ieee_wolffenbuttel_1990.

ieee_wolffenbuttel_1990.
Io08
IEEE T R A N S A C T I O N S O N INSTRUMENTATION A N D M E A S U R E M E N T . VOL. 39. N O . 6. D E C E M B E R 1990
Noncontact Capacitive Torque Sensor For Use on a
Rotating Axle
REINOUD F. WOLFFENBUTTEL,
MEMBER, IEEE, A N D
Abstruct-The measurement of the torque in a mechanically loaded
axle is often required for automotive power-train and engine control
systems. Up to the present, torque sensing has been performed by
mainly using strain gauges connected to the axle with slip rings to enable the electrical contacting. Noncontact magnetic and optical techniques have also been employed. In the proposed capacitive torque sensor, two angular displacement sensors are spaced a well-defined
distance apart. The rotor of each of these capacitive displacement sensors is composed of an artay of electrodes and sinewave voltages with
phase angles in the sequence O " , 90", 180", 270" applied to it. These
voltages are capacitively coupled from the stator to the rotor. The stator is also equipped with a readout electrode. The phase angle of the
sinewave on this readout electrode is proportional to the rotor-to-stator
electrode overlapping and, thus proportional to the angular position.
The phase difference between the output signals of the two angular
displacement transducers is a direct measure of the twist angle and,
thus of the torque in the axle. The sensor enables the noncontact torque
measurement bn a IO-mm diameter steel axle in the 0-100 Nm range.
I. INTRODUCTION
T
HE torque/speed relation of an engine is an important
parameter for fuel-consumption economy. Optimum
fuel economy would be obtained by keeping the engine at
the lowest possible gear during acceleration by changing
the gear ratio to give increased vehicle speed instead of
operating the throttle to increase the engine speed. The
throttle should only be operated to increase the power at
the lowest possible engine speed. Obviously, the engine
speed is not a suitable parameter for adjusting the transmission in such a strategy, so the torque should be used
to adjust the transmission ratio for operation within the
mechanical limitations [ 11. The engine crankshaft, or another axle where the torque is to be measured, is rotating,
which strongly favors a noncontacting measurement of
this torque. An electrical contact with the rotating axle
would require the use of slip rings, which would result in
a more expensive and maintenance demanding sensor system. Another boundary condition that restricts the range
of the possibilities originates from structural limitations.
The required mechanical properties of the axle usually
prohibit the milling of slots for placing the sensor electronics or a local stricture of the axle for realizing a larger
twist angle in the sensor. The milling of slots would be
Manuscript received February 14. 1990; revised June 30, 1990.
The authors are with the Department of Electrical Engineering, Laboratory for Electronic Instrumentation, Delft University of Technology, 2628
CD Delft, The Netherlands.
IEEE Log Number 9038787.
JENS A. FOERSTER
required in noncontact strain-gauge based torque measurement systems. The electric power for operation of
such a sensor can be supplied to the axle by inductive
means and the telemetry of sensor data is also quite feasible. However, practical constraints do usually not permit the weakening of the axle. Moreover, the relatively
high engine speed would require a careful mass balancing
in the axle to avoid vibrations caused by inertia. Nevertheless, such systems have been implemented in ship
axles, where the mass and diameter of the drive shaft and
the number of revolutions per minute permits the mounting of a strain-gauge based sensor and readout electronics
on the axle. A local stricture of the axle can be used to
enlarge the torque-induced twist angle. This would facilitate the measurement of the torque using two angular displacement sensors; one on either side of the stricture. As
the torque-induced twist angle is inversely proportional to
the fourth power of the axle diameter, a significant gain
in angular displacement can be obtained, however, structural problems usually prohibit the implementation of
these techniques.
