Shengao Wang

Bolt self-loosening under transverse vibration is governed by frictional contact and accumulated interfacial slip. In this study, transverse vibration tests were performed on M8 bolted joints under different initial preloads, displacement amplitudes, and excitation frequencies, with three tests per condition. Preload histories were analyzed using an operational four-stage framework comprising an initial abrupt decrease, lower-rate attenuation, a sustained acceleration interval, and a decelerating tail. N₂ denotes the operationally identified onset of sustained acceleration, rather than an instantaneous physical discontinuity. Stage-II/III rate contrasts vary between conditions and are modest for several 0.3 mm cases. A model with an independently estimated N₂ was favored over the specified alternative with acceleration starting at N₁, subject to the comparison assumptions and conditional uncertainty analysis. Quantitative comparisons use repeat-test statistics normalized to each test’s own initial preload. At 5 Hz and 0.3 mm, the mean cycle counts to 50% preload are 206.20 ± 25.35 and 116.25 ± 17.75 cycles for nominal initial preloads of 10 and 12 kN, respectively. At 10 kN and 5 Hz, reducing amplitude from 0.3 to 0.2 mm increases this milestone to 922.25 ± 97.15 cycles. For nominal 12 kN and 0.3 mm, the values at 5, 7 and 10 Hz are 116.25 ± 17.75, 137.34 ± 17.36 and 267.70 ± 32.00 cycles, respectively. Values are means ± sample SDs. In the illustrated records, an independently identifiable later acceleration interval was not observed within 1110 cycles at 15 kN (Group 5) or within 1405 cycles at 0.1 mm (Group 7). The finite element model reproduces the overall staged form but shows substantial transition-time mismatch and is used to interpret representative contact-state evolution. The four-stage framework is a conditional description of the tested histories; it does not establish universally discrete mechanisms or a stage sequence applicable to every condition.

Bolted flange joints are critical load-bearing connection components of complex mechanical equipment, whose service performance is dominated by the coupled evolution of bolt preload relaxation and interfacial stiffness degradation under long-term cyclic combined loads. Under cyclic transverse excitation, the contact interfaces experience successive full-stick, partial microslip and macroslip states, accompanied by embedding, creep and friction-induced wear, resulting in time-varying preload attenuation and the continuous degradation of joint mechanical properties. Distinguishing preload relaxation without nut rotation from rotational self-loosening is essential for revealing multi-bolt flange degradation mechanisms. This paper presents a systematic review of physics-driven constitutive modeling and degradation characterization of bolted flange connections. A unified classification framework for joint interface models is established, covering static friction models; velocity-dependent dynamic friction models; hysteresis stick–slip models, represented by the four-parameter Iwan model and Valanis endochronic model; and reduced-order equivalent joint models. The inherent differences between the Dahl model and LuGre model regarding the Stribeck velocity–friction characteristics are clarified. The representative models are comprehensively evaluated from the perspectives of physical interpretability, hysteresis reproduction accuracy, preload–degradation correlation and engineering applicability. A further comparative analysis is conducted of parameter identification bottlenecks of the Iwan, LuGre and Valanis models, focusing on multi-solution risk, anti-noise robustness and cross-working-condition transferability. Compared with single-bolt lap specimens, multi-bolt annular flanges exhibit prominent inter-bolt elastic interaction, circumferential contact pressure non-uniformity and local-to-global chain-reaction degradation behaviors. The common experimental test-beds and sensing techniques for joint degradation monitoring are summarized, and the measurement limitations, including sensor drift, synchronization error and installation constraints, and their influences on model parameter identification, are discussed. The existing machine-learning, digital-twin and physics-informed modeling applications for bolted joints are briefly outlined. Finally, this review summarizes the existing research consensus, unresolved contradictions and open research challenges. Special attention is paid to the limitations of existing time-variant Iwan-type models for multi-bolt flange degradation. Potential future research directions include multi-channel synchronous sensing matching time-varying constitutive models, quantification of inter-bolt load redistribution, and robust identification strategies under noisy experimental data.

Based on actual topography measurement data, this study adopts a paraboloid of revolution to characterize asperity geometry and establishes a lateral contact model that accounts for substrate deformation and covers the full elastic–plastic process. The proposed model achieves smooth transitions in contact behavior, effectively avoiding non-physical oscillations and discontinuities in the elastoplastic regime exhibited by existing models. Comparative results with multiple classical models demonstrate that the proposed model maintains strict monotonicity and continuity in predicting contact load, average contact pressure, and contact stiffness. This significantly improves prediction accuracy and physical consistency, providing a more reliable theoretical tool for modeling precision mechanical joint interfaces.

