Design integration for nonstandard flanges for pressure vessels.
Process equipment such as pressure vessels and heat exchangers are employed with Flanged joints and these must be detachable type. Standard flanges do not require much consideration of behavior of gaskets, bolts and flanges in detail, as these aspects are implicit within the standard codes. When standard flanges cannot be used, or are not appropriate to the circumstances, then it becomes necessary to design the joint in detail to match specific requirements. The joint between pair of flanges must have structural rigidity and integrity with negligible leakage during service. This will be a challenging task to the designer to arrive final design in an accurate way at lesser time.
Reflecting growing trend of computers numerous investigators like CADEM SOFTWARES, OHMTECH, have presented the standard flange design as part of the process equipment design. The Pi Engineering Softwares Inc. developed K Flange, a window based software, for the design of bolted flanges as per ASME code requirement. COPCOLT.com presented online program for the design of non standard flanges. However, this program requires large input data which is not required. Perhaps, all these programs have been developed in the languages other than Auto Lisp, which suffers poor graphic representation. Besides the higher cost, these programs do not provide editable drawing for future modification.
A software module, which integrates Mechanical and drafting design for nonstandard flanges using Auto Lisp compatible with AutoCAD is presented. The output is available as standard calculation sheet and detailed drawing. The detailed drawing of the flange can be used as template for fabrication / manufacturing when plotted. This could be the user friendly and cheaper program for various types of Non Standard flanges used in pressure vessels in accordance with ASME pressure Vessel Code .
Deign method for ASME  and Australian Standard  is similar in approach. These methods are adopted from Taylor and forge method developed by Waters .et. al  of the Taylor and forge company in Chicago the 1930s and substantially formed the basis of the ASME . After determining the design pressure and design temperature, the various steps involved in flange design are
1. Select the Flange material and bolt material and determine the allowable stress at both ambient and operating temperature.
2. Estimate the dimensions, including thickness, and select the flange facing and gasket details.
3. Determine an equivalent pressure if external loads exist by converting the external loads to a pressure and adding it to the internal pressure. Calculate required bolt area and select the bolt size.
4. Calculate all flange loads, moment arms, and moments for both gasket seating and operating conditions.
5. With flange dimensions, calculate the shape constants and read appropriate factors from the curves or calculate using equations.
6. Calculate longitude hub stress, radial flange stress, tangential flange stress and the required combinations.
7. Compare the calculated stresses to the allowable stresses. If the calculated or actual stresses are greater than the allowable, adjust the dimensions and repeat the process until the stresses are within an acceptable range.
[FIGURE 1 OMITTED]
Figure 1 Shows nomenclature for typical Hubbed Flange. Two bolt loads exists: that developed by tightening up of the loads, Wm2 is given by equation 1, and that which exists under operating condition, Wm1 is given by equation 2. The maximum of the two calculated forces, Wm1 and Wm2 is used to set the minimum required bolt force.
[W.sub.m2] = [pi] b G y = [H.sub.y] (1)
[W.sub.m1]= H + H P = 0.785[G.sub.2] P + 2b[pi]GmP (2)
Flange design bolt force, W is the maximum of and above. [W.sub.m1] and [W.sub.m2] Total flange moment acting on the flange, for the operating conditions [M.sub.o] is given by:
[M.sub.o] = [M.sub.D] + [M.sub.T]+ [M.sub.G] (3)
[W.sub.m1] =H + H P = 0.785[G.sub.2] P+ 2b[pi]GmP (4)
and for gasket seating condition [M.sub.o] is given by:
[M.sub.o] = [W.sub.F] [h.sub.G] (5)
The Three flange stresses are acted on flange are longitudinal hub stress, Radial stress, and Tangential stress. Longitudinal Hub Stress [f.sub.B] (equation 5) is the bending stress that varies through the hub thickness. Singh et. al  described this stress as essentially a bending stress with the maximum stress being nearly always at either extremity of the hub. Paulin  indicated that the maximum longitudinal hub stress could be up to be 2 times the material yield stress in this region.
