HO CHI MINH CITY UNIVERSITY OF TECHNOLOGY AND EDUCATION FACULTY FOR HIGH QUALITY TRAINING GRADUATION PROJECT OPTIMIZE INJECTION TIMING BY PEAK AND HOLD METHOD NGUYEN GIA HUY Student ID 16145018 VO MINH KHANG Student ID 16145022 Major AUTOMOTIVE ENGINEERING Advisor Assoc Pro Dr DO VAN DUNG Ho Chi Minh City, August 2020 HO CHI MINH CITY UNIVERSITY OF TECHNOLOGY AND EDUCATION FACULTY FOR HIGH QUALITY TRAINING GRADUATION PROJECT OPTIMIZE INJECTION TIMING BY PEAK AND HOLD METHOD NGUYEN GIA HUY Studen.
INTRODUCTION
The Project Background
Fuel injection timing is crucial for optimizing atomization and combustion, significantly impacting a gasoline engine's performance and emissions Despite the inherent delay time in coil operation, optimizing injectors can enhance efficiency The research team focused on two primary methods: peak and hold, and saturated injection Ultimately, they selected the "peak and hold" method for injector optimization, based on the specific injector type and the advantages it offers.
Electrical devices like ignition coils, injectors, relays, and solenoid valves generate significant electric voltages ranging from 80V to 400V when active This high voltage can adversely affect the lifespan of electrical components, leading to increased heat generation and unnecessary energy waste.
The focus of this article is on the innovative approach of recovering and regenerating inductive energy to charge a capacitor, which is then utilized to apply high voltage for optimizing injector timing This method aims to enhance the efficiency and performance of the injection system.
The project purpose
The research team perform this project with these goals:
- Evaluate the total energy due to the inductive energy
- Evaluate the regenerative energy and reuse this source of energy
- Evaluate the injection timing after applied high voltage
- Evaluate the possibility of the injector control system using
The Object and Scope of the Study
- Research objects: Electrical circuits, electrical loads, power source in car
- Research scope: Electrical system in automobile.
Research Methods
- Research, evaluate, and analysis theory
Relevant Research
1.5.1 Research about optimize injection timing
Wen-Chang Tsai and Tung-Sheng Zhan have optimized high-pressure injection timing using the peak and hold method Their developed injector drive circuit demonstrated excellent performance in both experimental settings and practical applications, specifically tested on a 500 c.c Kymco motorcycle engine.
An injector drive circuit was developed with three-stage current 12/5/2.5 A, coupled with adjustable pulse width modulation (PWM) duties
The research demonstrates that the 12A current generated effectively retracts the nozzle needle of the GDI injector at a fuel injection pressure of 100 bar Following this, a 5A holding current maintains continuous injection, while the final pulse of the drive circuit delivers a 3A current to secure the nozzle needle This three-stage control injector drive circuit enhances the performance of high-pressure fuel injectors and extends the lifespan of solenoid coils within the injector actuator during operation.
The three-stage power metal oxide semiconductor field effect transistor (MOSFET) drive circuit for the HP GDI Injector incorporates pulse width modulation (PWM) control, enhancing the last pulse duration for improved performance.
Recent research on energy regeneration systems emphasizes several key areas, including the calculation and simulation of energy recovery during excess energy generation, the development of control algorithms for energy recovery systems, and the optimization of energy storage capacities Additionally, studies focus on managing energy produced by the main system across various vehicle types, such as electric vehicles (EVs), hybrid electric vehicles (HEVs), and internal combustion engine vehicles.
Research on energy recovery in the form of Mechanical – Heat
Mechatronic energy recovery research prominently features regenerative braking systems in electric vehicles (EVs) and hybrid electric vehicles (HEVs) Key areas of focus include energy recovery during braking, the balance of brake force between regenerative and mechanical systems, the development of control algorithms for regenerative braking, optimization of regenerative braking force, and adaptive control of State of Charge (SOC) based on vehicle braking conditions.
Research conducted by Li-qiang Jin, utilizing AMESim software to simulate energy recovery from regenerative braking in electric vehicles, demonstrated a 30% improvement in energy efficiency This enhancement is particularly evident in four-wheeled electric vehicles, which are powered by four electric motors.
The study focuses on a four-wheeled electric vehicle equipped with integrated motors, as researched by G Le Solliec, A Chasse, and M Geamanu Their work emphasizes an algorithm designed to optimize energy recovery during braking, ensuring an efficient distribution of both regenerative and mechanical brake forces to the wheels.
Jinhyun Park, Houn Jeong, In Gyu Jang, and Sung-Ho Hwang employed MATLAB/Simulink and CarSim to simulate brake torque distribution control in electric vehicles through the fuzzy logic control method.
Eindhoven University of Technology's research from 2001 to 2006 introduced the innovative "Zero Inertia Powertrain (ZI)" concept, designed to enhance vehicle fuel efficiency This system optimizes engine performance by utilizing a continuously variable transmission (CVT) and an energy storage flywheel, effectively sharing the load with the motor through advanced control methods.
Figure 1.2: The system stores energy while braking ZI
The "Idle Stop and Go" drivetrain enhances vehicle efficiency by enabling start-stop operation, allowing the engine to shut off when power from the flywheel is released This system precharges the flywheel to store energy during braking, significantly reducing fuel consumption.
Ayala's research developed an innovative energy storage system that harnesses a carbon fiber flywheel to capture energy during braking This flywheel, featuring a moment of inertia of 0.11 kg·m², is integrated with a Planetary Gear System (PGS) that connects seamlessly to a conventional vehicle's powertrain.
Figure 1.3: The system stores energy while mechanically braking
Recent studies on hybrid electric vehicles (HEVs) emphasize the calculation of energy recovered from regenerative braking and the implementation of dark-based control algorithms These efforts aim to optimize the energy recovery during braking while adhering to brake force distribution rules Key research includes the work by Xiao Wen-yong, Wang Feng, and Zhuo Bin, which focuses on a regenerative brake system control algorithm based on the principle of brake force optimization for HEVs.
Sanketh S Shetty investigates control algorithms for regenerative brakes in hybrid electric vehicles (HEVs) using artificial neural networks, achieving energy recovery rates of 30% to 37% based on simulation cycles Additionally, Piranavan Suntharalingam's research focuses on recovering and managing regenerative braking energy in HEVs, utilizing an ultra-capacitor to store energy during braking Experimental findings indicate that the recovered energy varies between 16.33% and 17.46%, depending on the vehicle's deceleration speed.
Research on energy recovery in the form of Heat
Internal combustion engines, including gasoline and diesel variants, are prevalent in everyday vehicles, yet they waste a significant amount of heat energy—two-thirds is lost through exhaust, with 40% escaping as exhaust gas This inefficiency means that only about 25% of the fuel is converted into usable power However, a thermoelectric generator (TEG) can harness this waste heat and convert it into electrical energy, which can then recharge the vehicle's secondary battery By implementing TEG technology, vehicle efficiency can be enhanced, leading to improved fuel economy.
The system aims to reduce power consumption by up to 5%, while future versions capable of operating at high heat levels will achieve reductions of up to 10%
Researchers are optimizing materials to function efficiently at varying heat levels, which decrease as air moves through the system They are addressing challenges related to enhancing performance and reliability while integrating complex materials with diverse heating capabilities The goal is to maximize heat extraction from flue gas The materials heat up on one side while remaining cooler on the outside, creating a consistent current Currently, the team utilizes an electrothermal material known as skutterudite, composed of cobalt, arsenide, and either nickel or iron.