The relation between the twist angle r , over an axle
length L in an axle of uniform diameter D and a modulus
of rigidity G , at an applied torque T can be described by
r/T
= 3 2 L [rad/Nm]
rGD4
which results for a 10-mm thick steel axle (G,,,,, = 8.10"
N/m*) and a sensing distance L = 100 mm in: r / T =
lop3 rad/Nm. The torque can, therefore, be determined
using two angular displacement sensors spaced a distance
L apart to measure this twist angle. For direct torque sensing, with an inaccuracy smaller than 1 Nm and without
stricture of the mechanical structure, displacement sensors are required with a circumferential inaccuracy smaller
than 6 pm. The simplest differential noncontact angular
displacement sensing technique is based on the mutual
displacements of two flanges that are clamped on the axle
spaced a certain distance apart. Optical, magnetic, and
capacitive displacement sensing techniques can be applied. An optical torque sensor is shown schematically in
Fig. 1. Two disks, each with a slit, are mounted on an
axle a distance L apart. The twist angle controls the overlapping between the slits and thus pulsewidth modulates
the transmission from a LED lightsource to a photodetector. Disks are implemented for pursuing a mechanical am-
0018-9456/90/1200-1008$01.OO @ 1990 IEEE
1009
WOLFFENBUTTEL A N D FOERSTER: SENSOR FOR USE O N AXLE
hghlsaurce
S
Fig. 1 . Optical torque sensing using two disks with a torque-modulated
slit width.
plification of the torque induced angular displacement in
this sensor in order to enable torque sensing using conventional displacement sensors. The use of disks is restricted by the available space, which is limited by mechanical boundary conditions such as those imposed by
bearings.
A noncontact magnetic torque sensor is possible, based
on the magnetostrictive effect which is basically a straininduced magnetic field line deflection. The torque-induced compressive and tensile stresses distort the magnetic field lines as shown in Fig. 2. Applying a magnetic
field in the axial direction using external coils makes it
possible to measure the perpendicular field component. A
second pair of coils can be used for noncontact sensing of
the perpendicular field and thus enable the noncontact
sensing of the torque. A disadvantage of this method is
the power dissipation and the dependence of the sensitivity on the type of steel used. It is possible to get around
the latter disadvantage by using the ferroelectric properties of amorphous ribbons instead of the magnetostriction
of the axle itself. Groups of amorphous iron-based ribbons can be bonded to the axle with the longitudinal direction of one half of the ribbons at 45" with respect to
the axial direction and the other half perpendicular to that
as shown in Fig. 3 [2]. When applying a torque to the
axle, half of the ribbons will be subjected to tensile stress
and the other half to compressive stress. The magnetostriction changes the permeability of the ribbons and
causes a change in the mutual inductances between the
drive coil that drives both groups of ribbons, and the two
sense coils that detect the torque-induced magnetic anisotropy in the two perpendicular groups of ribbons. This
method, therefore, enables a noncontact torque sensing
[31, [41.
A disadvantage of the differential angular displacement
method for measuring the twist angle is that the difference
between the output signals of two sensors is generally used
to determine the twist angle in the readout circuitry rather
than the response of one differential sensor. A very interesting noncontact capacitive torque sensor that overcomes
this drawback has recently been reported in literature and
describes a noncontact torque sensor based on a differential capacitive displacement sensor. This sensor is
shown in Fig. 4 [5] and consists of two sets of serrated
teeth. One set is applied to the outside to a cylindrical
tube of dielectric material. The tube is clamped around
the shaft at a distance L from the teeth on the axle in such
CO11
(b)
Fig. 2 . Operating principle of (a) the magnetostrictive torque sensor and
(b) the basic sensor structure.
'I \ - I \ (
c
011.
Fig 3 Magnetic torque sensor using amorphous ribbons [ 2 ]
Capacitor plot
Oielec t ;ic tube
(a)
Free wd
Flxed
- -
Dielectric
Sensing
tube
copci tor
(b)
Fig. 4. Capacitive torque sensor described in 151. (a) Cross section and (b)
longitudinal section.
Shoft
1010
IEEE TRANSACTIONS ON INSTRUMENTATION A N D MEASUREMENT. VOL. 39. NO. 6. DECEMBER 1990
a way that the teeth on the axle and those on the tube are
overlapping. A twist angle results in a movement of one
set of teeth with respect to the other, which enables the
measurement of the torque by measuring the change in
capacitance. The readout is based on the change of an LC
product using a grid dip principle. Although this method
results in a noncontact, low-cost, and reliable sensor, it
requires a rather complicated mechanical structure composed of two coaxial cylinders with a rubber bearing at
the free end. Apart from this sensor, research is directed
towards inductive torque sensors based on amorphous ribbons. The response of the capacitive torque sensor discussed here is solely determined by the overlap between
two electrode patterns that are directly connected to their
respective substrates, the axle and the casing, and is
therefore based on a very simple mechanical structure
which is tolerant to the spatial limitations that are imposed
by e.g., bearings.