[f.sub.H] = [fM.sub.o]/[Lg.sup.2.sub.1]B (6)
Singh et. al describe the radial stress [f.sub.R] (equation 6) in the flange ring consists of two components, the bending stress caused by the radial bending moment and the membrane stress caused by in-plane surface loads on the inside diameter. Waters et. al. demonstrated the maximum stress always occurs at the inside diameter of the ring. Singh et. al also indicated the tangential stress [f.sub.T] (equation 7)in the ring is made up of two parts, the bending stress caused by the circumferential bending moment and the circumferential stress due to membrane stress caused by in-plane surface loads on the inside diameter. Waters et. al  demonstrated that the maximum stress always occurs at the inside diameter of the ring. Maximum radial and tangential stresses allowable are 1.0 times the material yield stress [Paulin ].
[f.sub.H] = (1.33te + 1)[M.sub.o]/[Lt.sup.2.]B (7)
[f.sub.T] = [YM.sub.o]/[t.sup.2]B - [Zf.sub.R] (8)
Equations 5 through 7 give the induced stress in integral type and all hubbed flanges. For the designing purpose these stresses should not exceed the corresponding allowable values given equation 8 through equation 12:
The maximum induced radial flange stress is.
[f.sub.H] 1.5 [less than or equal to] [f.sub.allow] (8)
[f.sub.R] 1.5 [less than or equal to] [f.sub.allow] (9)
[f.sub.T] 1.5 [less than or equal to] [f.sub.allow] (10)
0.5([f.sub.H] + [f.sub.R] [less than or equal to] [f.sub.allow] (11)
0.5([f.sub.H] + [f.sub.T] [less than or equal to] [f.sub.allow] (12)
[FIGURE 2 OMITTED]
[FIGURE 3 OMITTED]
Rusty Genser et. al , describes Auto CAD has greatest adaptability and key element of this adaptability is AutoCAD's built in programming language, Auto LISP. With Auto LISP user can virtually write own commands and redefine others. The non standard flange design automation program is written in Auto LISP language compatible with AutoCAD Drawing package. Further, use of Dialog control language boxes enriches the program and provides user friendly environment. Figure. 2 shows flow chart for design Automation of non standard flange. This program consists of two main modules namely mechanical design and detailed drawing. Mechanical design generally involves safe design of the nonstandard Flanges for the given input flange material, bolt material, bolt size, gasket material, gasket facing etc.. Once the safe design is obtained the program will draw the flange drawing with various dimensions.
Selection of flange material, bolt material and bolt size.
Figure 3 shows Flange input dialog box, provides selection for flange material, bolt material and bolt size. The material database has been considered from ASME pressure vessel code, where as bolt size from courtesy of Taylor--forge and pipe works. Selection of material automatically evaluates material stresses at design temperature and atmospheric temperature. Bolt size selection automatically evaluates parameters related to bolts such as bolt spacing, minimum radial distance, etc. and stores in temporary variable, which can be used, for future calculations.
Gaskets are interposed between two adjacent flange faces and are held tight by a series of bolts. The gasket is therefore compressed, which cases a yielding of its surface, thus seating the irregularity surface of the flange faces. According to the properties and the shape different types gaskets can be made. Various gasket materials can be easily selected from Gasket material selection dialog box (figure 4). This automatically gives gasket factor (m) and minimum gasket seating stress(y). Further gasket face selection for particular gasket can be done using gasket face selection dialog box (figure 5). The slide library of various gasket facings will make the user to understand the type of contact in better way.
[FIGURE 4 OMITTED]
[FIGURE 5 OMITTED]
Flange factors evaluation
Based on the type of flange, various flange factors [f.sup.1], F, [F.sub.L], V and [V.sub.L] are present both in the form of Charts and equations in ASME section VIII, Division 1. However, this program uses mathematical equations to speed up the program. After defining proper shape constants program automatically calculates above factors [figure.6].
[FIGURE 6 OMITTED]
Unlike the other commercial packages listed earlier, this program gives the output in both calculation sheet drawing and flange detailed drawing. Prior to the final output program asks user to make any modifications if inevitable by the user by the design out put Dialog Box. The Figure 5 specification sheet (figure 7) used as future reference for flange Detail drawing. These two are obtained on two different drawing sheets simultaneously using multiple drawing environment technique supported by a Script file.
