9.8
`
`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 MEASQREMENT
`
`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 measurement of the instan-
`taneous crank angle position. Much work is in progress in a variety of locations to make these
`methods into practical instantaneous torque control 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
`deve10pment. 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 development of a mass—producable on—board cyiinder
`pressure sensor? One of 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 present is filtered, the
`pressure signal is multiplied by an instantaneous shaft angle term, and integrated over the
`angle range representative of the power stroke of the cylinder. From this a measure of torque
`contribution from that cytinder is obtained. The best digital signal processing (DSP) chips
`available in the early 19905 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 905, the
`microcomputer chip performance required will be available and cost effective too.
`
`9.4.2 Digital Period Analysis [DPA]
`
`When. an engine is run at low speed and heavy load, the instantaneous angular velocity of its
`output shaft on the engine side of the flywheel varies at the fundamental frequency of the
`cylinders, since the compressiou stroke of each cylinder abstracts torque and the power stroke
`adds a larger amount. The signal—to-noise ratio of the measurement of instantaneous angular
`velocity (or rather of its reciprocal, instantaneous period) degrades with increasing engine
`speed and lighter load, but is a useful way to infer torque-like measures of engine performance.
`Figure 9.4 shows an idealized plot of instantaneous crankshaft period against crank angle
`under constant speed, lean conditions. The instantaneous period wave is seen to be a variation
`about the mean period value. This waveform can actually be measured using a precision, roul-
`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 EPA. The general case of the variation in crankshaft velocity in a four-
`cylinder engine can be described by:
`
`TN = AL PN (a) sin e 2 AL Par”, (3) sin a + n (e) + n + is
`
`(9.1)
`
`176
`
`176
`
`

`

`ENGINE TORQUE SENSORS
`
`9.9
`
`245m
`
`23.500
`
`one
`0
`BETWEEN PULSES 22.5 °
`
`21.500
`
`20.5130
`
`lDL E N EUTRAL
`
`D
`
`270
`
`360
`CRANK ANGLE
`
`5‘0
`
`T20
`
`FIGURE 9.4 Dig'tal period input.
`
`where
`
`TN = instantaneous torque due to burning gases in cylinder N at angle 9
`A = area of piston
`L = maximum effective crank lever arm
`
`PM (9} 2 pressure in cylinder N (a function of crank angle and many other variables)
`Pan 3, (9) 2 pressure in third cylinder to fire after N which is in its compression stroke
`when cylinder N is in its power stroke
`TF (8) = so-called “fixed load” torque due to friction, accessories, etc., and is gener-
`ally a function of deficit
`TL = torque delivered to the load
`I = inertia of the engine, drivetrain, and vehicle reaction through the wheels
`9 = instantaneous angular acceleration of the crankshaft
`
`In order for Eq. (9.1) to remain valid, as TN varies with angle 9 due to the variations of PM
`(9) and the sin 9 term, some term in the right-hand side of the equation must vary corre—
`spondingly. In fact, the major effect is upon 6, the angular acceleration, which varies both in
`magnitude and sign; being positive when PM is large and 6 is near M2, and negative when PN is
`small and 8 is near 0 and at. If Eq. (9.1) is integrated as a function of 9 from 0 = 0 to 9 = 1t and
`
`177
`
`177
`
`