11. THE CAPACITIVE
TORQUESENSOR
The capacitive torque sensor is basically a differential
angular displacement sensor and is composed of two capacitive displacement sensors mounted on the axle and
spaced a certain distance apart in order to enable the measurement of the twist angle.The operation of each of the
capacitive displacement sensors is based on the combined
capacitive coupling of four sinewaves to the readout electrode. The rotor is composed of an array of electrodes
organized as a bar-space type of grating and the stator
consists of a single bar-shaped readout electrode. The array of rotor electrodes are connected to sinewaves with
the same amplitude, however, adjacent electrodes have a
phase difference of 90". In this way the repetitive phase
pattern 0", 90", 180", 270", is generated along the rotor
with a periodicity over four electrodes of the array. The
phase of the sinewave on the stator electrode is determined by the superimposed coupling between the individual stator electrodes and the readout bar, which depends
on the mutual spacings, and is therefore a direct measure
of the position of the stator with respect to the rotor [6].
The fringing fields can be disregarded in case of a rotorto-stator spacing much smaller than the width of the electrode bars and at relatively low angular velocities. For a
10-mm diameter axle with a spacing of about 1 mm this
implies that only one set of four driving electrodes is allowed along the circumference. An almost linear relation
between the output phase and the angular position can be
obtained when using a rotor pattern with a spacing equal
to the bar width, a , and a stator electrode width equal to
((D+ 2 s ) / D ) X ( 3 a ) , as shown in cross section in Fig.
5. The electrical phase at the readout electrode changes
over 360" when the rotor completes one full mechanical
revolution. This sensor, therefore, enables the dimensionless transduction from mechanical rotation over a certain
angle into an electrical phase shift. The sensor is intended
for application in the 0-100 Nm torque range. The associated maximum angle of rotation between the two angular displacement sensors spaced a distance L = 100 mm
ROTOR
ELECTRODE
Fig. 5 . Basic capacitive angular displacement sensor.
apart can easily be derived from (1) and is equal to 7 =
5.7". A minimum resolvable torque equal to 0.2 Nm can
be detected when using a phase meter with a 0.01 " resolution. This performance is more than adequate for practical torque measurement in the intended application area,
however, the eventual objective of the torque sensor presented here is the integration of the sensor readout circuitry with a simple analog-to-digital (AD) converter in a
single chip. This 'smart sensor' will enable on-chip phase
readout with 0.1 resolution without having to resort to
external professional equipment, by using a phase-topulsewidth conversion to drive an integrated counter for
a gated AD conversion based on counting. This miniaturization is pursued at the expense of a reduced resolution
of the phase measurement and an unmodified sensor configuration would yield a torque resolution of only 2 Nm.
To compensate for this detrimental effect, a differential
sensor structure should be designed with an intrinsic better resolution. Such an objective can be met by changing
the number of electrodes and the electrode dimensions,
which results in a sensor where the effect of fringing fields
can no longer be disregarded. A sensor with an improved
performance is presented in the next section.
O
111. IMPROVED
SENSOR
The resulting sensor structure would be composed of
16 rotor electrodes and 4 stator electrodes as shown schematically in cross section in Fig. 6. In this way a phase
pattern of four times 360" is generated along the circumference of the rotor. Basically, this method implies the
transformation of the mechanical rotation over an angle 7
into an electrical phase change equal to 47.The four readout bars are distributed equidistant over the stator. The
detected phases are, therefore, synchronous and the four
readout strips can be connected in parallel in order to increase the nominal transducer capacitance and, thus, also
the signal amplitude of the sinewave at the input of the
readout circuitry is enhanced. This concept can be extended to 4 n rotor bars and n stator bars. Photolithographic constraints limit the bar width, a , and the bar
spacing to about amin= 0.4 mm. This limits n to nmax=
T ( D + s ) / ( 2 n X amin)= ( x x 1 1 ) / ( 8 x 0.4) = 10.
This results in a torque resolution in the practical sensor
exceeding 0 . 2 Nm, which is well within the range of the
target values. Unfortunately, extreme accuracy requirements should be imposed on the tolerances and the excen-
101 1
WOLFFENBUTTEL A N D FOERSTER: SENSOR FOR USE ON AXLE
ROTOR
@
Fig. 6. Capacitive angular displacement sensor with an enhanced resolution.
tricity of the rotor-to-stator spacing, s, for obtaining synchronized phases at all readout bars. A cancellation of the
readout signals will occur instead of reinforcement if such
requirements are not met and the signal level enhancement, pursued by the synchronization, is largely undone
by the tolerances in a practical structure.
