Analysis of a Capacitive Mass Flow Sensor for a Screw Conveyor

Excerpt from the Proceedings of the COMSOL Users Conference 2007 Grenoble Analysis of a Capacitive Mass Flow Sensor for a Screw Conveyor Anton Fuchs* and Hubert Zangl Institute of Electrical Measurement and Measurement Signal Processing Graz University of Technology, Austria *Kopernikusgasse 24/IV, A-8010 Graz, Austria, Email: anton.fuchs@tugraz.at $EVWUDFW This paper presents an analysis of a measurement principle for the determination of the mass flow of material through screw conveyors. The flow sensor design is based on capacitive sensing with the characteristic that the pipe content can be analyzed in a spatially resolving manner. Finite Element Analysis is used to investigate the sensor head and to estimate the performance of the sensor. Main aim of the paper is to estimate the range of capacitance values that can be expected for such a setup. .H\ZRUGV Finite Element Analysis, Screw Conveyor, Capacitive Sensing individual "pocket") in such a horizontal setup may vary dramatically, leading to erroneous results for the transported mass. Figure 1 shows the principle of material transportation by means of a screw conveyor and illustrates the different batches of material separated by the screw blades. Ma te ria l Inle t Tra nsp orta tio n Pip e Sc re w Bla d e Be a ring Moto r Ma te ria l O utlet  ,QWURGXFWLRQ In a variety of different applications in industry as well as in agriculture and shipping, large amounts of material have to be transported in a save and cost-efficient way. Depending on the requirements and types of transportation (e.g. conveying length, required mass flow, lifting height to overcome) and the material properties itself (i.e. state, size, abrasiveness, etc.), materials handling has developed certain suitable transportation techniques. The principle of transporting media by means of an Archimedes screw is very well known, especially in bulk materials handling. Practical realizations of this principle are one of the oldest machines still in use [1]. Such a conveyor basically consists of screw-shaped blades on a rotating axis in a closed pipe [2]. With the blade movement, the material is pushed through the transportation pipe. This conveyor type can be employed in horizontal, in slightly or steeply inclined as well as in vertical configurations. Further advantages are a steady operation principle and the control of mass flow via revolution speed of the screw. The transported mass can only be roughly estimated by knowing the revolution speed of the screw drive and the mean mass (or volume) of the transported material per revolution of a blade. The material fill level (i.e. the height of material in each )LJXUH  Screw conveyor principle for horizontal use with unequal material fill levels per blade, resulting in erroneous estimations of the transported masses. This paper discusses the sensor geometry for a novel, cost-effective capacitive sensor principle for mass flow measurement in screw conveyors [3] and gives a detailed analysis for the sensor by means of Finite Element Method (FEM). The range of capacitance values that can be expected for such a setup as well as the impact of material and screw on these capacitances are analyzed to allow for well-defined requirements of the circuitry to be developed.  3URSRVHG 6HQVRU $SSURDFK Several embodiments of the capacitive sensor front-end are supposable [4] - a functional embodiment of the sensor is presented in Figure 2. The sensor head consists of a segmented ring of transmitter electrodes and one continuous receiver ring mounted on a nonconducting pipe section. Transmitter electrodes are subsequently supplied with a signal of several MHz and either the electric potential or the charge at the receiver electrode [5] is measured to determine the inter-electrode capacitance between active transmitter segment and receiver ring. Since every transported bulk material features a dielectric permittivity r higher than the one of air ( r,mat is typically about Excerpt from the Proceedings of the COMSOL Users Conference 2007 Grenoble 3 to 4 while r,air is 1), the inter-electrode capacitance is over a wide range linearly affected by the presence of material in the vicinity of a capacitive