Sensor, system and method for determining Z-directional properties of a sheet

A sensor, system and method for determining the various Z-directional properties of a sheet by measuring the caliper of a moving sheet of material at a plurality of pressures. The invention employs a caliper gauge and a set of pressure transducers that can measure and send signals indicative of the caliper as well as pressures exerted on the sheet. The signals are then digitized by an analog-to-digital converter and sent to a computer. The computer uses the compressibility data to construct a compression stress-strain diagram where the slope of the curve in the linear region of the curve is defined as the compression modulus of elasticity which can be empirically correlated to the tensile modulus of elasticity for various grades of paper. The tensile modulus of elasticity can be then used in various formulas to determine other Z-directional physical properties of the sheet, such as tensile strength, extensional stiffness and Scott bonding.

BACKGROUND OF THE INVENTION 
(1) Field of the Invention 
The present invention relates to the field of sensors for measuring the 
properties of a sheet, and more particularly to a sensor and system 
including a caliper gauge for measuring sheet compressibility subjected to 
a plurality of pressures. 
The invention uses the compressibility measurements to compute a 
compression modulus of elasticity which can be used to derive various 
Z-directional properties of the sheet, such as the tensile modulus of 
elasticity, the Z-directional tensile strength, extensional stiffness and 
Scott bonding. 
(2) Description of the Related Art 
Various types of caliper gauges are known in sensor technology and are used 
for measuring the thickness of rapidly moving sheet material. One type of 
caliper gauge is called a "contacting caliper gauge." Contacting caliper 
gauges typically have two opposing pads which are forced into contact with 
opposite sides of a sheet. The distance between the pads is measured and 
directly relates to the sheet thickness or "caliper." 
It has been recognized that the aerodynamic design of the caliper pads must 
be considered if the pads are to be maintained on or near the sheet 
surface with relatively little external force. A previous caliper gauge 
having aerodynamically designed caliper pads is disclosed in the commonly 
assigned U.S. Pat. No. 4,901,445 to Mathew G. Boissevain, et al. This 
patent is incorporated herein by reference. 
However, applicants are not aware of caliper gauges being used to 
simultaneously measure the compressibility of a sheet at a plurality of 
pressures or using such measurements to compute a compression modulus of 
elasticity which can be used to compute the tensile modulus of elasticity 
and to derive various Z-directional physical properties of the sheet, such 
as Z-directional tensile strength, extensional stiffness and Scott 
bonding. 
One of the most critical properties involved in the manufacture of paper is 
its strength. Virtually all paper manufactured is sold with a strength 
specification of some sort, and acceptance of a manufacturer's paper 
depends on being able to meet this requirement. Paper strength has three 
basic orientations: 1) the machine direction, 2) the cross-direction, and 
3) the Z-direction. The machine direction refers to the primary direction 
of sheet travel through the papermaking machinery. The cross-direction 
refers to the direction across the width of the sheet, in the plane of the 
sheet and perpendicular to the machine direction. The Z-direction extends 
perpendicular to the plane defined by the machine and cross-direction and 
is also referred to as the thickness direction. 
A previous system for continuous determination of sheet strength in the 
cross-direction and machine direction is disclosed in the commonly 
assigned U.S. Pat. No. 4,866,984 to Paul J. Houghton which is incorporated 
by reference. This system does not, however, determine sheet strength in 
the Z-direction, and therefore does not provide a complete picture of 
paper strength. In addition, due to the alignment of wood fibers, which 
are the main constituent of paper, the strength for each orientation is 
substantially different. 
The Z-directional strength of paper is usually given in terms of an 
empirical, destructive test. A common test is the Scott bond test where 
the Z-directional strength is determined by measuring the bonding between 
the different layers of fibers through the sheet. In the Scott bond test, 
a strip of paper or sample is delaminated by applying an in-plane shear 
force. One side of the sample is double-taped to a fixed support. The 
other side is taped to an "L" bracket. A pendulum is then released to hit 
the vertical side of the bracket and shear the sample. The energy lost in 
the delamination can be measured from the stopping position of the 
pendulum. 
