No-Feed-Roll Corrugated Board or Paperboard Sheet Feeder Retrofit Apparatus and Method

Abstract

A method is provided for supplying a corrugated board article or a paperboard sheet article from a feeder apparatus for receipt by an article processing host machine. The method includes feeding the article to a feeder apparatus including a sheet supporting feed table surface having a feed end and a delivery end, feed elements, and a control surface selectively movable between a covering state and an exposing state. In the exposing state the feed elements are exposed to contact and drive the article along the sheet supporting feed table. The control surface is selectively movable to an angled state to selectively angle the control surface to consecutively conceal the respective feed elements as the article moves over the feed elements.

Claims

1. A method for supplying a corrugated board article or a paperboard sheet article from a feeder apparatus for receipt by an article processing host machine, the method comprising: feeding the corrugated board article or the paperboard sheet article to a feed end of the feeder apparatus, the feeder apparatus comprising: a feed table supporting surface having the feed end and a delivery end; feed elements; and a control surface selectively movable into a first state in which the feed elements are exposed to contact and drive the article along the feed table supporting surface, the control surface further being selectively movable to an angled state; and selectively moving the control surface into the angled state to selectively angle the control surface to consecutively conceal the respective feed elements from contact with the corrugated board article or the paperboard sheet article as the corrugated board article or the paperboard sheet article moves over the feed elements.

2. The method of claim 1, wherein the feed elements comprise a first plurality of first feed elements and a second plurality of second feed elements, the first feed elements being positioned in a first velocity zone and arranged in a first plurality of rows which extend transversely to a direction of travel of the corrugated board article or the paperboard sheet article through the feeder apparatus, the second feed elements being positioned in a second velocity zone positioned adjacent the first velocity zone and arranged in a second plurality of rows which extend transversely to the direction of travel of the corrugated board article or the paperboard sheet article through the feeder apparatus.

3. The method of claim 2, wherein the feeder apparatus further comprises a first vacuum powered suction section and a second vacuum powered section, the first vacuum powered suction section being located below the feed table supporting surface and corresponding to the first velocity zone for holding the corrugated board article or the paperboard sheet article against the first plurality of first feed elements while being fed thereby, the second vacuum powered suction section being located below the feed table supporting surface and corresponding to the second velocity zone for holding the corrugated board article or the paperboard sheet article against the second plurality of second feed elements while being fed thereby.

4. The method of claim 3, wherein the feeder apparatus further comprises airflow restrictors for the first and second vacuum powered suction sections, the airflow restrictors being movable to alter respective vacuum areas of the first and second vacuum powered suction sections based on article size to hold the corrugated board article or the paperboard sheet article against the feed elements.

5. The method of claim 2, wherein the feeder apparatus further comprises a first dedicated controlled motor or servo system to drive the first plurality of feed elements in a controllable first motion profile.

6. The method of claim 5, wherein the feeder apparatus further comprises a second dedicated controlled motor or servo system to drive the second plurality of feed elements in a controllable second motion profile.

7. The method of claim 6, wherein the feeder apparatus further comprises a controller configured to receive an article velocity signal from a host machine and to generate (i) a first control signal for the first dedicated controlled motor or servo system and (ii) a second control signal for the second dedicated controlled motor or servo system in response to the velocity signal to feed the corrugated board article or the paperboard sheet article through the feeder apparatus at selected velocity profiles in the first velocity zone and the second velocity zone.

8. A method for supplying a corrugated board article or a paperboard sheet article from a feeder apparatus to an article processing host machine operating at a velocity, the method comprising: feeding the corrugated board article or the paperboard sheet article to a feed end of the feeder apparatus, the feeder apparatus comprising: a feed table supporting surface having the feed end and a delivery end; and feed elements comprising a first plurality of first feed elements and a second plurality of second feed elements, the first feed elements being positioned in a first velocity zone, the second feed elements being positioned in a second velocity zone positioned adjacent to and downstream relative to the first velocity zone; supplying first drive signals to the first plurality of first feed elements to control velocity of the corrugated board article or the paperboard sheet article in the first velocity zone in a first motion profile having an initial first article velocity lower than the velocity of the article processing host machine and a subsequent second article velocity that is greater than the velocity of the article processing host machine as the corrugated board article or the paperboard sheet article passes over the first feed elements in the first velocity zone; and supplying second drive signals to the second plurality of second feed elements to control the velocity of the article in the second velocity zone in a second motion profile having an adjustable constant velocity equal to the velocity of the article processing host machine to deliver the corrugated board article or the paperboard sheet article to the host machine at the velocity of the article processing host machine.

9. The method of claim 8, wherein the feeder apparatus further comprises first and second control surfaces in the first and second velocity zones, respectively, the first and second control surfaces being movable to expose or conceal the said first feed elements and the second feed elements, respectively.

