13. J: 31...... ill... wnfiérflfia !! v)- 2.4.. l . $5.»... inflicf xx «.1... L1 ....h ..a&u\xx . it! “.2. .cl‘t «KL-“fl ,. a! .wwxnl. .. w; z is? . . FEVER! . . . ‘ ‘ _ . é} abil. «n» R :‘2 3 Fun... . 'l 9 '3 .x41)1?..5 . 11...... _. z 2. 5. .1 >7" 3 .3 ‘6 $5 ta 3... ...\ 5 513 5| :1?" . 1 \ . jimmy, 5.4mm u WI\T ”A nu- masts ‘. Date 0-7639 SETAT llllllllllllllll lllllllllNllllflllUllllllll 293 01399 6560 This is to certify that the thesis entitled MODELING AND PERFORMANCE OF A HYDRAULIC ACTUATOR SYSTEM presented by BAS IL JACOB JOSEPH has been accepted towards fulfillment of the requirements for M S . MECHANICAL ENGINEERING degree in 77. C, 43mm” 5 Major professor MAY _ 10 - 1995 MS U is an Affirmative Action/Equal Opportunity Institution » - -.-» i ~v—v‘.A w._~__~_ _r_' - fiW—“,—-- ‘— -WWW M— '“ w— v— ‘— v— LIBRARY Michigan State Unlverslty PLACE It RETURN BOXto manuals Momma. your "cord. To AVOID FINES Mum on or Moro duo duo. DATE DDE , DATE DUE DATE DUE __,__.— MODELING AND PERFORMANCE OF A HYDRAULIC ACTUATOR SYSTEM By Basil Jacob Joseph A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Mechanical Engineering 1995 The do and stone} it should lx of represer 1mm is cal defining mOdeling i advem of i The foe $31631 Eh; PTOject Si [he SUi’Sw um hm. the design The 5-551 [he ”mart tempera” Te: WW6 run Um ABSTRACT MODELING AND PERFORMANCE OF A HYDRAULIC ACTUATOR SYSTEM By Basil Jacob Joseph The design engineer Of today is invariably faced with the challenges Of speed, accuracy and economy in his work. Not only does he or she have to generate the best design, but it should be done within the least amount of time and with the least expense. The science of representing components and systems by expressing their physics in mathematical terms is called mathematical modeling. Such models can be built with varying complexity depending on which aspect of the design the engineer wishes to study. Mathematical modeling is fast becoming an indispensable ally in the design field, especially with the advent of powerful personal computers and relatively inexpensive work stations. The focus of this thesis is a Hydraulic Actuator Subsystem. The design Of the larger system that includes the Hydraulic Actuator Subsystem is part of an ongoing design project. Structured modeling techniques were used to develop a mathematical model Of the subsystem. Once the model was developed it was validated by comparing its behavior with known hardware performance. This validated model was a powerful tool in testing the design and improving the design. The system was modeled using bond graphs and the simulations were conducted using the software package ENPORT. The effects of entrained air in the fluid, various operating temperatures, and material properties Of key components were investigated. Simulations were run under various conditions and the system performance was evaluated. Dedication To my dearest mother and father: I am the arrow sent forth from their bow. The powerful how will bend and flex to give an arrow the gift of flight. iii l mu CBC Dill 32:. at supp: l ex; Of his t M} memb M: Mich, F i. the o ('I ACKNOWLEDGEMENTS I would like to sincerely thank Dr. Ronald Rosenberg, for his advice, guidance and encouragement during my academic program. His immense knowledge was both a source of support and motivation. I express deep gratitude to Julian LORusso of the FORD, API‘E division who went out of his way many a time to help me on mine. My appreciation goes out to Dr. Clark Radcliffe for his valuable suggestions as a member of my thesis committee. My colleagues in the Computational Design Laboratory, especially Joe DeROse and Michael Hales have been a great source Of support and encouragement. Finally special thanks to my dear brother who always kept me going, especially when the going got tough. iv Cha; LlSI LlST NOM 1A TABLE OF CONTENTS Chapter Page LIST OF FIGURES ......................................................................................... viii LIST OF TABLES ........................................................................................ xii NOMENCLATURE ........................................................................................ xiii 1. INTRODUCTION ........................................................................................ 1 1.1 Problem Definition .................................................................................. 1 1.1.1 The Importance Of Modeling in Design ................................... 1 1.1.2 Structured Modeling of Systems ............................................... 3 1.1.3 The System Under Study ........................................................... 4 1.2 Research Objectives ............................................................................ 11 1.3 Organization of the Thesis ................................................................ 13 2. A SET OF HYDRAULIC MODELS ................................................................ 14 2.1 Model Evolution ............................................................................. 14 2.2 The Two Modes of Operation ................................................................ 15 2.3 Model # 1 : The Initial Model .............................................................. 19 2.4 Model # 2 A Qualitative Model With More Details ........................ 22 labl F Chat. N N 3.D Table of Contents (cont'd.) Clnpter Page 2.5 Model # 3 : Model with Actual Design Parameters ............................ 24 2.6 Model # 4 : Model with Solenoid Details and Air in the Fluid ........... 27 2.7 Model # 5 : Model with Flow Limited Pump ....................................... 30 2.8 Model # 6 : The Most Complete Model ...................................... 31 3. DESCRIPTION OF COMPONENTS AND THEIR PHYSICS ..................... 34 3.1 Introduction .................................................................................... 34 3.2 Spool Valve .................................................................................... 34 3.2.1 The Geometry ........................................................................... 35 3.2.2 General Physics ....................................................................... 37 3.2.3 Detailed Physics and Modeling Assumptions ....................... 40 3.3 Solenoid Valve ........................................................................ 55 3.4 Buffer Volume ........................................................................ 58 3.5 Pump ............................................................................................. 58 3.6 Actuator ......................................................................... 58 vi REF APP APP APP APP APP Table of Contents (cont'd.) Chapter Page 4. RESULTS AND DICUSSIONS ................................................................. 60 4.1 Air Fraction Study .......................................................................... 61 4.2 Leakage Load Variation .............................................................. 62 4.3 Viscosity Variation Study .............................................................. 63 4.4 Spool Spring Variation Study .................................................. 64 5. CONCLUSIONS ....................................................................................... 65 REFERENCES ...................................................................................... 68 APPENDIX A Equations, Derivations and Named Parameters ......... 69 APPENDIX B System Bond Graphs and Simulation Plots .............. 79 APPENDIX C EN PORT Model File For Nominal Design .............. 105 APPENDIX D Node Descriptions for Nominal Design .............. 118 APPENDIX E User Defined Subroutines for Nominal Design .......... 163 vii ligu. LIST OF FIGURES Figure Page 1.1 Detailed Schematic of Hydraulic System ..................................................... 6 2.1 Spool Valve Steady States ............................................................................. 16 2.2 Actuator Steady States ............................................................................ 17 2.3 Model # 1: Initial Model ............................................................................. 20 2.4 Model # 2: Qualitative Model with More Details ..................................... 23 2.5 Model # 3: Model w/ Actual Parameters ................................................. 26 2.6 Model # 4: Macro Bond Graph ............................................................... 27 3.1 Spool Valve Cross-Section ........................................................................... 35 3.2 The Three Pressure Regions in the Spool Valve ........................................ 36 3.3 The Spool Dimensions ............................................................................ 37 3.4 Spool shown at ”Zero” with Chamber Dimensions ........................... 39 3.5 Hydraulic Resistances Identified .............................................................. 41 3.6 Dimensions for Hydraulic Resistances ................................................... 44 3.7 Spool Off The ”zero” Position ......................................................... 46 3.8 Rx1 in Transition ........................................................................................ 48 3.9 Solenoid Valve ................................................................................. 56 3.10 The Actuator ........................................................................................ 59 viii List Figu 81-1 81—2 81-3 Bl-4 81-5 81-6 82—1 List of Figures (cont'd.) Figures Page Bl-l Bond Graph Model for Flow Limited Pump ........................................... 79 81-2 Bond Graph Representation Of the Spool Valve ........................................... 79 31-3 Bond Graph Representation of the Solenoid Valve ........................................ 80 B 1-4 Bond Graph Representation of the Actuator ........................................... 80 81-5 Bond Graph Representation of the Leakage ........................................... 81 31-6 Bond Graph of the Function Blocks ........................................................ 81 82-1 Spool Movement in Disengagement Mode- For Model Described in Section 2.2 ....................................................................................................... 82 82—2 Pressure Profile in Disengagement Mode- For Model Described in Section 2.2 ...................................................................................................... 82 32-3 Pin Movement in Disengagement MOde- For Model Described in Section 2.2 ....................................................................................................... 82 82-4 Spool Movement in Engagement Mode- For Model Described in Section 22 ...................................................................................................... 83 82-5 Pressure Profile in Engagement Mode- For Model Described in Section 2.2 ...................................................................................................... 83 32-6 Pin Movement in Engagement Mode- For Model Described in Section 2.2 ...................................................................................................... 83 82-7 Spool Movement and Pressure Profile in Disengagement Mode- For Model Described in Section 2.3 ................................................................................ 84 32-8 Spool Movement and Pin Movement in Disengagement Mode- For Model Described in Section 2.3 ................................................................................ 84 List of Figures (cont'd.) Figures ’ Page 82-9 Spool Movement and Pressure Profile in Engagement Mode- For Model Described in Section 2.3 ................................................................................. 85 82-10 Spool Movement and Pin Movement in Engagement Mode- For Model Described in Section 2.3 ................................................................................ 85 82-11 Pin Movement and Pressure Profile in Disengagement Mode- For Model Described in Section 2.4 ................................................................................... 86 82-12 Pin Movement and Pressure Profile in Engagement Mode— For Model Described in Section 2.4 .............................................................................. 87 32- 13 Spool Movement, Pin Movement and Pressure Profile in both Engagement and Disengagement Mode- For Model Described in Section 2.5 .................. 88 82—14 Spool Movement, Pin Movement and Pressure Profile in both Engagement and Disengagement Mode- For Model Described in Section 2.6 .................. 89 82-15 Spool Movement, Pin Movement and Pressure Profile in both Engagement and Disengagement Mode— For Model Described in Section 26- Another Pump .................................................... 90 82-16 Spool Movement, Pin Movement and Pressure Profile in both Engagement and Disengagement Mode- For Model Described in Section 2.6— Nominal Design ..... 91 83-1 Spool Movement in Engagement Mode- For Model Described in Section 4.1 ...... 92 83-2 Pressure Profile sin Engagement Mode- For Model Described in Section 4.1 ...... 93 33-3 Pin Movement in Disengagement Mode- For Model Described in Section 4.1 ...... 94 83-4 Pressure Profile in Disengagement Mode- For Model Described in Section 4.1 ...... 95 list Tigr- 83-5 List of Figures (cont'd.) Figures B3-5 Pressure Profile in Engagement Mode- For Model Described in Section 4.2 ...... B3-6 Pin Movement in Disengagement Mode- For Model Described in Section 4.2 ...... B3-7 Pressure Profile in Disengagement Mode- For Model Described in Section 4.2 ...... B3-8 Spool Movement in Engagement Mode- For Model Described in Section 4.3 ...... 83-9 Pressure Profile in Engagement Mode- For Model Described in Section 4.3 ...... B3-10 Pin Movement in Disengagement Mode- For Model Described in Section 4.3 ...... B3-11 Pressure Profile in Engagement Mode- For Model Described in Section 4.4 ...... B3—l2 Spool Movement in Engagement MOde- For Model Described in Section 4.4 ...... B3-l3 Pin Movement in Disengagement Mode- For Model Described in Section 4.4 ...... xi Page 96 97 98 99 100 101 102 103 104 Tabl] Tablc T'eibi LIST OF TABLES Table Page Table 2.1 ................................................................................................................... 18 Table 4.1 ................................................................................................................... 61 xii SSV HS NOMENCLATURE Area Eccentricity Spring Stiffness Pressure Hydraulic Resistance Volume Spool Displacement Actuator Piston Movement Bulk Modulus Ratio Of Specific Heats Kinematic Visosity Density ABBREVIATIONS Solenoid-Spool Valve Hydraulic Subsystem xiii 1.1 PR 111 T. and in 11 engineer had 10 [3 Verify a would t in the c r001“ ft 903le '1 to 311334 Comm: the ”123 firs Chapter 1 INTRODUCTION 1.1 Problem Definition 1.1.1 The importance Of Modeling in Design For a long time design engineers have used physical models and mock-ups to help them while designing a new device. Thus we had scaled physical models of huge pumps, buildings, airplanes and so on. Such models are helpful in visualizing the final product and in investigating the behavior Of the device under different conditions. Frequently an engineer was also required to improve the performance of an existing design. He or she had to understand the current design precisely and then suggest changes to be made. To verify the innovations, a sample component of the existing design (or a scaled model) would be modified to incorporate the changes and then tested. This was true, for example, in the case of automobile engines and other expensive systems. There was little or no room for oversight, especially if considerable machining was needed, as this would prove costly in terms of both time and money. Engineers have long been using the physics of systems, expressed mathematically, to analyze them under extreme conditions. For example, stress analysis would be used to compute the maximum allowable load on a bridge or any such load supporting member, the maximum compression viable in a reciprocating gasoline engine cylinder before the flash point Of the fuel is reached, the maximum pressure a gas cylinder can contain, the 2Murat P51? at 2 maximum current a conductor can carry, the maximum number of revolutions that an engine can sustain, and so on. The mathematical principles were always used to predict the outer limits of safe operation. Yet when complex engineering systems were built there were Often surprises in the first few trials - sometimes accompanied by extreme consequences. These might have been avoided if the systems engineer would have analyzed the behavior of each and every component during the entire Operation of the system For even slightly complicated systems, this would require considerable amounts of time and effort in manual computing — till the advent of the modern computer. The computer could do complex calculations not only faster but even more accurately than the average engineer. And it could do them endlessly without ”inadvertent” (human) errors. The engineer could program all the mathematical formulae into a computer and punch in different values for different variables and the computer would retm'n the state of the system at each instant in time. This concept can then be taken a step further to study the whole system during the entire period of operation - at every instant in time. One only had to instruct the computer as to how different parameters changed in time (if at all they did). A computer model obviates the necessity of constructing hardware experiments that consumed time and effort. An accurate model that captures all the relevant physics can be used to identify the dominant factors so that designers can concentrate on those parts of the system. Multiple simulations of the model can provide answers to a whole range of ”what if?" questions which would otherwise require costly and sometimes dangerous hardware experiments. Powerful personal computers have now made it possible for any design engineer to use modeling techniques ‘ lithav incur; featu maxi Con . ;‘ UL! pm Te [’1 A ‘4 in his design. 