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Significant effects of the bolt arrangement on the contact characteristics of bolted joints have been demonstrated, which are strongly associated with the dynamic performance of mechanical structures. However, the complexity of interfacial pressure distribution and the randomness of surface microtopography bring challenges to the accurate characterization of the multi-scale contact mechanics. Herein, a hybrid method combining fractal theory with the finite element method (FT-FEM) is proposed, which formulates the interfacial contact evolution in the elastic, elastic-plastic, and fully plastic stages. The complementarity of these two methods makes it possible to reveal the contact mechanism at both micro and macro scales and overcomes difficulties in reflecting the detailed joint contact characteristics in the overall dynamic model. To explore broader implications, FT-FEM is applied to the optimal design of bolt arrangement in an ultra-precision machine tool. Good agreements in calculation results and experimental data validate the accuracy of the proposed FT-FEM and the dynamic simulation. Replacing 15-M10 bolts with 19-M8 bolts results in a 2.9% enhancement in the contact stiffness and a 2.283% attenuation in the vibration response of the workpiece. The results also show that adjusting the bolt arrangement according to the working condition can strengthen the bolted joint effectively. FT-FEM contributes to solving contact problems in various mechanical structures, and the findings have wide practical applications in bolt arrangement optimization. [Display omitted] • A hybrid method for bolted joint modeling considering multi-scale contact mechanics. • New method combines improved fractal theory and finite element method. • Bolt arrangement optimization is carried out applying the method in dynamic analysis. • Experimental validation is done with bolted structures and machine tool. [ABSTRACT FROM AUTHOR]

The contact stiffness of the joint interface significantly affects the dynamic characteristics of a machine tool structure. Herein, an improved theoretical model is proposed to calculate the joint interfacial contact stiffness. This model is established based on fractal theory. To mitigate the plastic and elastic contact problems, the Stronge contact model is adopted to express the contact force in the plastic regime innovatively, whereas the elastic contact force is interpreted using Hertz theory; the domain extension factor is compensated to revise the microcontact size distribution. Furthermore, the rotational contact stiffness is first derived, which renders the contact model more comprehensive. A representative test structure is designed, and the contact model is validated by comparing the simulated contact stiffness with experimental results. The transfer matrix method for multibody systems is incorporated with fractal contact model to establish a dynamic model of an ultra-precision machine tool; this ensures that the dynamic characteristics of the machine tool can be predicted more precisely. Experiments involving a vibration response test and a modal test demonstrate the feasibility of the fractal contact and dynamic models. Based on these two models, the effect of the interfacial contact stiffness on the structural dynamics is investigated. As the preloads at two joints loosen by 15%, the maximum vibration displacements increase by 1.74% and 2.90%, respectively, indicating that the joint interface between the column and lathe bed is more sensitive. The procedure presented herein will facilitate the design and optimization of the complex structures. Image 1 • Stronge contact model and domain extension factor are adopted to improve the joint interfacial contact stiffness model. • The rotational contact stiffness is first derived and validated by a representative test structure. • Transfer matrix method for multibody systems and fractal contact model are used jointly to establish the dynamic model. • One method to ensure the structural stability is proposed by discovering the sensitive joints and restraining bolt loosening. [ABSTRACT FROM AUTHOR]