6. Performance Testing of Bellows

Transcription

1 6. Performance Testing of Bellows Bellows are correlated with actual test results to demonstrate predictability of design parameters like rupture pressure, meridional yielding, squirm and cycle life for a consistent series of bellows of same basic design. [0] Minimum five meridional yield rupture tests on bellows of varying sizes are recommended by EJMA. [0] A minimum of ten squirm tests on bellows of varying diameters and number of convolutions are required. A minimum of twenty five fatigue test on bellows of varying diameters, thicknesses, convolution profiles are required to construct a fatigue life versus combined stress plot. The test bellows must be representative of typical bellows design and manufacturing process. Hence lot of cost is incurred in testing facilities of bellows. Many times special purpose test rigs are required to be prepared for experimental verification or testing of bellows. Testing results can be used for the foolproof design of expansion joints. Frequent testing is essential for the manufacturers as customized design approach. 6.1 Purpose of Testing: To assure a purchaser (user) that the product has been properly designed and manufactured; which requires some method of examination and testing of the product. The user may specify the kind of test required in the acceptance criterion. Type of testing may be depending upon individual application. To ensure that the product has been precisely designed and carefully manufactured, certain tests are required. To ensure that the product is totally defect free, some method of examination of the product is also required. The testing can be categorized in to two groups, destructive testing and non-destructive testing. All tests are not required for bellows, but the required types of tests are selected for individual application. Some standard non-destructive examinations are mentioned below. 6. Non-destructive Testing: 1. Radiographic examination. Liquid penetration examination 3. Fluorescent penetrant examination 190

2 4. Magnetic particle examination 5. Ultrasonic examination 6. Halogen leak examination 7. Mass Spectrometer examination 8. Air jet leak examination 9. Pressure Testing A. Hydrostatic testing B. Pneumatic testing 10. Spring rate test Pressure tests are useful for detecting leaks, and also way to test bellows squirm, meridional yield and rupture 6..1 Radiographic Examination: This method is based on the principle that extremely high frequency light waves, usually x rays will penetrate solid materials and, when projected on to photosensitive film, will reveal voids, areas of discontinuity, and lack of homogeneity. This examination is widely used to evaluate the soundness of welds. Unless required by the purchaser, radiographic examination of the longitudinal seam of a bellow need not be specified. 6.. Liquid Penetrant Test: This method consists of cleaning a surface, coating it with a dye, wiping the dye off and coating the surface with a developer which after sufficient time will draw the dye from the cracks, pin holes, and make them apparent to the observer. Liquid penetrant examination is limited in the scope to detecting the surface defects Flourcent Penetrant Examination: Flourcent penetrant examination is similar in purpose to the liquid penetrant examination but is accomplished by the use of a dye which contains a flourcent material and developer Magnetic Particle Examination: Magnetic particle examination consists of coating a surface with finely powdered iron and establishing a magnetic field in the material being examined. The 191

3 presence of discontinuities and irregularities in the magnetic field, as indicated by the lines of powdered iron, will indicate surface and subsurface defects Ultrasonic Examination: Ultrasonic examination used high frequency sound waves to detect flaws, and is useful in determining thickness, depth and exact location of defects. Interpretation of indications in sections of sharply varying thickness is difficult Halogen leak Examination: Halogen leak examination utilizes a probe of suitable design which selectively indicates the presence of halogen gases. This examination is more sensitive than a hydrostatic test or air jet leak examination but since it is done at low pressure, it can only determine the presence of a leak and can not validate the structural integrity of the item being examined Mass Spectrometer Examination: Mass spectrometer examination is an extremely sensitive means of determining the presence of a leak. The gas used is helium. This test is only recommended for explosive service requirements. 6.3 Hydrostatic Pressure Testing: The hydrostatic pressure testing is necessary to check the pressure withstanding capability of bellow and detection of any leakage in the bellow. This test is carried out in a suitable fixture as shown in the figure 6.1 or in case of large diameter; it can be carried out without fixture with necessary fabrication. The bellows ends must be closed and free length of the bellow should be made fixed with extra leg support at three or four sides of the diameter. This test involves filling of the expansion joint with a liquid, usually water. After filling, it can be pressurized up to the test pressure. The test pressure is usually 1.5 times the design pressure at ambient temperature. Expansion joints placed in high temperature service may require the pressure test to be performed at an adjusted pressure. It is imperative that the test pressure does not produce any membrane stress in excess of yield strength or cause permanent deformation or instability of the bellows at test temperature. The observer has to take care about 19