`

`9.1!;I
`
`SENSORS AND ACTUATORS
`
`then the summation is extended to angles larger than It by adding in the contributions of cylin—
`ders N + 1 and N + 3, the term in It} becomes an average angular velocity over a complete
`engine cycle.
`One important consequence of the preceding analysis is that, upon integration of the equa-
`tion, the sin 3 term becomes cos B—that is, the angular velocity wave lags the torque impulses
`causing it by m'2. Another consequence is that the amplitude of the period wave reflects the
`net contribution of the cylinders—if the load increases, and FAQ) increases to keep average
`angular velocity constant, the amplitude of the period wave must increase. The 10 term has
`become an In), it is the reciprocal of this term which was plotted in Fig. 9.4.
`When a spark plug fires or fuel is injected into a diesel cylinder, the pressure in the cylin—
`der takes a finite length of time to build—first, because of a delay to get the fire started and
`then because of 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 9 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 running faster.
`Further experiments by the Stanford researchers and others confirmed the suspicion that
`the period wave is 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-
`nent of the period wave measured with respect to a crankshaft angle index point, say t0p dead
`center of cylinder no. 1. The period wave is measured with a sensor which is a precision ver~
`sion of a crankshaft position sensor.” It produces a 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 arctari 311A]. To perform this com—
`putation in real time is 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
`wave appears to lead the torque impulses that cause it by M2, 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—TDC point.
`It is instructive to consider what performance is 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 sensor is a function of the diameter of the sensing disc. For the various mag—
`netic sensors, 3 repeatability better than 1:05 degree can be achieved with a ID—cm—diameter
`disc. In the DPA sensor, the concern is for the period-to~period jitter. 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 more fidelity the period wave will
`have for its high—frequency components. The period—to—period jitter of the magnetic sensor in
`this example is about 10.5 degree. This is satisfactory for 24 periods per revolution but
`marginal for 60 periods; a typical period wave amplitude is only i3 percent of the average
`period. On the other hand, even 60 periods per revolution is marginal for ignition or injection
`timing control.
`The granularity due to counting roundoff also needs to be considered. Today’s low-cost
`LSI circuits can count reliably at 20 MHz, so that is a practical clock frequency. If a four—cylin-
`
`178
`
`178
`
`

`

`ENGINE TORQUE SENSORS
`
`9.1 1
`
`der engine is running at 1800 revirnin (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 i3 percent amplitude period wave,
`this jitter amounts to $2 percent of the peak value of the period wave (not of the period itself),
`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 i one crankshaft degree is feasible.
`Figure 9.5 shows an actual period wave measured using an electromagnetic DPA sensor
`with one—degree increments and a 10—MHz clock. Both the jitter described previously and a
`fixed pattern noise can be discerned in 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 consume integration
`time. The better solution is to design a precision DPA sensor which minimizes fixed pattern
`nmse.
`
`DPA Used for Diagnostics. During the 19805, 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 toad the engine
`
`2200 —
`
`2nd 360 degrees
`
`IP11
`
`
`
`Jitter
`
`
`
`
`1st 360 degrees
`
`
`
`
`
`
`2100 i i
`
`
`
`
`
`10MHzpulsesbetweenteeth 8D0
`
`2100 '
`
`2000
`
`1940
`
`20
`
`40
`
`50
`
`80
`
`ILL—lltllltt1_trl_1_;_|_;_J_1_L_g__1_l__u
`100
`120
`140
`160
`130 200
`220 240 260 280 300 320 340
`360
`Gear tooth number
`
`FIGURE 9.5 Actual period wave data from engine crankshaft; unsmoothed data. {Courtesy ofThe Bendix Corn, Diesel! Operation)
`
`179
`
`179
`
`

`

`9.12
`
`SENSORS AND ACI UA'I‘ORS
`
`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 sensor is 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 next tooth is sensed by the first circuit. Virtually all of the fixed
`pattern noise is eliminated.
`What would be achieved in an on-board DPA system would be real~tin1e, 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 propagation is 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 number of cylinder pulses in order to
`obtain a good phase estimator. Under transient conditions, the shape of the pressure pulse
`may change enough so 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. As the airr'fue] 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 (SKN) is always a problem, since a differencing
`process always yields a poorer SIN than that of the original function. Hence, the DPA tech-
`nique yields poorer results the nearer the engine is to stoichiometry and the higher the engine
`speed.
`Referring to Fig. 9.6, if a figure of merit is formed
`
`T2— T1
`£1+t2
`
`R:
`
`
`
`
`
`(9.2)
`
`TDC
`
`TDC
`
`TDC
`
`INSTANTANEOUSENGINE
`PERIOD
`
` CRANK ANGLE
`
`I T1
`
`I T2
`
`———D-
`
`T1 —T2
`ROUGHNESS a F —
`
`t1 +t2
`
`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, whether direct 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 number of 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 control will first appear, and what kind or kinds will ultimately be successful, is
`not yet ciear.
`
`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 become essentially synonymous with control law for automotive engineers.
`Compression leveling A (theoretical) type of engine control which would cause each piston
`in each cylinder to compress its air charge to the same maximum pressure.
`Dynamometer A machine to absorb power in a controlled manner, especially from an
`engine under test.
`Hooke’s law A relationship for an ideal elastic member which says that the displacement is
`proportional to 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 in which the fuel
`for each cylinder is injected into 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 nor fuel left over, and all the reaction products such as carbon
`monoxide would be oxidized to their highest state-carbon dioxide.
`Torsional Hooke’s law A relationship 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 center of rota—
`tion. Its units are Newton—meters (pound force-feet).
`Unit injector A type of fuel conUol 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 hypodermic syringe.
`
`181
`
`181
`
`