sensor. Due to the segmented structure of the transmitter electrodes, information about the permittivity- and hence the material distribution in the measurement section can be obtained [6] [7]. T nsm itter Elec trod es ra Rec eiver Elec trod e )LJXUH  Geometry model of the screw with tetrahedron mesh. )LJXUH  Principle sensor setup in front- and sideview. The segmented layer of transmitter electrodes are subsequently set active to determine the capacitance between transmitter and receiver. The segmented ring of transmitter electrodes and the continuous receiver electrode ring were included as composite objects. A grounded shield in the far distance from the sensor geometry allows for a reference to ground. For the analysis, the COMSOL electrostatics model with the basic equation For a totally filled pipe within the measurement section, all inter-electrode capacitances are at a maximum. If the pipe is not fully filled, the measurement signal, which is proportional to the inter-electrode capacitance, will decrease. Field draining effects are expected that cause a "suction" of field lines from transmitting to receiving electrode whenever the blade passes the fixed electrodes (i.e. with every full turn of the blade). If these field draining effects can be detected reliably in the capacitive measurement signals, the revolution speed of the screw can be determined independently from the engine speed. This allows for a compact sensor with short wiring. − ∇ ⋅ ε 0ε r,mat ∇9 = ρ (1)  6HQVRU $QDO\VLV E\ 0HDQV RI )($ To analyze the capacitive sensor with respect to expected signal levels, FEM is applied. Therefore, the commercial FEM software COMSOL Multiphysics version 3.3 was used to develop a 3D geometrical model of the assembly. For the geometry of the screw-shaped auger the blades are drawn in 2D and this geometry was extruded with a certain twist along the axis. A rod was fused with the blades to form the entire auger geometry as shown in Figure 3. for the subdomain settings was used (no polarization is expected). The permittivity value r,mat of the material is set to 4 in all the simulations and the permittivity of the metal components like electrodes or the auger are set to 1e7 to ensure that electric field lines are perpendicular to metal surfaces. The electric potential 9 was the dependent variable in this model. Instead of subsequently setting all transmitter electrodes to an electrode potential 9 of 1 V (i.e. to “activate” the transmitter signals one after the other) and keep the receiver ring on ground, the boundary settings were interchanged. With these settings all inter-electrode capacitances &i between segmented transmitter electrodes and receiver ring can be calculated in one single simulation step. The surface charge densities σ of the grounded segmented electrodes L are individually integrated by means of calculating the surface LQWHJUDO RYHU WKH HOHFWURGH ERXQGDULHV i: &i = 1 ⋅ σ (Γi )⋅ dΓi 9 ∫Γ (2) The geometry of the setup, comprising a segmented layer of eight transmitter electrodes, a continuous receiver ring, and the screw, is shown in Figure 4. Figure 4a shows the profile of the setup with the denomination of the electrodes, for better demonstration the grounded shield Excerpt from the Proceedings of the COMSOL Users Conference 2007 Grenoble around the entire assembly is not shown in Figures 4a and 4b. to calculate the solution on an Intel Core2Duo computer with 2.4 GHz and 2 GB main memory. Figure 5 shows simulation results for a specific fill level: Figure 5a plots the permittivity distribution (truncated for better visibility due to the high permittivity of metal parts), Figure 5b the distribution of the magnitude of electric displacement and Figure 5c the cross-sectional potential distribution. (a) (a) )LJXUH  3D geometry model of the setup comprising a segmented layer of eight transmitter electrodes, a continuous receiver ring, and the screw in (a): Profile with denomination of electrodes and (b): Oblique view (b)  'HWHUPLQDWLRQ RI WKH )LOO /HYHO To estimate the impact of varying material fill levels within the sensitive volume, the pipe content is subdivided into ten equidistant, horizontal fill levels. This discrete division is done to avoid remeshing and the subdivision into