4 pressure drop in the bellow, leakages if any in the bellow. Bellow should come to its original shape after removal of pressure. Figure 6.1: Set up diagram for Hydro test 6.4 Pneumatic Pressure Testing: This test is having similar objectives as to check the pressure withstanding capability of bellow and detection of leakage. This test involves filling of the expansion joint with air or other gas. After filling, it can be pressurized up to the test pressure. The test pressure is usually 1.1 times the design pressure at ambient temperature. Expansion joints placed in high temperature service may require the pressure test to be performed at an adjusted pressure. It is imperative that the test pressure does not produce any membrane stress in excess of yield strength or cause permanent deformation or instability of the bellows at test temperature. 6.5 Spring Rate Test: The force required to deflect (usually compress) a bellow is a function of the dimensions of the bellows and the material from which it is made. It can be measured as load per unit deflection. The curve of force versus deflection for most 193

5 bellows indicates motion extending into the plastic range, since material thickness is taken very less in order to get higher flexibility. Spring rate determination of a bellow becomes more critical as variation in geometric parameters and bellow deforms in elastic range as well as plastic range. Many times due to higher deflection taking place in piping length, deformation stresses becomes very significant. But assuming the movement of bellows deformation is within elastic limit, the axial theoretical spring rate can be determined experimentally, which can be useful for the limit of axial deformations of bellows. Figure: 6. Setup diagram for spring rate test A simple press type fixture is necessary for the spring rate test. Following procedure can be used for test. The diagram is shown in figure The expansion bellow to be tested is placed in vertical position in the fixture as shown in the figure 6.. The bellow is held in place by means of fastening clamps.. Measurement of the length of bellow should be feasible with fixed or free scale at different loadings. 194

6 3. Measurement of force, which is created by operating screw or bringing ram downwards, should be through electronic load cell. 4. The initial position or free length of bellow is measured on the scale or using separate scale. 5. Force is gradually applied in the steps by rotation of the screw or pressurizing the ram. 6. Measure the load readings with reference to bellow length at various intervals. 7. Plot the curve of force vs deflection, which is the spring rate of the bellow. 8. Compare the spring rate with theoretical designed value. 6.6 Destructive Testing: 1. Squirm testing. Meridional yield- rupture testing 3. Fatigue life testing Squirm Testing: Main objective of the test is to determine the internal pressure which will cause a bellows to become unstable. Squirm is defined on the basis of change in pitch of the bellows convolutions under internal pressure. Test Procedure: 1. Expansion joint should be placed in a suitable fixture, with bellows in straight position.. Bellows should be effectively sealed at the ends during pressurization. 3. End movements must be prevented. 4. Bellows can be tested either in horizontal or vertical position. Horizontal is preferred. 5. Testing medium should be water for safety. 6. No restrictions to convolutions. 195

7 7. Use two dial gauges in perpendicular direction (on outer surface of convolution), to observe deflection of end centers of a bellow. 8. Change in pitch of all convolutions. 9. Pressurize the specimen in steps without releasing the pressure between steps. 10. Each interval should not exceed 10% of the final anticipated instability pressure, although smaller intervals are preferred. 11. Instability of axially aligned bellows is generally characterized by a sudden acceleration of either the change in resultant lateral deflection and/or change in convolution pitch Meridional yield rupture testing: Rupture test is to determine the internal pressure which will cause yielding and rupture of bellows. Place the expansion joint in any suitable fixture, with the bellows fixed in the straight position which will effectively seal the ends during pressurization, and most importantly will prevent any movement of the ends during testing. Test medium should be limited to water as safety precautions. Pressurize the specimen in steps, retaining to zero pressure after each step, up to at least twice the yield pressure. Instrumentation should be arranged such as pressure time recorder, strain gauges etc Fatigue Life Testing: This test must be on proto type bellows. Fatigue life testing is a verification of the ability of a bellow to withstand a given number of flexing cycles. With all other shape factors remaining constant, cycle life will generally increase with diameter. But for prototype testing it may be acceptable to cycle test the smaller size of expansion joint being furnished for a given series of identical service condition. Figure 6.3 shows the arrangement required for cycle life test of a bellow. Test Procedure: 1. Place the bellow element in the suitable fixture as shown in the figure Bellows should be effectively sealed at the ends during pressurization. Apply pressure gradually till it reaches design pressure. 196

8 3. Set axial movement of bellow as per designed permissible limit. Check whether the bellow test is as per free length or extended length. Set limits according to these values. 4. Pressurize the bellow with water. 5. Start fatigue testing at room temperature, keeping it pressurized at design pressure. The fatigue life frequency shall be kept constant as far as possible. Figure 6.3: Set up diagram for cycle life test 6. Continue cycle life testing till it reaches 10,000 cycles. 7. Check for any leakage in the bellow. 8. Carry out Die penetrant examination for any surface cracks after the fatigue test. 197

