FEM SEMESTER PROJECT

SUBMITTED TO: MISS SANA ZULFIQAR

SUBMITTED BY : WAQAR SIDDIQUE AWAN (09-ME-108)

RAMEEZ ANWAR (09-ME-100)

MUHAMMAD UMAR (09-ME-84)

DEPARTMENT OF MECHANICAL ENGINEERING

UNIVERSITY OF ENGINEERING AND TECHNOLOGY TAXILA

SUMMARY

Finite element analysis and its calculations in the realm of practice is very lengthy and long process and we cannot find all the values and calculations by hand without any mistake. So in order to do this assignment fastly and accurately software like ANSYS is employed and for modeling PRO-engineer is used . At every step of modeling and bending all the parameters are followed and the proper commands are used to ensure the quality of analysis and results.

ABSTRACT:

The fatigue analysis of the shaft is done on ANSYS and the modeling was done by professional engineer wildfire 5.0 . The first module consisting of modeling and the second consists of analysis through application of continuous load in the shaft.

DEDICATION:

“THIS WORK IS DEDICATED TO SIR ALI NASIR FOR HIS CONTINUOUS EFFORTS WHICH RESULTS IN THE FORMATION OF THE MOST UPDATED LAB IN THE UNIVERSITY”

CONTENTS:

INTRODUCTION TO ANSYS………………. ……………………………………………………..01

INTRODUCTION TO PRO-E…………………………………………………………………..……02

INTRODUCTION TO FATIGUE ANALYSIS …………………………………………………..….02

MODELING OF THE SHAFT………………………………………………………………….……04

ANALYSIS OF THE SHAFT…………………………………………………………………….…..11

DATA SHEETS………………………………………………………………………………………..18

REFRENCES………………………………………………………………………………………….at end

FATIGUE ANALYSIS OF A SHAFT

. 1.0. INTRODUCTION TO ANSYS:

ANSYS, Inc. is an engineering simulation software (computer-aided engineering, or CAE) ANSYS offers a comprehensive range of engineering simulation solution sets providing access to virtually any field of engineering simulation that a design process requires. Companies in a wide variety of industries use ANSYS software. The tools put a virtual product through a rigorous testing procedure.

The software provides two main modules:

1.0.1. Simulation Technology: Structural Mechanics, Multiphysics, Fluid Dynamics, Explicit Dynamics, Electromagnetics.

1.0.2.Workflow Technology: ANSYS Workbench Platform, High-Performance Computing, Geometry Interfaces, Simulation Process & Data Management.

ANSYS also provides integration directly to:

Autodesk Catia v4 and v5 Creo elements/Pro-E Creo parametric Solid edge Solid works NX

2.0. INTRODUCTION TO PRO-E/Creo elements pro:

 Pro/Engineer  is a parametric, integrated 3D CAD/CAM/CAE solution used by discrete manufacturers for mechanical engineering, design and manufacturing. The parametric modeling approach uses parameters,

dimensions, features, and relationships to capture intended product behavior and create a recipe which enables design automation and the optimization of design and product development processes.  Creo Elements/Pro provides a complete set of design, analysis and manufacturing capabilities on one, integral, scalable platform. These required capabilities include Solid Modeling, Surfacing, Rendering, Data Interoperability, Routed Systems Design, Simulation, Tolerance Analysis, and NC and Tooling Design. Companies use Creo Elements/Pro to create a complete 3D digital model of their products. The models consist of 2D and 3D solid model data which can also be used downstream in finite element analysis, rapid prototyping, tooling design, and CNC manufacturing.

All data is associative and interchangeable between the CAD, CAE and CAM modules withoutconversion. A product and its entire bill of materials (BOM) can be modeled accurately with fully associative engineering drawings, and revision control information.