`

`9.14
`
`SENSORS AND ACTUATORS
`
`REFERENCES
`
`1.
`
`J. A. "Remnant, Rat), H. 8., and Powell, J. David, “Engine characterization and optimal control,” Pro-
`ceedings ofthe IEEE Conference on Decisions and Contra! (including the 18th Symposium on Adap-
`tive Processes), Ft. Lauderdale, Fla, Dec. 12—14. 1979. IEEE 79CH 7486-0CS. Vol. I, 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 I. Fleming and Wood, P. W., “Non-contact miniature torque sensor for automotive applica-
`tions,” SAE Paper No. 820206.
`. Yutaka Nonomura; Sugiyarna, 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. 7’60007.
`Charles D. Hoyt, “DC excited capacitive shaft position transducer," US. 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 Otter, Kevin C, “On—line engine torque measurement utilizing crankshaft
`speed fluctuations," SAE Paper No. 850496.
`Clarence E. Kincaid, “Computerized diagnostics for Cummins engines,” Proceedbigs of Convergence
`’84, IEEE ’84 CH 1988—5.
`
`10.
`
`11.
`
`ABOUT THE AUTHOR
`
`For biographical information on William G. Wolber, see Chap. 8.
`
`182
`
`182
`
`

`

`CHAPTER 10
`
`
`ACTUATORS _
`
`Klaus Miiller
`Manager; Development ofMagnet Valves, Pressure Supply
`Automotive Equipment Division 1
`Robert Bosch GmbH, Stuttgart
`
`ion menace
`
`10.1.1
`
`Introductory Remarks
`
`Numerous open- and closed-loop controI 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
`
`Conventional finalazontrol elements (standard and spool valves, etc.) have been familiar for
`some time. A provision for electronic control is 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 conventional final—control element
`which it governs. (See Fig. 10.1.)
`
`'
`Electr. contr. signal
`
`
`
`Final-control
`element
`
`Mass or volume or
`energy flow
`
`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 Fm is calculated as
`
`2
`
`Fm = A B
`2%
`
`(10.1)
`
`where A = pole face area
`B = magnetic induction
`no 2 permeability constant (no 2 4 7t 10‘7 Vs/Am)
`
`On the flat-armature solenoid illustrated in Fig. 10.2a, the total solenoid force is 2 Fm. 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 determined for this force.
`
`
` """"
`
`vvvvv
`
`(a)
`
`(b)
`
`FIGURE 10.2 Flat—armature solenoid featuring field excitation (11) 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 magnitude greater than in air. For this reason, the iron
`regions conduct the field. If the effects of leakage flux are discounted, the absence of magnetic
`charge, gfii B dA = 0, means that the magnetic flux (Ilm remains constant for all cross sections A
`in the magnetic circuit:
`
`on. = ”A B dA1= ”A B dAz = “A B dA,- = const.
`1
`2
`i
`
`(10.2)
`
`If the magnetic induction is assumed to be homogeneous for all cross sections A, then Eq.
`(10.2) can be simplified to:
`
`(13m 2 31 A1: 32 A2 2 Bi 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 1 is
`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
`
`1 0.3
`
`armature
`
`air gap
`yoke
`
`1.5
`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 tug) of the section in question. Field strength l-L:
`
`B; = “.0 uni Hi
`
`(10'4)
`
`In air, u, = i. In ferromagnetic materials, u, 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 -—II-
`
`FIGURE 10.4 Progression of permeability and B-H curve
`
`Using the magnetic voltage Vm, = I H,- ds for the individual section, it is possible to calculate
`the peripheral magnetic voltage as the sum of the individual magnetic voltages Vm. Accord—
`ing to Ampere’s law,
`
`this magnetic peripheral voltage is equal to the magnetomotive force 8. It defines the total
`current of the coil, (9 = I w. (I = current, w = number of windings.)
`
`9 =1 H ds
`
`(10.5)
`
`185
`
`185
`
`

