05/448869

05/13/1975

03/07/1974

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Westinghouse Electric Corporation (Pittsburgh, PA)

72/10.400

72/10.700

B21B37/66; B21B37/58; B21B37/00

72/8,11,21,29,16

Mehr, Milton S.

Brodahl R. G.

I claim

1. A method of controlling the delivery gauge of a workpiece passing through a rolling mill stand having a pair of work rolls between which said workpiece is passed, with said work rolls respectively being operative with a pair of back-up rolls having eccentricity, said method including the steps of:

2. The method of claim 1, with said predetermined relationship including a determined average roll force between said work rolls.

3. The method of claim 1, with said respective values of said eccentricity being established for each of a top back-up roll operative with a top work roll and a bottom back-up roll operative with a bottom work roll.

4. The method of claim 1, with said predetermined relationship including the force between said work rolls for a predetermined angular rotation of said other back-up roll.

5. The method of claim 1, with said step of controlling the delivery gauge being in accordance with the following relationship

6. An apparatus for controlling the delivery gauge of a workpiece leaving a roll stand having a pair of work rolls respectively positioned between a pair of back-up rolls, the combination of:

7. The apparatus of claim 6, with said first error being determined by the relationship

8. The apparatus of claim 6, with said second error including a determined average roll force between said work rolls.

9. The apparatus of claim 6, with said predetermined relationship being

BACKGROUND OF THE INVENTION

Hot mill and cold mill automatic gauge control design has advanced to the state where the eccentricity of the back-up rolls has become a major problem. As the back-up rolls rotate, their eccentricity introduces a change in the exit gauge of each stand. Furthermore, the eccentricity causes the measured stand roll force to fluctuate. The well known roll force gauge control equation for automatic gauge control or AGC is based on the premise that an increase in roll force indicates an increase in exit gauge from the stand, but in the case of back-up roll eccentricity, the opposite is true. Therefore back-up roll eccentricity not only causes a delivery gauge error, it also causes the AGC to double the error.

Previous solutions to the problem have involved giving the AGC a deadband larger than the gauge error caused by the back-up roll eccentricity, or simulating the back-up roll eccentricity with a mechanical cam and lever, and feeding the simulated eccentricty to the AGC, as a correction signal. Neither of these solutions has been satisfactory.

In the operation of a rolling mill stand, the unloaded roll opening and the speed at each tandem mill stand or for each reversing mill pass are set up by the operator to produce successive workpiece (strip or plate) reductions resulting in work product delivered at the desired gauge. Generally, the loaded roll opening at a stand equals the stand delivery gauge on the basis of the usually justifiable assumption that there is little or no elastic workpiece recovery.

Since the operator provided initial setup conditions, or the initial roll opening setting provided by an associated computer control system operative with model equation information to calculate the setup screwdown schedule for the rolling mill, can be in error and since in any event certain mill parameters affect the stand loaded roll opening during rolling and after setup conditions have been establish, a stand automatic gauge control system is employed such that the stand delivery gauge can be closely controlled. Thus, at the present state of the rolling mill art and particularly the steel rolling mill art, a stand gauge control system is normally used for a reversing mill stand and for predetermined stands in tandem rolling mills.

More particularly, the well known gauge meter or roll force gauge control system has been widely used to produce stand gauge control in metal rolling mills, and particularly in tandem hot steel strip rolling mills and reversing plate mills where experience has demonstrated that roll force control is particularly effective. Earlier publications and patents such as an article entitled Installation and Operating Experience with Computer and Programmed Mill Controls by M. D. McMahon and M. A. Davis in the 1963 Iron and Steel Engineer Yearbook at pages 726 and 733, an article entitled Automatic Gauge Control for Modern Hot Strip Mills by J. W. Wallace in the December 1967 Iron and Steel Engineer at pages 75 to 86, U.S. Pat. No. 3,561,237 issued Feb. 9, 1971 to Eggers et al. and U.S. Pat. No. 2,726,541, issued Dec. 13, 1955 to R. B. Sims describe the theory upon which operation of the roll force and related gauge control systems is based. Attention is also called to U.S. Pat. No. 3,568,637 issued Mar. 9, 1971, U.S. Pat. No. 3,574,279 and 3,574,280 issued Apr. 13, 1971, and U.S. Pat. No. 3,600,920 issued Aug. 24, 1971 to A. W. Smith, which relate to roll force automation gauge control systems.

