US3401891A

US3401891A - Control system for a closed circuit grinding system for finish cement

Info

Publication number: US3401891A
Application number: US589346A
Authority: US
Inventors: Philip J Fleeman; Brand Willem
Original assignee: General Electric Co
Current assignee: Eaton Corp; General Electric Co
Priority date: 1966-10-25
Filing date: 1966-10-25
Publication date: 1968-09-17
Anticipated expiration: 1985-09-17
Also published as: DE1607460A1; DE1607460B2; GB1160789A; SE312261B

Description

Sept. 17, 1968 P. J. FLEEMAN ET AL CONTROL SYSTEM FOR A CLOSED CIRCUIT GRINDING SYSTEM FOR FINISH CEMENT Filed Oct. 25, 1966 I CUNKER HARDNE5S :BIGNALS H NEW MATERmL FLOW RATE EMGNALS REJECT MATERlAL PARTlCLE 5\ZE.

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A 7T RNE YS P.J. FLEEMAN ET AL 3,401,891 CONTROL SYSTEM FOR A CLOSED CIRCUIT GRINDING Sept. 17, 1968 SYSTEM FOR FINISH CEMENT Filed Oct. 25, 1966 4 Sheets-Sheet 4 a o o INVENTORS PHIL/P J. FLEEMAN W/LLEM BRA/VD BY j c A77'OANEYS United States Patent 3,401,891 CONTROL SYSTEM FOR A CLOSED CIRCUIT GRINDING SYSTEM FOR FINISH CEMENT Philip J. Fleeman, Calabasas, Calif., and Willem Brand,

Phoenix, Ariz., assignors, by mesne assignments, to The General Electric Company, New York, N.Y., a corporation of New York Filed Oct. 25, 1966, Ser. No. 589,346 8 Claims. (Cl. 241-64) This invention relates to computer controlled industrial processes and more particularly to a system for using computer control of a closed circuit grinding system for finish cement.

The reduction of clinker to finish grind cement is one of the most important and complex operations in the manufacture of cement. A size reduction of about 1000 to l is necessary to get a particle agglomeration which can be changed chemically into a mass with usable load bearing properties. Those properties are directly dependent upon the type of size reducer and upon the length of time the clinker is ground.

It has been found, mostly by experiment, that a closed circuit ball mill gives the finished material the properties which are desired. The ball mill is a cylindrical tube which contains a number of steel balls. The tube is caused to rotate at a speed which will cause the balls and the clinker both to strike each other and to rub against each other. By both actions, enough energy is put into the clinker particles to break them and thus reduce their size. The properties contributed by the method of grinding, then, are a result of geometric and physical relationships between the clinker, the balls, and the cylindrical tube. More obvious, perhaps, is the fact that the properties are also dependent upon the length of time a particle is ground. A piece of clinker could be struck once and be broken into pieces much smaller than the original piece, but still not be useful as finished grind cement. It could be ground indefinitely into particle sizes which cannot be seen except through a powerful microscope and which would also not be useful as finished grind cement. At some time between, the correct properties may be obtained. As a result of studies, standards of particle size distribution and specific surface area have been established for finished grind cement which are known as ASTM types I, II, or III. As is well known, ASTM stands for the American Society for Testing Materials.

An object of this invention is the provision of a system whereby a finished grinding cement mill is controlled automatically to produce a desired particle size distribution and surface area for the product.

Another object of this invention is the provision of a computer controlled finish grind cement operation which produces a specified type of output product at a maximum possible production rate.

Still another object of the present invention is to produce a novel and useful computer control system for an industrial process.

The foregoing and other objects of this invention are achieved in an arrangement wherein a digital computer has inserted therein data concerning the product being milled and performs certain mathematical computations thereon. The results of these computations together with information derived from incoming material are used in the solution of equations derived from a mathematical representation of the mill. As a result of the equation solutions, signals are generated which actuate controls for the purpose of altering certain equipment operation in the mill so that the output product is optimized in line with the desired product.

More specifically, the coefficients in equations in the computer which are solved are periodically updated from 3,401,891 Patented Sept. 17, 1968 input data representing the hardness of clinker material being fed to the ball mill, ball mill input and output particle size distribution, particle size distribution of the separator reject material and output product. The computer functions to produce output signals for controlling the fresh feed input rate and separator blade position whereby production is maximized from input signals representing the hardness and particle size distribution of the incoming new materials.

The novel features that are considered characteristic of this invention are set forth with particularly in the appended claims. The invention itself both as to its organization and method of operation, as well as additional objects and advantages thereof, will best be understood from the following description when read in connection with the accompanying drawings, in which:

FIGURE 1 is a schematic diagram of a finish grind cement installation equipped with sensors and controls in accordance with this invention;

FIG. 2 is a block schematic diagram of a computer installation in accordance with this invention;

FIG. 3 is a curve of the log of weight percent of passing particle size vs. size in microns;

FIG. 4 is a modified mill matrix representation;

FIG. 5 is a breakage function curve;

FIG. 6 is a separator matrix representation; and

FIG. 7 is an abbreviated representation of the combined mill and separator matrix.

The installation FIG. 1 is a schematic diagram of a finish grind cement installation which is controlled in accordance with this invention. Also shown schematically in FIG. 1 are the online sensors and controls which are required in accordance with this invention. Clinkers are usually held in a hopper and are fed through the bottom to a moving belt 12. The belt is rotatably supported in the usual, and well known, manner by a number of Spaced rollers 14, which are driven by a motor 16. The speed at which the belt moves determines the amount of clinkers which are delivered to a collector belt 18, also rotatably supported by rollers 20, which are driven by a motor 22. A source of gypsum is contained in a hopper 24, which feeds out of the bottom onto a moving belt 26. The belt is supported on rollers 28, which are controllably driven by a motor 30. The belt 26 also has its speed varied to determine the amount of gypsum delivered to the collecting belt 18.

