Figure 4-7 Controller scheme of the cam-less intake process. ........................ ..... The cylinders and end-plugs are made from aluminum 6061, the ultimate tensile.
FACULTY OF ENGINEERING AND TECHNOLOGY
DEPARTMENT OF MECHANICAL AND MECHATRONICS ENGINEERING
CAM-LESS ENGINE MANAGEMENT UNIT
Prepared by: AbdelRahman A Hijawi 1132067
Supervised by: Dr. Mohammad Kara’een
A Graduation Project submitted to the Mechanical and Mechatronics Engineering Department in partial fulfillment of the Requirements for the degree of B.Sc. in Mechanical/Mechatronics Engineering Birzeit © June, 2018
TABLE OF CONTENTS
Table of Contents ............................................................................................. I LIST OF ABBREVIATIONS........................................................................ IV NOTATIONS................................................................................................. V LIST OF TABLES ....................................................................................... VII LIST OF FIGURES.................................................................................... VIII ABSTRACT ................................................................................................... 1 الملخص.............................................................................................................. 2
CHAPTER 1 : LITERATURE REVIEW ...................................................... 3 CHAPTER 2 : PROBLEM FORMULATION .............................................. 5 2.1
Expected Benefits .............................................................................. 6
2.2
Limitations ......................................................................................... 6
2.3
Test Engine ........................................................................................ 7
CHAPTER 3 : CAM-LESS ENGINE EHVT DESIGN ................................. 8 3.1
Valve Train CAD Model .................................................................... 9
3.1.1 3.2
Cylinder Train........................................................................... 10
Hydraulic System ............................................................................. 10
3.2.1
Hydraulic Circuit ...................................................................... 12
3.2.2
Cylinder Design ........................................................................ 13
3.2.3
Piston and Rod Design .............................................................. 15
3.2.4
Seals ......................................................................................... 17
3.3
Electrical Circuits of the ECU .......................................................... 18
3.3.1
Sensors’ Circuits ....................................................................... 18
3.3.2
High Power Circuits .................................................................. 20
3.3.3
Electrical Circuits Components ................................................. 22
I
CHAPTER 4 : MODELLING AND CONTROLLING ............................... 25 4.1
Model Derivation ............................................................................. 26
4.1.1
System Equations ...................................................................... 27
4.1.2
State Equations ......................................................................... 36
4.2
Controller Design ............................................................................. 37
4.2.1
Plant Subsystems ...................................................................... 39
4.2.2
Inner Loop Adaptive PID Control ............................................. 39
4.3
Single Cylinder Simulation .............................................................. 41
4.3.1
Intake Dynamics ....................................................................... 42
4.3.2
Pumping Losses ........................................................................ 45
4.3.3
Piston Dynamic Analysis .......................................................... 46
CHAPTER 5 : ENGINE MANAGEMENT UNIT ...................................... 48 5.1
Position Signals ................................................................................ 49
5.2
Setting Real Time Engine Parameters............................................... 52
5.2.1
Volumetric Efficiency (VE) ...................................................... 52
5.2.2
Air to Fuel Ratio (AFR) ............................................................ 53
5.2.3
Injector’s Pulse-width (𝝉𝒊) ........................................................ 54
5.2.4
Ignition Pulse ............................................................................ 56
5.3
FPGA Processor ............................................................................... 58
5.3.1
CKP Interpreting Loop .............................................................. 59
5.3.2
Pulse Generation ....................................................................... 60
5.3.3
EHVT Controller Implementation ............................................. 62
5.3.4
Sequence Halting ...................................................................... 64
5.4
RT Processor .................................................................................... 64
5.4.1
Main Loop ................................................................................ 65
5.4.2
Input and Output Loop .............................................................. 66
5.4.3
Components Loop ..................................................................... 67
II
5.4.4
Run and Error Logging ............................................................. 67
CHAPTER 6 : EXPERIMENT AND VALIDATION ................................. 69 CHAPTER 7 : CONCLUSIONS................................................................. 70 REFERENCES ............................................................................................. 71 APPENDIX A ............................................................................................... 76 APPENDIX B ............................................................................................... 77 APPENDIX C ............................................................................................... 79 APPENDIX D ............................................................................................... 81
III
LIST OF ABBREVIATIONS
ABDC After bottom dead center
IAT
Inlet air temperature
ADC
Analog to digital converter
ICE
Internal combustion engine
ATDC
After top dead center
IGBT
Insulated gate bipolar transistor
BBDC
Before bottom dead center
ISO
International standardization organization
BDC
Bottom dead center
IVC
Intake valve opens
BTDC
Before top dead center
IVO
Intake valve opens
CAD
Computer aided design
MAF
Manifold air flow
CKP
Crankshaft position
MAP
Manifold Absolute pressure
CLT
Coolant temperature
CMP
Camshaft position
MOSFET Metal-oxide semiconductor fieldeffect transistor PID Proportional integral derivative
DAQ
Data Acquisition
PWM
Pulse-width modulation
DOHC Dual overhead camshaft
RPM
Revolutions per minute
ECU
Engine control unit
TDC
Top dead center
EHVT
Electrohydraulic valvetrain
VE
Volumetric efficiency
FPGA
Field-programmable gate array
VR
Variable Reluctance
IV
NOTATIONS
[𝑚 ]
𝑙
The piston rod length
[𝑚]
[𝑚 ]
𝑚
𝐴
Intake port area
[𝑚 ]
𝑚
Cylinder air mass charge Mass of fuel in the cylinder Mass of leftover fuel
[𝐾𝑔]
𝐴
Inner area of hydraulic cylinder Orifice area of the directional valve Runner area
𝐷
Bore diameter of the cylinder The modulus of elasticity Flow force
[𝑚]
𝑚
[𝑃𝑎]
𝑚
[𝑁]
𝑟
Approximated runner [𝐾𝑔] mass Manifold air mass [𝐾𝑔] charge Critical pressure ratio -
[𝑁]
𝑟
The crank radius
[𝑚]
[𝑚 ]
𝑟
Internal radius of the cylinder
[𝑚]
𝐿
Electromagnetic force The smallest area moment of inertia of the cross section Column length
[𝑚]
𝑟
[𝑚]
𝑃
𝑖 th cylinder pressure
[𝑃𝑎]
𝑡
External radius of the cylinder Injector opening time
[ms]
𝑃
Load pressure
[𝑃𝑎]
𝑥
Load displacement
[𝑚]
Supply pressure of system Atmospheric pressure ~1*105 Cylinder pressure
[𝑃𝑎]
𝑥
[𝑚]
[𝑃𝑎]
𝑥
Engine’s piston position Spool displacement
[𝑃𝑎]
𝜁
-
Exhaust pressure
[𝑃𝑎]
𝜂
𝑃
Manifold pressure
[𝑃𝑎]
𝜎
Damping coefficient of the gas velocity model Volumetric efficiency Radial stress
𝑄
Flow rate in system
[𝑚 / 𝑠]
𝜎
Tangential stress
[𝑃𝑎]
𝑅
Gas constant
[𝐽/ 𝐾𝑔𝐾]
𝜏
Injector pulse-width
[ms]
𝑇
Inlet air temperature
[𝐾]
𝜔
[𝑟𝑎𝑑/ 𝑠]
𝑇
Sampling time
[𝑠]
𝐸
Natural frequency of the gas velocity model Pumping losses
𝐴 𝐴
𝐸 𝐹 𝐹 𝐼
𝑃 𝑃 𝑃
𝑃
[𝑚 ]
𝑚
V
[𝐾𝑔] [𝐾𝑔]