1.1.2 Structured Modeling of Systems ”Models of systems are simplified, abstracted constructs used to predict their behavior" [1]. Even while engineers constructed scaled physical models, they did not incorporate every detail - only the relevant ones were reproduced. This is a characteristic feature of all modeling - physical or mathematical. One could incorporate a myriad of mathematical relations that pertain to a large system and construct a computational mammoth. The computations can then sometimes become nearly impossible - even by computers, or if at all possible they will only generate a great deal of unnecessary information together with the relevant. For example the calculation of frictional heat produced when a piston moves inside a cylinder once in five minutes may be totally irrelevant from a particular systems viewpoint, even though such a formula can be programmed into the model. Albeit, over simplification of a system should be avoided, for that may fail to capture important physical effects. So there is some degree of skill involved in breaking down a complex system into its component mathematical relations. A competent system designer needs a procedure for constructing different models (if required) of a large system that can all together predict the complete behavior of the system under study. Many approaches have been developed over the years for the effective modeling Of systems. The Bond Graph theory [1] is particularly useful for systems spanning multiple energy domains. The bonds represent the power transfer between various J represen possible understz ENPOF their be 1.1.3 3 hydr.’ i5 bein of the “as vi Within mOdel 4 elements in the system and if compatible units are used, power can be equated across different energy domains. The nature of the various parts of the system are captured by any one of a small set of ideal elements that can be used across the board for all energy types. For example a mechanical spring, an electric capacitance and a hydraulic compliance are all energy storage elements. In bond graph theory, all of them are represented by the same ideal element - the capacitor (or C element). Thus it becomes possible to perceive the overall structure of a large and complex system model. This understanding will be invaluable in studying the system behavior. The software package ENPORT [2] allows us to build bond graph models for nonlinear systems and simulate their behavior. 1.1.3 The System under Study In this thesis we apply structured modeling techniques to the evolving design of a hydraulic subsystem. This particular subsystem is part of a larger system which itself is being designed at the same time. Even though we were not involved in the modeling of the larger system, good communication with groups designing the other subsystems was vital to the success of the overall project. Limitations, changes and new possibilities within each subsystem may directly or indirectly affect the design (and hence the modeling) of our hydraulic subsystem. Propose of the System The hydraulic subsystem has two main functions to perform as listed below. The reader COUlpl't‘ Overt Oil to lead 5 reader should also read the next section (Overview of the Hydraulic System ) to fully comprehend the terms used here: 1. Cause a latch pin (in the actuator) to engage or disengage subject to a command signal. 2. Maintain the oil pressure in the external load circuit above a minimum mark at all times. Overview of the Hydraulic System The hydraulic subsystem (HS) consists of a pump which supplies high pressure oil to a Solenoid-Spool Valve (SSV) which in turn controls the oil flow to an external load circuit. The SSV consists of a solenoid valve and a spool valve housed in one unit. The solenoid controls the position of the spool inside the spool valve, which in turn changes some port openings in the spool valve chamber. These ports control the inflow of fluid from the pump (into the SSV) and out into the external load circuit. The external load circuit consists of a buffer volume, an actuator and a leakage demand. The actuator and the leakage are fed from the buffer volume. To drain out any excess oil in the subsystem, the SSV has a port that communicates with a sump. In all the discussions that follow in this thesis, the term system refers to the Hydraulic Subsystem, unless otherwise noted. The complete system schematic is shown in Figure 1.1. In the figure VC is an electrical signal line. All other lines between the various components are hydraulic. The SSV operates in two distinct modes which are dictated by the electrical signal ttutt ‘\ allow 1‘. 515). T causing- change the pte positit: load c leaka- 6 input (V C). A high voltage signal makes the solenoid valve change the spool position to allow maximum inflow from the pump (through SPLY) and out into the buffer (through SIS). This leads to a high pressure in the buffer which pushes a piston inside the actuator causing the actuator pin to disengage. A low voltage signal makes the solenoid valve change the spool position to let the least amount of flow into the buffer, thus dropping the pressure. A low pressure in the buffer will cause the actuator pin to move to the other position (engage). By virtue of the solenoid-spool valve design, this low pressure in the load circuit is not allowed below a certain minimum mark that is needed to supply the leakage demand that is also part of the external load. Slight increases in this leakage Solenoid—Spool Valve 6' w j / l SPLY Spool V1 Solenoid Pump 81 Valve ‘ Valve \ 1... 1.. __ ______ ______ __ I $15 I - EXTLK ~\ Dim—— a A2A O _.I it [ % P2H _, Actuator ! — —-- ——— _ ._ ___ . _ Figure 1.1 Detailed Schematic of Hydraulic Subsystem demar; SOlent‘ inside I amQ-u: the m 7 demand will not affect the system low pressure regulation mark. The regulation by the solenoid-spool valve is further explained in Chapter 3. The detailed physical dynamics inside the HS are dealt with in Chapter 3. To summarize, the two states of operation for the HS are: High Pressure State: When the spool valve configuration results in a high pressure in the external load circuit. This is the pump supply pressure. The actuator pin is then in the disengaged mode. Low Pressure State: When the spool valve configuration results in a low pressure in the load circuit. The actuator pin is then in engaged mode. In this state any small variation in the leakage demand is met by regulating action by the spool valve. Hence this is also called regulation mode. A simple description of the major Pump An ideal pump would be a source of high pressure oil capable of providing any amount of flow at the same pressure. But in reality fluctuations in flow demand can cause the output pressure from the pump to vary. The system is modeled with such a realistic a single oil sup; valve '1 entitled VC. lllc' Selenoi ValVe C of the Pen 0; (throug fiOW tl. 8 pump. In Figure 1.1 we show the pump drawing oil from the sump (FRSMP) and supplying it at a higher pressure to the SSV through the line marked SPLY. Solenoid-Spool Valve The spool valve and the solenoid valve are two virtually independent units inside a single housing. Oil from the pump flows into both these valves. The solenoid valve uses oil supplied by the pump (through V7) to perform its controlling action on the spool valve. The solenoid valve and the spool valve are both described in detail in Chapter 3 entitled Description of the Model. Depending upon the voltage signal received through VC, the solenoid either charges up or discharges. This opens or closes a valve inside the solenoid valve which controls the flow of oil (through V1) into one side of the spool valve chamber. The pressure thus built up on one side of the spool controls the position of the spool inside its chamber. The position of the spool determines the spool valve’s port openings to the pump, the actuator and the drain - thus controlling the inflow (through SPLY) and outflow through SIS and S31. When the solenoid valve closes the flow through V1 the oil is drained out of it through V5. The Bufi’er Volume The buffer is simply a large volume with an inlet port and one or more outlet ports. Oil from the SSV flows in through the inlet (SIS) and flows out through the outlet port to the actuator (A2A). on: sit. of it an PIOIIUS Oil the 13 mm leak; The Actuator The actuator consists of a piston in a cylinder. Oil from the buffer (line A2A) flows into one side of the piston and pushes it against a spring. The piston has a pin projecting out of it and which is long enough to protrude outside the actuator body; and the amount of protrusion outside the body depends upon the position of the piston inside the cylinder. Oil that flows past the piston is drained out into the sump through line P211 The actuator is more fully described in Chapter 3. Leakage A typical HS such as this provides the oil for forced lubrication to moving parts. One of the duties of the SSV is to maintain the minimum pressure needed for this purpose. Such a lubrication demand is modeled here as a simple orifice that is fed from the buffer (EXTLK) and which drains into the sump (LKFLO). The area of the orifice can be varied to emulate a higher flow demand. Sump In a typical closed system such as the HS, the sump will be a reservoir (usually at atmospheric pressure) of oil that may be shared by other subsystems in the larger system. The pump will draw oil from this (FRSMP) and all excess oil in the subsystem drains out into this sump (S31, V5, LKFLO, P211). Throughout our modeling we have assumed that the sump is at atmospheric pressure. fiflhr OWN] Other tr Sdh§fl funnier anar 10 Performance Specifications The two equilibrium states of the system have been described earlier under Overview of the System. The system needs to change (and stabilize) from one state to the other in a relatively short time for the satisfactory performance of the Hydraulic Actuator Subsystem within the larger system. The system is expected to perform a set of primary functions after which a set of secondary performance criteria also need to be satisfied. Primary Specifications 1. Complete engagement of the actuator pin should be achieved within 27 milliseconds. 2. Complete disengagement of the actuator pin should be achieved within 27 milliseconds. 3. The regulation pressure in the disengaged mode should be above 22.034 N/cm2 absolute (17 psi gage). Secondary Specifications 1. Meet all the primary specifications when the operating conditions vary : a. Fluid temperature varies from 150 °F to 250 °F b. Percentage of air in the fluid varies from 3.5% to 7% ll 2. Meet all the primary specifications when manufacturing tolerances vary on: a. Geometric dimensions b. Spring stiffness c. Surface finishes 3. Consideration of possible failure: Achieve a safe mode of operation if the oil supply were to be interrupted. In this case the pin should attain engagement. An acceptable computer model should be able to perform the above functions as well. The system performance in the model is studied by monitoring three key variables: 1. The position Of the spool inside the spool valve. 2. The position of the pin inside the actuator. 3. The pressure in the external load circuit. 1.2 Research Objectives The principal objective of this research was to develop a reliable computer model for the Hydraulic Actuator System using structured modeling techniques and then to use the model to aid in the ongoing design process. Towards this end we had to accomplish the following four steps: under idem \Ve ; gene to 1 Con CCU asrl 12 Study the Complete System: The contribution of every component to the overall system behavior needed to be grasped completely. The more important and the less important properties of components from a systems viewpoint needed to be distinguished. The crucial effects that require detailed modeling had to be identified as opposed to those that called for simpler treatment. The expected system performance also needed to be understood. Develop a Model: Once the nature of the different parts of the system were understood and the various physical effects relevant to the system’s performance were identified, structured modeling techniques had to be applied to develop a system model. We chose bond graphs as our modeling tool and used the software package ENPORT to generate the model of the system and simulate its behavior on the computer. Validate the Model: Once the model had been built on the computer, then it needed to be tested and validated. Validation entailed simulating the model under known conditions and recording its performance. The performance of the model was then compared to available test results of hardware experiments. The validated model is chosen as the nominal design. Parametric Studies: The nominal design was used to run various parametric studies to ensure that the model performed its primary and secondary functions. The effects of operating conditions like temperature and air fraction in the hydraulic fluid were investigated. Some system design parameters were changed slightly to see how the model behaved. These model parametric studies were used to improve the design and perfor 1.3 Paran figure discus model Appel Plovjd EXPO 13 performance of the subsystem. 1.3 Organization of the Thesis The thesis is organized into five chapters and a set of appendices. The current chapter contains the motivation for this research, the introduction to the problem, the research objectives and the outline of the thesis. Chapter 2 records the evolution of the model from one that had a very basic representation of the various component parts to one with the quite detailed modeling of the dominant effects. Chapter 3 describes in detail the various parts and their physical effects that were considered [important from a system point of view. Chapter 4 discusses some comparative results of parametric studies conducted with the fully evolved model. Chapter 5 draws a set of conclusions from the whole modeling effort. Appendix A contains some important equations, mathematical derivations, and a list of key (named) parameters used by the system model. Named parameters are symbolic constants used in various equations. Appendix B contains all the figures pertaining to the model bond graph and the results of the comparative studies discussed in chapter 4. Appendix C lists the ENPORT model file for the fully evolved model. Appendix D separately defines the various nodes in the model bond graph. Appendix E lists the user defined subroutines used by the model. These subroutines provide function definitions to pertinent nodes that cannot be adequately described by the ENPORT software library functions. l..l ‘.\lt brush a gooc be ab inthc‘ We V his a: (I? Chapter 2 A SET OF HYDRAULIC MODELS 2.1 Model Evolution Successful mathematical modeling requires a great deal of skill besides a knowledge of the physical and mathematical principles. An experienced modeler will have a good understanding of the various energy domains he or she deals with. He or she will be able to quickly identify the more important physical effects that need to be captured in the model of any system. In this research, work besides developing an accurate model, we were also seeking an insight and some experience in structural modeling. As implied in Section 1.1.2, a simpler model with less computations is preferable to a more complex model - if both of them can predict the system's behavior with reasonable accuracy. Our goal was to develop a model that has the fewest number of elements with the simplest possible mathematics and yet which can predict system behavior with a satisfactory degree of accuracy. The hydraulic system described in chapter 1 was modeled in progressive stages starting from a very basic model. Detailed and complete design data was not available to us as the hardware itself was being designed. So we started our efforts with models where we tried to emulate the qualitative behavior of the key components. This was very useful as a preliminary step as it helped us build a ”skeleton” for the system model. As we gained a better understanding of the system more physical effects were added to the 14 15 model. After arriving at a model that truthfully portrayed the qualitative behavior, we incorporated actual hardware design details into the model. When this model could not predict actual hardware behavior satisfactorily, we were faced with two modeling issues: 1. Should we add more physical effects to the model in order to improve its accuracy? This included questions such as whether we should consider the flow forces on the spool when the oil flows through the spool valve ports and whether we should consider the inertial effects of the fluid in the lines and the buffer volume. 2. Should we use better parameters and more complex mathematical expressions for the physical effects already modeled? This included questions such as whether we should model the hydraulic compliances in the chambers such that they vary with pressure and whether we should compute a more accurate value for the coefficient of discharge (Cd) at the various orifices. These are issues that any modeler has to contend with and they require both experience and skill to resolve efficiently. A major benefit from this research work was such an experience. This chapter briefly documents our efforts during the evolution of the model. 2.2 The Two Modes of Operation Before the progression of models is described, some conventions need to be l6 established. As briefly described in Section 1.1.3 under ”Detailed Operation of the System" the system being modeled has two distinct steady states of operation. These states are described in detail with reference to Figures 2.1 and 2.2 which show the nomenclature of the solenoid-spool valve and the actuator. In Figure 2.1 Xs denmes the PZChambcr SPOOL SPRING /’ SOLENOID VALVE (I) INLET PORT Figure 2.1 Spool Valve steady States spool movement and in Figure 2.2 Xp denotes the pin movement. When Xs is zero as 17 shown in Figure 2.1 (a), the inlet port is wide open leading to a high control port pressure and consequently the external load circuit is in a high pressure state. The actuator configuration in this state is shown in Figure 2.2 (b) where Xp equals Xpd. When the spool valve is in regulation mode, the spool is at or around Xse as shown in Figure 2.1 (b). This sets a low control port pressure and hence a low pressure state in the external / / //// / / / El 77’ / \: l“ \ 7 M ‘ \\ / / ,“\l\ Ill . , 7 / ~ , {:1 (a) Pin Figure 2.2 Actuator Steady States. 