Open Journal of Safety Science and Technology, 2012, 2, 1-7
http://dx.doi.org/10.4236/ojsst.2012.21001 Published Online March 2012 (http://www.SciRP.org/journal/ojsst)
Design Optimization of Stress Relief Grooves in Lever
Guide of Pressure Vessel for Food Processing
Yuichi Otsuka1*, Hamirdin Bin Baron2, Yoshiharu Mutoh3
1Top Runner Incubation Center for Academia-Industry Fusion, Nagaoka University of Technology,
Niigata, Japan
2Undergraduate School of Mechanical Engineering, Nagaoka University of Technology,
Niigata, Japan
3Department of System Safety, Nagaoka University of Technology, Niigata, Japan
Received November 20, 2011; revised February 7, 2012; accepted February 15, 2012
ABSTRACT
A stress relief groove is introduced in the R area and the stress is analyzed using a finite element method (FEM). Then
the relief of the stress concentration in the vicinity of the pressure vessel is measured based on these results. When de-
signing a stress relief groove, the lever must overhang the groove (L > 0). By introducing a stress relief groove to the R
area, maximum stress on the lever guide can be reduced by 10%. This enables the reduction of the maximum stress
(Mises stress) to be less than the fatigue strength. Furthermore, the location where maximum stress occurs on the lever
guide changes in accordance with the clearance between the lever and lever guide. This identified the need to take into
account the deviation factor such as design clearance in modeling process.
Keywords: Stress Relief Groove; Stress Concentration Factor; Finite Element Analysis; Pressure Vessel
1. Introduction
From the late 1980s, in preparation for the utilization of
high-pressure processing in the Japanese domestic food
industry, high-pressure processing was first utilized in
the commercialization of jam and fruit juice drinks. Today,
high-pressure food has become an increasingly familiar
product as a result of the commercialization of highly-
functional foods such as cooked rice in aseptic packaging
and pressure-steamed brown rice. Research is currently
being conducted with regards to the use of high-pressure
treatment as a food-processing method, with the aim of
improving the productivity and quality, as well as adding
a hypoallergenic quality [1].
Experiments have proven that there are various bene-
fits at pressures higher than 100 MPa (called ultra-high
pressure in many cases); however, the cost of ultra-high
pressure processing equipment is high and its production
is small. Moreover, because operating the ultra-high
pressure processing equipment requires specialized know-
ledge or skills, such small-scale equipment for everyday
use is not yet widely available. In addition, the develop-
ment of new equipment requires advanced technical ca-
pabilities and a definitive plan, and there are many other
complications such as securing an appropriate sales chan-
nel as well as obtaining financial investment for high
developmental and manufacturing costs.
With the conventional seal mechanism for ultra-high
pressure equipment, a push-type structure for the cover,
similar to that for a press, was used [1]. When this method is
used, the structure of the vessel and lid is simple, and the
structure is easily able to withstand ultra-high pressure.
However, the cost of a press mechanism is high and its
installation increases the overall size of the equipment. In
order to reduce the cost and size, the seal method shown
in Figures 1 and 2 was proposed. This consists of a cy-
lindrical vessel with a cover at each end fitted with a gas-
ket to maintain the pressure and the cover is closed by a
lever, which ensures that a firm seal is established. In the
upper part of the vessel, the lever is inserted into the lever
guide that has been processed using a wire cut (EDM).
Using this structure, a concentration of stress [2] oc-
curs in the vicinity of the area R because of the contact
between the lever and lever guide. The stress concentra-
tions at the R area of the lever guide will easily become
the origin of fracture. Therefore, it is vital to implement a
design that eases the stress in the vicinity of the R area.
In this study, a stress relief groove [3] is introduced in
the R area, as shown in Figure 3. The stress is subse-
quently analyzed using a finite element method (FEM) [4].
Then the relief of the stress concentration in the vicinity
of the pressure vessel is measured based on these results.
*Corresponding author.
C
opyright © 2012 SciRes. OJSST

Y. OTSUKA ET AL.
2
Figure 1. Pin-arm sealed pressure vessel structure for food
processing. Figure 2. Upper view of pressure vessel.
r
(lever contact area) are shown in Table 2.
