US3444713A - Volume flow automatic gage control - Google Patents

Description

May 20, 19 9 Sheet of2 Filed July 15, 1966 304! 205.50 33 ciouiSom L S u WA PM 1 mt m M M E A 0 V B U W U F A HT u 502;: T 8 n m. 0 Al E i A W M4 332 @5305 A ow fl NW mm Tom i u L L a u 3. m

United States Patent VOLUME FLOW AUTOMATIC GAGE CONTROL Peter J. Barnikel, New London, Conn., assiguor to General Dynamics Corporation, New York, N.Y., a corporation of Delaware Filed July 15, 1966, Ser. No. 565,526 Int. Cl. B21b 37/12 US. Cl. 72-8 15 Claims ABSTRACT OF THE DISCLOSURE A control system for the output gage in a rolling mill operating in accordance with the constant volume flow principle uses the input and output speed of the material together with the actual input thickness of the material to calculate the output thickness of the material and generate an error signal controlling the working means.

This invention relates to processes where material is passed between adjustable dies or rolls or other working means for the purpose of reducing the thickness of that material in a dimension transverse to the direction or passage of the material through the working means. More particularly, this invention relates to rolling mills wherein material such as steel is passed between the rolls of the stand for the purpose of obtaining a specific thickness of gage in the output product.

A number of factors influence the gage of the output product. Among these are the thickness and thickness variations of the incoming product, the resistance to deformation of the incoming product as governed by its temperature, metallurgical properties, etc., and the characteristics of the mill stand employed to produce the product. If there are no variations in thickness or resistance to deformation of the incoming product, an output product with no gage variation could be produced on a quality mill stand. These input variations occur, however, and the compliance of the mill stand permits the roll separation to change thus producing variations in the outgoing product gage.

In the past, a number of methods have been employed in an attempt to achieve the desired output gage over the length of the output rolled product. Those methods have varied greatly in complexity, cost, and the tolerance to which they can hold the output product. A fundamental approach taken was to make the mill stand massive and stiff. Later, continuous gaging of the output product was employed to adjust the roll separation in an attempt to maintain gage. This method proved unsatisfactory in most applications because of the transport delay between the action of the rolls on the strip and the time the strip is gaged. A well known gage control method infers changes in roll separation during the rolling process by measuring the roll separating force and adjusting the roll separation on this basis to maintain output gage. Other systems such as taught in Freedman et al. United States Patent No. 3,197,986, use a predictive approach wherein the characteristics of the incoming product are measured and, when that portion of the strip is in the roll bite, adjustments in roll gap are made to produce the desired output product.

A number of systems have been proposed which employ a continuity of volume flow principle. That is since there is no place to store material in the roll bite, the instantaneous volume flow of material entering the rolls must equal the instantaneous volume flow leaving the rolls. As examples of such systems, United States Patents Nos. 3,015,- 974, 3,054,311 and 3,121,354 to Orbom et al., Murtland and Weremeychik, respectively, propose to use the constant volume flow principally to compute the entrance 3,444,713 Patented May 20, 1969 gage whcih hypothetically would be necessary to provide the desired exit gage. Those proposals have the shortcoming that such hypothetically necessary entrance gage is not a direct measure of the correction in roll bite which must be effected to attain the desired output gage. It is preferable as proposed in United States Reissue Patent No. 25,075 to Hessenberg to compute the inferred deviation of the output gage from a desired value and to employ that deviation to efiect a correction in the roll 'bite. The Hessenberg proposal is, however, disadvantageous in that the correction signal is obtained by analog division of one dynamically varying quantity by another, and division cannot be effected as accurately by analog means as can addition or subtraction.

A further proposal for a gage control system using the constant volume principle is contained in United State Patent No. 3,000,243 to Stringer. Also, copending application Serial No. 525,036 filed Feb. 4, 1966 now Patent No. 3,387,471, issued June 11, 1968 and owned by the assignee hereof discloses a gage control system based on the constant volume principle.

An object of this invention is to provide a gage control system based on the constant volume flow principle which will produce a product with improved gage and yet be economically practical for use on small low production mills as well as on high production mills.

Another object of this invention is to provide a gage control system of such sort wherein a correction signal representative of the inferred deviation in output gage from a desired value is produced by a computaton which does not involve either the multiplication or the division of two or more dynamically varying input quantities.

Still another object of the invention is to provide for monitoring of the operation of a primary gage control system of the sort described by a follow-on thickness gauging system compatible with such primary system.

These and other objects are realized in accordance with the invention by providing a gage control system which responds in the following manner to signals which are measures of the input speed, output speed, and desired output thickness value of material passing through working means to be reduced in thickness by such means in a dimension transverse to the direction of passage and in an amount controlled by the adjustment of the working means. From the signals which are measures of the input speed, output speed and the desired output thickness, the system derives a signal which is a measure of an output length of the material and which varies directly with the desired output thickness. That output length signal is then combined in subtractive relation with a signal which is a measure of the actual input thickness of the material. The resulting signal is a correction signal representative of the deviation in the output thickness of the material from the desired output thickness therefor. By the use of appropriate signal-proportioning techniques, the magnitude of that correction signal may be made to represent such deviation to the same scale as the desired output thickness is represented by the magnitude of the signal corresponding thereto. The correction signal is adapted to control the adjustment of the working means so as to produce exact or approximate correspondence between the desired output thickness and the actually obtained output thickness of the material.

