Patent Application: US-73661903-A

Abstract:
a wood drying installation for a wood drying kiln including a pair of electrodes adapted to be inserted into a wood stack contained in the kiln , a resistance connected in a series circuit with the electrodes , an ac voltage source connected to apply an ac voltage across the series circuit , a phase detecting circuit connected to the series circuit operable to generate a signal representing the phase angle between ac voltages applied to different parts of the series circuit , and a processor to receive the signal . the system is operable to determine a moisture value corresponding to a capacitive component of the reactive impedance between the electrodes in accordance with a predetermined arithmetic algorithm relating the value to the phase angle .

Description:
referring to fig6 in more detail , reference numeral 10 indicates a wood - drying kiln in which there is a stack of timber 12 . the timber 12 is arranged in layers which are spaced from one another by means of spacers . the environment inside the kiln is controlled according to the moisture content of the timber . to determine the moisture content of the timber accurately , the kiln is provided with measuring means comprising an electronics module 14 outside but in close proximity to the kiln , a pair of electrodes 16 inside the kiln and coupled to the module 14 by means of electrical connections 18 , and a remote data processor 20 which is connected to the electronics module 14 by means of a data link 22 . where there are a number of kilns 10 , each with its own electronics module 14 , the various electronics modules may all be connected to the same data processor 20 . the electrodes 16 are in the form of metal plates and are simply inserted into the spaces between layers in the stack 12 . it is an important feature of the invention that the electrodes 16 need not be cleaned prior to insertion into the stack , as operation of the apparatus is not affected by the degree of physical contact with the timber . the size and exact position of the electrodes is also not important . if the size and / or position of the electrodes is changed , all that will be required is for the system to be recalibrated . the electronics module 14 serves to measure the values that are required to determine the capacitance and resistance of the complex impedance between the electrodes 16 . this is achieved in the following manner . the electronics module , as shown in fig7 includes a resistive element 24 , connected in series with one of the electrodes , and an oscillator 26 and associated driver 28 whereby a sinusoidal voltage can be applied to the electrodes via the resistive element . the oscillator 26 has a frequency which is in the ultra - sonic range , for example in the order of 40 khz . the impedance indicated at 30 represents the impedance between the electrodes 16 . the electronics module 14 further comprises a super - fast comparator 32 which is connected via a precision buffer 34 to the output of the driver 28 , and via a precision buffer 36 to one of the electrodes , the other electrodes being connected to ground . the waveform of the applied voltage ( i . e . the output of the driver 28 ) is indicated at 38 in fig8 whereas the waveform of the voltage across the electrodes 16 ( i . e . after the resistive element 24 ) is indicated by reference numeral 40 in fig8 . in fig9 the applied voltage 38 is indicated by the phasor v 1 and the voltage across the electrodes by the phasor v 2 . because the impedance 30 is a complex impedance , there is a phase difference between the voltages v 1 and v 2 , this being indicated by the angle φ in fig4 . v x in fig4 is the voltage across the resistive element 24 . the comparator 32 serves to convert the sinusoidal voltage 38 and 40 to square - wave voltages 42 and 44 respectively . the electronics module 14 further comprises an exclusive or ( xor ) circuit 46 whose output is indicated at 48 in fig3 . the rms value of the output 48 varies in proportion to the phase difference between the voltages 38 and 40 . the outputs of the buffers 34 and 36 and the output of the xor circuit 46 are fed via a multiplexer 50 to an rms - to - dc converter 52 . the multiplexer 50 has a relatively slow sampling rate as compared with the frequency of the applied signal . output 54 of the rms - to - dc converter 52 is relayed to the data processor 20 via the data link 22 . the phase angle of the impedance 30 is determined by making use of the following equations : φ is the phase difference between the voltage v 1 and v 2 ; c x is the value of the capacitive component of the complex impedance 30 ; and r x is the resistive component of the complex impedance 30 . assuming that the capacitive and resistive components of the impedance are in parallel as shown in fig2 . in the event