3.0. INTRODUCTION TO FATIGUE ANALYSIS:

Fatigue is the progressive and localized structural damage that occurs when a material is subjected to cyclic loading. Fatigue occurs when a material is subjected to repeated loading and unloading. If the loads are above a certain threshold, microscopic cracks will begin to form at the surface. Eventually a crack will reach a critical size, and the structure will suddenly fracture. The shape of the structure will significantly affect the fatigue life; square holes or sharp corners will lead to elevated local stresses where fatigue cracks can initiate. Round holes and smooth transitions or fillets are therefore important to increase the fatigue strength of the 

Fatigue life

ASTM defines fatigue life, nf, as the number of stress cycles of a specified character that a specimen sustains before failure of a specified nature occurs.

3.1.0. Characteristics of fatigue:

In metals and alloys, the process starts with dislocation movements, eventually forming

persistent slip bands that nucleate short cracks.

Fatigue is a stochastic process, often showing considerable scatter even in controlled

environments.

The greater the applied stress range, the shorter the life.

Fatigue life scatter tends to increase for longer fatigue lives.

Damage is cumulative. Materials do not recover when rested.

Fatigue life is influenced by a variety of factors, such as temperature, surface finish,

microstructure, presence of oxidizing or inertchemicals, residual stresses, contact (fretting), etc.

Some materials (e.g., some steel and titanium alloys) exhibit a theoretical fatigue limit below

which continued loading does not lead to structural failure.

In recent years, researchers (see, for example, the work of bathias, murakami, and stanzl-

tschegg) have found that failures occur below the theoretical fatigue limit at very high fatigue

lives (109 to 1010 cycles). An ultrasonic resonance technique is used in these experiments with

frequencies around 10–20 khz.

High cycle fatigue strength (about 103 to 108 cycles) can be described by stress-based parameters.

A load-controlled servo-hydraulic test rig is commonly used in these tests, with frequencies of

around 20–50 hz. Other sorts of machines—like resonant magnetic machines—can also be used,

achieving frequencies up to 250 hz.

Low cycle fatigue (typically less than 103 cycles) is associated with widespread plasticity in

metals; thus, a strain-based parameter should be used for fatigue life prediction in metals and

alloys. Testing is conducted with constant strain amplitudes typically at 0.01–5 hz.

High cycle fatigue:

Historically, most attention has focused on situations that require more than 104 cycles to failure where stress is low and deformation is primarily elastic.

The SN curve

In high-cycle fatigue situations, materials performance is commonly characterized by an s-n curve, also

known as a wöhler curve . This is a graph of the magnitude of a cyclic stress (s) against the logarithmic

scale of cycles to failure (n).

4.0. MODELING OF A SHAFT IN PRO -E :

4.0.1. DIMENTIONS FOR CRANK SHAFT:

CRANK JOURNAL DAIMETER 100 mm

CRANK JOURNAL LENGTH 140 mm

MAIN JOURNAL DIAMETER 150 mm

MAIN JOURNAL LENGTH 77.38 mm

COUNTER WEIGHTS THICKNESS 60 mm

PCD 201.2 mm

FILLETS 15 mm (at each sharp end of the counter weights)

4.0.2. DIMENTIONS FOR CRANK CONNECTING ROD:

CRANK ROD THICKNESS 80 mm

CRANK ROD LENGTH 631.6 mm

CRANK OIL PIN HOLE 21.2 mm

MODULUS OF ELASTICITY 175 e 9

POISION RATIO 0.3

NOW:

FOLLOWING THE FOLLOWING CODE WE’LL GET THE MODELED PART

4.1.0. FORMING BAIC GEOMETRY:

4.2.0. COUNTER WEIGHTS/ BALANCING WEIGHTS:

4.3.0. CRANK PIN JOURNAL EXTRUSION:

4.4.0. MIRROR MODEL OF COUTER WEIGHTS:

4.5.0. FINALISED MODEL OF THE CRANK SHAFT:

4.6.0. MODELLING OF THE CONNECTING ROD:

4.7.0. CRANK PIN OIL HOLE EXTRUSION:

4.8.0. FINALISED MODEL OF COONECTING ROD:

4.9.0. ASSEMPLY IN PROFESSIONAL ENGINEERS WILDFIRE 5.0:

4.10.0. SAVING FILE IN IGES FORMAT:

NOW WHAT WE GET IS:

