Bolted joints structures are critical fastening components widely used in mechanical equipment. Under long-term loading conditions, the bolted joints interface generates strong nonlinearities within the system. The nonlinear stiffness inside the bolt leads to changes in the stiffness of the whole system. This affects the dynamic characteristics of the whole system. It brings challenges and difficulties to the performance prediction and reliability assessment of the equipment. A cross-scale theoretical model study based on the microscopic contact mechanism can provide a more comprehensive understanding and cognition of the degradation behavior of bolted joints interfaces. The current development status and deformation process of asperity models are summarized. The research progress of statistical summation model and contact fractal model based on microscopic contact mechanism is analyzed. The experimental methods for parameter identification of connection interfaces are reviewed. The study of numerical modelling of bolted joints structures from the surface contact mechanism is briefly described. Future research directions for cross-scale modelling of bolted joints structures are outlined.

In this study, based on the Iwan model, the connection interface of the bolted joint structure subjected to lateral loads was simulated and comparatively analyzed. Commercial finite element software was used to model the bolted joint structure. Monotonic lateral loads and cyclic displacement loads were applied to the model. The changes in the preload force of the bolted connection structure, as well as the changes in the sticking zone and stress state of the connection interface, were analyzed, and the loading results of monotonic load and cyclic displacement load were compared. The results show that the contact interface stress decreases with the increase in displacement load, and this increase is also a nonlinear relationship, which is approximately in phase with the trend of the contact surface slip curve. The amount of contact surface stress loss and the amount of preload loss are not directly related to the magnitude of the initial preload, regardless of the loading conditions. The contact surface is also circular under any form of displacement loading, whether it is stressed or slipped. The amount of preload loss is proportional to the amount of bolt compression for that variable.

Stress concentration often occurs around bolt holes in load-bearing joint structures of large complex equipment, ships, aerospace and other complex machinery fields, which is an important mechanical factor leading to the failure of joint structures. It is of great engineering significance to study the phenomenon of stress concentration on connected structures for the safety of large and complex equipment; meanwhile, the layout of bolts seriously affects the stress around holes. Many scholars have studied the layout optimization of multi-bolted structures through experiments and simulations, but few algorithms have been applied to the layout optimization of bolted structures. And most of the studied types of multi-bolt structures are symmetrical. Therefore, in this paper, the gray wolf algorithm is used to optimize the layout of nickel steel plate connectors with a bolt layout in triangular position, and the optimal objective function is found based on the hole circumferential stress of the nickel steel plate, maximum shear stress of the bolt and bending stress of the nickel steel plate. Comparing the optimal values obtained by the fruit fly optimization algorithm, particle swarm optimization algorithm, gray wolf optimization algorithm, multiverse optimization algorithm and wind driven optimization algorithm, the accuracy of selecting the gray wolf algorithm for optimization is verified. A multi-bolt connection structure model was established in ABAQUS, and the surface stress before and after optimization was compared to verify the correctness of the gray wolf algorithm applied to the structure layout optimization of the nickel steel flat bolt connection. The results show that under the force of 15 KN, compared with the original bolt structure layout, the optimized upper side nickel steel plate bore peripheral stress is reduced by 73.1 MPa, and the optimization rate is 24%; bolt stress is reduced by 47.7 MPa, and the optimization rate is 12.5%; when the load is less than 18 KN, the optimization effect of both the upper nickel steel plate and bolt group is more than 10%. When the load is greater than 18 KN, the optimization effect is reduced, and when the load is greater than 21 KN, the nickel steel plate has exceeded the yield limit. Due to the existence of fixed constraints, the optimization of the lower nickel steel plate is not obvious. The results of this study can provide data and theoretical support for the layout optimization of the nickel steel flat bolt connection structure, and help to improve reliability analysis and health monitoring in complex assembly fields such as large complex equipment and aerospace.

Engineering equipment is an important material foundation for supporting national defense security and promoting the development of the national economy. Large and complex mechanical equipment has a complex structural composition and a large number of components, with a great deal of connection structures such as bolts and flanges inside. Affected by long-term loading conditions, phenomena like the degradation of contact stiffness will occur at the connection interfaces between components. This, in turn, will affect the dynamic characteristics of the entire system and seriously impact the reliability and performance of the equipment. By combining the microscopic contact mechanism with the cross-scale modeling method, the proposed contact framework can study the contact behavior of the connection interfaces more comprehensively. This paper classifies and summarizes the research status of the asperity contact model from the perspective of geometric modeling, classifies and summarizes the research status of the statistical contact model of rough surfaces according to different height distributions of asperities, and looks ahead to the research directions of the cross-scale model of connection structures in the future.

In order to study the influencing factors of friction coefficient in an M-B model, based on the basic model of fractal theory, the distribution function and probability distribution density of the micro-convex body truncation area are derived by using mathematical and statistical means, and a new model of critical truncation area and friction coefficient in fractal surface contact process are proposed. Considering the differences between the actual contact area and the truncated area during plastic deformation of the micro-convex body, a correction factor is introduced. Focusing on the mechanism of the elastic-plastic transition phase, and finally a friction coefficient model based on the fractal dimension, the normal force and correction factor is derived. Finally, the friction coefficient of fractal surface is simulated and verified by taking nickel as an example, and it is proved that the new model is correct in predicting the change trend of friction coefficient in the M-B model.

Bolts have the advantages of simple installation and easy removal. They are widely applied in aerospace and high-speed railway traffic. However, the loosening of bolts under mixed loads can lead to nonlinear decreases in pre-loading. This affects the safety performance of the structure and may lead to catastrophic consequences. Existing techniques cannot be used to monitor the bolt performance status in time. This has caused significant problems with the safety and reliability of equipment. In order to study the relaxation law of bolt pre-loading, this paper carries out an experimental analysis for 8.8-grade hexagonal bolts and calibrates the torque coefficient. We also studied different loading waveforms, nickel steel plate surface roughnesses, tangential displacement frequencies, four different strengths and bolt head contact areas of the bolt, the initial pre-loading, and the effects of tangential cyclic displacement on pre-loading relaxation. This was done in order to accurately predict the degree of bolt pre-loading loosening under external loads. The laws are described using the allometric model function and the nine-stage polynomial function. The least squares method is used to identify the parameters in the function. The results show that bolts with a smooth surface of the connected structure nickel steel flat plate, high-frequency working conditions, half-sine wave, and a high-strength have better anti-loosening properties. Taking 5–10 cycles of cyclic loading as a boundary, the pre-loading relaxation is divided into two stages. The first stage is a stage of rapid decrease in bolt pre-loading, and the second stage is the slow decrease process. The performance prediction study shows that the allometric model function is the worst fitted, at 71.7% for the small displacement condition. Other than that, the allometric model function and the nine-stage polynomial function can predict more than 85.5% and 90.4%, which require the use of least squares to identify two and ten unknown parameters, respectively. The complexity of the two is different, but both can by better indicators than the pre-loading relaxation law under specific conditions. It helps to improve the monitoring of bolt loosening and the system use cycle, and it can provide theoretical support for complex equipment working for a long time.