`
`SENSORS AND ACTUATORS
`
`sor. This sensor can also yield an accurate crankshaft position measurement. Nevertheless, an
`on-board version is not available today.
`
`9.4 INFERRED TORQUE MEASUREMENT
`
`Indirect measurements of torque-related parameters can be made with a view to inferring
`torque from the measurements.Typically, such measurements require considerable real-time
`computation in the control microcomputer, along with precision measurementof the instan-
`taneous crank angle position. Much workis in progress in a variety of locations to make these
`methodsinto practical instantaneous torque contro] signals.
`
`9.4.1
`
`Instantaneous Cylinder Pressure Sensors
`
`Engine development engineers have long used piezoelectric crystal cylinder pressure sensors
`in the laboratory to make engine power and heat release measurements and as an aid to
`development. The best of these sensors use doped quartz single crystals. They are accurate
`and reasonably robust, but expensive and unforgiving if overranged or subjected to excessive
`temperatures. Much work continues on developmentof a mass-producable on-board cylinder
`pressure sensor.’ Oneof the Japanese car manufacturers is reported to have a top-of-the-line
`passenger car model, available only in Japan, with engine control using piezoceramic cylinder
`pressure sensors.
`The signals from cylinder pressure sensors need considerable real-time data processing to
`produce inferred “torque”signals. In one method, the noise always presentis filtered, the
`pressure signal is multiplied by an instantaneous shaft angle term, and integrated over the
`angle range representative of the powerstrokeofthe cylinder. From this a measure of torque
`contribution from that cylinder is obtained. The best digital signal processing (DSP) chips
`available in the early 1990s are barely able to keep up with cylinder events in such a process.
`Nevertheless, we can be confident that if the proper sensors are available in the late 90s, the
`microcomputer chip performance required will be available and cost effective too.
`
`9.4.2 Digital Period Analysis (DPA)
`
`Whenan engineis run at low speed and heavy load, the instantaneous angular velocity ofits
`output shaft on the engine side of the flywheel varies at the fundamental frequency of the
`cylinders, since the compression stroke of each cylinder abstracts torque and the power stroke
`adds a larger amount. Thesignal-to-noise ratio of the measurementof instantaneous angular
`velocity (or rather of its reciprocal, instantaneous period) degrades with increasing engine
`speed andlighter load, butis a useful way to infer torque-like measures of engine performance.
`Figure 9.4 showsan idealized plot of instantaneous crankshaft period against crank angle
`under constant speed, lean conditions. The instantaneous period waveis seen to be a variation
`about the mean period value. This waveform can actually be measured using a precision, mul-
`titoothed crankshaft position sensor, For reasons which will be explained later, the instanta-
`neous angular velocity lags the torque inputs producing it. As a result, the period wave
`appears to lead the torque or cylinder pressure variations.
`
`Timing Control by DPA. The general case of the variation in crankshaft velocity in a four-
`cylinder engine can be described by:
`
`Ty = AL Py (8) sin @= AL Pex.s (8) sin 0+ Ty (0) + T+ 16
`
`(9.1)
`
`176
`
`176
`
`
`
`ENGINE TORQUE SENSORS
`
`9.9
`
`24,500
`
`23,500
`
`TINE
`BETWEEN PULSES
`
`22,500
`
`217,500
`
`20,500 0
`
`IDLE NEUTRAL
`
`270
`
`360
`CRANK ANGLE
`
`540
`
`720
`
`FIGURE 9.4 Digital period input.
`
`Ty = instantaneous torque due to burning gases in cylinder N at angle 0
`where
`A=area of piston
`L =maximum effective crank lever arm
`Py (8) = pressure in cylinder N (a function of crank angle and manyothervariables)
`Poss) (8) = pressure in third cylinder to fire after N whichis in its compression stroke
`when cylinder N is in its power stroke
`Ts (8) =so-called “fixed load” torque due to friction, accessories, etc., and is gener-
`ally a function of d6/dt
`T, = torque delivered to the load
`J = inertia of the engine,drivetrain, and vehicle reaction through the wheels
`§ = instantaneous angularacceleration of the crankshaft
`
`In order for Eq.(9.1) to remain valid, as Ty varies with angle 6 due to the variations of Py
`(9) and the sin 6 term, some term in the right-handside of the equation must vary corre-
`spondingly. In fact, the major effect is upon 8, the angular acceleration, which varies both in
`magnitude andsign; being positive when Py is large and 6 is near x/2, and negative when Py is
`small and @ is near 0 and a.If Eq. (9.1) is integrated as a function of 8 from 8 =0 to 8 =n and
`
`177
`
`177
`
`
`
`9.10
`
`SENSORS AND ACTUATORS
`
`then the summationis extendedto angles larger than x by addingin the contributionsof cylin-
`ders N+ 1 and N +3, the term in J becomes an average angular velocity over a complete
`enginecycle.
