8. Conclusions. 8.1 Final Conclusions:

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1 8. Conclusions As discussed earlier design of expansion joints is unique for every individual application. For each application type of inside fluid, its properties, pressure and its fluctuations, temperature variations, etc. parameters are different. There are different technical requirements from each expansion joint depending on its layout and application and length of piping. Hence, designer has to select geometric parameters in order to achieve the desired movement or compensate the axial, lateral or angular deflection due to thermal expansion. First the user decides the expected axial, lateral movement and accordingly the supplier suggests the technical specifications of expansion joint, which fulfill the requirement. From the previous study it is observed that each geometric parameter like diameter of bellow, material thickness, shape of convolutions, number of convolutions, pitch of convolutions, height of convolution, number of plies, etc. has several implications on the stresses behavior, design factors and performance. For an example thickness of material has effects on the strength, stability and fatigue life cycle of bellow. Also the design of expansion joint involves structural and thermal aspects. Hence, the determination of an acceptable design is very critical and complicated. In the present study each geometric parameter is studied for the performance aspect and several performance tests indicates effect of design parameters. Final conclusions from the study are mentioned below. 8.1 Final Conclusions: Final conclusions are elaborated in four groups. Stress behavior of bellows, squirm failure and critical pressure limit, axial spring rate and fatigue life cycle of bellow. These conclusions are combined outcomes of analytical study, Finite Element Analysis and experimental performance testing. These outcomes are with reference to the constraints of the study mentioned thereafter. These comments are useful for designers, researchers and manufacturers of expansion joints for further understanding of the design procedure. 253

2 8.1.1 Geometric parameters - Stress Relationship: 1. Inside fluid pressure produces circumferential membrane stress in the bellows tangent and convolutions. Axial pressure force (thrust force) also produces longitudinal membrane and bending stresses in the convolutions. Bending stresses becomes significant, while the bellows deflects axially (expansion / contraction) or laterally. 2. The major stresses in bellows results from the effect of pressure and deflection. Normally the deflection stresses are higher than the pressure stresses, and are generally above the yield point of the bellows material. 3. Longitudinal stresses are always higher than circumferential stresses. Since, bending stress produced because of pressure force at convolution faces. It is obvious that, stresses because of bending are always higher than direct stresses. Longitudinal bending stresses are directly proportional to square of height of convolution (w). (Figure 5.8) Referring equation Longitudinal bending stress, S 4 = P 2n w tp 2 Cp 4. Maximum longitudinal stresses are produced at root section and maximum circumferential stresses are produced at crest area of bellows. (Refer figure 7.5 and 7.6) These areas are having maximum stress concentration effect. Infect U shape geometry of convolutions, produces minimum stress concentration effect compared to any other shape of convolutions. 5. FEA methodology may be used by designers, for additional verification of design parameters. Stresses evaluated using Finite Element Analysis are near to analytical results. Since customized design approach of expansion joint suggested by EJMA; FEA is very useful. Any minor change in geometry can be made and stresses can be predicted. 6. Multiple plies of the bellow material, increases the overall thickness of the material, by which strength of bellow increases. It is obvious that higher thickness bellows can withstand higher pressure. But multiply arrangement is advantageous, as the inner ply can be used as high corrosion resistant material and outer ply will be higher strength material for load resistance. 254

3 But if simply taking higher thickness in single ply will reduce its fatigue life; as bellows undergo low cycle fatigue. The following table suggests performance of stresses while compared with equivalent single ply bellow. (Figure 4.4 and 4.5) Table 8.1: Multiply Response Design feature spt = tt spt = tt / n Circumferential stress Same Decreases Logitudinal bending stress Increases Decreases Fatigue life Increases Little change Where, tt = total thickness, and spt = single ply thickness 7. Number of convolutions is an important parameter with the designers. If higher number of convolution are selected, higher axial movement is feasible. Since desired axial movement, is shared by all convolutions, unit axial deflection per convolution should be considered in the design of bellow. However, for higher number of convolutions, length of bellow will be increases, and stresses due to deflection are reduces in individual convolutions. The number of convolution should be selected optimum based on the stresses distribution uniformly amongst all convolutions. Designer should keep in mind that the higher length bellow may become unstable (squirm) at critical pressure. (Figure 4.8) 8. Height of convolution is the most significant parameter for axial spring rate of the bellows. If height of convolutions increases, bellow can take higher axial and lateral movements. But this will increase the longitudinal stress in the bellow. Height of convolutions also affects the stability of bellows. As height of convolutions increases, column stability increases, while in-plane stability decreases. So, height of convolutions should be selected optimum in the bellow. (Figure 4.10 and 4.11) 9. As the pitch of bellows increases, circumferential membrane stress increases. But increase in pitch distance will enhance the length of bellow and its column in-stability reduces. Chances of squirm failure are always higher in case of higher pitch bellows. Here equalizing rings can be used, if 255

4 pitch and length of bellow are essential parameters for the specific application. Equalizing rings in the pitch slots will increase the overall column strength of bellows. Pitch of convolutions should be optimum. (Figure 4.15 and 4.16) 10. For high internal pressure applications, toroidal shaped bellows should be used. Since toroidal convolutions (spherical shape) possess higher strength compare to any other shape of convolution. But, toroidal shaped expansion joints provide minimum axial movements. (Table 7.5) 11. The most preferred convolution shape is U type. This U shaped expansion joints should be selected, where more axial / displacement movement is required. Also U shape convolutions are having minimum stress concentration effect due to uniform radius at root and crest sections. 12. Bellows should be always designed on actual metal temperature expected during operation. At elevated temperature, the modulus property is getting reduced. EJMA suggests that the modulus of elasticity of maximum operating temperature should be considered to evaluate permissible stresses of bellow material Squirm failure of bellows: 1. Bellows may fail by squirm, if number of convolutions and pitch of bellow parameters are selected on higher side. Critical pressure of the bellows should be checked or estimated using analytical approach. The design pressure of bellow should be well within the limit of critical pressure. 2. While fluctuation of pressure and thermal expansion/contraction takes place in the bellow, convolutions moves alternately left and right due to its elastic property. This movement continues till the motion remains in the desired limit. When the deflection further increases because of either critical pressure intensity or thermal movement there will be sudden deflection of convolution. The convolutions are deflected beyond elastic range in the permanent mode. These consequences may lead to squirm failure of bellow. 256

