To control the meshing performance of hypoid gear drive, current local conjugate theory and local synthesis method establish a relationship between the relative motion and local geometrical properties of the mating surfaces at one reference point. Theoretically, both local conjugate theory and local synthesis method cannot ensure the contact performance on the entire tooth surface resulting in uncontrolled contact pattern and undesirable transmission error. A global synthesis approach consisting of a machine-tool settings calculation model, a tooth contact analysis model, a meshing quality assessment function, and a swarm intelligence algorithm are proposed. The direction, area, and shape of the contact pattern and the amplitude of the intersection of two adjacent transmission error curves are taken as the evaluation indexes. Three curvatures of the design pitch cone of the pinion are taken as the control variables. A global selection space is then established within the reasonable range of the curvatures. An improved multiple population genetic algorithm is employed to find the optimal set of the curvatures to achieve the target values of the evaluation indexes. To avoid the edge contact and corner contact condition, a feasible region is defined on tooth surface and the contact patterns on the gear and pinion surfaces are all confined within the area. The optimized contact patterns obtained by the loaded tooth contact analysis method are similar to those obtained by the proposed approach, thus demonstrating the effectiveness of this methodology. The main novelty of this approach is to translate the derivation of the mathematical relation between the curvatures of the mating surfaces and the contact properties to solving a multi-objective optimization problem of the meshing quality indexes by the intelligence algorithm.
A new hybrid fuzzy clustering algorithm that incorporates the Fuzzy C-means (FCM) into the Quantum-behaved Particle Swarm Optimization (QPSO) algorithm is proposed in this paper (QPSO+FCM). The QPSO has less parameters and higher convergent capability of the global optimizing than Particle Swarm Optimization algorithm (PSO). So the iteration algorithm is replaced by the QPSO based on the gradient descent of FCM, which makes the algorithm have a strong global searching capacity and avoids the local minimum problems of FCM and in a large degree avoids depending on the initializationvalues. This paper also investigates the ability of FCM algorithm, PSO+FCM algorithm and GA+FCM algorithm with Iris testing data and Wine testing data. The simulation result proves that compared with other algorithms, the new algorithm not only has the favorable convergence but also has been obviously improved the clustering effect.
A major problem with most of swarm intelligent algorithms in multimodal optimization is premature convergence (PC), which results in great performance loss and sub-optimal solutions. To avoid premature convergence by maintaining diversity in the population, many kinds of optimization algorithms are proposed. However, to the best of our knowledge, few of the swarm intelligent techniques focus on the individual competition. The development of individual competition plays an important role of the diversity conservation in the population because it could increase individual independent consciousness and reduce the rapid social collaboration process. In this paper, a new algorithm, Fitness Predator Optimizer (FPO), is proposed based on the conceptions of predators. In an FPO system, all of the individuals are seen as predators. Each of the individuals is depicted only by its position. Then the individual is named as a "position" in FPO. Only the competitive, powerful positions selected as elites could achieve the limited opportunity to update. The elite team reduces the possibility of all of the individuals moving toward the same place. Eight well-known benchmark functions are used to test the performance of FPO. Four typical multimodal benchmark functions are used to test the global search ability of FPO and four fixed-dimension multimodal optimization problems are selected to make a comparison of the convergence rate between several well-known algorithms. The experimental results show that the FPO algorithm is able to provide excellent exploitation, utilizing local minima avoidance and exploration simultaneously.
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