A Hall-effect sensor based instrument for measuring the door-seal gap ofheavy trucks on the production line

Daniel P. Koch

Department of Mechanical Engineering (Undergraduate)Brigham Young University

Provo, Utah 84602Email: daniel.p.koch@gmail.com

Abstract

A proof-of-concept design for an instrument to measure the door-seal gap width on heavy trucks is presented.The door-seal gap is an important specification because if it is too small, the seal becomes over-compressedwhen the door is closed and exerts too much pressure on the door latch. The proposed design uses aHall-effect sensor and a permanent magnet in a unipolar, head-on configuration to measure the gap width.Because the relationship between the gap width and sensor output voltage is non-linear, the instrument fitsa curve through two calibration data points, and uses this curve to calculate the measured distance fromthe sensor output voltage. The measurement uncertainty of the instrument was within ±0.5mm over themajority of the desired measurement range, which is within the accuracy range required for this application.

1. Introduction

The door-seal gap width is an important, thoughoften overlooked, specification in the heavy truckindustry. The door-seal gap width is the distancebetween the door opening panel on the truck bodyand the door itself, in the location where the door-seal will later be installed. This gap has to be ad-justed by technicians on the production line to bewithin specification. If the gap is out of specifica-tion, it can cause several issues. A gap that is toolarge allows water and excessive road noise to en-ter the truck cabin because the door does not sealproperly. A gap that is too small, however, over-compresses the door-seal as the door is closed. Thiscondition requires the operator to apply an exces-sive amount of force to close the door, which canlead to operator fatigue or discomfort and to ex-cessive wear on other truck components. The over-compressed seal also applies excessive force on thedoor latching mechanism, which causes the mecha-nism to wear quickly and possibly fail over time.

No reliable methods currently exist for measur-ing the door-seal gap. Traditional measuring de-vices such as calipers and micrometers cannot beused because the gap must be measured while thedoor is closed. Current methods consist of placing a

piece of clay in the appropriate location on the dooropening panel, closing the door on it, opening thedoor and removing the clay, and then measuringthe thickness of the clay. This method is unreli-able, however, because the door can over-compressthe clay as it closes or, if the clay adheres to thedoor, can deform the clay as it opens, resulting inan inaccurate measurement. In addition, this mea-surement is often made before the truck is painted,and the clay can leave residues that adversely af-fect paint adhesion. This method is also slow, andsince it requires the use of clay it is not particularlysuitable for a production environment. As a re-sult of these limitations, the door-seal gap width isnot currently measured on the production line, andtrucks are consequently shipped with doors that arepositioned out of specification.

An instrument for measuring the door-seal gapwidth must satisfy several conditions to be suit-able for use on the production line. The instru-ment must be accurate and reliable. In addition,it must be portable and easy to use so that themeasurement can be made as quickly as possible.This paper presents a proof-of-concept design fora proposed instrument that fulfills these require-ments. The instrument uses a Hall-effect sensor as

May 2, 2012

its data acquisition mechanism. A Hall-effect sen-sor was chosen because it reduces the mechanicalcomplexity of the proposed instrument, is inexpen-sive, and gives reasonably accurate and repeatableresults. The instrument was designed specificallyfor use on the Freightliner Cascadia, which is thecurrent model Class 8 heavy truck manufacturedby Freightliner Trucks, a division of Daimler TrucksNorth America LLC.

2. Theory and Background

In order to take into account all of the necessaryconsiderations in the design of the subject, a ba-sic understanding of the theory behind Hall-effectsensors and their applications is required. This in-cludes an understanding of the basic principle be-hind the operation of Hall-effect sensors and theeffect of magnet orientations on the reading fromthe sensor.

2.1. Hall-Effect Sensors

A Hall-effect sensor produces an output voltageproportional to the strength of the magnetic fieldpassing through it. These sensors work on the prin-ciple of the Hall effect, which acts on a conduc-tor with current flowing through it. When a mag-netic field passes through the conductor, it producesa force on the charge carriers (the electrons in ametal or n-type semiconductor) that is perpendic-ular both to the direction of the magnetic field andto the direction of the current flow. This causes thecharge carriers to become concentrated on one sideof the conductor, producing an electric potential orvoltage. This voltage varies linearly with the mag-netic flux density, β, and with the magnitude of thecurrent, I, according to the relationship

VH =KHβI

z(1)

where KH is the Hall constant for the specific con-ductor and z is the thickness of the conductor. Inthe case of a Hall-effect sensor, where both KH andz are fixed, equation (1) can be written as

VH = KβI (2)

where K is the magnetic sensitivity [1]. The valueof K for a specific device is specified by the man-ufacturer, and is usually given in either volts pergauss or volts per millitesla (mT). From (2), the

strength of the magnetic field can be determinedby measuring the Hall voltage VH .