18 load circuit. Then the pin is in engaged mode (Xp now equals 0) as shown in Figure 2.2 (b). The high pressure state of the system is also referred to as the Pin Disengaged (or Retracted) Mode; and the low pressure state of the system is also called the Pin Engaged Mode. These states have been summarized in Table 2.1. Pressure Control _ : (Xp) High Disengaged Xp = Xpd Low Pressure Low Low llIiagle 2.1 Stea y tates Some points the reader should note about the modeling: Engaged 1. The spool and actuator piston spring in the actual hardware are installed such that they exert a preload force on the spool and piston even when they are at their 'zero’ positions. 2. Instead of measuring the actual displacement of the spool and actuator piston, we chose to track the deflection of their respective springs. These springs were defined such that they are at ’zero deflection’ position when the spool and piston are at their ’zero’ positions respectively. 3. In order to track the control pressure (which is also the pressure in the external 19 load circuit), we chose to track the pressure at the control port. 4. P1, P2 and P3 are pressures that exist in the respective chambers shown in Figure 2.1. 23 Model #1: The Initial Model A very basic model was constructed which had all the representative elements of the system (as envisioned at the time). This model concentrated primarily on the spool valve and we wanted to capture its structure and qualitative behavior. The elements, such as springs, masses, and resistances, did not have the exact nature as those in the real system. They were assumed to be very simple, linear and completely independent of each others’ behavior. None of the parameters were actual although values used were comparable to each other in magnitude. For example, the hydraulic resistances (R,) at the port openings were assumed to have either one of two fixed values at either steady state; and these numbers were computed manually, even though these resistances actually depend upon the position of the spool. The model is shown in Figure 2.3 below. Some points to note about the model: # The fluid was assumed to have no entrained air and the hydraulic chambers were assumed to behave like simple springs. 20 # The hydraulic chamber formed by the right side of the spool and the right chamber walls was not modeled. # The end walls of the chambers were not modeled - so the spool and actuator piston were never restricted in their range of movement. # The same pressure as in the control chamber (P3) was assumed to exist on the left face of the spool. C1STAR \11/ l 18 15 19 --~ P---': lld L20. ' __‘ SEF’S—:—8E{OPS-—8110NTL30P3-—J>°1EX—J¥20EX‘——2-2—1ANN¢2-0P2<1__ __ §lS_l_a_><2__!sexl L 2c3_ _ __. SOLENO “ " "‘ "’ T 7 "‘ " 3POOL VALVE VALVE? l TFPlNr l l l IPIN1 <1PIN1\CPIN1 : | RPIVN1 1 AC TU ATO'R Figure 2.3 Model # 1: Initial Model # The pump was assumed to be a pressure source (SEPS) and have unlimited flow capability. # The solenoid valve was not modeled and a separate pressure source (SECNTL) was included to set the pressure on the right side of the spool - just as the Then: (at let" pressu snnula side of Now t2 equah PTEViC in the “‘35 r and 5 beha Teal 21 solenoid valve would. # The buffer volume was not modeled. The model was exercised in the following manner. The spool was set at zero displacement (at left wall). The inlet pressure (SEPS) was set to a high value and the solenoid valve pressure port (SECNTL) was set to a very low value. With these initial conditions the simulation was started. The low pressure on the right side and high pressure on the left side of the spool caused it to move to the right. Now the initial conditions were changed : the pressures on either side of the spool were equalized and the spool was placed in the final position attained by it at the end of the previous simulation. The spool moved towards the left wall because of the preload force in the spool spring. In both of the above cases, the piston displacement in the actuator was not tracked as the hydraulic resistances were not being varied when the spool moved and so the pressure profile seen by the piston would not be representative of the actual behavior. This model was developed as a preliminary to one that had more complex (but real) element behavior. The purpose was to establish the model’s qualitative behavior - specifically the spool’s behavior. As noted before, the spool displacement is tracked by the spool spring (CSPL) deflection. The response of the model was found to generally agree with our expectations of the spool valve's behavior. Although, maybe due to errors in parameters used or relative scaling the behavior was not very pronounced. The reader 22 is reminded that for lack of actual design data, all our parameters were ”intelligent guesses". 2.4 Model #2: A qualitative model with more details Upon confirming that the general behavior of the spool was as expected, the next step was to model the relation between the spool position and the hydraulic resistances at the spool valve ports. Thus the model shown in Figure 2.4 was developed. It is the same model as in Figure 2.3, except that some of the element definitions were changed and some more elements were added. These changes are summarized below: # The value for the hydraulic resistance (Rx ) was re—computed each time the spool position changed. The spool positions and the resistances were assumed to have a linear relationship with a non-zero minimum value. # The chamber walls were added. These were modeled as extremely stiff springs (CW ALL and CSTP) on either side of the spool and piston. Again none of the elements used actual parameters - only ones with comparable magnitudes. This model was also exercised in both modes as described earlier. The control pressure (effort on 815) seen by the actuator was also tracked as was the piston movement (deflection of CPINl) in the actuator. The behavior of the model was found to be even more realistic than Model #1. These results are included in Figure 32-1 to Figure 82-6 in Appendix B. It should be noted that none of the values have exact 23 physical significance; only the general trends were of interest. Figure 32-1 to B2-3 show the spool, control pressure and pin behavior in the disengagement mode. In this mode the spool is initially in the regulation position (Xse in Figure 2.1 (b) ) the pin is fully engaged (Xp = O). The pressures on the two sides of j. T CWAu. CSPL 18|SPL RSPL I ' l 4&5. '7 l l 01 STAR TFF’Z kljoop‘ig'nma :r' 25 "' - -‘ ! SPLY:\ §1 A 14 22 21 If“ v1 J} BEPS , .. ops lousy-l. 093Mg<\0ls.,><\—lll.9lr~lor=r2x I. SEONTL L__J l er szsexr nxa " ,_____‘ PUMP I no,“ 1 season i VALVE l_ __m__ £15.__ __ __.___. 7 Spoor. wave — -— -_ -— 1 /° l 1HN1§CPIN1 I l |lt=lN1 7 a CSTP E I l ACTUATOR mm r I Figure 2.4 Model # 2: Qualitative model with more details. the spool are then equated and this causes the spool to move towards 'zero’ (pushed by its spring force) as seen in Figure 82-1, and the spool valve port openings to change. The Rfl resistance opens and the control pressure rises as seen in Figure B2-2. This rise in control port pressure pushes the piston in the actuator towards Xpd as seen in Figure 82- 3. Figure 32-4 to 82-6 show the spool, control pressure and pin behavior in the mg dis l0l 24 engagement mode. In this mode the spool is initially at Xs = 0; the pin is fully disengaged (Xp = Xpd). The pressure in the P2 chamber of the spool valve is then lowered and this causes the spool to move towards Xse - pushed by the pressure force in the P1 chamber, as seen in Figure B2-4, and the spool valve port openings change. The inlet port almost closes (ILl increases steeply) and the control pressure falls as seen in Figure 82—5. This fall in control port pressure allows the piston in the actuator to move towards the ’zero’ position as seen in Figure 82-6. 2.5 Model # 3: Model with realistic design parameters In the previous section, we developed a model that had all the qualitative behavior of the three major components of the system. We could now incorporate actual design values for parameters and change the mathematical expressions for the element behaviors to follow the real system more closely. We introduced the nonlinear nature of some key elements. The parameters were taken from existing hardware and the following changes were made to the previous model. # The sliding resistance between the spool and the inner diameter of the chamber (RSPL) was modeled as a viscous friction. The equation used for this computation is included in Equation A.1 in Appendix A. # The hydraulic resistances of the ports were changed to be either annular or orifice in nature depending on the spool position. These are included as Equation A2 and Equation A.3 in Appendix A. 25 # Actual values were used for the bulk modulus, the density and the viscosity of the oil. Actual values were also used for the mass of the spool and piston, all geometric dimensions, spring stiffness and preloads. These values with their units are listed as Table A.1 and Table A2 in Appendix A under Named Parameters and they are also included in Appendix D. # When incorporating actual design values, it was noticed that when the spool or piston struck the chamber walls they tended to bounce back a few times. This was on account of the walls being modeled as very stiff springs. In order to compensate for this effect, a damping (RWALL and RSTP) was introduced when the spool or piston impacted into the walls. # The hydraulic compliance of the fluid in the chamber on the left side of the spool (ClSTAR) was modeled as that of a chamber with changing volume. The theory is described for Equation A.4 in Appendix A # A resistance (R,. ) between the supply port and the left side of the spool was identified and assumed to act in parallel with the already existing R,l . The model is shown in Figure 2.5. This model was exercised like the earlier ones, with similar initial conditions. The results of these simulations are included as Figure 82-7 to Figure 82-10 in Appendix 8. The most important observation about this model was that the fluid in the hydraulic 26 ] 1618131. RSPL RWALL' -- --l I C1STAFI aft-:10“ : l— _ — 14 o | 8593 L saqxopsflléot1§bog<éhAvaok\ [Ll/1 fSECNTL I L30 le2 SEX1 lea '____J ' RX4gJOFtX1 : L——._. To M P I R152 315 SOLENo ID F_~———4~———————_—-—- v SPOOL VALVE ALVE __ _ .l- ... .— l- VNt -} N11“ FF. R1HN1%CPIN1 \\ | : IPIN‘I 34 a CSTP l l RSTP RF’IN‘I ‘ ACTU ATOR Figure 2.5 Model # 3 : Model w/ Actual parameters chambers on either side of the spool and piston was too stiff which prevented it from quickly expanding to fill the volume created when the spool or piston moved. This effect was not seen in earlier models because in those cases the chamber volume was assumed to be constant, which in effect translated to a constant compliance fluid spring. In this model since the volume of the chamber is recomputed continuously, the fluid spring compliance changed continuously. Thus the pressure computations in the chambers sometimes yielded impossibly large numbers; here the fluid can be perceived as "tearing I! up. We also notice that the ”bouncing" when the spool or piston strikes the wall was not entirely eliminated. It was later realized that a greater damping coupled with higher precision while computing eliminated this problem 27 2.6 Model # 4 : Model With Solenoid Characteristics and Air in Fluid Since the above model’s predictions were different from the hardware performance, especially with regards to the fluids behavior, the modeling assumptions were re- evaluated and another model was built with some major modifications. The macro level model graph is shown in Figure 2.6. The individual unit bond graphs are included in Appendix 8 (Figure 81-1 to Figure 81-5). The major bonds connecting these components are shown and labeled in the macro graph. There is one exception to be noted. The pump are shown and labeled in the macro graph. There is one exception to be noted. The pump model as shown in Figure 81-1 is not used for this model. Here we used a simple Control \ Panel Solenoid-Spool Valve Vc r W a“ SPLY SI W Mp \ o ‘——> Spool Solenoid L Valve Valve lssr Mid I c -——>.. 2 515 l Buffer / Leak [0 ———\C _. -- .___\1——\R EXTLK FRSMP LKFLO AZA P211 i —- h / Actuator 1’ I ” W Sump Figure 2.6 Model # 4: Macro 80nd Graph 28 constant source of pressure (SEPS) to represent the pump. The drain shown in the macro graph is just a source of effort set to atmospheric pressure. It should be noted that in the actual hardware, the solenoid valve and the spool valve both drain into a common line which then drains into the sump - as shown in Figure 1.1 and 2.6. For clarity of the model, we show them as draining separately into the sump as shown in Figures 81-2 and 81-3. The buffer is a zero junction with a large volume hydraulic compliance. The line FRSMP is shown dashed because it is never modeled. This line represents the supply of oil from the sump into the pump. Since the pump in our model is a simple source of effort which can be set to any pressure, we need not have a line of supply from the sump in our model. # In any hydraulic system it is impossible to avoid the entrapment of air in the working fluid - either dissolved or as bubbles. The fluid in this system was assumed to have 3.5% air (by volume) present as bubbles. This would dramatically increase the compliance of the fluid as is discussed in Appendix 8 (Hydraulic Compliance with air - Equation A5 in Appendix A). This theory was applied to the definitions of the hydraulic compliances on either side of the spool (C1 and C2) in Figure 81-2 and in the actuator (CARM2) in Figure 81-4. # The chamber formed between the left face of the spool and the left wall was identified as a separate pressure region (0P1) with a compliance (0C1). This chamber is referred to as the P1 chamber. 29 # A resistance to flow due to the pressure equalizing passage was included (Rmm) - between the Pl chamber and the inlet port. # When the spool is at 0 and touching the wall, the complete area of the spool cannot be acted upon by the pressure in the Pl region. There is an ”X” groove cut into this face of the spool so that the pressure has some surface area to work on. This detail was added to the model. More details are discussed in the chapter describing the physics (Chapter 3). # The solenoid part dynamics were modeled partially (Figure 81-3). Since the design details of the solenoid valve were not available, only the pressure-flow characteristics together with the triggering mechanism were modeled to represent the solenoid. See Chapter 3 for further details. # The large buffer volume between the SSV and the actuator was included in the model. This buffer will dampen any sudden spikes in the pressure profile and would also serve as a convenient take-off point for any more actuators. # A large leakage into the atmosphere was added to the output to see what effect it had on the performance of the system, especially in the low pressure regulation mode. This model seemed accurate and the simulation results are included in Figures 82- 1 1 to 82-12 in Appendix 8. Yet upon examining the fluid flow profiles especially at the 30 inlet to the SSV, some extremely large flow numbers were seen. The actual pump used in the hardware was incapable of these flows. These numbers were seen in the model because the pump was modeled as a source of pressure capable of providing almost infinite flows. The oscillations in pressure in the engagement mode are due to the large leakage introduced in the buffer circuit. This leakage flow demand during the low pressure mode causes the spool to drift towards 0 allowing more flow via R", which may prove to be too much inflow - thus we can see the spool "hunt" for an equilibrium position The hardware was found to ave the same behavior. 