JJMIE Jordan Journal of Mechanical and Industrial Engineering

JJMIE Jordan Journal of Mechanical and Industrial Engineering Volue, Nuber 3,Sep. 008 ISSN 995-6665 Pages 57-6 Matheatical Modeling for Pup Controlled Syste of Hydraulic Drive Unit of Single Bucket Excavator Digging Mechanis Jua Yousuf Alaydi * Industrial Eng. Dept., IUG, Palestine Abstract Industrial robots have turned out to be an everyday occurrence for engineers during the last twenty years. Increasing efficiency is one of the hottest research topics in hydraulic syste. The coparison between two types of hydraulic control systes, which are the valve, controlled syste and the pup-controlled syste is essential area of researching. Hydraulic actuator with pup-controlled syste is uipped in high power ining excavators and forestry uipent in order to increase efficiency. The purpose of this paper is to build a atheatical odel for a hydraulic actuator with pup-controlled syste. The boo of single bucket excavator is odeled and siulated as an exaple. The schee of this syste is presented and iteized. The odel of these ites is siulated and the control circuits are presented as well as the siulation results. 008 Jordan Journal of Mechanical and Industrial Engineering. All rights reserved Keywords: Hydraulic syste; Pup controlled syste; Valve controlled syste; hydraulic drive unit; single bucket excavator; atheatical odeling; and siulation;. Introduction Hydraulic actuation devices ay be linear or rotary and are usually referred to as pistons or otors, respectively. A pup or a valve giving four basic hydraulic power eleents and two basic over-all systes ay control these two actuation devices: pup controlled and valve controlled. Such hydraulic power eleents is siply a cobination the of principal power device in all hydraulic systes []. The pup-controlled syste consists of a variable delivery pup supplying fluid to an actuation device. The fluid flow is controlled by the stroke of the pup to vary output speed and the pressure generated atches the load. It is usually difficult to closely couple the pup to the actuator and this causes large contained volues and slow response []. The valve-controlled syste consists of a servo valve controlling the flow fro a hydraulic power supply to an actuation device. The hydraulic power supply is usually a constant pressure type (as opposed to constant flow) and there are two basic configurations. One consists of a constant delivery pup with a relief valve to regulate pressure whereas the other is uch ore efficient because it uses a variable delivery pup with a stroke control to regulate pressure. The features of each syste tend to copleent the other so that application ruireents would dictate the choice to be ade. Generally, there is not a cost advantage to either because the need for a replenishing arrangeent and a stroke servo for the pup controlled syste offset the costly servo valve and heat exchangers ruired for the valve controlled syste. However the faster response capability of valve controlled systes both to valve and load inputs akes this arrangeent preferred in the ajority of applications in spite of its lower theoretical axiu operation efficiency of 67% in low power applications where the inefficiency is coparatively less iportant, use of valve controlled syste is nearly universal. Applications, which ruire large horsepower for control purposes usually, do not ruire fast response so that a pup-controlled syste is preferred because of its superior theoretical axiu operating efficiency of 00% [3]. The pup-controlled actuator represents a further alternative. A siplified structure is depicted in Figure. This actuator uses a servo pup as a final control eleent in the actuator closed loop control. Siilar to the classical circuit of a hydrostatic transission, a closed hydraulic circuit design is eployed for the realization of a four- * Corresponding author. e-ail: jalaydi@ail.iugaza.edu

58 008 Jordan Journal of Mechanical and Industrial Engineering. All rights reserved - Volue, Nuber 3 (ISSN 995-6665) quadrant operation. This akes the utilization of brake energy in case of aiding loads generally possible. The pup controller adjusts the pup displaceent according to the deanded voluetric flow, which depends on the actuator velocity. The pressure difference between the high pressure and the low-pressure line is autoatically given by the actuator load. Mostly, the low pressure is set constant with the help of an external pup, which can also be eployed for the supply of the pup control syste. Thereby the hydraulic output power of the pup is siultaneously adapted to the ruired echanical output power of the actuator. Due to its siple design characterized by sall nuber of parts, and excellent achievable dynaic perforance, the swash plate of the axial piston pup would be usually the best choice for the servo pup [4]. The application of the displaceent control principle for actuators of heavy-duty obile anipulators has the following three iportant advantages: The iproved utilization of priary energy due to the oitted valves, The possibility of the additional use of brake energy