- Email: [email protected]
Development of a capacitive mass measuring system
Sensors and Actuators A 151 (2009) 113–117
Contents lists available at ScienceDirect
Sensors and Actuators A: Physical journal homepage: www.elsevier.com/locate/sna
Development of a capacitive mass measuring system Amir Abu Al Aish ∗ , Mahfoozur Rehman School of Electric and Electronic Engineering, University Science Malaysia, Engineering Campus, 14300 Nibong Tebal, P. Pinang, Malaysia
a r t i c l e
i n f o
Article history: Received 14 October 2008 Received in revised form 2 February 2009 Accepted 6 February 2009 Available online 28 February 2009 Keywords: Capacitive mass sensor Temperature errors Capacitance measuring system Spring
a b s t r a c t The paper deals with the theory, design, fabrication and test results of a robust, linear and accurate capacitive mass sensor. The change in capacitance, with increased mass, takes place due to the shielding effect of a conducting cylinder which moves in between the stationary concentric co-axial cylinders. A direct capacitance measuring system, developed by the authors, is used in the calibration of the mass sensor. Presented sensor is linear, immune to temperature errors, highly flexible in the design and can cover different weighing ranges by selecting proper springs only. For the spring, used in the system, mass sensor can weigh up to 4 kg. © 2009 Elsevier B.V. All rights reserved.
1. Introduction
2. Theory and design
Mass is a fundamental quantity and helps in the absolute measurement of several other quantities hence its accurate measurement plays very important role in the field of instrumentation. Mass measuring systems are as old as human civilization. Generally, equal arm or unequal armed beam balances have been used in the accurate and precise measurement of masses. The automatic measurement of mass started with the help of strain gauge load cells and still it is prevailing in most of the automatic systems. However, strain gauge is temperature sensitive and over all deflection, in load cell, is very small. Hence weighing errors due to temperature changes may arise and proper compensation should be provided for precise measurement of mass [1,2]. Fiber Optic sensor is also developed for the measurement of small masses [3]. It is based on the light intensity modulation and has non-linear response. In this paper we have proposed a capacitive mass sensor based on concentric co-axial cylinders. Change in the capacitance takes place due to the movement of the grounded cylindrical shield between the stationary concentric higher and lower potential cylinders. The change in capacitance is highly linear and can be calibrated in terms of mass with high precision. The capacitance to voltage converter which is used in this system can be easily interfaced with an analogue to digital converter (ADC) and a microcontroller to measure mass automatically [4].
Capacitive sensors have been used successfully in the measurement of a number of physical quantities due to their small size, accuracy, low power of consumption and simple circuits to convert it into voltages [5]. In most of the sensors, capacitances involved, are very small and are affected by earth admittances. Hence special techniques are used to eliminate the effect of earth admittances [5]. For this purpose, sensor is provided with a conducting shield (third terminal) and is represented by the circuit shown in Fig. 1(a) is the designed and its equivalent circuit is shown in Fig. 1(b). C12 capacitance of the sensor while C13 and C23 are undesirable capacitances and measuring circuit should be so chosen that the earth admittances do not affect the final results. In the recent past, Threewinding Transformer Ratio-arm Bridges were used to eliminate the effect of earth admittances [5,6]. For varying the value of capacitance, with physical quantity, sometimes conducting grounded shield is extended axially between the active area of the main electrodes [5,6]. This type of variation has two major advantages. Firstly, the relationship between the physical quantity to be investigated and the change in capacitance may be strictly linear and secondly the radial movement of shield towards the electrodes will not cause any variation in the value of the direct capacitance of the sensor. It is a very important aspect with respect to the fabrication of the sensor [5]. Furthermore the variation in the direct capacitance will be free from the fringing effect because the electrical field distribution will remain the same regardless of the position of the grounded shield [5]. Therefore in the development of the proposed mass sensor, this type of variation is used. The cross-sectional elevation of the proposed sensor is shown in Fig. 2. Two co-axial cylinders (1 and 2)
∗ Corresponding author. Tel.: +60 174014361. E-mail address: [email protected] (A. Abu Al Aish). 0924-4247/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.sna.2009.02.023
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Fig. 1. (a) Three-terminal capacitor. (b) Equivalent circuit of the capacitor.
Fig. 4. Proposed active bridge.