A saved file in .igs extension

4.11.0. OPENING THE FILE IN ANSYS:

File > import > IGES

Then ok> browse> (give path where saved) > ok

And as a result we’ll get the designed part opened in pro engineer

5.0.0 ANALYSIS IN ANSYS:

So the code is:

(Go to Main Menu)Preprocessor > perefrences > structural > h method

(Go to Main Menu)Preprocessor>Element Type>Add/Edit/Delete>Add>Structural & Solid &20 node 95 or 20node186 & OK

Material Prop>Material Models>Structural>Linear>Elastic>IsotropicEX = 210e5PRXY = 0.3 & OK

The part of modeling has already been done in pro engineer so there is no need to do modeling here so just skiping that step and moving to meshing

Meshing>Mesh Tool>Click on the Lines Set button

Choose smart size and level down to mesh 1 > select volume in mesh scroll down and tet and click meshWhen it will demand volume to be meshed select as:

After two processing boxes as:

It will lead to meshing of the part as:

Now coming towards the next phase:Solution>Analysis> Type New Analysis>Choose Transient & OK &> OKSol’n Controls>Basic Tab>Time at end of loadstep: 10

Transient Tab>Choose Stepped Loading >& OKDefine Loads>Apply>Structural>Displacement>On keypoints>Pick keypoint & OK>Select All DOFs>Displacement Value = 0 & OK(the keypoint at centre of the crank shaft outer notch are fixes in all degrees of freedoms)

Force/Moment>On Keypoints>Pick keypoints at outer edges of the connecting rod top & OK>Direction of Force/Moment: FY>Force/Moment Value: -60e9 & OK

Load Step Opts > Write LS File > Load step file number n: 1 & OK

Analysis Type> Sol’n Controls>Basic Tab > Time at end of loadstep: 20 & OK

Define Loads>Delete>Structural>Force/Moment > On Keypoints>Pick All & OK

Apply>Structural>Force/Moment>On Keypoints>Pick keypoints 2 & 3 & OK>Direction of Force/Moment: FY>Force/Moment Value: -60e9 & OK

Load Step Opts > Write LS File > Load step file number n: 2 & OK

Analysis Type > Sol’n Controls>Basic Tab > Time at end of loadstep: 30 & OK

Define Loads > Delete > Structural > Force/Moment > On Keypoints > Pick All & OK

Apply > Structural > Force/Moment > On Keypoints > Pick keypoints & OK >Direction of Force/Moment: FY>Force/Moment Value: 60e9 & OK

Load Step Opts > Write LS File > Load step file number n: 3 & OK Analysis Type > Sol’n Controls > Basic Tab > Time at end of loadstep: 40 & OK

Define Loads >Delete > Structural > Force/Moment > On Keypoints > Pick All & OK

Appl y> Structural > Force/Moment > On Keypoints > Pick keypoints & OK > Direction of Force/Moment: FY>Force/Moment Value: -60e9 & OK

Load Step Opts > Write LS File > Load step file number n: 4 & OKSolve > From LS Files > Starting LS file number: 1> Ending LS file number: 4 >File number increment: 1 & OK

Go to Main Menu) > General Postproc > Read Results > By Pick >Select Set 1 & Read & Close.(Go to Main Menu)General Postproc>Fatigue>Property Table>S-N Table

(Click N1) 100 (Click S1) 6.21e10(Click N2) 1000 (Click S2) 5.4e10(Click N3) 10000 (Click S3) 4.6e10(Click N4) 1000000 (Click S4) 3.8e10(Click N5) 10000000 (Click S5) 12e10

