- Email: [email protected]
Ultrasonic density sensor—analysis of errors due to thin layers of deposits on the sensor surface
Sensors and Actuators 76 Ž1999. 122–126 www.elsevier.nlrlocatersna
Ultrasonic density sensor—analysis of errors due to thin layers of deposits on the sensor surface A. Puttmer ¨ a
a,)
, N. Hoppe a , B. Henning b, P. Hauptmann
a,b
Otto-Õon-Guericke-UniÕersity Magdeburg, Institute for Measurement Technology and Electronics (IPE), P.O. Box 4120, 39016 Magdeburg, Germany b Institute for Automation and Communication, Steinfeldstr. 3 (IGZ), 39179 Barleben, Germany Accepted 25 November 1998
Abstract The density of liquids can be measured with ultrasonic techniques. Such sensors determine the reflection coefficient of ultrasound at the boundary between a reference material and the investigated liquid. An important question for application of these sensors is the influence of thin layers which may be deposited at the sensor–liquid interface. This article analyses the measurement errors of an ultrasonic liquid density sensor utilising simulation techniques. q 1999 Elsevier Science S.A. All rights reserved. Keywords: Ultrasound; Density sensor; Error analysis
1. Introduction
2. Ultrasonic measurement of the density of liquids
The density r of a substance is related to its acoustic parameters sound velocity c and acoustic impedance Z with Z s r c. The acoustic impedance Z can be determined from the reflection or transmission coefficient of sound, the velocity c can be determined from the time of flight of a pulse along a known path. Different sensors which use this acoustic principle have been introduced w1–5x. These sensors determine the acoustic impedance with a pulseecho-technique utilising the amplitude of an acoustic pulse, that is back-reflected from the interface between a reference material of known parameters and the liquid. Under industrial conditions, it is possible that thin layers are deposited on the surface of the sensor. Layers of deposited materials cause a change of the signal amplitude and phase leading to errors. Otherwise, sensors might be coated with thin layers to improve their durability to aggressive substances. This article aims to analyse the error of the ultrasonic density measurement in dependence on the layer properties thickness and acoustic impedance.
Sensor construction of Ref. w5x is given in Fig. 1a. Both, the piezoceramic transducer and the buffer rods of the reference material have cylindrical shapes. The piezoceramic transducer consists of lead-metaniobate. Both buffer rods are made of quartz glass Ž Z0 s 13.1 MRayl.. As the lengths l 1 and l 2 are different, the reference A ref and measurement echoes A meas are received separated in time ŽFig. 1b.. The measurement is done by measuring the acoustic impedance Zl with the help of the sound reflection coefficient R: Rsy
A ref k
Zl s r 0 c 0
,
1qR
Ž 1. Ž 2.
1yR
with r 0 c0 s Z0 and a calibration factor k related to the acoustic losses in the buffer rods. The value of k is determined with Eq. Ž1. in a calibration measurement of A meas and A ref with air substituting the liquid, when R s y1. The sound velocity of the reference material c 0 is measured from the zero-crossing times t ref and t meas : c0 s
)
A meas 1
Corresponding author. E-mail: [email protected]
0924-4247r99r$ - see front matter q 1999 Elsevier Science S.A. All rights reserved. PII: S 0 9 2 4 - 4 2 4 7 Ž 9 8 . 0 0 3 6 5 - 3
2 Ž l 2 y l1 . t meas y t ref
.
Ž 3.
A. Puttmer et al.r Sensors and Actuators 76 (1999) 122–126 ¨
123
Fig. 1. Construction of the ultrasonic density sensor Ža. and signals observed at the transducers of Z- and c-sensor for l1 s 17 mm, l 2 s 31 mm, l 3 s 22 mm and quartz glass as the reference material Žb..
The liquid’s sound velocity c l is determined with the help of a separate receiver, the c-sensor. The relation of c l and zero-crossing times t l and t meas is given by: l3
cl s tl y
1 2
.
Ž 4.
t meas y t offset
Here, t offset is a value that includes the time between actual pulse beginning and detected zero-crossing of the pulse and time delays of the electronic system. It is determined in a calibration procedure with a liquid of well known acoustic parameters, e.g., water. Finally, the density is calculated from the rearranged definition of the acoustic impedance:
rl s
Zl cl
.