`One important consequence of the preceding analysisis that, upon integration of the equa-
`tion, the sin @ term becomes cos @—thatis, the angular velocity wave lags the torque impulses
`causing it by x/2. Another consequenceis that the amplitude of the period wavereflects the
`net contribution of the cylinders—if the load increases, and P,(8) increases to keep average
`angular velocity constant, the amplitude of the period wave must increase. The I@ term has
`becomeanIq,it is the reciprocal of this term which wasplottedin Fig. 9.4.
`Whena spark plug fires or fuel is injected into a diesel cylinder, the pressure in the cylin-
`dertakesa finite length of time to build—first, because of a delay to getthefire started and
`then becauseof the finite and relatively constant flame propagation time, and second, because
`the temperature rise which causes pressure to rise, peaks only shortly before combustion is
`completed. Thereafter, pressure falls as the piston displaces under the pressure of the gases.
`Mean best torque (MBT) will be achieved from that cylinder when the pressure pulse, con-
`volved with sin 6 yields a maximum upon integration. As described previously, researchers at
`Stanford University have found analytically and confirmed experimentally that this condition
`prevails for a fairly wide range of engine conditions when the centroid of the pressure pulse
`occurs at 15 degrees past top dead center (TDC). Because of the delays described previously,
`ignition must occur early enough to position the pressure peak near this value.It is this “antic-
`ipation” in spark plug firing that is termed ignition advance. The reason why advance angle
`has to be larger at higher speeds is now obvious: the flame propagation delay time covers
`more degrees of crank angle when the engine is runningfaster.
`Further experiments by the Stanford researchers and others confirmed the suspicion that
`the period waveis a strong function of the crank angle, and that the angle associated with the
`centroid of the pressure wave is a unique function of the phase of the fundamental compo-
`nentof the period wave measuredwith respect to a crankshaft angle index point, say top dead
`center of cylinder no. 1. The period wave is measured with a sensor which is a precision ver-
`sion of a crankshaftposition sensor." It producesa fast, sharp pulse for every small and equal
`angle increment—say one degree—through which the shaft turns. Pulses from a high-fre-
`quency quartz crystal clock are counted to measure each period. The crankshaft angle index
`is available from the crankshaft position sensor.In principle, the period wave could be Fourier
`analyzed into the Fourier integral coefficients A, and B,, by computing the Fourier integrals,
`and the phase of the fundamental (first harmonic) is then arctan B,/A,. To perform this com-
`putationin real timeis a bit much to ask of today’s microcomputer (but not tomorrow’s!) and
`various shortcuts are utilized to achieve an approximate result. Remembering that the period
`waveappears to lead the torque impulses that cause it by 7/2, the spark timing can now be var-
`ied so as to place the centroid of the pressure wave, on the average, at or very near the 15-
`degree-after-TDCpoint.
`It is instructive to consider what performanceis required of the DPA and crankshaft posi-
`tion sensors to achieve a given signal-to-noise ratio. The repeatability of the crankshaft angle
`marked by the sensoris a function of the diameter of the sensing disc. For the various mag-
`netic sensors, a repeatability better than 40.5 degree can be achieved with a 10-cm-diameter
`disc. In the DPA sensor, the concern is for the period-to-periodjitter. It is obviously worse for
`smaller angle increments both because the angle jitter is a larger part of the period, and also
`because the period-counting roundoff error is larger for any given clock frequency. At the
`same time, the more periods measured per revolution, the morefidelity the period wave will
`havefor its high-frequency components. The period-to-periadjitter of the magnetic sensor in
`this example is about +0.5 degree. This is satisfactory for 24 periods per revolution but
`marginal for 60 periods; a typical period wave amplitude is only +3 percent of the average
`period. On the other hand, even 60 periods per revolution is marginalfor ignition or injection
`timing control.