An experimental study has been performed, the system includes:
Figure 1.5: Cutaway of a typical Thermoelectric Module
Figure 1.6: Temperature and Power of system
OVERVIEW
Power System Inductor
An inductor is a crucial passive component that operates alongside resistors (R) and capacitors (C), represented by the symbol "L," which derives from Lenz's Law related to electromagnetic induction Its fundamental design consists of a conductor coiled to convert electrical energy into magnetic energy, effectively storing it within the inductor The amount of magnetic energy stored is determined by the inductance, measured in henries (H).
Basic Characteristics of an Inductor
Inductors have the following basic characteristics
① Current flows to generate a magnetic field, and a change of the magnetic field generates an opposing current
② Changes electrical energy to magnetic energy and stores it
③ DC can pass through but AC cannot easily pass through at higher frequencies
An inductor generates a magnetic field when current flows through it, and this magnetic flux persists even after the current ceases, due to the inductor's magnetization Essentially, an inductor is capable of storing electrical energy in the form of magnetic energy.
The characteristics of ③ work as a conductor when DC is applied, but with
AC, the higher the frequency, it becomes more difficult to flow through This characteristic comes from the impedance of the inductor
Impedance (Z) of an inductor is expressed by the following formula
In addition, the absolute value of impedance can be calculated by the following equation
Z : Impedance (Ω) R : DC resistance component (Ω) j : Imaginary number
𝝅: Circular constant (3.14) f : Frequency (Hz) L : Inductance (H)
Higher frequencies result in increased impedance, making it more challenging for current to flow Additionally, a larger inductance (L) further complicates the flow of current.
Basic Structure of an Inductor and Inductance
An inductor is fundamentally a coil-shaped conductor with external terminals at both ends In recent years, most inductors have incorporated a core, around which the conductor is wound.
Figure 2.1: (a) Basic image of an Inductor
(b) Example of actual inductors Inductance of an inductor can be obtained by using the following formula
S: Cross-section of the coil (m 2 ) l: Coil length (m) Figure 2.2: Inductor
Principal Function of an Inductor
How an inductor works in a real application? Specific example is shown by using the basic characteristics ①, ②, ③ of the inductor described earlier
① Current flow generates a magnetic field, and a change of the magnetic field generates an opposing current ⇒Transformer principle
The structure with 2 windings of the primary and secondary sides can be interpreted as a transformer
When current flows through the primary winding, it creates a magnetic field that induces current in the secondary winding By adjusting the winding ratio between the primary and secondary windings, voltage can be effectively transformed.
② Changing electrical energy into magnetic energy for storing ⇒ Principle of a choke coil
Inductors play a crucial role in DC/DC converters by generating a magnetic field when the switch is activated and current flows through the inductor This process allows the inductor to store energy as magnetic energy, which is essential for efficient power conversion.
By turning off the switch to stop current supply, the stored magnetic energy is released (change of the magnetic field) and current flows
③ DC can pass through but AC cannot easily pass through at higher frequencies ⇒ Filter function
By adjusting the difficulty of AC flow in response to frequency-induced changes in impedance, it is possible to configure a low-pass or high-pass filter using a capacitor.
Figure 2.5: Example Low – High pass fitter
Type of Inductor
Inductors come in various types, and their classification depends on different perspectives The chart below categorizes inductors based on their applications in signal and power systems, as well as their magnetic core materials and manufacturing processes.
Power system inductors are increasingly crucial in meeting the growing market demand for larger capacity, higher efficiency, and compact power supplies While ferrite materials have traditionally been used for the magnetic cores of these inductors, there is a rising interest in metal composite power inductors that utilize metal magnetic materials These innovative inductors are gaining attention as effective solutions to the challenges faced in power system applications.
Figure 2.6: The classification made by application to the signal system and power system, and by magnetic (core) material and process
Metal magnetic Material Transformer Line filter
High power choke coil Chip choke coil Chip inductor Voltage Step-up
The MC type is highly regarded for its exceptional characteristics and reliability, making it a popular choice for automotive applications Primarily, it is utilized in DC/DC converters and input filters within power supply circuits across various Electronic Control Units (ECUs).
Panasonic intends to expand the variability of the MC type and deploy in other automotive applications in the future.
Figure 2.7: MC type power inductor application examples
THEORETICAL BASIS: RECOVERING ELECTRICAL ENERGY
Fuel Injector
Figure 3.1: Circuit cutting of the injector
When current flows through the injector coil, a strong magnetic force overcomes the spring tension, gravity, and fuel pressure, lifting the needle approximately 0.1mm to spray fuel Once the electric current is disconnected, the magnetic field vanishes, allowing the spring force to push the needle down and stop the injection process.
Table 3.1: Characteristic of Fuel Injector
Voltage impulse in the injector coil
Figure 3.2: Pulse voltage of the injector (1000 rpm - 2000 injection pulses)
• Section A: voltage level is applied to the injector, this voltage is normally working battery voltage
• Section B: the time of the power transistor in the ignition controller, connect the mass to seal the circuit, with current flowing through the injector
In Section C, when the power transistor conducts current through the injector, it reaches its peak value, causing the needle valve to disengage from the base and remain fully open.
• Section D: Time to stop supplying current to injectors Electromotive force induces a spontaneous voltage pulse generated by an unexpectedly interrupted magnetic field
• Section F: Nozzle energy is consumed End of a cycle
R is the total resistance of the coil
L is the inductance of the coil
At time t = 0, when lock K is closed, a direct current flows from the positive pole of the battery through resistor R and inductor L, returning to the negative pole of the battery This process generates an inductive electromotive force across inductor L.
𝑑𝑡 ξ carry the positive sign because 𝑑𝑖
𝑑𝑡 > 0, the current in the circuit is increasing now
Applying Kirchoff's law to the above circuit diagram we have:
𝑑𝑡 Perform the Laplace transform for the equation we will get:
Because the circuit does not store energy initially i(0 + ) = 0 The equation will be rewritten as follows:
The form of I s is not the basic form, so we will continue to transform the above equation:
A and B are constants to be determined, converging the right-hand denominator and balancing the two sides:
Carry out the Laplace reverse transformation for the above equation, we get the current equation through the solenoid at the time the transistor is turned off:
Energy RL Circuit
When the coil is imposed with a voltage, the voltage balance equation during the current rising process is expressed by:
When a voltage is applied to a solenoid, energy transfer occurs, with some energy being stored in the magnetic fields while a portion is lost as heat due to resistance, represented by the equation \( dt + iR = U \).
Magnetic field energy can be divided into three main components: the generation of eddy currents, hysteresis loss, and the conversion of the remaining energy into mechanical energy When the armature is constrained, the total energy input is calculated accordingly.
The control time for opening and closing the transistor at 1000 rpm is 3ms → t = 3.10 -3
The energy dissipated in heat:
The total energy input is:
Figure 3.4: Flowchart of energy Consumption and Accumulation
The diagram and formula indicate that the injector coil accumulates approximately 0.0093 joules of energy with each pulse Consequently, after six injection pulses, this energy equates to a single injection's energy requirement.
With a large number of pulses, the accumulated energy generated by the injector is not small
Formula for calculating the number of pulses (times) in the injector according to the number of revolutions for a 4-stroke gasoline engine
Where: X: the number of pulses of the coil per minute
N: engine revs (rpm) k: spray control mode i: number of injectors
Spray in groups i group number
Table 3.2: Spray control mode coefficient
Engine Revs (rpm) Number of pulses per injector per minute
Table 3.3: Number of pulses per injector
Thus, if we consider the motor in the state of 1000 rpm, equivalent to 500 injection pulses per minute of an injector, the energy consumption of the injector in 1 minute is:
Energy consumption per injector per minute (J))
Energy can be recovered per injector one per minute (J)
Table 3.4: Energy consumption and recovered
Realizing that this is a large source of energy that can be recovered for renewable use, the team relied on the theoretical basis to create the inductive energy recovery device.
