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Finite Element Analysis of Gear Contact and Bending Stresses
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Finite Element Analysis of Gear Contact and Bending Stresses
1.
International Research Journal
of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 06 Issue: 07 | July 2019 www.irjet.net p-ISSN: 2395-0072 © 2019, IRJET | Impact Factor value: 7.211 | ISO 9001:2008 Certified Journal | Page 1416 ERROR IDENTIFICATION AND COMPARISON WITH AGMA STANDARD IN GEARS USING FINITE ELEMENT ANALYSIS Dr. N. Nandakumar1, T. Allwin Raja2 1Associate Professor, Department of mechanical Engineering, Government College of Technology, Coimbatore, Tamilnadu, India. 2PG Scholar, Department of Engineering Design, Government College of Technology Coimbatore, Tamilnadu, India ---------------------------------------------------------------------***---------------------------------------------------------------------- Abstract - The objectives of this thesis are to use a algebraical style to progress theoretic replicas of thebehavior of helical gears and rack and pinion in mesh, to help to predict the effect of gear contact stresses and bending stress error. The core attention of the existing study as established to govern proper representations of contact rudiments, to analyze bending stresses and contact stressofhelicalgear and rack and pinion respectively by ANSYS and equate the outcomes with AGMA theoretic standards. Key Words: Helical gear, rack and pinion, contact stress analysis, bending stress analysis 1. INTRODUCTION Gearing is one of the most critical components in a mechanical power transmission system, and in most industrial rotating machinery. It is possible that gears will predominate as the most effective means of transmitting power in future machines due to their high degree of reliability and compactness. In addition,the rapidshiftinthe industry from heavy industries such as shipbuilding to industries such as automobile manufacture and office automation tools will necessitate a refined application of gear technology. The increasing demand for quiet power transmissioninmachines,vehicles,elevatorsandgenerators, has created a growing demand for a more precise analysisof the characteristics of gear systems. In the automobile industry, the largest manufacturerofgears,higherreliability and lighter weight gears are necessary as lighter automobiles continue to be in demand. In addition, the success in engine noise reduction promotes the production of quieter gear pairs for further noise reduction. Noise reduction in gear pairs is especially critical in the rapidly growing field of office-automation equipment as the office environment is adversely affected by noise, and machines are playing widening role in that environment. The finite element method is very often used to analyze the stress state of an elastic body with complicated geometry, such as a gear. In this thesis, first, the finite element models and solution methods needed for the accurate calculation of two dimensional Rack and pinion contact stresses and Helical gear bending stresses were determined. Then, the contact and bending stresses calculated using ANSYS 19.2 were equated to the outcomes gained from present approaches. The purpose of this thesis is to develop a model to learning and forecast the typical counting the connection stresses and the Bending stress of gears in mesh by the ANSYS 19.2 Tool packagegroundedonmathematical system. The aim is to find the amount of stress error inthegears,and thereby reduce the amount of failure rate generated. 2. CONTACT STRESS 2.1. IMPORTANCE OF CONTACT STRESS Despite the importance of contact in the mechanics of solids and its engineering applications, contact effects are rarely seriously taken into account in conventional engineering analysis, because of the extreme complexity involved. Mechanical problems involving contacts are inherently nonlinear .Usually the loading causes significant changes in stiffness, which results in a structure that is nonlinear. Nonlinear structural behavior arises for a number of reasons, which can be reduced to three main categories (1) Geometric Nonlinearities, (2) Material Nonlinearities, (3) Change in Status Nonlinearities, Throughthe quick change of computational mechanism, but, excessive advancement has been finished in geometric study of the tricky. Using the finite element way, several connection glitches, oscillating after moderately humble ones to quite difficult ones, can be resolved with high precision. TheFiniteElementMethodcan be restrained the desired technique to treat interaction problems, since of its confirmed achievement in giving a extensive variety of engineering delinquent in zones of solid mechanics, fluid flow, heat transfer, and for electromagnetic field and coupled field problems. 2.2. CONTACT PROBLEM OF RACK AND PINION The fig 1 shows Rack and pinion are hard-pressedcounter to each other. This prototype was constructedgroundedonthe Hertz contact stress theoretic delinquent. The ranges were premeditated beginning from the pitch diameters of the pinion and gear .The contact stress of this prototype should characterize the contact stress amongtwogears.Intheinput file, first, the geometry of Rack andpinionmustbedescribed. Then the geometry areas were meshed. In contact areas a fine mesh was built. The boundary conditions were applied in this model. The loads also were applied .In eachstepthere are a lot of sub-steps. In each sub-step the number of equilibrium iterations was set.
