ON THE DYNAMIC REGULATION OF PROGRAMMING MOTION ELECTROMECHANICAL LINEAR ACTUATOR

Transcription

1 THE ANNALS OF UNIVERSITY DUNĂREA DE JOS OF GALAŢI 61 Paper present at International Conference on Diagnosis and Prediction in Mechanical Engineering Systems (DIPRE 07) October 2007, Galati, Romania ON THE DYNAMIC REGULATION OF PROGRAMMING MOTION ELECTROMECHANICAL LINEAR ACTUATOR Vasile NĂSUI North University of Baia Mare, Romania ABSTRACT The paper presents the effect of dynamic regulation of the functional parameters on the performances of the linear-motion electromechanical actuator. This is essential taking into account the technical and technological importance of actuators in the intelligent flexible industrial systems of refinement. This research offers a new concept concerning the development of new systems of linear actuation and simulation using adding numerical programs and virtual instrumentation. The dynamic mechanical modeling and the virtual modeling conducted to a convergence of the obtained results. In the future the research may continue for developing new applications on other types of mechanical transmissions, using this method and different modular control laboratory. KEYWORDS: Linear actuator, dynamic modeling, intelligent flexible systems. 1. INTRODUCTION The work refers to theoretical, experimental researches and dynamic modeling of electromechanical linear actuators equipped with mechanical drive, through ball screws and roller screws. The large range of machine-tools, as well as the requests imposed on the technological processes, make necessary the new instruction of linear actuator with individual changing actions, even more compact in order to increase the quality and the flexibility of the products [1, 3, 4]. The charges of such systems are much more complex than those selected on the existing patterns requiring the construction of systems with intelligent actions in order to optimize the chosen solution [6, 8]. The new generation of machine-tools requires greater powers and very high speeds, precision of regulating the position but also a rational coordination of the composing individual action. The technical and technological evolution towards the integration in mechatronics included the development stages of the linear acting module of the actuator type marked by integrating the microprocessors. The development of mechatronics technology within this context contributed to the development of actuators as elements of execution, which have, besides the kinematics chain, energetic and informational material. In the dynamic study of the actuators I have to consider the whole linear actuators in spite of the effects of the transitory functional regime [3, 9]. The modular mechanical actuators represent a new concept in mechanical transmissions of various types and destinations that efficiently replace classical systems, mechanically, hydraulically and/or pneumatically actuated [9]. These provide the optimal solution for the construction of quantitative and qualitative mechanical transmissions for a wide range of applications having high efficiency, kinematics, dynamic capacities and high precision. The electromechanical linear actuators that are mechatronic products are part of the intelligent flexible systems of manufacture; they have to fulfil special requirements which impose new

