Theoretical derivation and analysis of strength calculation formulas of internal gear pair with double contact points

Abstract

To describing the strength conditions of tooth surfaces of internal gear pair with double contact points (IGPDCP) accurately, theoretical calculation method of the strength of tooth surfaces is proposed in this paper. Theoretical derivation and analysis of strength calculation formulas of the IGPDCP drive are carried out. For contact strength analysis, based on Hertz point contact theory, general calculation idea of contact strength is provided. The main curvature of the active contact line on tooth surfaces of the pinion and internal gear are derived, respectively. Furtherly, according to theoretical calculation and derivation, the formula for calculating the contact strength of the IGPDCP drive is obtained. Orthogonal test method is used to derive the calculation formula of bending strength of the IGPDCP drive, considering test factors include the modulus, tooth number of gear, transmission ratio, helix angle, contact angle, pressure angle, and torque. Nonlinear regression equations of bending stress of the pinion and internal gear are derived, respectively. The discussion of results of contact and bending strength between formula calculation and finite element analysis are present. The conclusions show that the proposed formulas can satisfy theoretical analysis and engineering application.

Keywords

Internal gear pair with double contact points contact strength bending strength calculation formula finite element analysis

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References

Singh

Kahraman

Ligata

. Internal gear strains and load sharing in planetary transmissions: model and experiments. J Mech Des 2008; 130(7): 917–928.

Tavassoli

Poursina

. An analytical determining the internal ring gear rim stiffness for practical purpose. J Mech Sci Technol 2021; 35(10): 4617–4625.

Ghosh

Chakraborty

. On optimal tooth profile modification for reduction of vibration and noise in spur gear pairs. Mech Mach Theory 2016; 105: 145–163.

Litvin

Kim

. Computerized design, generation and simulation of meshing of modified involute spur gears with localized bearing contact and reduced level of transmission errors. J Mech Des 1997; 119: 96–100.

Litvin

Fuents

. Gear geometry and applied theory. Cambridge: Cambridge University Press, 2004, pp.304–314.

Yang

. Study on an internal gear with asymmetric involute teeth. Mech Mach Theory 2007; 42(8): 977–994.

Choi

Kim

Lee

, et al. Design of rotor for internal gear pump using cycloid and circular-arc curves. J Mech Des 2012; 134(1): 011005-1–011005-12.

Lee

. Design and meshing analysis of a non-involute internal gear for counters. J Korean Soc Tribologists Lubrication Eng 2014; 30(4): 212–217.

Kim

Lee

Jung

, et al. Development of rotor for internal gear pump using cycloid and polycircular-arc curves. J Korean Soc Precis Eng 2012; 29(9): 1003–1011.

10.

Wang

Ren

. Design and manufacturing of a novel high contact ratio internal gear with a circular arc contact path. Int J Mech Sci 2019; 153-154: 143–153.

11.

Chen

Lei

Zeng

, et al. Computerized design, simulation of meshing and stress analysis of pure rolling internal helical gear drives with combined tooth profiles. Mech Mach Theory 2022; 176: 104959-1-104959-20.

12.

Song

Yang

, et al. Parameter design of double-circular-arc tooth profile and its influence on meshing characteristics of harmonic drive. Mech Mach Theory 2022; 167(4): 104567-1-104567-19.

13.

Peng

Chen

Liang

, et al. Mathematical model and tooth contact analysis of an internal helical gear pair with selectable contact path. Int J Precis Eng Manuf 2018; 19(6): 837–848.

14.

Liang

Meng

Gao

. Design principle and meshing analysis of internal gear drive with three contact points. Adv Mech Eng 2022; 14(2): 1658–1676.

15.

Sánchez

Pleguezuelos

Pedrero

. Strength model for bending and pitting calculations of internal spur gears. Mech Mach Theory 2019; 133: 691–705.

16.

Chen

Shao

. Mesh stiffness of an internal spur gear pair with ring gear rim deformation. Mech Mach Theory 2013; 69(11): 1–12.

17.

Tsai

. Integrated mathematical approach for design and manufacturing of power-skiving tool for interference-free involute internal gear cutting. Mech Mach Theory 2023; 180(2): 105172-1-105172-19.

18.

Chen

Song

Zhu

, et al. Manufacturing and contact characteristics analysis of internal straight beveloid gear pair. Mech Mach Theory 2017; 114(8): 60–73.

19.

Han

Zhang

. Investigation on formation mechanism of surface texture and modeling of surface roughness with internal gear power honing. Int J Adv Manuf Technol 2018; 98: 603–615.

20.

Liang

, ZW, Chen

, et al. Mathematical model and deviation analysis of machining cutters for internal gears with double contact points. Proc IMechE, Part C: J Mechanical Engineering Science 2023; 237(13): 3103–3114.

21.

Liang

Jiang

, et al. Optimization design and analysis of internal gear transmission with double contact points. Proc IMechE, Part C: J Mechanical Engineering Science 2023; 237: 5788–5798.

22.

Pleguezuelos

Pedrero

Sanchez

. Load Sharing and contact stress calculation of high contact ratio internal spur gears. In: Flores

(ed.) New trends in mechanism and machine science, Springer: Cham, Switzerland, vol. 24, 2015, pp.771–778.

23.

Sánchez

Pleguezuelos

Pedrero

. Calculation of tooth bending strength and surface durability of internal spur gear drives. Mech Mach Theory 2016; 95(1): 102–113.

24.

Cui

. Meshing stress analysis of straight conjugate internal gear pair. Mech Eng Autom 2015; 188(1): 56–58. (in Chinese)

25.

Johnson

. Contact mechanics. New York: Cambridge University Press, 1985, pp.84–90.