The solutions have been and are being used to treat inductively automatic electric
Method of suppressing the inductance of electromotive force appearing in electronic components when switching on or off the circuit:
To protect electronic components from damage caused by inductive voltage, three methods can be used:
- Use Resistors of great value
High-resistance resistors can serve as alternatives to diodes due to their durability and ability to suppress inductance voltage However, unlike diodes, these resistors allow current to flow whenever the relay is open Therefore, it is crucial to ensure that the resistor's resistance is sufficiently high to limit excessive current flow.
Figure 3.5: Circuit diagram of self-inductive electromotive force suppression by resistor 3.4.2 Capacitor method
Figure 3.6: Circuit diagram of inductance electromotive force suppression by capacitors
When the team cam activates the KK contact, the primary coil generates inductance, which leads to the creation of an electromotive force This force is then stored in capacitor C1, effectively suppressing the spark on the screw that results from the inductive electromotive force.
In addition to safeguarding circuit components, the capacitor in the ignition system plays a crucial role in enhancing the voltage on the secondary coil, which boosts ignition efficiency and optimizes injector performance.
Figure 3.7: Circuit diagram of inductance electromotive force suppression by diode 3.4.3 Diode method
An inductive current-blocking diode is installed in parallel to a coil, oriented in the reverse direction When the contact is closed, the diode prevents current from flowing through it However, once the control circuit interrupts the current, the flow through the coil ceases, leading to a reduction in the magnetic field.
The magnetic field lines within the coil generate a reverse voltage that begins to increase Once this reverse voltage exceeds the positive source voltage of 0.7V across the diode, the diode conducts, allowing the high voltage to pass through This process effectively suppresses the inductance voltage, as the reverse voltage is discharged through the diode and resistor R.
Figure 3.8: Circuit diagram of electromotive force recovery by high voltage capacitors
To protect electronic equipment, it is essential to include a sufficiently large resistor in systems with coils suppressed by diodes This resistor absorbs the reverse inductance electromotive force, preventing potential damage to the electronics.
Realizing that instead of using a resistor to cancel out the electromotive force, the team used a high voltage capacitor to absorb the electrodynamic force, used for renewable energy purposes.
Scientific judgment
On the basis of observing the variation of the inductance electromotive force on the coils, we give some hypotheses as follows:
- We found that the source of energy from the coils generated during operation is very large
- We found that the solutions to suppress the electromotive force in the coil are extremely wasteful
- We confirm that the above inductance pulses can be recovered and the recovery efficiency is relative.
THEORETICAL BASIS: IMPROVING INJECTOR'S SENSITIVITY
Characteristic of Solenoid
A solenoid is an electrical device composed of a coil of wire wrapped around a cylindrical tube, featuring a movable ferromagnetic actuator or plunger that can slide in and out of the coil's body.
Figure 4.1: Pintle free body diagram [2]
The force exerted on a solenoid's armature is directly proportional to the current and inversely proportional to the square of the gap between the armature and core Consequently, two-state solenoids generally incorporate a return spring with a linear response, while proportional solenoids utilize a nonlinear spring that ensures armature displacement correlates with solenoid current Although armature movement influences solenoid current, it usually does not significantly affect the overall circuit operation.
Figure 4.2: Current Properties of the Fuel Injector
The equation describing increase in the current on the coil in the RL circuit is obtained:
L – inductance of the coil t – time form beginning of the control pulse
The graph in Figure (a) illustrates how current in the coil varies over time, revealing an exponential growth pattern during the smooth sections of the plot The rate of this current increase is influenced by the coil's time constant τ and the factor ε0 /R, as indicated in the equation.
Figure 4.3: (a) relationship I(t) in the coil
(b) relationship UL (t) in the coil [3]
Voltage UL of the inductance L is described by equation:
𝜉 𝑜 = 𝑅𝐼 + |𝑈 𝐿 | Where UL – voltage on the coil
The equation describing voltage decay on the coil is obtained:
The voltage across the coil in an RL circuit is represented by the equation |U L| = ξ o 𝑒 − 𝑡 𝜏, indicating how it varies over time As illustrated in Figure (b), the electromagnetic force (Fe) in the injector coil is directly influenced by the current passing through it, which fluctuates over time due to the induction electromotive force (ξo).
Analyzing delays in injector needle travel can be effectively achieved by examining the current waveform flowing through the injector coil, rather than evaluating all the forces as outlined in Eq (21) [9] The current in the injector coil reflects the total forces that need to be balanced by the electrodynamic force generated The opening time of the injector is influenced by several factors.
• Injection pressure – pressure “before” the injector
• Pressure in the tank, into which the does is injected – pressure “after” the injector
• Density of the agent passing through
• Current and Voltage supplying the injector coil
When the injector needle closes the nozzle, upstream pressure counteracts its opening Initially, as the needle partially lifts, the flow of the agent begins, reducing the opposing force on the needle Consequently, the injector opening time does not change linearly with variations in injection time, pressure, and gas density Several factors influence the delay in the lifting of the injector needle, as illustrated in Figure 4.4.
Figure 4.4: Sum of Force Affecting the needle
F e - electromagnetic force in the injector coil (N)
F s – force of the injector spring (N)
F G – force generated by the injection pressure (N)
F B – inertial force of the injector needle (N)
F T – friction force between the needle surfaces and the needle cylinder surface (N)
The spring force applied by an elastic element on the valve is influenced by the type of spring and its deformation due to the valve's movement This force can be quantified based on these factors.
Where: c – constant of the elastic element f cl – spring deflection with the valve closed
The force generated by the pressure difference above and below the valve element is influenced by the injector's operating conditions, including supply and pickup pressure, as well as the injector's design, such as the valve seat surface area and pressure distribution during flow This force can be calculated accordingly.
A – area of the valve opening, Δp – pressure difference above and below the valve element
Inertial force, also known as virtual force, acts on all masses within a non-inertial reference frame This force arises not from physical interactions but from the translational acceleration present in such frames According to Newton's second law, the inertial force is directly proportional to the mass involved, as expressed by the equation F = -ma.
Where: m – mass of injector needle a – translational acceleration
Mixed friction involves at least two types of friction: dry friction and boundary or liquid friction The overall frictional force results from the interaction of micro-contact friction and both external and internal friction within lubricant microstrips This mixed friction force can be quantified as the difference between dry friction and liquid friction.
T L – liquid friction force ρ – dynamic viscosity of the lubricating liquid c – slip velocity with relative motion h – oil layer thickness
Mixed friction exists under conditions of insufficient quantity of lubricant, and when it is sufficient to fill all unevenness of both surfaces, taking into account the contact deformation
► The electromagnetic force attracting the valve element to the electromagnetic coil according to the Maxwell's law; this force can be defined as:
The current flowing through the coil is influenced by a constant that reflects the design, which is determined by the shape of the magnetic circuit components, the coil's configuration, and the gap between the jumper and the magnetic core.
Effecting flowchart of Input Parameter
To analyze the impact of input parameters on the electromagnetic force and the performance of solenoid injectors, an effective flowchart is essential This flowchart visually represents how various structural and operational parameters influence the electromagnetic force Key parameters, including spring stiffness, plunger mass, coil turns, input voltage, and current, significantly affect the electromagnetic force, as previously explored in this study.
