Експериментальне вимірювання жорсткості моделі гексапода
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Date
2012
Authors
Кириченко, А. М.
Journal Title
Journal ISSN
Volume Title
Publisher
ТНТУ
Abstract
Розроблено модель гексапода і конструкцію вимірювального стенда, запропоновано методику опрацювання результатів вимірювання, що дозволяє визначити вектор узагальненого пружного переміщення платформи гексапода при навантаженні та жорсткість, приведену до точки навантаження. Встановлено залежність приведеної жорсткості від положення рухомої платформи та координат прикладення навантаження.
The parallel machine tools stiffness is the most important as to their high accuracy and performance. The hexapods stiffness is considered in the article, as the hexapod is one of the effective machine tools for multiaxis processing.
The objective is to experimentally measure the elastic deformation of hexapod platform under loading by the force, to determine the spatial stiffness depending on the position of the moving platform and loading force, to calculate the reduced stiffness at the loading point.
The simplified hexapod model is developed and manufactured. The model consists of solid base and the moving platform connected to the base with six variable length struts. Each strut consists of two telescopic tubes with collet clamping device to lock its length.
The struts also have the universal joints at both ends. It is possible to change the platform position and orientation arbitrarily within certain range by changing the struts length. Then the platform position can be locked by tightening the collet clamps of each strut. The stiffness of each hexapod strut is measured and its average value is calculated.
The measuring bench is designed to measure the solely displacement of platform caused by the struts deformation and exclude the base deformation. With the manufactured equipment it is possible to apply the force to the platform at an arbitrary direction and angle, to simulate the load on the different height of the platform, from the top or the bottom of the platform. The force is created by the screw tensioner and measured with spring force gage dynamometer. The 6x1 spatial force vector is calculated with the force value and its position within the reference frame.
The platform displacement is measured by six gages placed around the platform in the particular order. The procedure of experimental data analysis is developed to obtain the generalized spatial displacement from the indicators readings and their position around the movable platform.
The 6x1 vector of spatial displacement is obtained for each load and the reduced stiffness is calculated. The relations of elastic deformations from the platform position with the reference to the base and the force position with the reference to the platform are obtained.
It is found that when the distance between the loading force and the platform is increased, the longitudinal displacement of the platform center decreases, but the angular displacement increases. This testifies that the longitudinal displacement at the load point is compensated by the displacement caused by the rotation of the moving platform relatively to the center of stiffness.
The measurements testified that the maximum stiffness is observed when the moving platform approaches the base. The maximum stiffness is observed when the load is applied at 0.05 to 0.1 m from the joints plane. In this case the stiffness approximately equals the strut stiffness.
Description
Keywords
механізм паралельної структури, гексапод, пружні переміщення, приведена жорсткість, parallel manipulator, hexapod, elastic deformation, reduced stiffness
Citation
Кириченко, А. Експериментальне вимірювання жорсткості моделі гексапода / А. Кириченко // Вісник Тернопільського національного технічного університету. – Тернопіль : ТНТУ, 2012. – № 2 (66). – С.114-120.