COMPUTER SIMULATION OF A LABORATORY HYDRAULIC SYSTEM WITH MATLAB-SIMULINK

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1 DVNCED ENGINEERING 4(20101, ISSN COMPUTER SIMULTION OF LORTORY HYDRULIC SYSTEM WITH MTL-SIMULINK Grego, G. & Siminiati, D. bstract: The article resents some selected roblems related to modeling and simulation of hydraulic sero-systems (ale + cylinder, using MTL-Simulink ackage. For this urose, is taken into account the basic mathematical model of certain selected elements and henomena that occur in a hydraulic sero system. Models are reresented as block diagrams adated to the software ackage requirements. fterward, the simulation results are comared with laboratory measurements. Laboratory measurements hae been erformed in Laboratory for hydraulics and neumatics at Faculty of Engineering, Uniersity of Rijeka. Keywords: hydraulic sero-systems, Simulink, differential cylinder, direction control ale, laboratory measurement 1 INTRODUCTION lthough electrical dries are becoming increasingly oular for high-erformance motion control, hydraulic sero-systems are still a wide ariety of alications in today's industrial motion systems, for examle: machining, robotics, motion simulators, fatigue testing systems, metal rocessing lants, mining, construction and agricultural machinery, etc [1]. The main disadantages of hydraulic sero-system are a nonlinear dynamical behaior of system, which stems from the comressibility of liquids, roerties of comlex flow ales and friction in hydraulic actuators. They deend on factors, which are difficult to measure, such as oil bulk modulus, iscosity and temerature. General aailability of increasingly sohisticated comuter hardware and comuter software with a better mathematical and simulation rograms allow simulation of ery comlex systems. MTL-Simulink [2] is often used in simulation tests because of the following adantages [3]: - Simlified rocedure that allows the designer to encode mathematical models in the aroriate rogramming language - The ossibility of multile use of the basic mathematical model, using secific libraries and their combinations, - a ossibility of examining systems with models haing areciably extended ranges of coefficients, in articular for hydraulic systems, The article is aimed at resenting modeling and simulation of hydraulic serosystems, directional control ale and differential cylinder, by means of MTL- Simulink. First, the basic mathematical models of ale and cylinder and henomena occurring in hydraulic sero-systems hae been considered. The models are shown both as block and detailed diagrams adated to the requirements of the MTL- Simulink grahical editor. Then, there hae been described a laboratory hydraulic system and laboratory measurements of ressure in the cylinder chambers. 17

2 Final comarison of simulation result and laboratory measurements will roe the accuracy of the simulation. 2 MTHEMTICL MODEL OF HYDRULIC SERVO-SYSTEM mong the arious combinations of hydraulic actuators and ales, a secific case of the cylinder and ale configuration is considered. The configuration includes a directional control ale or roortional ale and a differential cylinder, referred to as an +α configuration [4], which is robably the most widely used combinations of ale-actuator because of its comactness. To reduce the comlexity of the system modeling, within the limits defined by the system, it is useful to distinguish seeral subsystems: ower suly, ale, cylinder + load, tank and iing. For low-frequency behaiour, where ieline effect do not lay a role in the inut-outut behaiour, and for ideal oil suly, the model of a hydraulic sero-system is reduced to only two subsystems (ale + cylinder, what Fig. 1. shows [1]. x, x x Q, F f α Q m Fext Q Li x T S Q T Fig. 1. Schematic reresentation of ale-cylinder combination with definition of the ariables 2.1 Directional control ale Vales are the most imortant mechanical (or electrical link to the fluid interface in hydraulic systems. The flow through the ale is described in the equation of flow through the orifice (1, which takes into account the ressure dro direction: Q = Q x, Δ = c x Δ sign( Δ. (1 ( If we consider the four-way sool ale with an ideal critical centre, then the flow equation can be written as: Q Q = Q Q 1 2 = Q Q 3 = c c 4 2 = c 1 sg( x sg( x 3 c 4 sg( x sg( x sign( sign( S sign( sign( S T T S S T T, (2. (3 18