Briefly, the roll force gauge control system uses Hooke's law in controlling the screwdown position at a rolling stand, i.e. the loaded roll opening under workpiece rolling conditions equals the unloaded roll opening or screwdown position plus the mill spring stretch caused by the separating force applied to the rolls by the workpiece. To embody this rolling principle in the roll force gauge control system, a load cell or other force detector measures the roll separating force at each controlled roll stand and the screwdown position is controlled to balance roll force changes from a reference value and thereby hold the loaded roll openinig at a substantially constant value. Typically, the roll force gauge control system is an analog arrangement including analog comparison and amplification circuitry which responds to the roll force signal F and the screwdown position signal SD to control the screwdown position and hold the following equality:

ΔSD = - Δ F.K (1)

where:

ΔF = measured change in roll from an initial force

ΔSD = controlled change in screwdown position from an initial screwdown position.

K = predetermined stand mill spring modulus.

After the unloaded roll opening setup and the stand speed setup are determined by the mill operator for a particular workpiece pass or series of passes, the rolling operation is begun and the screwdowns are controlled to regulate the workpiece delivery gauge from the reversing mill stand or from each roll force controlled tandem mill stand, such that the loaded roll opening SD is maintained constant or nearly constant.

As the head end of the workpiece strip enters each roll stand of the mill, the lock-on screwdown position and the lock-on roll separating force are measured to establish what strip gauge should be maintained out of that roll stand. As the strip rolling operation proceeds, the roll stand separating force and the roll stand screwdown position values are monitored and any undesired change in roll separating force is detected and compensated for by a corresponding correction change in screwdown position. The lock-on gauge LOG is equal to the lock-on screwdown LOSD plus the lock-on force LOF multiplied by the mill stand spring modulus K. The workpiece strip delivery gauge G leaving the roll stand at any time during the rolling operation is equal to the unloaded screwdown position SD plus the roll separating force F multiplied by the mill spring modulus K. The gauge error is derived by subtracting the lock-on gauge from the delivery gauge. The following Equations 2, 3 and 4 set forth these relationships.

LOG = LOSD + K*LOF (2)

g = sd + k*f (3)

g - log = gauge error = sd - losd + (f-lof)*k (4)

a background teaching of stored program digital computer system operation can be found in a book entitled Electronic Digital Systems by R. K. Richards and published in 1966 by John Wiley and Sons.

A detailed description of computer programming techniques in relation to the control of metal rolling mills can be found in an article in the Iron and Steel Engineer Yearbook for 1966 at pages 328 through 334 entitled "Computer Program Organization for an Automatically Controlled Rolling mill" by John S. Deliyannides and A. H. Green, and in another article in the Westinghouse Engineer for January 1965 at pages 13 through 19 and entitled "Programming for Process Control" by P. E. Lego.

CROSS REFERENCE TO RELATED APPLICATION

The present invention is related to the invention disclosed in U.S. Pat. 3,793,860 which was filed Dec. 4, 1972 by A. V. Silva and the invention disclosed in concurrently filed patent application Ser. No. 448,868, filed Mar. 7, 1974, by J. W. Cook, and assigned to the same assignee as the present invention.

SUMMARY OF THE INVENTION

In accordance with the broad principles of the present invention, a control system and method for controlling delivery gauge or thickness of workstrip product leaving a metal rolling mill stand includes the measurement of the eccentricity of each back-up roll when there is no workstrip positioned between the work rolls of the roll stand, with the work rolls rotating at a relatively slow speed such as thread speed of operation and the control of the roll stand in accordance with that eccentricity. The measured eccentricity is then used in the control of the product delivery thickness .

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a schematic diagram of a roll stand and a gauge control system arranged for operation in accordance with the present invention;

FIG. 2 illustrates a mill spring curve and a workpiece reduction curve for a rolling mill stand, and the determination of a roll force screwdown correction in relation to a change in the stand load force;

FIG. 3 shows an illustrative logic flow chart of the eccentricity determination program operative in relation to a roll stand;

FIG. 4 shows a logic flow chart to illustrate the operation of the back-up roll eccentricity measurement program operative with the gauge control system shown in FIG. 1;

FIG. 5 shows a flow chart to illustrate the operation of the back-up roll eccentricity implementation program operative with the gauge control system shown in FIG. 1; and

FIG. 6 is a functional illustration of the eccentricity determination and the control of workpiece delivery gauge in accordance with the present invention.

GENERAL DESCRIPTION OF THE GAUGE CONTROL SYSTEM AND ITS OPERATION

There is shown in FIG. 1 a four high rolling mill stand 10 operative with a gauge control system 12 in accordance with the principles of the present invention. Generally, the invention is applicable to various types of rolling mill stands in which roll force gauge control is employed. Thus, the invention can be suitably adapted for application in hot steel plate reversing and other rolling mills.

A workpiece 14 enters the roll stand 10 at the entry end and it is reduced in thickness as it is transported through one or more roll stands to the delivery end of the rolling mill. The entry workpiece would be of known steel grade and it typically would have a known gauge or thickness. The delivered workpiece would have a desired thickness based upon the production order for which it is intended.

In the reduction rolling process, the one or more roll stands operate at successively higher speeds to maintain proper workpiece mass flow. Each stand produces a predetermined reduction or draft such that the total mill draft reduces the entry workpiece to strip with the desired gauge or thickness.

Each stand is conventionally provided with a pair of back-up rolls 16 and 18 and a pair of work rolls 20 and 22 between which the workpiece 14 is passed. A large DC drive motor 24 is controllably energized at each stand to drive the corresponding work rolls at a controlled speed.

As previously described, the sum of the unloaded work roll opening and the mill stretch substantially defines the workpiece gauge delivered from any particular stand in accordance with Hooke's law. To vary the unloaded work roll opening at each stand, a pair of screwdown motors 26 (only one shown for the roll stand) position respective screwdowns 28 (only one shown for the roll stand) which clamp against opposite ends of the back-up rolls and thereby apply pressure to the work rolls. It should be understood that the screwdown motors 26 are merely illustrative of roll opening positioning devices, and well known hydraulic positioning cylinder devices having a faster response to gauge error may be preferred in actual practice. Normally, the two screwdowns 28 at a particular stand would be in identical positions, but they can be located in different positions for strip guidance during threading, for flatness or other strip shape control purposes or possibly for other purposes. A conventional roll opening position detector or encoder 30 provides an electrical signal representation of screwdown position.

Roll force detection is provided at the roll stand 10 by a conventional load cell 32 which generates an electrical analog signal proportional to the roll separating force between the work rolls 20 and 22. At the very least, for a tandem rolling mill, each roll force controlled stand is provided with a load cell 32 and in many cases stands without roll force gauge control would also be equipped with load cells. The number of stands to which roll force gauge control is applied is predetermined during the mill design in accordance with cost-performance standards, and increasingly there is a tendency to apply roll force gauge control to all of the stands in a tandem hot strip steel mill.

The gauge control system 12 provides automatic gauge or thickness control for the operation of the mill stand 10. The gauge control system 12 can include a programmed general purpose process control digital computer system, which is interfaced with the various mill sensors and the various mill control devices to provide control over the operation of the mill stand 10. According to user preference, the gauge control system 12 can also include well known and conventional manual and/or automatic analog controls for back-up operation in performing other preselected mill functions.

