The Immune Self-adjusting Contour Error Coupled Control in Machining Based on Grating Ruler Sensors

Sensors & Transducers Vol. 181 Issue 10 October 014 pp. 37-44 Sensors & Transducers 014 b IFSA Publishing S. L. http://www.sensorsportal.com The Immune Self-adjusting Contour Error Coupled Control in Machining Based on Grating Ruler Sensors Guoong Zhao Qingu Li Binguan Zhuang Department of Mechanical Engineering Shandong Universit of Technolog Zibo 55049 China Tel.: 86-533767917 fa: 86-533786910 E-mail: g709@16.com Received: 3 Jul 014 /Accepted: 30 September 014 /Published: 31 October 014 Abstract: The actual dnamic performance of each feed ais can t match well usuall which will destro machine tool contour accurac seriousl. The immune self-adjusting coupled control method based on grating ruler sensors is developed to improve machine tool contour accurac in the paper. Firstl measure and convert the feed ais actual displacement into pulse signals with grating ruler sensors on each sampling period; then calculate the and compensation control quantit. The method combines the advantages of immune mechanism and classical Proportion Integration Differentiation (PID) control algorithm. The introduced method is testified on the three-ais computer numerical control (CNC) milling machine with three high precision grating ruler sensors. And the eperimental results show that the proposed immune self-adjusting coupled control method can improve machine tool contour accurac remarabl. Copright 014 IFSA Publishing S. L. Kewords: Grating ruler sensor Displacement measurement Contour error Immune mechanism Contour precision. 1. Introduction In manufacturing fields man parts have comple profile [1]. For these comple parts machining one wa is to approimate parts profile with linear segments and adopt linear interpolation. Another approach is to directl use curve interpolation method. Compared with the linear segments approimation and linear interpolation the curve direct interpolation method can improve machining accurac and processing speed snchronousl in theor []. For multi-ais CNC machine tool the contour precision is the most important factor to determine the machining accurac. In CNC machining the is defined as the shortest distance between the current cutter position and the command tool path curve [3]. The contour precision relates to the dnamic characteristics matching degree of each feed ais and depends on the multi-ais lined precision [4]. The CNC machine tool servo drive sstem is much comple and the transmission parts friction and electrical components parameters ma change in machining. So the actual dnamic performance of each ais can t match well usuall which will destro the machine tool contour accurac seriousl. Compared with advanced single ais servo controller the coupled control is more effective to improve contour accurac [5-6]. Man researchers conduct in-depth stud on the contour http://www.sensorsportal.com/html/digest/p_467.htm 37

Sensors & Transducers Vol. 181 Issue 10 October 014 pp. 37-44 error calculation and compensation approach in CNC machining. For plane and space curves Geng et al. defined the distance as from the actual cutter location to the line through the two interpolation points on the current sampling period and the last sampling period [7]. Yeh et al. put forward a tangent approimation algorithm which defined the distance from the actual cutter position to the tangent through the current ideal interpolation point on the command tool path [8]. LEE et al. developed a vector control method for the parameter curve which calculated the through solving nonlinear equations with bisection algorithm and Newton iterative algorithm on each sampling period [9]. In the coupled control the most important thing is to calculate the compensation control quantit which is a voltage signal. Then compute the sum of compensation control quantit and following error position control quantit and output to each ais servo sstem [10]. The PID controller is adopted to compute CNC machine tool following error position control quantit usuall. And man researchers use intelligent methods such as neural networs to calculate compensation control quantit. But the neural networ algorithm is slow sometimes which will destro the CNC sstem realtime performance [11 1]. Furthermore the tracing curve curvature changes and disturbances reduce the compensation effect. So it is urgent to put forward a method with predictive function and adaptive abilit to achieve compensation control quantit. Consequentl the immune self-adjusting contour error coupled control method in machining is developed in the paper. Firstl the CNC machine tool coupled control principle and the commonl used computing models are discussed in details; Secondl the immune self-adjusting contour error coupled control method based on grating ruler sensors is introduced to improve machine tool contour accurac; Finall the introduced method is testified on the three-ais CNC milling machine. And the eperimental results show that the proposed method can improve efficientl the machine tool contour accurac. The Contour Error Coupled Control Principle and Commonl Used Contour Error Computing Models.1. The Contour Error Coupled Control Principle With the two-ais lined machining arc profile as eample discuss the when the actual servo gains of two feed ais are inconsistent. Suppose the center of arc profile at origin and the ideal position loop gain of both X ais and Y ais servo sstem is s. However the actual position loop gain of each ais can't match well usuall in CNC machining because of mechanical transmission parts friction and various disturbances. Suppose the servo gains of X ais and Y ais is s and s respectivel the feed speed be v and the radius of arc profile be R. Then the radial error between the actual circle profile and the ideal circle profile caused b the inconsistent X ais and Y ais servo gain is as follows: v s s Δ R = ± ( )sin θ (1) s s where θ is the angle between the actual cutter position vector and X ais vector. The radial error ΔR is negative when machining arc profile clocwise; And the radial error ΔR is positive when machining arc profile anticlocwise. The actual tool path is an ellipse curve. As shown in Equation (1) the radial error ΔR has connection with feed speed and the actual feed ais servo gains. The long ais of the ellipse in the 45 line through origin when machining arc profile counterclocwise in XY plane; While the long ais of the ellipse in the 135 line through origin when machining arc profile clocwise in XY plane. This ma destro the machining qualit and precision. Consequentl it is necessar to stud the multi-ais coordinated control approach to improve the sstem contour precision. Compared with the advanced single ais servo controller the coupled control is a more effective wa to improve machine tool contour accurac. The coupled control steps are shown in Fig. 1. each ais actual displacement measurement computing model coupled control algorithm compensation control quantit Fig. 1. The coupled control steps... The Commonl Used Contour Error Computing Models The tangent approimation computing model is shown in Fig. [1]. For the general two-dimensional curve suppose point P be the actual cutter position on some sampling period point P be the ideal cutter position on the moment line L be the tangent through point P on the ideal tool path the angle between line L and X ais be θ 38

