Title:
Roll eccentricity correction system and method
United States Patent 3881335
Abstract:
A control system and method are disclosed to operate with at least one roll stand of a rolling mill to determine the magnitude and phase relationship of the eccentricity of each back-up roll of a four high roll stand, to monitor the rotation of the back-up rolls during the rolling process, and for each back up roll to correct the roll vertical position as a function of the roll angular position to compensate for the eccentricity of the respective back-up rolls as they rotate. This correction will remove the workpiece delivery gauge error induced by the eccentricity, and the gauge error induced by the improper response of the roll force gauge control equation to the eccentricity, particularly for application of a roll force gauge control system.
US Patent References:
System for eliminating cyclic variations in rolling mill gauge errors
Smith - July 1965 - 3194035
/3331229.html
Neumann et al. - July 1967 - 3331229
ROLLING MILLS
Howard - August 1969 - 3460365
MOTOR DRIVE SYSTEM FOR ROLLING MILL
Cox - August 1972 - 3683653
METHOD FOR DETECTING ECCENTRICITY AND PHASE ANGLE OF WORKING OR BACKING ROLL IN ROLLING MILL
Shiozaki et al. - January 1973 - 3709009
System for eliminating cyclic variations in rolling mill gauge errors
Smith - July 1965 - 3194035
/3331229.html
Neumann et al. - July 1967 - 3331229
ROLLING MILLS
Howard - August 1969 - 3460365
MOTOR DRIVE SYSTEM FOR ROLLING MILL
Cox - August 1972 - 3683653
METHOD FOR DETECTING ECCENTRICITY AND PHASE ANGLE OF WORKING OR BACKING ROLL IN ROLLING MILL
Shiozaki et al. - January 1973 - 3709009
Application Number:
05/448868
Publication Date:
05/06/1975
Filing Date:
03/07/1974
View Patent Images:
Export Citation:
Assignee:
Westinghouse Electric Corp. (Pittsburgh, PA)
Primary Class:
Other Classes:
72/10.700, 72/9.200
International Classes:
B21B37/66; B21B37/58; B21B37/00
Field of Search:
72/8,21,29,16,11
Primary Examiner:
Mehr, Milton S.
Attorney, Agent or Firm:
Brodahl R. G.
Claims:
I claim
1. A method of controlling the delivery gauge of a workpiece operative with a rolling mill stand having a pair of work rolls between which said workpiece is passed, and a pair of back-up rolls, with each said work roll being operative with a different back-up roll having eccentricity, said method including the steps of:
2. The method of claim 1, with said step of determining a portion of said maximum value of eccentricity of said back-up roll including the provision of an output signal in accordance with said portion, and
3. The method of claim 1, with said step of establishing the maximum value of said eccentricity operating in accordance with the roll force between said work rolls.
4. The method of claim 1, including the step of positioning said one back-up roll in accordance with a predetermined angular position of at least said one back-up roll.
5. The method of claim 1, with said step of determining a portion of said maximum value of eccentricity of said back-up roll being in relation to a predetermined position of said back-up roll where said portion is substantially equal to said maximum value of said eccentricity.
6. An apparatus for controlling the delivery gauge of a workpiece passing through a roll stand having a pair of work rolls positioned between respective back-up rolls, the combination of:
7. The apparatus of claim 6, including means for positioning said one back-up roll in each of a plurality of predetermined angular positions, with said means for determining the maximum eccentricity being operative in relation to each of said predetermined angular positions
8. The apparatus of claim 6, with said means for determining the maximum eccentricity being operative in relation to a predetermined zero angular position of said one back-up roll.
9. The apparatus of claim 6, with said means for determining the maximum eccentricity of one of said back-up rolls being operative to determine the maximum eccentricity of the other of said back-up rolls in relation to predetermined angular positions of said other back-up roll.
1. A method of controlling the delivery gauge of a workpiece operative with a rolling mill stand having a pair of work rolls between which said workpiece is passed, and a pair of back-up rolls, with each said work roll being operative with a different back-up roll having eccentricity, said method including the steps of:
2. The method of claim 1, with said step of determining a portion of said maximum value of eccentricity of said back-up roll including the provision of an output signal in accordance with said portion, and
3. The method of claim 1, with said step of establishing the maximum value of said eccentricity operating in accordance with the roll force between said work rolls.
4. The method of claim 1, including the step of positioning said one back-up roll in accordance with a predetermined angular position of at least said one back-up roll.
5. The method of claim 1, with said step of determining a portion of said maximum value of eccentricity of said back-up roll being in relation to a predetermined position of said back-up roll where said portion is substantially equal to said maximum value of said eccentricity.
6. An apparatus for controlling the delivery gauge of a workpiece passing through a roll stand having a pair of work rolls positioned between respective back-up rolls, the combination of:
7. The apparatus of claim 6, including means for positioning said one back-up roll in each of a plurality of predetermined angular positions, with said means for determining the maximum eccentricity being operative in relation to each of said predetermined angular positions
8. The apparatus of claim 6, with said means for determining the maximum eccentricity being operative in relation to a predetermined zero angular position of said one back-up roll.
9. The apparatus of claim 6, with said means for determining the maximum eccentricity of one of said back-up rolls being operative to determine the maximum eccentricity of the other of said back-up rolls in relation to predetermined angular positions of said other back-up roll.
Description:
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 backup 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 roll force AGC to amplify the error.
Back-up roll eccentricity has been a problem on metal rolling mills for many years. However with the trend to wide mills with large diameter back-up rolls the eccentricity problem is becoming somewhat more pronounced. The increase in roll eccentricity, combined with fast acting hydraulic roll force automatic gauge control, presents a major problem on mills such as tandem cold mills and wide plate mills. The gauge control which uses hydraulic roll gap actuators is fast in response (cut-off frequency approximately 20 Hz) and is capable of reacting to changes in roll gap very rapidly. However, the roll eccentricity causes the AGC to correct in the wrong direction so that the eccentricity in the roll causes its profile to be rolled into the work piece. As an axample, if the roll eccentricity causes the piece to be rolled slightly under gauge with no corrective action, the fast acting roll force AGC system will increase the undergauge condition to the extent that the variation in the delivery gauge being rolled will have the same magnitude as the roll eccentricity. The net roll eccentricity which acts on the roll gap at any time is the algebraic sum of four eccentricities for a four high mill and of two eccentricities for a two high mill. It is generally accepted that the eccentricity of a ground roll exhibits itself as a sine wave which completes one cycle for every revolution of the roll. In mathematical terms
E = X sin wt (1)
where
E = Eccentricity acting on gap at time t.