3 with the flow coefficient c. In the ractice, the flow coefficient may best be determined exerimentally, or be calculated using the catalogue data (Q N, Δ N, and x max of the ale manufacturer. QN 1 c =. (4 ΔN / 2 x,max Using the equation (2 a block diagram in MTL-Simulink for directional control ale has been deeloed (Fig. 2.. Fig. 2. block diagram of direction control ale The block diagram has been deeloed only for the flow Q which is connected to a differential cylinder, while the Q flow deends on the geometry of the cylinder, Q = αq. Suly ressure s = 210 bar, was chosen to facilitate comarison of exerimental and simulation results, since it is the alue of maximum ressure on the laboratory hydro aggregate. Control ale signal is defined, using equation (4, as the roduct of the maximum sool dislacement x max and flow coefficient c, whereby the alue of maximum sool dislacement has been disaeared, and now control signal deends of alues Q N and Δ N. The alues hae been taken from catalogue data of the ale manufacturer [5]. 2.2 Hydraulic differential cylinder Theoretical modelling of the hydraulic cylinder is less inoled than the ale. The rincial model relations hae been taken from [1], [6] and [7]. For this urose, a theoretical model is a slightly simlified, neglecting irreleant dynamics and nonlinearity, resulting in a comact cylinder model, which can easily be identified with exeriments. Pressure dynamics equations for differential cylinder are gien by: ( Q x + Q Q 1 = Li Le, (5 Ch 1 = ( Q + α x QLi QLe. (6 C h 19

4 The hydraulic caacitance of each chamber is gien with: C C h h V ( x V l, + ( x0 + x = Ch (, x = =, (7 E' ( E' ( V( x V l, + ( x0 x α = Ch (, x = =, (8 E' ( E' ( where V l, and V l, are the ieline olumes at the at the -side and -side resectiely and E is the effectie bulk modulus. The internal or cross chamber leakage flow (leakage from one chamber to the another can be calculated by: Q Li = C (, (9 Li where C Li is the internal leakage flow coefficient. External leakage (leakage from each cylinder chambers either to the drain or to tank in neglected, i.e. Q Le = Q Le = 0. The equation of iston motion goerning the load motion arises by alying Newton s second law to the forces on the iston. m ( F. (10 t x + Ff x = ( α Friction force is a function of elocity, equation (11, which is referred to as a Stribeck friction cure [1]. x F f ( x = F ( x + Fc ( x + Fs ( x = σ x + sign( x Fc0 + Fs0ex. (11 c s The tree characteristic arts of this cure are: iscous friction F, static friction F s and Coulomb friction F c. σ is the arameter for iscous friction, F c0 is the arameter for Coulomb friction, F s0 and c s are the arameters for static friction. Equations (5, (10 and (11 can be combined in a block diagram of a hydraulic differential cylinder as shown in Fig. 3. Pressure has been determined from the equilibrium equation of forces on the iston. It is assumed that no effects of external forces and friction forces, and = /α remains. Internal and external leakage failures are ignored, too. Cylinder dimension hae been chosen according to the laboratory cylinder, D = 40 mm, d = 25 mm, x max = 200 mm, continues α = 0,625 and = 0,00125 m 2. Pielines between ale and cylinder hae the characteristic: d l = 8 mm, l l = 2 m, continues V l, = V l, = 0,001 m 3. Effectie bulk modulus hae been chosen according [1] and it is E =18000 bar. Friction force has next arameters: σ = 220 Ns/m, F c0 = 200 N, F s0 = 600 N and c s = 0,015 m/s [1]. External force F ext has been neglected and the load mass m t = 2 kg (only iston mass. Cylinder osition and elocity are usually hysically limited. This kind of saturation cannot be taken into account by including a double integrator with saturation block into the model, as it does not realistically describe the real hysical behaiour of the system. lthough the osition has reached its uer saturation limit, the elocity is ext 20

5 still internally integrated. Instead, non-linear elements (logical oerations hae to be added to the model to ensure that elocity is immediately set to zero as soon as the cylinder reach its uer or lower saturation limit. Fig. 3. lock diagram of differential cylinder 2.3 Simulation results fter the simulation, next results hae been achieed, Fig From these results it is concluded that the inut signal takes one second, Fig. 4., which results in flow through the ale Q = 15,9 l/min and Q = 9,9 l/min, Fig. 5. fter 1.95 seconds, the flow stos, because the iston reached the maximum osition and came to the cylinder coer, Fig. 6. t the beginning the iston elocity raidly increases, due to increased ressure, and then it is moing with constant elocity of 0.2 m / s, Fig. 7. t the same time when entering hydraulic fluid into the cylinder, ressure is increasing raidly, until the ressure force to the iston becomes greater than the sum of the load force and friction force, Fig. 8 and Fig. 9. fter oercoming the reaction forces, the iston is moed and the ressure becomes constant ( =4 bar, = 6,5 bar until iston hits the cylinder ca, whereby the ressure increases until 210 bar, and dros to zero. Fig. 4. Inut signal Fig. 5. Flow through the ale Q 21

