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Stress analysis of a composite centrifugal fan impeller using the cyclic symmetric approach
Computers & Structures Vol. 48, No. 5, pp. 781-785, 1993
0045-7949/93 $6.00 + 0.00 ~ 1993 Pergamon Press Ltd
Printed in Great Britain.
STRESS ANALYSIS OF A COMPOSITE C E N T R I F U G A L FAN IMPELLER USING THE CYCLIC SYMMETRIC APPROACH S. MOHAMED NABI and N. GANESAN Machine Dynamics Laboratory, Department of Applied Mechanics, Indian Institute of Technology, Madras-600 036, India (Received 12 August 1992)
Abstract--The aim of this paper is to analyse the stress levels in a composite centrifugal fan impeller in a steady-state condition. In the solution procedure a cyclic symmetric approach is used, coupled with a modified Potter's scheme of solving simultaneous equations. This means less computer time and memory are required. Two composite materials, namely glass-epoxy and boron-epoxy, have been studied. Radial and circumferential fibre orientations are analysed. Maximum stress levels at different speeds have been calculated. Maximum deflections and factor of safety at 2000 rpm under both fibre orientations for the above materials are obtained.
INTRODUCTION
SUMMARYOF CYCLICSYMMETRICAPPROACH
The large computation time and memory needed are the main obstacles in the analysis of large-sized structures by the finite element method. The feature of geometrical periodicity of some mechanical components such as centrifugal fan impellers, automotive wheels and tyres, and turbine-blade disk, etc. can be used to minimize the above requirements. A structure with circumferential periodicity consists of a number of identical sectors to form a closed ring; many researchers have used this concept in the recent past. Wildheim [1] derived this principle and applied it to vibrations of a rotating regular polygon. Thomas [2] has used this approach for the dynamics of turbine blades and alternator end windings. The above authors used a conventional solution procedure, where the entire stiffness and mass matrix are assembled and used in the solution procedure. Ramamurti and Balasubramanium [3] modified Potter's method of solving simultaneous equations to solve the equations of steady-state analysis of circumferentially periodic structures. The same authors[4] have analysed a centrifugal fan impeller using the abovementioned solution procedure and verified the results with experimental values. This paper aims to develop a steady-state stress analysis of a composite centrifugal fan impeller with aid of the cyclic symmetic approach. In the finite element analysis a triangular plate element with six degrees of freedom per node is used. The solution procedure from [3, 4] has been followed here to solve the steady-state equation. Two types of composite material, namely glass-epoxy and boron-epoxy, with radial and circumferential fibre orientation have been used for the impeller. Maximum stress levels at 2000 rpm have been evaluated. Criteria of maximum deflection and factor of safety of the structure under the above speeds are discussed.
The principle used in this approach is that the deflection of any substructure is related to the deflection of preceding substructure by means of wave propagation theory. Since the deflection of each substructure is extrapolated from a single sector, only one sector is used for the analysis. Figure 1 shows a repetitive sector of a geometrically periodic structure, where N is the total number of sectors and n is number of stations in each sector. The static equilibrium of each station can be represented as follows [3]. For the first station
781
Cldn + Bldl + Aid2 = gl,
(1)
where B~ and A~ are stiffness submatrices of the stations, C~ is the coupling stiffness matrix between successive stations, ds are the nodal displacement vectors, and gs are the force vectors. Equation (1) can be written in general form Cidi_l+Bidi+Aidi+l=gi,
i = 2 , 3 , 4 . . . . . n. (2)
Equations (1) and (2) can be modified as dl = - Pld2 + ql + Qld,
d~=-Pid~+~+qi+Q~d,,
where p = B-IAI
ql = B/-lg I Q1 = - B ? I C I
p~= (B,- CP~_~)-~A,
i = 2 , 3 . . . . . n,
(3)
782
S. MOHAMEDNABI and N. GANESAN
5(n)
Equation (7) can be substituted into (11) to give
I V ( N ) ~ ~ - ~ ~
1
d. = - - ~ . d , + #..