On the basis of these considerations, a suitable digital computer system for the on-line roll force gauge control system 12 would be a Prodac 2000 (P2000) sold by Westinghouse Electric Corporatiton. A descriptive book entitled Prodac 2000 Computer Systems Reference Manual has been published in 1970 by Westinghouse Electric Corporation and made available for the purpose of describing in greater detail this computer system and its operation.

The digital computer system is associated with well known predetermined input systems, typically including a conventional contact closure input system which scans contact or other signals representing the sensed status of various process conditions, a conventional analog input system which scans and converts process analog signals, and operator controlled and other information input devices and systems such as paper tape, teletypewriter and dial input systems. Various kinds of information can be entered into the computer system through the input devices including, for example, desired strip delivery gauge and temperature, strip entry gauge and width and temperature (by entry detectors if desired), grade of steel being rolled, plasticity tables, hardware oriented programs and control programs for programming system, and so forth. The contact closure input systems and the analog input systems interface the computer system with the process through the medium of measured or detected variables, which include the following:

1. A roll force signal from the load cell 32 at the roll stand 10 proportional to stand roll separating force for use in roll force gauge control.

2. Roll opening position signal generated by the respective position detector 30 for use in roll force gauge control.

3. A position signal from rotary transducer or pulse generator 34 in relation to the angle of rotation of the top back-up roll 16.

4. A position signal from rotary transducer or pulse generator 36 in relation to the angle of rotation of the bottom back-up roll 18.

It is noted at this point in the description, that the measured stand roll force and the measured stand roll opening position in relation to the workpiece head end are stored and used as references for roll force gauge control system functioning if it is desired to operate in the well known lock-on mode of roll force gauge control operation.

To effect determined output control actions, controlled devices are operated directly by means of output system contact closures or by means of analog signals derived from output system contact closures through a digital to analog converter. The principal control action outputs from the gauge control system 12 includes a roll opening positioning command signal applied to roll opening position control 40 in operating the screwdown motor 26 for desired screw movement, and a speed control signal applied to the drive motor 24 to cause a change in drive speed to compensate the force on the workpiece strip for a change in thickness being made by a screwdown movement.

Display and printout systems such as numeral display, tape punch, and teletypewriter systems can be also associated with the outputs of the digital computer system in order to keep the mill operator generally informed about the mill operation and in order to signal the operator regarding an event or alarm condition which may require some action on his part.

Generally, the gauge control system 12 uses Hooke's law to determine the total amount of screwdown movement required at the roll force controlled stand 10 at the calculating point in time for roll force and gauge error correction, i.e. for loaded roll opening and stand delivery gauge correction to the desired value. The calculation defines the total change in the unloaded roll opening required to correct for determined back-up roll eccentricity or other roll force and gauge error causing conditions.

In FIG. 2, curves are shown to illustrate the application of Hooke's law to a rolling mill stand and to illustrate the basis upon which the gauge control system 12 provides improved roll force gauge control. A mill spring curve 62 defines the separation between a pair of mill stand work rolls as a function of roll separating force and as a function of screwdown position. The slope of the mill spring curve 62 is the well known mill spring constant K. When a correct screwdown calibration is known and the screwdowns are positioned such that the empty work rolls are just facing, the unloaded screwdown zero position is defined. The zero screwdown location mill spring curve is indicated by the reference character 60.

At the correct calibration condition, the indicated theoretical face intersect represents theoretical roll facing and it is for this theoretical condition that the screwdown position is assigned to a zero value. Under the correct calibration condition, roll facing actually occurs when the screwdown position is at a slightly negative value because of the non-linearity of the lower part of the mill spring curve. A definition of the screwdown calibration as being correct for the indicated theoretical conditions is, however, convenient and appropriate for mill operation.

When the screwdowns are opened (positive movement) the unloaded roll opening increases as reflected by a change to the right in the graphical location of the mill spring curve 62 such that the theoretical spring curve intersect equals the new unloaded roll opening. With screwdown closing, the mill spring curve 62 is shifted to the left in a similar manner.

