Modeling And Simulation Swash Plate Pump Response Characteristics in Load Sensing And Pressure Compensated Hydraulic System

Transcription

1 International OPEN ACCESS Journal Of Modern Engineering Research (IJMER) Modeling And Simulation Swash Plate Pum Resonse Characteristics in Load Sensing And Pressure Comensated Hydraulic System * Molham Chikhalsouk 1,4,Khalid Zouhri 2,3,4,*, Omar Khondker 4, Luis Ferreira 4 1 Deartment of Mechanical Engineering, Concordia University, Montreal, CANADA 2 Deartment of Mechanical Engineering-Engineering Mechanics, Michigan Technological University, Townsend Dr., Houghton, USA 3 Deartment of Mechanical Engineering, University of New Haven, Boston Post RoadWest Haven,. 4 Deartment of Mechanical Engineering, Higher College of Technology Abu Dhabi, UAE Corresonding author: *Molham Chikhalsouk ABSTRACT: Fluid Power is widely emloyed in alications required high loads such as tractors, cranes, and airlanes. In load sensing hydraulic systems, loads are controlled by adjusting a um-valve arrangement. In this aer, the swash late um hydraulic characteristics will be determined, the um and its fluid gains will be derived to obtain the um overall transfer function. Firstly, the swash late um mechanism is analyzed and its dynamic model is constructed; the um ressure and flow rate are lotted and the ossible imrovement is introduced. The load sensing unit arameters such as orifice width, orifice area, maximum assage area, and iston area at X and Y will be examined to identify their influence on the um characteristics; and the otimum arameters will be introduced. All results are develoed and simulated numerically. Keywords: Swashlate um, load sensing control, um characteristics, um flow rate, um delivery ressure. I. INTRODUCTION In the ast twenty years, a remarkable attention has been directed toward the variable dislacement swash late ums. These studies covered several asects of the um such as the um kinematics and um characteristics control to achieve the otimum erformance. One interesting study has been resented by Tanglin [1]. Tanglin roosal based on controlling the um characteristics by controlling the rime mover seed. Akers and Lin [2]have modeled the axial iston um and controller the um ressure as they have used a single stage electro-hydraulic valve to control the um flow rate. They used a ste function and tested the non-stationary resonse by imlementing the otimum control theory for the control oen loo. There was a remarkable imrovement in the um erformance. One more study was conducted by Kaliftas and Costoolus [3]. They modeled and tested the dynamic and static um characteristics. The um was equied with a ressure regulator. The results have been collected numerically and matched with the um oerations curves. In [4], Johnson and Manring have modeled the axial swash late um and investigated the effect of a defined loads on the um characteristics. In the last few years, the swash late um with the conical arrangement was introduced. In the conical arrangement, there is an angle between axial coordinate and the istons axis. This arrangement has a remarkable advantage over the cylindrical arrangement as the detachment force has been reduced. The detachment force tends to remove the iston from its slier ad. The conical um has been studied extensively, some good examles can be obtained in [5,6,7,8]. Khalil el al. [6] has modeled and simulated the swash late and investigated the effect of the um kinematics on the um flow rate and ressure riles. Also, Khalil in another study has investigated the influence of the controller secifications on the um characteristics [6,7, 9]. Further study has been conducted by Chikhalsouk. The study has concluded a simlified geometrical um kinematic exressions and accordingly, the um characteristics have been investigated. Another imortant technique in swash late um characteristics control is load sensing control. The load sensing swash late um consists of the um and control valves, which automatically adjust the um characteristics i.e. the um flow rate and ressure to meet the load requirements, and this maintains the hydraulic flow quality, the um efficiency and avoids the throttling overflow losses. Thus, the load sensing IJMER ISSN: Vol. 7 Iss. 8 August

