Engineering Failure Analysis 18 (2011) 2019–2027

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Engineering Failure Analysis

journal homepage: www.elsevier .com/locate /engfai lanal

Fatigue failure analysis of holding U-bolts of a cooling fan blade

M. Reihanian a,⇑, K. Sherafatnia b, M. Sajjadnejad c

a Department of Materials Science and Engineering, Faculty of Engineering, Shahid Chamran University, Ahvaz, Iranb School of Mechanical Engineering, Sharif University of Technology, P.O. Box 11365-11155, Tehran, Iranc Department of Materials Science and Engineering, Sharif University of Technology, P.O. Box 11155-9466, Tehran, Iran

a r t i c l e i n f o a b s t r a c t

Article history:Received 23 February 2011Received in revised form 2 June 2011Accepted 2 June 2011Available online 14 June 2011

Keywords:Fatigue failureFatigue lifeFractographyFinite element analysis

1350-6307/$ - see front matter � 2011 Elsevier Ltddoi:10.1016/j.engfailanal.2011.06.004

⇑ Corresponding author. Tel.: +98 611 3330010 1E-mail address: reihanian@scu.ac.ir (M. Reihania

Fatigue failure of holding U-bolt of a cooling fan blade is analyzed. Fractography of the frac-ture surface reveals the characteristics of a fatigue fracture. Finite element modeling isused for stress analyzing. Analysis of the loading conditions indicates that the bolts areunder multiaxial fatigue. Effective alternating and mean stresses are obtained based onthe multiaxial fatigue criteria. By using the modified Goodman approach and consideringthe notch effect, effective stress amplitude, is obtained for all nodes. The highest stressamplitude is obtained at six critical nodes. Fatigue life for the most critical node is deter-mined as 3.63 million cycles.

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1. Introduction

Industrial cooling fans are used in a wide range of applications such as cooling towers, air-cooled steam condensers andair-cooled heat exchangers. The basic parts of a fan assembly include fan blades, hub plate and holding U-bolts. During itsoperation, a fan blade sustains many forces such as gravitational, centrifugal and air resistance force. These forces can causethe failure of the blade [1] or holding U-bolts especially in large industrial fans where a large volume of air is used. Manyfactors such as variation of the centrifugal stress, shut up/down of the cooling system and mass imbalance make the fatigueto be the most probable cause of failure in cooling fan systems.

It is reported that about 90% of all mechanical failures is caused by fatigue [2]. Fatigue is one of the most dangerousmechanical failures because it occurs under loads that are lower than the static strength of the material [3]. The case studieson the fatigue fracture can be found in many sources such as Refs. [4–7]. In the present study, fatigue fracture of holding U-bolt of a cooling fan is analyzed using fractography examinations and finite element modeling. Fig. 1 shows a schematicdrawing of the fan blade. A holding U-bolt and fracture position are also schematically presented in Fig. 1. The fracture posi-tion is near the nuts and below the hub plate.

2. Material and methods

The chemical composition of the U-bolt material is presented in Table 1. This indicates that the bolts are made by304-type stainless steel. Typical values of ultimate tensile stress and yield stress for this type of stainless steel are givenas 505 and 205 MPa, respectively [8]. The microstructure of the U-bolt was examined by cutting a sample from the fracturedbolt, mechanical grinding and polishing to a mirror-like surface using alumina powder solution. The etching solution was a

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9x5684; fax: +98 611 3336642.n).

Fig. 1. Schematic representation of the cooling fan assembly, U-bolt and fracture position.

Table 1Chemical composition of the U-bolt material.

Element Fe Cr Ni Mn Si C

Weight percent Balanced 18.8 8 1.7 0.5 0.07

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mixture of 60 ml HCl and 20 ml HNO3 (Aquaregia solution). The fracture surface of the U-bolt was investigated by visualinspection and scanning electron microscopy (SEM), using secondary electron detectors.

3. Finite element modeling

A structural analysis of U-bolts of a cooling tower fan is performed using finite element modeling. SolidWorks software isused for geometry modeling of the cooling fan including fan blade, hub plate and U-bolts as shown in Fig. 2.

Finite element software ANSYS 12 is used for stress analysis. The elements used in U-bolt model are all 8-node solid brickelements Solid45. Finite element model for stress analysis is consisted of 10,000 elements and 16,200 nodes for each U-boltas shown in Fig. 3. All parts of the cooling fan assembly except the hub plate are considered flexible. Since blade model musttransfer forces to the U-bolts, it is not considered rigid in this analysis. To model the contact between the U-bolts, blade andhub surfaces, CONTA174 and TARGE170 elements are used. In this analysis, CONTA174 elements are used to model contactsurfaces for bolt–blade, bolt–hub plate, and blade–hub plate contacts.

