As a new type of transmission, the single-roller enveloping hourglass worm gear (SEHWG) is widely used in precision mechanical transmission systems. Time-varying mesh stiffness (TVMS) is one of the most important excitations, which has great influences on the dynamic characteristics of SEHWG systems. In this paper, a model for calculating the TVMS of the SEHWG is proposed, in which bending stiffness, shear stiffness, radial compression stiffness, and foundation stiffness are considered in the worm stiffness calculation. And bending stiffness, shear stiffness, and foundation stiffness are considered in the worm wheel stiffness calculation. The process of calculating the periodical TVMS of the SEHWG is also presented. Then, the TVMS of the SEHWG by the proposed method is compared with that of the finite element method for the model validation. Finally, the influences of the roller radii on TVMS are analyzed. The results show that the mesh stiffness of the TVMS has a tendency to rise first and then fall with the increasing roller radii.
DengXWangJHorstemeyerMFet al.Parametric study of meshing characteristics with respect to different meshing rollers of the antibacklash double-roller enveloping worm gear. J Mech Des2012; 134: 081004–081004.
2.
WanZCaoHZiYet al.An improved time-varying mesh stiffness algorithm and dynamic modeling of gear-rotor system with tooth root crack. Eng Fail Anal2014; 42: 157–177.
3.
MaHZengJFengRet al.Review on dynamics of cracked gear systems. Eng Fail Anal2015; 55: 224–245.
4.
LiangXZuoMJFengZ. Dynamic modeling of gearbox faults: A review. Mech Syst Signal Process2018; 98: 852–876.
5.
MacLennanLD. An analytical method to determine the influence of shape deviation on load distribution and mesh stiffness for spur gears. Proc IMechE, Part C: J Mechanical Engineering Science2002; 216: 1005–1016.
6.
WangJHowardI. Finite element analysis of high contact ratio spur gears in mesh. Trans ASME-F-J Tribol2005; 127: 469–483.
7.
WangJHowardI. The torsional stiffness of involute spur gears. Proc IMechE, Part C: J Mechanical Engineering Science2004; 218: 131–142.
8.
Del RinconAFViaderoFIglesiasMet al.A model for the study of meshing stiffness in spur gear transmissions. Mech Mach Theory2013; 61: 30–58.
9.
LitvinFLFuentesAGonzalez-PerezIet al.New version of Novikov–Wildhaber helical gears: Computerized design, simulation of meshing and stress analysis. Comput Methods Appl Mech Eng2002; 191: 5707–5740.
10.
LinTOuHLiR. A finite element method for 3D static and dynamic contact/impact analysis of gear drives. Comput Methods Appl Mech Eng2007; 196: 1716–1728.
11.
LiS. Effects of misalignment error, tooth modifications and transmitted torque on tooth engagements of a pair of spur gears. Mech Mach Theory2015; 83: 125–136.
SimonV. Stress analysis in double enveloping worm gears by finite element method. J Mech Des Trans ASME1993; 115: 179–185.
14.
ChungMYShawD. Parametric study of dynamics of worm and worm-gear set under suddenly applied rotating angle. J Sound Vib2007; 304: 246–262.
15.
LiangXZuoMJPandeyM. Analytically evaluating the influence of crack on the mesh stiffness of a planetary gear set. Mech Mach Theory2014; 76: 20–38.
16.
ZhouXShaoYLeiYet 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: 011011–011011.
17.
ChaariFFakhfakhTHaddarM. Analytical modelling of spur gear tooth crack and influence on gearmesh stiffness. Eur J Mech A/Solids2009; 28: 461–468.
18.
WalhaLFakhfakhTHaddarM. Nonlinear dynamics of a two-stage gear system with mesh stiffness fluctuation, bearing flexibility and backlash. Mech Mach Theory2009; 44: 1058–1069.
19.
LeiYWangDLiuZet al.A new model for calculating time-varying gearmesh stiffness. J Vibroeng2017, pp. 14–14.
20.
LeiYLiNLinJet al.Two new features for condition monitoring and fault diagnosis of planetary gearboxes. J Vib Control2015; 21: 755–764.
21.
WangQLiZMaHet al.Effects of different coupling models of a helical gear system on vibration characteristics. J Mech Sci Technol2017; 31: 2143–2154.
22.
ChenZZhaiWShaoYet al.Mesh stiffness evaluation of an internal spur gear pair with tooth profile shift. Sci China Technol Sci2016; 59: 1328–1339.
23.
ChenZZhaiWShaoYet al.Analytical model for mesh stiffness calculation of spur gear pair with non-uniformly distributed tooth root crack. Eng Fail Anal2016; 66: 502–514.
24.
YangDCHLinJY. Hertzian damping, tooth friction and bending elasticity in gear impact dynamics. J Mech Transm Autom Des1987; 109: 189–196.
25.
TianX. Dynamic simulation for system response of gearbox including localized gear faults, Canada: Dissertation, University of Alberta Edmonton, 2004.
26.
SainsotPVelexPDuvergerO. Contribution of gear body to tooth deflections-A new bidimensional analytical formula. J Mech Des Trans ASME2004; 126: 748–752.
27.
ChenZShaoY. Dynamic simulation of spur gear with tooth root crack propagating along tooth width and crack depth. Eng Fail Anal2011; 18: 2149–2164.
28.
ChenZShaoY. Mesh stiffness calculation of a spur gear pair with tooth profile modification and tooth root crack. Mech Mach Theory2013; 62: 63–74.
29.
ChenZZhangJZhaiWet al.Improved analytical methods for calculation of gear tooth fillet-foundation stiffness with tooth root crack. Eng Fail Anal2017; 82: 72–81.
30.
MaHSongRPangXet al.Time-varying mesh stiffness calculation of cracked spur gears. Eng Fail Anal2014; 44: 179–194.
31.
WanZCaoHZiYet al.Mesh stiffness calculation using an accumulated integral potential energy method and dynamic analysis of helical gears. Mech Mach Theory2015; 92: 447–463.
32.
WangQHuPZhangYet al.A model to determine mesh characteristics in a gear pair with tooth profile error. Adv Mech Eng2014; 6: 751476–751476.
33.
WangQZhangY. A model for analyzing stiffness and stress in a helical gear pair with tooth profile errors. J Vib Control2017; 23: 272–289.
34.
GuXVelexPSainsotPet al.Analytical investigations on the mesh stiffness function of solid spur and helical gears. J Mech Des2015; 137: 063301–063301.
35.
FalahAHElkholyAH. Load and stress analysis of cylindrical worm gearing using tooth slicing method. Trans Can Soc Mech Eng2006; 30: 97–111.
36.
FalahAHElkholyAH. Load sharing and stress analysis of single enveloping worm gearing considering transmission errors. Int J Adv Manuf Technol2008; 37: 211–220.