While the invention is specifically disclosed herein as embodied in a gage control system for a rolling mill installation, it is to be understood that the invention has other applications as, say, in gage control systems for wire drawing installations, tube drawing installations and so on.

For a better understanding of the invention, reference is made to the following description of an exemplary embodiment thereof (in the form of a gage control system for a rolling mill) and to the accompanying drawings wherein:

FIG. 1 is a schematic view of a single stand rolling mill and of agage control system according to the invention; and

FIG. 2 is a timing diagram explanatory of the operation of the gage control system of FIG. 1.

Considering first the mathematics appertaining to the gage control system described herein, because the volume flow of strip entering a rolling mill must equal the volume flow of strip leaving the mill, and because the entering and leaving widths of the strip can be considered to be substantially the same, it follows that:

where G =the actual instantaneous gage of the product entering the mill V =the actual instantaneous velocity of the product entering the mill G =the actual instantaneous gage of the product leaving the mill V =the actual instantaneous velocity of the product leaving the mill Ordinarily, the variation in gage can be considered negligible over the period of interest. In that instance and when:

=the nominal gage of the product entering the mill =the ordered or desired gage of the product leaving the mill where AG is the actual deviation in input gage from 6 and A6 is the inferred deviation in output gage from the ordered gage 6 We can postulate a velocity value V which is based on the achievement of ordered output gage from nominal input gage, and which is given by the expression:

V =V,fi Evidently:

V =7 +AV Now using (4) to substitute for V in (2) and then expanding (2), we obtain:

a fV1dl+AG fV dt=azfvzdt+AGgfi zdt +E IAV dz+AG IAV dr (5) But, as indicated by Expression 3, V =V Z$ Therefore,

G' 1J V1dl=( 2W2dt and, (5) reduces to:

To simplify the mechanics of solution, let

.l 1 2 Then:

which upon being divided by '5 yields AGI=i /(V +AV2)dt+ fAV dt (r2 which in turn can be rewritten as:

AG' AG, /AV,dt- /(V +AV )dt (10) From Equation 10, it is evident that the equation establishes an exact value for the term AG when all the other terms in the equation are fixed. It is also evident that, assuming the left-hand side of (10) has a fixed constant value, the value of term AG varies vinversely with that of the term (V +AV Let us now consider the effect on AG of omitting from (10) the right-hand term AV while the left-hand side of (10) is held constant. If AV is, say, positive and 5% of V the omission of AV requires (for continuing balance of Equation 10) that A6 assume a new value which will be about 5% greater than that which AG had before AV was omitted. That is, the omission of the right-hand term AV causes an error of about 0.05 A6 in the value of A6 as determined by Equation 10. Now, the value of AG may he, say 5% of 5 Hence, as expressed in relation to fi such error is about 0.05 (0:05 (5 or about 0.25% of E The foregoing figure of 0.25% is well within the gaging accuracy required for even high quality strip. Also, as A6 becomes a smaller and smaller percentage of (5 there -is a corresponding decrease in the error as a percentage of E which is produced by omission of the right-hand term AV For practical purposes, therefore, the right-hand term AV in Equation 10 can be neglected so that such rigorous equation can be rewritten as the approximate equation:

Equation 11 can be further simplified as follows. From 3, it is evident that:

f7 dt /V dz 2 2 1 and, by applying (12) to (11), we obtain:

A2 2 AG, jAV dt E2 fV dt (13) Then, applying (7) to (13), the expression simplifies to:

and, by transposing terms in (14), we get:

E [AG fAV dt] AG (15) From (4), it follows in (15) that:

[AV- 1ft: f V dt W d:

and, applying (12) to the right-hand term of (16), we get:

Adverting again however, to the step indicated by (7) of setting fV dr equal to GT we can rewrite (17) as:

fV2dI=IV2dt-@1 whence Expression 15 simplifies to:

Equation 15 or Equation 18 or one equivalent to either provides the mathematical basis for gage control systems according to the invention. The quantities directly involved in (18) are the nomical input gage E the ordered or desired output gage fi the deviation A6 of the actual input gage from the nominal value G1 for the input gage, the integral (f) of the actual output speed V with respect to time over a selected time period and the correction signal AG which is the inferred deviation in output gage from its ordered or desired value fi When Equation 18 is utilized for a gage control system according to the invention, the quantities and G are provided by inputs to the system which are each of constant but resettable value. Thus, the only dynamically varying input quantities involved in the application of (18) to a gage control system are the inputs which represent AG and -JV dt, respectively.

As compared to earlier prior art systems proposing to control output gage in accordance with a correction signal AG representinginferred deviation of output gage from desired value, a system based on Equation 18 or an equivalent equation is advantageous because the correction signal A6 of the system is obtained in a manner not requiring either the division or the multiplication of two dynamically varying inputs. To so avoid multiplication or division of dynamically varying quantities is particularly desirable when the gaging equation is solved by an analog computing system because it is difficult if not impossible by analog techniques to carry out multiplication or division of dynamic quantities to the accuracy with which such quantities can be added or subtracted by analog means. While in Equation 18, it might be con-- sidered that time t is a dynamic quantity and, hence, that the operation IV dt is equivalent to a multiplication of two dynamic quantities, ordinarily there is no difficulty even in a low cost analog system in accurately integrating a variable input quantity with respect to time.