in case of aiding loads, The reduction of total syste weight due to the replaceent of one or two large pups by a nuber of saller pups [5]. The realization of pup control is uncoplicated for rotary actuators and linear actuators with double rod cylinders. Several industrial applications have been developed recently. The kineatics and the whole achine design of obile anipulators ruire very often the use of differential cylinders. The unual areas of the differential cylinder have to be copensated, if the differential cylinder ay run within a pup-controlled actuator in a closed hydraulic circuit as shown in Figure B. The closed hydraulic circuit perits the four-quadrant operation of the pup-controlled actuator. Different circuit solutions allowing the copensation of the unual cylinder areas were developed recently. The first solution shown in Figure A was developed by Lodewyks at the University of Aachen in 993. A hydraulic transforer (5) serves as a flow copensator. The servo pup () has been used as a final control eleent in the closed loop position control of the linear actuator. The second solution is shown in Figure B characterized by two variable displaceent pup units (l, ) for one cylinder. This concept ruires a ulti-variable control concept for the siultaneous pressure and position control of the actuator to guarantee the ruired flow copensation. A third solution showed that in Figure C represents an enlargeent of the solution with two servo pups. The circuit is suppleented by a third variable displaceent pup (3) and a proportional pressure valve allowing the adjustent of the pressure level. This solution ruires a high nuber of coponents but does not need a ultivariable control concept. These actuator solutions were developed for special industrial applications. For the ajority of applications in obile achines, the replaceent of a valve controlled actuator by a displaceent-controlled actuator, which ruires two and ore variable displaceent pups and perhaps even further eleents, which increase the cost [4]. Figure. Circuit solutions for pup controlled actuator with differential cylinder The purpose of this paper is to build a atheatical odel for a hydraulic actuator with pup-controlled syste. The schee of this syste is presented and iteized. Models of ites and siulation of control circuits are also presented as well as the result of the siulation. Hydraulic Drive Unit of Single Bucket Excavator Digging Mechanis Kineatics and hydraulic circuit diagra of the hydraulic excavator digging echanis is shown in Figure and Figure 3. The hydraulic excavator digging echanis consists of four links, boo S, connecting eleent V, stick R, and bucket K ; each is set in otion by its own hydraulic cylinder. A variable displaceent pup controls the velocity of the piston rod of the cylinder. After investigating the load of each cylinder, it was shown that the boo cylinder is carrying the highest load []. Each eleent has its own ass, which in turn has its own reaction on the boo cylinder. Kineatics of digging echanis and structure design show that the reaction of the ass of each digging eleent changes with the stroke of boo cylinder. As shown in Figure, it is clear that any change in the echanis eleent position will result in substantial changes in the position of the ass center consuently this will cause changes in inertia and the uivalent ass as well as the total contained oil volue.

008 Jordan Journal of Mechanical and Industrial Engineering. All rights reserved - Volue, Nuber 3 (ISSN 995-6665) 59 Figure Excavator Digging Mechanis, (Boo S, Connecting eleent V, Stick R, and Bucket K) []. 3. Matheatical Modeling of the Hydraulic Drive Unit with Pup Controlled Syste Matheatical odel describes in details the boo hydro cylinder forward stroke and displays all-iportant characteristics of the investigated object. The scheatic diagra of the odel is shown in Figure 4. Figure 3. Hydraulic Unit and cineatic circuit diagra of the boo echanis Thus, this syste is characterized by variable paraeters depending on the eleents position. The control syste with dynaic characteristics ruires designing a control algorith structure (dynaic controller), which ust be efficient to copensate the dynaic variation of the controlled object paraeters. The following assuptions were ade during this paper: The friction force at the hinges and the seals are neglected. The link of each echanis is considered as a rigid body. The return pressure is constant and ual the replenishing pressure P =0. The paraeters changing range of the boo echanis can be coputed fro its atheatical odel. The atheatical odel of the boo hydraulic cylinder is set up for forward stroke oveent since digging process and consuently the highest load occurs during forward stroke. Figure 4. Model of the hydraulic actuator with pup controlled syste The odel incorporates: a) Control object cylinder HC and speed sensor SS to easure the rod speed. The cylinder is loaded by active force R (h) and ass (h), since these paraeters are a function of the cylinder stroke position h. b) Power supply unit, which is represented by the variable displaceent, pup P.

