Stress Analysis of Axial Flow Fan

Transcription

1 Adv. Theor. Appl. Mech., Vol. 5, 2012, no. 6, Stress Analysis of Axial Flow Fan Oday I. Abdullah Laser and System Technologies (AmP) Technical University Hamburg-Harburg, Germany Josef Schlattmann Laser and System Technologies (AmP) Technical University Hamburg-Harburg, Germany Abstract In this paper the finite element method has been used to determine the stresses and deformations of an axial fan blade. Three dimensional, finite element programs have been developed using eight-node superparametric shell element as a discretization element for the blade structure. All the formulations and computations are coded in Fortran-77. This work was achieved by modeling the fan blade as a rotating shell. The investigation covers the effect of centrifugal forces on stresses and deformations of rotating fan blades. Extensive analysis has been done for various values, speed of rotation, thickness, skew angle, and the effect of the curvature on the stress and deformation. The numerical results have shown a good agreement compared with the available investigations using other methods. Keywords: Axial flow fan, FEM, Stresses and deformations, Rotating blade. 1 Introduction Axial fans are widely used in ventilation, cooling, and compression. Different Types of fans such as free ducted and diaphragms mounted are employed to satisfy the various needs and conditions. Parameters like speed of rotation, skew angle and

2 264 O. I. Abdullah and J. Schlattmann the aerodynamic effects are taken into consideration in the design of fan blades. Knowledge of the steady state behavior of axial fans is consider essential for design purposes, because of that the results from this analysis will illustrate the values of maximum stresses and deformations and their locations. The failures of rotating blade are quite often due to the fatigue, thus the increasing requirements on the quality, durability, reliability and the life of blades directed the designers to have a clear indication of the deformations and stresses induced in the rotating blades, in addition to the knowledge of their steady-state characteristics. The centrifugal forces are of considerable magnitude due to high speeds of rotation. They also stiffen the structure and this has to be taken into account. Gross untwisting results from these forces can cause changes in the velocity triangles of the fluid flow, for the leading and trailing edges, also tip clearance can be changed drastically due to blade untwist; and both effects cause degradation in machine performance. Therefore, the steadystate analysis is important to both fluid and stress analysis; and vibratory stresses can be considered after the evaluating of the steady-state stresses and deformations; since at higher rotating speeds a new static equilibrium position will be generated. The mechanical failures occur due to fatigue and creep are problems for rotating blades, and when a turbomachine is started (at every running), the stresses due to rotation go from low value to the peak value and so constitute one component of low-cycle fatigue, provided that peak value is larger than the fatigue limit. While high cycle fatigue is due to blade vibration. Low cycle fatigue affects at the tip and pitch of the blade; while high cycle fatigue affects at the root. Creep occurs due to the effect of centrifugal loading at high temperature. A limiting value of creep often used for design is 0.2% strain. Most of the available literature deal with the determination of natural frequencies and mode shapes of the rotating blades and only few papers exist on the static behavior of the turbomachinery blades. This encourages the researchers to work in this field, but most of the researchers neglect the effect of centrifugal and geometric stiffness and assume the blade as beam such as Raylieh-Rits and Gulerkin methods this may affect on the prediction of the stresses and deformation, this assumption will lead the blade to failure before the expected lifetime for blade. Carngie [1] was examined a static bending of pre-twist cantilever blading. The blading is pre-twist linearly about the centered of its cross-section to a maximum angle of (π/2) radius, and is considered as mounted fixed at the root. He applied variation calculus, static equilibrium equations were derived from expressions for the total energy of blades subjected to either concentrated or uniformly distributed bending load. Walker [2] studied the vibration of combined helicoidal fan blade, in his study a conforming finite shell element suitable for the analysis of curved twisted fan blades was developed and applied to a number of blade models. The thin shell element was used in this study to predict the natural frequencies and mode shapes of a number of

