*Article* **Identification of Pre-Tightening Torque Dependent Parameters for Empirical Modeling of Bolted Joints**

**Yu Tian 1, Hui Qian 1, Zhifu Cao 2, Dahai Zhang <sup>3</sup> and Dong Jiang 1,\***


**Abstract:** The vibration characteristics of bolted structures are crucially affected by the pre-tightening torque. An approach for identifying the pre-tightening torque dependent stiffness parameters of bolted joints is proposed in this paper. Firstly, the interface of the bolted joint is characterized by the thin layer element with the isotropic material property, and the parameter value of the property is assigned relative to the distance from the center of the bolt; the influence of the bolt is ignored. Secondly, the model updating method is adopted to identify the parameters of thin layer elements using experimental data, and modal data under different values of pre-tightening torque in the range of 2 N·m~22 N·m are obtained; the torque wrench is used to determine the pre-tightening torque in the modal test. Finally, after identifying the material parameters using partial experimental data on pre-tightening torque range, the empirical equation of the interface parameters with the pre-tightening torque parameter is obtained by curve fitting and the rest of the experimental data are used to verify the accuracy of the fitted empirical equations. It is concluded that this method can obtain all the parameters of the equivalent thin layer elements within a certain range of pretightening torque, which can provide a reference for the empirical modeling of bolted structures, improve modeling efficiency and reflect the characteristic performance of real structural dynamics.

**Keywords:** bolted joints; parameter identification; thin-layer element; pre-tightening torque; contact interface