Ž 5.
reflection of the pulse A meas at single boundary between reference material and liquid. However, the mechanism of sound wave reflection and transmission is modified when a layer separates reference material and liquid ŽFig. 2.. Here, a part of the incident wave is reflected at the boundary reference material-layer Ž A R .. Another part is reflected at the layer-liquid interface causing the wave AXR inside the layer. Obviously, this wave is partially transmitted into reference material and liquid after travelling through the layer. These transmitted waves contribute to both A R and AT with amplitude and phase shift depending on the layer thickness x and acoustic parameters c and Z. Distortion of the pulses is observed as the result of this mechanism ŽFig. 3.. The example in Fig. 3 shows a strong influence of the layer impedance. Since layers may be deposited in a wide variety of thickness and acoustic impedance, it required huge effort
Operating with this principle, the amplitudes A meas and A ref as well as the times t l , t ref and tmeas must be measured and the parameters l 1 , l 2 , l 3 , k, r 0 and t offset must be known for calculating the density of the liquid with this sensor.
3. Error analysis Layers of deposits on the sensor surface have a certain influence on A meas , t l and tmeas resulting in errors of R, c 0 , c l and r l . Basically, Eqs. Ž1. – Ž5. are valid only for
Fig. 2. Origin of pulse distortion due to thin layers at the interface between sensor and liquid.
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A. Puttmer et al.r Sensors and Actuators 76 (1999) 122–126 ¨
Fig. 3. Pulse distortion due to a thin layer at the interface between sensor and liquid with the thickness x and acoustic impedance Z of 3 MRayl Ža. and 30 MRayl Žb..
to do the analysis completely experimentally. Simulations instead of experiments are used for error analysis in the work presented in this paper. Relative errors dZl and dc l are computed separately. Their contribution to the relative error of the density can be calculated with the help of: d r l s dZl q dc l .
Ž 6.
This allows the determination of the dominating contribution under given conditions.
F1 0 3 V1 1.32 F2 0 4 V2 1.81E9 R1 4 0 1E3 C1 4 0 1 .ENDS .SUBCKT SOURCE A B V1 A 1 PULSE Ž0,14,0,10N,10N,240N,1. V2 B 1 PULSE Ž0,14,260N,10N,10N,240N,1. .ENDS X4 1 0 SOURCE R1 1 3 50 X1 3 13 14 PZ35; Z-transducer RB 13 0 4.11K; quartz glass T1 14 0 16 0 Z0 s 4.11K TD s 2.86U; buffer rod T2 16 0 17 0 Z0 s 570 TD s TOF4 ; layer T3 17 0 20 0 Z0 s 449 TD s 2U y TOF4 ; water T4 20 0 21 0 Z0 s 5.43K TD s 250N; encapsulation X3 2 21 22 PZ35; c-transducer R3 22 0 1K; epoxy backing R4 2 0 50; termination .TRAN 8NS 6000NS 0 0 .PARAM TOF 1N .STEP PARAM TOF 1N 20N 1N .PROBE .END The subcircuit PZ35 represents the piezoceramic disc and subcircuit SOURCE models the electric excitation. The layer between buffer rod ŽT1 . and liquid ŽT3 . is represented by transmission line T2 with the parameters Z0 —impedance of the layer and TD —the time a pulse needs to travel through the layer. Since the sound velocity c of the layer is known, the layer thickness is x s cTD . Even though good agreement between simulation and experiment was proved in Ref. w6x for the transducer and the complete sensor, the SPICE model of the sensor with a layer was tested for the case of a polystyrene layer. The results of simulation and experiment are compared in
3.1. Sensor model Simulations were done using a unidimensional model for the circuit analyser SPICE. The model is based on lossy or lossless equivalent circuits for all piezoelectric and acoustic elements w6x. Layers are described by their acoustic impedance, thickness and velocity. All parameters can easily be varied in the range of interest and multilayered transducer layouts are easily possible by stacking the equivalent circuits. The source code is given below: ERROR ANALYSIS .SUBCKT PZ35 E B F; 2 MHz transducer T1 B 1 F 1 LEN s 0.74M R s 1470K L s 1.76 G s 0 C s 65N V1 1 2 E1 2 0 4 0 1 V2 E 3 C0 3 0 735P
Fig. 4. Relative errors d R, dc 0 , dc l and dZl for a boundary of quartz glass Ž Z0 s13.1 MRayl. to water Ž Zl s1.48 MRayl. with a polystyrene layer Ž Zl s 2.52 MRayl, cs 2400 mrs.. Lines indicate simulated graphs while symbols show experimental measurements.
