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

Abstract

To improve the dynamic load-sharing performance and achieve lightweight, the twin rotors concentric face gear power-split transmission system (TRFGPSTS) was optimized. The gear tooth matching conditions of the system based on the design characteristics of power flow closed-loop and virtual constraint configuration of the system are established, and the basic parameters of each gear meet the requirements of the system load-sharing layout and synchronous meshing of each branch movement are calculated. Based on the lumped mass parameter method, combined with the calculation results of gear tooth matching, the 45-DOF bending torsional coupling dynamic model of the system was established considering time-varying meshing stiffness, support stiffness, manufacturing and installation errors, and other factors, and the influence of each factor on the dynamic load-sharing performance of the system was analyzed. Combined with the influence law of various factors, a multi-objective dynamic load-sharing optimization design model was established with the best dynamic load-sharing performance and the minimum system quality as the objective function. Through the weighted combination method, the global optimal solution of the system optimization design was determined, and the influence of each parameter on the optimization objective function was analyzed. The correctness of the results was verified by using the genetic algorithm based on Pareto frontier distribution. The results show that the dynamic load-sharing characteristics of the system become worse with the increase of error and torsional stiffness, and are more sensitive to the influence of various error parameters. The optimization process focuses on the geometric parameters such as the Module, the teeth Number, the Pressure angle, and the Tooth width of each gear, which can reflect the degree of influence on the dynamic load-sharing and lightweight of the system. After optimization, the dynamic load sharing coefficient (DLSC) was reduced to 1.017, and the overall geometric volume was reduced to 1.473 × 10⁸ mm³. It provides a theoretical basis for the design and research of a new type of helicopter power transmission system with a compact structure, good maneuverability, and high reliability.

Keywords

Gear tooth matching concentric face gear load-sharing light weight optimization

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References

Litvin

Wang

Bossler

, et al. Application of face-gear drives in helicopter transmissions. J Mech Des 1994; 116: 672–676.

White

. Split torque helicopter transmissions with widely separated engines. Proc IMechE, Part G: J Aerospace Engineering 1989; 203(1): 53–65.

Bottiglione

De Pinto

Mantriota

. Infinitely variable transmissions in neutral gear: torque ratio and power re-circulation. Mech Mach Theory 2014; 74: 285–298.

Kahraman

. Load sharing characteristics of planetary transmissions. Mech Mach Theory 1994; 29(8): 1151–1165.

Krantz

Rashidi

. Vibration Analysis of a Split Path Gearbox. AIAA-95-3048, July 1995. DOI: 10.2514/6.1995-3048

Lopatin

Plotnikova

. Helical-bevel gearing with small wheel axles angles. Procedia Eng 2017; 206: 1189–1194.

Zschippang

Lanz

Küçük

, et al. Face-gear drive: assessment of load sharing, transmission characteristics and root stress based on a quasi-static analysis. Mech Mach Theory 2020; 151: 103914.

Chen

Tan

Guo

, et al. Study on excitation and time-varying mesh characteristics of straight bevel gears considering modification and friction. Mech Mach Theory 2022; 176: 105028.

Liang

Zuo

Patel

. Evaluating the time-varying mesh stiffness of a planetary gear set using the potential energy method. Proc IMechE, Part C: J Mechanical Engineering Science 2014; 228(3): 535–547.

10.

Dong

Tang

. Dynamic characteristics of the face gear transmission system based on a rotor-shaft-bearing model with multiple nodes. Int J Non Linear Mech 2021; 137: 103825.

11.

Geng

Spanos

. Stochastic dynamic load-sharing analysis of the closed differential planetary transmission gear system by the Monte Carlo method. Mech Mach Theory 2021; 165: 104420.

12.

Pleguezuelos

Sánchez

Pedrero

. Analytical model for meshing stiffness, load sharing, and transmission error for spur gears with profile modification under non-nominal load conditions. Appl Math Model 2021; 97: 344–365.

13.

Kim

Moon

Sohn

, et al. Macro geometry optimization of a helical gear pair for mass, efficiency, and transmission error. Mech Mach Theory 2020; 144: 103634.

14.

Choi

Ahn

Park

, et al. Influence of gear tooth addendum and dedendum on the helical gear optimization considering mass, efficiency, and transmission error. Mech Mach Theory 2021; 166(1): 104476.

15.

Kulangara

Rao

CSP

Subhash Chandra Bose

. Generation and optimization of lattice structure on a spur gear. Mater Today Proc 2018; 5(2): 5068–5073.

16.

Kishore

Reddy

AVV

Rao

. Design and optimization of spur gears in a single stage reduction gear box. Mater Today Proc 2022; 60: 2010–2017.

17.

Lei

Hou

, et al. Research on vibration and noise reduction of electric bus gearbox based on multi-objective optimization. Appl Acoust 2020; 158: 107037.

18.

Parmar

Ramkumar

Shankar

. Macro geometry multi-objective optimization of planetary gearbox considering scuffing constraint. Mech Mach Theory 2020; 154: 104045.

19.

Younes

Changenet

Bruyère

, et al. Multi-objective optimization of gear unit design to improve efficiency and transmission error. Mech Mach Theory 2022; 167: 104499.

20.

Choi

Ahn

, et al. Optimization of gear macro-geometry for reducing gear whine noise in agricultural tractor transmission. Comput Electron Agric 2021; 188: 106358.

21.

Marjanovic

Isailovic

Marjanovic

, et al. A practical approach to the optimization of gear trains with spur gears. Mech Mach Theory 2012; 53: 1–16.

22.

Simon

. Multi-objective optimization of the manufacture of face-milled hypoid gears on numerical controlled machine tool. Proc IMechE, Part B: J Engineering Manufacture 2021; 235(6–7): 1120–1130.

23.

Simon

. Multi-objective optimization of hypoid gears to improve operating characteristics. Mech Mach Theory 2020; 146: 103727.

24.

Zhang

Qin

Xie

, et al. Optimization design on dynamic load sharing performance for an in-wheel motor speed reducer based on genetic algorithm. Mech Mach Theory 2018; 122: 132–147.

25.

Artoni

. A methodology for simulation-based, multiobjective gear design optimization. Mech Mach Theory 2019; 133: 95–111.

26.

Zhang

Wang

, et al. Global optimization of reliability design for large ball mill gear transmission based on the Kriging model and genetic algorithm. Mech Mach Theory 2013; 69(Complete): 321–336.

27.

Cui

Wang

, et al. Reliability design and optimization of the planetary gear by a GA based on the DEM and Kriging model. Reliab Eng Syst Saf 2020; 203: 107074.

28.

Ding

Zhang

, et al. High-performance tooth flank collaborative optimization model for spiral bevel and hypoid gears. Adv Eng Inform 2023; 57: 102059.