Although (apart from time t), only the quantities '6 E A6 V and A6 are directly involved in Equation 18, the input speed V is indirectly involved. That is, it will be evident from the foregoing mathematical derivation that Equation 18 was arrived at by utilizing Equation 7 wherein the quantity fv dt is set equal to quantity 'GT That condition specified by Equation 7 is also a boundary condition for Equation 18 in that the time period of integration for the quantity fv a't in (18) is the same as and is determined by the period of integration required for the quantity fV dt to equal E The determination in such wise of the integration period for jV dt enables a gage control system operating in accordance with Equation 18 to provide an accurate correction signal AG despite changes in V or V or in the ratio of V to V Considering alternative ways of stating the gaging Equation 18, because the actual input gage G is the sum of the nominal input gage G1 and the actual deviation AG; of the input gage from nominal value. Expression 18 can be rewritten as:

Also, the quantities fv dt and fV dt correspond, respectively, to a length L of material entering the rolls and a length L of material exiting from the rolls during a time interval of which the value is determined by V and @2- Hence, the gaging equation can also be written as:

G2 T 1 2l 2 (21) where, in both (20) and (21), the length L is determined by setting the length L equal to G Lastly, while the inferred deviation in output gage from desired value has so far been denoted by the symbol AG from now on it will be designated by the symbol A6 in order to distinguish such inferred deviation from the actual deviation A6 in output gage from the desired value E Turning now to the specifics of the apparatus disclosed herein, FIG. 1 shows an embodiment of this invention applied to a single stand 4-high rolling mill. It is understood that the system could readily be applied to tandem mills as well or any rolling process wherein tension is maintained in the strip on either side of the control stand.

The drawing shows a schematic representation of a 4- high mill 8 rolling from left to right. The strip 7 is taken from pay ofr reel 5, reduced in stand 8, and recoiled on take-up reel 6. Tachometer wheels 3 and 4 are placed in contact with the strip at the input and output sides of the mill stands, respectively. Wheels 3 and 4 are drivers, respectively, of pulse tachometers-IS and 16, which produce pulse trains with repetition rates proportional to the input and output velocity of the strip. Tachometer 15 drives a single shot multivibrator 17 producing a controlled pulse of known width and amplitude for each pulse produced by tachometer 15. The output of single shot 17 is then fed to analog integrator 19'. The output of this integrator is equal to fv dt. In a similar manner, output pulse tachometer 16 drives single shot multivibrator 18, which in turn feeds integrator 20 to produce at the output of integrator 20 a signal proportional to fv dt. The output of integrator 19 is compared with the desired output gage GT as set on potentiometer 25, in the coincidence circuit comprised of amplifier 21, Zener diode 22, and resistors 23 and 24. When -fv dt is equal in magnitude to E the condition required for the gaging equation to apply, the circuit triggers producing a voltage at the output of amplifier 21 which is employed to block single shots 17 and 18 thus bringing the inputs of integrators 19 and 20 to zero. These integrators then hold their output values until they are reset for the next sampling cycle.

Since is equal in magnitude to fv dt, the signal representing is passed through amplifier 26 and potentiometer 27 to be modified by the factor fi /fi and produce a signal proportional to -f17 dt. From Equations 3 and 7, it will be evident that 1 1 2 412 is equal to signal level. Hence, in lieu of energizing potentiometer 27 by a G r signal from amplifier 26, element 27 may be energized from a negative voltage source and the potentiometer 27 set to yield directly an output of a -'G signal level.

The deviation AG from nominal input gage E is measured by gauge 1, which may take the form of an X-ray gauge. The deviation signal A6 is fed through a polarity-reversing and time-delay mechanism 55 (later described in more detail) of which the output is a-AG signal. The mechanism 55 (in combination with other components) synchronizes the introduction of the gage deviation signal AG into the computation of AG when that portion of the strip which was measured by the gauge 1 is in the roll bite. The output of potentiometer 27 is summed with -AG in amplifier 29. The output fv dt of integrator 20 is in turn summed with AG in amplifier 28. The output of amplifier 28 is modified with coefiicient potentiometer 30 by the coefficient fi /fi to produce a primary correction signal proportional to AG Since the AGgi signal is developed by a sampling process and is valid under the conditions when -fv dt= care must be exercised in employing A6 to achieve adjustment of rolling parameters to bring the output product on gage. One satisfactory method is to employ the output from amplifier 21, which signals the fact that fv dr= to trigger single shot multivibrator 32. The output of single shot 32 gates amplifier 31 open for a period equal to the width of the single shot output pulse. Ignoring for the moment the effect of the shown input to amplifier 31 from integrator 57, the output during that period of amplifier 31 is a control signal pulse AG with an energy level determined by the magnitude of A6 The A6 pulse of each sample period is then integrated in integrator 50 to produce a roll gap adjustment command signal fAG which is used for adjusting the roll gap setting to correct for deviations in the output gage of the strip from the desired value E This controlled time integration at the end 'of the sampling insures that the roll gap adjustments made will be proportioned to A6 and independent of strip velocity, which would not be the case if continuous integration were employed.

