MATHEMATICAL MODELING AND SIMULATION OF AN EXCAVATOR LOADER A Research Thesis written at KETTERING UNIVERSITY and submitted to KETTERING UNIVERSITY in partial fulfillment of the requirements for the degree of BACHELOR OF SCIENCE IN MECHANICAL ENGINEERING written by JOEL D. LABER 2014 Student Faculty Thesis Advisor Committee Member DISCLAIMER This thesis is submitted as partial and final fulfillment of the cooperative work experience requirements of Kettering University needed to obtain a Bachelor of Science in Mechanical Engineering Degree. The conclusions and opinions expressed in this thesis are those of the writer and do not necessarily represent the position of Kettering University, or any of its directors, officers, agents, or employees with respect to the matters discussed. 2 PREFACE This thesis represents the capstone of my five years combined academic work at Kettering University and job experience. Academic experiences in Mathematical Modeling, Dynamic Systems, and Controls proved to be valuable assets while I developed this thesis and addressed the problem it concerns. Although this thesis represents the compilation of my own efforts, I would like to acknowledge and extend my sincere gratitude to the following persons for their valuable time and assistance, without whom the completion of this thesis would not have been possible: 1. Dr. Ram S. Chandran, Professor of Mechanical Engineering and Faculty Thesis Advisor, Kettering University 2. LMS Corporation 3 TABLE OF CONTENTS DISCLAIMER ........................................................................................................................2 PREFACE ...............................................................................................................................3 LIST OF ILLUSTRATIONS ..................................................................................................5 I. INTRODUCTION ......................................................................................................7 Problem Topic ...............................................................................................7 Background .....................................................................................................7 Criteria and Parameter Restrictions ................................................................9 Methodology ...................................................................................................9 Primary Purpose ...........................................................................................10 Overview ......................................................................................................10 II. EXCAVATOR LOADER SCHEMATIC ..................................................................11 III. VALVE CONTROL HYDRAULIC CIRCUIT .........................................................13 IV. PUMP CONTROL HYDRAULIC CIRCUIT............................................................15 V. BOND GRAPH MODEL OF VALVE CONTROL...................................................17 VI. BOND GRAPH MODEL OF PUMP CONTROL .....................................................24 VII. VALVE CONTROL SIMULATION.........................................................................34 VIII. PUMP CONTROL SIMULATION............................................................................48 IX. CONCLUSIONS AND RECOMMENDATIONS.....................................................56 REFERENCES .......................................................................................................................58 GLOSSARY .........................................................................................................................59 APPENDIX: ABET PROGRAM OUTCOMES ..................................................................61 4 LIST OF ILLUSTRATIONS Figures Page 1. Excavator boom..................................................................................................................11 2. Simplified excavator boom.................................................................................................12 3. Valve control hydraulic circuit ...........................................................................................14 4. Pump control hydraulic circuit ...........................................................................................15 5. Valve control bond graph ...................................................................................................18 6. Pump control bond graph ...................................................................................................25 7. Hydraulic cylinder ..............................................................................................................35 8. Valve control AMESIM model ..........................................................................................38 9. Valve control signal generator settings ..............................................................................39 10. Valve control gain settings ...............................................................................................40 11. Valve control pressure source settings .............................................................................40 12. Valve control reservoir settings ........................................................................................41 13. Valve control fluid settings...............................................................................................41 14. Control valve settings .......................................................................................................42 15. Valve control cylinder settings .........................................................................................43 16. Valve control Mass Settings .............................................................................................43 17. Control valve spool displacement.....................................................................................44 18. Control valve port A flow Rate ........................................................................................45 19. Control valve port A pressure...........................................................................................45 20. Valve control cylinder displacement ................................................................................46 5 21. Valve control cylinder velocity ........................................................................................46 22. Pump control AMESIM model.........................................................................................49 23. Pump control prime mover settings..................................................................................50 24. Pump settings....................................................................................................................50 25. Pump controller gain settings ...........................................................................................51 26. Pump swashplate displacement ........................................................................................52 27. Pump flow rate..................................................................................................................52 28. Pump pressure...................................................................................................................53 29. Pump control cylinder displacement ................................................................................53 30. Pump control cylinder velocity.........................................................................................54 6 I. INTRODUCTION The objective of this thesis is to present a comparative analysis of position control performance of a valve controlled and pump controlled hydraulic system, used in an excavator loader. Problem Topic Currently, the demand for construction and agricultural equipment are growing at a faster pace, and there is a need to understand their performance in real systems. The specific portion discussed in this thesis deals with modeling and simulation of hydraulic systems used in these equipments. Background Modern excavators trace their roots back to the invention of the steam shovel in 1839 by William Otis Smith, which was controlled by pulleys (Parker). Today, these equipments are controlled by hydraulic circuits powered by diesel engines. They are capable of lifting far more than the original steam shovel. Excavators are used around the world primarily for construction, demolition, mining, recycling, and logging. One of the most notable manufacturers of excavators, Caterpillar Inc, produces excavators that have a lifting capacity varying from 1 to 90 metric tons. These units are fitted with engines producing over 500 horsepower and weigh over 190,000 lbs. Caterpillars' largest unit, the 390D L, has a hydraulic operating pressure of over 5000 psi and a flow rate of over 250 GPM. The boom is driven by two cylinders with a bore over 8 inches and a stroke of 75 inches. (Caterpillar, 2014). 7 Hydraulic actuators can be controlled two ways; they include valve control and pump control systems. In valve control systems, a pump, a pressure relief valve, and an accumulator maintain a constant pressure to a proportional valve or servo valve. The control valves provide throttling and directional control. The operator controls the valve, which in turn controls the boom position, velocity, and direction of travel of the actuator. Valve control circuits provide a fast response time, but they are limited by a operating efficiency of ≈67%. Despite this characteristic, valve control circuits are very widely implemented due to their fast response time. In a pump control circuit, a variable delivery pump is used to provide flow control and directional control; this mimics the operation of a control valve. Typically, these variable delivery pumps will be of over-the-center, axial-piston geometry, that uses a swash plate to vary the stroke of the pump. Pump control circuits are capable of extremely high power outputs and have a theoretical efficiency of 100%, but they have rather slow response times. This is primarily due to the rotating inertias within the pump itself. Large equipment does not necessarily have to move fast; therefore pump control circuits may be preferred. In many circumstances and applications, valve control circuits and pump control circuits may also cost about the same. In valve control, the major costs lie in the servo valve and heat exchangers. Whereas in pump control circuits, the costs are in the charging circuit, the control circuit that strokes the variable delivery pump, and the variable delivery pump. In this thesis, two mathematical models were developed using classical bond graph approach developed by Henry M. Paynter from MIT. These models show power 8 flow through the components of the circuit(s), and are extremely useful. One can generate the governing equations from them. They give a better understanding of what is happening in the circuit at the component level. Simulations were run that showed the performance curves. One may ask, "Why are simulations run to predict the performance of hydraulics?” and "Why are simulations important?” In modern engineering, with advances in computer programming, simulations have gotten so powerful, that before one can build a physical model, it is possible to tell exactly how that specific system will perform. In other words, we no longer have extensive trial times and costly initial prototype builds. Instead, we can identify a problem, design a circuit, simulate the system using a program such as AMESIM, and see the effects immediately for variables such as: working pressure, working flow rate, and actuator displacement. In the world of hydraulic simulation, the output will also tell you exactly how the circuit will behave dynamically, which has been mostly marginalized, as the emphasis has typically been on the steady state condition, and not the transient response and/or whether or not the system will be stable. Criteria and Parameter