Spring is provided with a guide made of iron (7) so that spring may apply uniform force against the weight to be investigated. A screw (8), with fine threads, is provided to adjust the position of the shield as well as to replace the spring to cover different weighing ranges. Over all system is contained in a metallic container (9) which provides stable base as well as acts as a shield against external fields. The guide of the shield is provided with a hole covered by a screw (10) which may help in the adjustment of the damping of the system. When hole is open, the air friction damping will be nearly negligible because air pressure will be quickly equalized on both sides. However when hole is partially blocked, trapped air will provide some order of damping. The position of screw may be adjusted to provide critical damping. Electrical connections are taken from the main cylinders (1) and (2), and the outer metallic container (shield and container are at same potential and kept at earth potential). 2.1. An active bridge for the measurement of small capacitances Fig. 2. (a) Cross-sectional view of the mass sensor. (b) Cut-opened view of the shield.
make the main capacitor which is designed for a capacitance of 18 pF. These are fixed on a base made of acrylic glass (Perspex) and terminals are taken out through fixing screws. Shielding cylinder (3) is fixed on the mass carrying platform (4) and rests on the spring (5) which serves as a load carrier for the weight to be investigated. Fig. 3 shows the three dimensional shape of the coaxial shielding cylinder. A Teflon guide (6) is provided to keep the movement of the shield vertical and in between the main cylinders (1) and (2).
In Fig. 4 is shown the schematic diagram of the bridge for the measurement of small capacitances. At balance, the sum of currents in the two branches (I1 and I2 ) will be zero which is indicated by the output voltage (V0 ) of the current to voltage converter. Assuming ideal conditions, the balance equation may be written as: V0 = (I2 + I1 )R3 = 0
(1)
where R3 is the feedback resistance of the current to voltage converter. The values of the branch currents may be written as I1 = −i2f
R2 Vs C12 R1
(2)
I2 = i2fVs C12
(3)
where Vs is the supply voltage of the bridge, R1 and R2 are the resistances used to control the gain of the inverter and f is the operating frequency. ) and stanThe relationship between unknown capacitance (C12 dard capacitance (C12 ) can be developed by substituting the values of I1 and I2 in Eq. (1) we get:
i2fVs C12 − i2f
R2 Vs C12 R3 = 0 R1
(4)
or = C12
Fig. 3. Three-dimensional shape of the coaxial shielding cylinder.
R1 C12 R2
(5)
can be measured in Eq. (5) shows that different values of C12 terms of the standard capacitor C12 , by varying the resistances R1 and R2 of the inverter. In this way appreciable range of capacitances
A. Abu Al Aish, M. Rehman / Sensors and Actuators A 151 (2009) 113–117 and C can be measured. Stray capacitances C23 23 will appear across the virtual ground and ground terminals of the current to voltage converter hence will not affect the results. On the other hand, C13 will appear across supply and will not affect the balance equation because change in supply voltage due to loading will affect will appear across the output both branches simultaneously. C13 of the opamp and will not affect the balance because the output impedance of the OpAmp (50–60 ) is 10−7 times smaller than the . The accuracy of the capacitance measurement and reactance of C13 hence mass, will depend upon the accuracy of the standard capacitor as well as on the accuracy of ratio provided by the resistances R1 and R2 . The relationship between mass and capacitance can be developed as follows: As the mass is increased, depending upon its spring constant, some down ward movement of the shield will take place. Shield is designed and placed to provide zero capacitance at the condition of zero mass. When mass is added on the top of the sensor, shielding effect of the shield decreases linearly and hence capacitance increases linearly. Relation ship between mass and capacitance, if Hooke’s law holds, can be given by following expression: C12 = GM
(6)
is the direct capacitance, M is the mass under measurewhere C12 ment and G is the factor which depends upon the spring constant. However, due to fringing effect, some error may be introduced which will remain same in all positions and hence proportional in ity constant will take care of it. Now substituting the value of C12 Eq. (5) in Eq. (6) we get:
GM =
R1 C12 R2
(7)
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from Eq. Now, substituting the value of direct capacitance C12 (4) in Eq. (7) we get:
V0 = −i2fGR4 Vs M
(10)
Eq. (10) shows that output voltage of the differentiator V0 is directly proportional to mass under measurement and hence it may be calibrated in terms of mass. However, frequency and applied voltage should be maintained constant. 2.3. Estimation of temperature errors The temperature rise will affect the main cylinders (1) and (2), shield (3) and the spring (5). The increase in length of active electrodes will not have any effect on the final results because length is defined by shield only. Increase in length of shield, made of brass, has been estimated and comes out to be 18.7 × 10−7 m K−1 which will change the effective capacitance by a factor of 2.95 × 10−4 pF K−1 . It will give rise to a full scale error of 0.0016% K−1 which is acceptable in the present design. However, it can be further reduced by making the shield of a material which has still lower value of the coefficient of linear expansion like invar36. Spiral spring will also be affected by the temperature and proper selection of material for spring, may reduce temperature errors. Phosphor bronze is one of the suitable materials for making spiral springs which are free of temperature errors. 3. Constructional details A prototype model of the proposed system is designed and fabricated to study its working. The cross-sectional view of the unit is shown in Fig. 2(a).
