19MTZ worldwide 7-8/2002 Volume 63

MATERIALSTitanium

Engine speed is an indispensable input parameter for theelectronic control unit of an internal combustion engine.Measurement of the engine speed is carried out by sensorwheels mounted on the crankshaft. In particular, geometrictolerances of the engine speed sensor wheel cause system-atic deviations that reduce the quality of engine speed sens-ing. This article by the Ingenieurgesellschaft Auto und Ver-kehr GmbH (IAV), the Fraunhofer-Institut für Informations-und Datenverarbeitung (IITB) and the Audi AG presents twoprocedures that allow the determination and in-service com-pensation of sensor wheel tolerances.

By Hermann Fehrenbach,

Carsten Hohmann,

Thorsten Schmidt,

Winfried Schultalbers

and Henning Rasche

Kompensation

des Geberradfehlers

im Fahrbetrieb

You will find the figures mentioned in this article in the German issue of MTZ 7-8/2002 beginning on page 588.

Inservice Compensationof Sensor Wheel Tolerance

20 MTZ worldwide 7-8/2002 Volume 63

1 Introduction

Engine speed is an indispensable input pa-rameter for the control of internal combus-tion engines. In particular, geometric toler-ances of the engine speed sensor wheelcause systematic deviations which reducethe quality of engine speed sensing. Withinthe scope of a co-operative project aimed atthe development of new speed-based diag-nostic and engine management methods,IAV GmbH, the Fraunhofer-Institut für In-formations- und Datenverarbeitung (IITB)and Audi AG have developed two differentmethods that allow the determination andin-service compensation of sensor wheeltolerances.

2 Task and Motivation

Among other functions, the control ofidling speed and engine smoothness isbased on the engine speed signal. Misfiringcan be detected by evaluating the enginespeed curve of individual cylinder seg-ments. In addition, modern angle-con-trolled diesel injection systems (commonrail and unit injectors) need a crank-anglereference for fuel metering. For controllingthe start and end of injection, the angle ref-erence is sensed with the aid of ferromag-netic pulse-generator wheels. Figure 1shows an example of this sensor wheel – a60-2-2 sensor wheel for diesel engines with56 teeth and two gaps.

When sensor wheels are manufacturedand installed, tolerances occur. Geometrictooth pitch tolerance, in particular, causes asystematic deviation in engine speedwhich is different for each sensor wheel. Itis desirable to have a method to compen-sate for this engine speed deviation in theengine control unit in order to increase thequality of the speed-dependent controlfunctions. Furthermore, such a method al-lows the quality requirements for sensorwheels to be reduced, allowing them to bemanufactured at a lower cost. It is particu-larly important to correct the engine speeddeviation in the event of tooth-synchro-nous evaluation of the engine speed signal.This mode of evaluation has been appliedin more recent methods such as cylinder-selective engine management or speed-based torque estimation.

3 Properties of the Sensor Signal

As an example, Figure 2 shows an outputsignal of an inductive sensor as used for en-gine speed sensing via sensor wheel. Thecurve of the signal in the gap, which herereveals a strong non-linear dependence on

the engine speed, is striking. For further sig-nal processing, it is useful to interpolate themissing teeth in the gap.

The engine speed is evaluated by mea-suring the intervals between the zero tran-sitions of the voltage signal. The interval ΔTthus determined allows the angular speedωmeas to be calculated using Equation (1):

A constant tooth interval Δϕsoll is usedfor the evaluation. However, the tooth in-terval is different for each tooth due to thetooth pitch tolerance. This difference re-sults in the systematic sensor wheel devia-tion which, with the aid of the true angularspeed ωref, can also be described as the rela-tive engine speed deviation in Equation 2:

4 Existing EstimationMethods

Contemporary publications describe onlyfew methods which allow the geometrictolerance of the engine speed sensorwheels to be estimated. The option of re-moving the sensor wheel for measurementmust be generally excluded on grounds ofthe effort and cost required. In addition,this option would not take into account thetolerance caused by mounting the sensor.

There are only few concepts that allow acorrection of the deviation with the sensorwheel mounted. Certain methods are limit-ed to a segmented correction of the geo-metric tolerance. This is not suitable forcontrol and diagnostic functions, since theangle resolution of the engine speed mea-surement is severely restricted. When esti-mating the tolerance, some of the othermethods do not sufficiently allow for devi-ations of an order equal to or lower thanthe ignition frequency. However, these de-viations are what make cylinder-specific di-agnosis or control so difficult.

