Engineering International Conference 2013 Proceeding p-ISBN: 97925-2784 November 21st, 2013, Semarang, Indonesia
Finite Element Analysis Analysis Of Pressure Pressure Cooker Kriswanto
Sunyoto
Master of Mechanical Engineering Diponegoro University Semarang, Indonesia
[email protected]
Mechanical Engineering Semarang State University Semarang, Indonesia
[email protected]
This Abstract — This
paper presents stress analysis and deformations using 3D CAD models pressure cooker assembly and finite element analysis (FEA) simulation of various wall thickness of the pressure cooker parts at workload conditions using CATIA V5 software. FEA to calculate stress and displacement that occur cause of load applied. Design of pressure cooker with 30 kg soft spines milkfish capacity has a geometry in 500 mm diameter, total high of 900 mm, design based on ASME using CATIA V5. Evaluation results using FEA CATIA show that 5 mm thickness is the acceptable minimum thickness from accaptance criteria where von mises stress is less than allowable strength material (SA 240 Grade 304). FEA analysis produces displacement 4.55 mm at 5mm pressure cooker wall thickness are assembled with a rubber gasket. When the rubber gasket removed, displacement generated only by 0.9 mm. The pressure cooker design has been analyzed in several acceptable thicknesses in term of safe design, so design with 5mm thickness of pressure cooker can be safe to use. The 5 mm thickness of the pressure cooker is the most economically wall thickness.
KeywordsKeywords- stress stress anal ysis; ysis; F EA ; pr essure essure cooker; cooker; ASM E code; code; CATI A V5
I. I NTRODUCTION Pressure Cooker is a cookware that utilizing hot steam for cooking food. The pressure cooker which made by Unnes has been applied by small and medium-sized enterprises (SMEs) of soft spines milkfish in Central Java. The SMEs of soft spines milkfish needs a pressure cooker that produces high quality, safe, and energy efficient. The pressure cooker which made by Unnes has several advantages over existing pressure cooker, among others: higher productivity (big capacity), efficient of time, low energy and low cost of production needed [1]. The research about the quality of the production pressure cooker based on parameters of temperature and pressure, show that pressure cooker is capable of producing soft spines milkfish with relative higher protein levels than the pressure cooking process conducted by another entrepreneurs [2]. Working system of a pressure cooker similarly with pressure vessel, so in designing a pressure cooker based on ASME Boiler and Pressure Vessel Code section VIII. The design method of pressure cooker according to ASME (American Society of Mechanical Engineers) code as known as "design by rule" uses design pressure, allowable stress and a design formula compatible with the geometry to calculate the minimum eic.ft.unnes.ac.id
required of tube and head thickness of the pressure cooker. The pressure cooker design has been using ASME Code, but the stress analysis of design has not been performed. Stress is one of the main causes of failure of a pressure vessel [3]. Pressure cooker similarly with pressure vessel, so stress is the main component that must be analysis.If the stress on a part at a critical location (the applied stress) is also known precisely, if the material’s strength (the allowable strength) is also known with precision and the allowable strength is greater than the applied stress, then the part will not fail [4]. Stress analysis is performed in order to ensure that a design will fulfill its intended function in a given loads environment. This paper presents stress analysis and deformations using three dimentional (3D) CAD (Computer Aided Design) models pressure cooker assembly and finite element analysis (FEA) simulation of the various thickness of a pressure cooker wall at workload conditions. The FEA is a numerical procedure that can be applied to obtain solutions to a large class of engineering problems involving stress analysis, heat transfer, electromagnetism, and fluid flow. The 3D CAD models and FEA simulations is used in this work is CATIA V5 software. II. DESIGN AND A NALYSIS PRESSURE COOKER A. Design by Rule To design a pressure cooker with 30 kg capacity soft spines milkfish requires geometric shell in 500 mm diameter and high of 780 mm. Its volume can contain 6 racks, which each of them can accommodate 5 kg soft spines milkfish. Design of pressure cooker according to ASME code. The formula in ASME Section I and Section VIII are used to determine the minimum required thickness and design pressure of shells and headers using the Maximum Allowable Working Pressure (MAWP) [5]. The maximum allowable stress values to be use in the calculation of the pressure cooker wall thickness are given in the ASME Code for many different materials. These stress values are a function of temperature.The material material of food equipment allowed are stainless steel, type in the AISI 200 series, AISI 300 series, or AISI 400 series [6]. The material that used in pressure cooker design is AISI 304. The rules for cylindrical shells in ASME section VIII1 and VIII-2 assumse a circular cross section with uniform
Engineering International Conference 2013 Proceeding p-ISBN: 97925-2784 November 21st, 2013, Semarang, Indonesia thickness in directions.
