Spur Gear Crack Propagation Path Analysis Using Finite Element . - IAENG
Proceedings of the International MultiConference of Engineers and Computer Scientists 2012 Vol II,IMECS 2012, March 14 - 16, 2012, Hong KongSpur Gear Crack Propagation Path AnalysisUsing Finite Element MethodAnanda Kumar Eriki, Member, IAENG, Ravichandra R, Member, IAENG and Mohd.Edilan Mustaffa Abstract— An effective gear design balances strength,durability, reliability, size, weight and cost. Howeverunexpected gear failure may occur even with adequate geartooth design. Failure of the engineering structures is caused bycrack, which depends on the design and operating conditionsand can be avoided by analyzing and understanding themanner it originates. To develop design guidelines to preventfailure modes considering gear tooth fracture, by studying thecrack propagation path in a spur gear. Crack propagationpaths are predicted for a variety of gear tooth geometry atvarious crack initiation location. The effects of gear tooththickness, pitch radius, and tooth pressure angle areconsidered. Analysis is being carried out using FEM with theprinciples of linear elastic fracture mechanics and mixed modefracture criteria. The stress intensity factors are the keyparameters to estimate the characteristics of a crack. Designcharts & Design guidelines or fracture mechanics will beformed considering the effects or gear geometry, applied load,crack size and material property.Keywords—Spur gear, Crack propagation path, LEFM, SIFFEMfunction of time, leading to the evaluation of the life of thecrack to reach their maximum permissible size from safeoperational life of the structure is defined.Fracture mechanics has developed into a useful disciplinefor predicting strength and life of cracked structures. Linearelastic fracture mechanics can be used in damage toleranceanalysis to describe the behavior of crack. The fundamentalassumption of linear elastic fracture mechanics is that thecrack behavior is determined solely by the values of thestress intensity factors which area function of the appliedload and the geometry of the cracked structure. The stressintensity factors thus play a fundamental role in linear elasticfracture mechanics applications. Fracture mechanics dealswith the study of how a crack in a structure propagates underapplied loads. It involves correlating analytical predictionsof crack propagation and failure with experimental results.Calculating fracture parameters such as stress intensityfactor in the crack region, which is used to estimate thecrack growth, makes the analytical predictions. Some typicalparameters are: Stress intensity factors (Open mode (a) KI,Shear mode (b) KII, Tear mode (c) KIII)I. INTRODUCTIONFAILURE of the engineering structures is caused by cracks,which is depending on the design and operatingconditions that extend beyond a safe size. Cracks present tosome extent in all structures, either as a result ofmanufacturing defects or localized damage in service. Thecrack growth leads to a decrease in the structural strength.Thus, when the service loading to the failure of the structure.Fracture, the final catastrophic event takes place very rapidlyand is preceded by crack growth, which develops slowlyduring normal service conditions.Damage Tolerance (DT) assessment is a procedure thatdefines whether a crack can be sustained safely during theprojected service life of the structure. DT assessment istherefore required as a basis for any fracture control plan,generating the following information upon which fracturecontrol decision can be made: the effect of cracks on thestructural residual strength, leading to the evaluation of theirmaximum permissible size, and the crack growth as aAnanda Kumar Eriki, Senior Lecturer, School of Engineering Scienceand Technology, Nilai University College, Nilai, Negri Sembilan, 71800,Malaysia; fax: 606-8502339, (e-mail: eriki@nilai.edu.my).Ravichandra. R, Senior Lecturer, School of Engineering Science andTechnology, Nilai University College, Nilai, Negri Sembilan, 71800,Malaysia; Tel: 606-8502338, (e-mail: ravichandra@nilai.edu.my).Mohd. Edilan Mustaffa, Head of Automotive Technology, UniversityKuala Lumpur Malaysia France Institute, Bangi, Selangor, 43650,Malaysia; Tel: 063-89262022 (e-mail: edilan@mfi.unikl.edu.my).ISBN: 978-988-19251-9-0ISSN: 2078-0958 (Print); ISSN: 2078-0966 (Online)Figure 1: Three types of loading on a cracked body;(a) Mode I; (b) Mode II and (c) Mode IIIJ-Integral: Path independent line integral that measuresthe strength of the singular stresses and strains near the cracktip. G integral path; N crack direction; x, y coordinates.Figure 2: J-integral,Crack tip and Crack faceIMECS 2012