`The granularity due to counting roundoff also needs to be considered. Today’s low-cost
`LSIcircuits can countreliably at 20 MHz,so thatis a practical clock frequency. If a four-cylin-
`
`178
`
`178
`
`
`
`ENGINE TORQUE SENSORS
`
`9.11
`
`der engine is running at 1800 rev/min (30 Hz), the associated period wave will have a funda-
`mental of 60 Hz. If the DPA sensor has one degree angle indices, referred to the crankshaft,
`each period will have about 2000 counts from the clock. Therefore, the period counting round-
`off noise will be +1 part per 2000. Referred to a nominal 43 percent amplitude period wave,
`this jitter amounts to +2 percent of the peak value of the period wave (notof the perioditself),
`not counting any smoothing.
`For the fundamental of the period wave, the phase of which is used for DPA timing con-
`trol, a good deal of smoothing can be realized, so that for a “clean” engine, estimation of the
`correct angle to + one crankshaft degreeis feasible.
`Figure 9.5 shows an actual period wave measured using an electromagnetic DPA sensor
`with one-degree increments and a 10-MHzclock. Both the jitter described previously and a
`fixed pattern noise can be discernedin the signal. The latter effect is due to slight imperfec-
`tions in the tooth spacing of the precision gear used as the sensing disc. Such systematic errors
`can be eliminated in the microcomputer, but they are troublesome and consumeintegration
`time. The better solution is to design a precision DPA sensor which minimizesfixed pattern
`noise.
`
`DPA Used for Diagnostics. During the 1980s, one of the heavy duty diesel engine manu-
`facturers introduced an off-board diagnostic instrument capable of doing DPA on the engine
`with the clutch disengaged and using snap acceleration and deceleration to load the engine
`
`
`
`2nd 360 degrees
`
`poe
`
`
`
`Jitter
`
`
`
`
`
`1st 360 degrees
`
`1940
`
`20
`
`40
`
`60
`
`80
`
`
`Ee ee
`120
`140
`160
`180 200
`220 240 260 280 300 320 340
`360
`Gear tooth number
`
`100
`
`FIGURE 9.5 Actual period wave data from engine crankshaft; unsmoothed data. (Courtesy of The Bendix Corp., Diesel Operation)
`
`179
`
`2200 +
`
`2100 r \
`
`
`
`
`
`
`2100 Ff
`10MHzpulsesbetweenteeth Ss=o
`
`179
`
`
`
`9.12
`
`SENSORS AND ACTUATORS
`
`inertially. This instrument used the very imperfect engine ring gear as the DPA target but
`solved the fixed pattern noise problem in a very elegant way."' The position sensoris actually
`a dual sensor, with the two magnetic circuits disposed tangential to the ring gear and closer
`together than one tooth pitch. A particular tooth is sensed by the first magnetic circuit and
`then by the second before the nexttooth is sensed bythefirst circuit. Virtually all of the fixed
`pattern noise is eliminated.
`What would be achieved in an on-board DPA system would be real-time, nearly ideal
`closed-loop control of spark timing. As with most controls for spark-ignited engines, there
`are some trims required to make the system work. Flame front propagationis in fact a com-
`plex process which has a substantial jitter in the time of propagation,so it is necessary to
`average the computation of the phase angle over a numberof cylinder pulses in order to
`obtain a good phase estimator. Undertransient conditions, the shape of the pressure pulse
`may change enoughso that the angle for mean best torque (MBT)shifts slightly. These fac-
`tors can also be incorporated in the control. A similar method could be used for compres-
`sion-ignition engines; in fact, the period wave has a more reproducible signature than for a
`spark-ignited engine.
`It is useful at this point to emphasize again that these principles hold under any conditions,
`but that the control works well only in the lean regime.Astheair/fuel ratio nears stoichiom-
`etry, the amplitude of the period wave becomes quite small. Because the method of measur-
`ing the instantaneous period—counting clock pulses over a finite angle increment—is a
`differencing method, the signal-to-noise ratio (S/N) is always a problem,since a differencing
`process always yields a poorer S/N than that of the original function. Hence, the DPA tech-
`nique yields poorer results the nearer the engineis to stoichiometry and the higher the engine
`speed.
