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.

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.

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.

Saul Bellow's Adherence and Breakthrough to Jewish Tradition

As one of the most significant American Jewish writers in the 20th century, Saul Bellow was influenced by the Jewish tradition and American mainstream thoughts in his writing creations. The conflicts and amalgamation between these two different cultures in his novels indicate that Bellow not only adheres to the Jewish traditional culture, but also breaks through the narrowmindedness of it.

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 (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.

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 (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 (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.

The Cultural Elements in Saul Bellow's The Adventure of Augie March

The United States of America is uniquely a country of immigrants, a civilization made up of people whose culture origins are in other societies with their own languages, religious customs and fundamental values.This paper will mainly discuss a great Jewish American writer- Saul Bellow focusing on his special ethnic background and analyze the cultural elements in his work The Adventure of Augie March from the perspectives of its main characters and cultural themes.

Superplastic forming gas pressure of titanium alloy bellows

The complex superplastic forming (SPF) technology applying gas pressure and compressive axial load is an advanced forming method for titanium alloy bellows,whose forming process consists of the three main forming phases namely bulging, clamping and calibrating phase. The influence of forming gas pressure in various phases on the forming process was analyzed and the models of forming gas pressure for bellows were derived according to the thin shell theory and the plasticity deformation theory. Using the model values, taking a two-convolution DN250 Ti-6Al-4V titanium alloy bellows as an example, a series of superplastic forming tests were performed to evaluate the influence of the variation of forming gas pressure on the forming process. According to the experimental results these models were corrected to make the forming gas pressures prediction more accurate.

电阻缝焊在多层波纹管膨胀节制造中的非典型应用

因薄壁多层的波纹管刚度小,补偿量大,寿命长而得到广泛应用。但薄壁多层的波纹管与其连接件的环缝焊接难度较大。为了方便多层波纹管的环缝焊接,多采用电阻缝焊将波纹管的直边段封焊在一起。电阻焊缝普遍存在2种状态,即熔合状态和塑性粘合状态。在生产实践中和通过试验研究发现,塑性粘合状态的电阻焊缝大量存在,但并没有显著影响环缝的焊接,采用分散热输入的多层焊是可以克服的。此种电阻缝焊的目的和要求与通常意义上的2层电阻缝焊不同,不要求有承压强度和密封性,只要将多层波纹管端部塑性粘合成整体,当波纹管与连接件焊接时,使下层起到对上层的衬垫作用,不致烧穿即可。此处电阻焊缝是工艺过程焊缝,不是终极焊缝,是在波纹管膨胀节制造过程中的非典型应用。生产实践中不分层的塑性粘合状态的电阻焊缝也可以满足环缝焊接。