The sign of the Hall voltage depends on the di-rection of the magnetic field (i.e. if a magnetic fieldemanating from the north pole of a magnet gener-ates a positive Hall voltage for a specific sensor andconfiguration, then a magnetic field emanating fromthe south pole of a magnet will produce a negativeHall voltage for the same sensor and configuration).In addition, because the voltage produced is per-pendicular to both the current and the magneticfield, a Hall sensor is sensitive to magnetic fieldsacting only along one specific axis (in commerciallyavailable Hall sensor integrated circuits, this axis isgenerally perpendicular to the face of the sensor).This axis is referred to as the sensitive axis of thesensor.

2.2. The Effect of Magnet Orientation

Using a Hall-effect sensor to measure displace-ment poses a special challenge because even thoughthe output voltage of the sensor varies linearly withthe magnetic flux density passing through it, thisflux density does not vary linearly with the distancefrom the magnet to the sensor. The displacementof an object is generally measured by placing thesensor in a fixed location, then affixing one or morepermanent magnets to the moving object such thatthe magnets are in close proximity to the sensor.

By varying the combination of the number of per-manent magnets and their orientations, the non-linearity of the flux density passing through thesensor with respect to distance can be alleviatedto a certain degree. The combinations commonlyused in practice generally fall into two sets of cate-gories: head-on vs. slide-by, and unipolar vs. bipo-lar [1–3]. “Head-on” refers to the condition wherethe direction of motion of the magnets is parallelto the axis of the magnets’ poles. In this config-uration the Hall-effect sensor is placed such thatits sensitive axis is coincident with this polar axis.“Slide-by” refers to the condition where the sensoris still placed with its sensitive axis parallel to theaxis of the magnets’ poles, but now the directionof motion of the magnets is perpendicular to thisaxis. In a “unipolar” configuration only one mag-net is used, while in a “bipolar” configuration twomagnets are used. For the “bipolar head-on” casethe sensor is generally placed between the two mag-nets, and the magnets’ poles are aligned with eachother, while in the “bipolar slide-by” case the mag-

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nets are placed side-by-side with their poles alignedin opposite directions.

The configuration that tends to yield the mostlinear relationship between displacement and mag-netic flux density passing through the sensor isbipolar slide-by [2]. Due to the geometric con-straints for this application, however, it is not fea-sible to use this configuration. The only feasibleconfiguration for this application is unipolar head-on. In this configuration, the magnetic flux densityvaries approximately with the inverse square of thedistance, d [1]:

β ∝ 1

d2(3)

While this relationship is not ideal, a reasonablyaccurate displacement sensor can still be made us-ing this configuration. McCall and Rohan [4] de-scribe a position transducer that uses this configu-ration. By using appropriate conditioning circuitry,they were able to obtain a voltage output that wasapproximately linear with respect to displacement,and that was reasonably accurate at distances of upto 30 to 60mm. A similar approach was taken inthe design of the proposed instrument.

2.3. Effect of Magnetic Materials

Ferromagnetic materials such as steel and ironinteract with and affect magnetic field lines. Oneof the ways in which they do this is by redirectingthe magnetic field lines. For example, if a ferrousplate is placed between a permanent magnet and aHall-effect sensor, the magnetic field lines will takethe shorter path through the plate and back to themagnetic pole. As a result, the Hall-effect sensorwill no longer sense any magnetic field. Anotherresult of this effect is that if a Hall-effect sensorin head-on configuration with a permanent magnetis backed by a piece of ferromagnetic material, themagnetic field that the sensor sees will be intensified[3]. This effect may need to be taken into consider-ation as many heavy truck bodies are manufacturedout of steel.

3. Specifications

The instrument needs to meet several specifi-cations to be suitable for use on the productionline. These specifications fit into the categoriesof geometric requirements, accuracy requirements,human interface requirements, and other miscella-neous specifications. The technical specifications

for the door and requirements for the instrumentwere obtained in a private communication with aFreightliner engineer [5].