Stress Locations>NLOC = 1>NODE = 10129 = Fixed End & Apply

NLOC = 2>NODE = 9008

NLOC = 1>NODE = 7000 = Free End & OK

Store StressesFrom result File>NODE: 10129>Event: 1>Loading: 1 & Apply

NODE: 9008>Event: 1>Loading: 1 & Apply

NODE: 7000Event: 1>Loading: 1 & OK

Read Results>By Pick>Select Set 2 & Read & Close

Fatigue>Store Stresses>From result FileNODE: 10129>Event: 2>Loading: 1 & Apply

NODE: 9008>Event: 2>Loading: 1 & Apply

NODE: 7000>Event: 2>Loading: 1 & OK

Read Results>By Pick>Select Set 4 & Read & Close

Fatigue>Store Stresses>From rst FileNODE: 10129>Event: 2>Loading: 2 & ApplyNODE: 9008>Event: 2>Loading: 2 & ApplyNODE: 7000>Event: 2>Loading: 2 & OK

Assign Events>NEV = 1>CYCLE =100>TITLE = Load 1 & Apply

NEV = 2>CYCLE = 1000>TITLE = Load 2 & OK>Calculate Fatigue & OK

Similarly putting the values for no. of cycles for other events. And then compiling the results:

5.1.0. ELEMENT SOLUTION

5.2.0. VECTOR DIAGRAM

5.3.0. DEFORMED SHAPE

5.4.0. Von Misses Stresses

5.5.0. Graphs made by using ansys 13 work bench:

5.5.1. No of cycles vs stresses (using mean stress value):

5.5.2. Graph of strain life parameters:

5.5.3. Graph of no. Of cycles vs stresses(using alternate stress R ratio)

5.5.0. Other results:

LOCATIONS 1 TO 5 IN STEPS OF 1. LOCATION 1 IS NODE 10129

STRESS CONC. FACTORS (X,Y,Z) = 1.000 1.000 1.000 LABEL =

LOCATION 2 IS NODE 9008 STRESS CONC. FACTORS (X,Y,Z) = 1.000 1.000 1.000 LABEL =

LOCATION 3 IS NODE 7000 STRESS CONC. FACTORS (X,Y,Z) = 1.000 1.000 1.000 LABEL =

LOCATION 4 IS NODE 5450 STRESS CONC. FACTORS (X,Y,Z) = 1.000 1.000 1.000 LABEL =

LOCATION 5 IS NODE 2450 STRESS CONC. FACTORS (X,Y,Z) = 1.000 1.000 1.000 LABEL = LIST FATIGUE PROPERTIES

N 1 ( 1) N 2 ( 2) N 3 ( 3) N 4 ( 4) N 5 ( 5) 100.00 1000.0 10000. 0.10000E+06 0.10000E+07 S 1 (21) S 2 (22) S 3 (23) S 4 (24) S 5 (25) 0.62000E+11 0.54000E+10 0.38000E+08 0.17000E+06 1200.0 FATIGUE STRESSES FOR LOCATIONS 1 TO 5 IN STEPS OF 1 EVENTS 1 TO 10 - LOADS 1 TO 3

*** POST1 FATIGUE STRESSES ***

LOCATION 1 NODE 10129 EVENT 1 (TOTAL STRESS - ITEMS 1-7) LOCATION 1 EVENT 1 LOAD 1 SX,SY,SZ -0.10336 0.10227E-02 -0.25447E-01 SXY,SYZ,SXZ,TEMP 0.61275E-02 -0.71514E-02 0.19712E-01 0.0000 EVENT 2 EVENT 3 EVENT 4 EVENT 5

LOCATION 2 NODE 9008 EVENT 1 EVENT 2 (TOTAL STRESS - ITEMS 1-7) LOCATION 2 EVENT 2 LOAD 2 SX,SY,SZ -0.70012E-01 0.47520E-02 0.22098E-01 SXY,SYZ,SXZ,TEMP 0.54930E-02 0.11001E-01 0.11581E-01 0.0000 EVENT 3 EVENT 4 EVENT 5

