Flow Measurement and Instrumentation 16 (2005) 1–6

www.elsevier.com/locate/flowmeasinst

flowmeterntelligentprototype

Smart floating element flowmeter based on a capacitive angulardisplacement transducer

Ying Xu∗, Tao Zhang, Huaxiang Wang, Deyu Chen

School of Electrical Engineering & Automation, Tianjin University, Tianjin 300072, China

Received 11 April 2003; received in revised form 21 October 2004; accepted 26 November 2004

Abstract

Based on the detection mechanism of a capacitive angular displacement transducer, a new type of smart floating elementwith a higher accuracy is provided in this paper. It mainly describes the principle of the flowmeter, design of the transducer, the isignal processor, the calibration of the prototype and analysis of errors. Experiment results show that the accuracy of the kind ofinvestigated is better than 1%.© 2004 Elsevier Ltd. All rights reserved.

Keywords: Smart; Floating element flowmeter; Capacitive angular displacement transducer

heaticanr

theg.

by

onium

cy?ehehe

eir

nthe

orantonsgesost, the

lthei.e.inst

1. Introduction

Precision measurement of flow is widely used in tfields of energy saving, economic accounting and automcontrol, etc. The floating element flowmeter playsimportant role in the measurement for medium and lowespeed flow.

At present, the research on the floating element flowmeteris theoretically based on Miller’s method [1], while thecorresponding nonlinearity correction is based onmechanical cam-plate in the process of practical designinTherefore it results in the following shortcomings:

(1) It’s impossible to make precision measurementmechanical structure; (2) The complexity of design andmanufacture of those products, for they have to be madeby one depending on the density of the measured medworking conditions and changeable range of the flow.

So, how do we improve the measurement accuraMeanwhile, how do we improve the flexibility in thmanufacture and application? It’s really important for tdevelopment of the floating element flowmeter. In t

∗ Corresponding author.E-mail address: xuying_tju@yahoo.com.cn (Y. Xu).

0955-5986/$ - see front matter © 2004 Elsevier Ltd. All rights reserved.doi:10.1016/j.flowmeasinst.2004.11.002

ntisces

e,

paper [2] of Baker and Sorbie, the authors presented thsimilar views on this.

Here, thedesign combines with a robust high-precisiocapacitive angular displacement transducer to detectposition of the floating element and microprocesstechnique for smart signals processing. The relevparameters of measured mediums and working conditiare stored in the processor for the conversion of flow ranin situ. Furthermore, the smart design will also meet the cexpectations of users of these flow meters. Consequentlyproblems mentioned above can be solved.

2. Measurement principle & system design

2.1. Measurement principle

As shown inFig. 1, a floating element is put into a verticacone-shape metal tube and moved up and down withchange in the flow speed. Four forces act on the float,gravity, buoyancy, resistance of pressure difference agathe flow direction and viscous stress. The floating elemewill reach an equilibrium position until the resultant forcezero, which means the upward and downward acting for

2 Y. Xu et al. / Flow Measurement and Instrumentation 16 (2005) 1–6

one

;

arodto

ngthacht ine.

ehet isaticighrw,s a

er,eter

neticownionofticfn

lar

ere,cer

ular

alns

y.

allitiveeIC

-er.es-

y ac-

ved

ic

h, a

sorsor

Fig. 1. Measurement principle of the floating element flowmeter (1 cmetal tube, 2 floating element, 3inner magnet steel).

are balanced. The flow equation is:

Qv = απ[Dhtgφ + (htgφ)2]√

2gV f

S f[(ρ f − ρ)/ρ] (1)

where, Qv—volume flow; α—flow coefficient; D—maximum diameter of floating element; h—height offloating element;φ—cone semi-angle of conical tube;V f —volume of floating element;ρ f —density of floating elementρ—fluid density;S f —maximum sectional area of floatingelement perpendicular to flow direction.