Sensors & Transducers Vol. 181 Issue 10 October 014 pp. 37-44 and the following error which epresses the distance between the actual and the ideal cutter position be E then it can be obtained: E = P P () Suppose the projection of following error E along X ais and Y ais be E and E respectivel and the closest point from point P to the target contour be P 1. Then the can be obtained: ε = P 1 P (3) The calculation of point P 1 coordinates is ver complicated for the comple curve. So man researchers use the tangent approimation computing model. Let PP 1 perpendicular to tangent L. When the following error is smaller the can be calculated approimatel with Equation (4): O ε = P P (4) 1 Fig.. The tangent approimation calculation. For the general curve the curvature radius of certain point can be obtained: d [1 + ( ) ] 3 / ρ d = (5) d d d d where and are the first derivative and d d second derivative respectivel. Consequentl the can be obtained with Equation (6) for general profile curve: ε = E c + E c ε (6) c P 1 P 1 P P E = sinθ /(ρ ) (7) E P E E L c = cosθ + /(ρ ) (8) E d / d sinθ = (9) 1+ ( d / d) sgn( d / d) cosθ = (10) 1+ ( d / d) 3. The Immune Self-adjusting Contour Error Coupled Control Method As shown in Fig. 1 the which calculated according to interpolation instruction and actual tool position on each sampling period should be converted into compensation control quantit. The commonl used compensation control method is shown in Fig. 3. On each sampling period adopt following error PID position controller to calculate compensation control quantit. This method is simple but the compensation effect is unsatisfactor in machining. Fig. 3. The commonl used compensation control method. There are T cells and B cells in the immune sstem of organisms. And B cells can secrete antibod to eliminate eternal invasion antigen [13]. In immune response process T cells can promote or inhibit the proliferation and differentiation of B cells which plas an important role in immune regulation. Adopting the biological sstems immune mechanism the immune self-adjusting coupled control method is developed in the paper which combining the advantages of the immune mechanism and classical PID control algorithm. The introduced method can obtain satisfactor sstem accurac and sstem robustness even curve curvature change and eternal disturbances. The structure of the immune self-adjusting coupled control is shown in Fig. 4. contour error PID controller following error PID controller Fig. 4. The immune self-adjusting coupled control structure. compensation control quantit immune selfadjusting control First order differential compensation control quantit 39