LOCATION 3 NODE 7000 EVENT 1 EVENT 2 EVENT 3 (TOTAL STRESS - ITEMS 1-7) LOCATION 3 EVENT 3 LOAD 3 SX,SY,SZ -0.88124E-01 -0.29325E-02 -0.81212E-02 SXY,SYZ,SXZ,TEMP 0.73567E-02 -0.54888E-02 0.11555E-01 0.0000 EVENT 4 EVENT 5

LOCATION 4 NODE 5450 EVENT 1 EVENT 2 EVENT 3 EVENT 4 (TOTAL STRESS - ITEMS 1-7) LOCATION 4 EVENT 4 LOAD 1 SX,SY,SZ 0.97641E-01 -0.47786E-02 -0.47826E-02 SXY,SYZ,SXZ,TEMP -0.20722E-01 -0.38477E-02 -0.24958E-01 0.0000 EVENT 5

LOCATION 5 NODE 2450

EVENT 1 EVENT 2 EVENT 3 EVENT 4 EVENT 5 (TOTAL STRESS - ITEMS 1-7) LOCATION 5 EVENT 5 LOAD 1 SX,SY,SZ -0.12107 0.51454E-02 -0.15930E-01 SXY,SYZ,SXZ,TEMP 0.57484E-02 -0.58497E-02 0.19447E-01 0.0000

ELEMENT SOLUTION PER ELEMENT ***** POST1 ELEMENT NODAL STRESS LISTING ***** LOAD STEP= 4 SUBSTEP= 1 TIME= 40.000 LOAD CASE= 0 THE FOLLOWING X,Y,Z VALUES ARE IN GLOBAL COORDINATES

ELEMENT= 1 SOLID45 NODE S1 S2 S3 SINT SEQV 5804 0.17477E-01 -0.66693E-02 -0.22189E-01 0.39666E-01 0.34621E-01 3840 0.13645E-01 -0.14106E-01 -0.21275E-01 0.34920E-01 0.31945E-01 5805 0.11023E-01 -0.17451E-01 -0.34311E-01 0.45334E-01 0.39688E-01 5805 0.11023E-01 -0.17451E-01 -0.34311E-01 0.45334E-01 0.39688E-01 3797 0.56160E-02 -0.15248E-01 -0.35440E-01 0.41056E-01 0.35557E-01 3797 0.56160E-02 -0.15248E-01 -0.35440E-01 0.41056E-01 0.35557E-01 3797 0.56160E-02 -0.15248E-01 -0.35440E-01 0.41056E-01 0.35557E-01 3797 0.56160E-02-0.15248E-01-0.35440E-01 0.41056E-01 0.35557E-01

ELEMENT= 2 SOLID45 NODE S1 S2 S3 SINT SEQV 5806 0.22533E-01 0.13111E-01 -0.30239E-01 0.52772E-01 0.48749E-01 4163 0.21071E-01 0.36237E-02 -0.37869E-01 0.58939E-01 0.52440E-01 5807 0.11301E-01 -0.28468E-02 -0.43497E-01 0.54798E-01 0.49271E-01 5807 0.11301E-01 -0.28468E-02 -0.43497E-01 0.54798E-01 0.49271E-01 5808 0.26853E-01 0.12621E-01 -0.28574E-01 0.55427E-01 0.49859E-01 5808 0.26853E-01 0.12621E-01 -0.28574E-01 0.55427E-01 0.49859E-01 5808 0.26853E-01 0.12621E-01 -0.28574E-01 0.55427E-01 0.49859E-01 5808 0.26853E-01 0.12621E-01 -0.28574E-01 0.55427E-01 0.49859E-01