A. Puttmer et al.r Sensors and Actuators 76 (1999) 122–126 ¨
125
Fig. 4. Good agreement between simulated and measured relative errors of R, c 0 , c l , and Zl is shown. 3.2. Computations The error analysis was done for layers with following properties: Ø Acoustic impedance Z s 0.05Z0 . . . 3Z0 , which corresponds to 0.65 . . . 39 MRayl ranging from polymers Ž1.7 . . . 4 MRayl. to metals Ž) 17 MRayl., Ø thickness x s lr50 and x s lr100 Ž l is the wavelength., Ø only smooth layers Žno scattering effects. on the surface of both Z-sensor and c-sensor with equal thickness. The analysed layer thickness is limited to the values x s lr50 and x s lr100 because sensor development is focused in this project on sensors with an accuracy better 1%. Referring to Fig. 4, the error dZl is increasing with the layer thickness and exceeds this limit at about x s lr50. Another important question is that of the opportunity of Žpartial. error compensation with the help of calibration. The mechanism of sound reflection shown in Fig. 2 acts in a similar fashion when the liquid is substituted by air. That is the case during the calibration measurement for determination of k. Thus, a layer will affect the calibration measurement and k will cover a difference caused by this layer. This difference of k can partially compensate the error of R generated by the layer. The calibrations of r 0 and t offset are affected by layers in analogous fashion.
Fig. 6. Error dZl caused by dc 0 for three different liquids and varying layer thickness without calibration Ža. and for two liquids after Žb. calibration of the sensor with water.
All error computations were done for two cases: 1. The sensor was calibrated with clean surface to the liquid and 2. the analysed layer on the surface was present during the calibration procedure. 3.3. Results
Fig. 5. Error dZl caused by d R for three different liquids and varying layer thickness without Ža. and with Žb. previous calibration of the sensor.
The measurement error dZl caused by an erroneous R is shown in Fig. 5a for three different liquids Ž0.7 MRayl–ethylether, 1.43 MRayls–water, 2.34 MRayl– glycerine.. For each considered liquid it is zero at two points Z s Z0 and Z s Zl . That are the points where the reflections between layer-reference material and layerliquid vanish. The error is negative for Z ) Z0 , which corresponds to layers of metal, and is negative for Z - Zl , which seems to be unlikely in practice. The range between both zero-error points corresponds to layers like polymers and shows a positive error. Here, the highest error in the graph is that of the measurement with Zl s 0.7 MRayl with up to q2.6% for a lr50-layer. However, the layer has an influence on the calibration factor k, too. When the sensor with the layer is first calibrated in air, the error is partially compensated with the help of the calibration factor k. As shown in Fig. 5b, the error is reduced from q2.6 to q1% for a lr50-layer and from q0.5 to q0.38% for a lr100-layer. The second impact of layers on the sensor surface on the measurement error of r is that caused by the errors of
126
A. Puttmer et al.r Sensors and Actuators 76 (1999) 122–126 ¨
an unidimensional model of the sensor. A comparative study for one layer material with varied thickness shows good agreement between simulation and experiment. Thin layers on the sensor surface affect the measurement of times Žsound velocity. much less than that of amplitudes Žreflection coefficient.. Therefore, the limit of layer thickness is set by the error of the amplitudes. Despite the significant improvement due to calibration, metal layers still cause high errors even when their thickness is only a tiny fraction of a wavelength, layers like polymers can be tolerated with a thickness up to lr50.