The output of integrator 50 is fed as a roll gap correction signal JAG into the conventional screwdown position loop formed by dilTerential amplifier 51, screwdown actuator 9, and roll gap feedback sensor 10. As shown, the inputs to amplifier 51 are the JAG screwdown adjustment command signal, a screwdown preset command signal and a feedback signal from device 10. The output of amplifier 51 is an error signal e which actuates the positioning of the screwdown actuator.

FIG. 1 shows in schematic form a conventional screwdown actuating system. In practice, however, the slow response of the screwdown actuators would tend to limit the performance which could be achieved by the gage control system, and a fast response actuator such as that described in pending United States continuation-in-part application Ser. No. 405,749 now Patent No. 3,355,925, issued Dec. 5, 1967 (owned by the assignee hereof) would be more desirable.

In the system of FIG. 1, the input gauge 1 is located, say, approximately 3' ahead of the roll bite, and it is desired to sample and obtain an inferred gage deviation output for approximately every foot of strip input. Those conditions establish the number of signal storage devices required in the time delay mechanism. As shown in FIG. 1, the input thickness gage 1 develops in a well known manner a signal A6 proportional to the actual deviation in input gage from the nominal input gage E. The signal 4G is fed to the integrator unit 55 comprised of a group of integrators 14-1, 14-2, 14-3 and 14-4. Those integrators are employed in their reset mode, i.e., switches 12-1 through 12-4 operate in consecutive order to set the value AG into the integrators as an initial condition while the switches are closed. When those switches are open, the integrators hold the values set into them. Those values are then read out at some later time when switches I l-1 through 11-4 are closed in consecutive order.

The sy nchronizing switches 12-1 through 12-4 and 11-1 through 11-4 are mercury wetted reed contacts. Contacts 11-1 through 11-4 are arranged around rotating disc 11 in synchronizing switch assembly 54 at the positions indicated by the corresponding numbered circles disposed around disc 11. Likewise, contacts 12-1 through 12-4 are arranged around disc 12 in assembly 54 at the position indicated by the corresponding numbered circles surrounding disc 12.

The shaded portion of each of discs 11 and 12 is magnetized, and activates each associated reed switch when the magnetized portion is in juxtaposition with the switch. The cooperative relations between the magnetized sector of disc 11 and switches 11-1 through 11-4 and between the magnetized sector of disc 12 and switches 12-1 through 12-4 are relations indicated by the dot-dash lines 11a and 12a, respectively. The switching arrangement shown employs the'group 12 switches to set AG into the integrators and the group 11 switches to read out the corresponding value of AG after a delay corresponding to 270 rotation of the synchronizing switch assembly shaft 56.

Shaft rotation of discs 11, 12 and 13 is synchronized to the input strip speed by driving shaft 56 with a stepping motor 53 which is in turn driven by the input pulse tachometer 15 through a pulse amplifier 52. Where the physical parameters of the rolling mill (e.g. space availability, speed, distance d desired sample length, etc.), permit, the synchronizing switch assembly could be driven by tachometer wheel 30 through a suitable gearing arrangement.

Disc 13 in synchronizing switch assembly 54 has associated switches 13-1 through 13-4 which provide cycle control by acting through lea-d 57 to reset integrators 19 and at the end of each cycle and to then activate those integrators to start the next cycle. As shown, switches 13-1 through 13-4 are wired in parallel and are represented in the drawing by the corresponding numbered circles around disc 13. (Details of the integrator reset arrangement are conventional and, hence, are not shown in FIG. 1.) The resetting of integrator 19 to zero causes the coincidence circuit composed of amplifier 21, Zener diode 22, and resistors 23 and 24 to return to its untriggered state, thus unblocking single shots 17 and 18 and permitting the integrating cycle of integrators 19 and 20 to start again.

The system lends itself to the use of conventional follow-on gage control techniques to insure obtaining ordered gage in the event that a mismatch of tachometers, tachometer wheels, or gains in integrators 19 and 20, etc. would tend to cause a steady-state error in AG This correction is accomplished by combining in amplifier 31 the integral of the actual deviation AG from the ordered output as measured by the follow-on output gauge 2 with the inferred value of gage deviation AG If the value of inferred gage deviation A6 determined by the basic system has no steady state error, the output gage deviation measured by gauge 2 will be zero when the obtained output gage is at desired value which results from the roll gap adjustment action bring AG;, to a value of zero. Any steady state error in the determination of AG will be measured as an output gage deviation A6 by output gauge 2 and combined with the inferred gage error A6 in amplifier 31 to bring the output product to ordered gage G Care must be taken in applying the gage deviation signal A6 measured by output gauge 2 in order to prevent excessive hunting of the overall gage control system. One method of applying the follow-on type gage correction is shown in FIG. 1. The output of pulse tachometer 16 triggers single shot multivibrator 46. The output of single shot 46 is in turn integrated by integrator 33 to produce a signal proportional to the quantity fv dt. When that signal is equal to the distance d between the roll bite and the follow-on gauge 2, as set on potentiometer 42, coincidence is sensed by the circuit consisting of amplifier 38, Zener diode 36 and resistors 34 and 40. The output of amplifier 38 triggers single shot multivibrator 44 to gate open amplifier 49 for a period equal to the width of the single shot pulse from element 44 thus permitting the gage deviation as measured by the follow-on gauge 2 to be integrated by integrator 57 to produce from the integrator a held output fAG The held output of integrator 57 is then additively combined with the inferred gage deviation AG in amplifier 31 to determine the energy level of control signal pulse AG The A6 pulse of each sample period of the basic system is then integrated in integrator 50 to produce a change in the roll gap adjustment command signal -fAG The efiect of the resulting roll gap adjustment is to produce a change in the output gage such that AG as determined by the basic system is equal to in magnitude but opposite in sign to fAG the held output of integrator 57. This action is repeated each sampling period of follow-on gauge 2 until (while integrator 57 continues to provide its output of fAG the measured value of A6 has been reduced to zero and the steady-state value of A6 is equal in magnitude and opposite in sign to the steadystate error of the basic system. Perturbations in the output gage are then seen as changes in the value of AG and produce control signal pulses AG with an energy level determined by the value of the change in A6 to eifect control in the manner previously described. Additional time is allowed for the follow-on corrective action just described to take place before initiating the next follow-on on sample period. That is, potentiometer 43 is set to a value proportional to d plus an increment Aa large enough to provide under all circumstances the time necessary for corrective action to take place. When the output of integrator 33 and the value set on potentiometer 43 coincide, the coincidence circuit consisting of amplifier 39, Zener diode 37, and resistors 35 and 41 triggers. The