(a) (b)
Figure 3. Conventional (a) and with stress relief groove design (b) at the corner side of lever guide. (a) Without groove; (b)
With groove.
2. Examination of the Optimal Groove
Shape Using 2-D Analysis
In order to select an optimal shape for the stress relief
groove, a simplified 2-D model of the pressure vessel was
created and analysis was carried out using this model.
2.1. Examination of the Optimal Groove Shape
Using 2-D Analysis
The commonly used FEM program MARC/MENTAT was
used in this analysis. We analyzed the data using 2-D
elasticity, and three contact point stress elements were
used.
Figures 4-6 show the boundary parameters and FEM
model used in this analysis. The FEM model was cut in
half longitudinally to obtain a cross-section and four models
were created. One was a conventional shape without a
groove, and the other three had semicircular grooves of
radii 1, 2 and 3 mm, respectively. The friction between
the lever guide and lever was defined, and the Lagrange
friction algorithm was used to define the friction behavior.
Table 1 shows the values for the properties of the material
used in the analysis model. To simulate a highpressure
during the operation of the equipment, a step-shaped mov-
ing velocity, Vy = 0.35 m/s, was provided to the rigid lever
in the y direction. This moving velocity is an assumed
value when the pressure is increased to 200 MPa.
2.2. 2-D Analysis Results
2.2.1. Mises Stress and Maximum Principal Stress
Distribution
Figure 7 shows the Mises stress distribution and maxi-
mum principal stress distribution in the vicinity of the R
area for the conventional model without a groove and for
the models with a groove of radii = 1, 2 and 3 mm. The
predicted stress concentration points A (R area) and B

Y. OTSUKA ET AL. 3
Fi gure 4. 2-dimentional FEM model of lever gue. The model id
is half of the upper side because of its symmetric structure.
Figure 5. Boundary conditions of the FEM model l.
(a) (b)
ith groove a (r = 3 mm).
n Coefficient
Figure 6. Detailed meshing conditions around the root of corner or groove. (a) Without groove; (b) W
Table 1. Material properties of JISUS630 used for the lever guide. S
Young’s ModulusPoisson’s Ratio Density Frictio
JIS SUS630 205 GPa 0.3 7 800 kg/m30.2
(a)
ss distributions (relat-
(b)
Figure 7. Effect of radius r for stress conce ntrating conditions and the contact point. (a) Mises stre
ing to plastic deformation); (b) Max principal stress distributions (relating to brittle fracture).
rou

Y. OTSUKA ET AL.
4
According to the stress distribution in Figure 7, the
maximum stress that occurs on the lever guide decreases
Table 2. Mises and max principal stress at point A and B;
point A is the root of the cor
in
in the model
wi
in
verhang Range L and
Stress Distribution
nge L
and the created models having dis-
ner and point B is the edge of
Mises Stress [MPa] Max Principal Stress [MPa]
a model having a stress relief groove as compared with
the one without the groove. The degree of reduction of
maximum stresses becomes higher according to the in-
crease of the groove radius from 1 to 3 mm.
Table 2 shows that the Mises stress at points A and B
and the maximum principal stress at point A
th a 3 mm groove radius. The maximum stress becomes
60% less than that of the model without a groove. The
maximum principle stress at point B in the models with 2
mm and 3 mm groove radii are approximately 90% less
than that of the conventional model and/or the model
with a 1 mm groove radius. The results indicate that the
location of the lever contact edges have a significant ef-
fect on the stress on the inner surface of the lever guide.
Table 3 shows the result of maximum stresses at the
root of grooves in the cases of eclipse shape. Interest-
gly, stresses show their lowest values in the cases of t
= b, which means the groove shape is half circle. The
reason is not clear. Probably the changes in contacting area
between the lever guides and the lever can affect the stress
concentration conditions.
2.2.2. Relation between O
To examine the relation between the overhang ra
e stress distribution, w
tances from the lever edge to the lever contact edge (over-
hang) L of 4, 2, 0 and −2 mm, and analyzed the stress
data. The results of the analyses for the Mises stress and
maximum stress distribution are shown in Figure 8. The
results show that there is no significant change in the
magnitude of stress at both point A and point B for the
models with L = 0, 2 and 4 mm, but for the model with L
= −2 mm, there is concentrated compressive stress. We
believe that when the overhang is L < 0, the stress is
concentrated at the contact edge, and thus the concen-
trated compressive stress is seen only in the model with L
= −2 mm.
contact regions.
