FIELD OF THE INVENTION
The present invention relates to a system and method for producing improved casting in a continuous casting process of steel manufacture by synthesizing optimum oscillation parameters.
In particular it relates to synthesizing oscillation parametric variation with casting speed in a continuous caster for minimizing adverse effects on performance and quality of castings in comparison to parametric schedules available currently that are provided by original equipment manufacturers (OEMs).
BACKGROUND OF THE INVENTION
In continuous casting process of steel manufacture the steel from a ladle is teemed to a tundish that acts like a buffer vessel. From the tundish, through a bifurcated submerged entry nozzle, the liquid steel is poured into a water-cooled copper mold about a meter in length. Water is circulated through slots in the mold to extract heat transferred from the liquid steel. Consequently, a thin solidified steel shell develops next to the mold inner walls whereas the steel remains liquid inside this shell. The solidified shell grows in

thickness even as it is continuously withdrawn from the mold on rollers and further cooled using water sprays. Finally, the completely solidified slab of required length is cut from the continuously cast strand.
Continuous casting is a critical process in steel manufacture where molten metal is solidified in the form of slabs of rectangular cross-section. Minor variations in this process can impact the production process widely - from excellent product quality to breakdown in the production chain.
The continuous casting process itself is facilitated by two interlinked sub-processes, namely, mold oscillation and lubricant addition. These essentially seek to neutralize two major problems associated with continuous casting, namely, sticking of the formative steel shell to the internal walls of the mold, and non-uniform development of shell across the strand perimeter due to uneven heat transfer.
The mold is made to oscillate along its longitudinal axis with amplitude less than 10 mm and frequency between 50 and 400 cycles per minute (cpm). The oscillation directly helps in detaching the solidified shell from the mold wall (like an AC current 'throws

back' a human finger in touch with a live wire), and indirectly enables the lubricant placed at the meniscus of the strand to penetrate uniformly further down into the small gap between the shell and mold.
Lubricant in the form of solid powder is poured from the top onto the meniscus where it melts in contact with the hot material. The liquid 'lubricant' then penetrates into the gap between strand and mold. Both upward and downward movements in the oscillation cycle enable this penetration. Since the strand inside the mold is always moving downwards with a certain speed (the 'casting speed*), in relative terms the mold moves downward only when its downward speed is greater than strand speed. This part of the oscillation cycle is referred to as "negative strip" while its supplement is "positive strip".
While negative strip aids in deeper penetration of lubricant, the positive strip pulls the lubricant from meniscus top towards the sides and also enables uniformity of spread within this gap.
Neutralization of the prime problems of continuous casting using oscillations leaves certain side effects. These are, firstly, the formation of 'oscillation marks' on the slab surface during negative strip [2] that look like cracks. Apart from being a quality issue in

itself, these marks also tend to degenerate into fault lines for the formation of transverse cracks. Secondly, during the positive strip the relative speed between strand and mold maximizes leading to a 'peak friction', which is higher than what would have been under non-oscillating conditions. This peak friction can potentially cause tearing of the formative shell near the meniscus, leading to sticking. Thus, it is apparent that the designer of oscillation strategy has to plan for maximizing the desirable effects, while minimizing the undesirable ones.
The oscillation designer does not have too many degrees of freedom in his hand for effecting an optimization as above. Only the oscillation frequency / and amplitude s (stroke) are available. Suzuki and others [3] showed that the wafeform could also be varied from the sinusoidal with gainful effects. Slower speed and longer time for upward movement, accompanied by faster and shorter downward movement will result in smaller negative strip time (time spent in negative strip within one cycle) as well as lower peak friction. The reduction in peak friction with lower upward maximum speed is obvious. Using x (= 0.5 for sinusoidal and 0.5 < x < 1 for gainful non-sinusoidal) to indicate degree of variation from sinusoidal, the designer now has s, f and x as free parameters.

