Bolted Joint Structure Research Articles

In-Situ Estimation of Bolt Clamping Force by Utilization of Its Effects on Flexural Vibration Propagation

After a bolt assembling process, non-destructive identification of the clamping force is important to minimize unexpected failure of the assembled joint structures. For in-situ inspection for every parts, a detachable device which allows generation and detection of vibration propagation was proposed in this study. Tone burst excitation was transmitted through the bolted-joint structure. The vibration propagation characteristics depended on the clamping force. With an increase in the clamping force, the surface vibration propagation speed increased. The vibration magnitude decreased due to increasing constraint. A band-pass filter was used to remove noise component. The filtered vibration propagation responses were used in convolutional long short-term memory (CLSTM) training. The performance of CLSTM model was verified through comparison with actual clamping force. With minimal physical influence on the assembled parts, the clamping force of bolted-joint was measured using the surface vibration propagation characteristics.

Development of a portable damage detection system based on electromechanical impedance technique for monitoring of bolted joint structures

Structural health monitoring of structures in general usually require an expert to permanently attach a sensor onto a specific area. This would be important for mechanical structures with bolted joints, such as in aircrafts or even machines as human lives depend on its structural integrity. However, for large civil infrastructures with bolted joints, such as in cable stayed bridges, installing a monitoring system with a large number of sensors would be unrealistic as the cost of the system would be significantly high. In addition, the time frame for certain bolts to loosen for civil structures can be quite long and one could say that a real time monitoring system is unnecessary as a routine maintenance is conducted for civil structures. An effective way of identifying bolt loosening would be vital for safety inspectors to inspect the target structure with minimized time. Thus, in this study, a piezoelectric transducer based non-destructive testing method is introduced to identify bolt loosening. The concept of real time online monitoring could be replaced with the portable damage detection concept shown in this study as the proposed idea could minimize the overall cost of the maintenance process.

Uncertain Parameters Estimation using Multi-Dimensional Analysis and Stochastic Model Updating

Stochastic model updating based on perturbation theory has been widely applied to quantify uncertain parameters in structural systems due to its simplicity and straightforward approach. Nevertheless, the significant requirements for establishing a good correlation in the initial prediction of structural responses and small perturbations in uncertain parameters have become influential in stochastic model updating. The initial assumptions of structural parameters are often unavailable to quantify the input properties due to insufficient information about the structural system. These problems contribute to large errors in initial prediction, causing ill-posedness in sensitivity matrices and convergence difficulties caused by the local minima function in the stochastic model updating approach. In these circumstances, this study attempts to propose a novel scheme to overcome the ill-posed and converging problems in the stochastic model updating by quantifying structural parameters of the assembled structure encompassing high uncertainties such as the stiffness term of the contact joint interface by using a combination of the lattice-based exploration approach and the perturbation-based stochastic model updating method. The lattice-based exploration approach is adopted for generating samples of predicted responses from the assumed initial distribution of random parameters in the interest of improving the initial correlation of the predicted responses for producing well-condition sensitivity. Responses from each sample are evaluated in light of their experimental counterparts to estimate the optimum initial distribution of the random parameters. Then, the initial statistical properties of the parameters can be estimated by rerunning the sampling approach using the optimum distribution. As a result, stochastic model updating using the perturbation approach can be applied efficiently with the new initial distribution. The proposed scheme has been demonstrated on an assembled bolted joint structure, focusing on the contact interfaces. It is found that the proposed scheme managed to produce satisfactory predictions on the distribution of natural frequencies with only 12.5 % of total errors are recorded in comparison with the experimental data.