At any particular screwdown position and with the correct screwdown calibration, the stand workpiece delivery gauge equals the unloaded roll opening as defined by the screwdown position SD plus the mill stretch caused by the workpiece. If the screwdown calibration is incorrect, i.e. if the number assigned to the theoretical roll facing screwdown position is something other than zero because of roll crown wear or other causes, the stand workpiece delivery gauge equals the unloaded roll opening plus the mill stretch plus or minus the calibration drift.

The amount of mill stretch depends on the characteristic reduction curve for the workpiece. As shown in FIG. 2, a reduction curve 64 for a workpiece strip of predetermined width represents the amount of force required to reduce the workpiece from a stand entry thickness (height) of H _IN . The workpiece plasticity P is the slope of the curve 64, and in this case the curve 64 is shown as being linear although a small amount of non-linearity would normally exist.

Desired workpiece deliver gauge H _D is the initial condition IC produced in this case since the amount of force required to reduce the workpiece from H _IN to H _D is equal to the amount of roll separating force required to stretch the rolls to a loaded roll opening H _D , i.e. the intersection of the mill spring curve at an initial screwdown opening SD indicated by mill spring curve 62 and the workpiece reduction curve 64 lies at the desired gauge value.

As shown in FIG. 2, if the stand delivery gauge increases by a gauge error amount GE to H _X during a workpiece pass to produce a present condition PC, in this instance because the workpiece plasticity decreases and because the workpiece entry thickness increases to H _XIN as represented by the reduction curve 66, the stand screwdowns must be closed to a value which causes a future correct gauge condition FC. At the condition FC, the intersection of the mill spring curve and the new reduction curve 66 lies at the desired gauge H _D as provided by a spring curve location indicated by the reference character 68. In other words, corrective screwdown closing causes the unloaded screw opening to be reduced by an amount ΔS _RF to a new value which adds with the new mill stretch to equal the desired gauge H _D .

The desired screwdown correction ΔS _RF is calculated to enable roll force gauge control operation in accordance with the following programmed relationship algorithm: ##EQU1## where: GE = gauge error

K = mill spring constant (in/10 ⁶ lb)

P = workpiece plasticity (in/10 ⁶ lb)

Generally the operative value of each stand spring constant K is relatively accurately known. It is the first determined by the conventional work roll screwdown test, and it can be recalculated prior to each workpiece pass on the basis of the workpiece width and the back-up roll diameter. Each resultant spring curve is stored for on line gauge control use.

The operative value of the workpiece plasticity P at each stand is also relatively accurately determined. If desired, P tables can be stored in the storage memory of the digital computer system associated with the gauge control system 12 shown in FIG. 1 to identify the various values of P which apply to the mill stand 10 for various grade class and gauge class workpieces under various operating conditions and at various operating times during the rolling of the workpiece strip 14.

A main advantage of using the roll force gauge control system is the ability to detect error changes in strip gauge the instant they take place as the product is being rolled in the roll stand. A shift in strip delivery gauge or thickness can be caused by a change in entry thickness, or a change in hardness as usually caused by a change in temperature. This change in delivery gauge can be immediately detected by feedback information monitoring of the roll separating force on the roll stand.

The screwdown correction ΔS _RF can be determined by the relationship:

ΔS _RF = X + GE (6)

where:

X is the amount of roll opening change and hence strip delivery gauge change due to the stretch of the roll stand

Ge is the gauge error.

The roll stand stretch X can be determined by the relationship:

X = K* ΔF (7)

where:

ΔF is the change in roll force when the gauge error GE is corrected.

GE = P* ΔF (8) ##EQU2## now combining Equation 9 with Equation 7 will give ##EQU3## and combining Equation 10 with Equation 6 will give

The screwdown correction ΔS _RF is shown in FIG. 2 in relation to the gauge error GE, the desired gauge H _D and the present gauge H _X .

DESCRIPTION OF BACK-UP ROLL ECCENTRICITY CORRECTION

The measurement of the back-up roll eccentricity can be done any time that is desired by the operator when there is not a workpiece strip in a stand. The hardware required consists of a force measuring load cell operative with the stand, and rotary transducers operative with each back-up roll. An analog or digital computer can be used in conjunction with the gauge control system 12 to implement the required calculations.

The eccentricity measurement is accomplished by facing the work rolls 20 and 22 shown in FIG. 1 to a predetermined force and rotating them at a typical operating speed. The rotary transducers 34 and 36 will respectively indicate the exact position of each back-up roll as it rotates, and the load cell 32 will indicate the force fluctuations caused by the eccentricity of the back-up rolls. The control system records the force reading F for every few degrees of rotation of the back-up rolls. Mathematically this force reading is in accordance with the following equation:

Force ₁ = Average Force + (A*sin θ) + B*sin (θ + C) (13)

where:

θ is the angle of rotation of a selected back-up roll, such as the top back-up roll.

A is the maximum force component caused by the eccentricity of the top back-up roll, and

B is the maximum force component caused by the eccentricity of the bottom back-up roll.

C is the angular offset between the top and bottom back-up roll eccentric axes.

Since the back-up rolls are not physically coupled to each other, and are never the same diameter, they are not actually rotating at the same frequency but the above equation is valid over short periods of time.

The second step is to allow the back-up rolls to rotate until the slight difference in rotational frequency has caused the bottom roll to be 180° offset from its initial relationship to the top roll. The equation for this condition would be:

Force ₂ = Average Force + (A*sin θ) + B*sin (θ + C + 180°) (14)

the rotary transducers 34 and 36 can each be monitored to detect when this condition has occurred, and the control system 12 would then record the force reading for every predetermined number of degrees of rotation of the back-up rolls.

The control system 12 now has enough information to permit the determination of the eccentricity of the top and bottom back-up rolls. The eccentricity of the bottom roll is determined as follows:

Force ₁ - Force ₂ = 2B* sin (θ + C) (15) ##EQU4##

Eccentricity _B = B * sin(θ+C) * mill spring (17) ##EQU5##

In other words, if the control system 12 subtracts the data of the Force ₂ measurements from the data of the Force ₁ measurements, and divides by 2, it has a record of the force components of the bottom roll for every few degrees of rotation, as desired in relation to selected values of the angle θ, and this force component is proportional to the eccentricity of the bottom roll.

The eccentricity of the top roll is determined as follows:

A*sin θ = Force ₁ - Average Force - B * sin (θ + C) (19)

eccentricity _T = A * (sin θ) * mill spring (20)

where Average Force is the integral from 0° to 360° of the measured values of F ₁ and divided by the number of samples, as follows: ##SPC1##

A*sinθ = F ₁ - B*sin(θ + C) - F _AV (22) ##EQU6##

The above equations allow the control system to utilize the recorded data to provide a record of the force component of the top roll for selected values of the angle θ in degrees of rotation.

The next step is to apply this information to the above roll force gauge control equation 4 for the workpiece gauge control as follows:

Gauge Error = (Screwdown - Lock-on Screw Down) + Eccentricity of top roll + eccentricity of bottom roll + (Force-Lock-on force) * mill spring. (26)

Where the eccentricity correction is a function of the angular position of each of the back-up rolls, and the angular positions are measured by the respective rotary transducers 34 and 36, this revised equation responds properly to roll eccentricity. When eccentricity causes the roll gap to close, the equation accounts for this, and when the measured roll force increases as a result of the eccentricity, the equation indicates the true gauge error.

If the above roll force gauge control equation is implemented in an analog automatic gauge control instead of a digital AGC, a digital computer can be used if desired to output an analog signal to the analog AGC corresponding to each value of eccentricity.