Figure 4.5: Effecting flowchart of the input parameters to electromagnetic force
Previous studies have rarely addressed key parameters such as sleeve thickness, coil shape, and the relative position of the coil, which significantly influence magnetic field strength and electromagnetic force This study aims to demonstrate their impact on electromagnetic force, as illustrated in the effecting flowchart in Figure 4.5 Additionally, the results derived from these key parameters will be optimized to enhance the performance of a solenoid injector.
According to the Maxwell’s Law:
In power-off mode, the needle is held against the cone-shaped valve seat by a spring and the force of fuel pressure, effectively sealing the fuel supply system against the manifold.
When powered on, the coil generates an electromagnetic field that retracts the armature, lifting the needle and allowing fuel injection Deactivating the current causes the injector to close Figure 4.6 illustrates the correlation between the actuation pulse, current, needle lift, and the volume of fuel injected.
Figure 4.6: Actuation of injector, current, lift and approximate amount of fuel
Each fuel injector exhibits a unique dynamic, with a delay time (dt opening) before the needle reaches full lift, influenced by various factors such as actuation voltage, fuel pressure, manifold pressure, temperature, and individual injector variations like spring force A similar delay occurs during injector closing, as the electromagnetic field takes time to dissipate, resulting in a dead time that, combined with the needle's flight time, contributes to the total closing delay (dt closing) The amount of fuel injected is directly proportional to the opening duration (t open), necessitating compensation for nonlinearities associated with flight times through the overall opening process.
Figure 4.7: Power electronics for injector actuation
The differential equations illustrate the connection between the electrical and mechanical components of the system, indicating that any alteration in the armature position results in a measurable change in electrical signals As depicted in Figure 4.7, there is a clear relationship between the injector needle position (lift), current, and voltage, with measurement points for voltage and current identified in the electric circuit as V.
The voltage signal at the end of the actuation, as shown in figure 4.7, is influenced by the extinction voltage of the Zener diode When the low-side switch opens, the current through the injector's coil collapses, leading to a negative voltage across the injector due to electromagnetic induction This negative voltage is capped by the Zener voltage, and once this threshold is exceeded, the diode enters breakdown, halting current flow through the injector The energy stored in the coil is then dissipated as eddy currents in the metal core, with the induced voltage observable at the coil's terminals.
Figure 4.8: Relationship between injector needle lift, current and voltage [4]
The solenoid valve of the injector must operate at high speed due to its inherent inductance, which prevents the current from instantly reaching the stable level, Iw, when energized The current's rising process, illustrated in Figure 4.8, includes a specific duration, termed the attracting time (t01), during which the current increases from 0 to Icd During this attracting time, the magnetic force generated becomes sufficient to lift the armature.
As the coil current reaches Icd, the electromagnetic force (FE) surpasses the difference between the armature spring force and the fuel pressure, prompting the armature to ascend The duration, t02, during which the armature moves to the fully closed position is referred to as the valve action time Consequently, the total response time of the solenoid, t, comprises two components: the attracting time (t01) and the valve action time (t02).
I w is a steady-state current of the coil and I w = U / R.
T is the constant time of the solenoid coil, which is related to the rising rate and
Figure 4.9: Current rising process of the injector solenoid
Let i = I cd Substitute this into Eq (4) and taking the eddy current effect into account, a coefficient α is used (generally, α is within 1.1∼1.3.), and thus, the attracting time is obtained
When the armature moves, the magnetic flux increases due to the decreasing air gap, leading to the generation of a counter electromotive force (EMF) in the coil This generated EMF, along with the self-induced EMF, inhibits current growth in the coil as its inductance changes Consequently, this scenario impacts the voltage balance equation of the solenoid coil.
𝑑𝑡 and the motion equation of the armature are expressed by mathematical model for a mechanical subsystem is defined by Newton’s second law
𝑑𝑡 2 Where: m is the total mass of the armature and other moving parts a is the acceleration of the needle v is the velocity of the needle x is the displacement of the armature
The injector testing bench allows for the measurement of two key forces: the self-induction electromotive force and the back electromotive force resulting from changes in inductance Consequently, the current growth time is shorter than that of an exponential function, enabling the determination of the solenoid valve's action time.
The relationship between force (F) and the variable U is evident, as an increase in U leads to a proportional rise in the coefficient k and consequently in force F E, specifically k 2 This correlation among U, time (t), and group F E is further supported by data from real experiments.
Figure 4.10: Current graph of injector in the circuit RL with 14 voltage
With the parameters of the needle we have R = 15.6 (Ω), L = 0.03 (H), U = 14 (V) is the battery voltage at the time of measurement, so the amperage through the injector is:
𝑅 = 14 15.6 = 0.89 (𝐴) Observing the measured graph, you realize that, I cd ≈ 0.45 (A) Thus, it takes time for the injector to reach its voltage I cd = 0.45 (A) is:
Based on the analysis, increasing the applied voltage reduces the time t01, leading to a shorter growth time for lifting the needle This enhancement improves the injector's sensitivity by replacing the voltage converter.
Experiment, use a valid voltage has U = 30 (V), Time is calculated as follows:
With I cd = 0.45 (A) is the amount of current required for the needle to be lifted
Based on the obtained results, carry out the experimental measurement of the process, the results obtained are as shown below:
Figure: 4.11: Current graph of injector in the circuit RL with 30 voltage
Realizing that the obtained result is feasible, the team relied on the theoretical basis to improve the injector's sensitivity by varying the voltage.
Current Waveform of Injector in RL Circuit
Key parameters include the current intensity at the needle opening point and the time interval after which the opening occurs, reflecting the change in the injector's time constant (𝜏).
Changes in the injector's technical state, represented by 𝜏 = 𝐿 𝑅, can indicate either damage or normal functioning Fuel injector damage is categorized into two main types: mechanical and electrical Analyzing current-related parameters helps define these damage types The characteristic current points of the injector, such as the nozzle opening (Point ON) and closing (Point CN), are illustrated in Figure 4.12, along with labels 1 to 6 that denote various cases of injector injuries.
• 4- short circuit in coil winding
• 5- break in the coil circuit
• 6- fatigue changes in the needle spring
Labels have been assigned to points that will change with given damage
Figure 4.12: Characteristic diagnostic points in the current waveform
When the injector's needle seizes, the smoothness at points ON and CN remains unchanged despite an increase in the current waveform controlling the injector This indicates that even with rising current and magnetic flux, the needle fails to lift, preventing any flow The current increase until the termination of the pulse follows an exponential curve without any bending point, accurately reflecting the underlying equation.
Figure 4.13: Steady increase in the current intensity due to the needle seizure
When the needle experiences a partial failure, the points where the current intensity and voltage decay plot bends (referred to as point ON and OC) will shift to injection parameters that do not align with these changes This misalignment can lead to misfiring or an imbalanced air-fuel mixture, resulting in either a lean or rich condition, depending on the needle's position.
Figure 4.14: Shifting of the needle opening point (ON) and needle closing point (CN)
Soiling the electrical connection of the injector coil leads to increased contact resistance, resulting in a decrease in current intensity and magnetic flux, or causing irregular pulsating changes.
4.3.4 Short-circuit in coil winding
A short circuit in coil winding, often caused by a connection to the negative terminal, leads to a reduction in the number of winding turns This reduction decreases the inductance of the injector coil, which can significantly impact its performance.
𝑙 Where μ o – magnetic permeability of the vacuum μ R – the relative permeability of a substance that fills the solenoid
𝑙 – the length of the coil
The extent of damage affects the magnetic flux, which may decrease or vanish entirely In instances of partial short-circuiting, the inductance diminishes while the coil resistance also decreases Consequently, to generate the required flux to lift the needle, a higher current is necessary.
Figure 4.15: Greater current value at the point of lifting the needle 4.3.5 Break in the coil circuit
Break in the coil circuit is the lack of the current flow and of the magnetic flux This is a type of change defined by the on-board diagnostic system
4.3.6 Fatigue changes in the needle spring
If the force of the spring closing the needle is decreased, point CN from Figure 4.12 will be shifted to the right, towards the subsequent closing (Figure 4.15)
Figure 4.16: Shift of the point of the injector needle closing
Increasing the mass flow will result in a time shift of the injection, as illustrated in Figure 10 Additionally, the ON point of the needle lift will also be adjusted, as shown in Figure 5, leading to a quicker lift at a lower current intensity.
Figure 4.17: Injection phase shift Preset injection time 2ms
A crucial aspect of the diagnostics discussed is the real-time control of various current-related parameters The Hall effect sensor is utilized to monitor magnetic flux and current intensity, while voltage measurements are taken directly within the controller An algorithm can be integrated into the controller to identify the needle's opening and closing points based on specific current intensity and voltage values during optimal operation To effectively detect these changes, a sufficiently high sampling rate of 51 kHz is required, necessitating the use of analog-to-digital converters with an operational frequency of at least this level.
Parameters Definition
This article defines key terms related to fuel injection timing in engines The Injection Opening Delay (IOD) refers to the time between the ECU's "start injection" signal and the actual commencement of fuel injection Conversely, the Injection Closing Delay (ICD) measures the interval from the ECU's "end injection" signal to the termination of fuel injection Additionally, the Set Injection Duration (SID) is the timeframe from the appearance to the disappearance of the ECU signal, while the Real Injection Duration (RID) captures the duration from when the spray exits the nozzle tip until it leaves completely.
The parameters of spray tip penetration (S) and spray cone angle (θ) are essential for characterizing spray features, as illustrated in the accompanying figure The spray cone angle represents the maximum angle created by the spray boundaries and the nozzle within the defined calculation range.
Figure 4.18: Definitions of spray core angle
This study examines the injection delay of the spray, specifically focusing on the spray cone angle The movement of the injector needle is reflected in the changes of the spray cone angle, particularly during needle closure As illustrated in Figure 4.19, the spray core angle curve of a typical injection event shows that the angle emerges after the injection signal, indicating that a core angle is established once the spray is released.
The core angle curve initially experiences a sharp increase, indicating a rapid rise in spray intensity Once the spray stabilizes, the angle gradually decreases to a consistent level However, when the needle closes, it disrupts this stability, causing the angle to rise once more Ultimately, at the conclusion of the injection, as the spray detaches from the nozzle tip, the calculation program registers the angle as zero.
Figure 4.19: Spray core angle curve of the injection event [6]
ECU to control pulse
By monitoring the under-swing signal, the ECU can determine when the dead-time concludes for each injection pulse, effectively identifying when the armature has lifted from its seat during the injection process.
Figure 4.20: Injector Control Signal and its Open Delay
In figure 4.20 & 4.21, in order to inject accurate fuel amount, compensation for injector dead time must be considered and undertaken by the EMS
To effectively compensate for injector dead time, it is essential to add an equivalent duration at the end of the injection process This dead time can fluctuate primarily based on battery voltage, where higher voltage results in a shorter injector dead time, while lower voltage extends it.
Figure 4.22: Injector Dead Time Compensation
Although Injector dead time is the function of battery voltage, in real EMS, injector dead time is derived through data table below
Figure 4.23: Calibrated Data for Injector Dead Time Compensation
Table 4.1: Example Data for Injector Dead Time Compensation
The data table of injector dead time is provided by injector manufacturer as typical values based on device electric characteristic, and accurate data needs to be calibrated during development.
INJECTOR CONTROL CIRCUIT
Saturated injector strategy
Most electronic fuel injection (EFI) systems utilize a 12-volt saturated circuit driver within their ECU, making them cost-effective, straightforward, and dependable This driver operates by delivering 12 volts to the fuel injectors, with the ECU controlling the on-off cycle to create a fuel injector pulse Typically, saturated injectors possess a higher impedance, ranging from 10 to 16 ohms, compared to peak and hold injectors.
Modern high impedance injectors utilize advanced technology that enables significantly higher flow rates, improved response times, and more reliable low pulse width operation without the risk of overheating As a result, low impedance injectors are no longer considered the pinnacle of fuel injector performance.
Principle of operation of the saturated injectors
A saturated signal is utilized to operate high impedance fuel injectors by sending a continuous intensity signal that keeps the valve open for the duration of the pulse width Unlike peak/hold injectors, which operate intermittently, saturated injectors maintain an "on" state throughout the signal, resulting in lower current flow in the driver and injector circuit This design minimizes heat generation, contributing to the longevity of the components.
Saturated circuit drivers exhibit slower response times compared to peak and hold drivers, with injector reaction times of 2 milliseconds versus 1.5 milliseconds, respectively This slower response can limit the usable operating range of injectors powered by saturated circuit drivers Additionally, saturated injectors are unable to accommodate larger CC or lb/hr styles due to their speed limitations.
Peak and hold injector strategy
Injectors are electrically controlled valves that precisely regulate the amount of fuel delivered to the engine They mix fuel with the air intake to achieve the optimal fuel-to-air ratio necessary for efficient combustion.
Peak/hold injectors are low impedance injectors commonly utilized in aftermarket high-performance systems due to their complexity and higher cost compared to saturated circuit drivers These injectors are typically not compatible with domestic production ECUs When the ECU signals for fuel injection, it transmits voltage through wire clips until a specific current level is achieved (the peak phase), which varies based on injector size and manufacturer During the pulse width duration, the current is then slightly reduced and maintained (the hold phase).
Principle of operation of the peak and hold injector
Peak and hold injectors, also known as current sensing or current limiting injectors, operate with low impedance (0.5-5 ohms) and require a specialized peak and hold driver for activation This system initially delivers a high current pulse to quickly open the injector (Peak), followed by a reduced current (Hold) to maintain its open state during the ECU command Due to their larger physical components and operation against high fuel pressure, these injectors need the initial high current to ensure stable opening and closing times, effectively managing higher fuel flow rates.
The initial current needed to activate a fuel injector solenoid is typically four times higher than what is required to keep it open Once activated, the current is automatically reduced to a lower holding level for the duration of the input pulse This design offers the advantage of minimizing the injector's "on" time, leading to a quicker response and significantly lower overall power consumption However, a notable drawback is the increased heat generated in the coil, which may result in potential failures over time.
Purpose and Function
Fuel injectors play a crucial role in the precise measurement and atomization of fuel, acting as electro-mechanical valves that respond within milliseconds This rapid operation allows the Engine Control Unit (ECU) to maintain optimal control over the fuel flow to the engine, ensuring efficient performance.
Method of Measurement
Fuel flow specifications are measured in grams per minute (g/min), which is the internationally recognized standard in vehicle manufacturing Vehicle development engineers focus on the mass of air inducted by an engine rather than its power rating, making the weight of fuel delivered by an injector a crucial metric.
Power Rating of Fuel Injector
In the aftermarket performance industry, it is common to rate fuel injectors based on anticipated engine power outputs, particularly horsepower However, this measurement approach faces several challenges, including inconsistencies in calculation methods, accuracy, and subjective interpretations, leading many fuel injector suppliers to reject this specification method Instead, various design requirements are considered during the design and manufacturing process of fuel injectors tailored for specific applications.