the
circumferential
and
longitudinal
1. Thin Cylindrical Shells Pressure cooker using thin cylindrical shells, the Geometry of the pressure cooker shell is:
Diameter (D) and high of shell = 500 mm= 19.685 in. Desain pressure of pressure cooker is (P): 2 bar (29 Psi) obtained from effective working of pressure cooker [5]. Maximum Allowable Stress According to ASME Section II for material SA 240 Grade 304 = 11200 Psi [5].
Shell radius of wall (R) = 250 mm = 9.84 in.
Welding factor for welded pipe (E) = 0.85
surfaces, deforms to fill in the valleys and compress on the high points. The gasket must be soft enough to deform, yet strong enough to resist being squeezed out by the pressure carried in the machinery. Geometry of gasket of pressure cooker is:
Inside diameter of gasket = 500 mm
Thickness of gasket= 13mm
B. Modeling of Pressure Cooker Drawing parts of pressure cooker are using CATIA V5 software. The Geometry of drawing obtained from geometry calculation of pressure cooker part that refers to ASME section VII. Fig. 1 show the detail drawing of pressure cooker.
Circumferential Stress (longitudinal welds), when, 29 psi < 0.385 x 20000 psi x 0.85.
The equation for the required thickness in the circumference direction, due to internal pressure is given as: t
PR
SE 0.6P
, when t 0.5 RorP 0.385 SE
29 Psix9.84in 11200 Psix0.85 0.6 x29 Psi
(a)
(1)
0.03 in = 0.76 mm
2. Dished Heads Formulae ASME section VIII-1 determines the rules for dished heads. Head of pressure cooker using elliptical head.The commonly used ellipsoidal head has a ratio of base radius to depth of 2:1. The actual shape can be approximated by a spherical radius of 0.9 D and a knuckle radius of 0.17 D. Geometry of head of pressure cooker is Straight Skirt Length (h) = ¼ D = ¼ x 19.685 in = 4.92 in Radius L = 0.9 D = 0.9 x 19.685 = 17.72 in Radius r1 = 0.17 D = 0.17 x 19.685= 3.35 in The required thickness of 2:1 heads with pressure on the concave side is given below:
(b)
Figure 1. Detail drawing of pressure cooker (a) shell with end cap support (b) elliptical head.
t
PD
2SE 0.2 P 29 Psix19.685in 2 x11200Psix0.85 0.2x 29Psi
From the 3D model of pressure cooker using software CATIA V5 we can get a data of volume, mass, and inertia of the pressure cooker part. The mass of pressure cooker be use as applied load for the FEA simulation.
(2)
0.03 in = 0.76 mm
3. Gasket A gasket is used to create a seal between mating surfaces of machines or piping assemblies. The seal is necessary to prevent leakage of gas, liquid, or dust into or out of these assemblies [7]. When a gasket is clamped between the mating surfaces of a joint it must deform enough to compensate for the imperfections in the finish of the mating surfaces. The clamping pressure applied to these joints does not create enough distortion in the flanges to effect a seal, so a gasket, placed between these eic.ft.unnes.ac.id
(a)
(b)
Figure 2. Three dimensional model of pressure cooker (a) shell (b) elliptical head.