4. Loading conditions

Load applied to the finite element model is chosen according to the information of Hawden cooling fans data sheet for9900 ENF 6 types. An axial fan blade can be seen as a one-time blocked beam on which air pressure and centrifugal forceare applied. The primary component of the blade force on the air is directed axially from inlet to outlet. The blade force nec-essarily has an additional component in the tangential direction, providing the reaction to the driving torque. Since mount-ing orientation of cooling fan shaft is horizontal, weight of blades and its moment must be considered in analysis.

From input data and detailed results for 9900 ENF 6 fan type, weight, Fw; centrifugal, Fc; axial, Fa; and tangential, Ft; forceacting on blades are calculated as follows:

Fw ¼mg ¼ ð78 kgÞ � 9:81ms2

� �¼ 765 N ð1Þ

Fc ¼ mrmx2 ¼ ð78 kgÞ � ð1:93 mÞ � 10:7rad

s

� �2

¼ 17;235 N ð2Þ

Fa ¼Axial thrust

6¼ 11;760 N

6¼ 1960 N ð3Þ

Fig. 2. Geometry modeling of the cooling fan including fan blades, hub plate and U-bolts.

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Ft ¼Fan shaft power

6� rA �x¼ 123;700 W

6� 2:58 m� 10:7 rads

¼ 746 N ð4Þ

where m is the mass of each blade and x is the angular velocity of blades. rm is the distance between the origin of the coor-dinate in the center of the hub plate and mass center. rA is the distance between the origin of the coordinate in the center ofthe hub plate and area center of blades. After the blade is modeled, rm and rA are calculated using SolidWorks software.

The directions of applied forces on blades of the cooling fan are shown in Fig. 4. It is noted that the condition of loading ismultiaxial. Among all forces, the only alternating force is weight force. Except the weight, all forces acting on the blades havefixed direction in relative coordinate system whose axes are rotating with the blade. To obtain the stresses of the U-bolts asrealistic as possible, first, U-bolts are stretched with a tension of 45 MPa in the normal direction to the hub plate from sec-tions near the nuts. Then, forces are exerted to the blade, which contact with hub plate and U-bolts. Therefore, the bladereaction forces in contact zone lead to stresses in U-bolts. The coefficient of friction for contact areas between fiberglass rein-forced polyester blade and mild steel hub plate is deemed to be 0.35 [9] and for other contact surfaces is considered to be 0.2.

Fig. 3. Typical mesh model of (a) U-bolt and (b) assembly of the blade and U-bolts.

Fig. 4. Applied forces on the cooling fan assembly.

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5. Results and discussion

5.1. Microstructure and fractograpghy

The micrograph of the U-bolt material is shown in Fig. 5, which is a typical microstructure of the austenitic stainless steel.Fig. 6 shows the macrograph and the corresponding SEM images at different stages of fracture. Visual inspection (Fig. 6a)designates that there is not any distortion near the fracture surface indicating that fracture is not proceed by macroscopicplastic deformation. In addition, fracture originates at the bottom side of the fracture surface (Fig. 6b) and progresses tothe up, where the final failure occurs. At this level, the surface morphology can be divided into two distinct areas. One rep-resents the fracture surface over which crack propagation is gradual. The other is the final area of the fracture surface thatcorresponds to the fast fracture stage. These observations are the characteristics of the fatigue fracture surface and point outthat fatigue is the most probable cause of failure. It should be noted that crack initiation stage of fatigue fracture is very smalland cannot extend for more than two to five grains [10]. However, its location can be found at low magnifications.

Fig. 6c shows the SEM micrograph of slow crack growth area with more details. The crack propagation path is in the direc-tion of the black arrow. As it is observed, fatigue striations are not clearly visible. However, the micrograph shows someroughly inclined ridges, which are perpendicular to the direction of crack propagation. These ridges are the evidence ofthe crack front advance with each load application [11,12]. Inspection of Fig. 6c illustrates that fatigue crack propagationoccurred by a ductile mechanism. This indicates that local plastic deformation occurred at the crack tip during slow crackpropagation, though the overall plastic deformation is not obvious. Another important feature of Fig. 6c is the presence ofmicrocracks that are indicated by white arrows. These microcracks may be formed due to the strain incompatibility atthe plastic zone ahead of the main crack [13].