3 Stress analysis of axial flow fan 265 fabricated fan blade structures and the results were compared with the experimental results. Ramamurti and sreenivasamurthy [3] studied the dynamic stress analysis of rotating twisted and tapered blades. The finite element method was used to determine the stresses and deformations.three-dimensional, twenty-node isoparametric elements have been used for the analysis. Extensive analysis has been done for various pretwist angles, skew angles, breadth to length ratios, and breadth to thickness ratios of the blades. Experiments were carried out to determine the stresses for the verification of the numerical results. Omprakash and Ramamurti [4] carried out the steady state dynamic stress and deformation analysis of high pressure stage turbomachinery bladed disks taking into account all the geometric complexities involved and included the contributions due to initial stress and membrane behavior. They used a triangular shell element with six degrees of freedom per node. Yoo et al. [5] studied the vibration analysis of rotating pre-twisted blade with a concentrated mass. The blade has an arbitrary orientation with respect to the rigid hub to which it is fixed.the equation of motion are derived based on a modeling method that employs hybrid deformation variables. The resulting equation for the vibration analysis is transformed into a dimension less parameters on the model characteristics of the rotating blade are investigated through numerical analysis. 2 Finite element analyses Analysis has been done for curvature and s with skew angles (0, 15, 30, 45, 60, 75 ) and it has been assumed a homogeneous and isotropic material. A superparametric 768 elements three- dimensional is used in the analysis. The stresses and deformations are computed for different mesh, a mesh sensitivity study was done to choose the optimum mesh from computational accuracy point of view. It is very well established by zienkiewicz [6] that the superparametric three-dimensional element is more convenient and suitable for the present finite element analysis than the triangular or rectangular flat elements usually used in shell problems, because the shell structure can be modeled truly in the analysis with very good accuracy for results. The equations of stress strain and transverse shear strain components are [6]: ε x [ σ υ ( σ σ )] = 1 (1) x y z E [ σ υ ( σ σ )] ε y = 1 (2) y x z E

4 266 O. I. Abdullah and J. Schlattmann [ σ υ ( σ σ )] ε z = 1 z x + (3) y E [ τ υ ( υ) ] 2 γ xy = xy 1+ E 2 γ xz = xz 1+ E [ τ υ ( υ) ] [ τ υ ( υ) ] 2 γ yz = yz 1+ E (4) (5) (6) 3 Verification test The current results that are exhibited in Table 1 & 2 compared with the numerical study in reference [3]. Table. 1 shows the maximum dimensionless tip deflection for different pre-twist angle and thickness to width ratio. And Table. 2 demonstrates the maximum dimensionless radial stresses for three aspect ratios at different pre-twist angles (0, 15, 30, and 45 ). In both tables the maximum error not exceeds 1.69%. 4 Case study The aim of this study is to fill in the gap by furnishing the information about the behavior of axial fan blades regarding deformations and stresses having different skew angles and thickness due to centrifugal loading. Analysis has been done for flat and s, the geometry of fan blade as shown in Fig. 1.a. Fig. 2.b shows the 768 elements (plane view) for the blades. The material properties are: E=69 G pa, υ= Numerical studies a- Effect of the speed of rotation: The variation of stresses and deformations with speed of rotation (150, 450, 750, 1050, 1350, and 1850 r.p.m) for different radius of the disc (0.1, 0.2, and 0.3m) are

5 Stress analysis of axial flow fan 267 investigated. Fig. 2 shows the variation of v-deflection with speed of rotation. Figs. 3, 4 & 5 show the variation of xx-stresses, yy-stresses, xy-stresses with speed of rotation. It can be noted from this figure, when the speed of rotation increases all stresses and deformations increases too. Also we presented the compared between the curvature and, the variation of xx-stresses, yy-stresses, and xy-stresses with the speed of rotation are shows in Figs. 7, 8 and 9. Fig. 6 shows the variation of v- deflection with the speed of rotation. b- Effect of skew angle: The stresses and deformations computed for the have different combinations of skew angles (0,15, 30, 45, 60, and 75 ) for different speed of rotations (500, 750, and 1000 r.p.m). Fig. 10 exhibits the variation of v-deflections with skew angle. It can be seen from this figure, when skew angle enlarges the v- deformation increases and then decreases. Figs. 11, 12 & 13 display the variations of xx-stresses, yy-stresses, and xy-stresses respectively with skew angle. Fig. 14 shows the plot of v-deflection for the curvature and with skew angle. The xxstresses, yy-stresses, and xy-stresses are plots with the skew angle as shown in the Figs. 15, 16 & 17 respectively. c- Effect of thickness: In order to investigate the thickness of the it was selected five different thickness (1.5, 2.5, 3.5, 4.5, and 5 mm). Fig. 18 shows the variation of v- deflection with thickness. It can be recognized, that when the thickness increases, the v-deflection decreases. Figs 19, 20 & 21 demonstrate the variations of xx-stresses, yy-stresses, and xy-stresses respectively with thickness. 6 Discussions The numerical results of the selected problems are discussed in this section. Using the standard finite element procedure, the stresses and deformations are computed for axial fan blade. The study has covered the effect of the speed of rotation, skew angle, thickness, and curvature effects on the performance of fan blade. It has been found that the xx- stress is predominant among normal stress components and shear stresses in xy plane compared to the other components of the stresses. But in the the stress in y-direction is predominant at all cases. When computed the stresses and deformations at various skew angles for curvature blade (0, 15, 30, 45, 60, and 75 ), It can be notes, when the skew angle is 45 the yy-stresses, xy-stresses and deformations are maximum except the xx-stresses is

