Abstract
In order to meet the requirements of the ideal kinematics characteristics of the driven gear, a new kind of uniform-variable non-circular gear is proposed. According to the ideal speed curve and acceleration curve, the concept of the uniform-variable non-circular gear is analyzed. The pitch curve equations are derived and the formulas for calculating the gear’s section length and center distance are established. A design procedure is developed and a simplified derivation of the mathematical model is presented. A few characteristics, such as pressure angles, the undercut and the contact ratio, of this new drive are analyzed. The results confirm that the proposed design method is more flexible to control the shape of the pitch curves by changing the parameters of the given speed curve and acceleration curve.
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References
Liu, D.W., Ren, T.Z.: Study on deformed limacon gear and motion optimization of its serial mechanism. J. Mech. Des. Trans. ASME 133(6), 061004-1-8 (2011)
Tong, S.H., Yang, D.C.H.: Generation of identical noncircular pitch curves. J. Mech. Des. Trans. ASME 120(2), 337–341 (1998)
Tsay, M.F., Fong, Z.H.: Study on the generalized mathematical model of noncircular gears. Math. Comput. Model. 41(4), 555–569 (2005)
Liu, D.W., Ren, T.Z.: Creating pitch curve of closed noncircular gear by compensation method. J. Mech. Eng. 47(13), 147–152 (2011)
Zhang, X., Fan, S.: Synthesis of the steepest rotation pitch curve design for noncircular gear. Mech. Mach. Theory 102(4), 16–35 (2016)
Hector, F.Q.R., Salvador, C.F., Liuisa, J.N.: The synthesis of a N-lobe noncircular gear using Bézier and B-spline nonparametric curve on the design of its displacement law. J. Mech. Des. Trans. ASME 129(9), 982–985 (2007)
Li, H.W.: Design of noncircular gears with pitch curves variations through parabola. J. Shandong Univ. Technol. 26(6), 63–65 (2012). (in Chinese)
Xu, G.H., Chen, J.N.: Modeling and simulation of fourier section curves of non-circular gear and study on impact of parameters. Hydromechatronics Eng. 41(12), 69–73 (2013)
Ottaviano, E., Mundo, D., Danieli, G.A., et al.: Numerical and experimental analysis of non-circular gears and cam-follower systems as function generators. Mech. Mach. Theory 43(8), 996–1008 (2008)
Guo, C.Z., Fu, W., Zhu, J.C., et al.: Design of the pitch curves of noncircular gears for quick return mechanism. Chin. J. Mech. Eng. 141(11), 221–227 (2005). (in Chinese)
Niu, S.C., Li, G., Li, G.Y., et al.: The design of new transmission in automatic fixation-shaping machine. J. Agric. Mech. Res. 33(2), 58–61 (2011). (in Chinese)
Lei, C.Y., Chen, J.N., Li, P.P., et al.: Reverse design of non-circular gear-crank slider hay baler mechanism. Trans. Chin. Soc. Agric. Eng. 28(13), 22–27 (2012). (in Chinese)
Fischer, X., Nadeau, J.P.: Integrated Design and Manufacturing in Mechanical Engineering. Springer, Paris (2011)
Lanzotti, A., Carbone, F., Grazioso, S., et al.: A new interactive design approach for concept selection based on expert opinion. Int. J. Interact. Des. Manuf. 12(4), 1189–1199 (2018)
Yang, S.C.: Applying envelope theory and deviation function to tooth profile design. Mech. Mach. Theory 42(5), 262–274 (2007)
Chao, L.C., Tsay, C.B.: Tooth flank, undercutting and tooth pointing of spherical gears. Mech. Mach. Theory 46(4), 534–543 (2011)
Kapelevich, A.: Direct Gear Design. CRC Press, Boca Raton (2013)
Sekar, R.P., Muthuveerappan, G.: Load sharing based maximum fillet stress analysis of asymmetric helical gears designed through direct design—a parametric study. Mech. Mach. Theory 80(10), 84–102 (2014)
Muni, D.V., Kumar, V.S., Muthuveerappan, G.: Optimization of asymmetric spur gear drives for maximum bending strength using direct gear design method. Mech. Based Des. Struct. Mach. 35(2), 127–145 (2007)
Marimuthu, P., Muthuveerappan, G.: Design of asymmetric normal contact ratio spur gear drive through direct design to enhance the load carrying capacity. Mech. Mach. Theory 95(1), 22–34 (2016)
Wang, J., Hou, L., Luo, S.M., et al.: Active design of tooth profiles using parabolic curve as the line of action. Mech. Mach. Theory 61(9), 47–63 (2013)
Wang, J., Luo, S.M., Wu, Y.: A method for the preliminary geometric design of gear tooth profiles with small sliding coefficients. ASME J. Mech. Des. 132(5), 054501-1-8 (2010)
Wang, J., Luo, S.M., Su, D.Y.: Active design and characteristics analysis of high contact ratio gears based on pressure angle. J. Cent. South Univ. 45(11), 3792–3799 (2014). (in Chinese)
Litvin, F.L., Gonzalez-Perez, I., Fuentes, A., et al.: Design and investigation of gear drives with non-circular gears applied for speed variation and generation of functions. Comput. Methods Appl. Mech. Eng. 197(45), 3783–3802 (2008)
Litvin, F.L., Fuentes, A.: Gear Geometry and Applied Theory, 2nd edn. Cambridge University Press, Cambridge (2004)
Acknowledgements
The work was supported by the National Natural Science Foundation of China under No. 51205335 and No. 51375411, the Scientific Research for the High Level Talent of Nanjing Institute of Technology under No. YKJ201702. These financial supports are gratefully acknowledged. The authors also sincerely appreciate the comments and modification suggestions made by the editors and anonymous referees.
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Wang, J., Fan, J. & Feng, Y. The design methodology and characteristics analysis of a uniform-variable non-circular gear drive. Int J Interact Des Manuf 13, 821–830 (2019). https://doi.org/10.1007/s12008-019-00535-0
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DOI: https://doi.org/10.1007/s12008-019-00535-0