Patent Number: 061335789
Section: description

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT FIG. 1 illustrates the scanner unit 10 which has a pair of cross beams 11 perpendicular to the machine direction (MD) (also designated y) 12 or the moving web 13. In this particular case this is a paper sheet being manufactured by a paper making machine. Mounted to travel across the sheet in a cross direction (CD), also designated x, is a pair of measuring heads or transducers 14a and 14b (see also FIG. 2). The top transducer 14a includes a radiation source 16 and the bottom transducer 14b a radiation detector 17. As is well-known in the art, the amount of radiation passing through the moving web 13 is indicative of a characteristic of the web such as basis weight. Referring to FIGS. 3 and 4 radiation detector 17 includes a circular plate 21 mounted to the transducer 14b with a open aperture 22 which has a 4 segment detector array 1, 2, 3, and 4 in a planar format. Such array is also shown in FIG. 5 and how it is aligned with the machine direction (MD) (or y direction) and cross direction (CD) (or x). Each of the segments of the array is a silicon photo voltaic cell with a uniform radiation response having good dynamic range. Each of the elements or segments 1, 2, 3 and 4 is symmetrically arranged around a center detector axis 23. This axis is nominally coincident with the axis of the radiation source (or the center axis of the aperture over which it is superimposed) assuming there is no misalignment. Each detector segment 1, 2, 3, and 4 is nominally square in configuration with the diagonals of elements 1 and 2 being co-linear and passing through the center detector axis 23. The center detector 23 is also nominally coincident with the radiation axis. This arrangement of detectors will provide compensation for the lateral misalignment that is commonly caused by the drive belt arrangement that moves the source and detector across the sheet in a cross direction. As illustrated in FIG. 5 each square detector has, of course, a center indicated with the centers of detectors 3 and 4 being offset in the y direction a distance designated "a"; similarly the detectors 1 and 2 have their centers offset in the x direction a distance "a." As illustrated in FIG. 6, radiation received by the each of the detectors is in the form of the four currents I.sub.1, I.sub.2, I.sub.3 and I.sub.4. These are input into a processor 26 to provide a measurement such as basis weight (B.W.) which has been compensated for any misalignment of the source and detector. Now referring specifically (FIGS. 7 and 8) to the top transducer head 14a a circular plate 30 which faces the moving web 13 includes an aperture 31 which has a center axis 32. FIG. 8 is the opposite side of plate 30 showing mounted on it an encapsulated radiation source 33 (Promethium 147) which is mounted for rotation on an axis 34 to move along the locus 35 from a stowed position where the radiation from the nuclear source is shielded by the plate 30 to a first position where the radiation source and its radiation axis is actually coincident with the center axis 32. Similarly also illustrated in FIG. 8 is clear transparent radiation standardization flag 36, for example made of a thin sheet of clear plastic, which is mounted for rotation on an axis 37 along from a stowed position and along a locus of movement 38 so that flag may be rotated between the radiation source and the moving web for standardization purposes. Thus referring back to FIG. 7 both the offset axis 34 of rotation of the encapsulated radiation source and flag axis 37 are on the line 39 which is a diameter of aperture 31 and of course passes through the center axis 32 of the aperture. FIGS. 9 and 11 illustrate the rotating parts and the mounting for encapsulated radiation source 33 which rotates in the direction shown by the arrow on the axis 34 and the standardization flag 36 rotates in the direction shown around the axis 37. FIGS. 10 and 12 are side views of the source and standardization flag, respectively. Referring to FIG. 10, the radiation source includes a substantially large area of radiation emission, for example 15.6 mm, which radiates in a substantially parabolic pattern 41 having a radiation axis 40. Mounted to provide movement to the radiation source and the standardization flag are ball-type connectors 42 and 43, respectively. And referring to FIG. 13 these connectors are again shown connected to pistons 44 and 45 to rotate the radiation source 33 and standardization flag 36 from a stowed positions to an active positions. With the mounting of the radiation source 33 for movement in a plane parallel to that of the web or perpendicular to that of the radiation axis even though a fairly large area of radiation is present necessitating a relatively larger encapsulated radiation source 33, effective shielding (or shuttering) is provided for the radiation source in the stowed position illustrated in FIG. 8. Here the open-ended encapsulated radiation source faces the circular disk 30. At the same time, there is adequate spacing 51 (FIG. 10) between the circular disk 30 and the bottom of the transducer 33 to allow space for standardization flag 36 to slide there between. Although the detector ideally is shown as having 4 segments (this is because the error correction process is believed to be relatively simple in this case) three segments in the form of 120.degree. wedges could be used. All that is necessary is that a planar array of three or more segments be used which are symmetrically arranged around a center axis. Referring now to FIGS. 5 and 6 and the set of equations following below, as discussed above the four detectors arranged symmetrically around the center 23 provides compensation for lateral