97
Views
1
CrossRef citations to date
0
Altmetric
Research Article

An extensive analysis of frequency and transient responses in S and C-shaped gears

ORCID Icon, ORCID Icon, ORCID Icon, ORCID Icon, ORCID Icon & ORCID Icon
Pages 825-837 | Received 24 Jan 2020, Accepted 08 Apr 2020, Published online: 26 Apr 2020

References

  • Ahmad, A. 2009. “Parametric Spiral and Its Application as Transition Curve.” Ph.D. Thesis, UniversitiSains Malaysia.
  • Åkerblom, M. 2001. Gear Noise and Vibration - A Literature Survey. Stockholm, Sweden: Maskinkonstruktion.
  • Ali, J., H. Said, and A. Majid. 1996. “Shape Control of Parametric Cubic Curves.” In SPIE, Fourth International Conference on Computer-Aided Design and Computer Graphics, edited by J. Zhou, 128–133. China.
  • Alpers, B. 2006. “Mathematical Qualifications for Using a CAD Program.” In IMA Conference on Mathematical Education of Engineers, edited by S. Hibberd and L. Mustoe. London: Loughborough, Engineering Council.
  • Artin, E. 1957. Geometric Algebra. New York: Interscience.
  • Baass, K. 1984. “The Use of Clothoid Templates in Highway Design.” Transportation Forum 1: 47–52.
  • Babu, V., and A. Tsegaw. 2009. “Involute Spur Gear Template Development by Parametric Technique Using Computer Aided Design.” African Research Review 3 (2): 415–429. doi:https://doi.org/10.4314/afrrev.v3i2.43640.
  • Barbieri, M., A. Zippo, and F. Pellicano. 2014. “Adaptive Grid-size Finite Element Modeling of Helical Gear Pairs.” Mechanism and Machine Theory 82: 17–32. doi:https://doi.org/10.1016/j.mechmachtheory.2014.07.009.
  • Barnett, H. 1985. “Criteria of Smoothness.” Journal of the Institute of Actuaries 112 (3): 331–367. doi:https://doi.org/10.1017/S0020268100042189.
  • Barone, S. 2001. “Gear Geometric Design by B-spline Curve Fitting and Sweep Surface Modelling.” Engineering with Computers 17 (1): 66–74. doi:https://doi.org/10.1007/s003660170024.
  • Beghini, M., F. Presicce, and C. Santus. 2006. “Proposal for Tip Relief Modification to Reduce Noise in Spur Gears and Sensitivity to Meshing Conditions.” Gear Technology 23 (2): 34–40.
  • Belyaev, A. 2004. Plane and Space Curves. Curvature. Curvature-based Features. Saarbrücken: Max-Planck-InstitutfürInformatik.
  • Bies, D., and C. Hansen. 2009. Engineering Noise Control: Theory and Practice. Florida: CRC Press.
  • Blake, R. 1961. Basic Vibration Theory, Shock and Vibration Handbook. 1st ed. New York: McGraw-Hill.
  • Brand, L., and E. Schwab. 2005. “General Science Note: The Rainbow Is All in Your Head.” Origins 58: 45–56.
  • Costa, L. 2002. “Estimating Derivatives and Curvature of Open Curves.” Pattern Recognition 35 (11): 2445–2451. doi:https://doi.org/10.1016/S0031-3203(01)00212-6.
  • Dejnozkova, E. and Dokladal, P., 2004, Modelling of overlapping circular objects based on level set approach. In International Conference Image Analysis and Recognition, Berlin, Heidelberg:  Springer Publisher, pp. 416-423.
  • Dooner, D. 2012. Kinematic Geometry of Gearing. New Jersey: John Wiley & Sons.
  • Du Sautoy, M. 2009. Symmetry: A Journey into the Patterns of Nature. New York: HarperCollins.
  • Fang, S., L. Wang, M. Komori, and A. Kubo. 2010. “Simulation Method for Interference Fringe Patterns in Measuring Gear Tooth Flanks by Laser Interferometry.” Applied Optics 49 (33): 6409–6415. doi:https://doi.org/10.1364/AO.49.006409.
  • Farin, G. 2002. Curves and Surfaces for CAGD: A Practical Guide. Massachusetts: Morgan Kaufmann.
  • Faux, I., and M. Pratt. 1988. Computational Geometry for Design and Manufacture. Chichester: Ellis Horwood.
  • Gomm, W. 1987. “Stability Analysis of Explicit Multirate Methods.” Mathematics and Computers in Simulation 23 (1): 34–50. doi:https://doi.org/10.1016/0378-4754(81)90005-7.
  • Habib, Z., and M. Sakai. 2003. “G2 Planar Cubic Transition between Two Circles.” International Journal of Computer Mathematics 8: 959–967.
  • Habib, Z., Sakai, M., 2005. Family of G2 spiral transition between two circles. In: Advances in Geometric Design. John Wiley & Sons, Ltd., pp. 133–151.
