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1516 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013 ε y = ε ∗ M y − O ( M − O ) + ( M − O ) + ( M −O ) 2 2 2 x x y y z z y . (17) ε z = ε ∗ M z − O ( M − O ) + ( M − O ) + ( M −O ) 2 2 2 x x y y z z z . (18) In conclusion, the contour error computing model approximates curve L in locality with arc properly, so higher precision will be achieved. V. CONTOUR ERROR COMPENSATION APPROACH Except for the three PID position controller for X axis, Y axis and Z axis, Myung-Hoon LEE sets up an additional PID contour error controller [17]. The calculation approach is rather complicated. In the paper the contour error control compensation approach is developed, which adds the obtained contour error to the following error of current sampling period, and sends the result to CNC PID position controller to calculate position controlled quantity. The CNC contour error calculation and compensation program flow chart is shown in Figure 7. L Ci-1 M O Ci r Ci+1 Figure 6. The contour error computing model based on curve interpolation Firstly, after receiving the N th machining program segment coding and pretreatment results on the K th sampling period, interpolate and obtain following error E x , E y , E z ; Secondly, adopt the contour error computing model, and calculate contour error ε with Equation (8), Equation (9) or Equation (15) ; Thirdly, decompose ε to ε x , ε y , ε z along X, Y, Z coordinate axes, and compute each axis optimal displacement of current sampling period after contour error compensation, which is μ , μ , μ ; Finally, input the μ , μ , y z x y μ z to X, Y, Z coordinate axes PID position controller respectively, and compute the correction quantity to control X, Y, Z coordinate axes servo motors. x Figure 7. The CNC contour error calculation and compensation program flow chart VI. EXPERIMENTATIONS ON CONTOUR ERROR COMPENSATION CONTROL A. The Three-axis Linked CNC Test Table The three-axis linked CNC test table hardware structure is shown in Figure 8. The CNC controller is made up of PC and programmable DSP movement control card. The PC and DSP movement control card communicate through USB2.0. The PC acts as the man-machine interface, which implements instruction control, code compilation, states display and other functions; And the interpolation, position control and contour error compensation control function are carried out on the programmable DSP movement control card. The Panasonic servo drivers and motors are adopted in the X, Y, Z axes. Both the interpolation period and sampling period are 4 ms. Figure 8. The three-axis linked CNC test table hardware structure B. The Contrast Experimentations on Contour Error Compensation Interpolate and machine a block of three order NURBS curve. The control knots are: © 2013 ACADEMY PUBLISHER
JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013 1517 A (15, 0, 15) B (15, 15, 15) C (0, 15, 0) D (-15, 15, -15) E (-15, 0, -15) F (-15, -15, -15) G (0, -15, 0) H (15, -15, 15) I (15, 0, 15) ; The scale factors are: (1, 0.6, 1, 0.5, 1, 0.5, 1, 0.6, 1) ; The knot vector is: (0, 0, 0, 0, 0.25, 0.375, 0.5, 0.625, 0.75, 1, 1, 1, 1). Firstly, interpolate and machine this NURBS profile when not adopting the introduced contour error coupledcontrol approach. The ideal profile curve and real profile are shown in Figure 9, where the contour error is magnified 12 times to display. The contour error when machining the curve is shown in Figure 10. From Figure 10 it can be seen, the maximal contour error is near to 0.104mm. Figure 11. The profile when adopting the introduced contour error coupled-control approach based on linear interpolation Finally, interpolate and machine this NURBS profile when adopting the introduced contour error coupledcontrol approach based on curve interpolation. The ideal profile curve and real profile are shown in Figure 13, where the contour error is magnified 12 times to display. The contour error when machining the curve is shown in Figure 14. From Figure 14 it can be seen, the maximal contour error is near to 0.044mm. Figure 9. The profile when not adopting the introduced contour error coupled-control approach Figure 12. The contour error when adopting the introduced contour error coupled-control approach based on linear interpolation Figure 10. The contour error when not adopting the introduced contour error coupled-control approach Secondly, interpolate and machine this NURBS profile when adopting the introduced contour error coupled-control approach based on linear interpolation. The ideal profile curve and real profile are shown in Figure 11, where the contour error is magnified 12 times to display. The contour error when machining the curve is shown in Figure 12. From Figure 12 it can be seen, the maximal contour error is near to 0.054mm. Figure 13. The profile when adopting the introduced contour error coupled-control approach based on curve interpolation © 2013 ACADEMY PUBLISHER
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Journal of Computers ISSN 1796-203X
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Corn Moisture Measurement using a C
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Call for Papers and Special Issues
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(Contents Continued from Back Cover
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