It is customary to determine the feed flow rate of fresh feed materials on the collector belt 18 using a device which can be purchased on the open market, known as a weigh-belt 32. This device effectively determines the flow rate of the material per unit of time and produces an analog signal indicative thereof. This analog signal is used to deflect a meter in the commercial device.

The fresh feed material on the belt 18 is next dumped onto a second collector belt 34. This belt is also supported on rollers 36, which are driven at a controllable speed by a motor 38. The second collector belt 34 receives the reject material which is being returned, from a belt 40. This reject belt also is supported on rollers 42, which are driven at a controllable speed by a motor 44. The reject belt 40 also has a weigh-belt mechanism 46 coupled thereto. The second collector belt 34 feeds the fresh feed and reject material into a ball mill 48 wherein the material is to be ground to have a desired particle size.

In accordance with the usual practice in cement mill systems of this type, water in a container 52 is added to the material being fed to the ball mill in a quantity which may be controlled by -a valve 54. Also, oil in a container 56 is added to the material being introduced into the ball mill in a quantity controlled by means of a valve 58. It is also customary to add balls to the ball mill through a ball dispenser 60 by controlling the valve 62. A ball is added in the usual operation of the mill whenever it is felt that the balls within the mill have been worn down to a diameter where they are beginning to become inefiective for the purpose of grinding the material within the ball mill.

The ball mill 48 is rotatably driven by a motor 64. As iscustomary, the amount of power which the motor takes to drive the ball mill is measured by a kilowatt hour meter 66. The source of power 68 is connected through the kilowatt hour meter to the motor 64.

The output of the ball mill is delivered to a belt 70. This belt is supported on rollers 72, which are driven at a speed as determined by the controllable motor 74. The belt 70 delivers the material received from the ball mill to an elevator 76. The elevator carries the material up to another belt 78. The belt 78, which is supported and driven by rollers 80, which in turn are driven by a. controllable motor 82, delivers the material received from the elevator to a separator 84.

The mechanical separator or classifier 84 is a well known device which causes separation between particles by imparting differences in their rate of movement and air. The basic forces used are gravity and inertia. The relative strength of the two forces are usually adjustable. In one type of commercially purchasable separator known as the Raymond Double-Whizzer, the material enters through the top and falls onto a whirling disc which causes an initial or rough separation. The lighter particles are swept upward by the forces produced by air movement which are generated by two fans contained within the separator. A secondary separation is caused by turbulence set up by one of the fans. The turbulence and thus the amount of separation are influenced by damper blades which can be moved out into the stream of air and finish grind material.

The position of the damper blades may be controlled by a damper blade positioner 86. The angle which the damper baldes make is sensed by a damper blade position sensor 88, which produces an electrical signal indicative thereof. Such damper blade position sensor may simply be a potentiometer having a slidable arm along the fixed resistance thereof. A predetermined voltage is applied across the fixed resistance of the potentiometer. The position of the slider arm and thus the voltage representative of the position of the damper blade are established responsive to the position of the damper blade.

The whirling disc and fans are driven by a motor 90. The power supplied to the motor from a source 92 is measured by a kilowatt hour meter 94.

The separator 84 separates the particles having the desired size from those not having the desired size. The particles having the desired size are passed through the bottom of the separator onto a belt 96, which carries the accepted material to a product storage location. The belt 96 is moved at a controlled speed by rollers 98, which in turn are driven by a control motor 100. A weigh-belt device 102 measures the finished product flow. The separator 84 dumps the reject material on the reject belt 40, which carries this material down to the second collector belt 34 in order that it be returned to the ball mill 48.

The computer input FIG. 2 is a block schematic diagram of the arrangement in accordance with this invention for automatically controlling the operation of the finish cement mill which has been described. Basically, signals from the various transducers and/ or sensors at the various locations around the cement finish mill are fed to a digital computer 110. In addition, measurements are made at various locations to be described of the particle size distribution, and signals representative of the data are fed to the computer. The computer proceeds to process these signals, as directed by a program, and then supplies, as an output,

- 4 signals which serve to control the separator damper blade position and the rate of flow of incoming new material which, as will be shown, under a predetermined particle size constraint, serves to determine what the finished product of the finish cement mill will be.

Since the present control scheme is basically a predictive type, the frequency of measurement to be performed on the incoming clinker will be higher than that for the reject material and the product. The hardness of the incoming clinker material should be known. This can be measured on the average of once per hour using standard hardness measuring apparatus. One of these is known as the Hardgrove Grindability Test, or, alternatively, the usual ASTM M. O. H. Test may be used, wherein the depth penetration of a standard weight is measured. This data is converted into a digital representation which may be entered into punched paper tape or magnetic tape, if desired, to render the information in a convenient form for entrance into the computer. The tape reader of this information on punched paper tape is represented in FIG. 2 by the rectangle 112, which bears the nomenclature Clinker Hardness Signals.

On the average of once every four hours (once per shift), the percentage residue of the ball mill input is measured on four screen sizes. The percentage residue of the reject material output of the separator and also the accepted or product stream of the separator is measured. This is a standard measuring procedure in the present operation of these types of mills. These percentage residue figures, which are also known as particle size distribution, may be digitized by entry into punched paper tape or on magnetic tape for the purpose of entering this information into the computer. The punched paper tape reader or magnetic tape reader for reading and generating the computer input signals for new material particle size data is represented by a rectangle bearing reference numeral 114 and designated as New Material Particle Size Distribution Signals, [i] There is also a rectangle 116 designated Reject Material Particle Size Distribution Signals, [r], indicative of the reader of punched paper tape or magnetic tape which generates computer input signals. The rectangle 118, designated Product Particle Size Distribution Signals, [12], represents the signals produced by the reader input to the computer.

