Note: Descriptions are shown in the official language in which they were submitted.
r.)4~
ROTARY KNIFE CONTROL
The present invention relates to the control system of a
rotating knife, actuating the knife to effic;ently cut a moving
sheet of material into predetermined lengths. More
particularly~ the invention relates to programming a knife
motor with an electric network responding to the movement of a
sheet of material being cut by the knife, and the knife
rotation.
Baekground Art
Rotating knives for cutting wallboard have been inadequately
controlled and resulted in "paper pulling". This undesirable
paper pulling has required up to 2 inches of each board to be
trimmed before sealing with end tape, and, of course, the
portion which was trimmed was scrap.
Attempts to overcome paper pulling were first made by
installing an eccentric gear arrangement in the motor-to-knife
gear train. This arrangement, when driven in a servo
configuration with velocity and position Feedback taken before
the eccentric gears, yielded a desired position/velocity
variation profil~ of the knife operation. The knife profile
was synchronized with the board movement so as to reach their
relative zero speeds at the 180 degree point of knife
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rotation. This is also the point of maximum kniEe penetration
when cutting the wallboard.
The above modification corrected the slight error caused
when the knife tip (which is synchronized with the moving
wallboard) first entered the surface of the wallboard. At t~is
point, the knife tip path was not peryendicular to the plane of
the wallboard but rather the knife tip path was at an acute
angle with the plane of the wallboard. Therefore, a
position/velocity error between the knife tip and the wallboard
(in an uncorrected system) was present during the cut, except
when the knife tip is at the 6 o'clock, or 180, posltion.
This difference between the knife and wallboard positions
caused the paper pulling and the position/velocity correction
provided by the eccentric gears eliminated the paper pulling
problem.
There is an inherent difficulty in the use of eccentric
gearing between ~he knife and its ~otor to achieve the
variation in the velocity/position profile of the knife
necessary to carry out efficient cuts of wallboard sheets which
have significant thickness. The gearing must be formed to
change the velocity profile of the knife quickly and
efflciently before the knife edge reaches the surface target on
the board. The problem of the inevitable mechanical wear of
the eccentric gearing should be eliminated and a direct control
of the knife motor be carried out from an electr~nic system
responsive to board travel under the knife and the knife
rotation.
Summary of the Xnvention
The present invention provides a feedback control syste~
that controls the position of a rotating knife to emulate a
rotating knife having eccentric gears. The rotary knife is
held in a park position until a sufficient length of wallboard
passes the location where the wallboard is cut such that when
the rotary knife starts to rotate, assuming the rotary knife
rotates synchronously with the wallboard line, the rotary knife
would cut the wallboard line at the appropriate location. The
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position and velocity of both the wallboard line and the
rotary knife are measured and compared. A rotary knife drive
signal comprised of the following terms is generated:
A synchronous drive term that controls main-taininy the
rotary knife in park position and contributes to the knife
drive signal when the knife is not in park position to drive
the knife synchronously with the wallboard line.
The velocity and position error terms correct for
velocity and position errors, for example, a change in
wallboard line velocity and the inability to start the knife
from rest to a speed synchronous with the wallboard line
instantly.
Finally, a correction term is added to the knife drive
signal just prior to, during and immediately following the
knife penetrating the wallboard to emulate the effects of
using eccentric gears to rotate the knife.
Thus, in accordance with the present invention there
is provided a system for cutting an elongated sheet of
material, including a continuous sheet of elongated material
~o with means to advance the sheet in a horizontal plane, a
first electrical pulse generator engaging the sheet to
detect the velocity/position of the advancing sheet and
establish a first train of pulses representative of the
velocity/position of the sheet, a rotating knife positioned
~5 at a point in the path traveled by the sheet to cut the sheet
in predetermined lengths, a motor connected to the knife for
rotating the knife in accordance with an electrical analog
signal, a second electrical pulse generator engaging the
knife to generate a second train of pulses representative of
the angular velocity/position of the knife, and means respon-
sive to the first and second pulse trains for generating a
knife motor signal to produce a knife blade rotation having
a rotation velocity that is substantially sinusoidal as a
function of a knife rotary position while the knife is engaged
with the sheet which cuts the sheet into predetermined lengths
without distortion of the sheet material at the cut.
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Brief Description of the Drawing.
Figure 1 is a aiagrammatic and schematic of a control
system for a wallboard knife in accordance with the in~enkion;
Figure 2 is a representation of the knife and board
position/velocity, including the portion of kn~e rotation
where the wallboard is cut.
