Mechanical Behavior Of Bolted Joints Research Articles

Finite element analysis of bolted joints under torsional loads

The presence of service torque, which is generated after tightening, directly affects the mechanical properties of bolted joint. In this work, the mechanical behavior of bolted joints under torsional loads is investigated using finite element analysis (FEA). Models with two plates and multiple plates are established separately to investigate the mechanical properties of different kinds of bolted joints. Three analysis steps involving the entire process from tightening to torsional loading are adopted, namely tightening step, initial loss step and loading step. Torsional loads in two directions along the thread axis are considered and defined as loosening torsional load and tightening torsional load. The clamping force, as well as the friction torques of various contact surfaces, of the bolted joint are extracted in all the analysis steps. Different scenarios of friction torque combinations for bolted joints are obtained by means of adjusting the friction coefficient of the corresponding contact surfaces. On this basis, the mechanical properties of bolted joints and the corresponding torque thresholds are extracted on various scenarios. FEA results showed that how the service torque makes the directional characteristic of the mechanical properties of bolted joints under torsional loads. Moreover, the service reliability of bolted joint can be further improved based on the directional characteristics and the extracted torque thresholds.

An investigation of vibration responses for bolted composite flanged-cylindrical shells considering material and joint nonlinearity

In this paper, a thorough investigation into the vibration response of bolted composite flanged-cylindrical shell structures, considering the material nonlinearity of carbon fiber-reinforced polymer composites (CFRP) and the joint nonlinearity of bolt connections, is presented. Firstly, a general semi-analytical modeling method for bolted composite flanged-cylindrical shell is developed based on the first-order shear deformation theory (FSDT) and the energy method. In this method, material nonlinearity is introduced by accounting for the frequency-strain dependency of material parameters. A joint model with non-uniform distribution parameters and dynamic boundaries is proposed to simulate the interface pressure distribution and nonlinear mechanical behavior of bolted joints. Then, for the general numerical model that incorporates both types of nonlinearities, the ability to accurately predict the nonlinear vibration behavior of a bolted composite flanged-cylindrical shell is demonstrated through experimental testing. Finally, an in-depth discussion is conducted on the influence of fiber layup patterns and bolt numbers on the nonlinear vibration response of the bolted composite flanged-cylindrical shells. The conducted analysis indicates that the proposed method can offer utility to designers, empowering them with the insights necessary for the dynamic optimization of such structures.

Critical load determination for preventing rotational loosening in bolted joints under dynamic transverse loads

To ensure the reliability of bolted joints, it is essential to accurately determine the critical load that prevents rotational loosening of the nuts. In this paper, the mechanical behavior of bolted joints during tightening, after tightening, and under transverse loading was analyzed. The contact status of two mating surfaces, including the thread and nut bearing surfaces, and their ability to withstand transverse loads were calculated. Based on the conditions leading to rotational loosening, defined by the occurrence of sliding across both sets of contact surfaces, the critical condition for transverse force that precipitates rotational loosening in bolted joints has been established. Furthermore, a systematic procedure for determining this critical state of rotational loosening in bolted joint assemblies has been developed. Finite element simulations on bolted joints subjected to dynamic transverse loads, using various combinations of friction coefficients, showed results in good agreement with theoretical predictions. Finally, experimental measurements of the critical rotational loosening loads were conducted. The experimental results highlight that the decrease in clamping force due to non-rotational factors has a significant impact on the critical loads. Considering this influence and adjusting the preload accordingly, the calculated results for the critical loads are in good agreement with the experimental data.

Coupled vibration analysis of bolted variable angle tow plates under combined nonlinear effects

To establish a dynamical modal of variable angle tow (VAT) plate accurately, the fiber path and fiber orientation of the VAT plate are described by high-order polynomials. Then, a simplified nonlinear joint model with interface dynamic partitioning is proposed to simulate the interface mechanical behavior of bolted joints. Based on these, a nonlinear semi-analytic dynamic model of the bolted VAT plate is built, which considers both material and joint nonlinearity and can accurately predict nonlinear vibration response. After verifying the proposed modeling method, a special bolted VAT plate is used as the analysis object for free vibration and forced vibration analysis. Firstly, the frequency veering behavior of the VAT plate caused by variations in boundary stiffness, connection stiffness, and fiber orientation is studied. Then, by analyzing the forced vibration response of the bolted VAT plate, it is found that under the combined effect of the modal interaction, material nonlinearity, and joint nonlinearity, the bolted VAT plate exhibited complex but rule-based nonlinear dynamic behavior. More importantly, the research work done in this paper has certain guiding significance for the optimization design of vibration resistance of a bolted VAT thin-walled structure with variable stiffness parameters and joint parameters as design variables.

