Comprehensive Modeling of Automotive Ignition Systems

This paper presents a comprehensive approach to improve the analysis and design process of automotive ignition coils. The delivered voltage and energy of the coil to the spark plug load are the two essential requirements placed on a coil design. The prediction of these two quantities, derived from the simulated transient secondary current and voltage, is fundamental to the design process and allows early assessment of design robustness. With only the data required for electromagnetic finite element analysis (FEA), including material loss data, the magnetic and electrostatic interactions among the coil laminations and windings can be modeled. These field computations are converted to equivalent circuit elements employed in a systems model. The systems model allows the calculation of requisite transient signals. This approach is highly flexible and gives fast simulations. Good agreement was obtained between the test data and the simulation results in both the time-domain and the frequency-domain. INTRODUCTION The objective of this work is to provide tools and methods to improve the design process, and ultimately to improve the design and performance of automotive ignition coil systems. These modeling efforts allow the early assessment of design robustness and improve the reliability of the automotive ignition coil system. The analysis of the ignition coil system discussed here includes a driver, a coil, and a load. Ignition coils deliver the high voltage (several tens of kV) necessary to initiate the breakdown of the sparkplug gap, and then sufficient energy (several tens of mJ) to sustain the combustion, and overcome plug losses. The delivered kV and energy are the two essential requirements imposed on the ignition coil design. These two quantities, as well as other parameters, are derived from simulated transient signals of the coil, i.e., the primary and secondary currents and voltages. The accurate prediction of the time variation of these quantities is fundamental to the design process. The proposed approach is from first principles to the extent possible. The number of experimentally determined factors from actual coil prototypes was minimized in predicting the coil behavior. A coil design process was developed that begins with only dimensions, material properties, and topology. Then the non-linear magnetic and linear electrostatic interactions among the windings and laminations of the coil were modeled using electromagnetic finite element analysis (FEA). A simple model was developed to account for the winding resistance. The proposed approach is to convert field computations into equivalent circuit elements to be employed in a systems modeling program. The equivalent circuit approach allows a high degree of flexibility, and relatively fast time-transient simulations. The physical modeling is with static magnetic and electric fields, but the system simulator properly accounts for dynamic effects through an interpolation process. In addition to the coil model, the equivalent circuit models for the electronic driver and sparkplug load must be included. However, the parameters and physics of these two subsystems are less well known, or harder to obtain, than for the coil itself. The rest of the paper is arranged as follows: First, the motivation, objectives, and the approach of the proposed work are discussed. Next, the basic coil behavior is demonstrated in terms of a Fundamental Coil Model. Then more complex behavior is introduced in terms of Simple Coil Model. Simulations are given for the Simple Coil Model that illustrates the effects on signals from non-linear components. Following this Simple Coil Model, the detailed modeling of the individual components of the Comprehensive Systems Model is presented. Finally, the simulated results are compared with measured data, on a particular developmental coil, in the time domain and frequency domain. IGNITION COIL MODELING MOTIVATION, OBJECTIVES AND APPROACH Motivation: The motivation to pursue a comprehensive modeling effort for ignition coils is several-fold, and common to 2007-01-1589 Comprehensive Modeling of Automotive Ignition Systems Visteon/ACH-LLC, CAE University of Michigan, Dearborn C. S. Yang, S. K. Park and C. Mi R. C. Stevenson and R. Palma Licensed to University of Michigan Licensed from the SAE Digital Library Copyright 2009 SAE International E-mailing, copying and internet posting are prohibited Downloaded Thursday, January 15, 2009 8:22:26 PM Author:Gilligan-SID:1178-GUID:15736962-141.215.16.4 2 most engineering modeling efforts. A good model promotes basic physical understanding of the surprisingly complex operation of ignition coils. It allows the design engineer to pose “what if” questions, which can generally be answered relatively quickly. Most importantly, it reduces cost in terms of the number of prototypes, the testing, and the time dedicated to building physical prototypes. There is scant to non-existent literature on the modeling of automotive ignition coils [1]. There appears to be little or no literature on electromagnetic FEA modeling of ignition coils. Design methods for coils seem to be closely held secrets in the industry, and most design work appears to be done from historical precedence. Design modifications in the past have been guided by basic transformer theory, without resorting to detailed modeling. The construction of coil prototypes, typically with several design iterations, is an expensive and a time consuming process. It involves the specification and fabrication of annealed laminations, the design and fabrication of bobbins and packaging, the winding of the primary and secondary coils, the potting the coils, and the testing the coils. This type of prototyping can have cycle times of several months. By comparison, modeling can produce comparable answers with in a week or less. Objectives Given these prototyping costs, both temporal and financial, the objectives of this modeling work become apparent: reduce cost by minimizing the need to build prototypes. To this end, the electromagnetic engineer should create a modeling process whose short-term objective provides accurate guidance for the design engineer during initial screening of design variations. As a derivative of this goal, the prototypes that are built with the modeling guidance should be close