a prescribed sinusoidal transverse displacement is applied to the top plate while the bottom plate is fixed.

Figure 4 shows the bolt rotation for 4 cycles of transverse displacement. It was found that a cyclic bending moment due to the transverse load is responsible for the self-loosening. Using the insight obtained from the analysis, engineers were able to significantly reduce self-loosening in their designs.




Figure 4  Bolt rotation for 4 cycles of transverse displacement

This Tech Brief illustrates how ADINA is a powerful tool for engineering design. The robust contact capabilities and the reliable element formulations make ADINA the preferred solution program for the most difficult problems in industry.


Keywords:
Threaded fastener joints, bolted joints, bolts, preload, torque, self-loosening, contact, friction, mesh glueing


*Courtesy of Mr. Hoshi from Hitachi Construction Machinery, Japan

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