3. Metallic Bellows. 3.1 Construction of Bellows: There are mainly two types of bellows according to manufacturing method. [20]

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1 3. Metallic Bellows The main element of an expansion joint, which consists of one or more convolution, is called bellow. The performance of expansion joint is mainly depends on the geometric features of bellow. Hence, type of raw material and its properties, its geometric features, other influencing design factors, construction or manufacturing method, and performance testing of bellows are necessary to study. Study of theses parameters is helpful in achieving desirable performance of expansion joints. 3.1 Construction of Bellows: There are mainly two types of bellows according to manufacturing method. [0] 1. Formed bellows: The formed bellows are made from thin sheet metal. The bellows are formed either hydraulically or mechanically, from a thin walled tube. The tube contains longitudinal welds and exhibit significant flexibility as the thickness is very less. Formed bellows are made in a single or multiple plies according to requirement. The thickness of material is ranging from 0.0 to.5 mm and diameter of bellows from 0 mm to 3000mm. These bellows are usually categorized according to convolution shape. Figure 3.1 shows formed bellows and the initial thin wall tube of material. Figure 3.1: Formed bellow 8

2 . Fabricated bellows: Thin gauge diaphragms or discs are used in series and joined by welding process. Fabricated bellows are made from heavier gauge material than formed bellows. Hence fabricated bellows can withstand higher amount of pressure. Figure 3. shows constructional arrangement of fabricated bellows. Figure 3.: Fabricated bellow Welded bellows can be fabricated from a greater variety of exotic metals and alloys, whereas formed bellows are limited to alloys with good elongation. Welded bellows are not fabricated from brass because of its fundamentally poor weldability. Other advantages to welded bellows include compactness (higher performance in a smaller package), ability to be compressed to solid height with no damage, resistance to nicks and dents, and dramatically greater flexibility. The welding of metal bellows is a microscopic welding process, typically performed under laboratory conditions at high magnification. The bellows convolutions are formed either hydraulically or mechanically, from a thin walled tube. The forming method should be very precise so that material thinning should be controlled, in order to maintain uniform thickness. The similar size convolution shapes should be formed in a bellow. 3. Components of a bellow: The main components of bellows are convolutions, crest, root and tangent part. The other important configurations of bellows are pitch of convolutions, mean diameter of bellow, height of convolutions, convolution depth, tangent part etc. Figure 3.3 shows various components of a bellow. 83

3 Figure 3.3: Components of a bellow 3.3 Geometry of a bellow: For the precise design of a bellow important geometries should be defined. These are bellows mean diameter, height of convolutions, pitch of convolutions, tangent length, collar length etc. These parameters are shown in following figure 3.4. COLLAR Figure 3.4: Geometry of U shaped bellow Db = Inside diameter of bellows, n = Number of plies, w = Height of convolution, Lt = Tangent length of bellow, N = Number of Convolutions, Do = Outside diameter of bellows t = Thickness of material q = Pitch of convolutions Lc = Collar length of bellows r = Radius of root & crest (U type) 84

4 3.4 Convolution shapes of bellows: Bellows can be made using different shapes of convolutions. Performance behavior of bellows differs with reference to each convolution shape and other parameters. Mostly U shape of convolutions is preferred by designers because of its simplicity in design, manufacturing and also permits more amount of deformation in axial direction. Other shapes are V type, S shape, semi toroidal shape, toroidal shape, flat, stepped, sweep, ripple etc. Figure 3.5 shows various basic shapes of convolutions. As no standard machineries are developed for forming of convolutions, simple hydraulic or mechanical press is used in the industries. There is no standard dimensional sizes of convolutions are determined, and customized approach is adopted for the design there are different features amongst various manufacturers. Figure 3.5: Various Convolution shapes of bellows 3.5 Bellows materials: Mainly cold rolled carbon sheets are used in the manufacturing of bellows. Many times thin sheet of stainless steel or alloyed steel are used for bellows to avoid corrosion. Formability is the main criteria for the selection of material. Following are the material suggested as per the properties required from ASM hand book. [B] Classification of Cold rolled plain carbon steels sheets are shown in table

5 Table 3.1: Classification of Cold rolled plain carbon steels [B] Sr. Material Thickness Width Specification symbol / No. designation (mm) (mm) ASTM No. A366, A619, A60, 1 Cold rolled sheet A366M, A619 M, A 60 M A366, A619, A60, Cold rolled sheet > 0.35 > 300 A366M, A619 M, A 60 M 3 Cold rolled sheet < A506, A Mechanical properties of the material: The relationship between formability and values of the strain hardening exponent, n and the plastic strain ratio r (determined in tensile testing) is important. Plastic strain ratio (r) is the resistance of steel sheet to thinning during forming operations. This is the ratio of true strain in the width direction (ε w ) to the true strain in the thickness direction (ε t ) of the plastically strained sheet metal. [B] Plastic strain ratio (r) = ε w / ε t (3.1) This rate is related to the crystallographic orientation of low carbon steels. It can be decided by standard tension test. The strain hardening exponent (n) is the slope of the true stress strain curve when plotted on logarithmic co-ordinates. A significant portion of the curve is nearly a straight line for many low carbon steels. The approximately value is 0.. Many times for manufacturing of bellows annealed sheets are used as raw material. Annealing is low temperature recrystallization annealing or process annealing can be used to soften cold rolled low carbon steel. When done in batches process, this type of annealing is known as box annealing * B ASM Hand book (Formerly metal hand book), Volume 1; Properties and selection: iron, steels and high performance alloys; ASM International Hand Book Committee; USA; Seventh Print; December