Sensors & Transducers Vol. 181 Issue 10 October 014 pp. 37-44 The corresponding relationship between immune sstem and the compensation control sstem is shown in Table 1. Table 1. The corresponding relationship. Immune sstem The K generation of antigen and antibod breeding Antigen concentration Antibod concentration Contour error compensation control sstem The K sampling period of CNC sstem Contour error Contour error compensation control quantit The introduced immune self-adjusting contour error control method is a nonlinear PID controller essentiall. Suppose the variable gain in the sampling period be p1 () then p1 ( ) = N i= 1 ε ( ) ε ( i) / N (11) where N is the constant. Suppose the control coefficients of X ais following error PID controller be p i and d respectivel; Suppose the control coefficients of Y ais following error PID controller be p i and d respectivel; Suppose the control coefficients of Z ais following error PID controller be p i and d respectivel. Suppose the projection of ε () along X ais Y ais and Z ais be ε () ε () and ε () respectivel. Then the outputs of the immune selfadjusting coupled control in the sampling period along X ais Y ais and Z ais can be obtained: u c ( ) = uc( 1) + p1( ) (( ε ( ) ε ( 1)) + ε ( ) + ( ε ( ) ε ( 1) + ε ( ))) u c ε ( ) + d p (( ε ( ) ε ( 1)) + ε ( 1) + ε ( ))) ( ε ( ) i p ( ) = u ( 1) + 1( ) c d p p i p p p (1) (13) u c ( ) = uc ( 1) + p1( ) (( ε ( ) ε ( 1)) + ε ( ) + ( ε ( ) ε ( 1) + ε ( ))) d p i p p (14) Then the sum of compensation control quantit and the following error position control quantit is output to each ais servo sstem to achieve position control. 4. The Contour Error Coupled Control Eperiments 4.1. The Developed Three-ais CNC Milling Machine The three-ais high precision CNC milling machine is built up with personal computer (PC) and digital signal processing (DSP) motion card. The X ais Y ais and Z ais adopt Yasawa alternating current (AC) servo motors and drivers. The Z ais servo motor has brae function. All of the feed ais adopts grating ruler sensors for displacement measurement and feedbac and the pulse equivalent is 0.001 mm. As shown in Fig. 5 the grating ruler sensors are composed of instruction grating and grating reading head. The instruction gratings are fied in the milling machine moving parts and the grating reading head are arranged in the milling machine fied component. The three-ais high precision CNC milling machine hardware structure is shown in Fig. 6. In the three ais CNC milling machine the PC acts as upper computer and man-machine interface which performs the command control code editing state detection and displa function; And the DSP motion control card acts as lower machine which performs interpolation position control coupled control functions. The PC adopts the Windows XP as development platform and the data communication between PC and DSP is achieved through USB.0. The software function structure of the CNC milling machine is shown in Fig. 7. 4.. The Contour Error Coupled Control Eperiments As shown in Fig. 8 the tool path is epressed with NURBS curve: The control points be A 1 (55055 A (555555) A 3 (0 550) A 4 (-55 55-55) A 5 (-55 0-55) A 6 (-55-55-55) A 7 (0-550) A 8 (55-5555) A 9 (55055); The corresponding weights are (1 0.6 1 0. 1 0.5 1 0.3 1); 40

Sensors & Transducers Vol. 181 Issue 10 October 014 pp. 37-44 The not vector be (0 0 0 0 0.5 0.375 0.5 0.65 0.75 1 1 1 1). The feed speed is 700 mm/min. When adopting the eisting compensation control method shown in Fig. 3 the interpolation feed curve is shown in Fig. 9. Under the same woring conditions when adopting the developed immune self-adjusting control method the interpolation feed curve is shown in Fig. 10. The contour error curve between Fig. 9 and Fig. 10 is compared in Table. The eperiment results show that the proposed immune self-adjusting control method can improve machine tool contour accurac remarabl. Table. The curve comparison. Fig. 5. The grating ruler sensors structure. Figure Fig. 9 Fig. 10 Contour error ma / (mm) 0.081 0.05 Contour error mean / (mm) 0.034 0.06 Contour error std / (mm) 0.07 0.01 PC USB progra -mmable DSP motion card X Y and Z ais servo drivers pulse encoders velocit feedbac X Y and Z ais servo motors ball screw transmission X Y and Z ais wortable grating ruler sensors displacement measurement Fig. 6. The three-ais high precision CNC milling machine hardware structure. humancomputer interaction function module parameter settings machining path preview feed ais position displa three-ais CNC milling machine software function program process module manual control module new processing procedure select eisting processing procedure line interpolation arc interpolation and NURBS interpolation module X ais Y ais and Z ais step movement control X ais Y ais and Z ais manual control X ais Y ais and Z ais return reference point program running module coupled control processing pause and continue error recording file Fig. 7. The software function structure of the three-ais CNC milling machine. 41