5 Determination and Compensation of the SensorWheel Tolerance

If the reference engine speed is known, thesensor wheel tolerance δ’ can be deter-mined for each tooth using Equation 2. Thedeviation can then be corrected using Equa-tion 3:

It is particularly difficult to determinethe reference engine speed of an internal

combustion engine, since inertia and gasforces cause rotational non-uniformities. Inorder to solve this problem, IAV has devel-oped a method that specifies the referencespeed with the aid of a kinetic crankshaftenergy model. The crankshaft's moment ofinertia θ and the angular speed ωref deter-mine the kinetic crankshaft energy E inEquation 4:

All variables in Equation 4 depend onthe crank angle ϕ. The kinetic crankshaftenergy E varies in relation to the crank an-gle because of the compression and expan-sion work Egas(ϕ) of the cylinders. Duringthe overrun phase, the gas forces are not in-fluenced by combustion and can then beapproximated by means of a polytropiccompression. This model of the kinetic en-ergy approach and Equation 3 lead to themethod’s basic Equation 5:

The inertia forces are described with theaid of a variable moment of inertia θ(ϕ). E– represents the mean crankshaft energy atthe selected operating point. Equation 5 al-lows the calculation of the sensor wheel de-viation δ’(ϕ) for each tooth speed ωmeas(ϕ).In order to fully determine the sensorwheel deviation, the engine speed curveωmeas(ϕ) only needs to be recorded in theoverrun state for the length of one crank-shaft revolution.

The method developed by the IITB usesthe anti-phase properties of gas and inertiaforces to determine and compensate for thegeometric tolerance of the sensor wheel.The only parameters required for thismethod are the number of cylinders andteeth. The reference angular speed ωn(z) isdetermined on the basis of the mean angu-lar speed, which is in turn determined bymeasuring the engine speed. The angulardeviation is then calculated using the rela-tionship described in Equation 6:

Here is Δϕen (z) the incremental angulardeviation per revolution, ωn (z) the incre-mental angular speed per revolution (esti-mated), f (z) the increment frequency (mea-sured), Δϕi (z) the angle increment for a ide-al indrement and k and l the lower and the

DEVELOPMENT Measuring and Test Techniques

Eq. (1)

Eq. (3)

Eq. (4)

Eq. (6)

Eq. (2)

Eq. (5)

21MTZ worldwide 7-8/2002 Volume 63

upper engine-speed limit. For ensembleaveraging, an appropriate engine speedrange must be selected. If this range is se-lected correctly, the proportion of the signalthat is due to the rotational non-uniformi-ties is compensated for by averaging.

It is only necessary to ensure that thephase is sufficiently distributed statistical-ly. When adapting the sensor wheel, it istherefore useful to choose a run-down test,since this covers all engine speed ranges.The benefits of this method are that it re-quires little calculation and is parameter-independent.

6 Test Set-Up

The two compensation methods of IAV andIITB presented above were tested using afive-cylinder in-line engine. The referenceangular speed was recorded using an opti-cal reference sensor similar to those used asangle mark sensors for indication systems.For cylinder pressure indication, it is stan-dard practice to mount the sensor at thefree end of the crankshaft. However, mea-surements have revealed that, with thisset-up, a dynamic angle deviation falsifiesthe reference measurement due to crank-shaft torsion. For this reason, the referenceangle mark sensor was mounted directlyon the flywheel.

7 Test Results

Figure 3 shows the results of the estimatedsensor wheel tolerance gained using thetwo methods described above, compared tothe determination of tolerance using a ref-erence measurement. As expected, the tol-erance curve has its peak in the area of thetooth gap (tooth numbers 8 to 11; the gap it-self between numbers 9 and 10 is not de-picted). Both methods of tolerance estima-tion provide comparable results. In the caseillustrated, the maximum deviation fromthe reference is only 0.02 °CA.

In order to test the reproducibility of theestimated tolerance results, several testswere performed using the same engine andthe same sensor wheel. The maximum de-viations during the tests were less than0.008 °CA. Figure 4 shows the curve of theestimated tooth tolerance for five differentmeasurements in accordance with the IITBmethod.

8 Summary and Outlook

This article presents two methods devel-oped by IAV and IITB that allow the manu-facturing-related geometric tolerance ofengine speed sensor wheels to be deter-mined and compensated for during normal

operation. Both procedures allow a consid-erable increase in the accuracy of angularspeed measurements with minimum ef-fort.

As far as their structure is concerned,both methods can be integrated into theengine control system. This offers new per-spectives for all electronic control units anddiagnostic functions which can be solvedusing a precise engine speed signal. Im-provements are to be expected particularlyin the area of injection and in control sys-tems for engine smoothness. ■

MATERIALSTitanium