Analytical calculation of the CNC machines servo drives position loop gain

• Autorzy: Pandilov Z. , Dukovski V.
• Języki publikacji: EN

Abstrakty

EN

Purpose: One of the most important factors which influence on the dynamical behavior of the servo drives with rotary and linear motors for CNC machine tools is position loop gain or Kv factor. Design/methodology/approach: From the magnitude of the Kv-factor depends tracking or following error. In multi-axis contouring the following errors along the different axes may cause form deviations of the machined contours. Generally position loop gain Kv should be high for faster system response and higher accuracy, but the maximum gains allowable are limited due to undesirable oscillatory responses at high gains and low damping factor. Usually Kv factor is experimentally tuned on the already assembled machine tool. Findings: This paper presents a simple method for analytically calculation of the position loop gain Kv. A combined digital-analog models of the 6-th order (for rotary motors) and 4-th order (for linear motors) of the position loop are presented. In order to ease the calculation, the 6-th order system or 4-th order system is simplified with a second order model. With this approach it is very easy to calculate the Kv factor for necessary position loop damping. The difference of the replacement of the 6-th order system and 4-th order system with second order system is presented with the simulation program MATLAB. Analytically calculated Kv factor for the servo drives with rotary motors is function of the nominal angular frequency ů and damping D of the servo drive electrical parts (rotary motor and regulator), nominal angular frequency ům and damping Dm of the mechanical transmission elements, as well as sampling period T. Kv factor for the servo drives with linear motors is calculated as function of the nominal angular frequency ům and damping D of the linear motor servo drive electrical parts (motor and regulator) and sampling period T. Research limitations/implications: The influence of nonlinearities was taken with the correction factor Originality/value: Our investigations have proven that experimentally tuned Kv factor differs from analytically calculated Kv factor less than 10%, which is completely acceptable.

Słowa kluczowe

EN

numerical technique; CNC machine tool; servo-drive system; position loop gain

PL

technika nuneryczna; obrabiarka CNC; serwonapęd

• Wydawca: International OCSCO World Press
• Czasopismo: Journal of Achievements in Materials and Manufacturing Engineering
• Rocznik: 2009
• Tom: Vol. 37, nr 2
• Strony: 578--583
• Opis fizyczny: Bibliogr. 15 poz., rys., tabl.

Twórcy

autor

Pandilov Z.

autor

Dukovski V.

• Faculty of Mechanical Engineering, University “Sv. Kiril i Metodij”-Skopje, Karpos II b.b., P.O.Box 464, MK-1000, Skopje, Republic of Macedonia,

Bibliografia

• [1] H. Gao, Increase of Dynamic Contour Accuracy by Application of Contour Error Oriented Optimization Exemplified by a Linear Motor Feed Drive, Dissertation, TU Darmstadt, Germany, 1999 (In German).
• [2] T. B. Bullock, G. W. Younkin, Bode diagrams analyze servosystems, Machine Design, February 9 (1995) 49-54.
• [3] S. Gordon, M. T. Hillery, Development of a high-speed CNC cutting machine using linear motors, Journal of Materials Processing Technology 166 (2005) 321-329.
• [4] H. Gross, J. Hamann, G. Wiegaertner, Electrical Feed Drives in Automation: Basic, Computation, Dimensioning, MCD Corporate Publishing, Erlangen and Munich, 2009 (In German).
• [5] L. Harder, J.A. Isakssson, Robust PI-control of cutting forces in turning, Proceedings of 31 MATADOR Conference, United Kingdom, 1995, 261-266.
• [6] W. T. Lei , Y. Y. Hsu, Error measurement of five-axis CNC machines with 3D probe-ball, Journal of Materials Processing Technology 139 (2003) 127-133.
• [7] X. Luo, K. Cheng, D. Webb, F. Wardle, Design of ultraprecision machine tools with applications to manufacture of miniature and micro components, Journal of Materials Processing Technology 167 (2005) 515-528.
• [8] Z. Pandilov, V. Dukovski: Application of the double ball bar test for optimizing contouring accuracy of CNC milling machine, Proceedings of the 11th International Scientific Conference on Production Engineering, CIM 2007, Croatia, 2007, 251-256.
• [9] Z. Pandilov: Analytical determination of the position loop gain for linear motor CNC machine tool, Journal of Achievements in Materials and Manufacturing Engineering 26/2 (2008).171-174.
• [10] D. A. Smith, Wide bandwidth control of high-speed milling machine feed drives, Dissertation, University of Florida, USA, 1999.
• [11] P. Soucek , Servo mechanisms for machine tools, CVUT, Prague, 2009 (In Czech).
• [12] G. W. Younkin, Industrial Servo Control Systems: Fundamentals and Applications, Marcel Dekker Inc., 1996.
• [13] J. Wang, Robust Tracking Controller Design with Application to an X-Y Feed Table for High-Speed Machining, PhD dissertation, ISBN,90-5682-468-6, Katholieke Universiteit Leuven, Belgium, 2004.
• [14] M. Weck, Machine Tools and Machinig Systems, Volume 3, Mechatronics Systems: Feed Drives and Process Diagnosis, Springer, 2009 (In German).
• [15] M. Weck, P. Krueger, C. Brecher, Limits for controller settings with electric linear direct drives, International Journal of Machine Tools and Manufacture 41 (2001) 65-88.