Best Mode for Carrying Out the Invention
Overview
The present invention is embodied in a system which
controls a knife position to cleave a strip of material
passing beneath the knife into predetermined lengths. Although
not limited to the particular cutting duty disclosed, the knife
in Figure 1 is illustrated as actuated to cut green wallboard
into predetermined lengths prior to their removal from their
primary production line so they may be stacked on an assembly
line where they are cured by furnace heat. Further, the knife,
itself, is illustrated as comprised of two elongated cylinders,
each cylinder having a cutting edge mounted thereon. The
cylinders are geared together so they are simultaneously
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actuated by an electrical motor through a gear train.
Obviously, the knife may take various forms with the common
denominator of a cutting edge passed through the thickness of
the wallboard sheet to make the required cleavage. F~rther
details of this mechanical arrangement need not be disclosed
beyond the representations of Figure 1. The invention is
embodied in the complete system which extends from the sensing
structure of the wallboard travel and the knife rotation
through the electronic system responsive to these inputs to
produce an electric analog control signal for the knife motor
which actuates the knife in its required cutting.
Only two active measurements are made in Figure 1. A
first train of electrical pulses is generated to represent the
velocity/position of the wallboard line as i~ is moved by a
conveyor. A second train of pulses is generated to represent
the position/velocity of the knife edge in its rotat~ion. These
two trains of pulses, in electrical form, are fed into an
electric network to generate a single analog electrical output
signal to control the knife motor. The end result is actuation
of the cutting edge of the knife to give it the
position/velocity profile illustrated in Figure 2. Again, in
general, the profile determined for the knife will bring its
edge to each target on the wallboard surface, and thereafter,
with a predetermined speed, acceleration and deceleration, cut
through the body of the wallboard to avoid distortion of the
wallboard body. Following the cleavage action by the knife
edge, the knife edge will be accelerated sufficiently to avoid
interference with the wallboard body and thereby avoid
distortion of the wailboard body.
Specific Structure
The sheet of material, or wallboard line, 1 is viewed
~n elevation as it rests on the rollers of a conveyor. The
conveyor advances the line of wallboard 1 to the right, passing
the wallboard between cylinders 2 and 3 of knife 4. Cylinder 2
rotates counter-clockwise; cylinder 3 rotates clockwise. A
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single edge is shown on each knife cylinder, these edges being
brought together at the 6 o'clock, or 180, posi~ion o roller
2. When the edges are brought together, a cleavage is made
across the width of wallboard 1. When the travel of the
wallboard is coordinated with the actuation of the knife, the
wallboard is divided into lengths which are subsequently
removed at a station~ not shown, to the right.
A first train of pulses is generated by optical pulse
generator 5. Generator 5 may be mechanically connected to
roller 6 which is in direct contact with the surface of
wallboard 1 as the board travels to the right. Of course, the
generator 5 could be arran8ed in direct contact with the line
of wallboard, i~self. The output of generator 5 is placed on
conductor 7 as the first train of electrical pulsès,
representative of the position/veloclty of the board 1.
Optical generator 8 is mechanically connected to knife 4. A
second train of pulses is generated by pulse generator 8 and
placed on conductor 9 as the generator outputO
: The two trains of pulses on 7 and ~ are fed into the
electric network and registers in order to produce a single
analog electrical control signal placed on 10. This analog
electrical control signal is applied to regulate the speed of
motor 11 in order that motor 11 will actuate knife 4 through
gear train 12.
Computer System
First, the train of pulses representing the wallboard
line, on conductor 7, is connected to and conditioned by buffer
circuit 15. The conditioned output of buffer 15 is connected
to quadrature detector circuit 16. The output signal of
quadrature circuit 16 is connected to rate multiplier circuit
17. The output of the rate multiplier circuit 17 is connected,
in parallel, to up/down counter 18 and frequency-to-digital
converter 19.
Second, the train of pulses representing the knife
actuation, on conductor 9, is connected to buffer 20,
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quad~ature detector 21, rate multiplier 22, up/down counter 23
and frequency-to-digital converter 24. All of the outputs of
18, 19, 23 and 24 are connected to Difference Res~lver and
Processor (DRP) 25. It is within DRP 25 that the inputs o 18,
19, 23 and 2~ are processed into a digital value which i5
applied to a digital-to-analog converter (D/A) 26. The output
of D/A 26 i8 the analog signal, suitably amplified at 27, for
knife motor conductor 10.