60 008 Jordan Journal of Mechanical and Industrial Engineering. All rights reserved - Volue, Nuber 3 (ISSN 995-6665) c) Servo valve unit, which converts input signal U p and feedback signal fro sensor displaceent sensor DS into a control signal Y p. 3.. Model Description The odel consists of Electro hydraulic Servo valve C to control the flow of variable displaceent pup P. An input signal U p is activated by the excavator operator which enters the aplifier EPM, and then the servo valve spool starts to ove. Oil enters into the servo valve hydro cylinder piston chaber SC forcing the rod, which is linked to the pup swash plate forward and thus changing the pup flow. The rod displaceent Y P will keep changing until the electric signal of displaceent sensor DS balances the control signal U P. Oil flow fro the pup P enters into the cylinder chaber, creating force enough to ove the ass against external force R. Check valves CV prevent stagnation, copensate the shortage of the flow fro the replenishing flow, and allow the excess flow to pass through the pressure relief valve to the tank. 3.. Matheatical Modeling of the Actuator Equation of oveent Equivalent ass acting on hydro cylinder rod changes depending on digging echanis eleent positions as shown in uation a below. It is assued that all digging echanis eleents are joint rigidly as one unit and rotating as solid body with ass c around axis through O. c = + + 3 + 4. (h) can be coputed fro the kineatics and dynaics analysis of the syste given in []. h is the vector of digging echanis state position characterized by cylinder stroke, h boo, h insert, h 3 stick and h 4 bucket. In addition, fro [] the uivalent ass will have the following relationship: r d h r ( h) b crc ( h) w τ =, (a) Kineatics of Fig. 3 gives a d sinϕ b =, (b) a + d a d cosϕ a + d (h 0 + h) ϕ = arccos (c) ad Then the angular acceleration can be coputed as: dv = () ( h) A P R w τ d ϕ = rc = r (h c 0 + h ) 4a d [a + d (h 0 + h ) ] d h (e) Continuity uation of the oil in the cylinders chabers V dp E = k y C P A v () Servo valve uation p e dyp Tp + yp = K p U (3) p Where: (h) is the ass as a function of the digging eleent position (h), v is the velocity of piston rod easured by speed sensor SS, A area of the piston, R external force, V volue of hydro cylinder chaber, E oil bulk odulus, k pup coefficient (which can be coputed experientally fro the relationship of the pup flow Q and the servo valve displaceent Y p ), K p controller coefficient (which can be coputed experientally fro the relationship of the servo valve displaceent Y p and input signal U P ), t tie. Cobining uations,, and 3, the atheatical odel will have the following for: dv = (4) dp = kψ (Ce + Ci )(P P ) Av, (5) ( h) A P A P R( h) ( ) V h E Where: is the uivalent or the effective ass of the digging echanis eleents acting on the cylinder piston rod, kg. Fro uation (b), (c) and (e), it is possible to copute the axiu and iniu liits of uation (a) which can be rewritten as: a = + d a d cosϕ rc a d sin ϕ Where: r c, is the radius of rotation around hinge O, w τ is the angular acceleration of the center of ass, c is the ass of the syste. A, A are the areas of forward and return stroke of the piston,. P, P are the pressure at the piston and rod chabers, Pa. P uals the replenishing pressure P =0 (assued). k is the pup control eleent (swash plate) gain coefficient 3 /rad/deg. v is the piston rod velocity, /s. V is the total contained volue including the chabers and the connecting hoses and anifolds. E is the liquid bulk odulus of elasticity (constant). ψ is the swash plate paraeter (0 ψ ). C e, C i is the luped external and internal leakage coefficients respectively. h 0 distance fro cylinder hinge B to the piston return stroke position. Equations 4 and 5 can be Lap laced and written in the general for as: C. (d)