or M=
R1 C12 R2 G
3.1. Co-axial cylindrical capacitor (8)
Eq. (6) shows that Mass may be calibrated in terms of resistances. Different weighing ranges may be obtained by varying standard capacitance in steps and continuous variation may be obtained by variable resistances. To avoid the effect of leakage resistances, balance condition should be checked with phase sensitive detector. 2.2. Direct reading small capacitance measuring system Fig. 5 shows the circuit which can be used to measure capacitance linearly. In the differentiator circuit, capacitor is replaced by the equivalent circuit of the three-terminal capacitive mass sen and C will not affect the output voltage sor. The capacitances, C13 23 will appear because C13 will appear across supply voltage and C23 across the input terminals of the operational amplifier [7]. Expression for output voltage may be written as follows: R4 Vs V 0 = −i2fC12
Fig. 5. Circuit diagram of the linear mass measuring system.
(9)
Main sensor is composed of a capacitor made of co-axial cylinders (1) and (2) and shielding (3) arrangement. Outer cylinder (1) and inner cylinder (2) of the main sensor have the radii of 4.3 cm and 3.8 cm, respectively. They have the working height of 4.0 cm. These are fixed on a Perspex plate to keep the distance constant as well as to provide good insulation between them. The uniformity of spacing between cylinders is very important and is checked with the help of standard spacers. This setup is placed in a metallic container which supports the system as well as acts as a shield. 3.2. Cylindrical conducting shield It is made of brass and it is designed to move between the main cylinders (1) and (2). It has windows with thin webs in the upper part of the cylindrical structure as shown in Figs. 2(b) and 3. The thin webs are the part of the shielding cylinder and are designed to supports the main part of the shield. However their presence will change the unshielded capacitance of the sensor. Under zero mass condition, shield is placed so that its Lower part completely shields the main cylinders, and sensor has zero direct capacitance. When mass is placed on the carrying platform (4), the position of the shield changes between the main cylinders, and windows of the shield comes in between the main cylinders and hence effective direct capacitance increases. The shield is so designed that increase in capacitance is directly proportional to the mass placed on the sensor. The shield is the integral part of the upper cover of the system. This shield is provided with a guide made of Teflon (6) which guides (solid lubricant) as well as insulate (best insulator) the shield from one of the electrodes.
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3.3. Controlling and damping system A spiral spring (5) serves as the load carrier for the mass to be investigated and is kept on the base whose movement can be adjusted by a screw (8) as shown in Fig. 2(a). It will provide definite value of deflection to the shield under steady state. The size and strength of the spring will decide the maximum value of mass which can be measured by the system. The material and construction of spring will affect the accuracy and linearity of the system. Springs made of steel have been used in the prototype of the capacitive mass measuring device, presented here. The movement of the shield, with mass, under transient condition, can be controlled by adjusting the air pressure between Teflon guide and the spring chamber. In other words, air pressure will control the damping of the system. A screw, placed in a small hole (10), may control the damping of the mass sensor, with out any extrainvestment. Fig. 7. Relationship between mass and output voltage of the direct capacitance measuring system.
4. Experimental methods and results To verify the developed theory, a proto-type model of mass sensor was designed and fabricated with a total movement of shield of 2.7 cm. The maximum mass measured, with the device, is 4.0 kg in steps of 250 g (6.25% of full scale). However, range can be changed by selecting a spring with different spring constant. It has been calibrated with the help of active bridge at 1 kHz and it was found that it has sensitivity of the order of 0.002 pF g−1 . Complete calibration curve is shown in Fig. 6. Exact zero position is achieved by using the screw in the bottom of the sensor. The graph is appreciably linear and non-linearity may be attributed to random effects only. Later on, to make direct measurement of the mass, the capacitance and mass relationship is recorded by using the simple differentiator circuit based upon opamp (LF 356) and the amplitude of the output voltage value (peak-to-peak) is measured by digital oscilloscope (Lecroy LT342). It was found that the standard deviation has a value of 0.009 V. The results are shown in Fig. 7. It has two curves. The first curve is drawn between values of measured output voltage and mass and the second curve is drawn between the output voltage calculated from Eq. (9) (magnitude only) by substituting the values of capacitances obtained from Fig. 6. The Eq. (11), given below, represents the least square fitting curve which is same for the calculated as well as measured data and have a sensitivity of 1.0 mV g−1 . y = 0.001x
(11)
R2
(correlation coefficient) are 0.998 and 0.994 for calculated and measured data, respectively, which indicate strong linear relationships. To estimate the temperature errors, system temperature was varied from 20 ◦ C to 35 ◦ C (which was possible in the laboratory) and no variation was recorded in the output voltages when the masses were measured.
