NO-FEED-ROLL CORRUGATED BOARD OR PAPERBOARD SHEET FEEDER RETROFIT APPARATUS AND METHOD

Abstract

A self-contained no-feed-roll computer controlled corrugated board or paperboard sheet feeder apparatus 200 is configured to upgrade an installed corrugated board processing machine (e.g., 10) and includes a feed table surface 210 for boards (e.g., 2) having drive wheels (222W, 224W, 226W) in an initial variable velocity zone 220 which drives the board in a first motion profile through a first vacuum zone, and a second velocity zone 230 which then drives the board in a second motion profile through a second vacuum zone Retrofittable sheet feeder 200 also includes a controller 300 configured to receive predetermined velocity signals 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.

Claims

1. A corrugated board or paperboard sheet feeder apparatus 200 and retrofitting method wherein the sheet feeding apparatus is capable of feeding a single sheet 2 from a stack of corrugated boards sheets that travels from a feed end to a delivery end, and into a host machine 10 comprising: a) a supporting feed table surface 210 for the sheet, said supporting feed table surface 210 including the feed end and the delivery end and having feed elements or drive wheels; b) said feed elements comprising a first plurality of feed elements in an initial variable velocity zone 220 which drive the board in a first motion profile, wherein the first feed elements are driven by a first dedicated computer controlled motor or servo system 220M; c) said feed elements also comprising a second plurality of feed elements in a second velocity zone 230 which drive the board in a second motion profile, wherein the second feed elements are driven by a second dedicated computer controlled motor or servo system 230M; d) said first plurality of feed elements arranged in a first plurality of rows which extend transverse to the direction of travel of the sheet from the feed end to said second plurality of feed elements which are arranged in a second plurality of rows which extend from said first plurality of feed elements to the delivery end; e) a first vacuum powered suction zone corresponding to said initial variable velocity zone 220 in supporting feed table surface 210 for holding the sheet against said first plurality of feed elements while being fed thereby; f) a second vacuum powered suction zones corresponding to said second velocity zone 230 for holding the sheet against said second plurality of feed elements while being fed thereby; and g) a controller 300 configured to receive 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 said host machine's predetermined velocity signal.

2. The corrugated board or paperboard sheet feeder apparatus 200 and retrofitting method wherein the sheet feeding apparatus is capable of feeding a single sheet 2 from a stack of corrugated boards sheets that travels from a feed end to a delivery end, and into a host machine 10 of claim 1, wherein said dedicated primary servo motor 220M in the initial variable velocity zone 220 is configured to perform a specific motion profile designed to reduce the peak torque requirements and accelerate the sheet at a lower rate (than what would normally be required over a specific distance), wherein said motor 220M accelerates the sheet above machine speed momentarily for it to catch up and then decelerates the board to machine velocity to ensure that the longest sheet that can be fed (maximum sheet) is not sacrificed.

3. The corrugated board or paperboard sheet feeder apparatus 200 and retrofitting method wherein the sheet feeding apparatus is capable of feeding a single sheet 2 from a stack of corrugated boards sheets that travels from a feed end to a delivery end, and into a host machine 10 of claim 1, wherein said sheet feeder apparatus 200, once the retrofit is complete, can accommodate an increased maximum feedable sheet size.

4. The corrugated board or paperboard sheet feeder apparatus 200 and retrofitting method wherein the sheet feeding apparatus is capable of feeding a single sheet 2 from a stack of corrugated boards sheets that travels from a feed end to a delivery end, and into a host machine 10 of claim 1, wherein said driving wheels need to assist and contact the sheet as much as possible, so a new linkage design, using unequal length members, angles the control surface (e.g., 240, 250) which sequentially conceals each wheel as the sheet is fed into the machine.

5. A self-contained no-feed-roll computer controlled corrugated board or paperboard sheet feeder apparatus 200 configured to upgrade an installed corrugated board processing machine (e.g., 10), comprising: a feed table surface 210 for boards (e.g., 2) having drive wheels (e.g., 222W, 224W, 226W) in an initial variable velocity zone (e.g., 220) which drives the board in a first motion profile through a first vacuum zone, and a second velocity zone (e.g., 230) which then drives the board in a second motion profile through a second vacuum zone; sheet feeder 200 also includes a controller 300 configured to receive predetermined velocity signals 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.

6. The self-contained no-feed-roll computer controlled corrugated board or paperboard sheet feeder apparatus 200 configured to upgrade an installed corrugated board processing machine (e.g., 10) of claim 5, further comprising a dedicated primary servo motor 220M in the initial variable velocity zone (e.g., 220) configured to perform a specific motion profile designed to reduce the peak torque requirements and accelerate the sheet at a lower rate (than what would normally be required over a specific distance), wherein said motor 220M accelerates the sheet above machine speed momentarily for it to catch up and then decelerates the board to machine velocity to ensure that the longest sheet that can be fed (maximum sheet) is not sacrificed.

