The calculation of time-varying meshing stiffness caused by the alternate contacting of the gear tooth is an essential prerequisite to obtain real and effective nonlinear dynamic characteristics of the transmission system, so that the significance of which cannot be overemphasized. Accordingly, this work proposes an improved method to get meshing stiffness with taking fillet-foundation and gear rim deflection into consideration. Compared to the traditional potential energy method, the proposed method has more superior accuracy and performance, and its effectiveness has been further verified by the finite element analytical model. After that, an ideal eight degree of freedoms (DOFs) dynamic model of one stage mass-spring-damper involute spur gear, including lateral and torsional motions, is established to study the dynamic characteristics. Due to the complexity of the gear system operating conditions, we also investigate the influence of various parameters including hub bore radius, transmitting load, and rotation speed on dynamic features, especially in heavy-load and high-speed conditions. From the results, it can be concluded that these parameters will play a prominent role in the spur gear pair dynamic behaviors, providing a certain guidance for gear design.
OuyangTCHuangHZZhouXR, et al. A finite line contact tribo-dynamic model of a spur gear pair. Tribol Int2018; 119: 753–765.
2.
ChenZGShaoYM.Dynamic simulation of spur gear with tooth root crack propagating along tooth width and crack depth. Eng Fail Anal2011; 18: 2149–2164.
3.
ChenZGShaoYM.Mesh stiffness calculation of a spur gear pair with tooth profile modification and tooth root crack. Mech Mach Theory2013; 62: 63–74.
4.
BrancatiRRoccaERussoR.A gear rattle model accounting for oil squeeze between the meshing gear teeth. Proc IMechE, Part D: J Automobile Engineering2005; 219: 1075–1083.
LiangXHZhangHSZuoMJ, et al. Three new models for evaluation of standard involute spur gear mesh stiffness. Mech Syst Signal Process2018; 101: 424–434.
7.
MaHSongRPangX, et al. Time-varying mesh stiffness calculation of cracked spur gears. Eng Fail Anal2014; 44: 179–194.
8.
XieCYHuaLLanJ, et al. Improved analytical models for mesh stiffness and load sharing ratio of spur gears considering structure coupling effect. Mech Syst Signal Process2018; 111: 331–347.
9.
TheodossiadesSGnanakumarrMRahnejatH, et al. Effect of a dual-mass flywheel on the impact-induced noise in vehicular powertrain systems. Proc IMechE, Part D: J Automobile Engineering2006; 220: 747–761.
10.
MaHZengJFengRJ, et al. An improved analytical method for mesh stiffness calculation of spur gears with tip relief. Mech Mach Theory2016; 98: 64–80.
11.
KarpatFYuceCDoğanO.Experimental measurement and numerical validation of single tooth stiffness for involute spur gears. Measurement2020; 150: 107043.
12.
YılmazTGDoğanOKarpatF.A comparative numerical study of forged bi-metal gears: bending strength and dynamic response. Mech Mach Theory2019; 141: 117–135.
13.
HaslCLiuHOsterP, et al. Method for calculating the tooth root stress of plastic spur gears meshing with steel gears under consideration of deflection-induced load sharing. Mech Mach Theory2017; 111: 152–163.
14.
OuyangTCHuangHZZhangN, et al. A model to predict tribo-dynamic performance of a spur gear pair. Tribol Int2017; 116: 449–459.
15.
YangYCaoLYLiH, et al. Nonlinear dynamic response of a spur gear pair based on the modeling of periodic mesh stiffness and static transmission error. Appl Math Model2019; 72: 444–469.
16.
MunroRGPalmerDMorrishL.An experimental method to measure gear tooth stiffness throughout and beyond the path of contact. Proc IMechE, Part C: J Mechanical Engineering Science2001; 215: 793–803.
17.
RaghuwanshiNKPareyA.Experimental measurement of gear mesh stiffness of cracked spur gear by strain gauge technique. Measurement2016; 86: 266–275.
18.
PandyaYPareyA.Experimental investigation of spur gear tooth mesh stiffness in the presence of crack using photo elasticity technique. Eng Fail Anal2013; 34: 488–500.
19.
LinTJOuHLiRF.A finite element method for 3D static and dynamic contact/impact analysis of gear drives. Comput Methods Appl Mech Eng2007; 196: 1716–1728.
20.
PandyaYPareyA.Failure path based modified gear mesh stiffness for spur gear pair with tooth root crack. Eng Fail Anal2013; 27: 286–296.
21.