In accordance with Eq. (1), if a floating element hasa fixed shape and conic tube, the flow is a nonlinerelationship with the floating element’s height. The methof reducing the influence of the quadratic term useddecrease the cone angular of the tube. Therefore the leof the conic tube would have to be extended to rethe expected flow measure range, which could resulmanufacturing difficulties and installation inconveniencAt present, the total height of a common metal tubfloating element flowmeter is up to 250 mm, and theight of the conic tube is 60–70 mm. Consequently, iimpossible to ignore the nonlinear influence of the quadrterm, especially for wider flow ranges, and to get a haccuracy just by using a nonlinear cam-plate. In this papea microprocessor is introduced for calculating the flotherefore it greatly improves the accuracy and providegood man–machine interface.

2.2. System design

Based on a capacitive angular displacement transducthe measurement principle of the floating element flowmis shown inFig. 2, comprising of three main parts, i.e. flowsensor, transducer and smart signal processor. The magsteel embedded in the floating element moves up and dwith its main body, which leads to the synchronous motof the small external magnetic steel fixed in one endthe mechanical link rod outside the tube through magneforce coupling and makes the rod rotate at an angle oθ ,therefore the linear-displacement of the floating element ca

Fig. 2. Principle of structure. (① floating element flow sensor;② angulardisplacement transducer;③ smart signal processor; as depicted② in Fig. 2,1 small external magnetic steel; 2 mechanical link rod; 3 capacitive angudisplacement transducer; 4 counterweight).

be converted to an angular-displacement of the rod. Han introduced capacitive angular displacement transducan accomplish the change of detecting signal from anginto capacitance (i.e.C) and theninto voltage signal (i.e.Vout) by a signal processing circuit. Finally, the output signamplitude of the circuit can represent the flow. The functioare as follows:

Vout = f1(C) = f2(θ) = f3(h) = f4(Q) (2)

where, f1– f4 stand for a monotonic function respectivelThe relationship betweenVout andQ is

Q = Q(Vout). (3)

The transducer consists of a mechanical link rod, a smmagnetic steel embedded in one end of the rod, a capacangular displacement transducer and a counterweight. Thsmart signal processor consists of the microcomputer Pand the peripheral circuit.

3. Transducer design

3.1. Sensing electrodes design

A high-precision capacitive angular displacement transducer with robust characteristics is provided in this papTopology structure and measurement principle of sometablished capacitive sensors have changed fundamentallcording to the following design method [3].

(1) Because of the complexity of the sinusoidal dricircuit, an impulse driving voltage is used insteaof the sinusoidal driving voltage, avoiding harmondistortions, amplitude mismatch, and phase errors.

(2) To decrease stray field influences, the shape of eacelectrode should have, compared to its own areaminimized circumference.

(3) In order to fulfill Electro Magnetic Compatibility(i.e. EMC) specification, the active area of the senshould be surrounded by guard rings connected to senground.

Y. Xu et al. / Flow Measurement and Instrumentation 16 (2005) 1–6 3

d

. It

ntich

r

45

ntertingteset aoringThenthe

ethe

tain

nt,

ularned

gletherthe

ventheula

di.e.en,new

e,tricealtion

entsor.l

theuitnce

nce

Fig. 3. Structure of capacitive sensor (1 rotary axle; 2, 3 grounded guarrings; 4 receiving plate; 5 rotary plate; 6 transmitting plate).

Fig. 3is the topology structure of the capacitive sensormainly consists of three coaxial and parallel plates:

(1) A stator (plate 6) is divided into eight equivaleconductive transmitting segments, s1–s8, all of whare electrically isolated from each other.

(2) A stator (plate4) is a concentric circle electrode foreceiving induced charge from transmitting segments.

(3) The rotor of the system consists of four blades (◦respectively) in the form of circle sectors.

