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UBC Theses and Dissertations

Finite element modeling of ballscrew feed drive systems for control purposes Okwudire, Chinedum


This thesis details a scheme, based on finite element methods, for modeling of the ballscrew drives of Cartesian-configured machine tools. Using this scheme, the structural dynamics of the ballscrew mechanism can be incorporated into the feed drive model, and thereby considered during high-bandwidth controller design, and interactive simulation of feed drive-controller performance in the virtual environment. The finite element method used in this thesis for modeling is a hybrid kind, whereby the more rigid components of the feed drive are modeled as lumped-parameter rigid bodies, while the flexible members, like the ballscrew, are modeled using distributed-parameter structural members. As a result, a feed drive model is developed which both maintains a reasonably low level of complexity while adequately capturing the relevant dynamics needed for controller design and simulation. This scheme also pays close attention to the modeling of the screw-nut interface, because it plays an important role in the functioning of ballscrew drives. Two methods are proposed for deriving the stiffness matrix of this interface - the Rigid Ballscrew Method and the Shape Function Method. The former method is shown to capture interesting dynamics of the interface, while the latter is derived in anticipation of situations where the former may not perform satisfactorily. In order to show the benefits of this modeling scheme, three high-bandwidth controllers are designed. The first controller is designed based on the traditional technique which considers only the rigid-body dynamics of the drive. On the other hand, the second and third controllers are designed considering the rigid-body and structural dynamics information obtained from the proposed modeling scheme. Analyses performed on the three controllers reveal that the two controllers designed based on the proposed scheme outperform that which is designed following the traditional technique. Finally, a simulation strategy is designed which allows the feed drive model, together with its non-linear dynamics to be combined with the controller dynamics and other dynamics of the feed drive system. In order to reduce simulation time, a novel method of performing model reduction based on a Component Mode Synthesis technique combined with Modal Acceleration recovery is described. This method is used to achieve an efficient reduction without compromising relevant dynamic properties of the full model. The potentials of the scheme presented in this thesis are demonstrated partly by experiments conducted on a test bed, and in other cases, by simulations performed on a model generated from the test bed.

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