This article presents ideas for contour error control of machine tools. A demonstration of these ideas is performed on a biaxial drive system exhibiting linear and circular contouring. A new independent contour error control (ICEC) strategy, which utilizes the equations of the well-known cross-coupling controller, is shown to diminish a linear contour error without using any cross-feeding signals between the driving axes. For circular contouring, new exact equations for contour error calculations are presented. These exact equations may lead to some significant control strategies that can be based on the cross-coupling control (CCC) concept. One new CCC strategy, based on one of these exact contour error equations, is shown to be very promising for circular contouring. Finally, the proposed strategies have been further developed for either independent or cross-coupling backlash compensation. These backlash compensation schemes may save complications of having special means for backlash control if CCC systems are intended for implementation.
KorenY.Cross-coupled biaxial computer control for manufacturing systemsTrans. ASME, J. Dynamic Systems, Measmt Control, 1980, 102, 265–272.
4.
KorenY.LoC. C.Variable-gain cross-coupling controller for contouringCIRP Annls, 1991, 40, 371–374.
5.
KorenY.LoC. C.Advanced controllers for feed drivesCIRP Annls, 1992, 41, 689–698.
6.
ZhongQ.ShiY.MoJ.HaungS.A linear cross-coupled control system for high speed machiningInt. J. Advd Mfg Technol., 2002, 19, 558–563.
7.
YehS.-S.HsuP.-L.Estimation of the contouring error vector for the cross-coupled control designIEEE/ASME Mechatronics, 2002, 7 (1), 44–51.
8.
YehS.-S.HsuP.-L.Analysis and design of integrated control for multi-axis motion systemsIEEE Trans. on Control System Technol., 2003, 11 (3), 375–382.
9.
ChengY.-M.ChinJ.-H.Machining errors as ensembles of cutting, feeding and machine structure effectsInt. J. Mach. Tools Mf., 2003, 43, 1001–1014.
10.
YookJ.TilburyD.ChervelaK.SoparkarN.Decentralized, modular real-time control for machining applications. In Proceedings of the 1998 American Control Conference, pp. 844–849 (IEEE Publications).
11.
ChiuG. T.-CTomizukaM.Contouring control of machine tool feed drive systems: A task coordinate frame approachIEEE Trans. on Control System Technol., 2001, 9 (1), 130–139.
12.
ShihY.-T.ChenC.-S.LeeA.-C.A novel cross-coupling control design for bi-axis motionInt. J. Mach. Tool Mf., 2002, 42, 1539–1548.
13.
De MarchiJ. A.Modeling of dynamic friction, impact backlash and elastic compliance nonlinearities in machine tools, with applications to asymmetric viscous and kinetic friction identification. PhD Thesis, Rensselaer Polytechnic Institute, Troy, New York, 1998.
14.
MackiJ. W.NistriP.ZeccaP.Mathematical models for hysteresisSIAM Rev., March 1993, 35 (1), 94–123.
15.
TaoG.KokotovicV.Adaptive control of systems with backlashAutomatica, 1993, 9 (2), 323–335.
16.
ReckerD. A.Indirect adaptive non-linear control of discrete time systems containing a dead-zoneInt. J. Adaptive Control Signal Processing, 1997, 11, 33–48.
17.
SeidlD. R.LamSui-LunPutmanJ. A.LorenzR. D.Neural network compensation of gear backlash hysteresis in position-controlled mechanismsIEEE Trans. on Applied Industry, 1995, 31 (6), 1475–1483.
18.
SteinJ. L.WangC.-H.Estimation of gear backlash: Theory and simulationTrans. ASME, J. Dynamic Systems, Measmt Control, 1998, 120, 74–82.
19.
GerdesJ. C.KumarV.An impact model of mechanical backlash for control system analysis. In Proceedings of the American Control Conference ACC, vol. 5, pp. 3311–3315.
20.
NordinM.GutmanP.-O.Controlling mechanical systems with backlash - a surveyAutomatica, 2002, 38 (10), 1633–1649.
21.
YounkinG. W.Modeling machine tool feed servo drives using simulation techniques to predict performanceIEEE Ind. Applics, 1991, 27 (2), 268–274.
22.
LingY.TaoG.Numerical design and analysis of backlash compensation for a multivariable nonlinear tracking system. In Proceedings of the 1999 American Control Conference, San Diego, California, pp. 3539–3543 (IEEE Publications).
23.
TarngY. S.KaoJ. Y.LinY. S.Identification of and compensation for backlash on the contouring accuracy of CNC machining centresInt. J. Adv. Mfg Technol., 1997, 13, 77–85.
24.
SugieH.IwasakiT.NakagawaH.KohdaS.Compensation for position-varying lost motion to improve the contouring accuracy of NC machine tools. In Proceedings of the Industrial Electronics Conference, 2000, Vol. 3, pp. 2213–2218 (IEEE Publications).
25.
NordinM.GalicJ.GutmanP.-O.New models for backlash and gear playInt. J. Adaptive Control Signal Processing, 1997, 11, 49–63.
26.
LagerbergA.EgardtB.Estimation of backlash with application to automotive powertrainsIn Proceedings of the 42nd Conference on Decision and control, Maui, Hawaii, December 2003, pp. 4521–4526.
27.
LagerbergA.EgardtB.Estimation of backlash in automotive powertrains - an experimental validationIn Proceedings of the 1st IFAC symposium on Advances in automotive control, Salermo, Italy, 19-23 April 2004, pp. 1–6.