Modal testing and modelling the dynamic characteristics of a plate with bolted joints

Modelling the dynamic characteristics of the bolted joints in a complex assembled structure with a high accuracy is very challenging due to the assumptions and uncertainties in the input data of the FE model. In this paper, the identification of the dynamic characteristics of the bolted joints structure using the CBUSH element connector is proposed. Modal testing and normal modes analysis are conducted on a thin plate assembled structure with bolted joints. In the simulation work, the CBUSH element connector is employed and the stiffness coefficient for six degrees of freedom is computed based on four flexibility formulae. The predicted natural frequencies and their corresponding mode shapes are compared against the results of the experimental work. A good agreement of the FE model is achieved by using the coefficient of stiffness as represented in the Swift flexibility formula. The study justifies that the dynamic characteristics of the bolt joints could be accurately modelled by using the CBUSH element connector. The obtained findings provided an alternative approach to modelling the dynamic characteristics of a thin plate assembled structure with bolted joints.

Fatigue failure simulation of a double-lap composites-metal bolted joint structure

The fatigue damage behavior and the failure characteristics of the T300/QY8911 laminate and 7050-T7451 aluminum single-bolt bolted joints were investigated by test and progressive damage analysis (PDA) in this article. The manufactured composites-to-metal bolted joints (CMBJs) with different thickness metal plates and lap-patterns have been tested in static and fatigue load case and the failure characteristics are compared. A modified Lemaitre fatigue damage model and a phenomenological composite fatigue damage model were proposed and applied simultaneously to capture the damage evolution in the laminate and the metal parts. The competition of the fatigue damage of the laminate and the metal parts in affecting the joint stiffness and the coupling of the damage accumulation were studied by PDA, and the results indicates that: the failing sequence of the CMBJs constructive parts may change between the static load case and the fatigue load case; the fatigue damage of the metal parts has little effect on the joint stiffness of the CMBJs, nevertheless, there is certain coupling of the laminates fatigue damage and metal fatigue damage in the CMBJs, the harden or soften of the metal parts by fatigue hardening or crack progression would promote or slow down the damage accumulation in laminate.

The method of bolt axial force looseness monitoring and control by piezoelectric ceramics in bolted joint structures

Aiming at the problem of bolt looseness in structures, this paper proposes an active control method of axial force monitoring through guided wave and axial force compensation via the inverse piezoelectric effect of a piezoelectric ceramic gasket. Based on the finite element model, the propagation process of guided wave wave in bolted connectors is analyzed, which shows that the transmitted wave energy increases with the increase of bolt clamping force. The analysis of the stress-strain characteristics of the axially polarized and radially polarized piezoelectric ceramic gasket shows that the axially polarized piezoelectric ceramic gasket is more suitable for the control of bolt clamping force. The finite element analysis of the application of piezoelectric ceramic gasket in bolt axial force control shows that the power of guided wave signal increases monotonously with the increase of loaded electric field strength. In accordance with these theoretical methods and research, an active control system for bolt axial force is established in this experiment. The system monitors the power of the guided wave signal in real time and controls the axial force of the bolt by adjusting the intensity of the piezoelectric effect, which achieves an accurate control effect.

Stochastic Model Updating of Bolt-Jointed Structure for Structural Dynamics Applications

Structural stiffness exerts from joint connections and contact interfaces are significantly affect the dynamic behaviour of the bolt-jointed structure. Randomness in the joint connections due to the manufacturing variability in the identical bolted joints and uncertainty in contact interfaces due to the assambled and reassambled of the joint structure make sets of the dynamic behaviour of the bolt-jointed structure always inconsistent. On this account, a stochastic analytical model needs to be developed for the bolt-jointed structure to be used for uncertain parameters quantification. Hence, this paper is intended to propose an accurate and efficient stochastic analytical modelling of bolt-jointed structure in predicting the dynamic behaviour of the structure due to the randomness in the joint connections and uncertainty in contact interfaces. The aim of the study was accomplished by investigating four different finite element (FE) models of bolt-jointed structure with different element connectors to represent the bolted joints connections, namely rigid element (RBE), beam element (CBEAM), and 2 types of spring elements namely CELAS and CBUSH. Stochastic modelling was conducted by coupled the appropriate FE models with Latin Hypercube Sampling (LHS) algorithm to provide variability sampling due to the randomness in the bolted joints. The experimental modal analysis was performed by reassembled and disassembled the bolted joints to extract the variability in the dynamic behaviour, and the results were compared with LHS using statistical characteristics. Stochastic model updating then was used to minimise the discrepancies between experimental result and predicted model. The result has shown that the CBUSH is the most appropriate connector to accurately predict the dynamic behaviour of the bolt-jointed structure under variability conditions using the stochastic model updating method.