The equations for Force ₁ and Force ₂ assume that the eccentricity is sinusoidal, for simplicity. However, the true eccentricity can actually be modeled by the sum of a number of sinusoidal terms of different amplitudes and different phases but common frequency, therefore, the results derived from the equations would still be true. The operator initially faces the rolls to a high force and rotates them. The signals supplied to the control system are the roll force signal from the load cell and the pulse signals from the pulse generator coupled to the upper back-up roll to indicate the rotational position of the upper roll and the pulse signals from the pulse generator coupled to the lower back-up roll to indicate the rotational position of the lower roll. The gauge control system is programmed to sample the force signal over one complete rotation of the upper and lower back-up rolls; for theoretical purposes only one complete rotation is needed but in actual practice for mechanical purposes the force signal for four or five rotations of the back-up rolls is sampled to provide statistical averages. The control system is programmed to sample the force signal and save a predetermined number such as 360 samples in memory, with one sample being made for each degree of rotation of the upper back-up roll, and in this way obtain roll force samples in memory for the rotation angle of the top back-up roll θ going from 0° to 360°, with no workpiece positioned between the work rolls and with a predetermined roll force such as 1000 metric tons being provided for the roll stand under consideration. The second step of measuring the back-up roll eccentricity is to separate the work rolls and rotate one of the back-up rolls, for example the bottom back-up roll, until the pulse generator operative with the bottom back-up roll indicates that the bottom back-up roll is now rotated substantially 180° from its relationship to the top back-up roll to in effect provide a 180° phase shift of the bottom back-up roll, and then again sample the roll force signal for each degree of rotation of a complete 360° rotation of the top back-up roll and save in memory the resulting 360 roll force signal samples. It is readily apparent that a fewer number of samples, such as 72 samples will give an approximation of the back-up roll eccentricity in this regard. These roll force signal measurements are all made with respect to the top back-up roll rotational position as a reference.

The back-up roll caused error in the measured roll force signal for a given rolling mill roll stand can be in the order of ± 10% of the desired delivery gauge, particularly in relation to the last roll stand of a rolling mill. For a rolling mill stand with hydraulic roll positioning apparatus, the speed of response is fast enough to actually remove the eccentricity impressions by changing the roll opening in phase with the eccentricity as required to correct the gauge error resulting from the eccentricity of either one or both of the back-up rolls.

In FIG. 3 there is illustrated the eccentricity correction to be applied to the roll opening of the mill stand in relation to the angular rotation position of a particular back-up roll. The roll force error caused by the back-up roll eccentricity is shown by the curve.

In FIG. 4 there is shown a flow chart to illustrate the eccentricity measurement program operation for the back-up roll eccentricity determination in accordance with the present invention. At step 75 the roll stand force is read and checked in relation to predetermined limits, such as high limit of 1500 metric tons and a low limit of 800 metric tons, and if the force reading is outside of those limits at step 77 an alarm is provided for the operator and the program ends. If the stand roll force reading is within the desired limits, at step 79 the roll stand speed is read and checked in relation to predetermined limits, such as a high limit of 100 RPM and a low limit of 50 RPM, and if the speed is outside of those limits at step 81 an alarm is provided for the operator and the program ends. If the roll stand speed is within the desired limits, at step 83 the eccentricity index is initialized and a program loop is begun at step 85 where the stand roll force is read as the work rolls are rotating. In practice the program operation is such that 90 force sample readings will be taken during one back-up roll rotation. At step 87 the angular position of the top back-up roll is read from the rotary transducer 34, and 90 such readings will be taken or one reading every 4° of rotation. At step 89 the angular position of the bottom back-up roll is read from the rotary transducer 36, and 90 such readings will be taken. At step 91 the position readings are stored in memory and a delay of about one-tenth second is provided, and at step 93 the index is incremented such that the next force and position sample readings are taken the next time through this loop. At step 95 a check is made to see if 90 sample readings have been taken, and if not the program loops back to step 85 and if so the program goes to step 97 for a delay of 5 seconds to wait until the bottom back-up roll has rotated 180° in relation to the top back-up roll. At step 99 a check is made to see if the bottom back-up roll is 180° out of phase in relation to the top back-up roll, and if not the program loops back to step 97 for another time delay of 5 seconds and then another check is made at step 99 until the 180 degrees out of phase condition has occurred. If the check at step 99 shows that the bottom back-up roll is 180° out of phase, the program goes to step 101 to initialize the 180° out of phase eccentricity index. At step 103 the stand roll force is read as the work rolls are rotating. Again, 90 force sample readings are taken during one back-up roll rotation. At step 105 the position of the top back-up roll is read from the rotary transducer 34, and 90 such readings will be taken or one reading every 4° of rotation. At step 107 the position of the bottom back-up roll is read from the rotary transducer 36, and ninety such readings will be taken. At step 109 the position readings are stored in memory and a delay of about one-tenth second is provided, and at step 111 the index is incremented such that the next force and position sample readings are taken the next time through this loop. At step 113 a check is made to see if 90 sample readings have been taken, and if not the program loops back to step 103 and if so the program goes to step 115 to calculate the average stand roll force by summing up all force readings taken during the first 90 samples and dividing by the number of such samples. At step 117 the top back-up roll eccentricity E _T is calculated in accordance with the relationship of above equation (25), at step 119 the bottom back-up roll eccentricity E _B is calculated in accordance with above equation (18), and then the program ends.

