The recent drive systems are considered as interactive systems containing a range of subsystems with different physical nature. This contribution deals with the modelling of mechatronic drive systems using numerical package DYNAST. The theoretical general observations are demonstrated on particular experiments on real system.Moderni pogonski sustavi smatraju se interaktivnim sustavima koji sadržavaju podsustave različitih fizikalnih svojstava. Ovaj dokument prikazuje modeliranje mehatroničkog pogonskog sustava korištenjem numeričkog paketa DYNAST. Načelna teorijska razmatranja demonstrirana su pomoću konkretnih eksperimenata na realnom sustavu

C. Kratochvíl

L. Houfek

R. Grepl

V. Fuis

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C. KRATOCHVÍL, L. HOUFEK, R. GREPL, V. FUISANALYSIS AND MODELING OF DYNAMICPROPERTIES OF INTERACTIVE DRIVE SYSTEMReceived – Prispjelo: 2009-02-10Accepted – Prihva}eno: 2009-08-20Original Scientific Paper – Izvorni znanstveni radINTRODUCTIONThis contribution shows the solution of mentionedproblems during the analysis of particular technical sys-tems with tooth wheels and gears. To model and simu-late such systems it is necessary: a) to create objectiveand partially structured model of basic mechanicalstructure; b) to create at least simplified models of mesh-ing conditions, transfer functions and kinematic excita-tion for tooth wheels and gears; c) to create model ofsurrounding environment; d) to formulate the concept ofdrive system control and e) to propose the way of inte-gration of basic drive structure, surrounding environ-ment and control.SYSTEM METHODOLOBY ANDITS USE IN DRIVE SYSTEMS MODELLINGThe system approach is usually understood in nar-rower concept than its real content. The most often itsreduced only to structural object examination, ob-ject-object and object-environment linkage consider-ation -and target behaviour formulation. Sometimesonly the creation of relevant quantities system is consid-ered as system approach. In detail one can find the infor-mation about these problems in 1-3, we will consideronly simplified limitations. Together with necessary un-derstanding of object structure we recommend at leastits intention consideration. That means that during theselection of structures elements, its properties and out-puts, linkage and interaction selection its essentiality de-termination is the most important. Among other attrib-utes of system approach which we recommend to con-sider is the requirement to examine the objects as open(non-isolated) systems with the linkages and interac-tions with the environment, as complex and interdisci-plinary problems and as hierarchic organized structures.Oriented examination respecting the preservation ofsubstantial relations input-output, cause-consequence,or superior solution - specific solution, time dependentdynamical examination and level balanced examinationare considered as inevitable, if we want to work on thecurrent - level of science and technology.Various types of modelling not just the technical sys-tems itself but its behaviour, dynamic properties and en-vironment effects appear to be the most progressive. Thebasic step during dynamic tasks solution using arbitrarytype of modelling is creation of essential variables set,containing variables describing the structure, states andeffects on technical objects and also variables describingthe effects, that means its expressions and behaviour.Methods for mathematical modelling of drive sys-tem, interactive in general can use:– applications of known physical principles for de-scription of phenomenon appearing in drive sys-tems (e.g. II. Newton’s law, Kirchhoffs law, etc.),or– application of mechatronics methods based onartificial intelligence algorithms (e.g. geneticalgorithms, neural networks, etc).Its clear that modelling of particular technical systemmust respect general recommendations mentionedMETALURGIJA 49 (2010) 2, 103-106 103The recent drive systems are considered as interactive systems containing a range of subsystems with differentphysical nature. This contribution deals with the modelling of mechatronic drive systems using numerical pac-kage DYNAST. The theoretical general observations are demonstrated on particular experiments on realsystem.Key words: drive system, experiment, modelling, DYNASTAnaliza i modeliranje dinami~kih svojstava interaktivnog pogonskog sustava. Moderni pogonskisustavi smatraju se interaktivnim sustavima koji sadr`avaju podsustave razli~itih fizikalnih svojstava. Ovaj docu-ment prikazuje modeliranje mehatroni~kog pogonskog sustava kori{tenjem numeri~kog paketa DYNAST.Na~elna teorijska razmatranja demonstrirana su pomo}u konkretnih eksperimenata na realnom sustavu.Klju~ne rije~i: pogonski sustav, eksperiment, modeliranje, DYNASTISSN 0543-5846METABK 49(2) 103-106 (2010)UDC – UDK 669.14-418:539.37:620.17=111C. Kratochvíl, L. Houfek, R. Grepl, V. Fuis; Faculty of Mechanical Engi-neering, Brno University of Technology, Brno, Czech Republicabove and at the same time it has to consider the particu-larities coming from the given system requirements def-initions and its purpose. In drive system we have to con-sider that the systems primary purpose is to work as thedrive for working machines. We can see that the drive asindependent structural subsystem is connected with cer-tain other subsystems, which must be considered in cor-responding model.That means that our aim is to create certainsubmodels of: electrical (hydraulical) parts of the motor,mechanical parts (motor, gearings, clutches), workingenvironment model, technological requirements model.That means that we must build: a) equations of motionof particular subsystems of the drive according to its physi-cal principle, that means for mechanical part, electricalpart, control, etc.; b) for gearing subsystems create at leastmodels of gearing conditions and kinematic excitation; c)model of surrounding environment effects; d) model ofalgoritmized requirements of technology and control andintegrate those into control submodel; e) formulate andmodel driving, parasitic and malfunction effects and fi-nally f) model subsystem of information elements.PROCEDURE FOR DESIGNAND CONTROL OF SYSTEMThe design procedure for designing a control systemis an orderly sequence of steps. Good engineering de-sign is interdisciplinary and requires that the engineerfirst thoroughly understand the requirements of custom-ers, the defined control system specifications, the envi-ronment that the control system will operate in, theavailable power, the schedule that it must be built in, andthe available budget.Due to the availability of a large number of techniquesto solve the great variety of control system problemspresent, the element of experience is very important to theapproach used for the solution of a specific problem.1. Obtain a complete understanding of the job re-quirements with respect to: a) general descriptionof the problem; overall control-system perfor-mance and accuracy with respect to the ste-ady-state and transient phases; b) identificationof the transfer function of the controlled process;c) miscellaneous requirements as to reliability,schedule, cost, maintainability, size, weight, andavailable power.2. Consider several alternative solutions, includingelectric and hydraulic power servo drives, the useof continuous control or digital control, etc.3. Choose the most desired approach based on thespecifications, requirements, and elements fixedby the customer.4. Interpret these requirements in terms of suchclosed-loop design characteristics as frequencyand transient response.5. Establish the approximate open-loop characteris-tics that will satisfy the closed-loop require-ments.6. Design the system and select the sensors, actua-tors, amplifier, and stabilization required (analogor digital) in order to satisfy step 5.7. Review, refine, and simplify steps 5 and 6.8. Simulate the system on a computer, including itslinear and nonlinear characteristics, to check thedesign. Make any necessary changes to the de-sign.9. Build a prototype, and check the design experi-mentally. Make any necessary changes to the de-sign.10.Refine the design in order to optimize perfor-mance and minimize cost.EXAMPLE: REAL DRIVESYSTEM AND ITS MODELLINGIn following text we will analyse the behaviour anddynamic properties of the real electromechanical drivesystem with controlled DC motor shown in Figure 1.Figure 2 shows idealized drive systems. The systemconsists of motor subsystem, transimission subsystemand technological subsystems. The model of drive mo-tor control is shown in Figure 2c and model of superiortechnological regulation is shown in Figure 2b.The model of mechanical subsystem, discretizedwith concentrated parameters and non-linear couplingsis shown in Figure 2a. Its parameters are as follows:I1=950 kg⋅m2; I2=55 kg⋅m2; I3=I4=120 kg⋅m2; k21=1.75N⋅m/rad; k32=1.97×107 N⋅m/rad, couplings allowance0,01/0,015 rad. Load levels: impulses 10 % of mediumvalue of driving torque; kinematic load and noise max25 % and 5 % of medium value of driving torque; im-pulse duration 0.01 sec, its frequency 1 and 10 Hz, ki-nematic load frequency 28.5 Hz.MATHEMATICAL MODELThe mathematical model of drive system is formu-lated using state vectorx(t) x (t), x (t)M RT  ,where vector xM defines the quality of mechanical sub-system and vector xR defines parameters of the motorand control circuits. Vector xM is defined by means of104 METALURGIJA 49 (2010) 2, 103-106C. KRATOCHVÍL et al.: ANALYSIS AND MODELING OF DYNAMIC PROPERTIES OF INTERACTIVE DRIVE SYSTEMFigure 1. Real drive systemx(t) (t), (t) T   ,where (t) represents the relative angular replacementsof mechanical parts of reduced model. The state equa-tion and output equation are expressed in the followingform: )x(t) (t), u(t), t h(xy(t) (t), u(t), tg(x )where u(t) is the vector of the input quantities.PARASITIC EXCITATION AND ITS MODELSWe can divide the parasitic excitations of drive sys-tem into two groups:– first group represents the kinematics excitation (socalled stress kinematics excitation). These matterswere discussed in our articles 4, 5.– second group represents balanced signal of motorsfeedback circuit.DRIVING KINEMATIC EXCITATIONDC motor produces periodic torque, which acts ontomotor’s rotor. The cause of rising of this moment couldbe a periodic fluctuant signal on the output of motorfeedback angular velocity sensor. The frequency of peri-odic driving moment is given by angular velocityofsensor’s shaft.Modeling function must involve real shape frompractical measuring and this function must have a defi-nite mathematical definiction. In our case, the modellingfunction is sin2, so parasite stress moments are de-scribed by expression:M(t) M (t)0  	   Mk t k ksin( ) , , ,202 2 0 1     ...where  ( ) ( )t t t  d0is angular defection and ( )t isspot angular velocity of rotating parts.NUMERICAL RESULTSThe courses of directive torques depending on timein particular couplings of the drive model structure areshown in Figure 3. We can found the states in which thepeak load torques appear and its characteristic coursesand conditions under which the “disconnection” of theparticular couplings appear.The representation of transient responses in phaseplane enables the detail study of transient phenomena.As the example we show the phase diagram in places 2and 3 in which one can see the limit cycles (characteriz-ing parasitic vibration on “free space borders” and tran-sient trajectories) shown in Figure 4 a, b.The size and the range of limit cycles characterizethe level of parasitic phenomena which complicates thecontrol of angular speed. It can be limited to the certainlevel by suitable selection of control parameters. At thesame time the courses of transient trajectories can be in-fluenced mainly by eliminating the uncontinuousnessand rapid changes. This operation is called qualitativeanalysis of dynamic properties.METALURGIJA 49 (2010) 2, 103-106 105C. KRATOCHVÍL et al.: ANALYSIS AND MODELING OF DYNAMIC PROPERTIES OF INTERACTIVE DRIVE SYSTEMFigure 2. Model of complex drive system (ELM - electricmotor, MS – mechanical subsystem (transmis-sions and working machines), VV - power cou-pling, RM - motor control, PTR – requirements oftechnological regulation, PP - failures, noise, TZ– techhnological load)a)b)c)Figure 3. Time dependending of directive torquesCONCLUSIONIn this contribution we described generalrequirments for the analysis of dynamical properties ofreal drive system using numerical simulations of theirmodels. The numerical package DYNAST was used.Problems of design of dynamic drive system withtoothed gearings and simulation of its dynamical prop-erties is extremely broad and complex. Today’s drivesrepresent interactive systems with elements or subsys-tems of various physical principles. Therefore we lim-ited the contribution onto selected problems includingbasic thoughts connected with creation of the model, itsfunction and control.Let us finaly summarize:– The pass from real technical system towardsmodel system is possible after selection and for-mulation of those properties of real system, whichare characteristic for required functions satisfac-tion and therefore must be performed by the modelsystem.– Only model system which is essentially simplerthan real system Is worth, and mainly the systemwhich enables creation of computational and com-puter models.More and more often one can see the design andmodelling “in variants”, based on sequential creation ofmodels or different complexity which are then used forperforming simulation experiments with the aim to se-lect the model as simple as possible, but keeping givenrequirements.REFERENCES1 A. H. Nayfeh, B. Balachandran: Applied Nonlinear Dyna-mics, John Wiley & Sons, Inc. New York, 1995.2 L. J. Kamm, Understanding Electro-Mechanical Enginee-ring (An Introduction to Mechatronics), IEEE Press, Inc.New York, 1996.3 F. C. Moon: Chaotic vibrations, John Wiley & Sons, Inc.New York, 1987.4 C. Kratochvíl, P. Heriban, L. Houfek, M. Houfek: Mecha-tronické pohonové soustavy, VUT Brno, 2008.5 C. Kratochvíl et all.: Bifurkace a chaos v technických sou-stavách a jejich modelování, ÚT AV ^R, Praha, 2008.Acknowledgement:This work has been supported by the research plan ofMinistry of Education, Youth and Sports, nr. MSM0021630518 – Simulation modeling of mechatronicssystems and Grant agency of Czech Republic, grant nr.101/08/0282 – Mechatronic drive systems with nonlin-ear couplings.Note: The responsible translator for English language is Prof. Ing. CtiradKratochvíl, DrSc., Brno University of Technology, Brno, Czech Republic.106 METALURGIJA 49 (2010) 2, 103-106C. KRATOCHVÍL et al.: ANALYSIS AND MODELING OF DYNAMIC PROPERTIES OF INTERACTIVE DRIVE SYSTEMFigure 4. Transient responses of system

Analiza i modeliranje dinamičkih svojstava interaktivnog pogonskog sustava

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