Primary measuring transducer of moisture content for grain quality control

The main task of the research is the development of the primary capacitive measuring transducer that can perform testing influences on the material under research, applied for automatic “type uncertainty” method error compensation, that takes place because of the method of measurement imperfection. To estimate the relevant level of testing influences a group of different materials with 2, 2.5, 3 and 3.5 dielectric permittivity values was taken for 0, 10, 20, 30 and 40% of moisture content control points. The primary measuring transducer of moisture content is organized with an electrode system in a form of V-type plates, which is fixed on the internal surface of two dielectric rings. Testing influences on the substance are reproduced directly in the capacitive primary transducer by simple metallic plates with fixed thickness introduction into the space between separate electrodes of an electrode system. A prototype product of the primary measuring transducer had been experimentally tested together with the new method of moisture measurement, which includes two additive, two multiplicative and two complementary testing influences on the material under research. Moisture content with nominal values 0, 10, 20 and 30% was reproduced by certain group of grains with different dielectric permittivity values. Experimental setup of an adaptive moisture meter was assembled using the substitution method of measurement to provide good accuracy for the conditions of capacitance measurement in substances with significant dielectric losses. The accuracy of moisture measurement was defined as discrepancy between average measured and nominal moisture content and as an uncertainty of this discrepancy in a form of type A uncertainty.

Introduction position, granulometric composition and temperature variation. Not only material's type or sort has an effect on its physicochemical composition, but conditions of extraction, processing, etc., that is the list of factors, complicated for analytic forecasting. Granulometric composition of different bulk materials is far from ideal what decreases the repeatability of measurements. Temperature influence, in its turn, can be taken into account by the introduction of correction coefficients into the result of moisture measurement.

Problem statement
Moisture control is typical for the significant number of operations in extracting, processing and production of different materials. Now we have approximately 33% of moisture meters represented by dielcometer instruments with capacitive primary transducers. Moisture meters of this type have complementary error of measurements (type uncertainty), connected with dif-ferent values of dielectric permittivity for the materials under research in dehydrated state. The influence of this error is usually significant and traditional ways of its compensation can be effective when we know the composition of the material under research.
In other cases the effectiveness of traditional compensation methods essentially decreases.
Mainly because of that further improvement of the existing methods of moisture measurement with a task to solve the problem of type uncertainty compensation is a relevant and perspective mission.

Analysis of recent researches and publications
In moisture meters, present on the modern market, different physicochemical composition in the most cases can be taken into account in the way of metering curves or rating coefficients introduction into the microprocessor block memory for maximal number of the materials under research with a possibility of separate calibration before each measurement [1][2][3]. But it is impossible to get analytic forecast of chemical composition and different features of all the materials under research. That is why mentioned above methods of type uncertainty compensation have local effectiveness and are not versatile.
Besides, the analysis of measurement methods based on dielcometer principle was carried out [4]. Separate group of methods was detected, where special testing influences should be fulfilled to define the initial moister value of the sample under research. Testing influences can be implemented in the form of measured out water volumes addition with further mixing, introduction of measured volume of a material with certain dielectric permittivity or capsules with water of a certain form.
Direct addition of water dozes into the material with further mixing can be hardly possible for some cases, for example, when we have measurements in a flow or when the material with high moisture content is under research. Besides that, for a big number of technological processes (grain softening, production of oil-water or coal-water slurries) it is necessary to maintain a certain value of moisture and measured out water volumes addition can't be accepted. Application of leak-proof capsules with water is ineffective from the production manufacturability point of view.
Main purpose of the research is to create a primary transducer of moisture content with a design, which could provide the most simple and manufacturable way to fulfill testing influences on the material under research with a task to compensate material's type influence on the result ofmeasurement.

Primary measuring transducer of moisture content
Before we discuss testing influences on the material, it's necessary to estimate their relevant level. For that purpose a group of different materials with dielectric permittivity values ε n , equal to 2, 2.5, 3 and 3.5 was taken. Then five control points of moisture content W were chosen for these materials with values 0, 10, 20, 30 and 40% of moisture.
Main purpose of such a check-up was to determine the percentage of binary mixture dielectric permittivity change for the certain volumes of water added to different materials.
Primary measuring transducer is organized with an electrode system 1 (Fig. 1) in a form of V-type plates. System of electrodes is fixed on the internal surface of two dielectric rings 2 and 3. To make the implementation of testing influences convenient, construction of the transducer has two internal dielectric rings 4 and 5.
Testing influences on the substance are reproduced directly in the capacitive primary transducer by simple metallic plates 6, 7 with fixed thickness introduction into the space between separate electrodes of an electrode system 1. To preform two additive testing influences on the material under research primary transducer can be conventionally divided into three measuring sections. In accordance with To provide second testing influence on the substance under research capacitance C of four capacitors from section 2 must be increased by 59.74% or in 1.5974 times. Gap between the electrodes, designated as Z, should be decreased by the same value. Primary transducer's prototype product has such geometrical dimensions ( Fig. 1): electrodes' length (distance between rings 2 and 3) is equal to l = 50 mm; gap between electrodes Z = 20 mm; internal diameter of dielectric rings D = 150 mm; electrodes' width (distance between rings 2 and 4) L = 0.5√(D 2 -Z 2 )--1.866Z = 37 mm.
In correspondence with [10], capacitance C of a flat capacitor with metallic plate between the electrodes will depend only from metallic plate thickness and can be calculated using the formula: where d is a distance from the edge of an electrode to the edge of metallic plate. Knowing that, it is possible to calculate thickness d 1 of one metallic plate 6 using formula (2) and thickness d 2 of one metallic plate 7 using formula (3): . Z . , 1 1 2764