2.7 Model it 5 : Model with Limited Flow Pump Characteristic Realizing that a real pump needed to be modeled for a true representation of the system, some more changes were made to the model: # The physical dimensions of the pump were not available, and moreover a model for the pump was beyond the scope of this project. So as in the case of the solenoid valve, a pressure flow curve was obtained for the actual pump used with the hardware and was included in the model. Again the line from the sump (FRSMP) was not modeled because we are not modeling the whole pump; instead we use a source of flow in conjunction with a resistance to emulate the pump's pressure-flow characteristics. Refer Figure 81-1. The macro model is exactly as shown in Figure 2.6. The individual units are expanded in the Figure 81-1 to Figure 81-5 in Appendix 8. The results of the simulations 31 of this model are shown in Figures 82-13 in Appendix 8. Now the model could not produce effective disengagement of the pin. During the disengagement of the pin, it was seen that too much time was taken up in building up the pressure in the piston chamber. The same behavior was seen in the actual hardware experiments. This led to the conclusion that the pump was too weak and required a lot of flow to build up enough pressure to disengage the piston completely. The large leakage was also felt to contribute to system failure. We also felt that we should consider the effects of the existing chamber pressure when computing the hydraulic compliance at each time step. 2.8 Model # 6: The Most Complete Model In all the previous models, we assumed that the model performance lacked accuracy because we did not model all the significant physical effects. But now, faced with the issues described in Section 2.2, we conclude that maybe we need to redefine the internal physics of some of the elements already modeled We recognized that the hydraulic compliance is a major factor in the system performance. The assumptions made in modeling the hydraulic compliance were considered again. The air in the chamber dramatically reduced the effective bulk modulus of the hydraulic fluid in the chamber. But the bulk modulus of this air was also constantly changing with both the pressure in the chamber and the volume of the chamber. The effect of the existing chamber pressure on the bulk modulus and volume of air were now included in the calculations. The theory is discussed in detail in chapter 3, Section 3.2.3.2 and Appendix A (Equation A.14). The system model is exactly as shown in Figure 2.6 except that function blocks were created 32 to compute the instantaneous values of B“, and V,,, as the pressures in the chambers changed. These re-computed values were used in the calculation of the final pressure in the chamber. The function blocks are shown in Figure 81-6 in Appendix 8. This is the "fully evolved” model capable of predicting projected hardware performance. Actual hardware reflecting this model was not built for an accurate comparison, but it was felt that such hardware could be built as the next step. The main performance measurement was the time taken by the model to achieve complete engagement or disengagement Of the piston pin after the command to switch modes had been issued. The performance of this model is given in Figures 82-14 to 82—16 in Appendix 8. In Figure 82-14 we see that the pin has no trouble disengaging within the time studied (50 milliseconds). Yet we notice that the piston movement and the pressure build- up seem slower. The supply pump characteristic was then changed tO simulate a more powerful pump. The system performance in Figure 82-15 shows how the disengagement process is much quicker now. Figure 82-16 shows the system performance after the large leakage in the buffer circuit had been reduced to a much smaller value. We see that the spool does not ”hunt" for an equilibrium any more in the low pressure regulation mode. The switching time of this model was found to fall within the bounds of the system’s primary and secondary specifications mentioned in Section 1.1.3. This model was then chosen as the nominal dc‘ 11C At S\: Di. 33 design on which parametric studies would be carried out. All the physics of this model’s major components viz: the Pump, the Solenoid- Spool Valve, the Buffer and the Actuator are fully described in Chapter 3. The various nodes and their specific subroutine definitions are detailed in Appendix D and E. Adopting this version as the nominal design, some parametric studies were done on the system and these together with their results are discussed in Chapter 4 - Results and Discussions. Chapter 3 DESCRIPTION OF COMPONENTS AND THEIR PHYSICS 3.1 Introduction This chapter describes in detail the five major components in the system, viz; Spool valve, Solenoid Valve, P111111), Buffer and Actuator. The geometric dimensions are included and the various physical effects assumed to exist in the components are also explained. 3.2. Spool Valve As mentioned earlier, the Solenoid-Spool Valve consists of the spool valve and the solenoid valve housed in one unit. The spool valve not only controls the Oil flow to move the actuator piston, it also regulates the minimum pressure of flow in the external load circuit. This minimum pressure value is decided by a combination of the supply pump capability and the spool valve design. This will be elaborated later in this section. The physical effects inside the spool valve are discussed here and the way they have been modeled are described. Even though there may be numerous effects involved only the dominant ones that are relevant to capture the dynamic behavior have been modeled. 34 3.2.1 The Geometry Before we describe the dynamics of the spool valve, we need to understand its geometry. A simple cross-section view of the spool valve is shown in Figure 3.1. /— SPOOL SPRING t /// / \ LDRAIN PORT CWTRO. PORT INLET PORT Figure 3.1 Spool Valve Cross-Section As we can see, the spool valve consists of only one moving part - the spool, which is essentially two equal diameter cylinders connected end-to-end by a smaller diameter cylinder. The spool is within a chamber that is cylindrical. On one side, between the wall and the spool is a spring, which seats into a small cavity on the spool. When the spool chamber is filled with fluid, we will assume that the spool floats in the middle of 36 the chamber with a small clearance all around. By virtue of its shape, the spool divides the chamber into three different regions as shown in Figure 3.2 below. The pressure in these regions are referred to as P1, P2 and P3 . PRESSURE EQUALIZING _ P2 /7 PASSAGE /[ “ u‘ P1 Figure 3.2 The Three Pressure Regions in the Spool Valve The spool valve has three hydraulic ports to communicate with the rest of the system (refer Figure 3.1). The inlet port is where the high pressure supply (e.g. from a pump) comes in, the control port shown in the middle is where the controlled output flow from the spool valve comes out. The drain port is to drain the valve chamber when required. In the cross-section figures of the spool valve there is a passage shown through the spool body that connects the Pl chamber and P3 chamber. This passage is referred to as the pressure equalizing passage, since it equalizes the pressure between those two chambers. As shown in Figure 3.3 it has two interconnected bores across the smaller diameter section (although only one of these can be shown in a cross-section view) and 37 one along the larger diameter section on the left side. The "X” groove (1 mm wide) on the face of the spool is designed so that when the spool touches the wall at its 'zero’ position, there is still a small area on which fluid pressure in the P1 chamber can act. .. , 5' :6 3 ‘ 10 i / Te l" W 15 __ a Figure 3.3 The Spool Dimensions 3.2.2 General Physics If we assume that the spring on the side of the spool is not present, then the spool becomes a body free to move as per the dictations of the three forces generated by the pressures P,, P2 and P3. But P3 acts equally on all sides and cancels itself out. Hence the position of the spool is dependent only on the forces due to Pl and P2. The effective areas Al and A2 of either face of the spool are equal. The spring on the P2 side of the spool has its maximum installed length lesser than the free length, and hence is always compressed, irrespective of where the spool is in its chamber. So for an equilibrium of forces on the spool, 38 m*m=m*m+n+x*m where X5 is the displacement of the spool as measured from the 'zero’ position of the chamber (refer Figure 2.1). F. is the preload force on the spool spring (by virtue of the shorter installed length) when the spool is touching the wall at 0. F.=K*(lo-IJ L-freelengthofthespring lI - installed length of spring K is the stiffness of the spring. So the values of P1 & P2 determine the position of the spool in its chamber. Here we ignored the flow forces generated by fluid flowing through narrow passages into and out of the three chambers. The pressure in the P2 chamber is controlled by the solenoid valve which is affixed on one side of the spool valve (as shown in Figure 3.1). The operation of the solenoid valve will be discussed later. Spool at “Zero“ Position Let us assume that the spool is at 'zero’ position and in contact with the wall. This configuration exists when P1 and P2 are equal. Then the preload force of the spool spring will push the spool to the wall. This spool valve configuration is shown in Figure 3.4. 39 35.815 j l” .0... (7,6755%? f’ Figure 3.4 Spool shown at ”Zero" with Chamber Dimensions We know that P, equals P3 due to the pressure equalizing passage when the spool is at 0. This in turn is the supply pressure coming in through the inlet port. P, cannot act on all of Al since the spool is assumed to be touching the wall. But there is the "X" groove cut into that face of the spool and so the size of the P1 chamber is only as big as the ”X” groove. The force in P1 chamber of the of the spool is Fm = P, * ( Area of the ”X”) The force on the other side (P2 chamber) of the spool is Fm=P,*A,+ F, 4O Spool moving away from “zero" Now if we were to maintain P, at the same high pressure and reduce P2, there will come a point when FM, is greater than Fm, . The spool will then start moving toward Xse (refer Figure 2.1). Note that as soon as the spool moves away from the wall, the area increases to the full area (A1) of the spool face. 3.2.3 Detailed Physics and Modeling Assumptions A general picture of the spool valve operation was outlined above. This section attempts to look at the details of how the various configurations of the spool valve are achieved and the assumptions involved while modeling the spool valve dynamics. 3.2.3.1 Hydraulic Resistances From the geometry of the spool valve (shown in Figure 3.4), we can deduce that the opening between the inlet port and the P3 chamber is the largest when the spool is at its ’zero’ position. It follows that the incoming flow will be greatest in this configuration. And at the other end of the P3 chamber, there will be a minuscule flow out into the drain. For ease of discussion we will name the hydraulic resistances that play a role in the flow of fluid in and out of the spool valve: 1;, : Hydraulic Resistance to flow between inlet port and P3 chamber Rn : Hydraulic Resistance to flow between P, chamber and Drain 41 R” : Hydraulic Resistance to flow between Drain and P2 chamber R“ : Hydraulic Resistance to flow between inlet port and P, chamber Figure 3.5 shows these resistances. From the spool valve geometry shown in Figure 3.4, we see that the spool can move a maximum of only about 2.8 mm. It follows that R” and Ru will always be annular resistances in their respective flow paths. In the configuration shown in Figure 3.4, R“ is the resistance offered by an orifice and R” is an annular resistance. The resistances are calculated in the following manner referencing Figure 3.6. .7 I A Figure 3.5 Hydraulic Resistances Identified 42 Ru The orifice area of Ru can be computed from the magnified view shown in the bottom of Figure 3.6. W W If c = Vaz+b2 Then we have: ....Eq 3.1 Area of Orifice, A0 = 1r * Diameter of the chamber * c L J Where ”a" and ”b” are as shown in Figure 3.6. Note that ”b” is the clearance between spool and chamber. It was calculated as the difference between the spool’s larger radius and the Chamber’s inner radius (Refer Figure 3.3 and 3.4). Now if the spool moves towards Xse (refer Figure 2.1 (b) ), ”a" changes and ”c” is recalculated, which changes A0. The orifice flow equation [3] is given by r W T P. —P How, 0: Cd*Area* \J2£—"”‘—"p——22 where Cd : Coefficient of Discharge ...Eq 32 Area : from Eq. 3.1 Pm, - P3: the pressure drop across the Orifice p : Density of Fluid P J 43 From the geometry shown in Figure 3.6, we see that Rx2 is the resistance offered by an annular passage of length L. This length of the annular tube decreases as the spool moves towards Xse. The laminar flow [3] through this tube is given by Equation 3.3. Elam Q = 72:“: [1+%(i;)2] (P3PDW)]...Eq. 3.3 where P3 - PM : the pressure drop in the direction of flow L : as shown in Figure 3.6 e : The eccentricity between the centers of spool and chamber c : The clearance between spool and chamber Po : The Fluid Kinematic Viscosity 44 ,, W4 @"7ng/% 5/7 lllll / // V 7 . x//., / , 7 /;,//////, , , . / 15/ ////% / /'/// / ’ 1 44 l Figure 3.6 Dimensions for Hydraulic Resistances 45 As mentioned in Section 3.1.1, we assumed that the spool floats in the middle of the chamber and so the eccentricity is zero. The flow equation then became: 3 l Flow, 0: ‘2’: (g-PDMHJ...Eq. 3.4 u Rxaand Ru The flows through these resistances are always annular in nature and were computed in the same manner as in Equation 3.4. The Figure 3.6 depicts the lengths of the passages in these cases. It is obvious that as the spool moves towards Xse, L3 increases and L4 decreases. Hydraulic Resistances - Spool 06' the ''zero" position When the pressure P2 is dropped very low, the spool is forced to move towards Xse. This occurs when the pressure force acting on the ”X” on the left face of the spool is large enough to overcome the spring preload and low pressure combination on the right Figure 3.7 shows the configuration in the spool valve when the spool has just started moving away from the ’zero’ position. 46 Looking at the various flow paths identified in Figure 3.5, we see the following trends: Ru : Still remains an orifice flow, but the dimension ’a’ has decreased - resulting in an increased resistance to flow from the inlet port to the P3 chamber. Rn : Still remains an annular passage flow; although the dimension ’L’ is now reduced resulting in a slight lowering of resistance to flow from the P3 chamber to the drain port. Rfl : With reference to Figures 3.6 and 3.7, the dimension ’L3' has increased, resulting in an increased Rfl resistance. RI4 : With reference to Figures 3.6 and 3.7, the dimension 'L4’ has decreased, resulting in a decreased R“ resistance. “ Tl” \ 7—, /, ‘/ ia_ Figure 3.7 Spool off the "zero" position 47 Figure 3.8 shows two configurations of IL, in the spool valve at instants following the one depicted in Figure 3.7. We see that Ru first reaches a thresh-hold point where the dimension ’a’ is zero. The flow is still an orifice flow. The continued movement of the spool towards Xse will change the nature of R“. It then turns into an armular passage resistance that keeps increasing as the spool continues to move in that direction. The flow through this resistance is then given by the annular flow equation described in Equation 3.4 - except that the pressure difference is now measured between the inlet and the P3 chamber; and the length of the passage is L1 as shown in Figure 3.8. A similar yet opposite flow transformation takes place in the case of Ra. It starts out being an annular passage (when the spool is at the 'zero’ position) whose length keeps decreasing till it reaches a thresh—hold point and then the annular flow equation ceases to apply when the flow path becomes an orifice. The correct mathematical description of these two flow transformations was a very important factor while developing the model for the spool valve. Let us consider the flow through R“. As described earlier, the initial flow was described by the orifice equation described in Equation 3.2. After the spool crosses the thresh-hold point, the final flow is described by the annular passage equation: 3 ‘leC Flow, 0 = 6:11. (PW—P3) 48 th at and of orifice regime Rx1 in annular regime Figure 3.8 Ru in Transition We see that the length of the passage appears in the denominator of the annular flow equation. Just after the cross-over, in the initial stages of the annular flow regime, when the length of passage is very close to zero, this equation is prone to produce some very large flow numbers (or the equation ”blows up” ) which are not indicative of the actual situation. This is because division by the length of passage might get very close to division by zero. Thus it became necessary to define a transition region, between the two flow regimes, that eliminated the huge numbers in the calculations and at the same time could effectively ”patch up” the flow curves produced by both equations - orifice and annular. The computations in this transition region were neither that of an orifice nor 49 of an annular flow. We decided on a length for the transition region making sure that outside this region, the annular flow equation did not "blow up”. Then we assumed that for one half of this region a ’constant area orifice equation’ would apply and for the other half, a weighted average of orifice and annular equations would apply. The weightage of each equation will depend on the position of the spool within the transition region The constant area orifice equation would apply in the half closer to the orifice flow regime and the weighted average would apply in the half closer to the annular flow regime. The definition of one half of the transition region as a ’constant area orifice’ was necessary because using a weighted average in that half did not eliminate the ’division by zero error’. Using R" as an example, the computations in the transition region are described below in detail. From the geometry of the spool valve chamber shown in Figure 3.4, it is evident that as the spool moves towards Xse, R" ceased to be an orifice type resistance after a spool displacement of 0.095cm. So the transition flow region for R“ begins after this point. The transition length was chosen as 0.0015cm. So for the first half (note that this is the half closer to the orifice flow regime )of this transition length ie. 0.00075cm, a constant area orifice flow was assumed to exist. And the area of this orifice was the last computed area by Equation 3.1 just before 11,, entered the transition region. After the spool had traversed the 0.00075cm, the flow through R“ was calculated as a weighted average of both orifice and annular flows as shown below: 50 [ How: [1 — {loom + {Om}... J...Eq.3.5 where x is the spool displacement past the 0.00075cm mark; L is 0.00075cm for R" Qua" is the same flow number as calculated in the first half of the transition region. Om“...Ir is calculated as in Equation 3.4; but the length of passage used in this equation was measured from the beginning of the transition region, ie. past 0.095cm of spool travel. Once the spool crossed over this transition region, the flow was calculated using a regular annular flow equation as in Equation 3.4. When the spool moves back from Xse to 0, the same set of computations are done in reverse order. These computations are done in ENPORT [2] by the sub-routine ZZSU69 (refer APPENDIX E). In the case of R,2 , the same techniques are applied in order to prevent the computations from ’blowing up’. These computations are carried out in ENPORT by the sub—routine ZZSU70. 