6 Fig. 6. Piston elocity Fig. 7. Piston osition Fig. 8. Pressures in cylinder chambers and Fig. 9. Detail of the cylinder chambers ressures and 3 LORTORY MESUREMENTS The laboratory hydraulic system consists of a hydro aggregate with control ales, differential hydraulic cylinder, PLC unit, measuring sensors and measuring instrument, as reresented in Fig. 10. Hydro aggregate with directional control ales, has the following technical characteristic: electromotor ower P = 5,5 kw, electromotor seed n = 1460 rm, um dislacement Q 1 = 10,8 cm 3, max. ressure of the system max = 210 bar [8]. With the PLC unit is fixed the inut signal for direction control ale. PLC rogramming is accomlished by entering alues of the signal eriod and auses between two signals, and the number of reetitions. Measurement equiment consists of a measurement instruments and sensors [9]. Measuring sensors determine ressure and temerature changes of the hydraulic fluid, which are then shown on the measuring instrument. Laboratory measurements were erformed on the differential cylinder, the aboe mentioned characteristics, wherein the measured alues are ressures i in the cylinder chambers. Inut signal had three arts. etween 0 and 1 and 2 to 3 seconds, there is no electric current on ale solenoid (ale is closed, while 1 to 2 seconds electricity owered solenoid, whereby the hydraulic fluid flow through the ale is achieed. 22

7 Measurement sensor PLC unit Hydraulic cylinder Control ale Measurement instrument Hydro aggregate Fig. 10. Laboratory hydraulic system Measurements were erformed for the case without loading cylinder with an external force, and without adding extra weight, which means that it is taken into account only the mass of the load iston and iston rod (about 2 kg. Measurement results of ressure in cylinder chambers ( i are shown in Fig. 11. from the initial moment until the third second. Fig. 12. shows the change of ressure in the cylinder chambers in the ale oening time t = 0,9 s to t = 1,2 s. Fig. 11. Measured alues of the cylinder chambers ressures and Fig. 12. Detail of the cylinder chambers ressures and during cylinder extraction 4 COMPRISON OF THE RESULTS Comaring the results obtained by laboratory measurements of cylinder ressure and the results obtained by simulation in MTL-Simulink, it can be concluded that the ressure behaior is similar, but not the same. Pressure in chamber on the iston side ( in laboratory measurements at the beginning raidly increases, and immediately falls, while the simulation doesn't show such a behaior, Fig. 13. This effect can be attributed to stick-sli effect [1], which is not taken into account in the simulation. Comaring the alue of increasing ressure at the beginning, shows a difference of 25% ( 2,5 bar. The initial ressure in the simulation is smaller, which can be 23

8 exlained by incomlete knowledge of the arameters of friction in a laboratory hydraulic cylinder. Obsering the ressure during the motion of the iston, the ressure is identical, which roes the accuracy of the simulation. Comaring the results for ressure it can be concluded that the ressure behaior is similar as s ressure behaior for, Fig. 14. The initial increasing of ressure is different by 20% ( 2 bar, and the ressures during the motion are equal. Fig. 13. Comarison of the ressure Fig. 14. Comarison of the ressure 5 CONCLUSION The main objectie of this study was to comare the dynamic roerties of hydraulic differential cylinders obtained by simulation with the simulation software MTL- Simulink and those measured in the laboratory. It was determined that the alues of ressure at a steady state corresond ery well. t the ending osition of the cylinder iston significant differences aear. The reason is requirement for recise determination of the coefficient of friction in the cylinder and the shock that occurs when oening a connection from the directional control ale. Such roblems would disaear if instead of on / off ale a roortional control ale be installed, which in combination with the PLC gies much better dynamic roerties of the cylinder. References: [1] Jelali M., Kroll.: Hydraulic Sero-systems, Modelling, Identification and Control, Sringer, London, [2] MTL: Reference Guide. The MathWorks, Inc, [3] Jędrzykiewicz Z., Pluta J., Stojek J.: lication of the MTL Simulink ackage in the simulation tests on hydrostatic systems, cta Montanistica Sloaca, Ročnik 3 (1998, 1, [4] acke W.: Serohydraulik, Technical Uniersity of achen, Germany, [5] TOS: htt:// ( [6] Merrit HE.: Hydraulic Control Systems, John Willey & Sons, 1967 [7] Viersma TJ.: nalysis, Synthesis and Design of Hydraulic Serosystems and Pieline, Elseier, [8] Hansa Flex: htt://cat.hansa-flex.com/hr/cat/1, ( [9] Parker, Senso Control, htt:// ( Receied: