Vibration-attenuation devices and methods are disclosed that utilize a bellows situated between a first and second mass and pressurized with a fluid to an internal fluid pressure substantially equal to a zero-stiffness pressure such that the bellows exhibits a substantially zero lateral stiffness The devices may include various components configured to measure, regulate, and control the internal pressure of the bellows in order to maintain a desired pressure The devices may include an active support, such as a secondary bellows or linear actuator, that provides a secondary support force The active support may be connected to various components configured to measure and control the secondary support force The vibration-attenuation devices disclosed may be used in a lithography exposure apparatus to attenuate vibrations between: (1) a support frame and a support surface; (2) a base and a stage-supporting platform; and (3) a supporting stage and a wafer stage

Vibration-attenuation devices and methods using pressurized bellows exhibiting substantially zero lateral stiffness

Application of the equivalent column concept to the stability of axially compressed bellows

Thin-walled bellows expansion joints are frequently applied in piping systems for absorbing thermal and mechanical movement. There have been several failures in service due to the lateral buckling of bellows under pressure, the most notable case being the Flixborough disaster in 1974. The problem of bellows squirming, as the phenomenon is more commonly termed, was first investigated by the Dutch engineer J. A. Haringx in 1952. In the intervening years there has been little additional research carried out and consequently there is a paucity of experimental data and practical theories on the subject. The present paper offers guidance to avoid bellows squirming and provides the design engineer with simple procedures for evaluating the stability of a pressurised bellows subject to either small or large lateral displacements. Formulae are also presented in order to determine the strength of bellows supports which limit and control the amount of bellows movement in service.

Analysis and design guidance for the lateral stiffness of bellows expansion joints

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 Tingxin, et al.

General solution for u-shaped bellows overall-bending problems

Bellows have wide applications in automobile, aerospace, piping systems and industrial systems. An optimised shape for the bellows is expected to give good guidelines for practical design. Metallic bellows expansion joints are subject to displacement loading, this frequently results in cyclic strains. The effects of convolution geometry and boundary conditions on the failure of bellows are analysed in this study. Lateral deflection is considered as a boundary condition and a FEM solution for bellows is obtained. The stress distribution and the number of cycles to failure in the conditions of lateral deflection are obtained. Comparing results, the relation between the number of load cycles to failure and the flexible tube radius is obtained. In addition, the relation between stress and boundary conditions for the model in this study is also obtained.

The Effects of Convolution Geometry and Boundary Condition on the Failure of Bellows

The Problem of bending deformation of U-shaped bellows has not been treated hitherto except by an approximate energy method, and the presentation of the data for this problem is being looked forward to by the designers in piping engineering at the present time. In this paper, the numerical method proposed by B. Budiansky and P.P. Radkowski for problems of unsymmetrical bending of axisymmetric shells, is applied to the problem mentioned above, and the design data for it are presented.

Kiyoshi Nakagawa

Papers

Bending Deformation of U-Shaped Bellows