The rotary axle (as depicted inFig. 3) fixed on tworolling bearings (not displayed) passes through the ceof those 3 plates respectively and drives the rotor rotasynchronously. While installing, the gap between pla4–6 should be as narrow as possible. In order to glarger capacitance, the isolated gap between the neighbtransmitting sectors should be as narrow as possible.transmitting & receiving electrodes are bound by both ainner and an outer-grounded guard ring so as to improveEMC, depicted as 2 and 3 inFig. 3. Depending upon therotary plate rotating angleθ , the capacitance between thtransmitting and the receiving plates can be detected bycharge detector with the pulse signal excitation of a cerfrequency.

Being the distance travelled of the floating elemethe relative changeablerange of the rotary angleθ ofthe mechanical link rod is about 30◦. Considering theelectric field edge effect, there should be a certain angredundancy in the practical design. Therefore, the desigcapacitive sensor has the ability to measure 45◦. The inducedelectric charge will increase four times as much as a sinsector capacitor by connecting s1, s3, s5 and s7 togeelectrically, and s2, s4, s6 and s8 together electrically. Ifexcitation signal acts on s1, s3, s5 and s7, the capacitancemodel between the three plates within 45◦ is shown inFig. 4.The calculating value of the capacitance is

C = 4 × (C1//C2) (4)

where,

C1 = εrε0s1

δ= 1

8π R2 θ

45◦εrε0

δ= F1(θ) (5)

Fig. 4. Equivalent capacitance model of 45◦ plate (δ: gap between 2 stators,d: thickness of rotor).

Fig. 5. Difference principle of the capacitor.

C2 = εrε0s′1

δ − d= 1

8π R2 45◦ − θ

45

εrε0

δ − d= F2(45◦ − θ). (6)

It shows that the change in angularθ can be gained bydetecting the capacitance change.

Furthermore, the capacitance value between the etransmitting electrodes (i.e. s2, s4, s6 and s8) andreceiving one is the same as the one calculated by form(4), except its increasing or decreasing direction. As depictein Fig. 5, if one curve (i.e. curve O) subtracts the other (curve E), a new one (i.e. curve F) can be formed. Ththe sensibility can be enhanced two times by using thecurve F.

3.2. Signal detection

However, given thecapacitance equivalent circuit abovthe simplified model ignored the stray capacitance of elecfield. Therefore, there is a deviation between the rvalues ofthe capacitance and those from simplified equa(4). This paper imported a micro-capacitance measuremcircuit to detect the real value of the capacitive senFig. 6② shows theprinciple block diagram of the signaprocessing. A micro-charge detector is in the front ofelectric circuit, which can reduce the sensitivity of the circto the high frequency signals and improve the performaof resistance electro-magnetic interference as well. Thispaper refers to having stray-immune micro-capacita

4 Y. Xu et al. / Flow Measurement and Instrumentation 16 (2005) 1–6

rge

t

orndderehege

ter

orore

re-

dt

te

dtheter

uregas

eur

erre

ameh-ers,

uren beionent

he

ingelyucernt,

nd

eter.ng

es7

int.e,

(only about 5 pF in this type of senor) charge–dischameasuring circuit (see Ref. [4]).

4. Smart design

4.1. Flow calculation and range conversion

As mentioned above, the flowQv in Eq. (1) is nonlinearwith its heighth. In addition, even if the floating elemenis at the same height in the cone tube, the measured flowis still different when the measured medium densitythe working conditions, e.g. environmental temperature apressure are different from the calibration status. In orto improve the calculating accuracy and convert the scalautomatically, microcomputer technology is applied to tflowmeter to guarantee its performance, which has chanthe situation of traditional design and manufacture procedureof this type of flowmeter completely, that is, each meshould be designed and made individually according to thedensity of the measured medium or working conditions,its ranges should be converted manually in situ. Therefthe smart level can be improved greatly.