X = Maximum magnitude of eccentricity.
W = Roll angular velocity.
For a four high mill there will be four separate equations of the same form as above, each of which may have different maximum values as well as phase angles. From a practical standpoint work roll eccentricity does exist, however, theoretically it is not exhibited into the roll gap problem, and for that reason the work roll eccentricity problem will be assumed to be negligible.
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 established, 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. Nos. 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 automatic 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 dectector 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 opening at a substantially constant value.
Typically, the roll force gauge control system can be 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:
ΔH = -ΔSD+(Δ F . K) (2)
where:
ΔH = delivery gauge error correction change in roll opening.
ΔF = measured change in roll force from an initial force.
ΔSD = measured change in roll opening or screwdown position from an initial screwdown position.
K = predetermined 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 is maintained constant or nearly constant.
As the head end of the workpiece strip enters each roll stand of the mill, the lock-on roll opening or screwdown position and the lock-on roll separating force are measured to establish what strip gauge should be maintained out of that roll stand. This can be done digitally by the storage of the lock on readings for roll opening position and roll force, and can be done with analog circuitry by signal integrator devices retaining these lock on reading values. 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. In the case of an analog workstrip gauge control system, the relationship of above equation (2) can be employed to maintain a desired delivery gauge from a roll stand. In the case of a digital gauge control system, the workstrip head end or lock on delivery gauge is compared to the present roll force delivery gauge for controlling the gauge leaving the roll stand. 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, as well known to persons skilled in this art, is derived by subtracting the lock-on gauge from the latter delivery gauge, for particularly the operation of a digital gauge control system, as follows:
GAUGE ERROR = (SD - LOSD) + (F-LOF)*K (3)
cross reference to related applications
the present invention is related to the inventions disclosed in U.S. Pat. No. 3,793,860, filed Dec. 4, 1972 by A. V. Silva and in concurrently filed patent application SN 448,869 filed Mar. 7, 1974 by R. Q. Fox, both of which applications are 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 determination of the eccentricity of each back-up roll for predetermined angular positions thereof when there is no workstrip positioned between the work rolls of the roll stand and with each back-up roll being sequentially rotated in relation to the other back-up roll, and the control of the roll stand in accordance with the eccentricity to determine the workstrip product delivery gauge.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 shows a schematic diagram of a roll stand and a roll force gauge control arranged for operation in accordance with the present invention;
FIG. 2 shows a schematic diagram of a tandem rolling mill and gauge control arranged for operation in accordance with the present invention;
FIG. 3 shows a curve to illustrate the eccentricity characteristic of a typical backup roll for a roll stand;
FIG. 4 shows a logic flow chart to illustrate the operation of the back-up roll eccentricity determination of the present invention;
FIG. 5 is a functional illustration of the digital determination of eccentricity and the control of workpiece delivery gauge in accordance with the present invention;
FIG. 6 is a functional illustration of the analog determination of eccentricity and gauge control in accordance with the present invention; and
FIG. 7 is a schematic showing of suitable analog signal apparatus for providing the eccentricity correction to the gauge control for each of the top and bottom back-up rolls.
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 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, however, in certain cases it may also be applicable when no such gauge control is used. Thus, the invention can be suitable 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 tandem mill reduction rolling process, the succeeding 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, or twin drive motors 23 and 24 as shown in FIG. 1, can be 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 roll opening control 26, which could be a pair of screwdown motors or a hydraulic positioning apparatus, position the back-up rolls and thereby apply pressure to the work rolls. A conventional roll opening position detector or encoder 30 provides an electrical signal representation of the roll opening 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.
The gauge control 12 provides automatic gauge or thickness control for the operation of the mill stand 10. The gauge control 12 can include a programmed general purpose process control digital computer system, which is interfaced with the various mill operational 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 12 can also include well known and conventional manual and/or automatic analog controls.
On the basis of these considerations, a suitable digital computer system for a digital embodiment of the on-line roll force gauge control system 12 would be a Prodac 2000 (P2000) sold by Westinghouse Electric Corporation. 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 the 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 the respective position detector 30 for use in roll force gauge control.
3. A position signal from angular transducer or pulse generator 34 in relation to the angle of rotation of the top back-up roll 16.
4. A position signal from angular 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 in the digital computer memory 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 closure through a digital to analog converter. The principal control action outputs from the gauge control system 12 includes a positioning command signal applied to roll opening control 26 for desired roll positioning movement.
Display and printout systems such as numeral display, tape punch, and teletypewriter systems also can be 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 acton on his part.
Generally, the gauge control 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 gauge error correction, i.e., for loaded roll opening and stand delivery gauge correction to the desired value.
As well known to persons skilled in the art, the desired roll opening corresction ΔS RF is calculated to enable roll force gauge control operation in accordance with the following programmed relationship algorithm:
ΔS RF = [(K/P) + 1] * GE (4)
where:
GE = gauge error
K = stand 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 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 12 to identify the various values of P which apply to the mill stand 10 for various grade class and gauge class workpieces under various operation 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 change 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.
DESCRIPTION OF BACK-UP ROLL ECCENTRICITY CORRECTION
The determination of the back-up roll eccentricities of a stand can be done any time desired by the operator when there is not a workpiece strip in that stand. The hardware required consists of a force measuring load cell operative with the stand, a roll opening position detector and rotary transducers operative with each back-up roll. An analog or digital computer can be used in conjunction with the gauge control 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 vertical position for each of predetermined rotational positions for the top back-up roll and for each of predetermined rotational positions for the bottom back-up roll. The rotary transducers 34 and 36 will respectively indicate the exact position of each back-up roll, and the load cell 32 will indicate the force variations caused by the eccentricity of the back-up rolls. The control system records the force reading F for each of the predetermined rotational positions of the respective back-up rolls.