Analysis of the mechanical behavior of bolted joints with slotted-in steel plate considering the move path of rotation center for single-layer timber reticulated shell

The mechanical behavior of the bolted joints with slotted-in steel plate plays an important role in maintaining the stability of single-layer timber reticulated shell, yet methods to estimate the mechanical behavior of the bolted joints still remains to be improved. Assuming that the ductile failure of the bolted joints and the compressive failure of the glulam beam end occurred, the move path of the rotation center was obtained through theoretical derivation and used to determine the ultimate moment and rotational stiffness of the bolted joints. The equations for calculating the ultimate moment of the bolted joints were derived based on the European Yield Modes, t. Moreover, employing the beam on elastic foundation theory, a simplified equation of slipping stiffness was obtained and used to calculate the rotational stiffness. Experimental investigations on bolted joints for single-layer timber reticulated shell were conducted to verify the accuracy of the proposed theoretical methods. The results showed the rotational stiffness and ultimate moment obtained from theoretical calculation were consistent with the results of experimental tests. Furthermore, by calculating the move path of the rotation center, it was found that the rotation center started from the geometrical center of bolts at earlier loading stage and moved towards the compressive region of the glulam beam end with the increase of the external force. And the moment-rotation curves predicted by the linear model was in good agreement with the moment-rotation curves obtained from experimental tests, showing a convenient and reliable way to the design of bolted joints for single-layer timber reticulated shell.

On dynamic behavior and failure of high lock bolted joints: Testing, analysis and predicting

A bidirectional synchronous dynamic loading technique based on electromagnetic split Hopkinson tensile bar (ESHTB) system was employed to investigate the dynamic behavior and failure of high lock bolted joints. Force-displacement curves over wide ranges of loading speed (5 × 10−6 m/s to 15 m/s) and loading state (tension, shear and three kinds of tension-shear coupling) were obtained by combining with results obtained from quasi-static tests. An obvious elevation of failure load levels when changing the loading state from shear to tension or improving the loading speed was observed. Meanwhile, such strengthening effect of loading state on failure loads presented positive correlation with the loading speed. Detailed analysis for effect of loading state on mechanical behavior of bolted joints was conducted by applying von Mises yield criterion together with failure load analysis. Moreover, on this base, the influence of loading speed on failure loads was reasonably defined by applying a relation equal to the different strain rate effect between shear and tension for bolt material. Finally, a failure criterion considering coupling effect of loading speed and loading state on failure load of bolted joint was proposed. Prediction results showed a good agreement with the experimental results, indicating the determination of failure loads for bolted joints under different loading states over a wide range of loading speeds can be achieved.

A fretting test apparatus for measuring friction hysteresis of bolted joints

This paper focuses on an experimental investigation of the mechanical behavior of bolted joints. A new test apparatus to measure friction hysteresis was designed to provide a reliable experimental database for the calibration of contact models. This apparatus uses a piezoelectric actuator to provide the contact interfaces with stable oscillatory relative displacement. The friction force and the bolt preload were continuously measured during the test, using a load cell and a force washer, respectively. The relative motion between the interfaces was measured using a single laser vibrometer. The influence of the bolt preload and excitation amplitude on friction hysteresis was investigated. A numerical model was developed to extract the tangential contact stiffness from the measured data.

Experimental and numerical analyses of the shimming effect on bolted joints with nonuniform gaps

In order to investigate the effect of shim compensation for nonuniform gaps in aircraft assembly, the influence of the shims with different material and parameters on bolted joints is studied in this paper. According to the real material and assembly conditions of the aircraft joint structures, the specimen and experiment are designed to obtain the tensile performance of the joint structures with different shims. A three-dimensional finite element model, which incorporates the Johnson–Cook material property of the alloys, traction-separation law of liquid shims, contact relationships between the joint elements, and boundary conditions of the tensile process, is established with the specimen configurations. After validating through comparing with the experimental results, the modeling method is adopted to simulate the tensile response of the bolted joints with shims. Furthermore, both the influence of the shim material and thickness on the mechanical behaviors of bolted joints is investigated in detail. Shims can considerably reduce the assembly stress of joint structures and improve the joint stiffness and load capacity, and this effect is more remarkable with the increase of gap values. Liquid shims improve the joint stiffness due to its cohesive ability, while solid shims improve the joint load capacity. Hybrid shims possess a composite shimming effect of liquid and solid shims. Whatever the shim material is applied, the joint stiffness and strength drop with the growth of shim thickness, so strict deviation control method should be taken to ensure the assembly gaps as small as possible. The research results enhance the knowledge of shimming effect on joint structures, and thus offer positive guidance for practical application in aircraft assembly.

