Method and device for measuring basis weight and moisture content amount

1. A method of measuring basis weight and moisture amount for calculating a basis weight and a moisture amount of a sample constituted by a paper sheet using a microwave resonator, the method comprising the steps S 1 to S 6 of;

(Step S 1 )

obtaining a resonance frequency and a resonance peak level of the microwave resonator in a case without a sample;

(Step S 2 )

obtaining a resonance frequency and a resonance peak level of the microwave resonator in the case where the sample is measured;

(Step S 3 )

obtaining a resonance frequency shift amount Δf as a difference between the resonance frequency obtained in the step S 1 and the resonance frequency obtained in the step S 2 ;

(Step S 4 )

obtaining a peak level change amount ΔP as a difference between the resonance peak level obtained in the step S 1 and the resonance peak level obtained in the step S 2 ;

(Step S 5 )

obtaining V 1 and V 2 using expressions:

V 1=(Δ f·∈″ 2 /Kf−Δp·∈′ 2 /Kp )/(∈′1·∈″2−∈″1·∈′2)  (3); and

V 2=(Δ f·∈″ 1 /Kf−Δp·∈′ 1 /Kp )/(∈″1·∈′2−∈′1·∈″2)  (4);

(Step S 6 )

obtaining an absolute dry basis weight and a moisture amount using expressions:

Absolute Dry Basis Weight=β· V 1  (5); and

Moisture Amount=γ· V 2  (6),

wherein

V 1 : a volume of absolute dry paper under a certain condition;

V 2 : a volume of water under a certain condition;

Kf: a proportional constant for matching dimensions;

Kp: a proportional constant for matching dimensions;

∈′1: a dielectric constant of the absolute dry paper−1;

∈′2: a dielectric constant of the water;

∈″1: a dielectric loss factor of the absolute dry paper;

∈″2: a dielectric loss factor of the water; and

β, γ: proportional constants, and

the constants Kf, Kp, ∈′1, ∈′2, ∈″1, and ∈″2 are determined through the following steps A and B, and the constants β and γ are previously determined:

(Step A) for each of a plurality of standard samples having different values for one of the basis weight and the moisture amount, measuring the resonance frequency shift amount Δf and the peak level change amount ΔP by a measurement apparatus using the microwave resonator through the steps S 1 to S 4 ; and

(Step B) obtaining ∈′1, ∈′2, ∈″1, and ∈″2 when variance values of Kf and Kp are smaller than a predetermined value in the relation of the expressions (3) and (4), by taking V 1 =BD/β and V 2 =WT/γ, BD being a predetermined absolute dry basis weight of each of the standard samples and WT being a predetermined moisture amount of each of the standard samples, and by using Δf and ΔP obtained in the step A.

2. The method of measuring basis weight and moisture amount according to claim 1 , wherein

an air dry basis weight and a moisture percentage are further obtained using the following expressions:

Air Dry Basis Weight=Absolute Dry Basis Weight+Moisture Amount; and

Moisture Percentage=Moisture Amount×100/Air Dry Basis Weight.

3. The method of measuring basis weight and moisture amount according to claim 1 , further comprising:

providing a plurality of rectangular dielectric resonators constituting the microwave resonator only on one side of a sample in the same plane such that long sides of the resonators are oriented to directions (θ) different from each other;

taking the directions (θ) as angles θ and the resonance frequency shift amounts Δf 1 to Δf r , of the resonators as r, plotting on a polar coordinate (r, θ) in which an angle is θ and a distance from the point of origin is r to draw an ellipse by an ellipse approximation process, obtaining a radius Δfr of a circle having an area identical to an area of the ellipse, and taking the obtained Δfr as Δf; and

obtaining peak level change amounts ΔP 1 to ΔP n of the resonators, and taking one of ΔPr(A), ΔPr(B), and ΔPr(C) as ΔP according to claim 1 , ΔPr(A), ΔPr(B), and ΔPr(C) being:

(A) ΔPr constituted by one of ΔP 2 to ΔP n ;

(B) ΔPr constituted by an average value of ΔP 1 to ΔP n ; and

(C) ΔPr constituted by a radius of a circle having an area identical to an area of an ellipse obtained by taking the directions (θ) as angles θ and ΔP 1 to ΔP n as r, plotting on the polar coordinate (r, θ) in which the angle is θ and a distance from the point of origin is r, and drawing the ellipse by the ellipse approximation process.

4. An apparatus of measuring basis weight and moisture amount comprising:

a microwave resonator;

a microwave exciting device configured to generate an electric field vector in the resonator;

a detecting device configured to detect one of a transmission energy and a reflected energy by the resonator; and

a data processing device configured to import resonance frequencies of the microwave resonator and peak levels at positions of the resonance frequencies in cases without a sample and with a sample from the detecting device, and to calculate a basis weight and a moisture amount of the sample, wherein

the data processing device includes:

a Δf·ΔP calculating unit configured to calculate a resonance frequency shift amount Δf and a peak level change amount ΔP respectively based on the resonance frequencies and the peak levels imported from the detecting device;

