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To meet the requirements of shorter synchronization time and higher life for the synchronizer in transmission, mathematical models aiming at synchronization time and synchronizer life were established separately based on Newton’s second law and adhesive wear theory, M-B fractal contact model. The evaluation function was constructed by ideal point method to establish a multi-objective parameter optimization model with the two objectives. Using the AHP to determine weight value of the target in the multi-objective optimization model, and using the improved particle swarm algorithm to optimize the multi-objective parameter optimization model. The results show that the synchronization time is reduced by 8% and the synchronizer life is increased by 9% compared with that before optimization, the two objectives are improved better. The using of the improved particle swarm algorithm improves the performance of the synchronizer, and the application of the ideal point method effectively avoids the problem that the high order of magnitude dominates the multi-objective optimization.

The foamed aluminum filled crash-box with induction grooves on the side wall was made finite element analysis in the impact process by LS-DYNA,and the parameters influence of induction grooves on the energy absorption characteristics of crash-box was studied. The results was dealt with the LS-Prepost, considering the energy absorption, peak impact force, the average impact force and energy absorption ratio, when crash-box was made two radius of 2.5 mm semicircle grooves in the upper 50% part of the side wall, in the impact process of a symmetrical stack the ideal type of shrinkage deformation, depressed peak impact force without affecting energy absorption, higher energy absorption ratio and compression efficiency wound be gotten. The finite element simulation of the impact process was feasible when the crash-box body was made the impact test by the vertical and horizontal hydraulic impact test platform.

In order to realize the protection of broken conveyer belt with different moving direction, the scheme of broken belt protector with bidirectional and arc shaped catching scheme was proposed, and the main parameters were designed taking the GX1000 type conveyer belt as application example. The virtual prototype simulation of the broken belt protector catching process was done, and the velocity characteristic of main components was obtained. The model prototype with 1/2 structure size of the prototype machine was manufactured, and the test of catching process and the catching force were carried out. And the catching force parameters of prototype machine were derived based on small-scale model similarity theory. Consequently, the virtual and model prototype of broken conveyer belt protector with bidirectional and arc shaped catching scheme can carry out catching motion by different directions acorrding to the direction of broken belt motion, and wedge-shaped space for catching is formed and catching brake is finished. The broken belt protector single machine can realizes bidirectional catching. The limit catching force of prototype machine is higher than 56.4 kN, and the limit catching force is higher than theoretical cutting force which is 23.15 kN, and the demand of catching brake safely is met.

To improve the problem that the conventional design results of planetary gear transmission could not guarantee all of objectives were the optimal, aiming at the shortcomings that adaptive particle swarm optimization algorithm easily produced infeasible solution and fell into local optimum, an adaptive particle swarm optimization algorithm based on multi-level penalty function with dynamic change penalty coefficient was proposed. The algorithm set the penalty function as a multi-level penalty function and the penalty coefficient could be adjusted with the iterative process. The reliability and others were taken as the constraint conditions, the volume, the contact ratio and the transmission efficiency as the objective functions. Combined with the ideal point method to construct the evaluation function for multi-objective optimization. The results show that the volume is decreased by 41.87%, the contact ratio is increased by 2.643%, and the transmission efficiency is increased by 0.1563%. The improved particle swarm optimization improves the defects of original algorithm, and each objective is reasonably optimized.

In this paper, the complete f-moment convergence for weighted sums of sequences of extended negatively dependent random variables is investigated. As a result, we not only extend and generalize some results on complete convergence obtained by Wu and Zhai (Journal of Mathematical Inequalities, 13(1): 251-260, 2019), but also get some results on the complete consistency for the estimator of nonparametric regression models and provide some simulations to assess the validity of our theoretical results. [ABSTRACT FROM AUTHOR]