9 Fatigue may be performed at constant pressure or varying pressure condition. It is also acceptable to cycle test at room temperature any expansion joint which will be furnished for operating temperatures up to the active creep range. For expansion joints operating above this range, consideration should be given to testing at elevated temperature. 6.7 Experimental Work All activities associated with the development of any product for the full satisfaction of the customer requires extensive planning and as well as conducting various research studies so that the optimum value of all decision variables can be achieved. The quality engineering techniques are very much helpful in producing robust design of the products. [B13] Many more quality engineering principles are helpful for making robust product. They are system design through innovations, parameter design, tolerance design, product design optimization, process design optimization, statistical quality control etc. 6.8 Design of Experiments In the present business scenario of globalization a revolution is taking place due to customers higher expectations and breakneck technical changes are taking place which are causing yesterday s realities as tomorrow s irrelevancies. Quality, reliability and durability are the primary factors in the customer s buying decisions in the present overall business revolution. The robust design of products is the fundamental requirement of the customers. Robust design means that the performance of the system is always acceptably close to the ideal function of the system. A systematic and efficient way to meet the challenge of developing a robust product is the statistical approach to the optimization of the product and process design which was originally developed by Sir Ronal A Fisher and later adapted by Genichi Taguchi for industrial products. This work is an attempt towards optimization of various geometric parameters for the spring rate of bellows. After that some tests are carried out and using results some meaningful conclusions are drawn Taguchi s philosophy: All products have characteristics that describe their performance relative to customer requirements or expectations. The quality of product is measured in 198

10 terms of these characteristics. Quality is related to the loss to society caused by a product during its life cycle. A truly high quality product will have a minimum loss to the society as it goes through this life cycle Purpose of Experimentation: The purpose of product or process development is to improve the performance characteristics of the product or process relative to customer needs and expectations. The purpose of experimentation should be to understand how to reduce and control variation of a product or process; subsequently, decisions must be made concerning which parameters affect the performance of a product or process. By adjusting the average and reducing variation, the product or process losses can be minimized Basis of experimentation: The basis of experimentation should be based on the use of orthogonal arrays to conduct small, highly fractional factorial experiments up to larger, full factorial experiments. The use of orthogonal arrays is just a methodology to design an experiment, but probably the most flexible in accommodating a variety of situations and yet easy for industry people to execute on a practical basis Introduction to Design of Experiments (DOE): Design of Experiments (DOE) is a statistical technique introduced by R A Fisher in England. This technique is useful for simultaneously study of multiple variables on the any parameter or outcomes. Dr. Taguchi has carried out significant research with DOE techniques in the field of electronics. This technique has many advantages over classical experimentation procedure. DOE is helpful in addressing quality of the product issue in the design phases of products. DOE is helpful in finding influence of individual parameters, determination of relative influence of individual factors and it leads to optimum design of the product or process. A designed experiment is the simultaneously evaluation of two or more factors (design parameters) for their ability to affect the resultant average or variability of particular product or process characteristics. To accomplish this in an effective and statistically proper fashion, the levels of the factors are varied in a strategic manner. The results of a particular test conditions are observed and a complete 199

11 set of results are analyzed to determine the influential factors and preferred levels, and weather increases or decreases of those levels will potentially leads to further improvement. Basically this is an iterative process. Later on experiments typically involve few factors at more than two levels to determine conditions of further improvement The process of Design of Experiments DOE: [B13] Following are the steps suggested for design of experiments by Taguchi philosophy. 1. State the problem or area of concern: A statement of problem should be critically framed so that will make clear and concise description of the problem. Expansion joints are manufactured with customized approach for individual application. The performance is mainly depending on precise design and manufacturing methodology. The expansion joint must perform expected flexibility while working. The flexibility of bellow is depending on its material property and selection geometric parameters. The initial theoretical axial spring rate can be evaluated from the parameters. The spring rate of bellow must maintain consistently within limits, so performance is assured. This testing will also help to reduce variation in manufacturing procedure and quality will improve. The statement of the problem is framed as Optimization of parameter design of expansion joints for the desired or expected value of initial axial spring rate using Design of Experiment (DOE) technique.. State the objectives of the experiment. The objectives of the experiment are (a) Effect of various geometric parameters on axial spring rate, (b) Study of percentage influence of each parameter, (c) To check expected performance of expansion joint, (d) To verify existing design procedure. 3. Select the quality characteristics and measurement system. 00

12 The initial axial spring rate of the bellow can be measured by spring rate test as suggested by EJMA. This test is basically non-destructive test. Here the spring rate is measured by movements of bellows at various pressure values. The convolution movement can be measured by variations of pitch of the convolutions. This movement can be measure by vernier caliper. The both ends must be welded with flanges and their movements should be restricted by a fixture. 4. Select the factors that may influence the selected quality characteristics. Here the list of factors to be evaluated in the experiment for their effect on the selected quality characteristics should be determined. The initial axial spring rate of bellows depends on following factors (a) Selection of material and its modulus of elasticity (b) Selection material thickness, (c) Design parameter - height of convolutions, (d) Design parameter - pitch of convolutions (e) Design parameter Mean diameter of bellow (f) Design parameter number of plies of material. 5. Identify control and noise factors. (Taguchi-specific) Control factors are those factors that a manufacturer can control the design of a product, the design of a process, or during a process. (a) Control on variations in thickness while forming convolutions. (b) Control on precise dimension of height of convolutions. (c) Control on pitch of convolutions. Noise factors are those things that a manufacturer can not or wishes not to control for cost reasons. 1. Very high precision level of dimensions 6. Select the levels for the factors. Basically the spring rate of bellows mainly depends on two parameters for a particular material. First parameter is thickness and number of plies. As higher 01