Before proceeding with an analysis of the manipulation
of the input signals to the DRP 25, agreement must be had on
the physical movement of knife 4 in rela~ion to line 1. Upper
cylinder 2 of knife 4 is discussed in terms of the position of
its single edge as it is carried counter-clockwise from its
park position at 3 o'clock. Obviously, the edge i9 carried
from i~s 3 oiclock park position to and through its 12 o'clock
position9 9 o'clock position, 6 o'clock position and returns to
its park position~ Immediately ~ollowing completion of each
cut by knife 4, cylinder 2 is held at its park position from
which it is rotated in its precise synchronization with the
linear travel of wallboard 1.
For the purpose of understanding the function of D~P 25 and
its input from circuits 18, 19, 23 and 24 as well as the output
of DRP 25, the following symbols are defined:
Tc: Target cut - is both a hypothetical point on the
wallboard line and a distance from the preceding
cut equal to the length of wallboard to be cut
Ts: Target start - is both a hypothetical point on the
wallboard line and a distance from the preceding
cut, closer to the preceding cut than Tc by a
distance equal to that portion of the
circumference of the circular knife that the knife
must pass through from the park pos~tion to the
cu~ position hence Ts = Tc ~ KxC
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Lp: Line position - the length of the wallboard line
which has passed the knife cut position subsequent
to the last cut
Kp: Xnife positio~ - the linear distance tra~ersed by
the circumference of the knife as measured from
the park position of the knife
Lv: Line velocity - the velocity of the wallboard line
in units of length per unit time
Kv: Knife velocity - the Iinear distance traversed by
: lO the knife per unit time
~ ~ Ko Knife output - the knife drive signal (digital)
; ~ presented to the digital-to-analog (D/A) converter
B: Bias - bias derived from a lookup table, has the
va~ue of zero except where the
knife/synchronization profile varies to emulate
: the curve shown in Figure 2
C: Circumference - circumference of the circular
knife path
: : D: Synchronous drive term - drive signal that
~ : 20 maintains the knife in park position until Ts
: passes the cut point, then contributes to the
knife output signal
Gv: Velocity error gain - a gain to weigh the
significance given the difference in velocity
'5 between the wallboard line and the knife
K: Fraction of circumference - a fraction, less than
unlty, which represents the portion of the
: circumference through which the knife must rotate
in going from the park position to the cut
position
M: Multiplier - multipl1er for system gain (overall)
The above defined variables are interrelated in the
following equation:
Ko = (((Lp -Ts) -Kp) M) + Gv(Lv -Kv) + B + D
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The variable K is dependent upon the location of the park
position. Variable K is a fraction less than one t~lat
represents the portion of the circumference through which the
knife must rotate in going from the park position to the cut
position. The park position can be located anywhere around the
circumference of the knife cylinder where the knife blade does
not interfere with the passing o~ continous wallboard line 1
that also allows rotating knife to accelerate to be synchronous
with wallboard line 1 and have reduced the position error to
~ero before bias B is introduced. Hence K can range from
approximately 1/8 to approximately 7/8. Generally a larger
mass of knife 4, motor 11, and gear train 12 will require a
larger K value because a larger mass, initially at rest, must
be brought up to a speed synchronous with wallboard line 1. In
lS the best mode, the park position of cylinder 2 was the 3
o'clock position, and since cylinder 2 rotated counter-
clockwise and since the cut position is at the 6 o'clock
position of cylinder 2, variable K has the value of 3/4.
~t the same time that up/down counters 18 and 23 accumulate
the pulses of their trains to provide a line positional
reference in terms of digital values for the DRP 25, frequency-
to-digtal converters 19 and 24 respond to the pulse trains to
provide digital values representative of their respective
velocities. The position/velocity reference values of the
knife and wallboard line are presented continuously to DRP 25.
DRP 25 i5 a digital computer. It consists of an adder/logic
element, memory, registers, and input/output ports. DRP 25
receives the outputs from 18, 19, 23 and 24 which respectively
represent the knife position, Kp, knife velocity, Kv, line
position, Lp, and line velocit~, Lv, from their respective
data paths from the processing of the train of pulses on
conductors 7 and 9. These digitals values are stored
temporarily in DRP 25 memory then the equation defining knife
output presented above is used to calculate an updated knife
output. The knife output equation contains four terms: a
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position error term, a velocity error term, a correction term
and a synchronous drive term.