[𝑚]
[𝑃𝑎]
[𝑊]
𝑉
𝑖 th cylinder volume
[𝑚 ]
𝐾
𝑉
Initial volume of driving chamber Clearance volume
[𝑚 ]
𝐿
[𝑚 ]
𝑁
[𝑚 ]
𝑊
𝑉
Displacement volume Manifold volume
[𝑚 ]
𝑎
𝑉
Runner volume
[𝑚 ]
𝑐
𝑉 𝑉
𝑐 𝑘
The column effective length factor Coil inductance
-
Revolutions per minute Load force on the end-plug Spool’s stroke
[RPM]
𝑏
Damping constant of the spool
[𝑁. 𝑠/ 𝑚]
Discharge coefficient of the directional valve Compression ratio -
𝑏′
Damping constant of the load
[𝑁. 𝑠/ 𝑚]
𝑘
[𝑁/𝑚]
Runner calibration factor
𝑘′
Spring constant of the spool Spring constant of the load
-
VI
[𝐻]
[𝑁] [𝑚]
[𝑁/𝑚]
LIST OF TABLES
Table 2-1 Test engine parameters. ................................................................... 7 Table 3-1 ISO 68 hydraulic oil characteristics. .............................................. 11 Table 3-2 D1VW DCV series specification. .................................................. 12 Table 3-3 Piston seals types, description and CAD. ....................................... 17 Table 3-4 IRFZ44n electrical characteristics. ................................................. 22 Table 3-5 IRG4PC50UD electrical characteristics. ........................................ 23 Table 3-6 BC557 electrical characteristics. .................................................... 23 Table 5-1 Test engine injectors' characteristics. ............................................. 56 Table 5-2 Error codes and description logged by the ECU in the components loop. .................................................................................................................. 68
VII
LIST OF FIGURES
Figure 3-1 CAD model of the assembly of the proposed EHVT. Consisting of two structures: (the hydraulic cylinders and cylinder train) and the DCVs array. .. 9 Figure 3-2 Cylinder train CAD based on the test engine's camshaft cover dimensions (usually where engine oil is poured in the engine). .......................... 10 Figure 3-3 DCV symbolic and detailed schematics. ....................................... 11 Figure 3-4 Hydraulic circuit of the proposed EHVT. ..................................... 12 Figure 3-5 Cutout section of the hydraulic cylinder. ...................................... 13 Figure 3-6 Stress distribution in thick walled cylinders. ................................. 14 Figure 3-7 Engine sensors connection circuit design. ..................................... 19 Figure 3-8 The differential input circuit for the CKP signal. .......................... 19 Figure 3-9 MOSFET driver power circuit design with load R5. ..................... 20 Figure 3-10 IGBT ignition coil driver power circuit design. .......................... 21 Figure 3-11 Schematic symbol and pinout of the IRFZ44z MOSFET. ........... 22 Figure 3-12 Schematic symbol and pinout of the IRG4PC50UD IGBT.......... 23 Figure 3-13 Schematic symbol and pinout of the BC557 BJT. ....................... 24 Figure 4-1 Series RL circuit. ......................................................................... 27 Figure 4-2 DCV servo valve section and free body diagram of the spool forces. .......................................................................................................................... 29 Figure 4-3 Free body diagram of the hydraulic piston and intake valves assembly. ........................................................................................................... 31 Figure 4-4 System variables on the EHVT and engine assembly.................... 33 Figure 4-5 The desired lift reference signal with 𝑢𝑙= 5 mm and 𝑢𝑑= 160o. .... 37
VIII
Figure 4-6 Desired air mass charge and valve profile requirements, the table can be found in appendix B. ..................................................................................... 38 Figure 4-7 Controller scheme of the cam-less intake process. ........................ 38 Figure 4-8 The plant subsystems layout. ........................................................ 39 Figure 4-9 PID gains at different operating points 𝑥𝑙. .................................... 40 Figure 4-10 Step response of the systems, comparing the response with a single nominal controller and the lift dependent controllers. ......................................... 40 Figure 4-11 Simscape simulation of a closed loop double acting hydraulic cylinder.............................................................................................................. 41 Figure 4-12 Comparison between camshaft generated profile and the 𝑥𝑙. ...... 42 Figure 4-13 The effect of changing oil pressure on the 𝑥𝑙. ............................. 42 Figure 4-14 Different 𝐷𝑐 effect on the response. ........................................... 42 Figure 4-15 𝑥𝑙 at different engine speeds. ...................................................... 42 Figure 4-16 𝑃𝑐4(𝜃) during the two cycles. .................................................... 43 Figure 4-17 Cylinder, manifold and runner pressures in the 𝜃 domain. .......... 43 Figure 4-18 The 𝑚𝑐𝑖 comparison between the proposed valve train (solid) and the camshaft (dashed). ....................................................................................... 44 Figure 4-19 Engine's PV diagram at 1000 RPM and 𝑢𝑙=3 mm and 𝑢𝑑=110o , both intake valve actuation methods are compared at the un-throttled operation. 45 Figure 4-20 Crankshaft and piston simplified geometry. ................................ 46 Figure 4-21 Fourth piston dynamics with 𝑙𝑝𝑟=8 cm and 𝑟𝑐𝑘=3 cm, at idle (800 RPM) for 720 degrees in the crankshaft domain. ................................................ 47 Figure 5-1 Application flow chart showing the interactions of each RT and FPGA programs. ................................................................................................ 48 Figure 5-2 Crankshaft position sensor configuration and conditioning circuit. [ [33], retrieved May 16, 2018)] ........................................................................... 50
IX
Figure 5-3 CKP and CMP sensors signals in the 𝜃 domain with (𝑇𝑠=5us). Processed variables show the program’s output after processing both signals. .... 51 Figure 5-4 VE map, the table can be found in appendix B. ............................ 53 Figure 5-5 Spark advance corresponding to engine speed plot, the table can be found in appendix B. .......................................................................................... 57 Figure 5-6 Loop flow chart of the FPGA program. ........................................ 58 Figure 5-7 CKP signal and the falling edge trigger together plotted against 𝜃. 59 Figure 5-8 SingalstoAngleStroke.vi inputs and outputs.................................. 59 Figure 5-9 Valve lift response to changing commands of the EHVT controller. .......................................................................................................................... 63 Figure 5-10 A loop flow chart of the real- time program. ............................... 64 Figure 5-11 Main screen interface with simulated idle signals. The log is also showing the cranking time and cranking temperature ......................................... 65 Figure 6-1 Experimental setup of the proposed EHVT................................... 69
X
ABSTRACT
In the days of microcontrollers and technological advancement, and with the inevitable energy crisis closing in, the persisting challenge to replace mechanical systems with more modern computer controlled actuators, and the need for reducing the human footprint on the environment as well as saving energy resources are all factors that drive innovation. Traditional internal combustion engines (ICE)s utilize camshafts to operate the intake and exhaust valve, which limits the valve’s lift to one profile as the camshafts are tied to the engine’s crankshaft by a timing belt. As a replacement to this mechanical setup, an electrohydraulic valve-train (EHVT) is designed, modelled and controlled in this paper. An engine operated by an EHVT, also referred to as cam-less, can achieve better combustion results by manipulating the intake air flow through varying the valve lift according to the pedal position, and calculating the required fuel to then operate the fuel injectors. The controller is implemented in a custom engine control unit (ECU). The air flow to the engine’s cylinders and their pressures are visualized and discussed. The EHVT intake system also gives the flexibility of independent control of the cylinders, furthermore, it reduces pumping losses, and as a result, fuel consumption is enhanced.