The signals generated by the weigh-belt 32, which are the new material flow-rate signals, are digitized by any suitable analog-to-digital converter and then provided to the computer 110. In FIG. 2 this is designated by the rectangle 120, which bears the legend New Material Flow-Rate Signals, I. Similarly, the weigh-belt signals from the reject weigh-belt 46 are digitized by apparatus represented by the rectangle 122, which bears the legend Reject Material Flow-Rate Signals, R.

The product weigh-belt 1102 produces signals which are fed to the computer after being digitized. This is represented by the rectangle 124, which bears the legend Product Flow-Rate Signals, P.

Two other particle size distribution inputs to the computer are measured at the input to the .ball mill and at the output to the ball mill. These are respectively designated in

rectangles

126 and 128 as Ball Mill Input Particle Size Distribution, [e], and Ball Mill Output Particle Size Distribution, f].

The output of the computer consists of a plurality of signals, the first of which is designated as 1 which is applied to a belt motor speed control 130 which controls the speed of the

motors

22, 16, and 30. The ratio of the belt drive speeds of

belts

12 and 26 by

motors

16 and 30 is normally set to establish a clinker-gypsum ratio. Thus, alterations in the speed of belt 34 by controlling the speed of motor 38 require proportionate control of the speeds of

motors

16 and 30. Thus the signal I determines the flow rate of new product or new clinker and gypsum to the ball mill.

The computer generates signals, D which establish the position of the damper in the separator. These signals are applied to a separator damper position control 132, which in turn actuates the damper blade positioner 86. Damper blade position signals are fed back from the sensor 88 to verify that the damper blade has been set as indicated by the computer output.

Grinding theory From the first time grinding or crushing was used for gainful purposes, someone has tried to analyze the process. The classical approach has been to analyzethe breakage of a single particle and to relate conclusions about this type of breakage to power requirements in a mill.

The process is started with the application of a force, either of impact or friction, which causes a load in shear, compression, ,or tension. In practical crushing, all are present in varying degrees. The effect of the force is to cause a deformationof the crystal lattice. When the deformation is great enough, the lattice will tear along paths which are weakened by previous processes, either of crushing or manufacture. The result of the tear is the creation of new surface.

The work which is done is used in three ways: (1) in deformation without breakage, (2 in deformation with breakage, and (3) in breakage. Work of the first kind is returned to the surroundings in the form of mechanical movement and heat as with rubber band. The second is converted completely to heat. The third, which experiment has shown to be about one percent of the total energy, is used in the breakage of the lattice.

The manner in which the lattice breaks is determined by the type of material. Rocks may be classified into two general structural classes, homogeneous and heterogeneous. Fracture will take place in a homogeneous rock through grains and grain boundaries alike. It will occur only along grain boundaries in a heterogeneous rock. Another distinction is that the particle size distribution which results from the breakage of a homogeneous material can be described by an exponential law. The size distribution from the breakage of a heterogeneous material must be described by a statistical relationship.

Cement clinker is effectively a homogeneous material in that fracture is equally likely to'occur through grains or through the material between grains. This is characteristic of harder materials in contrastto the softer .ones like sandstone and limestone.

Other factors influence the breakage. It is well established that in tensile tests of'brittle materials the resistance to fracture is a function of time. Crushing single particles by impact in a drop-weight crusher showed that the energy required to produce 1000 cm. of new surface was three times that to produce the same surface in slow compression. Also, slow compression produces more surface.

Another factor is temperature. As mentioned previously, much of the work done on a particle during the grinding process is converted to heat. The heat which is added causes expansion of the clinker particles, the pressures oppose-the expansion,..and. work is. done. The pressures, especially at the weaker junction planes of the material, do much of. the work of breakage, andless kinetic energy is required to produce new surface area at higher temperatures. 7

Another factor which influences the manner and extent of breakage is the state of the surface of the material. Experiments with glass, which has some of the properties of clinker, have shown that tensile strength in a dry vacuum is as much as 2.5 times the strength in normal ambient conditions. Similarly, the strength in a corrosive chemical atmosphere is reduced a large amount according to the chemical. In both cases, th e presence of a liquid, in the first case moisture, and, in the second, a chemical,

on the surface of the material seems to act as a catalyst to the lattice rearrangement. This catalytic action is probably one method by which grinding aids reduce the energy necessary to increase the surface of clinker.

A more practical factor which influences the breakage or grinding process is the type of equipment which is used. A particle crushed by a hammer mill will have characteristics similar to those measured when a single particle is crushed, i.e., abrasion will not have much influence, but broken particles moving with kinetic energy will cause secondary breakage. In a ball mill, two basic processes occur, crushing and abrading. The extent of each is determined by the size of the balls relative to the size of the clinker, the speed of the mill, the amount of material being ground, agglomeration, etc.

In a ball mill not every particle is broken as it passes through the mill; there is only a certain probability that it will be broken. Also, after a particle is broken, the sizes of the resulting particles are not uniform, but they will have a distribution, the form of which is also a probability function.

Whatever the machine or the type and conditions of breakage, the results of grinding must be measured in a useful and objective way. It is obvious that a change in size and number of particles occurs in any breakage process. Also, the amount of material at the mean size, and the range of sizes, decreases as more breakage occurs. The two measurable parameters which reflect these characteristics are size distribution and specific surface. These parameters will be the basis for all discussion and simulation of the process in the ball mill.

