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.
Highlights
Planetary gearboxes have a wide application in various mechanical systems, such as industrial drives, rotorcraft, automobiles, wind turbines, etc., where they can offer compact dimensions and higher power densities with less noise and higher torque-to-weight ratios, especially compared to standard parallel axis gear trains [1,2]
To analyze the optimization performance and to verify the performance of the modifications introduced in the proposed Multi-Objective Hybrid Particle Swarm Optimization Differential Evolution (MHPSODE) algorithm, in this paper, the statistical comparison has been performed between the proposed algorithm and several well-known algorithms, such as NSGA-II [42], MO_Ring_PSO_SCD [22] and DEMO [43] on CEC2009 benchmark problems
The considered multi-objective optimization test instances released in CEC2009 benchmark consist of 10 unconstrained optimization problems and 3 problems that deal with constrained optimization [45]
Summary
Planetary gearboxes have a wide application in various mechanical systems, such as industrial drives, rotorcraft, automobiles, wind turbines, etc., where they can offer compact dimensions and higher power densities with less noise and higher torque-to-weight ratios, especially compared to standard parallel axis gear trains [1,2]. To further enhance the optimization performance of PSO algorithm in solving MOO problems, in this paper an improved hybrid PSO and DE algorithm, called Multi-Objective Hybrid Particle Swarm Optimization Differential Evolution (MHPSODE) algorithm, has been proposed to deal with the complex MOO of planetary gearbox design. 2. Problem Formulation This paper considers the problem of MOO of the planetary gearbox with the aim to obtain the gear design parameters, which lead to construction with lower weight and volume while simultaneously having increased efficiency and service life. In this regard, in this paper the following objective functions have been formulated for the considered MOO optimization problem:. The different factors used in the above equations are given in the Appendix A
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