(12)
Comparing eqns (7) and (11) we can get d I -- [P. -- (1 -- Q . ) - t p . ] - l [ #
n
- -
(1 -- Q. )-tq.]. (13)
Substituting eqn (13) into (12) we can arrive at the value of d, and by backward substitutions in eqn (10) other unknown displacements are derived. RESULTS
Fig. I. Periodic structure.
q~ = (Bi -- Ci P i - l ) - l(g~ _ C~qi_ 1) Qi=(a,-ciPi_l)-t(CiQi_l)
,
i = 2 , 3 . . . . . n. (4)
The equilibrium at the nth station is (5)
d.= -P.d.+,+q.+Q.d..
Because of cyclic symmetry
a.+, =a,.
(6)
d. = 1 -- ( Q . ) - ' q . - (1 - Q , ) P ~ ' 4 .
(7)
Hence
AND DISCUSSION
The details of one sector of a centrifugal fan impeller having eight backward curve blades are given in Fig. 2. The finite element models of three components of the impeller are given in Fig. 3. For the blade and back plate, the fibre orientations are taken with respect to the back plate axis, and the details of orientations are explained in Fig. 4. The complete shape of the cover plate is considered as a truncated cone. The radial fibres are parallel to the generator of the truncated cone and the circumferential fibres are perpendicular to it; the inner edges of the back plate are fixed. The analysis of the impeller is carried out under steady-state conditions from 800 to 2000 rpm in steps of 200 rpm. The load vector neglects the effect of air flow and considers only the centrifugal load.
Equations (1) and (2) after simplification give (8)
dl = - P l d ~ + #1, where PI
: [BI
--
CI(1
--
O,,)-tP,]-IAl
41 = [B1-C1( 1 - - Q . ) - I P . ] - I [ g l - C , ( 1 - Q . ) - lg.] (9) similarly d,=
-P,d,+, + #,
204
i
/
I
P, = [B, -- C , ( l - P , _ , ) - t ] A , ~]l = [Bi--
Ci(1 -
P,-I) -1]
Hub [g,-- C,#,_ 1], i = 2 , 3 . . . . .
n.
(10)
The above equation can be written for the n th station as
\ 200
B~ackplate a.= -P.a.+,
+#..
(ll)
te
Fig. 2. Centrifugual fan impeller.
00
138
Stress analysis of a centrifugal fan impeller 6 No. of nodes
Table 1. Comparison of surface strains at 2000rpm:
Z ~
isotropic case
~
Components
~
!~
~N~N~ ~X[
i ~ r , ~ . - - - ~ - - ~ - , ~ r - , , , . J ~,a [~ 200
Blade
Back plate 8 cover No. No. No. No.
of of of of
nodes elements sectors stations
program
Cover plate outer surface
108
112
Back plate inner surface
128
131
Axial strain on convex surface of blade Axial strain on
176
157
- 294
- 271
of blade Maximum stresses
Validation
In order to validate the program, the results obtained for the isotropic case are compared with those reported in [4]. The maximum displacement and strains are compared. As reported in [4], the maximum deflection occurs at the midspan of the blade, the reported value is 0.155mm and the present analysis gives 0.1484mm at 1800 rpm. The strains at 2000 rpm for different components are given in Table 1. The referenced surface strains are read from the graphs reported in [4]. The cover plate and the back plate strains, and the blade strains have a difference of less than 5% and about 8% than that of reported values, respectively. V l
~
Present
Reference [4]
concave surface
: 88 :131 : 8 : 6
Fig. 3. Finite element model.