2 swash late um has relatively fewer energy losses and higher efficiency in comarison to other tyes of hydraulic ums. In order to imrove the um oerating stability and its erformance, it is very vital to otimize the um construction. The comlex structure for the swash late sensing um makes the mathematical modeling is retty challenging. Hence, the conventional develoment aroaches are hard to comly with the modern ums designrequirements. Load sensing systems have become very oular in the ast two decades, esecially in automobile and heavy duty machinery [10, 11, 12]. One imortant advantage of these systems is the high otential of energy saving; where is the um meets the ower requirements to the various loads with the least control losses. However, a kind of interaction amongst loads and an instability is reorted [13].In load sensing um, the ressure is sent back to the um controller to adjust the swash late swiveling angle and um flow rate accordingly. The remarkable advancements in comuter simulation grant researchers with an effective and convenient latform to design the um[14, 15]. The simulation tests enable the researchers to discover the otential design roblems and enhance the required arameters to achieve the desired erformance and then building the rototye. Some of the comuter simulations that can significantly simlify the develoment rocess and shorten its cycle, and substantially reducing the develoment costs which lead to the ideal design scheme [16, 17]. In the ast few years, the comuter simulation has been emloyed in imroving the design of the hydraulic um and has shown a remarkable success [18, 19]. For examle in [20], Cho et al. have used AMESim software to model and simulate the conical swash late um and studied and analyzed the iston ressure fluctuation. In [21],Baek et al. have extended their studies to include the iston behaviors under disk eccentricity ratio. The axial iston um characteristics and the effect of the internal leak on the um ressure and flow rate were investigated by Bergada [22]. Casoli et al. have modeled and simulated an excavator s arm owered by swash late um by using gray box technique, and have obtained fast excavation cycle[23]. The ressure control by ressure comensator for swash late um was studied by Mandal in [24]. In [25], Xu et al. have studied the otimum structure for anti-overturning slier of swash late um to enhance the service life and the swash late um reliability. Roccatello et al. have modeled and simulated multi subsystems of a swash late um based on software technology and tested the swash late um dynamic resonse characteristics [26]. The Zhu et al. s study has added a significant analysis of the swash late load sensing um [27], however, more work needs to be achieved.other studies have concentrated on the structure and otimum arameters of the load sensing swash late um [28, 29]. In this aer, the swash late um is selected for the research object. The load sensing and swash late um structure are exlained. The mathematical model is develoed. The test rig secification and structure are detailed. The um characteristics are obtained. The load sensing unit arameters influence on the um characteristics are studied. Finally, the otimum load sensing arameters are recommended. Load Sensing Unit with Swash Plate Pum The load sensing arrangement consists of a variable dislacement um i.e. swash late um, an actuatingyoke, a um control iston, and a critically laed adjusting valve. The orifice is controlled by two ressures, which are ustream(um ressure) and downstream (load ressure).when the load increases, there will be an increase in um feedback sensing load ressure. Hence, there will be a change in the ressure acting on the sool. The sool is exeriencinga unbalance force and shifting it to the right and connecting to the tank. On the other hand, a decrease in the fluid ressure will increase the swash late swivelingangle, which increases the um flow rate. This increase in the um flow exeriences a higher resistance in the controlling orifice, which increases the ressure. The um feedback line ressure is sensed, which affects the comensator iston right handed side. The ressure kees building u till the balance occurs through the comensator. Accordingly, the orifice ressure dros and the flow is adjusted reaching to its original level (control flow). In other words, in load sense control, the um flow increases or decreases to main the differential ressureacross the orifice. Thus, the flow will be constant for the same orifice oening regardless the load condition or the rime mover revolution. Accordingly, the um will use only the enough ower to maintain suitable flow. A limiting ressure control is a controlled method to set the maximum system ressure. The ressure limiting valve is installed to hinder um ressure to go beyond the reset ressure. The load sensing valve reloaded sring is calculated with the following equation as: fv. A (1) v where desired differential ressure across the control valve in Pa Av control valve cross-sectional area in m 2 IJMER ISSN: Vol. 7 Iss. 8 August

3 3. Pressure and Flow Control Arrangement for the Swash Plate Pum The control unit consists of a 3-way hydraulic directional valve and a double-acting servo cylinder that controls the um yoke. The load sensing is enabled by keeing a redetermined ressure differential through the flow control valve. These ressures act uon the sides of the directional valve and move it corresondingly to the ressure difference. The control unit elements are: A. Flow Control Variable Area Orifice: The variable orifice consists of a cylindrical shar-corner sool and a rectangular oening in a sleeve. The orifice flow rate is roortional to the ressure differential through the orifice faces and its oening. The connections A and B are maintaining hydraulic channels with the orifice inlet/outlet. The ositive direction is from A to B, where the ositive signal at sool S oens/closes the orifice according to the orifice orientation arameters. B. Load Sensing Fixed Orifice: Is s squared corner fixed area orifice. The flow rate is roortional to the ressure differential through t the orifice. Ports A and B are maintaining hydraulic channels linked with the orifice inlet/outlet. The ositive direction is from ort A to ort B, which means that when the flow from A to B is counted ositive, and the differential ressure is comuted as P = P A - P B. C. Pressure Relief Valve: it oens as the ressure exceeds the valve reset ressure, where value control member is ushed against its seat and initiating a ga between the outlet and inlet. This relief sends some of the fluid back to the tank and decreases the ressure at the inlet. Yet, the ressure starts to be built as the flow rate is insufficient. At this condition, the area increases till the control element reaches its eak. Connections A and B are maintaining channels and the working direction from A to B. D. Double Acting Calve Actuator: It uses as a ilot actuator for ressure/directional/flow control valves, where all flow consumtion and forces can be neglected excet sring force. The actuator has two single acting actuators advancing against each other. Each actuator contains a centering sring with its washer and a iston. When a ort is under a control ressure, one centering sring is comressed across its washer only, while will exert no force. When a ressure control is released on the both orts, the sool centers between them. This design enables each actuator to have its own design arameters. When a control ressure alies, the iston will move against its sring. The different control unit elements are listed in Figure Swash Plate PumStructure As shown in Figure 1, the swash late um consists of a certain number of istons moving inside their cylinders and combined in a common block named the cylinders block. The cylinders/istons are enclosed in an annular array within the cylinders block at an equal interval around the axial coordinate. The cylinders block is retained securely aginst the ort late by the aid of the cylinder block sring comressed force. A ball and socket joint links the iston base to its slier. The sliers are maintained in touch with the swash late and the swash lates swiveling angle is controlled by a servomechanism deending on the delivery ressure/ flow rate demands. In actual alications, the loadon the hydraulic actuator may alter from instance to instance, which will require the swash late um to roduce a several oerating ressure/ flow rate accordingly. II. Mathematical Modeling The analytic method is the most oular method to model and analyzes the hydraulic ums in general and swash late ums in articular [ 30, 31], state sace method [32], and bond grah aroach [ 33]. In this work, the dynamic model for the load sensing um will be built based on analytic aroach. 1) Load Sensing Valve Dynamic Equation: The load sensing valve dynamic exression can be written as: M.&& x + C. x& + K. x = ( P P ) A F v v v v v v s l v 0 (2) Let s name total inuts as transform f e, hence, the load sensing valve transform function can be obtained by Lalace 1 X ( s) Kv G ( s) = = s + 2. ς v + 1 ω v 1 2 Fe ( s) s 2 ω nv nv (3) IJMER ISSN: Vol. 7 Iss. 8 August

4 2) Swash late dynamic equation: The dynamic equation of swash late[20] can be exressed as:.. 1. J V J k x = A x& +.&&& x ( K C 2 0 ). x 2 A. l. + + && A. l q v 1 0 β 1 0 (4) Hence, the swash late transferfunction can be obtained by Lalace transform Kq X ( s) A1 G2( s) = = 2 X v ( s) s s s( ) ω 3) Pum outut flow rate characteristics. The um flow gain equation of the um [ 34] can be written as: Q 2 n ς ω n = K. n. x (6) um Q The um outut flow rate gain can be obtained by Lalace transform as Qum ( s) G3( s) = = KQ. n X ( s) 4) Pum ressure characteristics. The um flow rate variation causes the ressure variation. Hence, the ressure differential equation can be written as follows: t l l. V (8) Q + Q c Ps = P& s β Consequently, the um ressure may be exressed as 1 (9) Ps ( s) cl G4( s) = = Q ( s) + Ql ( s) s 1+ ωt Oen loo transfer function of the load sensing swash late um is the roduct of the four gains i.e. 1 Kq 1 ( ) ( ) ( KQ. n)( ) (10) Kv A1 cl G( s) = s s s s s ( + 2. ς 1) ( 2. 1) (1 ) 2 v + s + ς ω ω ω ω ω nv nv n n Equation (10) reresents the load sensing swash late um transfer function. Two oscillatoryelements, one inertial element, and one amlifying element are the cascade gains for the oen loo of the equivalent transfer function for the um. The um resonse in the time domain can be reresented by the fundamental frequency of the elements, at the same time, the vibration characteristics of the system can be figured out by the elements daming coefficients. Hence and in order to imrove the system erformance, there is a need to lessen the influence of the first order inertial element and secure that the second order vibratory element lays the leading role in the system. Increasing the corner frequency of the first order to increase the ressure/ flow coefficient of the load system can be one a suitable aroach. Also, decreasing the load sensing valve sring stiffness or decreasing the iston area of the variable hydraulic cylinder are other owerful aroaches. 5. Test Rig Construction The objective of the test rig is to investigate the interaction between the swash late um and the control unit, and the same time achieving the load sensing and the ressure control goals. To secure the vital accuracy, the um model should be derived in the way that considers this interaction among the istons, the swash late, and the ort lates, which makes it very critical to constructing the comrehensive um model. t (5) (7) IJMER ISSN: Vol. 7 Iss. 8 August

5 5. 1Test Rig Outline The schematic reresentation of the system test rig is illustrated in Figure 3. The um model is symbolized with the name Swash Plate Pum. The rime mover, which is the source of um mechanical ower, is simulated with the Ideal Angular Velocity source. The um oututs/ delivery are a hydraulic ieline and two variable orifices. The flow rate is adjusted by the flow control orifices; in this work, the oening is remained fixed during the simulation. The load sensing um needs to reserve a constant differential ressure across the orifice regardless the swash late loading. The loading um is reresented in the simulation as the load orifice block. In order to investigate the control unit for several load conditions, the load orifice area is changed during the simulation. The changing rofile is utilized by the Load Signal Builder block. The control unit is symbolized in the test rig by a three-way valve ressure controlled, a ressure relief valve, flow control orifice, and an orifice. The control unit senses signals on the um ressure and the load ressure, measured ost the valve of flow control. According to these ressures, the yoke dislacement is generated, which limits the angular swash late swiveling angle i.e. the iston stroke. In this way, the differential ressuresmaintained across the flow control valve and eliminate the um to generate an excessive ressure set by the manufacturers. The fundamental test rigs arameters are listed in Table : Test Rig Model The models of the swash late um and the control unit are built Swash Plate um Model The um under investigation is a swash late um. The um block diagram is illustrated in Figure (4). In Figure (4), S is symbolizing the um driving shaft (ort 3), Y for the yoke linked to the inclined swash late (ort 1), and B is the um discharge ressure (ort 2). All istons are symbolized by a subsystem named iston. These istons models are identicals and linked to um external um s orts. Every iston is linked to the low ort (suction ort i.e. A), which is simulated by with the Ideal Hydraulic Pressure Source block. The booster ressure set oint is 5 bar. The yoke is linked to the istons actuator orts, hence oerating on the inclined swash late. The yoke dislacement is controlled by the hard sto function : Pressure and Flow Control Subdivision Model The control subsystem is exhibited on Figure (2), such that is constructed by a three-way directional valve, double acting hydraulic valve actuator, ressure relief valve, and non-variable orifice blocks. The ort B and A are linked to the u and downstream of the control orifice in Figure 2. The flow control orifice differential ressure is selected to be 20bar. In Figure (2), the lower osition of the 3-way directional valve needs to be reliminary oen, to ush the swash late um to boost its dislacement at the beginning of the oeration. To conduct the load sensing objective, the ressure rise at the LSP oening have to oen the 3- directional valve lower osition. These are the major consideration in valve ort to system connection. The other arameters such as orifice area, valve length, and sring stiffness are adjusted during the simulation to guarantee the effectiveness and numerical stability. The um needs to be oerated within the ower limitations, and hence, the ressure limiting function is alied in joint with the non-variable orifice and ressure relief valve blocks. The relief valve set value is selected to be 250bars. This value is suitable to decrease the ressure of the double acting valve actuator, which is linked to the yoke, as the ressure increases at the non-variable orifice. This action decreases the um dislacement. 5.3: Test Rig Data The load sensing system is investigated by simulating the derived models with aroriate arameters, which are summarized in Table (2) : Simulation Data and Results The simulation cycle contains several elements defined by several load conditions that affect the variable area block whose oening is adjusted by sool osition in Load Signal Builder block, as illustratedin Figures(5)Figure (6)shows the load sensing evolution with resect to time. From the figure, the simulation cycle starts with zero oening for 0.25 sec, and then, the oening increases linearly and becomes 2.8 mm at 0.31 sec. This oening remains constant for 0.20 sec, and another linear increase takes lace and reaching the maximum valve 5.2 mm at 0.52 sec. it remains constant for 0.25 sec and then decreases to 1, and another decrease (-0.8 mm). Finally, the oening settles at 2.5 mm. At the beginning of the cycle, the um shaft rotates at 260 rad/sec and the initial osition of the yoke is selected to be 5 mm. The um flow rate and ressure are illustrated in Figures (7-1) and (7-2). As can be noticed from the Pressure Profile, the servo cylinder begins to increase the um dislacement, the um ressure increase to reach 200 bars at 0.24 sec, where the differential ressure across the flow control valve gets close to the ressure set value; the load sensing valve oens at this instant. IJMER ISSN: Vol. 7 Iss. 8 August

6 Afterward, the ressure settles at 75 bars and this lasts till 0.5 sec, hence, the um ressure dros to 50 bars and this last for 0.25 sec (till 0.75 sec). Another two ressure increase cycles take lace at 0.85 sec and 1.1 sec, resectively. Through these three cycles, the um holds almost the same flow rate in site of alternations of the oening of the load valve. The limiting function dominates the ressure rise as it reaches 270 bars and the um reacts to the load sensing regime allowing the ressure to decrease. The simulation results exhibit that the um flow rate and ressure characteristics and the load sensing variable um are comatible. Hence, the swash late um characteristics can be dynamically simulated and analyzed by using the model. 6. Load Sensing System Comonents Simulation and Otimization In this section, the um flow and ressure characteristics govern the um fundamental arameters are discussed; then, a series of simulation runs are conducted to investigate the imact of the several loads sensing unit arameters on the um external characteristics i.e. the um flow rate and the ressure. As mentioned earlier, the load sensing unit consists of the 3-way directional valve, the double acting servo cylinder which stroke/ stroke the control iston, the variable control orifice, the load sensing fixed orifice, and the ressure relief valve. The objective of this simulation is to identify the most sensitive arameter for imroving the um characteristics. The simulation matrix is formulated and the arameters are selected. The arameters are Flow Control Orifice with Variable Area Slot /Orifice Width, Load Sensing Fixed Orifice/ Orifice Area, Pressure Relief Valve/ Maximum Passage Area, and Hydraulic Double Acting Valve Actuator/ Piston Area at X and Y. The arameters are groued in Table (1), and the simulation results are lotted accordingly in Figure (8). Figure (8-1) illustrates the influence of flow control orifice width on the um ressure. The orifice width is increased consecutively starting from the original value and increased to 1.2, 1.3, 1.4, 1.5, and 2 cm. Increasing the orifice width imroves the um ressure and the ressure fluctuation can be noticed at a high value of the width, which is 2 cm. Figure (8-2) shows the influence of flow control orifice width on the um flow rate. It is notable that um flow rate increase as the orifice width increase and the maximum width generates an excessive flow fluctuation which is not recommended for hydraulic systems. Figures (8-3 and 8-4) demonstrate the um characteristics at different values for Load Sensing Fixed Orifice areas. The selected areas are 4, 6, 8, and 10 mm 2, resectively. The increase in the area has an imact on the um flow rate at 1.1 sec and increases of the flow rate, however, there is a minimal fluctuation in the flow rate. Moreover, increasing the area has a ositive imact on the ressure and the ressure overshooting droed by 50 %. The effect of the ressure relief maximum area on the um flow rate and ressure are reresented in Figures (8-5 and 8-6). The simulation results show that there is no imact on the relief valve area on the um characteristics. Figures (8-7 and 8-8) establish the relationshis between the um characteristics and the actuator area. Increasing the area would decrease the um flow rate and ressure by 5% with every 5 mm 2 area increase. For otimum um characteristics, it can be summarized the following observations: Increasing the variable orifice width u to 1.5 cm, increasing the fixed orifice area u to 10 mm 2, and the small increase in actuator area (u to 85 mm 2 ). On the other hand, no imact on the relief valve area on the um characteristics as used for maintaining the um ressure at the reset value. 7. Conclusions The swash late um hydraulic characteristics were determined, the um several gains and overall transfer functions were derived and determined. The load sensing unit arameters such as orifice width, orifice area, maximum assage area, and iston area at X and Y were first identified to simulate the um characteristics. Then a set of simulation runs were conducted to obtain the otimum characteristics. It was found that increasing the orifice width reasonably would imrove the um characteristics. Also, the increase in the fixed orifice area has a ositive imact. Moreover, the small increase in the actuator area could imrove the um flow rate and the ressure. However, there is no influence for the relief valve on the um erformance. Figures Cations: Figure 1: Load sensing unit with swash late Figure 2: Schematic Reresentation of the Swash Plate Resonse Characteristics Control Unit Figure 3: Schematic Reresentation of the Test Rig Figure 4: Schematic Reresentation of the Swash Plate Figure 5: Schematic Reresentation of thesool Block Figure 6: Load Sensing Valve Oening with Time Figure 7-1: Pum Flow Rate Profile Figure 7-2: Pum Pressure Profile Figure 8-1: Pum Pressure Profile with Several Control Orifice Widths Figure 8-2: Pum Flow Rate Profile with Several Control Orifice Widths Figure 8-3: Pum Outut Flow Rate with Several Load Sensing Fixed Orifice/ Orifice Area Values Figure 8-4: Pum Outut Pressure with Several Load Sensing Fixed Orifice/ Orifice Area Values IJMER ISSN: Vol. 7 Iss. 8 August

7 Figure 8-5: Pum Outut Flow Rate with Different Pressure Relief Valve/ Maximum Passage Area Values Figure 8-6: Pum Outut Pressure with Different Pressure Relief Valve/ Maximum Passage Area Values Figure 8-7: Pum Outut Flow Rate with Several Double Acting Valve Actuator/ Piston Area Values Figure 8-8: Pum Outut Pressure with Several Double Acting Valve Actuator/ Piston Area Values LIST OF FIGURES Figure 1: Load sensing unit with swash late Figure 2: Schematic Reresentation of the Swash Plate Resonse Characteristics Control Unit IJMER ISSN: Vol. 7 Iss. 8 August

8 Figure 3: Schematic Reresentation of the Test Rig Figure 4: Schematic Reresentation of the Swash Plate IJMER ISSN: Vol. 7 Iss. 8 August

9 Figure 5: Schematic Reresentation of thesool Block Figure 6: Load Sensing Valve Oening with Time Figure 7-1: Pum Flow Rate Profile IJMER ISSN: Vol. 7 Iss. 8 August

10 Figure 7-2: Pum Pressure Profile Figure 8-1: Pum Pressure Profile with Several Control Orifice Widths Figure 8-2: Pum Flow Rate Profile with Several Control Orifice Widths IJMER ISSN: Vol. 7 Iss. 8 August

11 Figure 8-3:Pum Outut Flow Rate with Several Load Sensing Fixed Orifice/ Orifice Area Values Figure 8-4: Pum Outut Pressure with Several Load Sensing Fixed Orifice/ Orifice Area Values Figure 8-5:Pum Outut Flow Rate with Different Pressure Relief Valve/ Maximum Passage Area Values IJMER ISSN: Vol. 7 Iss. 8 August

12 Figure 8-6:Pum Outut Pressure with Different Pressure Relief Valve/ Maximum Passage Area Values Figure 8-7: Pum Outut Flow Rate with Several Double Acting Valve Actuator/ Piston Area Values Figure 8-8:Pum Outut Pressure with Several Double Acting Valve Actuator/ Piston Area Values IJMER ISSN: Vol. 7 Iss. 8 August

13 Flow Control Orifice with Variable Area Slot /Orifice Width Load Sensing Fixed Orifice/ Orifice Area Pressure Relief Valve/ Maximum Passage Area Hydraulic Double Acting Valve Actuator/ Piston Area at X/ Y Aendix Comonent Parameter Unit #1 #2 #3 #4 #5 #6 Flow Control Orifice with Variable Area Orifice Width cm Slot Load Sensing Fixed Orifice Orifice Area mm 2 2 Pressure Relief Valve Maximum Passage mm 2 20 Area Hydraulic Double Acting Valve Piston Area at X/ Y mm 2 80 Actuator Flow Control Orifice with Variable Area Orifice Width cm 1 Slot Load Sensing Fixed Orifice Orifice Area mm Pressure Relief Valve Maximum Passage mm 2 20 Area Hydraulic Double Acting Valve Piston Area at X/ Y mm 2 80 Actuator Flow Control Orifice with Variable Area Orifice Width cm 1 Slot Load Sensing Fixed Orifice Orifice Area mm 2 2 Pressure Relief Valve Maximum Passage mm Area Hydraulic Double Acting Valve Piston Area at X/ Y mm 2 80 Actuator Flow Control Orifice with Variable Area Orifice Width cm 1 Slot Load Sensing Fixed Orifice Orifice Area mm 2 2 Pressure Relief Valve Hydraulic Double Acting Valve Actuator Maximum Passage Area mm 2 20 Piston Area at X/ Y mm Table 1: Load Sensing Comonents Simulation Matrix Nomenclature: Flow Control Orifice with Variable Area Width 1 cm Load Sensing Fixed Orifice Area 2 mm 2 Pressure Relief ValveArea 20 mm 2 Hydraulic Double Acting Valve Actuator Piston Area at X and Y 80 mm 2 f : Load sensing valve reload force N v x&& v, x& v, x v ( x&&, x&, M v : Proortional valve sool mass C v : Proortional valve viscous friction coefficient K v : Proortional valve sring stiffness P l : Leak Pressure A v : Sool cross-sectional area ς v, ς : Daming coefficient (sool, swash late) ω nv, x ): Acceleration/Velocity/ dislacement of the sool (n th iston) ω, ω n t : Natural frequency (valve, swash late, and ressure ) Q : Pum volume flow rate A 1 : Control iston cross-sectional area J : Average Swash late inertia V : Volume of um at the high-ressure side β : Effective bulk modulus K : swash late equivalent stiffness Q l : Volumetric leak 0.1 kg 90 N.m/s 20 kn/m m 2 Rad/sec m 3 /sec m X10-3 N.m. sec 2 /rad m 3 1X10 9 Pa N/m m 3 /sec IJMER ISSN: Vol. 7 Iss. 8 August

14 c l : Leak coefficient P s, V : Volume of the um P & : suction ressure, instantaneous suction ressure s 4.3 X10-13 m 3 /Pa.sec Pa, Pa/s m 3 t Pum maximum dislacement 7.9 cm 3 /rad Pitch radius 5 cm Piton diameter 2.8 cm n: Pistons number 9 Maximum iston stroke 6 cm Maximum swash late angle 37 0 Arm length between the swash late ivoting oint and the actuator 5.6 cm Swash late actuator stroke 5 cm Orifice diameter at the BDC 7 mm Prime mover seed 260 rad/sec Hydraulic fluid tye Skydrol LD-4 Pum maximum ressure 260 bar Pum maximum volume flow rate 1.1 l/s Piston dead volume 1 cm 3 Leakage area 1X10-12 m 2 Pressure control unit iston area A/B 9/4.2 m 2 Orifice with variable area slot orifice width Flow discharge coefficient 0.7 Orifice with variable area slot orifice initial direction Critical Reynolds number 12 Orifice with variable area slot orifice leakage area 1X10-9 m 2 Table 2: Imortant Parameters References [1]. Tonglin Shang Imroving Performance of an Energy Efficient Hydraulic Circuit, Thesis, University of Saskatchewan, Aril [2]. Akers, A., & Lin, S. J. (1987, June). Control of an axial iston um using a single-stage electrohydraulic servo valve. In American Control Conference, 1987 ( ). IEEE. [3]. Kaliafetis, P., &Costooulos, T. (1995). Modeling and simulation of an axial iston variable dislacement um with ressure control. Mechanism and machine theory, 30(4), [4]. Johnson, R. E. (1996). Modeling and designing a variable-dislacement oen-loo um. Journal of dynamic systems, measurement, and control, 118, 267. [5]. Bahr, M. K., &Kassem, S. A. (2000, August). On the Dynamics of Swash Plate Axial Piston Pums with Conical Cylinder Blocks. In Proceeding of Flucome 2000 Conference, Sherbrooke University, Sherbrooke, Canada. [6]. Khalil, M. K. B., Yurkevich, V. D., Svoboda, J., & Bhat, R. B. (2002). Imlementation of single feedback control loo for constant ower regulated swash late axial iston ums. International Journal of fluid ower, 3(3), [7]. Khalil, M. (2003). Performance investigation of the swash late axial iston ums with conical cylinder blocks (Doctoral dissertation, Concordia University) [8]. Chikhalsouk, M. H. and Bhat, R. B. (2007). Reduction of Noise Levels in Hydraulic System Driven by Swash Plate Pums by Imroving Design of Port Plate, Proceedings of the Canadian Acoustics Week in Canada 2007, Vol. 35, No. 3, , Montreal, Canada. [9]. S. Hata, T. Muro, R. Fukagawa, Wear of um arts in slurry transortation system, Journal of Terramechanics, Volume 21, Issue 3, 1984, Page 306 [10]. Book, R., & Goering, C. E. (1997). Load sensing hydraulic system simulation. Alied Engineering in Agriculture, 13(1), [11]. I.R. Ehrlich, D. Sloss, B. Hanamoto, C.J. Nuttall, The wheel um roulsion system for floating vehicles, Journal of Terramechanics, Volume 8, Issue 4, 1972, Pages [12]. ShojiroHata, TatsuroMuro, Ryoichi Fukagawa, Wear of unshrouded centrifugal um due to slurry transortation in a shield tunnelling work, Journal of Terramechanics, Volume 24, Issue 1, 1987, Pages [13]. Lantto, B., Krus, P. and Palmberg, J.O The interaction between Loads in Load sensing Systems. Proceeding of the 2nd Tamere International Conference on Fluid Power. Linkoing, Sweden, 53. [14]. Bojinović, M., Mole, N., &Štok, B. (2015). A comuter simulation study of the effects of temerature change rate on austenite kinetics in laser hardening. Surface and Coatings Technology, 273, [15]. Yokoyama, M. (1985). Automated comuter simulation of two dimensional elastostatic roblems by the finite element method. International journal for numerical methods in engineering, 21(12), [16]. He, B., Han, L., Wang, Y., Huang, S., & Liu, L. (2014). Kinematics analysis and numerical simulation of a maniulator based on virtual rototying. The International Journal of Advanced Manufacturing Technology, 71(5-8), IJMER ISSN: Vol. 7 Iss. 8 August

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