  • Hassan, A., G. Thanigaiyarasu, and V. Ramamurti. 2008. “Effects of Natural Frequency and Rotational Speed on Dynamic Stress in Spur Gear.” In:WorldAcademy of Science, Engineering and Technology 36: 1279–1287.
  • Higuchi, F., S. Gofuku, T. Maekawa, H. Mukundan, and N. Patrikalakis. 2007. “Approximation of Involute Curves for CAD-system Processing.” Engineering with Computers 23 (3): 207–214. doi:https://doi.org/10.1007/s00366-007-0060-3.
  • Hirani, H. 2014. Applications of Tribology. Delhi, India: Lecture notes distributed in Tribology at Indian Institute of Technology.
  • Hoschek, J., and D. Lasser. 1993. Fundamentals of Computer Aided Geometric Design. (Translation by L. L. Schumaker). Massachusetts: A.K. Peters Wellesley.
  • Hwang, Y., and C. Hsieh. 2007. “Determination of Surface Singularities of a Cycloidal Gear Drive with Inner Meshing.” Mathematical and Computer Modelling 45 (3): 340–354. doi:https://doi.org/10.1016/j.mcm.2006.05.010.
  • Jacobsen, T., R. Schubotz, L. Höfel, and D. Cramon. 2006. “Brain Correlates of Aesthetic Judgment of Beauty.” Neuroimage 29 (1): 276–285. doi:https://doi.org/10.1016/j.neuroimage.2005.07.010.
  • Juhász, I. 1998. “Cubic Parametric Curves of Given Tangent and Curvature.” Journal of Computer Aided Design 25 (1): 1–9. doi:https://doi.org/10.1016/S0010-4485(97)00046-8.
  • Kapelevich, A. 2000. “Geometry and Design of Involute Spur Gears with Asymmetric Teeth.” Mechanism and Machine Theory 35 (1): 117–130. doi:https://doi.org/10.1016/S0094-114X(99)00002-6.
  • Kapelevich, A., and R. Kleiss. 2002. “Direct Gear Design for Spur and Helical Involute Gears.” Gear Technology 19 (5): 29–35.
  • Klubnik, R. 2008. “Measuring Displacement Using Accelerometers.” Maintenance Technology 21 (3): 30–33.
  • Kolivand, A. 2014. “Involute Straight Bevel Gear Surface and Contact Lines Calculation Utilizing ease-Off Topography Approach.” SAE Technical Paper, 1–1765.
  • Komzsik, L. 2009. What Every Engineer Should Know about Computational Techniques of Finite Element Analysis. 2nd ed. New York: CRC Press.
  • Kouibia, A., and M. Pasadas. 2000. “Smoothing Variational Splines.” Applied Mathematics Letters 13 (2): 71–75. doi:https://doi.org/10.1016/S0893-9659(99)00167-6.
  • Levy, J. 2011. Your Options Handbook: The Practical Reference and Strategy Guide to Trading Options. New Jersey: John Wiley & Sons.
  • Lin, H. 2009. “On the Derivative Formula of a Rational Bezier Curve at a Corner.” Applied Mathematics and Computation 210 (1): 197–201. doi:https://doi.org/10.1016/j.amc.2008.12.078.
  • Litvin, F., I. Gonzalez-Perez, A. Fuentes, K. Hayasaka, and K. Yukishima. 2005. “Topology of Modified Surfaces of Involute Helical Gears with Line Contact Developed for Improvement of Bearing Contact, Reduction of Transmission Errors, and Stress Analysis.” Mathematical and Computer Modelling 42 (9): 1063–1078. doi:https://doi.org/10.1016/j.mcm.2004.10.028.
  • Martinsson, H., F. Gaspard, A. Bartoli, and J. Lavest. 2007. “Reconstruction of 3D Curves for Quality Control. In Image Analysis, 760–769. Berlin, Heidelberg: Springer Publisher.
  • Matsuura, A., J. Hashimoto, and K. Okuno. 2013. “Geometric Visual Instruments Based on Object Rolling.” In Bridges 2013: Mathematics, Music, Art, Architecture, Culture, 303–310. Netherlands: Tessellations Publishing.
  • McConnell, K. 1995. Vibration Testing: Theory and Practice. New Jersey: John Wiley & Sons.
  • Michalski, J., P. Pawlus, and W. Żelasko. 2011. “Surface Topography of Cylindrical Gear Wheels after Smoothing in Abrasive Mass, Honing and Shot Peening.” Journal of Physics 311 (1): 012022. IOP Publishing.
  • Ognjanović, M., and S. Kostić. 2012. “Gear Unit Housing Effect on the Noise Generation Caused by Gear Teeth Impacts.” Strojniškivestnik-Journal of Mechanical Engineering 58 (5): 327–337. doi:https://doi.org/10.5545/sv-jme.2010.232.
  • Palermo, A., D. Mundo, A. Lentini, R. Hadjit, P. Mas, and W. Desmet. 2010. “Gear Noise Evaluation through Multibody TE-based Simulations: In. Proceedings of International Conference on Noise and Vibration Engineering, Leauven, Belgium, 3033–3046.