It should be noted in the discussion of grinding theory that the mill process has two parts. The first is one of separation, or selection, in which some particles are selected by chance for breakage; the particles not selected merely pass through the mill and separator and back into the mill. The second process is that of actual breakage.

Neither the process of breakage nor the process of separation can be observed directly, but information about them may be deduced from measurements of size distribution of the particles at certain points in the system. This is made practical through the use of sieves or, indirectly, from measurements of specific surface area. In addition, mass flow rates can be obtained from suitable instruments.

These ideas and process characteristics have led to the adoption of a mathematical technique which conveniently represents distributions and the processes which change distributions. This technique is the use of matrix methods, where vectors are used to describe distributions, and matrices are used to describe the processes of selection, breakage, and separation. The approximation by vectors replaces the use of functions; instead of differentiation and integration, only addition, subtration, and multiplication are used. This technique is ideally suited to use in a digital computer. The basic ideas and an example of how a process may be simulated follow.

The matrix method The matrix method will use vectors to describe distributions and matrices to describe the processes of selection, breakage, and separation. The approximation by vectors replaces the use of functions; instead of differentiation and integration, only addition, subtraction, and multiplication are used. At the same time, there will be no loss of accuracy because the precision of the analysis is at least as good as that of the data used. The examples which are presented are based on the following definitions and manipulations:

(a) Vect0r.A vector is a group of numbers listed in a certain order. The numbers are called elements of the vector. A vector can be a row vector or a column vector.

Row vector [r]=[r,, r r 7,,]

Column vector (0):

(b) Matrix.A matrix is a group of numbers arranged in a rectangular array of m rows and n columns. It will have an order of (m, n). If m =n, it is a square matrix.

(c) Scalar.-A scalar is a matrix of order (1, 1), i.e. a single element, or number.

(d) Addition of matrices.The addition of two matrices of the same order is performed by adding their compounding elements and writing the sums as the corresponding elements of the resultant matrix. (e) Multiplication of two vect0rs.-Only multiplication of a row vector and a column vector is noted. The corresponding elements are multiplied and then added. The product is a scalar.

(f) Multiplication of two matrices-Two matrices can be multiplied together only when the number of columns of the first equals the number of rows of the second.

Mum: 11 12 11 12 l1 ll+ l2 2l l1 l2+ l2 22 21 22 21 22 21 1l+ 22 2l 21 12+ 22 22 The matrix method, as it will be used in the mathematical description of the mill and separator, can be explained best with a series of examples:

Size vector The size distribution of an assembly of particles is measured with a sieve analysis. The results of the sieve analysis can be plotted as the Residues (r), Passing (p), or Distribution (d) characteristics.

The size distribution can also be represented by a vector. A vector is a group of numbers listed in a certain order. The numbers are called elements of the vector. A vector can be a column vector or a row vector.

As an example, a sieve analysis of the feed to a millseparator system was found to be as follows:

X inches 1(ar), weight p(x), weight 11(1), weight percent percent percent From this, the following table can be made:

Aperture, Weight, percent Size Class Weight, percent microns Passing Distribution 853 46 a 22 422 24 a 211 14 a 14 From this, then, the Distribution Vector is seen to be d 54 d d2 d 10 and percent undersize =100-86=14.

Note: For simplication, percentages are given for only three increments. It is likely, however, that an actual size vector will have to contain six elements.

, Suppose also that half the feed in each incoming size increment is selected for breakage 'and half passes through the mill unchanged. The selection matrix will be the following:

8 O 0 O. 5 0 0 S: O 822 0 0 0. 5 0

The purpose of the diagonal for-m becomes obvious when the selection matrix is multiplied by the feed distribution vector:

1 11 O 0 1 11 (is d 0 22 0 2 22 d3 0 0 8 d3 33 If the matrix were not diagonal, the selection would be unnaturally complex. 'In the example selected above, the scalar 0.5 could be used, but this would not illustrate the general case where s s and .1 will usually all be different because they are functions of flow rate and geometric conditions in the mill.

Thus:

54 0. 5 0 0 54X0. 5 27 d8: 22 0 0.5 0 22X0.5 11 10 0 0 0. 5 10 X0. 5 5

Again, suppose that the breakagematrix is This matrix is a numerical expression of the breakage law; it describes what happens to particles of each size in the feed which have been selected for breakage. In this matrix there can be no numbers above the diagonal be cause the feed increment is always decreased, never increased in size.

When the feed distribution vector, the selection matrix, and the breakage matrix are all multiplied together, the result is a vector which describes one cycle of breakage:

dSB

To this product of one cycle of breakage, there must be added the clinker which was not selected for breakage:

54 O. 5 0 O 10. 8 T0ta1= 22 0 0. 5 0 10. 2 10 O 0 0. 5 10. 0

Percent Undersize: -74:26

The procedure can be summarized in the following table:

*Undersize. The effect of breakage simulation can be seen even more Input Output 14% Undersize 26% Undersize Residue Veet0r=r= 12 Passing Vector= p Distribution Vector=d= The other important characteristic of an assembly of particles, besides its size distribution, is its weight. Let the flow-rate of feed to the mill-separator system be P tons/ hr. F is called a scalar. The weight of each size of feed being fed to the mill will then be the product of F and the weight percentage of each size. In other words, the scalar F will be multiplied by each element of the size vector to produce a weight vector.

Fx 11 Fd Fat (12 Fdg Fd=w or Fm d a i t t F d W Change in size vector A change in the size distribution, for example, the size reduction caused by a breakage process, is represented by a matrix multiplying the vector.

