Generic placeholder image

Recent Patents on Mechanical Engineering

Author(s): Lili Zhu, Guangxin Wang*, Wenjie He and Wenzhong Fan

DOI: 10.2174/2212797613666200206152545

DownloadDownload PDF Flyer Cite As
Analysis of Contact Strength for Nutation Transmission with Conical Movable Teeth by Fractal Theory

Page: [141 - 155] Pages: 15

  • * (Excluding Mailing and Handling)

Abstract

Background: Nutation transmission with conical movable teeth is a patent about a new type of spacial movable tooth drive that was developed based on the bevel planetary gear drive with a difference in the number of small teeth.

Objective: The aim of this study was to establish the fractal contact model and calculate the contact strength of the center gear in the nutation transmission with conical movable teeth based on the M-B fractal contact theory and also to demonstrate the validity of the present solution by comparing it with the FEM results and the Hertz contact results.

Methods: Based on the fractal theory, the relationship between the loads and the area for the tapered roller teeth in contact with the center disk was obtained, and the four basic parameters were simulated to analyze the effect of the fractal contact model in MATLAB.

Results: The accuracy of the fractal contact model was verified using numerical simulation and analysis of the relationship diagram for the real contact area and load and the contact area ratio chart with different parameters.

Conclusion: Based on the FEM theory, the Hertz elastic contact theory, and the fractal theory, the tooth surface contact strength of the center disk was compared and analyzed, which enabled us to demonstrate the validity of the present solution, and measures were taken to optimize and improve the followup design of the nutation drive.

Keywords: Conical movable teeth, contact strength, finite element analysis, fractal theory, Hertz elastic contact theory, nutation.