5 3. Short bellows having L b /D b less than transition point factor; the in-plane critical pressure is always less than column squirm critical pressure. [3] This observation agrees with the analytical approach of EJMA. 4. From experiments it has been observed that, the short bellows (L b /D b C z ), initially deformed by in-plane squirm and subsequently deformed by column squirm. Using equation Longitudinal bending stress, S 4 = P n w t 2 p 2 C p The maximum meredional (longitudinal) stresses will develop squirm in the bellows, and that will be at the yield stress of the material, hence deriving for maximum conditions. Maximum Yield stress, S y = P w t cr 2n p 2 C p (8.1) Rearranging above equation, Critical pressure, P cr = S y 2n t p C p w 2 (8.2) EJMA relation is very near to this equation, along with end condition constants, which are used for design of columns. (Equation 3.5) Column critical pressure, P sc = 0.87 Ac S y 0. 73L 1 Db q C z Db b Axial Spring rate of Bellows: 1. Bellows with less spring rate are soft (flexible), while bellows with higher spring rate are stiffer. We desire more flexibility and higher strength from expansion joints. 2. As per analytical approach of EJMA, axial spring rate increases with increase in diameter, thickness of material, number of plies and elasticity property of material, while decreases with decrease in height of convolutions. So, stiffness of bellow is function of following parameters. Stiffness of bellow = f Dm, t, E, w, N, q, n 257

6 Normally stiffness (spring rate) is evaluated for each convolution, hence, number of convolution (N) and pitch (q) will be unity. 3. U shapes convolutions permits higher axial deflection, compared to toroidal convolution bellows, for the same material thickness. 4. The stiffness is directly proportional to cubic rate of thickness and inversely proportional to cubic rate of height of convolutions. In case of precise requirement of stiffness of bellow, thickness and height of convolution are significant parameters. From Design of Experiment it is proved that out of these two parameters thickness is the most significant parameter. 5. It is observed that the working spring rate (f w ) of bellow is always higher than initial spring rate of bellow. The working spring rate (f w ) depends on the amount of axial deformation made by each convolutions and static force of inside fluid. Increase in convolution movement and static pressure leads towards higher working spring rate. This is a dynamic parameter of a bellow. 6. It is also observed that working spring rate of bellow is a continuously changing parameter. While the deflection is beyond the stiffness, then permanent deformation takes place Fatigue Life of Bellows: 1. For ductile materials subjected to cyclic loading, the stress concentration factor has to be included in the factors that reduce the fatigue strength of a component. EJMA has introduced material thinning factor and stiffness factor. It is not possible to determine stress concentration factor due to large variations in shapes and features of bellows. 2. The fatigue life expectancy through stress fatigue life relationship phenomena is an approximate method. This method includes only elastic properties effect in the prediction of life cycles. The stresses developed in the expansion joints are elastic as well as plastic deformation. Hence consideration of plastic stress-strain will make prediction more precise. But it is very difficult to estimate stresses due to permanent deformation. 258

7 3. Fatigue life of a bellows is influenced by the combined stress range induced by pressure and deflection. The multiply construction with lower thickness enhances the fatigue life of bellows. 8.2 Limitations of Study: Following are the limitations of the study: 1. There are large variations in manufacturing methodology of bellows from industry to industry. Hence analytical validation of results may not be very precise. Also the geometric dimensions of bellow are not very much precise (in terms of microns). Hence, precise validation of the results is difficult. 2. FEA may be used as additional verification of design process. Also the prototype testing can be avoided in some cases. But it can not eliminate conventional design process. 3. FEA may be used for stress analysis for the expected results, but periodically validation of results by experimental methods is necessary. Experimentation gives more reliable verification of design process. The experimental testing gives assurance to the customers. 4. Measurement of stresses is only possible through strain measurement, but here strain gauges instrumentation facility was not feasible. The cost of strain gauges is not very high, but precise measurement requires high electrical network. This involves very high cost. 5. Bellows undergo low cycle fatigue. To evaluate the number of life cycles of a bellow requires a special test rig. Reliable experimental test data can be generated only after multiple tests. But due to lack of experimental test facility, fatigue tests are not included in the study. Also multiple tests require many test specimens, which involves very high cost is definitely a constraint. Hence, experimental study of individual parameters of fatigue life is not covered. 259

8 8.3 Future Scope of Study: This study is mainly based on design aspects of expansion joints. The further study can be enhanced by following ways. 1. More number of experiments may be conducted for few more samples in each case, to make exhaustive and critical review of the performance of bellows. 2. Stress measurement is difficult in the experimentation, but introducing some strain gauges for the accurate measurement of strain with reference to design parameters can be evaluated. 3. Fatigue life tests are very costly affairs for even industry people, hence using fatigue module of FEA software to bellows, can be more useful for the industry for prototype of experimentations. 4. Developing computerized control program based (CNC) machines to form convolutions in the bellows is a challenging task. Since, convolution geometry differs from industry to industry; some standardization in shapes can be established. 5. Identifying more critical parameters of bellows and adding more features in the expansion joints to improve or enhance the performance of expansion joints in the real life applications. 260