output of amplifier 3 then triggers single shOt multivibrator 45 which in turn activates a reed relay composed of inductor 48 and a mercury wetted reed switch 47. Switch 47 acts through lead 58 to reset integrator 33- to zero and reinitiate the follow-on gage sampling process.

The overall operation of the FIG. 1 system will now be described with reference to the timing diagram of FIG. 2. That diagram illustrates schematically and in a qualitative manner some of the more important waveforms involved in the operation. The shown waveforms are idealized in shape and in other respects such as, for example, omitting the small time delay involved in changing an integrator from its hold-signal state to its reset state.

Some preliminaries to a run of strip 7 through the mill 8 are as follows. The input thickness gauge 1 is set in accordance with the nominal input thickness E of the strip so that the AG signal from the gage is a true measure of the deviation in the actual input thickness of the strip from the value E Moreover, the gauge 1 is spaced ahead of the roll bite of mill 8 by a distance d such that the full travel (at any speed) of the strip 7 through that distance causes the disc -13 to be driven through one full revolution.

The screwdown actuator 9 is preset to provide for mill 8 a roll bite which should yield on the output side of the mill an output gauge of strip 7 which approximates the desired output gage T1}. The follow-on page is set in accordance with E to provide an output A6 signal which is a true measure of the deviation in the actual output gage of the strip from the value 6 The potentiometers 25, 27 and 30 are set to tap settings providing signal levels proportional to 6 fi /fi and d /E respectively.

Following those preliminaries, the mill 8 and its gauge control system are turned on, and the strip 7 is passed through the mill to be reduced in gage. In so passing through the mill, the strip 7 is assumed to have input and output speeds relative to the mill which are of a typical value, and which are designated as V and V respectively.

Consider at a given moment of operation a section S of strip which has a length equal to A1 of d and which is positioned at that moment to have its leading edge directly under gauge 1. During the time required for such leading edge to travel from gauge 1 into the roll bite of mill 8, the timing disc 13 is driven by the means earlier described to undergo one full revolution. In the course of that revolution, the magnetized sector of disc 13 causes the switches 13-1 through 13-4 to successively develop four respective trigger pulses (FIG. 2, waveform A) by which the integrators 19 and 20 are reset a corresponding number of times to provide four sampling cycles within 1 period p of revolution of the disc. Each sampling cycle is of the same duration c. Because the speed of rotation of disc 13 is proportional to the input speed V of the strip, the time quantities p and c are each inversely proportional to V As shown by waveform A, the duration of the period p of the timing disc 13 is an integral multiple of the duration of each sampling cycle.

During the initial portion of each sampling cycle, multivibrator .17 generates constant energy pulses at a rate proporional to V and those pulses are integrated by integrator -19 to develop at its output a progressively increasing signal fV dt (waveform B). When the magnitude of that signal arrives at time t at coincidence with the G2 level established by the setting of potentiometer 25, amplifier 21 produces a blocking square wave (waveform C) of which the leading edge occurs at time t.

The input speed V of the strip may vary between a normal minimum limit V and a normal maximum limit V For the maximum normal input speed, the V integral is fV "dt and, for the minimum normal input speed, the V integral signal is --fV 'dt. In waveform B, the typical V integral signal is shown by a solid line,

10 and the minimum and maximum V and V integral signals are shown by dot-dash lines.