[1]
Kedrowski DK, Slimak SP. Nutating gear drive train for a cordless screwdriver. Mech Eng 1994; 1: 70-1.
[2]
Maroth AM. Counterbalanced mechanical speed change mechanism. US3935750 (1976)..
[3]
Robert DL, James ESL. Nutating drive mechanisms having roller driving elements. US4620457 (1986)..
[4]
Mlendini P, Perrone M, Stam S, Barbagelate A, Primavori MD, Appolonia S. Wobbling gears achieve high ratios. ESA 2000; 10(3): 34-7.
[5]
Suzumori K, Hashimoto T, Uzuka K, Enomoto I. Pneumatic direct-drive stepping motor for robots. Intel Robot Syst 2002; 2(5): 2031-6.
[6]
Uzuka K, Enomoto I, Suzumori K. Development of nutation motors (2nd report, development of practical model by the OF type bevel gears and diaphragm). Trans JSME (Part C) 2006; 72(4): 1200-6.
[http://dx.doi.org/10.1299/kikaic.72.1200]
[7]
Uzuka K, Enomoto I, Suzumori K. Development of nutation motors (1st report, driving principle and basic characteristics of pneumatic nutation motor). Trans JSME (Part C) 2006; 72(4): 1194-9.
[http://dx.doi.org/10.1299/kikaic.72.1194]
[8]
Uzuka K, Enomoto I, Suzumori K. Development of nutation motors (4th report, development of small-sized and high torque pneumatic nutation motor by the OFW type bevel gears and principle of lever). Trans JSME (Part C) 2007; 73(6): 1731-7.
[http://dx.doi.org/10.1299/kikaic.72.1194]
[9]
Uzuka K, Enomoto I, Suzumori K, Nagata T. Development of nutation motors (3rd report, development of electromagnetic nutation motor by the OF1 type bevel gears and electromagnets). Trans JSME (Part C) 2007; 73(4): 1188-95.
[http://dx.doi.org/10.1299/kikaic.73.1188]
[10]
Oda S, Suzumori K, Uzuka K, Enomoto I. Development of nutation motors (improvement of pneumatic nutation motor by optimizing diaphragm design). J Mech Sci Technol 2010; 24(1): 25-8.
[http://dx.doi.org/10.1007/s12206-009-1157-y]
[11]
Yamamori M. Nutation gear device, transmission ratio variable mechanism and steering device for vehicle. ZL201010129312 (2010)..
[12]
Zihni BS, Robert CB. Design analysis of pericyclic mechanical transmission system. Mechanism Mach Theory 2013; 61(1): 102-22.
[13]
Wang GX, Guan TM. Modeling of nutation drive with rolling teeth. Appl Mech Mater 2009; 16-19: 708-12.
[http://dx.doi.org/10.4028/www.scientific.net/AMM.16-19.708]
[14]
Wang GX, Li LJ, Guan H, Guan TM. Modeling and simulation for nutation drive with rolling teeth. Adv Mat Res 2012; 538-541: 470-3.
[http://dx.doi.org/10.4028/www.scientific.net/AMR.538-541.470]
[15]
Wang GX, Deng J, Wang P, Li LJ. Meshing principle and dynamic simulation of nutation drive with face-gear. J Dalian Jiaotong Univ 2017; 38(2): 48-54.
[16]
Mark JR, Eric K. Power transmissions having pericyclic motion converters. US9765853 (2015).
[17]
Barbagelata A, Ellero S, Landò R. Planetary gearbox. EP2975296 (2015).
[18]
Mark JR, Eric K. Power transmissions. US20160341282 (2016).
[19]
Johann B. Regenerative drive system. US20180244156 (2018).
[20]
Singleton JC, McCullough DH, Hartz RJ. Nutating-type actuator. US3428839 (1969).
[21]
Foskett RD. Stepping motor with nutating Gear. US3492515 (1970).
[22]
Gong ZX. Space planetary waveguide reducer. Liaoning Jixie 1983; 21(5): 31-3.
[23]
Sun YC. Working principle and design of harmonic bevel gear reducer. Gear J 1984; 8(5): 34-7.
[24]
Yan SY, Zhan Y, He SJ. The internal involute cone gears. J Shenyang Polytech Univ 1986; 8(4): 67-80.
[25]
Mao SM, Wu XT, Yue DQ. A high-performance gear transmission- internally-toothed bevel gear transmission. Heavy Machin 1989; 13(5): 24-8.
[26]
Huo JP, Mao SM, Wu XT. Tooth contact analysis of internal spiral bevel gears cut by full formate method. Mech Transm 1994; 18(2): 4-13.
[27]
Liu HR, Zhou Y, Li GS. Varieties of the offset planetary drive of bevel gear. J Changsha Railway Univ 1997; 15(4): 50-2.
[28]
Liu HR, Li GS. Efficiency analysis and testing of offset planetary drive of bevel gear. J Changsha Railway Univ 1998; 16(3): 44-7.
[29]
Yu YB, Zhu JC, Hu LR. Optimization of internal bevel gear nutation drive. J Hubei Polytech Univ 2000; 15(2): 48-51.
[30]