3.1. Geometric Requirements

The instrument must be able to fit entirely withinthe door-seal gap when the door is closed. Figure 1shows a CAD model of the door and door openingpanel, and Figure 2 shows a typical cross-sectionof the door, door opening panel, and door-seals.Note that there are two door-seals, and hence twodoor-seal gaps. The door-seal shown in cyan is theprimary door-seal, while the door-seal shown in ma-genta is the secondary door-seal. Because the doorand door opening panels themselves will have beenpreviously checked to verify that they are withinspecification, it will only be necessary to measurethe primary door-seal gap to ensure that both gapsare within specifications.

The instrument would be used by mounting it(using a clip or some other means) on the flat por-tion of the door opening panel where the primaryseal will later be attached (this is the location ofthe primary seal in Figure 2). The nominal widthof the door-seal gap is 15mm, with a tolerance of±3mm. In practice, deviations of up to ±6mm maybe encountered, which means that the instrumentmust be able to measure distances ranging from 9to 21mm. In addition, the height of the instrument,when fully compressed, must be no more than 9mm.The width of the flat portion of the door openingpanel on which the instrument will be mounted isapproximately 20mm, which defines the maximumallowable width of the instrument. Because the in-strument could be placed on relatively straight sec-tions of the door opening, there is no fixed limit onthe length of the instrument.

3.2. Accuracy Requirements

Because the tolerance range on the door-seal gapspecification is fairly large (±3mm), the proposedinstrument does not need to be particularly accu-rate. As long as the absolute error is within ap-proximately ±0.5mm, the instrument will be morethan accurate enough for the intended application.Because the body of the Cascadia is made of alu-minum, the effect of ferromagnetic materials suchas steel on the accuracy of the instrument does notneed to be considered.

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Figure 1: CAD model of the Cascadia’s door (green) anddoor opening panel (gray)

Figure 2: Typical section cut of the door (red), door openingpanel (dark blue), primary door-seal (cyan), and secondarydoor-seal (magenta). The widths of the door-seal gaps arehighlighted in green.

3.3. Human Interface Requirements

Technicians would place between 3 and 6 of theproposed instruments at crucial locations aroundthe door opening to acquire the information re-quired to adjust the door properly. The device musttherefore be easy to mount on the door openingpanel so that technicians can make the measure-ments quickly. The instrument must also providesome type display that can be read quickly andeasily. This would ideally consist of a numericaldisplay that indicates the actual width of the door-seal gap. Because the tolerance range is so large, nomore than three significant digits would be neces-sary on the display. The display should also updatein real time.

3.4. Other Requirements

The instrument should be as small and self-contained as possible so that it is easy to use ina production environment. Ideally the instrumentwould be battery powered, and would either incor-porate a display directly onto the instrument orwould provide wireless connectivity to eliminate ca-bles. In addition, the instrument should be as in-expensive as possible, which means that it shouldbe easy to manufacture and should use inexpensivecomponents.

4. Methods

There were three main phases to the design ofthis instrument. The fist phase consisted of de-signing the mechanical and electrical aspects of theinstrument and building a physical prototype. Thenext phase involved designing, implementing, andvalidating a calibration method. The final phaseconsisted of collecting data with the device and per-forming an uncertainty analysis to quantify the ac-curacy of the instrument.

4.1. Mechanical Design

The final mechanical design of the instrumentwas chosen for its simplicity. A simple design waschosen to ensure the durability of the instrumentand to decrease manufacturing costs. Figure 3shows a CAD rendering of the proposed design.The instrument consists of a steel arm that is at-tached at one end to an aluminum base. A plasticor metal clip would be attached to this base so thatthe instrument can clip onto the door or door open-ing panel. The Hall-effect sensor is mounted on the

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Figure 3: CAD model of the mechanical design of the instru-ment. The permanent magnet is mounted on the underneathside of the arm such that it is positioned directly above theHall-effect sensor. Note that the clip can be modified asneeded to fit the specific application.

base below the free end of the stainless steel arm,and a permanent magnet is affixed to the free endof the arm. This arm serves as a spring that holdsthe magnet up away from the sensor. As the instru-ment is compressed by the door, the arm bends sothat the magnet comes into closer proximity to theHall-effect sensor, and the sensor then produces acorresponding output voltage.

This design does introduce some additional non-linearities into the relationship between the sensoroutput and the distance being measured. Thesenon-linearities occur because the output voltage ofthe sensor is sensitive to both translational and an-gular misalignments of the sensitive axis of the sen-sor with the polar axis of the magnet. The effectof these irregularities, however, es relatively smalland does not significantly affect the accuracy of theinstrument. This is demonstrated in Section 5.