5. Conclusions A linear and accurate capacitive mass measuring system is presented in this paper. Results on a proto-type model are included which confirm the theory. In comparison of load cells having embedded strain gauges and LVDT based system, presented system have some distinct advantages. Firstly the repair of the presented system is much easier as well economical than load cell having embedded strain gauges. Secondly, strain gauge based load cell do not have any sort of flexibility which is a very important aspect of mechatronic system design. In the presented sensor, errors due to temperature are nearly negligible in comparison of load cells employing strain gauges since the change in capacitance of the sensor, with temperature, is very small as explained in Section 2.2, while resistance of the strain gauge changes with temperature appreciably [8]. Materials used in the fabrication of the presented system are easily available and their properties do not affect the accuracy unlike LVDT. The magnetic core plays important role in the accuracy and sensitivity of the LVDT system. The presented system does not require separate damping arrangement. It can also be used in the measurement of masses from few grams to hundreds of kilograms by selecting proper springs. Zero error, if any, can be adjusted with the help of the corresponding screw (8). The mechanical and Electronic parts of the system are quite simple and may be prepared at low cost. It can be interfaced with microcontroller to develop an intelligent mass sensor. The proto-type model is tested up to 4 kg mass due to the availability of spring and weights of good accuracy. However, it needs calibration according to the international recommendations OIML R-76 [9] and OIML R-111 [10]. Acknowledgment The authors would like to thank University Science Malaysia for providing the short term grant No. 304/PELECT/6035171 to carry out the research work. References
Fig. 6. Relation ship between mass and capacitance.
[1] V.V. Athani, R. Vaswani, PC based electronic weighing system, Proceedings of IEEE Industry Applications Society Annual Meeting 2 (1990) 1856–1861. [2] N.H. Norton, Handbook of Transducer, Prentice Hall, Inc., New Jercy, 1989, 72, 190-199. [3] H. Gonlabi, Mass measurement using light intensity modulated optical fiber sensor, Optics and Lasers in Engineering 38 (2002) 537–548. [4] D.V. Hall, Microprocessors and Interfacing, Macmillan/McGraw-Hill, USA, 1992, 308-316. [5] B. Hague, T.R. Foord, Alternating Current Bridge Methods, 6th ed., Pitman, London, 1971, 484-535.
A. Abu Al Aish, M. Rehman / Sensors and Actuators A 151 (2009) 113–117 [6] M. Rehman, V.G.K. Murti, A sensitive and linear pressure transducer, Journal of Physics E: Scientific Instruments (England) 14 (1981) 988–992. [7] W.Q. Yang, A self-balancing circuit to measure capacitance and loss conductance for industrial transducer applications, IEEE Transactions on Instrumentation and Measurement 45 (1996) 955–957. [8] E. Doebelin, Measurement Systems Application and Design, 5th ed., McGrawHill, New York, 2003, 247. [9] International recommendation OIML R76-1, Metrological and technical requirements, 2006. [10] International Recommendation, 111—Weights of Classes E1, E2, F1, F2, M1, M12, M2, M2-3 and M3, International Organization of Legal Metrology (OIML), Paris, Draft of 12 August 2004.
Biographies Mahfoozur Rehman received B.Sc. Engg. (Electrical) and M.Sc. Engg. (Instrumentation and Control) from Z.H. College of Engineering and Technology, Aligarh Muslim
117
University, Aligarh, India, in 1966 and 1972, respectively, and Ph.D. (Electrical) from Indian Institute of Technology Madras, Chennai, India, in 1981. He has been working in the field of Sensor Technology and has published nearly 75 papers in International Journals, Conferences, National journals and refereed National Conferences. He took voluntary retirement from the post of professor in Electronics Engg. Dept. in 2004 and joined School of Electric and Electronics Engg., USM, Pulau Pinang, Malaysia. Amir Abu Al Aish received B.Sc. Engg. (Electronic Technology) from Yarmouk University, Irbid, Jordan, in 2003 and M.Sc. Engg. (Electronic system design) in 2006 from university Science Malaysia, Pulau Pinang, Malaysia. At present, he is working for his Ph.D. degree in the School of Electric and Electronics Engineering, USM, Pulau Pinang, Malaysia. He is working in the field of sensors technology and electronic instrumentation and so far he has published four papers in refereed International conferences.
Contents lists available at ScienceDirect
Sensors and Actuators A: Physical journal homepage: www.elsevier.com/locate/sna
Development of a capacitive mass measuring system Amir Abu Al Aish ∗ , Mahfoozur Rehman School of Electric and Electronic Engineering, University Science Malaysia, Engineering Campus, 14300 Nibong Tebal, P. Pinang, Malaysia
a r t i c l e
i n f o
Article history: Received 14 October 2008 Received in revised form 2 February 2009 Accepted 6 February 2009 Available online 28 February 2009 Keywords: Capacitive mass sensor Temperature errors Capacitance measuring system Spring
a b s t r a c t The paper deals with the theory, design, fabrication and test results of a robust, linear and accurate capacitive mass sensor. The change in capacitance, with increased mass, takes place due to the shielding effect of a conducting cylinder which moves in between the stationary concentric co-axial cylinders. A direct capacitance measuring system, developed by the authors, is used in the calibration of the mass sensor. Presented sensor is linear, immune to temperature errors, highly flexible in the design and can cover different weighing ranges by selecting proper springs only. For the spring, used in the system, mass sensor can weigh up to 4 kg. © 2009 Elsevier B.V. All rights reserved.
1. Introduction
2. Theory and design
Mass is a fundamental quantity and helps in the absolute measurement of several other quantities hence its accurate measurement plays very important role in the field of instrumentation. Mass measuring systems are as old as human civilization. Generally, equal arm or unequal armed beam balances have been used in the accurate and precise measurement of masses. The automatic measurement of mass started with the help of strain gauge load cells and still it is prevailing in most of the automatic systems. However, strain gauge is temperature sensitive and over all deflection, in load cell, is very small. Hence weighing errors due to temperature changes may arise and proper compensation should be provided for precise measurement of mass [1,2]. Fiber Optic sensor is also developed for the measurement of small masses [3]. It is based on the light intensity modulation and has non-linear response. In this paper we have proposed a capacitive mass sensor based on concentric co-axial cylinders. Change in the capacitance takes place due to the movement of the grounded cylindrical shield between the stationary concentric higher and lower potential cylinders. The change in capacitance is highly linear and can be calibrated in terms of mass with high precision. The capacitance to voltage converter which is used in this system can be easily interfaced with an analogue to digital converter (ADC) and a microcontroller to measure mass automatically [4].
Capacitive sensors have been used successfully in the measurement of a number of physical quantities due to their small size, accuracy, low power of consumption and simple circuits to convert it into voltages [5]. In most of the sensors, capacitances involved, are very small and are affected by earth admittances. Hence special techniques are used to eliminate the effect of earth admittances [5]. For this purpose, sensor is provided with a conducting shield (third terminal) and is represented by the circuit shown in Fig. 1(a) is the designed and its equivalent circuit is shown in Fig. 1(b). C12 capacitance of the sensor while C13 and C23 are undesirable capacitances and measuring circuit should be so chosen that the earth admittances do not affect the final results. In the recent past, Threewinding Transformer Ratio-arm Bridges were used to eliminate the effect of earth admittances [5,6]. For varying the value of capacitance, with physical quantity, sometimes conducting grounded shield is extended axially between the active area of the main electrodes [5,6]. This type of variation has two major advantages. Firstly, the relationship between the physical quantity to be investigated and the change in capacitance may be strictly linear and secondly the radial movement of shield towards the electrodes will not cause any variation in the value of the direct capacitance of the sensor. It is a very important aspect with respect to the fabrication of the sensor [5]. Furthermore the variation in the direct capacitance will be free from the fringing effect because the electrical field distribution will remain the same regardless of the position of the grounded shield [5]. Therefore in the development of the proposed mass sensor, this type of variation is used. The cross-sectional elevation of the proposed sensor is shown in Fig. 2. Two co-axial cylinders (1 and 2)
∗ Corresponding author. Tel.: +60 174014361. E-mail address: [email protected] (A. Abu Al Aish). 0924-4247/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.sna.2009.02.023
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Fig. 1. (a) Three-terminal capacitor. (b) Equivalent circuit of the capacitor.
Fig. 4. Proposed active bridge.