10. The method of claim 9, further comprising generating first and second control surface signals to move the first and second control surfaces, respectively, through a sequence of positions to selectively provide contact between the first and second feed elements and the corrugated board article or the paperboard sheet article to drive the corrugated board article or the paperboard sheet article through the first and second motion profiles.

11. The method of claim 8, wherein the first feed elements are arranged in a first plurality of rows which extend transversely to a direction of travel of the corrugated board article or the paperboard sheet article through the feeder apparatus, and wherein the second feed elements are arranged in a second plurality of rows which extend transversely to the direction of travel of the corrugated board article or the paperboard sheet article through the feeder apparatus.

12. The method of claim 8, wherein the feeder apparatus further comprises a first controllable vacuum associated with the first velocity zone and a second controllable vacuum associated with the second velocity zone to engage the corrugated board article or the paperboard sheet article against the first feed elements and the second feed elements, respectively.

13. The method of claim 8, wherein the first feed elements comprise first drive wheels and the second feed elements comprise second drive wheels.

14. A method for supplying a corrugated board article or a paperboard sheet article from a feeder apparatus to an article processing host machine operating at a velocity, the method comprising: feeding the corrugated board article or the paperboard sheet article to a feed end of the feeder apparatus, the feeder apparatus comprising: a feed table supporting surface having the feed end and a delivery end; and feed elements comprising a first plurality of first feed elements and a second plurality of second feed elements, the first feed elements being positioned in a first velocity zone, the second feed elements being positioned in a second velocity zone positioned adjacent to and downstream of the first velocity zone; operating the feed elements to accelerate the corrugated board article or the paperboard sheet article to a velocity above the velocity of the article processing host machine and then decelerate the corrugated board article or the paperboard sheet article to the velocity of the article processing host machine.

15. The method of claim 14, wherein the feeder apparatus further comprises a controller configured to receive velocity signals from the article processing host machine to generate a first variable velocity control signal for the first velocity zone and a second velocity control signal for the second velocity zone based on the velocity signals from the article processing host machine.

16. The method of claim 14, wherein the feed elements comprise first drive wheels mounted in the first velocity zone of the feed table supporting surface and second drive wheels mounted in the second velocity zone of the feed table supporting surface, and wherein the method further comprises operating the first drive wheels to drive the corrugated board article or the paperboard sheet article in a first motion profile through a first vacuum zone of the feeder apparatus, and operating the second drive wheels to drive the corrugated board article or the paperboard sheet article received from the first velocity zone in a second motion profile through a second vacuum zone of the feeder element to the delivery end.

17. The method of claim 16, wherein the feeder apparatus further comprises a dedicated primary servo motor in the first velocity zone configured to perform the first motion profile based on the first variable velocity control signal.

18. The method of claim 16, wherein the feeder apparatus further comprises a variable vacuum generator and variable control surfaces in each of the first and second velocity zones, and wherein the method further comprises selectively moving the variable control surfaces in the first and second velocity zones above the first drive wheels and the second drive wheels to prevent the corrugated board article or the paperboard sheet article from contacting the first and second drive wheels, respectively.

19. The method of claim 18, wherein the feeder apparatus further comprises first and second drive mechanisms, and wherein the method further comprises operating the first and second drive mechanisms to independently lower and raise the control surfaces to consecutively engage corrugated board articles or the paperboard sheet articles with selected drive wheels as the corrugated board articles or the paperboard sheet articles are fed through the feeder apparatus and into the article processing host machine.

20. The method of claim 19, further comprising selectively moving the control surfaces into an angled state to selectively angle the control surfaces to consecutively conceal the respective feed elements as the corrugated board articles or the paperboard sheet articles move over the feed elements.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0019] The above and still further objects, features and advantages of the present invention will become apparent upon consideration of the following detailed description of a specific embodiment thereof, particularly when taken in conjunction with the accompanying drawings, wherein like reference numerals in the various figures are utilized to designate like components, wherein:

[0020] FIG. 1A illustrates a diagrammatic side view of the feed end portion of a typical finishing machine for feeding corrugated sheets from a hopper to following machine sections, in accordance with the Prior Art.

[0021] FIG. 1B illustrates a diagrammatic side view of a typical sheet feeder for feeding sheets into the finishing machine of FIG. 1A, in accordance with the Prior Art.

[0022] FIG. 1C illustrates a diagrammatic side view of a second type of sheet feeder for feeding sheets into the finishing machine of FIG. 1A, in accordance with the Prior Art.

[0023] FIG. 2 is a perspective view in elevation illustrating the No-Feed-Roll sheet feeder apparatus configured and programmed for use with the typical finishing machine for feeding corrugated sheets from a hopper to following machine sections of FIG. 1, once the prior art sheet feeder 12 is removed for replacement as part of the upgrading or retrofitting method of the present invention.