Restrictions The bond graph models are presented, and simulations were run. They depict the main lift cylinder, as this provides the macro position control of the excavator loader body. All other cylinders were held fixed. Methodology In this thesis, hydraulic circuits used in valve control and pump control for this specific application are presented. Bond graph models were developed for a valve control 9 circuit and a pump control circuit. Simulations were performed for these hydraulic circuits to understand their performance and operating characteristics. Primary Purpose The objective of this thesis is to show the fundamental differences between two primary hydraulic control methodologies: valve control and pump control. Overview For the content of this thesis, Chapter 2 focuses on physical schematics of the excavator itself. Chapters 3 and 4 discuss the operation and development of the two hydraulic circuits created for this application. Chapters 5 and 6 focus on the development of the Bond Graph models for the two cases and the equations derived from them. Chapters 7 and 8 present results of the simulations for the two control cases. And finally, Chapter 9 discusses the results and presents the conclusions. 10 II. EXCAVATOR LOADER SCHEMATIC Figure 1 depicts the excavator loader geometry that was analyzed. The loader contains four cylinders, two cross members, a central carriage, and a bucket. Cylinder A Figure 1. Excavator boom. Note (Alaydi, 2008). The comparative study presented in this thesis focuses on Cylinder A marked in Figure 1. The other three cylinders are assumed to be fixed, just as if the operator wished to operate one cylinder to adjust the main position of the bucket. The actuator that 11 connects point Os1 to Os2, cylinder A, is the focus of this thesis. A detailed schematic of this setup is shown in Figure 2. Cylinder A Figure 2. Simplified excavator boom. Note (Alaydi, 2008). A close up view of the arrangement under study is shown in Figure 2. The area of focus is the cylinder connected between the points A and B, cylinder A. This cylinder provides the position control of the boom assembly. 12 III. VALVE CONTROL HYDRAULIC CIRCUIT A valve controlled hydraulic circuit that is commonly used in an excavator boom control application is depicted in Figure 3. The circuit shown in Figure 3 includes a fixed displacement pump combined with a relief valve and an accumulator. This arrangement maintains a constant pressure to the control valve. The control valve could be a proportional or a servo valve. This valve regulates the speed and direction of motion of the actuator. The actuator is the position control cylinder that is located between points A and B, as shown in Figure 2. A counterbalance valve is also used in the circuit. It is located on the rod side of the actuator, between the actuator and the control valve. In the neutral position, the control valve's load ports are blocked, but they still may leak. This leads to cylinder creep and prevents the cylinder from holding its position. The counterbalance valve locks the cylinder by forcing the hydraulic fluid to flow through a pressure relief valve and check valve combination. This action holds the cylinder rod side pressure just above the cracking pressure of the relief valve. 13 Figure 3. Valve control hydraulic circuit 14 IV. PUMP CONTROL HYDRAULIC CIRCUIT A pump controlled hydraulic circuit considered for the application, excavator boom position control, is shown in Figure 4. Figure 4. Pump control hydraulic circuit As depicted in Figure 4, the variable delivery pump controls the velocity and displacement of the cylinder. The cylinder is connected between points A and B as shown in Figure 2. What is unique with this circuit however is that it is a closed loop, where as the valve control system is an open loop circuit. In an open loop circuit, load pressure is sent directly to tank immediately after its energy has been consumed in the actuators. In a closed loop circuit, the circuit is continuous, and does not return to tank. Due to this 15 nature of the pump control circuit, an additional circuit is required to supplement or make up for any lost fluid. This is known as the charging circuit, and it brings in fluid directly from a reservoir into the main circuit, and allows the main circuit to replenish itself as need be using an array of check valves, pressure relief valves, and a charge pump. Another important feature of this circuit that is unique, are the twin pressure relief valves. These valves are set up so that as the two lines to the cylinder switch back and forth between load pressure and return pressure, the system will always release the higherpressure side to the lower pressure side. This is special to closed loop circuits due to the reversibility of the main pump. 16 V. BOND GRAPH MODEL OF VALVE CONTROL Bond graphs provide a means to model multidiscipline, dynamic systems. They express the power flow through a system, and provide means to develop governing equations that model a system under study. A Bond Graph of the valve control system, developed for this study, is in Figure 5. This bond graph includes a simple spool valve model connected to a cylinder model, and a load model. 