4.2. Electrical Design

Because the output voltage of the Hall-effect sen-sor depends on the magnitude of the power supplyvoltage, it is essential that the power supply volt-age coming into the sensor be consistent. This isaccomplished with the filtering circuitry shown inFigure 4. The input voltage to this circuitry wouldbe in the range of 9V, and could come from eithera battery or from a wall adapter. The circuitryfilters high-frequency noise out of the input, andoutputs a constant 5V to the Hall-effect sensor andother electronics. The Hall-Effect sensor chosen forthis prototype was the A1302 continuous time, ra-tiometric, linear Hall effect sensor manufactured by

IN1

OUT3

GND

2

7805

100μF 10μF

1N4001

Green LED

330Ω

VCC1

GND2

3VOUT

A1302

Sensor Voltage Out

0.1μF

115V AC to 9V DCWall Adapter

115VAC

Figure 4: Schematic of the power supply circuitry. An ap-proximately 9V input is connected to the power plug to sup-ply a constant 5V source to the A1302 Hall-effect sensor.The output value is read from pin 3 of the sensor.

Figure 5: Photograph of the realized hardware implementingthe proposed design. The actual measurement device canbe seen in the foreground on the right; the power supplycircuitry can be seen on the left.

Allegro MicroSystems, Inc. (for the full specifica-tions for this sensor, see reference [6]).

Figure 5 shows a photograph of the realized hard-ware implementing both the proposed mechanicaland the proposed electrical design. For the pur-poses of this proof-of-concept report, all data ac-quisition and real-time calculations were performedusing LabVIEW.

4.3. Calibration

The Hall-effect sensor produces an output voltagethat is non-linear with respect to the distance be-tween the sensor and the magnet. A simple curve-fitting method was employed to perform the cal-ibration required to obtain an accurate measure-ment of the distance from the output voltage fromthe sensor. This method was chosen because it re-quires only two data points and so the calibrationcan be performed very quickly, and because the nec-essary calculations are relatively simple and so can

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be easily implemented on a microprocessor.From equations (2) and (3),the relationship be-

tween the output voltage and the distance beingmeasured is expected to be of the form

V =C

(d− d0)2 + VQ (4)

where C and d0 are constants to be determined andVQ is the quiescent output voltage, or the voltagethat the Hall-effect sensor outputs when there is nomagnetic field present. The value of VQ is suppliedby the manufacturer, and for the A1302 Hall-effectsensor is equal to [6]

VQ = 2.5 V (5)

Solving equation (4) for d yields

d =C√

V − VQ+ d0 (6)

where the arbitrary constant C has been taken out-side of the square root. Collecting two data points,(V1, d1) and (V2, d2), and substituting them intoequation (6) produces the system of equations

d1 =C√

V1 − VQ+ d0 (7a)

d2 =C√

V2 − VQ+ d0 (7b)

which needs to be solved for the two unknowns Cand d0. Subtracting (7b) from (7a) and solving forC gives

C =d1 − d2

1√V1−VQ

− 1√V2−VQ

(8)

Solving (7b) for d0 then yields

d0 = d2 −C√

V2 − VQ(9)

where the value of C is obtained from equation (8).For both (8) and (9), the value of VQ is obtainedfrom (5).

After the calibration is complete, the instrumentdisplays the distance being measured in real time byreading the output voltage from the Hall-effect sen-sor and plugging it into equation (6) along with thevalues of C, d0, and VQ. This calibration methodwas validated by also collecting data points alongthe entire measuring range of the instrument at in-tervals of approximately 0.1mm, and then compar-ing these measured values with the values predictedby the calibration curve fit.

4.4. Effect of Magnetic Materials

In order to gain a basic understanding of how fer-romagnetic materials, such as steel and iron, affectthe reading of the instrument, a second calibrationcurve was collected after mounting the instrumenton a steel base. This calibration curve was thencompared to the original calibration curve. Becausethe Cascadia has an aluminum body, this issue isnot particularly relevant and so was not exploredin detail. However, this is an issue that should beexplored in subsequent design iterations and so itmerits at least a mention here.

4.5. Uncertainty Analysis

The sources of error in the proposed measure-ment system include sensitivity and linearity er-rors in the Hall-effect sensor, irregularities in thepower supply voltage, non-linearities introduced bythe mechanical design of the device, errors in dataacquisition and digital-to-analog conversion, errorsin the calibration equipment, and errors caused bythe calibration method itself. A simple uncertaintyanalysis was performed to quantify the aggregateeffect of these sources of error and to provide anestimate of the accuracy of the device.