Engineering International Conference 2013 Proceeding p-ISBN: 97925-2784 November 21st, 2013, Semarang, Indonesia TABLE I.
C. Finite Element Analysis (FEA) of Pressure Cooker Failure of thin cylindrical pressure vessel occurs in two ways, it may fail along the longitudinal section i.e. circumferentially or it may fail along the transverse section i.e. longitudinally. Two types of tensile stresses occur in pressure vessels. One is circumferential or hoop stress and the other one is longitudinal stress. Longitudinal stress is half of the circumferential or hoop stress. Therefore, the design of the pressure vessel must be based on the circumferential or hoop stress [8]. The finite element analysis (FEA) is a numerical technique for finding approximate solutions of partial differential equations (PDE) as well as of integral equations. The solution approach is based either on eliminating the differential equation completely, or rendering the PDE into an approximating system of ordinary differential equations, which are then numerically integrated using standard techniques such as Euler's method, Runge-Kutta, etc [9]. The uniform cylinders having axis of symmetry are analized using axisymmentric elements. These elements adapt a different stress strain matrix & stiffness matrix is derived a/c the following formula. k
∬
T
B .D.B. dr.d .
(3)
Finite element method software that is used in the stress analysis of pressure cooker is software CATIA V5. FEA simulation using CATIA V5 to calculate stress and displacement of the thickness variety of pressure cooker design. Analysis only performed on assembly of three main part (shell, head and gasket). Assembly of pressure cooker is then subjected to an internal pressure, load the content applied, temperature field when operate, mass off the pressure cooker and then corresponding maximum von mises stress values and deformation are noted from the analysis results. The iterative procedure is continued till the von mises stress reaches near about yield strength values. While modeling and carrying analysis in CATIA the following cylinder with specified dimensions are chosen and modeled in the software CATIA. The assumptions are made: 1. Material is perfectly elastic. 2. Default tetrahedral mesh gives enough accuracy. The factor of safety is a factor of ignorance. If the allowable strength is greater than the applied stress, then the part will not fail. Design will be accept if the factor of safety is more than 1. Factor of safety formula is: FS
Sallow σ
(4)
ap
The material considered used for pressure cooker sheel and head is SA 240 Grade 304 refer to ASME section II Table 1, with main properties as specified in Table I.
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MATERIAL PROPERTIES OF PRESSURE COOKER PART [11]
Material Properties Material
Shells SA 240 Grade 304
Head SA 240 Grade 304
Gasket Natural Rubber
Young's modulus (N/m2)
1.93e+011
1.93e+011
2e+006
0.29 8030
0.29 8030
0.49 910
9.4e-006
9.4e-006
1.62e-004
2.05e+008
2.05e+008
-
Poisson's ratio Density (kg/m3) Coef. of thermal expansion ºK Yield strength (N/m2)
The load cases of pressure cooker to be considered during the analysis are listed in Table II. TABLE II.