`

`1 0.4
`
`SENSORS AND AC1"UATORS
`
`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 magnetic circuit as a general network (with gaps and iron regions
`as reluctance elements) instead of as a series circuit. The results will then reflect the 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 8 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
`determine the field coil’s specifications. For a graphic interpretation, see Fig. 10.6.
`
`Aw = h -
`
`I
`
`Winding cross section area:
`
`h
`
`|
`
`A z
`w
`
`n a: p (da+di)(1+0t as)? 92
`2 kw U2
`
`Winding number:
`
`
`w:
`
`( 2A...ka
`
`H 9 (demo
`
`Wire diameter:
`
`
`
`1:2
`
`d:
`
`(apida+diiAwkw}“4
`
`11: R
`
`AW Winding cross section area
`Ft
`Coil resistance
`9
`Specific resistance
`of coil wire
`da Outer diameter of windings
`d-
`Inside diameter of windin s
`'
`9
`a
`Thermal resistivity coefficient
`of coil wire
`
`ac Temperature differential between
`coil and room temperature
`8 Magnetomotive force
`kW Coil space factor (ratio of total
`wire area {w/o Insulatlon} to winding
`cross section area)
`Voitage at coil
`
`U
`
`FIGURE 10.5 Determining coil data for specified coil resistance and voltage levels.
`
`
`
`
`
`
`WindingcrosssectionareaAW—|-
`
`
`
`Magnetomotive force 0 —h-
`
`FIGURE 10.6 Area of winding Aw as function of magneto—
`moljve force El (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 (Hg. 10.?)
`can be used to minimize the volume of pot—shaped solenoids.
`
`ACTUATORS
`
`10.5
`
`
`
`FIGURE 10.? Selecting coil dimensions for pot~shapcd solenoids
`
`In general, the solenoid is iteratively optimized by changing geometry in those critical
`areas within the magnetic circuit requiring a high magnetic voltage ij. The magnetomotive
`force 8 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.
`
`
`
` Soienoid
`diameterD—>
`
`L = const.
`
`
`
`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, Arnpere’s law [Eq. (10.5)] and Eq. (10.4) provide the following:
`
`o 2 H5 5 = fit?
`
`(10.6)
`
`where 5 : working gap
`
`187
`
`187
`
`

`

`10.6
`
`SENSORS AND ACHIATORS
`
`Together with the force relationship, Eq. (10.1), the following result is obtained:
`
`92
`A .
`1
`Fm = ——2l3§2—',1.e.,rm ~ g
`
`(10.7)
`
`The substantial dmp 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 current in the coil
`or by means of design modifications to the armature and base (see Fig. 10.9).
`
`2
`
`
`
`F
`
`(b)
`
`8
`
`FIGURE 10.9 Design modifications and force curve.
`
`F
`
`(a)
`
`F
`
`(6)
`
`3
`
`5
`
`The areas below the force-travel curves, a measure of the work performed, are always the
`same.
`
`farm (a) as: const.
`D
`with
`I = const.
`
`(10.8)
`
`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 mechanical friction, 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 more clearly, Fig. 10.11 pro-
`vides a schematic illustration of the progression over time of three parameters: voltage 11 at
`the excitation coil, excitation current i, and armature position 5.
`The dynamic response pattern can be calculated using computer programs that apply
`Maxwell’s equations (field propagation with eddy currents, self—induction) in corijunction
`with the motion equation.
`Approximation formulas can be employed to derive rapid estimates (eddy currents and
`magnetic resistance in the iron regions are not taken into account):
`
`188
`
`188
`
`

