Gear vibration reduction using genetic algorithms

Abstract — In the present paper, two different techniques are proposed to design spur gear profile modifications for noise reduction: an iterative “Heuristic” approach and an optimization approach based on Genetic Algorithms. Different objective functions are investigated and dynamic simulations are carried out to check the effectiveness of the new design solutions. Keywords: Profile modification, gear, optimization, genetic algorithm. efficiency. The genetic algor I. Introduction The reduction of vibration and noise is nowadays a very important issue in the design of gear power transmissions. The main reasons are the increase of performance, standard noise restrictions and market competitors. Experimental tests [1] proved that several nonlinear phenomena, such as sub and super harmonic resonances and chaotic motions, occur when the dynamic transmission error is present. The literature offers a large number of paper regarding the simulation of the dynamic behaviour of gears: Kahraman and Singh [2] focused the attention on the effect of time varying mesh stiffness using the harmonic balance method for a gear system with clearance; Amabili and Rivola [3] proposed a different approach based on Hill infinite determinant to predict transition curves and stability regions; Parker et al. [4] used a semi-analytical technique to capture the non linear dynamic response of a gear pair. Many authors underlined the effect of modifications on the dynamics of gears: Kahraman and Blankenship [5] experimentally measured the effect of the involute tip relief on the dynamic response, while Bonori et al. [6] simulated the effect of different profile modifications and manufacturing errors on gear noise. A key point on the design process of spur gears is the choice of the best profile modification; it is not trivial difficult to define design guidelines for profile modifications. In 1999, Smith [7] suggested the application of Harris maps on tip and root relief, improving the work of Harris [8] and Niemann [9]. New approaches where proposed by Beghini et al. [10] and Fonseca et al. [11], they used iterative and genetic approaches respectively; such papers did not provide the effect on the dynamics. In the present work two optimization techniques are presented to find suitable profile modifications for a spur gear pair. Both optimization approaches are based on the minimization of the peak to peak of the static transmission error (PPTE). The first method searches the optimum solution by means of iterative calculations of the PPTE, using many combinations of the parameters, which define the profile modifications. The second method uses a genetic algorithm approach, able to provide strong reduction of the PPTE, with a higher computational ithm approach is also used with a different objective function, i.e. the averaging of mesh stiffness harmonic content. In order to evaluate the effectiveness of the optimization techniques, an actual gear pair is considered as case study and dynamic simulations are performed. For this purpose a simple spur gear dynamic model is developed, including a smoothing technique for the clearance type non-linearity. Numerical integrations allow to obtain the whole dynamic scenario.