to the design objectives. These goals require that the modeling effort should be based on “first principles” to the extent possible. It is to predict accurate transient behavior, not to fit the model to data gathered after prototypes are built, that the modeling effort is directed. However, because of the magnetic, electrical, and geometrical complexity of the coils, modeling approximations are inherent. Thus, some adjustment of systems and models to test data may be necessary. The longer-term objective is to advance from an analysis of design to a synthesis of design. That is, given a set of specifications, produce an optimized design that accounts for constraints on performance, material costs, package space, etc. This type of design work requires having an analysis procedure coupled to the ability to iterate, sample, or search many designs subject to the constraints. There is likely no unique solution. This longer-term objective will be accomplished in future work. Approach With regard to the modeling approaches, there are at least three potentially viable schemes. The first scheme, and the most physically accurate, would be to solve the complete set of Maxwell equations, beyond the lowfrequency approximation which is generally used for electric machine modeling. In this complete formulation, Ampere’s Law ( t H D J ) includes the displacement current density, t D , while in the lowfrequency case, the displacement current density is ignored. For this scheme, the full coupling of the electric and magnetic fields is obtained, i.e., the magnetic inductive and capacitive effects are automatically accounted. For the current state of the art in electromagnetic solvers, the direct solution of the complete set of Maxwell equations, with strong material nonlinearity, is not practical. A second approach is to solve a transient FEA model of the magnetics, including external circuitry for the driver, the load, and capacitive effects. This approach is feasible but cumbersome, since a transient magnetic FEA problem would need to be solved for changes in any minor model parameter. A third approach, detailed in this paper, is a more flexible method. In this third approach, the model includes an equivalent circuit of the driver, the load, and the coil. The lumped circuit elements for inductive, capacitive, and resistive effects are obtained from FEA. The inductive elements account for non-linear material properties. The flexibility of this approach comes with studies requiring changes to circuit elements, other than those derived from FEA. These changes can be accommodated quickly and easily. Simulations can be run in a matter of a few minutes. IGNITION COIL OPERATION OVERVIEW Automotive ignition system requirements and operation with regard to engine and spark plug performance is discussed in [2]. For the modeling effort described in this section, the focus is more narrowly on describing how the coil works. The ignition coil system consists of a coil, which acts as a transient voltage transformer; a driver, which “charges” the primary winding; and a load (a spark plug) to which the coil delivers a high voltage pulse. The coil system block diagram is shown Fig. 1. The basic job of an ignition coil system is to convert a low-voltage DC source into a very high voltage and very fast transient at the spark plug gap. Driver The driver part of the system consists of a voltage source (the automotive battery, nominally 14.4 V) and a controlled switch. The switching device is commonly an IGBT [3]. However, this simple switch will not suffice, because the large voltage that develops in the Licensed to University of Michigan Licensed from the SAE Digital Library Copyright 2009 SAE International E-mailing, copying and internet posting are prohibited Downloaded Thursday, January 15, 2009 8:22:26 PM Author:Gilligan-SID:1178-GUID:15736962-141.215.16.4 3 secondary is transformed by the coil to the so-called “flyback voltage” in the primary. The fly-back voltage may be over 1,000V. IGBTs used for ignition can withstand no more than approximately 600 V across the EmitterCollector ports. Thus, the IGBT must be protected against the fly-back voltages. This protection comes in the form of a clamping Zener diode added across the IGBT. This diode has an avalanche voltage of about 500 V. This diode has a major effect on the signal dynamics. Fig. 1. Component for ignition coil system. Coil The ignition coil is a (transient) voltage transformer. A schematic representation of the ignition coil is shown Fig. 2. The primary and secondary windings are coupled through a magnetic circuit of laminated steel, which channels magnetic flux much like a wire conducts current. However, the magnetic “conductivity,” i.e., the permeability of the laminations, is much lower than the corresponding electrical conductivity of wire. Thus, magnetic fields leak more from a magnetic circuit than the electric fields leak from an electrical wire. Fig. 2 represents this leakage as a primary and a secondary leakage flux. Leakage flux represents a loss of coupling between the primary and the secondary windings. Not all the flux generated by the primary winding links the secondary winding, and vice versa. Leakage flux may appear to be innocuous, since the non-ideal coupling for an ignition coil can approach 99%. However, it can be seen that the leakage flux results in a mode that appears in transient operation, but is not apparent in steady state operation. Arguably, the most significant parameter of a transformer is the turns ratio, / s p N N r , where p N and s N are the number of turns of the primary and the secondary winding, respectively. Given a primary winding, typically with ~100 p N turns, and a secondary winding, typically with 10,000 ~ s N turns, the turns ratio is about 100 r . Power conservation implies that the primary voltage and the secondary voltage are related by s s v v r , while the primary current and secondary current are related by, / s p i i r . For example, if the avalanche voltage of the clamping Zener Diode is about 500 volts, with 100 r , the peak secondary voltage is no more than 50 kV. Correspondingly, if the peak primary current is 10 A, then the peak secondary current is 100 mA. Fig. 2. Transformer magnetic circuit model In practice, the so-called “negative” voltage n v is measured instead of p v . Since for peak values, n b v V , then