3.2.3.2 Hydrach Compliances The hydraulic compliance of a fluid is its ability to be compressed under pressure. It is quantified by the compressibility or the bulk modulus of the fluid - one being the reciprocal of the other. Bulk modulus denoted as B is defined as change in pressure divided by the fractional change in volume. As described by Merritt [3], an isothermal 51 as well as adiabatic bulk modulus can be defined for a fluid. It can be shown that the adiabatic bulk modulus is the product of the isothermal bulk modulus and the ratio of specific heats. In most hydraulic design applications we use the adiabatic expression for bulk modulus, especially when the bulk modulus of air is to be calculated. Bulk modulus is the most important fluid property in determining the dynamic performance of a hydraulic system because it relates to the "stiffness” of the fluid and hence directly alters the "response time” in a hydraulic circuit. It is always a positive number. Bulk modulus is significantly altered by the slightest amount of air entrained in the fluid. Merritt and others have developed expressions for the effective bulk modulus of a fluid-air mixture inside a chamber as 1 2 V“ -1— + V0” ._1_ Be” VTaral(Bai) VTml(Bar'l) and ...Eq. 3.6 811'! 301'] 3st? : VTotal Bur Va? ‘ Baa Va where we ignore the effects of container expansion. The effect that entrained air has on the fluid bulk modulus is dependent not only on the volume of the chamber, but also on the pressure inside the chamber as we will see shortly. 52 Spool at 'Zero' Position Revisited When oil under pressure flows into a chamber it gets compressed. If there is any air entrained, the mixture gets compressed to a greater degree. We have seen that when the spool is at 0, a tiny chamber exists between the face of the spool and the wall of the chamber. This is the volume of the ”X” groove. Oil forced into this chamber gets compressed due to its own compressibility and also due to the compressibility of the air entrained (if any) in the oil. The pressure in the chamber at any given time is the pressure of this compressed oil and air mixture. In the case of the spool valve, the inflow of oil raises the pressure in the chamber and after attaining a certain pressure within the chamber, the spool is pushed outward from the wall. This causes the volume of the chamber to increase, leading to a drop in the pressure. This will in turn allow more oil to flow into the chamber till the pressure builds up enough to move the spool again, and the whole process gets repeated. Ofcourse the activities inside the chamber do not repeat themselves in the same order; it is a dynamically changing situation. At the same time the mass of oil capable of flowing into the chamber is continually changing due to the changes in the hydraulic resistances caused by the spool movement. These changing pressures and volumes affect the hydraulic compliance of the fluid inside the two chambers formed by either face of the spool and the respective chamber walls. An expression that relates the effective bulk modulus of a fluid-air mixture in a chamber when both the volume and the pressure are changing is developed in Appendix A (Equation A.13). These effects have been modeled by the ports C1 and C2 in the 53 system bond graph (Figure Bl-2). These ports are only sources of efforts whose value is assigned to them after a complex set of calculations have been carried out by the function blocks shown in Figure Bl—6 of Appendix B. ( W AP : _ Beff VT VT or LP * d1 ___ _ B at?“ d! d V7. VT 01' .45 . _ B... _"_"r dt V, J! and g = Be” * Flow L J The Equation A. 13 shown in Appendix A together with the existing chamber pressure and the flow rate into the chamber is used by the block DPCl to obtain the pressure differential in that time step— as shown above; this differential is then integrated by the block INTCl to obtain the final pressure at that time step. 3.2.3.3 The End Walls of the Chamber The two end walls of the spool chamber are modeled as very stiff springs with heavy one-way damping. The damping is active only when the spool strikes the wall and flies to "move into" it. The nodes that model these effects are RWALLl and CWALLl. 54 We have used only one resistance element and one spring element to model both walls together. They are both defined in such a way that they are inactive within a certain range of spool movement (which is the chamber length). If the spool attempts to cross over this range on either side, then these spring and damper properties take effect. 3.2.3.4 Viscous Friction on the sides When the spool slides in its chamber filled with fluid, the fluid gets sheared. This fluid shearing causes viscous friction between the side walls and the spool. We assumed that only the larger diameter sections of the spool experienced significant viscous friction. The node RSPL models this effect. The equation used is included in Appendix A. 3.2.3.5 Pressure Equalizing Passage This passage as described earlier has three interconnected bores. The passage offers a combined resistance and it is calculated as follows. Four coplanar short cylindrical passages join at a common point, from where a longer passage begins in a direction perpendicular to the other four. 80 the resistances of the four short passages act in parallel, and this combined resistance acts in series with the long passage. The corner resistance is also considered, where the fluid coming in from the four pipes has to ”turn” a corner and flow into the longer pipe or vice versa. The corner resistance is assumed to be a multiple of the minimum resistance. The node Rm“, models this resistance 55 3.2.3.6 Regulating Action of the Spool In the regulation mode, the pressure force (due to fluid flowing in from the solenoid valve) on the P2 chamber side of the spool is almost non-existent. The spool is pushed towards Xse by the pressure force in the Pl chamber, which is also the pressure in the control chamber (P3) - due to the pressure equalizing passage. At a certain spool position, the force pushing the spool towards Xse gets balanced by the spring force (which includes preload) acting on the other side of the spool. Now when there is an increased flow demand from the actuator circuit ( for e.g. caused by a greater leakage), the pressure in the control chamber drops leading to a drop in pressure in the Pl chamber. This upsets the balance of forces on either side of the spool and the spring forces now dominate. The spool will be pushed towards the 0 position. This in turn opens up the L, path and allows more inflow from the pump, building up pressure in the control chamber. When the pressure force in the Pl chamber of the spool rises high enough it prevents the spool from being pushed any farther by the spring forces; the spool has then found its new regulating position. This is how the spool valve meets any reasonable demands of flow and always maintains a minimum low pressure. 3.3 Solenoid Valve The solenoid valve is not modeled with all its dynamics. Only the hydraulic resistances of its ports are varied according to the manufacturer’s data. This is simulated 56 as a rate of change of orifice area with time. The solenoid valve shares the oil supply from the pump (with the spool valve) to control the spool position. When the solenoid in the valve is charged up by a high voltage, it attracts an armature from a default position. The armature is coupled to a ball which controls the port openings to the spool valve chamber and the drain. See Figure 3.11. {—r "" To Spool Valve Ball Valve Armature //. . ,rz / "237.4 ,’ .. ,4 , i, q, S. ,. .. .- . a f} . ' A z . z). is... .4/ // \\ k.-. To Drain BEE From Pump Figure 3.9 Solenoid Valve - in principle No details of the solenoid valve geometry are known - except the time taken for the solenoid to charge or discharge. The manufacturer also provided the maximum flow through either port for a given pressure difference. So from the Orifice Flow Equation: 57 2 (Ir—P.) Flow, 0 = Cd * Area * p where C(, : Coefficient of Discharge Area : of orifice P, —P2: the pressure drop across the Orifice p : Density of Fluid which we can rewrite as 0: Cd*Area* %*m knowing Q, P,-P,, and p and assuming Area is 1 unit, we calculate a value for Cd * Area * \J—g Using this value as CNOT and assuming that Area changes from 0 to 1 within the time taken to charge or discharge the solenoid, we can compute the flow through the ports at all times. The solenoid is known to take 6 milliseconds to charge up and 3 milliwconds to discharge. The area is assumed to change between 0 and 1 during this time in an exponential manner. A transfer function is used to model these openings to the two ports - one to the spool valve and the other to the drain. When one port opens, the other closes within the same span of time. It is assumed that during charge-up of the solenoid, the port to the spool chamber opens and the drain port closes. In the model, RSE and RSC are assumed to be orifice resistances ( as described above) with their areas changing exponentially. 58 3.4 Bufl’er Vohrme The buffer volume is just a large chamber of constant volume. It can be considered as a plenum for supply to more than one actuator and also as an absorber for any pressure spikes. The fluid inside this chamber acts like a huge compliance. 3.5 Pump The pump is not modeled in its entirety. The combination of SFPMP and RPMP together emulate the pressure-flow curve of the actual pump. CINLT can be considered as the hydraulic compliance of the line between the pump and the SSV. 3.6 Actuator The actuator shown in Figure 3.12 has more or less the same mechanical elements as the spool valve. The piston slides in the cylinder and the pin slides in the hole on the body. The sliding friction of these elements is modeled by RFRNZ and RFREZ respectively. Their equations are exactly as those for RSPL. The end walls are modeled by a combination of CPIN2 and RPINZ. CPIN2 is defined to have two different properties in two ranges of operation - one as the pin spring and the other as the end wall. When the piston moves within its allowed range (ie. within the two walls) it acts as a simple retainer spring, with a certain stiffness and preload. But once the piston strikes either wall, then the spring stiffness changes to a very high number to imitate a metal 59 wall. E5 // W 325nm “01 Figure 3.10 The Actuator Atmospheric pressure exists on the right side of the piston. The small stops seen between the piston and the left cylinder wall are stops which help to serve the same purpose as the "X" groove on the spool - to provide an area for the pressure force to act on when the piston is at "zero" (refer Figure 2.2). As in the case of the spool spring, the piston spring has a preload force keeping the piston against the 0 position unless and until the pressure force exceeds this spring force. Chapter 4 RESULTS AND DISCUSSIONS As mentioned earlier, the actual design of the system was also being carried out in parallel with the model development. Hardware experiments were set up only for the design modeled in Section 2.7. As we already saw in the model performance, this design was not satisfactory, mostly because the pump was not powerful enough to build up the required disengagement pressure. The design team then decided to reduce the leakage and improve the pump performance. The pump curve used in Section 2.8 reflects this new pump and leakage. The model described in Section 2.8 was then chosen as the nominal design because its performance was close to the actual hardware’s projected performance with the new pump and leakage. The model file (for ENPORT) is listed in Appendix C and the individual node descriptions and subroutine definitions are in Appendices D and E. This chapter describes some parametric studies conducted on this nominal design. The studies were done to ensure that the system met the primary and secondary performance specifications. To have complete faith in the model, it is important to build the actual hardware and duplicate its performance in the model. The studies discussed here help in establishing the methods and reasoning involved. The system response to different conditions is studied by monitoring mainly the control pressure P3, the pin movement and the spool movement. As and when required, other variables are compared. A key of the various parameters that have been varied is 60 61 given in Table 4.1 and a discussion of the studies and their results follow. The plots for the various results are given in Appendix B. Some of these plots are shown for a much longer time than is necessary to observe the system behavior because there are other plots that did require such a long time to observe all the trends. l Study Seri; # Parameter Nomiml Value New Value 1 Air Fraction 3.5% by Volume 7% by Volume 2 Leakage Load 0.05 cm2 orifice 0.5 cm2 orifice 3 Viscosity 1.092E-06 N-sl cm2 2.37E—06 N-s/ cm2 4 Spool Spring 18 N/cm 27 N/cm Stiffness(KSPOOL) 5 Oil Bulk Modulus 1.72E+05 N/cm2 5.8E+05 N/cm2 Table 4.1 Key for Parametric Study 4.1 Air Fraction Study As discussed in earlier chapters, the presence of air in the working fluid has a marked effect on the system performance. In the nominal design we assume that 3.5% air(by volume) is present as bubbles(i.e. undissolved) in the oil. It is not possible to keep this percentage of air a constant, more often than not it tends to increase. So we study the effect of 7%(by volume) air in the oil. This would make the oil softer than the nominal. As far as system performance we can expect a slight increase in the disengagement time of the piston pin. The softer fluid will take more time to build enough pressure in the 62 chamber to offset the preload force in the spring. We will also see that the spool tends to oscillate with a larger amplitude while ”hunting" to find the regulating pressure in the engagement mode - because the fluid has become more compliant. These variables for the nominal design and the parametric study have been plotted in Appendix B for comparison. Looking at the comparative plots, we realize that the model behaved as expected. During the pin engagement, we do see the greater amplitude in the spool movement and the pressure oscillations in the control chamber - Figures BZ-l and BZ-Z in Appendix B. After all that we see the pressure being regulated to nearly the same value - Figure BZ—Z in Appendix B. But the pin disengagement (Figure 32—3 in Appendix B) is not affected because the small size of the chamber when the piston is hard left allows the pressure to be built up rapidly; moreover the softer fluid flows faster to fill that chamber. But once the pin starts moving, we see that the pressure in the system climbs much slower than in the Nominal Design - see Figure 824 in Appendix B. 4.2 Leakage Load Variation As mentioned in Chapter 3, the spool valve settles to a constant low pressure in the regulation mode. One of the purposes of the spool valve is to always guarantee this minimum regulation pressure in the actuator circuit. The leakage added to the buffer volume is meant to simulate a constant flow draining. So even if the leakage orifice area were to be increased from the nominal, the spool valve should regulate the flow into the 63 actuator circuit to maintain the same minimum pressure as the nominal design does. The control chamber pressure and the pin movement in either mode are compared below for both the nominal design and the higher leakage model. In the case of the higher leakage model, it can be seen that the pressure regulates to about the same level as in the nominal design during the regulation mode(engagement mode) - see Figure 32-5 in Appendix B. During the disengagement mode we see that due to the higher drainage from the actuator circuit, it takes more time for the control pressure to build up to the maximum and the pin thus takes slightly longer to disengage fully - see Figures BZ-6 and BZ-7 in Appendix B respectively. 