In relation to the curve shown in FIG. 3, the horizontal line R represents the average roll force. This curve is greatly amplified just to point out the problem.
In actual practice a back-up roll average radius may be in the order of 30 inches, whereas the eccentricity may be only about 0.010 inches sin wt or less. However the thickness of the strip being rolled may be in the order of 0.100 inches down to 0.030 inches on a wide tandem cold mill rolling sheet product. Therefore it can be seen that although the eccentricity is small compared to the roll radius it is large compared to the strip thickness.
For the here disclosed determination of back-up roll eccentricity the following assumptions are made:
A. the stand in question has a twin drive arrangement, or suitable apparatus such as clutches to allow turning the top back-up roll without turning the bottom back-up roll and to allow turning the bottom back-up roll without turning the top back-up roll.
B. the stand is equipped with roll force measuring equipment to allow accurate reading of roll force.
C. the stand is equipped with a roll opening control for accurately positioning the roll gap either manually or preferable automatically.
D. it is desirable that the mill be equipped with a suitable computer apparatus which can be used to make the required calculations.
E. the out of roundness of the work rolls is assumed small compared to back-up roll eccentricity and is ignored.
The stand will be assumed to be of a type in which the gap is adjusted for initial set up by moving the top roll, however it can be one in which the gap is controlled by moving the bottom roll.
The top back-up roll eccentricity and its phasing will be first determined in the following manner.
First --close the work rolls to some force which is sufficient to insure that the rolls are well below face. Read a first force F 1 , which will be one point on the top back-up roll eccentricity curve of the form:
F 1 = R + X Sin θ
where R corresponds to an average roll force which would be obtained if θ were allowed to vary over a range of zero to 360° and X is one half the peak to peak variation as θ covers this same range, as shown in FIG. 3.
Second -- open the work rolls and rotate the top back-up roll 90° in the direction it turns when the mill runs in the forward direction. The bottom rolls are maintained in the same exact position as they were when the first force reading was made. Close rolls again to the same position they were for the first force reading and read the second roll force F 2 for this condition.
Third -- open the work rolls again and rotate the top back-up roll an additional 90° so that it is now at a value of 180° from where it was for the initial force reading. Close rolls to same position as previously closed for the readings at θ = θ and θ + 90°, and record this third force reading F 3 .
Fourth -- now there are three independent force readings for three different but known values of the angles of the back-up roll. The bottom rolls were not moved throughout the entire procedure, therefore if it is assumed that the top work roll out of roundness is negligible, the difference in force reading for the different angles of the top back-up roll are due to the eccentricity of the top back-up roll. The following equations now exist.
F 1 = R + X Sin θ (5) F 2 = R + X Sin (θ + 90°) (6)
F 3 = R + X Sin (θ + 180°) (7)
The following trigonometric identities can be used to aid in the solution of these equations.
Sin (θ + 90°) = Cos θ (8) Sin (θ + 180°) = -Sin (9) eta.
Substitution of equation 9 in equation 7 results in
F 3 = R -X Sin θ (10)
Adding together equations 5 and 10, gives the following:
F 1 + F 3 = 2R (11) R = (F 1 + F 3 /2) (12)
substitution of equation 12 in equations 5 and 6 result in
F 1 = (F 1 + F 3 /2) + X Sin θ (13) F 2 = (F 1 + F 3 /2) + X Cos θ (14)
Rearranging equations (13) and (14),
F 1 -(F 1 + F 3 /2) = X Sin θ (15) F 2 -(F 1 + F 3 /2) = X Cos θ (16)
Dividing equation 15 by equation 16 will give
Tan θ =[F 1 - (F 1 + F 3 /2) /F 2 -(F 1 + F 3 /2)] = [2F 1 - (F 1 + F 3 )/2F 2 - (F 1 + F 3 )] (17)
solution of this equation will result in two values of
θ = φ (18) θ = φ + 180° (19)
X can be solved for by use of φ or (φ + 180°). The absolute magnitude of X will be the same in either case, except the sign will be opposite depending on whether φ or (φ + 180°) is used.
Use the absolute value of X to solve for θ. Again two values of θ will be found but only one of them will be the same as one of the values determined before. This will be the correct value of θ.
As an example of the above calculations assume that force values are read of F 1 = 1000 tons, F 2 = 800 tons and F 3 = 800 tons for the three respective force readings. The initial above equations 5, 6 and 7 would then be:
F 1 = 1,000 = R + X Sin θ (20) F 2 = 800 = R + X Sin (θ + 90°) (21)
F 3 = 800 = R + X Sin (θ + 180°) (22) 800 = R - X Sin (23) 1,800 = 2R (24)
R = 900
1,000-900 = 100 = X Sin θ (26) 800-900 = -100 = X (27) -1 = Tan (28) ta.
θ = [135° and 315°]
Solving for X in above equation 26, using θ = 135°, will give
100 = X Sin θ = X Sin 135° (29) 100 = 0.707X (30) (31) 141
substituting this value of X in equation 23 will give
800 = 900 - 141 Sin θ (32) -100 = -141 Sin (33) Sin θ = 0.707 (34)
θ = [45° and 135°]
Therefore θ = 135°
The values X = 141 and θ = 135 are known to define how the eccentricity will exhibit itself. The force value X caused by the eccentricity can be converted directly to a value of roll eccentricity by use of the mill modulus at the value of force measured. The top back-up roll is now positioned at 135° + 180° =315°, so the top back-up roll can be rotated at additional 45° to bring it to θ = zero degrees.
A similar procedure can be followed to determine the bottom back-up roll eccentricity and its phase relationship.
If a programmed digital computer is included as part of the gauge control 12 it can be used to carry out the roll positioning, force readings and the calculation as outlined and to set each of the top back-up roll and the bottom back-up roll to a zero degree phase position. When both rolls have been positioned so that their respective θ = 0, the eccentricity correction system 33 shown in FIG. 1 will then be adjusted so that the eccentricity signals will be entered into the gauge control 12 in phase with the eccentricity and of a magnitude equal to the eccentricity.