[FIGURE 7 OMITTED]
Validation of The Program
Benchmark problems serve to ensure that the values obtained from the developed software are correct and accurate. Program is validated with the bench mark problem  and shown good correlation. The design specifications the bench mark problem are Design Pressure 1 Mpa, Design Temperature 150[degrees]C, Flange Material IS : 2004-1962 Class 2, Bolting Material 5% Cr Mo Steel, Gasket material Asbestos, Shell Diameter 1m, Shell Thickness 0.01m and Weld neck Flange. The results of the design can be noted from the figures 7 and 8.
[FIGURE 8 OMITTED]
A computer code for Mechanical and Drafting Design of Non standard flanges is developed in Auto LISP compatible with AutoCAD. The output Drawings can be exported in any format supported by AutoCAD. The large database is available at the hands of designer and user friendly environment created by dialog control language boxes of the program makes the designer to feel very simple. The editable specification sheet and detailed drawing provides the designer for future modification if necessary. Further, this can be used as template for fabrication / manufacturing when plotted.
A = outside diameter of flange, in m (inch).
[A.sub.b] = actual total cross-sectional area of bolts at root of thread or section of least diameter under stress, in square m (square inch).
[A.sub.m]= total required cross-sectional area of bolts, taken as the greater of [A.sub.m1] and [A.sub.m2], in square m (square inch).
[A.sub.m1]= total cross-sectional area of bolts at root of thread or section of least diameter under
Stress, required for the operating conditions, in square m (square inch). = [W.sup.m1]/[S.sub.b]
[A.sub.m2] = total cross-sectional area of bolts at root of thread or section of least diameter under stress, required for gasket seating, in square m (square inch) = W m1/ Sa
B = inside diameter of flange, in m (inch).
[B.sub.1] = B+ [g.sub.o] for integral-type flanges when f is equal to or greater than 1.
b = effective gasket or joint-contact-surface seating width, in m (inch). = 2.52 [square root of ([b.sub.0])]
2b = effective gasket or joint-contact-surface pressure width, in m (inch).
[b.sub.0] = basic gasket seating width, in m (inch) = N/2
C = bolt circle diameter, in m (inch).
D = diameter of bolt hole, in m (inch).
[D.sub.b] = bolt outside diameter, in m (inch).
d = factor, in m (inch) to the 3rd power, for integral-type flanges = U/V [h.sub.0][g.sup.2.sub.0]
For loose-type flanges = U/[V.sub.L] [h.sub.0][g.sup.2.sub.0]
e = factor, in m (inch) to the power of minus 1 for integral flanges. = F/[h.sub.0]
F = factor for integral-type flanges
[F.sub.L] = factor for loose-type flanges
[f.sup.1] = hub stress-correction factor for integral flanges (when greater than 1, this is the ratio of the stress in the small end of hub to the stress in the large end), (for values below limit of figure use [f.sup.1] = 1).
G = diameter at location of gasket-force, in m (inch); it is defined as follows:
When [b.sub.o] > 6 m (1/4 inch.), G = outside diameter of gasket contact-face minus 2b.
[g.sub.o] = thickness of hub at small end, in m (inch).
[g.sub.1] = thickness of hub at back of flange, in m (inch).
H = total hydrostatic end-force, in Newton (pounds), = 0.785[G.sup.2]P
[H.sub.d] = hydrostatic end-force on area inside of flange, in Newton (pounds). = 0.785[B.sup.2]P
[H.sub.G] = gasket-force (difference between flange design bolt-force and total hydrostatic end-force), in Newton (pounds), = W-H
[H.sub.p] = total joint-contact surface compression force, in Newton (pounds),= 2b[pi]GmP
[H.sub.T] = difference between total hydrostatic end-force and the hydrostatic end-force on area inside of flange, in Newton (pounds), = H- [H.sub.D]
h= hub length, in m (inch).
