Transfer functions of the automatic electrohydraulic drive. Ya. Sokolova, O. Krol, T. Tavanuk, V. Sokolov
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1 ТЕKA. COMMISSION OF MOTORIZATION AND ENERGETICS IN AGRICULTURE 05 Vol. 5 No. 3-8 Transfer functions of the automatic electrohydraulic drive Ya. Soolova O. Krol T. Tavanu V. Soolov Volodymyr Dahl East-Urainian National University rolos@yandex.ru Received July. 05: accepted July Summary. The linear mathematical model is presented and transfer functions of the automatic electrohydraulic drive with throttle regulation are defined. The mathematical model is adapted on drives of the special technological equipment for machining materials constructed on the basis of standard modules. Key words: automatic electrohydraulic drive linear mathematical model throttle regulation transfer functions. INTRODUCTION The modern technological equipment for mechanical processing of materials demands much of characteristics of drives on accuracy of realization of the set laws of movement of a target lin that is reached by use of ерlу electrohydraulic watching drive (AEHD) []. The important stage in AEHD designing is the estimation of stability quality of regulation and correction of dynamic properties of a drive. Performance of the given stage is connected with woring out of mathematical model of the non-stationary woring processes proceeding in a drive. The mathematical models of dynamic processes presented in the literature [ 5 ] cannot be generalized on all class considered AEHD. A number from them is focused on certain designs of devices of a drive (Fig. ) in particular electrohydraulic amplifier (EHA). In the majority of model definition of parameters which cannot be estimated from nameplate data of standard devices demand or are revealed at a stage of preliminary designing. Fig.. Settlement scheme AEHD (a) and target cascade EHA (b) At small deviations of parameters of system from static values use of linear models for the mathematical description of non-stationary processes is admissible. It allows to receive the analytical decisions giving the chance to find out and present prominent features of studied process for any combination of parameters of system. Besides analytical decisions are "standards" for an estimation of accuracy of analytical decisions. The wor purpose is woring out of linear mathematical model and definition of transfer functions of an electrohydraulic watching drive with the throttle regulation adapted on drives of the equipment for processing by the pressure constructed on the basis of standard modules with use for an estimation of dynamic characteristics of nameplate data of devices of a drive. OBJECTS AND PROBLEMS Let's allocate basic elements of the AEHD: a hydraulic engine (HE) the electrohydraulic amplifier (EHA) the including electromechanical converter (EMC) and the hydraulic booster (HB) the feedbac gauge (FBG) the electronic bloc (EB). Further it is considered the settlement scheme of a drive presented on fig.. In wors [ 6] typical nonlinear mathematical model of the AEHD with throttle regulation which includes following equations and dependences is considered: U OC = OC Y U УС = УС (U-U ОС ) L У diу d xз dxз y y З xi y R i U E У T T x i Ç dçï õç hï ðí ð sign pí ð õç hï Q 0 õç hï Ç dçï õ Ç hï ð ð Ñ sign p ðñ õç hï Ç dçï õç hï ð ðc sign p ðc õç hï Q 0 õç hï Ç dçï õ Ç hï ð Í ð sign pí ð õç hï УС
2 4 Ya. Soolova O. Krol T. Tavanu V. Soolov dv m p F p F cy T V R CT signv R dy V H / Y H / HO F ( H / Y ) dp Q F V E el dp HO F ( H / Y ) dp Q F V E el dp where: Y V - moving and speed of the piston; р р - pressure in hydrocylinder cavities; m - the resulted weight of mobile parts; F F - the effective areas; c - rigidity of item loading; к Т - factor of force of a viscous friction; R СТ - force of a dry friction; R - loading; Н - a piston course; E el - the module of elasticity of a woring liquid; HO CO - "dead" volumes of pressure head and drain highways; OC - factor of FBG transfer; xi - factor of EHA transfer; constants of time Т У Т У which are defined on shift frequencies 90 hailstones: on a phase on 45 and Т у ; Ту where: р Н р С - pressure of pump station and on plum; h п - size of positive overlapping; З - factor of the expense of a crac of a valve; d З - diameter of a valve; п - factor of completeness of use of perimeter of a valve; - density of a woring liquid; U - entrance (operating) pressure; U УС - pressure on EB exit; УС - factor of EB strengthening; L У - inductance of a winding of management; R E - active resistance of the electric chain. Let's mae the linearization of the received nonlinear mathematical model preliminary having excluded as a first approximation force of a dry friction and item loading. Usually at drawing up of linear mathematical models of hydrodrives [9 0 ] the assumption of equality of "dead" volumes of pressure head and drain highways is accepted: нo co o. () And the indissolubility equations register for average position of the piston and also equality of the effective areas of the hydrocylinder: FF F. () Last assumption is the most essential however allows to simplify considerably model for the account of following possibility to admit equality of expenses in EHA lines: QQ Q. (3) ith the account of the above-stated the equation of movement and balance of expenses become: dy V (4) o F H dp Q FV (5) Eel o F H dp Q FV. (6) Eel By linear lins are described FBG EB and operating winding EHA: U y (7) oc oc U ( U U ). (8) yc yc oc The linear accepts communication of displacement of HB valve with a current in a management winding: d x3 dx3 y y 3 xi y T T x i. (9) e use the traditional approach [6 8] to linearization of the flow-transfer EHA characteristics: Q x3 ( p p ) (0) where: factors of transfers are defined on expressions: 0 0 Q x Q x in a general view Q x x Q x x p p x p p p p p p 3 30 x x x ( p p) p p p p Q p x x p p p p p () () Q x p p зo static values of variables. As a first approximation in calculations it is possible to put values and defined at x 0 p 0 p 0 for valve HB with zero: зo 0 0 pn 3 dçn (3) p 0 (4) where: pn pn pc brought to EHA pressure.