a first constant determining unit configured to determine constants Kf, Kp, ∈′ 1 , ∈′ 2 , ∈″ 1 , and ∈″ 2 by obtaining ∈′ 1 , ∈′ 2 , ∈″ 1 , and ∈″ 2 when variance values of Kf and Kp are smaller than a predetermined value in the relation of the expressions (3) and (4) according to claim 1 , using Δf and ΔP obtained by the Δf·ΔP calculating unit when each of a plurality of standard samples having different values for one of the basis weight and the moisture amount is measured by the microwave resonator, and taking a predeterminded absolute dry basis weight of each of the standard samples as V 1 /β and a predetermined moisture amount of each of the standard samples as V 2 /γ by measuring the standard samples;

a constant recording unit configured to record the constants Kf, Kp, ∈′ 1 , ∈′ 2 , ∈″ 1 , and ∈″ 2 determined by the first constant determining unit ( 112 ), and the proportional constants β and γ;

a V 1 ·V 2 calculating unit configured to calculate V 1 and V 2 based on the expressions (3) and (4) according to claim 1 using the constants Kf, Kp, ∈′ 1 , ∈′ 2 , ∈″ 1 , and ∈″ 2 recorded in the constant recording unit, and Δf and ΔP obtained by the Δf·ΔP calculating unit when the samples are measured by the microwave resonator; and

an absolute dry basis weight and moisture amount calculating unit configured to calculate an absolute dry basis weight and a moisture amount based on the expressions (5) and (6) according to claim 1 from V 1 and V 2 obtained by the V 1 ·V 2 calculating unit when the samples are measured by the microwave resonator and the proportional constants β and γ recorded in the constant recording unit.

5. The apparatus of measuring basis weight and moisture amount according to claim 4 , further comprising:

an air dry basis weight and moisture percentage calculating unit configured to calculate an air dry basis weight and a moisture percentage based on the expressions according to claim 2 from the absolute dry basis weight and the moisture amount obtained by the absolute dry basis weight and moisture amount calculating unit.

6. The apparatus of measuring basis weight and moisture amount according to claim 4 , wherein

the microwave resonator is constituted by a plurality of rectangular dielectric resonators provided only on one side of a sample in the same plane such that long sides of the resonators are oriented to directions (θ) different from each other,

the Δf·ΔP calculating unit is configured to calculate Δfr and ΔPr according to claim 3 , and

the absolute dry basis weight and moisture amount calculating unit is configured to perform calculation using Δfr and ΔPr calculated by the Δf·ΔP calculating unit.

7. The method of measuring basis weight and moisture amount according to claim 2 , further comprising:

providing a plurality of rectangular dielectric resonators constituting the microwave resonator only on one side of a sample in the same plane such that long sides of the resonators are oriented to directions (θ) different from each other;

taking the directions (θ) as angles θ and the resonance frequency shift amounts Δf 1 to Δf r , of the resonators as r, plotting on a polar coordinate (r, θ) in which an angle is θ and a distance from the point of origin is r to draw an ellipse by an ellipse approximation process, obtaining a radius Δfr of a circle having an area identical to an area of the ellipse, and taking the obtained Δfr as Δf according to claim 1 ; and

obtaining peak level change amounts ΔP 1 to ΔP n of the resonators, and taking one of ΔPr(A), ΔPr(B), and ΔPr(C) as ΔP according to claim 1 , ΔPr(A), ΔPr(B), and ΔPr(C) being:

(A) ΔPr constituted by one of ΔP 1 to ΔP n ;

(B) ΔPr constituted by an average value of ΔP 1 to ΔP n ; and

(C) ΔPr constituted by a radius of a circle having an area identical to an area of an ellipse obtained by taking the directions (θ) as angles θ and ΔP 1 to ΔP n as r, plotting on the polar coordinate (r, θ) in which the angle is 0 and a distance from the point of origin is r, and drawing the ellipse by the ellipse approximation process.

8. The apparatus of measuring basis weight and moisture amount according to claim 5 , wherein

the microwave resonator is constituted by a plurality of rectangular dielectric resonators provided only on one side of a sample in the same plane such that long sides of the resonators are oriented to directions (θ) different from each other,

the Δf·ΔP calculating unit is configured to calculate Δfr and ΔPr according to claim 3 , and

the absolute dry basis weight and moisture amount calculating unit is configured to perform calculation using Δfr and ΔPr calculated by the Δf·ΔP calculating unit.

9. The apparatus of measuring basis weight and moisture amount according to claim 4 , wherein

the microwave resonator is constituted by a plurality of rectangular dielectric resonators provided only on one side of a sample in the same plane such that long sides of the resonators are oriented to directions (θ) different from each other,

the Δf·ΔP calculating unit is configured to calculate Δfr and ΔPr according to claim 7 , and

the absolute dry basis weight and moisture amount calculating unit is configured to perform calculation using Δfr and ΔPr calculated by the Δf·ΔP calculating unit.

10. The apparatus of measuring basis weight and moisture amount according to claim 5 , wherein

the microwave resonator is constituted by a plurality of rectangular dielectric resonators provided only on one side of a sample in the same plane such that long sides of the resonators are oriented to directions (θ) different from each other,

the Δf·ΔP calculating unit is configured to calculate Δfr and ΔPr according to claim 7 , and

the absolute dry basis weight and moisture amount calculating unit is configured to perform calculation using Δfr and ΔPr calculated by the Δf·ΔP calculating unit.