1
الملخص
في ظل تطور وحدات التحكم والمعالجات ,ومع اقتراب أزمة الطاقة المحتمة ,يصبح التحدي ﻻستبدال اﻻنظمة الميكانيكية بمشغﻼت حديثة متمحكم بها عن طريق حواسيب ,والحاجة ﻻيجاد حلول طاقة بديلة لتقليل بصمة اﻻنسان على البيئة؛ يصبحون دافعا ً لﻼبتكار الفعّال .محركات اﻹحتراق الداخلي التقليدية تعتمد على عواميد الكام لتفعيل محابس شكل واحد كنيتجة لربط التحكم بالهواء الى داخل أو خارج حجرة اﻻشتعال ,مما يح ّد شكل وارتفاع فتح المحابس الى ٍ ميكانيكي ثابت لعامود الكام مع عامود الكرانك بواسطة حزام التوقيت .يأتي هذا البحث لدراسة بديل للنظام الميكانيكي, صف محابس إلكتروهيدروليكية لتحريك محابس هواء المحرك .المحركات حيث يتم تصميم ,تجسيد ,والتحكم في ّ المفعلة بهذه الطريقة يمكن أن تحرز إحتراقا ً أفضل عن طريق التحكم بالهواء الداخل خﻼل تغيير ارتفاع فتحة المحبس دواسة التسارع في المركبة .إضافة الى ذلك ,يتم حساب كمية الوقود المسؤول عن إدخال الهواء نسبة الى مكان ّ ق كامل .يتم تطبيق المتحكم على وحدة تحكم المحرك المخصصة .يتم أيضا ً المحتاجو من كل بخاخ وقود ﻹحراز احترا ٍ كل من تدفق الهواء الداخل و ضغط اسطوانات المحرك وتأثرها بالنظام البديل .تستعرض مرونة دراسة وعرض ٍ النظام اﻹلكتروهيدروليكي في التحكم المنفصل بكل اسطوانة ,باﻻضافة الى أنها تقلل من خسائر بستون المحرك وكنتيجة تحسن استهﻼك الوقود.
2
CHAPTER 1 :
LITERATURE REVIEW
Cam-less engines have been introduced and studied through various experiments on engines with modified EHVT systems , such as the electronically controlled intake EHVT developed in [1]. The studies demonstrated that controlling cylinder air charge (𝑚 ) in consequence to intake valve motion reduces the pumping losses associated with the intake and exhaust strokes of the engine’s pistons; hence enhances the fuel economy [2] [3]. Traditionally, air flow is controlled by varying the throttle position (𝜙) prior to the intake manifold, however, the throttle body becomes dispensable in cam-less engines as air flow is controlled by varying the lift of the intake valve, this is referred to as an un-throttled operation. A comprehensive study of the cam-less intake process can be found in [4], the authors develop a control oriented dynamic model of the process and examine the sensitivity of the system to high order dynamics. They, also, connect the intake process to an ideal valve lift achieved by the hydraulic actuators. A study of a closed loop controller for the valves can be found in [5], the authors tested an adaptive maximum valve lift controller for the EHVT designed in [1] and modelled in [6]. Actuator designs can be found in [3] and [1] Performance enhancement and the effect of the un-throttled operation can be found in [4], [3] and [7]. Analysis of a variable hydraulic valve train can also be found in [8], the authors developed an interesting feedback loop that utilizes the oxygen sensor on the exhaust valve to adjust the AFR and varying the intake valve timing of each cylinder, their results showed an 80% decrease in the pumping losses, as well as a 7% reduction in fuel consumption. Early intake valve closing was tested on a single cylinder test bed in [9] . The authors tested an EHVT variable lift’s implication on the gas emissions and the intake specific fuel consumption. A recent design of an EHVT can be found in [10] where the authors studied the sensitivity of the EHVT to oil temperature changes . By observing the operation of the hydraulic actuators at cold oil temperatures and recognized it was lethargic. The
3
authors develop a valve opening and closing controller robust against temperature changes; the EHVT was designed to operate at 4000 RPM. However, most of the previous studies and the proposed EHVTs were implemented using a controller that is distinguished from current ECUs on production vehicles, which caused an impediment in implementing the valve-train on the vehicles directly. Moreover, the studies were limited to four-cylinder engines. This project is intended to link the operation of the EHVT to the rest of the engine’s operations.
4
CHAPTER 2 :
PROBLEM FORMULATION
Engines’ intake process significantly affects the performance; the intake valve is conventionally operated by camshafts that do not offer variable control of the intake valves’ lift, duration or timing, and therefore the intake air of the engine in the throttled operation is controlled by varying 𝜙 to the pedal position. A properly controlled EHVT varies the lift of the intake valves according to the engine’s air requirement. Controlling the air intake in the un-throttled operation along with air to fuel (AFR) ratio manipulation can be achieved, these can enhance some engine characteristics such as fuel economy, maximum torque and performance. Designing and controlling an EHVT that is synchronized with the engine’s operation requires understanding an ECU and its functions. Modelling the system is essential to develop the controller, the behavior of the system and its response to changes in the intake valves’ lift is visualized in a high order mathematical model developed in subsystems that allows studying the system responses closely; to adapt to them in the control algorithm despite the fact that experimental data of the intake system is not available. This project is divided as follows: chapter 3 contains the EHVT mechanical design as well as the required electrical circuits for implementing the system. The EHVT’s parameters and dimensions were used to simulate the system model derived in CHAPTER 4 :chapter 4, the behavior of the system is studied and a control method is proposed for the cam-less engine operation. The effect of intake valve lift variation in the un-throttled process on the pumping losses and the 𝑚 is also visualized and discussed. The EHVT control is integrated within the custom ECU developed in chapter 5, the main programming language of the ECU is National Instruments’ LabVIEW, deployed on its own MyRio controller. The EHVT response is tested using an experimental setup designed and discussed in chapter 6.
5
2.1 Expected Benefits Cam-less intake process is un-throttled; the air flow is controlled directly by the intake valve which decreases pumping losses. The un-throttled operation and pumping losses development are further discussed in [2]. Achieving better air flow means better combustion of fuel and higher power output [3]. On the other hand, individual control of the intake valve lift and the injector pulse-width of each cylinder expresses the flexibility of the proposed system.
2.2 Limitations The proposed EHVT is limited to 3000 RPM due to hardware limitations, the achieved rising time restricts valve opening and closing times at higher speeds. Moreover, the valve overlap between the intake and exhaust valve is not considered. The proposed EHVT replaces the intake valve-train, leaving the exhaust camshaft operating with the geometry and timing set by the original equipment manufacturer (OEM) of the test engine. The timing of the new mechanism is not discussed in this study, however, it can be adapted from the current timing system by attaching a speed reducer on top of the exhaust camshaft pulley and tightening the timing belt connecting it with the crankshaft to match the original speed ratio.
6
2.3 Test Engine The ECU was developed to run a vehicle of make: Peugeot - 407 - 2.0i 16V; engine Code: EW10J4 (RFN). The engine has the parameters shown in Table 2-1 [11]. Table 2-1 Test engine parameters.
Parameter
Value
Idle RPM
800 RPM
Estimated idle vacuum is 24 “Hg
Notes
The most vacuum to expect from the engine ~24 for stock ~15 for street/strip ~10 for race engine
Maximum RPM
5200 [RPM]
Peak flywheel horsepower
136 [𝐻𝑝]
At 6000 RPM
Peak torque
191 [𝑁. 𝑚]
At 4100 RPM
Engine Displacement 𝑉
1.997 [𝐿]
Engine maximum boost level
0 [psi]
0 for naturally aspirated, max. boost [psi] for turbo/supercharged, 21 psi maximum
7
CHAPTER 3 :
CAM-LESS ENGINE EHVT DESIGN
Replacing the intake camshaft valve-train, the designed EHVT is aligned normally to the intake poppet valves. The proposed hydraulic system for valve actuation operates at high oil pressures due to the fast opening and closing required. Mechanical designs including the high pressure double acting cylinderical vessels and the cylinder train are explored in this chapter, as well as the electrical circuit designs of the ECU. Modern engines feature four valves per cylinder, two for the intake valves and two for the exhaust valves simply to achieve better air flow; this valve arrangement is referred to as “Pent Roof”. Each hydraulic actuator is used to operate an intake poppet valves pair, regulating air flow into the combusiton chamber. Valve motion is consequent to oil flow to the hydraulic actuator chambers which is controlled by a directional control valve (DCV). At any instant of the engine’s operation, there is a pair of intake valves pressed ,and therefore there is at least one hydraulic piston in an extended postion.