3 TRANSFER FUNCTIONS OF THE AUTOMATIC ELECTROHYDRAULIC DRIVE 5 For deviations of variables from static values it is had the following system of the linear equations: Uoc oc y U U U diy L R i U yc yc oc y E y yc d x3 d x3 T y T y x3 xi iy Q x3 p p 0 FH /dp Q Eel FV 0 FH /dp Q Eel FV dv m p p F T V R; dy V. (5) (6) (7) (8) (9) (0) () () (3) e subtract (Еq. ) of (Еq. 0) we substitute result in (Еq. 9) then system it is transformed on Laplas [3 4 7] and it is led to a ind: Uoc ( s) ocy( s) U yc ( s) yc ( U ( s) Uoc ( s)) Rý iy ( s) Ly U yc ( s) Toys xi x3 ( s) i y Tys Tys ( p( s) p( s)) FH s 4E x3 ( s) F V ( s) F( p ( s) V( s) ms T p ( s)) R y( s) V ( s) s (4) where: s Laplas variable Т оу a constant of time of a winding of management: Toy Ly Rэ (5) Е the resulted module of elasticity of the hydrocylinder: Еel Е. (6) o FH To system (Еq. 4) there corresponds the bloc diagram presented on Fig.. Let's transform the bloc diagram for what we will enter factor of transfer EB [5 9]: Keb Kyc Ke. (7) And factor of strengthening EHA under the expense: KQi Kxi K. (8) Value K Qi it is possible to establish on nameplate data EHA: [6 0 ]: KQi Qn in (9) where: Q n i n - the nominal expense and rated current management EHA. The transformed bloc diagram is shown on fig. 3. Let's receive transfer function of a drive on an operating signal for what we will transform the bloc diagram (fig. 4) see having excluded from consideration ΔR. Let's define a hydromechanical constant of time of the hydrocylinder: Т mh 4E F. (30) And factor relative damping of the hydrocylinder: Km HKT. Т ц F EF In real drives [6]: T (3) K K F. (3) Therefore it is definitively possible [3 4] to offer the bloc diagram of transfer of the operating signal resulted on fig. 5.