Fuel injector Driver
Fuel injectors are controlled by one of two possible injector control circuits called drivers: saturated (high impedance) and peak-and-hold (low impedance or current regulated)
At short pulse widths, injectors experience a phenomenon known as dead time, where there is no flow due to the inertia of the pintle valve, which is significantly influenced by the operating voltage When the magnetic flux field around a coil collapses, a reverse polarity spike occurs; however, if the release of stored energy is slowed, the entire process, including the injector's closing time, is delayed While we initially focused solely on optimizing the opening time, we now realize the importance of also managing the closing time to ensure efficient injector performance.
Figure 5.3: Voltage of two types fuel injector
Low impedance injectors, with a DC resistance of less than 2 ohms, necessitate higher currents, resulting in elevated energy levels and potential issues In contrast, high impedance injectors, characterized by a DC resistance greater than 8 ohms, exhibit low inductance, leading to lower current and energy spikes However, low impedance injectors are essential for achieving higher fuel flows at increased pressures.
To minimize opening dead time, a full high current hit is essential; however, once the injector is open, we can significantly reduce the current This "hold current" is considerably lower than the opening current, resulting in reduced stored energy Consequently, the injector closes quickly and consistently, leading to minimal noise spikes.
Peak and Hold Saturated Specification 1-4 Ohms range 10-15 Ohms range
"on" time, resulting in faster response
Disadvantages Increases coil heat, which can lead to failure over time
• Can't handel large CC or lb/hr styles due to limitations in its speed
Table 5.1: Advantages and Disadvantages two types
A peak-and-hold driver circuit is designed for fuel injectors with low resistance coils (2-2.5 ohms) that require higher current (4-5 amps) to open To prevent overheating from constant operation at 4 amps, the circuit incorporates a switching mechanism that reduces the current to a safer level after the injector is activated This allows the injector to remain open with significantly less current, leading to the term "peak-and-hold." Initially, the circuit delivers a peak current of 4 amps to open the injector, then reduces it to 1 amp to maintain its open state for the duration of the pulse width.
In peak-and-hold Multi-Port applications, a single driver controls two injectors, delivering a peak current of 2 amps and a hold current of 0.5 amps This configuration offers a rapid response time, as the high initial current generates the necessary magnetic force to lift the valve quickly Consequently, peak-and-hold systems provide a wide dynamic range, making them ideal for small displacement, high horsepower engines, such as turbocharged four-cylinder engines.
Figure 5.4: Driver current and Opening/Closing time of two type
DESIGN SYSTEM
Design inductance energy recovery circuit from ignition coil
This device is designed to adjust the power supply voltage for the injector, and our research indicates that supercapacitors effectively meet the necessary requirements for voltage, charging time, lifespan, energy, and capacity Notably, supercapacitors also provide high recovery efficiency for our collector, leading us to choose them as the preferred storage solution for this project.
Snap In Radial Electrolytic Capacitors
- Highest ripple current capability for demanding inverter applications
Max ESR: 0.603 ohms Dimensions: 35mm x 30mm Manufacturer by: Panasonic Part Number: EET-ED2W22
Leakage Current 3√CV (àA) max after 5 minutes; C Capacitance in àF, V = WV
Endurance 3000 hours at +105°C with maximum specified ripple current
6.1.2 Design and compute inductance energy recovery circuit from solenoid
Figure 6.2: Design inductance energy recovery circuit
When the ECU does not output a signal, the transistor remains in the off state, creating an open circuit that keeps the injector inactive During this time, the battery charges the capacitor to a voltage equal to the source voltage Once the ECU sends a signal, the transistor becomes conductive, transforming the injector circuit into a closed circuit, which activates the injector.
At the moment the power transistor is turned off, the magnetic field energy accumulated in the coil is converted to energy stored in capacitor C
2 When the transistor is switched off, an inductance is generated on the coil (L) against the increase in current The current is shown in the following formula: i(t) =1
0.03𝑡 (A ms⁄ ) When the transistor cuts off at the moment t= 3ms: i(t) = 14
Figure 6.3: The presence of inductance electromotive force when switching on-off the transistor t = 3ms 120V
Current varies from 2.2 (A / ms) to 0A when the transistor is turned off The electromotive force is calculated by the same formula:
0.35 𝑚𝑠 = 120 (𝑉) t = 0.35 ms is the time of the circuit from the overvoltage due to the self-induction, which occurs when the energization of the injector coil is stopped At this time the energy stored in the inductor is released, as well as the lifetime of the electromotive force, the faster the switching speed, the greater the electromotive force
Electromotive force serves as a source that charges the capacitor When the transistor is inactive, the capacitor reaches a voltage equivalent to the battery voltage However, when the transistor becomes active, it continuously switches on, allowing the capacitor to recharge using the stored energy from the inductor.
≈ 120V The capacitor will be loaded corresponding to the number of switching pulses of the transistor:
The electromotive force of 120V is brief, lasting approximately 0.01ms, as indicated by the measured pulse The capacitor's charge voltage is calculated using the formula: uC = ξ (1 − e^(-t)).
Where: u c is the instantaneous Voltage of the Capacitor (V) ξ is the Electromotive Force (V) t is the lifetime of the Electromotive Force (s)
R L is the internal Resistance of the injector (Ω)
R C is the internal Rsistance of the capacitor (Ω)
The above formula shows that, for every turn of the transistor, the capacitor will increase 0.33 (V)
A capacitor is considered fully charged when its voltage matches the voltage supplied by the battery For a capacitor charged to 14 volts, the number of pulses required for it to reach full charge can be determined based on the battery voltage.
→ 𝑝𝑢𝑙𝑠𝑒 ≈ 321 Formula for calculating capacitance of the capacitor
Q is the charge on the two plates (Coulomb)
C is the capacitance of the capacitor (F)
U is the voltage difference between the two plates (V)
Charge of the capacitor at the time the capacitor voltage reaches its value U = 120V and C = 220μF :
Design capacitor discharge and control circuit
The natural response of a resistor-inductor-capacitor circuit (RLC) can take on three different forms, depending on the specific component values
In previous articles, we provided an intuitive overview of RLC circuit behavior and derived a second-order differential equation to analyze a specific example This article focuses on examining the characteristic equation in detail and naming the various solutions it presents.
For each individual element, we can write i-v equations
Kirchhoff's Voltage Law (KVL) can be applied by starting in the lower left corner and summing the voltages around the loop in a clockwise direction In this process, the inductor exhibits a voltage rise, whereas both the resistor and capacitor demonstrate voltage drops.
𝑈 𝐿 − 𝑈 𝑅 − 𝑈 𝐶 = 0 Replacing the v terms with the corresponding I terms gives us:
To simplify the equation, we can take the derivative of both sides, which allows us to eliminate the challenging integral term.
This gives us the following equation with a second derivative term, a first derivative term, and a plain i term, all still equal to 0
A homogeneous second-order ordinary differential equation is defined by the equation \( C_i = 0 \), where all terms are related to the variable \( i \) and its derivatives It is categorized as second-order due to the presence of the highest derivative being a second derivative, and it is termed ordinary because it involves only one independent variable, with no partial derivatives The next step involves solving this differential equation.
In addressing natural response problems such as RC, RL, and LC circuits, we begin by assuming a solution in exponential form Exponential functions are unique because their derivatives closely resemble the original function, which simplifies the analysis of differential equations involving multiple derivatives This similarity enhances the ease of solving these equations effectively.