6 ASTM Specifications A 611 A 366 A 619 A 414 Table 3. : Compositions of Cold rolled plain carbon steels [B] Type of material C Mn P S CR, SQ Grades A, B, C, E CR, SQ Commercial quality CR, SQ Drawing quality Pressure Vessel Grade A Grade B Grade C Grade D Grade E Grade F Grade G CR = Cold Rolled, SQ = Structural Quality Following commercial named materials are used for manufacturing metallic bellows. Table 3.3 : Bellow materials according to temperature range Bellows material Temperature range 0 F (ASME Sec. VII) 304 Stainless steel -300 to Stainless steel -300 to Stainless steel -300 to Stainless steel -300 to 1400 Nickle to 600 Monel to 900 Inconel to 100 Inconel to 100 Inconel to 1500 Incol to Stainless Steel Stainless steel 304 is an austenitic grade that can be severely deep drawn. This property has resulted in 304 being the dominant grade used in applications like sinks and saucepans. 87

7 304L Stainless Steel Type 304L is the low carbon version of Stainless steel 304. It is used in heavy gauge components for improved weldability. Some products such as plate and pipe may be available as dual certified material that meets the criteria for both 304 and 304L. 304H Stainless Steel 304H, a high carbon content variant, is also available for use at high temperatures. Property data given in this document is typical for flat rolled products covered by ASTM A40/A40M. ASTM, EN or other standards may cover products sold by Aalco. It is reasonable to expect specifications in these standards to be similar but not necessarily identical to those given in this datasheet. Table 3.4: Composition of SS 304 [W4] Material C Mn Si P S Cr Ni N S S max SS 304L 0.03 max SS 304H 0.1 max Material Table 3.5: Mechanical Properties of Stainless steel sheets [W4] Tensile strength (MPa) Compression strength (MPa) Proof stress 0.% (MPa) Elongation A 5 (%) Hardness Rockwell B S S SS 304L SS 304H Table 3.6: Physical Properties of Stainless steel sheets SS 304 [W4] Property Value Density 8.00 g/cm 3 Melting point C Modulus of elasticity MPa Thermal conductivity 16. W/m.K at 100 C Thermal expansion 17.x10-6 /K at 100 C 88

8 Table 3.7: Physical Properties of Inconel sheets inconel 600 Property Value Density 8.47 g/cm 3 Melting point C Modulus of elasticity Thermal conductivity Thermal expansion MPa 14.9 W/m.K 13.3 µm/mk Inconel 600: Inconel 600 is a nickel- chromium alloy with good oxidation resistance at high temperatures and resistance to chloride ion stress corrosion cracking, corrosion by high purity water, and caustic corrosion. It is used for furnace components, in chemical and food processing, in nuclear engineering and for sparking electrodes. Inconel 800: A Ni-Cr-Fe alloy resists the high temperature oxidation. This alloy is a first choice for an upgrade from the 300 series stainless steels when improved performance or strength at temperature is required. For higher ASME Boiler and Pressure Code design values, consider Alloy 800HT Properties of Inconel alloys: [W4] 1. Inconel alloys are oxidation and corrosion resistant materials well suited for service in extreme environment.. When heated or at elevated temperature, inconel forms a thick, stable, passivating oxide layer protecting the surface from further attack. 3. Inconel retains strength over a wide temperature range, attractive for high temperature applications. 4. Inconel s high temperature strength is developed by solid solution strengthening or precipitation strengthening, depending on the alloy. 5. Inconel is difficult metal to shape and machine using traditional techniques due to rapid work hardening. 6. Welding of inconel alloys is difficult due to cracking and microstructural segregation of alloying elements in the heat affected zone. However some alloys are designed for welding to overcome this problem. 89

9 3.5.3 General applications of inconel sheets: Iconel sheets are often used in extreme environments. It is common in gas turbine blades, seals, combustors, turbocharger rotors and seals, pressure vessels, heat exchanger tubing, etc. 3.6 Manufacturing of bellows: Hydraulic forming or mechanical forming process is used for forming convolutions. A welded cylinder is placed in the center of a stack of split dies, which are machined to determine the final convolution shape. Internal pressure and controlled axial compression is applied. A high pressure is used in forming process, which thus imposes a leak test on the final bellows; however, because this pressure is applied against external rings, the structural strength and stability of the bellows are not proven in the forming process. Initially sheet metal is welded in longitudinal direction. The weld efficiency is tested during convolution forming process. If welding is not effective, then material will fail from welding during forming process. Manufacturing methods are varying with different manufacturers, as special purpose machinery is not developed for the forming of convolutions. 3.7 Single or multi-ply material: [0] Bellows are made from thin sheet metal in order to get higher flexibility. But these bellows can not withstand higher amount of pressure. Hence to reduce the risk of sudden failure or complete failure, multiple plies are used for high pressure applications. The inner ply is high corrosion resistant material and outer ply is less costly higher strength material for load resistance. Also if thick material is used, its fatigue life is reduced. So its overall life is also reduced. For multi-ply, fatigue resistance is limited ply. Depending on the wall thickness and convolution size, single wall thin bellows may be limited by stress or stability to lower pressure application. To overcome this limitation, multi-ply bellows can be made by telescoping two or more cylinders and forming together. Multi-ply bellows may be advantageous for reducing the risk of sudden and complete failure. Also, in case of multi-ply the inner ply highly corrosion resistance material is used and as outer ply less costly high strength material can be used. Here, the fatigue resistance is limited by the inner ply. The multi-ply can be used in many applications. It is important to understand the functional characteristics of each type of constructions. 90