13 the thickness, spring rate is increases and for lower thickness the spring rate will be reduces. These two parameters must be considered as a common parameter named as total thickness. This will simplify the understanding as a common parameter. So, Total thickness = Material thickness x number of plies. Second important parameter is height of convolutions, as the height of convolution increases, spring rate reduces and for lower height of convolution spring rate is always higher. Here, two levels of parameters can be selected for the total thickness and height of convolution parameters for the design of experiment. [B13, B4] 7. Select the appropriate orthogonal array. The determination of appropriate orthogonal array for the experiment is major criteria for the experiment. Since two parameters are selected for two levels, following orthogonal array may be selected for the experimentation. Parameter A = Thickness of bellow material Parameter B = Height of convolutions Table 6.1: Experimental parameters for Axial Spring Rate Thickness of bellow material t (cm) A1 Height of convolutions w (cm) B1 A1 B A B1 A B 8. Select interactions that may influence the selected quality characteristics, or go to step 4. (iterative process) 9. Assign factors to orthogonal array and locate interactions. 10. Conduct tests described by trials in orthogonal arrays. 11. Analyze and interpret results of the experimental trials. 1. Conduct confirmation experiment. Steps 8 to 1 are performed in the experiment as per experimental results. 0

14 6.9 Applying DOE on Spring Rate of Bellows: The force required to deflect a bellow is a function of the geometric parameters of the bellows and the material from which it is made. The curve of force versus deflection for bellows may be represented by straight line, based on Hook s law of elasticity (within elastic region). Here lower material thickness will permit higher flexibility and leads to higher spring rate. Spring rate will not be consistent because of large variations in geometric parameters. U shape of convolutions permits higher spring rate, while toroidal shape of convolutions will not. Hence for expected movement of expansion joint, determination of spring rate of bellow becomes essential. The influencing parameters for the spring rate of bellows are mean diameter, thickness of material, number of plies, height of convolution, number of convolutions and elastic modulus of the material. If the spring rate of bellows is evaluated in force required per unit deflection, per convolution, than number of convolution parameter can be reduced from the analysis. The initial theoretical spring rate of bellows can be evaluated analytically using following relationship which is suggested by EJMA. [0] Theoretical initial spring rate, 3 p Dm Eb t n fiu 1.7 (6.1) 3 w C where, D m = Mean diameter of the bellow, cm. E b = Elasticity of the bellow at room temperature, N/cm t p = Thickness of bellow material, cm n = Number of plies, 3 w = Height of convolutions, 3.8cm. C f = Constant based on inside dia. and pitch of convolutions, Axial Spring Rate of Metallic Bellows The factors, which can influence axial spring rate, are thickness of material (t), number of ply (n), convolution height (w), mean diameter of bellow (Dm), elastic property of material, and constants. Table 6.1 shows the factors considered and its corresponding levels along with the interactions. The inner array along with the experimental results is given in Table 6.. Experimental results are taken by manual measurement. The movement of convolution is measured by distance between two end flanges using Vernier calliper. For the analysis smaller is better f 03

15 quality characteristic is selected. Due to economic reasons, one test result for each trial is used in this investigation only the interactions between two factors are considered and all other interactions are ignored. Table 6. Factors and Levels No. Factors Level 1 Level 1 t x n w t x w INTERACTION Table 6.3 Experimental Results Sr. t w Axial Spring Rate (N/cm) Axial Spring Rate (N/cm) No. (cm) (cm) Experimental data Table 6.4: Experimental Results (In two level formats) Parameter Parameter Total (A 1 ) (A ) Parameter 3100, , (B 1 ) Parameter 408, , (B ) Total = Analytical Approach: Sum of Squares (SS): SS T = N y i 1 i T N (6.) = = = Variations due to thickness (t): T N ka A SS A = i T i 1 nai N (6.3) = =

16 SS A = A A 1 = N 8 = (6.4) Variations due to convolution height (w) : SS B = B B 1 = N 8 = (6.5) Variations due to combined effect (t and w): A 1 B 1 = (A x B) 1 = 6310 A B = (A x B) = 8630 A 1 B = (A x B) 3 = 4668 A B = (A x B) 4 = 7000 SS (AxB) = C i 1 ( AxB) i ( naxb) i T SS N A SS B (6.6) = = 18 SS (AxB) = AxB AxB 1 = 18 N SS T = SS A + SS B + SS (AxB) + SS e = SS e SSe = 4105 Degree of freedom: V T = N 1 = 8 1 = 7 V T = V A + V B + V AxB + Ve V A = k A 1 = 1 = 1 V B = k B 1 = 1 = 1 V AxB = V A x V B = 1 x 1 = 1 V e = V T V A V B V AxB = = 4 05