In FIG. 4 there is shown a logic flow chart to illustrate the operation of the back-up roll eccentricity determination of the present invention by a programmed digital computer. At step 100 the first force (F1) T is read for the top back-up roll 16, as shown in FIG. 1. At step 102 the work rolls are separated and the top back-up roll is rotated 90°. At step 104 the second force (F2) T is read for the top back-up roll. At step 106 the work rolls are separated and the top back-up roll is rotated another 90°. . At step 108 the third force (F3) T is read. At step 110 is set forth the relationships of above equations (5), (6) and (7) to be used for determination at step 112 of the maximum top back-up roll eccentricity X T and the phase relationship θ T of same, and the top back-up roll is now rotated until θ T equals the zero position. At steps 114 and 126 as shown in FIG. 4, the same procedure is followed in determination of the maximum back-up roll eccentricity X B and the phase relationship θ B of same. The bottom back-up roll is now rotated in position until the angular position of same corresponds to θ B equal to zero. At step 128 the eccentricity correction E T is output to the gauge control 12 as shown in FIG. 1. At step 130 the eccentricity correction E B is output to the gauge control 12.
In FIG. 2 there is shown a tandem rolling mill and gauge control arranged for operation in accordance with the present invention. The first roll stand S 1 is controlled to deliver an absolute gauge or thickness H 1 , as determined through operation of a roll force gauge control operation, in accordance with the relationship
H 1 = SD + (F * K) (35)
where H 1 is the roll force determined actual delivery gauge from the roll stand S 1 , SD is the unloaded roll opening setting as indicated by the roll opening position detector 52, F is the stand roll force as measured by the load cell 55, K is the known mill spring characteristic of the roll stand Sl and the asterisk is the Fortran representation for multiplication. A reference roll force F R is supplied by the operator as an input to the gauge control 54, such that the delivery gauge of the first stand S 1 is controlled by the roll force difference as follows
FR - F = roll force error (36)
and this is applied in a well known manner by the gauge control 54 for correcting the roll opening of stand S 1 through operation of roll opening control 56. The X-ray gauge 58 is operative to adjust the calibration of the roll opening control 56 in accordance with the well known X-ray offset operation. A load cell is operative with each of the other roll stands for the fast acting and well known control of its associated stand for a substantially constant roll force in relation to the measured lock on roll force of each roll stand. An interstand tension sensing device is positioned between the adjacent roll stands as shown in FIG. 2 for providing a well known slower acting substantially constant tension mass flow control for the succeeding roll stands. The load cell operation is fast enough to follow the individual roll stand force changes caused by the respective back-up roll eccentricities of that roll stand. For a typical five stand tandem mill, where the last stand SX is passing work product at 5,000 FPM, the back-up rolls can be in the order of 60 inches in diameter to result in about 5 1/2 rotations and hence 5 1/2 eccentricity signal cycles of each back-up roll per second. A hydraulic roll opening control can follow up to about 20 signal cycles per second, so it can readily follow the 5 1/2 cycles eccentricity signal for the last roll stand SX, and the earlier roll stands operate slower in number of rotations per second.
In FIG. 5 there is functionally illustrated the eccentricity determination and the control of workpiece delivery gauge in accordance with the principles of the present invention. The roll stand 150 to be controlled is provided with suitable sensor devices to provide output signals in accordance with the top back-up roll angular position in relation to the established zero location of the angular position θ T , the bottom back-up roll angular position in relation to the established zero location of the angualr position θ B , the stand roll force F and the unloaded roll opening position SD. The stand spring characteristic K and the workpiece plasticity P are predetermined and known as well understood by persons skilled in this art. At step 152 the eccentricity correction E T is determined by the relationship
E T = X T sin θ T (37)
where E T is the top back-up roll correction and θ T is the measured angular position of the top back-up roll, with the maximum eccentricity X T being established as previously decribed. At step 154 the eccentricity correction E B for the bottom back-up roll is determined by the relationship
E B = X B sin θ B (38)
where E B is the bottom back-up roll correction and θ B is the measured angular position of the bottom back-up roll, with the maximum eccentricity X B being established as previously described. At step 156 the stand gauge error is determined using the relationship of above equation (3) including the top back-up roll correction E T and the bottom back-up roll correction E B . At step 158 the roll opening correction ΔS RF is determined using the relationship of above equation (4).
In FIG. 6 there is functionally illustrated the determination of the respective values of back-up roll eccentricity for each of the top and bottom back-up rolls. The roll stand 151, including a pair of work rolls operative with respective back-up rolls having eccentricity, is provided with well known sensor devices to supply the indicated output signals. The top roll position control 153 can be a closed loop feedback control apparatus responsive to the presently indicated angular position of the top back-up roll for supplying an output signal to control the separation and angular position of the top back-up roll successively as desired, for example, after the reading of roll force F 1 for the initial top back-up roll angular position, then a second angular position including an additional 90° and subsequently followed by a third angular position including a second additional 90° would be provided in accordance with the relationships of above equations (5), (6) and (7). The maximum eccentricity and zero position determination apparatus 155 can be operative to solve the latter relationships of equations (5), (6) and (7 ) for the maxiumum eccentricity value X T and the angular position of the top back-up roll where θ T = 0°, which is then supplied to the top roll position control 153 to result in the top back-up roll being positioned such that θ T = 0°. The present eccentricity determination apparatus 157 is operative to determine the present eccentricity error E T introduced by the present angular position of the top back-up roll in accordance with above equation (37), and to supply this as an output signal to the roll opening control apparatus 159. Similarly, the bottom roll position control 161, the maximum eccentricity and zero position determination apparatus 163 and the present eccentricity determination apparatus 165 are operative to supply the present eccentricity error E B as an output signal to the roll opening control apparatus 159. It should be understood that the roll stand 151 can be operative with a suitable apparatus for providing a desired delivery thickness workpiece therefrom in accordance with above equation (35), such as the roll opening control 26 shown in FIG. 1 which can be a well known feedback control apparatus responsive to an operator provided delivery gauge reference signal HR as compared with a roll force (or X-ray gauge) determined actual delivery gauge H to determine a workstrip delivery gauge error to be corrected. On the other hand, if it is assumed that the initial roll opening setting and the initial roll force conditions were correct, such that the whole length of the workstrip is to be rolled to substantially the same thickness, then the relationship of above equation (2) can be followed as indicated in FIG. 6, with the addition of the respective eccentricity caused thickness errors E T and E B for the top and bottom back-up rolls.
