Bellow Design Guide [PDF]

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BELLOW DESIGN GUIDE Design guide for bellows An expansion joint is a device containing one or more bellows used to absorb dimensional changes in the piping system while maintaining pressure integrity .Design of bellow involves the evaluation of many often conflicting criteria such as pressure capacity, fatigue life , & spring rate. A bellow is a flexible element of the expansion joint consisting of one or more convolutions & the end tangents with Lb/Db < 3 .Total movement capacity of a bellows is proportional to the number of convolutions. Bellow expansion joints are employed in piping systems to absorb differential thermal expansion while containing the system pressure . The ability of bellow to carry pressure is limited by hoop stress or S2 (defined in EJMA- this is the stress that runs circumferentially around the bellows due to the pressure difference between the inside & the outside of the bellows) . hoop stress holds the bellow together & should be limited to code stress level. The bellows ability to carry pressure is also limited by bulge stress S4 (this stress runs logitudinal to the bellows centreline , it is located in the bellow side wall & is measure of the tendency of convolutions to become less U shaped or more spherical.For bellows that are not annealed after forming ,S4 is allowed by EJMA to exceed the initial yield strength of the bellows material by a large margin because it is cold worked . If a bellow is annealed after forming , S4 must be severly limited because the bellows sidewall material is no longer cold worked. Heat treatment of bellows after forming convolutions can lower bellow spring rate “squirm” pressure, & cycle life The value of (S3 +S4 ) must be limited to 1.5 times the allowable stress for annealed bellows & 3 times the allowable stress for bellows in the as formed condition. When a bellow deflects , bending of the side walls of each convolutions absorb the motion. The associated stress caused by this motion is deflection stress S6.(this stress runs longitudinal to the bellow centreline. Deflection bending stress is the primary bending stress influencing fatigue life .The maximum value of S6 is located in the sidewall of each convolutions near the crest or root.Expansion joints are designed to operate with a value of S6 that far exceeds the yield strength of the bellow material . This means that most expansion joints will take permanent set at the rated axial , angular or lateral motion. Expansion joint bellows are rarely designed to operate in the elastic stress range . There fore the bellow will eventually fatigue after a finite number of movement cycles . The total deflection stress range in the bellows for a typical cyclic movement application will exceed the yield strength & may have a total strain range in excess of 1%.



For a bellow , instability corresponds to a condition where a small increase in the internal pressure will result in a large change in shape. Squirm is said to occur when the bellow deforms such that the ratio of the maximum convolution pitch under internal pressure to the convolution pitch before application of pressure exceeds 1.15 .For a single bellow , column squirm is defined as a gross lateral shift of the centre section of a bellow while the end remain fixed.F or a universal type expansion joint with two bellows,column squirm results in curvature of the bellows centrelines & lateral movement or rotation of the centre pipe spool .For universal expansion joint with initial lateral offset pressure forces are resisted by combined axial & angular spring stiffness. Each increase in pressure produce a corresponding nonlinear jump in lateral deflection .There are two types of squirm or instability that can occur for internally pressurised bellows. One is called column squirm & the other is called in-plane squirm (localised plastic deformation). Limiting design pressure based upon squirm for a universal expansion joint with initial lateral offset, straight centre spool & fixed ends Ps =0 .44 Pe Where Pe= The following acceptance criteria should be used to evaluate bellow squirm at design pressure P< Ps Where Ps is based upon the actual measured or calculated bellows metal temperature under operating conditions To evaluate bellow squirm at test pressure , the following acceptance criteria should be used Pt