We assume a solution with this form:
K is a variable that adjusts the amplitude of the current, while the exponent s indicates a frequency, requiring s to have units of 1.
𝑡 ) We call this the natural frequency
Next, substitute the proposed solution into the differential equation If the equation turns out to be true, then our solution is a winner
𝐶𝐾𝑒 𝑠𝑡 = 0 Now let's work on the terms with derivatives
Middle term: The first derivative of the R term is
𝑑𝑡𝐾𝑒 𝑠𝑡 = 𝑠𝑅𝐾𝑒 𝑠𝑡 Leading term: We take the derivative if the leading 𝐾𝑒 𝑠𝑡 term two times:
So the leading term becomes:
Plug these back into the differential equation:
𝐶𝐾𝑒 𝑠𝑡 = 0 Now we can factor out the common 𝐾𝑒 𝑠𝑡 term:
Now let's figure out how many ways we can make this equation true
We could set K equal to 0 That means i = 0 and we are putting nothing into the circuit and getting nothing out Pretty boring
The term e^st approaches zero only as t approaches infinity, which takes a considerable amount of time Therefore, an intriguing solution to satisfy the equation is to set the term containing all the s variables to zero.
This is called the characteristic equation of the RLC circuit
We solved for s, the roots of the RLC characteristic equation, using the quadratic formula
By substituting variables α and ωo whe wrote s a little simpler as:
√𝐿𝐶 α is called the damping factor ωo is called the resonant frequency
The quadratic formula yields two solutions for s, designated as s1 and s2 To incorporate both solutions into our proposed model, we revise it to represent a linear combination, or superposition, of two distinct exponential terms, which include four adjustable parameters.
We now take a close look at the expression for s, the roots of the RLC characteristic equation, and the impact it has on the solution for i
If we want an exact answer for particular values of R, L, and C, we perform a computation like the one we did in the previous article for the example circuit
We can get an impression of the full richness of the natural response by looking three possible outcomes in a qualitative sense
The solution for s, depends on the sign of the subtraction that happens under the square root term in the equation:
Relation Sign of α 2 – ω 2 Nickname s i(t) α > ωo + Overdamped 2 real roots 2 decaying exponentials α = ωo 0 Critically damped
2 repeated roots t decaying exponential α < ωo - Underdamped 2 complex roots
Table 6.2:the oscillation patterns depend on α and ωo
In this scenario, the term 𝜔 0 2 is negligible compared to α 2, ensuring that the expression within the square root remains positive Additionally, since the square root value is less than α, it follows that the resulting values of s will be two negative real numbers.
𝑠 1,2 = −𝛼 ± √𝛼 2 − 𝜔 0 2 s1 = - real number1 and s2 = - real number2
(Convince yourself that s1 and s2 will both be negative.)
The current will be the superposition of two real exponentials that both decay to zero
An overdamped circuit is characterized by two superimposed exponential functions that work to drive the current towards zero This condition occurs when the resistance in the circuit is relatively high compared to the resonant frequency.
Figure 6.7: Current of Overdamped case Critically damped case (α = ω o )
The boundary between underdamped and overdamped systems occurs when the damping factor α equals the resonant frequency ω₀ At this point, the terms under the square root cancel each other out, resulting in two identical real numbers known as repeated roots This relationship can be expressed by the equation α² - ω₀² = 0, leading to the roots s₁,₂ = -α.
Solving a 2 nd -order differential equation with repeated roots is a bit tricky With repeated roots, the answer is an exponential term multiplied by t
𝒊 = (𝑲 𝟏 + 𝑲 𝟐 𝒕)𝒆 −𝜶𝒕 This response is said to be critically damped
Figure 6.8: Current of Critically damped case
The under damped case is when α < ω o The solution ends up as a decaying sine wave
When 𝛼 2 is less than 𝜔 𝑜 2 the expression inside the square root is negative,
The square root of a negative number is an imaginary number, j something So s will be two complex numbers with the same real part,- α and the same imaginary part,
√𝛼 2 − 𝜔 𝑜 2 but with opposite signs That means s1 and s2 are complex conjugates If you start out with real-world values for R, L, and C, s is always complex conjugates
At this point we introduce an optional frequency variable It makes the upcoming equations slightly more compact
𝜔 𝑑 = √𝛼 2 − 𝜔 𝑜 2 (ωd is called the damped natural frequency)
The term "d" refers to damped oscillations, where the variables ωo and α are rearranged in the subtraction to ensure a positive value under the square root This adjustment results in a positive damped frequency, denoted as ωd, and is represented as jωd to account for the reversed subtraction.
With this bit of notation, s becomes:
(j for the imaginary unit √−1 since we use i for current)
Notice: if R = 0, then α = 0 and ωd is the same as ωo If R is finite, then ωd < ωo
𝑖 = 𝐾 1 𝑒 𝑠 1 𝑡 + 𝐾 2 𝑒 𝑠 2 𝑡 turns into the sum of two exponentials whose exponents are complex conjugates,
We tease apart the real and imaginary parts of the exponents,
𝑖 = 𝐾 1 𝑒 −𝛼𝑡 𝑒 +𝑗𝜔 𝑑 𝑡 + 𝐾 1 𝑒 −𝛼𝑡 𝑒 −𝑗𝜔 𝑑 𝑡 and pull the common e -αt term out in front,
The primary focus of the analysis lies in the leading term, e^(-α), while the two imaginary exponents are combined in the second significant term within parentheses This approach mirrors the method used in the LC natural response To effectively manage the imaginary exponents, we can utilize Euler’s formula, just as we did previously.
Figure 6.9: Current of Over damped case Conclusions:
① The damping effect is due to the presence of resistance R
• The damping factor α determines the rate at which the response is damped
• If R = 0, then α = 0 and we have an LC circuit with as the undamped natural frequency The response in such a case is undamped and purely oscillatory
• The circuit is said to be lossless because the dissipating or damping element (R) is absent
• By adjusting the value of R, the response may be made undamped, overdamped, critically damped or underdamped
② Oscillatory response is possible due to the presence L and C
The phenomenon of ringing in underdamped responses is characterized by damped oscillation, resulting from the energy transfer between the storage elements, inductance (L) and capacitance (C).
③ The overdamped has the longest settling time because it takes the longest time to dissipate the initial stored energy
• If we desire the fastest response without oscillation or ringing, the critically damped circuit is the right choice
Table 6.3: Current of three types Oscilation
Realizing that, the Critically damped RLC oscillator circuit will match the properties of the project, the Critically damped type has a current property similar to that in the RL circuit
Figure 6.10: Comparation of current between the RL and RLC circuit segments
To ensure the injector operates effectively by lifting the needle, the RLC circuit must achieve a stable and maintainable current This circuit is characterized as critically damped, where the condition α² equals ω².
In order for the RLC to oscillate critically damped, the capacitor needs to be calculated to satisfy the conditions, the RLC oscillates critically when and only α = ωo
Design System
The Arduino Mega 2560 is a microcontroller board based on the ATmega2560 (datasheet) It has 54 digital input/output pins (of which 14 can be used as PWM outputs),
The Mega features 16 analog inputs, 4 UARTs, a 16 MHz crystal oscillator, USB connectivity, a power jack, an ICSP header, and a reset button, providing comprehensive support for the microcontroller Users can easily connect it to a computer via USB or power it with an AC-to-DC adapter or battery to begin their projects Additionally, the Mega is compatible with most shields designed for the Arduino Duemilanove and Diecimila, enhancing its versatility for various applications.