In FIG. 7 there is shown an analog signal apparatus for providing the eccentricity correction, suitable for application to the gauge control 16 as shown in FIG. 1, in relation to each of the top and bottom back-up rolls. A selsyn transmitter 170, control transformer 172 and demodulator 174 will be used for each of the two back-up rolls. The selsyn transmitter 170 will be driven by the back-up roll so that one revolution of the back-up roll corresponds to one revolution of the selsyn transmitter. The selsyn will have one electrical degree equal to one mechanical degree.
With the associated back-up roll set for θ = 0, the control transformer 172 will have its rotor turned to have zero volts on the demodulator output voltmeter 176. This voltage should start to go positive as the angle θ is increased. If it goes negative the control transformer is 180° out of phase and should be recalibrated by rotating it 180°.
Setting the angle on the control transformer takes care of properly phasing the corrective signal with respect to the eccentricity. The magnitude of the eccentricity signal is adjusted by the pot 178 on the demodulator 174 output. The pot 178 should be calibrated such that the full output would be proportional to the maximum eccentricity to be expected, for example, 0.010 inches. Then any lesser amount desired could be set by a suitable adjustment to provide a direct reading on the pot. The output signal from the pot would be introduced into the analog position control for the stand roll opening control. Due to slight differences in back-up roll diameter there can be a drift in the phase relation of the eccentricity of one roll with respect to the other, however, each roll eccentricity signal will take care of its own roll signal so that the sum of the two signals should always be correct in this regard.
The positioning of the respective back-up roll angles during the determination of E T , E B , θ T and θ B can be controlled automatically by the digital computer with suitable sequencing and feedback devices or it can be done manually with suitable position indication. The same is also true of the required vertical positioning of the rolls with respect to each other.
A suitable stand initial roll force range in relation to the determination of the eccentricity correction and phase angle θ would be in order of 500 metric tons. The determination of the eccentricity correction and phase angle relationship for each back-up roll should be made when the back-up rolls are changed or whenever the operator desires this determination be done for some reason.
GENERAL DESCRIPTION OF INSTRUCTION PROGRAM LISTING
In the Appendix there is included an instruction program listing that has been prepared to determine and compensate the eccentricity of each back-up roll in relation to the roll force automatic gauge control operation of a rolling mill in accordance with the here disclosed control system and method. The instruction program listing is written in a programming language suitable for 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. This instruction program listing is included to provide an illustration of one suitable embodiment of the present control system and method that has actually been prepared. This instruction program listing has 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 listing included in the Appendix was prepared in relation to the flow chart shown in FIG. 4. ##SPC1##
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 backup 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 roll force AGC to amplify the error.
Back-up roll eccentricity has been a problem on metal rolling mills for many years. However with the trend to wide mills with large diameter back-up rolls the eccentricity problem is becoming somewhat more pronounced. The increase in roll eccentricity, combined with fast acting hydraulic roll force automatic gauge control, presents a major problem on mills such as tandem cold mills and wide plate mills. The gauge control which uses hydraulic roll gap actuators is fast in response (cut-off frequency approximately 20 Hz) and is capable of reacting to changes in roll gap very rapidly. However, the roll eccentricity causes the AGC to correct in the wrong direction so that the eccentricity in the roll causes its profile to be rolled into the work piece. As an axample, if the roll eccentricity causes the piece to be rolled slightly under gauge with no corrective action, the fast acting roll force AGC system will increase the undergauge condition to the extent that the variation in the delivery gauge being rolled will have the same magnitude as the roll eccentricity. The net roll eccentricity which acts on the roll gap at any time is the algebraic sum of four eccentricities for a four high mill and of two eccentricities for a two high mill. It is generally accepted that the eccentricity of a ground roll exhibits itself as a sine wave which completes one cycle for every revolution of the roll. In mathematical terms
E = X sin wt (1)
where
E = Eccentricity acting on gap at time t.
X = Maximum magnitude of eccentricity.
W = Roll angular velocity.
For a four high mill there will be four separate equations of the same form as above, each of which may have different maximum values as well as phase angles. From a practical standpoint work roll eccentricity does exist, however, theoretically it is not exhibited into the roll gap problem, and for that reason the work roll eccentricity problem will be assumed to be negligible.
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 established, 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. Nos. 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 automatic 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 dectector 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 opening at a substantially constant value.
Typically, the roll force gauge control system can be 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:
ΔH = -ΔSD+(Δ F . K) (2)
where:
ΔH = delivery gauge error correction change in roll opening.
ΔF = measured change in roll force from an initial force.
ΔSD = measured change in roll opening or screwdown position from an initial screwdown position.
K = predetermined 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 is maintained constant or nearly constant.
As the head end of the workpiece strip enters each roll stand of the mill, the lock-on roll opening or screwdown position and the lock-on roll separating force are measured to establish what strip gauge should be maintained out of that roll stand. This can be done digitally by the storage of the lock on readings for roll opening position and roll force, and can be done with analog circuitry by signal integrator devices retaining these lock on reading values. 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. In the case of an analog workstrip gauge control system, the relationship of above equation (2) can be employed to maintain a desired delivery gauge from a roll stand. In the case of a digital gauge control system, the workstrip head end or lock on delivery gauge is compared to the present roll force delivery gauge for controlling the gauge leaving the roll stand. 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, as well known to persons skilled in this art, is derived by subtracting the lock-on gauge from the latter delivery gauge, for particularly the operation of a digital gauge control system, as follows:
GAUGE ERROR = (SD - LOSD) + (F-LOF)*K (3)
cross reference to related applications
the present invention is related to the inventions disclosed in U.S. Pat. No. 3,793,860, filed Dec. 4, 1972 by A. V. Silva and in concurrently filed patent application SN 448,869 filed Mar. 7, 1974 by R. Q. Fox, both of which applications are 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 determination of the eccentricity of each back-up roll for predetermined angular positions thereof when there is no workstrip positioned between the work rolls of the roll stand and with each back-up roll being sequentially rotated in relation to the other back-up roll, and the control of the roll stand in accordance with the eccentricity to determine the workstrip product delivery gauge.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 shows a schematic diagram of a roll stand and a roll force gauge control arranged for operation in accordance with the present invention;
FIG. 2 shows a schematic diagram of a tandem rolling mill and gauge control arranged for operation in accordance with the present invention;
FIG. 3 shows a curve to illustrate the eccentricity characteristic of a typical backup roll for a roll stand;
FIG. 4 shows a logic flow chart to illustrate the operation of the back-up roll eccentricity determination of the present invention;
FIG. 5 is a functional illustration of the digital determination of eccentricity and the control of workpiece delivery gauge in accordance with the present invention;
FIG. 6 is a functional illustration of the analog determination of eccentricity and gauge control in accordance with the present invention; and
FIG. 7 is a schematic showing of suitable analog signal apparatus for providing the eccentricity correction to the gauge control for each of the top and bottom back-up rolls.