`Referring to Fig. 9.6,if a figure of merit is formed
`
`
`
`r,-T,
`hth
`
`
`
`(9.2)
`
`TDC
`
`TDC
`
`INSTANTANEOUSENGINE
`PERIOD
`
`TDC CRANK ANGLE
`
`1T4
`
`'T>
`
`>
`
`ROUGHNESS @ F
`
`T,—T2
`—_——_
`ty +tg
`
`FIGURE 9.6 Digital roughness control.
`
`180
`
`180
`
`
`
`we have a measure of the “roughness” of the engine useful for lean limit control or misfire
`detection. This is one example of many such optimizing algorithms which may be derived
`from DPA
`
`ENGINE TORQUE SENSORS
`
`9.13
`
`9.5 SUMMARY
`
`One can conclude from this chapter that torque measurement, whetherdirect or inferred, is a
`useful parameter for engine evaluation off-board, but that the proper sensors and computer
`analysis equipment for on-board control are not yet available. Yet the numberof facilities
`working to advance this art, the resources being added, and the sporadic reports of progress
`are such that one can predict with some confidence that a breakthrough is imminent. Just
`what kind of controlwill first appear, and what kind or kindswill ultimately be successful,is
`notyet clear.
`
`GLOSSARY
`
`Algorithm A set of software instructions causing a digital computer to go through a pre-
`scribed routine. Because embedded computer engine controls have become so common,algo-
`rithm has becomeessentially synonymous with control law for automotive engineers.
`Compression leveling A (theoretical) type of engine control which would cause each piston
`in each cylinder to compressits air charge to the same maximum pressure.
`Dynamometer A machine to absorb power in a controlled manner, especially from an
`engine undertest.
`Hooke’s law A relationship for an ideal elastic member whichsays that the displacementis
`proportionalto the force.
`Interdigitated An arrangement of two multiple-finger structures such that each pair of fin-
`gers from one structure has a finger from the other interposed.
`Pulse sequential A type of fuel control for gasoline spark-ignited engines m whichthe fuel
`for each cylinderis injectedinto the air manifold near the intake valve for that cylinder just as
`it opens.
`Robust Able to survive and operate properly in a severe environment.
`Stoichiometric Pertaining to a combustion process in which the oxidizing agent (oxygen)
`and the reducing agent(fuel) are in balance such that, were the reaction to go to completion,
`there would be neither oxygen norfuel left over, and all the reaction products such as carbon
`monoxide would be oxidized to their highest state—carbon dioxide.
`Torsional Hooke’s lawArelationship for an ideal elastic shaft which says that the angle
`through which the shaft twists is proportional to the torque.
`Torque The moment tending to make the output shaft of an engine turn. Torque can be
`expressed as a force acting perpendicular to a lever arm at a distance from the centerof rota-
`tion. Its units are Newton-meters (pound force-feet).
`Unit injector A type of fuel control for diesel engines which has fuel metered into a piston-
`barrel injector for injection into a specific cylinder at a specific time. Each engine cylinder has
`its own cam-driven injector, which operates something like a hypodermicsyringe.
`
`181
`
`181
`
`
`
`9.14
`
`SENSORS AND ACTUATORS
`
`REFERENCES
`
`1. J. A. Tennant, Rao, H.S., and Powell, J. David, “Engine characterization and optimal control,” Pro-
`ceedings of the IEEE Conference on Decisions and Control(including the 18th Symposium on Adap-
`tive Processes), Ft. Lauderdale, Fla., Dec. 12-14, 1979. IEEE 79CH 7486-OCS, vol. 1, pp. 114-119.
`. Itshak Glaser and Powell, J. David, “Optimal closed-loop spark control of an automotive engine,”
`SAE Paper No. 810058, Society of Automotive Engineers Inc., Warrendale, Pa.
`. Anders Unger and Smith, Kent, “Second-generation on-board diagnostics,” Automotive Engineering
`vol. 102, no. 1, Jan. 1994, pp. 107-111.
`. William J. Fleming, “Automotive torque measurement: a summary of seven different methods,” IEEE
`Transactions on Vehicular Technology, VT-31, No.3, Aug. 1982, pp. 117-124.
`. William J. Fleming and Wood, P. W.,“Non-contact miniature torque sensor for automotive applica-
`tions,” SAE Paper No. 820206.