Analytical Expression of Cross Sectional Geometry of Various Screw Threads and Finite Element Analysis of the Mechanical Behavior of Multiple-Thread Screws

Distinctive mechanical behavior of bolted joints is caused by the helical shape of thread geometry. Mathematical expression of the helical thread geometry of a single-thread screw has successfully been derived in the previous study. Using the derived equations, finite element models were constructed by taking account of the effect of the helix, and it is clarified how the stress distributes along the thread root and where the maximum stress occurs. Meanwhile, there are various thread forms other than a single-thread triangular screw. In this study, mathematical expressions of the helical thread geometry and the cross sectional area of multiple-thread screws, trapezoidal thread and pipe thread are derived in the same manner as in the case of a single-thread screw. Using the equations thus obtained, finite element models with multiple-thread screws are constructed, and its tightening process by torque method is analyzed. Numerical results show that the stress distribution patterns are basically identical along all helixes for each multiple-thread screw. It is also found that the maximum Mises stress occurs at the first bolt thread root and it increases as the lead of multiple-thread screw increases.

True Cross Sectional Area of Screw Threads With Helix and Root Radius Geometries Taken Into Consideration

When evaluating the strength of threaded fasteners under external loads, stress area is commonly used. However, in order to elucidate the mechanical behavior of bolted joints more rigorously and extensively, it is desired to derive an analytical expression of the true cross sectional area of screw threads, with the effects of the helix and root radius taken into account. In this paper, a series of closed-form algebraic equations, which can calculate true cross sectional areas of internal and external screw threads, is derived. The equations obtained can be applied to both metric and inch screw threads with a coarse or a fine pitch. Then, the equivalent diameter of the true sectional area is defined and compared with the pitch diameter and stress area diameter.

Proposition of Helical Thread Modeling With Accurate Geometry and Finite Element Analysis

Distinctive mechanical behavior of bolted joints is caused by the helical shape of thread geometry. Recently, a number of papers have been published to elucidate the strength or loosening phenomena of bolted joints using three-dimensional finite element analysis. In most cases, mesh generations of the bolted joints are implemented with the help of commercial software. The mesh patterns so obtained are, therefore, not necessarily adequate for analyzing the stress concentration and contact pressure distributions, which are the primary concerns when designing bolted joints. In this paper, an effective mesh generation scheme is proposed, which can provide helical thread models with accurate geometry to analyze specific characteristics of stress concentrations and contact pressure distributions caused by the helical thread geometry. Using the finite element (FE) models with accurate thread geometry, it is shown how the thread root stress and contact pressure vary along the helix and at the nut loaded surface in the circumferential direction and why the second peak appears in the distribution of Mises stress at thread root. The maximum stress occurs at the bolt thread root located half a pitch from nut loaded surface, and the axial load along engaged threads shows a different distribution pattern from those obtained by axisymmetric FE analysis and elastic theory. It is found that the second peak of Mises stress around the top face of nut is due to the distinctive distribution pattern of σz.

Analytical Expression of True Cross Sectional Area of Screw Thread with the Effects of Root Radius Taken into Consideration

The cross sectional area of threaded fastener has a complicated configuration due to the helix that characterizes its essential function of tightening structural members. When estimating the strength of threaded fasteners under external loads, the use of “stress area” is recommended in JIS B 0251. It is desired, however, to establish a procedure to calculate the true cross sectional area of screw thread by taking account of the effects of root radius in order to elucidate the various mechanical behaviors of bolted joints. In this paper, an analytical expression is presented to calculate the true cross sectional area with simple algebraic equations. Then, its “equivalent diameter” is defined and compared to effective diameter corresponding to the stress area defined in JIS B 0251.