that the complex impedance includes an inductive component ( l x ) in parallel with the capacitive component c x , the value of l x can be determined independently from c x by measuring the complex impedance at two different frequencies . the capacitive and resistive components of the complex dielectric as depicted in fig7 is obtained rigorously by means of the following procedure . element 30 in fig7 is represented as z x , meaning the parallel combination of the resistive r x and capacitive c x properties of the wood sample . the load impedance z x ( 30 ) is connected in series with the resistor r s ( 24 ) and the voltage v 2 is measured across the load . the principle measurement is then the comparison between the applied voltage { overscore ( v )} 1 connected to the remaining side of r s and the load voltage { overscore ( v )} 2 which also involves a phase detection . expressing the impedance in terms of the dielectric elements c x and r x and the angular frequency ω , the impedance of the dielectric medium can be obtained in terms of r x and c x as z x = r x  z c z c + r x ( 1 ) z c = 1 j   ω   c x z x = r x 1 + ω 2  c x 2  r x 2 - j  r x 2  c x  ω 1 + ω 2  c x 2  r x 2 ( 2 ) rewriting this in terms of magnitude and angular components using the euler description yields ,  where    z x  = r x ( 1 + ω 2  c x 2  r x 2 )  1 + r x 2  c x 2  ω 2   and   θ = arctan  ( - ω   rxcx ) . ( 3 ) z x = r s  v _ 2 v _ 1 - v _ 2 ( 4 ) since { overscore ( v )} 1 is the oscillator voltage , the phase angle of this sinusoid is zero . the waveform obtained at v 2 will display some amplitude decrease due to e . g . the dielectric loss of the medium ( wood ) and also display a phase difference φ due to the 80 | 1 polarization ratio of the h 2 o molecules and the cell - wall structure in the presence of the electromagnetic field . therefore define , { overscore ( v )} 1 = v 1 and { overscore ( v )} 2 = v 2 e jθ . by substitution for { overscore ( v )} 1 and { overscore ( v )} 2 in equation ( 4 ) into and after expanding into { overscore ( v )} 1 and { overscore ( v )} 2 real and complex parts and finally rewriting in euler form , the following is obtained . z x = r s  v 2  e j  ( φ + δ ) v 1 2 + v 2 2 - 2  v 1  v 2  cos   φ  ( 5 ) δ = arctan  v 2  sin   φ v 1 - v 2  cos   φ ( 6 ) since the impedances of equation ( 7 ) and ( 3 ) and are the same in magnitude and phase angle it follows that , θ = φδ + 2kπ and r s  v 2 v 1 2 + v 2 2  2  v 1  v 2  cos   φ = r x ( 1 + ω 2  c x 2  r x 2 )  1 + r x 2  c x 2  ω 2 ignoring multiple solutions , assuming k = 0 and substituting for θ and δ in the phase equation , and obtain , arctan  ( - r x  c x  ω ) = φ + arctan  v 2  sin   φ v 1 - v 2  cos   φ ( 8 ) by taking tan on both sides of the equation and using the identity , tan  ( a + b ) = tan   a + tan   b 1 - tan   a   tan   b ( 9 ) - ω   r x  c x = sin   φ   v 1  v 1  cos   φ - v 2 ( 10 ) which is the reciprocal of the loss tangent . the equation ( 10 ) substituted into equation ( 2 ) is sufficient to obtain r x uniquely in terms of the amplitudes v 1 , v 2 and their relative phase shift φ . after some extended simplifications it is found that r x = r s   v 2  v 1  cos   φ - v 2 ( 11 ) c x is obtained in turn by substituting equation 11 into equation 10 . after some trivial simplifications the capacitance c x is obtained as , c x = v 1  sin   φ  v 2  2  π   f   r s ( 12 ) take note that capacitive phase angles are negative , therefore φ would be negative resulting in the capacitance c x to be positive . it is clear from the above derivation and equations and that by only measuring the magnitudes v 1 , v 2 and the phase angle φ between these two sinusoids , that the capacitance c x and the resistance r x can be obtained exactly within the resolution of the measurement of v 1 , v 2 and the φ . it must be stressed that c x is obtained independently r x and that variations of one do not influence the other due to inaccuracies introduced by the method and vice versa . the only dependence that can be introduced is due to the minute errors created during measuring of these three quantities . a method is therefore established whereby the pure values of r x and c x are obtained independently , instantaneously and simultaneously once v 1 , v 2 and φ are known . it can also operate at a specified frequency within its frequency range . the mathematical model obtains exact values of r x and c x not depending on any hardware except r s and of measurement principles to obtain v 1 and v 2 accurately . it is clear from the equations 11 and 12 obtained that r s can be dynamically altered to suit for measurements without loss of accuracy as it is contained in the equations . there is therefore a minimal dependence on hardware reference restricted to only that of r s and the accurate measurement of two voltages v 1 and v 2 . the