7. The self-contained no-feed-roll computer controlled corrugated board or paperboard sheet feeder apparatus 200 configured to upgrade an installed corrugated board processing machine (e.g., 10) of claim 6, wherein said sheet feeder apparatus 200, once the retrofit is complete, can accommodate an increased maximum feedable sheet size.

8. The self-contained no-feed-roll computer controlled corrugated board or paperboard sheet feeder apparatus 200 configured to upgrade an installed corrugated board processing machine (e.g., 10) of claim 7, wherein said driving wheels assist and contact the sheet as much as possible through separately controllable control surfaces (e.g., 240, 250) which can sequentially conceal each wheel as the sheet is fed into the machine.

9. The self-contained no-feed-roll computer controlled corrugated board or paperboard sheet feeder apparatus 200 configured to upgrade an installed corrugated board processing machine (e.g., 10) of claim 8, further comprising a controller 300 configured to receive a selected board or machine 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 said host machine's predetermined velocity signal.

10. A method for retrofitting and controlling an upgraded self-contained corrugated board or paperboard sheet feeder apparatus 200 on an installed operating corrugated board processing or host machine 10 such as a box making machine, comprising the method steps of: (a) providing a corrugated board or paperboard sheet feeder apparatus 200 capable of feeding a single sheet 2 from a stack of corrugated boards sheets that travels from a feed end to a delivery end, and into a host machine 10 comprising a supporting feed table surface 210 for the sheet, said supporting feed table surface 210 including the feed end and the delivery end and having feed elements or drive wheels; said feed elements comprising a first plurality of feed elements in an initial variable velocity zone 220 which drive the board in a first motion profile, wherein the first feed elements are driven by a first dedicated computer controlled motor or servo system 220M; said feed elements also comprising a second plurality of feed elements in a second velocity zone 230 which drive the board in a second motion profile, wherein the second feed elements are driven by a second dedicated computer controlled motor or servo system 230M; said first plurality of feed elements arranged in a first plurality of rows which extend transverse to the direction of travel of the sheet from the feed end to said second plurality of feed elements which are arranged in a second plurality of rows which extend from said first plurality of feed elements to the delivery end; a first vacuum powered suction zone corresponding to said initial variable velocity zone 220 in supporting feed table surface 210 for holding the sheet against said first plurality of feed elements while being fed thereby; a second vacuum powered suction zones corresponding to said second velocity zone 230 for holding the sheet against said second plurality of feed elements while being fed thereby; and a controller 300 configured to receive 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 said host machine's predetermined velocity signal; (b) connecting said host machine 10 to said sheet feeder apparatus 200 and providing a host machine desired board speed signal to said controller 300.

11. The method for retrofitting and controlling an upgraded self-contained corrugated board or paperboard sheet feeder apparatus 200 on an installed operating corrugated board processing or host machine 10, further comprising the method steps of: controlling a primary servo motor 220M in the initial variable velocity zone 220 to perform a specific motion profile designed to reduce the peak torque requirements of the machine, wherein said motion profile is programmed to accelerate the sheet at a selected lower rate (than what would normally be required over a specific distance) where dedicated motor 220M makes up for this by accelerating the sheet above machine speed momentarily for it to catch up and then decelerates the board to machine velocity; wherein 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.

12. The method for retrofitting and controlling an upgraded self-contained corrugated board or paperboard sheet feeder apparatus 200 on an installed operating corrugated board processing or host machine 10, further comprising the method steps of: providing separately controllable angled control surfaces (240, 250) over each velocity zone (220, 230) and controlling the elevation and angle of the control surfaces (e.g., 240, 250) in a manner which sequentially exposes or conceals each drive wheel (e.g., 222W, 224W, 226W) as each sheet is fed into the host machine.

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 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 is 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) is 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 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 ) 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]$\begin{array}{cc}{V}_1\left(C\right)=V,V_1+V_3=V_2,=\frac{B^1}{2}+\frac{B^2}{2},\mathrm{and}h=\mathrm{chase},& \left(\mathrm{Eqs}.1\mathrm{and}2\right)\end{array}$
V.sub.4(C)=V, V.sub.4+V.sub.6=V.sub.5, .sub.1=X.Math..sub.2(Eqs. 3 and 4)

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.

[0042] To derive the desired control signals for each velocity zone in sheet or board feeding system 200, the applicant's development work Assumed/Defined:

The displacement of 1 is directly related to that of .sub.2 by a constant, X.