This paper proposes an improved wave function asperity elastic–plastic model. A cosine function that could better fit the geometric morphology was selected to construct the asperity, the elastic phase was controlled by the Hertz contact theory, the elastoplastic transition phase was corrected by the hyperbolic tangent function, and the fully plastic phase was improved by the projected area theory. The model broke through the limitations of the spherical assumption and was able to capture the stress concentration and plastic flow phenomena. The results show that the contact pressure in the elastic phase was 22% higher than that of the spherical shape, the plastic strain in the elastoplastic phase was 52% lower than that of the spherical shape, and the fully plastic phase reduced the contact area error by 20%. The improved hyperbolic tangent function eliminated the unphysical oscillation phenomenon in the elastoplastic phase and ensured the continuity and monotonicity of the contact variables, with an error of <5% from the finite element analysis. Meanwhile, extending the proposed model, we developed a rough surface contact model, and it was verified that the wavy asperity could better match the mechanical properties of the real rough surface and exhibited progressive stiffness reduction during the plastic flow process. The model in this paper can provide a theoretical basis for predicting stress distribution, plastic evolution, and multi-scale mechanical behavior in the connection interface.

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.

Engineering equipment is an important material basis for supporting national defense security and promoting the development of the national economy. Large and complex mechanical equipment has a complex structural composition and numerous components, with a large number of connection structures such as bolts and flanges inside. Affected by long-term loading conditions, phenomena such as contact stiffness degradation will occur at the joint interface between components, thereby influencing the dynamic characteristics of the entire system and seriously affecting the reliability and performance of the equipment. By integrating microscopic contact mechanisms with cross-scale modelling approaches, the proposed contact framework can study the contact behavior of the joint interface more comprehensively. This paper summarizes the research status of the asperity contact model under two modeling methods, summarizes the research status of the statistical summation contact model from the assumptions of different asperity height distributions, outlines the current situation of the engineering application of the joint interface contact model, and looks forward to the research directions of the cross-scale model of connection structures in the future.

Bolted joints, with their advantages of simple structure and convenient disassembly and assembly, are widely used in complex equipment fields such as aerospace systems and weaponry. Subject to complex mechanical loads, the contact surfaces may undergo nonlinear behaviors such as contact–separation and viscous slip, leading to the nonlinear degradation of the connection stiffness, which severely threatens the safety and reliability. These have driven research on bolted joints to span multiple disciplines, from interfacial micro-friction to macro-structural dynamics. Therefore, from the field of micro-friction to macro-dynamics, this review summarizes and analyzes three major degradation models, outlines the experimental development in connected structures, and provides an overview of the numerical analysis methods for degradation simulation. This paper also looks forward to the development directions for future research on the degradation of connected structures.

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.

Bolt connection structure is a common form of connecting large and complex equipment. Its object contact surfaces under normal and tangential loads will appear in the form of slip and adhesion, which affects the service life of mechanical equipment. Bolted connection structures cause changes in stiffness and damping, which have great impacts on the dynamic characteristics. Experimental studies and numerical simulations have difficulty predicting the overall performance of bolts in a timely manner, hence cannot ensure the reliability and safety of complex equipment. In order to improve the overall performance of complex equipment, it is necessary to study the contact theory model of bolt connection structures. Based on the relationship between friction force and velocity in the classical friction model, the mathematical expressions of restoring force and tangential displacement in the kinetic theory model are deduced to predict the stiffness degradation of the bolted structure and to characterise the kinetic properties and laws of the bolted structure. From the perspective of theoretical calculation, it makes up for the situation in which it is difficult to measure the performance of bolts due to the existence of spanning scale and provides theoretical support for the reliability of connecting complex equipment. This paper summarises and analyses the contact theory model of bolt connection structures, ranging from macroscopic to microscopic; describes the static friction model, kinetic friction model, statistical summation contact model, fractal contact model; and analyses the influencing factors of the microscopic contact mechanism. The advantages and disadvantages of the kinetic theoretical models are described, the manifestation of friction and the relationship between tangential force–displacement are discussed, and the key research directions of the kinetic theoretical models of bolted structures in the future are elucidated.

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.