4.3 Viscosity Variation Study The viscosity of the working fluid affects the viscous friction when the spool or the piston slides in the chamber. It also affects the flow rate through the annular passages. High viscosity conditions will exist when the system operates at lower temperatures. When operating in such conditions, the nominal design tends to be a little sluggish as will all hydraulic systems. Given in Appendix B are the comparative plots for the nominal design and the lower temperature simulation. It is seen during the engagement mode, that the oscillations of the spool movement and control pressure are very subdued before the spool valve finds the regulation pressure - see Figures 828 and BZ-9. During disengagement, the control pressure takes longer to build up to the maximum value. the pin takes slightly longer to 64 complete disengagement - see Figure BZ-lO in Appendix B. 4.4 Spool Spring Variation The three previous studies can be classified as robustness studies; the system may be called upon to operate under those conditions sometimes and it is important that the system not fail. A useful computer model should also be able to help in the modifications of an existing design; changing geometry or material properties of components in the model should yield results that faithfully replicate the hardware performance if these same properties were changed physically. It has already been mentioned in Chapter 3 that the regulating pressure achieved by the spool valve is decided by a combination of the supply pump capacity, the spool spring characteristic and the geometry of the spool valve ports(size and position). By choosing a stiffer spool spring, we should be able to raise this regulated pressure mark. We chose a spring that was 1.5 times as stiff as the nominal design but has the same free length. The comparative system response is shown in Figures BZ-ll and 82-12 in Appendix B. We see that in the engagement mode, the regulation pressure has been raised As can be inferred from section 3.2.3.6, a stiffer spring will push the spool towards 0 even more than in the nominal design. This opens up the R“ path even more and lets more oil to flow in through the inlet port and thus raising the pressure. During the disengagement, the quicker movement of the spool to the left builds up the control pressure faster and the pin disengages faster than the nominal - see Figures 82-13 in Appendix B. Chapter 5 CONCLUSIONS 5.] Summary In Section 1.2 there were four broad steps that were to be completed to achieve the principal objective of this research. Below we restate the steps and summarize our accomplishments. Study the Complete System: The system was studied in detail and all the physical effects that needed to be modeled to capture the relevant behavior to sufficient accuracy were identified. The individual components and their important applicable physics were treated in detail in Chapter 3. Develop a Model: Chapter 2 records the evolution of the initial model into the final model. The several iterations in this modeling process are of interest from a modeling education perspective. In the context of learning about a hydraulic control system one can also gain insight into the process of structured modeling. Some very important modeling issues were: - The inclusion of air in the fluid, - The effect of chamber pressure on the hydraulic compliance, 65 66 - The pump characteristics - Flow versus Pressure curve - The effective definition of the hydraulic resistance of the ports, - The leakage in the load circuit and the resistance of the pressure equalizing passage. Validate the Model: During the period when we were developing our computer models for an evolving system design, there were no reliable detailed results of systematic hardware experiments available to us. It was agreed by the engineering group that the model performed in a satisfactory manner. The most critical performance characteristic was the time (5) taken to switch from engagement to disengagement (and reverse), once the command to switch modes was issued. Both switching times were found to occur within the time frame of 27 milliseconds. The regulation pressure in the model was about 20 N/cm2 absolute. Parametric Studies: The system model was used for performing some parametric studies as discussed in Chapter 4, based on the understanding gained about the model as reported in the second and third chapters. These parametric studies produced results that were judged reasonable by the engineering group. Once the model can be verified in some detail by comparison with reliable hardware test results, it will be a powerful tool for improving the design of the system. Both parametric studies and design innovations can be performed on the model with great confidence. 67 Since all the steps were completed satisfactorily within a reasonable time period, we conclude that the research objectives were met. 5.2 Topics for Further Research Pump The pump was not modeled to include any internal dynamics in this work. It is possible that the pump dynamics may play a role of some importance in the system performance. Modeling the pump more completely and incorporating that in the system should be the next step to pursue. Solenoid We must consider including the solenoid dynamics of the SSV in the model. In our study it was only modeled as a pair of controlled resistances to flow. System Leakages The various individual leakages back to drain can be modeled in detail. A more thorough study of the leakages could be conducted. The leakages were all lumped together in this work. The total leakage is an important parameter when sizing the pump. Note: REFERENCES Karnopp D. C. , Margolis D. and R. C. Rosenberg. System Dynamics: A Umfied Approach. John Wiley & Sons, Inc. : New York, 1990. ENPORT/pc Professional User's Manual. Rosencode Associates, Inc. May 1994. Merritt H. E. Hydraulic Control Systems. John Wiley & Sons, Inc. : New York, Inc. New York, 1967. A considerable amount of engineering information about the device being designed was provided by FORD Motor Co. in informal technical reports, not cited herein. 68 APPENDIX A EQUATIONS, DERIV ATION S AND NAMED PARAMETERS Equation for Viscous Sliding Friction: The spool can be considered as a flat plate that is rolled up. So we can use the viscous friction equation for two plates sliding over each other[3]. The drag effects due to the pressure differences on either side are neglected. The friction force is given as: r W F = u. U.L. W b where ll 3 Kinematic ViSCOSity ...Equation A.l U : Velocity of moving plate L: Length of moving Plate w : Width of moving Plate h : Distance between Plates Orifice Flow Equation : This equation [3] is to compute the turbulent liquid flow rate through an orifice. We need to know the area of the orifice, the Coefficient of Discharge (which we assume for the system), the pressure difference between either side of the orifice and the density of the liquid. HOW, Q = Cd at: A133 a: 2% ...Equation A2 J p Where : 69 70 Appendix A Cd : Coefficient of Discharge Area : Area of Orifice P1 - P2 : Pressure drop across Orifice p : Density of fluid Annular Flow Equation Again from the same reference as above, this equation computes the rate of flow through an annular passage. 3 P7 =77” 1332 - t' A.3 Low, 0 6uL [ +2(c)](1>l 132)] Equaron where P, - P, : the pressure drop in the direction of flow. L : Length of the passage e : The eccentricity between the centers of the two cylindrical bodies; it is zero if they are concentric c : The clearance between the outer cylinder and the inner one u : The Fluid Kinematic Viscosity Pressm Calcuhtion in a Hydraulic Chamber with Changing Volume: We need an equation to compute the pressure at each time step in a chamber 71 Appendix A where a compressible fluid is flowing in and the volume is changing. We know from books on hydraulic power [3] that for a fluid compressed inside a chamber: dP_B TV : T/ where the negative sign can be omitted when the volume is increasing. Here, P : pressure in the chamber 0 : the bulk modulus of the fluid V : the total volume in the chamber Now (11’ = P - P0 ; where P0 is the initial pressure and P is the final pressure, and if we assume gage pressures, then I PL . P V dV ...(A) In the case of the spool valve chambers, we have a changing total volume as the spool moves. This is computed as : V = V() + AW * Xspm, where V0 is the initial chamber volume (when XW, = 0) Aw, is the area of the spool face Xspool is the displacement of the spool from its zero position. By defining the chamber as a C element [1], we have Effort = Stiffness * displacement (B) 72 Appendix A where displacement is the time integral of Flow. Drawing a parallel between (A) and (B); the pressure at each time step is given by: P = B + I( flow into the chamber for that time step) Vo + Aquaf Xsmor where the second term on the right is the change in fluid Volume for that time step. Thus the relation we are looking for is: * ‘— B + . e — chan e m volume . [ Vo + A X g Equation A 4 The Effect of Air Entrainment on the Bulk Modulus of the fluid in a Chamber When there is undissolved air trapped in the fluid, the effective bulk modulus is calculated [3] as follows: 1 z _1_ Befl’ Bait + _1_ Bay where we ignore the container. The bulk modulus of air may be calculated [3] as : B“, = Ratio of specific heats * Pressure The supply pressure from the pump is used for this calculation. We assume 0,, is constant at all chamber pressures. Thus we arrive at 73 Appendix A P: Bet? Vo + Aw* Xgml + change in volume ...Equation A.5 Since [5,, is much smaller than [30,, , it dominates the calculation leading to a very compliant fluid. An Expression for Bulk Modulus of Oil-Air Mixture in a Chamber when Pressure and Volume are Changing Let x be the volume fraction of air in the oil at STP VT”, be the Total Volume of chamber( VT”, = V0,, + V,,,r ) AV,“ be the change in Total Volume of the oil P be the pressure in the chamber [50,, be the bulk modulus of the oil with no air entrained B6,, be the effective bulk modulus of oil with air entrained We know [3] When we substitute the expression for lid, [3], and re-write in discrete form we have 74 Appendix A AP _ B?” = — ‘8‘” ’9‘” ....Equation A.6 fl.) Val l Ba] Vu’r where V,,, and V,,, are the respective volumes under current chamber conditions. Now V,,, can be calculated from the initial volume fraction of air in oil at STP with the equation for isentropic compression p, v," = p, V2” ...Equation A.7 where states (1) and (2) refer to STP and the present chamber conditions respectively; P, in Equation A.7 Pumaspm. Then P, l/a V2 * Vila] which can be rte-written as ...Equatron A.8 P. a ll» Var‘r : Vmesnvlp J P being the current Chamber Pressure Recalling that x is the volume fraction of air in oil at STP, we have V8,, @ 57? = x VT”, ...Equation A.9 Which is the volume the entrained air would occupy at STP; Then 75 Appendix A V, 2 V. Z x me’lpmwig ...Equation A.10 1” P Also since VI = V0,, + Vdr, we have P l 1 _ Ag); ...Equation A.ll p Vou : VTotal and knowing that for isentropic compression of air, the bulk modulus [3] is given by Barr : P *Yair Where . ...Equatron A.12 P a the current chamber pressure 7 w is the ratio of specific heats where we will assume that 70,, = 1.4 ; From Equations A.6, A.10, A.11 and A.12 we have AP _ - Yair P8017 . A VTW ‘ P ...Equatron A.13 l/ Pal/r1 [30H VM( 3;") ” + ywl’ V7041 ~ x(—;,—) J rearranging terms and simplifying, we arrive at Appendix A ...Equation A.14 r A i 77 Appendix A Par-cor Vb I l'llhs Datum A 1 cm RetalofiueotSpnolVflwGeueI-ytfus 10-24) 5mm 3.5 '5 ARM.“ 8 1.5 an Rebirth" or Spool \‘dveC-eunenvtl-‘iue 10-24) BRKI 0.05m mormmmmmuhm WmtuMmzm-wuuhm C 0.! lens Return m. ot'Spool Valve (m (Fm-e 10-24) CD 0.8 enema-«Wham CNOT 17.0316 CummeImMIrSch-dde CORNER IS TnWMcmmmRPOPG CREI. 0.5 MWFm-rarmflowm D 0.5 can RefirtofmeotSpndVMGeuae-yG-i-e 10-241 d1 0.2 cm Refit» his :1me Valve MW" 10-24) d2 0.15 an Refibhdsm VMMW-‘m 10-24) DAMPRT 150 N-ecm mmmtorMp-mm DCHMBR 0.80165 cur mum-d8“ “Nether-surf" 10-241 DPIN 0.605 cm limelight”: DEM-"ED Milli-01cm Dimef feedhdefororluohsDRA DSMALL 0.54 cm Referlohnotsm \‘elvetmrfiale 10-241 DSPOOL 0.79913 can Rattan-earshot VelveGeu-ytfwe 10-24) E 0.2 an mahndSpeddeGuya-‘m 10-26) EMOD LEE-OS Nisan 2 MMdOMIOWJm F 0.62:: 11*»de Vineuu-th'e 10-24) m 1.129“ mehduwm FLL'XBILD 0.1113“: Tufl-tahbde-q-WVIMCOI mm 01113.: T-ehk-hhfich-piuWV‘nCoi G 0.843 cm MbhdwvmeMG-‘m 10-24) GAMMA 1.4 Rn'ootSpeuficHeen H 1.093 an RefatoheofSpool Venetian-NF": 10-2‘) 1 0.973 cm mnmdsmvunomyrrm 10-24) ILSPSPR 0.9627! cm “Wrists-ads" KSPOOL 18 Nlcm Sims-“Spoolsmtfieu COLETECH) KSPRING r Nicer: scan-«155" KWALL 1.008006 N/crn Shotmc'flhteSonCh-fier KWALLl 1.00E'06 Ncm smuuwumm LCHMBR 3.3315 can Referlofmeot'Soool VMGeuuytI-"m I0-241 U’LV 0775 cm Mathew“ U’LVCHMBR 1.1 cu: ”dwell-lumen” LSPOOL 3.3 cm Relation-10159001 \eMWtI-‘m 10-241 MATLDNSTY “NE-05 .\'-e 2cm 4 Dave! Spud A“ ($5 3031 \DRAl-‘D 5.005411 cm Matted holeeuoNDIu PAT.“ 111.14 Ncur 2 .Wm PSL'PLY 41.162 New 2 Stank-neural“ RHO 8.50506 Nos 2 Dumat'Oil LNSEATPRS 25H” Themau‘hchmem-dmrommmm X'ISCOS 1091-2-06 Nessa: 2 Viecmotoilrd 200F \‘OLSPL 1.1372 cm 3 \‘ohlneotSpool hWfl-Mflflbolfigln WALDMP 130 N-ecrn 0mm“ “will \OTE SomorwmnmaWmet-NPORTMI Table A. 1: Spread Sheet of Namedl—“arameters Appendix A 78 ...e 825...... ...8... 2...... 3.2.535 M... 5%: . ... .5 ”Se... 2 2.5:; 9.9. e. 5.6 .22.. 9.8. 2.. 22...... 25...... 2:. a .8 E : 2:? +2: as»: ... .22 8.. ua... ...... a .8... 2.. .33.. a... a»: 2.. .... 25...... 2:. n .8 3:2 e :5 _. 5 ...... 2.. ... .8 2.. a. a... ...... 22 a. .8... 2.. :2? a... a... 2.. 8 has... 2...... 25...... 2F a .8 828 e :5. :5 {a 38v. 2.. ..e 8...»... 2:28.“ : 3 new ...... 2.. :83... .26.. e8 .8... 2.. 8.3... 5.5.2 H.593. 75.2.5. .5 a .2 e .9: ...v. =3 =2 .8... 9232.. :5 as... ......a 5... as... 8.35.. e28 3. “a . <12... . : . E. 42: 2a.: :3. .5 .e. .. ... 3. .2. :2, =2 .8... 3.3a... ...: use... .8... :2? as... 8:35.. cu...u .5. 2:: A. . :32: as»: 3.3. .8 3.5 ... ...: z a a__2 83...... .32. :3 ...... 2.. 3.. 85w... 525...... 2: U2r: -z=2__oz_._._ a .8 .33., 5.27.: 8.88 gametes . 8a e... 2.:e .2. 2F 4 ".239... ~ .6 25:: e 43:... as ...: @355918... .832. Bee-22.5.5: - $2.52 .8 2.8.. .....5: an 3. e. 3.5... a: .8... .922. Beast ”...xxm: . $.28: .5 2.8 e N. am: 2.... case... 2.4.. ... 2.22.. .82... ... 88:61:38 2.. . 8:8 e: .... 859...: 2 as: :2. . : ... ...: 538.2. 2:580 a. .58 as... 3 2.. 3:5; as 2... 0:... 5.53.8 23.5.2.5. 381...... EN 2.. 33:5 8.. .... 3...: ages... ...... .... Baa! 2.... 2.. a. 8. 8e... :2? .5996 _. z . 3...: as 8. .e 2. .2. =2 5:25.. .3: .... e332 2.... 2.. 2 8. n8... 22? ... E. .57.. _. z . 3:... a8 3:. ... E .... 8.. .8... .388 2...... 8.. 2: 6.5...235 . ... N . .6 .38.“ .....54. 81:8... an: 81> halt... Table A.2: Spread Sheet of Named Parameters (...continued) SYSTEM BOND GRAPES AND SIMULATION PLOTS APPENDIX B EWPMP e~>opMp S FLY Figure Bl-l: Bond Graph Model for the Flow Limited Pmnp S10 I1 86 S4 F0136 I S1 S1 828 FUqJFEB ..1 S OMr—‘IH‘IaT 2 8 S7 1RX4r—OPSA1 1 F00 1 6L3:*HH3EX?¥OEX‘:1PEDCZ<3 D ELA Appendix B Figure Ill-3: Bond Graph Representation of the Solenoid Valve /—fiE§-FISHF2 CARMZ 1 SHF2 AZE ‘\ AC OARMZ A2PIN TFPIN2 P2A RFREZ PRFRNZ /PIN2V1'>P2F P2E P2 PPIN2 CPIN2 IPIN2 TFRMZG P2H SEARMZ Figure 31-4: Bond Graph Representation of the Actuator 81 Appendix B r—OSFH / EXTLK E> lNTSF-‘r' > SINK1 DC1DT \ E2 \ EPCH ,, INTC1 7 SINKZ DCZDT E3 §P02} >|INT02} >:SINK3| DPMDT r____., E4 EPFth} >IINTCRMS” >}SINK4| DINLDT E8 DPINL § INTLT > INKS Figure 31-6: Bond Graph of the Function Blocks 82 Appendix B Figure 32-1: Spool Movement in WMode-ForModel - -huihedinSectionZA t - - «I 2m: 30 J. u _Flgm82-2:PtessueProfilein g .Dlsenpgauthode-ForModel a jdaaihedinSectionZA g - a. - O‘r 1 ESL J Fig-11324: PinMovementin ow Mode-ForModel ~.Wm5¢cfim2.4 83 Appendix B . // 1 t / x L / ‘ Figure 32-4: Spool Movement in ' 1 Engagement Mode-For Model . _ described in Section 2.4 O Pun-‘3': 1. 12mm 132-5: Pressure Profile in 3‘; F \ Engagement Mode- For Model 3 - \ described in Section 2.4 a r \‘\\ _ z >- \ ‘F/ M_ V“ . o ' t. in ' r-o ’ ‘ Figure 3245: Pin Movement in o F ' Engagement Mode- For Model 2 ‘ 4 described in Section 2.4 a: b l J '4 ° rm: * 5‘ 20m ‘3‘353035 7 [I SPOOL —-—-> TRESSOIE —-) o é rive a» FigmBZ.7:SpmlMovememandenfiomeMWMode-FaModddaaihedm sectiouZS z-o 3-5 -- -- - - - z ‘ b .- j/K/‘af ‘ SPOOL 5-) -% PIN - o I O i 5 M () *- mm:8poolmdPianementmDBmpgmModeFmModelda:dibedeecnm25~ 85 Appendix B 2'6 +m T I V f T I ' l { SPOOL. [PRESSURE ‘ We; SPOOL —-—§ FPRESSURE -) o 0 g. r .\ ~Tme ZS; Figure 32-9: Spool Movement and Preusure Profile in Engagement Mode-For Model described in section 2.5 20 3s , - _ SPOOLW _ e - A. A l- . VJ _ ‘l O O 2 251‘ Figure 32-10: Spool and Pin Movement in Engagement Mode- For Model described in Section 25' 86 Appendix B ”’32 ' F ' ‘2: ' * t_ " mess / ul '3". XD/N £2“? - (/ - L l . l . l . l L 0 a nun: 8..l-03 Figure 32-11: Pin Movement and Pressure Profile in Disengagement Mode-For Model described in section 2.6 8 7 Appendix B ..- “...”? P IN —~—_.__._5 PK! 0 TI"! 5..l-.3 Figure 132-12: Pin Movement and Pressure Profile in Engagement Mode- For Model described in Section 2.6 88 Appendix B 0.4 0.. '1? -. A Command to Discharge coo tone-oz zone-m sous-m woe-oz sane-oz omen: 1.00242 noose: once-oz tooem TIME- Figure 32-13: Spool Movement, Pin Movement and Pressure Profile in both Engagement and Disengagement Modes - for the Model desaibed in Section 2.7. 89 Appendix B 9 t -, _ _ — __._—-.—-— i" Iwoouotoanun 1 . Unscrew“. :. o cmncoroun . ONE-01 '- l ' ::. ‘ .0 O .. (“E-01 0v . o . . A . .I . g H zone-01 -- . . I i C H o . J .) omeooo ~ ' 10 2° 30 ‘0 -2.00E-01 nmmflow Command +0 :DI'SeKfl 19¢ x O 5 Mmm' Omaha-””0”.- Figure 32-14: Spool Movement, Pin Movement and Pressure Profile in both Engagement and DisengaganentModm- forthetheCompleteModeldmcribedinSection 2.8. Theeerwultspeflaintoa low power pump. 90 Appendix B new» ‘" Comma {a ' SNOHOIOZIZM) “<3 ° cmwtommm) raccoon W " Plnposmtolzsmm) 08¢“ —. ..u-O‘I ..WE-OI 4 “-0. III-0' ONE.” 10 20 30 40 $0 00 70 N 00 100 Figure 32-15: Spool Movement, Pin Movement and Pressure Profile in both Engagement and Disengagement Modes - for the Complete Model described in Section 2.8. 'llteee results pertain to a more powerful pump in the circuit. AppendixB 91 68.62 53 BE :85 8338 05 89c ems—«2 2:. .wN 830m S @858... 3qu Boa—EU 2.. 5.. - 832 .aoaowamaofin v5 EoEowuwnm £3 E chE 8585 2a .5826: Em ...—08262 Boom 673 9:5,.— misusezw All! 35.5 9N .. .. .. .... .. I .. .. N, ...-'l’itvdi‘ifllil a Ilia-‘21....8u: .. ...: .14 g C _ pd Nd _ _ _" __ _ _ ‘ to i..- - -- _ 3 Eczema . _ .Eoz.z_m ...Ialul —— 9o 562-4% I III _ - — _ _ . "I'l'-l'|l"flullii ‘l' — —- 0.0 K. _ _ 3 _ _ . ._ . .02.; 15:52 05 88.. 33:3. 53 m2 2:: 2a 5 885 a 2: .3. 880m s 3.8% .082 2.. a. - 8oz Esaafi a scans: 38m ”......— 95»: Appendix B 92 menu“: .0550: I I I. SE A v N—N 93 Appendix B 8.9 38oz 2: 88 83:8 53 as. 2:: 2., 5 882. a 2F .3. 880m 5 Erase .082 2a .8 - 8oz ~550ng a nae; 2385 $8 £3: 8. .81....erF o I. . _ no 0 a s a o a .. a o o . e . a a u o .. $5 a“? .. .aEEoz .. I I .- mv AppendixB 94 2...; 3.82 2: .8: 838.. 83 as. 2:: ea 5 88.5 a 2F .2. 888 a 3:83 382 2.. .e - as: aoaaasao a 32882 as 3.8 8.5,.— «gun? .2552 II I. _ eat a." Appendix B 95 83 22 2a: 2.. a .583 a 2F .3 82on a excuse .252 2: a. - 252 .saouaafia a east 2385 3.8 3:3,.— o=_a> 13:82 2: 89¢ 33:2. 8. .25 2...» _§ue< _ _QC.EOZ I I '_ c Awe—:22 ‘50-‘35. Appendix B 96 .932 2.. Ba: :2 a. 9584 2: a... 880m 5 Eaves .082 2.. a. - 33> ave—2 .Baomawam 5 ...—act 2.52m “Wm.— «...—ur— cc— .2505; c ad "to 5025- I .... 0.50.0350 we 2:9, 35:52 8. 8a: 8. a 9584 2F .2. 88% s excuse E52 as 5. - 252 .8538er s .8582 a: 6.8 5»: 8F Appendix B 97 €§5 ac ., ,A no» :6 ....... 35502 I I I -.- ' - .Iu..0'oo'no.no--n'nn'l-.-..Ic'ui...-u'.l'n.'u-o-o-o|n-o-oa. mud Appendix B 98 2:3 35:52 2: BE: :2 m_ ems—84 2:. .~.v 880m. 5 acetone—c .252 3.. he .. 352 8050:30me E 2:05 2:895 Kan: 95mg— 8. $5.2...» o _mdut0 _ .GEEOZ I I I QBOOI35. co Appendix B 99 25; .8282 on. 30—3 8896 on m_ o§§8§ 2:. .3. 53% S costume—e .252 2: he - £52 anowamam E 808052 3on "98 953,”— OOx “M‘§3UM\\C 35:52 I I I QBOCISHO n9 Appendix B 101 .2505... 8? 3.352 2.. 328 ”83% on 3 ”Engage 2: .3 83% s 3.58“. .082 as .8 - as: .8803..er a .8808: as 5.8 2:5 cop .85 222 35:52 a I I. mm. Appendix B 102 2:: .anz 2: 3 Eu 3 83. m. «saw 325 2F .3. 88% a excuse Ea: 2.. é - 082 .8538 a use.