misalignment caused by the drive belt arrangement which moves the source and detector across the sheet. As illustrated and discussed above two of the detectors 1 and 2 have their centers on the x axis and detectors 3 and 4 have their centers on the y axis. These centers are all at the nominal distance "a" from the center detector axis 23. When the detector and the source are perfectly aligned individual detector signals I.sub.1 through I.sub.4 can be modeled by the equations (1) through (4) as a function of misalignment in the x-y plane. Referring specifically to these equations, x and y are the misalignment coordinates, a is the distance of the individual detectors from the center detector axis 23, S is a signal from an any one individual detector when the center such detector is coincident with the radiation axis of the source, and k is a factor that depends on the size and distance of the source, and to some degree on the basis weight to be measured. Thus, for example, referring to equation (1) if the radiation axis is centered on the center of the detector 1, then x=a and y=0 and I.sub.1 is equal to S. However, when it moves to the center axis 23, as shown illustrated in FIG. 10, the radiation source has an emission in the shape of a parabola and therefore the equations (1) through (4) are in the form of a parabolic function. Equation (5) is the sum of equations (1) through (4) and the sum is indicated as I.sub.T. It is apparent that if x and y are equal to 0 (that is there is no misalignment) that equation (5) provides accurate measure of received radiation which is the term 4S(1-ka.sup.2). In other words, the actual radiation received and the constants k and a. However, where there is an alignment, x and y must be taken into account. Since there is no direct way of measuring x and y, the error must be eliminated by a mathematical manipulation of the various currents I.sub.1 through I.sub.4. From an inspection of FIG. 5 it can be seen that detectors 1 and 2 and their equations represent errors in the cross direction (the most significant misalignment) and that detectors 3 and 4 and their equations (3) and (4) errors in the machine direction. And it is also obvious that the error term is, as illustrated in equation (5), as an x.sup.2 plus y.sup.2 type of factor. Thus the mathematical entity is created of equation (6) which matches the error term k(x.sup.2 +y.sup.2). And in addition this error correcting entity must also eliminate the S term. It has been found that this can be accomplished as indicated in equation (6) by taking the square of the cross directional signals that is (I.sub.1 -I.sub.2).sup.2, the square of the difference of the machine direction signals (I.sub.3 -I.sub.4).sup.2 and dividing it by the square of the I.sub.T. Referring to the result of that computation, because of the division by I.sub.T.sup.2 no S is in the result. Furthermore in the denominator of equation (6) all of the latter terms have less than 1% effect on the total value of the expression which may be therefore reduced to the expression of equation (7). Therefore, the error term in equation (5) containing the x.sup.2 +y.sup.2 can be rewritten as shown in equation (8). What has been done is that the k(x.sup.2 +y.sup.2) term of equation (7) which is the other half of equation (6), has been solved and has been substituted in equation (8). Then the right side of the equation (8) is substituted in equation (5) to produce a misalignment corrected signal I.sub.T. Noted that equation (9) is a re-arrangement of equation (5) where the term 4S(1-ka.sup.2) is solved for and thus the correction term is all in the denominator. The constant term (viz. ka.sup.2) of equation (9) as illustrated in the left-hand side of the equation (10) depends slightly on the amount of mass between the source and detector due to scattering of the radiation beam. Experiments have shown one possible way to model this term is as illustrated in the right side of equation (10) where p and q are constants and I.sub.T0 is the value of I with no web in the measuring gap. When it is taken into account that denominator of equation (9) is almost one the final correction algorithm is equation (11). This corrected signal is processed by the processor 26 illustrated in FIG. 6. The calculation of basis weight is done in the same manner as uncompensated signals have been used previously. That is a corrected form of Beer's laws. Thus to summarize the processing means for eliminating the misalignment error takes the sum of the signals from the four detectors and the square of difference of the pairs of machine direction and cross directional signals. And this directly eliminates the error term. Thus an improved nuclear gauge for measuring a characteristic of moving sheet material and alignment compensation has been provided. Equations EQU I.sub.1 =S{1-k[(x-a).sup.2 +y.sup.2 ]} (1) EQU I.sub.2 =S-{1-k[(x+a).sup.2 +y.sup.2 ]} (2) EQU I.sub.3 =S{1-k[x.sup.2 +(y-a).sup.2 ]} (3) EQU I.sub.4 =S{1-k[x.sup.2 +(y+a).sup.2 ]} (4) EQU I.sub.T =4S(1-ka.sup.2)[1-k(x.sup.2 +y.sup.2)/(1-ka.sup.2)](5) EQU [(I.sub.1 -I.sub.2).sup.2 +(I.sub.3 -I.sub.4).sup.2 ]/I.sub.T.sup.2 =k(x.sup.2 +y.sup.2)/{(1-ka.sup.2)[(1-ka.sup.2)/ka.sup.2 -2(x.sup.2 +y.sup.2)/a.sup.2 +(ka.sup.2 /(1-ka.sup.2))((x.sup.2 +y.sup.2)/a.sup.2).sup.2 ]} (6) ##EQU1## EQU [1-k(x.sup.2 +y.sup.2)/(1-ka.sup.2)]=1-[(1-ka.sup.2)/ka.sup.2 ][(I.sub.1 -I.sub.2).sup.2 +(I.sub.3 -I.sub.4).sup.2 ]/I.sub.T.sup.2 (8) EQU I'.sub.T =I.sub.T /{1-[(1-ka.sup.2)/ka.sup.2 ][(I.sub.1 -I.sub.3).sup.2 +(I.sub.3 -I.sub.4).sup.2 ]/I.sub.T.sup.2 }=4S(1-ka.sup.2)(9) EQU (1-ka.sup.2)/ka.sup.2 =p+q(I.sub.T /I.sub.T.sbsb.0) (10) EQU I'.sub.T =I.sub.T {1+[p+q(I.sub.T /I.sub.T.sbsb.0)][(I.sub.1 -I.sub.2).sup.2 +(I.sub.3 -I.sub.4).sup.2 ]/I.sub.T.sup.2 }(11)