Yu YB, Zhang JM, Yu WB. Analysis and optimization of gyro moment in nutation drive of bevel differential. Mach Tool Hydraul 2001; 29(6): 32-3.
[31]
Li KQ, Yu YB, Yi J, Gong FY, Hu L. Kinematics analysis of a new planetary bevel gear drive device with small teeth difference and inclined plate. J Hubei Polytech Univ 2002; 17(2): 108-9.
[32]
Jin YL, Wang JJ, Ding JY, Yang SR. Study on the spherical surface cone- cycloid nutation drive 2K-H. Des Res 2006; 56(3): 37-9.
[33]
Huang W. Design and Simulation of nutation gear transmission deceleration mechanism. MSc Dissertation, Kunming University of Science and Technology, Yunnan, PR China, November 2007.
[34]
Zajac TS, George HE. Hydraulic moter. US003675539 (1972).
[35]
Molyneux WG. The internal bevel gear and its applications. Proc Inst Mech Eng G J Aerosp Eng 1997; 211(1): 39-61.
[http://dx.doi.org/10.1243/0954410971532488]
[36]
Nelson CA, Cipra RJ. Similarity and equivalence of nutating mechanisms to bevel epicyclic gear trains for modeling and analysis. J Mech Des 2015; 127(2): 1305-11.
[37]
Nelson CA, Cipra RJ. Simplified kinematic analysis of bevel epicyclic gear trains with application to power-flow and efficiency analyses. J Mech Des 2015; 127(2): 278-86.
[http://dx.doi.org/10.1115/1.1814392]
[38]
Kedrowski DK, Slimak SP. Wobbling gear drive train for cordless screwdriver. Proceedings of the ASME Winter Conference. New Orleans, LA, USA, April,.. 1993.
[39]
Kedrowski DK, Slimak SP. Nutating gear drivetrain for a cordless screwdriver. Mech Eng ASME 1994; 116(1): 70-4.
[40]
Meng XZ. Theoretical and experimental study on nutation gear drive. MSc Dissertation, Northeastern University, PR China, June 1998.
[41]
Litvin FL, Wang AG, Handschuh RF. Computerized generation and simulation of meshing and contact of spiral bevel gears with improved geometry. Comput Methods Appl Mech Eng 1998; 1581(2): 35-64.
[http://dx.doi.org/10.1016/S0045-7825(97)00229-6]
[42]
Litvin FL, Fuentes A, Fan Q, Handschuh RF. Computerized design, simulation of meshing, and contact and stress analysis of face milled formate generated spiral bevel gears. Mechanism Mach Theory 2002; 375: 441-59.
[http://dx.doi.org/10.1016/S0094-114X(01)00086-6]
[43]
Litvin FL, Fuentes A, Hayasaka K. Design, manufacture, stress analysis, and experimental tests of low-noise high endurance helical bevel gears. Mechanism Mach Theory 2006; 41(1): 83-118.
[http://dx.doi.org/10.1016/j.mechmachtheory.2005.03.001]
[44]
Gu B, Yao LG, Wei GW, Cai YJ. The analysis and modeling for nutation drives with double circular-arc helical bevel gears. International Conference on Advanced Manufacture. Taipei, P.R. China. January, 2006..
[http://dx.doi.org/10.4028/0-87849-990-3.949]
[45]
Cai YJ, Yao LG, Gu B. Kinematical and dynamical simulations nutation drive with double circular-arc helical bevel gears. Drive Syst Tech 2007; 21(4): 22-5.
[46]
Yao LG, Gu B, Haung SJ, Wei GW. Mathematical modeling and simulation of the external and internal double circular-arc spiral bevel gears for the nutation drive. J Mech Design T ASME 2010; 132: 1-10.
[http://dx.doi.org/10.1115/1.4001003]
[47]
Lin Z, Yao LG. General mathematical model of internal meshing spiral bevel gears for nutation drive. Appl Mech Mater 2012; 101-102: 708-12.
[http://dx.doi.org/10.4028/www.scientific.net/AMM.101-102.708]
[48]
Lin Z, Yao LG. Mathematical model and 3D modeling of involute spiral bevel gears for nutation drive. Adv Mat Res 2013; 694-697: 503-6.
[http://dx.doi.org/10.4028/www.scientific.net/AMR.694-697.503]
[49]
Lin Z, Yao LG, Lin Q. Contact trace of internal meshing double circular-arc spiral bevel gears. Adv Mat Res 2014; 945-949: 822-5.
[http://dx.doi.org/10.4028/www.scientific.net/AMR.945-949.822]
[50]
Zhang J, Yao LG, Huang SJ, Gu B. Tooth profile accurate modeling of internal and external double circular-arc spiral bevel gears. Mod Manuf Eng 2015; 1: 119-24.
[51]
Tao JW, Yao LG, Zhang J. Mathematical modeling and characteristics analysis for the nutation gear drive based on error parameters. J Chongqing Univ 2016; 15(4): 149-58.
[52]