Theoretically, the correction equations on flow measument of liquid and gas are as follows:

(1) Correction equation of liquid flowThe correction equation of liquid flow can be derive

from Eq. (1) when the density of measured liquid is differenfrom that of the calibrated, that is

Qv = Qv0α

α0

√(ρ f − ρ)ρ0

(ρ f − ρ0)ρ(7)

where, Qv0, ρ0, α0 are volume flow, fluid density andflow coefficient of the flowmeter under the standard sta(temperaturet = 20 ◦C, pressurep = 101 325 Pa)respectively. Qv , ρ, α are the items of the measuremedium under the practical working state respectively. Ifviscosity of the measured medium is similar to that of waunder standard state, thenα = α0.

(2) Correction equation of gas flowWith the gas,ρ f � ρ, Eq. (1) can be simplified as

follows:

Qv = απ[D0htgφ + (htgφ)2]√

2gV f

S f

ρ f

ρ. (8)

According to Eq. (8), if the measured gas is different fromthe air and the working conditions are different from thecalibration state, e.g. with different temperature, pressand compressive coefficient, a corrective equation offlow will be as follows:

Qv = Qv0α

α0

√ρ0

ρ

√T

T0

√P0

P

√Z0

Z(9)

where, Z is the compressive coefficient of measured gasunder working state.

d

Fig. 6. Principle block diagram of system hardware.

4.2. Hardware design

Fig. 6shows theprinciple block diagram of the hardwarof the intelligent signal processor, which consists of fodifferent units, i.e. microprocessor unit① , detecting unit② ,output unit ③ and power unit④ . With embedded ROM,RAM, timer, AD, watchdog, etc., one PIC microcomputof USA Microchip Company is used as the counit.

4.3. Software design

Here, the software enables the flowmeter to indicate boththe accumulated flow and the instantaneous flow at the stime with double rows and 8-digit LCD. By means of 3 pusbuttons on the instrument panel, the working parametsuchas the coefficients of the rating curve (i.e.A, B1, B2, B3of Eq. (10)), decimal digits, density, temperature, pressand compressive coefficient of the measured medium, caset into the microcomputer, and then the range converscan be done automatically to make precision measuremof the flow, which can bring great convenience to tmanufacturers and users for different requirements.

5. Prototypes calibration

Three prototypes of the smart metal tube floatelement flowmeter with 15, 50, 80 mm caliber respectivbased on the capacitive angular displacement transdwere calibrated by experimental calibrating equipmeas depicted in Fig. 7. There is a 36 m high-levelwater tower to keep a stable hydraulic pressure aa stable flow. An electromagnetic flowmeter with 0.2%measurement accuracy is used as a standard mCalibrating experiments were performed in the followisteps:

(1) The process of calibration was carried out 5 timfor increasing & decreasing flow rate respectively,calibration points for one travel and 3 times for each poInstantaneous voltages(V ) of the prototype and the flow ratdisplayed in the standard flowmeter(m3/h) are recorded

Y. Xu et al. / Flow Measurement and Instrumentation 16 (2005) 1–6 5

.71

.798573.24

Table 1Test datalist for three prototypes

Instrument with 15 mm caliber Instrument with 50 mm caliber Instrument with 80 mm caliberQS Q P QM δP δM QS Q P QM δP δM QS Q P QM δP δM

(m3/h) (%) (m3/h) (%) (m3/h) (%)

0.0404 0.0421 0.045 0.43 1.1 0.63 0.674 0.7 0.7 1.1 4.01 4.12 4.3 0.27 00.0507 0.0522 0.055 0.38 1.0 1.26 1.28 1.4 0.35 2.2 8.01 8.09 8.7 0.2 10.1 0.097 0.11 0.75 2.4 2.52 2.5 2.6 0.24 1.3 16.0 15.9 16.4 0.15 0.0.15 0.151 0.16 0.25 2.4 3.05 3.06 3.2 0.18 2.3 20.5 20.4 21.1 0.25 1.0.201 0.199 0.21 0.5 2.2 3.78 3.76 3.9 0.3 1.9 24.0 24.1 23.7 0.2 0.0.301 0.302 0.31 0.25 2.2 5.04 5.03 4.9 0.22 2.2 32.0 31.6 32.5 0.94 10.401 0.399 0.41 0.5 2.2 6.3 6.25 6.4 0.83 1.6 40.0 40.3 41 0.79 2.

