Duality in the analysis of responses to nonlinear systems

The paper provides a new view on the averaging procedure and equivalent linearization in the study of nonlinear mechanics. It is shown that the duality of those techniques can be used to obtain better approximate solutions or to separate the original nonlinear systems subjected to periodic and random excitations into deterministic and stochastic ones. | Vietnam Journal of Mechanics, VAST, Vol. 32, No. 3 (2010), pp. 135 – 144 A NEW ALGORITHM FOR KINEMATIC PROGRAM CONTROL OF OPTICAL PARTS BY GRINDING Nguyen Van Khang1 , Nguyen Trong Hung2 1 Hanoi University of Technology 2 Hung Yen University of Technology and Education Abstract. Based on the definition of the local coating coefficient, the average local coating coefficient and the speed coefficient in grinding of optical parts, and on theory of multibody kinematics, an algorithm for kinematic program control during the grinding process of optical parts has been developed at Hanoi University of Technology. Using this algorithm, the results of the improvement in the precision of processed surfaces of optical parts by grinding under kinematic program control have been obtained and will be presented in the present paper. 1. INTRODUCTION With the development of high precision mechanic and optical sectors, optical tools and devices have been playing an important role in many industrial fields. Key components in optical tools and devices are parts made by optical glasses, hereunder called as optical parts. Among processing methods, grinding is one of the most effective methods to achieve high precision, even though the facilities are not at the same level of precision. The problem to improve processed surface’s precision of optical parts by grinding is widely interested. It’s related to a lot of technological factors. The study on the influence of kinematics on precision of the processed part’s surface is one of effective methods by improving processed surface’s precision of optical parts. Study on kinematic program of processed optical parts is still limited [1, 2]. By applying kinematics of multibody systems [3, 4, 5, 6], the present paper’s authors established a kinematic program for processing optical parts on grinding equipment to improve processed surface’s precision of optical parts. Experiments were carried out on optical part grinding equipment with four - .

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