Proceedings of the International MultiConference of Engineers and Computer Scientists 2012 Vol II,IMECS 2012, March 14 - 16, 2012, Hong KongEnergy release rate is the amount of work associated witha crack opening or closure. The evaluation of the stress fieldaround the crack tip to show that, for pure opening mode andin the limit of linear elastic fracture mechanics, the vanishingsmall fields fracture zone is surrounded by a linear elasticmaterial with stress and strain fields uniquely determined,for any type of loading, geometry or structure size, by thestress intensity factor KI,. It flows that a critical value KICmust exist so that when the actual KI, is lower, no crackgrowth can take place. This reasoning may be extended toother fracture mode to obtain fracture criteria. Hence, forpure shear mode and tear mode, critical stress intensityfactors KIIC, KIIIC may be defined such that the crack growthmay occur when the critical value are reached. But theseparameters give only information for pure mode loadings,and do not allow following the cracking process, which ingeneral involve change from pure to mixed modes. Formixed modes, the straight approaches consist that fracturemay initiate the value of KI, KII, KIII a critical condition.II. MODELED IN SOLIDWORKSThe basic spur gear tooth geometry data was input to atooth coordinate generation. The output was toothcoordinate data, which defines a single tooth sector or agear. From that single tooth sector coordinate, the completegear model was generated.Figure 3: Isometric spur gear model using SolidWorksThe gear design parameters are: Number of teeth 28;Diametric pitch 201mm; Pitch radius 44mm; Pressureangle 20deg. The tooth load was placed at the highest pointof single tooth contact (HPSTC), normal to the surface.Although the tooth load changes in magnitude and directionin actual gear operations, a static analysis with the load atthe HPSTC has given accurate results with respect to crackpropagation analysis. The gear inner diameter was fixed toground for boundary conditions.A. Pre-ProcessingAnsys helps to build a complete finite element mode,including physical and material properties, loads andboundary conditions, and analysis the various behaviors ofmechanical components and structure. Preprocessingcomprises of building, meshing and loading the modelcreated.B. MeshingAnsys offers a complete set of tools for automatic meshgeneration including mapped meshing and free meshing canaccess geometric information in the form of point, curvesand surface. With all parts of model defined, nodes,elements, restraints and loads, the analysis part of the modelis ready to begin. The system can determine approximatevalue of stress, deflections, temperatures, pressures andvibrations nodes.An analysis requires Nodal point, Elements connectingthe nodal points, Material and physical properties, Boundaryconditions which consist of loads and constraint, Analysisoption: how the problem will evaluated.After creation of solid modeling the model has convertedto FEM model, i.e. generating of nodes and elements: Setelement attributes, Set mesh control, Generate the mesh.Before generating the mesh, definition of appropriateelement attributes needed. The element attributes includeElement type, Real constants, Material properties, Elementcoordinate system.C. Element TypesPlane82-8 Node structural solid-a higher order version ofthe two dimensional, four-node element (plane 42) Itprovides more accurate results for mixed (quadrilateraltriangular) automatic meshes and can tolerate irregularshapes without as much loss of accuracy. The 8nodeelements have compatible displacement shapes and are wellsuited to model curved boundaries. The 8-node element isdefined by eight nodes having two degrees of freedom ateach node, translations in the nodal x and y directions. Thearea of the element must the positive. The element must liein global X-Y plane in plane 82 and Y-axis must be the axisof symmetry for axis symmetric analysis.III. FEA PROCEDURE IN ANSYSFigure 4: Finite element model for rim compliance effecton crack propagation;8diametral pitch, 28teeth,445mmpitch radius200, pressure angle, mb 0.9 with standard filletISBN: 978-988-19251-9-0ISSN: 2078-0958 (Print); ISSN: 2078-0966 (Online)Figure 5: Element shapeNodes: I,J,K,L,M,N,OPDegrees of freedom: UX, UYMesh control may produce a mesh that is adequate for themodel, which is going to be analyzed with the help of meshof mesh control it is easy to specify the mesh type either freeor mapped mesh and element shape. Free mesh has noIMECS 2012