8
3.1 Valve Train CAD Model The CAD model shown in Figure 3-1 was drawn according to the test engine’s dimensions. Taking advantage of the dual overhead camshaft (DOHC) setup, the hydraulic cylinders actuate the intake valves while leaving no effect on the exhaust camshaft operation. The model is conservative and neglects the DCVs block and camshaft timing mechanism for simple illustration. Hydraulic Cylinder Cylinder Train Camshaft Case
4-Way DCV
Intake Valve
Figure 3-1 CAD model of the assembly of the proposed EHVT. Consisting of two structures: (the hydraulic cylinders and cylinder train) and the DCVs array.
9
3.1.1 Cylinder Train The hydraulic actuators are fixed in place by threads embedded in the designed cylinder train shown in Figure 3-2. The sealed threads setup provides the cylinders with rigidity and sustains high vibrations of the engine at high speeds. The cylinder train is bolted to the engine using the manufacturer’s bolts used to hold the camshaft cover.
Figure 3-2 Cylinder train CAD based on the test engine's camshaft cover dimensions (usually where engine oil is poured in the engine).
3.2 Hydraulic System The parameters of the simulated hydraulic circuit are based on design criteria discussed in this section. Hydraulic Fluid Standard
International Standardization Organization (ISO) established a viscosity grading system for industrial hydraulic oils, the organization classifies mineral based hydraulic oil like the ISO 68 has a median viscosity and is available in the market. Table 3-1 shows some of the ISO 68 hydraulic oil characteristics. According to the system hydraulic oils are designated by the letters ISO followed by a number equal to the oil viscosity measured in centistokes at 40°C. The viscosity of a hydraulic fluid depends on its composition and the temperature. Common viscosity of hydraulic oils is in the range 16 - 100 centistokes and the optimum viscosity value is 16 - 36 centistokes [12].
10
Table 3-1 ISO 68 hydraulic oil characteristics.
Property
Value
Density at 15.6°C
0.880 *10³ [𝑘𝑔/𝑚 ]
Kinematic viscosity at 40°C
68.0 [𝑐𝑆𝑡]
Kinematic viscosity at 100°C 10.2 [𝑐𝑆𝑡] Viscosity index
135
Pressure Source
The selected pump must be able to deliver high pressures, but modern fourcylinder engines lack high pressure pumps. As such, an electrical driven pump was chosen as an external pressure source to maintain a stable response of the hydraulic actuators, which affects the airflow. The pump has to operate at high flow rates to keep up with the fast operation. Response variations with different pressures are discussed later in section 4.3. DCV Selection
Solenoid actuated hydraulic DCV described in [13] is selected, the D1VW series features three positions, four ports and is spring centered. This series can withstand the high pressure fluid associated with the EHVT actuators. Figure 3-3 shows the DCV’s both symbolic and detailed schematics.
Figure 3-3 DCV symbolic and detailed schematics.
The valve has the specifications shown in Table 3-2, these parameters are also used for simulating the hydraulic system in section 4.3.
11
Table 3-2 D1VW DCV series specification.
Parameter
Value
Maximum Pressure
34.5 [𝑀𝑃𝑎]
Maximum Allowable Leakage (at 49oC)
26.2 𝑐𝑐 [at 34.5 𝑀𝑃𝑎]
Response Time at (34.5 𝑀𝑃𝑎 and 32 𝑙/𝑚𝑖𝑛) Pull-in: 51 ms, Drop-out: 21 ms
3.2.1 Hydraulic Circuit The EHVT’s oil flow is controlled by four solenoid actuated DCVs, the solenoids receive the control voltage from the circuit module which receives trigger pulses from the ECU, the duration of the pulses is determined by the controller’s output and the position of the corresponding engine piston. Figure 3-4 shows the connection of the DCVs and the hydraulic pistons.
Figure 3-4 Hydraulic circuit of the proposed EHVT.
12
3.2.2 Cylinder Design Designing a hydraulic cylinder is based on the stress that is a result of the oil pressure the cylinder has to withstand. Design criteria is introduced in [14]. The author discusses the requirements needed to design a double acting cylinders. The hydraulic actuators must keep up with the fast operation; oil pressure is directed to either of the cylinder’s chamber to open or close the intake valve. Threaded construction is used due to its rigidity and ease of manufacturing. Designed working pressure requirement is at least 50 𝑀𝑃𝑎, selected according to the size constraints and pump and valves size. End Plug
A
Piston Seal
B
Plug Static Seal
Rod End Plug
Piston Rod
Piston
Piston Guide Ring
Plastic Piston Seal
Rod Seal
Wiper Seal
Figure 3-5 Cutout section of the hydraulic cylinder.
Failure in the cylinder may cause a leak allowing a very fast jet of hydraulic fluid which may cause extensive damage to the surroundings. Thus, a pressure relief valve must be used while testing the cylinder, the valve is set to open and release the oil pressure if it exceeded a pressure limit. The limit is manipulated remotely and gradually increased to test the designed piston’s pressure rating. The design has to also consider the critical area that allows the oil pressure to exert the required force to overcome the spring’s force and press the intake poppet valve.
13
3.2.2.1 Cylinder Vessel Cylinder vessel’s diameter and wall thickness are designed according to the load pressure and oil capacity of the cylinder. A valid thin-walled assumption requires the vessel to have a wall thickness of no more than about one-tenth of its radius (often cited as Diameter / t > 20) [15]. The designed cylinders have an internal radius (𝑟 = 1.2 cm), an external radius (𝑟 = 2.5 cm) and wall thickness (𝑡 =1.3 cm). Hence, the current cylinders have a thick-wall stress distribution.
𝑟
𝑟
Tangential Stress 𝝈𝒕
Radial Stress 𝝈𝒓
Figure 3-6 Stress distribution in thick walled cylinders.
The oil pressure inside the cylinder exerts stresses in the tangential and radial directions 𝜎 and 𝜎 . The magnitude of these stresses is the highest near the inner surface at (𝑟 = 𝑟 ) and decreases as the radius approaches the outer surface (𝑟 = 𝑟 ) as Figure 3-6 shows. The resulting stresses are studied using an element-wise approach of the cylinder wall in [16]. Neglecting the axial stress caused by The average stresses through the cylinder wall are given by (3-1) and (3-2). 𝜎 =
𝑃𝑟 𝑟 −𝑟
1−
𝑟 𝑟
(3-1)
𝜎 =
𝑃𝑟 𝑟 −𝑟
1+
𝑟 𝑟
(3-2)
The cylinders and end-plugs are made from aluminum 6061, the ultimate tensile strength (𝑓 ) of this aluminum alloy is 310 MPa, and the ultimate shear strength (𝑓 ) is 276 MPa [17].
14
3.2.2.2 End-Plugs Two end plugs are required to seal the hydraulic cylinder, one of the plugs has a centric hole for the piston rod to pass through. The end-plugs’ thickness is first calculated in (3-3). 𝑘𝑃 𝑡 = 2𝑟 𝑓
(3-3)
𝑃 is the load pressure on the end-plug and 𝑘 is an empirical value and is approximately 0.162. End-plugs are threaded and static seals are utilized to insulate the cylinder. The number of threads required for the design can be calculated according to the pressure inside the cylinder, the load force on the end plug (𝑊) is calculated by (3-4). 𝑊=
𝜋 (2𝑟) 𝑃 4
(3-4)
Generally, the number of threads required to withstand a load is calculated by (3-5). 𝑛=
𝑊 𝜋𝑝 𝑓 𝐷
(3-5)
Where:
𝐷 is the diameter of the pitch circle [𝑚𝑚]
𝑝 is the pitch
𝑛 is the number of threads
3.2.3 Piston and Rod Design Extending the piston is achieved by directing the oil pressure to chamber A of the hydraulic cylinder, this pressure exerts a force on the piston opening the intake valve. Changing the spool position of the DCV to direct high pressure oil to chamber B reverses the force on the piston and causes the intake valve to close. Hydraulic pistons have to accommodate the high pressure inside the vessel and ensure no leakage between the two chambers. The force on the piston is transferred
15
to the intake valves by the piston rod. The piston rod is attached to the piston by a bolt; a rigid and inexpensive method for attaching them1. Piston rod is designed to withstand the force it will transfer along its axial axis, with no side loading causing bending. The rod has to have a surface finish between 0.1 and 0.4 [Ra µm] and chrome plating to avoid friction losses. Rod failure may occur due to column buckling, the failure comes in the form of sudden sideways deflection of the structural member. “The theory of the behavior of columns was investigated in 1757 by mathematician Leonhard Euler. He derived the formula, the Euler formula, that gives the maximum axial load that a long, slender, ideal column can carry without buckling” [18]. (3-6) calculates the maximum critical force (𝐹 ) in cylindrical columns. 𝐹 =
𝜋 𝐸𝐼 (𝐾𝐿 )
(3-6)
Where:
𝐸 is the modulus of elasticity of the rod material [𝑃𝑎]
𝐼 is the smallest area moment of inertia of the cross section of the rod [𝑚 ]
𝐿 is the unsupported length of the column [𝑚]
𝐾 is the column effective length factor, 𝐾 = 2 for one end fixed and the other end free to move laterally
1
Some industrial pistons and piston rods are made from the same shaft with different diameters, it is an expensive process and does not affect rigidity for the required application.
16
3.2.4 Seals Hydraulic cylinders are prone to leakage between the two cylinder chambers, along with leakage of the end plugs. Hydraulic seals are required to prevent any leakage and to sustain the high pressure within the vessel. Table 3-3 shows the seals as described in [19], along with their CAD. Seals are available in variations of inner and outer standard diameters, the designed cylinder bears in mind the available standard seals to decrease manufacturing cost and ensure easy maintainability of the hydraulic cylinder. Table 3-3 Piston seals types, description and CAD.
Seal
Description
Piston
Prevent fluid from passing the piston and are essential for maintaining the position at rest and controlling the motion of the cylinder.
seals
CAD
Rod seals
They act as a pressure barrier and maintain the operating fluid inside the cylinder. The rod seal regulates the fluid layer, which extends with the surface of the piston rod. This is important to prevent rod corrosion, lubricate the wiper seal, and lubricate the rod seal itself. Rod seals are also lubricated with the same fluid layer.
Plug
Static seals are used to prevent fluid leaking out of the cylinder assembly.
static seal
17
Wiper seals
Guide rings
Wiper seals are important due to their ability to block external contaminants from entering the hydraulic system and cylinder assembly, they accept the lubrication layer in the cylinder as the rod retracts.
Guide rings prevent metal-to-metal contacts between cylinder components. They keep the piston rod and piston position accurately centered. This is crucial to the performance of the rod sealing and piston sealing system. They react against the radial load caused by side loads acted upon the cylinder assembly.
3.3 Electrical Circuits of the ECU Driver circuits for injectors and ignition coils employ transistors for fast switching. Circuit components were selected to withstand the operation’s load voltage and current. The driver circuit also has a 20 pin auxiliary input to communicate engine sensors from the engine to the board during the operation. The manifold absolute pressure (MAP), inlet air temperature (IAT), coolant temperature (CLT) and the oxygen level (O2) are acquired. 3.3.1 Sensors’ Circuits Signal conditioning and filtering is implemented in the ECU and not conditioned electronically. Therefore, the designed circuit for all sensors only features a voltage divider to limit the voltage to MyRio’s expansion port (MXP) ‘connector A’ maximum input voltage (±5 volts). The sensors’ circuit is shown in Figure 3-7.
18
Figure 3-7 Engine sensors connection circuit design.
The CKP sensor is connected through the mini system port (MSP) differential input pins of the controller; as they can read within ±10 volts with high impedance. The signal, shown in Figure 3-8, is an alternating sine wave that affects how the engine performs, if the controller pins had low impedance, the performance of the test engine’s ECU will be affected significantly as the signal will be altered while scoping, causing a gap between the outputs of the custom ECU and the test engine’s ECU . Figure 3-8 shows the differential circuit for the CKP sensor.
Figure 3-8 The differential input circuit for the CKP signal.
19
Figure 3-9 CKP signal in the crank angle domain.
3.3.2 High Power Circuits Solenoid DCVs and fuel injectors operate using the same physical principle; voltage passing through the coils causes an induced magnetic force on a ferromagnetic member. Therefore they can be driven using the same circuit. Figure 3-10 shows the designed metal-oxide semiconductor field-effect transistor (MOSFET) driver power circuit to operate both actuators, R5 in the figure represents the load (either the solenoid DCV or the injector). The circuits were simulated using ISIS 7 Proteus electronics simulator.
Figure 3-10 MOSFET driver power circuit design with load R5.
Driving the ignition coils requires the insulated gate bipolar transistor (IGBT) as a driver, Figure 3-11 shows the driving circuit of the ignition coils.
20
Figure 3-11 IGBT ignition coil driver power circuit design.
21
3.3.3 Electrical Circuits Components IRFZ44z
High power N-Channel MOSFET, it is used in automotive operations as it can withstand high voltage and current. The drain and source terminals are connected when the voltage on the gate exceeds 4.5 volts. MyRio’s MSP connectors use a 3.3volt logic, therefore a gate driver circuit is required to switch the MOSFETs. Table 3-4 shows the absolute maximum ratings of the transistor [20]. Table 3-4 IRFZ44n electrical characteristics.
Parameter
Value
Drain to Source Breakdown Voltage (VDSS) 55V Static Drain to Source Resistance (RDS)
17.5mΩ
Drain Current (ID)
49A maximum
Figure 3-12 Schematic symbol and pinout of the IRFZ44z MOSFET.
IRG4PC50UD
High power N-channel IGBT is used in the ignition coils driving circuit, as ignition coils can hold up to 400 volts of return voltage after firing a spark plug. This IGBT withstand the high return voltage, the gate voltage required for this transistor is 15 volts, this also calls for a gate driving circuit to switch the IGBTs. Table 3-5 shows the absolute maximum ratings of the transistor [21].
22
Table 3-5 IRG4PC50UD electrical characteristics.
Parameter
Value
Collector to Emitter Voltage (VCES) 600V maximum Collector Current (Ic)
55A maximum
Gate to Emitter Voltage (VGE)
15V
G
C
E
Figure 3-13 Schematic symbol and pinout of the IRG4PC50UD IGBT.
BC557
Bipolar junction transistor (BJT), PNP type, used to drive the MOSFETs and IGBTs. This transistor has to only withstand the gate triggering signals’ voltage (5 or 15 volts). Table 3-6 shows the absolute maximum rating of the transistor [22]. Table 3-6 BC557 electrical characteristics.
Parameter
Value
DC Current Gain (hFE)
300V maximum
Continuous Collector Current (IC) 100mA Emitter Base Voltage (VBE)
6V
Base Current (IB)
5mA maximum
23
Figure 3-14 Schematic symbol and pinout of the BC557 BJT.
