Stability and nonlinear vibrations of couped discrete and continuous dynamical systems  Page description

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Details of project

  
Identifier
43368
Type K
Principal investigator Stépán, Gábor
Title in Hungarian Csatolt diszkrét és folytonos dinamikai rendszerek stabilitása és nemlineáris rezgései
Title in English Stability and nonlinear vibrations of couped discrete and continuous dynamical systems
Panel Engineering, Metallurgy, Architecture and Transport Sciences
Department or equivalent Műszaki Mechanikai Tanszék (Budapest University of Technology and Economics)
Participants Csernák, Gábor
Insperger, Tamás
Kollár, László E.
Kovács, László
Szabó, Zsolt
Szolgay, Péterné
Starting date 2003-01-01
Closing date 2007-12-31
Funding (in million HUF) 10.872
FTE (full time equivalent) 0.00
state closed project





 

Final report

  
Results in Hungarian
Gépészmérnöki feladatok megoldásakor, ahol mozgások leírása, tervezése a cél, hagyományosan folytonos szemlélet dominál. A műszaki-technológiai fejlesztés azonban sok olyan rezgési problémába ütközött az utóbbi évtizedben, ahol a fejlődés további korlátját jelentő rezgéseket diszkrét hatások okozzák. Ennek alappéldái a robotika rezgési jelenségei, ahol a newtoni dinamikával leírható, folytonosan viselkedő rendszert mikroprocesszorok segítségével szabályoznak, és így a mintavételezésen és kerekítési hibákon keresztül időbeli és térbeli digitális hatásokat kapcsolnak hozzá. Diszkrét és folytonos rendszerek dinamikájának együttes vizsgálatára szükség van akkor is, ha a fizikai rendszer maga szabályozza a folytonos rendszert diszkrét módon, mint a nagy amplitúdójú szerszámgéprezgések, a gyorsan forgó tengelyek rubbing jelensége, vagy a kerekek térbeli gördülése és csúszása során jelentkező kapcsolgatás esetén. Olyan algoritmusokat dolgoztunk ki, amelyek a lehető legkevesebb numerikus közelítést tartalmazva, pontosan és egyszerűen adják meg az ilyen rendszerek stabilitásának feltételeit, illetve a stabilitásvesztéskor kialakuló rezgések jellegét, frekvenciáit, amplitúdóit. Ezekkel a módszerekkel sikerült pl. robotok emberekkel való érintkezéséhez szükséges erőszabályozásokat terveznünk az EU rehabilitációs robot projektjében, új nagysebességű marási technológiákat javasolnunk, magyarázatot adnunk kerekek fékezéskor kialakuló laterális (simmiző) rezgésére.
Results in English
Time-continuous approach dominates the solution of those problems of mechanical engineering where the goal is the analysis or design of certain motions. The technological development, however, has often been set back during the last decade by vibration problems originated in discrete effects. Basic example is the vibration phenomenon of robots, where the continuous physical system described the Newtonian laws is subjected to control by means of microprocessors. These introduce digital effects both in time and space via the sampling and the round-off, respectively. The coupled discrete and continuous systems dynamics are in the focus of critical vibration phenomena also in those cases when the physical system regulates itself in a discrete way. This happens during the large amplitude oscillations of machine tools, the rubbing phenomenon of rotors, or the subsequent switches between the rolling and sliding dynamics of wheels. We developed algorithms that give the stability conditions of these systems in a reliable, efficient and still simple way. Moreover, these methods also describe the nature of these vibrations, provide their frequency content and amplitude range. This way, for example, we designed the force control of rehabilitation robots in an EU project where human and robot must interact by touching each other, suggested new technological parameter domains for high-speed milling, or explained the lateral vibrations (shimmy) of wheels during braking.