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 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, however, in certain cases it may also be applicable when no such gauge control is used. Thus, the invention can be suitable 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 tandem mill reduction rolling process, the succeeding 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, or twin drive motors 23 and 24 as shown in FIG. 1, can be 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 roll opening control 26, which could be a pair of screwdown motors or a hydraulic positioning apparatus, position the back-up rolls and thereby apply pressure to the work rolls. A conventional roll opening position detector or encoder 30 provides an electrical signal representation of the roll opening 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.
The gauge control 12 provides automatic gauge or thickness control for the operation of the mill stand 10. The gauge control 12 can include a programmed general purpose process control digital computer system, which is interfaced with the various mill operational 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 12 can also include well known and conventional manual and/or automatic analog controls.
On the basis of these considerations, a suitable digital computer system for a digital embodiment of the on-line roll force gauge control system 12 would be a Prodac 2000 (P2000) sold by Westinghouse Electric Corporation. 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 the 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 the respective position detector 30 for use in roll force gauge control.
3. A position signal from angular transducer or pulse generator 34 in relation to the angle of rotation of the top back-up roll 16.
4. A position signal from angular 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 in the digital computer memory 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 closure through a digital to analog converter. The principal control action outputs from the gauge control system 12 includes a positioning command signal applied to roll opening control 26 for desired roll positioning movement.
Display and printout systems such as numeral display, tape punch, and teletypewriter systems also can be 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 acton on his part.
Generally, the gauge control 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 gauge error correction, i.e., for loaded roll opening and stand delivery gauge correction to the desired value.
As well known to persons skilled in the art, the desired roll opening corresction ΔS RF is calculated to enable roll force gauge control operation in accordance with the following programmed relationship algorithm:
ΔS RF = [(K/P) + 1] * GE (4)
where:
GE = gauge error
K = stand 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 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 12 to identify the various values of P which apply to the mill stand 10 for various grade class and gauge class workpieces under various operation 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 change 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.
DESCRIPTION OF BACK-UP ROLL ECCENTRICITY CORRECTION
The determination of the back-up roll eccentricities of a stand can be done any time desired by the operator when there is not a workpiece strip in that stand. The hardware required consists of a force measuring load cell operative with the stand, a roll opening position detector and rotary transducers operative with each back-up roll. An analog or digital computer can be used in conjunction with the gauge control 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 vertical position for each of predetermined rotational positions for the top back-up roll and for each of predetermined rotational positions for the bottom back-up roll. The rotary transducers 34 and 36 will respectively indicate the exact position of each back-up roll, and the load cell 32 will indicate the force variations caused by the eccentricity of the back-up rolls. The control system records the force reading F for each of the predetermined rotational positions of the respective back-up rolls.
In relation to the curve shown in FIG. 3, the horizontal line R represents the average roll force. This curve is greatly amplified just to point out the problem.
In actual practice a back-up roll average radius may be in the order of 30 inches, whereas the eccentricity may be only about 0.010 inches sin wt or less. However the thickness of the strip being rolled may be in the order of 0.100 inches down to 0.030 inches on a wide tandem cold mill rolling sheet product. Therefore it can be seen that although the eccentricity is small compared to the roll radius it is large compared to the strip thickness.
For the here disclosed determination of back-up roll eccentricity the following assumptions are made:
A. the stand in question has a twin drive arrangement, or suitable apparatus such as clutches to allow turning the top back-up roll without turning the bottom back-up roll and to allow turning the bottom back-up roll without turning the top back-up roll.
B. the stand is equipped with roll force measuring equipment to allow accurate reading of roll force.
C. the stand is equipped with a roll opening control for accurately positioning the roll gap either manually or preferable automatically.
D. it is desirable that the mill be equipped with a suitable computer apparatus which can be used to make the required calculations.
E. the out of roundness of the work rolls is assumed small compared to back-up roll eccentricity and is ignored.
The stand will be assumed to be of a type in which the gap is adjusted for initial set up by moving the top roll, however it can be one in which the gap is controlled by moving the bottom roll.
The top back-up roll eccentricity and its phasing will be first determined in the following manner.
First --close the work rolls to some force which is sufficient to insure that the rolls are well below face. Read a first force F 1 , which will be one point on the top back-up roll eccentricity curve of the form:
F 1 = R + X Sin θ
where R corresponds to an average roll force which would be obtained if θ were allowed to vary over a range of zero to 360° and X is one half the peak to peak variation as θ covers this same range, as shown in FIG. 3.
Second -- open the work rolls and rotate the top back-up roll 90° in the direction it turns when the mill runs in the forward direction. The bottom rolls are maintained in the same exact position as they were when the first force reading was made. Close rolls again to the same position they were for the first force reading and read the second roll force F 2 for this condition.
Third -- open the work rolls again and rotate the top back-up roll an additional 90° so that it is now at a value of 180° from where it was for the initial force reading. Close rolls to same position as previously closed for the readings at θ = θ and θ + 90°, and record this third force reading F 3 .
Fourth -- now there are three independent force readings for three different but known values of the angles of the back-up roll. The bottom rolls were not moved throughout the entire procedure, therefore if it is assumed that the top work roll out of roundness is negligible, the difference in force reading for the different angles of the top back-up roll are due to the eccentricity of the top back-up roll. The following equations now exist.