17 6.9.3 Results and discussions: The results are evaluated by Taguchi method and the methodology is shown earlier. The results are tabulated in the ANOVA table 6.5. The influence of each parameters can be observed easily by referring last column. Figure 6.4 and 6.5 shows effect of both geometric parameters by line graph. Table 6.5: ANOVA Table Factor Sum of squares (S S) Degree of freedom (v) Variance (V) F-Ratio (F) Percent contribution ( % ) t w t x w Error Total Variance = SS / degree of freedom Factor F = Variance / Variance (error) SS A = SS A (V e ) v A = = Percent contribution = (SS A / SS T ) x 100 = ( / ) x 100 = Effect of t ASR, N/cm t, cm Figure 6.4 Influence of thickness of material 06

18 Effect of w ASR, N/cm w, cm Figure 6.5 Influence of height of convolution Observations: 1. The experiment investigation and the subsequent analysis bring out the influence of dominancy of selected geometric parameters (thickness and height of convolution) for the axial spring rate of bellows.. The thickness is being the most significant parameter (65.98%), followed by convolution height plays influence of (3.51%) and the combination of these two parameters affects very negligible (-0.36%) for achievement of axial spring rate in metallic bellows. 3. The factors are predominant for a confidence level of 95%, since error part is very negligible, the results may consider reliable. 4. The most significant parameter is thickness of material (t) for desired axial spring rate Limitation: Spring rate measurement is carried out on four bellows and results are extrapolated for L-8 orthogonal array. Further if all eight experimental data are available, influence can be evaluated more precisely. 07

19 6.10 Spring Rate Test: The force required to deflect a bellow is a function of the dimensions of the bellows and the material from which it is made. The curve of force versus deflection for most bellows indicates motion extending into the plastic range, since material thickness is taken very less in order to get higher flexibility. Spring rate determination of a bellow becomes more difficult as variation in geometric parameters and bellow deforms in elastic range as well as plastic range. Many times due to higher deflection taking place in piping length, deformation stresses becomes very significant. Bellows are loaded by internal pressure, which may cause a bellow to become deflect axially, laterally or angularly. Bellows performance is depending on critical pressure and temperature and their fluctuations. The bellow convolution may get expand or contract axially and laterally. Figure 6.6: General curve of Bellows Force vs Deflection The curve shown in figure 6.6 shows the curve of force vs deflection for most bellows indicates motion extending into the plastic range. The first portion of the curve is a straight line as the bellows is deflected through its elastic range (Hooke s law). As bellows deflection continues and extends into plastic range, the 08

20 force vs deflection relationship becomes non-linear until the point of maximum deflection is reached. When the restraining force is released, the curve again becomes linear until the applied force is zero at which point the residual deflection of the bellows still has a positive value. To return the bellows to its initial position, a restoring force must be applied in the opposite direction as shown by the curve below the abscissa. This phenomenon is similar to hystersis loop behavior of materials while supplying electric or magnetic energy. Line A represents theoretical initial elastic spring rate, which can be determined analytically with reasonable accuracy. This equation is mentioned in analytical approach and for U shape convolution as shown in figure 6.7. Figure 6.7: Convolutions of bellows Experimental method to check Spring Rate: An experimental set up requires a bellow with both ends blind. This bellow is mounted between two end plates with fixed lungs. The bellow can not expand but due to pressure force, it can contract. The whole set up is made vertical and at the top, pressure gauge is mounted. Same side one opening is kept through water pump. The water is filled till it overflows, and then the hole is closed. Now using water pump inside pressure can be increased at different values and the movements of convolutions can be observed and measured. The length 09

21 variations can be measured with reference to convolution tip. It can also be termed as pitch. The pitch variation is taken at 4 sides, 90 0 to each other, named as A, B, C and D Assumptions of Analysis: 1. Bellow material is having uniform thickness.. Bellow material is homogeneous. 3. Pitch measurement is carried out with vernier caliper, but due to manual approach, measurement error can be approximately ± 0. mm. Geometric Dimensions of a bellow: A bellow with following dimensions is taken for experiment for the spring rate measurement. Table 6.6: Geometric dimensions of a bellow Db Dm t w q N n E (cm) (cm) (cm) (cm) (cm) (N/cm ) Mean diameter, D m = D b + w + (n x t) = (3x0.06) = cm Cylinder bore = 10 cm. Figure 6.8: Measurement indication of a bellow 10

22 Experimental Results: Table 6.7: Experimental Results Sr. Change in length between convolutions, cm Average Pressure No N/cm change, A B C D. cm Maximum variations between N/cm Result Analysis: Sr. No. Pressure N/cm Table 6.8: Computation of Axial Spring Rate Force = Pr. x Area (N) Unit Deflection (Reference : 45.7) (cm) Bellow Spring Rate =Force/Unit deflection (N/cm ) Average: = Sample calculations: Force at 100 N/cm pressure = Pr.xArea =100x 4 D bore Unit deflection at 100 N/cm pressure measured = 1.5 cm Spring rate = Force / unit deflection = 7850 / 1.5 = 680 N/cm =100 x (10) = 7850 N 4 11