24
CHAPTER 4 :
MODELLING AND CONTROLLING
Cam-less un-throttled intake process is modelled to develop the controller; a multi-cylinder air breathing model is developed in this chapter independently from the EHVT model. Air flow to the engine has great significance on how the fuel combustion process will end up, it is controlled by the intake poppet valve that is lifted as a result of the force exerted by high pressure oil acting on the piston in the designed electrohydraulic actuator. All simulations were done in MATLAB/Simulink. The models were integrated and the whole system is simulated in order to achieve robust control of the intake valve lift position based on the desired 𝑚 , the controller is then implemented within the ECU to synchronize the valve-train with the strokes of engine pistons in chapter 5. The desired 𝑚 will be set by the accelerator pedal position representing the torque demand from the engine.
25
4.1 Model Derivation Deriving the model will rely on previous efforts to describe the electrohydraulic system in [23], the intake process is described in [4]. The derived model of the EHVT designed in chapter 3 considers the response of the DCV and the resulting fluid flow, the load pressure, the intake valve’s dynamic response and the engine cylinders’ pressures and the corresponding 𝑚 ; where 𝑖 denotes to the cylinder number. The following assumptions were made while deriving the model: 1. Parameter values are assumed to be varying within a known range of nominal values. 2. Frictional forces between the cylinder walls and piston are neglected. 3. Leakage of the hydraulic oil in the DCV and cylinder is also ignored. 4. Spool in the DCV has zero overlap as shown in Figure 4-2. 5. Intake manifold pressure is assumed to be isothermal and show accurate dynamics, the same isothermal assumption is applied in the engine’s cylinders.
26
4.1.1 System Equations The EHVT’s response and the resulting intake air dynamics are described in this section, two multi-cylinder models were developed independently to be later integrated to aid the controller design. 4.1.1.1 EHVT Model The input of the EHVT model is the DCV’s solenoid voltage, the DCV consists of a coil wrapped around a permanent magnet pin. DC voltage applied to the solenoid induces a magnetic field on the coil, the induced magnetic field exerts a force on the pin that pushes the spool in the desired direction. Two solenoids are required to manipulate the spool’s position. Controlling the solenoid requires the high power MOSFET driving circuit introduced in section 3.3.2. However, for the sake of simplicity, the voltage in this section is assumed to be coming from a battery source with a time varying voltage 𝑣 (𝑡). The coil can be also represented as an inductor, the simplified control RL circuit is shown in Figure 4-1. 𝑅 𝑖(𝑡)
𝐿(𝑥 ) 𝑣(𝑡)
Figure 4-1 Series RL circuit.
Applying Kirchhoff voltage loop on this circuit yields: 𝑣 (𝑡) = 𝑖𝑅 + 𝐿(𝑥 ).
𝑑 𝑖(𝑡) 𝑑𝐿 (𝑥 ) 𝑑𝑥 +𝑖 . 𝑑𝑡 𝑑𝑥 𝑑𝑡
(4-1)
The inductance of the coil (𝐿) is a function of the spool’s displacement (𝑥 ), to reduce model non-linearity, (4-1) is simplified by assuming 𝐿(𝑥 ) as a first order function of (𝐿 )
27
𝑣 (𝑡) = 𝑖𝑅 + 𝐿
𝑥 𝑎+𝑥
.
𝑑 𝑖(𝑡 ) 𝑖𝑎𝐿 𝑑𝑥 + . (𝑎 + 𝑥 ) 𝑑𝑡 𝑑𝑡
The magnitude of the electromagnetic force (𝐹
(4-2)
) exerted on the spool is given
by (4-3). The direction of the force depends on which solenoid is acting. 𝐹
=
𝑖 𝑑𝐿 (𝑥 ) . 2 𝑑𝑥
(4-3)
Hence, the force is related to the 𝐿 and the 𝑥 . Using the same assumption about 𝐿(𝑥 ), (4-3) becomes: 𝐹
=
𝑖 𝑎𝐿 2(𝑎 + 𝑥 )
Where:
𝑣 (𝑡 ) is the applied voltage [𝑉]
𝑖(𝑡) is the current through the valve [𝐴]
𝑅 is the resistance of the coil [𝛺]
𝐿 is the inductance of the coil as a function of 𝑥 [𝐻]
𝑥 is the spool’s displacement [𝑚]
𝑎 is the stroke length [𝑚]
28
(4-4)
The DCV has two springs on both ends to center the spool as shown in damping force is defined as a function of the spool’s velocity (𝑥̇ ) and the damping constant (𝑏). The spring and damping forces oppose the 𝐹
in direction. Spool
𝐹
B
A
𝑥
Casing T
P
𝐹 T
𝑘𝑥 𝑏𝑥̇
T
Figure 4-2 DCV servo valve section and free body diagram of the spool forces.
Applying the momentum equation on the spool yields: 𝑖 𝑎𝐿 = 𝑚𝑥̈ + 𝑏𝑥̇ + 𝑘𝑥 + 𝐹 2(𝑎 + 𝑥 )
(4-5)
Where:
𝑚 is the spool’s mass[𝐾𝑔]
𝑏 is the spool’s damping constant [𝑁. 𝑠/𝑚]
𝑘 is the spool’s spring constant [𝑁/𝑚]
And the flow force (𝐹
) is opposing 𝐹
, due to building up of oil pressure
normal to the spool through the DCV’s orifice; it is defined as a function of the pressure difference and 𝑥 . 𝐹
= 0.43𝛼 𝑃
−𝑃 𝑥
(4-6)
As the spool moves, flow of the hydraulic fluid starts in to either chamber A or B, determined by the direction of 𝑥 . Fluid flow rate (𝑄 ) is a function of the source and load pressures (𝑃
) and (𝑃 ) respectively, as well as the orifice area (𝐴 ) as
a function of 𝑥 .
29
𝑄 = 𝑐 𝛼𝑥
(𝑃
− 𝑠𝑔𝑛(𝑥 ). 𝑃 )/𝜌
(4-7)
Where:
𝑐 is the flow discharge coefficient
𝛼 is the area gradient of the orifice [𝑚 /𝑚]
𝜌 is the fluid density [𝐾𝑔/𝑚 ]
Assuming that the maximum spool displacement is 1 cm in the positive and negative directions, boundaries of 𝐴 can be generated using (4-8). (4-8)
𝐴 = 𝛼𝑥
When the valve is completely closed (spool is at zero position) the orifice area is zero and thus there will be no flow. The maximum 𝐴 is assumed to be half way through the displacement of the spool (5 mm). At 0 and 10 mm the orifice area is zero and the flow is blocked. To consider this area change behavior, equation (4-7) becomes: 𝑄 = 𝑐 𝛼(0.005 − (𝑥 − 0.005)) (𝑃
− 𝑠𝑔𝑛(𝑥 ). 𝑃 )/𝜌
(4-9)
After the fluid flow begins, pressure accumulates in the cylinder chamber, the continuity equation applied on this system in (4-10). The hydraulic cylinder’s volume (𝑉) is changing as the load is moving, it is given by (4-11). 𝑃̇ =
4𝛽 (𝑄 − 𝐴 𝑥̇ ) 𝑉(𝑡)
𝑉 (𝑡 ) = 𝑉 + 𝐴 𝑥
(4-10)
(4-11)
Where:
𝛽 is the fluid’s bulk modulus [𝑁/𝑚 ]
𝑉 is the initial volume in the cylinder [𝑚 ]
𝐴 is the internal area of the cylinders [𝑚 ]
The 𝐴 is assumed constant in both chambers, neglecting the rod’s area. The 𝑃 inside either of the cylinder chambers will exert a force on the piston that varies
30
with the 𝐴 . Figure 4-3 shows the free body diagram of the piston and forces acting in the direction of 𝑥 .
Figure 4-3 Free body diagram of the hydraulic piston and intake valves assembly.
