To enhance the bending resistance of bellows,an environmentally friendly electric pulse heat treatment(EPHT)method was used.The strengthening mechanism was systematically studied by microstructure characterization,fin...To enhance the bending resistance of bellows,an environmentally friendly electric pulse heat treatment(EPHT)method was used.The strengthening mechanism was systematically studied by microstructure characterization,finite element simulation and bending test.The results showed that during EPHT process,the cross-sectional area of the trough was small,so that the current density was large,which made the temperature of the trough significantly higher than those of other regions.The temperature difference between the peak and the trough was most influenced by frequency.Empirical formulas were derived to predict the temperature and current density of the trough under varying parameters.The dislocation elimination and grain growth of the trough achieved the optimal balance at 800℃and 7 A/mm2,obtaining the best bending resistance.Bellows prepared by general heat treatment process(GHTP)had coarse grains and local high dislocation density areas.In contrast,the grains of EPHT bellows were fine,the dislocations were eliminated completely and uniformly,and the crack propagation path was more tortuous.Compared with GHTP,EPHT significantly reduced the dislocation density and eliminated oxide inclusions.This microstructural optimization altered the crack propagation behavior from simultaneous bidirectional growth(initiating from both high-strain surfaces and wall center)to unidirectional propagation(surface to center)of GHTP,thereby greatly reducing the crack propagation rate.Notably,the fracture mechanism changed from quasi-cleavage to ductile fracture.Compared with GHTP,the number of bending cycles of EPHT bellows increased by about 200%before fracture.展开更多
To advance the understanding of the corrosion behavior of stainless steel bellows in marine atmospheric environments and enhance the precision of service life predictions,this study employs finite element simulations ...To advance the understanding of the corrosion behavior of stainless steel bellows in marine atmospheric environments and enhance the precision of service life predictions,this study employs finite element simulations to investigate the pitting corrosion rates and pit morphologies of bellows peaks and troughs under varying electrolyte film thicknesses.The model incorporates localized electrochemical reactions,oxygen concentration,and homogeneous solution reactions.For improved computational accuracy,the fitted polarization curve data were directly applied as nonlinear boundary conditions on the electrode surface via interpolation functions.Simulation results reveal that the peak regions exhibit faster corrosion rates than the trough regions.With increasing electrolyte film thickness(from 10μm to 500μm),corrosion rates at both peaks and troughs decrease progressively,and after 120 hours of simulation,the maximum corrosion rate at the peaks declines from 0.720 mm/a to 0.130 mm/a,and at the troughs from 0.520 mm/a to 0.120 mm/a,with the disparity in corrosion rates diminishing over time.Furthermore,as corrosion progresses,pits propagate deeper into the substrate,exhibiting both vertical penetration and lateral expansion along the passive film interface,ultimately breaching the substrate.This research offers valuable insights into designing corrosion mitigation strategies for stainless steel bellows in marine environments.展开更多
The formulae for stresses and angular displacements of U-shaped bellows overall bending in a meridian plane under pure bending moments are presented based on the general solution for slender ring shells proposed by Zh...The formulae for stresses and angular displacements of U-shaped bellows overall bending in a meridian plane under pure bending moments are presented based on the general solution for slender ring shells proposed by Zhu Weiping, et al. and the solution for ring plates. The results evaluated in this paper are compared with those on EJMA (standards of the expansion joint manufacturers association) and of the experiment given by Li Tingxilz, et al.展开更多
A novel buckling-induced forming method is proposed to produce metal bellows.The tube billet is firstly treated by local heating and cooling,and the axial loading is applied on both ends of the tube,then the buckling ...A novel buckling-induced forming method is proposed to produce metal bellows.The tube billet is firstly treated by local heating and cooling,and the axial loading is applied on both ends of the tube,then the buckling occurs at the designated position and forms a convolution.In this paper,a forming apparatus is designed and developed to produce both discontinuous and continuous bellows of 304 stainless steel,and their characteristics are discussed respectively.Furthermore,the influences of process parameters and geometric parameters on the final convolution profile are deeply studied based on FEM analysis.The results suggest that the steel bellows fabricated by the presented buckling-induced forming method have a uniform shape and no obvious reduction of wall thickness.Meanwhile,the forming force required in the process is quite small.展开更多
In this study,the pressure compensation mechanism of a reducer bellows is analyzed.This device is typically used to reduce the size of undersea instruments and improve related pressure resistance and sealing capabilit...In this study,the pressure compensation mechanism of a reducer bellows is analyzed.This device is typically used to reduce the size of undersea instruments and improve related pressure resistance and sealing capabilities.Here,its axial stiffness is studied through a multi-fold approach based on theory,simulations and experiments.The results indicate that the mechanical strength of the reducer bellows,together with the oil volume and temperature are the main factors influencing its performances.In particular,the wall thickness,wave number,middle distance,and wave height are the most influential parameters.For a certain type of reducer bellows,the compensation capacity attains a maximum when the wave number ratio is between 6:6 and 8:4,the wall thickness is 0.3 mm,and the wave height is between 4–5 mm and 5–6 mm.Moreover,the maximum allowable ambient pres-sure of the optimized reducer bellows can reach 62.6 MPa without failure,and the maximum working water depth is 6284 m.展开更多