17 18 The pump, relief valve, and accumulator combination is modeled as a source of pressure; this is indicated in the Bond Graph in Figure 5. When basic bond graph algebra is applied to the whole Bond Graph model, the relationships below are developed: (1) QP = QA + QB (2) PP − PA RA (3) QA = RA = QAT = RAT = ρ Pp − PA 2 1 Cd ωx v PA − PT RAT (5) ρ P − PT 2 A 1 Cd ωx v (4) PA = ( β V ) ∫ ΔQC dt + PA (0) (6) (7) TP VTP = AP X 0 + AP ∫v Mp dt (8) ΔQC = Qe + Ql − QRp − Q1 (9) Qe = QA + QAT (10) Ql = PA − PB Rl (11) PA Rp (12) QRp = Q1 = 19 v Mp Ap (13) v Mp = ( 1 M ) ∫ ΔFMp dt + v Mp (0) p (14) ΔFMp = F1 − F2 − FS (15) F1 = PA A p (16) F2 = PB AR (17) FS = K[ ∫ ΔvC dt + xC (0)] ΔvC = v Mp − v Mld (18) (19) v Mld = ( 1 M ) ∫ ΔFMld dt + v Mld (0) (20) ld ΔFMld = FS − v Mld RB PB = ( β V ) ∫ ΔQCr dt + PB (0) (21) (22) TR VTR = AR X 0 + AR ∫v dt (23) ΔQCr = Q2 + Ql − QRr − Qex (24) Mp Q2 = v Mp AR QRr = PB Rr Qex = QB − QRbT PB − PT RbT QRbT = RbT = 1 Cd ωx v QB = Rb = ρ P − PT 2 B Pp − PB 1 Cd ωx v 20 Rb ρ Pp − PB 2 (25) (26) (27) (28) (29) (30) (31) And the variable definitions are: PP = System pressure from pump, pressure relief valve, and accumulator QP = Pump flow QA = Flow at the "A" port in the control valve QB = Flow at the "B" port in the control valve PA = Pressure at control valve port "A" RA = Valve pressure-flow gain for port "A" Cd = Orifice discharge coefficient ω = Width of valve port xν = Control valve spool travel ρ = Mass density of hydraulic oil QAT = Flow at control valve port "AT" PT = Hydraulic oil pressure in system reservoir RAT = Pressure-flow gain for control valve port "AT" β = Hydraulic oil bulk modulus VTP = Total Hydraulic oil volume on piston side of actuator VTR = Total Hydraulic oil volume on rod side of actuator QC = Flow in piston side compliance element AP = Area of piston in actuator X0 = Initial displacement of actuator νMp = Velocity of actuator piston-rod assembly Qe = Flow entering piston side of actuator Ql = Leakage flow in actuator across piston 21 QRp = Flow in piston side resistance element Q1 = Flow acting against piston in actuator PB = Pressure at "B" port in control valve Rl = Leakage coefficient for piston in actuator RP = Pressure resistance at piston side port in actuator MP = Mass of piston-rod assembly in actuator FMp = Force in IMp element F1 = Force on piston side of actuator F2 = Force on rod side of actuator FS = Force transmitted to shaft of piston-rod assembly AR = Area of the rod side of the piston K = Stiffness of shaft in piston-rod assembly νC = Velocity in shaft compliance element νMld = Velocity of the load against the actuator Mld = Mass of the load against the actuator FMld = Force in IMld element RB = Damping resistance in pin joints in mechanical linkage attached to actuator QCR = Flow in rod side compliance element Q2 = Flow on rod side of actuator QRr = Flow in rod side resistance element Qex = Flow leaving rod side of actuator to valve Rr = Pressure resistance at rod side in actuator QRbT = Flow in RbT element 22 RbT = Pressure-flow gain at control valve port "BT" Rb = Pressure-flow gain at control valve port "B" The segment of the Bond Graph containing Junctions 1 through 5 illustrate the control valve. This sub model contains four resistance elements that represent the four orifices in the control valve. The equations that are associated with this portion of the Bond Graph are (1) through (6), and (28) through (31). Other parts of the Bond Graph containing Junctions 6 through Junction 11 depict the hydraulic actuator and associated elements. This sub model contains the following: compliance elements to depict the volume of fluid on both sides of the actuator, resistance elements to illustrate pressure drop due to piping geometry and a pin joint that would be connected to the actuator, inertance elements representing the mass of the cylinder rod and the applied load to the cylinder, and transformer elements illustrating the physical action of converting hydraulic pressure and flow into mechanical force and speed. Equations that are associated with this sub model are (7) through (27). 23 VI. BOND GRAPH MODEL OF PUMP CONTROL The bond graph model of a pump controlled hydraulic system is given in Figure 6. This model was developed based on the work reported by Dransfield (1981). This model has about the same level of abstraction as that of the valve control system discussed in the earlier chapter. The actuator model used is the same developed for the valve controlled system. A variable delivery, axial piston pump is employed in the circuit. Pump stroke is controlled via an auxiliary hydraulic circuit. The model represents the electric motor/prime mover as a source of flow, also included are models for piping, inertia of the pump, and internal leakage of the pump. 24 25 The governing equations representing the pump-controlled system were developed by applying rules of equation development as applied to Bond Graphs. The Bond Graph model given in Figure 6 is used. S f (t) = Sω (t) (32) τ o = ( 1 C ) ∫ Δω C sp dt + τ o (0) sp (33) Δω C sp = Sω − ω p (34) ω p = ( 1 I ) ∫ Δτ I p dt + ω p (0) p (35) τI p = τo − τ fp − τ p (36) τ fp = R fpω p (37) τ p = PpVD (38) VD = (πrp Br tan θ )N p (39) Pp = Pc − Pre −enter (40) Pc = ( β V ) ∫ ΔQC cp dt + Pc (0) (41) ΔQC cp = Qp − QR lp − QR v − Qout (42) c QR lp = QR v = Pc Pc Rlp Rv Qp = ω pVD 26 (43) (44) (45) Qout = PR L 1 RL1 (46) 128 µL1 πd 4 (47) PR L 1 = Pc − PL1 (48) PL1 = ( β V ) ∫ ΔQC L 1 dt + PL1 (0) (49) RL1 = L1 VL1 = π ( d 2 ) 2 LL1 (50) ΔQC L 1 = Qout − QL1 (51) PR L 2 (52) QL1 = RL 2 128 µL2 πd 4 (53) PR L 2 = PL1 − Ps (54) RL 2 = Ps = ( β V ) ∫ ΔQC p dt + Ps (0) (55) TP VTP = AP X 0 + AP ∫v Mp dt ΔQC p = QL1 − QR p − Ql − Q1 QR p = Ql = Ps Pl Rp Rl (56) (57) (58) (59) Pl = −Ps − Preturn (60) Q1 = υ M p A p (61) υ M p = ( 1 M ) ∫ ΔFM p dt + υ M p (0) p (62) ΔFM p = F1 − F2 − Fs (63) 27 F1 = Ps A p (64) F2 = Preturn Ar (65) Fs = ( 1 C ) ∫ ΔυC s dt + Fs (0) (66) ΔυC s = υ M p − υ M ld (67) s υ M ld = ( 1 M ) ∫ ΔFM ld dt + υ M ld (0) (68) ld ΔFM ld = Fs − FR B (69) FR B = RBυ M ld (70) Preturn = ( β V ) ∫ ΔQC r dt + Preturn (0) (71) VTr = Ar X 0 + Ar ∫ v Mp dt (72) Tr ΔQC r = Q2 − Ql − QR r − Qreturn (73) Q2 = υ M p Ar (74) QR r = Preturn Qreturn = RL 3 = Rr PR L 3 RL 3 128 µL3 πd 4 (75) (76) (77) PR L 3 = Preturn − PL 3 (78) PL 3 = ( β V ) ∫ ΔQC L 2 dt + PL 3 (0) (79) VL 2 = π ( d 2 ) 2 LL 2 (80) ΔQC L 2 = Qreturn − QL 2 (81) L2 28 QL 2 = PR L 4 RL 4 = RL 4 128 µL4 πd 4 Pre −enter = PL 3 − PR l 4 And the variable definitions are: Sω (t) = Flow supply from diesel engine τ o = Torque from diesel engine entering pump Csp = Compliance of pump input shaft ω C sp = Flow in Csp element ω p = Flow of the pump's rotating assembly I p = Inertia of the pump's rotating assembly τ I p = Torque in I p element τ f p = Torque in R f p element τ p = Torque applied to pump's piston array to develop outbound pressure R f p = Resistance due to friction acting on the pump's rotating assembly Pp = Pressure developed by the pump VD = Volumetric displacement of the pump rp = Radius of a piston in the pump's piston array Br = Radius of the pump's barrel θ = Angular displacement of the pump's swashplate 29 (82) (83) (84) N p = Number of pistons in the pump Pc = Pressure in the pump's compression chamber Pre −enter = Pressure returning into the pump from the system β = Bulk modulus of the hydraulic fluid Vc = Volume of the pump's compression chamber QC cp = Flow in the Ccp element Qp = Flow developed by the pump QR lp = Flow in the Rlp element QR v = Flow in the Rv element Qout = Flow leaving the pump's compression chamber Rlp = Resistance due to the pump's leakage Rv = Resistance due to the pump's internal relief valve PR L 1 = Pressure in the RL1 element RL1 = Resistance due to the pressure drop in the first segment of the supply line to the system L1 = Length of the first segment of the supply line to the system µ = Viscosity of the hydraulic fluid LL1 = Length of the supply line to the system d = Diameter of the pressure line to the system PL1 = Outbound pressure of the first pressure drop in the supply line to the system VL1 = Volume of the supply line to the system QC L 1 = Flow in CL1 element 30 QL1 = Flow into second pressure drop in the supply line to the system PR L 2 = Pressure in the RL 2 element RL 2 = Resistance due to the second pressure drop in the supply line to the system L2 = Length of the second segment of the supply line to the system Ps = Supply pressure entering the actuator VTP = Total hydraulic oil volume on piston side of actuator QCp = Flow in piston side compliance element A p = Area of piston in actuator X o = Initial displacement of actuator υ Mp = Velocity of actuator piston-rod assembly QR p = Flow in piston side resistance in actuator Ql = Leakage flow in actuator across piston Q1 = Flow acting against piston in actuator R p = Pressure resistance at piston side port in actuator Rl = Leakage coefficient for piston in actuator Pl = Pressure difference between supply pressure and return pressure in actuator Preturn = Pressure leaving actuator M p = Mass of piston-rod assembly in actuator FM p = Force in IM p element F1 = Force on piston side of actuator F2 = Force on rod side of actuator Fs = Force transmitted to shaft of piston rod assembly 31 Ar = Area of the rod side of the piston Cs = Compliance of shaft in piston-rod assembly υC s = Velocity in shaft compliance element υ M ld = Velocity of the load against the actuator M ld = Mass of the load against the actuator FM ld = Force in IM ld element RB = Damping resistance in pin joints in mechanical linkage attached to actuator VTR = Total volume on rod side of actuator QC r = Flow in rod side compliance element Q2 = Flow on rod side of actuator QR r = Flow in rod side resistance element Qreturn = Flow leaving rod side of actuator Rr = Pressure resistance at rod side in actuator PR L 3 = Pressure in RL 3 element RL 3 = Resistance due to the first pressure drop in the return line from the system L3 = Length of the first segment of the return line from the system QC L 2 = Flow in the CL 2 element VL 2 = Volume of the return line from the system LL 2 = Length of the return line from the system QL 2 = Flow into second pressure drop in the return line from the system PR L 4 = Pressure in RL 4 element RL 4 = Resistance due to the second pressure drop in the return line from the system 32 L4 = Length of the second segment of the return line from the system The segment of the Bond graph containing Junctions 1 through 4 illustrate the variable delivery, axial piston pump. This sub model contains the source of flow from the diesel engine, compliance of the pump's input shaft and compression chamber, inertance of the pump's rotating assembly, resistances due to the pump's friction and leakage, and a transformer due to the pump's ability to translate torque and rotational velocity into pressure and a flow rate. The equations that correspond to this sub model are (32) though (42). The next segments of the bond graph are the supply line and return line that connect the system. Each sub model contains two resistances, that together, show pressure drop across each line. Also, each sub model contains a compliance to represent the volume of each line. The equations that are associated with these sub models are (43) through (50), and (72) through (80). The segment of the bond graph which illustrates the actuator is the same that was used in the valve control Bond Graph shown in Figure 5. The equations that are associated with this sub model are (51) through (74). 33 VII. VALVE CONTROL SIMULATION In preparation for simulating the valve control circuit, certain system parameters need to be defined beforehand. First, for the excavator mechanism shown in Figure 3, the boom lift cylinder stroke had to be determined. The cylinder stroke "s" is the third side of a triangle with the other sides being lengths "d" and "a". With sides "d" and "a" defined, d = 5.5 m and a = 3.0 m respectively (Alaydi, 2008), maximum stroke of the boom could be determined. Using simple trigonometry, the minimum and maximum value for φ, the angle between sides "d" and "a", was determined to be 60° and 88°. For these two values, the minimum and maximum cylinder lengths were found to be 4.81 m and 6.21 m, respectively. The appropriate cylinder stroke can be found using the formula: s = H Max − H Min (85) and the stroke was found to be 1.4 m. The next step was to determine the maximum load encountered by the cylinder. To find this value, a free body diagram was constructed, with the cylinder direction being along the y-axis. With the cylinder in this position, maximum load on the cylinder can be determined. In this setting, the full force of the weight will be acting in this direction, as shown by the free body diagram Figure 7. 34 Figure 7. Hydraulic cylinder Following values are assumed: AP = 0.125m 2 AR = 0.06m 2 P1 = 207 Bar 35 Applying elementary statics to the free body diagram along the y-axis, the following expression was derived: ∑F Y = P1 AP − P2 AR − Mg = 0 (86) Neglecting the rod side pressure and the resulting force, (7-2) can be simplified, leading to: P1 AP = M = M critical g (87) Where M critical is the specific load that will put the cylinder into static equilibrium, at a selected pressure, where no motion will occur. For this application in this thesis, M critical = 26,376.15 kg. The next step is to find the load pressure, PL , which is the pressure exerted by the load in the piston-side chamber of the cylinder. This is found using the following equation: 36 PL = Mg AP (88) Assuming a mass of 25,000 kg acting on the cylinder, the load pressure is equal to 196 Bar. This means that there is a differential pressure across the control valve. The following equation is used to find this: PDiff = PS − PL (89) For this model, the differential pressure is 11 Bar, when the supply pressure is 207 Bar. Using all this information, the control valve can be sized utilizing the valve's linearized pressure-flow gain. This flow is related to the load flow going into the cylinder. This yields the following relationship: KC PDiff = QL = νAP (90) With the cylinder assumed to extend at a steady velocity of 0.1 m/s and further algebraic manipulation, KC is found to be 68.18 L/min/Bar. 37 The next step is to develop the model for simulation. Using this model, one can simulate both the transient and steady state response of the system. To facilitate simulation of the system described earlier in Chapter 5, simulation software AMESIM is used in this thesis. In AMESIM, a model of a multi-domain dynamic system can be written using macro or micro components. Another software, MATLAB/SIMULINK can also be used; in this method the equations are typed or GUI can be developed and a computer code is used to solve them. Also, AMESIM software is based on the Bond Graph technique; so the equations shown in chapter 5, are embedded in the sub-models shown in the user's interface. In both Figure 3 and Figure 5, there is a source of pressure connected to the control valve, which in turn in connected to a hydraulic cylinder. The same arrangement is used in AMESIM, as shown in Figure 8. Figure 8. Valve control AMESIM model 38 Figure 8 also calls out the specific types of components that were used. The only detail that may not be obvious is choice of the mass element sub-model shown in Figure 8. A sub-model that included coulomb friction was used, as this would best illustrate the effects of the pin joints that sustain and join the excavator boom to the actuator. The next set of figures portray the settings of the simulation model. The signal generator is shown in Figure 9, the gain multiplier in Figure 10, the pressure source in Figure 11, the reservoir in Figure 12, the fluid properties in Figure 13, the control valve settings in Figure 14, the cylinder in Figure 15, and then the load in Figure 16. Figure 9. Valve control signal generator settings 39 Figure 10. Valve control gain settings Figure 11. Valve control pressure source settings 40 Figure 12. Valve control reservoir settings Figure 13. Valve control fluid settings 41 Figure 14. Control valve settings 42 Figure 15. Valve control cylinder settings Figure 16. Valve control mass settings 43 The schematic of the model written in AMESIM reflects the valve control system bond graph model; specific sub-models are defined as shown in Figure 8. Figures 9 through Figure 14 depict the settings of all of the components. The simulation was ran to show the actuator perform a full extend and retract cycle. The next series of figures depict the results of the simulation. First is the spool position in the control valve in Figure 17, the flow rate from Port A on the control valve in Figure 18, the pressure at Port A at the control valve in Figure 19, the actuator rod displacement in Figure 20, and then the actuator rod velocity in Figure 21. Figure 17. Control valve spool displacement 44 Figure 18. Control valve port A flow rate Figure 19. Control valve port A pressure 45 Figure 20. Valve control cylinder displacement Figure 21. Valve control cylinder velocity 46 As shown, there is a fairly close correlation between the preliminary hand calculations and what the computer model shows. The extension velocity and flow into the piston side of the cylinder are close to what was originally predicted, given the volumes. One of the important parameters that is very revealing about the stability of this system is the pressure plot. Since the pressure shown in Figure 19 is very clean, that means that there are no pressure spikes present in the system. Meaning that when the valve spool is shifted quickly, as illustrated in Figure 17, the system responds in a nicely damped manner with no oscillations, and also exhibiting a short response time. Meaning that, when the system receives a sudden input, the system does not violently respond, but reacts instantly and naturally. 47 VIII. PUMP CONTROL SIMULATION As in the case of the valve control scenario, certain system parameters must be evaluated prior to simulating the pump-controlled system. A number of subsystems used in this case are the same used in the previous case, leading to the use of the same parameter values. Parameter values that are required to be evaluated for the pump control circuit are rotational speed of the pump and the volumetric displacement of the pump. Using the same cylinder piston area of 0.125 m2, and extension velocity of 0.1 m/s, and assuming a pump speed of 1500 rpm, the volumetric displacement of the pump can be found using equation (91). APυ = VD N (91) Volumetric displacement needed was found to be 500 cc/rev. The bond graph model depicted in Chapter 6, Figure 6, shows an over-the-center, variable displacement, axial piston pump directly connected to a double acting cylinder. The AMESIM model developed to simulate this situation is shown in Figure 22. 