In another such destructive test, the Z-directional tensile test, a sample 
is delaminated by pulling on both surfaces in the Z-direction with an 
equal force. Double-sided tape is used on each side to transfer the stress 
to the sample. The paper strength is determined by measuring the force 
exerted on the paper when it ruptures. 
Of course, neither test can be performed "on-line" as the paper is being 
manufactured in order to avoid the production of substandard material. 
Instead, the sample must be taken from the end of a reel after the reel 
has been completed. Since papermaking is a high speed continuous process, 
large amounts of paper can be easily produced before strength can be 
confirmed by a later measurement. The result of the time-consuming, 
off-line testing is that the strength measurement provided by perhaps 
several square feet must be accepted as representative of the thousands of 
square feet making up the reel. Consequently, it would be highly desirable 
to measure paper strength on-line while it is being manufactured. 
An article by Hall, On-Line ultrasonic Measurement of Paper Strength, 
Sensors (1990), based on research at the Institute of Paper Science and 
Technology, describes the use of commercial fluid filled wheels which are 
adapted for out-of-plane ultrasound velocity measurements and caliper 
measurements for moving paper webs. However, no on-line data is presented 
and there is no apparent disclosure of how to correlate these measurements 
with Z-directional paper strength. 
Nonetheless, Z-directional strength is important to monitor and control 
on-line, both to the efficiency of the paper mill and the efficiency of 
the processes in the converting operations. In a paper mill, there are 
several processes, such as those employing sizing presses and coaters, 
where highly viscous materials are applied to the paper. In the process of 
applying and drying these materials, the sheet or portions of the sheet 
can be pulled apart in the Z-direction, causing build-up on the 
applicators and dryers. In addition, there are other areas where either 
the surface of a calender roll or the surface of the sheet is dampened 
which causes the sheet to adhere to the roll. 
However, too high a value of Z-directional strength can also cause 
problems. For example, if the Z-directional strength is obtained from too 
much densification of the sheet by wet pressing, or other means, then 
certain properties such as opacity, folding stiffness and tear strength 
will be reduced. Also, it can be generally stated that the higher the 
strength, the higher the cost of manufacturing the paper. 
The company that buys the paper and converts it into a product has similar 
types of Z-directional strength requirements. Many of the converting 
operations, such as corrugators, printers, coaters and laminators, also 
apply substances of high viscosity that create a Z-directional force on 
the sheet of paper. Here again, if the Z-directional strength in the paper 
is too low, portions of the sheet will be pulled apart or delaminate in 
the Z-direction causing either sheet breaks or build-up on the applicator 
rolls or drying equipment. 
Thus, it would be desirable to be able to obtain the Z-directional 
strength, as well as other Z-directional properties such as tensile 
strength, extensional stiffness and Scott bonding on-line to achieve the 
strength required by both the papermaker and the converter, while at the 
same time optimizing cost and manufacturing efficiency. 
SUMMARY OF THE INVENTION 
An object of the present invention is to provide a sensor, system and 
method for determining various Z-directional properties of a sheet by 
measuring the compressibility of the sheet subjected to a plurality of 
pressures. For example, the compressibility data can be used to compute 
the Z-directional compression modulus of elasticity. Such data also can be 
used to derive other Z-directional physical properties of the sheet, such 
as tensile strength, extensional stiffness and Scott bonding. 
In one example of the invention, these and other objects are achieved by 
pressing a first and second major surface of a sheet on opposite sides at 
a plurality of pressures and measuring and sending signals indicative of 
the caliper of the sheet at each of these pressures to an 
analog-to-digital converter. The digitized signals are then sent to a 
computer which generates a stress-strain diagram. The ordinate of the 
diagram is the pressure or stress exerted upon the sheet. The abscissa of 
the diagram is the strain exerted on the sheet which is defined as the 
reduction in sheet thickness resulting from the difference in pressure 
divided by the thickness of the sheet at the lower pressure. From this 
data a Z-directional compression modulus of elasticity can be computed, 
which is defined as the slope of the stress-strain curve within the linear 
region of the curve. The Z-directional tensile modulus of elasticity can 
then be determined empirically. As stated earlier, such information can 
then be used to derive various other Z-directional properties of the 
sheet. 