  • Paul, I., and G. Bhole. 2010. “Modification of Spur Gear Using Computational Method-involutes Profile Being Modify.” 2010 International Conference on Industrial Engineering and Operations Management, 197–203. Dhaka, Bangladesh.
  • Peckner, D., and I. Bernstein. 1977. Handbook of Stainless Steels. New York: McGraw-Hill.
  • Prvan, T. 1997. “Smoothing Splines with Variable Continuity Properties and Degree.” Applied Mathematics Letters 10 (2): 75–80. doi:https://doi.org/10.1016/S0893-9659(97)00014-1.
  • Quinn, D. W. 1987. “A Finite Method for Computing Sound Propagation in Ducts.” Mathematics and Computers in Simulation 29 (1): 51–64. doi:https://doi.org/10.1016/0378-4754(87)90066-8.
  • Radzevich, S. 2012. Dudley’s Handbook of Practical Gear Design and Manufacture. 2nd ed. London: Taylor & Francis Group.
  • Reyes, O., A. Rebolledo, and G. Sanchez. 2008. “Algorithm to Describe the Ideal Spur Gear Profile.” World Congress on Engineering (WCE) II, London, U.K.
  • Said, H. 1990. “The Bézier-Ball Type Cubic Curves and Surfaces.” SainsMalaysiana 19 (4): 85–95.
  • Sankar, S., M. Raj, and M. Nataraj. 2010. “Profile Modification for Increasing the Tooth Strength in Spur Gear Using CAD.” Journal of mechanical engineering Science 2 (9): 740–749.
  • Shen, T., C. Chang, K. Chang, and C. Lu. 2013. “A Numerical Study of Cubic Parabolas on Railway Transition Curves.” Journal of Marine Science and Technology 21 (2): 191–197.
  • Srikanth, N., A. Jeevanantham, and Nirmal. 2014. “Determination of Lock Slippage in Gear Tooth Using Quasi-static Analysis.” IOSR Journal of Mechanical and Civil Engineering (IOSR-JMCE) 2(3): 19–22.
  • Tuma, J. 2009. “Gearbox Noise and Vibration Prediction and Control.” International Journal of Acoustics and Vibration 14 (2): 99–108. doi:https://doi.org/10.20855/ijav.2009.14.2242.
  • Vermeij, I. 2000. “Design of a High Speed Track.” HERON 45 (1): 9–23.
  • Walton, D., and D. Meek. 1989. “Computer-aided Design for Horizontal Alignment.” Journal of Transportation Engineering 115 (4): 411–424. doi:https://doi.org/10.1061/(ASCE)0733-947X(1989)115:4(411).
  • Walton, D., and D. Meek. 1996. “A planar cubic Bézier spiral.” Journal of Computational and Applied Mathematics 72 (1): 85–100. doi:https://doi.org/10.1016/0377-0427(95)00246-4.
  • Walton, D., and D. Meek. 1999. “Planar G2 Transition between Two Circles with a Fair Cubic Bezier Curve.” Computer Aided Design 31 (14): 857–866. doi:https://doi.org/10.1016/S0010-4485(99)00073-1.
  • Walton, D., D. Meek, and J. Ali. 2003. “Planar G2 Transition Curves Composed of Cubic Bézier Spiral Segments.” Journal of Computational and Applied Mathematics 157 (2): 453–476. doi:https://doi.org/10.1016/S0377-0427(03)00435-7.
  • Wu, W., C. Yin, and S. Zhao. 2013. “New Involute Interpolation Method Based on Arc Length.” Computer Engineering and Design 34 (1): 314–317.
  • Xianzhang, F. 2011. “Analysis of Field of Stress and Displacement in Process of Meshing Gears.” International Journal of Digital Content Technology and Its Applications 5 (6): 345–357. doi:https://doi.org/10.4156/jdcta.vol5.issue6.42.
  • Xiao, J., X. Deng, J. He, W. Ma, Y. Li, and J. Li. 2014. “Simulation and Analysis about Different Pressure Angle in Involute Gears Based on Neural Network.” Applied Mechanics and Materials 540: 88–91.
  • Yahaya, S. 2015. “Said-Ball Cubic Transition Curve and Its Application to Spur Gear Design.” Ph.D. Thesis, UniversitiSains Malaysia.
  • Yan, K., J. Wang, and R. Zhou. 2014. “A New Method of Point-to-point Comparison Interpolation for Involute.” Key Engineering Materials 589: 708–711.
  • Zehe, M., S. Gordon, and B. McBride. 2002. CAP: Computer Code for Generating Tabular Thermodynamic Functions from NASA Lewis Coefficients. NASA/TP–2001–210959/REV1. Ohio, USA: Glenn Research Center.
  • Zeller, T. 2007. Driving Germany: The Landscape of the German Autobahn, 1930–1970. Vol. 5. New York: Berghahn Books.
  • Zhou, J., W. Sun, and Q. Tao. 2014. “Gearbox Low-noise Design Method Based on Panel Acoustic Contribution.” Mathematical Problems in Engineering Article ID 850549, 10.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.