Open Journal Systems

Developments and progresses of meshing theory for gearing

Yaping Zhao, Jiayue Ma

Article ID: 2290
Vol 1, Issue 1, 2023

DOI: https://doi.org/10.54517/mss.v1i1.2290
VIEWS - 79 (Abstract)

Abstract

Gear drive dominates in mechanical transmissions and has comprehensive advantages of high precision, high efficiency, high reliability, long life and the ability to realize large drive ratios. The main purpose of this article is to review research development in meshing theory, which involves the meshing theory of the one degree-of-freedom (1DOF) line-conjugate tooth surface couple, the 1DOF point-conjugate tooth surface couple and the two degree-of freedom (2DOF) conjugate tooth surface couple. Some compendious discussions are made on the significant results and progresses in meshing theory developments of gearing.

Keywords

gear drive; meshing theory; research developments and progresses

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References

1. Radzevich SP. Theory of Gearing: Kinematics, Geometry, and Synthesis. CRC Press; 2012.

2. Litvin FL. Development of Gear Technology and Theory of Gearing. NASA Reference Publication; 1997.

3. Litvin FL, Fuentes A. Gear Geometry and Applied Theory, 2nd ed. Cambridge University Press; 2011.

4. Willis R. Principles of Mechanism. Pitt Press; 1841.

5. Dudley DW, Poritsky H. On cutting and hobbing gears and worms. Journal of Applied Mechanics 1943; 3-4: 139-146. doi: 101115/1.4009283

6. Poritsky H. Stresses and deflections of cylindrical bodies in contact with application to contact of gears and of locomotive wheels. Journal of Applied Mechanics 1950; 17: 191-201. doi: 10.1115/1.4010099

7. Litvin FL. Theory of Gearing, 2nd ed (Russian). Nauka; 1968.

8. Litvin FL. Theory of Gearing. NASA reference publication 1212; 1989.

9. Litvin FL, Fuentes A, Demenego A, et al. New developments in the design and generation of gear drives. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 2001; 215(7): 747-757. doi: 10.1243/0954406011524117

10. Gear Meshing Research Group, Department of Mathematics, Nankai University. Mathematical basis of gear meshing theory, part Ⅰ (Chinese). Gearing 1977; 2: 5-15. doi: 10.16578/j.issn.1004.2539.1977.02.002

11. Gear Meshing Research Group, Department of Mathematics, Nankai University. Mathematical basis of gear meshing theory, part Ⅱ (Chinese). Gearing 1977; 3: 35-54. doi: 10.16578/j.issn.1004.2539.1977.03.004

12. Gear Meshing Research Group, Department of Mathematics, Nankai University. Mathematical basis of gear meshing theory, part Ⅲ (Chinese). Acta Mathematicae Applicatae Sinica 1976; 2: 84-88.

13. Yan ZD. Mathematical basis of gear meshing theory, part Ⅳ (Chinese). Acta Mathematicae Applicatae Sinica 1980; 3: 195-203.

14. Wu DR, Luo JS. Meshing Theory for Gear Drives (Chinese). Science Press; 1985.

15. Zhao YP, Su DZ, Wei WJ, et al. Lubrication characteristics of dual-tori double-enveloping toroidal worm drive. Tribology Transactions 2010; 53(2): 266-273. doi: 10.1080/10402000903312349

16. Zhao YP, Su DZ, Zhang Z. Meshing analysis and technological parameters selection of dual tori double-enveloping toroidal worm drive. Mechanism and Machine Theory 2010; 45: 1269-1285. doi: 10.1016/j.mechmachtheory.2010.04.004

17. Mu SB, Zhao YP, Zhang X. Meshing theory of involute worm drive. Mechanism and Machine Theory 2021; 165: 1-23. doi: 10.1016/j.mechmachtheory.2021.104425

18. Zhu XY, Zhao YP, Chi YF, et al. Manufacturing principle and meshing limit line of toroidal surface enveloping cylindrical worm drive with arc toothed worm. International Journal of Precision Engineering and Manufacturing 2022; 23: 319-332. doi: 10.1007/s12541-022-00618-1

19. Huai CF, Zhao YP. Meshing theory and tooth profile geometry of toroidal surface enveloping conical worm drive. Mechanism and Machine Theory 2021; 165: 1-23. doi: 10.1016/j.mechmachtheory.2019.01.006

20. Zhao YP. Engineering Differential Geometry of Curves and Surfaces (Chinese). China Science Publishing; 2023.

21. Litvin FL, Kin V. Computerized simulation of meshing and bearing contact for single-enveloping worm-gear drives. ASME Journal of Mechanical Design 1992; 114(2): 313-316. doi: 10.1115/1.2916948

22. Zhao YP, Kong JY, Li GF, et al. Computerized simulation of tooth contact and error sensitivity investigation for ease-off hourglass worm drives. Computer-Aided Design 2012; 44(8): 778-790. doi: 10.1016/j.cad.2012.03.010

23. Meng QX, Zhao YP, Yang ZY, et al. Meshing theory and error sensitivity of mismatched conical surface enveloping conical worm pair. Mechanism and Machine Theory 2020; 145: 1-33. doi: 10.1016/j.mechmachtheory.2019.103681

24. Meng QX, Zhao YP, Cui J, et al. Kinematics of point-conjugate tooth surface couple and its application in mixed mismatched conical worm drive. Mechanism and Machine Theory 2022; 167: 1-30. doi: 10.1016/j.mechmachtheory.2021.104528

25. Chi YF, Zhao YP, Zhu XY, et al. Geometry, kinematics and synthesis of abnormal hourglass worm gearing with centering bearing contact and lower error sensitivity. Mechanism and Machine Theory 2022; 178: 1-24. doi: 10.1016/j.mechmachtheory.2022.105089

26. Chi YF, Zhao YP, Zhu XY, et al. Mismatched gearing composed of hourglass worm and spur gear: Meshing theory, tooth contact simulation, comprehensive design. Mechanism and Machine Theory 2022; 174: 1-23. doi: 10.1016/j.mechmachtheory.2022.104883

27. Litvin FL, Krylov NN, Erikhov ML. Generation of Tooth Surfaces by Two-Parameter Enveloping. Mechanism and Machine Theory 1975; 10(5): 365–373. doi: 10.1016/0094-114X(75)90036-1

28. Gao YT, Li HM. Theory of Conjugate Surface with Two-parameter (Chinese). Journal of Harbin Institute of Technology 1989; 20(4): 66-76. doi: HEBX.0.1989-04-011

29. Zhao YP, Wei WJ, Dong XZ. Some problems on the 2DOF theory of gearing. Mechanism and Machine Theory 2008; 43: 1024-1037. doi: 10.1016/j.mechmachtheory.2007.07.002

30. Dong XZ, Li HT, Wei WJ. Gear meshing theory and application with two degrees of freedom (Chinese). China Machine Press; 2011.

31. Dong XZ. Research on gear meshing with two degrees of freedom, part Ⅰ (Chinese). Gearing 1990; 4: 1-6,42. doi: 10.16578/j.issn.1004.2539.1990.04.002

32. Dong XZ. Research on gear meshing with two degrees of freedom, part Ⅱ (Chinese). Gearing 1991; 1: 1-6. doi: 10.16578/j.issn.1004.2539.1991.01.001

33. Zhao YP, Su D, Wei WJ, et al. A meshing principle for generating a cylindrical gear using an Archimedes hob with two degrees of freedom. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 2010; 224(1): 169-181. doi: 10.1243/09544062JMES1535