`. Yutaka Nonomura; Sugiyama, Jun; Tsukado, Koja; Masahoru, Takeuchi; Itoh, Koji: and Konami,
`Toshiaki; “Measurements of engine torque with the intra-bearing torque sensor,” SAE Paper No.
`87042.
`
`. G.W. Pratt Jr.,“An opto-electronic torquemeter for engine control,” SAE Paper No. 760007.
`. Charles D. Hoyt, “DC excited capacitive shaft position transducer,” U.S. Patent No. 4 862 752 Sept.5,
`1989.
`
`. Hiroki Kusakabe; Okauchi, Tohru; and Takigawa, Masuo; “A cylinder pressure sensor for internal
`combustion engine,” SAE Paper No. 92071.
`. Stephen J. Citron and Orter, Kevin C., “On-line engine torque measurement utilizing crankshaft
`speed fluctuations,” SAE Paper No. 850496.
`. Clarence E. Kincaid, “Computerized diagnostics for Cummins engines,” Proceedings of Convergence
`‘84, TEEE °84 CH 1988-5.
`
`ABOUT THE AUTHOR
`
`For biographical information on William G. Wolber, see Chap.8.
`
`182
`
`182
`
`
`
`
`
`CHAPTER10
`ACTUATORS
`
`Klaus Muller
`Manager, Development ofMagnetValves, Pressure Supply
`Automotive Equipment Division I
`Robert Bosch GmbH,Stuttgart
`
`10.1 PREFACE
`
`10.1.1
`
`Introductory Remarks
`
`Numerous open- and closed-loop control systems find application in modern production
`vehicles, where they provide improved operating characteristics together with enhanced
`safety, comfort, and environmental compatibility.
`The actuators respond to position commands from the electronic control unit to regulate
`energy, mass, and volume flows.
`
`10.1.2 Actuators: Basic Design and Operating Principles
`
`Conventionalfinal-control elements (standard and spoolvalves, etc.) have been familiar for
`some time. A provision for electronic controlis required for actuator applications in modern
`vehicles. The actuator consists of a transformer to convert the input signal from the control
`unit into (usually) mechanical output quantities, and the conventionalfinal-control element
`which it governs. (See Fig. 10.1.)
`
`i
`Electr. contr. signal
`
`
`
`Final-control
`on
`
`Mass or volume or
`oe
`
`Stage 1
`FIGURE 10.1 Basic actuator elements.
`
`Stage 2
`
`Either the control unit or the actuator itself will feature an integral electronic output
`amplifier. The energy conversion principles (stage 1) determine the classification of the actu-
`ators. Electromechanical actuators will also be discussed in the following pages.
`
`10.1
`
`183
`
`183
`
`
`
`10.2
`
`SENSORS AND ACTUATORS
`
`10.2 TYPES OF ELECTROMECHANICAL ACTUATORS
`
`10.2.1 Magnetic Actuators
`
`dc Solenoids
`
`In order to operate, actuators depend on the forces found at the
`Actuator Principles.
`interfaces in a coil-generated magnetic field when current passes through it. The solenoid
`actuation force F,, is calculated as
`
`F,,=
`
`
`AB
`
`2 Wo
`
`(10.1)
`
`where A = pole face area
`B= magnetic induction
`Ll, = permeability constant (u, = 4 2 107’ Vs/Am)
`
`On the flat-armature solenoid illustrated in Fig. 10.2a, the total solenoid force is 2 F,,. Equa-
`tion (10.1) can also be applied to versions equipped with a permanent magnet(Fig. 10.2b). A
`particular solenoid force is specified for each technical application. The pole face area, the
`magnetic circuit, and the coil are then determinedforthis force.
`
`'
`
`»
`
`(a)
`
`(b)
`
`FIGURE 10.2 Flat-armature solenoid featuring field excitation (a) via coil;
`(b) via permanent magnet.
`
`Determining Magnetic Circuit and Coil Specifications. The magnetic circuit consists of
`the working gap (between the armature and the base) and the ferrous regions. Permeability
`in iron is approximately three orders of magnitudegreater than in air. For this reason,the iron
`regions conductthefield. If the effects of leakage flux are discounted, the absence of magnetic
`charge, ¢6 B dA = 0, meansthat the magnetic flux ®,, remains constantforall cross sections A
`in the magnetic circuit:
`
`©,=|I. BdA,=|J. BdA,=|I. B dA, =const.