In another example of the invention, a system is provided for measuring a 
physical property of a moving sheet with a first and second major surface. 
A first sheet-contacting pad is disposed adjacent to the first major 
surface, while a second sheet-contacting pad opposing the first pad is 
disposed adjacent to the second major surface. A third sheet-contacting 
pad is disposed downstream from the first pad adjacent to the first major 
surface, while a fourth sheet-contacting pad opposing the third pad is 
disposed adjacent to the second major surface. Means operatively coupled 
to the first pad measure and generate a signal indicative of the distance 
between the first and second pads. Another means operatively coupled to 
the third pad measure and generate a signal indicative of the distance 
between the third and fourth pads. Means are provided for pressing the 
first and second pads against the sheet at a first pressure and the third 
and fourth pads at a second higher pressure. A transducer measures and 
generates signals indicative of these pressures. An analog-to-digital 
converter then digitizes the signals which are sent to a computer. The 
computer receives the digitized signals and converts them into 
compressibility data to construct a compression stress-strain diagram. The 
slope of the curve in the linear region is defined as the compression 
modulus of elasticity, which is empirically related to tensile modulus of 
elasticity which can then be used to derive various other Z-directional 
sheet properties.

DESCRIPTION OF THE PREFERRED EMBODIMENTS 
The following description is the best contemplated mode of carrying out the 
invention. This description is made for the purpose of illustrating the 
general principles of the invention and should not be taken in a limiting 
sense. The scope of the invention is best determined by reference to the 
appended claims. In the accompanying drawings, like numerals designate 
like parts. 
FIG. 1 illustrates one embodiment of a sheet thickness or caliper gauge 10 
of the present invention carried by a scanner 12 which scans back and 
forth across a longitudinally moving paper sheet 14 being produced by a 
papermaking machine (not shown). The scanner 12 is of a conventional type, 
such as that described in the commonly assigned U.S. Pat. No. 3,621,259 to 
Mathew G. Boissevain. This patent is incorporated herein by reference. 
The scanner 12 consists generally of a framework having a pair of spaced, 
transverse upper and lower beams 16, 18 and a pair of opposing upper and 
lower carriages 20, 22 which move back and forth along the beams 16, 18 in 
the cross-direction, that is the direction indicated by the arrows 29. The 
upper carriage 20 carries an upper head 24 of the caliper gauge 10, while 
the lower carriage 22 carries a lower head 26. The two carriages 20, 22, 
and thus the two caliper heads 24, 26 are juxtaposed to provide a gap 
through which the sheet 14 freely moves in the machine direction, that is, 
the direction shown by arrow 28. 
Although FIG. 1 shows only the caliper gauge 10 used to measure paper 
thickness, the carriages 20, 22 would typically also carry additional 
devices for measuring other physical properties of the sheet 14. 
FIG. 2 illustrates, in partial cross-section, the upper and lower heads 24, 
26 of the caliper gauge 10. The sheet 14 moves rapidly between the upper 
and lower heads 24, 26 in the machine direction, that is, the direction 
shown by arrow 28. Thus, the sheet 14 moves from the front to the rear of 
the caliper gauge 10. 
The upper head 24 of the caliper gauge 10 includes a sturdy, relatively 
massive base 34 (also shown in FIG. 1). One end of a support arm 36 is 
hinged toward the front of base 34. The other end of the support arm 36 is 
connected to a bellows 38. The bellows 38 connects the other end of the 
support arm 36 to the base 34 near the back of the gauge 10. The bellows 
38 is disposed substantially perpendicular to the sheet 14. A first 
sheet-contacting pad 40 is attached to the end of the bellows 38. 
As shown in FIG. 4, the first pad 40 has a sheet contacting surface 42 
which is substantially parallel to the sheet 14. The pad 40 has a rounded 
portion 44 at the front to guide the paper 14 between the first pad 40 and 
a second pad 46. When pressurized, the bellows 38 forces the first pad 40 
into contact with the upper surface of the sheet 14. 
