A bellow pressure fiber optic sensor for static ice pressure measurements

Static ice pressure affects safe operation of hydraulic structures. However, current detection methods are hindered by the following limitations： poor real-time performance and errors owing to the partial pressure of the surrounding wall on traditional electrical resistance strain bellow pressure sensors. We developed a fiber optic sensor with a special pressure bellow to monitor the static ice pressure on hydraulic structures and used the sensor to measure static pressure in laboratory ice growth and melting tests from -30℃ to 5℃. The sensor resolution is 0.02 kPa and its sensitivity is 2.74 × 10-4/kPa. The experiments suggest that the static ice pressure peaks twice during ice growth and melting. The first peak appears when the ice temperature drops to -15℃ owing to the liquid water to solid ice transition. The second peak appears at 0℃ owing to the thermal expansion of the ice during ice melting. The novel fiber optic sensor exhibits stable performance, high resolution, and high sensitivity and it can be used to monitor the static ice pressure during ice growth and melting.

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.

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.

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.

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.

Development of a non-cable whole tectorial membrane micro-robot for an endoscope

A novel non-cable whole tectorial membrane micro-robot for an endoscope is developed. The micro-robot we have fabricated and tested can propel itself in the intestine tract of a pig in an autonomous manner by earthworm-like locomotion. The silicone of bellow shape is laid over the outer surface of the micro-robot to reduce the affection of the viscoelastic properties of the intestine. Wireless power transfer and communication systems are employed to realize the non-cable locomotion of the mi-cro-robot. The prototype of the micro-robot is 13.5 mm in diameter and 108 mm in length. The experimental results show that the towing force for the micro-robot is about 0.8 N, which is much smaller than the maximum driving force 2.55 N of the linear actuator. The supplying power of the wireless power transfer system fulfills the needs of the micro-robot system and the mi-cro-robot can creep reliably in the large intestine of a pig and other contact environments.

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.

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.

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.

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.

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.

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%.

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.

Existence of periodic orbits and shift-invariant curve sequences near multiple homoclinics

In this paper, the complicated dynamics is studied near a double homoclinic loops with bellows configuration for general systems. For the non-twisted multiple homoclinics, the existence of periodic orbit with the specified route and the existence of shift-invariant curve sequences defined on the cross sections of multiple homoclinics corresponding to any specified one-side infinite sequences are given. In addition, the existence regions are also located.

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.