On the use of the GP-NARX model for predicting hysteresis effects of bolted joint structures

Structures joined by lap-joints can present complex nonlinear dynamic behavior as a function of the stress to which the lap-joint is subjected, including contact stiffness variations and softening, along with hysteresis effects related to frictional dissipation at the contact interface. Considering applications where the use of non-parametric models that depend only on input and output data is required, this work proposes and details the GP-NARX model’s use to approximate systems’ dynamics with hysteresis. Initially, the proposed model’s predictive applicability is evaluated on a numerical application involving the Bouc-Wen oscillator with hysteretic damping. Then, this work proposes a GP-NARX model to describe the dynamics of the BERT benchmark, an experimental system that contains a symmetric double bolted joint that is nonlinearly dependent upon the applied excitation amplitudes, presenting as a friction joint’s well-known softening effect. The structure also presents data variation related to the presence of uncertainties in the measurement process. Thus, to accommodate the experimental variability, the training step of the GP-NARX model considers several experimental realizations. The results indicate that GP-NARX can make accurate predictions of the response of both investigated applications, emphasizing its practical ability, where the confidence intervals of the proposed model were able to accommodate the noisy experimental data, learning the nonlinear relation between the input and output data points.

Digital Twin‐Assisted Simulation of Complex Assembly Models in Descending Process and Implementation of Key Link Characterization

In this paper, the simulation and key link characterization of the complex assembly model step‐down process are studied and analysed in depth using the digital twin approach, and the method is used in the practical process. The physical model step‐down method MORA algorithm and its physical interpretation in various simplified cases are given, and the MORA method is improved on this basis. The concept of local activeness based on knot structure is introduced, and the process of model transformation and downscaling and decomposition based on local activeness is explained in detail. The high‐fidelity mapping of solid equipment is completed in virtual space, which can accurately reproduce and predict the health state of engineering equipment throughout its life cycle, effectively avoiding the huge property losses and safety risks caused by early failure of vulnerable structures and providing a safe and stable working environment for offshore oil and gas production. With the prototype monitoring data as reference, the response surface method is used to identify the parameters of the finite element model of the hinge node, which improves the fidelity of the virtual model of the hinge node. Considering the friction coefficient changes and load characteristics during the degradation of the hinge node, the dynamics simulation conditions are set, and the operating states of the hinge node at different stages of its whole life cycle are simulated by using the high‐fidelity virtual model of the hinge node, and the prediction model of the hot spot stress of the hinge node is established to monitor its in‐position state in real time, and the operation and maintenance overhaul method based on the health state of the hinge node is proposed. The system is divided into four modules: multilevel inverse modelling of the assembly twin, statistical shape characterization and analysis of batch parts, optimization of fixture positioning and flexible assembly of thin‐walled parts, and optimization of low‐stress assembly of bolted joint structure, which verifies the feasibility of the method and provides guidance for the actual product forming process.

Improvement in the accuracy of the dynamic behaviour prediction of a bolted structure using a simplified finite element model and model updating

Bolted joints in assembled structures contribute to the dynamic behaviour of the structures but also increase uncertainties in modelling and prediction of the dynamic behaviour. This paper presents a modelling scheme able to reduce uncertainties and increase the accuracy of the prediction. A finite element (FE) model of a bolted joint structure was developed using CBUSH, CBEAM and 3D elements representing the bolts, contacting interfaces, and structural components, respectively. Normal modes analysis was performed on the FE model to calculate the natural frequencies and mode shapes. Sensitivity analysis was formulated and used in identifying the highly sensitive design parameters of the FE model. Model updating was adopted in correlating the FE model with experimental modal analysis (EMA) and producing an updated FE model. It was found that the updated FE model is capable of predicting the dynamic behaviour of the bolted joint structure with 95 per cent accuracy. This proposed scheme demonstrated potential for applicability to the dynamic behaviour analysis of complex bolted structures.