ELEMENT= 3 SOLID45 NODE S1 S2 S3 SINT SEQV 4163 0.22314E-01 0.52125E-02 -0.38744E-01 0.61058E-01 0.54556E-01 5807 0.22596E-01 0.73147E-02 -0.33489E-01 0.56085E-01 0.50220E-01 5808 0.23201E-01 0.92415E-02 -0.33943E-01 0.57144E-01 0.51600E-01 5808 0.23201E-01 0.92415E-02 -0.33943E-01 0.57144E-01 0.51600E-01 5809 0.26891E-01 0.11318E-01 -0.33148E-01 0.60039E-01 0.53965E-01 5809 0.26891E-01 0.11318E-01 -0.33148E-01 0.60039E-01 0.53965E-01 5809 0.26891E-01 0.11318E-01 -0.33148E-01 0.60039E-01 0.53965E-01 5809 0.26891E-01 0.11318E-01 -0.33148E-01 0.60039E-01 0.53965E-01 ***** POST1 ELEMENT NODAL STRESS LISTING ***** LOAD STEP= 4 SUBSTEP= 1 TIME= 40.000 LOAD CASE= 0 THE FOLLOWING X,Y,Z VALUES ARE IN GLOBAL COORDINATES

ELEMENT= 4 SOLID45

NODE S1 S2 S3 SINT SEQV 5809 0.22373E-02 -0.59557E-02 -0.43292E-01 0.45529E-01 0.42036E-01 5808 0.94282E-02 0.70012E-02 -0.40343E-01 0.49771E-01 0.48603E-01 2095 0.66089E-02 -0.13164E-02 -0.43495E-01 0.50104E-01 0.46649E-01 2095 0.66089E-02 -0.13164E-02-0.43495E-01 0.50104E-01 0.46649E-01 5807 0.80664E-02 0.31612E-02-0.38945E-01 0.47011E-01 0.44761E-01 5807 0.80664E-02 0.31612E-02-0.38945E-01 0.47011E-01 0.44761E-01 5807 0.80664E-02 0.31612E-02-0.38945E-01 0.47011E-01 0.44761E-01 5807 0.80664E-02 0.31612E-02-0.38945E-01 0.47011E-01 0.44761E-01

ELEMENT= 5 SOLID45 NODE S1 S2 S3 SINT SEQV 5809 -0.92058E-02 -0.12963E-01 -0.70925E-01 0.61719E-01 0.59929E-01 2095 -0.43985E-02 -0.99530E-02 -0.74373E-01 0.69975E-01 0.67370E-01 4164 0.61513E-02 -0.34330E-03 -0.50465E-01 0.56617E-01 0.53665E-01 4164 0.61513E-02 -0.34330E-03 -0.50465E-01 0.56617E-01 0.53665E-01 5807 -0.65156E-02 -0.10967E-01 -0.73641E-01 0.67125E-01 0.65014E-01 5807 -0.65156E-02 -0.10967E-01 -0.73641E-01 0.67125E-01 0.65014E-01 5807 -0.65156E-02 -0.10967E-01 -0.73641E-01 0.67125E-01 0.65014E-01 5807 -0.65156E-02 -0.10967E-01 -0.73641E-01 0.67125E-01 0.65014E-01

ELEMENT= 6 SOLID45 NODE S1 S2 S3 SINT SEQV 5809 0.47010E-02 -0.21754E-01 -0.64382E-01 0.69083E-01 0.60372E-01 4163 0.10209E-01 -0.14085E-01 -0.59679E-01 0.69888E-01 0.61454E-01 5807 0.56891E-02 -0.19623E-01 -0.62725E-01 0.68414E-01 0.59912E-01 5807 0.56891E-02 -0.19623E-01 -0.62725E-01 0.68414E-01 0.59912E-01 4164 0.51908E-02 -0.15015E-01 -0.63054E-01 0.68244E-01 0.60718E-01 4164 0.51908E-02 -0.15015E-01 -0.63054E-01 0.68244E-01 0.60718E-01 4164 0.51908E-02 -0.15015E-01 -0.63054E-01 0.68244E-01 0.60718E-01 4164 0.51908E-02 -0.15015E-01 -0.63054E-01 0.68244E-01 0.60718E-01