At 1mm intervals along the entire measurementrange of the instrument (9mm to 21mm), sets of 50data points (N = 50) consisting of the measureddistances were collected. This was accomplished byrepeatedly inserting the device into a fixed gap andrecording the measured distance. The mean (d̄) andstandard deviation (Sd) of each of these sets wasthen calculated, and the interval within which—with 95% probability—any single measurement diis likely to fall was estimated using the formula

di = d̄± tν,95Sd (95%) (10)

where tν,95 is the Student’s-t distribution, and thenumber of degrees of freedom, ν, is equal to N − 1.The term ±tν,95Sd is the uncertainty.

5. Results

There are two main important results obtainedfrom the methods described above: the validationresults for the calibration method, and the resultsfrom the uncertainty analysis.

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2.5 3 3.5 4 4.5 5 5.58

10

12

14

16

18

20

22Calibration Curve Fit

voltage [V]

dist

ance

[mm

]

calibration datacurve fitcurve fit sample points

Figure 6: Plot of the recorded calibration data points andthe calibration curve fit. The blue points are the individualdata points, the green line is the curve fit, and the red pointsare the data points used for the curve fit. Note that the axesdo not start at zero in order to show more detail.

5.1. Calibration

Figure 6 shows the recorded calibration datapoints along with the curve fit given by equations(6), (8), and (9). Data points were collected atintervals of approximately 0.1mm. The nominaldistances of the sample points for equations (8)and (9) were chosen to be 10mm and 18mm. Thedata points that were actually used are (V1, d1)= (3.9206 V, 10.0447 mm) and (V2, d2) = (2.7164V, 18.0647 mm). As can be seen from the figure,equation (6) approximates the actual calibrationdata very well. There are a few irregularities inthe recorded data points compared to the predictedcurve; these irregularities are most likely causedby the mechanical design of the instrument as dis-cussed previously.

Figure 7 shows the absolute error between thedistance calculated from the output voltage usingequation (6) and the distance actually recorded inthe calibration points. As is apparent, the erroris within the desired ±0.5mm bounds over the en-tire measurement range, and over the majority ofthe measurement range the error is within approx-imately ±0.2mm. This result is encouraging, asit suggests that the total final error will likely bewithin the desired bounds over the majority of thecalibration range.

8 10 12 14 16 18 20 22−0.2

−0.1

0

0.1

0.2

0.3

0.4

0.5Error between calibration data and curve fit

nominal distance [mm]

abso

lute

err

or [m

m]

Figure 7: Plot of the absolute error in distance between thecalibration data and the estimate given by the curve fit. Notethat the axes do not start at zero in order to show moredetail.

5.2. Effect of Magnetic Materials

When a steel plate was placed under the baseof the instrument, the Hall-effect output voltagechanged and the instrument’s calibration curveshifted. This new calibration curve is plotted along-side the original calibration curve in Figure 8. Ascan be seen, there is a significant difference betweenthe two curves. This suggests that at the least theinstrument needs to be recalibrated before beingused on magnetic materials, or that in future de-sign iterations measures should be taken to elimi-nate this effect.

5.3. Uncertainty Analysis

Table 1 summarizes the results of the uncertaintyanalysis calculated from equation (10). These re-sults are also displayed graphically in Figure 9,where the acceptable ±0.5mm error bound is alsosuperimposed. As can be seen, the measured un-certainty is within the ±0.5mm error target overmost of the measurement range. The reason forthe large uncertainties at 16mm and 17mm is notknown, but these results appear to be atypical andnon-representative of the accuracy of the instru-ment in that range. As the nominal distance in-creases, the uncertainty generally also increases.This is consistent with the calibration curve shownin Figure 6. At small distances, a small change involtage leads to a very small change in the resultof the distance calculation, while at large distancesa small change in voltage corresponds to a larger

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2.5 3 3.5 4 4.5 58

10

12

14

16

18

20

22

24Ferromagnetic Effect

voltage [V]

dist

ance

[mm

]

AluminumSteel

Figure 8: Plot of the calibration curves obtained with analuminum backing and with a steel backing. Note that theaxes do not start at zero in order to show more detail.

nominal dis-tance [mm]

mean [mm] uncertainty[mm]

9 9.1654 0.03992110 9.9529 0.05633811 10.8414 0.05976612 12.1508 0.01566813 12.798 0.04416714 13.6625 0.09389415 15.0744 0.06562716 15.533 0.3313817 16.3714 0.5817218 18.4192 0.1316719 18.788 0.476420 19.8281 0.7291421 20.3684 1.2769

Table 1: Mean value and uncertainty range for each of thenominal distances chosen for the uncertainty analysis

8 10 12 14 16 18 20 228

10

12

14

16

18

20

22Uncertainty vs. Nominal Distance

nominal distance [mm]

mea

sure

me

dist

ance

[mm

]

nominal distance0.5mm error range1.0mm error rangemeasurement uncertainty

Figure 9: Plot of the results from the uncertainty analysis.The blue lines represent the nominal distance, the ±0.5mmerror range, and ±1.0mm error range respectively. The redx’s represent the mean values, and the green error bars showthe uncertainty.

change in the result. This implies that the accuracyof the instrument is better at smaller distances.