Spring is provided with a guide made of iron (7) so that spring may apply uniform force against the weight to be investigated. A screw (8), with fine threads, is provided to adjust the position of the shield as well as to replace the spring to cover different weighing ranges. Over all system is contained in a metallic container (9) which provides stable base as well as acts as a shield against external fields. The guide of the shield is provided with a hole covered by a screw (10) which may help in the adjustment of the damping of the system. When hole is open, the air friction damping will be nearly negligible because air pressure will be quickly equalized on both sides. However when hole is partially blocked, trapped air will provide some order of damping. The position of screw may be adjusted to provide critical damping. Electrical connections are taken from the main cylinders (1) and (2), and the outer metallic container (shield and container are at same potential and kept at earth potential). 2.1. An active bridge for the measurement of small capacitances Fig. 2. (a) Cross-sectional view of the mass sensor. (b) Cut-opened view of the shield.
make the main capacitor which is designed for a capacitance of 18 pF. These are fixed on a base made of acrylic glass (Perspex) and terminals are taken out through fixing screws. Shielding cylinder (3) is fixed on the mass carrying platform (4) and rests on the spring (5) which serves as a load carrier for the weight to be investigated. Fig. 3 shows the three dimensional shape of the coaxial shielding cylinder. A Teflon guide (6) is provided to keep the movement of the shield vertical and in between the main cylinders (1) and (2).
In Fig. 4 is shown the schematic diagram of the bridge for the measurement of small capacitances. At balance, the sum of currents in the two branches (I1 and I2 ) will be zero which is indicated by the output voltage (V0 ) of the current to voltage converter. Assuming ideal conditions, the balance equation may be written as: V0 = (I2 + I1 )R3 = 0
(1)
where R3 is the feedback resistance of the current to voltage converter. The values of the branch currents may be written as I1 = −i2f
R2 Vs C12 R1
(2)
I2 = i2fVs C12
(3)
where Vs is the supply voltage of the bridge, R1 and R2 are the resistances used to control the gain of the inverter and f is the operating frequency. ) and stanThe relationship between unknown capacitance (C12 dard capacitance (C12 ) can be developed by substituting the values of I1 and I2 in Eq. (1) we get:
i2fVs C12 − i2f
R2 Vs C12 R3 = 0 R1
(4)
or = C12
Fig. 3. Three-dimensional shape of the coaxial shielding cylinder.
R1 C12 R2
(5)
can be measured in Eq. (5) shows that different values of C12 terms of the standard capacitor C12 , by varying the resistances R1 and R2 of the inverter. In this way appreciable range of capacitances
A. Abu Al Aish, M. Rehman / Sensors and Actuators A 151 (2009) 113–117 and C can be measured. Stray capacitances C23 23 will appear across the virtual ground and ground terminals of the current to voltage converter hence will not affect the results. On the other hand, C13 will appear across supply and will not affect the balance equation because change in supply voltage due to loading will affect will appear across the output both branches simultaneously. C13 of the opamp and will not affect the balance because the output impedance of the OpAmp (50–60 ) is 10−7 times smaller than the . The accuracy of the capacitance measurement and reactance of C13 hence mass, will depend upon the accuracy of the standard capacitor as well as on the accuracy of ratio provided by the resistances R1 and R2 . The relationship between mass and capacitance can be developed as follows: As the mass is increased, depending upon its spring constant, some down ward movement of the shield will take place. Shield is designed and placed to provide zero capacitance at the condition of zero mass. When mass is added on the top of the sensor, shielding effect of the shield decreases linearly and hence capacitance increases linearly. Relation ship between mass and capacitance, if Hooke’s law holds, can be given by following expression: C12 = GM
(6)
is the direct capacitance, M is the mass under measurewhere C12 ment and G is the factor which depends upon the spring constant. However, due to fringing effect, some error may be introduced which will remain same in all positions and hence proportional in ity constant will take care of it. Now substituting the value of C12 Eq. (5) in Eq. (6) we get:
GM =
R1 C12 R2
(7)
115
from Eq. Now, substituting the value of direct capacitance C12 (4) in Eq. (7) we get:
V0 = −i2fGR4 Vs M
(10)
Eq. (10) shows that output voltage of the differentiator V0 is directly proportional to mass under measurement and hence it may be calibrated in terms of mass. However, frequency and applied voltage should be maintained constant. 2.3. Estimation of temperature errors The temperature rise will affect the main cylinders (1) and (2), shield (3) and the spring (5). The increase in length of active electrodes will not have any effect on the final results because length is defined by shield only. Increase in length of shield, made of brass, has been estimated and comes out to be 18.7 × 10−7 m K−1 which will change the effective capacitance by a factor of 2.95 × 10−4 pF K−1 . It will give rise to a full scale error of 0.0016% K−1 which is acceptable in the present design. However, it can be further reduced by making the shield of a material which has still lower value of the coefficient of linear expansion like invar36. Spiral spring will also be affected by the temperature and proper selection of material for spring, may reduce temperature errors. Phosphor bronze is one of the suitable materials for making spiral springs which are free of temperature errors. 3. Constructional details A prototype model of the proposed system is designed and fabricated to study its working. The cross-sectional view of the unit is shown in Fig. 2(a).