Origami bellows are formed by folding flat sheets into closed cylindrical structures along predefined creases.As the bellows unfold,the volume of the origami structure will change significantly,offering potential for ...Origami bellows are formed by folding flat sheets into closed cylindrical structures along predefined creases.As the bellows unfold,the volume of the origami structure will change significantly,offering potential for use as inflatable deployable structures.This paper presents a geometric study of the volume of multi-stable Miura-ori and Kresling bellows,focusing on their application as deployable space habitats.Such habitats would be compactly stowed during launch,before expanding once in orbit.The internal volume ratio between different deployed states is investigated across the geometric design space.As a case study,the SpaceX Falcon 9 payload fairing is chosen for the transportation of space habitats.The stowed volume and effective deployed volume of the origami space habitats are calculated to enable comparison with conventional habitat designs.Optimal designs for the deployment of Miura-ori and Kresling patterned tubular space habitats are obtained using particle swarm optimisation(PSO)techniques.Configurations with significant volume expansion can be found in both patterns,with the Miura-ori patterns achieving higher volume expansion due to their additional radial deployment.A multi-objective PSO(MOPSO)is adopted to identify trade-offs between volumetric deployment and radial expansion ratios for the Miura-ori pattern.展开更多
According to the characteristics of fluid-structure interaction( FSI) in the process of metal bellows inflating to disperse bomblets,a 3D dynamical FSI model( W model) which describes the interaction between a viscous...According to the characteristics of fluid-structure interaction( FSI) in the process of metal bellows inflating to disperse bomblets,a 3D dynamical FSI model( W model) which describes the interaction between a viscous compressible flow and a structure undergoing large deformationis established. Then the dynamic characteristics of the metal bellows deformation,the changing law of the internal flow field and the motion law of the bombs are acquired.Where the internal pressure and bombs' moving law are approximate to interior ballistic results,which indicates the W model established reasonably. Besides,considering gaps existing atthe bellows' tow ends,the dynamical FSI modelcontaining gaps( Y model) is also built. The results of the W and Y models are compared and the results show that the existence of the gaps has little influence to the flow field and the stress distributionin the bellows,but obviously reduces the separation speed of the bomblets about 10%.展开更多
This paper follows the work of[1,2].There are some progress in dealing with moderately small rotations(the squares of rotation angles are the order of magnitude of strains)of middle surface normals of inside and outsi...This paper follows the work of[1,2].There are some progress in dealing with moderately small rotations(the squares of rotation angles are the order of magnitude of strains)of middle surface normals of inside and outside ring shells and compressed angle of bellows.Calculation results agree with experiments well.To bellow design,the method given in this paper is of practical value and the discussion of the influence of compressed angle on characteristic relation is helpful.展开更多
Because of the complex constraint effects among layers in multi-layered metallic bellows hydroforming,the stress concentration and defects such as wrinkling and fracture may easily occur.It is a key to reveal the defo...Because of the complex constraint effects among layers in multi-layered metallic bellows hydroforming,the stress concentration and defects such as wrinkling and fracture may easily occur.It is a key to reveal the deformation behaviors in order to obtain a sound product.Based on the ABAQUS platform,a 3 D-FE model of the four-layered U-shaped metallic bellow hydroforming process is established and validated by experiment.The stress and strain distributions,wall thickness variations and bellow profiles of each layer in the whole process,including bulging,folding and springback stages,are studied.Then deformation behaviors of bellows under different forming conditions are discussed.It is found that the wall thinning degrees of different layer vary after hydroforming,and is the largest for the inner layer and smallest for the outer layer.At folding stage,the wall thinning degree of the crown point increases lineally,and the difference among layers increases as the process going.The displacements of the crown point decrease from the inner layer to the outer layer.After springback,the U-shaped cross section changes to a tongue shape,the change of convolution pitch is much larger than the change of convolution height,and the springback values of the inner layer are smaller than the outer layer.An increase in the internal pressure and die spacing cause the maximum wall thinning degree and springback increase.With changing of process parameters,bellows with deep convolution are easily encountered wall thinning during hydroforming and convolution distortion after springback.This research is helpful for precision forming of multi-layered bellows.展开更多