In a practical system, however, particularly a double compartment mill, the range of size distribution is about 1000:1. This wide range must be described with a vector of from three to six elements it computation is not to be cumbersome. For this reason, size classes will be assigned which are in a geometric progression with a common ratio of a. If the largest size is 1, then the next is a, the next is a etc. These size classes are assigned on the basis of the Passing Characteristic, or cumulative distribution. If the PC is plotted in the form of a log of wt. percent passing versus log of size, a curve 150 such as shown in FIG. 3 is obtained. The size classes can be assigned by dividing the curve equally into classes of equal size.

Once the coefiicient and exponent of the Rosin-Rammler characteristics are found, this procedure will become quite simple if two sieves with a geometric ratio are used for making the two size measurements. Tyler screens are rrlilanufactured and sold commercially with this relations 1p.

When a number a is picked (a 1) which will conveniently cover the size range of material being examined, Passing and Distribution vectors, may be found. It should be noted at this point that the weight percent undersize must always be included in any calculations in order to balance material relationships. The percent undersize can be found by summing the Distribution vector and subtracting it from 100.

System equation derivations based on statistical techniques The breakage functi0n.-In the foregoing Matrix Method description, there is illustrated that if the elements of the selection matrix and the elements of the breakage matrix are known, this representation will provide a means of predicting the size distribution of the mill output material. The basic variables consist of flow rate, input size distribution vector, and hardness of material. With the notation given in FIG. 4, which is a drawing of a modified ball mill matrix, the input E is the breakable material in tons/hour, [e] is the particle size distribution. The output F is output material in tons/hr., and [f] is the particle size distribution. Assume that the a elements of the selection matrix are functions of the flow rate, and the b elements of the breakage matrix are functions of the hardness. It should be recognized that this division is arbitrary and that there is just as much justification in representing the operation by a single matrix with elements being functions of both flow rate and hardness. For updating reasons, however, the second representation has distinctive advances which will be shown later.

A form which has been used successfully for representing breakage phenomena is one which describes the passing characteristic, or cumulative function, of all particles below a given size, resulting from the breakage of material of one given diameter y. This breakage function, B, will be function of y the size of the particle being broken, and x the varying size of the particles resulting from the breakage.

The equation which is suggested is:

The purpose of the denominator is to provide an answer when no breakage occurs, i.e., when It should be noted that this representation of breakage in the mill-separator process equations precludes any change for variations of any other process variable. All breakage occurs in the same way: the effects of geometry, flow-rate, etc., can only be shown via the selection function. The breakage function, then, is the source of the numerical values which will form the elements of the breakage matrix B. The formation of the matrix can be shown best with an example.

Assume that a particle in the range from a to a is broken. Let the particle have the size y=a fl When it is broken according to B(x, y), the cumulative distribution of the product will be where l-e- =0.63.

From this a table can be made which shows the weight percent passing, or cumulative, character as a function of x:

. Average size of Weight Percent Group X Passing Note that as a result of the use of the ratio x/y, the r disappears from the calculation, andthe result is a function only of a.

The weight percentage in each size range, with respect to the originalgroup started with, can be found by taking the differences between the values for the passing characteristic above. In this way, the elements of the distribution characteristic are found. As an example, the weigth percent between u and a is In this way another table can be formed:

Thus, when a particle in the a to a size range is broken, there will result a new group of particles which will be distributed in the proportions b b b over the size ranges from 1 to a, when a is selected, numerical values can be found.

With the proportional values, the breakage matrix can be formed. The matrix will have n rows and n columns.

The element of the ith row and jth column will be the proportion of a particle in the jth size grade before breakage, which falls in the ith grade after breakage. The matrix will appear as follows:

The efiect of hardness The effect of hardness can be taken into account by introducing the parameter n to the breakage function:

-(x/y ,y, (5)

where n: f(H); H=hardness.

It can be seen that the elements of the breakage matrix will not be constants, but functions of hardness, or n, as follows:

-n el 1=e (6) The effect of hardness on n in this definition of the breakage function can be seen in FIG. 5, which is a curve of breakage function B versus particle size x. For values of n 1, the contribution to the larger size groups becomes less and less, and for values of n l the opposite takes place. Returning again to FIG. 4, we can write the output vector components f in the following way:

The percentage of material in the smallest'group, f follows from the condition s f 2fi In this set of equations, the a elements represent the effects of mill geometry and feed rate, E, and the single coefiicient It shows the effect of hardness,'H. If both the input vector, [i], and the hardness of the feed are known, the equation set (7) can be used for predicting the output size distribution, [f].

Mill matrix element calculations The mill matrix simulation as shown in FIG. 4 consists of a selection matrix, its complement, and a breakage matrix. The elements of the selection matrix are the a and the elements of the breakage matrix are the b It is noted that the b are a function of n, which is, in turn, a function of hardness, H. Before the control system can be used, a complete set of elements a to a and n, must be determined. After start-up, then, it will be changed with an updating procedure which will be described later.

All elements, a to a and n, can be found from test runs for p q r different mill conditions. The number p indicates the number of flow rate, e, which should be measured; q is the number of types of clinker which will be used, where type is defined by hardness, H; and r is the number of test runs which will be made for each value of E and H.

From each of the test runs noted, size distribution data will be taken at the mill input and output. This will be put into the following expression and minimized:

+ =SSE(an G38 The minimization of this expression for the sum of the square of the errors of 8 balances will give the values for a to a and n for each individual set of E and H values. The p values of a then in its turn will be used for determination of its own linear coefficients according to the equation? ii( l1+ il When n is available from the above tests, it must be related to hardness, H. This can conveniently be either linear or of the form The constants a, b, and 0 can be found from three of the above test runs. When all constants are found from these off-line tests, the on-line control system may be started.