Proceedings of the International MultiConference of Engineers and Computer Scientists 2012 Vol II,IMECS 2012, March 14 - 16, 2012, Hong Kongrestrictions in terms of element shapes in case of mappedmesh it is not so. When using free mesh type element shapeis allowed to take only triangular shapes for 2D andtetrahedral for 3D, for mapped mesh it is allowed to takequadrilateral and triangular for 2D and hexahedral for 3D.According to element size selection accuracy of results hasvaried.The second approach recently developed is to use dualboundary elements to represent the crack, the model of theedge crack using this approach. In this case the modeling isextremely simple and economical. The crack is representedby two elements occupying the same physical location, eachelement representing of face of the crack. The maxD. Gear MeshAfter the specifications of element attributes, and meshingControl, the mesh has been generated automatically bypicking the areas, which is going to mesh. In a crack modelstructure, near the crack tip node “delete and fill” meshingmethod is used. In the “delete and fill” meshing method sixnode triangular elements are used.F. MethodologyFigure 6: Spur gear meshed modelElement attributes:Element name-PLANE 82; Element shape-2D six nodetriangular and 2D eight node quadrilateral elements; NodesI,J,K,L,M,N,O,P; Degree of freedom-UX, UY; Materialproperty-EX 2e11; Poison’s ratio-NUXY-0.3.E. Crack modelingA crack can be represented in a boundary element modelusing two main approaches. The traditional approachrequires the user to define a zone boundary along the cracksurfaces and continue this through the body of thecomponents being studied.Figure 9: Flow chart of crack propagation path predictionG. Crack direction angleStress intensity factor values are KI, 22.5900 andKII, 2.6802, finding crack direction angle calculation [ c ]Tan c / 2 / (4 [1 1 8 / ]2Tan c / 2 22.590 / 4 2.6802 [1 1 8 22.590 / 2.6802 ]2Tan c / 2 52.380 c 44.50 0Figure7: Boundary element modes of edge crackWhere the problem is split into two zones and the edgecrack is extended by a zone interface (dotted line) across toanother external boundary.Figure 10: Geometric parametersFigure 8: Dual boundary element representations of crackISBN: 978-988-19251-9-0ISSN: 2078-0958 (Print); ISSN: 2078-0966 (Online)IMECS 2012
Proceedings of the International MultiConference of Engineers and Computer Scientists 2012 Vol II,IMECS 2012, March 14 - 16, 2012, Hong KongNomenclatureKI, KII & KIIIx, yGNarI, J, K, M, N, O, PUX, UYEXNUXY cStress intensity factorsCo-ordinatesIntegral pathCrack directionCrack lengthCrack tip distanceNodesDegrees of freedomYoung’s modulusPoisson’s ratioCrack dirction angleH. Crack-Extension criterionThe maximum principal stress criterion states that thegrowth of the crack will occur in a direction perpendicular tothe maximum principal stress. Thus, the local crack growthdirection is determined by the condition that the local shearstress is zero.IV. SIMULATION OF CRACK GROWTHIt provides a powerful productivity tool to evaluating thebehavior of existing cracks. The boundary element methodoffers several advantages in crack growth simulationbecause high stress gradients at the crack tip can beaccurately modeled and continues re-meshing required, tosimulating the crack growth.I. Incremental crack extension analysisThe incremental crack extension analysis assumes a piecewise linear discrimination of the unknown crack path. Foreach increment of the crack extension, the dual boundaryelement method is applied to carry out a stress analysis ofthe cracked structure and the J-integral is the technique usedfor the evaluation of the stress intensity factor.Figure 12: Crack tip modelFigure 11: Predicted crack propogation path in a spurgearThe steps of this basic computational cycle, repeatedlyexecuted for any number of crack extension increments are:a) Carry out the stress analysis of structure,b) Compute the stress intensity factors,c) Compute the direction of the crack extension incrementd) Extend the crack one increment along the directione) Repeat all the above steps sequentially until aspecified number of crack extension increments arereachedIn practice this requirement gives a unique directionirrespective of the length of the crack extension increment.Therefore the procedure adopted in this system is to use apredictor corrector technique to ensure the crack path isunique and independent of the crack extension incrementused.A. Crack Propagation Computational ProcedureFirst define an initial crack by identifying the node of thecrack