On the basis of paper[1],assuming the logarithm of thickness at arbitrary point on a U-shaped bellows meridian is linear with the logarithm of distance between that point and axis of symmetry,perturbation solutions of...On the basis of paper[1],assuming the logarithm of thickness at arbitrary point on a U-shaped bellows meridian is linear with the logarithm of distance between that point and axis of symmetry,perturbation solutions of the corresponding problems of large axisymmetrical deflection are given.The effects of thickness distribution variation,which result from technology factors,on stiffness of bellows are discussed.展开更多
In order to analyze bellows effectively and practically, the finite_element_displacement_perturbation method (FEDPM) is proposed for the geometric nonlinear behaviors of shells of revolution subjected to pure bending ...In order to analyze bellows effectively and practically, the finite_element_displacement_perturbation method (FEDPM) is proposed for the geometric nonlinear behaviors of shells of revolution subjected to pure bending moments or lateral forces in one of their meridional planes. The formulations are mainly based upon the idea of perturba_ tion that the nodal displacement vector and the nodal force vector of each finite element are expanded by taking root_mean_square value of circumferential strains of the shells as a perturbation parameter. The load steps and the iteration times are not as arbitrary and unpredictable as in usual nonlinear analysis. Instead, there are certain relations between the load steps and the displacement increments, and no need of iteration for each load step. Besides, in the formulations, the shell is idealized into a series of conical frusta for the convenience of practice, Sander's nonlinear geometric equations of moderate small rotation are used, and the shell made of more than one material ply is also considered.展开更多
This is one of the applications of Part (Ⅰ),in which the angular stiffness, and the corresponding stress distributions of U_shaped bellows were discussed. The bellows was divided into protruding sections, concave sec...This is one of the applications of Part (Ⅰ),in which the angular stiffness, and the corresponding stress distributions of U_shaped bellows were discussed. The bellows was divided into protruding sections, concave sections and ring plates for the calculation that the general solution (Ⅰ) with its reduced form to ring plates were used respectively, but the continuity of the surface stresses and the meridian rotations at each joint of the sections were entirely satisfied. The present results were compared with those of the slender ring shell solution proposed earlier by the authors, the standards of the Expansion Joint Manufacturers Association (EJMA), the experiment and the finite element method. It is shown that the governing equation and the general solution (Ⅰ) are very effective.展开更多
This is one of the applications of Part (Ⅰ), in which the angular stiffness, the lateral stiffness and the corresponding stress distributions of C_shaped bellows were calculated. The bellows was divided into protrudi...This is one of the applications of Part (Ⅰ), in which the angular stiffness, the lateral stiffness and the corresponding stress distributions of C_shaped bellows were calculated. The bellows was divided into protruding sections and concave sections for the use of the general solution (Ⅰ), but the continuity of the stress resultants and the deformations at each joint of the sections were entirely satisfied. The present results were compared with those of the other theories and experiments, and are also tested by the numerically integral method. It is shown that the governing equation and the general solution (Ⅰ) are very effective.展开更多
The overall bending of circular ring shells subjected to bending moments and lateral forces is discussed. The derivation of the equations was based upon the theory of flexible shells generalized by E.L. Axelrad and th...The overall bending of circular ring shells subjected to bending moments and lateral forces is discussed. The derivation of the equations was based upon the theory of flexible shells generalized by E.L. Axelrad and the assumption of the moderately slender ratio less than 1/3 (i.e., ratio between curvature radius of the meridian and distance from the meridional curvature center to the axis of revolution). The present general solution is an analytical one convergent in the whole domain of the shell and with the necessary integral constants for the boundary value problems. It can be used to calculate the stresses and displacements of the related bellows. The whole work is arranged into four parts: (Ⅰ) Governing equation and general solution; (Ⅱ) Calculation for Omega_shaped bellows; (Ⅲ) Calculation for C_shaped bellows; (Ⅳ) Calculation for U_shaped bellows. This paper is the first part.展开更多
is one of the applications of (Ⅰ), in which the angular stiffness, the lateral stiffness and the corresponding stress distributions of Omega_shaped bellows were calculated, and the present results were compared with ...is one of the applications of (Ⅰ), in which the angular stiffness, the lateral stiffness and the corresponding stress distributions of Omega_shaped bellows were calculated, and the present results were compared with those of the other theories and experiments. It is shown that the non_homogeneous solution of (Ⅰ) can solve the pure bending problem of the bellows by itself, and be more effective than by the theory of slender ring shells; but if a lateral slide of the bellows support exists the non_homogeneous solution will no longer entirely satisfy the boundary conditions of the problem, in this case the homogeneous solution of (Ⅰ) should be included, that is to say, the full solution of (Ⅰ) can meet all the requirements.展开更多