6. Discussion and Conclusions

The proposed design and prototype was success-ful as a proof-of-concept demonstration for usinga Hall-effect sensor based instrument to measurethe door-seal gap. The device generally performedwell, although there are still a few issues that needto be resolved. In addition, there are still some im-provements that should be implemented to makethe device ready for commercial use.

The calibration results shown in Figures 6 and7 demonstrate that the curve-fitting calibrationmethod is reasonably accurate and closely matchesthe empirical data. In addition, the two-point cal-ibration method can be performed quickly, and iscomputationally inexpensive and so can easily beimplemented using a microprocessor. Furthermore,Figure 9 shows that over the majority of the de-sired measurement range (9mm to 21mm), the un-certainty associated with the instrument’s measure-ment is within the ±0.5mm error bound target forthe device. This level of accuracy obtained withthe first prototype suggests that further researchand development of this device would be justified.

While the instrument performed well overall,there are still some significant issues that need tobe resolved. The first is that at the upper end of

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the measurement range (between about 18mm and21mm), the uncertainty associated with the mea-surement result increases sharply. Further workneeds to be done to resolve this issue. This may in-clude refining the electrical design of the device, ormodifying the mechanical design to keep the mag-net at a more appropriate distance from the sensoreven when large gaps are being measured. Anotherproblem that still needs to be addressed is that thereading from the Hall-effect sensor changes whenthe instrument is placed on a steel (or any otherferromagnetic) surface. This would obviously bean issue for trucks whose bodies are made of steel.Since the Cascadia has an aluminum body, this is-sue is not immediately relevant. However, it wouldbe worthwhile to conduct further research into solv-ing this issue so that the instrument could be usedon truck bodies of any material.

Aside from these major issues, a few minor im-provements would still need to made to transformthis prototype design into a commercially viable so-lution. Certain manufacturing processes could beimproved, such as using printed circuit boards anda surface-mount Hall-effect sensor to fix the sen-sor more securely to the base. In addition, thedata processing functionality needs to be imple-mented on a microprocessor to replace the currentLabVIEW implementation. Furthermore, the de-vice should be converted to run on battery power,and could also possibly transmit data using wirelesstechnologies.

While there are still various improvements andrefinements to be made, this prototype design func-tioned extremely well, and serves as a good startingpoint for developing a commercially viable systemfor measuring the door-seal gaps on the productionline for heavy trucks.

7. Acknowledgments

I would like to thank John Koch for providingtechnical information and details regarding the re-quirements for the measurement system. John isa Senior Development Engineer in the Door Sys-tems Integration and Optimization group at Daim-ler Trucks North America LLC.

References

[1] D. S. Nyce, Linear Position Sensors: Theory and Ap-plication. Hoboken, New Jersey: John Wiley & Sons,Inc., 2004.

[2] D. Ferrazzin, G. Di Domizio, F. Salsedo, C. A. Avizzano,F. Tecchia, and M. Bergamasco, “Hall Effect Sensor-Based Linear Transducer,” Proceedings of the 1999 IEEEInternational Workshop on Robot and Human Interac-tion, vol. 219-224, 1999.

[3] E. Ramsden, Hall-Effect Sensors: Theory and Applica-tion, 2nd ed. Amsterdam: Elsevier, 2006.

[4] W. D. McCall and E. J. Rohan, “A Linear PositionTransducer Using a Magnet and Hall Effect Devices,”IEEE Transactions on Instrumentation and Measure-ment, vol. 26, no. 2, pp. 133–136, 1977.

[5] J. G. Koch, Senior Development Engineer, DaimlerTrucks North America LLC, Mar. 2012, private commu-nication.

[6] Allegro MicroSystems, Inc., “A1301 and A1302Continuous-Time Ratiometric Linear Hall Effect SensorICs,” datasheet, Worcester, Massachusetts, 2010.

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