10 A. Multi-ply construction with the same total thickness as a single ply construction (tt=spt) B. Multi-ply construction with the same thickness for each ply as a single ply construction (tt=n x spt) C. Multi-ply construction with greater thickness for each ply than for single ply construction (tt > n x spt) Table 3.8 : Behavior of multi-ply bellows Parameter Multi-ply construction characteristics Design feature tt = spt tt = n x spt tt > n x spt Circumferential stress same decreases Decreases Longitudinal bending increases decreases Decreases stress Fatigue life increases little change Decreases 3.8 Reinforcement of bellows: [0] Sometimes reinforcing or equalizing rings are added while the bellow material is very thin. Reinforcing rings resist any distortion of the convolution root and are easily fitted to bellows that are formed hydraulically. Equalizing rings can be of cast or fabricated construction, generally in two halves bolted together. These rings also prevent convolution root distortion but additionally limit the compressive axial deflection taken by each element. Both types of rings are claimed to improve fatigue life. Figure 3.6 shows the arrangement of equalizing rings in thin wall bellows. Figure 3.6: Reinforcing rings and equalizing rings details 91

11 3.9 Internal Sleeve: [0] Bellows can be sleeved for various reasons. First is to reduce turbulence and thus pressure drop, to minimize erosion on the walls and to restrict entry of foreign material. Sleeves should be designed with the minimum practical clearance to restrict entry of foreign material. There should be sufficient overlap at the free end to ensure that with all possible movements, especially if lateral movement is involved, there is no chance of the sleeve end fouling the convolutions. It is wrong to assume that a sleeve can completely prevent deposition of solid material in the convolutions, since back eddies can easily result in sedimentation behind the sleeve. In fact, a sleeve can frequently help to trap solid material against the bellows, where it might otherwise have been carried away in the turbulent flow. The most practical way to prevent solid from getting into the bellows/sleeve space is by use of purge medium continuously supplied to this space. The draining of this space of any corrosive products must be considered Criteria affecting Bellows Design: The designer is having freedom in deciding the geometric parameters of bellows, but he has to take care about the cumulative effect of these parameters on the various performance criteria. They are internal pressure capacity, squirm failure, stability of bellow, fatigue life etc. Each criterion affects on the performance of expansion joint. They are elaborated as following Internal Pressure Capacity: Excessive hoop stress in the straight cylindrical end tangents of a bellow will cause circumferential yielding. This stress is calculated by a modification of the Barlow s equation. For un-reinforced bellows straight tangents can be reinforced by collars. Excessive hoop stress in the convoluted section of the bellows can produce circumferential yielding and possible rupture. As in any cylindrical shell, this stress is inversely proportional to the cross sectional areas and material properties. Excessive longitudinal pressure stress in the convoluted section of a U shaped bellows will produce bulging of the side wall. Any gross change in the convolution shape will decrease the space between convolutions, and the ability of the bellows to absorb movement. Such change in shape will also affect the fatigue life. 9

12 Deflection stresses are produced in the convoluted section due to deflection. Typical stress range values are very high. These values are not true stresses, since they exceed the elastic limit of the material. They are useful for the prediction of fatigue life Fatigue life Expectancy: The fatigue life expectancy can be defined as the total number of complete cycles which can be expected from the expansion joint based on data tabulated from tests performed at room temperature under simulated conditions. A cycle is defined as one complete movement from initial positioning the piping system to the operating position and back to initial position. Fatigue life is dependent upon the maximum stress range which the bellows is subjected, the maximum stress amplitude being the far less significant factor. The fatigue life expectancy of an expansion joint is affected by various factors such as operating pressure, operating temperature, material of bellows, movement per convolution, the convolution pitch, the depth and shape of the convolutions and bellows heat treatment. Any change in these factors will result in a change of fatigue life of the expansion joint. The fatigue life expectancy can be evaluated from the total number of complete cycles which can be expected from the expansion joint based on data tabulated from tests performed at room temperature under simulated conditions. The fatigue life expectancy of an expansion joint is affected by various factors such as operating pressure, operating temperature, material of bellows, movement per convolution, the convolution pitch, the depth and shape of the convolutions and bellows heat treatment. Any change in these factors will result in a change of fatigue life of the expansion joint. The work hardening of austenitic stainless steel, induced during the forming of convolutions, generally improves the fatigue life of an expansion joint. The fatigue life of a bellows is a function of the sum of the meridional pressure stress range and the total meridional deflection stress range. The number of cycles to failure may be evaluated using total stress range (St) versus number of cycles (Nc) to failure from actual fatigue tests of a series of bellows of similar materials at room temperature. In actual practice bellows are subjected to varieties of stress cycles during its operating life. Hence, EJMA suggests Miner s 93

