INTERNATIONAL DESIGN CONFERENCE - DESIGN 2000 Dubrovnik, May 23 - 26, 2000.
MULTIDISCIPLINARY APPROACH TO THE PROBLEM OF THE HYPERBARIC CHAMBER DOOR DESIGN Zvonko Herold, Nenad Bojčetić, Damir Deković Keywords: Hyparbaric chamber, Design, Finite Elements Method, Thorispherical head Abstract: The work exposes problems of the frame shaping and dimensions with rectangular rounded angles door the two-piece hyperbaric chamber, using ASME standards, and also the computer programs for stress and deformation modelling analysis. The calculation performed according to the standard enabled only stress control in particular frame points, whereas numerical calculation, using final elements method gives larger span of stress and deformation results in graphoanalitytical form. One of the essential goals in solving the task was the usability of computer approach analysis with method of final polynomials Pro/MECHANICA in finding the solution of cited type of problem and the deviation valorisation of solution obtained by computer and classical calculation method.
1. Introduction The two-piece hyperbaric chamber for 5 bar working pressure was designed according to the American standard in construction of vessels under pressure, containing the special supplement for vessels under pressure for human use. This is a horizontal cylindrical vessel and it consists of the main camber (volume V = 12,5 m3) intended for treatment, the pre-combustion camber (volume V = 4,6 m3) with the passing part and the conduct control panel. The cambers are dividend outwards and reciprocally by a deep thorispherical heads. They are equipped and foreseen for hyperbasic oxygen therapy, or for oxygen application under the increased pressure in clinical medicine. To make easier to get in and out of the chamber for disabled patients in wheelchair, or for these ones who have to be transported in bed into the chamber, the main chamber slot in the level of floor must be flat. Therefore the main chamber entry door has to be of rectangular form with rounded angles, whereas all other doors are classical round form. This paper presents one aproach in design and calculation of the rectangle entry door with rounded angles positioned on the thorispherical head of the main chamber.
2. Calculation observing asme regulations In designing and shaping rectangular rounded frame in dished head of hyperbaric chamber the American regulations have been used for calculation of vessels under pressure, because our regulations do not determine calculation of quoted openings. American standard has the special requirements for designing, fabrication, inspection and testing of vessels for human use.
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2.1 Dimensioning of the frame wall with reinforcement in the dished head Since the same frame shape is used for stiffening of opening in the sphere of head and for the door shell frame, this calculation of independent frame becomes the base for constructional shaping of fundamental dimensions of frames in both cases. This method is only used for calculation of stiffening in particular points of frame on the head, whereas this standard can not be used in the door calculation of such a complex geometrically shape. Calculation observing ASME regulations in performed in Anglo-Saxon units, because of unprocessed formulas and calculational factors on SI system of units and measures. Project data: Project pressure P = 0.5 MPa = 72.5 psi Head and frame material Č 0563 (St 52 – 3) Allowable stress S = 236.6 MPa = 34314 psi Welded connection factor E = 1.0
Figure 2.1.1 Attachments disposition The total stresses are superimposed membrane and stresses on the bending and they have to be less than allowable stress. 2.1.1 Membrane Stress Short-Side Plates
(S m )F = (S m )H
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=
P (L2 + L21 + R ) t1
(1)
Long- Side Plates
(S m )A = (S m )B = P (L1 + R )
(2)
t1
Corner Section
(S m )C − F
=
P t1
(L2 + L21 )2 + L12
+ R
(3)
2.1.2 Bending Stress (index A, B, C, F, H – Stress places)
(S b ) F
=
c I1
(L2 + L21 )2 M pP + + R (L2 + L21 − L1 ) A 2
(4)
Auxiliary calculation sizes (derived calculation or from table): c = 0.785in , I1 = I 2 = 1.02in 4 , K 4 = −294 ,
Θ = 24.38° ,
w = 0.54in ,
S y = 51470psi ,
c´= 2.08in ,
∆2 = 6000 psi , I 21 = 5.04in 4 .
Bending moment:
M A = pPK 4
(5)
L + L21 M r = M A + pP{(L2 + L21 ) 2 + R ⋅ cos Θ + (1 − sin Θ )(− RL1 )} 2
(6)
(S b )H
=
c I1
[
]
pP (L2 + L21 )2 + 2 R(L2 + L21 − L1 ) − L12 M A + 2
(S b ) A =
M A ⋅ c´ I 21
(S b )B
=
c I2
pPL22 M A + 2
(S b )C
=
c I1
pP 2 M A + 2 (L2 + L21 )
(7)
(8)
(9)
(10)
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(S b )24.38° = M r ⋅ c
(11)
I1
2.1.3 Total Stress (index A, B, C, F, H – Stress places)
(ST )F = (S m )F + (Sb )F
= 20791psi = 143MPa
(S T ) H = (S m ) H + (S b ) H
= 9330psi = 64MPa
(12)
(13)
(ST )A = (S m )A + (Sb )A = 28527psi = 197 MPa
(14)
(ST )B = (S m )B + (S b )B
= 8266psi = 57 MPa
(15)
(ST )C = (S m )C + (S b )C
= 4908psi = 34 MPa
(16)
(ST )C − F = (S m )C − F + (S b )24.38° = 23646psi = 163MPa
(17)
The chosen thickness of frame wall as the dimensions of fins area satisfactory, because no total stress exceeds the value of allowable stress S = 236.6 MPa.