_e Position Error Term : (((Lp-TS)-Kp)M)
Upon making the preceding cut, up/down counters 18 and
23 are reset to zero, variable Lp is reset to zero and a
new hypothetical point Tc and hence a new hypothetical point
Ts are defined. Ts defines the point which when passing
between the axes of the knife cylinders 2 and 3 the knife must
start rotating in order to cut the wallboard line at
hypothetical point Tc when Tc is directly between the axes
of knife cylinders 2 and 3 assumlng that the knife tip will
move in synchronization with the wallboard line. Since DRP 25
repeatedly processes the input values and calculates an updated
knife drive sign~l Ko at a rapid rate, a continuous record of
the systems status exists. To determlne when hypothetical
point Ts passes between the axes of knife cylinders 2 and 3,
Lp is repeatedly compared to Ts~ TS remains fixed; Lp
increases from ~ero at the preceding cut to the value of Tc
at the subsequent cut. As long as Ts is greater than Lp,
DRP 25 holds knife 4 in the parked position because Ts has
not passed under the knife. When Lp equals T8, Ts is
directly between the axes of cylinders 2 and 3 of knife 4 and
the knife is started to rotate.
Once Ts passes between the axes of cylinders 2 and 3
of knife 4, the quantities (Lp - Ts~ and variable Kp are
compared repeatedly to determine whether the knife 4 is in the
proper position relative to the wallboard line to make a cut at
Tc. The quantity (Lp-TS) represents the length of
wallboard that has passed between the axes of knife 4 since
Ts was between the axes of knife 4. ~ represents the
linear distance traversed by the circumference of the knife as
measured from the park position of the knife. When there is a
difference between the quantities (Lp-TS) and Kp, a
position error exists and unless the position of the knife is
changed relative to the wallboard, the wallboard will not be
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cut at point Tc. The position error term contributes to the
knife output signal Ko to correct the position o the knie
relative to the wallboard. When the knife posltion Kp is
smaller than the length of wallboard that has passed between
the axes of knife 4 since Ts, the position error term
contributes positively to the knife output Ko causing ~he
knife to rotate more rapidly and hence to catch up to the
; wallboard line position. When the knife position is greater
than the length of wallboard that has passed between the axes
of knife 4 since Ts, the position error term subtracts from
the knife output Ko causing the knife to rotate more slowly
and hence to allow the wallboard line position to catch up to
the knife position. When there is no difference between
(Lp - Ts) and variable Kp, i.e. when ~Lp ~ Ts) - Kp
~ 0, knife 4 is in the proper position with respect to the
wallboard line to make a cut in the wallboard line at
hypothetical point Tc. The position error term reduces to
zero and the knife ouput, Ko~ consists of only the remaining
terms provided they are non zero. N is an adjustable bias
variable used to determine overall system gain.
The Velocity Error Term : GV(Lv- ~)
A velocity error exists when the wallboard line
velocity differs from the knife velocity. When the knife
velocity is less than the line velocity, the velocity error
term contributes positively to the knife output Ko to cause
the knife to increase in velocity ~o catch up to the line
velocity. When the knife velocity is greater than the line
velocity, the velocity error term subtracts from the knife
output Ko to allow the line velocity to catch up to the knife
velocity. Obviously since the knife was initially at rest in
the park position, the knife must travel faster than the line
velocity to catch up to and become synchronous with the
wallboard line. Thus, the velocity error gain Gv weighs the
significance given the velocity error term contribution to the
knife drive signal. When the line velocity is the same as the
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knife velocity, that i89 when the knife i5 synchronous with the
line velocity, the velocity error term reduces to zero and thus
does not contribute to the knife drive signal knie output
Ko consis~s of only the remaining terms provlded they are non-
zero.