`

`
`
`ACTUATORS
`
`'I 0.7
`
`
`
`
`
`5—b-
`
`I—I-
`
`FIGURE 10.10 Operating points of a proportional solenoid.
`
`S:
`
`
`
`_
`
`(109a)
`
`(10.95)
`
`1
`L
`s u —21 ~————
`
`R n 1_£(2Fm50)m
`
`1
`
`U
`
`Lo
`
`....
`tr ————§9————31;"
`
`
`U( Fmech )
`__ R quh
`2 SOLD
`Lu
`
`U3
`
`where
`
`1..., = initial inductance
`R = coil resistance
`
`U = voltage at solenoid
`5., = gap with armature lowered
`th = armature counterforce (treated as constant)
`t1, :2, see Fig. 10.11
`
`and
`
`189
`
`189
`
`

`

`10.8
`
`SENSORS AND ACfUATORS
`
`t2
`
`’1:
`
`FIGURE 10.12 Relationships of I, and t2.
`
`Figure 10.12 provides an overview of the relationships between :1 and t; 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 current is
`applied suddenly, the progress over time for the magnetic force is
`
`F," (t) z FmD (1 — e‘”‘)2
`
`for field generation
`
`and
`
`with
`
`with
`
`Fm(t) = Fmo ed”:
`
`for field dissipation
`
`“t —ML for rectan ular cross sections
`‘ n2 p s (at; + an)
`g
`
`’L’ =M for circular cross sections
`4 (2.405)2 p a
`“
`
`where PM = static solenoid force according to Eq. (10.1)
`r = time
`
`in, = length of iron core in which eddy currents occur
`nib : heightl‘width of iron core (rectangular cross section)
`at 2 diameter of iron core (circular cross section)
`p 2 specific resistance
`3 = working gap
`
`Lamination to inhibit eddy currents in dc solenoids is not a standard precedure; 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 power loss P, = (FIR. The coil is thus designed to operate at the
`maximum permissible temperature.
`
`Torque Motors. The torque motor consists of a stator and an armature—both made of soft
`magnetic material—and a permanent magnet. The pivoting armature can be equipped with
`either one or two coils.
`
`Figure 10.13.21 shows only the magnetic flux generated by the permanent magnet.'Ihe arma-
`ture is resting at the center position.The magnitude of the magnetic induction is the same at all
`
`190
`
`190
`
`

`

`ACTUATORS
`
`10.9
`
`
`
`(a)
`
`(b)
`
`FIGURE 10.13 Design and operation of the torque motor.
`
`Center of rotation
`
`(C)
`
`gaps. Because equal amounts of force are generated at the armature ends, the forces acting on
`it exercise a mutual canceling effect.
`Figure 10.13.!) 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 (dip/2 + (DJZ) accompanied by reductions at gaps 1 and 4 (Clap/2 — (DJ2). Using Eq. (10.1),
`the torque in the center position is
`
`M=Fmr=flggswr,i.e.,rr~r
`
`(10.10)
`
`where
`
`r 2 armature radius
`
`A = pole face area
`3,, = magnetic induction in gap generated by permanent magnet
`s = length of gap
`w = number of coil windings
`I = 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 performance as 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 control signals to carry out rotary or
`linear stepped movements. Thus one complete rotation of the motor shaft will be composed
`of a precisely defined number of increments, step angles $0. The magnitude of these angles is
`determined by the phase number q, the pole pair number p, and by the number of teeth I, in
`the step motor. The step motor is thus capable of transforming digital control signals directly
`into discontinuous rotary motion. In principle, the step motor is essentially a combination of
`do solenoids. The calculations employed for do 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 magnetic circuit), and hybrid devices.
`
`191
`
`191
`
`

`

`10.10
`
`SENSORS AND ACIUATORS
`
`CE
`
`
`
`
`
`(b)
`
`FIGURE 10.14
`
`{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 come to be the most widely applied (see Fig. 10.14).
`Drive systems featuring electromagnetic step motors combine the following characteristics:
`
`. Field forces induce controllable, incremental movements (minimal wear).
`0 Precisely graduated movements can be generated using an open~loop control circuit (with-
`out position monitors or feedback signals).
`
`' High torque remains available at low angular velocities and in single-step Operation.
`- Brushless motor design makes it possible to create drive systems which combine reliabi