For this reason a sensor is constructed with several
electrical periods over the rotor circumference, however,
with only one stator readout strip irrespective of the number of rotor electrodes. The bar width, a = 0.4 mm and
the rotor-to-stator spacing s = 1 mm. These dimensions
indicate that the parallel-plate approximation is utterly inadequate for describing the sensor characteristics. The angular displacement sensor with improved resolution is basically of the incremental type. Therefore, an ambiguity
can occur in the readout of extremely high torques. A
small torque is indicated if the angular displacement exceeds four rotor strips. The practical torque sensor is designed to exhibit a sufficiently large safety margin.
The angular displacement sensor is composed of a
coaxial stator and rotor electrode as depicted at several
cross sections along the axial direction in Fig. 7. The
schematic diagram of the equivalent electrical circuit is
shown in Fig. 8. The values of the capacitors C,through
C4 depend on the angular displacement. C, is the return
coupling capacitor between the rotor and the stator and CO
is the capacitance between the rotor and the conductive
axle. When assuming CO >> C,, C , , C,, C3, C4, an output voltage U, is generated that can be described by
+ ( C , - C 3 ) U cos ut).
(2)
The phase of the output voltage contains the desired angular position information, hence
arg (U,)= arctan
(21 :).
~
(3)
As the fringing-fields can no longer be disregarded, it is
not possible to derive a simple analytical expression for
the relation between arg (U,)and the angle of rotation.
Equation (3) has been solved numerically and the result
is shown for one period of the repetitive stator pattern in
Fig. 9. The torque sensor is composed of two sets of these
o
~
o
@
@
o
o
ELECTRODE
READOUT
~
o
o
Fig. 7 . Practical capacitive angular displacement sensor for different cross
sections along the axial direction.
Fig. 8 . Equivalent electrical circuit of the sensor capacitors with the parasitics and the readout charge amplifier.
0
075
05
075
1
4a
Fig. 9. Calculated response of an angular displacement sensor with a rotor-to-stator spacing, s, much larger than the electrode spacing, a . The
phase angle on the readout electrode is shown versus the position X.
angular displacement sensors spaced a well-known distance apart and { arg ( U,, ) - arg ( U,,)} is used as a
measure of the torque-induced twist angle 7.As arg ( U,)
is not a linear function of the angle of rotation, a modulation of { arg ( U,,) - arg ( U O 2}) occurs when measuring the torque on a rotating axle. This property prevents
the direct torque measurement and the average value of
{ arg ( U,,) - arg (U,,)
} is used instead. The measurement of the average of the difference in phase can easily
be implemented in the readout circuits, using a phase-topulsewidth modulation and a counter for the pulsewidthto-digital conversion, by counting over the time that is
needed to travel over at least one set of 4 bars. The measurement time depends on the angular velocity and gives
a minimum measurement delay equal to: the time per revolution/n. An improved signal-to-noise ratio can be obtained by counting over n / m revolutions, however, the
increased measurement time will give an extra delay
IEEE TRANSACTIONS ON INSTRUMENTATION A N D MEASUREMENT. VOL 39. NO. 6. DECEMBER 1990
1012
CiGnal
90'
Gnd
0'
Gnd
cut
Gnd 180° G n d - 5 7 0 '
(a)
(b)
Fig. 10. (a) Stator pattern and (b) rotor pattern used for the angular displacement sensors that are implemented in the practical torque sensor.
I
-
.
axle
[
; sensor
\
;
'\ .
shielding
,
/ I
,
-
-I
1
,1
case
stator electrode
rotor electrode
I$
bay
bearing
~~~
Fig. 1 I . Capacitive torque sensor
which might affect the stability of a closed-loop system
that is based on this sensor.
The electrodes are realized on flexible printed circuit
board material and are attached to their respective substrates using a special cement that is customarily used for
creep-resistant bonding of strain gauges. A dielectric is
required in between the rotor electrode and the axle with
a thickness in the same order of magnitude as the rotorstator spacing. This measurement prevents the loss capacitance, C,, between the interdigitized rotor electrode and
the conductive axle from severely reducing the amplitude
of the ac voltage before return coupling to the detector.