3. Numerical calculation The numerical calculation of the main entry door of the two-piece hyperbaric camber is obtained by means of computer, using the program package Pro/ENGINEER. Pro/MECHANICA modulus for stress analysis and simulation, as well as for deformation was used in this calculation.
Figure 3.1 Assembly model, head with frame and set of door
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Each separate element of welded construction has been modelled in particular, and the parts have been joined in the assembly in figure 3.1. The assembly model is divided in two parts, making separate functional units appropriate for calculation: • head model (figure 3.1.1), • door model (figure 3.2.1). These spatial models are the base for load setting and boundary conditions definition indispensable for making numerical calculation. The calculation results are shown graphically on the spatial model, and they can be divided in two groups: • stress: maximum stress, reduced stress, and line of the same stress, • deformations: disposition of displacements, line of the same displacements. 3.1 Head with frame calculation
Figure 3.1.1 Model of the head with loads and limitations drawn in
Figure 3.1.2 Program generated elements net on the model of the head
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Figure 3.1.3 Reduced stress on the head, view from inside
Figure 3.1.4 Displacements on the head, view from inside
3.1.1 Results of the head calculation analysis The results of the head with frame calculation show the following values: ! maximum stress 1.7693E–01 kN/mm2 = 176.93 MPa ! maximum reduced stress 1.3820E–01 kN/mm2 = 138.20 MPa The relevant stress in comparison with the allowable one is the reduced stress. We can conclude that all dimensions of head and frame satisfy, because the maximum reduced stress is less then allowably S = 236.36 MPa. If we look at the deformation results: ! the maximum displacement is 1.02 mm. This displacement has been noted on the shell of the head, whereas the ring displacements are significantly smaller (0.34mm), what is important for high-quality packing. The displacements are in the limits of allowable sizes. 3.2 Door calculation from the shell of the head with rectangular frame
Figure 3.2.1 The door model with loads and limitations drawn in
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Figure 3.2.2 Program generated net of elements on the door model
Figure 3.2.3 Reduced stress in the door, view from inside
Figure 3.2.4 Lines of the same displacements, view from outside
3.2.1 Results of the door calculation analysis Results of the slot calculation show the following values: ! maximum stress 2.2741E–01 kN/mm2 = 227.41 MPa ! maximum reduced stress 2.1424E–01 kN/mm2 = 214.24 MPa The relevant stress in comparison with the allowable one is the reduced stress. We can conclude that all dimensions of the frame and spherical shell satisfy, because the maximum reduced stress is less then allowably S = 236.36 MPa. If we look at the deformation results: ! the maximum displacement is 1.1 mm. This displacement is noted on the spherical shell, whereas the ring displacements are significantly smaller (0.4mm) in Y-axis, but in Z-axis direction they are insignificant, that is important for highquality packing. The displacements are in the limits of allowable sizes.
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4. Conclusion With this paper we achieved the desired goal, because except the stress control in particular points of the frame on the head observing the standard, numerical calculation by the method of final elements gave the spectrum of stress results and deformations in the grapho-analytical form on the special model. Namely, such complexly shaped door construction, without using numerical methods, could be calculated with difficulty in totality. Analysing and synthesising the results, the used program package even in such a complex problem gives the solution, that totally satisfies the criteria from the cited standard, with greater reliability and shorter time necessary for conduction and co-ordination of all relevant parameters in the construction shaping. Reference Herold Z., Bojčetić N., Konstrukcijsko rješenje i proračun glavnih vrata dvodijelne hiperbarične komore, OXYPula, Zagreb 1999. Vilke M., Dvodijelna hiperbarična komora, Emproinženjering - Rijeka, 1998. ASME SECTION VIII, Rules for Construction of Pressure Vessels, Division 1, Appendix 13, New York, 1992. Zvonko Herold, PhD ME University of Zagreb Faculty of Mechanical Engineering and Naval Architecture Chair of Design Theory Ivana Lučića 5, Zagreb, Croatia Tel: +385 1 6168 145 Fax: +385 1 6156 949 e-mail:
[email protected]
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