Y
783
/~"
"X
"X
Radial
Circumferential (a) Back plate
The maximum stresses for the two composite materials are obtained at 2000 rpm and are listed in Table 2. tL, a 0, and Zr0 values are picked from different points of the structure, where they are found to be maximum. The stresses are derived from the displacement arrived using the cyclic symmetric approach. Comparison of in-plane and bending stresses reveals that the predominant stresses are bending stresses. As the back plate thickness is higher than that of the cover plate, stresses are higher in the blade area nearer to the back plate than at the cover plate. The above facts are true for both fibre orientations. For the blade, the radial stress is predominant when the fibres are radially oriented. The tangential stress has a comparatively low value as seen from Table 2. The circumferential fibre orientation shows a stress variation which is quite different from that of the radial fibre orientation. Here, the tangential stress is high and its maximum value is less than the maximum radial stress for glass-epoxy and vice versa for boron-epoxy. Comparatively, boron-epoxy has higher stress levels than glass-epoxy for both orientations. The stress levels across the blade are shown in Fig. 5. The sign change in the stresses occurs twice when m o v i n g across the blade f r o m the back plate to
Zt
l
.. Radial
X
the cover plate. As the stresses are higher in the blade than in the other components, the blade stresses are plotted for different speeds in Figs 6 and 7.
I Circumferential
=X
Maximum deflection
(b) Cover plate
As in the case o f an isotropic fan impeller, here the m a x i m u m deflection also occurs at the midspan o f the
(c) Blade Fig. 4. Fibre orientation,
ameter because too high a deflection, compared to the isotropic case, would render the composite application unsafe. The maximum deflections calculated for different cases are presented in Table 3. The boron-epoxy material with circumferential fibre orientation give less deflection than any other combination; even lower than the maximum deflection of a mild steel impeller.
Radial
-~X Circumferential
784
S. MOHAMEDNABI and N. GANESAN Table 2. Maximum stresses of impeller components at 2000 rpm (kgf/mm2) Back plate
Material
Cover plate
o"r
o"0
-c~
Glass-epoxy Radial Circum.
0.85 0.99
0.64 0.67
0.42 -0.47
Boron -epoxy Radial Circum.
1.20 1.38
0.74 1.04
0.72 -0.65
ar
o0
"Or0
ar
1.05 0.73
0.95 -0.79
0.47 0.44
1.60 - 1.87
!.26 - 1.60
0.92 1.11
3.0
2.0
Blade GO
ZrO
- 1.94 - i.14
0.55 - 1.75
0.82 -0.66
-2.01 -0.97
0.951 -2.25
0.76 -0.55
-0.0
**~.~
Radial fiber orientation
(%)
~,~..~.~,
-0.5
\
\
~
°~.~
~
"<.)Y,,
1.0 E E
}
0.0
~, -1.o t
-2.0
-2.0
on (cro)
* Glass--Epoxy -3.0 * Boron- Epoxy -4.0
°
~
2'0 '
4b
do
' 8'0 '1~o
,~o'do
Distance from back plate in mm Fig. 5. Stresses across the blade.
% t
-2.5
° Glass - Epoxy • Boron- Epoxy
-3.,
B~O
12'oo 1~o Speed (rpm)
' 2000
' 2400
Fig. 7. Variation of blade stresses with speed (circumferential fibres).
Factor of safety
Tsai-Hill theory [5] has been used to calculate the factor o f safety o f different c o m b i n a t i o n s o f material and fibre orientation. A l t h o u g h this theory generally is used only for glass-epoxy material, it has also been used for b o r o n - e x p o y to study the comparative advantages o f b o t h materials. The factor o f safety is calculated in all the elements and the lowest value is given in Table 4 for different cases. In every c o m b i n a t i o n o f material and fibre orientation,
although the maximum stress level occurs in the blade, the lowest factor of safety occurs in the cover plate, except when glass-epoxy material with circumferential fibre orientation is used. This clearly shows that the combination of different stresses is the critical parameter for the design of this composite centrifugal fan impeller. In both fibre orier~tations the glass--epoxy material gives a higher factor of safety than the other. CONCLUSIONS
1.0
Composite centrifugal fan impeller steady-state stress analysis has been carried out using the cyclic symmetric approach. By using the composite material the weight of the impeller can be reduced to one quarter of the mild steel impeller. By analysing
0.0
E -1.0 E Table 3. Maximum radial deflection of blade at different configurations at 2000 rpm
~ -2.0
-3.0 = Glass- Epoxy * Boron - Epoxy
-40
~0
'
' 1200
'
Speed
in rpm
140
2doo
2400 '
Fig. 6. Variation of blade stresses with speed (radial fibres).