Model
A B B
Without groove1742 788 –705 667
Groove, r = 1 mm508 1614 621 –664
Groove, r = 2 mm426 960 507 –37
Groove, r = 3 mm255 526 302 –17
d mincipess incases ose
shape grooves.
2b; diameter Maxinum stress ]MPa[
Table 3. Mises anax pral str the f eclip
Shape of eclipse t; depth,
t 2b Mises Stress Max Principal
1 2 539 473
1 1 766 601
0.5 2 592 656
2 4 667 332
2 2 507 426
1 4 1011 475
3 6 557 262
3 3 513 350
1.5 6 869 363
Figure 8. Effect of over-hang in contact region for max principal stresses in the cases of L = 4, 2, 0, –2 models.

Y. OTSUKA ET AL. 5
Therefore, when selecting the profile of the stress re-
lief groove, the overhang L has to be greater than 0 in
order to reduce the compressive stress on the inner surface
of the lever guide, and thus we chose a stress relief groove
with radius r = 3 mm (L = 0).
3. 3-D Analysis
We performed 3-D analysis to measure the stress at the
six locations where stress concentration is predicted dur-
ing the pressurization of the pressure vessel as shown in
Figure 9: points F, H, E, and C on the inner side of the
lever guide; and points G and D on the outer side of the
lever gu
oove and Model 2 with a 3-mm
s selected based on 2-D analysis
each lever guide, which means that the lever
was inserted into the center of the lever guide space.
e of
th
pa-
ra
Groove
Fi
ide.
3.1. 3-D Analysis Method and Model
Stress analysis was performed for Case 1 and Case 2
below, as shown in Figures 10 and 11, respectively.
1) Case 1
Model 1 without a gr
radius groove, which wa
were compared. The stress concentration relief obtained
by using the stress relief groove was investigated. The
maximum tolerance for the machining dimensions be-
tween the lever and lever guide was 0.6 mm. In Case 1, a
fit tolerance of 0.3 mm was set for the inner side and
outer side of
2) Case 2
In Case 2, stress analysis was performed on the R area
when, using the dimensional tolerance of the lever, the
levontact with the surface of the outer sider made c
e lever guide with a clearance of 0.6 mm from surface
of the inner side (model 3) and when the lever made
contact with the surface of the inner side of the lever
guide with a clearance of 0.6 mm from the surface of the
outer side (model 4). Model 3 and model 4 are shown in
Figure 11.
The dimensions of the 3-D model are shown in Figure
9. The analysis was performed using 3-D elasticity, and
four contact point stress elements were used, as shown in
Fi gure 12 shows the model and boundarygure 9. Fi
meters for the 3-D analysis. The friction conditions and
e values for the material properties were the same as th
those for the 2-D analysis. The numbers of elements are
as the follows; Model 1 = 103,389, Model 2 = 102,706,
Model 3 = 103,528, Model 4 = 103,528, respectively.
3.2. 3-D Analysis Results
3.2.1. Case 1: Ef f ec t of Stress C on c entration Relie f
by the
gure 13 shows the Mises stress distribution for model
1 without a groove in Case 1. The stress values for points
C, D, E, F, G, and H are shown in Table 4.
Figure 9. 3-dimensional finite element model of pressure vessel.
Red circles show possible initial failure point.
Figure 10. Models for case l. Con ventional mod el (model 1) and
with stress relief groove 3 mm model (model 2).
Figure 11. Models for case 2. Clearance 0.6 mm at outer
side (model 3) and inner side (model 4) of the vessel.
Figure 12. Meshing and boundary conditions of FE models.
Number of elements; Model 1 = 103,389, Model 2 = 102,706,
Modle 3 = 103,528, Model 4 = 103,528.

Y. OTSUKA ET AL.
6
Figure 13. Mises stress distribution of Mo del 1.
Table 4. Stress analysis result for case 1; effect of stress
relief grooves for reducing maximum stresses.