A typical G' signal level is shown in waveform B by a solid line. Dotted lines are employed to show the signal levels corresponding to a nominal minimum setting 'G and to a nominal maximum setting G Because, in waveform B, the integral signal may have various slopes as shown and the signal level E of desired output thickness may also vary as represented by the different levels of the solid and dotted horizontal lines, the arrival at coincidence of the magnitude of the integral signal with the signal level may occur at various times of which some are indicated by the intersection points (VIII: 82): 1 2) 1: 2): 1 g2 (V1,, g2) and (v g appearing from left to right in waveform B. Each of these points corresponds to a different possible time of occurrence t of the leading edge of the blocking square wave waveform C). The one of such points which is earliest in time is the point (v g which corresponds to a time t, and which occurs when (a) V is of maximum value V to yield an integral fV "dt of maximum slope, and (b) the setting for the desired output gauge is of the minimum value E The one of such points which is latest in time is the point (v g which corresponds to a time t" and which occurs when (a) V is of minimum value V to yield an integral signal J'V 'dt of minimum slope, and (b) the setting for desired output gauge is of the maximum value G Hence, the time t of occurrence of the leading edge of the square wave may normally vary (waveform C) between an early limit t and a late limit 2''.

Turning now to waveform D, during the initial portion of each sampling cycle, the multivibrator 1-8 generates constant energy pulses at a rate proportional to V and those pulses are integrated with respect to time by integrator 20 to produce an output signal -fV dt of progressively increasing magnitude. The integrating action of element 20- is arrested by the blocking square wave from amplifier 21 (waveform C) so that the signal fV dt is stabilized at the value it reaches the time t of occurrence of the leading edge of the square wave. Thereafter, the square wave acts to hold such signal at its stabilized value until integrator 20 is reset at the end of the sampling cycle.

In waveform D, an integral signal -fV dt of typical value is shown by a solid line which reaches at the time t the signal level 1 which corresponds to the typical level G in waveform B, and at which level the integral signal becomes stabilized in value by the action of the blocking square wave. Such typical V integral signal fV dt is a concomitant of the typical V integral signal fV dz shown in waveform B. The minimum and maximum V integral signals -fV dt and fV "dt of waveform B have as concomitants, nominal, minimum and maximum V signals designated as, respectively, fv dt and -J"v "dt and represented by dot-dash lines.

Consider now the effect in waveform D of changing the speed of the strip so as to change the slope of the signals fV a't and JV dt while maintaining constant in waveform B the G signal level. Assume that the change in speed is from the typical values V V to either the normal minimum values V V or the normal maximum vales V V In waveform D the signals fV "dt and W 'dt have, respectively, a greater and lesser slope than the typical signal jV dt. Hence, if the time t were to stay fixed (waveform C), the signals -JV "dt and J'V 'dt would result in stabilized values for the V integral signal which would be greater and less, respectively, than the' typical stabilized value 1 Referring to waveform B, however, it will be seen that, in the instance where stays set at its typical level (solid line), a concomitant of the production of the signal -fV "dt is an advancing of the stabilizing time t to a time t corresponding to the point (1 g in waveform B. Conversely, a concomitant of the production of the signal fV dt is a retarding of the stabilizing time t to a time t represented by the point (11 g in waveform B.

In other words, the stabilizing time t shifts so as to compensate for changes which would otherwise be caused in the stabilized value of the v integral signal by changes from typical value in the input and output speeds of the strip. Thus, at any particular setting of desired output gage, the level at which the V integral signal stabilizes is substantially independent of changes in the velocity of the strip. This fact is illustrated in waveform D wherein (for the same signal level E in waveform B), the signals fV "dt, JV dt and jV 'dt all stabilize at the same level 1 despite the difference in the respective slopes of those three signals.

If the ratio k of V to V stays constant, the described compensation is full so that the level l becomes wholly independent of V and V If k does not stay constant, the compensation will not longer be full but will be in an amount to produce (ultimately) a correction signal AG of a value which appropriately reflects the change in k.

On the other hand, when the input and output speeds V and V of the strip stay constant but the setting 5 for desired output gage is varied, the level at which the V integral signal stabilizes is a function of the value set for desired output gage. This latter fact is illustrated in connection with the typical fV dt signal in waveform D and the concomitant typical IV dt signal in waveform B. A shift in waveform B in the setting for desired output gage from the typical value G to the minimum value 5' causes the stabilizing time t to advance to point (v g The result in waveform D is a stabilizing of the signal J'V dt at an advanced time t such that the stabilized level of the signal is of a value 1 less than Conversely, a shift in waveform B in the setting for desired output gage from the typical value 5 to the maximum value G causes the stabilizing time t to retard to point (v g The result then following in waveform D is a stabilizing of the signal fV dt at a retarded time t, such that the stabilized level of the signal is of a value 1 greater than Accordingly, it will be seen that the magnitude of the stabilized V integral signal varies directly with the value E of desired output gage which is set into the system.

To put it another way, since the integral of speed with respect of time is dimensionally equivalent to distance or length, the stabilized value of the V integral signal represents an output length L of the strip, and the value of the quantity L varies directly with the quantity G While integrators 19 and 20 and amplifier 21 are operating as described, the A6 signal is fed from gauge 1 through mechanism 55 to emerge therefrom as a AG signal in the form of successive samples of square wave shape (waveform E). The leading edge of each such sample occurs before the earliest time t (waveform C) at which the V integral signal (Waveform B) could normally arrive at coincidence with a G}, signal level of any normal value. Within the mechanism 55, the sequential closing of switches 12-1 through 124 and the sequential closing of switches 11-1 through 11-4 are controlled by, respectively, discs 11 and 12 (rotating synchronously with disc 13) with a timing such that the AG sample from section S of strip is not available at the output of the mechanism until the leading edge of that section is within the roll bite of mill 8. Note in this connection that the AG sample from strip section S i held in integrator 14-4 of the mechanism.