`
`1
`
`2
`
`i
`
`(10.2)
`
`If the magnetic induction is assumed to be homogeneousforall cross sections A;, then Eq.
`(10.2) can be simplified to:
`
`®,, = B, A, = Bz A, = B; A; = const.
`
`(10.3)
`
`184
`
`184
`
`
`
`The induction lines run at a 90° angle to the surfaces A;. Equation (10.3) defines the magnetic
`induction in each section of the magnetic circuit (Fig. 10.3). If, as an example, Index 1is
`assigned to the gap section, then B, and A, are derived with the assistance of Eq. (10.1), and
`one can proceed to calculate B; for the other sections.
`
`ACTUATORS
`
`10.3
`
`armature
`
`air gap
`yoke
`
`15
`2,3,4
`6
`
`FIGURE 10.3 Magnetic circuit divided into individual sections.
`
`The magnitude of the magnetic field strength H; is determined by the material properties
`(permeability u,;) of the section in question. Field strength H;:
`B; = Lo Ly H,
`
`(10.4)
`
`In air, u, = 1. In ferromagnetic materials, 1, does not remain constant. Rather, it varies as a
`function of the magnetic field strength H (see Fig. 10.4). The relationship between B and H is
`defined by the B-H-curve.
`
`
`
`
`
`H ——
`
`FIGURE 10.4 Progression of permeability and B-H curve.
`
`Using the magnetic voltage Vqi= JH, ds for the individualsection,it is possible to calculate
`the peripheral magnetic voltage as the sum of the individual magnetic voltages V,,;. Accord-
`ing to Ampere’s law,
`
`(10.5)
`0=)Hds
`this magnetic peripheral voltage is equal to the magnetomotive force ©. It defines the total
`current of the coil, © = J w. (J = current, w = numberof windings.)
`
`185
`
`185
`
`
`
`10.4
`
`SENSORS AND ACTUATORS
`
`Because the preceding calculation fails to consider leakage flux, the results must fre-
`quently be treated as approximations only. It is possible to increase the precision of the cal-
`culations by portraying the magneticcircuit as a general network (with gaps and iron regions
`as reluctance elements) instead of as a series circuit. The results will then reflectthe effects of
`a large proportion of the leakage flux. Maximum precision is achieved with numeric field cal-
`culations, which provide numerical solution of Maxwell's equations.
`After magnetomotive force © has been determined,the field coil must be dimensioned to
`produce the required magnetic field. The formulas contained in Fig. 10.5 can be employed to
`determinethefield coil’s specifications. For a graphic interpretation, see Fig. 10.6.
`
`Aw=h-!
`
`Winding cross section area:
`
`h
`
`|
`
`R mp (da+d))(1+a Ad)* 0?
`Aw = SS
`2kywU
`
`Winding number:
`
`Wire diameter:
`
`
`
`
`
`Tp (da+di)
`
` es | 2AwkwR|1/2 ‘be [ SeesAi
`
`
`
`mR
`
`Aw Winding cross section area
`R__
`Coil resistance
`p
`Specific resistance
`of coil wire
`da Outer diameter of windings
`d;
`Inside diameter of windings
`a
`Thermalresistivity coefficient
`of coil wire
`
`©
`ky
`
`Aj Temperature differential between
`coil and room temperature
` Magnetomotive force
`Coil space factor(ratio of total
`wire area (w/o insulation) to winding
`cross sectionarea)
`Voltage at coil
`
`U
`
`FIGURE10.5 Determining coil data for specified coil resistance and voltagelevels.
`
`
`
`
`
`
`WindingcrosssectionareaAy,—»
`
`
`
`
`
`Magnetomotive force © ——»
`
`FIGURE 10.6 Area of winding A, as function of magneto-
`motive force © (parameter coil resistance).
`
`186
`
`186
`
`
`
`To minimize the size of the solenoid assembly, the magnetic circuit and the coil must be
`dimensioned to produce the smallest overall size. The formulas for coil dimensions(Fig. 10.7)
`can be used to minimize the volumeofpot-shapedsolenoids.
`
`ACTUATORS
`
`10.5
`
`FIGURE10.7 Selecting coil dimensions for pot-shaped solenoids.