The stator and rotor electrode patterns of the capacitive
angular displacement sensor are shown in Fig. 10. The
__
rotor pattern basically consists of a structure with large
area pads for the capacitive coupling of the ac voltages to
the rotor. The driving and readout electrodes are separated using a ground electrode in between to prevent direct coupling to the stator and to minimize stray-field coupling between stator and rotor.
IV. SENSORPERFORMANCE
The sensor performance for static torques has been
measured using the sensor with a 10-mm diameter steel
axle that is clamped on one side, as depicted in Fig. 11.
On the other side, a lever is connected to the axle. A
charge amplifier has been used for the readout of the out-
1013
WOLFFENBUTTEL AND FOERSTER: SENSOR FOR USE ON AXLE
’ O0T
output
0°--
Phase
[Dew1
oo-.
2
oo--
1 00--
o
----
,>i
Oecr
torque
l
00
0
4
8
12
16
20
Torque [Nml
Fig. 12. Results of measurements performed on the capacitive torque sensor at increasing and decreasing torque.
put phase. A torque can be applied to the axle using standard weights connected to the end of the lever. The response of the sensor to a torque increasing from 0 to 20
Nm and subsequently decreasing again to 0 Nm is shown
in Fig. 12. Preliminary measurements have been performed on a rotating axis at low angular velocities. The
results are in agreement with the static response curves,
however, the accuracy of these measurements was not yet
sufficient to give quantitative results. The measurements
indicate a hysteresis. Increasing the load and subsequently reducing the load again at a certain value of the
applied torque does not immediately give the initial phase
angle. The error decreases after a few minutes. This behavior is characteristic for creep. The bonding technique
used to cement the rotor electrode to the axle is critical
for this effect and a substantial improvement can be expected when using a thick-film printing technique for the
realization of the rotor electrodes. As no saturation occurs, this sensor is suitable for a wider range of torques.
In the present measurement setup, it was not yet possible
to apply such torques.
V . CONCLUSIONS
Noncontact capacitive torque sensing is possible based
solely on the capacitive coupling between a stator and a
rotor electrode pattern. A very robust and simple torque
sensor can be constructed in this way. A sensitive angular
displacement-to-phase angle conversion has been implemented for the readout with a sensitivity exceeding
0.3”/Nm. Present prototypes suffer from hysteresis,
which can be reduced when using a different technique
for the bonding of the rotor electrode. As the phase difference between two capacitive displacement transducers
is measured, the torque indication is not affected by the
angular velocity of the axle. A fixed angular mismatch
between the two displacement sensors gives rise to an offset, which can easily be compensated by an initial torque
measurement prior to the mechanical loading of the axle.
The mechanical power supplied by the axle can also be
determined when using the rate of change in the phase of
one of the displacement sensors as the velocity signal.
Future research will be focussed on a reduction of the
creep behavior and a widening of the operating range by
testing different bonding techniques as well as by optimizing the electrode geometry. The research will also aim
at the realization of a custom silicon chip that will contain
the electronic circuitry required for the driving and the
readout of the sensor.
REFERENCES
M . H. Westbrook, “Sensors for automotive application,” J . Phys. E:
Sci. Instrum., vol. 18, pp. 751-758, 1985.
I . Sasada, E. Sakai, S . Uramoto and K . Harada, “Noncontact torque
sensor employing synchronized switching process,” in Proc. 5rh Sensor Symp., Japan, pp. 115-120, 1985.
H . Hase and M . Wakamiya, “Torque sensor,” in Proc. 8th Sensor
Symp., Japan, pp. 279-282, 1989.
Y . Nishibe, Y . Nonomura, M . Abe, K . Tsukada, M . Takeuchi, and 1.
Igarashi, “Real time measurement of instantaneous torque with high
accuracy using magnetostrictive sensor,” in Proc. 8th Sensor Symp.,
Japan, pp. 1 1 1-1 14, 1989.
J . D.Turner, “The development of a thick-film noncontact shaft torque
sensor for automotive applications,” J . Phys. E: Sci. Instrum., vol.
22, pp. 82-88, 1989.
K . B. Klaassen and J . C . L. van Peppen, “Linear capacitive displacement transduction using phase readout,” Sensors and Actuators, vol.
3, pp. 209-220, 1982183.
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