Applying the momentum equation on the piston and valves yields: 𝐴 𝑃 = 𝑚 𝑥̈ + 𝑏 𝑥̇ + 𝑘 𝑥
(4-12)
Where:
𝑚 is the load mass [𝐾𝑔]
𝑏 is the load damping constant [𝑁. 𝑠/𝑚]
𝑘 is the load spring constant [𝑁/𝑚 ]
And 𝑥 in (4-13) is the load displacement, the valve lift in this chapter will also be referred to by 𝑥 as the piston rod and the intake poppet valve are assumed to be one rigid body, neglecting vibrations. 4.1.1.2 Intake Process Considering a control volume at the manifold, and given that air follows the ideal gas theorem, then for an 𝑛-cylinder engine, the manifold and cylinders pressures (𝑃 and 𝑃 ) can be calculated using (4-13) and (4-14) respectively.
31
𝑃 = 𝑚 −
𝑚
𝑃 =𝑚 .
.
(4-13)
𝑅 𝑇 𝑉
𝑅 𝑇 𝑉 (𝜃)
(4-14)
Where:
𝑅 is the gas constant of air [J kg
𝑇 is the IAT [𝐾]
𝑉 is the manifold volume [𝑚 ]
And the term (𝑚 − ∑
]
𝑚 ) is the total mass trapped within the manifold,
given by the throttle air charge 𝑚 cylinder, and
K
and the total mass of air that entered each
are constants based on the isothermal assumption. 𝑉 (𝜃 ) is the
volume of cylinder 𝑖 as a function of 𝜃, it can be found using the piston position introduced in section 4.3.3 or using the simplified function in (4-15). 𝑉 (𝜃 ) =
𝑉 720 1 − 𝑐𝑜𝑠 𝜃 − 𝑖 2 𝑛
32
+𝑉
(4-15)
𝑥
𝑚
𝑃 𝑚
𝑃 𝑉
𝐴 (𝜙)
𝑃
𝜃
Figure 4-4 System variables on the EHVT and engine assembly.
Cylinder displacement (𝑉 ) and clearance volume (𝑉 ) are constants that depend on the geometry of the engine. Crank angle (𝜃) is found by integrating the speed of the engine over the four cycle duration (720°) in (4-16). 𝜃=(
𝑁 360. 𝑑𝜏 𝑚𝑜𝑑 720° 60
(4-16)
𝜃 can be estimated as a linear function for constant RPM (𝑁); the rate of change in 𝜃 is assumed to be constant during the simulation.
33
Differentiating (4-13) and (4-14): (4-17)
𝑃̇ =
𝑅 𝑇 𝑚̇ − 𝑉
𝑃̇ =
1 𝑅 𝑇 𝑚̇ − 𝑉̇ 𝑃 𝑉
𝑚̇ (4-18)
The air mass flow is captured using a quasi-steady model of flow through an orifice [24]. The model will estimate the flow through the throttle body area (𝐴 ), and the flow through the intake port area (𝐴 ) which is a function of the 𝑥 . )
(4-19)
𝑚̇ = 𝐴 (𝑥 ) 𝑑(𝑃 , 𝑃 )
(4-20)
𝑚̇ = 𝐴 (ϕ) 𝑑(𝑃 , 𝑃
And 𝐴 can be estimated as a function of 𝜙 using (4-21). 𝐴 = 1.268𝑒
(−0.2215 − 2.275ϕ + 0.23ϕ )
(4-21)
The air flow through the orifice is modelled as one dimensional compressible ideal gas using standard orifice flow function (4-22) while assuming a constant 𝑇 [25]. 𝑝 𝑝 ⎧ 𝛿 𝑝 ⎪ 𝑅 𝑇 𝑑(𝑝 , 𝑝 , 𝑇 , 𝑇 ) = ⎨ 𝑝 𝛿 𝑝 ⎪ 𝑅 𝑇 𝑝 ⎩
𝛿(𝑥) =
(
)/ (
⎧ γ ⎪
2 γ+1
⎨ ⎪x ⎩
2𝛾 (1 − 𝑥 ( 𝛾−1
/
𝑖𝑓 𝑝 ≤ 𝑝 ⎫ ⎪ 𝑖𝑓 𝑝 > 𝑝 ⎬ ⎪ ⎭
)
𝑖𝑓 𝑥 ≤ r )/
(4-22)
⎫ ⎪
(4-23)
⎬ ) 𝑖𝑓 𝑥 > r ⎪ ⎭
Where the critical pressure ratio 𝑟 = 2/(𝛾 + 1) functions can be simplified by linearization at 𝑃 = 𝑃
/(
)
and 𝛾 for air is 1.4, the
, using the assumption that
the system will always operate at that point during the un-throttled operation. Intake port area is determined by the 𝑥 , they are linearly related by the intake valve and runner geometry factor (𝜓) as shown in (4-24). 34
𝐴
(4-24)
= 𝜓𝑥
The pressure is estimated to be spatially uniform and homogenous within the intake manifold and the cylinders, they are modelled as one container due to the high volumes associated with the process, the intake runner undergoes standing waves forced on it by the piston force as it is going down after intake valve opens (IVO). This spatial pressure is evaluated per intake runner, is captured by a onedimensional model introduced in [26] and in [27], and was later implemented in [28]. The pressure drop in each port (∆𝑃 ) is studied as a function of spatially distributed gas velocity 𝑣 (𝑥 , 𝑡), this function is evaluated at the inlet port (𝑥 ). (4-25)
𝑃 = 𝑃 − ∆𝑃
The pressure drop can be found by evaluating the runner mass (𝑚 ) at a constant manifold pressure, so that: ∆𝑃 =
𝑚 𝑘 𝑑𝑣 (𝑥 , 𝑡) . 𝐴 𝑑𝑡
(4-26)
∆𝑃 =
𝑚 𝑘 𝑑𝑣 (𝑥 , 𝑡) . 𝐴 𝑑𝑡
(4-27)
Where 𝐴 , 𝑉 are the runners area and volume respectively. And 𝑘 is a calibration factor that describes the geometry of the runners. The time dependent gas velocity at the inlet port (𝑣 (𝑥 , 𝑡)) can be approximated to be 𝑣 , by solving the second order differential equation with known initial values. [26] [29] 𝐴
1 𝑑 1 𝑑 𝑣 + 2𝜁 𝑣 +𝑣 𝜔 𝑑𝑡 𝜔 𝑑𝑡
=
𝜋𝐵 𝑣 4
(4-28)
The gas velocity at the port is a damped oscillation based on a Helmholtz resonator equivalent model, the natural frequency (𝜔 ) and damping ratio (𝜁 ) can be found experimentally. Values used for 1500 RPM are found by engine data in [29]. Where 𝜔 =2𝜋*176 and 𝜁=0.005. Assuming that the runner velocity and acceleration start at zero, initial conditions are given in (4-29). 𝑣 (𝑡 = 𝑡
)=0
𝑎𝑛𝑑
35
𝑑 𝑣 (𝑡 = 𝑡 𝑑𝑡
)=0
(4-29)
4.1.2 State Equations The system’s model can be described using the following set of states: 𝑎 = 𝑖 𝑠𝑜, 𝑎̇ = 𝑑 𝑎 =𝑥
𝑖 (𝑡 ) 𝑑𝑡
𝑎 = 𝑥̇
𝑠𝑜, 𝑎̇ = 𝑥̈
𝑎 = 𝑃 𝑠𝑜, 𝑎̇ = 𝑃̇
𝑠𝑜, 𝑎̇ = 𝑥̇ = 𝑎
𝑎 = 𝑥̇
𝑠𝑜, 𝑎̇ = 𝑥̈
𝑎 =𝑚
𝑎 =𝑃
𝑠𝑜, 𝑎̇ = 𝑃̇
𝑎 = 𝑃 𝑠𝑜, 𝑎̇
𝑎 =𝑥
𝑎
𝑠𝑜, 𝑎̇ = 𝑥̇ = 𝑎
=𝑚
𝑠𝑜, 𝑎̇ = 𝑚̇
𝑠𝑜, 𝑎̇
= 𝑃̇ = 𝑚̇
And 𝑢 is the voltage input. Hence, substituting the states in (4-2), (4-5), (4-7), (4-12),(4-17),(4-18),(4-19) and (4-20) results in the following state equations: 𝑎̇ =
𝑎+𝑎 𝐿𝑎
. 𝑢−𝑎 𝑅−
𝑎 𝑎𝐿 .𝑎 (𝑎 + 𝑎 )
(4-31)
𝑎̇ = 𝑎 𝑎̇ =
𝑎 𝑎𝐿 𝑘 𝑏 − 𝑎 − 𝑎 2𝑚(𝑎 + 𝑎 ) 𝑚 𝑚
𝛽 𝑎̇ = 𝑉 +𝐴 𝑎
𝑐 𝛼. 𝑎
− 𝑠𝑔𝑛(𝑎 )𝑎 𝜌
𝑃
𝐴 𝑘 𝑎 − 𝑚 𝑚 𝑎̇ =
𝑎 −
= 𝑎̇
1 𝑅 𝑇𝑎̇ 𝑉
𝑏 𝑚
𝑎
(4-35)
𝑎̇ )
− 𝑉̇ 𝑎
= 𝛼 ∗ 𝑎 𝑑 𝑎 ,𝑎
36
(4-33)
(4-36)
𝑅𝑇 𝑎̇ − 𝑉
𝑎̇ = 𝐴 𝑑(𝑎 , 𝑝 𝑎̇
(4-32)
(4-34)
𝑎̇ = 𝑎 𝑎̇ =
(4-30)
(4-37) (4-38) (4-39)
4.2 Controller Design In the throttled operation, the pedal position is related to 𝜙 which determines the area of exposure of the manifold to the atmosphere. As introduced earlier in chapter 2, the cam-less intake is an un-throttled operation (𝜙=90o), hence the manifold sustains atmospheric pressure during the run.