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International Research Journal
of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 06 Issue: 07 | July 2019 www.irjet.net p-ISSN: 2395-0072 © 2019, IRJET | Impact Factor value: 7.211 | ISO 9001:2008 Certified Journal | Page 1417 Fig.1. RACK AND PINION 2.3 . CONTACT STRESS ANALYSIS The fig 2 shows the usual connection stress laterally on the interaction parts. The similar process is ended for dissimilar materials and the outcomesareequatedwithAGMAordinary outcome and discourse around the stress difference. FIG.2.CONTACT STRESS ANALYSIS 3. BENDING STRESS When one investigates actual gears inservice,theconditions of the surface and bending failure are two of the most important features to be considered. The finite element method is very often used to analyze the stress states of elastic bodies with complicated geometries, such as gears. There are published papers, which have calculated the elastic stress distributions in gears. In these works, various calculation methods for the analysis of elastic contact problems have been presented. The finite element method for two-dimensional analysis is used very often. It is essential to use a three-dimensional analysisifgearpairs are under partial and non uniform contact. However, in the three-dimensional calculation, a problem is created due to the large computer memory space that is necessary. In the technique for producing a FEM typical for bending stress analyses, the calculations secondhand to produce the gear tooth shape curve. When meshing the teeth in ANSYS, if “SMART SIZE” is used the number of elementsneartheroots of the teeth are automatically much greater than in other places. It also indicates that only one tooth is enough for the bending stress analysis for the 3-D model. FIG.3.HELICAL GEAR 3.1. BENDING STRESS ANALYSIS The Figure 4 displays how to mesh the 3D model and how to place happening the load on the sample. Here are internal side nodes on the individually side of apiece part. So a great number of degrees of free movement in this 3D model take a lengthier period to enclose running.It similarlyspecifiesthat only one tooth is sufficient for the bending stress study for the 3-D model. The investigation displays one tooth FEM prototype and display how abundant Von Mises stress is on the base of tooth when the number of teeth is 37 forthegear. FIG.4.BENDING STRESS ANALYSIS In this unit the tooth base stressesand thetoothdeflectionof one tooth of helical gear is designed using an ANSYS model. 4. AGMA ANALYSIS In this section, a comparison of the tooth root stresses obtained in the three dimensional model and in the two
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International Research Journal
of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 06 Issue: 07 | July 2019 www.irjet.net p-ISSN: 2395-0072 © 2019, IRJET | Impact Factor value: 7.211 | ISO 9001:2008 Certified Journal | Page 1418 dimensional model using ANSYS with the results given by the standards of the AGMA is carried out. is recommended by the AGMA and the other coefficients, such as the dynamic factor, are set at 1.2. Where σ(c) and σ(f) are contact and bending stress respectively. 5. BENDING STRESS COMPARISON The Von Mises stresses on the root of tooth were carried out in order to know if they match the results from ANSYS. The above calculations of the Von Mises stresses on the root of tooth were carried out in order to know if they match the results from ANSYS In this Table 1 the maximum values of the tooth root stress obtained by the ANSYS method. TABLE.1.BENDING STRESS ANALYSIS 5.2. CONTACT STRESS COMPARISON TABLE.2.CONTACT STRESS ANALYSIS NUMBER OF TEETH AGMA (MPa) ANSYS (MPa) % ERROR 33 85.050 84.429 0.74 35 91.129 91.770 0.69 37 115.126 110.78 3.97 40 116.86 113.79 2.63 42 128.86 124.80 2.93 44 141.97 132.15 7.43 These changes are supposed to be produced by aspects such as the mesh design and the limited circumstances on the finite element analysis, and the supposed location of the dangerous unit in the values are shown in Table 2. 