NODAL SOLUTION PER NODE ***** POST1 NODAL DEGREE OF FREEDOM LISTING ***** LOAD STEP= 4 SUBSTEP= 1 TIME= 40.000 LOAD CASE= 0 THE FOLLOWING DEGREE OF FREEDOM RESULTS ARE IN GLOBAL COORDINATES NODE UX UY UZ USUM 1 93.360 88.959 145.54 194.45 2 84.593 88.959 120.66 172.13 3 93.360 101.23 70.189 154.57 4 84.593 101.23 45.307 139.49 5 94.237 88.959 148.03 196.74 6 83.716 88.959 118.17 169.96 7 93.360 96.026 102.15 168.44 8 98.972 97.736 107.58 175.85 9 90.405 97.736 83.267 157.03 10 84.593 96.026 77.272 149.49 11 84.593 94.165 88.695 154.56

12 93.360 94.165 113.58 174.59 13 99.865 97.736 110.12 177.91 14 89.511 97.736 80.731 155.18 15 78.981 92.455 83.267 147.38 16 78.088 92.455 80.731 145.48 17 88.442 92.455 110.12 168.81 18 87.549 92.455 107.58 166.69 19 83.716 96.026 74.784 147.72 20 83.716 101.23 42.819 138.17 21 94.237 96.026 104.64 170.45 22 94.237 94.165 116.07 176.69 23 83.716 94.165 86.207 152.67 24 84.405 88.907 120.45 171.86 25 74.360 88.907 91.934 147.94 26 74.360 92.414 70.405 137.94 27 84.405 92.414 98.916 159.53 28 94.237 101.23 72.678 156.24 29 -79.158 14.585 112.52 138.34 30 -257.52 -67.870 112.52 289.11 31 -83.617 14.585 99.862 131.06 32 -79.158 18.091 90.988 121.95 33 -257.52 -64.364 90.988 280.60 34 -83.617 18.091 78.333 116.00 35 -261.98 -64.364 78.333 280.91

REFERENCES:

http://www.algor.com/news_pub/tech_reports/2005/fatigue/

http://www.google.com.pk/url?sa=t&rct=j&q=fatigue%20analysis%20of%20a %20shaft&source=web&cd=2&ved=0CGwQFjAB&url=http%3A%2F%2Fweb.deu.edu.tr%2Fansys%2Fsayac3.php%3Fid%3D12&ei=fka5T5HpIIvZsgae4dH2Bw&usg=AFQjCNG3e5Kp91T3h1fGYdxU8r_6VtNZUg&cad=rja

http://www.dewi.de/dewi/fileadmin/pdf/publications/Magazin_35/03.pdf

http://www.google.com.pk/url?sa=t&rct=j&q=fatigue%20analysis%20of%20a %20shaft&source=web&cd=6&ved=0CH4QFjAF&url=http%3A%2F%2Fopencourseware.kfupm.edu.sa%2Fcolleges%2Fces%2Fme%2Fme307%2Ffiles%255C2-Lectures_LEC_30_CH-18_Shafts_and_Axles.ppt&ei=fka5T5HpIIvZsgae4dH2Bw&usg=AFQjCNG8VT_bi5RizopvTdhB2e-k2akkPA&cad=rja

http://www.ascent-journals.com/IJMRAE/Vol3No1/Paper-8.pdf

http://feadomain.com/index.php/articles/11-tutorials/3-fatigue-analysis-using-fe-fatigue

http://www.kxcad.net/romaxdesigner/RMXknow_web%5CShaft%20Fatigue%20Analysis.htm