— oaeee ":8 5»: 8. .2525 IIllIllIIllll'ullnIIIIIIIII-ll-II) 8.5m :8 35:62 .. I I ow [ Appendix B 103 8.: .anz 05 8 Eu 3 8:2 a mean saw 2: .3. 88% a 388a .822 0a a. - as: .8335 a .8503: .88 £8 8.3: c .2505; o. 2.5m Em 35502 I I I Appendix B 104 . . 8E .8252 2. a E5 a 85. a 2:8 38m 2:. ¢ ¢ 888 a 3.8.8 .082 2.. .2 - 8oz “850:9.an a 58582 5.. "2.8 8.3.. S: , .25th . o 83m :3 _OC.EOZ I I I ”nun“““0“““”“””““”“”””““”l““ “N.“ APPENDIX C ENPORT MODEL FILE FOR NOMINAL DESIGN READING FILE MODEL 02:05:09 02/24/95 ENPORT/PC 5.2 NOHDES_E.ENP Model_name: NOMDES_E TITLE The VDE with only the 1 DRA latching pin and the flow limited pump. DESCRIPTION This model has the flow limited pump. The solenoid valve feeds oil only to the 1 latching pin and none of the leakages associated with the pins are considered. The model is created only to generate results for the thesis document. The results may not be accurate from a FORD point of view. This is the pin engagement mode. I have added a leakage to the shaft to simulate the varying flow demand. This is the nominal Design: Flow limited pump, Low Leak, AF 3.5%; Beta if. varies with Pressure . SY STEM GRAPH DESCRIPTION NODE TYPE xLoc YLOC ACT MACRO 01p2 MOGV 900. 100. T max nocv 300. 100. T mar-3x mcv o. 100. T 1HI-zx2 MIGV 600. 100. T sz MRGV o. -100. T Rx3 MRGV 600. —200. T 83x1 uscv 300. -200. T 1Rx1 MIGV -300. -100. T 0193 uocv —300. 100. T Rx1 uncv -300. -300. T OPS uocv -600. —100. T 0P1 uosv -1200. 100. T 1Rx4 mcv -1200. -100. T 1813 msv —600. 100. T RPQPG MRGV -600. 400. T TFPl 24ch -800. 800. T TFPZ 24ch 300. 800. T OSP'I-i nocv 100. -1800. T o<31 MOGV -1200. 800. T lsPL MW -100. 800. T RSPL MRGV -700. 1300. T RWALm MRGV -700. 1000. T 105 CSPL ISPL ISHFZ RSHFZ 0P21 0P2 IRSE RSE IRSC SE13 RSC OARMZ {PFPINZ 1PIN2 IIFREZ IIFRNZ (IPINZ IIPINZ IIPINZ TPFRMZ SHEARHZ IIX4 (JINLT ENJH \KSEN DELAY INSEN JHSENZ IIIST CHSFTI (21 (22 IlflrSFT IN'I'Cl INTCZ INTCan SINRI 81m SINRB tSIbnxg Ilsiflr IDFK21 IDszz DPan SFPMP (IP’EP RPMP (:Ilttflr HEGV MEGV 500. 500. ~100. -3300. -2000. 900. 4300. 4300. 5100. 4300. 4300. 6100. -l400. -4400. -3600. -3600. -4300. -2800. -2800. -4300. -3600. -2900. -2900. -1200. —8000. 7800. 7800. 7800. 7000. 5100. 6100. -7600. -1800. 1600. -5200. —12900. -12900. -12900. -12900. -10700. -10700. ~10700. -10700. -17600. -17600. -17600. -17600. -18100. -14700. -14700. ~8000. 1300. 1000. 1400. -2800. -2800. 800. 100. -300. -300. 1000. -1000. 1000. 1200. ~3200. —3800. -4700. -4500. -4500. -5200. -5200. -5400. -5800. -6700. -300. 2500. -600. 600. -1600. -600. -600. -600. -1500. 900. 1000. -2900. -8200. —8700. -9200. -9700. -8200. -8700. —9200. -9700. -8200. -8700. -9200. ~9700. 2500. 2500. 5200. 5300. vii-36888689688868HHHHHHHHHHHHHHHHHHHHGGHabitat-38888868804 106 Appendix C ..fiT DPINLT INTLT SINKB ILEAK SEATMLK ORFAREA (33NNECTOR S4 86 S7 :58 £39 £511 £313 £314 £516 £317 £518 £319 £320 £531 £312 £515 EKBOA. £329 £523 £524 :325 £326 5E2? £528 IUZA IUZB 811) £321 ESZJLA ‘13 \ld \IS ‘76 I?21\ l?2]3 I?2(: P21) P213 B+GV BQGV B-GV MIGV HRGV MEGV B+GV TYPE w W U U m m mgmgmgmgmgm '< < <:‘< < ‘=‘< < <31< < ‘3 < <='< < ‘:.< < ‘3 < <:'< < ‘='< < <:‘< < <:‘< < <=‘< < ¢:.< < EEEEEQEEEEEEEESEEEEEEEEEEEEng -17600. -12900. -10700. 2800. 6000. 2800. 7500. FROM -12000. -12000. -12000. -3200. -3200. -6000. -5700. TO OPS 1RX4 OPS 1RX1 IRXI 1813 0P3 0P3 13331 183EX IBEXZ IHEXZ 01P2 GE! 1313 0P3 0C1 TFPl ISPL 1$PL ISPL ISPL ISPL ISPL OSFTI ISHFZ 0P1 0P21 TFPZ 0P2 IRSE IRSE IRSC AREA TFPIN2 1PIN2 1PIN2 1PIN2 1PIN2 1RX4 0P1 1RX1 RXl 0P3 0P1 1813 lH3EX RXZ OEX DEX RX3 IHEXZ SEXI RPQPG OSFTI TFPl ISPL TFP2 CHALLI CSPL ISPL RSPL RWALLI ISHFZ RSHFZ 0C1 01P2 0P21 1RSE RSE SEX3 RSC TFPI 1PIN2 RFREZ RPINZ IPINZ CPIN2 iii-3889046 107 VERTICES 100. 100. -400 o -300. —1100. 1000. 1300. 1300. 1000. 1200. Appendix C 108 P2P BM V 1PIN2 RFRNZ AZPIN 88 V OARMZ TFPIN2 A2C 88 V ISHFZ OARMZ PZG BM V 1PIN2 TFRMZ —2900. -5500. P23 BH V TFRMZ SEARMZ 55 BB V 1RX4 RX4 51 BB V OINLT OPS -3800. -600. -600. V 86 V VGEN SUM D 56 V DELAY SUM V2 BB V IRSC 0P2 V1 BH V 0P2 01P2 VC 86 V SUM AGEN AA 86 V AGEN DIST A1 86 V DIST RSC AZA 56 V DIST AGEN2 A2 SG V AGENZ RSE V7 BH V OINLT IRSC 4300. 2500. SlD BB V OSFTl CSFTl S30 BH V 0C1 C1 322 BE V 0P21 C2 AZE BH V OARMZ CARMZ El 56 V INTSFT SINKl 82 56 V INTCl SINKZ E3 86 V INTC2 SINK3 E4 56 V INTCRMZ SINK4 DSFTDT 86 V DSFT INTSFT DC1DT 86 V DPCl INTCl DCZDT 86 V DPC2 INTC2 DRMDT 86 V DPRMZ INTCRHZ P1 88 V SFPMP 0PMP P2 BH V 0PMP RPMP SPLY BH V 0PM? CINLT P3 BB V OINLT CINLT DINLDT SG V DPINLT INTLT 38 86 V INTLT SINKB EXTLK 88 V OSFTI 1LEAK 800. -3200. LKFLO BB V 1LEAK SEATMLK ORIF BB V 1LEAK RLEAK ORFARE 56 V ORFAREA RLEAK 7500. —4100. NODE EQUATIONS Named_parameters: 43 1 CD 8.00000E-01 2 VISCOS 1.092008-06 3 RHO 8.50000E-06 4 AIRFRA 3.500008-02 5 WALDMP 1.SOOOOE+02 6 XWALL 1.00000E+06 _6000 Appendix C 9'“ JUL. :‘~.§\.‘_.‘..( :K-fl. -t_' HSPOOL HSPOOL 9 ASPOOL 10 WIDSPL 11 SPLMXX 12 KSPOOL 13 SPRELO 14 DCHMBR 15 VOLCHI 16 VOLCHZ 17 DRAFED 18 DAHPRT 19 PAREA 20 KSPRNG 21 FPRELD 22 PINMAX 23 KWALLZ 24 PMASS 25 CNOT 26 PATH 27 PSUPLY 28 NDRAFD 29 RIOVLP 30 R2OVLP 31 HSPLZ 32 CORNER 33 BRKI 34 BRKZ 35 BRK3 36 BILDUP 37 BLDUPZ 38 VSHFT 39 GAMMA 40 EMOD 41 PHPCVL 42 CREL 43 ORIFIC Number of outputs: Node: 3x2 Equation: Y_list F.816 Node: RX3 1.25000E-03 9.097603-05 5.015908-01 2.5106OE+00 2.815008-01 1.80000E+01 ‘ 2.992003+oo 50 Y - ZZSU70 X_list 0.825 E.Sl6 8.016508-01 3.36960E—02 2.024603-01 4.00000E—01 1.50000E+02 2.875003-01 4.00000E+00 4.95560E+00 3.250003-01 1.00000E+06 9.892803-05 1.70316E+01 1.014OOE+01 4.1162OE+01 5.00000E-01 9.50000E-02 1.61000E-01 1.250003-03 1.500003+01 1.000008-01 2.000008-01 3.000008-01 1.030003-01 2.03000E-01 1.727BOE+01 1.4000OE+00 1.72000E+05 1.727BOE+01 5.000008-01 5.000008-02 ( X: P ) 1(M9 1 2 6 Parameters HSPLZ RZOVLP CD VISCOS DCHMBR RHO Appnnhtc * 1'. Who-DI“! 1 10 Appendix C Equation: Y - ZZSU71 ( X, P ) 1 2 6 Y_list Y_list Parameters F.Sl9 Q.S25 HSPOOL E.Sl9 1.390008-01 CD VISCOS DCHMBR RHO Node: SEXI Equation: Y = CON ( x, P ) 1 0 1 Y_list X_list Parameters E.S31 PATM Node: R11 Equation: Y - 228069 ( X, P ) 1 2 6 Y_list x_list Parameters F.88 0.825 HSPOOL E.SB RIOVLP CD VISCOS DCHMBR RHO Node: RPQPG Equation: Y = 225076 ( x, P ) l 1 2 Y_list X_list Parameters F.812 H.812 VISCOS CORNER Node: TFPl Equation: Y a MUL ( x, P ) 1 2 1 Y_list x_1ist Parameters P.530A P.829 1.00000E+00 A Equation: Y - MUL ( X, P ) 1 2 1 Y_list x_list Parameters E.829 E.S3OA 1.00000E+00 A Node: TFPZ Equation: Y = GAIN ( x, P ) 1 1 1 Y_list x_list Parameters F.822A F.823 ASPOOL Equation: Y = GAIN ( x, P ) 1 1 1 Y_list x_list Parameters 8.823 E.822A ASPOOL Node: RSPL Equation: Y = ZZSU62 ( x, P ) l 1 4 Y_list Y_list Parameters ... f- 3? '1“.. 111 AppendixC E.827 F.827 VISCOS 1.80000E+00 WIDSPL HSPOOL Node: RWALLl Equation: Y - ZZSUGB ( x, P ) 1 2 4 Y_list x_list Parameters 8.828 0.825 WALDMP F.825 WALDMP 0.00000E+00 SPLMXX Node: CSPL Equation: Y - LIN ( x, P ) 1 1 2 Y_list x_list Parameters 3.825 0.825 SPRELO KSPOOL Node: CHALLl Equation: Y - ZZSU61 ( x, P ) 1 1 4 Y_list x_list Parameters E.824 0.524 0.00000E+00 SPLMXX KWALL KWALL Node: ISPL Equation: Y - ATT ( x, P ) 1 1 1 Y_list x_list Parameters P.826 P.826 MSPOOL Node: RSHF2 Equation: Y - ZZSU32 ( x, P ) l 1 3 Y_list x_list Parameters F.AZB E.AZB DRAFED 5.00000E-01 VISCOS Node: RSE Equation: Y = 225064 ( x, P ) 1 2 1 Y_list x_list Parameters F.V4 A2 CNOT E.V4 Node: SEX3 Equation: Y - CON ( x, P ) 1 0 1 Y_list x_1ist Parameters E.V5 PATH Node: RSC 1 12 Appendix C Equation: Y = 225064 ( x, P ) 1 2 1 Y_list x_list Parameters F.V6 A1 CNOT E.V6 Node: AREA Equation: Y = TABLE ( x, P ) 1 1 9 N 0.825 A -S.00000E+00 3.81760E-01 0.000008+00 3.817603—01 1.00000E-08 ASPOOL 1.00000E+01 ASPOOL OWNH Extend option: OFF Node: TFPINZ Equation: Y - GAIN ( x, P ) 1 1 1 Y_list X_list Parameters E.P2A E.A2PIN PAREA Equation: Y - GAIN ( x, P ) 1 l 1 Y_list x_1ist Parameters F.A2PIN F.P2A PAREA Node: RFREZ Equation: Y - 225054 ( x, P ) 1 2 6 Y_list x_1ist Parameters E.PZB F.PZB 1.16800E+00 F.PZB 1.00000E+00 5.50000E-01 1.00000E+00 3.50000E—03 VISCOS Node: RFRN2 Equation: Y - 225054 ( X, P ) l 2 6 Y_list x_list Parameters E.P2F F.P2P 9.99100E-01 F.P2F 1.00000E+00 7.50000E-01 1.00000E+00 8.500005—04 VISCOS Node: CPIN2 Equation: Y - 225019 ( X, P ) 1 1 8 Y_list X_1ist Parameters E.P2E 0.PZE KSPRNG FPRELD KWALLZ KWALL2 1 13 Appendix C 0.00000E+00 PINHAX 1.00000E+00 1.00000E+00 Node: RPINZ Equation: Y = 225020 ( x, P ) l 2 5 Y_list X_list Parameters E.P2C Q.P2E 0.00000E+00 P.PZC DAHPRT DAHPRT 0.00000E+00 PINHAX Node: IPIN2 Equation: Y - ATT ( x, P ) 1 1 1 Y_list x_list Parameters P.P2D P.P2D PHASS Node: TFRHZ Equation: Y - GAIN ( x, P ) 1 l 1 Y_list x_list Parameters E.PZG E.PZH PAREA Equation: Y = GAIN ( x, P ) 1 1 l Y_list x_list Parameters P.P2H P.PZG PAREA Node: 5EARM2 Equation: Y - CON ( x, P ) 1 O 1 Y_list x_list Parameters E.PZH PATH Node: 3x4 Equation: Y - 225072 ( x, P ) l 2 6 Y_list x_list Parameters F.85 0.825 HSPOOL 5.55 5.95000E-01 CD VISCOS DCHHBR RHO Node: SUM Equation: Y = SUM ( x, P ) 1 2 2 Y_list x_list Parameters VC D 1.00000E+OO V 1.00000E+00 Node: VGEN Equation: Y - POLSETRN( x, P ) 1 1 5 Y_list X_list Parameters Node: DELAY Equation: Y_list D Node: AGEN Equation: Y_list AA Node: AGEN2 Equation: Y_list A2 Node: CSFTl Equation: Y_list E.SlD Node: C1 Equation: Y_list E.530 Node: C2 Equation: Y_list E.522 Node: CARMZ Equation: Y_list E.A2E Node: DSFT Equation: 114 TIME BRKI 1.ZOOOOE+01 BRK2 0.00000E+00 BRK3 Y=PULSETRN(X,P) 1 1 5 x_list Parameters TIHE BRKl -1.2000OE+01 BILDUP 0.00000E+00 BLDUP2 Y - TRANSFER( x, P ) 1 1 4 X_list Parameters VC 1.00000E+03 1.00000E+00 8.33333E+01 0.00000E+OO Y = LIN ( x, ) 1 1 2 x_list Parameters A2A 1.00000E+OO -1.00000E+OO Y = ASGN ( x, ) 1 1 0 x_list Parameters E1 Y = ASGN ( x, ) 1 1 0 X_list Parameters E2 Y = ASGN ( x, ) 1 1 0 x_list Parameters E3 Y = ASGN ( x, ) 1 1 0 x_list Parameters E4 Y - 225012 ( AppaxfixC? Y_list DSFTDT Node: DPCl Equation: Y_list DClDT Node: DPC2 Equation: Y_list DC2DT Node: DPRMZ Equation: Y_list DRMDT Node: SFPMP Equation: Y_list P.Pl Node: RPMP Equation: N E.Pl x_list E Q E .SlD .825 1 Y - 225012 ( x, P ) x_list E Q E .830 .825 2 Y = 225085 ( x, P ) Y_list P Q E .822 .825 3 Y - 225012 ( x, P ) X_list F .A2C 0.PZE E Y - CON 4 ( x: P ) x_list Y-TABLE (11,9) 1 2.16400E+01 2 2.305008+01 3 2.458003+01 4 2.68400E+01 P.PZ 0.00000E+OO 8.200003-01 1.67000E+00 2.36500E+00 115 Parameters VSHFT 0.00000E+00 GAMMA 1.00000B+00 EMOD AIRFRA 1 3 6 Parameters VOLCHI ASPOOL GAMMA 1.00000E+00 EMOD AIRFRA 1 3 6 Parameters VOLCHZ ASPOOL GAMMA l.OOOOOE+00 EMOD AIRFRA 1 3 6 Parameters 2.75700E-01 PAREA GAMMA 1.00000E+00 EMOD AIRFRA 1 0 1 Parameters 1.022008+01 1 1 31 Appendix c ‘OQNJOUI 10 11 12 13 14 15 3.01600E+01 3.48200E+01 4.158OOE+01 4.39500E+01 4.580003+01 4.73300E+01 4.86IOOE+01 4.963OOE+01 5.046OOE+01 5.094OOE+01 5.11900E+01 2.80500E+00 3.220008+00 3.69000E+00 5.04SOOE+00 6.310003+00 7.44SOOE+OO 8.420003+00 9.180002+00 9.74SOOE+00 1.009SOE+01 1.022008+01 Extend option: OFF Node: CINLT Equation: Y - ASGN ( x, P ) Y_list X_list E.P3 EB Node: DPINLT Equation: Y = 22 Y_list DINLDT Node: RLEAK Equation: Y = ORIFICE ( X, P ) Y_list X_list F.0RIF E.ORIF ORFARE Node: SEATHLK Equation: Y - CON ( x, P ) Y_list x_1ist E.LKFLO Node: ORFAREA Equation: Y = CON ( x, P ) Y_list x_1ist ORFARE SORTED SYSTEM EQUATIONS 144 145 48 48 48 48 5012 ( x, P ) X_list P.P3 0.525 EB 48 48 48 1 16 Appendix C 1 1 0 Parameters 1 3 6 Parameters PMPCVL 0.00000E+00 GAMMA 1.00000E+00 EMOD AIRFRA 1 2 2 Parameters CD 5.00000E-Ol 1 0 1 Parameters PATM 1 0 1 Parameters ORIFIC 48 48 48 "'5; 121 122 123 124 136 137 138 139 INITIAL CONDITIONS 0825 - 0824 - P826 3 0P2E - PP2D ' XTFOOI - E1 = E2 8 E3 ‘ E4 = E8 = ALGEBRAIC VARIABLES Loops: 0 Nbr OUTPUT VARIABLES 1 0825 TIME CONTROLS Initial time - Final time = Number saved 8 END-OF-FILE 117 125 126 127 128 129 130 131 132 133 134 135 140 141 142 143 144 -6.2810E-06 -6.28108-06 1.3983E-07 3.2500E-01 3.2649E-08 1.20008-02 4.1343E+01 4.1341E+01 4.1344E+01 4.1343E+01 4.1344E+01 vbls: 0 0.0000E+00 9.5000E-02 951 AppnflhtC APPENDIX D NODE DESCRIPTIONS FOR NOMINAL DESIGN MODEL Node Name AREA Type SRC (Block) Power Domain Hydraulic Description Dictates the area available for pressure to act on the left side of the spool. When the spool is hard left (ie, touching i the wall), there is almost no surface on which the fluid ’ pressure can act except on a 1mm wide "X” provided on 32 the left face of the spool for this purpose. This block generates an area value for this surface depending on the '1‘... position of the spool. It is approximated by a table that 2’ assumes the full face of the spool is available to act upon only after the spool has moved 1.00E—08 cm away from the left wall. Equations Function TABLE Outputs Inputs Parameters A: QS25: None 3.81760E-01 —5.00 3.81760E-01 0.00 ASPOOL 1.00E-08 ASPOOL 10.00 A - Function of QSZS( varies from 0.38 to ASPOOL ) 118 Node Name 119 Appendix D Type SE Power Domain Hydraulic Description Even though this is an SE type node, it actually represents '-~ the hydraulic compliance of the fluid in the chamber on the left side of the spool. The hydraulic compliance of the fluid ‘ E depends on the air in the fluid, the bulk modulus of the i fluid, and the pressure on the fluid volume. Since there will . "‘ be both change in volume, and mass of the fluid in the volume the compliance of the fluid will keep changing. So the existing pressure, volume and flow are used to re- ‘ 5, compute the final pressure in this chamber. This complex set V of computation is achieved with a combination of this SE ' type node, and a set of signal blocks that are given seperately elsewhere on the system bond graph (to make the graph easier to read). The signal blocks related to this node are DPCl, INTCl and SINKZ. Equations Function ‘ ASSIGN 120 Appendix D Node Name C2 Type SE Power Domain Hydraulic Description Even though this is an SE type node, it actually represents the hydraulic compliance of the fluid in the chamber on the right side of the spool. The hydraulic compliance of the fluid depends on the air in the fluid, the bulk modulus of the fluid, and the pressure on the fluid volume. Since there will be both change in volume, and mass of the fluid in the volume the compliance of the fluid will keep changing. So the existing pressure, volume and flow are used to re- compute the final pressure in this chamber. This complex set of computation is achieved with a combination of this SE type node, and a set of signal blocks that are given seperately elsewhere on the system bond graph (to make the graph easier to read). The signal blocks related to this node are DPC2, INTC2 and SINKB. Equations Function ASSIGN Outputs Inputs Parameters ,5 13322 E3 NONE 1 i 3 Equation 5822 - E3 Description 121 Appendix D I Node Name C SPL ‘ I Type C Power Domain Mechanical Description This capacitance element represents the spool spring on the 11' ght side of the spool. This spring is preloaded with a certain force and pushes the spool against the left wall in the absence of any other imbalance of forces. E? F .11 Equations Function LIN . Outputs Inputs Parameters , E825 QSZS SPRELO KSPOOL Equation E825 = SPRELO + KSPOOL * QSZS 122 Appendix D Node Name CWALLl Type C Power Domain Mechanical Description Represents the wall on either end of the spool chamber. The wall is modelled as a very stiff spring. {... Equations Function ' ZZSU61 it Outputs Inputs Parameters E824 Q824 0.00 If SPLMXX KWALL KWALL Equation E824 - ZZSU61 (Q824; Parameters) Node Name 123 Appendix D DPCl . Type SRC (Block) Power Domain Hydraulic Parameters 3' Description This is a computational node directly linked and to support C1. It considers the existing pressure in the C1 chamber , E". the mass of fluid flowing in/out, and the size of the ' chamber in order to calculate the pressure difference in the chamber as a result of the fluid flow. Equations VOLCHI ASPOOL GAMMA 1.00 EMOD AIRFRA Equation DClDT - ZZSU12 ( F830, Q825, E2; Parameters) Description 124 Appendix D Node Name DPC2 Type SRC (Block) Power Domain Hydraulic Description This is a computational node directly linked and to support C2. It considers the existing pressure in the C2 chamber , the mass of fluid flowing in/out, and the size of the chamber in order to calculate the pressure difference in the chamber as a result of the fluid flow. Equations . Equation ; Description I Function ZZSU85 Outputs Inputs Parameters DC2DT F822 VOLCHl QSZS ASPOOL E3 GAMMA l .00 EMOD AIRFRA DC2DT - ZZSU85 (F822, Q825, E3; Parameters) 125 Appendix D INTCl Type INT (Block) Power Domain Hydraulic Description This node integrates the output of the DPCl node to compute the final pressure in the Cl chamber. Equations [ is set by software ] E2 - INTEGRAL (DClDT) Node Name 126 Appendix D Type INT (Block) Power Domain Hydraulic Description This node integrates the output of the DPC2 node to compute the final pressure in the C2 chamber. Equations [ is set by software ] Equation 127 Appendix D Power Domain Mechanical Description Represents the inertia of the spool body. The mass of the spool is calculated from the density of the material and the volume of the spool. Equations Function Equation Description 128 Appendix D Node Name RPQPG Type R Power Domain Hydraulic Description This is the resistance to fluid flow in the pressure equalizing passage that connects the chamber on the left hand side of the spool to the control port chamber of the spool valve. The side view (as seen in various figures of the spool valve) of this passage is like a ”'1‘". This passage is considered as three different resistance paths in series. Since the fluid tums a corner, the comer resistance is estimated as being a multiple of the least resistance. Equations Function I ZZSU76 Outputs Inputs Parameters F812 E812 VISCOS CORNER Equation F812 - ZZSU76 (E812; Parameters) Type Power Domain Mechanical Description This is the translational resistance on the spool. It is a fluid friction effect. Fluid layers are sheared when the spool moves within the chamber filled with oil. 80 this resistnace is proprotional to fluid viscosity. ZSSU62 Parameters VISCOS 1.800 WIDSPL 130 Appendix D RWALLl R Power Domain Mechanical Description This resistive element represents