4 6 Ya. Soolova O. Krol T. Tavanu V. Soolov Fig.. The Bloc diagram Fig. 3. The Bloc diagram Fig. 4. To definition of transfer function AEHD on an operating signal Fig. 5. The Bloc diagram of transfer of an operating signal According to the bloc diagram it is established transfer function AEHD on an operating signal: where: signal: yu K yu ( s) s ( Toy s )( Ty s Ty s ) D EHD ц ( T s T s ) (33) K yu factor of transfer AEHD on an operating K K yu (34) oc D EHD good quality AEHD (factor of strengthening of the opened system) DEHD KEBKQi Koc F. (35) For reception of transfer function AEHD on loading [8] we will exclude from the bloc diagram presented on fig. 3 ΔU and we will transform the scheme as is shown in Fig. 6. Let's designate a constant of time of a lin of forestalling: T R FH. 4E K (36) ith the account (Еq Еq. 3) we transform the bloc diagram to a ind it agree Fig. 7. Under the bloc diagram it is found transfer function AEHD on loading influence: yr where: influence: yr or y y oy K ( T s )( T s T s )( T s ) ( s) (37) s ( Toy s )( Ty s Ty s )( T s D уr EHD T s) K - factor of transfer AEHD on loading K K уr. (38) F DEHD The target size is defined generally by result of operating and loading influence [6 7] according to a superposition principle: y( s) ( s) U ( s) ( s) R( s). (39) yu yr
5 TRANSFER FUNCTIONS OF THE AUTOMATIC ELECTROHYDRAULIC DRIVE 7 Fig. 6. To definition of transfer function AEHD on loading Fig. 7. The Bloc diagram of transfer of loading influence CONCLUSIONS. The mathematical model of the dynamic features automatic electrohydraulic drive of the special technological equipment is designed.. Transmission functions are received for moving output lin on controlling signal and loading influence. 3. Mathematical model and transmission functions which are received in this article prescribed in base for designing of system the auto control equipment. REFERENCES. Abramov E. Kolesnicheno K. Maslov V Hydrodrive elements: the Directory Кiev "Technics" 30. (in Russian).. Alexeev A. Imayev D. Kuzmin N. Yaovlev V Control theory St. Petersburg ETU "LETI" 5. (in Russian). 3. Andrijchu N. Soolov V Aerohydrodynamics: textboo for universities Lugans Publishing house of Volodymyr Dahl East- Urainian National University 56. (in Russian). 4. Chernetsaya-Beletsaya N. Kushcheno A. Varauta E. Shvorniova A. Kapustin D. 04. Define the operational hydro-solid vaste handing system TEKA Commision of Motorization and Power Industry in agriculturevol. 9 No Chupraov Ju Electrohydraulic watching drives Мoscow MADI 88. (in Russian). 6. Chupraov Ju. 975.: Electrohydraulic amplifiers Мoscow MADI 4 (in Russian) 7. Dorf R. Bishop R. 00. Modern systems of management Мoscow Laboratory of Base Knowledge Gamynin N. 97. Hydraulic drive control systems Moscow: Machine building 756. (in Russian). 9. Goodwin G. Grefe F. Salgado M Design of Control Systems Moscow Knowledge Lab Hohlov V. 964.: Electrohydraulic watching drive Мoscow the Science 73. (in Russian).. Leshcheno V Hydraulic servo drives Moscow Mashinostroenie 8. (in Russian).. Leshcheno V Hydraulic servo system and drive machines with computer control. M.: Engineering. 67 (in Russian). 3. Navrotsy K. 99. Theory and designing hydroand pneumodrives Мoscow Mechanical engineering 38. (in Russian). 4. Popov D. 98. Non-stationary's hydromechanical processes Мoscow Mechanical engineering 40. (in Russian). 5. Popov D Dynamics and regulation hydroand pneumatic systems Мoscow Mechanical engineering 464. (in Russian). 6. Soolova Ya. Ramazanov S. Tavanu T. 00. Nonlinear modeling of the electrohydraulic watching drive TEKA Commision of Motorization and Power Industry in agriculture Vol. XC Soolova Ya. Tavanu T. Greshnoy D. Soolov V. 0. Linear modelling of the electrohydraulic watching drive TEKA Commision of Motorization and Power Industry in agriculture Vol XІ В Soolova Ya. Tavanu T. Soolov V. 00. Nonlinear mathematical model of the electrohydraulic watching drive with throttle regulation Messenger of the East-Urainian National University named by V. Dahl Vol. 0 (5) (in Russian). 9. Sveshniov V. Usov A Moustaches hydrodrives: the Directory. - publ. Мoscow Mechanical engineering 5. (in Russian). 0. Syomin D. Rogovoy A. 00. Power characteristics of super-chargets with vortex wor chamber TEKA Commision of Motorization and Power Industry in agriculture Vol Tersyh V Comparative analysis of dynamic properties of throttle hydrodrives Publishing house of high schools. Mechanical engineering (in Russian). Yaovlev V. 984.: Adaptive Cruise Control: A Textboo Leningrad Len. University 4. (in Russian).
6 8 Ya. Soolova O. Krol T. Tavanu V. Soolov ПЕРЕДАТОЧНЫЕ ФУНКЦИИ АВТОМАТИЧЕСКОГО ЭЛЕКТРОГИДРАВЛИЧЕСКОГО ПРИВОДА Я. Соколова О. Кроль Т. Таванюк В. Соколов Аннотация. Представлена линейная математическая модель и определены передаточные функции автоматического электрогидравлического привода с дроссельным регулированием. Математическая модель адаптирована на приводы специального технологического оборудования для механической обработки материалов построенные на основе стандартных модулей. Ключевые слова: автоматический электрогидравлический привод линейная математическая модель дроссельное регулирование передаточные функции.
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