008 Jordan Journal of Mechanical and Industrial Engineering. All rights reserved - Volue, Nuber 3 (ISSN 995-6665) 6 r r ( h) V( h ) ()( h C + C ) EA s + A e i s + δv = k δψ Where: δ deviation fro steady state value, s Lap lace operator. The dynaic behavior of this second order syste can be then described in ters of two paraeters, T which is the characteristic tie, and ξ which is the daping ratio. The syste characteristic uation can be rewritten to give: ( h) V( h) EA ( h)( C + C ) A e (6) = T (7) i = Tξ 4. Siulation Exaple. The given analysis allows coputing the iportant paraeters of the controlled object at any digging echanis position resulting fro changing vector h. All the data are collected fro real ining excavator. The calculations were perfored for the following real diensions collected fro 5-3 single bucket excavator in []. Pup leakage coefficients were evaluated based on lab experient fro [] as follow: (8) The following coefficients were collected fro anufacturers catalogues for the boo cylinder and the pressure relief valve. Relief valve external leakage coefficient C er =0.06 0-5 /(N s), no internal leakage coefficient was considered. Hydraulic cylinder internal leakage coefficient C ic =0.37 0-5 /(N.s), no external leakage coefficient was considered. The luped leakage coefficients are: Total external leakage coefficient C e = C ep +C er ; and Total internal leakage coefficient C i = C ip +C ic.for MEXZ 4APM-5 ining excavator shown in Fig.. l =l 3 =6.5; l =.9; r 4 =.4; a=3.0; d=5.54; h =3.3; = 3 =.5*0 3 kg; =8.5*0 3 kg; 4 =40*0 3 kg (ass bucket with full load); A =*0.5 ; E=.*0 3 MPa; Siulation of the syste of uations 6,7 and 8 for T and ξ were accoplished with step Δh =0.H for the boo digging echanis eleent (H is the axiu stroke of the boo cylinder). In Figure 5 the result of siulation of the pup controlled syste which have been ade for the given data fro real ining excavator, the pup Hytos MLPD/G7D, the proportional valve Bosch NG6, the linear hydraulic actuator Mannesann Rexroth CYW 60 B 63/45-0, volue of the pipe 0.00 3 and the dynaical load described above. Maxiu and iniu values of T and their corresponding ξ,, V, were obtained as follows: T ax =0.0; ξ=0.05; =.5*0 6 ; V=0.68; T in =0.0066; ξ=0.0; =0.066 0 6 ; V=0.050; C ep =.4 0-5 /(N s); C ip =5. 0-5 /(N s) δv ax.8.6.4. in 0.8 0.6 0.4 0. T=0.0s T=0.0066s 0 0 0. 0.4 0.6 0.8..4.6.8 t (s) Figure (5) Transient response for hydraulic drive

6 008 Jordan Journal of Mechanical and Industrial Engineering. All rights reserved - Volue, Nuber 3 (ISSN 995-6665) 5. Discussion And Conclusion The transient response for two extree boo positions in copliance with actuator atheatical odel was resolved and analyzed to give the following results: The digging echanis load acting on the boo cylinder rod was changed fro 0.3*0 6 N to.38*0 6 N. The value of the characteristic tie of the linearized odel of the control object was changed fro T in =6.6*0-3 s to T ax =0*0-3 s. The daping coefficient was also changed fro ξ in =0.0 to ξ ax =0.05. The dynaic behavior of the load, the characteristic tie, and the daping coefficient would greatly affect the transient process paraeters thus, for each piston oveent, a new transient process with different paraeters would appear. The digging echanis and hydraulic unit atheatical odel represents a dynaic syste with variable paraeters because the coefficients are deterined by the digging echanis position. The siulation of the hydraulic actuator with pup controlled odel shown in Fig.5 were obtained without correction for two extree digging echanis positions and it was clearly shown the weak daping of hydraulic unit resulted in sustained vibration. The siulation of the odel is eployed to show that hydraulic actuator with open loop control syste is not relevant for hydraulic unit with pup controlled syste. It is necessary to construct a rational dynaic regulator to control the pup flow in order to stabilize the syste. The next step is to look for a suitable controller for the hydraulic drive digging echanis to eliinate the vibration resulting fro the weak daping. References [] Jua Y. Alaydi. Optiization of Pup Controlled Syste of Hydraulic Unit of Single Bucket Excavator Digging Mechanis. PhD thesis Kharkov Polytechnic University, Kharkov Ukraine, 000. [] Gladky P.M., Alaydi J.Y. Application of hydraulic actuators with pup controlled syste in hydraulic excavators. Vestnic Journal of National Technology, University of Ukraine, Machine building, Kiev Polytechnic Institute, Kiev. Ukraine, 000.00-03. [3] Herbert E. Merritt, Hydraulic Control Systes, J. Wiley, and Sons967. [4] Backe W. Trends in Mobile Hydraulics, Fourth International Conference on Fluid Power, Teper, Finland, 995. [5] Oshina M., The tendency of servo control for hydraulic excavator. Fifth Scandinavian International Conference on Fluid Power, Linkoping, Sweden, 997.