[0024] FIG. 3 is a top-side plan view illustrating the No-Feed-Roll sheet feeder apparatus of FIG. 2 and the retrofitting method of the present invention.

[0025] FIG. 4A is a side view in elevation illustrating the No-Feed-Roll sheet feeder apparatus and retrofitting method of FIGS. 2 and 3, in accordance with the present invention.

[0026] FIG. 4B is a multi-part diagram including a sheet velocity data plot diagram illustrating the sheet's velocity as a function of position (A-F) for the corrugated boards or sheets fed by the No-Feed-Roll sheet feeder apparatus of FIGS. 2-4A, and below that diagram are eight diagrams illustrating the orientations of the sheet and the control surfaces as sheets are fed from initial position A through position E to position F, in sequence, in accordance with the retrofitting and sheet feeding method of the present invention.

[0027] FIG. 5A is a sheet velocity data plot diagram illustrating the sheet's velocity as a function of time for the corrugated boards or sheets fed by the No-Feed-Roll sheet feeder apparatus of FIGS. 2-4 in accordance with the retrofitting and sheet feeding method of the present invention.

[0028] FIG. 5B is a diagram illustrating six (6) velocity profiles (machine velocity as a function of machine displacement 13 and position (A-E)) illustrating the machine speed profiles for the No-Feed-Roll sheet feeder apparatus of FIGS. 2-4B and retrofitting method of the present invention.

[0029] FIG. 5C is a diagram illustrating six (6) board displacement profiles (board or sheet displacement h as a function of position) illustrating the board displacement profiles for the No-Feed-Roll sheet feeder apparatus of FIGS. 2-4B and retrofitting method of the present invention.

[0030] FIG. 5D is a diagram illustrating board displacement profiles (velocity as a function of position, illustrating three areas, namely, board displacement from A to C, board displacement due to the second half of the h6 curve and the area under the velocity curve due to shifting of the second part of h6 up to match h2) for the No-Feed-Roll sheet feeder apparatus of FIGS. 2-4B and retrofitting method of the present invention.

[0031] FIG. 5E is a second velocity zone motion profile data plot diagram illustrating the feed wheel velocity (in RPM) as a function of machine displacement (in meters) for the No-Feed-Roll sheet feeder apparatus of FIGS. 2-4B in accordance with the retrofitting and sheet feeding method of the present invention.

[0032] FIG. 6 is a plan view in elevation illustrating a vacuum section's air flow for the No-Feed-Roll sheet feeder apparatus of FIGS. 2-4B and retrofitting method of the present invention.

[0033] FIG. 7 is a block diagram illustrating the signal flow between a controller or computer and data input, sensor motor and pump components of the No-Feed-Roll sheet feeder apparatus of FIGS. 2-6 illustrating the retrofitting and sheet feeding controls and method of the present invention.

DESCRIPTION OF THE PREFERRED EMBODIMENT

[0034] Turning now to a more detailed description of the present invention, as illustrated in FIGS. 2-7, the sheet or board feeding system 200 and method of the present invention does not require a mechanical drive input from or mechanical coupling with the host machine (e.g., a finishing machine for folding or making boxes from corrugated boards or sheets 10 or M) and instead is an entirely self-contained unit 200 which is driven with one or more motors, using sensed velocity or speed data from the host machine (10 or M) only as a speed reference. Critical functions performed by a feed table of sheet feeding system 200 are parameterized such that they can be scaled to different machinery with a change in a program stored in and executed by controller 300 in sheet feeding system 200. The host machine (e.g., 10 or M) is preferably modified or configured to be attached to the system's feed table 210. In the event that one or more nip or feed rolls (e.g., 3U, 3L) is a necessary component of the to-be-upgraded host machine's pre-existing or legacy drive train, feeding system 200 can be configured to work with and maintain that pre-existing or legacy drive train.