13 hypothesis for predicting the effect of cumulative fatigue based on different stress cycles. The relation is mentioned as follows. Cumulative usage factor, U = U1 + U + U3 + U Un (3.) n1 n n3 n4 U... (3.3) N N N N 1 3 This factor should not exceed 1. Where, Stress cycle = St 1, St, St 3 Variations in stresses (absolute values) n 1, n, n 3... = Number of each stress cycles N 1, N, N 3. = Maximum number of stress cycles which would be allowable if this type of cycle were acting alone Bellows Stability: Excessive internal pressure may cause a bellow to become unstable and squirm. Squirm is determining parameter to bellows performance in that it can greatly reduce both fatigue life and pressure capacity. This phenomenon is similar to buckling of long columns. The buckling of bellows is called squirm. Squirm harmful to the performance of bellows as it can reduce both pressure capacity and fatigue life. The two most common type of There are two basic types of squirm, column squirm and in-plane squirm. 4 Figure 3. 7 : Column Squirm Figure 3.8 : In-plane squirm Column squirm is defined as a gross lateral shift of the middle section of the bellow. It results in a curvature of the bellows centerline as shown in figure 3.7. This type of squirm is associated with length to diameter ratio. According to this ratio, bellows can be categorized in long or short columns. Failure of column is 94

14 depends on the kind of column. Squirm is similar to buckling of column under compressive load. Buckling failure consists of an elastic and in-elastic region. Since bellows are made from thin sheet metal, deformation of bellows can be in elastic and plastic mode. Hence determination of stresses is much more difficult. Figure 3.9: Force vs. Deflection curve Figure 3.9 shows a graph which indicates critical column squirm pressure for series of bellows having same diameter, thickness and convolution shapes. As the number of convolution is increases, the curve passes through a transition from inelastic to elastic behavior. The other condition which is related to column squirm is end condition. Usually expansion joint is rigidly supported (fixed) at both the ends. The equations suggested by EJMA for buckling pressure to avoid column squirm is Buckling Pressure = P sc = 0.34 C f N q iu when L b C (3.4) z Db Buckling Pressure = Psc = 0.87 A c S y 0. 73L 1 Db q C z D b b when L b C (3.5) z Db In-plane squirm is defined as deflection occurred in individual convolutions, parallel to the surface of bellow materials. It looks like warping of perpendicular faces of convolutions. This deflection is associated with high meridional bending stress and the formation of plastic hinges at root and crest of convolutions. It is more likely to occur in small length to diameter ratio bellows. For the estimation of critical pressure to avoid in-plane squirm EJMA has given following relation Critical pressure, P si = 0.51S i (3.6) K 95

15 Squirm failure also depends on end conditions of the bellows. Normally bellows ends are welded to collars and they are further welded to flanges of pipes. Generally both ends rigidly fixed condition is considered. This may vary for other application. Bellows when subjected to internal pressure is acted upon by an unbalance pressure force or couple which, is sufficiently large, could result in distortion of the bellows. The magnitude of the unbalance pressure force or couple is proportional to the internal pressure and the displacement of the convolutions, a reduction in either of these values will improve the stability of expansion joint Spring Rate of bellows: The force required to deflect a bellows axially is a function of the dimensions of the bellows and the material from which it is made. The flexibility of bellows is measured by spring rate of bellows. This is also helpful for expected movement of piping for the design purpose. The curve of force versus deflection for most bellows indicates motion extending into the plastic range. Initially the bellow is deflected through elastic range. But as bellows continuous and extends into plastic range, the force versus 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 to bellows to its initial position, a restoring force must be applied in the opposite direction as shown by the curve below abscissa. Figure 3.10: General curve of Bellows Force vs. Deflection The use of the initial elastic spring rate in place of the working spring rate for a bellows whose deflection extends into the plastic range predicts forces which can 96

16 be considerably higher than actual. Line B, drawn from the origin to the point of maximum force and deflection, is used as the bellows working spring rate, fw. But this has a disadvantage of underestimating the actual force over the full range. Line C drawn from the point of maximum force and deflection to the value of the restoring force required to return the bellows to zero deflection, becomes line C when transferred to the origin. A working spring rate based on line C can be used. This reduces the discrepancy between the indicated and true values although the difference can still be significant. A relation to estimate the bellows theoretical axial elastic spring rate suggested by EJMA is as follows. Bellows theoretical axial elastic spring rate = 3 p Dm Eb t n fiu 1.7 (3.7) 3 w C f Cold Springing of bellows: Actually cold springing is defined as the prestraining of the elements of a piping system at the time of installation, so that the thermal stresses in the piping in the operating positions are appreciably reduced. Foe expansion joints, cold springing is defined as the lateral or angular offset of the ends of an expansion joint when installed and should not be considered as axial pre-compressing or pre-extending. Where expansion joint is used to relieve loading on sensitive equipment, or anchor structures are limited to extremely small loads, cold springing the expansion joint at installation will effect a reduction in the maximum deflection force value of as much as 50%. In other cases, 100% cold spring may be used to provide minimum lateral deflection forces at the operating position Vibration in bellows: [0] The metallic bellow component will have its own natural frequency. Metallic bellows are used in the applications where there are low amplitudes and high frequencies. Expansion joints should not be used to absorb vibrations created by reciprocating machines or pumps. There will be two kinds of vibrations. The vibration will depend on number of convolutions of bellows. Since both ends of bellows will be rigidly connected with pipe ends, vibration area will be between first and last convolution of bellows. The vibration will develop in axial direction and lateral direction. This natural frequency of metallic bellows can be measured using following mathematical relation. 97

17 Axial vibration, f n K sr Cn Hertz (3.8) W Where, Ksr = Overall bellow spring rate, (kg/cm) W = weight of bellows including reinforcement, flanges, liquid, kg. Cn = Constant used for calculation of frequencies. Where, n = 1,, 3, 4, 5. Number of convolution C 1 (first mode) , , 6, 7, 8, 9, 10 etc Lateral vibrations: Vibration induced in the perpendicular direction of bellows axis is called lateral vibrations. It is also known as beam mode of vibration. It can be calculated using following relationship. Lateral vibrations, f n Cn Dm K sr Hertz (3.9) L W b Where, C1 = 4.8 (For first mode) The predicted amplitude and frequency of external mechanical vibrations to be imposed on the bellows, such as caused by reciprocating or pulsating machinery (kind of pump) shall be specified. The expansion joint must be designed to avoid the resonant vibration of the bellows to prevent the possibility of sudden fatigue failure. Many times layout and anchor position, alteration may be done in order to control the vibration amplitudes Design approach: Every individual application of bellows is unique considering type of internal fluid, its temperature variations, its pressure, pipe diameter, fluctuations in pressure, corrosion, pipe length and many others. Hence expansion joints design and manufacturing prefers customized approach. For a specific application it is designed, than individually manufactured and non destructive testing is carried out. Here high degree of understanding is required between manufacturer and user in order to assure a safe and reliable installation. 98

18 The user is asked to give basic technical information about the requirements, pressure, temperature, maximum possible axial movement, maximum lateral movement etc. Then according to this requirement, the manufacturer suggests the technical design of expansion joint, which includes the dimensions and its technical capabilities. If the user is satisfied with this design, then only commercial aspect or rates are quoted. This approach is suggested by Expansion Joint Manufacturing Association. 3.1 Design procedure: The design of a bellows is complex in that it involves an evaluation of pressure capacity, stress due to deflection, fatigue life, spring forces and column instability. The determination of a suitable design is further complicated by the numerous variables involved such as diameter, material thickness, pitch, height, number of plies, method of reinforcement, manufacturing technique, material type and heat treatment. In many cases, the design for a particular application will involve a compromise of conflicting requirements. EJMA has developed theoretical stress analysis of bellows. The analysis is based on certain assumptions. These assumptions are idealized bellow configuration, a uniform thickness, a homogeneous and isotropic material and elastic behavior. These assumptions are not precisely correct for most applications. A bellows usually operates in the elastic and plastic stress region and cold work, due to forming, alters the mechanical properties of the material. Few investigators have employed computerized analysis technique to more accurately consider the effect of thickness and shape variations as well as plasticity. This procedure is obviously more complex than a simple elastic analysis and yet does not fully solve the design problem in the absence of experimental verification. Also a bellow design should be based on the actual bellows metal temperature expected during operation. Design of bellows includes evaluation of major stresses in the circumferential membrane and longitudinal membrane and bending stress with reference to pressure and deflection. It also requires estimating spring forces and fatiguing life of bellows. The detailed theoretical design is elaborated at later stage Testing of bellows: [0] Bellows are correlated with actual test results to demonstrate predictability of rupture pressure, meridional yielding, squirm and 99

19 cycle life for a consistent series of bellows of same basic design. Usually, five meridional yield rupture tests on bellows of varying sizes with not less than three convolutions are required. 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 needs to be prepared for experimental verification or testing of bellows. Testing results can be used for the foolproof design of expansion joints. The testing is necessary to for the verification of the design procedure. After manufacturing bellows are necessary to test or specific inspection procedure is decided and which is followed. This testing is required to assure the user about the satisfactory design and performance verification. Usually following non-destructive examinations are recommended for the inspection and testing after manufacturing. 1. Radiographic examination. Liquid penetration examination 3. Flourscent penetrant examination 4. Magnetic particle examination 5. Ultrasonic examination 6. Halogen leak examination 7. Mass Spectrometer examination 8. Air jet leak examination Following non-destructive tests are also recommended depending upon the application. 1. Pressure Testing (a) Hydrostatic test (b) Pneumatic test 100

20 Following destructive tests are also recommended depending upon the application. 1. Squirm testing. Meridional yield rupture testing 3. Fatigue life testing 3.14 Failure of Bellows: Bellows are loaded with combined tensile and compressive loadings during its service life. Bellows may fail due following reasons during its application. 1. Stress corrosion: Stress-corrosion which is evidenced by cracking of the material as the result of a combination of stress and corrosive environment. This is occurring because of chlorides of austenitic stainless steel. Corrosion can significantly reduce the service life of expansion joints.. Fatigue failure: Bellows undergoes low cycle fatigue during its service life. Bellows may fail due to fatigue because of its randomly occurring (different stress ranges) thermal expansion and compression movements. The fatigue life may be estimated based on its expected stresses due to deflection. The bellows should be designed for finite number of life cycles. 3. Carbide Precipitation: Bellow material becomes unstable at elevated temperature and due to vibrations occurring in the bellows. The designer has to insure that vibrations loads will not be detrimental to the function of the bellows. Vibrations should be controlled by providing external damping devices or system mass adjustment. 4. Squirm Failure: Excessive internal pressure may cause a bellow to become unstable and squirm. The buckling of bellows is called squirm. This phenomenon is similar to buckling of long columns. Squirm reduces pressure capacity and fatigue life. The two most common type of There are two basic types of squirm, column squirm and in-plane squirm. This failure can be avoided by suitable geometric parameters pitch, height of convolution and material properties. 5. Rupture failure: Bellows may yield (shear cracks) due to excessive internal pressure, is called rupture failure. This failure is normally 101

21 successive failure after squirm failure. This failure can be avoided by over pressurization and material properties General Applications of Bellows: Convoluted (formed) bellows are used in a large number of industrial applications other than piping. Some applications are mentioned below. 1. Load cells: A load cell deforms if a certain load in the form of a pressure or a strain is imposed on it. This deformation is then detected by a strain gauge through which a low voltage direct current is flowing. The change in voltage is detected and made visible on a control panel. To protect this strain gauge from outside damages or weather influences a bellow is mounted over the gauge to protect it from outside influences.. Vacuum interrupters: For the switching of very high voltages in transformer stations sparks should be avoided. To prevent any danger that the surrounding atmosphere will explode, oxygen has to be removed in the area where the sparks occur. This can be done by sealing the spark area completely. Bellows are used to seal this confined area and the inside of the bellow is vacuumized or an inert gas is filled into the bellow. 3. Mechanical Seals: These are mostly used to close the inside of a pump from the outside world to prevent leakage. For that purpose, a mechanical seal is mounted on the pump shaft. As the pump shaft is turning, there has to a rotating sealing element consisting of a stationary and a rotating ring. To enforce sufficient pressure on the two rings one is fitted with a spring. This spring can also have the form of a diaphragm (welded) bellow. 4. Pressure gauges: If the pressure of aggressive fluids or gases has to be measured, the gauge has to be isolated from the flow. For critical applications a diaphragm sealing is used instead of a bourdon tube in the gauge. This gives more security that the aggressive media cannot leak. The diaphragm is a self contained sensor, transmitting the displacement to the measuring device. 5. Sensors: In this application diaphragm or convoluted bellows are completely sealed and filled with a certain gas. Two electrical poles are penetrating the inside of the bellow. By variation the current of those two poles the temperature inside 10

22 the bellow can be regulated. The expansion or contraction of the bellow is used as an actuator to control a certain movement. 6. Valve Sealing: A bellow is used between the housing and the rising stem to seal the inside completely from the outside world. In Europe this is of particular importance as regulations such as TA Luft prohibit any leakage. 7. Couplings for stepper motors and servomotors: The flexible part, capable of compensating for misalignment is made by a bellow. It ensures that there is no angular positioning difference between the two coupling halves. This is essential if the positioning accuracy should be extremely precise. 8. Exhaust pipe expansion joints: Running engines cause self vibration. To compensate for those movements and temperature differences resulting in thermal expansion, bellows are used to connect the exhaust gas pipes to the funnel. Metal bellows are also used other products and marketplaces, including medical applications like implantable drug pumps, to industrial actuators, to aerospace applications such as altitude sensors and fluid management devices (accumulators, surge arresters, volume compensators, and fluid storage). Metal bellows are also found in space applications, providing reservoirs with potable water as well as accumulators to collect wastewater Characteristics of Metallic Bellows used in Instrumentations: 1. Absolute leak tightness zero permeation to mass spectrometer sensitivity. High reliability 3. Compatibility with many environments 4. High humidity 5. Salt spray 6. Corrosive fluids 7. Liquid or gas applications 8. Wide temperature extremes 103

23 9. Long predictable life at operating conditions 10. No degradation in performance after long storage periods 11. Maintenance free service 1. Contaminant free operation 3.17 Conventional Design of Bellows: (As suggested by EJMA) Design for strength is an essential criterion for any mechanical system. The objective of this design is to avoid failure at minimum cross section areas for the required loading conditions. Design of bellows, since they are made from thin sheets, the design for thin cylinders methodology is useful. For thin cylindrical objects with some distinguish geometric features can be designed with reference to Barlow s equation Design methodology single expansion joint : Data: Design pressure (P) = 5 kg/cm = 50 N/cm Design temperature (T) = 50 0 C Modulus of elasticity at room temperature (E b ) = N/cm Modulus of Elasticity at 50 0 C (E b ) = N/cm Yield strength of material (S y )= 0300 N/cm Allowable stress (S ab ) = 1730 N/cm Thickness of material (t) = 0.08 cm Number of plies (n) = 1 no. Number of convolutions (N) = 15 nos. Inside diameter (Db) = cm Height of convolutions (h) =.30 cm Pitch of convolutions (p) =.6 cm Tangent length (Lt) =.5 cm Collar length (Lc) =.5 cm Collar thickness (tc) = 0.16 cm 104

24 Length of a below (Lb) = (N x p) = cm (3.10) Mean diameter of bellow (Dm) = Db + h + ( n x t ) = 4.98 cm (3.11) Collar diameter (Dc) = Db + ( x tc) = 40.9 cm (3.1) Thickness after thinning (tp) = t Db Dm = cm (3.13) Cross section area of a convolution (Ac) =(0.571 x pitch) + ( x h) x tp x n (3.14) = cm Stiffening factor (k) = 1.5 Lt Db xt = 0.95 Values taken from Graph, Cp = 0.65, Cd = 1.75, Cf = Design calculations: [0] Bellows tangent circumferential membrane stress (S 1 ) S 1 = P Db nt nt Eb Lt Db Lt Lt Ebk tc k Ec Lc Dc = 4110 N/cm (3.15) Collar circumferential membrane stress (S 11 ) S 11 = P Dc Lt Ec k nt Eb Lt Db nt tc k Ec Lc Dc = 4160 N/cm (3.16) Bellows circumferential membrane stress (S ) S = P Dm Kr = 7137 N/cm (3.17) ntp w / q Here, S 1 & S < S ab * C w ; (3.18) Where, C w = Longitudinal weld efficiency factor, may be taken as 1. Bellows meridional membrane stress due to pressure (S 3 ) S 3 = P w ntp = 740 N/cm (3.19) Bellows meridional bending stress due to pressure (S 4 ) 105

25 S 4 = P n w tp Cp = 140 N/cm (3.0) Here, (S 3 + S 4 ) should be < S ab * C m (3.1) Where, C m = Material strength factor, C m = 1.5 for annealed condition and 3 for as formed condition. Bellows meridional membrane stress due to deflection (S 5 ) S 5 = E b tp e 3 w Cf = 0 (As e = 0) (3.) Bellows meridional bending stress due to deflection (S 6 ) S 6 = 5 tp e E b 3w Cd = 0 (As e = 0) (3.3) For bellow to be designed for 5 cm axial motion. Total axial motion x = 5 cm Axial motion per convolution, ex = X N 5 15 = 0.34 cm (3.4) Axial force = Fa = Spring rate x movement / convolution (3.5) = x = N. Axial spring rate = Axial force Axial deflection = 10 N/cm (3.6) Bellows meridional membrane stress due to deflection (S5) S 5 = E b tp e 3 w Cf = x x0.34 = 987 N/cm 3 x.3 x1.70 Bellows meridional bending stress due to deflection (S6) S 6 = 5 tp e E b 3w Cd = 5 x x x x.3 x 1.75 = N/cm For bellow to be designed for 5 cm axial motion and cm lateral motion. Axial motion, X = 5 cm Lateral motion, Y = cm 106

26 Axial motion per convolution, ex = X N 5 15 = 0.34 m 3DmY Lateral motion/convolution, ey= = N Lb X x4.98x =0.454 cm/con. (3.7) 15 Vertical lateral force = Vl = fw Dmey Lb X = 33080x4.98x0.454 = 896 N. (3.8) Equivalent movement, ee = ey + et + [ex] = =0.794 cm (3.9) Equivalent movement, ec = ey + et - [ex] = =0.114 cm (3.30) Bellows meridional membrane stress due to deflection (S5) S 5 = E b tp e 3 w Cf = x x = 303 N/cm 3 x.3 x1.70 Bellows meridional bending stress due to deflection (S6) S 6 = 5 tp e E b 3w Cd = 5 x x x x.3 x 1.75 = 1997 N/cm Thermal Considerations in design: Metallic bellow movement occurs because of temperature and pressure variations in the piping. The bellow deformation depends on piping layout and position of anchors. Figure 3.11: Lay out of piping Figure 3.11 shows one layout of piping with a bellow. Bellow will be fluctuating along X direction (towards anchor B) as the flow of fluid is in this direction, but the expansion effect will be developed due to region between 107

27 bellow and anchor B. The temperature of fluid will increase the temperature of pipe materials as well as bellow. Due thermal expansion of the pipe material, its length will be increased. Hence, thermal aspect is important in the design of bellow. The pipe and bellow materials approach the temperature equivalent to fluid temperature. The elastic modulus of the bellow material is decreases at elevated temperature. Hence, an elastic modulus should be considered at particular temperature during the design. For the higher temperature applications, as the elastic modulus reduces, its yield stress reduces, and finally the permissible stress limit is reduces. Hence, the designer should control the developed stresses corresponding to permissible stresses at designed temperature Estimation of Stresses as per EJMA: A program is prepared in excel worksheet using EJMA relations to evaluate the stresses, transition parameter, spring rate, critical pressure of bellow considering column buckling and in-plane squirm etc. First part is data sheet, all data related to bellows and its requirements is required to feed as input. Part is an evaluation. 108

28 Part 1: Data input: Estimation of Stresses developed in Matallic Bellows as per EJMA Pressure, P 50 N/cm q/w Inside Dia, Db 40.6 cm q/.(dm*tp)1/ 0.56 No. of Ply, n 1 nos. Yield stress, Ys 0310 N/cm Read from Graphs Thickness, t 0.08 cm Cd 1.75 Reduced thickness, tp cm Cp 0.65 Height of convolution, w.3 cm Cf 1.7 Elasticity (bellow), Eb N/cm Tangent length, Lt.5 cm Material Properties data Collar Thickness, tc 0.16 cm Sy 0310 Elasticity (Collar), Ec N/cm Sab 1730 Length of collar, Lc.5 m Eb Stiffening Factor, k 0.95 Collar. Dia, Dc 40.9 cm Mean Dia., Dm 4.98 cm Pitch, q.6 cm No. of Convolution, N 15 Area of convo., Ac cm Axial deflection, ex cm Lateral deflection, ey 0 m Factor, Kr 1.95 Part : Calculation of Stresses S1 S Num E+1 Num1 149 D Num D Den Den = (D1+D) S1=Num/Den S = Num/Den S3 S4 Num 115 Num1 5 Den Num S3 = Num/Den Cp 0.65 S S5 S6 Num Num Den Den S S S1 + S Sab = 1738 S3 + S Sab = 3814 (cold formed bellow) S5 + S Total stress, St

29 3.19 Design of Components of Expansion Joints: The basic unit of every expansion joint is the bellows. By adding additional components expansion joints of increasing complexity and capability are created which are suitable for wide range of applications. These components are limit rods, lugs, hinge plates, clevis plates, flanges, collar, cover, etc. Fundamental design rules should refer to design these components. For a specific application, these component logical design methodology is developed as follows. Material = Carbon Steel Permissible tensile stress = 8500 N/cm Permissible shear stress = 0.8 x 8500 = 6800 N/cm Permissible average shear stress = 0.6 x 8500 = 5100 N/cm Permissible crushing stress = 1.5 x 8500 N/cm Inside Pressure = 30 N/cm Mean diameter of Bellow = 3.4 cm. Thrust force = Pressure x Area (3.31) = 30 x 4 [3.4] = 4740 N Tie rod or Limit rod: Limit rods are used to limit the maximum movements of expansion joint as per design. Bellow is not supposed to take up the additional expansion or contraction movement. Cross section of tie rod = circular Type of Loading = Tension or compression Maximum tensile stress = Thrust load (3.3) x d x no. of tie rods Diameter of tie rod = 4740 = 1.36 cm. = 15 mm 8500 x x 110

30 3.19. Lugs: Lugs are provided for the support of tie rods. Normally square cross section plates are used here. Basically it acts as a base of the tie rod assembly. Cross section of lugs = rectangle Type of loading = Membrane and bending Number of lugs = 4 Height of lugs, distance from outer diameter = 10 cm. Bending moment = 4740 x 10 = N-cm. Section modulus = (b x t / 6) Cross section (b x t) = x 6 = 45 cm x 4 If we take width =15 cm, thickness of plate should be 3 = 1.71 cm = 17.1 mm Hinge Plates: Hinge assembly is provided to get lateral movement of expansion joints. Rectangle cross section is used for hinge plates. Plates are joined by rivets at the middle of bellow. Figure 3.11 shows schematic arrangement. Number of hinges = Hinge plates ( nos.) Clevis plate (1 no.) Thrust load = 4740 N Figure 3.1 : Hinge plate assembly Cross section b x t = x = 1.5 cm If width 3 cm is selected, thickness required is 0.5 cm. 111

31 Design of Pin Pins are made from structural steel and its function is permit lateral and angular motion to ends of the pipe. Cross section of Pin = circular Type of loading = double shear Pin diameter = 4740 = 1.5 cms. = 1.5 mm x x 6800 x Clevis Plates: It is also a part of hinge assembly. Cross section dimensions will be similar to hinge plates, but crushing failure will be required to check. Crushing stress = Thrust load X xt x noof plates (3.33) Distance x = x x1750 = 1.96 = cms. = 0 mm x Figure 3.13 : Clevis plate Figure 3.1 shows schematic arrangement of clevis plate, designed for distance x Hinge Support Plates: Hinge plates are fixed at the top of support plates. The plate is under tension as well as bending moment. Figure 3.14 shows schematic arrangement of hinge support plates. 11

32 h A B b Figure 3.14 : Hinge support plates A and B Bending moment = Thrust force x height of plate (h) 4740 x 10 cms = N-cm. Section modulus = (b x t / 6) Cross Section (b x t ) = 47400x x x 4 (considering plates opposite sides) = 15 cm We can take width = 15 cm and thickness = 1 cm Gimbal ring: Gimbal ring is floated over the bellow with the support of four pins. Gimbal plates may be square loop or circular section. Cross section : Rectangular plate (b x t) Loading: Tension plus bending Cross section of gimbal plate = (b x t /6 )= Thrust load Permissible stress x no. of pins = 4740 x10 x x 4 = 45 cm. We can take width as 30 cms, thickness = 1.5 cms = 1.5 mm Design of Pin: Type of cross section = Circular Type of loading = double shear Pin diameter = 4740 = 0.76 cms. = 8 mm x x 6800 x 4 113

33 Check for crushing: Crushing stress = Thrust load X xt x noof plates Distance x = x 4 x1750 = 0.97 = 1 cm. = 10 mm Design of Pantograph linkages: Fa Figure 3.15: Links arrangements for hinged expansion joint Figure 3.15 shows the arrangement of pantograph linkages in the hinge type expansion joints. The type of loading is axial due to thrust force. In one bellow, there will be four linkages are joined by pins. Thrust force = 5000 N. Maximum load on the each linkage will depend on the angular position, which is achieved after expansion effects. Assuming that the angle is 45 0 as shown in figure Actual link 0 cm B X cm Fa A 45 0 C Sin 45 0 = BC / 0 Figure 3.16: Load distribution in the links Dimension BC = Sin 45 0 x 0 = cm. 114

34 Force on link AB = 5000 x sin 45 0 = N Load on each link = / 4 = 440 N Assuming factor of safety as 4 Critical load = 440 x 4 = N Taking thickness of link = t and width of link = b; and assuming b = 5 t Cross section area of the link = b x t = 5 t x t = 5t Moment of inertia of cross section of link = (1/1) (b) (t 3 ) = (1/1) (t) (5t) 3 = (t 4 ) Radius of gyration; k = I A t = 5t 4 = 1.44 t (3.34) Checking the cross section for buckling, Considering both ends hinged, L = l = 00 mm Using Rankine s relation f Critical load = c A 100 x 5t = l a 1 k t (3.35) = 500t.57 1 t 4 t 36 = t.57 t 4 36 t 9.5 = 0 t = hence; t = 5.76 = 10 mm; b = 5 t = 50 mm (Taking positive sign) Considering perpendicular direction I = (1/1) (b) (t 3 ) = (1/1) (5 t) (t 3 ) = t 4 Cross section area = t x b = 5 t 115