With the development of gear transmission to high speed and heavy load, the effect of temperature rise on gear transmission system cannot be ignored. In this paper, the thermal deformation and time-varying thermal stiffness of spur gear are derived under steady-state temperature field by considering the material characteristics and real tooth profile. The rules of thermal deformation and non-involute errors at different temperatures are summarized. A dynamic model of two-stage gear system considering temperature is established. The numerical method is used to solve this model, carrying out experiments to verify the reasonability of the model. The vibration response characteristics of two-stage gear under different temperature and rotational speeds are analyzed. The results show that the effect of temperature on meshing stiffness is more obvious in double tooth meshing region. The temperature rise highlights the main periodic characteristics of the vibration. The effect of temperature on vibration strength is closely related to rotational speed.
BlokH (1937) Theoretical study of temperature rise at surfaces of actual contact under oiliness lubrication conditions. Proceedings - Institution of Mechanical Engineers1(2): 14–20.
2.
DongNZhouJTongR, et al. (2023) Study on the coupling relationship between wear and dynamics under steady uniform temperature field of planetary gear system. Journal of Mechanical Science and Technology37(12): 6405–6428, Seoul: Korean Soc Mechanical Engineers.
3.
GB/T 11348.2:2012 (2012) Measure and evaluate the vibration of the machine on the rotating shaft. Part 2: steam turbines and generators installed on land.
4.
GB/T 19936.1:2005 (2005) Gear FZG test procedure. Part 1: FZG test method A/8.3/90 for relative gluing load bearing capacity of oils.
5.
GouXZhuLQiC (2017) Nonlinear dynamic model of a gear-rotor-bearing system considering the flash temperature. Journal of Sound and Vibration410: 187–208, London: Academic Press Ltd- Elsevier Science Ltd.
6.
HeYYangH (2023a) Analytical model of gear thermal stiffness based on the potential energy method. Applied Sciences13(6): 3599, Basel: MDPI.
7.
HeYYangH (2023b) Novel meshing stiffness model for spur gear pairs considering the temperature effect. Mechanics29(4): 274–284, Kaunas: Kaunas Univ Technol.
8.
HoehnBRMichaelisKOttoHP (2006) Influence of immersion depth of dip lubricated gears on power loss, bulk temperature and scuffing load carrying capacity. In: DatongQBingkuiCChaoL (eds) Proceedings of the international conference on mechanical transmissions, Vols 1 and 2, 30 July 2007; Science Press Beijing, China, 837–845. https://webofscience.clarivate.cn/wos/alldb/full-record/WOS:000245459700166(accessed 2 December 2024).
9.
HöhnBRMichaelisK (2004) Influence of oil temperature on gear failures. Tribology International37(2): 103–109, Oxford: Elsevier Sci Ltd.
10.
HuBZhouCWangH, et al. (2021) Nonlinear tribo-dynamic model and experimental verification of a spur gear drive under loss-of-lubrication condition. Mechanical Systems and Signal Processing153: 107509, London: Academic Press Ltd- Elsevier Science Ltd.
11.
KalinMKupecA (2017) The dominant effect of temperature on the fatigue behaviour of polymer gears. Wear376–377: 1339–1346, 21st International Conference on Wear of Materials.
12.
LetzelterEGuingandMVaujanyJ-P, et al. (2010) A new experimental approach for measuring thermal behaviour in the case of nylon 6/6 cylindrical gears. Polymer Testing29(8): 1041–1051.
13.
LiWZhaiPDingL (2019) Analysis of thermal characteristic of spur/helica gear transmission. Journal of Thermal Science and Engineering Applications11(2): 021003, New York: Asme.
14.
LiuHYanPGaoP (2020) Effects of temperature on the time-varying mesh stiffness, vibration response, and support force of a multi-stage planetary gear. Journal of Vibration and Acoustics142(5): 051110, New York: Asme.
15.