The Arduino Mega can be powered via the USB connection or with an external power supply The power source is selected automatically
External power sources for devices can be supplied through an AC-to-DC adapter or a battery To connect the adapter, simply plug a 2.1mm center-positive connector into the power jack on the board Alternatively, battery leads can be attached to the Gnd and Vin pin headers of the POWER connector.
The board functions effectively with an external power supply ranging from 6 to 20 volts However, supplying less than 7 volts may result in the 5V pin delivering insufficient voltage, potentially leading to instability in the board's operation.
If using more than 12V, the voltage regulator may overheat and damage the board The recommended range is 7 to 12 volts
The Mega2560 stands out from earlier boards by utilizing the Atmega8U2 as a USB-to-serial converter, rather than the FTDI USB-to-serial driver chip.
The power pins are as follows:
The Vin pin on an Arduino board serves as the input voltage source when using an external power supply, rather than the standard 5 volts from a USB connection This pin allows you to supply voltage directly or access the voltage supplied through the power jack.
The 5V regulated power supply is essential for powering the microcontroller and other components on the board This power can be sourced from VIN through an on-board regulator, or it may be supplied via USB or another regulated 5V source.
3V3: A 3.3volt supply generated by the on-board regulator Maximum current draw is 50 mA
The ATmega2560 microcontroller features 256 KB of flash memory for code storage, including 8 KB allocated for the bootloader, along with 8 KB of SRAM and 4 KB of EEPROM, which can be accessed using the EEPROM library for both reading and writing operations.
The Mega features 54 digital pins that can function as either inputs or outputs, utilizing the pinMode(), digitalWrite(), and digitalRead() functions Operating at 5 volts, each pin can supply or accept up to 40 mA and is equipped with an internal pull-up resistor, which is typically disabled by default, ranging from 20 to 50 kOhms.
Digital I/O Pins 54 (of which 14 provide PWM output)
DC Current per I/O Pin 40 mA
DC Current for 3.3V Pin 50 mA
Flash Memory 256 KB of which 8 KB used by bootloader
Figure 6.17: Voltage Devider Calculator Circuit
A voltage divider circuit is a widely used configuration that reduces a higher voltage to a lower level using two resistors The output voltage can be calculated using Ohm's Law, which provides a fundamental formula for this process.
VS is the source voltage, measured in volts (V),
R1 is the resistance of the 1st resistor, measured in Ohms (Ω)
R2 is the resistance of the 2nd resistor, measured in Ohms (Ω)
Vout is the output voltage, measured in volts (V).
Component
A transistor is a crucial electronic component utilized in circuits for amplifying or switching electrical signals and power, making it essential for various electronic devices It comprises two PN diodes arranged back to back and features three terminals: emitter, base, and collector The fundamental principle of a transistor lies in its ability to control the current flow in one channel by adjusting the intensity of a smaller current in a separate channel.
Understanding the maximum ratings and electrical characteristics of power semiconductors is crucial for their effective application, as detailed in the device data sheet Adhering to data sheet specifications is essential for good design practice, rather than relying on data from limited sample lots.
A rating defines the upper or lower limits of a device's capability, and exceeding these limits can lead to permanent damage or failure Maximum ratings indicate the extreme performance thresholds of a device and should not be considered as standard operating conditions during design.
A characteristic is a measure of device performance under specified operating conditions expressed by minimum, typical, and/or maximum values, or shown graphically
A thermistor is a crucial component in heat-operated switch circuits, functioning as a temperature-sensitive resistor Its resistance decreases with rising temperatures and increases as temperatures drop, allowing for precise temperature regulation in various applications.
When heat is applied to the thermistor, its resistance decreases, causing a larger portion of the supply voltage to drop across the resistor R This leads to an increase in base current, which subsequently raises the collector current As a result, the bulb illuminates, and the siren activates.
6.5.1.1 Transistor NPN (Negative-Positive-Negative)
Figure 6.19: Symbol of Transistor NPN
The NPN transistor is designed to amplify weak signals entering the base, resulting in strong amplified signals at the collector In this type of transistor, electrons flow from the emitter to the collector, with the collector connected to a positive power supply and the base linked to the negative pole of the power source.
6.5.1.2 Transistor PNP (Positive-Negative-Positive)
The PNP transistor is a type of Bipolar Junction Transistor (BJT), similar to the NPN transistor, featuring three key terminals: Emitter (E), Collector (C), and Base (B) In a PNP configuration, the emitter is connected to a positive voltage, while the collector is grounded.
The MOSFET (Metal Oxide Semiconductor Field Effect Transistor) is a crucial semiconductor device commonly utilized for switching applications and amplifying electronic signals in various electronic devices This four-terminal device consists of source (S), gate (G), drain (D), and body (B) terminals, making it essential for modern electronics.
The main principle of the MOSFET device is to be able to control the voltage and current flow between the source and drain terminals
The N-Channel MOSFET features an N-channel region situated between the source and drain terminals When a positive voltage is applied to the gate terminal, it repels holes beneath the oxide layer, pushing them into the substrate and creating a depletion region filled with bound negative charges from acceptor atoms This process allows electrons to populate the channel, forming it effectively Additionally, the positive gate voltage attracts electrons from the n+ source and drain regions into the channel Consequently, when a voltage is applied between the drain and source, current flows freely, with the gate voltage regulating the electron flow within the channel.
Figure 6.24: Symbol of IRF630N – MOSFET
𝑅 𝐷𝑆𝑆 Drain-to-Source Resistance 0.30 ohms
The Insulated Gate Bipolar Transistor (IGBT) is a three-terminal semiconductor switching device known for its fast switching capabilities and high efficiency in various electronic applications By integrating a MOS structure control input with a bipolar power transistor output switch, IGBTs effectively manage high-voltage and high-current scenarios These devices are specifically engineered to drive high-power applications while requiring only a low-power input.
VGE = 0, the device is turned off since there is no inversion layer is formed in p-type body region This is cut-off region
To ensure optimal performance, apply a gate-to-source voltage (VGE) greater than 0 but less than the threshold voltage (VGET) In this range, minimal leakage current occurs, primarily from the flow of minority carriers, while the device remains in the cut-off region.
VCE is almost equal to VCC
The increase in gate-emitter voltage (VGE) beyond the threshold value (VGET) activates the device, placing it in the active region This increase in voltage generates an n-type inversion layer within the p-type body region, thereby creating a channel that facilitates current flow.
An increase in the gate-to-source voltage (VGE) significantly elevates the gate-to-emitter voltage (VGET), pushing the MOSFET into the ohmic region and driving the output PNP transistor into saturation In this saturation region, the collector current (ic) rises, leading to a reduction in the collector-emitter voltage (VCE).
When the power supply is connected, current flows through the windings of the electromagnet coil, with the final current level determined by the DC resistance of the coil and wires This current generates a magnetic field that aligns the magnetic domains in the metal core, enhancing the magnetic force and storing more energy Upon switching off the supply, the magnetic field collapses, generating an Electromotive Force (EMF) or Counter Electromotive Force (CEMF) in the coil windings.
If this back EMF is not controlled or suppressed it will generate very large voltages that in turn can:
- Cause arcing at contacts, reducing switch life
Metal Oxide Varistor (MOV) prevents EMF
When the power supply is interrupted, the Back EMF increases to the rated voltage of the Metal Oxide Varistor (MOV) At this moment, the MOV begins to conduct electricity, effectively clamping the voltage to just above this threshold.
When clamping the back EMF, the voltage drop will typically be in the order of 30V or so Using the same equation: