“…For the analysis, the manufacturing errors listed in Table 2 were applied to all gears, pinions and wheels of gear pairs 1 and 2. The operating conditions are an input speed of 1383 rpm, an input torque of 300 Nm, and an operating time of 777 h, which are for the 4th gear pair in the main shift part of the transmission error of a 75-kW agricultural tractor 33 . Figure 2 Frequency distribution of safety factor for tooth root stress of pinion and wheel of each gear pair using random robustness analysis.…”
In gear design, gear performance metrics such as safety factors for tooth root stress and surface durability, peak-to-peak static transmission error (PPSTE), efficiency, mass, and volume are considered. They are calculated by the geometric parameters of gear macro- and micro-geometry, and manufacturing errors related to gear geometry significantly affect gear performance. However, previous studies have only focused on the micro-geometry errors. In this study, Monte Carlo-type robustness analysis was performed considering the manufacturing errors for tooth thickness, tip diameter, and center distance. Gear performance metrics except PPSTE were calculated based on the international standards and geometric characteristics. PPSTE was evaluated analytically due to lack of standards. When the errors were considered, two gear pairs with the safety factors satisfying the design requirements and similar performance for PPSTE, efficiency, mass, and volume showed different gear performances. There were many samples in gear pair 1 that could not satisfy the design requirements of safety factors, and gear pair 2 had the robustness of PPSTE not only at the specific torque but also with wide torque range when compared to gear pair 1. These results imply that considering the gear macro-geometry errors and robustness of PPSTE is significantly important when designing gears.
“…For the analysis, the manufacturing errors listed in Table 2 were applied to all gears, pinions and wheels of gear pairs 1 and 2. The operating conditions are an input speed of 1383 rpm, an input torque of 300 Nm, and an operating time of 777 h, which are for the 4th gear pair in the main shift part of the transmission error of a 75-kW agricultural tractor 33 . Figure 2 Frequency distribution of safety factor for tooth root stress of pinion and wheel of each gear pair using random robustness analysis.…”
In gear design, gear performance metrics such as safety factors for tooth root stress and surface durability, peak-to-peak static transmission error (PPSTE), efficiency, mass, and volume are considered. They are calculated by the geometric parameters of gear macro- and micro-geometry, and manufacturing errors related to gear geometry significantly affect gear performance. However, previous studies have only focused on the micro-geometry errors. In this study, Monte Carlo-type robustness analysis was performed considering the manufacturing errors for tooth thickness, tip diameter, and center distance. Gear performance metrics except PPSTE were calculated based on the international standards and geometric characteristics. PPSTE was evaluated analytically due to lack of standards. When the errors were considered, two gear pairs with the safety factors satisfying the design requirements and similar performance for PPSTE, efficiency, mass, and volume showed different gear performances. There were many samples in gear pair 1 that could not satisfy the design requirements of safety factors, and gear pair 2 had the robustness of PPSTE not only at the specific torque but also with wide torque range when compared to gear pair 1. These results imply that considering the gear macro-geometry errors and robustness of PPSTE is significantly important when designing gears.
“…First, the initial population (candidate solution) is obtained through the initial parameter x of each gear of the system determined in Figure 15 and the constraint conditions obtained from equations ( 23)- (25). Secondly, after the genetic operation (selection, crossover, mutation), some candidate solutions are retained according to the fitness (constraint conditions) according to the adaptive conditions (equation (20), equation ( 21)). The reserved candidate solution and the eliminated solution are coevolutionary through the longitudinal population, and better individuals are selected according to the fitness function.…”
Section: Solution Based On Genetic Algorithmmentioning
confidence: 99%
“…Through the multi-scale method from gear contact to complete transmission, multi-objective optimization based on non-dominated sequencing genetic algorithm II (NSGA-II) is realized. Choi et al 20 optimized the macro geometry of the two gear pairs of the agricultural tractor gearbox by using the non-dominated sorting genetic algorithm III (NSGA-III) with the goal of minimizing PPSTE. Marjanovic et al 21 introduced the characteristics and problems of gear system optimization with spur gears, provided the best concept selection description based on the selection matrix, the best material selection, the best gear ratio and the best position, further introduced the definition of mathematical model, and used the original software to optimize the gear system with spur gears.…”
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.
“…Xiang and Zuo (2013) determined the noise of the manual transmission and analyzed the noise signals of the transmission under multiple working conditions. Choi et al (2021) optimized the gear macro-geometry of a tractor transmission through a genetic algorithm to minimize peak-to-peak static transmission errors. The overall noise level in the transmission operating range was found to reduce by 3.1 dBA, and all the noise levels of the gear harmonic components were reduced effectively (Choi et al, 2021).…”
Abstract. In this study, the noise of the gear transmission system for two-speed automatic transmission (2EAT) of pure electric vehicles was analyzed and optimized. Firstly, through vehicle noise tests, poor working conditions and noise contribution of each gear pair were determined with the order analysis method. Secondly, a dynamics calculation model and a simulation model of the gear transmission system were established and the poor meshing state of the main reducer gear pair under specific conditions was determined as the main cause of noise. Finally, a genetic algorithm combined the weight method was used for gear modification. After gear
modifications, the fluctuation range of transmission error was reduced and
the contact condition of the tooth surface was significantly improved.
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