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1、附錄Control of a Non-Orthogonal Reconfigurable Machine ToolReuven KatzJohn YookYoram KorenReceived: January 3, 2003; revised: September 16, 2003AbstractComputerized control systems for machine tools must generate coordinat

2、ed movements of the separately driven axes of motion in order to trace accurately a predetermined path of the cutting tool relative to the workpiece. However, since the dynamic properties of the individual machine axes

3、are not exactly equal, undesired contour errors are generated. The contour error is defined as the distance between the predetermined and actual path of the cutting tool. The cross-coupling controller (CCC) strategy was

4、 introduced to effectively decrease the contour errors in conventional, orthogonal machine tools. This paper, however, deals with a new class of machines that have non-orthogonal axes of motion and called reconfigurable

5、machine tools (RMTs). These machines may be included in large-scale reconfigurable machining systems (RMSs). When the axes of the machine are non-orthogonal, the movement between the axes is tightly coupled and the impo

6、rtance of coordinated movement among the axes becomes even greater. In the case of a non-orthogonal RMT, in addition to the contour error, another machining error called in-depth error is also generated due to the non-or

7、thogonal nature of the machine. The focus of this study is on the conceptual design of a new type of cross-coupling controller for a non- orthogonal machine tool that decreases both the contour and the in-depth machining

8、 errors. Various types of cross-coupling controllers, symmetric and non-symmetric, with and without feedforward, are suggested and studied. The stability of the control system is investigated, and simulation is used to

9、compare the different types of controllers. We show that by using cross-coupling controllers the reduction of machining errors are significantly reduced in comparison with the conventional de- coupled controller. Furth

10、ermore, it is shown that the non-symmetric cross-coupling feedforward (NS-CC-FF) controller demonstrates the best results and is the leading concept for non-orthogonal machine tools. ©2004 ASME Contributed by the Dy

11、namic Systems, Measurement, and Control Division of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS for publication in the ASME JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received by the ASME Dynamic S

12、ystems and Control Division January 3, 2003; final revision September 16, 2003. Associate Editor: J. Tu. Keywords:machine tool, cross-coupling controller, non-orthogonal, RMTstrategy to improve the controller performanc

13、e. The latest trend of cross-coupling controller improvement is the application of fuzzy logic . All these methods, however, do not work for machines with non-orthogonal axes. Surface cut (e.g., a circular cut in the

14、X-Y plane) on a 3-axis orthogonal milling machine requires a motion of two axes (e.g., X and Y). However, surface cuts in the non-orthogonal RMT require simultaneous motion of all three axes. Therefore, in addition to t

15、he contour error, this motion creates another error, called the in-depth error, which is in the Z direction. This error affects the surface finish quality of the workpiece. While contouring, the tool tip of the RMT has

16、not only to follow the predetermined path, but also to control continuously the depth of cut. The simultaneous control of both errors, the conventional contour error and the in-depth error, requires a new control strate

17、gy since the standard CCC algorithms cannot be directly applied. In other words, the RMT control design problem requires a new control approach that is able to correct simultaneously two types of cutting errors. This pr

18、oblem has not been addressed in the literature. In this paper, we describe three types of controllers aimed at reducing the contour and in-depth error simultaneously. First we investigate a symmetrical cross-coupling (S

19、-CC) controller, which unfortunately does not show good performance in reducing both errors. The poor performance is due to the conflicting demands in reducing the two errors and the lack of information sharing between

20、the two pairs of axes (X-Y and Y-Z), which are responsible for error compensation. To overcome this problem, the required motion information of one pair of axes is fed forward to the other. This idea results in two new

21、controller types, symmetrical cross-coupling feedforward (S-CC-FF) controller and non-symmetrical cross-coupling feedforward (NS-CC-FF) controller. Finally, the influence of the reconfigurable angular position of the cu

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