2 62 THE ANNALS OF UNIVERSITY DUNĂREA DE JOS OF GALAŢI concepts of design. All these can be best achieved only using the methods of modern design, including the technique of numerical computations, such as that of the virtual prototype. Setting up the best of solutions by virtual modeling offers the idea of the overall technical conception of the actuator product, its possible composition by the appropriate structural solutions, such as the functions of its elements. The technical system of the linear actuator, perfected through this method, has a few basic characteristics expressed by particular indicators, such as: adjustable acting, high precision and efficiency, loading capacity, a rank of high speeds, numerical control etc. The actuator has a complex structure, the mechanical part being composed of some elements that ensure a high kinematic and dynamic precision, and the commanding part being represented by a computer-led system, based on an appropriate software. In order to optimize the functioning of a tool, the actions must be able to regulate the speed continuously by converting the reduced dissipation of electric energy into mechanical energy. The regulating electric actions consisted in an element of electronic execution, of the electric machine, a mechanical transmission and the working machine (fig. 1). The main component parts of an actuator are presented in figure 1, including the acting electric engine, the transmission itself, the filling and the control devices: 1 - planetary reducer (servomechanism); 2 - asynchronous electric engine and 3 - static converter of frequency. Fig. 1. The linear actuators with converter: 1- servomechanism, 2- electric engine, 3- converter. positioning in machines used for manufacturing or testing. One type is the electromechanical actuator, which converts the torque of an electric rotary engine into a linear mechanical thrust. For the moment of training the screw, the average force is needed to load the system, the pace of the screw and the efficiency which the rollscrew offers. The function of coordination and mechanical timing is replaced with the electronic alternative, using a new concept of dynamic regulation, which improves the performances of the system. The modern actions replace even more frequently the regulating mechanical transmission because its performances does not fit anymore the demands imposed by the user, such as increasing the power per volume unit of the active materials. Today, the electrical regulating actions are important parts of the machine-tools with quick evolution, from the actions of continuous electric power to those with alternative electric power [7]. The realization of this work led to the modeling of some translation systems using virtual simulating programs Simulink and LabView and also to the modular control laboratory, with these transmissions in which I did the experimental researches. Also, by this dynamic modeling it is given the equation of the system performances and the way of applying the concept of dynamic regulation system [10]. For the new criteria of performances called errors of trajectories of machine-tools with numerical control it is required the reconsideration of the main parameters of tracing servomechanisms which should correspond to the transitory and critical working regimes. The positioning systems with good dynamics and great possibilities of torque regulating, which satisfy the mentioned requests, are programming servomechanisms with a regulating action [5]. The test stand of industrial linear actuator is presented in figure THE THEORETICAL DYNAMIC MODEL OF THE ACTUATOR This system can be used in advanced mechanisms, elevators and manipulators, rotation devices etc. The linear actuator is composed of an engine turning a screw in which the nut is not allowed to rotate against the screw. This allows a linear motion of the nut for the length of the screw. A position at some point along the screw is commanded by the user and the engine turns the screw until the nut reaches that particular position. The engine rotates the driven screw by a synchronous timing belt drive, worm gear drive, or a coupling direct inline drive, connected from the engine shaft to the screw. Thrust is transmitted from the drive nut, to the translating tube. An actuator's function is to provide thrust and Fig. 2. The test stand of an automatic actuator. There it can be memorized different stages of rotations in both directions and also there can be assured the passing over the frequencies of resonance, memorized by the converter. The present day advances in software field allows the development of some solutions for multifunctional universal machines of the servo-converting type, for positioning and movement actions. The use of digital technique allows such a bi-directional transfer of data without supplementary elements (just-in-time) through a parametric serial interface at a central leading system,

3 THE ANNALS OF UNIVERSITY DUNĂREA DE JOS OF GALAŢI 63 which can interrogate the real values of the parameters at any hierarchic level. This study makes possible to solve some aspects characterising the dynamics of actuators, useful for research and general design of these transmissions, as well as for their exploitation under very safe conditions. The requirements of mechanical construction of the actuator are more often dynamic ones, which generate the acceleration of the movement and of the inertia force which can cause vibrations. If the system loses its state of stability due to an impulse and if this impulse is eliminated, then the system executes free oscillations, during which, there is a continuous exchange of kinetic and distortion energy. For the case of continuous action of the disturbing force, the system executes forced oscillations. According to these dynamic loading coefficients there can be appreciated the endurance of the actuator and the degree of their loading. Based on the dynamic coefficient there can be followed: the exact limitation of the work purpose, according to the maximum dynamic loading which appears within the flexible links in the mechanisms, the values of the maximum accelerations and of the minimum functioning time in the period of the start-up, of braking and the oscillation frequencies of the supports. A control block diagram of the system is shown below, in figure 3. The scheme of the regulating action in the alternative electric power is presented in figure 4. The Simulink program allows the creation of dynamic patterns using some blocks, subsystems which define those particular patterns. It is necessary to know the system to be modeled, and the physical and mathematical rules, according to which the system works. The blocks which can be used, are found in the library within the program that can define or create other blocks or can turn to the use of external functions used in the MatLab program. After creating the model, this is run, and the simulation can be visualized using a display where there can be read the numerical values of the analysed signal or the signal can be analysed using the graphics with the aid of one of the blocks of type SCOPE, this making possible the analysis of the results. For the moment of training the screw, it is necessary the average force which loads the system, the pace of the screw and the efficiency which the screw on rolls offers. For the calculus of the necessary moment to overcome the friction in the rolling bearing it is taken into account the average force which is supported by the system, the axial force which can be overtaken by the rolling bearing. For its construction it is recommended a type of rolling bearing which overtake the radial and axial forces; the inner diameter of the cap, the friction force between the bolt nuts should be constant. For calculating the acceleration moment, the algorithm of calculus differs, having more many values at different moments of the circuit while calculating the angular acceleration, the reduced inertia moment of the engine shaft, the inertia moment of the screw, the angular speed, the linear speed, the pace of the screw, the inertia moment of the engine and the necessary rotational speed. Position display COMPUTER Signal generator Position command Feedback display Position feedback DC-Motor LabVEW RS- xxx Controller Power command Amplifier Power Armature Codor Signal end of travel Rotation Multiplexer End of travel Nut Linear motion Screw Fig. 3. Control block diagram of actuator. Fig. 4. The scheme of the regulating action.

4 64 THE ANNALS OF UNIVERSITY DUNĂREA DE JOS OF GALAŢI In order to see this equation under a simple shape, the Simulink MatLab program gives the possibility to insert it in the so-called subsystems; there will be no difference in the way they function, but it will be possible to insert other values; the subsystems are added to give the total moment, for the operation of the linear actuators [7]. The static converter of frequency achieves the electric drive engine feeding, of the asynchronous type of general use, with a variable frequency voltage, maintaining a certain voltage-frequency characteristic. Thus, the variation of the engine rotations number and the output rotations number of the reducer are achieved (fig. 5). The ratio between the maximum and minimum number of rotations, as output, is the biggest. The variation of the output number of rotations is achieved at a constant torque, up to the nominal number of rotations, and the number of rotation above the nominal one, at constant power (by torque decrease). It can be used at any planetary reducer drive where a continuous output number of rotations control is required. Fig. 5. The characteristics of parameters regime. The correct definition of the economical functioning regime of an electromechanical linear actuator must take into account the hints from the economical regime. There are shown below two diagrams depicting the basic elements of the two most common electric motion control systems: stepping engine-based one and servomotor-based one. Each one has advantages, some of which are highlighted in the diagram: the training electric power and the efficiency of all the structural components. In the transitory dynamic regime, in order to maintain a constant efficiency at the nominal power for the power dissipations supposes the knowledge of a weight graphic, as precise as possible (fig. 6). The appreciation of the functioning economical regime should be done separately for each type of acting engine, as well as for every nominal parameter which changes, that is for each artificial characteristic. Saving the electric energy can be done by important measures in the whole chain of the actuator system, starting from the filling point, passing to the control one or the regulating one and going on with the acting engine and the kinematic transmission. For the majority of electric engines, the efficiency has small variations around its nominal value, exchanges of power between the nominal value and approximate 50% out of the nominal value. However [9], for the actuators, to establish the acting power due to the conditions of transitory regime of work is very important. 3. DYNAMIC MODELING For the dynamic calculus of an actuator with a ball screw it is chosen the same mathematical model of synthesis as in the case of roll screw, but with different values of pre-pressing forces, different values of axial forces taken over by a ball screw which has a theoretical and practical efficiency approaching 93%, to be able to get the value as close as possible to the values taken from the experimental stand. Transposing this model which visualizes the equation under a simpler program Mat Lab, gives the possibility of introducing them under the so-called subsystems, where they work the same way having the possibility of implementing some values according to the pattern of the ball screw (fig. 7). The program Simulink allows creating some dynamic models using some blocks; it also allows reducing the material part by minimization and raising the informational one; the energetic density within the smaller and smaller quantity of material contributed to a reduced energetic consumption. It is important to establish the value function, relevant for an objectively chosen criterion of optimization and to appreciate its characteristic. The experience shows that the focus should be done on finding appropriate mathematical expressions of appreciation. Choosing this concept for a solution which fits best the criteria of the list of requirements, it is offered the perspective of on optimal achievement. For this purpose, there is necessary information on the predictable behaviour, respectively on the characteristics of the product which is to be developed on the basis of the proposed concept. An appreciation done on the basis of this information can have as objective either the comparison to the ideal solution or establishing an optimization degree. In order to comprehend more completely the properties and to make the product a concept it is necessary to regulate the characteristics