Maximum stress [MPa]
Model 1
(without groove)
Model 2
(with groove r = 3 mm)
Point
Mises Max Principal Mises Max Principal
C 105 91 108 103
D 332 263 433 413
109 103
G 249 192 286 302
H 744 704 561 627
E 773 801 670 512
F 105 94
When the vessel is pressurized, the lever is subjected
to a bending moment and because the R area for point E
and point H acts as a fulcrum for a lever-bending defor-
mation, it is evident from Figure 13 and Table 4 that the
stress is greater at points E and H than at points C, D, F,
and G. If model 1 and model 2 are compared, the stress
on the R area is reduced by approximately 10% by in-
troducing a groove with a 3-mm radius to the R area at
pointsial is
700 MPa [5], and therefore the durability can be ex-
3.2.2. C as e 2: Relati on between Cl earance and
Maximum Stres s
Thes stresand th
stress distributis sim
ure 13. The ss ,
are swn in T 5.
In model 3 when the lever makes contact with the sur-
face of the inner side oe, the s is
grea at poin, H, E,C on thrface o
ner side and ispoiG, D on the surface
Table 5. Stressysis resor case ect of clnces
for the locationaximutress.
Maximum stress [MPa]
E and H. The fatigue strength of this mater
pected to be 107 cycles.
Locat ions
e Miss don
ion for Case 2
istributie maxrincipal
ilar as shown in Fig-
imum p
tress values for pointC, D, E F, G, and H
ho abl e
f the lever guidstres
terts F
less at
and
nts
e suf the in-
of the
anal
s of mult f m s2; effeara
Model 3
(outer side clearan)
Model 4
(inner side clearance)
Point ce
Mises Max Principal Mises Max Principal
C 202 191 104 111
D 237 200 653 542
E 795 805 621 636
F 159 165 104 113
G 236 195 642 514
H 783 796 583 601
). The
maximn addition, it can be
H, E, and C on the surface of the
in
oints of stress cannot
be considered because thoccurs on the
surface of the inner side fracture test
the fracture originnt on the outehis ex-
presses a reqerinas
deviated fromacnse
using the FEMisis
Tcalculated results been duced he
desiof modi vesselhe mod one c de-
monate high6] expental
result can cleaemonsffectiveness ress
relierooves we designe
4. Conclusions
The selection optimape to support the lop-
ment of high-pressure contaiers for use in high-pressure
um stress
(M
3) The location where maximum stress occurs on the
outer side than that in Case 1 (clearance 0.3 mm
um stress exists at point E. I
seen that for model 4 when the lever makes contact with
the surface of the outer side of the lever guide, the stress
is greater at points G and C on the surface of the outer
and is less at points F,
ner side. The maximum stress is at point D.
Based on the results, the clearance between the lever
and lever guide is an important factor in determining the
points of maximum stress (Mises stress and maximum
principal stress). When the clearance is not taken into ac-
count, a countermeasure for those p
e maximum stress
. However, even in a
is preser side. T
uirement for considg how the model h
the
model
tual conditio
ng for fracture
s of u
analy
, even when
.
he haveintrointo t
gn
str
fied
er stress to
and t
fracture [
difie
. This
ould
rime
rly dtrate the eof st
f gd.
of the al shdeve
n
processing of food was implemented using finite element
analysis. The main results are the follows;
1) When designing a stress relief groove, the lever must
overhang the groove (L ≥ 0).
2) By introducing a stress relief groove to the R area,
maximum stress on the lever guide can be reduced by
10%. This enables the reduction of the maxim
ises stress) to be less than the fatigue strength.

Y. OTSUKA ET AL.
7
lever guide changes in accordance with the clearance be-
tween the lever and lever guide. This identified the need
to take into account the deviation factor such as design
clearance in modeling process.
5. Acknowledgements
One of the authors (Y.O.) was partially supported by the
Top Runner Incubation System through the Academia-
Industry Fusion Training in the Promotion of Independent
Research Environment for Young Researchers, MEXT,
Japan. The authors also appreciate the critical advice of
Assoc. Prof. Yukio Miyashita at Nagaoka University of
Technology. This research was financially supported by
JST project “Development of Technology for Promoting
Food Quality”.
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