A linear complex equation for slender ring shells overall bending in a meridian plane is given based on E. L. Axelrad's theory of flexible shells. And the non homogeneous solution is obtained from W. Z. Chien'...A linear complex equation for slender ring shells overall bending in a meridian plane is given based on E. L. Axelrad's theory of flexible shells. And the non homogeneous solution is obtained from W. Z. Chien's solution for axial symmetrical slender ring shells to investigate the overall bending problem of Ω shaped bellows subjected to pure bending moments. The values calculated in the present paper are very close to the existing experiment. Thus Chien's work on axial symmetrical problems for ring shells has been extended to overall bending problems.展开更多
In ITER facilities, there are some special expansion joints connected with the openings of cryostat. Expect for the assemblies connected with NB openings, others are rectangular section with big dimensions and severe ...In ITER facilities, there are some special expansion joints connected with the openings of cryostat. Expect for the assemblies connected with NB openings, others are rectangular section with big dimensions and severe working conditions and they are important for ITER safe runing.展开更多
Currently,the main optimization of pneumatic conveying seed-discharge systems targets distributors,ignoring the important role of pipelines.In this study,simulations were used to determine an improved structure of the...Currently,the main optimization of pneumatic conveying seed-discharge systems targets distributors,ignoring the important role of pipelines.In this study,simulations were used to determine an improved structure of the conveying pipe.The horizontal pipe was determined to be a 300 mm straight pipe,which was connected under the vertical bellows as a transition.This study adopted the L9(34)orthogonal test method to optimize the bellows parameters,using as index the coefficient of variation of the uniformity of the bellow outlets.The indoor bench test was designed to validate different flow rate and bellows length combinations.The optimal bellows parameter combination of the corrugated circle had a radius of 8 mm,bellows length of 500 mm,corrugation distance of 40 mm and corrugation length of 16 mm,achieving a 3.46%coefficient of variation of the particle distribution in the plumbing.Under various particle mass flow rates(33.5,67.0,101 g·s−1),the bellows length of the optimal solution was verified to be in the interval of 400−500 mm,and the consistency coefficients of the variations in row displacements of the system satisfied the requirements.This study provides guidance for the design and application of piping in pneumatic seed-discharge systems.展开更多
Grouted Bellows Connect Rebar(GBR)technology is critical for ensuring reliable connections in precast concrete components.The bond-slip behaviour,a core metric for assessing GBR connection performance,presents signifi...Grouted Bellows Connect Rebar(GBR)technology is critical for ensuring reliable connections in precast concrete components.The bond-slip behaviour,a core metric for assessing GBR connection performance,presents significant complexity,and existing empirical models often fall short in prediction accuracy to meet engineering demands.Addressing this challenge,this study introduces an innovative hybrid model(CNN-LSTM)that integrates convolutional neural networks with long shortterm memory networks.Utilizing eight critical parameters,such as grouting strength,reinforcement ultimate strength,and the anchorage length-to-diameter ratio of the reinforcement,the model achieves precise predictions of GBR bond stress.This study systematically collected data from 114 sets of GBR pull-out tests,constructing a dataset comprising 2,272 bond-slip samples for model training and validation.Additionally,15 GBR independent samples were independently fabricated and multiple samples were extracted to assess the model generalization capability.Experimental results demonstrate that the CNN-LSTM model significantly outperforms traditional empirical models in predicting bond stress and exhibits superior generalization across key metrics,including total energy consumption,maximum bond stress,failure modulus,and residual energy.Parameter importance analysis reveals that grouting strength,reinforcement ultimate strength,and the anchorage length-to-diameter ratio are the most influential factors in bond stress prediction.Building on the CNN-LSTM model predictions,this study establishes an improved empirical model with clear physical significance,offering a reliable computational foundation for engineering applications.展开更多
A metal bellows-based fiber Bragg grating (FBG) accelerometer is proposed and experimentally demonstrated. The optical fiber (containing the FBG) is pre-tensioned, and the two ends of the optical fiber are fixed d...A metal bellows-based fiber Bragg grating (FBG) accelerometer is proposed and experimentally demonstrated. The optical fiber (containing the FBG) is pre-tensioned, and the two ends of the optical fiber are fixed directly from the shell to the inertial mass. In this design, the FBG is uniformly tensioned to obtain a constant strain distribution over it. By employing this configuration, the FBG always has a sharp reflection characteristic with no broadening in its reflection spectrum during wavelength shifting. Dynamic vibration measurements show that the proposed FBG accelerometer has a wide frequency response range (5-110 Hz) and an extremely high sensitivity (548.7 pro/g). The two important indicators of FBG accelerometer can be tuned by the addition of mass to tailor the sensor performance to specific applications, identifying it as a good candidate for structural health monitoring.展开更多
基金financial supports from the National Natural Science Foundation of China(Nos.52204406 and 52375390)the Science and Technology Program of Hebei Province,China(Nos.E2025203087,E2024203229 and E2023203260)the Key S&T Special Projects of Xingtai City(No.2023ZZ017).