FIG. 4 also shows a second pad 46 opposing the first pad 40, having a sheet 
contact surface 54, being substantially parallel to the sheet 14 and 
having a rounded portion 62 at the front to guide the paper 14 between the 
first and second pad 40 and 46. 
As shown in FIG. 2, the upper head 24 of the caliper gauge 10 also includes 
a support arm 35 hinged at one end to the front of base 34. The other end 
of the support arm 35 is attached to a bellows 37. The bellows 37 connects 
the other end of the support arm 35 to the base 34 near the center of the 
caliper gauge 10. The bellows 37 is disposed substantially perpendicular 
to the sheet 14. A third sheet-contacting pad 39 is attached to the end of 
the bellows 37. 
As shown in FIG. 2, the third pad 39 is similar in construction to the 
first pad 40. The third pad 39 has a sheet-contacting surface 41 which is 
substantially parallel to the sheet 14 and a rounded portion at the front 
of the pad to guide the sheet 14 between the third pad 39 and a fourth pad 
45. When pressurized, the bellows 37 forces the third pad 39 into contact 
with the upper surface of the sheet 14. 
The lower head 26 is similar in construction to the upper head 24. Like the 
upper head 24, the lower head 26 includes a second sturdy, relatively 
massive base 48, a second sheet-contacting pad 46 connected to a bellows 
50 and support arm 51. A fourth sheet-contacting pad 45 is connected to a 
bellows 47 and a support arm 33. Each of these elements is connected in 
substantially the same manner as that described above for the upper head 
24, except, of course, the lower head 26 is mounted to the lower carriage 
22. 
FIG. 3 illustrates the relationship between the support arms 33, 51 which 
are hinged at their ends to the lower base 48. The other ends of the 
support arms are connected to both bellows 47, 50 as well as pads 45, 46, 
respectively. 
As shown in FIG. 2, the upper and the lower heads 24, 26 are positioned 
such that the upper and lower bellows 38, 50 as well as the upper and 
lower bellows 37, 47 are in a substantially linear, opposing relationship. 
Thus, during operation of the caliper gauge 10, the first and second pads 
40, 46 and the third and fourth pads 39, 45 are disposed in substantial 
opposing relationship on opposite sides of the sheet 14. The pads 45, 46 
should be sufficiently broad in lateral extent so that slight lateral 
misalignments between the upper and lower heads 24, 26 will not induce a 
falsely large caliper measurement. 
In general, any resiliently extendible means could be used in place of each 
bellows. However, a bellows is preferred because the electromagnetic 
circuit used to measure the thickness of the sheet material may be placed 
within the hollow interior of the bellows. One such circuit is fully 
described in the commonly assigned U.S. Pat. No. 3,828,248 to Gunnar 
Wennerberg which is incorporated herein by reference. 
Briefly, however, the caliper gauge 10 is equipped with an electromagnetic 
proximity sensing device for accurately measuring the distance between the 
opposing pads. For example, as shown in FIGS. 4-5, with respect to the 
opposing pads 40, 46, the device includes an electromagnetic core 52 
mounted to the first pad 40 and disposed within the upper bellows 38. The 
electromagnetic core 52 is disposed so that its two pole faces 53, 55 are 
mounted to that portion of the first pad 40 which remains in closest 
proximity with the sheet 14. When the first pad 40 has a vacuum notch 68, 
the electromagnetic core 52 is disposed so that its two pole faces 53, 55 
are located in the rear half of the first pad 40. The two pole faces 53, 
55 are preferably mounted transverse to the direction of sheet travel and 
straddle the vacuum notch 68. Favorable results have been obtained when 
the two pole faces 53, 55 are located near the rear edge of the first pad 
40, where a pad 40, having a vacuum notch 68, remains closest to the sheet 
14. 