or M=
R1 C12 R2 G
3.1. Co-axial cylindrical capacitor (8)
Eq. (6) shows that Mass may be calibrated in terms of resistances. Different weighing ranges may be obtained by varying standard capacitance in steps and continuous variation may be obtained by variable resistances. To avoid the effect of leakage resistances, balance condition should be checked with phase sensitive detector. 2.2. Direct reading small capacitance measuring system Fig. 5 shows the circuit which can be used to measure capacitance linearly. In the differentiator circuit, capacitor is replaced by the equivalent circuit of the three-terminal capacitive mass sen and C will not affect the output voltage sor. The capacitances, C13 23 will appear because C13 will appear across supply voltage and C23 across the input terminals of the operational amplifier [7]. Expression for output voltage may be written as follows: R4 Vs V 0 = −i2fC12
Fig. 5. Circuit diagram of the linear mass measuring system.
(9)
Main sensor is composed of a capacitor made of co-axial cylinders (1) and (2) and shielding (3) arrangement. Outer cylinder (1) and inner cylinder (2) of the main sensor have the radii of 4.3 cm and 3.8 cm, respectively. They have the working height of 4.0 cm. These are fixed on a Perspex plate to keep the distance constant as well as to provide good insulation between them. The uniformity of spacing between cylinders is very important and is checked with the help of standard spacers. This setup is placed in a metallic container which supports the system as well as acts as a shield. 3.2. Cylindrical conducting shield It is made of brass and it is designed to move between the main cylinders (1) and (2). It has windows with thin webs in the upper part of the cylindrical structure as shown in Figs. 2(b) and 3. The thin webs are the part of the shielding cylinder and are designed to supports the main part of the shield. However their presence will change the unshielded capacitance of the sensor. Under zero mass condition, shield is placed so that its Lower part completely shields the main cylinders, and sensor has zero direct capacitance. When mass is placed on the carrying platform (4), the position of the shield changes between the main cylinders, and windows of the shield comes in between the main cylinders and hence effective direct capacitance increases. The shield is so designed that increase in capacitance is directly proportional to the mass placed on the sensor. The shield is the integral part of the upper cover of the system. This shield is provided with a guide made of Teflon (6) which guides (solid lubricant) as well as insulate (best insulator) the shield from one of the electrodes.
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3.3. Controlling and damping system A spiral spring (5) serves as the load carrier for the mass to be investigated and is kept on the base whose movement can be adjusted by a screw (8) as shown in Fig. 2(a). It will provide definite value of deflection to the shield under steady state. The size and strength of the spring will decide the maximum value of mass which can be measured by the system. The material and construction of spring will affect the accuracy and linearity of the system. Springs made of steel have been used in the prototype of the capacitive mass measuring device, presented here. The movement of the shield, with mass, under transient condition, can be controlled by adjusting the air pressure between Teflon guide and the spring chamber. In other words, air pressure will control the damping of the system. A screw, placed in a small hole (10), may control the damping of the mass sensor, with out any extrainvestment. Fig. 7. Relationship between mass and output voltage of the direct capacitance measuring system.
4. Experimental methods and results To verify the developed theory, a proto-type model of mass sensor was designed and fabricated with a total movement of shield of 2.7 cm. The maximum mass measured, with the device, is 4.0 kg in steps of 250 g (6.25% of full scale). However, range can be changed by selecting a spring with different spring constant. It has been calibrated with the help of active bridge at 1 kHz and it was found that it has sensitivity of the order of 0.002 pF g−1 . Complete calibration curve is shown in Fig. 6. Exact zero position is achieved by using the screw in the bottom of the sensor. The graph is appreciably linear and non-linearity may be attributed to random effects only. Later on, to make direct measurement of the mass, the capacitance and mass relationship is recorded by using the simple differentiator circuit based upon opamp (LF 356) and the amplitude of the output voltage value (peak-to-peak) is measured by digital oscilloscope (Lecroy LT342). It was found that the standard deviation has a value of 0.009 V. The results are shown in Fig. 7. It has two curves. The first curve is drawn between values of measured output voltage and mass and the second curve is drawn between the output voltage calculated from Eq. (9) (magnitude only) by substituting the values of capacitances obtained from Fig. 6. The Eq. (11), given below, represents the least square fitting curve which is same for the calculated as well as measured data and have a sensitivity of 1.0 mV g−1 . y = 0.001x
(11)
R2
(correlation coefficient) are 0.998 and 0.994 for calculated and measured data, respectively, which indicate strong linear relationships. To estimate the temperature errors, system temperature was varied from 20 ◦ C to 35 ◦ C (which was possible in the laboratory) and no variation was recorded in the output voltages when the masses were measured.