Sensors & Transducers Vol. 181 Issue 10 October 014 pp. 37-44 ( ) Contour error mm 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.0 0.01 Fig. 8. The tool path curve. 0 0 3 6 9 1 15 18 1 4 7 30 Time ( sec) Fig. 9. The curve when adopting the eisting compensation method shown in Fig. 3. ( ) Contour error mm 0.06 0.05 0.04 0.03 0.0 0.01 0 0 3 6 9 1 15 18 1 4 7 30 Time ( sec ) Fig. 10. Contour error curve when adopting the developed immune self-adjusting control method. 5. Conclusions The CNC machine tool servo drive sstem is much comple and the transmission parts friction and electrical components parameters ma change in machining which will destro the contour accurac. The CNC machine tool coupled control principle is analed in details with the arc profile machining as eample and the commonl used computing models are discussed. Adopting the biological sstems immune mechanism the immune self-adjusting coupled control method based on grating ruler sensors is developed in the paper combining the advantages of the immune mechanism and classical PID control algorithm. The introduced method is testified on the three-ais CNC milling machine. And the results show that the proposed immune self-adjusting control method can improve machine tool contour accurac remarabl. Acnowledgements The authors are grateful to the Project of the National Natural Science Foundation of China (No. 5110536) and the Project of the Taishan Scholar Program of China. References [1]. Bung-Sub Kim Seung-Koo Ro Jong-Kweon Par Development of a 3-ais destop milling machine and a CNC sstem using advanced modern control algorithms International Journal of Precision Engineering and Manufacturing Issue 11 010 pp. 39-47. []. Xu Zhiiang Zhao Guoong Zhao Fuling A multiais cross-coupling control approach based on NURBS curve interpolation Mechanical Science and Technolog Vol. 5 Issue 1 006 pp. 1451-1453. [3]. Peng Chao-Chung Chen Chieh-Li Biaial contouring control with friction dnamics using a contour inde approach International Journal of Machine Tools and Manufacture Vol. 47 Issue 10 007 pp. 154-1555. [4]. Ming-Yang Cheng Ke-Han Su Shu-Feng Wang Contour error reduction for free-form contour following tass of biaial motion control sstems Robotics and Computer-Integrated Manufacturing Vol. 5 Issue 009 pp. 33-333. [5]. Zhao Ximei Guo Qingding Zero phase adaptive robust cross coupling control for NC machine multiple lined servo motor Proceedings of the China Electrical Engineering Vol. 8 Issue 1 008 pp. 19-133. [6]. Liu Yi Cong Shuang Optimal contouring control based on tas coordinate frame and its simulation Journal of Sstem Simulation Vol. 1 Issue 11 009 pp. 3381-3386. [7]. Geng Lirong Zhou Kai Research on real time compensation method based on time series predictive technolog for of CNC machine tool Manufacturing Technolog & Machine Tool Issue 6 004 pp. -5. [8]. Sh-Shiuh Yeh Pau-Lo Hsu Analsis and design of integrated control for multi-ais motion sstems IEEE Transactions on Control Sstems Technolog Vol. 11 Issue 3 003 pp. 375-38. [9]. Mung-Hoon Lee Seung-Han Yang Young-Su Kim A multi-ais controller for free form Curves JSME International Journal Vol. 47 Issue 1 004 pp. 144-149. 4

Sensors & Transducers Vol. 181 Issue 10 October 014 pp. 37-44 [10]. Song Bao Zhou Yunfei Research of the multi-ais integrated control Machine Tool & Hdraulics Issue 10 004 pp. 141-143. [11]. Ke-Han Su Ming-Yang Cheng Contouring accurac improvement using cross-coupled control and position error Compensator International Journal of Machine Tools and Manufacture Vol. 48 Issue 1 008 pp. 1444-1453. [1]. Sh-Shiuh Yeh Pau-Lo Hsu Estimation of the contouring error vector for the cross-coupled control design IEEE/ASME Transactions on Mechatronics Vol. 7 Issue 1 00 pp. 44-50. [13]. Wang Bin Li Aiping Optimal design of fu immune nonlinear PID control Control Engineering of China Issue 14 007 pp. 81-83. 014 Copright International Frequenc Sensor Association (IFSA) Publishing S. L. All rights reserved. (http://www.sensorsportal.com) 43

44 Sensors & Transducers Vol. 181 Issue 10 October 014 pp. 37-44