摘要To enhance the bending resistance of bellows,an environmentally friendly electric pulse heat treatment(EPHT)method was used.The strengthening mechanism was systematically studied by microstructure characterization,finite element simulation and bending test.The results showed that during EPHT process,the cross-sectional area of the trough was small,so that the current density was large,which made the temperature of the trough significantly higher than those of other regions.The temperature difference between the peak and the trough was most influenced by frequency.Empirical formulas were derived to predict the temperature and current density of the trough under varying parameters.The dislocation elimination and grain growth of the trough achieved the optimal balance at 800℃and 7 A/mm2,obtaining the best bending resistance.Bellows prepared by general heat treatment process(GHTP)had coarse grains and local high dislocation density areas.In contrast,the grains of EPHT bellows were fine,the dislocations were eliminated completely and uniformly,and the crack propagation path was more tortuous.Compared with GHTP,EPHT significantly reduced the dislocation density and eliminated oxide inclusions.This microstructural optimization altered the crack propagation behavior from simultaneous bidirectional growth(initiating from both high-strain surfaces and wall center)to unidirectional propagation(surface to center)of GHTP,thereby greatly reducing the crack propagation rate.Notably,the fracture mechanism changed from quasi-cleavage to ductile fracture.Compared with GHTP,the number of bending cycles of EPHT bellows increased by about 200%before fracture.
基金supported by the National Natural Science Foundation of China(No.52074130)Engineering Research Center of Resource Utilization of Carbon-containing Waste with Carbon Neutrality,Ministry of Education,200237 Shanghai,PR China.
摘要To advance the understanding of the corrosion behavior of stainless steel bellows in marine atmospheric environments and enhance the precision of service life predictions,this study employs finite element simulations to investigate the pitting corrosion rates and pit morphologies of bellows peaks and troughs under varying electrolyte film thicknesses.The model incorporates localized electrochemical reactions,oxygen concentration,and homogeneous solution reactions.For improved computational accuracy,the fitted polarization curve data were directly applied as nonlinear boundary conditions on the electrode surface via interpolation functions.Simulation results reveal that the peak regions exhibit faster corrosion rates than the trough regions.With increasing electrolyte film thickness(from 10μm to 500μm),corrosion rates at both peaks and troughs decrease progressively,and after 120 hours of simulation,the maximum corrosion rate at the peaks declines from 0.720 mm/a to 0.130 mm/a,and at the troughs from 0.520 mm/a to 0.120 mm/a,with the disparity in corrosion rates diminishing over time.Furthermore,as corrosion progresses,pits propagate deeper into the substrate,exhibiting both vertical penetration and lateral expansion along the passive film interface,ultimately breaching the substrate.This research offers valuable insights into designing corrosion mitigation strategies for stainless steel bellows in marine environments.
摘要The formulae for stresses and angular displacements of U-shaped bellows overall bending in a meridian plane under pure bending moments are presented based on the general solution for slender ring shells proposed by Zhu Weiping, et al. and the solution for ring plates. The results evaluated in this paper are compared with those on EJMA (standards of the expansion joint manufacturers association) and of the experiment given by Li Tingxilz, et al.