References
Fig. 7. Error dc l for three different liquids and varying layer thickness without calibration Ža. and for two liquids after Žb. calibration of the sensor with water.
c 0 and c l . Both measurements become erroneous due to a shift in zero-crossing time of t meas and t l . The impact of layers on the measurement error of Zl caused by an erroneous c 0 is shown in Fig. 6a. Considering one layer thickness, it has similar behaviour for all investigated liquids and layers with Z ) 0.5Z0 . It has different behaviour in the practically unlikely case Z - Zl . The similarity of all graphs allows an effective error compensation when water is used for sensor calibration when the layer is present. Errors after calibration are given in Fig. 6b. The measurement error of c l caused by thin layers on the sensor surface is shown in Fig. 7a. It is zero for layers with Z s Zl , the point where layer and liquid have the same acoustic behaviour. After recalibration of the sensor with a layer and water as the calibration medium, the error graph is that of Fig. 7b. Since the layer causes an absolute error, the relative error < dc l < can be reduced when the length l 3 of the sensor is increased. It was 22 mm in the simulation.
4. Conclusions Thin layers of deposits at the interface of an ultrasonic density sensor have great influence on the measurement. The analysis of such effects can be done with the help of
w1x D.J. McClements, P. Fairley, Ultrasonic pulse echo reflectometer, Ultrasonics 29 Ž1991. 58–62. w2x B. Fisher, V. Magori, A. von Jena, Ultraschall ŽUS.-Dichtemesser ´ zum Messen der spezifischen Dichte eines Fluid, Patent EP 0 483 491 B1, 1995. w3x B. Jensen, Gerat ¨ zur akustischen Messung der Dichte einer Flussigkeit, ¨ Patent DE 30 16 323 A1, 1979. w4x J.C. Adamowski, F. Buiochi, C. Simon, E.C.N. Silva, R.A. Sigelmann, Ultrasonic measurement of density of liquids, J. Acoust. Soc. Am. 97 Ž1. Ž1995. 354–361. w5x A. Puttmer, B. Henning, K. Dierks, P. Hauptmann, Vorrichtung zur ¨ Messung und Bestimmung der akustischen Impedanz von flussigen ¨ Medien, Pat. DE 19535848, 1996. w6x A. Puttmer, P. Hauptmann, R. Lucklum, O. Krause, B. Henning, ¨ SPICE model for lossy piezoceramic transducers, IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control 44 Ž1. Ž1997. 60–65. Alf Puttmer was born in Magdeburg, Germany, on May 6, 1970. He ¨ graduated in electrical engineering at Otto-von-Guericke-University Magdeburg in 1994. In 1994, he joined the Department of Electrical Engineering of the Otto-von-Guericke-University Magdeburg as a PhD student. His current research interests include development and modeling of ultrasonic sensors for liquids. Niels Hoppe was born in Magdeburg, Germany, on August 28, 1972. He received the Diploma degree in electrical engineering from the Otto-vonGuericke-University Magdeburg in 1998. In 1998, he joined the Department of Electrical Engineering of the Otto-von-Guericke-University Magdeburg as a PhD student. His research interests are modeling and signal processing of ultrasonic sensor signals. Bernd Henning was born in Wriezen, Germany, on March 25, 1960. He graduated in 1986 in electrical engineering and received the PhD in 1991 from the Otto-von-Guericke-University Magdeburg, Germany. From 1986 to 1993, he worked at the Department of Electrical Engineering of the Otto-von-Guericke-University Magdeburg. In 1993, he joined the Institute for Automation and Communication Magdeburg. His research interests are sensor design of ultrasonic sensors for fluids, new ultrasonic sensors, quartz crystal microbalance sensors and torque sensors. Peter R. Hauptmann was born on July 20, 1944 in Sandau, Germany. He received the Diploma degree in physics from the Technical University Dresden, Germany, in 1968 and the PhD from the Technische Hochschule Leuna-Merseburg, Germany, in 1973 in polymer physics. From 1968 to 1985, he worked at the Technische Hochschule Leuna-Merseburg as a senior lecturer. Since 1985, he has been a Professor at the Otto-vonGuericke-University Magdeburg, Germany. His research interests are chemical sensors and sensors for machinery, basically based on resonant principles.
Ultrasonic density sensor—analysis of errors due to thin layers of deposits on the sensor surface A. Puttmer ¨ a
a,)
, N. Hoppe a , B. Henning b, P. Hauptmann
a,b
Otto-Õon-Guericke-UniÕersity Magdeburg, Institute for Measurement Technology and Electronics (IPE), P.O. Box 4120, 39016 Magdeburg, Germany b Institute for Automation and Communication, Steinfeldstr. 3 (IGZ), 39179 Barleben, Germany Accepted 25 November 1998
Abstract The density of liquids can be measured with ultrasonic techniques. Such sensors determine the reflection coefficient of ultrasound at the boundary between a reference material and the investigated liquid. An important question for application of these sensors is the influence of thin layers which may be deposited at the sensor–liquid interface. This article analyses the measurement errors of an ultrasonic liquid density sensor utilising simulation techniques. q 1999 Elsevier Science S.A. All rights reserved. Keywords: Ultrasound; Density sensor; Error analysis
1. Introduction
2. Ultrasonic measurement of the density of liquids
The density r of a substance is related to its acoustic parameters sound velocity c and acoustic impedance Z with Z s r c. The acoustic impedance Z can be determined from the reflection or transmission coefficient of sound, the velocity c can be determined from the time of flight of a pulse along a known path. Different sensors which use this acoustic principle have been introduced w1–5x. These sensors determine the acoustic impedance with a pulseecho-technique utilising the amplitude of an acoustic pulse, that is back-reflected from the interface between a reference material of known parameters and the liquid. Under industrial conditions, it is possible that thin layers are deposited on the surface of the sensor. Layers of deposited materials cause a change of the signal amplitude and phase leading to errors. Otherwise, sensors might be coated with thin layers to improve their durability to aggressive substances. This article aims to analyse the error of the ultrasonic density measurement in dependence on the layer properties thickness and acoustic impedance.
Sensor construction of Ref. w5x is given in Fig. 1a. Both, the piezoceramic transducer and the buffer rods of the reference material have cylindrical shapes. The piezoceramic transducer consists of lead-metaniobate. Both buffer rods are made of quartz glass Ž Z0 s 13.1 MRayl.. As the lengths l 1 and l 2 are different, the reference A ref and measurement echoes A meas are received separated in time ŽFig. 1b.. The measurement is done by measuring the acoustic impedance Zl with the help of the sound reflection coefficient R: Rsy
A ref k
Zl s r 0 c 0
,
1qR
Ž 1. Ž 2.
1yR
with r 0 c0 s Z0 and a calibration factor k related to the acoustic losses in the buffer rods. The value of k is determined with Eq. Ž1. in a calibration measurement of A meas and A ref with air substituting the liquid, when R s y1. The sound velocity of the reference material c 0 is measured from the zero-crossing times t ref and t meas : c0 s
)
A meas 1
Corresponding author. E-mail: [email protected]
0924-4247r99r$ - see front matter q 1999 Elsevier Science S.A. All rights reserved. PII: S 0 9 2 4 - 4 2 4 7 Ž 9 8 . 0 0 3 6 5 - 3
2 Ž l 2 y l1 . t meas y t ref
.
Ž 3.
A. Puttmer et al.r Sensors and Actuators 76 (1999) 122–126 ¨
123
Fig. 1. Construction of the ultrasonic density sensor Ža. and signals observed at the transducers of Z- and c-sensor for l1 s 17 mm, l 2 s 31 mm, l 3 s 22 mm and quartz glass as the reference material Žb..
The liquid’s sound velocity c l is determined with the help of a separate receiver, the c-sensor. The relation of c l and zero-crossing times t l and t meas is given by: l3
cl s tl y
1 2
.
Ž 4.
t meas y t offset
Here, t offset is a value that includes the time between actual pulse beginning and detected zero-crossing of the pulse and time delays of the electronic system. It is determined in a calibration procedure with a liquid of well known acoustic parameters, e.g., water. Finally, the density is calculated from the rearranged definition of the acoustic impedance:
rl s
Zl cl
.
Ž 5.
reflection of the pulse A meas at single boundary between reference material and liquid. However, the mechanism of sound wave reflection and transmission is modified when a layer separates reference material and liquid ŽFig. 2.. Here, a part of the incident wave is reflected at the boundary reference material-layer Ž A R .. Another part is reflected at the layer-liquid interface causing the wave AXR inside the layer. Obviously, this wave is partially transmitted into reference material and liquid after travelling through the layer. These transmitted waves contribute to both A R and AT with amplitude and phase shift depending on the layer thickness x and acoustic parameters c and Z. Distortion of the pulses is observed as the result of this mechanism ŽFig. 3.. The example in Fig. 3 shows a strong influence of the layer impedance. Since layers may be deposited in a wide variety of thickness and acoustic impedance, it required huge effort
Operating with this principle, the amplitudes A meas and A ref as well as the times t l , t ref and tmeas must be measured and the parameters l 1 , l 2 , l 3 , k, r 0 and t offset must be known for calculating the density of the liquid with this sensor.
3. Error analysis Layers of deposits on the sensor surface have a certain influence on A meas , t l and tmeas resulting in errors of R, c 0 , c l and r l . Basically, Eqs. Ž1. – Ž5. are valid only for
Fig. 2. Origin of pulse distortion due to thin layers at the interface between sensor and liquid.
124
A. Puttmer et al.r Sensors and Actuators 76 (1999) 122–126 ¨
Fig. 3. Pulse distortion due to a thin layer at the interface between sensor and liquid with the thickness x and acoustic impedance Z of 3 MRayl Ža. and 30 MRayl Žb..
to do the analysis completely experimentally. Simulations instead of experiments are used for error analysis in the work presented in this paper. Relative errors dZl and dc l are computed separately. Their contribution to the relative error of the density can be calculated with the help of: d r l s dZl q dc l .
Ž 6.
This allows the determination of the dominating contribution under given conditions.
F1 0 3 V1 1.32 F2 0 4 V2 1.81E9 R1 4 0 1E3 C1 4 0 1 .ENDS .SUBCKT SOURCE A B V1 A 1 PULSE Ž0,14,0,10N,10N,240N,1. V2 B 1 PULSE Ž0,14,260N,10N,10N,240N,1. .ENDS X4 1 0 SOURCE R1 1 3 50 X1 3 13 14 PZ35; Z-transducer RB 13 0 4.11K; quartz glass T1 14 0 16 0 Z0 s 4.11K TD s 2.86U; buffer rod T2 16 0 17 0 Z0 s 570 TD s TOF4 ; layer T3 17 0 20 0 Z0 s 449 TD s 2U y TOF4 ; water T4 20 0 21 0 Z0 s 5.43K TD s 250N; encapsulation X3 2 21 22 PZ35; c-transducer R3 22 0 1K; epoxy backing R4 2 0 50; termination .TRAN 8NS 6000NS 0 0 .PARAM TOF 1N .STEP PARAM TOF 1N 20N 1N .PROBE .END The subcircuit PZ35 represents the piezoceramic disc and subcircuit SOURCE models the electric excitation. The layer between buffer rod ŽT1 . and liquid ŽT3 . is represented by transmission line T2 with the parameters Z0 —impedance of the layer and TD —the time a pulse needs to travel through the layer. Since the sound velocity c of the layer is known, the layer thickness is x s cTD . Even though good agreement between simulation and experiment was proved in Ref. w6x for the transducer and the complete sensor, the SPICE model of the sensor with a layer was tested for the case of a polystyrene layer. The results of simulation and experiment are compared in
3.1. Sensor model Simulations were done using a unidimensional model for the circuit analyser SPICE. The model is based on lossy or lossless equivalent circuits for all piezoelectric and acoustic elements w6x. Layers are described by their acoustic impedance, thickness and velocity. All parameters can easily be varied in the range of interest and multilayered transducer layouts are easily possible by stacking the equivalent circuits. The source code is given below: ERROR ANALYSIS .SUBCKT PZ35 E B F; 2 MHz transducer T1 B 1 F 1 LEN s 0.74M R s 1470K L s 1.76 G s 0 C s 65N V1 1 2 E1 2 0 4 0 1 V2 E 3 C0 3 0 735P
Fig. 4. Relative errors d R, dc 0 , dc l and dZl for a boundary of quartz glass Ž Z0 s13.1 MRayl. to water Ž Zl s1.48 MRayl. with a polystyrene layer Ž Zl s 2.52 MRayl, cs 2400 mrs.. Lines indicate simulated graphs while symbols show experimental measurements.