As the fatigue crack propagates, the effective cross section area is reduced until the final rupture of the component occurs.The transition from these stages is revealed on SEM micrograph of Fig. 6d. The fracture mode at final stage may be eitherductile (with a dimpled fracture surface) or brittle (with cleavage or intergranular fracture surface) or a combination of both[12]. Fig. 6e shows SEM image of the fracture surface at the final stage. The presence of dimples indicates that the fracturemode at this stage is ductile.

5.2. Stress analysis

Stress analysis is done for 16 directions of blade in vertical plane by finite element analysis. The order of U-bolts place-ment in fan assembly is shown in Fig. 7a. Fig. 7b–e illustrates equivalent von Mises nodal stress distribution for particular

Fig. 5. Micrograph of the blade material.

Fig. 6. Macrograph and the corresponding SEM images of the fracture surface at different stages of fracture.

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four situations of blade having angles of 0�, 90�, 180� and 270� respect to gravity direction. It is observed that the nodes havethe high stress values near the nuts and below the contact zone with hub plate. The maximum and minimum stress statesare detected in Fig. 7c and e, respectively; that is in situations 90� and 270�. It is noted that the maximum nodal stress iscalculated in the second bolt of the fan assembly shown in Fig. 7a.

5.3. Fatigue analysis

Because of the complexity of loading condition, a multiaxial state of stress is formed in U-bolts. Since, the greatest Misesnodal stress is less than the material yield strength, (Sy = 205 MPa), general yielding cannot occur in this analysis. This is con-sistent with the results of fractography examinations obtained in the previous sections. Since the bolt is actually loaded withdynamic forces, fatigue analysis is performed. Because the applied stresses are within the elastic range of the material, thestress-life approach is used to determine the fatigue life of U-bolts [11].

Principal stresses obtained from ANSYS analysis are utilized in fatigue life calculations. Finite life and mean stress effectscan be approximated with the modified Goodman stress equation as follow

Sa

SNfþ Sm

Su¼ 1 ð5Þ

where Su is the ultimate tensile stress, Sa is the stress amplitude corresponding to a certain life, Sm is the mean stress, and SNf

is the stress amplitude that would give the same life if Sm were zero. For simplicity, SNf is called the fatigue stress in thisanalysis. The expression relating the fatigue stress, SNf, to the number of load reversal to failure, 2Nf is expressed by Basquin’sequation as

SNf ¼ r0fð2Nf Þb ð6Þ

where r0f and b are defined as the fatigue strength coefficient and fatigue strength exponent, respectively. Values of r0f and bfor 304 type stainless steel are 1267 MPa and �0.139 MPa, respectively [14].

Fig. 7. (a) Order of the U-bolts placement in fan assembly. (b–e) Equivalent von-Mises stress distribution on the U-bolts for four different orientations of fanblade respect to the direction of gravity.

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The classical multiaxial approaches in fatigue are based on three criteria [11]: (i) maximum principal stress/strain, (ii) vonMises theory, and (iii) maximum shear stress (Tresca theory). Among all these criteria, von Mises or effective stress approachis the most widely used approach for multiaxial fatigue of materials with ductile behavior. According to von Mises criterion,the effective stress amplitude, Sae, for multiaxial fatigue is defined as

Sae ¼1ffiffiffi2p

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðSa1 � Sa2Þ2 þ ðSa2 � Sa3Þ2 þ ðSa3 � Sa1Þ2

qð7Þ

Table 2Stresses in critical nodes. All stresses are in MPa.

Node number Node position Minimum principal stresses Maximum principal stresses Sae � K f Sme SNf

S1 S2 S3 S1 S2 S3

6416 2nd U-bolt 131.3 49.4 45.2 189.3 72.1 64.6 70.4 276.0 155.26417 2nd U-bolt 148.9 57.4 52.4 199.3 76.9 69.5 61.1 302.2 152.26425 2nd U-bolt 118.9 5.5 �8.5 173.0 8.3 �5.9 97.7 145.6 137.36824 2nd U-bolt 93.8 4.4 �7.0 150.5 7.4 �4.3 102.4 122.3 135.14773 2nd U-bolt 22.2 0.3 �0.2 83.8 0.5 �0.1 116.8 53.3 130.64433 2nd U-bolt 25.1 1.2 �0.5 90.3 2.4 0.7 113.2 64.0 129.6

Fig. 8. Position of the critical nodes that lie on the lateral surface of the second U-bolt.