remainder is done by exact formulas to obtain r x and c x . furthermore the loss - tangent can be constructed from c x and r x by the equation tan   δ = 1 ω   r x  c x or instantly from the same measurement of v 1 , v 2 and the phase angle φ using the equation tan   δ = v 2 - v 1  cos   φ v 1  sin   φ the model also takes care of oscillator variations in a fundamental way . the equations are such , that any variations of oscillator amplitude due to power fluctuations etc are compensated for elegantly and intrinsically without the need for any hardware implementation . the magnitudes v 1 and v 2 are related as follows . v 2 v 1 =  z r s + z  ( 13 ) from this it is clear to see that c x and r x in equations 11 and 12 will be invariant under any variations of v 1 and as a consequence also tan δ as it is constructed uniquely from c x and r x . since the measurement principle can detect r x and c x independently , the resistance and capacitance of the probe wiring can be elegantly removed . since capacitances add in parallel , the probe wire capacitance can simply be subtracted from the capacitance measured with a load attached in order to obtain the capacitance of the wood sample as c l = c t − c c , where c l , c t and c c are the load , total and cable capacitances respectively . the parallel resistance of lossy probe systems is also accurately measured and can be trivially removed by means of where r t is the total resistance measured , r l is the load resistance and r p is the probe parallel resistance . the instantaneous measurement of capacitance and resistance by the method therefore easily systematically and clearly removes the cable dielectric properties in order to obtain the dielectric properties of the medium independent from cable dielectric influences . from the valve of c x the moisture context of the wood can not be determined as indicated by fig5 . since the pure value of c x can be measured by this method , measurement of moister content above f . s . p . is immediately evident as the influence of r x , which obscures this measurement , is removed . similarly , since the pure value of r x can be obtained , the exact value of f . s . p . can be correlated as the influences of c x , which obscures detection of f . s . p . on r x is eliminated . the method elegantly removes the probe dielectric influences on the measurements as the probe dielectrics can be measured and the capacitance subtracted from the capacitance obtained with a dielectric connected and probe resistance obtained removed from the resistance obtained with a dielectric connected by means of the formula for two resistances in parallel . furthermore , since c x and r x are obtained in their pure form by this method and since the probing system is just a proportionality between the c x and ∈ r and r x and σ it can be related directly with public data . the application of a measuring system to constitute a meter to perform the tasks as described in this method is described in detail in the parent application ser . no . 08 / 913 , 429 and will be understood to apply to this continuation in part thereof . the following notational difference is introduced . in this continuation in part ω shall mean the angular frequency ω = 2 πf , where f is the frequency . in the parent application ω was understood to mean the phase difference between the sinusoids related to v 1 and v 2 which is rather indicated as φ in this continuation . the series resistor r in the parent application is renamed to r s . by substitution of the equations a , b , d and b as found in the parent application , c x and r x obtained yields exactly the equations as derived in this continuation application . the above described system measures the capacitance and resistive of a reactive load represented by a stack of wood produced between two probes . in accordance with the invention , the reactive load is connected in a series circuit with a known resistance and the voltage across the reactive load and across the series current are detected . the phase angle between the two voltages is determined and from the values of the known resistance , the voltages , and phase angle between the detected voltages , the capacitance and resistance are determined in accordance with arithmetic equations expressing the capacitance and resistance in terms of the measured values . it will be appreciated that instead of detecting the voltage across the series circuit , the voltage across the known resistance could be detected , and the phase angle between this voltage and the voltage across the reactive load measured . from these voltages , the value of the known resistance , and the phase angle , the capacitance and the resistance of the reactive load could be determined from arithmetic equations in a similar manner . 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