Local Buckling-Induced Forming Method to Produce Metal Bellows

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.

Subsea Compensation of Pressure Based on Reducer Bellows

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.

GENERAL SOLUTION FOR U-SHAPED BELLOWS OVERALL-BENDING PROBLEMS

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.

Application of Non-homogeneous Solution for Equations of Slender Ring Shells to Overall-Bending Problem of Ω-Shaped Bellows

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.

The Dynamical FSI Simulation for Bellows Inflating to Disperse Bomblets

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%.

PROBLEMS OF U-SHAPED BELLOWS WITH NONLINEAR DEFORM TION OF LARGE AXISYMMETRICAL DEFLECTION(Ⅰ)—COUNTING NONLINEAR DEFORMATIONS OF RING SHELLS AND COMPRESSED ANGLE OF BELLOWS

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.

ON PROBLEMS OF U-SHAPED BELLOWS WITH NONLINEAR DEFORMATION OF LARGE AXISYMMETRICAL DEFLECTION(Ⅱ)——COUNTING VARIATION OF THICKNESS DISTRIBUTION

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.

GENERAL SOLUTION OF THE OVERALL BENDING OF FLEXIBLE CIRCULAR RING SHELLS WITH MODERATELY SLENDER RATIO AND APPLICATIONS TO THE BELLOWS (Ⅰ)-GOVERNING EQUATION AND GENERAL SOLUTION

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.

FINITE ELEMENT DISPLACEMENT PERTURBATION METHOD FOR GEOMETRIC NONLINEAR BEHAVIORS OF SHELLS OF REVOLUTION OVERALL BENDING IN A MERIDIONAL PLANE AND APPLICATION TO BELLOWS (Ⅰ)

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.

GENERAL SOLUTION OF THE OVERALL BENDING OF FLEXIBLE CIRCULAR RING SHELLS WITH MODERATELY SLENDER RATIO AND APPLICATIONS TO THE BELLOWS (Ⅳ)-CALCULATION FOR U-SHAPED BELLOWS

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.

GENERAL SOLUTION OF THE OVERALL BENDING OF FLEXIBLE CIRCULAR RING SHELLS WITH MODERATELY SLENDER RATIO AND APPLICATIONS TO THE BELLOWS (Ⅲ)-CALCULATION FOR C-SHAPED BELLOWS

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.

GENERAL SOLUTION OF THE OVERALL BENDING OF FLEXIBLE CIRCULAR RING SHELLS WITH MODERATELY SLENDER RATIO AND APPLICATIONS TO THE BELLOWS (Ⅱ)- CALCULATION FOR OMEGA-SHAPED BELLOWS

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.

Proposal of metal bellows-based fiber Bragg grating accelerometer

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.

Deformation behaviors of four-layered U-shaped metallic bellows in hydroforming

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.

Analysis and Optimization of Flow-Guided Structure Based on Fluid-Structure Interaction

Gases containing sulfur oxides can cause corrosion and failure of bellows used as furnace blowers in high-temperature environments.In order to mitigate this issue,the behavior of an effective blast furnace blower has been examined in detail.Firstly,the Sereda corrosion model has been introduced to simulate the corrosion rate of the related bellows taking into account the effects of temperature and SO_(2) gas;such results have been compared with effective measurements;then,the average gas velocity in the pipeline and the von Mises stress distribution of the inner draft tube have been analyzed using a Fluid-Structure Interaction model.Finally,the semi-closed internal corrosion environment caused by a 5 mm radial gap between the inner draft tube and the bellows has been considered.The gas flow rate in the residential space has been found to be low(0.5 ms–this value leads to a stable semi-closed internal corrosion environment for exhaust gas exchange);water phase in the exhaust gas is prone to accelerate the corrosion rate.On this basis,a bellows with an optimized inner draft tube has proposed,which includes corrosion-resistant honeycomb buffer rings.