6. CONCLUSION It was exposed that an FEA prototype could be helped to analyze the interaction among two physiques exactly by confirmation of contact stresses among two cylinders in contact and comparison with the Hertzian equations. Active approaches to approximation the tooth interaction stress using a 3D interaction stress prototype and to guesstheroot bending stresses via 3D FEA prototype are anticipated. The expansion of a innovative mathematical way for FEA showing of the full gear figure which can alternate in mesh together with the contact problem is offered.Themotionless stress fault was too attained after running the replicas in ANSYS. REFERENCES [1] Norton, R. L., “MachineDesign:AnIntegratedApproach”, New Jersey: Prentice-Hall Inc. [2] Hamrock, B. J., Jacobson, S.R., “FundamentalsofMachine Elements”. [3] Buckingham, E., 1949, “Analytical Mechanics of Gears”, McGraw-Hill, New York. [4] Coy, J. J., Chao, C. H. S., 1982, “A method of selecting grid size to account for Hertz deformation in finite element analysis of spur gears”, Trans. ASME,J.Mech.Design104 759-766. [5] Gatcombe, E.K., Prowell, R.W., 1960, “Rocket motorgear tooth analysis”, (Hertzian contact stresses and times) Trans. ASMA, J. Engng Industry. [6] Umezawa, K., 1988, “Recent Trends in Gearing Technology”, JSME International Journal Series III Vol.31, No. 2, pp 357-362. [7] Klenz, S. R., 1999, “Finite Element Analyses of A Spur Gear Set”, M.Sc. Thesis, Dept. of Mechanical Engineering, University of Saskatchewan. [8] Smith, J. O. Liu, C. K., “Stresses Due to Tangential and Normal Loads on an Elastic Solid with Applications to Some Contact Stress Problems”, Journal of Applied Mechanics [9] Wang, J., 2003, “Survey of Nonlinear Vibration of Gear Transmission Systems” Appl Mech Rev vol 56, No 3. [10] Chong, T. H., Bar, I., 2001,“Multiobjectiveoptimal Design of Cylindrical Gear Pairs for the Reduction of Gear Size NUMBER OF TEETH AGMA (MPa) ANSYS (MPa) % ERROR 28 650.43 671.24 3.2 30 670.32 690.43 3 34 732.65 757.12 3.34 37 745.59 771.69 3.5 40 765.76 797.92 4.2 42 788.77 820.32 4
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International Research Journal
of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 06 Issue: 07 | July 2019 www.irjet.net p-ISSN: 2395-0072 © 2019, IRJET | Impact Factor value: 7.211 | ISO 9001:2008 Certified Journal | Page 1419 and Meshing Vibration”, JSME International Journal,Vol. 44, No. 1, pp 291-292 [11] B.Bloomfield, Designing facegears, Mach.Design19(1947) 129134. [12] G.F. Heath, R.B. BosslerJr., Advanced rotorcraft transmission (ART) program final report, NASA Contractor Report 191057, January 1993. [13] G.F.Heath,R.R.Filler,J.Tan,Developmentoffacegeartechnol ogyforindustrialandaerospacepowertransmission,NASA /CR2002211320,May2002. [14] R.R.Filler, G.F.Heath, S.C.Slaughter, D.G.Lewicki, Torque Splitting By a Concentric Face Gear Transmission, the American Helicopter Society 58th Annual Forum, Montreal, 2002June1113. [15] G.F. Heath, S.C. Slaughter, M.T.Morris, J.Fetty, D.G. Lewicki, D.J. Fisher, Face Gear Development under the Rotor craft Drive System for the 21st Century Program, the American Helicopter Society 65th Annual Forum, 2009 May 27-29.
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