He has to select an optimum schedule of these parameters across the range of casting speed v to achieve maximum lubrication with minimum peak friction and oscillation mark depth. The quality and productivity of steel manufacture depends significantly on this choice.
SUMMARY OF THE INVENTION
The main object of the present invention is to provide a new method for optimal synthesization of the different oscillation parameters of the mold oscillation system in a continuous casting process of steel manufacture. The optimality is addressed from the perspective of enhancing the mold lubrication, especially during higher casting speed.
Another object of the invention is to reduce the intensity of oscillation marks.
Yet another object is to reduce peak friction within an oscillation cycle.
These and other objects can be achieved with the aid of a genetic rule to optimize the amplitude, frequency, and waveform, i.e. degree of deviation from the sinusoidal form of the oscillation of the continuous casting mold, based on objective functions that maximize the lubrication, and minimize the depth of oscillation marks and the cycle peak friction.

The optimization is performed within constraints imposed by machine limits. The objective function and constraints are extracted from analysis of the physics of oscillation, lubrication and heat transfer within the continuous casting process, and expressed as a set of algebraic relations.
In the present invention a genetic rule or algorithm (GA) is used for optimization of oscillation parameters. The oscillation parameters stroke, frequency and deviation from sinusoidal form are denoted by s, f and x respectively. Oscillation performance metrics are constructed based on calculated lubrication index and predicted peak friction and depth of oscillation marks. These metrics are used within an objective function to be optimized to achieve that scheduling of s, f and T with v that provides best oscillation performance. The objective function is defined in terms of the 'free' parameters s, f and x. In each generation of the GA, the fitness (objective) function for each member of the population of chromosomes (i.e. potential solutions expressed as concatenated bit mappings of stroke, frequency and waveform) is calculated using the above relations and compared with fitness of other members. Selection of a member to the next generation is dependent on this relative fitness - thus imposing the 'survival of the fittest' principle. In a new generation, population members are split and cross-combined ("crossover") and also bit-flipped ("mutated") occasionally to generate new solutions, which are then

compared for relative fitness and the cycle is repeated till the highest fitness attained converges. This 'highest fitness solution' corresponds to a certain combination of s, f and T. The above-mentioned procedure is repeated for different values of the casting speed.
Following the above procedure an optimal free parameter set consisting of stroke s, frequency f and deviation from sinusoidal waveform x, for the oscillating mold in the continuous casting process of steel manufacturing, has been designed by coupling a genetic algorithm with synthesized prior knowledge of cross-parametric physical relationships. Compared to the parameter set implemented according to the original equipment manufacturer, the GA set provides favorable performance for all individual oscillation effects like lubrication, peak friction and depth of oscillation mark, as results indicate.
In a preferred embodiment, the present invention provides a method for producing improved castings in a continuous casting process of steel manufacture, said method comprising the steps of: passing molten steel through a substantially vertically-aligned hydraulically operated oscillating mold of rectangular section to emerge in the form of a continuous strand comprising a solidified shell encapsulating molten material; imposing oscillation on the oscillating mold with a waveform having frequency less than 300

cycles / min and stroke below 10 mm for preventing sticking / attachment between downward moving strand and mold and for uniform penetration of lubricant film between said moving strand and said mold; and regulating the oscillation parameters based on casting speed; wherein the parametric variation of oscillation schedule is synthesized with the casting speed with the aid of a genetic rule for maximizing lubrication benefits and minimizing adverse effects of peak cyclical friction and depth of oscillation mark.
The oscillation waveform is either sinusoidal or non-sinusoidal. The oscillation parameters like waveform, frequency and stroke are desirably regulated with casting speed. The desire being to attain an oscillation parameter schedule with casting speed for a given mold with geometrical and performance specifications, oscillatory speed and acceleration limits, such that lubrication is maximized and peak friction and depth of oscillation marks minimized over all casting speed regimes.
The invention provides a method for synthesizing that parametric variation with casting speed which maximizes benefits of lubrication and minimizes all adverse effects on performance and quality of casting, in comparison to parametric schedules available currently that are provided by original equipment manufacturers (OEMs).