基金National Natural Science Foundation of China(Grant No.52175349)Aeronautical Science Foundation of China(Grant No.20200009057004)。
摘要A novel buckling-induced forming method is proposed to produce metal bellows.The tube billet is firstly treated by local heating and cooling,and the axial loading is applied on both ends of the tube,then the buckling occurs at the designated position and forms a convolution.In this paper,a forming apparatus is designed and developed to produce both discontinuous and continuous bellows of 304 stainless steel,and their characteristics are discussed respectively.Furthermore,the influences of process parameters and geometric parameters on the final convolution profile are deeply studied based on FEM analysis.The results suggest that the steel bellows fabricated by the presented buckling-induced forming method have a uniform shape and no obvious reduction of wall thickness.Meanwhile,the forming force required in the process is quite small.
基金Key Laboratory of Petroleum and Natural Gas Equipment of Ministry of Education.
摘要In this study,the pressure compensation mechanism of a reducer bellows is analyzed.This device is typically used to reduce the size of undersea instruments and improve related pressure resistance and sealing capabilities.Here,its axial stiffness is studied through a multi-fold approach based on theory,simulations and experiments.The results indicate that the mechanical strength of the reducer bellows,together with the oil volume and temperature are the main factors influencing its performances.In particular,the wall thickness,wave number,middle distance,and wave height are the most influential parameters.For a certain type of reducer bellows,the compensation capacity attains a maximum when the wave number ratio is between 6:6 and 8:4,the wall thickness is 0.3 mm,and the wave height is between 4–5 mm and 5–6 mm.Moreover,the maximum allowable ambient pres-sure of the optimized reducer bellows can reach 62.6 MPa without failure,and the maximum working water depth is 6284 m.
摘要Origami bellows are formed by folding flat sheets into closed cylindrical structures along predefined creases.As the bellows unfold,the volume of the origami structure will change significantly,offering potential for use as inflatable deployable structures.This paper presents a geometric study of the volume of multi-stable Miura-ori and Kresling bellows,focusing on their application as deployable space habitats.Such habitats would be compactly stowed during launch,before expanding once in orbit.The internal volume ratio between different deployed states is investigated across the geometric design space.As a case study,the SpaceX Falcon 9 payload fairing is chosen for the transportation of space habitats.The stowed volume and effective deployed volume of the origami space habitats are calculated to enable comparison with conventional habitat designs.Optimal designs for the deployment of Miura-ori and Kresling patterned tubular space habitats are obtained using particle swarm optimisation(PSO)techniques.Configurations with significant volume expansion can be found in both patterns,with the Miura-ori patterns achieving higher volume expansion due to their additional radial deployment.A multi-objective PSO(MOPSO)is adopted to identify trade-offs between volumetric deployment and radial expansion ratios for the Miura-ori pattern.
摘要According to the characteristics of fluid-structure interaction( FSI) in the process of metal bellows inflating to disperse bomblets,a 3D dynamical FSI model( W model) which describes the interaction between a viscous compressible flow and a structure undergoing large deformationis established. Then the dynamic characteristics of the metal bellows deformation,the changing law of the internal flow field and the motion law of the bombs are acquired.Where the internal pressure and bombs' moving law are approximate to interior ballistic results,which indicates the W model established reasonably. Besides,considering gaps existing atthe bellows' tow ends,the dynamical FSI modelcontaining gaps( Y model) is also built. The results of the W and Y models are compared and the results show that the existence of the gaps has little influence to the flow field and the stress distributionin the bellows,but obviously reduces the separation speed of the bomblets about 10%.
摘要This paper follows the work of[1,2].There are some progress in dealing with moderately small rotations(the squares of rotation angles are the order of magnitude of strains)of middle surface normals of inside and outside ring shells and compressed angle of bellows.Calculation results agree with experiments well.To bellow design,the method given in this paper is of practical value and the discussion of the influence of compressed angle on characteristic relation is helpful.
基金the funds of the National Natural Science Foundation of China(No.51875456)the Natural Science Basic Research Plan in Shaanxi Province of China(No.2019JM-450)+3 种基金the Young Talent fund of University Association for Science and Technology in Shaanxi,China(No.20170518)the Key Laboratory of Advanced Manufacture Technology for Automobile Parts(Chongqing University of Technology),Ministry of Education(No.2018KLMT03)Materials Science and Engineering provincial-level superior discipline funding project of Xi'an Shiyou Universitythe Program for Young Innovative Research Team in Xi'an Shiyou University(No.2015QNKYCXTD02)。
摘要Because of the complex constraint effects among layers in multi-layered metallic bellows hydroforming,the stress concentration and defects such as wrinkling and fracture may easily occur.It is a key to reveal the deformation behaviors in order to obtain a sound product.Based on the ABAQUS platform,a 3 D-FE model of the four-layered U-shaped metallic bellow hydroforming process is established and validated by experiment.The stress and strain distributions,wall thickness variations and bellow profiles of each layer in the whole process,including bulging,folding and springback stages,are studied.Then deformation behaviors of bellows under different forming conditions are discussed.It is found that the wall thinning degrees of different layer vary after hydroforming,and is the largest for the inner layer and smallest for the outer layer.At folding stage,the wall thinning degree of the crown point increases lineally,and the difference among layers increases as the process going.The displacements of the crown point decrease from the inner layer to the outer layer.After springback,the U-shaped cross section changes to a tongue shape,the change of convolution pitch is much larger than the change of convolution height,and the springback values of the inner layer are smaller than the outer layer.An increase in the internal pressure and die spacing cause the maximum wall thinning degree and springback increase.With changing of process parameters,bellows with deep convolution are easily encountered wall thinning during hydroforming and convolution distortion after springback.This research is helpful for precision forming of multi-layered bellows.