[0035] The sheet feeding apparatus of the present invention 200 (as illustrated in FIGS. 2-7) consists of a plurality (e.g., 2 or more) divided vacuum sections with chambers or boxes (e.g., 220, 230) with a plurality of wheeled shafts (e.g., 222, 224, 226, 232 and 234) driving grippy elastomeric covered feed wheels (e.g., 222W, 224W, 226W, 232W and 234W) which impart driving force to accelerate the lowermost sheet. Each of the sections has a movable control surface (e.g., 240, 250) with apertures configured to allow the feed wheels to project upwardly therethrough (e.g., as shown in FIG. 4A) and those movable control surfaces (e.g., 240, 250) can be raised or lowered to prevent or allow contact of a board or sheet with the feed wheels (e.g., 222W, 224W, 226W, 232W and 234W). These wheeled shafts are divided into one or more variable velocity zones leading to a constant velocity zone residing above (not shown) or below (see FIGS. 2-4A) the board or sheet's path of travel. Each velocity zone is independently driven with a dedicated and separately controlled electric motor. An initial variable velocity zone will always perform the entire motion profile to accelerate the sheet into the machine. Optionally, a second variable velocity zone, following the first, comes in contact with the sheet some distance after the sheet begins accelerating (due to driving force from the prior or first variable velocity zone). This second variable velocity zone only needs to perform a fraction of that velocity profile due to the nonzero initial velocity of the sheet as it enters the second variable velocity zone. During inactive periods, this second variable velocity zone decelerates to the nonzero initial sheet velocity, rather than zero, in anticipation of the next cycle. The final zone is driven at constant velocity, matching the machine velocity. The final zone is located such that the previous zone(s) will have already accelerated the sheet to constant velocity some distance before making contact with the wheels. In FIG. 4A, velocity zone 220 is illustrated with three shafts (222, 224, 226), velocity zone 230 is illustrated with two shafts (232, 234) and the final velocity zone is within host machine 10. FIG. 6 illustrates air flows in the vacuum box(es) of sheet feeder 200 and FIG. 7 is a signal flow diagram illustrating how the vacuum pumps are controlled for each vacuum box and how speed and other control data are used in sheet feeder 200. A controller (or feeder computer or CPU) 300 receives signal and data inputs from the host machine 10 and sensors and components in sheet feeder 200 as well as control signal outputs (e.g., to servo motors and to vacuum pumps.)

[0036] The primary servo motor 220M in the initial variable velocity zone 220 will perform a specific sheet or board motion profile (e.g., as illustrated and defined in FIGS. 5A-5F) designed to reduce the peak torque requirements of the machine. The motion profile generated using the apparatus of the present invention is a uniquely advantageous characteristic of the present invention. Peak torque specification is one of the leading limitations of commercially available servo motors. At the same time, traditional feeders need a significant amount of power to accelerate a sheet to machine velocity over a relatively short distance. To reduce peak torque, the velocity profile for sheet or board feeding system 200 is designed to accelerate the sheet at a lower rate than what would normally be required over a specific distance. The motor makes up for this by accelerating the sheet above machine speed momentarily for it to catch up. The motor then decelerates the board to machine velocity. A servo motor performing such a motion profile will require a higher maximum velocity, but a lower peak torque rating. By returning the board to machine velocity at the proper time, it is ensured that the longest sheet that can be fed (maximum sheet) is not sacrificed. So the first plurality of feed elements or drive wheels (222W, 224W, 226W) in initial variable velocity zone 220 drive the board (e.g., 2) in a first motion profile, and are driven by a first dedicated computer controlled motor or servo system 220M (see FIG. 4A), while the second plurality drive wheels (232W, 234W) in second velocity zone 230 drive the board in a second motion profile, and are driven by a second dedicated computer controlled motor or servo system 230M.

[0037] The position, velocity and acceleration of each board (e.g., 2) are controlled with a dedicated computer controlled motor in each velocity zone (e.g., 220), as illustrated in FIG. 4B, a multi-part diagram including a sheet velocity data plot diagram illustrating the sheet's velocity as a function of position (A-F) for the corrugated boards or sheets (e.g., 2) fed by the No-Feed-Roll sheet feeder apparatus 200, and below that diagram are eight diagrams illustrating the orientations of the sheet (e.g., 2) and the control surfaces (e.g., 240, 250) as sheets are fed from initial position A through position E to position F, in sequence, in accordance with the retrofitting and sheet feeding method of the present invention. FIG. 5A is a sheet velocity data plot diagram illustrating the sheet's velocity as a function of time for the corrugated boards or sheets fed by the No-Feed-Roll sheet feeder apparatus of FIGS. 2-4B in accordance with the retrofitting and sheet feeding method of the present invention. FIG. 5B is a diagram illustrating six (6) velocity profiles (machine velocity as a function of machine displacement 13 and position (A-E)) illustrating the machine speed profiles for the No-Feed-Roll sheet feeder apparatus of FIGS. 2-4B and retrofitting method of the present invention, as will be described in more detail below.

[0038] While vacuum pressure is needed throughout the feed table 210, it must be divided into at least two sections (e.g., 220, 230). One section (230) handles the environment of the initial vacuum box, where the stack of sheets always restricts the airflow and high pressure holds the sheets down. The next section (220) is an open-air vacuum box that is only covered for a fraction of the machine cycle by the sheet being fed. This section needs to be maintained with a separate high flow vacuum blower. Both vacuum boxes have a lateral restricting mechanism to alter the vacuum area based on the sheet size. This restriction is performed by manually operating a series of flaps on the outside of the feed table. Alternatively, an electrically-controlled mechanism that adjusts two opposing baffles (see, e.g., FIG. 6) symmetrically is using a single source of motion. An automated system using a pressure transducer to monitor vacuum and stop moving the baffles when the desired vacuum is preferred, for simplicity, reliability, ease of maintenance and economy.

[0039] Previous feed table designs have used a four-bar linkage mechanism to control the sheet. The sheet being fed needs to contact the driving wheels, but the following sheet cannot make contact with rotating wheels without causing a jam. A mechanism raised a series of control surfaces in unison above the driving wheels when contact was not desired. At the start of the next cycle, an alternating shaft would lower the surfaces and the sheet would make contact with the wheels moving at a minimal safe velocity. The linkage members were designed such that the control surfaces remained horizontal and exposed or concealed the driving wheels all at once. The prior art design relied on the machine's feed rolls to control the sheet, and any additional driving force from the feed table wheels was nonessential extra support. In the system of the present invention, without feed rolls, the driving wheels need to contact the sheet as much as possible. A new linkage design, using unequal length members, angles each control surface (e.g., 240, 250) which sequentially conceals each wheel as the sheet is fed into the machine. Subsequently, the sheet is driven for a longer period of time and distance. In a resting position, the control surface (e.g., 240, 250) sits horizontally above the driving wheels and prevents contact with the sheet. This motion can also be performed with cams raising and lowering each end of any control surface control surface (e.g., 240, 250) independently to create the desired angle. Either mechanism is controlled by a single servo motor performing a variable motion profile. Each variable velocity zone will require one or more control surface mechanisms. Only the constant velocity zone does not require such a mechanism.

[0040] Another advantageous feature of the servo motion profile illustrated in FIGS. 5A-5E is the adjustable dwell period. As long as the sheet or board (e.g., 2) being fed is still over the driving wheels, the wheels can continue to drive the board. This can continue until either the edge of the board passes, or a specific time where the wheels need to begin decelerating in preparation for the next cycle. At this time a selected control surface (e.g., 240, 250) defined in feed table 210 rises into place to break contact between the board and the wheels. Referring next to FIGS. 5A and 5B, each board or sheet (e.g., 2) is taken from a hopper or is initially at rest and then is accelerated over a sequence of points (A, B, C, D, and E) to a velocity which will as nearly as possible exactly match the desired selected machine speed for host machine 10. This acceleration happened over the sequence of velocity zones (e.g. 220, 230).

[0041] Referring specifically to the diagram of FIG. 5B, a diagram illustrating six (6) velocity profiles (machine velocity as a function of machine displacement 13) illustrating the machine speed profiles for the No-Feed-Roll sheet feeder apparatus 200 of FIGS. 2-4B and retrofitting method of the present invention, the Initial conditions may be defined as:

[00001]$\begin{array}{cc}{V}_1\left(C\right)=V,V_1+V_3=V_2,?=\frac{B^1}{2}+\frac{B^2}{2},\mathrm{and}h=\mathrm{chase}?,& \left(\mathrm{Eqs}.1\mathrm{and}2\right)\end{array}$$\begin{array}{cc}V4\left(C\right)=V,V_4+V_6=V_5,{?}_1=X.Math.{?}_2& \left(\mathrm{Eqs}.3\mathrm{and}4\right)\end{array}$

[0042] Referring next to FIG. 5C, it was desired to control board velocity and displacement in such a way as to effectively take the first half of velocity curve 2, connect the second half of velocity curve 6 to the end of velocity curve 2. The area under the velocity curve, which total displacement, h then becomes:

[00002]$\begin{array}{cc}\left(I\right)& ?\\ h=\frac{h^2}{2}+\frac{h^6}{2}+\left(\frac{B_2}{2}.Math.V_1\left(C\right)\right)& \left(\mathrm{Eq}.5\right)\end{array}$

With Sun's Extend-o-Feed? system (as shown in FIG. 1B and described in commonly owned U.S. Pat. No. 5,184,811), using a 120? modified-sine acceleration curve, each board (e.g., 2) covers about 92% of the machine displacement due to feeding acceleration. This machine displacement coverage is called the Chase.

[0043] To derive the desired control signals for each velocity zone in sheet or board feeding system 200, the applicant's development work Assumed/Defined:

[0044] The displacement of ?1 is directly related to that of ?.sub.2 by a constant, X. (where

[00003]$\frac{B_1}{B_2}=X$

).