Full text http://real.mtak.hu/1040/
Decision
Yes





 

List of publications

  
Insperger, T., Stépán, G., Bayley, P. V., Mann, B. P.: Multiple chatter frequencies in milling processes, Journal of Sound and Vibration 262 (2003) 333-345, 2003
Insperger, T., Stépán, G.: Stability of the damped Mathieu equation with time delay, ASME Journal of Dynamic Systems, Measurement and Control 125 (2003) 166-171, 2003
Insperger, T., Mann, B. P., Stépán, G., Bayley, P. V.: Stability of up-milling and down-milling, Part 1: Alternative analytical methods, International Journal of Machine Tools and Manufacture, 43 (2003) 25-34, 2003
Mann, B. P., Insperger, T., Bayley, P. V., Stépán, G.: Stability of up-milling and down-milling, Part 2: Experimental verification, International Journal of Machine Tools and Manufacture, 43 (2003) 35-40, 2003
Stréli T., Kisfalusi, K., Stépán, G.: Stability of digital force control in the presence of damping, Proceedings of GaMM Tagung (Dresden, 2004) PAMM Volume 4, Issue 1, pp. 143-144 (Published Online: 24 Nov 2004 Copyright © 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim), 2004
Kovács, L. L., Stépán, G.: Dynamics of digital force control applied in rehabilitation robotics, Meccanica 38 (2003) 213-226, 2003
Insperger, T., Stépán, G.: Comparison of the Fargue-type analytical approximation and the numerical semi-discretization method for delayed systems, Journal of Computational and Applied Mechanics 4 (2003) 203-215, 2003
Insperger, T., Stépán, G.: Semi-discretization of time-periodic delay-differential equations, 7th SIAM Conference on Applications of Dynamical Systems (Salt Lake City, Utah, 2003), 2003
Baksa, I., Stépán G.: Motion analysis of digitally controlled machines, Proceedings of GaMM Tagung (Dresden, 2004) PAMM Volume 4, Issue 1, pp. 127-128 (Published Online: 24 Nov 2004 Copyright © 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim), 2004
Kovács, L. L., Stépán, G., Insperger, T.: Outer-loop force control of industrial robots, Proceedings of Eleventh IFToMM World Congress in Mechanism and Machine Science (Tianjin, 2004), China Machine Press (CD-ROM ISBN7-89492-107-6/TH-14) pp. 1746-1750, 2004
Olson, B. J., Shaw, S. W., Stépán, G.: Nonlinear dynamics of vehicle traction, Vehicle System Dynamics 40 (2003) 377-399, 2003
Stépán G.: Mikrokáosz, Természet Világa 135 (2004) 60-64, 2004
Insperger, T., Stépán, G.: Stability transition between 1 and 2 degree-of-freedom model of milling, Periodica Polytechnica, 48 (2004) 27-39, 2004
Csernák, G., Stépán, G.: Fractal dimension as measure of control time, Periodica Polytechnica, 48 (2004) 17-25, 2004
Kollár, L. E., Stépán, G., Turi, J.: Dynamics of piecewise linear discontinuous maps, International Journal of Bifurcation and Chaos 14 (2004) 2341-2351, 2004
Kollár, L. E., Stépán, G., Turi, J.: Dynamics of sampled systems with backlash, Proceedings of Eleventh IFToMM World Congress in Mechanism and Machine Science (Tianjin, 2004), China Machine Press (CD-ROM ISBN7-89492-107-6/TH-14) pp. 1498-1502, 2004
Insperger, T., Stépán, G.: Vibration frequencies in high-speed milling processes, or a positive answer to Davies, Pratt, Dutterer and Burns, ASME Journal of Manufacturing Science and Engineering 126 (2004) 481-487, 2004
Insperger, T., Stépán, G.: Updated semi-discretization method for periodic delay-differential equations with discrete delay, International Journal for Numerical Methods in Engineering 61 (2004) 117-141, 2004
Csernák, G., Stépán, G.: Lifetime of transient chaotic vibrations in digitally controlled systems, Proceedings of Eleventh IFToMM World Congress in Mechanism and Machine Science (Tianjin, 2004), China Machine Press (CD-ROM ISBN7-89492-107-6/TH-14) pp. 1465-1469, 2004