23 Graphs: Force (N) Deflection (cm) Figure 6.9: Force Vs Deflection curve Analytical Approach: EJMA suggests an analytical approach to check the initial spring rate of bellows. It also suggests that; since there is no standard manufacturing methodology at various industries, frequent experimental testing must be carried out to validate the design methodology. Dm Eb t p n Bellows initial Axial Elastic Spring Rate fiu 1.7 (4) 3 w C f 3 = 1.7 x x x x1.8 3 x 3 = N/cm/convolution. Axial spring rate of bellow = / 10 = 5454 N/cm. 1

24 Spring rate, N/cm/conv Pressure, N/cm Experimental Analytical Average Exp Figure 6.10 : Comparison of Spring Rate Results Comparison of Results: Table 6.9: Comparison of Results Average Experimental Spring rate Analytical Spring rate Deviation in spring rate % deviation (N/cm) (N/cm) (N/cm) Observations: 1. Experimental results shows that the spring rate of bellows vary with respect to internal pressure load. Hence, the average movement of convolution is considered for various pressure loadings in elastic range. As the pressure increases towards designed value, the spring rate also approaches to expected value. In the present study maximum deviation is up to 1.19%.. Bellows with lower value of spring rate are flexible, while bellows with higher spring rate value are stiffer. We desire more flexibility from expansion joints. 3. Stiffness of bellow is directly proportional to mean diameter of bellow, thickness of material, number of plies of bellow, while inversely proportional to height of convolutions. 13

25 6.11 Squirm Test: The purpose of squirm test is to check critical buckling pressure of a bellow. The objectives of the test are to find actual factor of safety, validation of the design procedure and confirmation of manufacturing process. The bellow is said to be squirmed on the basis of major (sudden) change in pitch of the bellows convolutions under internal pressure. The test will also be helpful to determine the critical internal pressure at which it will become unstable Geometric dimensions of a bellow: Material type = SS 304 Table 6.10: Geometric dimensions of a bellow Db Dm t w q N n E (cm) (cm) (cm) (cm) (cm) (N/cm ) Length of a bellow = N x q = 18.0 cm Design Pressure = 50 N/cm Estimation of Critical pressure: Ratio of Length to diameter of bellow = (18.0 / 16.90) = Transition Point factor, Cz = 4.7 f S y D i u b q A c =.5 Since Lb/Db ratio is less than transition point factor (1.0769<.5), it is short column. Where, fw = Theoretical spring rate = 1998 N/cm/convolution Sy = Yield strength of material = 0310 N/cm Ac = Cross section metal area of one bellow = cm Critical Pressure (In-plane) = 7 N/cm Critical Pressure (Column) Psc = 0.87 A c S y 0. 73L 1 Db q C z Db b = 95.4 N/cm 14

26 Experimental Readings: Table 6.11: Experimental Readings of Pitch dimensions

27 Summary of Results: Table 6.1: Summary of Pitch Dimensions Pressure, N/cm Average pitch, mm AVG. PITCH, mm PRESSURE, N/cm Figure 6.11: Graph showing pitch variations 16

28 Observations: 1. Experimental results of squirm test of bellows shows variations of pitch well within elastic limits up to the pressure 10 N/cm. But beyond that pressure, deformation exceeds continuously till squirm failure.. The pitch variation suddenly increases from 50 N/cm, i.e. because of drastic deformation of bellows beyond elastic limits. Here the pitch disturbs permanently even after releasing pressure. This is called squirm failure. 3. Bellow should be loaded well within the limits of critical pressure to avoid squirm failure. 4. In case of short column bellows, it is observed that the bellow initially failed by in-plane squirm, than subsequently by column squirm. 5. Critical value of pressure suggested by EJMA involves following safety factor. Factor of safety in in-plane squirm failure = (50 / 7) = 3.47 Factor of safety in column squirm failure = (90 / 95.4) =

29 6.1 In-Plane Stability Tests: In actual practice, piping are operates at various temperatures in a specific range. Like for a particular application of expansion joint, the piping operates between 5 0 F to F (-3 0 C to C). Now the installation of expansion joint should be carried out at minimum design temperature, and at minimum temperature, the bellow will be under compression mode. To facilitate the installation for such cases, bellows are initially pre-compressed axially by certain amount and than installation is carried out. The amount of pre-compression is calculated based on coefficient of thermal expansion at various temperatures. Pre-compression of bellows creates very high longitudinal bending stresses due to deflection. If the compression amount is higher, than permanent deformation of material takes place in the convolution area. The maximum stresses are develops at roots of convolutions. To analyze the amount of longitudinal stresses developed in the bellows, following calculations are made using EJMA relations. Table 6.13: Evaluation of longitudinal stresses under pre-compression Pre-compression (cms) Bellows meridional membrane stress due to deflection N/cm Bellows meridional bending stress due to deflection N/cm Total meridional stresses N/cm