Material
Radial deflection (mm)
Mild steel
0.155
Glass -epoxy Radial Circumferential
0.646 0.342
Boron -epoxy Radial Circumferential
0.287 0.133
785
Stress analysis of a centrifugal fan impeller Table 4. Factor of safety for a composite impeller at different configurations based on stresses obtained at 2000 rpm Material
To have the best design of this impeller, different layups may be analysed to get an efficient combination of desired results.
Factor of safety
Glass-epoxy Radial Circumferential
3.2 2.9
Boron -epoxy Radial Circumferential
1.9 1.7
glass-epoxy and boron-epoxy materials the following inferences can be drawn: (i) a glass-epoxy material with circumferential fibre orientation gives a higher factor of safety than a boron-epoxy material and (ii) a boron-epoxy material with circumferential fibre orientation gives a lower maximum deflection than a glass-epoxy material.
REFERENCES
1. J. Wildheim, Vibration of rotating circumferentially periodic structures. Quart. J. Mech. Appl. Math. 34, No. 2 (1981). 2. D. L. Thomas, Dynamics of rotationally periodic structures. Int. J. Numer. Meth. Engng 14, 81-102 (1979). 3. V. Ramamurti and P. Balasubramanium, Static analysis of circumferentially periodic structures with Potter's scheme. Comput. Struct. 22, 427-431 (1986). 4. V. Ramamurti and P. Balasubramanium, Steady state stress analysis of centrifugal fan impellers. Comput. Sruct. 25, 129-135 (1987). 5. R. M. Jones, Mechanics of Composite Materials. McGraw-Hill (1975).
0045-7949/93 $6.00 + 0.00 ~ 1993 Pergamon Press Ltd
Printed in Great Britain.
STRESS ANALYSIS OF A COMPOSITE C E N T R I F U G A L FAN IMPELLER USING THE CYCLIC SYMMETRIC APPROACH S. MOHAMED NABI and N. GANESAN Machine Dynamics Laboratory, Department of Applied Mechanics, Indian Institute of Technology, Madras-600 036, India (Received 12 August 1992)
Abstract--The aim of this paper is to analyse the stress levels in a composite centrifugal fan impeller in a steady-state condition. In the solution procedure a cyclic symmetric approach is used, coupled with a modified Potter's scheme of solving simultaneous equations. This means less computer time and memory are required. Two composite materials, namely glass-epoxy and boron-epoxy, have been studied. Radial and circumferential fibre orientations are analysed. Maximum stress levels at different speeds have been calculated. Maximum deflections and factor of safety at 2000 rpm under both fibre orientations for the above materials are obtained.
INTRODUCTION
SUMMARYOF CYCLICSYMMETRICAPPROACH
The large computation time and memory needed are the main obstacles in the analysis of large-sized structures by the finite element method. The feature of geometrical periodicity of some mechanical components such as centrifugal fan impellers, automotive wheels and tyres, and turbine-blade disk, etc. can be used to minimize the above requirements. A structure with circumferential periodicity consists of a number of identical sectors to form a closed ring; many researchers have used this concept in the recent past. Wildheim [1] derived this principle and applied it to vibrations of a rotating regular polygon. Thomas [2] has used this approach for the dynamics of turbine blades and alternator end windings. The above authors used a conventional solution procedure, where the entire stiffness and mass matrix are assembled and used in the solution procedure. Ramamurti and Balasubramanium [3] modified Potter's method of solving simultaneous equations to solve the equations of steady-state analysis of circumferentially periodic structures. The same authors[4] have analysed a centrifugal fan impeller using the abovementioned solution procedure and verified the results with experimental values. This paper aims to develop a steady-state stress analysis of a composite centrifugal fan impeller with aid of the cyclic symmetic approach. In the finite element analysis a triangular plate element with six degrees of freedom per node is used. The solution procedure from [3, 4] has been followed here to solve the steady-state equation. Two types of composite material, namely glass-epoxy and boron-epoxy, with radial and circumferential fibre orientation have been used for the impeller. Maximum stress levels at 2000 rpm have been evaluated. Criteria of maximum deflection and factor of safety of the structure under the above speeds are discussed.