Mill matrix element updating It has been mentioned that n will be updated on-line. If it is assumed that elements a and b have been determined from adequate test data, it can be updated with a once-a-shift measurement of the size distribution of the material entering and leaving the ball mill.

Equation 5 showed b expressed as a function of n. When the values of 1;,(n), as given by Equation 6, are

The best fitting n for this set of equations follows from minimizing which gives the requirement for n:

This value of n can be used also for updating the coefficients a, b, and c in the relationship between 11 and H.

The separator A mechanical separator, or classifier, causes separation between particles by imparting differences in their rate of movement in air. The basic forces used are gravity and inertia. The relative strengths of the two forces are usually adjustable.

In the Raymond Double Whizzer type of mechanical separator, the material enters through the top. It falls on the whirling disc which causes an initial or rough separation. The lighter particles are swept upward by the force of air movement of the two whizzer fans. A secondary separation is caused by the turbulence set up by the second fan. The turbulence above the second whizzer and thus the amount of separation are influenced by damper blades which can be moved out into the stream of air and finish grind material.

The variables which will change the size distribution and amount of the product are the speed of the rotating disk and Whizzers, the number of whizzer blades, the distance the damper blades protrude into the air stream, and the fiow rate of the incoming material. The speed of rotation of the disk and blades can be considered as constant. The number of whizzer blades will be set when the machine is installed so that the movement of the damper blades will cover the range of size distribution required at the flow rates the machine must handle. The two variables which must be shown in the process equations are damper position and flow rate. The model should show their influence on a size distribution vector.

The separator will be analyzed by representing it with two parallel matrices, one of which represents the selection of feed material for the reject stream, and the other the selection for the product stream. This is shown in FIG. 6, where the elements S in the diagonal for the reject matrix are complements of the elements (lS of the product matrix. With the disc and the whizzer blades rotating at constant speed, the elements of both matrices will be a function of product flow rate, F, and damper position, D.

The relationship S ,=S(F, D) can be derived with a conventional sieve analysis and material balance around the separator. This must be done with a suflicient number of tests to cover the number of unknown coefiicients and to cover the range of F and D over which the separator must operate.

For the purpose of making the simplest start, let

Since there are three sets of unknowns, S must be found with sieve analyses from at least three separate settings of F and D. For each setting, there will be a group of material balances where size range is signified by the subscript i. P and R may be found from a simultaneous solution of Equation 16 for two separate size ranges. They may be found with greater accuracy, however, with a weighted least squares curve fitting procedure using material balances from all available size ranges. The total error in the data fitting procedure will be distributed such that the error in the overall material balance is weighted least; the size dimension group smaller than 44 microns second, and the groups 200-325 mesh, -200 mesh, etc., weighted successively heavier.

From FIG. 6, which is illustrative of the separator matrix, it is seen that: Ff S =Rr or With the values of R and P found in the preceding paragraph, S may be found with Equation 17. When S is known for each size range, and for at least three combinations of D and F, Equation 15 may be used to find an, bu, and Cu.

The size dimension group 44 microns is given in the results of the test runs as cumulative passing percentage. This balance will be used with the corresponding material balance for this group to derive the separate coefiicient .9 which is of special importance since it determines the product specifications more than any of the other matrix coeflicients.

For reasons later to be explained, it seems advisable to perform more tests with finer mesh values, in order to arrive at a set of s values below the cutpoint of the material. Assuming for the moment that three additional sieve measurements are available giving the weight percentage for three additional size dimension groups, we would then be in a position to derive the additional coefiicients 810,10 to 512,12 from which specific surface could be calculated with a high degree of accuracy.

The coeflicients A shown in the abbreviated systems matrix represented by FIG. 7 are related to the a values of the mill-selection matrix and b,,- values of the breakage matrix via:

11*=( 11)+ 11 11 .1*== z1 21 22* 22)+ 22 22 etc.

The values a are only functions of E; the values 11,,- only of hardness H.

A control scheme Once the s elements have been derived from a wide variety of test conditions, the matrices can be used for on-line predictive control. This will be illustrated with the aid of FIGS. 4 and 7. For this optimization discussion, the elements of the breakage matrix have been assumed to be constant, though the arguments can be extended for more degrees of control. For the configuration shown, the following set of equations holds:

I ,f]=[ 11 1 f1 21 E X F o n ss 8 f8 19 Without mill dust losses, we have 8 F=E and f 100-Efi The value of p or the weight percentage of the smallest group, follows then from For the product size there is a prediction of total weight in the group 325 sieve, 200-325 and consecutively coarser groups. Since for this material, the groups 44 represent only a small percentage, and tests indicate that the product distribution approximates the Rosin-Rammler form, it can be assumed that this functional description holds for the whole passing curve and that a 44 micron cutpoint determines the b coefiicient of the distribution curve. A given specific surface requirement is then analogous to a specific value for the 44 micron cutpoint passing percentage. A similar cutpoint can be obtained for different choices of F and D.

For variations in the input vector [i], the problem is now reduced to one of finding values for D and I which will maximize production P under the constraint of Equation 213 for the percentage p Since F is coupled to the input I and the recycle R, which in its turn is a function of F, an iterative procedure is recommended for the optimization. For this purpose, Equations 15 to 23 can be written in the following form:

With s -s available as separation coefficients, the specific surface requirement on the product can be related to the control calculations in two ways. The first is based on the assumptions that the product can be described with the Rosin-Rammler Law, that n is constant, and that the weight percent passing 325 mesh will completely describe the size distribution of the product. Under these assumptions,

Equations

18, 19, and 21 are valid, with i=1 11, but Equations 22 and 23 must be changed to the following:

12 12 F=Z9 fii1-S; (D, MFR? (23a) where 12 ZQiPFC (23b) represents the product specification requirement.