Novel Discrete Particle Swarm Optimization Based on Huge Value Penalty for Solving Engineering Problem

For the purpose of solving the engineering constrained discrete optimization problem, a novel discrete particle swarm optimization（DPSO） is proposed. The proposed novel DPSO is based on the idea of normal particle swarm optimization（PSO）, but deals with the variables as discrete type, the discrete optimum solution is found through updating the location of discrete variable. To avoid long calculation time and improve the efficiency of algorithm, scheme of constraint level and huge value penalty are proposed to deal with the constraints, the stratagem of reproducing the new particles and best keeping model of particle are employed to increase the diversity of particles. The validity of the proposed DPSO is examined by benchmark numerical examples, the results show that the novel DPSO has great advantages over current algorithm. The optimum designs of the 100-1 500 mm bellows under 0.25 MPa are fulfilled by DPSO. Comparing the optimization results with the bellows in-service, optimization results by discrete penalty particle swarm optimization（DPPSO） and theory solution, the comparison result shows that the global discrete optima of bellows are obtained by proposed DPSO, and confirms that the proposed novel DPSO and schemes can be used to solve the engineering constrained discrete problem successfully.

COMPLEX EQUATIONS OF FLEXIBLE CIRCULAR RINGSHELLS OVERALL_BENDING IN A MERIDIAN PLANE AND GENERAL SOLUTION FOR THE SLENDER RING SHELLS

Complex equations of circular ring shells and slender ring shells overall-bending in a meridian plane are presented based on E. L. Axelrad's equations of flexible shells of revolution render asymmetrical lending. It turns out that the equations are analogous to Novozhilov's equations of symmetrical ring shells, where general sollutions have been given by W. Z. Chien. Therefore, by analogy with Chien's solution, a general solution for equations of the slender ring shells is put forward, which can be used to salve bellow's overall-bending problems.

Analytical approach for the design of convoluted air suspension and experimental validation

An improved analytical design to investigate the static stiffness of a convoluted air spring is developed and presented in this article.An air spring provides improved ride comfort by achieving variable volume at various strokes of the suspension.An analytical relation is derived to calculate the volume and the rate of change in the volume of the convoluted bellow with respect to various suspension heights.This expression is used in the equation to calculate the variable stiffness of the bellow.The obtained analytical characteristics are validated with a detailed experiment to test the static vertical stiffness of the air spring.The convoluted air bellow is tested in an Avery spring-testing apparatus for various loads.The bellow is modeled in the ABAQUS environment to perform finite element analysis(FEA)to understand and visualize the deflection of the bellow at various elevated internal pressures and external loads.The proposed air spring model is a fiber-reinforced rubber bellow enclosed between two metal plates.The Mooney-Rivlin material model was used to model the hyperelastic rubber material for FEA.From the results,it is observed that the experimental and analytical results match with a minor error of 7.54%.The derived relations and validations would provide design guidance at the developmental stage of air bellows.These expressions would also play a major role in designing an effective active air suspension system by accurately calculating the required stiffness at various loads.

柔软激光焊接波纹管

自动激光焊的新型和专利技术造就了"柔软"波纹管制造业,一种机械运动阻力低的波纹管.预期这些柔软波纹管有利于在真空和半导体设备中,需求精密定位而只允许最小的机械阻力的场合应用.

FINITE ELEMENT DISPLACEMENT PERTURBATION METHOD FOR GEOMETRIC NONLINEAR BEHAVIORS OF SHELLS OF REVOLUTION OVERALL BEDING IN A MERIDIONAL PLANE AND APPLICATION TO BELLOW (Ⅱ)

The finite_element_displacement_perturbation method (FEDPM)for the geometric nonlinear behaviors of shells of revolution subjected to pure bending moments or lateral forces in one of their meridional planes (Ⅰ) was employed to calculate the stress distributions and the stiffness of the bellows. Firstly, by applying the first_order perturbation solution (the linear solution)of the FEDPM to the bellows, the obtained results were compared with those of the general solution and the initial parameter integration solution proposed by the present authors earlier, as well as of the experiments and the FEA by others.It is shown that the FEDPM is with good precision and reliability, and as it was pointed out in (Ⅰ) the abrupt changes of the meridian curvature of bellows would not affect the use of the usual straight element. Then the nonlinear behaviors of the bellows were discussed. As expected, the nonlinear effects mainly come from the bellows ring plate,and the wider the ring plate is, the stronger the nonlinear effects are. Contrarily, the vanishing of the ring plate, like the C_shaped bellows, the nonlinear effects almost vanish. In addition, when the pure bending moments act on the bellows, each convolution has the same stress distributions calculated by the linear solution and other linear theories, but by the present nonlinear solution they vary with respect to the convolutions of the bellows. Yet for most bellows, the linear solutions are valid in practice.