The principle used in this approach is that the deflection of any substructure is related to the deflection of preceding substructure by means of wave propagation theory. Since the deflection of each substructure is extrapolated from a single sector, only one sector is used for the analysis. Figure 1 shows a repetitive sector of a geometrically periodic structure, where N is the total number of sectors and n is number of stations in each sector. The static equilibrium of each station can be represented as follows [3]. For the first station
781
Cldn + Bldl + Aid2 = gl,
(1)
where B~ and A~ are stiffness submatrices of the stations, C~ is the coupling stiffness matrix between successive stations, ds are the nodal displacement vectors, and gs are the force vectors. Equation (1) can be written in general form Cidi_l+Bidi+Aidi+l=gi,
i = 2 , 3 , 4 . . . . . n. (2)
Equations (1) and (2) can be modified as dl = - Pld2 + ql + Qld,
d~=-Pid~+~+qi+Q~d,,
where p = B-IAI
ql = B/-lg I Q1 = - B ? I C I
p~= (B,- CP~_~)-~A,
i = 2 , 3 . . . . . n,
(3)
782
S. MOHAMEDNABI and N. GANESAN
5(n)
Equation (7) can be substituted into (11) to give
I V ( N ) ~ ~ - ~ ~
1
d. = - - ~ . d , + #..
(12)
Comparing eqns (7) and (11) we can get d I -- [P. -- (1 -- Q . ) - t p . ] - l [ #
n
- -
(1 -- Q. )-tq.]. (13)
Substituting eqn (13) into (12) we can arrive at the value of d, and by backward substitutions in eqn (10) other unknown displacements are derived. RESULTS
Fig. I. Periodic structure.
q~ = (Bi -- Ci P i - l ) - l(g~ _ C~qi_ 1) Qi=(a,-ciPi_l)-t(CiQi_l)
,
i = 2 , 3 . . . . . n. (4)
The equilibrium at the nth station is (5)
d.= -P.d.+,+q.+Q.d..
Because of cyclic symmetry
a.+, =a,.
(6)
d. = 1 -- ( Q . ) - ' q . - (1 - Q , ) P ~ ' 4 .
(7)
Hence
AND DISCUSSION
The details of one sector of a centrifugal fan impeller having eight backward curve blades are given in Fig. 2. The finite element models of three components of the impeller are given in Fig. 3. For the blade and back plate, the fibre orientations are taken with respect to the back plate axis, and the details of orientations are explained in Fig. 4. The complete shape of the cover plate is considered as a truncated cone. The radial fibres are parallel to the generator of the truncated cone and the circumferential fibres are perpendicular to it; the inner edges of the back plate are fixed. The analysis of the impeller is carried out under steady-state conditions from 800 to 2000 rpm in steps of 200 rpm. The load vector neglects the effect of air flow and considers only the centrifugal load.
Equations (1) and (2) after simplification give (8)
dl = - P l d ~ + #1, where PI
: [BI
--
CI(1
--
O,,)-tP,]-IAl
41 = [B1-C1( 1 - - Q . ) - I P . ] - I [ g l - C , ( 1 - Q . ) - lg.] (9) similarly d,=
-P,d,+, + #,
204
i
/
I
P, = [B, -- C , ( l - P , _ , ) - t ] A , ~]l = [Bi--
Ci(1 -
P,-I) -1]
Hub [g,-- C,#,_ 1], i = 2 , 3 . . . . .
n.