If experimental data show that within the control range of interest for D and F the resulting product size distribution varies too much to allow a one-parameter relationship between specific surface and the passing weight percent for a 325 mesh sieve, another method must be used. For any set of F, -D values and input size dimension vector [f], the specific surface can be calculated from the resulting Pljp] values with the following equation:

With gram in this dimension group this makes surface or specific surface per gram ,g i l'i .-1

(6/ p to be replaced with K found from Blaine test on sample.)

For changes in input size dimension vector [i], a two dimensional search has to be performed now on I and D with the condition of Equation 29 to be taken into account. This search will take place in the computer program on the mathematical representation of the process as given by Equations 15 to 29.

Updating of the function S (D, F)

The above outlined control scheme will allow periodic updating in the following manner. Assume once-a-shift measurements of the size distribution of both recycle material [r] and product [p]. When the sample measurements are taken off the product and recycle stream, and the data entered into the computer, the computer will calculate and then store the predicted values for F and he vector [f]. The analysis data describing R and P will be manually inserted in the computer. A subroutine will then be called for to establish the best fitting values for P and R on the basis of nine (or twelve) available partial material balances and the over-all material balance around the separator. With P and R established this way, the values of s will be recalculated.

The recalculated s values will now be used to update the relationship s =a+bF+cD. The slopes of these relationships will not be altered on the basis of this single experiment. A weighting procedure to combine the present shift information with the last measurement results, applying a weighted intercept on the basis of the new information, can also be considered.

Summary To summarize the operation of the system, initially and before the computer is placed on line, the selection matrix elements a to a and the quantity n are found from test runs for different mill conditions. This is done by measuring the flow rate E and the hardness H of clinker which will 'be used in a number of test run conditions. Also, for each test run particle size distribution [e] and [f] is taken at the ball mill input and output. n is calculated from the data obtained using Equation 9 and minimizing to give values for a a to a and n. Then Equation 10A is used to obtain the linear coefficients of a and Equation 10B is solved in order to obtain the values for the constants a, b, and c in that equation.

In the separator the procedure previously indicated in connection with the description of Equations 15, 16, and 17 is followed to obtain a set of values for s and a bu and C11.

In operating on line, the present system maximizes production P (in tons/hour) by adjusting the fresh feed input 1 (in tons/ hour) and blade position D (inches insertion), with a fixed percentage p (or percentage of the smallest particle size group) as a constraint. The disturbances in the system are variations in the input particle size distribution characterized by the vector [i] and the hardness, H, of the feed material. Thus, these are read into the computer most frequently, say once per hour. Assuming that the product size approximates the Rosin- Rammler form (see Rosin, P. and Rammler, E., The Laws Governing the Fineness of Powdered Coal, published in the Journal of The Institute of Fuel, October 1933), it can be shown that the constant condition is equivalent with the requirement of a minimum specific surface. If this assumption is not allowed, the same optimization principle applies, but the constraint condition will be replaced with Equation 29. The result will then be a maximum production for a given minimum specific surface (material size).

With on-line operation, updating is necessary. The value it is updated on line by a once-a-shift measurement and entry into the computer of the values [e] and [f], which are the particle size distributions at the input to and output from the ball mill. The hardness, H, of the incoming clinker material is also measured at that time. The computer calculates the new value of n by solving Equation 14. It then updates the coeflicient a in Equation 10B. Then for subsequent optimization calculations, the updated predictive Equations and 6 for b are solved.

For updating the separator coeificients, there are required once-a-shift measurements of the size distribution of recycle material [r] and product [p], as well as the values of product flow rate P (tons/hour) and reject product air rate R (tons/hour). The procedure to be followed is specified on page 32.

The computer functions in response to the indicated inputs to update the ball mill and separator coeflicients and to use these together with the [i] and H inputs in Equations 24 through 28 for calculating and producing output signals I and D to give a maximum P for the constraint condition which has been imposed.

There has accordingly been described and shown herein a novel, useful, and improved system for computer controlled optimization of a closed circuit grinding system for a finish cement mill.

The embodiments of the invention in which an exclusive property or privilege is claimed are defined as follows:

1. Apparatus for optimizing the output product flow rate from a particulate processing system of the type wherein a controllable carrying means carries new material from a source to be mixed with rejected material and then fed to a grinding means the output from which is fed to a controllable means for separating said grinding means output into accepted material having a predetermined range of particle sizes and rejected material having particle sizes outside of said accepted range, said apparatus comprising:

means for measuring the hardness, H, of the new material and establishing H signals representative thereof;

means for measuring the particle size distribution, [i],

of the new material and establishing [i] signals representative thereof; and

means responsive to said H and [i] signals for controlling said controllable carrying means and said controllable separating means for optimizing the amount of accepted material within said predetermined range of particle sizes in accordance with specified criteria.

2. Apparatus as recited in claim 1 wherein said means responsive to said H and [i] signals for controlling said controllable carrying means and said controllable separating means includes computer means responsive to said H and [i] signals for generating a D electrical signal indicative of the maximum acceptable particle size and an I electrical signal representative of a rate of new material flow from said source for optimizing accepted material output from said separating means having predetermined particle sizes.

3. The combination as recited in claim 2 wherein there 18' is included means for measuring the particle size distribution of said rejected material and generating [r] signals representative thereof, means for measuring the particle size distribution of said accepted material and generating [p] signals representative thereof, and means for applying said [r] and [p] signals to said computer means for updating its response to said H and [r] signals.

