In the fields of high-end equipment such as aero engines and precision transmission systems, gear transmission needs to balance lightweight and high precision to meet the requirements of efficient and reliable operation under harsh working conditions. The gear meshing stiffness is regarded as one of the most critical system parameters in gear transmission systems, and higher gear meshing stiffness can more accurately transmit force. Therefore, based on the principle of load transfer contact analysis (LTCA), this paper constructs a calculation method for the meshing stiffness of laminated composite gears. Compared with the finite element simulation results, the verification error is about 5%, which confirms the effectiveness of this method. The paper systematically explores the influences of carbon nanotube (CNT) distribution patterns (X, O, U-shaped), mass fraction, aspect ratio, and reinforcement radius on the time-varying meshing stiffness. This paper can provide parameter optimization basis for the stiffness control of composite gears, lightweight and high-precision design of transmission systems, and contribute to the performance upgrade of equipment in aerospace and other fields, promoting the engineering application of advanced composite materials in precision transmission components.
ThomaneckPTerlauMEberlR, et al. In-process analysis of the dynamic deformation of a bionic lightweight gear. Mech Syst Signal Process2025; 228: 112446.
2.
LiTTangJHuZ, et al. Development and validation of a semi-analytical timoshenko-based model for resonance analysis in lightweight gear systems. J Sound Vib2025; 605: 119001.
3.
HaoDDong-boZZe-XuC, et al. Optimization design of load-sharing and light weight of the twin rotors concentric face gear power-split transmission system based on gear tooth matching condition. Proc Inst Mech Eng Part C: J Mech Eng Sci2024; 238(12): 6018–6041.
4.
XiaoZYanBHuB, et al. The enhanced mesh stiffness model and tribo-dynamics of cracked spur gears considering mixed lubrication contacts and irregular crack propagation. Eng Fract Mech2025; 326: 111427.
5.
SunZTangJChenS, et al. Mesh stiffness and dynamic response analysis of modified gear system with thin web and weight reduction holes. J Sound Vib2023; 546: 117437.
6.
PedreroJISánchezMBPleguezuelosM. Analytical model of meshing stiffness, load sharing, and transmission error for internal spur gears with profile modification. Mech Mach Theory2024; 197: 105650.
7.
TalakeshAHadian JaziSAriaeiA, et al. A new mesh stiffness determination method in a straight bevel gear system through experimental modal analysis and metaheuristic algorithms. Measurement2024; 238: 115352.
8.
ChuXShangZDongS. Tooth profile design and meshing characteristics analysis of internal meshing gears based on variable center meshing line. Proc Inst Mech Eng Part C: J Mech Eng Sci2024; 238(16): 8542–8560.
9.
HuJHuNZhangL, et al. Vibration signal modeling of planetary gearbox based on dynamics and finite element method for tooth crack diagnosis. Adv Mech Eng2022; 14(7): 16878132221114720.
10.
WangXYangYLuJ, et al. Comparison of meshing characteristics and dynamic behavior of hypoid gear drive under different load conditions. Adv Mech Eng2024; 16(12): 16878132241261471.
11.
YuXSunYLiH, et al. An improved meshing stiffness calculation algorithm for gear pair involving fractal contact stiffness based on dynamic contact force. Eur J Mech2022; 94: 104595.
12.
HuXLiuXZhangD, et al. An improved time-varying mesh stiffness calculation method and dynamic characteristic analysis for helical gears under variable torque conditions. Adv Mech Eng2023; 15(10): 16878132231203132.
13.
MoSWangLLiuM, et al. Study of the time-varying mesh stiffness of two-stage planetary gear train considering tooth surface wear. Proc Inst Mech Eng Part C: J Mech Eng Sci2024; 238(1): 279–297.
14.
LinTChenMYangJ. Calculation method of time-varying meshing stiffness of herringbone gear pair with tooth profile modification. J Vib Shock2021; 40(09): 175–183.
15.
LiuZWangHLuF, et al. A new fast calculating method for meshing stiffness of faulty gears based on loaded tooth contact analysis. Processes2023; 11(7): 2003.
16.
FlekJKarasTDubM, et al. Experimental identification of gear mesh stiffness and verification by theoretical models. Manuf Technol2024; 24(4): 552–566.
17.
RaghuwanshiNKPareyA. Mesh stiffness measurement of cracked spur gear by photoelasticity technique. Measurement2015; 73: 439–452.
18.
PandyaYPareyA. Experimental investigation of spur gear tooth mesh stiffness in the presence of crack using photoelasticity technique. Eng Fail Anal2013; 34: 488–500.
19.
ZhengSChenMZhangL, et al. Effects of spontaneous foaming methods on the mechanical, thermal insulation, and pore expansion behavior of phosphogypsum-based composite cementitious materials. J Build Eng2025; 111: 113228.
20.
ZhangYYanJRenZ, et al. Molecular dynamics simulation of thermal properties and morphological stability of biochar-based composite phase change materials. Int J Heat Mass Transf2025; 251: 127354.