The first pad 40 is preferably formed of a highly abrasion resistant, 
non-magnetic material, such as sapphire. The second pad 46 is formed of a 
magnetically susceptible abrasion resistant material, such as ferrite, 
preferably coated with sapphire or diamond. The pads 40, 46 are preferably 
abrasion resistant to avoid excessive wear caused by the friction between 
the moving sheet 14 and the sheet contacting surfaces 42, 54 of the pads 
40, 46. Pads 39, 45 are made of the same material and have the same 
construction (FIG. 2). 
As shown in FIG. 2, the coil 56 surrounding the electromagnetic core 52 may 
be electrically connected to an oscillator circuit 58 and used as the 
inductance of that circuit. Thus, movement of the magnetically susceptible 
ferrite pad 46 toward and away from the coil 56 due to sheet thickness 
variations modifies the inductance of the coil 56 and hence the resonant 
frequency of the oscillator 58. A frequency counter 60 is operatively 
coupled to the oscillator 58 to determine its resonant frequency. The 
counter 60 then sends a signal to a computer 30 indicative of this 
resonant frequency. The computer 30 computes the distance between the pad 
40 and the pad 46, and hence, sheet thickness based upon this resonant 
frequency. 
The first pad 40 should also be abrasion resistant because, as shown in 
FIG. 5, the electromagnetic core 52 is preferably recessed within the pad 
40 so that the pole faces 53, 55 are in close proximity to the sheet 
contacting surface 42 of the pad 40. The proximity sensing circuits are 
calibrated with the unworn pad. Therefore, if the sheet contacting surface 
42 of the pad 40 is worn down, the pole faces 53, 55 of the 
electromagnetic core 52 will move closer to the sheet 14 and produce an 
erroneous thickness measurement or tear the sheet. 
The support arm 36 shown in FIG. 5 is representative of the other support 
arms 33, 35, 51 and may be made of a lightweight material such as Mylar. 
The support arm 36 should preferably have a vent hole 76 to reduce the 
lifting effect of the air which moves along with the rapidly moving sheet 
14. 
The caliper gauge 10 is also equipped with a similar electromagnetic 
proximity sensing device for accurately measuring the distance between 
opposing pads 39, 45. As shown in FIG. 2, like the electromagnetic 
proximity sensing device for opposing pads 40, 46, the sensing device 
includes an electromagnetic core 49, a coil 57, an oscillator circuit 59 
and a frequency counter 61. Each of these elements operates and is 
connected in the same manner as that described above for the sensing 
device for measuring the distance between opposing pads 40, 46. 
As the caliper gauge 10 scans back and forth across the sheet 14, signals 
from the gauge 10 are sent via signal processing circuitry from the 
frequency counters 60, 61 to the computer 30. Because the opposing pads 
39, 45 are directly upstream from pads 40, 46, both sets of pads detect 
the thickness of the sheet 14 at the same cross-directional location. The 
computer 30 manipulates the signals from the frequency counters 60, 61 so 
that caliper of the sheet 14 is measured at the same machine directional 
location. For example, the signal offset may be computed from the distance 
between opposing pads 40, 46 and opposing pads 39, 45 and the machine 
directional velocity of the sheet 14 or obtained by cross-correlation 
where the signals are shifted in relation to each other until their 
correlation is maximal. 
In operation, the sheet 14 is threaded between the opposing caliper heads 
24, 26 and the computer 30 instructs the scanning station 12 to begin 
scanning the caliper gauge 10 back and forth along the cross-direction of 
the sheet 14. The bellows 37, 47 are pressurized to place opposing pads 
39, 45 in opposing contact with the sheet 14. A pressure P.sub.L of about 
5 inches of water (gauge) in 1-inch diameter bellows will provide 
sufficient pressure to maintain the pads 39, 45 of FIG. 2 in contact or in 
close proximity (less than about two microns) to the sheet 14 over a 
relatively wide range of sheet speeds. Bellows 38, 50 are also pressurized 
to place pads 40, 46 in opposing contact with the sheet 14. A higher 
pressure P.sub.H of about 10-20 inches of water (gauge) in 1-inch diameter 
bellows will provide sufficient pressure to maintain the pads 40, 46 of 
FIG. 2 in contact with the sheet 14 over a relatively wide range of sheet 
speeds. 
