Optimal design of 6-DOF vibration isolation platform based on transfer matrix method for multibody systems
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RESEARCH PAPER
Optimal design of 6-DOF vibration isolation platform based on transfer matrix method for multibody systems Min Jiang1 · Xiaoting Rui1 · Wei Zhu1 · Fufeng Yang1 · Yanni Zhang1 Received: 5 June 2020 / Revised: 10 August 2020 / Accepted: 8 September 2020 © The Chinese Society of Theoretical and Applied Mechanics and Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract The structure parameters of 6-degree of freedom (DOF) vibration isolation platform have a significant effect on its performance. To make the designed vibration isolation platform perform well, non-dominanted sorting genetic algorithm version II (NSGAII) was applied to optimize its structure based on the transfer matrix method for multibody systems. Firstly, the Jacobian matrix of 6-DOF vibration isolation platform was solved based on kinematics. Secondly, the transfer equation of 6-DOF vibration isolation system was established by the linear transfer matrix method for multibody systems. And the formula of its natural frequency was derived according to the boundary conditions of the system. Thirdly, the manipulability index was constructed based on a dimensionless Jacobian matrix. And a new performance index function was established considering the influence of dynamic isotropic and legs mass. Fourthly, genetic algorithm (GA) and NSGA-II were used to optimize the structure of the 6-DOF vibration isolation platform under the same conditions, respectively. It showed that NSGA-II had higher optimization efficiency, better calculation accuracy and shorter optimization time than that of GA. Finally, NSGA-II was adopted for multi-objective optimization design of 6-DOF vibration isolation platform based on the constraint conditions. Optimal Pareto solutions were obtained, which provides structural parameters for subsequent design work. Therefore, the proposed optimization method and the performance index in this paper provide a theoretical basis for the optimal design of relevant vibration isolation mechanism. Keywords Optimal design · 6-DOF vibration isolation · Transfer matrix method · Non-dominanted sorting genetic algorithm version II (NSGA-II)
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1 Introduction Compared with the traditional serial mechanism, the 6-DOF vibration isolation platform based on Stewart mechanism has advantages of high stiffness, strong bearing, high accuracy, good dynamic performance and simple solution of inverse kinematics. It can effectively reduce the vibration transmitted between the mechanisms at both ends of the platform. Therefore, it has been extensively applied in various areas of spacecraft [1, 2], telescope [3, 4], vehicle [5, 6] and sensor [7, 8]. However, the structure parameters of the 6-DOF vibration isolation platform are the main factors affecting its performance. Determining the optimal structure parameters that meets the specific environmental condition is urgent in
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Xiaoting Rui [email protected] Institute of Launch Dynamics, Nanjing University of Science and Technology, Nanjing 210094, China
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