Representation of bolted joints in a structure using finite element modelling and model updating

Efficient and accurate finite element (FE) modelling of bolted joints is essential for increasing confidence in the investigation of structural vibrations. However, modelling of bolted joints for the investigation is often found to be very challenging. This paper proposes an appropriate FE representation of bolted joints for the prediction of the dynamic behaviour of a bolted joint structure. Two different FE models of the bolted joint structure with two different FE element connectors, which are CBEAM and CBUSH, representing the bolted joints are developed. Modal updating is used to correlate the two FE models with the experimental model. The dynamic behaviour of the two FE models is compared with experimental modal analysis to evaluate and determine the most appropriate FE model of the bolted joint structure. The comparison reveals that the CBUSH element connectors based FE model has a greater capability in representing the bolted joints with 86 percent accuracy and greater efficiency in updating the model parameters. The proposed modelling technique will be useful in the modelling of a complex structure with a large number of bolted joints.

Fatigue Behavior of Bolted Joints: Comparative Analysis for the Effect of Fretting and Stress Concentration

Abstract In this paper, a methodology is developed to investigate the combined effect of some main factors (bolt pretension load, shear load, coefficient of friction, and bolted joints structure) on the fatigue performance of bolted joints. A parameter k, which reflects the ratio of bolt pretension load to shear load, is used to evaluate the competition effect of fretting and stress concentration on fatigue damage of bolted joints. The analysis result deduces that as the increase of k, the effect of stress concentration is decreased, while the influence of fretting is increased. At the increase of the bolt pretension load, the fatigue crack formation position will be far away from the hole center. This parameter k can be used as a design or assembly parameter to improve the strength performance of the bolted joints.

Modeling tangential friction based on contact pressure distribution for predicting dynamic responses of bolted joint structures

Subjected to dynamic excitations, bolted joint interfaces exhibit nonlinear characteristics that significantly affect the dynamic response of assembled structures. In this paper, a novel modeling method is developed to improve the prediction accuracy of the tangential contact behavior of bolted joint interfaces. This method is based on the framework of the Iwan model and builds the relationship between the Iwan density function and the distribution of the contact pressure. It is the first time to give an explicit physical significance of the Iwan density function. The effectiveness of the proposed model is validated well by comparing with published experiments. Then the proposed model is integrated into a numerical model of a bolted joint structure and combined with the alternating frequency/time method to study its applicability in dynamics analysis. The model is fully compatible with the current state-of-the-art numerical analysis tools. The results show that the simulated interface responses are in good agreement with the experiment.

Study on bearing strength and failure mode of a carbon-epoxy composite laminate for designing bolted joint structures

A composite single-lap bolted joint was experimentally studied and its bearing behavior was predicted numerically. Prior to performing the experiment, an appropriate e/D ratio of the composite material was determined via double-lap bolted joint tests. Using the obtained e/D ratio, specimens were manufactured, and single-lap composite bolted joint tests were subsequently performed. Various joint tests were conducted with the number of bolt holes, pre-torque, and thickness as experimental variables. The preferred bearing failure mode was observed with the designed e/D ratio and bearing strength increased with increasing tightening torque. The bearing strength was significantly affected by the projected bearing area and exhibited a linearly proportional relation with the joint bearing area. The fracture mechanism was observed using optical microscopy, indicating fiber buckling, breakage, and delamination induced from the initial damage. An energy-based progressive failure analysis (PFA) was implemented to predict the composite bolted joints strengths. The adopted PFA accurately predicted the strength of the bolted joint in range of 12%.