[00003]$\left(\mathrm{where}\frac{B_1}{B_2}=X\right).$
Therefore, h.sub.3=X.Math.h.sub.6(Eq. 6)

This leads to Modified Sine Equations, where: [0043] Y=Board displacement at any point in time. [0044] =Total machine displacement until board reaches const. velocity. [0045] h=Total board displacement until board reaches const. velocity. [0046] Chase:

[00004]$\frac{h}{}\%$ [0047] .sub.1=Total machine displacement for the first part of the accel. curve. [0048] .sub.2=Total machine displacement for the second part of the accel. curve. [0049] =Machine displacement at a specific point in time.

[00005]$\begin{array}{cc}\mathrm{Displacement},y=\mathrm{Kh}\left[\mathrm{radians}\right]& \left(\mathrm{II}\right)\end{array}$$\begin{array}{cc}\mathrm{Velocity},v=\left(\mathrm{Cv}\right)\left(h\right)\frac{V}{}\mathrm{where},& \left(\mathrm{III}\right)\end{array}$$V\mathrm{is}\mathrm{input}\mathrm{speed}\mathrm{in}\mathrm{radians}/\sec .\mathrm{and}h\mathrm{and}B\mathrm{are}\mathrm{in}\mathrm{radians}.$$\begin{array}{cc}\mathrm{Acceleration},a=\mathrm{Ca}h\frac{{\left(V\right)}^2}{}\left[\mathrm{radians}/{\sec }^2\right]& \left(\mathrm{IV}\right)\end{array}$$\mathrm{Where},\mathrm{for}0\frac{}{B}\frac{1}{B};$

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

Remembering:

[0050] Y=Board displacement at any point in time. [0051] =Total machine displacement until board reaches const. velocity. [0052] h=Total board displacement until board reaches const. velocity. [0053] Chase:

[00007]$\frac{h}{B}\%$ [0054] .sub.1=Total machine displacement for the first part of the accel. curve. [0055] .sub.2=Total machine displacement for the second part of the accel. curve. [0056] =Machine displacement at a specific point in time.
Taking the initial condition that V.sub.1(C)=V to solve for h.sub.1 in section III (above)

[00008]$\begin{array}{c}{V}_1\left(C\right)=V=C_v{h}_1\left(\frac{V}{B_1}\right)\mathrm{at}\mathrm{point}{}^{}{C}^{}\\ =1.75957=\frac{}{4+}+\frac{3}{4+}.Math.\sin (\frac{4}{3}\left(\frac{}{B}\right)-\frac{}{6}\end{array}$

[0057] Where is 0.5, and

[00009]$\begin{array}{cc}{h}_1=\left(\frac{B^1}{V}\right)\frac{V}{C_v},\mathrm{so}& \left(\mathrm{Eq}.16\right)\end{array}$$\begin{array}{cc}{h}_1=\text{?}\mathrm{and}\mathrm{so}& \left(V\right)\end{array}$$\begin{array}{cc}{h}_u=\text{?}& \left(\mathrm{VI}\right)\end{array}$$\text{?}\text{indicates text missing or illegible when filed}$

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

[00010]$\begin{array}{cc}\mathrm{Substitute}: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}$$\begin{array}{cc}h=\frac{h_2}{2}+\frac{h_{2-h1}}{2X}+\frac{B_{2}V}{2}.fwdarw.2\left(h\right)=\left(\frac{h_2}{2}+\frac{h_3}{2X}-\frac{h_1}{2X}+\frac{B_{2}V}{2}\right)2& \left(\mathrm{VII}\right)\end{array}$$2h=h_2+\frac{h_2}{X}-\frac{h_1}{X}+B_{2}V$$h_2\left(1+\frac{1}{X}\right)=2h+\frac{h_1}{X}-B_{2}V$$h_2=\frac{2h+\frac{h_1}{X}-B_{2}V}{1+\frac{1}{X}}$

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

(VIII) h.sub.3=h.sub.2h.sub.1,

[00011]$\begin{array}{cc}{h}_6=\frac{h_3}{X}& \left(\mathrm{IX}\right)\end{array}$

and (X)h.sub.5=.sub.4+h.sub.6
So, for Board Displacement: y.sub.1+Kh.sub.1 (piecewise) and for / (from point A to point C):

0(/)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+(y6y6.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 (y6y6.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, (21@c)V.

[0058] 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).
Finally, calculating Board Velocity:

[00012]$\begin{array}{cc}{v}_i=C_v{h}_i\frac{V}{B_i}& \left(\mathrm{Eq}.22\right)\end{array}$

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 h6 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.

[0059] 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: [0060] 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. [0061] 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. [0062] 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.

[0063] Persons of skill in the art will appreciate that the system 200 and method of the present invention provides 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.

[0064] 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.

[0065] 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).

[0066] 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.

[0067] 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.