30 6.1.1 Bellow subjected to compressive deformation: Bellows are used in free length installation, compression length installations or expanded length installations. These conditions are selected for space availability and for special requirements. This test is conducted on a bellow after 10 cm initial compression. The geometric dimensions of bellow are as following. The objectives of the test are to study convolution movement, in-plane behavior, and squirm failure (critical pressure) of bellows in compression mode Geometric dimensions of a bellow: Material type = SS 304 Design Pressure = 0.5 Pascal Table 6.14: Geometric dimensions of a bellow Db Dm t w q E N n (cm) (cm) (cm) (cm) (cm) (N/cm ) Length of a bellow = N x q = cm Initial compression of bellow = 10 cm Evaluation of Critical pressure: Ratio of Length to diameter of bellow = (3.90 / 40.60) = Transition Point factor, Cz = 4.7 f S D y b w q A c = Since Lb/Db ratio is less than transition point factor, it is short column. Where, fw = Theoretical spring rate = N/cm/convolution Sy = Yield strength of material = 0310 N/cm Ac = Cross section metal area of one bellow = cm Db = Inside diameter of bellow = 4.98 cm, Limiting critical pressure (in-plane) (Psi) = 53.3 N/cm Buckling pressure, (column) Psc = 0.87 A c S y 0. 73L 1 Db q C z Db b = 51.1 N/cm 19

31 6.1.4 Experimental Readings: Table 6.15: Experimental Readings of Pitch Dimensions Pr. Mode A B C D A B C D A B C D A B C D A B C D A B C D Summary of Results: Table 6.16: Summary of Pitch Dimensions Pressure, N/cm Average pitch, mm

32 Movement of convolutions, mm Pressure, N/cm Movement Figure 6.1: Movement of convolutions Observations: 1. In this experiment the pressure intervals are comparatively larger than previous column squirm test.. Experimental results of squirm test of bellows shows average pitch as 16.5 mm instead of.6 mm as bellow is compressed by 10 cm. 3. The pitch variations are almost negligible at all pressure values (64.3 to for the pressure 0 to 130 N/cm ). This is because all convolutions do not have space or room for the movement as the bellow is compressed. 4. Bellow squirm occurs at 130 N/cm pressure. 5. In case of short column bellows, it is observed that the bellow initially failed by in-plane squirm, than subsequently by column squirm. 6. Critical value of pressure suggested by EJMA includes factor of safety of as following. Factor of safety in in-plane squirm failure = (130 / 49.) =.64 and Factor of safety in column squirm failure = (130 / 5.11) = The factor of safety is less compared to normal bellow in earlier experiment. 1

33 6.1.7 In-Stability Test of Bellow Subjected To Tensile Mode Bellows are used in free length installation, compression length installations or expanded length installations. These conditions are selected for space management and for special requirements. The squirm test in pre-extension mode is conducted on an expansion joint of following dimensions. The objective of the test is to study convolution movement, and squirm failure of bellows in extension mode Geometric dimensions of a bellow: Material type = SS 304 Design Pressure = 0.5 Pascal Table 6.17: Geometric dimensions of a bellow Db Dm t w q E N n (cm) (cm) (cm) (cm) (cm) (N/cm ) Length of a bellow = cm Initial extension of bellow = 5 cm Evaluation of Critical pressure: Ratio of Length to diameter of bellow = (38.90 / 40.60) = Transition Point factor, Cz = 4.7 f S D y b w q A c = Since Lb/Db ratio is less than transition point factor, it is short column. Where, fw = Theoretical spring rate = N/cm/convolution Sy = Yield strength of material = 0310 N/cm Ac = Cross section metal area of one bellow = cm Db = Inside diameter of bellow = 4.98 cm, Limiting critical pressure (in-plane) (Psi) = 50 N/cm Buckling pressure, (column) Psc = 0.87 A c S y 0. 73L 1 Db q C z Db b = 51.1 N/cm

34 Experimental Readings: Table 6.18: Experimental Readings of Pitch Dimensions Pres A B C D A B C D A B C D A B C D A B C D Summary of Results: Table 6.19: Summary of Pitch Dimensions Pressure, N/cm Average pitch, mm

35 Movement of convolutions, mm Pressure, N/cm Movement Figure 6.13: Movement of convolutions Observations: 1. In this experiment the pressure intervals are comparatively larger than previous column squirm test.. Experimental results of squirm test of bellows shows average pitch as 5.93 mm instead of.6 mm as bellow is extended by 5 cm. 3. The pitch variations are almost negligible at all pressure values (98.75 to for the pressure 0 to 105 N/cm ). This is because of bellow is extended by 5 cm. and convolution movement is constrained by tension force. 4. The convolutions became unstable at around 135 N/cm pressure. This is called in-plane squirm. The critical pressure value for instability is 51.1 N/cm as per EJMA. 5. Critical value of pressure suggested by EJMA involves following safety factor. Factor of safety in in-plane squirm failure = (135 / 50.1) =.69 Factor of safety in column squirm failure = (135 / 51.1) = The factor of safety is lowest, while bellow is in compression mode, and highest when it is in normal mode. 4