the damping by a wall when an object hits the wall. Since the walls in the spool chamber are modeled as very stiff springs, some amount of bounce may be seen when the spool hits against the walls. This is damped out by this R element. The nature of the resistance is such that it damps only when the spool moves into the wall and not when it moves out. The damping co-efficient is a named parameter that can be tuned to obtain realistic responses of damping and bounce as observed in experiments. Equations Parameters WALDMP F825 WALDMP 0.00 Name Type 11 Power HYDRAULIC Domain Description This is the resistance between the inlet port and the control port of the spool valve. This R changes as the spool moves...the opening seen by the oil coming through the inlet gets bigger as the spool moves to the ‘1er wall of the chamber. The nature of the resistance changes from an orifice flow to be an annular type of flow. The flow calculations depending on the position of the spool and the pressure difference between the two regions are done in a subroutine. There is a transition region that is defined so that the two kinds of flow curves are smoothly patched up together. Equations Equation Description i I 132 Node Name RXZ Type R Power Domain Hydraulic Description This is the resistance to flow of oil between the control port and the drain port The nature of the resistance is the same as RX]. The flow calculations depending on the spool position and the pressure difference between the two regions are made in a subroutine. Again there is a transition region that is defined so that the two kinds of flow curves are smoothly patched up together. Equations Function ZZSU70 F816 - ZZSU70 (Q825, E816; Parameters) Node Name 133 Appendix D Type Power Domain Hydraulic Description This is the resistance between the control port and the port that talks to the solenoid valve part of the Solenoid-Spool valve combination. The flow through this resistance never becomes an orifice type by virtue of the geometry of the spool valve; it is always annular flow and allows a very small flow. The flow calculations according to the pressure difference between the chambers are made by a subroutine. Equations Function Parameters HSPOOL E819 1.39E-01 CD VISCOS DCHMBR RHO Appendix D Node Name RX4 Type R Power Domain Hydraulic Description This is the resistance to flow between the inlet port and the chamber on the left of the spool. By virtue of the geometry this will always be an annular type of flow, with the length of the passage changing with spool position. The flow calculations are made by a subroutine. Equations Function ZZSU72 Outputs Inputs Parameters F85 QSZS HSPOOL E85 5.95E-01 CD VISCOS DCHMBR RHO Equation F85 - ZZSU72 (0825, E85; Parameters) Description Node Name Type Power Domain Hydraulic Description Represents a drain. It is considered to be a port which is at atmospheric pressure. It is assumed to be a pressure source that can handle infinite flow. Function Node Name 136 Appendix D TFPI Type TF Power Domain Hydraulic <-> Mechanical Description This transformer represents the interface between the hydraulic and mechanical domains on the left side of the spool. It converts the pressure acting on the left side of the spool into a force acting on the left side of the spool. The area on which this pressure acts is determined by the AREA block described above. Equations Function I MUL Outputs Inputs Parameters FS30A F829, A 1.00 E829 ES30A, A 1.00 Equation F830A - 1.00 * A * F829 Description E829 - 1.00 * A * ES3OA Node Name Type Power Domain Hydraulic <-> Mechanical Description This transformer represents the interface between the hydraulic and mechanical domains on the right side of the spool. It converts the pressure acting on the right side of the spool into a force acting on the right side of the spool. The area on which this pressure acts is constant. Parameters ASPOOL ASPOOL Equation F822A - ASPOOL * F823 Description 5523 - ASPOOL * E822A Node Name Type FCN (Block) Power Domain Hydraulic Description Generates the area for the orifice functions RSC and RSE. What we know (from COLTECH) is that the ports open and close in a certain amount of time, once the command is given. The two openings of RSE and RSC are inversely related. When one closes, the other opens. This block generates the area curve for one of them according to a first order lag. The area for the other resistance is generated by a block Equations 1.00E+03 1.00 83.333 0.00 Equation AGEN2 139 Appendix D FCN (Block) Power Domain Hydraulic Description This block is directly tied to the block AGEN. Once AGEN generates a curve for the area for one of the resistances (RSC or RSE), since the other resistance is inversely tied to it, this block generates an inverse curve to that generated by AGEN. Equations Function Equation Node Name DELAY Type SRC (Block) Power Domain Electrical Description When there is a moded switch from the regulation mode to the high pressure mode of the spool valve, the solenoid valve opens the port between the supply and the control form nearly zero to maximum; and the port between supply and exhaust is closed simultaneously. There is a 3 millisecond flux build-up time required by the coil in the solenoid valve to build up the neccessary force to move the valve. This 3 millisecond delay is artificially built up by this DELAY node. It has to be mentioned that the delay is rigidly coupled with the pulsetrain from the VGEN block and hence any changes to the width of the pulse or the magnitudes in VGEN should be accompanied by a corresponding change in this block. Equations Equation Description 141 Appendix D Type R Power Domain Hydraulic Description The resitance between the supply to the solenoid valve and the control port that talks to the spool valve. Assumed to be an orifice type of flow through this resistance. The orifice equation is timed according to actual flow numbers obtained on a real solenoid valve by COLTECH engineers. We knew the maximum flow through the valve at a certain pressure of the supply. The flow is determined by the area of the orifice, which in turn is dictated by an area generating block called AGEN, where the area changes by a first order lag. Node Name 142 Appendix D Type Power Domain Hydraulic Description The resitance between the supply to the solenoid valve and the exhaust port that talks to the drain. Assumed to be an orifice type of flow through this resistance. The orifice equation is tuned according to actual flow numbers obtained on a real solenoid valve by COLTECH engineers. We knew the maximum flow through the valve at a certain pressure of the supply. The flow is determined by the area of the orifice, which in turn is dictated by an area generating block called AGENZ, where the area changes by a first order lag. Function 5 ZZSU64 Outputs Inputs FV4 A2 EV4 FV4 - ZZSU64(A2, EV4; CNOT) 143 Appendix D Node Name SEX3 Type SE Power Hydraulic Domain Description This represents the drain. The drain is assumed to be at atmospheric pressure. Equations Function . CON — —*——— —- —— ——— — —:=l-=_===g——— — —— — __,_ — —— Outputs Inputs Parameters { EVS None PATM i._ L __ __ _ ____________ - _ -___.____________ _ ___- ___ __ 3 Equation Evs - PATM 144 Appendix D ___l Node Name VGEN Type SRC (Block) Electrical Generates a pulse train of 50 milliseconds long of 0 volts and 12 volts alternately. It is meant only to switch between the two modes of the spool valve. This is not part of the real solenoid valve design. It has been included only so that various runs can be conducted between the two modes of operation of the VDE. Parameters 145 Appendix D Node Name CSFTl Type SE Power Domain Hydraulic Description It is like a hydraulic C element and represents the compliance effects of the fluid in the rocker shaft. The rocker shaft is considered to be a relatively large volume with no other effects. The compliance calculations are made in a similar manner to the C1 and C2 elements mentioned in the Spool valve description. There is no moving piston here and hence no volume changes need to be considered when computing the pressure due to fluid flow in/out. The signal block that does the computation for this node are DSFI‘, INTSFT and SINKl. Equations Function ASGN Outputs Inputs Parameters ll-i'ulu- r 1' {(15 0"“ In Node Name Type SRC (Block) Power Domain Hydraulic Description This is a computational node directly linked and to support CSFTl. It considers the existing pressure in the Cl chamber , the mass of fluid flowing in/out, and the size of the chamber in order to calculate the pressure difference in the chamber as a result of the fluid flow. Equations Parameters VSHFT 0.000 GAMMA 1.00 EMOD AIRFRA Equation DSFTDT - ZZSU12 (F81D,Q825,E1; Parameters) Description Note: The same function (ZZSU12) as in DPCI is used here to compute the change in pressure; the physical volume of the Rocker Shaft remains constant(VSHFT). In ZZSU12 the physical volume of the chamber is computed as: Vt = VSHFT + P(2)*QSZS, where the 1st term on the right is the initial volume and the 2nd term accounts for the geometric change in volume. So to maintain a constant volume for all computations by this subroutine for this node, we pass 0.0 as the area in the above equation - thus P(2)=0.0. 7.4- .____ ___. ___ _ _ _*_ _ . ,.fi.e_, _ _‘_.___.__,_______—. r _ ~_.__4 147 Appendix D Node Name INTSFT Type INT (Block) Power Domain Hydraulic Description This node integrates the output of the DSFI‘ node to compute the final pressure in the ROKER SHAFT chamber. 'F Equations Function [ is set by software ] Parameters None Equation Description Node Name 148 Appendix D CARM2 (CARMB) Type SE Power Domain Hydraulic Description This is the hydraulic compliance element for the fluid in the rocker arm. The details of the modelling are the same as in the case of C1. Except that in this case moving piston is the pin. The computing blocks related to this node are DPRM(2), INTCRMZONTCRM3) and SINK4 (SINKS). Equations Equation 149 Appendix D Node Name CPIN2 (C PIN3) I Type C 3 Power Domain Mechanical l 1 Description Models the pin spring. This spring has a preload which pushes the pin to the "left” wall such that the pin tends to stay in an engaged position with the other half of the rocker arm in l the absence of any unbalanced force. Equations £9213 (EP3E) QP2E (QP3E) KSPRING FPRELD KWALLZ KWALLZ 0.00 PINMAX l .0 l .0 __ _ A- _ .A v“. __ - L -_ L, -7- L 7. #_ L , , .7- v ,4- _ — ___ ... A. , ._e if _ if __‘ Equation EPZE - ZZSU19 (QPZE; Paramaters) Description 150 Appendix D Node Name DPRMZ (DPRM3) Type SRC (Block) Power Domain Hydraulic Description This is a computational node directly linked and to support CARM2(CARM3). It considers the existing pressure in the rocker arm chamber , the mass of fluid flowing in/out, and the size of the chamber in order to calculate the pressure difference in the chamber as a result of the fluid flow. Equations ' ZZSU12 Parameters FAZC (FA3C) 2.757e-01 QPZE (QP3E) PAREA E4 (ES) GAMMA 1.00 EMOD AIRFRA DRMDT - ZZSU12 (FA2C,QP2E,E4; Parameters) 151 Appendix D INT (Block) Power Domain Hydraulic Description This node integrates the output of the DPRM2 (DPRM3) node to compute the final pressure in the rocker arm chamber. Equations ' i [ is set by software ] Parameters E4 - INTEGRAL(DRMDT) Power Domain Mechanical Description Represents the inertial effects due to the mass of the pin. Equations 152 Appendix D _ Node Name “___—"__le _—.l Type R ll Power Domain Hydraulic ! Description This is the hydrodynamic damping force on the engagement 1 length of the pin. It is similar to RSPL in its physics. l Equations Function ZZSU54 E _ Outputs— 9v "___ ”We ' 7 i 153 Appendix D Node Name RFRNZ I Type R l Power Domain Mechanical Description This is the hydrodynamic damping force on the non-engagement length of the pin. It is similar to RSPL in its physics. l Equations Function ZZSUS4 : __ __ _____..___ .fi"_____ e__.___e_ _flme is _ _~___V_L --_ _-____L- Rafi Outputs Inputs Parameters l i EP2F FP2F 9.991E-01 l FP2P 1.00 l 7.5E-01 . 1.00 : 8.5E-04 l VISCOS l l Equation EPZF - ZZSU54 (FP2F; Parameters) Description l l 154 Appendix D Node Name RPINZ Type R Power Domain Mechanical Description This effect is exactly the same as RWALLl in the solenoid- spool. In this case the damping is meant for the bounding walls .. of the pin. 5 Equations Function zzs U20 L Outputs Inputs Parameters _ F EPZC QP2E 0.00 L FP2C DAMPRT “ DAMPRT 0.0 PINMAX Equation EP2C - ZZSU20 (QP2E, FP2C; Parameters) Description 155 Appendix 1) Node Name Type SE Power Domain Hydraulic Description Represents the atmospheric pressure acting on the mixture of oil and air on the ”right” side of the pin. Equations Equation EP2H - PATM Description Power Domain Hydraulic <-> Mechanical Description Transforms the pressure acting inside the pin chamber to a force on the pin piston according to the area of the pin(piston) face . Equations Function 3 GAIN Outputs Inputs Parameters L EP2A EA2P1N PAREA FA2PIN FP2A PAREA EP2A - PAREA * EAZPIN FA2PIN * PAREA * FP2A Node Name Type Power Domain Mechanical <-> Electrical 5 Description The interface between the pin piston and the oil and air on the L far (”right") side of the pin. Essentially atmospheric pressure L acts on the pin from this side. L l Equations Function . GAIN L __________ A- _ _ ___ ___L Outputs Inputs Parameters 1 EPZG EP2H PAREA FP2H mo PAREA L Equation EP2G - PAREA * EP2H L FP2H - PAREA * FPZG 157 Appendix D NAMED PARAMETERS The following is a listing of all the named parameters used in the model. The names, what they represent and the pertinent calculations ( if required ) are shown. A spread sheet in EXCEL that will automatically do all these calculations is also provided together with the model. Fixed Value NAMED PARAMETERS: l. AIRFRA The fraction (per 100 parts ) of air in the oil. 3.5% 2. BRKI This is a parameter developed only for simulation runs. Sets the length of the pulse train of the signals that switch between modes. In the current version, it was chosen as 50 milliseconds in each mode. 3. CD The coefficient of discharge for all the various orifices. It is assumed to be a constant 8.00E-01 4. CORNER The timing factor for the corner resistance in RPQPG: 15 times Rl( resistance of the shorter passage ) 5. CNOT The constant multiplier for the orifice flow in the solenoid valve. Knowing the maximum flow at a given pressure and assuming the area to be 1 unit, this constant is computed. 170 6. DAMPRT The damping coefficient of the pin chamber walls: 150 N sec/cm 7. DCHMBR The diameter of the spool chamber: 8.0165E-01 cm 10. ll. 12. 13. 14. 15. 16. 17. 158 Appendix D DSPOOL Spool diameter: (Larger section) 7.9915E-01 cm DRAFED The diameter of the feed hole that feeds oil into the DRA. This hole is in the rocker shaft; 4.00E-01 cm EMOD The bulk modulus of the oil (10 W 30) : 1.7200E+05 Nlcm’ FPRELD The preload on the pin spring: 4.9556 N (the equivalent of 25psig acting on the pin area) GAMMA The ratio of specific beats for air: 1.4 KSPOOL The stiffness of the spool spring. Given by COLTECH as 18 Nlcm KSPRING The stiffness of the pin spring: 4.00 Nlcm KWALL The stiffness of the wall ( which is modeled as a very stiff spring). 1.000E+06 Nlcm KWALL2 The stiffness of the wall in the pin chamber: 1.000E+06 Nlcm MSPOOL This mass of the spool was calculated knowing the spool geometry and the spool material density. Volume of spool - 1.137198 cm3 Material - SS 303: 18% Cr, 8% Ni Density = 8 grams / cm3 - 8.00E—05 N sec2/cm‘ l8. 19. 20. 21. 22. 23. 159 Appendix D Mass = 9.09760E-05 N sec’lcm NDRAFD The diameter of the feed hole that feeds oil into the DRA. This hole is in the rocker shaft: 5.00E-01 cm PATM The atmospheric pressure: 10.14 Nlcm’ PMASS The mass of the pin: 9.89280E-05 N sec’lcm PSUPLY The supply pressure from the pump: 41.162 Nlcm’ ( equivalent of 45 psig) R110 The density of oil. 0.85 grams] cm3 - 8.5 E-06 N sec’ [cm SPRELO The preload on the spool spring. 2.992 N 160 Appendix D 24. VISCOS The viscosity of the oil. It is temperature dependent. A table of viscosity VS temperature I L— .. . - -—_____ ___ ______~___‘__ _ ___—# 100 5.64 E-06 2.37 E—06 1.092 E-06 ===u=====a== 25. WALDMP The damping coefficient of the wall. 150 N sec/cm 161 Appendix D Derived NAMED PARAMETERS: l. ASPOOL The area of the spool face: 5.0159E-01 cm‘2 2. BILDUP BRKI + 3 millisec - 53E-02 sec. (where 3 ms is the time for flux buildup) 3. BRKZ The 2nd breakpoint for the pulsetrain: 2 * BRKl - 100 millisec 4. BRK3 The 3rd breakpoint for the pulsetrain: 3 * BRK] = 150 millisec 5. HSPLZ The clearance between the spool and its chamber at the RX2 end: 1.25E-03 cm 6. HSPOOL The clearance between the spool OD and the spool chamber l.D. Calculated from spool and chamber diameters: 1.2500E-03 cm 7. PAREA The area of the pin face: 2.875E-0l cm‘2 8. PINMAX The maximum distance that the pin can travel between walls: 325E-0l cm ‘2 10. 12. l3. 14 15 10. 11. 12. 13. 14. 15. 162 Appendix D RlOVLP The distance the spool travels till RXl enters into the transition region from orifice flow to annular flow. This is the distance that the spool travels before the larger diameter of the spool completely overlaps the inlet port: 9.5E-02 cm RZOVLP The same concept as in RIOVLP. Except that inthis case the flow regime changes from an annular to an orifice type, with a transition in between: 1.6lE-01 cm SPLMXX The maximum distance spool can travel between walls: 2.815E-01 cm VOLCIIl The volume of the chamber on the left side of the spool when the spool is hard left ( the "X” on this face ): 3.3696E—02 cm‘3 VOLCH2 The volume of the chamber on the right side of the spool when the spool is hard left: 2.0246E-01 cm‘3 VSHFI‘ The volume of the rocker shaft: 1 .7278E+0l cm “ 3 WIDSPL The cicumference of the spool's maximum diameter. 2.5106 cm m— X—a—Zfla—a~< 163 vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvadbmfld.DIIO an. I ausuou . n> \ anon . I an s I .n.u .Oooondhon o o‘.«. \ C I nu.- uoom vocauodcs u=o>oum _ .o.v.u .undavnul I 0306 luau c Icons I anon IUCQ I ‘ illouxov.u . ov.n. I o Anaouooafido.alldu.\AuuovOIIouacuv I A .IIIquou.H..aauIa I «u .u«ou.ou.u.\.uoau. 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