Therefore, h.sub.3=X.Math.h.sub.6(Eq. 6)

This leads to Modified Sine Equations, where: [0045] Y=Board displacement at any point in time. [0046] ?=Total machine displacement until board reaches const. velocity. [0047] h=Total board displacement until board reaches const. velocity. [0048] Chase: h/B % [0049] ?.sub.1=Total machine displacement for the first part of the accel. curve. [0050] ?.sub.2=Total machine displacement for the second part of the accel. curve. [0051] ?=Machine displacement at a specific point in time. [0052] (II) Displacement, y=Kh [radians] [0053] (III) Velocity,

[00004]$v=\left(\mathrm{Cv}\right)\left(h\right)\frac{V}{?}$

where, V is input speed in radians/sec. and h and B are in radians. [0054] (IV) Acceleration,

[00005]$a=\mathrm{Ca}h\frac{{\left(V\right)}^2}{?}\left[\mathrm{radians}/{\sec }^2\right]$

[00006]$\mathrm{Where},\mathrm{for}0?\frac{?}{?}?\frac{1}{8}:$$\begin{array}{cc}k=\frac{?}{4+?}.Math.\frac{?}{B}-\frac{1}{4\left(4+?\right)}.Math.\sin \left(4?\frac{?}{B}\right)& \left(\mathrm{Eq}.7\right)\end{array}$$\begin{array}{cc}{C}_v=\frac{?}{4+?}\left(1-\cos \left(4?\frac{?}{B}\right)\right)& \left(\mathrm{Eq}.8\right)\end{array}$$\begin{array}{cc}{C}_a=\frac{4{?}^2}{4+?}.Math.\sin \left(4?\frac{?}{B}\right)& \left(\mathrm{Eq}.9\right)\end{array}$$\mathrm{And}\mathrm{for}\frac{1}{8}?\frac{?}{B}?\frac{7}{8}:$$\begin{array}{cc}k=\frac{?}{4+?}.Math.\frac{?}{B}-\frac{9}{4+?}.Math.\cos \left(\frac{4?}{3}\frac{?}{B}-\frac{?}{6}\right)& \left(\mathrm{Eq}.10\right)\end{array}$$\begin{array}{cc}{C}_v=\frac{?}{4+?}+\frac{3?}{4+?}.Math.\sin \left(\frac{4?}{3}\frac{?}{B}-\frac{?}{6}\right)& \left(\mathrm{Eq}.11\right)\end{array}$$\begin{array}{cc}{C}_a=\frac{4{?}^2}{4+?}.Math.\cos \left(\frac{4?}{3}\frac{?}{B}-\frac{?}{6}\right)& \left(\mathrm{Eq}.12\right)\end{array}$$\mathrm{And}\mathrm{for}\frac{7}{8}?\frac{?}{B}?1:$$\begin{array}{cc}K=1-\frac{?}{4+?}+\frac{?}{4+?}\frac{?}{B}-\frac{1}{4\left(4+?\right)}.Math.\sin (2?\left(2\frac{?}{B}-1\right)& \left(\mathrm{Eq}.13\right)\end{array}$$\begin{array}{cc}{C}_v=\frac{?}{4+?}\left[1-\cos \left(2?\left(2\frac{?}{B}-1\right)\right)\right]& \left(\mathrm{Eq}.14\right)\end{array}$$\begin{array}{cc}{C}_a=\frac{4{?}^2}{4+?}.Math.\sin \left(2?\left(2\frac{?}{B}-1\right)\right)& \left(\mathrm{Eq}.15\right)\end{array}$

Remembering:

[0055] Y=Board displacement at any point in time. [0056] ?=Total machine displacement until board reaches const. velocity. [0057] h=Total board displacement until board reaches const. velocity. [0058] Chase: h/B % [0059] ?.sub.1=Total machine displacement for the first part of the accel. curve. [0060] ?.sub.2=Total machine displacement for the second part of the accel. curve. [0061] ?=Machine displacement at a specific point in time.

[0062] Taking the initial condition that V.sub.1(C)=V to solve for h.sub.1 in section III (above)

[00007]$\begin{array}{cc}{V}_1\left(C\right)=V=C_v{h}_1\left(\frac{V}{B_1}\right)\mathrm{at}\mathrm{point}C=1.75957=\frac{?}{4+?}+\frac{3?}{4+?}.Math.\sin (\frac{4?}{3}\left(\frac{?}{B}\right)-\frac{?}{6}& \left(\mathrm{Eq}.16\right)\end{array}$$\mathrm{Where}?\mathrm{is}0.5,\mathrm{and}{h}_1=\left(\frac{B^1}{V}\right)\frac{V}{C_v},$$\begin{array}{cc}\mathrm{so}{h}_1=\frac{B_1}{C_{v@C}}& \left(V\right)\end{array}$$\begin{array}{cc}\mathrm{and}\mathrm{so}{h}_u=\frac{B_2}{C_{v@C}}& \left(\mathrm{VI}\right)\end{array}$

Next, solving for h.sub.2 in equation 5 in section (I) in terms of h and ?:

[00008]$\begin{array}{cc}\mathrm{Substitue}:h_6=\frac{h_3}{X},h_3=h_2-h_1,V_1\left(c\right)=V& \left(\mathrm{Eq}.17\right)\end{array}$$h=\frac{h_2}{2}+\frac{h_{2-h1}}{2X}+\frac{B_{2}V}{2}.fwdarw.2\left(h\right)=\left(\frac{h_2}{2}+\frac{h_2}{2X}-\frac{h_1}{2X}+\frac{B_{2}V}{2}\right)2$$2h=h_2+\frac{h_2}{X}-\frac{h_1}{X}+B_{2}V$$h_2\left(1+\frac{1}{X}\right)=2h+\frac{h_1}{X}-B_{2}V$$\begin{array}{cc}{h}_2=\frac{2h+\frac{h_1}{X}-B2V}{1+\frac{1}{X}}& \left(\mathrm{VII}\right)\end{array}$

Assuming V=1 so h.sub.1 is per unit of machine velocity. It is known that:

[00009]$\begin{array}{cc}{h}_3=h_2-h_1,& \left(\mathrm{VIII}\right)\end{array}$$\begin{array}{cc}{h}_6=\frac{h_3}{X}& \left(\mathrm{IX}\right)\end{array}$$\begin{array}{cc}\mathrm{and}{h}_5=h_4+h_6& \left(X\right)\end{array}$

So, for Board Displacement: y.sub.1+Kh.sub.1 (piecewise) and for ?/? (from point A to point C):

0?(?/?)?? and

(XI) y=y.sub.2=Kh.sub.2(Eq. 18)

And where (?.sub.1/?.sub.1)=(?/?), so (XII) ?=?)?.sub.1(Eq. 19)

Thus, for ?/? from point C to point D, ??(?/?)?1, and (?.sub.2/?.sub.2)=(?/?)

Which leads to:

(XIII) y=y.sub.2@c+(y6?y6.sub.@c)+(?.sub.2??.sub.1@c)?V(Eq. 20)

Referring now to FIG. 5D, the total board displacement from A to C is represented by the area in section 400 (corresponding to y.sub.2@c) while the area 402 represents the board displacement due to the second half of the h.sub.6 curve (y.sub.6?y6.sub.@c) and the third area 404 represents the area under the velocity curve due to shifting the second part of h.sub.6 up to match h.sub.2 (which corresponds to the third part of Eq. 20, (?2??1@c)?V.

[0063] Starting with the total machine displacement occurring from A to C (e.g., as illustrated in FIGS. 4B and 5B) due to following the ?.sub.1 curve one can add the displacement due to ?.sub.2 and then subtract the first half of ?.sub.2 since it was desired to follow ?.sub.1 from point A to point C, which provides:

(XIV) ?.sub.2=((?.sub.@c/?)??.sub.1)+((?/?)??.sub.2)?((?.sub.@c/?)??.sub.2)(Eq. 21)

So the total machine displacement from point A to point C (due to ?.sub.1) is ((?.sub.@c/?)??.sub.1) and the machine displacement from point C due to ?.sub.2 (due to ?.sub.2) is represented by the second part of Eq. 21, ((?/?)??.sub.2)?((?.sub.@c/?)??.sub.2)

[0064] Finally, calculating Board Velocity:

[00010]$\begin{array}{cc}{v}_i=C_v{h}_i\frac{V}{B_i}& \left(\mathrm{Eq}.22\right)\end{array}$

As noted above, FIG. 5D illustrates the board displacement profiles (velocity as a function of position, illustrating three areas, namely, board displacement from A to C, board displacement due to the second half of the h.sub.6 curve and the area under the velocity curve due to shifting of the second part of h.sub.6 up to match h.sub.2), in accordance with the method of the present invention, while FIG. 5E is a second velocity zone motion profile data plot diagram illustrating the feed wheel velocity (in RPM) as a function of machine displacement (in meters) for the No-Feed-Roll sheet feeder apparatus 200 of FIGS. 2-4.

[0065] The advantages of sheet feeder 200 and the retrofit method of the present invention (for installing sheet feeder 200 into host machine 10) will enhance the host machine's operation, for a few reasons, including: [0066] a. On any feeder, the registration error caused by wheel tread wear depends on the location of the feed roll nip, which the sheet feeder 200 of the present invention machine does not have. Any speed deviation between the feeder 200 and the host machine 10 will accumulate until the machine takes control of the board. On a typical (prior art) feeder this is a couple of inches until the board reaches the feed rolls. With the sheet feeder 200 the board is controlled for a longer duration. In the system and method of the present invention, the interval during which the board is under positive control is at least double that of the prior art feeder (e.g., 12), probably more, until the vacuum transfer (e.g., in host machine 10) fully takes over. [0067] b. The program stored in the controller's memory may be adapted to compensate for this difference. Here, the method is similar to the compensation method in applicant's Microgrind? system which compensates for anvil blanket thickness after intentional removal of material. The system's controller (e.g., 300) is preferably programmed to automatically adjust feeder speed with a sensor at the end of the wheelbox. The sensor must react quickly enough to get an accurate reading depending on desired accuracy and machine speed. [0068] c. Given this data, one may estimate the average wheel tread diameter (e.g., for feed wheels 222W, 224W, 226W, 232W and 234W) and, at a selected diameter change threshold provide an indication recommending that the machine user prepare to change the wheel treads when required for performance, accuracy, or safety reasons.