The respective outputs of the integrator 20 (wave form D) and of the mechanism (waveform E) are continuously supplied to the computing means (amplifiers 28 and 29 and potentiometer 30) along with the G signal level from potentiometer 27. At each of successive stabilizing times it established by the times of occurrence of the leading edges of the blocking square waves from amplifier 21, the multivibrator 32 is triggered to ungate amplifier 31 so as to provide from the mentioned computing means a succession of output samples (waveform F). Those sample outputs form a train of pulses occurring at a rate proportional to the input speed V of the strip 7. Each of such pulses has a duration which is the same for all those pulses. The pulse duration is short enough so that, even though the formation of the leading edge of the pulse should be delayed until the late limit t" (waveform C) for occurrence of the stabilizing time t the lagging edge of the pulse occurs before termination of the contemporaneous AG sample (waveform E) from the delay mechanism 55.

In this way, under all normal conditions of operation of the described gauge control system, the magnitude of the output pulses AG from amplifier 31 is determined by the gauging Equation 18 as Moreover, since each of these AG pulses is of constant duration, the energy content of each such pulse is given by that equation.

As described, the respective energy contents of the A6 pulses are integrated by integrator 50 so as to provide a primary correction signal for adjustment of the screwdown actuator 9 and, accordingly, of the size of the roll bite.

The modification of the primary correction signal by the supplemental correction signal -AG from gauge 2 is accomplished in the following manner. The multivibrator 46 generates constant energy pulses which occur at a rate proportional to the output speed V of the strip. Those pulses are integrated with respect to time by integrator 33 so that the element 33 develops at its output a progressively increasing integral signal jV dt (waveform G). When the magnitude of that signal arrives at coincidence with the d signal level set on potentiometer 42, multivibrator 44 is triggered to ungate amplifier 49 to provide an output sample (waveform H) of the A6 signal. Such signal is in the form of a pulse having a magnitude and energy content proportional to AG and having a timing which is asynchronous in relation to that of the pulses shown by waveform (F). The duration of such AG pulse is constant. As described, the pulse is fed to integrator 57 which develops the signal --fAG Integrator 33 is reset by a trigger pulse produced as earlier described (by multivibrator 45) when the output integral signal of integrator 33 (waveform G) arrives at coincidence with (d +Ad signal set on potentiometer 43.

The above-described embodiment being exemplary only, it is to be understood that additions thereto, modifications thereof and omissions therefrom can be made without departing from the spirit of the invention and that the invention comprehends embodiments differing in form and/or detail from that specifically described. For example, the supplemental correction signal provided by the follow-on gauge 2 need not be used in all applications of the invention. Moreover, such signal, when used, can be introduced in a variety of dilferent ways to perform the function of compensating for the steady state errors of the basic system. For example, the signal fG may be fed with positive polarity to the input of amplifier 26 so as to modify the '6 signal.

Also, it will be apparent to anyone skilled in the art that the derived gaging equations could readily be solved by a small digital computer on a continuous basis. Therefore, no attempt will be made to describe such an embodiment. Generally speaking, it is normally more economical to solve simple equations with analog techniques if the accuracy and resolution of the analog components are satisfactory. Since analog components with accuracies of one part in a thousand or better and drift rates measured in parts per million are commercially available, the use of analog equipment is acceptable for most applications of the invention. As indicated, however, digital equipment may also be used.

In addition, while the FIG. 1 embodiment employs roll gap adjustment as a means for controlling reduction, it will be readily apparent to one skilled in the art that reduction control may also be obtained. by adjustment by suitable and well known means of the front and back tension of the strip in accordance with the fAG signal. Still further, for the purpose of timing the gating of the pulses derived from the follow-on gauge 2 and provided as an output from amplifier 49, it is evident that the timing circuit comprised of single shot multivibrator 46 and the components controlled thereby can be replaced by a switch device actuated through a gear train by the tachometer wheel 40 to provide a gating pulse to amplifier 49 at times separated by time intervals which are proportional to the output velocity of the strip, and which are each long enough to allow the full follow-on corrective action to take place before the next gating pulse occurs.

Accordingly, the invention is not to be considered as limited save as is consonant with the recitals of the following claims.

I claim:

1. A control system for an installation wherein material is passed through working means to be reduced in thickness in a dimension transverse to the direction of passage, the thickness reduction being a function of the adjustment of means controlling the reduction efiected by said working means, said system comprising, a first integrator means and second integrator means responsive to, respectively, a first signal and a second signal of, respectively, the input speed and the output speed of said material relative to said working means to separately integrate those signals with respect to time so as to respectively produce an increasing input length signal and an increasing output length signal, comparator means responsive to arrival at conicidence of said increasing input length signal with a signal representative of the desired output thickness for said material to terminate the increase in said output length signal to thereby stabilize its value, and computer means responsive to said stabilized output length signal and to a signal which is a measure of the actual input thickness of said material to combine said two last-named signals in subtractive relation so as to provide for adjustment of said controlling means by a primary correction signal derived from such combining and representative of the deviation in the output thickness of said material from said desired output thickness.