Simultaneously, when the caliper is measured, a pressure transducer 100 
sends signals indicative of the pressure P.sub.L in bellows 37, 47 to an 
analog-to-digital converter (not shown). The digitized signals are then 
sent to the computer 30. Similarly, a second pressure transducer 102, 
sends signals indicative of the pressure P.sub.H in bellows 38, 50 to the 
analog-to-digital converter (not shown), then the digitized signals are 
sent to a computer 30. Through cross-correlation of the signals described 
earlier, the sheet caliper measurements C.sub.H and C.sub.L, at pressures 
P.sub.H and P.sub.L, respectively, are measured at the same location of 
sheet 14. 
The resulting data can be stored in computer 30 to generate a compression 
stress-strain diagram (FIG. 6). The ordinate of the diagram is the stress 
exerted by the pads upon the sheet, which is proportional to the bellow's 
pressure. The higher pressure of bellows 38, 50 is still set low enough so 
that the compressibility data is within the linear region of the 
stress-strain curve. The abscissa of the diagram is the strain exerted on 
the sheet. The strain is defined as the caliper reduction resulting from 
the increase in pressure of bellows 38, 50 to that of bellows 37, 47 
divided by the caliper of the paper at the lower pressure in bellows 37, 
47. From this data, a Z-directional compression modulus of elasticity 
E.sub.ZC may defined by the following formula: 
##EQU1## 
Where E.sub.ZC =the Z-directional compression modulus of elasticity. 
A Z-directional tensile modulus of elasticity E.sub.ZT may be computed from 
the Z-directional compression modulus of elasticity E.sub.ZC for various 
grades of paper as follows: 
EQU E.sub.ZT =k.multidot.E.sub.ZC 
Where k is an experimental constant 
The tensile modulus of elasticity E.sub.ZT can be then used to empirically 
derive various Z-directional properties of the paper, such as the 
Z-directional tensile strength as follows: 
EQU S.sub.ZT =A.multidot.E.sub.ZT.sup.B +C.multidot.W.sup.D 
.multidot.C.sub.L.sup.E +F.multidot.V.sup.G 
Where 
S.sub.ZT is Z-directional tensile strength; 
E.sub.ZT is the Z-directional tensile modulus of elasticity; 
W is the basis weight of sheet 14; 
C.sub.L is the caliper of the sheet 14 subjected to the lower pressure 
P.sub.L of bellows 37, 47; 
V is velocity of the sheet 14 passing through the caliper gauge 10; and 
A, B, C, D, E, F and G are experimentally determined constants. 
Scott bonding can be computed by a similar formula with a different set of 
constants as follows: 
EQU S.sub.B =H.multidot.E.sub.ZT.sup.I +J.multidot.W.sup.K 
.multidot.C.sub.L.sup.L +M.multidot.V.sup.H 
Where 
S.sub.B is the Scott bonding value; and 
H, I, J, K, L, M and N are experimentally determined constants. 
Extensional stiffness can be computed by a similar formula with another set 
of constants as follows: 
EQU X.sub.Z =O.multidot.E.sub.ZT.sup.P +Q.multidot.W.sup.R 
.multidot.C.sub.L.sup.T +U.multidot.V.sup.Y 
Where 
X.sub.Z is the extensional stiffness of the sheet 14; and 
O, P, Q, R, T, U and Y are experimentally determined constants. 
The above equations are applicable to a wide variety of papers being 
manufactured. The constants A, B, C, D, E, F, G, H, I, J, K, L, M, N, 0, 
P, Q, R, T, U and Y vary depending on the particular paper being made, and 
on which test is being simulated. The constants for a given papermaking 
system can be determined by measuring the various parameters (e.g., 
velocity of the sheet 14 and basis weight, etc.) of the system during 
production and analyzing the above formulas with a linear regression 
program. 
A preferred embodiment of the present invention has been described. 
Nevertheless, it will be understood that various modifications may be made 
without departing from the spirit and scope of the invention, as 
determined by the appended claims.