Proposition of Helical Thread Modeling with Accurate Geometry and Finite Element Analysis

Distinctive mechanical behaviors of bolted joints are caused by the helical shape of thread geometry. Recently, a number of papers have been published to elucidate the strength or loosening phenomena of bolted joints using three-dimensional finite element analysis. In most cases, mesh generations of the bolted joints are implemented with the help of sophisticated commercial software. Therefore, the mesh patterns thus obtained are not necessarily adequate for analyzing the stress concentration and contact pressure distributions, which are the primary concerns when designing bolted joints. In this paper, an effective mesh generation scheme is proposed, which can provide helical thread models with accurate geometry in order to analyze such important characteristics as the stress distribution along the helix and the contact pressure distributions on the pressure flank. Using the FE models constructed according to the proposed procedure, it is shown how the thread root stress and contact pressure vary along the helix. Also shown is how the imperfect engagement of the mating threads, around the top and bearing surfaces of the nut, affects the circumferential contact pressure distribution at the nut loaded surface and the axial load distribution along engaged threads.

Elastic Plastic Finite Element Analysis of Bolted Joint During Tightening Process

Mechanical behavior of bolted joints during the tightening process with torque control is analyzed by FEM as elastic plastic contact problems. Three-dimensional analysis was conducted employing two-dimensional model with each node having three degrees of freedom that attains high computation efficiency. Such important factors as development of plastic zones, variations of load distributions along engaged threads, the relationships between axial bolt stress and nut rotation angle were analyzed in order to provide an effective guideline when tightening critical structures with high bolt preloads. It was also shown that the proposed numerical method can be applied to evaluate the tightening process by “plastic region tightening” used extensively in recent years. The validity of the numerical method is demonstrated by comparing the calculated bolt elongation with that obtained from experiment.

Mechanical Behaviors of Bolted Joint in Various Clamping Configurations

In a bolted joint, failures usually initiate at the first root of the bolt thread. However, rupture around the bolt head is sometimes reported for a tap bolt because of high stresses produced by tightening torque applied to the bolt head. It is also well known that manufacturing errors of internal threads in a tapped hole are generally much larger than those of external threads, thus leading to the failures concerned. In this paper, mechanical behaviors of bolted joints in various clamping configurations are analyzed using FEM as multi-body elastic contact problem, and the effects of nominal diameter, friction and pitch error upon stress concentrations are evaluated for through bolts, studs, and tap bolts. It is then quantitatively estimated on the effectiveness of “recessed internal threads” for reducing the stress concentration occurred around the far end of bolt hole. In addition, the tightening process and strength of a bottoming stud, which have seldom been studied despite favorable performance in preventing stress concentration at the runout of threads, are also investigated.

Mechanical Behaviors of Bolted Joint in Various Clamping Configurations.

In a bolted joint, failures usually initiate at the first root of the bolt thread. However, rupture around the bolt head is sometimes reported for a tap bolt because of high stresses produced by tightening torque applied to the bolt head. It is also well known that manufacturing errors of internal threads in a tapped hole are generally much larger than those of external threads. In this paper, mechanical behaviors of bolted joints in various clamping configurations are analyzed using FEM as an axisymmetric elastic contact problem, and the effects of nominal diameter, friction and pitch error upon stress concentrations are evaluated for through bolts, studs and tap bolts. In addition, the tightening process and strength of bottoming studs, which have seldom been studied despite of its good performance in preventing stress concentration at the runout of threads, are also investigated.

Mechanical Behavior of Bolted Joints Under Steady Heat Conduction

Bolted joints in heat exchangers, cylinder heads in combustion engines, and so on are subjected to heat fluxes. It is necessary to examine the mechanical behavior of such bolted joints under thermal changes in order to establish an optimal design. This paper deals with mechanical behavior of bolted joints, in which two hollow cylinders and two rectangular thick plates made of aluminum are fastened at room temperature by a bolt and nut made of steel, and are subjected to thermal changes or steady heat conduction. Temperature distributions of the joints are analyzed using the finite difference method. Then, methods for estimating an increment in axial bolt force and a maximum stress produced in the bolts are proposed. In the experiments, the aforementioned bolted joints are put in a furnace. Furthermore, the rectangular thick plates fastened by a bolt and nut are heated by an electric heater. Then, the temperatures on the surfaces of the clamped parts and the bolts are measured with thermocouples. The increase in axial bolt force and the maximum stress produced in the bolts under steady heat conduction or thermal changes are measured. The analytical results are in fairly good agreement with the experimental ones.