Szalai, R., Stépán, G., Hogan, S. J.: Global Dynamics of low immersion high-speed milling, Chaos 14 (2004) 1069-1077, 2004
Insperger, T., Stépán, G.: Stability analysis of turning with periodic spindle speed modulation via semi-discretisation, Journal of Vibration and Control 10 (2004) 1835-1855, 2004
Orosz, G., Stépán, G.: Hopf Bifurcation Calculations in Delayed Systems with Translational Symmetry, Journal of Nonlinear Science 14 (2004) 441-464, 2004
Kollár, L., Stépán, G., Turi, J.: Dynamics of delayed piece-wise linear systems, Proc of Fifth Mississippi State Conf on Diff Eqns & Comp Sim (Starkville, 2001), Electronic Journal of Differential Equations, Conference 10 (2003) pp. 163-185., 2003
Stépán, G., Szalai, R., Mann, B., Bayly, P., Insperger, T., Gradisek, J., Govekar, E.: Global attractors of high-speed milling – analysis, numerics and experiments, Proceedings of the 2003 ASME DETC, 19th Biennial Conference on Mechanical Vibration and Noise (Chicago, 2003) (Eds: S. Sinha, E. Butcher) DETC03/VIB-48572 (2003) pp. 1-8., 2003
Szalai, R., Stépán, G.: Stability boundaris of high-speed milling correspnding to period doubling are essentially closed curves, Proceedings of 2003 ASME International Mechanical Engineering Congress and R&D Expo (Washington D.C., 2003) IMECE2003-42122 (2003), pp. 1-6., 2003
Insperger, T., Schmitz, T. L., Burns, T. J., Stépán, G.: Comparison of analytical and numerical simulations for variable spindle speed turning, Proceedings of ASME International Mechanical Engineering Congress and R&D Expo, Washington, D.C. (2003), paper no. IMECE2003-41809 (CD-ROM) pp.1-8, 2003
Stépán, G.: Nonlinear dynamics, as a tool of technological development, microCAD 2003 International Scientific Conference (Miskolc, Hungary, 2003), 2003
Stépán, G.: How delay equations arise in engineering, Symposium on Delay Equations and their Applications (Bristol, 2003), 2003
Baksa, I., Stépán, G.: Motion analysis of digitally controlled machines, Proceedings of 4th Conference on Mechanical Engineering GÉPÉSZET 2004 (Budapest, 2004), pp. 338-342, 2004
Csernák, G., Stépán, G.: Simple Coulomb friction oscillator: asymmetric and sticking motions, Proceedings of 4th Conference on Mechanical Engineering GÉPÉSZET 2004 (Budapest, 2004), pp. 348-352, 2004
Insperger, T., Stépán, G.: Digital control of dynamical systems – stability problems due to time delay, Proceedings of 4th Conference on Mechanical Engineering GÉPÉSZET 2004 (Budapest, 2004), pp. 362-366, 2004
Kovács, L., Stépán, G.: Deadtime effect on indirect force control of industrial robots, Proceedings of 4th Conference on Mechanical Engineering GÉPÉSZET 2004 (Budapest, 2004), pp. 377-381, 2004
Triesz, P., Stépán, G.: Discrete-time mechanical model for the rubbing phenomenon of rotordynamics, Proceedings of 4th Conference on Mechanical Engineering GÉPÉSZET 2004 (Budapest, 2004), pp. 417-420, 2004
Stépán, G., Szalai, Insperger, T., R., Mann, B., Gradisek, J., Govekar, E., Bayly, P.: Dynamics and stability of high-speed milling, Proceedings of the 37th CIRP International seminar on Manufacturing Systems (Ed.: L. Monostori, ISBN 963 214 905 X), Budapest (2004) pp. 119-125, 2004
Stépán, G., Takács, D.: Dynamics of balancing, Proceedings of the First Conference on Biomechanics (Budapest, 2004) (Ed.: I. Bojtár, ISBN 963 420 799 5) pp. 415-422, 2004
Gradisek, J., Kalveram, M., Insperger, T., Weinert, K., Stépán, G., Govekar, E., Grabec, I.: On stability prediction for low radial immersion milling, Proceedings of the 7th CIRP International Workshop on Modeling of Machining Operations, 2004, (Cluny, France, 2004) (Eds.: Moisan, A., Poulachon, G.). pp. 227-233, 2004
Insperger, T., Stépán, G., Turi, J.: Comparison of zeroth- and first-order semi-discretizations for the delayed Mathieu equation, Proceedings of 43rd IEEE Conference on Decision and Control (Bahamas, 2004), pp. 1-5, 2004
Insperger, T., Lekien, F., Salman, H., Haller, G., Stépán, G.: Control of separation point in periodic flows including delay effects, Proceedings of IFAC Workshop on Periodic Control Systems (Yokohama, Japan, 2004) pp. 1-5, 2004
Stépán, G., Insperger, T.: Stability of time-periodic time-delay systems, Time Delay Systems (Eds.: W Michelis, D. Roose) Elsevier, NY, ISBN 0-08-044583-7, pp. 15-22, 2005
Stépán G, Kovács LL, Kövecses J: Bifurcations caused by sampling effects in robotic force control, Vibration Control of Nonlinear Mechanisms and Structures (Eds: Ulbrich H, Gunthner W, SMIA Series, Vol. 130) Springer, Dordrecht (ISBN-10 1-4020-4160-8 (HB)) pp. 331-342, 2005
Insperger, T., Gradisek, J., Kelveram, M., Stépán, G., Weinert, K., Govekar, E.: Machine tool chatter and surface quality in milling processes, Proceedings of ASME International Mechanical Engineering Congress (Anaheim, California, 2004) paper no. IMECE2004-59692 (CD ROM) pp. 1-13, 2004
Stépán, G.: Nonlinear dynamics of balancing with memory effects, Workshop on Stochastic Systems With Delay and Memory (Wittenberg-Lutherstadt, Germany, 2004), 2004
Stépán, G., Insperger, T., Szalai, R.: Nonlinear dynamics of high-speed milling, 21st International Congress of Theoretical and Applied Mechanics (extended abstracts on CD ROM, paper no. FSM2L_10252, ISBN 83-89697-01-1, pp 1-2.) (Warsaw, Poland, 2004), 2004
Stépán, G.: Micro-chaos, Invited plenary lecture at Dynamics Days 2004 (Palma de Mallorca, Spain, 2004), 2004
Csernák, G., Stépán, G.: Quick estimation of escape rate with the help of fractal dimension, Communications in Nonlinear Science and Numerical Simulation 11 (2005) 595-605., 2005
Insperger, T., Stépán, G.: Stability improvements of robot control by periodic variation of the gain parameters, Proceedings of Eleventh IFToMM World Congress in Mechanism and Machine Science (Tianjin, 2004), China Machine Press (CD-ROM ISBN7-89492-107-6/TH-14) pp. 1816-1820, 2004
Insperger, T., Stépán, G.: Optimization of digital control with delay by periodic variation of the gain parameters, Proceedings of IFAC Workshop on Periodic Control Systems (Yokohama, Japan, 2004) pp. 1-6., 2004
Stépán, G., Szalai, R., Insperger, T.: Nonlinear dynamics of high-speed milling subjected to regenerative effect, Nonlinear Dynamics of Production Systems (Eds.: G. Radons, R. Neugebauer) pp. 111-128, 2004
Kovács, L., Insperger, T., Stépán, G.: Teaching-in force control of industrial robots used in medical applications, Proceedigns of 14th CISM-FToMM Symposium on Robot Design, Dynamics and Control (Montreal, 2004) (Eds.: J. Angeles, Ph. Bidaud, ISBN 0-662-35997-6) pp. 1-10, 2004
Stréli, T., Kisfalusi, K., Stépán, G.: Stability of digital force control in the presence of damping, Proceedings of 4th Conference on Mechanical Engineering GÉPÉSZET 2004 (Budapest, 2004), pp. 407-411, 2004
Stépán G, Kovács LL, Kövecses J: Bifurcations caused by sampling effects in robotic force control, Vibration Control of Nonlinear Mechanisms and Structures (Eds: Ulbrich H, Gunthner W) Springer, Dordrecht, 2005 (ISBN-10 1-4020-4160-8 (HB)) 331-342, 2005
Stépán, G., Szalai, R., Hogan, J: The chaotic oscillations of high-speed milling, Chaotic Dynamics and Control of Systems and Processes in Mechanics (Eds.: G. Rega, F. Vestroni), Springer, Dordrecht, 2005 (ISBN I-4020-3267-6) 147-158., 2005