LOAD CASES ON PRESSURE COOKER
Type of Load
Magnitude
2e+005 N/m2 (2 bar) 300 N (30 kg)
Internal Pressure Axial Load (loadofcontents) Temperature Field Mass of pressure cooker
373.15 K (100 ºC) 950 N (95 kg)
III. R ESULTS The pressure cooker being designed ASME section VIII. From the formula in ASME section VIII can decide minimum thickness of wall thick cylinder sell through Eq. 1. Geometry of elliptical head obtained from Eq. 2. The formula based on design pressure. Minimum thickness of pressure cooker is 0.76 mm. Pressure cooker capacity 30 kg has a geometry in 500 mm diameter, total high of 900 mm. A. FEA Results of Pressure Cooker with Gasket No Load 300N and No Temperature Applied FEA results of pressure cooker in variety thickness with gasket where the applied load is 2e+005 N/m2 of internal pressure, 950 N of mass, without application of temperature and content load shown in the table III. TABLE III. FEA RESULTS OF PRESSURE COOKER IN VARIETY THICKNESS WITH GASKET, NO LOAD 300N AND NO TEMPERATURE APPLIED No
1 2 3
Thickness of Shell and Head (mm) 0.7
0.9 1.5
Von Mises Stress (N/m2)
5.6e+008 5.5e+007 4.34e+007
FEA results get the minimum thickness of the pressure cooker that suitable the acceptable criteria is 0.9 mm thickness. The von mises stress of 0.9 mm thickness 2 (5.5e+007 N/m ) is less than the allowable strength of pressure cooker material (2.05e+008 N/m2). Fig. 3 shown the 3D model von mises stress at nodal of pressure cooker, where maximum stress (5.5e+007 N/m2) is in the red area, while the minimum stress (0) is the blue area. The red area is stress distribution of tensile stress. The analysis did not reveal any compressive stress, so the stress that occurs in a pressure cooker only tensile stress.
Engineering International Conference 2013 Proceeding p-ISBN: 97925-2784 November 21st, 2013, Semarang, Indonesia The 3D model a von mises stress at nodal of pressure cooker shown in the fig. 4, where maximum stress 2 (1.97e+007 N/m ) is in the red area, while the minimum stress (0) is the blue area. The red area is stress distribution of tensile stress. The analysis did not reveal any compressive stress, so the stress that occurs in a pressure cooker only tensile stress. Maximum von mises stress as shown in contact area of assembly shell and head.
Figure 3. The von mises stress of 0.9 mm thickness pressure cooker with gasket no load 300N and no temperature applied
B. FEA Results of Pressure Cooker with Gasket Loaded 300N and No Temperature Applied FEA results of pressure cooker in variety thickness with gasket where the applied load is 300 N of load, 2e+005 N/m2 of internal pressure, 950 N of mass, no temperature applied shown in the table IV. TABLE IV. FEA R ESULTS OF PRESSURE COOKER IN VARIETY THICKNESS WITH GASKET LOADED 300N, NO TEMPERATURE APPLIED No
Thickness of Shell and Head (mm)
Von Mises Stress (N/m2)
1
0.7
5.6e+008
2 3
0.9 1.5
5.5e+007 4.34e+007
Figure 4. The von mises stress of 5mm thickness pressure cooker with gasket
The results of von mises stress of pressure cooker that apply a 300 N load compared with no applying a 300 N load is not different. These results suggest that loading 300 N (contents load) does not influence the results of the stress analysis. Based the FEA result, the minimum thickness of the pressure cooker that no temperature applied that suitable the acceptable criteria is 0.9 mm thickness
Von mises stress result from FEA CATIA V5 then being investigated in acceptable criteria with factor of safety. The respective design check of the method being investigated is accepted if the ratio is more than one. Fs
2.05e 008N / m 1.97e 008N / m
2
2
1.04
C. FEA Results of Pressure Cooker with Gasket Loaded 300N and Temperature Applied FEA results of pressure cooker in variety thickness with gasket where the applied load is 300 N of load, 2e+005 N/m2 of internal pressure, 950 N of mass, and 100˚C temperature applied shown in the table V. TABLE V. R ESULTS OF PRESSURE COOKER IN VARIETY THICKNESS WITH GASKET LOADED 300N, TEMPERATURE 100˚C APLLIED No
Von Mises Stress (N/m2) 2.42 e+008
Diplacement (mm)
1
Thickness of Shell and Head (mm) 3
2 3
3.5 4
2.34 e+008 2.2 e+008
4.64 4.63
4
4.5
2.14 e+008
4.62
5
5
1.97 e+008
4.55
4.65
The von mises stress that less than allowable strength (2.05e+008 N/m2) is 1.97e+008 N/m 2 which is pressure cooker on 5mm thickness. Thickness of pressure cooker that less than 5 mm produce von mises stress greater than allowable strength, so that thickness less than 5 mm is a design failure. eic.ft.unnes.ac.id
Figure 5. The translational diplacement of 5 mm thickness pressure cooker with gasket
Fig. 4 shows the 3D model deformation of pressure cooker, the maximum translantional diplacement vector is 4.55 mm. The maximum deformation shown in red arrows indicate the component gasket.