F 1 = R + X Sin θ (5) F 2 = R + X Sin (θ + 90°) (6)
F 3 = R + X Sin (θ + 180°) (7)
The following trigonometric identities can be used to aid in the solution of these equations.
Sin (θ + 90°) = Cos θ (8) Sin (θ + 180°) = -Sin (9) eta.
Substitution of equation 9 in equation 7 results in
F 3 = R -X Sin θ (10)
Adding together equations 5 and 10, gives the following:
F 1 + F 3 = 2R (11) R = (F 1 + F 3 /2) (12)
substitution of equation 12 in equations 5 and 6 result in
F 1 = (F 1 + F 3 /2) + X Sin θ (13) F 2 = (F 1 + F 3 /2) + X Cos θ (14)
Rearranging equations (13) and (14),
F 1 -(F 1 + F 3 /2) = X Sin θ (15) F 2 -(F 1 + F 3 /2) = X Cos θ (16)
Dividing equation 15 by equation 16 will give
Tan θ =[F 1 - (F 1 + F 3 /2) /F 2 -(F 1 + F 3 /2)] = [2F 1 - (F 1 + F 3 )/2F 2 - (F 1 + F 3 )] (17)
solution of this equation will result in two values of
θ = φ (18) θ = φ + 180° (19)
X can be solved for by use of φ or (φ + 180°). The absolute magnitude of X will be the same in either case, except the sign will be opposite depending on whether φ or (φ + 180°) is used.
Use the absolute value of X to solve for θ. Again two values of θ will be found but only one of them will be the same as one of the values determined before. This will be the correct value of θ.
As an example of the above calculations assume that force values are read of F 1 = 1000 tons, F 2 = 800 tons and F 3 = 800 tons for the three respective force readings. The initial above equations 5, 6 and 7 would then be:
F 1 = 1,000 = R + X Sin θ (20) F 2 = 800 = R + X Sin (θ + 90°) (21)
F 3 = 800 = R + X Sin (θ + 180°) (22) 800 = R - X Sin (23) 1,800 = 2R (24)
R = 900
1,000-900 = 100 = X Sin θ (26) 800-900 = -100 = X (27) -1 = Tan (28) ta.
θ = [135° and 315°]
Solving for X in above equation 26, using θ = 135°, will give
100 = X Sin θ = X Sin 135° (29) 100 = 0.707X (30) (31) 141
substituting this value of X in equation 23 will give
800 = 900 - 141 Sin θ (32) -100 = -141 Sin (33) Sin θ = 0.707 (34)
θ = [45° and 135°]
Therefore θ = 135°
The values X = 141 and θ = 135 are known to define how the eccentricity will exhibit itself. The force value X caused by the eccentricity can be converted directly to a value of roll eccentricity by use of the mill modulus at the value of force measured. The top back-up roll is now positioned at 135° + 180° =315°, so the top back-up roll can be rotated at additional 45° to bring it to θ = zero degrees.
A similar procedure can be followed to determine the bottom back-up roll eccentricity and its phase relationship.
If a programmed digital computer is included as part of the gauge control 12 it can be used to carry out the roll positioning, force readings and the calculation as outlined and to set each of the top back-up roll and the bottom back-up roll to a zero degree phase position. When both rolls have been positioned so that their respective θ = 0, the eccentricity correction system 33 shown in FIG. 1 will then be adjusted so that the eccentricity signals will be entered into the gauge control 12 in phase with the eccentricity and of a magnitude equal to the eccentricity.
In FIG. 4 there is shown a logic flow chart to illustrate the operation of the back-up roll eccentricity determination of the present invention by a programmed digital computer. At step 100 the first force (F1) T is read for the top back-up roll 16, as shown in FIG. 1. At step 102 the work rolls are separated and the top back-up roll is rotated 90°. At step 104 the second force (F2) T is read for the top back-up roll. At step 106 the work rolls are separated and the top back-up roll is rotated another 90°. . At step 108 the third force (F3) T is read. At step 110 is set forth the relationships of above equations (5), (6) and (7) to be used for determination at step 112 of the maximum top back-up roll eccentricity X T and the phase relationship θ T of same, and the top back-up roll is now rotated until θ T equals the zero position. At steps 114 and 126 as shown in FIG. 4, the same procedure is followed in determination of the maximum back-up roll eccentricity X B and the phase relationship θ B of same. The bottom back-up roll is now rotated in position until the angular position of same corresponds to θ B equal to zero. At step 128 the eccentricity correction E T is output to the gauge control 12 as shown in FIG. 1. At step 130 the eccentricity correction E B is output to the gauge control 12.
In FIG. 2 there is shown a tandem rolling mill and gauge control arranged for operation in accordance with the present invention. The first roll stand S 1 is controlled to deliver an absolute gauge or thickness H 1 , as determined through operation of a roll force gauge control operation, in accordance with the relationship
H 1 = SD + (F * K) (35)
where H 1 is the roll force determined actual delivery gauge from the roll stand S 1 , SD is the unloaded roll opening setting as indicated by the roll opening position detector 52, F is the stand roll force as measured by the load cell 55, K is the known mill spring characteristic of the roll stand Sl and the asterisk is the Fortran representation for multiplication. A reference roll force F R is supplied by the operator as an input to the gauge control 54, such that the delivery gauge of the first stand S 1 is controlled by the roll force difference as follows
FR - F = roll force error (36)
and this is applied in a well known manner by the gauge control 54 for correcting the roll opening of stand S 1 through operation of roll opening control 56. The X-ray gauge 58 is operative to adjust the calibration of the roll opening control 56 in accordance with the well known X-ray offset operation. A load cell is operative with each of the other roll stands for the fast acting and well known control of its associated stand for a substantially constant roll force in relation to the measured lock on roll force of each roll stand. An interstand tension sensing device is positioned between the adjacent roll stands as shown in FIG. 2 for providing a well known slower acting substantially constant tension mass flow control for the succeeding roll stands. The load cell operation is fast enough to follow the individual roll stand force changes caused by the respective back-up roll eccentricities of that roll stand. For a typical five stand tandem mill, where the last stand SX is passing work product at 5,000 FPM, the back-up rolls can be in the order of 60 inches in diameter to result in about 5 1/2 rotations and hence 5 1/2 eccentricity signal cycles of each back-up roll per second. A hydraulic roll opening control can follow up to about 20 signal cycles per second, so it can readily follow the 5 1/2 cycles eccentricity signal for the last roll stand SX, and the earlier roll stands operate slower in number of rotations per second.