`
`In general, the solenoid is iteratively optimized by changing geometry in thosecritical
`areas within the magnetic circuit requiring a high magnetic voltage V,,;. The magnetomotive
`force © is then recalculated for the modified magnetic circuit. Figure 10.8 shows the opti-
`mization of solenoid diameter D for a particular armature diameter d.
`
`
`6 =const. Solenoid
`diameterD———
`
`
`
`L =const.
`Fim = const.
`
`{
`
`5
`
`Armature diameter d ———®
`
`FIGURE 10.8 Relationship between solenoid and armature diameters.
`
`Magnetic Force Curve. When the unit is intended for use in an actuator, the relationship
`between magnetic force and stroke will be required. With a flat armature and base, and with-
`out including the iron regions, Ampere’s law [Eq. (10.5)] and Eq.(10.4) provide the following:
`
`@=H;8= ra
`
`(10.6)
`
`where 6 = working gap
`
`187
`
`187
`
`
`
`10.6
`
`SENSORS AND ACTUATORS
`
`Together with the force relationship, Eq. (10.1), the following result is obtained:
`
`Ou,
`
`A;
`
`.
`
`F,= aeits ~3
`
`1
`
`(10.7)
`
`The substantial drop in magnetic force will be undesirable in many applications. Modifica-
`tions to the curve for magnetic force versus stroke represent an alternative to increases in
`solenoid dimensions. This expedient can be effected through control of the currentin thecoil
`or by meansof design modifications to the armature and base (see Fig. 10.9).
`
` Zz
`
`F
`
`Zz
`
`(b)
`
`6
`
`FIGURE 10.9 Design modifications and force curve.
`
`F
`
`(a)
`
`F
`
`(c)
`
`6
`
`8
`
`The areas below the force-travel curves, a measure of the work performed,are always the
`same.
`
`
`
`[Fx (8) a3=const. (10.8)
`
`0
`
`with
`
`I=const.
`
`Configuration c can be employed together with a spring to produce a proportional solenoid in
`which armature travel can be regulated as a function of current. This type of system is sensi-
`tive to interference from extraneous factors such as mechanicalfriction, and hydraulic and
`pneumatic forces. Thus, final-control systems for high-precision applications must also incor-
`porate a position sensor and a controller (Fig. 10.10).
`Dynamic Response. To show the dynamic response pattern moreclearly, Fig. 10.11 pro-
`vides a schematic illustration of the progression over time of three parameters: voltage u at
`the excitation coil, excitation currenti, and armature positions.
`The dynamic response pattern can be calculated using computer programs that apply
`Maxwell’s equations (field propagation with eddy currents, self-induction) in conjunction
`with the motion equation.
`Approximation formulas can be employed to derive rapid estimates (eddy currents and
`magneticresistance in the iron regions are not taken into account):
`
`188
`
`188
`
`
`
`
`
`F_o§&—
`
`6
`
`10.7
`
`
`
`i
`
`FIGURE 10.10 Operatingpoints of a proportional solenoid.
`
`me
`
`ty|to
`
`FIGURE 10.11 Progressionof voltage, current, and armature travel.
`
`(10.9a)
`
`(10.9b)
`
`
`
`where L, = initial inductance
`R= coil resistance
`U = voltage at solenoid
`5, = gap with armature lowered
`Foch = armature counterforce (treated as constant)
`=, &, see Fig. 10.11
`
`and
`
`189
`
`189
`
`
`
`10.8
`
`SENSORS AND ACTUATORS
`
`hyets
`
`ty
`
`ty,
`
`FIGURE 10.12 Relationships of¢, and 6.
`
`Figure 10.12 provides an overview of the relationships between f, and 4, and the parameters.
`The eddy currents must also be considered in calculations dealing with electromagnets
`intended for operation at high speeds or switching frequencies. When the excitation currentis
`applied suddenly, the progress over time for the magnetic force is
`
`F,, (Q)=Fno(l1-e“y
`
`for field generation
`
`and
`
`with
`
`with
`
`Fi(D) = Foo for field dissipation
`
`= ates for rectangular cross sections
`
`t=
`
`brad?