48 Figure 22. Pump control AMESIM model A diesel engine, illustrated as a thermal engine, can provide a constant speed to the pump. This setup models the pump as a source of flow. The parameter values of, signal generator, double acting cylinder, the load mass and coulomb friction, are the same in AMESIM as in the earlier case. One of the distinct differences between valve control and pump control systems is, the valve control system had a constant supply pressure, and the pump control system is flow controlled. The majority of the subsystem models are the same for both cases. The settings used specifically for the pump control simulation are shown in following figures, with the thermal engine model in Figure 23, the variable delivery pump in Figure 24 and the pump controller gain in Figure 25. 49 Figure 23. Pump control prime mover settings Figure 24. Pump settings 50 Figure 25. Pump controller gain settings Simulation plots of the pump controlled system obtained using AMESIM are given below in Figures 26 through 30. With he pump displacement in Figure 26, pump flow rate in Figure 27, pump pressure shown in Figure 28, actuator displacement in Figure 29, and actuator velocity in Figure 30. 51 Figure 26. Pump swashplate displacement Figure 27. Pump flow rate 52 Figure 28. Pump pressure Figure 29. Pump control cylinder displacment 53 Figure 30. Pump control cylinder velocity Observations of the simulation results and plots are as follows. The results are different compared to the valve control simulation results. Pump displacment plot shown in Figure 26, is similar to that of the valve control spool position plot shown in Figure 18. The pump flow rate is shown in Figure 27, is different from the flow rate of the control valve in the earlier case; the flow immediately spikes to the peak flow, then begins to drop as pressure builds to move the piston. On the segment which depicts the return stroke, it is relatively constant, but has some ripples. The pressure plot shown in Figure 28 is very different. It is primarily constant and flat; around 0 Bar. The displacement graph shown in Figure 29, has a similar displacement profile of the valve control simulation depicted in Figure 20. However, when the actuator is pump controlled, the cylinder never reaches the full stroke, it goes to 0.7m; in the valve controled case it goes to 1.4m. Also, the displacement profile has fluctuations and ripples. 54 In the valve control setup, the actuator displacement is extremely constant and predictable. And finally, the actuator velocity plot is shown in Figure 30. This graph shows large pulsations. 55 IX. CONCLUSIONS AND RECOMMENDATIONS Based on observations and discussion of simulation results, the following conclusions are reached, they include: first, compared to a pump controlled hydraulic system, as seen in the performance curves, Figures 26-30, a valve controlled system shown in Figures 17-21, exhibits consistent and clean behavior. The flow rate curve correlates directly with the control valve spool position curve. The pressure at port A transitions instantaneously with very little oscillations or spikes, as seen in Figure 19. The displacement of the hydraulic cylinder exhibits a linear response with very little oscillations or pulsations. The second conclusion that can be made from these observations is, valve controlled hydraulic systems are more likely to produce a smooth operating cycle for the excavator machine. This is due to their dynamic behavior observed in Figures 17 through 21. When a major component, such as an excavator boom, has a clean operation cycle, there is less fatigue on the machine. This is likely to improve the life of the machine. And lastly, if a pump controlled hydraulic system is to be used for an application like that of an excavator boom lift, then an effective controller must be developed. This controller must be able to account for the error in the system, and should include a feedback signal to correct for cylinder position error, to properly stroke the pump accounting for load effects. This thesis offers a detailed study comparing two hydraulic control methods, recommendations are also made to improve the study. First, a separate, detailed AMESIM model should be developed for an over-the-center variable displacement axial 56 piston pump to accurately describe its dynamic characteristics. The bond graph shown in Chapter 6 that illustrates such a pump, contains three state variables in the pump segment of the model. The AMESIM model shown in Figure 22 contains an advanced, catalog hydraulic pump sub model, without temperature affects, that AMESIM offers; and the entire model has four state variables. For comparison, the valve control AMESIM model shown in Figure 8, contains six state variables, and the valve control bond graph model shown in Figure 5 contains five state variables. Another recommendation that can be made, is that it would be worthwhile to use a software tool such as MATLAB or MAPLE to simulate the two systems and compare the results against the AMESIM results. This could be used as a measure to further determine the accuracy of the AMESIM solutions, and this could be also used to provide a baseline or datum for any future simulations. And finally, another recommendation that can be made from this study is to develop an appropriate Bode Plot and Root Locus Plot of the system. These two plots hold a lot of clues about how a system performs. These plots are likely to provide a big picture and to help understand as to why these systems respond the way they do. 57 REFERENCES Alaydi, J. (2008). Mathematical modeling for pump controlled system of hydraulic drive unit of single bucket excavator digging mechanism. Jordan Journal of Mechanical and Industrial Engineering, 2(2), 157-162. Retrieved from http://jjmie.hu.edu.jo/files/JJMIE- V2-N3-press/6(42-47).pdf Caterpillar. (2014). 