different FEM meshes when variable fill levels are used – errors due to varying element sizes are hence avoided. Filled domains of the pipe content are set to r,mat=4 in the subdomain settings while unfilled GRPDLQV DUH VHW WR r,air=1. Since we are interested in the behavior of inter-electrode capacitances for increasing and decreasing fill levels at this stage, the screw geometry is replaced by a simplified rod in the pipe center. The boundary conditions of the rod are set to ground potential. The simplified geometry consists of about 48.000 elements and it takes less than 15 seconds (b) )LJXUH  Simulation results for a given horizontal fill level: Cross-sectional plots of (a): Permittivity distribution, (b): Distribution of the electric displacement and (c): Distribution of the electric potential. (c) Excerpt from the Proceedings of the COMSOL Users Conference 2007 Grenoble The calculated inter-electrode capacitances between receiver ring and transmitter electrode 1 to electrode 8 (electrode denomination according to Figure 4a) are plotted in Figure 6 over the material fill level. As can be expected, the two bottommost electrodes are affected first by the increasing material fill level. The topmost electrodes feature an increase in inter-electrode capacitance and hence in the measurement signal for high fill levels only. Due to the slight, clockwise inclination of the transmitter electrodes (out-of-symmetry, compare Figure 4a), a delay between corresponding transmitter electrodes can be observed in the simulation results in Figure 6. x 10 4.4 4.2 4 -13 reaches the most sensitive area of the top electrodes. For the intermediate transmitter electrodes (i.e. electrodes 2, 3, 6, and 7), both effects are superimposed and therefore the gradient is lower than for the bottom and top electrodes, where coupling and draining effects occur at different fill levels.  'HWHUPLQDWLRQ RI WKH 6FUHZ 5HYROXWLRQ The revolution speed of the screw can also be reliably determined by analyzing the motor rotation speed that drives the screw. However, to avoid expensive cabling and electromagnetic disturbances caused by long cable duct through industrial environment, an all-in-one sensor solution for both revolution speed and fill level is desirable. It is furthermore desirable to make use of a non-invasive sensor principle that can be easily implemented in existing screw conveyor systems and that features a clear separation between actuating and sensing elements. The geometry model shown in Figure 4 is used to estimate the sensitivity of the setup on the screw rotation angle. Therefore, the grounded screw is stepwise rotated in 5° steps and the FEM model is solved for several screw rotation angles using the electrostatic problem formulation in Eqn. (1). The 45° rotation symmetry of the setup is exploited for the analysis of the screw impact on the capacitances. For the calculation itself, the geometry is subdivided into a tetrahedron mesh with about 105.000 elements in total. It took about 30 seconds to solve the problem with one rotation angle on a Core2Due computer. Figure 7 shows simulation results for one specific rotation angle of the screw: Figure 7a plots the permittivity distribution (permittivities truncated for better visibility), Figure 7b the distribution of the magnitude of electric displacement and Figure 7c the cross-sectional potential distribution. The obtained interelectrode capacitances between individual transmitter electrodes and the common receiver ring are plotted over the screw rotation angle in Figure 8, following the denomination of electrodes according to Figure 4a. It can be seen that due to the helical geometry of the screw, the signals differ in their phase and that a capacitance variation of about 100 pF can be expected. Inter-Electrode Capacitances for Increasing Fill Level Electrode 5 Electrode 6 Electrode 7 Electrode 8 Electrode 1 Electrode 2 Electrode 3 Electrode 4 Field Draining Effect Inter-Electrode Capacitances [F] 3.8 3.6 3.4 3.2 3 2.8 2.6 2.4 0 Field Draining Effect 10 20 30 )LJXUH  Inter-electrode capacitances between individual transmitters and receiver ring for increasing material fill level (denomination of electrodes according to Figure 4a). Fill Level [mm] 40 50 60 70 80 90 For low fill levels, only a thin material layer exists in the vicinity of the two bottom electrodes. A raise of the fill level then causes a steep increase of the coupling capacitance since the electric field from transmitter to receiver electrode is predominantly coupled through the material. However, when the material layer becomes thicker, the capacitance between the material and grounded objects in the sensor (screw and shielding) goes up. As a consequence, the electric field is partly directed to grounded areas and kind of sucked off from the receiver electrode (field draining effect). This means that for a certain fill level the capacitance between bottom electrodes and the receiver decreases. Similarly for the top electrodes, a drain effect can be observed before the fill level Excerpt from the Proceedings of the COMSOL Users Conference 2007 Grenoble Inter-Electrode Capacitance [F] x 10 Inter-Electrode Capacitance [F] -13 Electrode 1 x 10 -13 Electrode 2 2 1.5 1 2 1.5 1 0 x 10 50 -13 Inter-Electrode Capacitance [F] Inter-Electrode Capacitance [F] 100 150 200 250 Screw Rotation Angle [° ] Electrode 3 300 350 0 x 10 50 -13 100 150 200 250 Screw Rotation Angle [° ] Electrode 4 300 350 2 1.5 1 2 1.5 1 0 x 10 50 -13 Inter-Electrode Capacitance [F] Inter-Electrode Capacitance [F] 100 150 200 250 Screw Rotation Angle [° ] Electrode 5 300 350 0 x 10 50 -13 100 150 200 250 Screw Rotation Angle [° ] Electrode 6 300 350 2 1.5 1 2 1.5 1 (a) 0 x 10 50 -13 Inter-Electrode Capacitance [F] Inter-Electrode Capacitance [F] 2.5 2 1.5 1 100 150 200 250 Screw Rotation Angle [° ] Electrode 7 300 350 0 x 10 50 -13 2.5 2 1.5 1 100 150 200 250 Screw Rotation Angle [° ] Electrode 8 300 350 0 50 )LJXUH  Inter-electrode capacitances between individual transmitters and receiver ring over the rotation angle of the screw (denomination of electrodes according to Figure 4a). 100 150 200 250 Screw Rotation Angle [° ] 300 350 0 50 100 150 200 250 Screw Rotation Angle [° ] 300 350  &RQFOXVLRQ (b) This paper presents a FEM simulation-based analysis of a capacitive sensor, intended for the measurement of the revolution speed of an auger in a screw conveyor as well as for the material fill level of the assembly. Due to the use of segmented transmitter electrodes, the sensor features spatially resolving measurement. Results from FEM show that capacitance variations of the proposed setup will be suitable to determine the material fill level and the revolution speed of the screw. Simulation results furthermore reveal that field draining effects due to metal parts in the setup have to be considered. )LJXUH  Simulation results for a given revolution angle of the screw: Cross-sectional plots of (a): Permittivity distribution, (b): Distribution of the electric displacement and (c): Distribution of the electric potential. (c)  5HIHUHQFHV 1. C. Rorres, The Turn of the Screw: Optimal Design of an Achimedes Screw, -RXUQDO RI +\GUDXOLF (QJLQHHULQJ, , no. 1, pp. 72-80 (2000). 2. G. Pajer, H. Kuhnt and F. Kurth, 6WHWLJI|UGHUHU, VEB Verlag Technik, Berlin, (1977). 3. A. Fuchs, H. Zangl, G. Brasseur, Mass Flowmeter for Screw Conveyors Based on Capacitive Sensing, 3URF RI ,((( ,QVWUXPHQWDWLRQ DQG 0HDVXUHPHQW 7HFKQRORJ\ Excerpt from the Proceedings of the COMSOL Users Conference 2007 Grenoble &RQIHUHQFH ,07& , Warsaw, Poland, May 1-3, 2007 pp. 1-5 (2007) 4. A. Fuchs, H. Zangl and G. Brasseur, Method and Device for a Reliable Determination of the Massflow in Screw Conveyors, $XVWULDQ 3DWHQW $SSOLFDWLRQ $ 5. H. Wegleiter, A. Fuchs, G. Holler and B. Kortschak, Analysis of Hardware Concepts for Electrical Capacitance Tomography Applications, 3URF RI WKH ,((( 6HQVRUV , Irvine, California, October 31-November 3, 2005, pp. 688-860 (2005). 6. L.K. Baxter, &DSDFLWLYH 6HQVRUV  'HVLJQ DQG $SSOLFDWLRQ, Chapter: Proximity Detectors, IEEE Press, New York, USA (1997). 7. M. Young, E. Pickup, R. Deloughry, T. Hartley, S.A. Nixon and L. Barratt, Development of a Variable Density Flowmeter for an Industrial Application Using Tomographic Imaging, ,(( &ROORTXLXP RQ $GYDQFHV LQ (OHFWULFDO 7RPRJUDSK\ (Digest No: 1196/143), pp. 14/1-14/3 (1996).  $FNQRZOHGJHPHQWV This work was partially funded by the Austrian Science Fund through the Translational Research Project number L355-N20.