`4 (2.405)? p 8
`
`for circular cross sections
`~
`
`where F,,. = static solenoid force according to Eq. (10.1)
`t= time
`de = length of iron core in which eddy currents occur
`a/b = height/width of iron core (rectangularcross section)
`d = diameter ofiron core (circular cross section)
`p = specific resistance
`6 = working gap
`
`Lamination to inhibit eddy currents in de solenoids is not a standard procedure; its applica-
`tion is restricted to extreme cases.
`Figures 10.6 and 10.12 illustrate the fact that at a given voltage, small coil resistances will
`furnish a small coil and short activation times. However, these benefits are accompanied by a
`simultaneous increase in the powerloss P, = U*/R. The coil is thus designed to operate at the
`maximum permissible temperature.
`
`Torque Motors. The torque motorconsists of a stator and an armature—both madeofsoft
`magnetic material—and a permanent magnet. The pivoting armature can be equipped with
`either one or two coils.
`Figure 10.13a showsonly the magnetic flux generated by the permanent magnet. The arma-
`ture is resting at the center position.The magnitude of the magnetic induction is the sameatall
`
`190
`
`190
`
`
`
`ACTUATORS
`
`10.9
`
`
`
`Centerof rotation
`
`(a)
`
`{b)
`
`(c)
`
`FIGURE 10.13 Design and operation of the torque motor.
`
`gaps. Because equal amounts of force are generated at the armature ends, the forces acting on
`it exercise a mutual canceling effect.
`Figure 10.130 illustrates only that magnetic flux which is generated at the coil. Figure
`10.13c shows the cumulative pattern for the fluxes from a and b, with increased flow at gaps 2
`and 3 (®,/2 + ®,/2) accompanied by reductions at gaps 1 and 4 (®,/2 — ®/2). Using Eq. (10.1),
`the torque in the centerposition is
`
`M= Fy r= 7292 wLie,M~I
`
`(10.10)
`
`where
`
`r=armature radius
`A =pole face area
`B, = magnetic induction in gap generated by permanent magnet
`s = length of gap
`w = numberof coil windings
`7=current.
`
`Torque motors are used for applications in which substantial forces are required over
`small operating angles. They react more rapidly than electromagnets. In hydraulic and pneu-
`matic applications, torque motors deliver good performanceas drive units for flapper and
`nozzle systems.
`
`Electromagnetic Step Motors. Electromagnetic step motors are drive elements in which a
`special design operates in conjunction with pulse-shaped controlsignals to carry out rotary or
`linear stepped movements. Thus, one complete rotation of the motor shaft will be composed
`of a precisely defined numberof increments, step angles 0). The magnitude of these angles is
`determined by the phase numberg, the pole pair number p, and by the numberofteeth z in
`the step motor. The step motoris thus capable of transforming digital control signals directly
`into discontinuous rotary motion. In principle, the step motoris essentially a combination of
`dc solenoids. The calculations employed for de solenoids are thus also suitable for application
`with electromagnetic step motors. Depending upon the configuration of the magnetic circuit,
`a distinction is made between three types of step motors: the variable-reluctance step motor
`(neutral magnetic circuit), heteropolar units (polarized magneticcircuit), and hybrid devices.
`
`191
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`191
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`
`
`10.10
`
`SENSORS AND ACTUATORS
`
`Ce (b)
`
`FIGURE10.14 (a) Heteropolar step motor and (b) hybrid step motor.
`
`Due to its positive operating characteristics (holding force available in power-off state,
`improved cushioning, lower control power requirement for a given volume), the polarized
`step motor has cometo be the most widely applied (see Fig. 10.14).
`Drive systems featuring electromagnetic step motors combine the following characteristics:
`
`e Field forces induce controllable, incremental movements (minimal wear).
`¢ Precisely graduated movements can be generated using an open-loop controlcircuit (with-
`out position monitors or feedbacksignals).
`¢ High torque remains available at low angular velocities and in single-step operation.
`¢ Brushless motor design makes it possible to create drive systems which combinereliability
`with long servicelife.
`
`The operating characteristics of the rotational step motor can be described with the aid of
`a stationary torque-angle (M-) curve. A reasonable approximation can be obtained using
`sinus-shaped curves with a phase displacement reflecting the switching states of the phase
`windings (A, B, C) (Fig. 10.15a). Assuming that external torque inputs can be excluded,the
`
`
`
`{a)
`
`(b)
`
`FIGURE 10.15
`
`