[h.sub.D] = radial distance from the bolt circle to the circle on which [H.sub.D] acts, in m (inch).
= C - D - [g.sub.1]/2
[h.sub.G] = radial distance from gasket-force reaction to the bolt circle, in m (inch), = C - D/2
[h.sub.o] = a factor. = [square root of (BgO)]
[h.sub.T] = radial distance from the bolt circle to the circle on which [H.sub.T] acts, in m (inch).
= C - B/4 + [h.sub.G]/2
K = ratio of outside diameter of flange to inside diameter of flange, = A/B
L = a factor = te + 1/T + [t.sup.3]/d
[M.sub.D] = component of moment due to [H.sub.D],in N-m (inch-pounds), = [H.sub.D] [h.sub.D]
[M.sub.G] = component of moment due to [H.sub.G], in N-m (inch-pounds), = [H.sub.G] [h.sub.G]
MG= total moment acting upon the flange, for operating conditions or gasket seating as may apply, in N-m(inch-pounds) = [Wh.sub.G]
MT = component of moment due to [H.sub.T], in N-m (inch-pounds), = [H.sub.T] [h.sub.T]
[M.sub.o] = Total Flange moment in N-m (inch-pounds),
m = gasket factor,
N = width used to determined the basic gasket seating-width [b.sub.o], based upon the possible contact width of the gasket in m (inch).
n = number of bolts.
P = Maximum allowable working pressure on flange, in MPa (Psi).
[f.sub.a] = design strength for bolt at atmospheric temperature, in MPa (Psi).
[f.sub.b] = design strength for bolt at design temperature, in Map (Psi).
[f.sub.f] = design strength for material of flange at design temperature (operating condition) or atmospheric temperature (gasket seating), as may apply, in MPa (Psi).
[f.sub.H] = calculated longitudinal stress in hub, in MPa (Psi), = [fM.sub.o]/[Lg.sup.2sub.1]B
[f.sub.R] = calculated radial stress in flange, in MPa (Psi), = (1.33te + 1)[M.sub.o]/[Lt.sup.2]B
[f.sub.T] = calculated tangential stress in flange, in MPa(Psi), = [YM.sub.o]/[t.sup.2]B - [ZS.sub.R]
T = factor involving K
t = flange thickness, in m (inch).
U = factor involving K.
V = factor for integral-type flanges
[V.sub.L] = factor for loose-type flanges
W = flange design bolt-force, in Newton (pounds)
[W.sub.F] = imparted load on flange, in Newton (pounds).
[W.sub.m1] = minimum required bolt-force for operating conditions, in Newton (pounds).
[W.sub.m2] = minimum required bolt-force for gasket seating in Newton (pounds).
Y = factor involving K.
y = gasket or joint-contact-surface seating stress in MPa (Psi).
Z = factors involving K
 American Society of Mechanical Engineers (2000) Boiler and Pressure Vessel Code, Section VIII Division 1, Appendix S.
 Australian Standard AS 1210, Pressure Vessels (1997). Appendix B, Standards Association of Australia.
 Waters E O; Wesstrom D B; Rossheim D B and Williams F S G: 'Formulas for Stresses in Bolted Flanged Connections, Transactions of American Society of Mechanical Engineers, Vol 59, 1937, p 161.
 Singh K P and Soler A I (1984) Mechanical Design of Heat Exchangers and Pressure Vessel Components, Arcturus, New Jersey, 1984, page 81-126.
 Paulin Research Group, (2003), Axipro 2.0 Program Manual. pp. 2.4.2-2.4.4.
 Rusty Genser and Joseph Smith, (1992) Maximizing Auto LISP, New Riders Publication
 B.C. Bhatta charya, (2005), Introduction to chemical equipment design Mechanical Aspects, CBS publishers.pp120-125.
Murali Saggarla (1) and Bhaskar Rao Yadavalli (2)
(1) Department of Mechanical Engineering, JPN College of Engineering, Mahabubnagar, Andhra Pradesh, India
(2) Design Engineering Division, IICT, Hyderabad, Andhra Pradesh, India