Engineering International Conference 2013 Proceeding p-ISBN: 97925-2784 November 21st, 2013, Semarang, Indonesia IV. CONCLUSION A. Summary
Figure 6. The translational diplacement of 5 mm thick pressure cooker without gasket.
When the gasket is removed from the pressure cooker on the thickness of 5mm, FEA results is shown in fig. 6 The smallest deformation (4.55 mm) is on 5 mm thickness of pressure cooker. The deformation shown o n component gasket. When the gasket is removed from the pressure cooker on the thickness of 5 mm, the displacement is 0.9 mm. Translantional displacement certainly be small because the rubber material has a high elasticity. Rubber material also serves as an additional safety when the pressure cooker produce over pressure, although here have been a safety valve.
Design of pressure cooker capacity of 30 kg soft spines milkfish based on ASME using CATIA V5. Pressure cooker has a geometry in 500 mm diameter, total high of 900 mm. Evaluation results using FEA CATIA V5 show 5 mm on thickness is the minimum thickness acceptable from acceptance criteria where von mises stress (1.97e+008 N/m2) is less than allowable strength material SA 240 Grade 304 ( 2.05e+008 N/m2). FEA result shown the smallest deformation is 4,55 mm at 5 mm wall thickness are assembled with rubber gasket, when a rubber gasket removed, displacement generated only by 0.9 mm. The pressure cooker design has been analyzed in several thickness acceptable in term of safe design (acceptance criteria), so design of 5 mm thickness of pressure cooker can be safe to use. The 5 mm thickness of the pressure cooker is the most economically wall thickness. B. Advice The minimum thickness of pressure cooker design that safe to use is 5 mm with SF 1.04, if we want to get a greater factor of safety (FS), we can use a thickness greater than 5 mm.
D. FEA results of pressure cooker at 5mm thickness when temperature variety applied TABLE VI.
FEA RESULTS OF PRESSURE COOKER AT 5MM
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THICKNESS WHEN TEMPERATURE VARIETY APPLIED
No 1 2 3 4
Temperature (ºC) 100 80 60 0
Von mises stress (N/m2) 1.97e+008 1.34+008 7.64e+007 2.07e+007
When the temperature in the pressure cooker was varied, von mises stress decreased corresponding to the decrease of the temperature. Maximum von mises stress as shown in contact area of assembly shell and head. When the temperature in the pressure cooker is 80 ºC, von mises stress resulted from FEA CATIA is 1.34+008 N/m2. The analysis as shown in fig. 7 did not reveal any compressive stress, so the stress that occurs ina pressure cooker only tensile stress. The von mises stress is stress distribution of tensile stress. The analysis did not reveal any compressive stress, so the stress that occurs in a pressure cooker only tensile stress.
Design
Guides
&
[8] N. Dwivedi and V. Kumar, “Burst Pressure Prediction of Pressure Vessel using FEA,” International Journal of Engineering Research & Technology. vol. 1 no7, 2012. [9]
C. Nagaraju, D.S. Sandeep, A. Kumar, and Mallikarjunarao, ”Application of HTT for Beam Element. International Journal of Engineering Science and Technology. Vol. 2(6), pp. 2051-2056.
[10] Finite element Analysis CATIA V5 tutorial. (DassaultSystemes, 2008). [11] Material of properties, product data sheet 304/304L stainless steel. www.aksteel.com
Figure 7. The von mises stress of 5 mm thickness pressure cooker at temperature 80ºC.
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