Nonlinear dynamic behaviors of a bolted joint rotor system supported by ball bearings

A dynamic model of the rotor-bearing system with bolted joint structure is set up based on the Lagrange’s equations, which considers the bearing clearance, the gyroscopic effect and the initial deformation due to the non-uniform preload. The nonlinear dynamic responses of the system were obtained by using the Runge–Kutta–Fehlberg method, and then the influence of the radial bearing clearance on the nonlinear dynamic behaviors of the rotor system is studied by means of bifurcation diagram, frequency spectrum, shaft orbits and Poincare maps. The results indicate that the larger bearing clearance will make the system enter into chaotic motion at a lower rotating speed. In addition, with the increase in bearing clearance, the duration of the chaotic motion becomes longer. Furthermore, the influence of initial deformation on the stability of the bolted joint rotor system with bearing clearance is studied. The results show that when the bearing clearance is present, the instability speed of the rotor system will gradually rise with the increase in initial deformation. Meanwhile, as the bearing clearance continuously increases, the regions of the chaotic motion become less and smaller, and the motion state should be completely changed under certain initial deformation. The related results can provide guidance for the optimization and design of the bolted joint rotor-bearing system.

Theoretical and Experimental Study on Electrical Contact Resistance of Metal Bolt Joints

As a kind of fixed connection, bolt joints are widely used in engineering. In this paper, the analytic equations of the contact resistance under different situations are deduced by approximating the Gaussian distribution and the asperity deformation process based on the Greenwood–Williamson model. The equations explicitly describe the theoretical dependences of contact resistance on mechanical and electrical parameters of materials, surface topographic features, and the property of the surface oxidation film. The characteristic curves of contact resistance versus contact pressure for brass, copper, and their silver-coated counterparts are measured by using a specially designed bolted-joints structure. The experimental results are consistent with the theoretical model, indicating that, in the log–log plot, the contact resistance depends linearly on contact pressure with a slope ranging from −0.5 to −1. The analytic equations and experimental observations of contact resistance revealed in this paper can be used as a guidance for electrical contact engineering.

Damage and Fracture Analysis of Bolted Joints of Composite Materials Based on Peridynamic Theory

Abstract It is clear that the advantages of fibre glass-reinforced plastics surpass those of steel, but the failure analysis of composite structures is much more complex than that of isotropic materials as composite materials may fail in a variety of ways. In order to simulate the damage and fracture of bolted joints of fibre reinforced composite, the bond-based peridynamic method suitable for elastic, brittle and anisotropic characteristics of composite material is used. The peridynamic model for composite laminate is validated by the finite element method. Then a peridynamic program of composite damage is applied to calculating the damage of bolted joint structure and the damage propagation process and failure mode of the structure is obtained.

The Failure Analysis of Composite Bolted Joint Structure Based on a Nonlinear Model

The Failure Analysis of Composite Bolted Joint Structure Based on a Nonlinear Model

Laser-based structural training algorithm for acoustic emission localization and damage accumulation visualization in a bolt joint structure

Acoustic emission caused by structural damage encompasses important information about structural integrity. In particular, acoustic emission can detect phenomena that are difficult to determine, such as microcracks and internal cracks. However, conventional acoustic emission has shown limitations in complex structure applications for years. In this article, we propose a Q-switched laser scan–based structural training technique to achieve accurate acoustic emission localization and visualize accumulated damage in complex structures with a single PZT sensor (acoustic emission sensor). The proposed method compensates for the difference in characteristics between the actual acoustic emission wave and the laser-induced elastic wave using laser-based structural training algorithm. Acoustic emission localization in complex structures is accomplished by cross-correlation in the time domain. Pencil-lead break method is used as the source for acoustic emission to simulate the real damage-induced acoustic emission event. The proposed laser-based structural training algorithm with a laser scanning interval of 2 mm achieved an average localization error of 1.84 mm in two Al-alloy layers with fastener structure. Finally, the accumulated damages were visualized by appending the damage index of the acoustic emission waves at accurately localized points.

Vibration Characteristics of Rotor Bearing System with Bolted Joint Structure

Vibration Characteristics of Rotor Bearing System with Bolted Joint Structure