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where Sa1, Sa2 and Sa3 are principal alternating stresses. The Tresca and Von Mises equivalent mean stresses are insensitive toa hydrostatic stress but fatigue life has been observed to be sensitive to hydrostatic stress. In the stress-based approach, theeffect of mean stresses in multiaxial fatigue is accounted for by using mean stress plots such as Goodman diagram. Theequivalent mean stress, Sme, for multiaxial fatigue can be defined as the sum of principal mean stresses as

Sme ¼ Sm1 þ Sm2 þ Sm3 ð8Þ

where Sm1, Sm2 and Sm3 are the principal mean stresses. By replacing Sa and Sm in Eq. (5) by Sae and Sme, respectively, thefatigue stress is estimated for multiaxial fatigue.

Principal alternating and mean nominal stresses are calculated for all nodes using FE software. Referring to Fig. 1, two endparts of U-bolts are threaded to permit the nuts to be screwed up to the hub plate bottom. Therefore, fatigue stress concen-tration due to threaded part raises the effective nominal stress amplitude, Sae. Fatigue stress concentration factor, Kf, is ob-tained from notch sensitivity factor, q, and stress concentration factor, Kt, by

K f ¼ 1þ qðKt � 1Þ ð9Þ

In order to choose the values of Kt and q, the values of the models used in Lehnhoff and Bunyard [15] work that has theclosest diameter to the present work are chosen here as 4.26 and 0.86, respectively. Therefore, fatigue stress concentrationfactor is calculated as 3.8.

Fatigue stress, SNf, leads to finite life when its value is less than the endurance limit Se; otherwise infinite life is occurred.For steels with ultimate strength, Su, less than 1400 MPa, an estimation for the ideal endurance limit, S0e is given by [16].

S0e ¼ 0:5Su ð10Þ

To predict the actual endurance limit, Se, Marin’s equation is used as below

Se ¼ kakbkckdkeS0e ð11Þ

where k values are the modifying factors that quantify the effects of surface condition, size, loading, temperature, and mis-cellaneous items, respectively. Most actual parts have a less well-finished surface that causes a reduction in endurance limitof the component. The surface factor, ka, is used to account for this. It is given by

ka ¼ aðSuÞb ð12Þ

Fig. 9. Distribution of the maximum (b) and minimum (c) of the largest principle stress (S1) at fracture region (a).

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For forged surface finish, recommended values for constants a and b are a = 272 and b = �0.995 [16]. Therefore, ka isdetermined as 0.556 for a typical 304 type stainless steel. For the given U-bolt with diameter of d = 30 mm, the size factor,kb, is given by

kb ¼ 1:24� d�0:107 ¼ 1:24� 30�0:107 ¼ 0:861 ð13Þ

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The values of other factors are considered to be equal to one. By substituting the modifying factors into Eq. (11), the fullycorrected endurance limit of the U-bolt is estimated as Se = 120.9 MPa.

After computation of principal alternating and mean stresses for all nodes, the effective alternating, Sae, and effectivemean stress, Sme, are obtained by utilizing Eqs. (7) and (8). By using the modified Goodman approach (Eq. (5)) and applyingfatigue stress concentration factor, Kf, fatigue stress, SNf, is obtained for all nodes. The fatigue stress for six critical nodes issummarized in Table 2. The position of these nodes is illustrated in Fig. 8. Among all critical nodes, node 6416 has the max-imum value of SNf = 155.2 MPa. Fatigue life for this critical node is obtained as 3.63 million cycles or 593 h using Basquin’sequation (Eq. (6)).

It is noted that the position of fracture is dictated by the maximum fatigue stress (SNf) that is near the highest stress re-gions (Figs. 7 and 8). Graphical representation of the fatigue stress distribution is impossible with the software used in thisstudy. Therefore, distribution of the maximum and minimum of the largest principal stress at fracture region is shown inFig. 9. The largest principal stress has the highest effect on fatigue stress.

6. Conclusions

Fractography of the fracture surface reveals that the fracture of U-bolt is caused by fatigue. Analysis of loading conditionindicates that the U-bolts are under multiaxial fatigue. The finite element analysis shows that the nodes having the highstress values are near the nuts and below the contact zone with hub plate. The maximum and minimum stress states aredetected in situations 90� and 270� of blade with respect to the direction of gravity. The principal alternating and mean stres-ses for all nodes are obtained by fatigue analysis. Fatigue stress is obtained by utilizing the modified Goodman approach andnotch effect. Results show that six critical nodes have the highest fatigue stress. Fatigue life for the most critical node is ob-tained as 3.63 million cycles or 593 h.

Acknowledgment

The authors would like to thank the financial support of the Shahid Chamran University through the Grant number89-3-02-44305.

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