5 THE ANNALS OF UNIVERSITY DUNĂREA DE JOS OF GALAŢI 65 and to establish the calculus methods or experimental models. The model can be improved step by step until it is obtained a physical and mathematical model which can fulfill the requirements of the study of the technical phenomenon. In order to come up with appropriate models the theory of systems is used. For the system elements there should be searched the modules of a model which have an analogue behaviour using analogies and similarities for the research of the whole behaviour. It is preceded to the systematic variation of system parameters, getting to a quantity optimization taking into account some objectives. Establishing a system of objectives and criteria of appreciation these objectives ordered in a matrix, is getting one step closer to the ordered representation of information. The blocks that can be used are found in the library within the program or they can be defined and create other blocks or they can appeal MathLab program. After creating the model, this is tested and the simulation can be visualized by the help of a display; the numerical values of the analysed signal can be read or the signal can be analysed by the help of some graphics using one of the blocks of type Scope, thus being possible the analysis of the results. The validation of the model is done by interpreting the results and comparing the behaviour of the elaborated model and the real system. Thus, the model may be improved step by step, obtaining one which can fulfill the requirements of the study of the technical phenomenon. These allow the experimental solving of some problems which can not be theoretically worked out, or it can be used to validate or generalize theoretical models. The use of techniques of the virtual prototype for optimizing the performances of the actuators is shown in figure 6 [6]. For calculating the acceleration moment, the calculus algorithm differs, having more values and for different moments of the circuit while calculating the angular acceleration, the reduced insertion moment of the engine shaft, the inertia moment of the screw, the angular speed, the linear speed, the pace of the screw, the inertia moment of the engine and the necessary rotational speed. After the graphical analysis of these two images, in figures 7 and 8 it is noticed that the amplitude is much greater at the return of the nut to the engine than that obtained in the direct pushing movement; searching to remove these differences is necessary to balance appropriately the pre-load and to achieve an assembly with particular bearings for the imposed precision transmission, which were mounted on the ball screw to bring within normal limits the differences among the two movement directions The elastic pattern starts the analysis of the deformations of the kinematic couples, as they are of great importance has a great importance. The deformation can be considered according to the axial force where: 1.4 Q = [ µ m] (1) d P z 3 1 where: Q is the axial force, P the pre-load force, z - the number of balls, d 1 - the nominal diameter of the balls, - the contact angle of the balls, λ - the angle of the sloping the propeller of the screw. Fig. 6. The dynamic modeling with virtual instruments.

6 66 THE ANNALS OF UNIVERSITY DUNĂREA DE JOS OF GALAŢI On the experimental stand the accelerating transducer to acquire data is mounted on top of the nut and it is interconnected to the computer by the help of a data acquisition system. The graphical visualization of the acceleration moment for electromechanical linear actuator is presented in figures 7 and 8. Fig. 9. The stand with virtual instrumental of linear electromechanical actuator. Fig. 7. The motion amplitude in the pushing direct movement. The applicative and experimental researches, the practical checking and the theoretical patterns used in this research can be applied in practice. The conception and its manufacture computer aided system have an application field for developing new products, covering the conception aspects, manufacture and the link between them. This research is part of modern preoccupations regarding the improvement of new systems of linear acting and of numerical modeling using algorithms and programs of numerical computation and virtual instrumentation. The sequence of special performances obtained through this regulatory system for the actuators makes possible their application to the machine-tools with numerical control, especially to those of the last generation with parallel kinematics as well as in the robot industry. The research is of great importance as it presents calculation algorithms for the main dynamic parameters, power and mechanical efficiency. REFERENCES Fig. 8. The motion amplitude in the nut return. 4. SUMMARY AND CONCLUSIONS The methodology presented in these paper confirms the convergence of theoretical results of simulation using combined techniques based on virtual instruments with the experimental ones on the trial stand equipped with a data acquisition system and processing the data with numerical order. The research results can assess immediately any system of linear movement because it has as a basis the newest techniques of modeling in the field. These have as objective the developing of a new system of electromechanical linear actuator as well as perfecting the existing ones in a very short time and in highly energetic and economical conditions. 1. Adrian, O. et al., 1999, Dinamica roboţilor industriali, Editura BREN, Bucureşti, Romania. 2. Borangiu, Th., 2003, Advanced Robot Motion Control, Editura AGIR. Editura Academiei Romane. 3. Gillinch, G. R., 2003, Dinamica maşinilor. Modelarea sistemelor tehnice, Editura AGIR. 4. Mohora, C., Cotet, E., Patrascu, G., 2001, Simularea sistemelor de producţie, Editura Academiei Romane. 5. Montgomery, D.C.,1996, Design of Analysis of Experiments, 4 th Edition, John Wiley & Sons, New York, 6. Năsui, V., 2006, Actuatori liniari electromecanici, Editura Risoprint, Cluj Napoca. 7. Năsui, V., Pay, G., About some dynamic parameters of telescopic linear actuators for machine-tools with parallel kinematics. Proc. of the Intern. Conf. on manufacturing systems ICMaS2002. În: Romanian Journal of Tehnical Sciences Tom. 47. Ed. Academiei Romane, pp Popa, A., 2002, Controlul digital al sistemelor mecatronice, Editura Orizonturi Universitare, Timisoara. 9. Vukobratovič, M., Applied Dynamics of Manipulation Robots-Modelling.. Springer-Verlag Berlin Heidelberg, Varanasi, K., Nayfeh, S Modelling, identification and control of ballscrew drives, Proceedings of the ASPE16 th Annual Meeting, Crystal City, Virginia.