In FIG. 5 there is functionally illustrated the eccentricity determination and the control of workpiece delivery gauge in accordance with the principles of the present invention. The roll stand 150 to be controlled is provided with suitable sensor devices to provide output signals in accordance with the top back-up roll angular position in relation to the established zero location of the angular position θ T , the bottom back-up roll angular position in relation to the established zero location of the angualr position θ B , the stand roll force F and the unloaded roll opening position SD. The stand spring characteristic K and the workpiece plasticity P are predetermined and known as well understood by persons skilled in this art. At step 152 the eccentricity correction E T is determined by the relationship
E T = X T sin θ T (37)
where E T is the top back-up roll correction and θ T is the measured angular position of the top back-up roll, with the maximum eccentricity X T being established as previously decribed. At step 154 the eccentricity correction E B for the bottom back-up roll is determined by the relationship
E B = X B sin θ B (38)
where E B is the bottom back-up roll correction and θ B is the measured angular position of the bottom back-up roll, with the maximum eccentricity X B being established as previously described. At step 156 the stand gauge error is determined using the relationship of above equation (3) including the top back-up roll correction E T and the bottom back-up roll correction E B . At step 158 the roll opening correction ΔS RF is determined using the relationship of above equation (4).
In FIG. 6 there is functionally illustrated the determination of the respective values of back-up roll eccentricity for each of the top and bottom back-up rolls. The roll stand 151, including a pair of work rolls operative with respective back-up rolls having eccentricity, is provided with well known sensor devices to supply the indicated output signals. The top roll position control 153 can be a closed loop feedback control apparatus responsive to the presently indicated angular position of the top back-up roll for supplying an output signal to control the separation and angular position of the top back-up roll successively as desired, for example, after the reading of roll force F 1 for the initial top back-up roll angular position, then a second angular position including an additional 90° and subsequently followed by a third angular position including a second additional 90° would be provided in accordance with the relationships of above equations (5), (6) and (7). The maximum eccentricity and zero position determination apparatus 155 can be operative to solve the latter relationships of equations (5), (6) and (7 ) for the maxiumum eccentricity value X T and the angular position of the top back-up roll where θ T = 0°, which is then supplied to the top roll position control 153 to result in the top back-up roll being positioned such that θ T = 0°. The present eccentricity determination apparatus 157 is operative to determine the present eccentricity error E T introduced by the present angular position of the top back-up roll in accordance with above equation (37), and to supply this as an output signal to the roll opening control apparatus 159. Similarly, the bottom roll position control 161, the maximum eccentricity and zero position determination apparatus 163 and the present eccentricity determination apparatus 165 are operative to supply the present eccentricity error E B as an output signal to the roll opening control apparatus 159. It should be understood that the roll stand 151 can be operative with a suitable apparatus for providing a desired delivery thickness workpiece therefrom in accordance with above equation (35), such as the roll opening control 26 shown in FIG. 1 which can be a well known feedback control apparatus responsive to an operator provided delivery gauge reference signal HR as compared with a roll force (or X-ray gauge) determined actual delivery gauge H to determine a workstrip delivery gauge error to be corrected. On the other hand, if it is assumed that the initial roll opening setting and the initial roll force conditions were correct, such that the whole length of the workstrip is to be rolled to substantially the same thickness, then the relationship of above equation (2) can be followed as indicated in FIG. 6, with the addition of the respective eccentricity caused thickness errors E T and E B for the top and bottom back-up rolls.
In FIG. 7 there is shown an analog signal apparatus for providing the eccentricity correction, suitable for application to the gauge control 16 as shown in FIG. 1, in relation to each of the top and bottom back-up rolls. A selsyn transmitter 170, control transformer 172 and demodulator 174 will be used for each of the two back-up rolls. The selsyn transmitter 170 will be driven by the back-up roll so that one revolution of the back-up roll corresponds to one revolution of the selsyn transmitter. The selsyn will have one electrical degree equal to one mechanical degree.
With the associated back-up roll set for θ = 0, the control transformer 172 will have its rotor turned to have zero volts on the demodulator output voltmeter 176. This voltage should start to go positive as the angle θ is increased. If it goes negative the control transformer is 180° out of phase and should be recalibrated by rotating it 180°.
Setting the angle on the control transformer takes care of properly phasing the corrective signal with respect to the eccentricity. The magnitude of the eccentricity signal is adjusted by the pot 178 on the demodulator 174 output. The pot 178 should be calibrated such that the full output would be proportional to the maximum eccentricity to be expected, for example, 0.010 inches. Then any lesser amount desired could be set by a suitable adjustment to provide a direct reading on the pot. The output signal from the pot would be introduced into the analog position control for the stand roll opening control. Due to slight differences in back-up roll diameter there can be a drift in the phase relation of the eccentricity of one roll with respect to the other, however, each roll eccentricity signal will take care of its own roll signal so that the sum of the two signals should always be correct in this regard.
The positioning of the respective back-up roll angles during the determination of E T , E B , θ T and θ B can be controlled automatically by the digital computer with suitable sequencing and feedback devices or it can be done manually with suitable position indication. The same is also true of the required vertical positioning of the rolls with respect to each other.
A suitable stand initial roll force range in relation to the determination of the eccentricity correction and phase angle θ would be in order of 500 metric tons. The determination of the eccentricity correction and phase angle relationship for each back-up roll should be made when the back-up rolls are changed or whenever the operator desires this determination be done for some reason.
GENERAL DESCRIPTION OF INSTRUCTION PROGRAM LISTING
In the Appendix there is included an instruction program listing that has been prepared to determine and compensate the eccentricity of each back-up roll in relation to the roll force automatic gauge control operation of a rolling mill in accordance with the here disclosed control system and method. The instruction program listing is written in a programming language suitable for 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. This instruction program listing is included to provide an illustration of one suitable embodiment of the present control system and method that has actually been prepared. This instruction program listing has 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 listing included in the Appendix was prepared in relation to the flow chart shown in FIG. 4. ##SPC1##