Multi-Objective Optimization of Planetary Gearbox with Adaptive Hybrid Particle Swarm Differential Evolution Algorithm

Abstract

This paper considers the problem of constrained multi-objective non-linear optimization of planetary gearbox based on hybrid metaheuristic algorithm. Optimal design of planetary gear trains requires simultaneous minimization of multiple conflicting objectives, such as gearbox volume, center distance, contact ratio, power loss, etc. In this regard, the theoretical formulation and numerical procedure for the calculation of the planetary gearbox power efficiency has been developed. To successfully solve the stated constrained multi-objective optimization problem, in this paper a hybrid algorithm between particle swarm optimization and differential evolution algorithms has been proposed and applied to considered problem. Here, the mutation operators from the differential evolution algorithm have been incorporated into the velocity update equation of the particle swarm optimization algorithm, with the adaptive population spacing parameter employed to select the appropriate mutation operator for the current optimization condition. It has been shown that the proposed algorithm successfully obtains the solutions of the non-convex Pareto set, and reveals key insights in reducing the weight, improving efficiency and preventing premature failure of gears. Compared to other well-known algorithms, the numerical simulation results indicate that the proposed algorithm shows improved optimization performance in terms of the quality of the obtained Pareto solutions.

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“…Modern researchers often apply hybrid approaches involving evolutionary (EA), particle swarm optimization (PSO), backtracking search optimization (BSA) algorithms, and neural networks to solve multicriteria optimization problems [17][18][19][20][21][22]. Y. Hu et al [17] presented a hybrid solution combining GA, PSO, and backpropagation neural networks (BPNN) to forecast electric load.…”

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“…3,5,9 The high torque transmission ratio and high power densities of planetary gears provide advantages over standard parallel axis gear sets. 10,11 Multistage planetary gears compose of a series of single stage planetary gears that are coupled together in a power flow configuration. 12 A multistage planetary gear mechanism consists of concentrically coupled stages, unlike parallel axis gear mechanisms such as spur, helical and bevel (Figure 2).…”

Optimization Design for the Planetary Gear Train of an Electric Vehicle under Uncertainties

“…Miler et al [4] chose transmission volume and power loss as design objectives, and they optimized the parameters of the planetary gear train with multi-objective optimization. Sedak et al [5] proposed a constrained multi-objective nonlinear optimization problem for planetary gearboxes, based on a hybrid element heuristic algorithm, considering gear volume, center distance, contact ratio, and power loss as optimization objectives. Patil et al [6] proposed a multi-objective optimization strategy to minimize the total volume and power loss of the two-stage helical gearbox and spur gearbox.…”