(10)
The above equation can be written for the n th station as
\ 200
B~ackplate a.= -P.a.+,
+#..
(ll)
te
Fig. 2. Centrifugual fan impeller.
00
138
Stress analysis of a centrifugal fan impeller 6 No. of nodes
Table 1. Comparison of surface strains at 2000rpm:
Z ~
isotropic case
~
Components
~
!~
~N~N~ ~X[
i ~ r , ~ . - - - ~ - - ~ - , ~ r - , , , . J ~,a [~ 200
Blade
Back plate 8 cover No. No. No. No.
of of of of
nodes elements sectors stations
program
Cover plate outer surface
108
112
Back plate inner surface
128
131
Axial strain on convex surface of blade Axial strain on
176
157
- 294
- 271
of blade Maximum stresses
Validation
In order to validate the program, the results obtained for the isotropic case are compared with those reported in [4]. The maximum displacement and strains are compared. As reported in [4], the maximum deflection occurs at the midspan of the blade, the reported value is 0.155mm and the present analysis gives 0.1484mm at 1800 rpm. The strains at 2000 rpm for different components are given in Table 1. The referenced surface strains are read from the graphs reported in [4]. The cover plate and the back plate strains, and the blade strains have a difference of less than 5% and about 8% than that of reported values, respectively. V l
~
Present
Reference [4]
concave surface
: 88 :131 : 8 : 6
Fig. 3. Finite element model.
Y
783
/~"
"X
"X
Radial
Circumferential (a) Back plate
The maximum stresses for the two composite materials are obtained at 2000 rpm and are listed in Table 2. tL, a 0, and Zr0 values are picked from different points of the structure, where they are found to be maximum. The stresses are derived from the displacement arrived using the cyclic symmetric approach. Comparison of in-plane and bending stresses reveals that the predominant stresses are bending stresses. As the back plate thickness is higher than that of the cover plate, stresses are higher in the blade area nearer to the back plate than at the cover plate. The above facts are true for both fibre orientations. For the blade, the radial stress is predominant when the fibres are radially oriented. The tangential stress has a comparatively low value as seen from Table 2. The circumferential fibre orientation shows a stress variation which is quite different from that of the radial fibre orientation. Here, the tangential stress is high and its maximum value is less than the maximum radial stress for glass-epoxy and vice versa for boron-epoxy. Comparatively, boron-epoxy has higher stress levels than glass-epoxy for both orientations. The stress levels across the blade are shown in Fig. 5. The sign change in the stresses occurs twice when m o v i n g across the blade f r o m the back plate to
Zt
l
.. Radial
X
the cover plate. As the stresses are higher in the blade than in the other components, the blade stresses are plotted for different speeds in Figs 6 and 7.
I Circumferential
=X
Maximum deflection
(b) Cover plate
As in the case o f an isotropic fan impeller, here the m a x i m u m deflection also occurs at the midspan o f the
(c) Blade Fig. 4. Fibre orientation,
ameter because too high a deflection, compared to the isotropic case, would render the composite application unsafe. The maximum deflections calculated for different cases are presented in Table 3. The boron-epoxy material with circumferential fibre orientation give less deflection than any other combination; even lower than the maximum deflection of a mild steel impeller.
Radial
-~X Circumferential
784
S. MOHAMEDNABI and N. GANESAN Table 2. Maximum stresses of impeller components at 2000 rpm (kgf/mm2) Back plate
Material
Cover plate
o"r
o"0
-c~
Glass-epoxy Radial Circum.
0.85 0.99
0.64 0.67
0.42 -0.47
Boron -epoxy Radial Circum.