21.
WuQKangYTangZ, et al. Preparation and properties of Ag nanoparticle-filled expanded graphite paraffin-based composite phase change materials with high temperature response properties. Diam Relat Mater2025; 157: 112561.
22.
ZhangYTongJGuoQ, et al. Hierarchical multiscale analysis for 3D woven composite leaf spring landing gear. Thin-Walled Struct2023; 189: 110913.
23.
LiuCBaiXCaoQ, et al. Safety properties of 3D framework loaded polyethylene glycol composite phase change materials with mxene. J Saf Sustain2025; 2: 171–180.
24.
MuzaqihAFAdiputraRPrabowoAR, et al. Analysis of ultimate capacity of sandwich composite material against impulse load: a study case of fluid-structure interaction by FE approach. Results Eng2025; 26: 105506.
25.
SilvaAOColomboPHotzaD. Chitosan-geopolymer composites: a synergistic approach to sustainable and functional materials. Ceram Int2025; 51(21): 33885–33896.
26.
TianBCuiKWenP, et al. Reinforcement of tribological performance assisted by in-situ carbon layer from the release, capture and tribo-chemistry of ionic liquid hydrotalcite composite lubricating materials. Carbon N Y2025; 243: 120532.
27.
ChenKTsamprasGCheruvalathS, et al. Experimental characterization of mechanical and tribological properties of composite materials for friction-based force-limiting structural components. Compos B Eng2025; 302: 112472.
28.
PawarPBUtpatAA. Analysis of composite material spur gear under static loading condition. Mater Today Proc2015; 2(4–5): 2968–2974.
29.
MojškercBBergantZŠturmR, et al. Fatigue and wear performance of bioepoxy vacuum-infused and autoclave-cured E-glass fiber reinforced polymer composite gears in mesh with a steel pinion. Polym Test2024; 140: 108600.
30.
MalikZHRifaiAPMuflikhunMA. Comparative study of process parameters’ influence on geometric accuracy and relative errors of lightweight compound gear printed by vat. photopolymerization and material extrusion. J Eng Res2025; 13(2): 949–961.
31.
Dhakshain BalajiVGopalakrishnanVAjayC, et al. Stress analysis of symmetric and asymmetric spur gears made of ceramic reinforced stainless steel matrix composites. Mater Today Proc2022; 50: 2111–2118.
32.
WangJSongTWenT, et al. Multi-objective process optimization of gear carburization and quenching based on ELM-MOPSO neural network. Mater Today Commun2025; 43: 111691.
33.
LoryuenyongVNakhloWSrikaenkaewP, et al. Optimization and performance prediction of carbon dioxide adsorption on chitosan/activated carbon/epichlorohydrin composite materials using Box–Behnken design and artificial neural network approaches. Case Stud Chem Environ Eng2025; 11: 101144.
34.
BelabedZTounsiABousahlaAA, et al. Mechanical behavior analysis of FG-CNTRC porous beams resting on Winkler and Pasternak elastic foundations: a finite element approach. Comput Concr2024; 34(4): 447–476.
35.
ZerroukiRZidourMTounsiA, et al. Buckling behavior of nonlinear FG-CNT reinforced nanocomposite beam reposed on Winkler/Pasternak foundation. Comput Concr2024; 34(3): 297.
36.
SemmahABellifaHBouradaF, et al. Exploring the effect of axial magnetic fields on the thermal stability of SWBNNTs resting on elastic medium using the N-TBT. Eur Phys J Plus2024; 139(6): 504.
37.
ZahraATRazzokovJKashifM, et al. Strained mechanical and fracture analyses of armchair-chiral-zigzag-based carbon nanotubes using molecular dynamics simulations. ACS Omega2024; 9(49): 48055–48069.
38.
NazAKashifMAin AsifQU, et al. Tuned structural and water diffusion in single-walled carbon nanotubes using molecular dynamics simulations. J Electron Mater2025; 54(9): 7081–7095.
39.
ZahraATShahzadAManzoorA, et al. Structural and thermal analyses in semiconducting and metallic zigzag single-walled carbon nanotubes using molecular dynamics simulations. PLoS One2024; 19(2): e0296916.
40.
BelabedZBousahlaAATounsiA. Vibrational and elastic stability responses of functionally graded carbon nanotube reinforced nanocomposite beams via a new Quasi-3D finite element model. Comput Concr2024; 34(5): 625.
41.
BakhaddaBBouiadjraMBBouradaF, et al. Dynamic and bending analysis of carbon nanotube-reinforced composite plates with elastic foundation. Wind Structures2018; 27(5): 311–324.
42.
AbualnourMYouzeraHChikhA, et al. On the dynamic behavior of cylindrical shell with graphene nanoplatelets (GNPs) faces and hexagonal honeycomb core layer. Mech Res Commun2026; 153: 104637.