Stépán, G., Insperger, T., Szalai, R.: Delay, parametric excitation, and the nonlinear dynamics of cutting processes, International Journal of Bifurcation and Chaos 15 (2005) 2783-2798, 2005
Stépán, G., Szalai, R., Mann, B. P., Bayly, P. V., Insperger, T., Gradisek, J., Govekar, E.: Nonlinear dynamics of high-speed milling – analysis, numerics, and experiments, ASME Journal of Vibration and Acoustics 127 (2005) 197-203., 2005
Govekar, E., Gradisek, J., Kalveram, M., Insperger, T., Weinert, K., Stépán, G., Grabec, I.: On stability and dynamics of milling at small radial immersion, CIRP Annals - Manufacturing Technology 54 (2005) 357-362., 2005
Csernák, G., Stépán, G.: Life expectancy of transient microchaotic behaviour, Journal of Nonlinear Science 15 (2005) 63-91., 2005
Olson, B. J., Shaw, S. W., Stépán, G.: Stability and bifurcation of longitudinal vehicle braking, Nonlinear Dynamics, 40 (2005) 339-365., 2005
Gradisek, J., Govekar, E., Grabec, I., Kalveram, M., Weinert, K., Insperger, T., Stépán, G.: On stability prediction for low radial immersion milling, Machine Science and Technology 9 (2005) 117-130., 2005
Gradisek, J., Kalveram, M., Insperger, T., Weinert, K., Stépán, G., Govekar, E., Grabec, I.: On stability prediction for milling, International Journal of Machine Tools and Manufacture 45 (2005) 769-781., 2005
Kovács L.L., Kövecses J., Stépán G.: Dynamic behaviour of robots with digital force control, Proceedings of the 8th Conference on Dynamical Systems Theory and Applications (Lodz, Poland, 2005), (eds. Awrejcewicz J., Sendkowski D., Mrozowski J.) Vol. 1, pp.335-342, 2005
Insperger, T., Stépán, G., Hartung, F., Turi, J.: State dependent regenerative delay in milling processes, Proceedings of ASME International Design Engineering Technical Conferences, (Long Beach, California, 2005), paper no. DETC2005-85282 (CD-ROM) pp. 1-6., 2005
Insperger, T., Stépán, G.: Act and wait control concept in force-controlled systems with discrete delayed feedback, Proceedings of ASME International Design Engineering Technical Conferences, (Long Beach, California, 2005), paper no. DETC2005-85036 (CD-ROM) pp. 1-8., 2005
Insperger, T., Stépán, G., Turi, J.: State-dependent delay model for regenerative cutting processes, Proceedigns of Fifth EUROMECH Nonlinear Dynamics Conference, ENOC 2005, (Eindhoven, The Netherlands, 2005), pp. 1124-1129., 2005
Csernák, G., Stépán, G.: Symmetric and Asymmetric Motions of a Harmonically Driven Dry-friction Oscillator, Proceedigns of Fifth EUROMECH Nonlinear Dynamics Conference, ENOC 2005, (Eindhoven, The Netherlands, 2005), pp. 258-263., 2005
Stépán, G.: Delay, parametric excitation and the nonlinear dynamics of cutting processes (keynote lecture), 5th Euromech Nonlinear Dynamics Conference (Eindhoven, The Netherlands, 2005)., 2005
Takács, D., Stépán, G.: Experimental study of the shimmy motion of wheels, 22nd Danubia-Adria Symposium on Experimental Methods in Solid Mechanics (Parma, Italy, 2005)., 2005
Stépán, G., Takács, D.: Wheel shimmy caused by distributed delays, 8th SIAM Conference on Applications of Dynamical Systems (Salt Lake City, Utah, 2005), 2005
Stépán, G.: Dynamics of rehabilitation robots – shake hands or hold hands? (keynote lecture), Recent Advances in Nonlinear Mechanics (Aberdeen, UK, 2005)., 2005
Kovács L.L., Stépán G., Kövecses J: Discrete-time stability and vibrations of systems with unidirectional force control, 2005 CCToMM Symposium on Mechanisms, Machines, and Mechatronics, (Longueuil, Québec, Canada, 2005) CCToMM05-P17 (CDROM) pp. 1-5., 2005