390d l. Retrieved from http://www.cat.com/en_US/products/ne w/equipment/excavators/large-excavators/17844667.html Dransfield, P. (1981). Hydraulic control systems - design and analysis of their dynamics. Berlin: Springer-Verlag. Parker, A. (n.d.). How steam shovels work. Retrieved from http://science.howstuffworks.com/transport/engines-equipment/steamshovel1.htm 58 GLOSSARY Accumulator: Hydraulic component that is used to store energy. This component is the hydraulic equivalent of an electrical capacitor or a mechanical spring. Actuator: Hydraulic component that performs work. Can be linear or rotary. Bond Graph: Mathematical modeling tool for dynamic systems that are used to procure equations of motion for a system by depicting the power flow through a system. Bulk Modulus: The relative stiffness of a specific hydraulic fluid. Compliance: A physical entity that possesses the characteristics of energy storage. In hydraulic systems, a chamber of fluid is compliance. In mechanical systems, a spring is a compliance. Counterbalance: A hydraulic valve specifically used for the application of vertical Valve cylinder position control. Element: Any element in bond graph modeling that carries power. Can be a resistance, inertance, compliance, transformer, or a gyrator. Governing: Equations An equation in dynamic systems that graphically shows how a segment of the system will respond. May also be referred to as an equation of motion. Inertia: Any quantity in a dynamic system that will resist a change in motion by relating a specific momentum with a specific flow. Examples of inertia consist of a mass, an inductor, and a pipe, for mechanical, electrical, and hydraulic systems. Junction: An entity in bond graph modeling that acts as a summation point for connecting eleme Pressure Relief: Valve A valve that is designed to limit the pressure in a segment of a hydraulic system by deferring excess pressure to a point of lower pressure; often the system reservoir. Pump: A pump is the prime mover in a hydraulic system and is a source of flow. Can be of varying types, usually they are external gear or axial piston. Proportional: Valve A directional control valve that possesses throttling capabilities due to the proportional solenoid that drives the spool laterally in the valve body. 59 Servo Valve: A valve that is similar in purpose and function to a proportional valve. However the drive unit in a servo valve is a servo torque motor. Transformer: An entity in bond graph modeling that directly relates the input effort to the output effort, and the input flow to the output flow, via a linear factor known as a modulus. 60 APPENDIX A ABET PROGRAM OUTCOMES 61 PROGRAM OUTCOMES MECHANICAL ENGINEERING (Updated for 2008/09 Academic Year) Upon graduation, students receiving the Bachelor of Science in Mechanical Engineering Degree from Kettering University will have the following knowledge, skills, and abilities: A. An ability to apply knowledge of mathematics, science and engineering. Engineering concepts and principles were exclusively used to correlate between variables and factors B. An ability to design and conduct experiments, as well as to analyze and interpret data. The ability to conduct experiments and interpret data was absolutely crucial to this project. C. An ability to design a system, component, or process to meet desired needs within realistic constraints such as economic, environmental, social, political, ethical, health and safety, manufacturability, and sustainability. The conclusions from the previous simulations were used to conduct an in depth comparison between valve controlled hydraulic systems and pump controlled hydraulic system. D. An ability to function on multi-disciplinary teams. The ability to work on a multi-disciplinary team was vital to this project. There was collaboration between dynamic systems, controls, and fluid power engineering to work together. E. An ability to identify, formulate, and solve engineering problems. As engineering problems and difficulties arose, such as diagnosing simulation results, were dealt with a logical and thought out manner. F. An understanding of professional and ethical responsibility. Professional and ethical responsibility is crucial in collecting and presenting simulations in the world of academia. 62 G. An ability to communicate effectively. Due to the complexity and skill level of the subject of this thesis, effective communication was vital to the success of the project. H. The broad education necessary to understand the impact of engineering solutions in a global, economic, environmental, and societal context. Poor dynamic system engineering decisions in the agricultural and construction industries, can have negative impacts on the industry equipment and their end users. I. A recognition of the need for, and an ability to engage in lifelong learning. There was a great appreciation for extensive and lifelong learning along with continuous education. J. A knowledge of contemporary issues. Knowledge of contemporary issues, such as modern simulation techniques, aide in the understanding for the improvements of a hydraulic system. K. An ability to use the techniques, skills, and modern engineering tools necessary for engineering practice. The ability to use modern computational tools was critical for the completion of this thesis. L. Familiarity with statistics and linear algebra. Linear algebra was used in the development of equations of motion for a system. M. A knowledge of chemistry and calculus-based physics with a depth in at least one of them. For this thesis, calculus-based physics were crucial as a tool for understanding hydraulic systems. 63 N. An ability to model and analyze inter-disciplinary mechanical/electrical/hydraulic systems. The ability to analyze inter-disciplinary systems was necessary due to the hydraulic and mechanical systems surrounding the focus area of the thesis. O. An ability to work professionally in the area of thermal systems including the design and realization of such systems. This thesis did not elaborate on a thermal system. AA. An ability to work professionally in the area of mechanical systems including the design and realization of such systems. The realizations of this thesis gave insights into mathematical modeling, dynamic systems, controls, and fluid power. 64