Cai YJ, Yao LG. Comparison analysis and verification on spur and helical three-lobe rotors with novel tooth profile in roots blower. 2016 2nd International Conference on Mechanical, Electronic and Information Technology Engineering. Chongqing, PR China. May, 2016.
[53]
Cai YW, Yao LG, Xie ZY, Zhang J. Influence analysis of system parameters on characteristics of the nutation drive with double circular arc spiral bevel gears. Forsch Ingenieurwes 2017; 81(2-3): 125-33.
[http://dx.doi.org/10.1007/s10010-017-0245-x]
[54]
Fanghella P, Bruzzone L, Ellero S. Dynamic balancing of a nutating planetary bevel gear train. Proceedings of the MUSME Conference. Huatulco, Mexico. October,. 2014.
[55]
Fanghella P, Bruzzone L, Ellero S, Lando R. Kinematics, efficiency and dynamic balancing of a planetary gear train based on nutating bevel gears. Mech Based Des Struc 2016; 44(1-2): 72-85.
[http://dx.doi.org/10.1080/15397734.2015.1047956]
[56]
Qu JF. Theory of Movable Tooth Transmission. China Machine Press: Beijing, P.R. China 1993.
[57]
Qu JF, An ZJ. Research on zero clearance cycloid ball transmission. Chin J Mech Eng 1994; 7(1): 17-23.
[58]
An ZJ, Qu ZG. No reverse error ball transmission and force analysis on hetero type single cycloid. Chin J Mech Eng 1996; (1): 16-20.
[59]
Hyun DC. A study on CAD application for design and machining of ball reducer. J Korean Soc Manuf Proc Eng 2004; 3(2): 44-52.
[60]
Zhou JJ, Chen ZC. Study and performance test of full complement cycloid ball reducer with ceramic balls as its gear teeth. Chin J Aeronauti 2001; 14(4): 245-51.
[61]
Wang GX, Zhu LL. Mechanism of nutation drive with movable taper teeth. CN200510078247.6 2005.
[62]
Wang GX, Zhu LL, Li LJ, He WJ. Design method of center gear teeth of mechanism of nutation drive with movable taper teeth. CN201310123210.5 2013.
[63]
Zhu LL, Wang GX, Fan WZ. Modeling and simulation of the nutation drive with movable taper teeth. Recent Pat Mech Eng 2019; 12: 72-82.
[http://dx.doi.org/10.2174/2212797612666181228124232]
[64]
Majumdar A, Bhushan B. Fractal model of elastic-plastic contact between rough surfaces. ASME J Tribol 1991; 113: 1-11.
[http://dx.doi.org/10.1115/1.2920588]
[65]
Ge SR, Zhu H. Fractal of Tribology. hina Machine Press: Beijing, P.R. China 2005.
[66]
Thomas L, Warren TL, Krajcinovic D. Random cantor set models for the elastic-perfectly plastic contact of rough surface. Wear 1996; 196: 1-15.
[http://dx.doi.org/10.1016/0043-1648(95)06785-X]
[67]
Huang K, Zhao H, Chen Q. Research of fractal contact model on contact carrying capacity of two cylinders’ surface. Tribology 2008; 28(6): 529-33.
[68]
Xu S. Study on the gear face contact model based on the fractal theory MS Dissertation, HeFei University of Technology, P.R. China, . 2008.
[69]
Chen Q, Zhao H, Huang K, Xu S. Application research on gear contact stress analysis by fractal theory. China Mech E 2010; 21(9): 1014-7.
[70]
Wei Z, He JN, Ma WX, Gao Y. The contact strength analysis of double-circular-arc modified cycloid gears based on fractal theory. IEEE International Conference on Oxide Material for Electronic Engineering. Lviv, Ukraine. September, 2012.
[71]
Chen Q, Huang K, Zhang Y, Sun H. Analysis of influence parameters on gear’s contact strength based on fractal contact model. China Mech E 2013; 24(16): 2208-21.
[72]
Zhao H, Wu QL. Application study of fractal theory in mechanical transmission. Chin J Mech Eng 2016; 29(5): 871-9.
[http://dx.doi.org/10.3901/CJME.2016.0818.094]
[73]
Xue PS, Zhu LD. A three-dimensional fractal prediction method for the normal contact stiffness of a bifractal joint surface. CN109446655 (2019)..
[74]
Ge SR. The fractal behavior and fractal characterization of rough surfaces. Tribology 1997; 17(1): 73-80.
[75]
Wang GX. Research on nutation transmission with movable teeth PhD Dissertation, Dalian Jiaotong University, P.R. China, . 2013.
[76]
Majumdar A, Tien CL. Fractal characterization and simulation of rough surfaces. Wear 1990; 136(2): 313-27.
[http://dx.doi.org/10.1016/0043-1648(90)90154-3]
[77]
Luo JW, Zhang JJ. Numerical solution of contact stress of tapered roller bearing. Bearing 2004; 9: 1-3.