摘要On the basis of paper[1],assuming the logarithm of thickness at arbitrary point on a U-shaped bellows meridian is linear with the logarithm of distance between that point and axis of symmetry,perturbation solutions of the corresponding problems of large axisymmetrical deflection are given.The effects of thickness distribution variation,which result from technology factors,on stiffness of bellows are discussed.
摘要In order to analyze bellows effectively and practically, the finite_element_displacement_perturbation method (FEDPM) is proposed for the geometric nonlinear behaviors of shells of revolution subjected to pure bending moments or lateral forces in one of their meridional planes. The formulations are mainly based upon the idea of perturba_ tion that the nodal displacement vector and the nodal force vector of each finite element are expanded by taking root_mean_square value of circumferential strains of the shells as a perturbation parameter. The load steps and the iteration times are not as arbitrary and unpredictable as in usual nonlinear analysis. Instead, there are certain relations between the load steps and the displacement increments, and no need of iteration for each load step. Besides, in the formulations, the shell is idealized into a series of conical frusta for the convenience of practice, Sander's nonlinear geometric equations of moderate small rotation are used, and the shell made of more than one material ply is also considered.
摘要This is one of the applications of Part (Ⅰ),in which the angular stiffness, and the corresponding stress distributions of U_shaped bellows were discussed. The bellows was divided into protruding sections, concave sections and ring plates for the calculation that the general solution (Ⅰ) with its reduced form to ring plates were used respectively, but the continuity of the surface stresses and the meridian rotations at each joint of the sections were entirely satisfied. The present results were compared with those of the slender ring shell solution proposed earlier by the authors, the standards of the Expansion Joint Manufacturers Association (EJMA), the experiment and the finite element method. It is shown that the governing equation and the general solution (Ⅰ) are very effective.
摘要This is one of the applications of Part (Ⅰ), in which the angular stiffness, the lateral stiffness and the corresponding stress distributions of C_shaped bellows were calculated. The bellows was divided into protruding sections and concave sections for the use of the general solution (Ⅰ), but the continuity of the stress resultants and the deformations at each joint of the sections were entirely satisfied. The present results were compared with those of the other theories and experiments, and are also tested by the numerically integral method. It is shown that the governing equation and the general solution (Ⅰ) are very effective.
摘要The overall bending of circular ring shells subjected to bending moments and lateral forces is discussed. The derivation of the equations was based upon the theory of flexible shells generalized by E.L. Axelrad and the assumption of the moderately slender ratio less than 1/3 (i.e., ratio between curvature radius of the meridian and distance from the meridional curvature center to the axis of revolution). The present general solution is an analytical one convergent in the whole domain of the shell and with the necessary integral constants for the boundary value problems. It can be used to calculate the stresses and displacements of the related bellows. The whole work is arranged into four parts: (Ⅰ) Governing equation and general solution; (Ⅱ) Calculation for Omega_shaped bellows; (Ⅲ) Calculation for C_shaped bellows; (Ⅳ) Calculation for U_shaped bellows. This paper is the first part.
摘要is one of the applications of (Ⅰ), in which the angular stiffness, the lateral stiffness and the corresponding stress distributions of Omega_shaped bellows were calculated, and the present results were compared with those of the other theories and experiments. It is shown that the non_homogeneous solution of (Ⅰ) can solve the pure bending problem of the bellows by itself, and be more effective than by the theory of slender ring shells; but if a lateral slide of the bellows support exists the non_homogeneous solution will no longer entirely satisfy the boundary conditions of the problem, in this case the homogeneous solution of (Ⅰ) should be included, that is to say, the full solution of (Ⅰ) can meet all the requirements.