5. Conclusions A linear and accurate capacitive mass measuring system is presented in this paper. Results on a proto-type model are included which confirm the theory. In comparison of load cells having embedded strain gauges and LVDT based system, presented system have some distinct advantages. Firstly the repair of the presented system is much easier as well economical than load cell having embedded strain gauges. Secondly, strain gauge based load cell do not have any sort of flexibility which is a very important aspect of mechatronic system design. In the presented sensor, errors due to temperature are nearly negligible in comparison of load cells employing strain gauges since the change in capacitance of the sensor, with temperature, is very small as explained in Section 2.2, while resistance of the strain gauge changes with temperature appreciably [8]. Materials used in the fabrication of the presented system are easily available and their properties do not affect the accuracy unlike LVDT. The magnetic core plays important role in the accuracy and sensitivity of the LVDT system. The presented system does not require separate damping arrangement. It can also be used in the measurement of masses from few grams to hundreds of kilograms by selecting proper springs. Zero error, if any, can be adjusted with the help of the corresponding screw (8). The mechanical and Electronic parts of the system are quite simple and may be prepared at low cost. It can be interfaced with microcontroller to develop an intelligent mass sensor. The proto-type model is tested up to 4 kg mass due to the availability of spring and weights of good accuracy. However, it needs calibration according to the international recommendations OIML R-76 [9] and OIML R-111 [10]. Acknowledgment The authors would like to thank University Science Malaysia for providing the short term grant No. 304/PELECT/6035171 to carry out the research work. References
Fig. 6. Relation ship between mass and capacitance.
[1] V.V. Athani, R. Vaswani, PC based electronic weighing system, Proceedings of IEEE Industry Applications Society Annual Meeting 2 (1990) 1856–1861. [2] N.H. Norton, Handbook of Transducer, Prentice Hall, Inc., New Jercy, 1989, 72, 190-199. [3] H. Gonlabi, Mass measurement using light intensity modulated optical fiber sensor, Optics and Lasers in Engineering 38 (2002) 537–548. [4] D.V. Hall, Microprocessors and Interfacing, Macmillan/McGraw-Hill, USA, 1992, 308-316. [5] B. Hague, T.R. Foord, Alternating Current Bridge Methods, 6th ed., Pitman, London, 1971, 484-535.
A. Abu Al Aish, M. Rehman / Sensors and Actuators A 151 (2009) 113–117 [6] M. Rehman, V.G.K. Murti, A sensitive and linear pressure transducer, Journal of Physics E: Scientific Instruments (England) 14 (1981) 988–992. [7] W.Q. Yang, A self-balancing circuit to measure capacitance and loss conductance for industrial transducer applications, IEEE Transactions on Instrumentation and Measurement 45 (1996) 955–957. [8] E. Doebelin, Measurement Systems Application and Design, 5th ed., McGrawHill, New York, 2003, 247. [9] International recommendation OIML R76-1, Metrological and technical requirements, 2006. [10] International Recommendation, 111—Weights of Classes E1, E2, F1, F2, M1, M12, M2, M2-3 and M3, International Organization of Legal Metrology (OIML), Paris, Draft of 12 August 2004.
Biographies Mahfoozur Rehman received B.Sc. Engg. (Electrical) and M.Sc. Engg. (Instrumentation and Control) from Z.H. College of Engineering and Technology, Aligarh Muslim
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University, Aligarh, India, in 1966 and 1972, respectively, and Ph.D. (Electrical) from Indian Institute of Technology Madras, Chennai, India, in 1981. He has been working in the field of Sensor Technology and has published nearly 75 papers in International Journals, Conferences, National journals and refereed National Conferences. He took voluntary retirement from the post of professor in Electronics Engg. Dept. in 2004 and joined School of Electric and Electronics Engg., USM, Pulau Pinang, Malaysia. Amir Abu Al Aish received B.Sc. Engg. (Electronic Technology) from Yarmouk University, Irbid, Jordan, in 2003 and M.Sc. Engg. (Electronic system design) in 2006 from university Science Malaysia, Pulau Pinang, Malaysia. At present, he is working for his Ph.D. degree in the School of Electric and Electronics Engineering, USM, Pulau Pinang, Malaysia. He is working in the field of sensors technology and electronic instrumentation and so far he has published four papers in refereed International conferences.