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Abstract: The
dynamic problem of the 3-TPS vertical—hor- izontal conversion hybrid CNC
machine tool is studied by using the Lagrange method to analyze the
dynamic behavior, study or realize the technology sectors, such as
selecting and optimizing the structure parameters, control the machine,
and so on. The Lagrange dynamic equation is firstly developed into a
standard form expressed in the Cartesian space according to the
machine’s structure feature. The machine tool is divided into three
subsystems: The moving platform, the three limbs and the parallel
locking mechanism according to the machine’s structure feature. Then the
kintic energy and potential energy models of the three subsystems are
deduced respectively. The dynamic equation expressed in the Cartesian
space of the machine is founded on the base of that. To compute the
terms of the dynamic equation, such as the inertia matrix M, the
Coriolis centrifugal term V, the gravity term G, and so on, of the three
subsystems, the recursion formulas are deduced according to the standard
form of the Lagrange dynamic equation. The recursive algorithm to
compute the terms is given finally. This dynamic model of the hybrid
machine is of clear concept and the calculation is relatively simple.
This can satisfy the needs of the machine’s control.
Key words: CNC
machine tool Hybrid dynamic Lagrange equation
CLC No: TP242.2
国家高技术研究发展计划基金(5123007)和辽宁省科学技术基金(20041013)资助项目
. Received 20050526, received in revised form 20051209
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