The Correction Term : B
~ ariable B is a correction term which makes no
contribution to the knife drive signal except where the
knife/llne synchroni~ation profile varies to emulate the curve
shown in Figure 2. The variable B is implemented by way of a
table look-up into the DRP 25. The contribution of variable B
remains zero until the knife position Kp equals a value which
represents the point of rotation where the knife position is
required to follow the profile of Figure 2. The portlon of
the knife circumference over which variable B is non-zero
varies depending on the mass of the knife, motor and gears as
well as the power rating of the motor. A large motor driving a
small knife and gears can introduce a correction more readily
than a small motor driving a large knife and gears. With
reference to cylinder 2, the variable B makes no contribution
to the knife drlve signal Ko from the park position through
the twelve o'clock position through the nine olclock position
to appro~imately the eight-thirty o'clock position as shown in
Figure 2. At the eight-thirty o'clock posltion of rotation of
knife cylinder 2, variable B contributes to the knife drive
signal Ko by way o~ table look-up to emulate the effect of
driving kinfe 4 with an eccentric gear arrangement. Thus,
variable B assu~es the value of the first location of the look-
up table and, as a result, biases Ko by that amount. As Lp
continues to increase by a measured a unt, say several pulse
increments, the first value of B fro~ the table look-up is
replaced by the second value of B in the table look-up, which
biases the value of Ko by the latter value of B. This
sequence continues as the wallboard line continues to pass
knife 4, i.e. as Lp increases, through the values
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representing the cut (and beyond) with the table of B values
being sequentially accessed and used in the equation solving
for the knife drive signal Ko until the knife tip is clear of
the board, approximately at the three-thirty o'clock position
as shown in Figure 2, at which time the con~ribution of the
variable B to the knife drive signal again returns to zero.
It is obvious that the table of B values is arranged in a
sequence which causes Ko (after conversion to an analog
signal in D/A 26) to cause the rotation of knife 4 to vary
from exact synchronization with the linear movement of wall-
board line 1, as shown-in Figure 2.
As shown in Figure 2, the contribution of the correction
term, B, to the knife drive signal Ko is symmetrical about
the 5iX o'clock knife tip position since the wallboard line
velocity is constant. The maximum contribution of the
correction term B to the knife drive signal Ko as the knife
enters the wallboard occurs when the knife blade is approxi-
mately one-half the distance between the knife position when
the variable B first makes a contribution to the knife drive
signal and the six olclock position. In the preferred
embodiment shown in Figure 2, the maximum contribution of
correction term B upon the knife entering the wallboard
occurs at approximately the seven-fifteen o'clock position.
Similarly, as the knife withdraws from the wallboard, having
the point of maximum knife penetration at the six o'clock
position, the point of maxiumum contribution to the knife
drive signal KO::by the correction term B upon withdrawal of
the knife occurs at approximately the halfway point between
the six o'cloc~ position and the last knife position contri-
buting a.non-zero correction term B to the knife drive signal.
In the preerred embodiment the maximum contribution of
correction term B occurs at approximately the four-forty-five
o'clock position. As stated above, the portion of the knife
circumference over which the correction term B is non-zero
varies depending upon the mass of the knife, motor and gears
as well as the power rating of the motor. Furthermore, the
correction term B contributes to the knife drive signal a
:~ZO~:~9~
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magnitude to emulate the effect of driving knife 4 with an
eccentric gear arrangement. Th-us, the correction term B is
curvilinear, symmetrical about the point of maximum knife
penetration, having a maximum value in each symmetrical half
that is approximately halfway between the point o~ maxiumum
penetration and the most distant non-zero correction term on
that symmetrical half of the curve and is effective to emulate
the effect of an eccentric gear arrangement.
The Synchronous Drive Term: D
As long as Ts is greater than Lp, DRP 25 holds knife 4
in the park position because Ts has no~ passed the cut point.
This is achieved by maintaining synchronous drive term D zero.
Since the velocity error and position error do not contribute
to Ko until Ts is greater than Lp and since B is zero until
cylinder 2 is at about the 8:3~ o'clock position, drive signal
Kois zero which maintains the knife in the park position. In
addition to the function of maintaining knife 4 in the park
position until Ts passes the cut point, after Ts passes the
cut point, that portion of knife output Ko contributed by D
rotates knife 4 synchronous with wallboard line l. Since
knife 4, motor ll and gear train 12 are initially at rest and
cannot be brought up to synchronous speed instantly, ve~ocity
and position errors develop as knife 4 is started to rotate
from the park position. The velocity error term and position
error term discussed above correct velocity and position
errors. When the velocity and position errors go to zero, it
is the contribution of synchronous drive term D to knife output
Ko that causes knife 4 to continue to rotate. Synchronous
drive term D also controls returning knife 4 to the park
position after cutting off a length of wallboard line 1.
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From the foregoing, it will be seen that thls invention is
one well adapted to attain all of the ends and objects
hereinabove set forth, together with other advantages which are
obvious and inherent to the apparatus.
It will be understood that certain features and
subcombinations are of utility and may be employed without
reference to other features and subcombinations. This is
contemplated by and is within the scope of the invention.
As many possible embodiments may be made of the invention
without departing from the scope thereof, it is to be
understood that all matter herein se~ forth or shown in the
accompanying drawing is to be interpreted in an illustrative
and not in a limiting sense.
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