6 268 O. I. Abdullah and J. Schlattmann maximum at 30, but if the skew angle greater than or little than 45 the yy-stresses, xy-stresses and deformations decreases. The xx-stresses decrease for the skew angle increases or decreases about 30. The same behavior for the with variation skew angles, but the stresses and deformations on are lower than stresses and deformations on the. Hence, the skew angle must be kept to a minimum, bearing in mind fluid dynamic requirement of the skew angle to achieve maximum efficiency and minimum stress level. It can be recognized that when the thickness increases the stresses and deformations decreases, this effect is due to the reduction in structural stiffness, and thus a large deflection and higher stresses are generated due to the reduction in the blade thickness. Also it can be observed the speed of rotation and radius of the disc are effect of a large part of results, which the stresses and deformations are proportional to the speed of rotation and disc radius. 7 Conclusions The conclusions obtained from the present analysis can be summarized as follows: 1. Generally for all types of axial flow fan blades, it can be concluded when the speed of rotation increases to twice, the von-misses stresses is increases by 300%. 2. The increases of the blade thickness leads to decrease in the stresses and deformations, (i. e. thin blades give greater stresses and deformations than the thick blades) and that is due to the higher reduction in structural stiffness. 3. The dominant stress is the stress in the lengthwise direction (xx-stresses) for both types of fan blades. 4. The increases in the disc radius result in higher stresses and deformations. This problem should be taken into consideration especially for thin blades having large aspect ratio. 5. The stresses and deformations in the larger than the under the same conditions except the xy-stresses at skew angle greater than 45º. 6. The maximum effect of skew angle occurs when the skew angle is 45 for the yystresses, xy-stresses, and deformations, but the maximum xx-stresses occurs at skew angle 30.

7 Stress analysis of axial flow fan 269 Table.1 verification test for tip deformation parameter in y-direction for rotating rectangular Blade, L/b=5, with different thickness ratios and twist angles (ρ=7850 Kg/m³, Ω=260 rad/sec, b=0.2, E=200 Gpa) Cases v-deformation/(ρω²b³/e) t/b=0.12 Present work 1200 d.o.f 1600 d.o.f Ref. [3] % Difference α = α = t/b=0.05 α = α = Table.2 verification test for predominant stress parameter near root for rotating rectangular blade for different aspect ratios and pre-twist angles, t/b=0.05 (ρ=7850 Kg/m³, Ω=260 rad/sec, b=0.2, E=200 Gpa) Cases yy-stresses/(ρ Ω² b²) L/b=5 Present work 1200 d.o.f 1600 d.o.f Ref. [3] % Difference α = α = α = α = L/b=4 α = α = α = α = L/b=3 α = α = α = α =

8 270 O. I. Abdullah and J. Schlattmann Hint: the maximum depth for the curvature is 16.6 mm in the side view. (R 1200 Center point P) 26 (R 370 Center point Q) (R 830 Center point R) φ 5 (Five Holes for B C D E F G H I J K L M N O A MRAK COORDINATES Fig. 1 (a) The dimension of an axial flow fan blade (practical application). X-direction Y-direction

9 Stress analysis of axial flow fan 271 Y X Fig (1.b) Suitable mesh size for practical fan blade v-deformation (m) *10^ xx-stress (Mpa) Fig.2 Variation of v-deformation with speed of rotation (skew angle=0, thickness=1.5 mm) Fig.3 Variation of xx-stresses with speed of rotation (skew angle=0, thickness=1.5 mm) yy-stress (Mpa) xy-shear stress (Mpa) Fig.4 Variation of yy-stresses with speed of rotation (Skew angle=0, thickness=1.5 mm ) speed of rotation(r.p.m) Fig.5 Variation of xy-stresses with speed of rotation (Skew angle=0, thickness=1.5 mm )