36 Comparison of Results Initial condition Compression by 10 cm Extension by 5 mm Table 6.0: Comparison of results of in-plane stability tests In-plane Column Actual S5+S6 critical Critical Acting squirm (Theo.) pressure, Pressure, f o s N/cm N/cm N/cm pressure, N/cm (in-plane) (Theoretical) (Theoretical) Acting f o s (column) Squirm failure mechanism: While performing above experiments, following observations are made about squirm phenomena in case of short column. The squirm failure for short column bellow may be explained in to three stages. 1. Bulging of flanks: The pressure inside the bellow is gradually increases at periodic intervals. The convolutions of bellow will remain in elastic limit up to the pressure for which it is designed. However, when the pressure is further increases, convolution flanks becomes inclined between their root and crest part of each convolution. The convolutions are bulging from flanks. At this stage the maximum axial force is developed at root and crest part of convolutions. These two sections provide strength to the convolutions of bellows. Figure 6.14: Bulging of flanks. Deformation along plane: The further increase in internal pressure will develop very high amount of force at root sections. This will create very high membrane and bending stresses in the convolution flanks. Practically, not all convolutions will have similar precise wall thickness and diameters, hence in-plane deformations occurs in weak areas. This deformation initiates in elastic region and may continue until plastic region. This 5

37 deformation will be non-uniform in convolutions only. This stage is in-plane squirm. Figure 6.15: In-plane deformation 3. Deformation along longitudinal axis: When further internal pressure is increases in the bellow, gradually the whole structure becomes unstable along its longitudinal axis. The end centers are slowly disturbs from its coinciding axis. An individual convolution may come closer to each other at one side and becomes spreader from opposite side. This stage is column squirm. Figure 6.16: Axial displacement Above three stages of failure of bellows are snapped and shown below. Initial condition of convolutions Convolutions planes are deformed within plane Figure 6.17: Photographic images: In-plane stability test Convolutions deformed laterally - Column squirm 6

38 Observations: 1. Actual squirm failure occurs at minimum.5 times the designed critical pressure. [4] This can be visualized by comparing values of actual critical pressure and design critical pressure. Hence, this may be considered as the factor of safety provided in the design procedure.. 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. This observation are agreed and verified with the analytical approach of EJMA. 3. By experimental observation we may conclude that the short bellows (L b /D b <C z ), initially deformed by in-plane squirm and subsequently deformed by column squirm. 4. Bellows may fail by column squirm, if number of convolutions and pitch of bellows are selected on higher side. As, these two parameters are directly proportional to the length of bellow. In addition, these bellows will be amongst the long column bellows. 7

39 6.14 Dynamic Analysis: Every individual metallic bellows are different in dimensions, and unique for the applications. The natural frequency of expansion joints must be evaluated analytically and designer should take care to avoid similar/near by natural frequency of expansion joint and frequency of vibration, because of pumping machinery in the piping. Overlapping of both frequencies will leads to resonant condition and very heavy vibration amplitudes may be created. A metallic bellow with following dimensions is selected for the analysis Geometric dimension of Flanges bellow: Material: SS 304 Table 6.1: Geometric dimensions of a bellow Db Dm t w q E N n (cm) (cm) (cm) (cm) (cm) (N/cm ) Initial spring rate, fi = 8.5 N/cm/convolution Overall spring rate of bellow, Ksr = fi / N = 8.5 / 8 = 35.3 N/cm Axial vibration, f n C n K W sr = = 4 Hertz The frequency of vibration can be measured with FFT analyzer. In this experiment FFT analyzer (make: Pruftechnique, Germany) is used to measure natural frequency. The vibrations are created with rubber coated hammer with manual hammering on the expansion joint. Total three sets of readings are taken to check the repeatability of the experiment. The readings are mentioned in table 6.. The objectives of an experiment are to measure natural frequency of vibration of expansion joint. The detailed specifications of FFT analyzer is mentioned in appendix E. 8

40 6.14. Experimental results: Table 6.: Experimental results of FFT Analyzer Reading Number First peak (Hz) Second Peak (Hz) FEA Approach: The metallic bellow which is tested for measurement of natural frequency earlier, same is modeled in the ANSYS software and analyzed for dynamic analysis. The model is shown in figure The results are mentioned in table 6.3. The result of natural frequency from FEA is shown in figure Figure 6.18: Axi-symmetry FEA model (Full view and close view) FEA results: Table 6.3: FEA Results Reading Number First peak (Hz) Second Peak (Hz)