A. Puttmer et al.r Sensors and Actuators 76 (1999) 122–126 ¨
125
Fig. 4. Good agreement between simulated and measured relative errors of R, c 0 , c l , and Zl is shown. 3.2. Computations The error analysis was done for layers with following properties: Ø Acoustic impedance Z s 0.05Z0 . . . 3Z0 , which corresponds to 0.65 . . . 39 MRayl ranging from polymers Ž1.7 . . . 4 MRayl. to metals Ž) 17 MRayl., Ø thickness x s lr50 and x s lr100 Ž l is the wavelength., Ø only smooth layers Žno scattering effects. on the surface of both Z-sensor and c-sensor with equal thickness. The analysed layer thickness is limited to the values x s lr50 and x s lr100 because sensor development is focused in this project on sensors with an accuracy better 1%. Referring to Fig. 4, the error dZl is increasing with the layer thickness and exceeds this limit at about x s lr50. Another important question is that of the opportunity of Žpartial. error compensation with the help of calibration. The mechanism of sound reflection shown in Fig. 2 acts in a similar fashion when the liquid is substituted by air. That is the case during the calibration measurement for determination of k. Thus, a layer will affect the calibration measurement and k will cover a difference caused by this layer. This difference of k can partially compensate the error of R generated by the layer. The calibrations of r 0 and t offset are affected by layers in analogous fashion.
Fig. 6. Error dZl caused by dc 0 for three different liquids and varying layer thickness without calibration Ža. and for two liquids after Žb. calibration of the sensor with water.
All error computations were done for two cases: 1. The sensor was calibrated with clean surface to the liquid and 2. the analysed layer on the surface was present during the calibration procedure. 3.3. Results
Fig. 5. Error dZl caused by d R for three different liquids and varying layer thickness without Ža. and with Žb. previous calibration of the sensor.
The measurement error dZl caused by an erroneous R is shown in Fig. 5a for three different liquids Ž0.7 MRayl–ethylether, 1.43 MRayls–water, 2.34 MRayl– glycerine.. For each considered liquid it is zero at two points Z s Z0 and Z s Zl . That are the points where the reflections between layer-reference material and layerliquid vanish. The error is negative for Z ) Z0 , which corresponds to layers of metal, and is negative for Z - Zl , which seems to be unlikely in practice. The range between both zero-error points corresponds to layers like polymers and shows a positive error. Here, the highest error in the graph is that of the measurement with Zl s 0.7 MRayl with up to q2.6% for a lr50-layer. However, the layer has an influence on the calibration factor k, too. When the sensor with the layer is first calibrated in air, the error is partially compensated with the help of the calibration factor k. As shown in Fig. 5b, the error is reduced from q2.6 to q1% for a lr50-layer and from q0.5 to q0.38% for a lr100-layer. The second impact of layers on the sensor surface on the measurement error of r is that caused by the errors of
126
A. Puttmer et al.r Sensors and Actuators 76 (1999) 122–126 ¨
an unidimensional model of the sensor. A comparative study for one layer material with varied thickness shows good agreement between simulation and experiment. Thin layers on the sensor surface affect the measurement of times Žsound velocity. much less than that of amplitudes Žreflection coefficient.. Therefore, the limit of layer thickness is set by the error of the amplitudes. Despite the significant improvement due to calibration, metal layers still cause high errors even when their thickness is only a tiny fraction of a wavelength, layers like polymers can be tolerated with a thickness up to lr50.