mouth and coordinates of crack tip. The element in thesurrounding area of the crack tip, insert a 6node triangularelements around the crack tip. Then fill the remaining areabetween the rosette and original mesh with conventional8node quadrilateral elements. Mode I & Mode II stressintensity factor, KI & KII respectively can be calculated. Thestress intensity factor was determined from the finite elementnodal displacements and forces using J-integral method.Mode I loading refer to loads applied normal to the crackplane, which tends to open the crack. Mode II refers to inplane shear loading. The stress intensity factors quantify thestate of stress in the region near the crack tip. The stressintensity factors can also be used to predict the crackpropagation angles used the mixed mode criteria.Figure13: Meshing of gear with crackISBN: 978-988-19251-9-0ISSN: 2078-0958 (Print); ISSN: 2078-0966 (Online)IMECS 2012
Proceedings of the International MultiConference of Engineers and Computer Scientists 2012 Vol II,IMECS 2012, March 14 - 16, 2012, Hong KongAfter the initial crack is inserted in a mesh, theincremental crack extension analysis is used to simulate thecrack propagation and calculate stress intensity factors,crack propagation angle. Then the places of new crack tip atthe calculated angle and define crack incremental length.The model is re-meshed using the delete and fill. Theprocedure is repeated a number of times.B. Computational cycle used to simulate crack growthThe tasks for the analysis:a)Compute crack initiation location,b)Compute the boundary element method of crackedstructure,Perform stress analysis of modelc)d) Compute stress intensity factors and crack growthdirectione) Compute the direction or angle or crack extensionf) Construct incremental crack surfaceThe crack propagation path was predicted for spur gearusing mixed mode criteria and crack extension criteria. Gearcrack propagation path analysis will be carried out for avariety of gear tooth geometry at various crack initiationlocations.Figure 14: Vonmesis stressIn order to mixed mode crack growth an incremental typeanalysis is used where knowledge of both the direction andsize of the crack increment extension is necessary. The crackgrowth algorithm incorporated in the calculation of directionangle for the crack extension. For each increment of crackextension, a stress analysis is performed using boundaryelement method and stress intensity factors are evaluated.The main objective of this paper is to predict the gearservice life in fatigue, in the presence of an intial crack in thetooth foot. The FEM has been used to simulate the crackpropagation based LEFM, and in the correlationdisplacement method to determine the relation betweenintensity factor and length of the crack.Figure 17: Failure stress with CrackC. Abbreviations:Mode I (KI): Opening or tensile mode, where the cracksurface move directly a part.Mode II (KII): Sliding or in-plane shear mode, where thecrack surfaces slide over one another in a directionperpendicular to the leading edge of the crackMode III (KIII): Tensile mode or Anti-plane shear mode,wher the crack surfaces move relative to one anotherparallel to the leading edge of the crack.Figure 15: Displacement DistributionThe incremental direction along the crack front for nextextension is determined by calculated stress intensity factors.The crack front is re-meshed and the next stress analysis iscarried out.Figure 18: Stress intensity factors and crack propagationFigure 16: Failure Displacement with CrackISBN: 978-988-19251-9-0ISSN: 2078-0958 (Print); ISSN: 2078-0966 (Online)A loss of stiffness is observed when crack are introduced.It is also noticed that the maximum of stiffness reduction isat the engagement of the cracked tooth of pinion which is anexpected result regarding to the relative flexibility of thetooth at the addendum circule compared with that at the basecircle.IMECS 2012