4. Apparatus as recited in claim 1 wherein said controllable carrying means is a conveyor belt, said grinding means is a ball mill, and said controllable means for separating saidgrinding means output into accepted material and rejected material includes a separator having a movable damper blade for determining the portion of incoming material which is accepted material having a predetermined particle size range.

5. Apparatus for optimizing the output product flow rate for a finish cement mill of the type wherein a controllable carrying means carries new material from a source to be mixed with rejected material and then fed to grinding means the output from which is fed to a controllable means for separating said grinding means output into accepted material having a predetermined range of particle sizes and rejected material having par ticle sizes outside of said accepted range, said apparatus comprising:

means for measuring the particle size distribution, [i],

of the new material and establishing [i] signals representative thereof;

means for measuring the particle size distribution, [e],

of the material entering said grinding means and establishing [e] signals representative thereof;

means for measuring the particle size distribution, [f],

of the material leaving said grinding means and establishing [f] signals representative thereof;

means for measuring the particle size distribution of the rejected material and producing [r] signals representative thereof;

means for measuring the particle size distribution of accepted material and producing [p] signals representative thereof;

means for measuring the flow rate of said rejected material from said controllable separating means and producing R signals representative thereof;

means for measuring the flow rate of new material from said source and producing I signals representative thereof;

means for measuring the flow rate of accepted material and producing P signals representative thereof; and means responsive to said H, [i], [e], [f], [r], [p], R, P, and I signals for controlling said controllable separating means and said controllable carrying means for optimizing accepted material output from said controllable separating means having predetermined particle sizes. 6. The combination with a cement mill of the type including a source of new material; a ball mill having an input and an output; a separator having an input, an accepted material output, a reject material output, and a movable damper blade for determining from the material supplied to its input the particle sizes of the material which will be directed to its accepted material output; belt means for carrying said new material from said source to said ball mill input; means for carrying output from said ball mill to said separator input; and means for carrying output from said separatorreject material output to said belt means to mix thereon with said new material, of:

means for measuring the hardness of the new material and establishing H signals representative thereof;

means for measuring the particle size distribution of said new material and for establishing [i] signals representative thereof; and

computer means to which said H and [i] signals are applied for positioning said movable damper blade and for controlling the speed of said belt means to optimize the accepted material obtained from said separator having predetermined particle sizes. 7. The combination as recited in claim wherein there is included means for meausring the particle size distribution of said rejected material and generating [r] signals representative thereof, means for measuring the particle size distribution of said accepted material and generating [p] signals representative thereof, and means for applying said [r] and [p] signals to said computer means for updating its response to said H and [i] signals.

8. The combination with a cement mill of the type including a source of new material; a ball mill having an input and an output; a separator having an input, an accepted material output, a reject material output, and a movable damper blade for determining from the material supplied to its input the particle sizes of the material which will be directed to its accepted material output; belt means for carrying said new material from said source to said ball mill input; means for carrying output from said ball mill to said separator input; and means for carrying output from said separator reject material output to said belt means to mix thereon with said new material, of:

means for measuring the particle size distribution of said new material and for establishing [i] signals representative thereof;

means for measuring the particle size distribution of the material entering said ball mill and establishing [e] signals representative thereof;

means for measuring the particle size distribution of the material leaving said ball mill and establishing [f] signals representative thereof;

means for measuring the flow rate of said rejected material from said separator and producing R signals representative thereof;

means for measuring the flow rate of accepted material and producing P signals representative thereof; and

means responsive to said H, [i], [e], [f], [r], [p], R, P, and I signals for positioning said movable damper blade and controlling the flow rate of new material for optimizing accepted material output from said separator having predetermined particle sizes.

References Cited UNITED STATES PATENTS 3,011,726 12/1961 Herz 24133 X 3,027,099 3/1962 Ludwig 241-33 3,145,935 8/1964 Wilson 241-34X ANDREW R. JUHASZ, Primary Examiner.

U.S. DEPARTMENT OF COMMERCE PATENT OFFICE Washington, D.C. 20231 UNITED STATES PATENT OFFICE CERTIFICATE OF CORRECTION Patent No. 3,401,891 September 17, 1968 Philip J. Fleeman et a1.

It is certified that error appears in the above identified patent and that said Letters Patent are hereby corrected as shown below:

In the heading to the printed specification, lines 5 to 7, "assignors, by mesne assignments, to The General Electric Company, New York, N. Y. a corporation of New York" should read assignors, by mesne assignments, of fifty percent to The Bunk Ramo Corporation, Canoga Park, Calif. a corporation of Delaware and fifty percent to The General Electric Company, New York,

N. Y. a corporation of New York Signed and sealed this 13th cfay of January 1970.

(SEAL) Attest:

Edward M. Fletcher, Jr. A J Attesting Officer Commissioner of Patents

Claims

1. APPARATUS FOR OPTIMIZING THE OUTPUT PRODUCT FLOW RATE FROM A PARTICULATE PROCESSING SYSTEM OF THE TYPE WHEREIN A CONTROLLABLE CARRYING MEANS CARRIES NEW MATERIAL FROM A SOURCE TO BE MIXED WITH REJECTED MATERIAL AND THEN FED TO A GRINDING MEANS THE OUTPUT FROM WHICH IS FED TO A CONTROLLABLE MEANS FOR SEPARATING SAID GRINDING MEANS OUTPUT INTO ACCEPTED MATERIAL HAVING A PREDETERMINED RANGE OF PARTICLE SIZES AND REJECTED MATERIAL HAVING PARTICLE SIZES OUTSIDE OF SAID ACCEPTED RANGE, SAID APPARATUS COMPRISING: MEANS FOR MEASURING THE HARDNESS, H, OF THE NEW MATERIAL AND ESTABLISHING H SIGNALS REPRESENTATIVE THEREOF;