1.20 1.38
0.74 1.04
0.72 -0.65
ar
o0
"Or0
ar
1.05 0.73
0.95 -0.79
0.47 0.44
1.60 - 1.87
!.26 - 1.60
0.92 1.11
3.0
2.0
Blade GO
ZrO
- 1.94 - i.14
0.55 - 1.75
0.82 -0.66
-2.01 -0.97
0.951 -2.25
0.76 -0.55
-0.0
**~.~
Radial fiber orientation
(%)
~,~..~.~,
-0.5
\
\
~
°~.~
~
"<.)Y,,
1.0 E E
}
0.0
~, -1.o t
-2.0
-2.0
on (cro)
* Glass--Epoxy -3.0 * Boron- Epoxy -4.0
°
~
2'0 '
4b
do
' 8'0 '1~o
,~o'do
Distance from back plate in mm Fig. 5. Stresses across the blade.
% t
-2.5
° Glass - Epoxy • Boron- Epoxy
-3.,
B~O
12'oo 1~o Speed (rpm)
' 2000
' 2400
Fig. 7. Variation of blade stresses with speed (circumferential fibres).
Factor of safety
Tsai-Hill theory [5] has been used to calculate the factor o f safety o f different c o m b i n a t i o n s o f material and fibre orientation. A l t h o u g h this theory generally is used only for glass-epoxy material, it has also been used for b o r o n - e x p o y to study the comparative advantages o f b o t h materials. The factor o f safety is calculated in all the elements and the lowest value is given in Table 4 for different cases. In every c o m b i n a t i o n o f material and fibre orientation,
although the maximum stress level occurs in the blade, the lowest factor of safety occurs in the cover plate, except when glass-epoxy material with circumferential fibre orientation is used. This clearly shows that the combination of different stresses is the critical parameter for the design of this composite centrifugal fan impeller. In both fibre orier~tations the glass--epoxy material gives a higher factor of safety than the other. CONCLUSIONS
1.0
Composite centrifugal fan impeller steady-state stress analysis has been carried out using the cyclic symmetric approach. By using the composite material the weight of the impeller can be reduced to one quarter of the mild steel impeller. By analysing
0.0
E -1.0 E Table 3. Maximum radial deflection of blade at different configurations at 2000 rpm
~ -2.0
-3.0 = Glass- Epoxy * Boron - Epoxy
-40
~0
'
' 1200
'
Speed
in rpm
140
2doo
2400 '
Fig. 6. Variation of blade stresses with speed (radial fibres).
Material
Radial deflection (mm)
Mild steel
0.155
Glass -epoxy Radial Circumferential
0.646 0.342
Boron -epoxy Radial Circumferential
0.287 0.133
785
Stress analysis of a centrifugal fan impeller Table 4. Factor of safety for a composite impeller at different configurations based on stresses obtained at 2000 rpm Material
To have the best design of this impeller, different layups may be analysed to get an efficient combination of desired results.
Factor of safety
Glass-epoxy Radial Circumferential
3.2 2.9
Boron -epoxy Radial Circumferential
1.9 1.7
glass-epoxy and boron-epoxy materials the following inferences can be drawn: (i) a glass-epoxy material with circumferential fibre orientation gives a higher factor of safety than a boron-epoxy material and (ii) a boron-epoxy material with circumferential fibre orientation gives a lower maximum deflection than a glass-epoxy material.
REFERENCES
1. J. Wildheim, Vibration of rotating circumferentially periodic structures. Quart. J. Mech. Appl. Math. 34, No. 2 (1981). 2. D. L. Thomas, Dynamics of rotationally periodic structures. Int. J. Numer. Meth. Engng 14, 81-102 (1979). 3. V. Ramamurti and P. Balasubramanium, Static analysis of circumferentially periodic structures with Potter's scheme. Comput. Struct. 22, 427-431 (1986). 4. V. Ramamurti and P. Balasubramanium, Steady state stress analysis of centrifugal fan impellers. Comput. Sruct. 25, 129-135 (1987). 5. R. M. Jones, Mechanics of Composite Materials. McGraw-Hill (1975).