l

set

e.ingne

ofetic

erare

antandown

is

eterrt

rsoso-

theis

het

r,ro-

%

entent

in,w,

hat

esn

is

and then the curve of 3-orderpolynomial fitting according tothe 7 calibration points (averaged value), i.e. the functionaequation (10) of V —m3/h, is

Q = A + B1 ∗ V + B2 ∗ V 2 + B3 ∗ V 3; (10)

(2) Function relationship coefficients from step (1) areinto the microcomputer so that the instantaneous flow m3/hand the accumulated flow m3 can be shown on the prototypCalibrate it again; with 3 times for increasing & decreasflow rate respectively, also 7 calibration points for otravel and once for each point. The instantaneous flowthe prototype is compared with that of the electromagnflowmeter, and then its error is analyzed.

Three prototypes with 5, 50 and 80 mm calibare calibrated respectively, and their flow ranges0.04–0.4 m3/h, 0.63–6.3 m3/h and4–40 m3/h respectively,and the measurement range ratio is 10:1. The significdigits of the flow rates of both meters (standard metercalibrated meter) equal to 3. The calibration data are shin Table 1.

The full-scale relative error of the smart prototypedefined as:

δP =∣∣∣∣ Q P − QS

Q P max

∣∣∣∣ × 100% (11)

where,δP—full-scale relative error;Q P , QS ,—instantane-ous flow rate of the smart prototype and the standard mrespectively;Q P max is the maximum flow rate of the smaprototype.

Furthermore, the test data of three mechanical rotamete(as depicted 4 inFig. 7) with corresponding caliber are alsshown in the table. The electromagnetic flowmeter is alused as a standard meter. After being calibrated, the camplates which indicate the flow curve performance offlowmeter can be obtained. The definition of the erroralmost the same as expression (11), except that,QM (flowrate reading of the mechanical meter) instead ofQ P shouldbe used.

A precision analysis is made in this paper for tflow rate at the calibrationpoints of the prototypes. Ican be seen fromTable 1 that the maximum full-scalerelative errors(δP ) of the three smart prototypes (with

Fig. 7. Calibrating equipment for flow test (1 water towe2 electric–magnetic flowmeter, 3 smart prototype, 4 mechanicaltameter, 5 pump, 6 ground, 7 water pool).

15, 50, 80 mm caliber respectively) are 0.75%, 0.83and 0.94% respectively. However, the errors(δM ) of thethree mechanical instruments, are 2.4%, 2.3% and 2.4%respectively.

6. Conclusion

The research results on the smart floating elemflowmeter based on the capacitive angular displacemtransducer indicate as follows:

(1) It is not necessary to make the flowmeter one by oneaccordance with the densityof the measured mediumworking conditions and changeable range of the flowhich brings great convenience to the makersand users.

(2) The accuracy of this smart instrument is higher than tbased on the mechanical structure.

(3) Having run for three months, the three prototypwith different calibers keep the same accuracy whecalibrated again, which verifies the reliability of thkind of smart instrument.

6 Y. Xu et al. / Flow Measurement and Instrumentation 16 (2005) 1–6

ha,pp.

nteter

EEJune

e21

References

[1] R.W. Miller, Engineering Manual of Flow Measurement (S. YanzTrans.), Mechanical & Industrial Publishing Firm, Beijing, 1990,637–644.

[2] R.C. Baker, I. Sorbie, A review of the impact of componevariation in the manufacturing process of variable area (VA) flowm

performance, Flow Meas. Instrum. 12 (2001) 101–112.[3] G. Brasseur, A robust capacitive angular position sensor, in: IE

Instrumentation Measurement Technol. Conf., Brussels, Belgium,1996.

[4] S.M. Huang, J. Fielden, R.G. Green, M.S. Beck, A new capacitanctransducer for industrial applications, J. Phys. E: Sci. Instrum.(1988) 251–256.