Figure 4-5 The desired lift reference signal with 𝑢 = 5 mm and 𝑢 = 160o.
Figure 4-5 shows the reference signal described by the lift magnitude 𝑢 and duration 𝑢 , where 𝑢 is in mm and 𝑢 is in degrees, this notation is used by various engine tuners [4]. The effects of varying 𝑢 and 𝑢 on the mass entering the cylinder is studied. The desired 𝑚 is proportionally related to the pedal position, as the pedal position increases, the desired 𝑚 also increases as more air is required to be delivered to the engine. the desired lift is generated at some angle BTDC and terminated at some angle before BBDC, this angle offset is done to ensure that the valve is closed in the following compression cycle to avoid air backflow (air going out of the cylinder through the intake valve during compression).
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Desired mc and Valve Profile Description
0.5
Desired mc
0.4 0.3 0.2 0.1 0 180 160 140 120 100
ud degrees
80
0
1
2
3
4
6
5 10-3
ul mm
Figure 4-6 Desired air mass charge and valve profile requirements, the table can be found in appendix B.
The controller interprets the desired 𝑚 requirements map shown in Figure 4-6, and decides what are the valve requirements to deliver the desired 𝑚 . This map is a simplified version of previous examples by engine manufacturers.
Figure 4-7 Controller scheme of the cam-less intake process, (The_Control.mdl).
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4.2.1 Plant Subsystems Controlling the hydraulic plant is achieved by this nested loop, the non-linear model derived in section 4.1 is implemented in Simulink subsystems. The plant has two inputs; control voltages for each of the DCV’s solenoids, the output is the 𝑥 .
Figure 4-8 The plant subsystems layout, (Plant.mdl).
The Non-linearity of the plant makes it harder to predict the system’s response; achieving robust controlling of the plant requires adapting to the physical changes of the system. 4.2.2 Inner Loop Adaptive PID Control Proportional Integral Derivative (PID) controllers are implemented in many applications in ICEs. The feedback based controller is also implemented in the inner loop of the designed controller. However, using the controller with one set of gains (𝑘 , 𝑘 and 𝑘 ) will neglect some of the changes that happened in the system. Therefore, the model was linearized at multiple operating points; these points were chosen at a lift range between (1 and 7 mm) and the corresponding states at each lift were snapped. Several linearized state space systems of the plant were obtained, and the closed loop PID controller of each model is auto-tuned in Gain_Switching_Controller.m, the result is an array of controllers with an index that corresponds to the operating point (lift). The script can be found in appendix C. Tuned PID gains that correspond to the linearized model at each operating point of the plant model are shown in Figure 4-9.
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Gains vs Lift x l
900 800 700 600
K
500
K K
400
p i d
300 200 100 0
1
2
3
4
5
x l (mm)
6
7 10-3
Figure 4-9 PID gains at different operating points 𝑥 .
Using the adaptive lift controller ensures fast settling of the system under different operating conditions, the system’s response to one nominal controller is compared to having the lift dependent gains shown in Figure 4-9.
Figure 4-10 Step response of the systems, comparing the response with a single nominal controller and the lift dependent controllers.
The single controller chosen and shown in Figure 4-10 was the controller at 𝑥 =1 mm, the controller lead to system stability at all operating conditions; however, the controller at 𝑥 =3 mm causes instability under some operating conditions. The lift dependent controller adapts to the operating point changes and ensures fast, robust response of the intake 𝑥 .
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4.3 Single Cylinder Simulation The intake process of the fourth engine cylinder is simulated, the hydraulic system and the air intake dynamics are studied in the 𝜃 domain, the intake event of the fourth cylinder occurs at 𝜃=180o. Simulink’s fluids library Simscape® [30] was used to simulate the proposed system to validate the model derived in section 4.1, a full model of the electrohydraulic system can be simulated with Simscape blocks while considering pressure losses due to piping and fittings. The lift is studied under different operating conditions and EHVT geometry, simulation parameters can be found in appendix A.
Figure 4-11 Simscape simulation of a closed loop double acting hydraulic cylinder, (closed_loop_pos.mdl).
The reference signal is generated in Simulation_Parameters.m, the script also includes the hydraulic circuits parameters. The actuator is tested in the 𝜃 domain, at 1000 RPM and oil pressure of 8 MPa and with a cylinder diameter (𝐷 =18 mm), the system’s response is shown in Figure 4-12. The system response will vary with different simulation parameters shown in the following figures. The desired 𝑥 was set to 𝑢 =5 mm and 𝑢 =180o (full duration) to test the maximum feasible duration at higher engine speeds.
41
10 -3 8 MPa 4 MPa 2 MPa
Lift xl (mm)
Lift xl (mm)
8
6
4
2
0
Figure 4-12 Comparison between camshaft generated profile and the 𝑥 .
0
180
360
540
720
Figure 4-13 The effect of changing oil pressure on the 𝑥 .
Figure 4-14 Different 𝐷 effect on the response.
Figure 4-15 𝑥 at different engine speeds.
4.3.1 Intake Dynamics Testing the model for a complete two cycles involves estimating the cylinder pressure 𝑃 (𝜃) at any given 𝜃. A Polytropic model for compression and expansion introduced in [31] is adapted, a simple but efficient method in describing gas pressure in the cylinder. 𝑃 (𝜃)𝑉 (𝜃 ) = 𝐶
42
(4-40)
In (4-40), 𝑛 is the polytropic exponent and 𝐶 being the cycle to cycle dependent constant. The cylinder pressure while it is undergoing the exhaust stroke is assumed to be (𝑃
=1.1 bar). Hence, each cylinder is initialized to this value right before
the intake model begins at IVO (𝑥 ≠ 0). 𝑃 (𝜃) is shown in Figure 4-16.
Figure 4-16 𝑃 (𝜃) during the two cycles.
Taking a closer look at the intake stroke (180