Baksa, I., Kisfalusi, K., Stépán, G.: Experiments with digital force control, Proceedings of the 20th Canadian Congress of Applied Mechanics (CANCAM 2005), (Montréal, Québec, Canada, 2005) pp. 394-395., 2005
Kovács L.L., Stépán G., Kövecses J.: A case study on the stability of digital force control of robotic manipulators, Proceedings of the 20th Canadian Congress of Applied Mechanics (CANCAM 2005), (Montréal, Québec, Canada, 2005) pp. 427-428., 2005
Stépán G.: Ember és gép - kezet fogunk vagy kezet rázunk?, Magyar Tudomány 5 (2005) 580-584, 2005
Insperger T, Stépán G, Turi J: State-dependent delay in regenerative turning processes, Nonlinear Dynamics 47 (2007) 275-283, 2007
Stépán G, Insperger T: Stability of time-periodic and delayed systems — a route to act-and-wait control, IFAC Annual Reviews in Control 30 (2006) 159-168, 2006
Insperger T, Gradisek J, Kalveram M, Stépán G, Weinert K, Govekar E: Machine tool chatter and surface location error in milling processes, ASME Journal of Manufacturing Science and Engineering, 128 (2006) 913-920, 2006
Szalai R, Stépán G, Hogan SJ: Continuation of bifurcations in periodic delay-differential equations using characteristic matrices, SIAM Journal on Scientific Computing 28 (2006) 1301-1317, 2006
Orosz G, Stépán G: Subcritical Hopf bifurcations in a car-following model with reaction-time delay, Proc. of the Royal Society London A 462 (2006) 2643-2670, 2006
Csernák G, Stépán G: On the periodic response of a harmonically excited dry friction oscillator, Journal of Sound and Vibration 295 (2006) 649-658, 2006
Hartung F, Insperger T, Stépán G, Turi J: Approximate stability charts for milling processes using semi-discretization, Applied Mathematics and Computation 174 (2006) 51–73, 2006
Insperger T, Stépán G: Act and wait control: case study of a double integrator with delayed feedback, Proceedings of 6th European Solid Mechanics Conference (ESMC 2006) (Budapest, Hungary, 2006) CD-ROM papers\S41\320_279.pdf, 2006
Stépán G, Orosz G: Hopf calculations in delayed car-following models, Proceedings of IFAC Time Delay Systems Workshop (L’Aquila, Italy, 2006) (Eds: Pepe P, Germani A) CD-ROM, pp. 1-6, 2006
Takács D, Stépán G: Theoretical and experimental investigation of tyre dynamics, Proceedings of Applied Mathematics and Mechanics 6 (2006) 847-848., 2006
Baksa I, Kisfalusi K, Stépán G: Experimental results on vibration frequencies of digital force control, Proceedings of 5th Conference on Mechanical Engineering GÉPÉSZET 2006 (Budapest, 2006), CD-ROM pp. 1-5, 2006
Takács D, Stépán G: Experimental study of quasi-periodic oscillations of towed wheels, 5th Conference on Mechanical Engineering GÉPÉSZET 2006 (Budapest, Hungary, 2006) CD-ROM pp. 1-5, 2006
Insperger T, Mann BP, Edes B, Stépán G: The effect of runout on the chatter frequencies of milling processes, , in Proceedings of 9th CIRP International Workshop on Modeling of Machining Operations (Bled, Slovenia, 2006), CD-ROM paper no. 033, 2006
Kovács LL, Kövecses J, Stépán G: Dynamic behaviour of robots with digital force control, Proceedings of the 8th Conference on Dynamical Systems Theory and Applications (Lodz, Poland, 2005), (eds. Awrejcewicz J., Sendkowski D., Mrozowski J.) Vol. 1, pp. 3, 2006
Kovács LL, Kövecses J, Stépán G: Dynamic behaviour of robots with digital force control, Proceedings of the 8th Conference on Dynamical Systems Theory and Applications (Lodz, Poland, 2005), (eds. Awrejcewicz J., Sendkowski D., Mrozowski J.) Vol 1, pp 335-342, 2006



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