References
Fig. 7. Error dc l for three different liquids and varying layer thickness without calibration Ža. and for two liquids after Žb. calibration of the sensor with water.
c 0 and c l . Both measurements become erroneous due to a shift in zero-crossing time of t meas and t l . The impact of layers on the measurement error of Zl caused by an erroneous c 0 is shown in Fig. 6a. Considering one layer thickness, it has similar behaviour for all investigated liquids and layers with Z ) 0.5Z0 . It has different behaviour in the practically unlikely case Z - Zl . The similarity of all graphs allows an effective error compensation when water is used for sensor calibration when the layer is present. Errors after calibration are given in Fig. 6b. The measurement error of c l caused by thin layers on the sensor surface is shown in Fig. 7a. It is zero for layers with Z s Zl , the point where layer and liquid have the same acoustic behaviour. After recalibration of the sensor with a layer and water as the calibration medium, the error graph is that of Fig. 7b. Since the layer causes an absolute error, the relative error < dc l < can be reduced when the length l 3 of the sensor is increased. It was 22 mm in the simulation.
4. Conclusions Thin layers of deposits at the interface of an ultrasonic density sensor have great influence on the measurement. The analysis of such effects can be done with the help of
w1x D.J. McClements, P. Fairley, Ultrasonic pulse echo reflectometer, Ultrasonics 29 Ž1991. 58–62. w2x B. Fisher, V. Magori, A. von Jena, Ultraschall ŽUS.-Dichtemesser ´ zum Messen der spezifischen Dichte eines Fluid, Patent EP 0 483 491 B1, 1995. w3x B. Jensen, Gerat ¨ zur akustischen Messung der Dichte einer Flussigkeit, ¨ Patent DE 30 16 323 A1, 1979. w4x J.C. Adamowski, F. Buiochi, C. Simon, E.C.N. Silva, R.A. Sigelmann, Ultrasonic measurement of density of liquids, J. Acoust. Soc. Am. 97 Ž1. Ž1995. 354–361. w5x A. Puttmer, B. Henning, K. Dierks, P. Hauptmann, Vorrichtung zur ¨ Messung und Bestimmung der akustischen Impedanz von flussigen ¨ Medien, Pat. DE 19535848, 1996. w6x A. Puttmer, P. Hauptmann, R. Lucklum, O. Krause, B. Henning, ¨ SPICE model for lossy piezoceramic transducers, IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control 44 Ž1. Ž1997. 60–65. Alf Puttmer was born in Magdeburg, Germany, on May 6, 1970. He ¨ graduated in electrical engineering at Otto-von-Guericke-University Magdeburg in 1994. In 1994, he joined the Department of Electrical Engineering of the Otto-von-Guericke-University Magdeburg as a PhD student. His current research interests include development and modeling of ultrasonic sensors for liquids. Niels Hoppe was born in Magdeburg, Germany, on August 28, 1972. He received the Diploma degree in electrical engineering from the Otto-vonGuericke-University Magdeburg in 1998. In 1998, he joined the Department of Electrical Engineering of the Otto-von-Guericke-University Magdeburg as a PhD student. His research interests are modeling and signal processing of ultrasonic sensor signals. Bernd Henning was born in Wriezen, Germany, on March 25, 1960. He graduated in 1986 in electrical engineering and received the PhD in 1991 from the Otto-von-Guericke-University Magdeburg, Germany. From 1986 to 1993, he worked at the Department of Electrical Engineering of the Otto-von-Guericke-University Magdeburg. In 1993, he joined the Institute for Automation and Communication Magdeburg. His research interests are sensor design of ultrasonic sensors for fluids, new ultrasonic sensors, quartz crystal microbalance sensors and torque sensors. Peter R. Hauptmann was born on July 20, 1944 in Sandau, Germany. He received the Diploma degree in physics from the Technical University Dresden, Germany, in 1968 and the PhD from the Technische Hochschule Leuna-Merseburg, Germany, in 1973 in polymer physics. From 1968 to 1985, he worked at the Technische Hochschule Leuna-Merseburg as a senior lecturer. Since 1985, he has been a Professor at the Otto-vonGuericke-University Magdeburg, Germany. His research interests are chemical sensors and sensors for machinery, basically based on resonant principles.