摘要A linear complex equation for slender ring shells overall bending in a meridian plane is given based on E. L. Axelrad's theory of flexible shells. And the non homogeneous solution is obtained from W. Z. Chien's solution for axial symmetrical slender ring shells to investigate the overall bending problem of Ω shaped bellows subjected to pure bending moments. The values calculated in the present paper are very close to the existing experiment. Thus Chien's work on axial symmetrical problems for ring shells has been extended to overall bending problems.
摘要In ITER facilities, there are some special expansion joints connected with the openings of cryostat. Expect for the assemblies connected with NB openings, others are rectangular section with big dimensions and severe working conditions and they are important for ITER safe runing.
基金funded by the National Key R&D Program of China(2022YFD2300700).
摘要Currently,the main optimization of pneumatic conveying seed-discharge systems targets distributors,ignoring the important role of pipelines.In this study,simulations were used to determine an improved structure of the conveying pipe.The horizontal pipe was determined to be a 300 mm straight pipe,which was connected under the vertical bellows as a transition.This study adopted the L9(34)orthogonal test method to optimize the bellows parameters,using as index the coefficient of variation of the uniformity of the bellow outlets.The indoor bench test was designed to validate different flow rate and bellows length combinations.The optimal bellows parameter combination of the corrugated circle had a radius of 8 mm,bellows length of 500 mm,corrugation distance of 40 mm and corrugation length of 16 mm,achieving a 3.46%coefficient of variation of the particle distribution in the plumbing.Under various particle mass flow rates(33.5,67.0,101 g·s−1),the bellows length of the optimal solution was verified to be in the interval of 400−500 mm,and the consistency coefficients of the variations in row displacements of the system satisfied the requirements.This study provides guidance for the design and application of piping in pneumatic seed-discharge systems.
基金the National Natural Science Foundation of China(Grant No.52478504)Guangxi Key Research Program(No.Guike AB22036001,Guike AB21220046)Hezhou Science and Technology Development Program(Hekeji 202229).
摘要Grouted Bellows Connect Rebar(GBR)technology is critical for ensuring reliable connections in precast concrete components.The bond-slip behaviour,a core metric for assessing GBR connection performance,presents significant complexity,and existing empirical models often fall short in prediction accuracy to meet engineering demands.Addressing this challenge,this study introduces an innovative hybrid model(CNN-LSTM)that integrates convolutional neural networks with long shortterm memory networks.Utilizing eight critical parameters,such as grouting strength,reinforcement ultimate strength,and the anchorage length-to-diameter ratio of the reinforcement,the model achieves precise predictions of GBR bond stress.This study systematically collected data from 114 sets of GBR pull-out tests,constructing a dataset comprising 2,272 bond-slip samples for model training and validation.Additionally,15 GBR independent samples were independently fabricated and multiple samples were extracted to assess the model generalization capability.Experimental results demonstrate that the CNN-LSTM model significantly outperforms traditional empirical models in predicting bond stress and exhibits superior generalization across key metrics,including total energy consumption,maximum bond stress,failure modulus,and residual energy.Parameter importance analysis reveals that grouting strength,reinforcement ultimate strength,and the anchorage length-to-diameter ratio are the most influential factors in bond stress prediction.Building on the CNN-LSTM model predictions,this study establishes an improved empirical model with clear physical significance,offering a reliable computational foundation for engineering applications.
基金supported by the International S&T Cooperation Project of China by the MOST of China (No. 2009DFG13050)the National "863" Program of China (Nos. 2007AA06Z413 and 2009AA06Z203)+1 种基金the Key Scientific and Technological Research Project of Shaanxi Province (Nos. 20092KC01-19 and 2008ZDGC-14)the National Natural Science Foundation of China ( Nos. 60727004 and 61077060)
摘要A metal bellows-based fiber Bragg grating (FBG) accelerometer is proposed and experimentally demonstrated. The optical fiber (containing the FBG) is pre-tensioned, and the two ends of the optical fiber are fixed directly from the shell to the inertial mass. In this design, the FBG is uniformly tensioned to obtain a constant strain distribution over it. By employing this configuration, the FBG always has a sharp reflection characteristic with no broadening in its reflection spectrum during wavelength shifting. Dynamic vibration measurements show that the proposed FBG accelerometer has a wide frequency response range (5-110 Hz) and an extremely high sensitivity (548.7 pro/g). The two important indicators of FBG accelerometer can be tuned by the addition of mass to tailor the sensor performance to specific applications, identifying it as a good candidate for structural health monitoring.