10 272 O. I. Abdullah and J. Schlattmann v-deformation (m)*10^ xx-stress (Mpa) Fig.6 Variation of v-deformation with speed of rotation (R=0.18, thickness=1.5 mm) Fig. 7 Variation of xx-stresses with speed of rotation (R=0.18, thickness=1.5 mm) yy-stress (Mpa) 12 8 xy-shear stress (Mpa) Fig. 8 Variation of yy-stresses with speed of rotation (R=0.18, thickness=1.5 mm) Fig. 9 Variation of xy-stresses with speed of rotation (R=0.18, thickness=1.5 mm) r.p.m 500 r.p.m 750 r.p.m 750 r.p.m r.p.m 1000 r.p.m v-deformation (m) *10^ xx-stress (Mpa) Fig. 10 Variation of v-deformation with skew angle (R=0.18, thickness=1.5 mm) Fig.11 Variation of xx-stresses with skew angle (R=0.18, thickness=1.5 mm)

11 Stress analysis of axial flow fan r.p.mэ 500 r.p.m r.p.m 1000 r.p.m r.p.m 1000 r.p.m yy-stress (Mpa) 20 xy-stress (Mpa) Fig.12 Variation of yy-stresses with skew angle (R=0.18, thickness=1.5 mm) Fig.13 Variation of xy-stresses with skew angle (R=0.18, thickness=1.5 mm) v-deformation (m)*10^ xx-stress (Mpa) Fig.14 Variation of v-deformation with skew angle (R=0.18, Thickness=1.5 mm, speed of rotation =1000 r.p.m) Fig.15 Variation of xx-stresses with skew angle (R=0.18, Thickness=1.5 mm, speed of rotation =1000 r.p.m) yy-stress (Mpa) xy-shear stress (Mpa) Fig.16 Variation of yy-stresses with skew angle (R=0.18, Thickness=1.5 mm, speed of rotation =1000 r.p.m) Fig.17 Variation of xy-stresses with skew angle (R=0.18, Thickness=1.5 mm, speed of rotation =1000 r.p.m)

12 274 O. I. Abdullah and J. Schlattmann v-deformation (m)*10^ xx-stress (Mpa) thickness (mm) Fig.18 Variation of v-deformation with blade thickness (speed of rotation=1000 r.p.m, skew angle=0) thickness (mm) Fig.19 Variation of xx-stresses with blade thickness (speed of rotation=1000 r.p.m, skew angle=0) 10 5 R 0.1m 8 4 yy-stress (Mpa) 6 4 xy-shear stress (Mpa) thickness (mm) Fig.20 Variation of yy-stresses with blade thickness (speed of rotation=1000 r.p.m, skew angle=0) thickness (mm) Fig.21 Variation of xy-stresses with blade thickness (speed of rotation=1000 r.p.m, skew angle=0)

13 Stress analysis of axial flow fan 275 Nomenclature ρ Ω b E L t R v- deformati on Density of material, [Kg/m³] Speed of rotation, [rad/s] The width of the blade, [m] Young s modulus, [N/m²] length of the blade, [m] Thickness of blade, [m] Disc radius, [m] The displacement in the y- direction, [m] xx-stress The normal stress in the x- direction, [N/m²] yy-stress The normal stress in the y- direction, [N/m²] σ The normal stress in the x- x direction, [N/m²] σ The normal stress in the y- y direction, [N/m²] σ The normal stress in the z- z direction, [N/m²] τ The shear stress in the xy-plane, xy [N/m²] τ The shear stress in the xz-plane, xz [N/m²] τ The shear stress in the yz-plane, yz [N/m²] x, ε y ε The strain in the x, y, and z z directions Transverse shear strain xy, γxzγyz components in the Cartesians coordinate system ε, γ, References [1] W. Carnegie., Static bending of pre-twisted cantilevers blading. 1957, J. of procedings of the institute of mechanical engineering, vol.171, pp [2] K.P.Walker., Vibrations of cambered helicaidal fan blades, J. of sound and vibration, vol.59, No.1, pp [3] V.Ramamurti and S.Sreenivasamurthy, Dynamic stress analysis of rotating twisted and tapered blades.1980, J.strain analysis, vol. 15, No.3, pp [4] V.Omprakash and V.Ramamurti., Dynamic stress analysis of rotating turbomachinery bladed-disc system 1989, J.computer and structure, vol. 32, No.2, pp [5] H.H.Yoo, J.K.Lee, and J.Chung., Vibration analysis of rotating pre-twisted blades a concentrated mass 2001, J. sound and vibration, vol.240, No.5, pp [6] William Weaver and Paul R.Johnston, (finite elements for structural analysis), standford university, Prentice-Hall, N, J.198. Received: May, 2012