LuoBLiWFuC, et al. (2020) Investigation of the thermal stiffness and thermal tooth profile modification of spur gears. Journal of the Brazilian Society of Mechanical Sciences and Engineering42(4): 150, Heidelberg: Springer Heidelberg.
16.
MaHLiZFengM, et al. (2016) Time-varying mesh stiffness calculation of spur gears with spalling defect. Engineering Failure Analysis66: 166–176, Oxford: Pergamon-Elsevier Science Ltd.
17.
MaoK (2007) A numerical method for polymer composite gear flash temperature prediction. Wear262(11–12): 1321–1329, Lausanne: Elsevier Science Sa.
18.
MarafonaJDMMarquesPMTMartinsRC, et al. (2021) Mesh stiffness models for cylindrical gears: a detailed review. Mechanism and Machine Theory166: 104472, Oxford: Pergamon-Elsevier Science Ltd.
19.
ParkCIL (2020) Dynamic behavior of the spur gear system with time varying stiffness by gear positions in the backlash. Journal of Mechanical Science and Technology34(2): 565–572, Seoul: Korean Soc Mechanical Engineers.
20.
Roda-CasanovaVGonzalez-PerezI (2021) Investigation of the effect of contact pattern design on the mechanical and thermal behaviors of plastic‐steel helical gear drives. Mechanism and Machine Theory164: 104401.
21.
ShiJ-FGouX-FZhuL-Y (2020) Calculation of time-varying backlash for an involute spur gear. Mechanism and Machine Theory152: 103956, Oxford: Pergamon-Elsevier Science Ltd.
22.
SunZChenSHuZ, et al. (2022a) Analytical models for thermal deformation and mesh stiffness of spur gears under steady temperature field. Engineering Failure Analysis133: 105972.
23.
SunZChenSTaoX, et al. (2022b) Research on dynamic characteristics of gear system considering the influence of temperature on material performance. Journal of Vibration and Control28(13–14): 1792–1803, London: SAGE Publications Ltd.
24.
SunZChenSHuZ, et al. (2022c) Vibration response analysis of a gear-rotor-bearing system considering steady-state temperature. Nonlinear Dynamics107(1): 477–493, Dordrecht: Springer.
25.
Townsend (1980) Analytical and experimental spur gear tooth temperature as affected by operating variables. ASME J. Mech103(1): 219–226.
26.
VanH (1947) Continuous as against intermittent fling-off cooling of gear teeth. Journal of Lubrication Technology96(4): 529–538.
27.
WangC (2019) A calculation method of thermal deformation for double helical gear. Mechanics & Industry20(6): 612, Les Ulis Cedex A: Edp Sciences S A.
28.
WangZPuWZhangY, et al. (2020) Transient behaviors of friction, temperature and fatigue in different contact trajectories for spiral bevel gears. Tribology International141: 105965.
29.
WangJShanZChenS (2022) Nonlinear dynamics analysis of multifactor low-speed heavy-load gear system with temperature effect considered. Nonlinear Dynamics110(1): 257–279, Dordrecht: Springer.
30.
XieCHuaLHanX, et al. (2018) Analytical formulas for gear body-induced tooth deflections of spur gears considering structure coupling effect. International Journal of Mechanical Sciences148: 174–190, Oxford: Pergamon-Elsevier Science Ltd.
31.
YazdaniMSoteriouMCSunF, et al. (2015) Prediction of the thermo-fluids of gearbox systems. International Journal of Heat and Mass Transfer81: 337–346.
32.
ZhouY (2020) Nonlinear dynamic analysis of a multi-degree-of-freedom gear system based on temperature effect. Modern Manufacturing Engineering5: 1–8.
33.
ZhouCPanLXuJ, et al. (2017) Non-Newtonian thermal elastohydrodynamic lubrication in point contact for a crowned herringbone gear drive. Tribology International116: 470–481, Oxford: Elsevier Sci Ltd.