[0069] Persons of skill in the art will appreciate that the system 200 and method of the present invention provide a new and surprisingly effective and cost efficient corrugated board or paperboard sheet feeder apparatus 200 and sheet feeder retrofitting method where the sheet feeding apparatus is capable of feeding a single sheet (e.g., 2) from a stack of corrugated boards sheets that travels from a feed end to a delivery end, and into a host machine 10. The sheet feeder 200 includes a supporting feed table surface 210 including a feed end and a delivery end and has rows of feed elements or drive wheels (e.g., 222W, 224W, 226W, 232W and 234W). As illustrated in FIGS. 2-4B, the feed elements or drive wheels are configured as a first plurality of feed elements in an initial variable velocity zone 220 which drive the board in a first motion profile, being driven by a first servo system 220M. A second plurality of feed elements in a second velocity zone 230 drive the board in a second motion profile, and are driven by a second servo system 230M in a second motion profile (see FIGS. 5A-5E). The first plurality of feed elements in initial variable velocity zone 220 are arranged in a first plurality of rows which extend transverse to the direction of travel of the sheet from the feed end to the second plurality of feed elements in second velocity zone 230 which are arranged in a second plurality of rows which extend from the first plurality of feed elements to the delivery end.

[0070] A first vacuum powered suction zone which acts on the board in initial variable velocity zone 220 and draws through supporting feed table surface 210 holds the board or sheet, holding it against the first plurality of feed elements while the board is being fed. A second vacuum powered suction zone corresponds to second velocity zone 230 and holds the sheet against the second plurality of feed elements while being fed. In sheet feeder system 200, all of these elements are controlled by a pre-programmed controller 300 (including a processor and memory), and signal receiving and signal transmission connections. The system's controller is programmed and configured to receive a predetermined velocity signal from the host machine 10 and generate (i) a first initial variable velocity control signal for initial variable velocity zone 220 and (ii) a second velocity control signal for second velocity zone 230 in response to the host machine's predetermined velocity signal.

[0071] Turning now to FIG. 6, a vacuum section's air flow for the No-Feed-Roll sheet feeder apparatus of FIGS. 2-4B is shown. As noted above, vacuum pressure is needed throughout the feed table 210 of the present invention, and it is preferably divided into two sections (e.g., 220, 230). In each initial vacuum section (which handles the environment of the initial vacuum box, where the stack of sheets (e.g., 2) always restricts the airflow) high pressure holds the sheets down. Both vacuum sections include boxes which have a lateral restricting mechanism to alter the vacuum area by moving vacuum doors based on the sheet size. As illustrated in FIG. 6, air flows in through apertures in the feed table surface and downwardly drawing the boards against the feed wheels (e.g., 222W, 224W, 226W, 232W and 234W). The vacuum doors preferably move symmetrically, and lateral vacuum restriction is preferably performed by operating a series of flaps on the outside of the feed table. In the preferred embodiment, an electrically-controlled mechanism adjusts two opposing baffles symmetrically using a single source of motion, and in applications or host machines of an asymmetrical configuration, two or more motors may be employed. An automated embodiment of the system of the present invention includes a pressure transducer to monitor vacuum and stop moving the baffles (or change the vacuum pump speed) when the desired vacuum is achieved. Alternatively, the baffles may be moved to a pre-selected and calibrated location based on input sheet size or a particular job's requirements (or recipe).

[0072] Turning next to the diagram of FIG. 7, the signal flow between a controller or computer 300 and data input, sensor motor and pump components of the No-Feed-Roll sheet feeder apparatus of FIGS. 2-6 is shown. The feeder CPU, PLC or controller 300 includes a memory and stores programs adapted for operating feeder system 200 to achieve the board movements described above. Feeder CPU inputs include sheet or board sensors, limit switch signal inputs, a master position and velocity sensor or signal input from host machine 10 and operator controls including inputs for start, stop, double/skip, material size and feed status inputs as well as interlock and safety circuit inputs. The Feeder CPU 300 is programmed and configured to generate several output signals including signals controlling the feeder motors in each zone or section (220M, 230M), control surface motors in each section (240M, 250M), vacuum dampers and motors in each section and vacuum baffle or door position servos in each section.

[0073] Having described preferred embodiments of a new and improved apparatus and method, it is believed that other modifications, variations and changes will be suggested to those skilled in the art in view of the teachings set forth herein. It is therefore to be understood that all such variations, modifications and changes are believed to fall within the scope of the present invention as set forth in the appended claims.