Research On Hydroforming Of Toroidal Bellows And Light-weight Design Of Bellows Based On Finite Element Analysis

As having higher capacity to undertake pressures and larger compensation ability compared with the convoluted bellows,toroidal bellows is more and more widely used in engineering.With more and more large bellows applied,manufacturing process and light-weight design of bellows is getting increasingly concerned.In this paper,hydroforming process of the toroidal bellows was simulated with the influencing factors studied based on the finite element analysis.Optimal design of the unreinforced convoluted bellows and reinforced toroidal bellows was also conducted.The main contents and conclusions are as follows:(1)Finite element simulations of hydroforming of a multi-layered and multi-corrugated toroidal bellows were carried out.The stress and strain distributions before and after unloading were analyzed and the structural parameters were obtained from numerical simulations and verified from the experimental measurements.Results showed that the differences of thinning ratio and wave height between simulations and tests are less than 4%implying that the numerical simulation with the finite element method is feasible and dependable for the hydroforming of the toroidal bellows.(2)The single factor analysis and the variance analysis of the orthogonal experiment were conducted to study the effect of the geometric factors and operating factors on the roundness of wave-shape.It was found that the ratio of wall thickness and radius of small arc(t/r0),the ratio of radius of large arc and diameter of tube blank(r/D)and pressure coefficient of forming stage(y2)have significant influence on the roundness of wave-shape.The range of t/r0 and y2 were given regarding the coefficient a/2h which represented the roundness.The curves of a/2h with different t/r0 and ?2 were provided for the reference of selecting parameters in manufacturing.(3)Wall thickness reduction during the hydroforming of the toroidal bellows was investigated with the influencing factors studied by performing single factor test and the orthogonal experiment.It was found that the ratio of radius of large arc and diameter of tube blank(r/D),the pressure coefficient of bulge stage(?1)and pressure coefficient of forming stage(y2)have remarkable effect on thinning rate of wall thickness.A formula of thinning rate of wall thickness was fitted based on the sufficient numerical simulations of the hydroforming process.Numerical verification showed that the formula had a high accuracy and can meet the requirements of engineering application.(4)The software for circular bellows optimal design was developed with VB,which can carry out the design by rules,finite element analysis and optimal design for unreinforced convoluted bellows and reinforced toroidal bellows.Application of some engineering cases showed that the weight was reduced significantly if applying optimal design,implying that the function of the software for the light-weight of bellows is effective.