Proceedings of the International MultiConference of Engineers and Computer Scientists 2012 Vol II,IMECS 2012, March 14 - 16, 2012, Hong KongV. CONCLUSIONAs concluded that, spur gear crack propagation path waspredicted using mixed mode criteria and crack extensioncriteria. Finite element spur gear model and crack model wasdeveloped, Crack propagation direction angle was calculatedusing intensity factors at the crack tip, Crack propagationpath was predicted for gear tooth using mixed mode criteriaand crack extension criteria, Finite element analysis has beencarried out for gear crack propagation, Gear crackpropagation path analysis will be carried out for a variety ofgear tooth geometry at various crack initiation locations. Theeffects of gear tooth thickness, crack initiation locations andgear tooth geometry factors will be considered. Designcharts for fracture mechanics will be formed considering theeffects of gear geometry, applied crack size and materialproperty.This paper focused on deterministic mechanic modelingof subsurface crack propagation. For the life prediction ofspur gear under realistic service conditions, a probabilisticapproach considering variabilities in loading spectra,material properties and structural details is required andneed further study. Also, other effects influencing the rootand internal diameter are failure, such as manufacturingprocess parameters, residual stress and barake thermalloading need to be investigated in the futureREFERENCES[1][2][3][4][5][6][7][8]Z. Chen, Y. Shao, “Dynamic simulation of spur gear with toothcrack propagating along tooth width and crack depth”, EngineeringFailure Analysis 18 (2011) 2149-2164.S.Zouari, M. Maatar, “Following spur gear propagation in the toothfoot by FEM” (2010) 10: 531-539.Fakher. Charri, Tahar F, Mohamed Haddar, “Analytical modeling ofspur gear tooth crack and influence on gearmesh stiffness”.European Journal of Mechanics a/Solids 28 (2009) 461-468.Wu S, Zuo KJ, Parey A. “Simulation of spur gear dynamics andestimation of fault growth”. J Sound Vib (2008);317:608-24A. Belsak, Joze Flasker, “Detecting cracks in the tooth root ofgears”. Engineering Failure Analysis 14 (2007) 1466-1475.Y Liu, L. Liming, S. Mahadevan, “Analysis of subsurface crackpropagation under rolling contact loading in railroad wheel usingFEM” Engineering Fracture Mechanics 74 (2007) 2659-2674.C. James Li, Hyungdae Lee, “Gear fatigue crack prognosis usingembedded model, gear dynamic model and fracture mechanics”,Mechanical systems and signal processing 19 (2005) 836-846.David G. Lewicki, “Gear crack propagation path studies-Guidelinesfor Ultra-safe design” U.S Army Research Laboratory, GlennResearch Center, Cleveland, Ohio.ISBN: 978-988-19251-9-0ISSN: 2078-0958 (Print); ISSN: 2078-0966 (Online)IMECS 2012
Analysis is being carried out using FEM with the principles of linear elastic fracture mechanics and mixed mode fracture criteria. The stress intensity factors are the key parameters to estimate the characteristics of a crack. Design charts & Design guidelines or fracture mechanics will be . Calculating fracture parameters such as stress .
Crack repair consists of crack sealing and crack filling. Usually, crack sealing re-fers to routing cracks and placing material on the routed channel. Crack filling, on the other hand, refers to the placement of mate-rial in/on an uncut crack. For the purposes of this manual, crack sealing will refer to both crack filling and sealing.
crack growth as a mutual competition between intrinsic mechanisms of crack advance ahead of the crack tip (e.g., alternating crack-tip blunting and resharpening), which promote crack growth, and extrinsic mechanisms of crack-tip shielding behind the tip (e.g., crack closure and bridging), which impede it. The widely differing
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Work out the gear ratios of these gears: (numbers inside the circles are the numbers of teeth on each gear) Blue drive gear, green driven gear, pink idler gear, yellow compound gear 1: Simple meshed gear 2: Simple gear train with idler gear 15 3: Compound gear train 4: Choose the correct words to make these statements true for these gear trains.
9 spur-gear-75t-5/8 5/8" spur gear on gear shaft 1 10 wdrfkey-5/32x5/8 woodruff key gear 1 11 main-shaft-locknut locknut 1 . parts breakdown for model tm-11 rice hydro, inc. when ordering 1" spur gear "wdrfkey-1/4x1" is also reco
Computer Aided Spur Gear Design and Analysis Edward M. Vavrek Purdue University North Central I. Introduction This paper describes a spur gear analysis program written in visual basic. The program is used to assist students to learn the procedures to size and select spur gears. The class t
3. Explain what a gear train does? 4. Explain what a simple gear train is? 5. Explain torque? 6. What does a larger gear driving a smaller gear achieve? 7. What does a smaller gear driving a larger gear achieve? 8. What is the driven gear? 9. What is the driver gear? 10. What is the idler gear? 11. What is the calculation for working out gear .
form a gear set or a gear train . In a gear set, the input gear is called _ gear. The output gear is called the _ gear. Note: An idler gear or intermediate gear changes direction of rotation without change in gear set speed or torque Spinner &