Calculation of primary measuring transducer's electric capacitance
At first electric capacitances of sections 1, 2 and 3 for empty primary measuring transducer were calculated. Section 1 contains four connected in parallel capacitors, where gap between electrodes is equal to Z 1 = Z -d 1 . Section 2 has four capacitors with a gap Z 2 = Z -d 2 . Section 3 is free from metallic plats and has four capacitors with a gap Z between electrodes. General electric capacitance for the capacitors of section 1 can be calculated using the formula: where g 01 -spatial characteristics of basic electric field, m; g 21 -spatial characteristics of external field in a form of half cylinder for the side l; g 41the same in a form of half cylinder for the side L; g 61 -the same in a form of half tube for the side l; g 81 -the same in a form of half tube for the side L; g 101 -the same in a form of spheric quadrants; g 121 -the same in a form of quadrants of the spheric shells.
Method of spatial characteristics calculation can be found in Table 2.
Capacitance value C 1 would be equal to: .
Spatial characteristics calculations for C 2 and C 3 capacitances of the primary measuring transducer sections 2 and 3 are given in Table 3. Described primary measuring transducer was developed as a part of moisture measurement method in bulk and liquid dielectric substances [11,12], where moisture content can be calculated using formula (5):   Main idea of the method is that we take a sample of material under research and get a first reading from the capacitance primary transducer C 3 (it will be the capacitance of section 3). Then we get a second reading from the initial transducer C 1 as a capacitance of section 1 with first group of metallic plates (they simulate adding 10% of water into the sample as a first additive test). To create the first multiplicative test and get a third reading from the initial transducer value of capacitance C 3 was increased two times ( C / 3 in the formula). First complementary test (reading number four) was received by two times increasing the capacitance C 1 ( C / 4 in the formula). Next, fifth reading from the capacitance primary transducer can be taken from section 2 as a capacitance C 2 (second additive test). Reading number six must be performed as a second multiplicative test 4•C 3 = C 3 // , and the last reading is a second complementary test 4•C 2 = C 2 // . Values of all capacitances were calculated for the conditions where moisture content W = 0% and W = 20%, and dielectric permittivity of a bulk material is equal to ɛ n = 3.5 (Table 4).
Obtained values were substituted into (5) with a result W = 0.77% for dehydrated substance and W = 20.157% for moist substance. We can see that method error is acceptable and formula (5) is workable.

Experimental researches
To fulfill experimental researches moisture content with nominal values 0, 10, 20 and 30% had to be reproduced for such substances as: pearl barley (ɛ = 3.68); poppy (ɛ = 3.56); millet (ɛ = 3.17); pea (ɛ = 2.97); wheat cereals (ɛ = 2.55) [12]. Mass of each sample was approximately 600 g, and for their preliminary dehydration 30 standard aluminum weighing bottles with 20 g weights of grain were used. Empty weighting bottles were weighed with ±0.01 g accuracy [13] using electronic scales "LEV 600-0.01". In accordance with [14], weighing bottles with opened leads should be placed in a drying oven to dry in 130 °С temperature during 120 minutes. Air sterilizer "GP-10" with required metrological characteristics was used for that purpose. Fig. 2 shows the experimental setup. It has a container with primary measuring transducer, secondary measuring transducer, oscilloscope Tektronix 2213A to control the shape and duration of pulses, taken from secondary measuring transducer's check point, variable air capacitor, digital multimeter UTM 18803 to measure dc voltage on the output of a secondary transducer and accurate RLC-meter UTM 1612 to measure capacitance value of the variable air capacitor [15].
Container with primary measuring transducer was filled with substance under research. Then capacitive sensors of three sections were connected one by one to the input of secondary measuring transducer and three values of dc voltage from its output were fixed. After that primary measuring transducer was substituted by variable air capacitor. Using method of substitution electric capacitances of each primary measuring transducer's section were defined.

Таble 4
Values of electric capacitances in picofarads for dehydrated and moist bulk material

Results and discussion
Averages of 10 measurements for primary transducer's electric capacitances C 1 , C 2 and C 3 , filled with materials under research in dehydrated state and with moisture content of W = 10%, W = 20% and W = 30% are shown in Table 5.
Rest of the capacitances, mentioned in Tables 4, 5, were calculated in accordance with the principle described right after formula (5). Now it became possible to check the testing algorithm (5) interaction with the results of capacitance measurement (averages) shown in Table 5. Results of moisture calculation for mentioned materials under research can be found in Table 6.
It is possible to estimate the method part of moisture measurement absolute uncertainty by using: discrepancy ∆ m of measured moisture content average W mi and standard moisture value W si , and uncertainty of that discrepancy in a form of type A uncertainty.

Conclusions
In the described model of primary measuring transducer we have metallic plates introduced into the gap between electrodes instead of capsules with water or direct water addition. It was divided into three sections.
First section is free from testing influences on the material under research, in second section 10% of water addition is simulated by increasing its capacitance into 27.64%. Third section simulates 20% addition of water and, to provide it, electrical capacitance of this section should be increased in 59.74%.
Experimental setup was assembled using the substitution method of measurement. As a result, the accuracy of moisture measurement was defined as a discrepancy ∆ m of measured moisture content average W mi and standard moisture value W si , and uncertainty of that discrepancy in a form of type A uncertainty. It helped to confirm that received accuracy values correspond with requirements to grain moisture meters set out in [16].