ChenTYWangYXChenZG.A novel distribution model of multiple teeth pits for evaluating time-varying mesh stiffness of external spur gears. Mech Syst Signal Process2019; 129: 479–501.
22.
MaHYangJSongRZ, et al. Effects of tip relief on vibration responses of a geared rotor system. Proc IMechE, Part C: J Mechanical Engineering Science2014; 228: 1132–1154.
23.
OuyangTCHuangGCChenJX, et al. Investigation of lubricating and dynamic performances for high-speed spur gear based on tribo-dynamic theory. Tribol Int2019; 136: 421–431.
24.
ChenKKHuangfuYFMaH, et al. Calculation of mesh stiffness of spur gears considering complex foundation types and crack propagation paths. Mech Syst Signal Process2019; 130: 273–292.
25.
CornellRW.Compliance and stress sensitivity of spur gear teeth. J Mech Des1981; 103: 447–459.
26.
YangDCHLinJY. Hertzian damping, tooth friction and bending elasticity in gear impact dynamics. J Mech Des1987; 109: 189–196.
27.
TianXH.Dynamic simulation for system response of gearbox including localized gear faults. Edmonton: University of Alberta, 2004.
28.
WuSYZuoMJPareyA.Simulation of spur gear dynamics and estimation of fault growth. J Sound Vib2008; 317: 608–624.
29.
WuSY.Gearbox dynamic simulation and estimation of fault growth. Edmonton: University of Alberta, 2007.
30.
SainsotPVelexPDuvergerO.Contribution of gear body to tooth deflections—a new bi dimensional analytical formula. J Mech Des2004; 126: 748–752.
31.
ChaariFBaccarWAbbesMS, et al. Effect of spalling or tooth breakage on gear mesh stiffness and dynamic response of a one-stage spur gear transmission. Eur J Mech A/Solids2008; 27: 691–705.
32.
ChaariFFakhfakhTHaddarM.Analytical modelling of spur gear tooth crack and influence on gearmesh stiffness. Eur J Mech A/Solids2009; 28: 461–468.
33.
ZhouXJShaoYMLeiYG, et al. Time-varying meshing stiffness calculation and vibration analysis for a 16DOF dynamic model with linear crack growth in a pinion. J Vib Acoust2012; 134: 1–11.
34.
LiangXHZuoMJPandeyM.Analytically evaluating the influence of crack on the mesh stiffness of a planetary gear set. Mech Mach Theory2014; 76: 20–38.
35.
LiangXHZuoMJHoseiniMR.Vibration signal modeling of a planetary gear set for tooth crack detection. Eng Fail Anal2015; 48: 185–200.
36.
SaxenaAChoukseyMPareyA.Effect of mesh stiffness of healthy and cracked gear tooth on modal and frequency response characteristics of geared rotor system. Mech Mach Theory2017; 107: 261−273.
37.
YangYXiaWKHanJM, et al. Vibration analysis for tooth crack detection in a spur gear system with clearance nonlinearity. Int J Mech Sci2019; 157−158: 648−661.
38.
YuWNMechefskeCKTimuskM.Influence of the addendum modification on spur gear back-side mesh stiffness and dynamics. J Sound Vib2017; 389: 183–201.
39.
YangXQDingKHeGL.Phenomenon-model-based AM-FM vibration mechanism of faulty spur gear. Mech Syst Signal Process2019; 134: 106366.
40.
KunduPDarpeAKKulkarniMS.A correlation coefficient based vibration indicator for detecting natural pitting progression in spur gears. Mech Syst Signal Process2019; 129: 741–763.
41.
PatilVChouhanVPandyaY.Geometrical complexity and crack trajectory based fatigue life prediction for a spur gear having tooth root crack. Eng Fail Anal2019; 105: 444–465.
42.
HeHFLiuHJZhuCC, et al. Study on the gear fatigue behavior considering the effect of residual stress based on the continuum damage approach. Eng Fail Anal2019; 104: 531–544.
43.
XiaoZLZhouCJLiZD, et al. Thermo-mechanical characteristics of high-speed and heavy-load modified gears with elasto-hydrodynamic contacts. Tribol Int2019; 131: 406–414.
44.
XiaoWQChenZWPanTL, et al. Research on the impact of surface properties of particle on damping effect in gear transmission under high speed and heavy load. Mech Syst Signal Process2018; 98: 1116–1131.
45.
HongIJKahramanAAndersonN.A rotating gear test methodology for evaluation of high-cycle tooth bending fatigue lives under fully reversed and fully released loading conditions. Internal J Fatigue2020; 133: 105432.