In FIG. 5 there is shown a flow chart to illustrate the eccentricity implementation program operation of the gauge control system 12 shown in FIG. 1. At step 131 the position of the top back-up roll 16 is read from the rotary transducer 34. At step 133, using the top back-up roll position as an index, the eccentricity E _T value is obtained from the look up table provided by the FIG. 4 program. At step 135 the position of the bottom back-up roll 18 is read from the rotary transducer 36. At step 137, using the bottom back-up roll position as an index, the eccentricity E _B value is obtained from the look up table provided by the FIG. 4 program. At step 139 the eccentricity correction is obtained by adding together the individual eccentricity values, in accordance with the relationship indicated by above equation (26), which is used to calculate the gauge error at step 141. At step 143 the roll opening correction is calculated in accordance with above equation (12), and at step 145 this roll opening correction is output to the roll opening position control 40 shown in FIG. 1.

In FIG. 6 there is functionally illustrated the eccentricity determination and the control of workpiece delivery gauge in relation to a roll stand 150. At block 152 the average stand roll force F _AV is determined. At block 154 the force reading F ₁ is established for in the order of every four degrees of rotation of the top back-up roll 16 in accordance with above equation (13). At block 156 the force reading F ₂ is established in accordance with above equation (14). At block 158 the eccentricity E _B of the bottom back-up roll 18 is established in accordance with above equation (18), and at block 160 the eccentricity E _T of the top back-up roll 16 is established in accordance with above equation (25). At block 162 the gauge error including eccentricity is established in accordance with above equation (26), and at block 164 the roll opening correction is established in accordance with above equation (12).

GENERAL DESCRIPTION OF INSTRUCTION PROGRAM LISTING

In the Appendix there are included two instruction program listings that have been prepared to determine and correct for the eccentricity of each back-up roll in relation to the roll force automatic gauge control operation of a tandem rolling mill in accordance with the here disclosed control system and method. The instruction program listings are written in the FORTRAN language of the PRODAC P2000 digital computer system, which is sold by Westinghouse Electric Corporation for real time process control computer applications. Many of these digital computer systems have already been supplied to customers, including computer instruction books and descriptive documentation to explain to persons skilled in this art the operation of the hardware logic and the executive software of this digital computer system. These instruction program listings are included to provide an illustration of one suitable embodiment of the present control system and method that has actually been prepared. The instruction program listings have not been extensively debugged through the course of extensive practical operation for the real time operational control of a rolling mill. It is well known by persons skilled in this art that most real time process control application programs contain some bugs or minor errors, and it is within the skill of such persons and takes varying periods of actual operation time to identify and correct these bugs.

The instruction program listings included in the Appendix were prepared in relation to the programmer's flow charts shown in FIG. 4 and in FIG. 5. ##SPC2##