2. A system as in claim 1 which is cyclically repetitive in operation to produce each of said input length, output length and correction signals in the form of successive samples, said system further comprising, means to integrate the successive correction signal samples and to provide an integral of such samples for correction of the adjustment of said controlling means.

3. A system as in claim 2 in which said signal which is a measure of the actual input thickness of said material is at least partly derived from thickness gauging means disposed ahead of said working means in sensing relation with said material, said system further comprising means responsive to the input speed of said material to time the sampling cycles of said system so as to render the duration of each such cycle inversely proportional to said input speed.

4. A system as in claim 3 in which the time interval required for said material to travel from said gauging means to said working means is a time interval of greater duration than that of any sampling cycle of said system.

5. A system as in claim 4 in which the sampling cycles of said system are of equal duration, and in which the duration of said time interval is an integral multiple of the duration of each sampling cycle.

6. A system as in claim 1 in which said first integrator means and said second integrator means is each analog integrator means, and in which said computer means includes analog operational amplifier means.

7. A system as in claim 1 further comprising means to modify by a proportioning factor said combination in subtractive relation of said output length signal and said actual input thickness signal, said proportioning factor being representative of the ratio of said desired output thickness for said material to the nominal input thickness for said material.

8. A system as in claim 1 further comprising, means to provide a signal representative of the nominal input thickness of said material, input thickness gauging means disposed ahead of said working means in sensing relation with said material to provide a signal representative of the deviation from said nominal thickness in the input thickness of said material, and means to additively combine such deviation signal and nominal input thickness signal to provide said signal which is a measure of the actual input thickness of said material.

9. A system as in claim 8 further comprising variable delay means for said input thickness deviation signal, said delay means being interposed between said gauging means and additive combining means and being responsive to said first signal to delay said additive combining of said deviation signal for a time period approximating that required for said material to travel from said thickness gauging means to said working means.

10. A system as in claim 1 further comprising output thickness gauging means disposed in sensing relation with said material at a position rearward of said working means in the direction of passage of said material, said output gauging means being responsive to the actual deviation in the output thickness of said material from said desired output thickness to provide a supplemental correction signal, and means to render the adjustment of said controlling means a partial function of said supplemental signal.

11. A gage control system for a mill wherein strip is reduced in gage by being passed through rolls having a roll gap of adjustable size, said system comprising, first integrator means responsive to a signal V of the input speed of said strip towards said rolls to integrate said V signal with respect to time so as to provide an increasing signal fV dt, second integrator means responsive to a signal V of the output speed of said strip away from said rolls to integrate said V signal with respect to time so as to provide an increasing signal jV dt, source means of a signal level E representative of the desired output gauge for said strip, comparator means responsive to arrival at coincidence of said fV dt signal with said level to terminate the increase of the JV dt signal so as to stabilize its value, and computing means responsive to said stabilized fV dt signal and to a signal G which is a measure of the actual input gauge of said strip to provide a A6 correction signal for adjustment of the size of said roll gap, said AG signal being representative of the deviation in output gage from Q, and said A6 signal being representative of the expression where 5 is the nominal input thickness of said strip.

12. A gage control system as in claim 11 further comprising, source means of a signal representative of said nominal input thickness G input thickness gauging means disposed ahead of said rolls in sensing relation with said strip to provide a signal A6 representative of the actual deviation in the input gauge of said strip from said nominal thickness Q, and means to additively combine said 15 G signal and said deviation signal A5 to provide said G signal.

13. A gage control system as in claim 11 further comprising output thickness gauging means disposed in sens-.

ing relation with said strip at a position rearward of said rolls in the direction of passage of said strip, said ouput gauging means providing a AG signal representative of the actual deviation in the output gauge of said strip from said desired output gauge a integrator means to derive from said IAG signal, a signal representative of IAG and means to additively combine said AG and fAG signals so as to thereby form a AG signal for adjustably correcting the size of said roll gap.

14. A gage control system for an installation wherein material is passed through Working means to be reduced in thickness in a dimension transverse to the direction of passage, the thickness reduction being a function of the adjustment of means controlling the reduction effected by said working means, said system comprising, means responsive to a signal of the input speed of said material towards said working means to produce synchronizing pulses at a rate proportional to said input speed, computer means triggered by said synchronizing pulses to produce corresponding constant duration pulses at said rate, said computer means being responsive to said input speed signal and to signals of the output speed of said material and of the desired output thickness of said material to render the magnitude of said constant duration pulses a function of said input and output speeds and of said desired thickness, and integrator means responsive to said constant duration pulses to integrate them so as to provide a correction signal for adjustment of said controlling means.

15. A gage control system as in claim 14 in which said computer is responsive to a signal which is a measure of the actual input thickness of said material to render the magnitude of said constant duration pulses a function also of said actual input thickness.

References Cited UNITED STATES PATENTS Re. 25,075 10/1961 Hessenberg 729 3,015,974 1/1962 Orbom et al 729 3,054,311 9/1962 Murtland 729 3,121,354 2/1964 Weremeychik et al. 728 3,169,424 2/ 1965 Branscon et al. 729 3,319,444 5/1967 Masterson 728 CHARLES W. LANHAM, Primary Examiner.

A. RUDERMAN, Assistant Examiner.

U.S. C1. X.R. 729

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