The synthesizing of oscillation parametric variation is performed with the help of a genetic rule or algorithm (GA) for its optimization. The fitness function for the GA being singularly constructed from synthesized prior knowledge of the physics of oscillation and associated phenomena, using interrelationships between derived quantities like positive and negative strip times, negative strip distance, lubrication index and independent parameters like waveform, frequency and stroke.
The constraints of the optimization being extracted from the functionality of mold displacement, velocity, acceleration and jerk with normalized time in a non-sinusoidal waveform, coupled with the limits on these imposed by mechanical constraints of mold machinery.
The synthesized oscillation schedule runs on a programmable logic controller (PLC) in the form of a control table.
The control table receives real time inputs of the speed of casting from sensors and controllers at various points of the plant wide network.

The control table generates real time outputs in the form of command signals from the PLC to actuators of the mold hydraulic oscillator to appropriately modify the stroke and frequency.
BREIF DESCRIPTION OF THE ACCOMPANYING DRAWINGS
The invention can now be described in detail with the help of the figures of the accompanying drawings in which
Figure 1 shows a slab caster machine configuration
Figure 2 shows displacements in sinusoidal and non-sinusoidal oscillations
Figure 3 shows negative strip time along with velocity
Figure 4 illustrates impacts of different parameters on described effects
Figure 5 shows variation of stroke with casting speed. GA synthesized solutions, low / mid-C mode and peritectic mode, versus OEM-supplied values for corresponding grade types.

Figure 6 shows variation of frequency with casting speed. GA synthesized solutions, low / mid-C mode and peritectic mode, versus OEM-supplied values for corresponding grade types.
Figure 7 shows variation of lubrication index (LI) with casting speed. Comparing GA synthesized solution at the two grades versus OEM provided values at the same grades.
Figure 8 shows variation of negative strip time (NST) with casting speed. Comparing GA synthesized solution at the two grades versus OEM provided values at the same grades.
Figure 9 shows variation of peak friction factor (PFF) with casting speed. Comparing GA synthesized solution at the two grades versus OEM provided values at the same grades.
Figure 10 shows variation of negative strip distance (NSD) with casting speed. Comparing GA synthesized solution at the two grades versus OEM provided values at the same grades.

Figure 11 shows variation of positive strip time (PST) with casting speed. Comparing GA synthesized solution at the two grades versus OEM provided values at the same grades.
DETAIUP PESCRIPTION
In the slab caster machine configuration illustrated in Figure 1, reference 1 represents a ladle turret. A tundish / tundish car is represented by reference 2. A mold 3, first zone (secondary cooling) 4, strand guide (plus secondary cooling) 5 and straightener withdrawal units 6 are also shown.
Within the continuous casting process of the steel manufacture molten steel is passed through a water-cooled substantially vertically-aligned oscillating mold of rectangular cross-section about a meter long to emerge in the form of a continuous strand consisting of a solidified shell encapsulating molten material.

Figure 2 illustrates the displacement of sinusoidal and non-sinusoidal oscillation. Slower speed and longer time for upward movement, accompanied by faster and shorter downward movement as shown in Figure 2, will result in smaller negative strip time. This is illustrated in Figure 3, while the reduction in peak friction with lower upward maximum speed is obvious.
In this section the mathematical relationship between lubrication index (LI) and the parameter set S = { v, s, ƒ,τ) is described, which enables an explicit expression for fitness function to be constructed. The constraints based on machine limits are stated. Features of the genetic algorithm (GA) used for optimization are then described.
The primary function of oscillation is to maximize lubrication between the strand and mold. As explained in the last section, this is effected in two ways, first, by creating a detachment between the strand and mold, and second, by facilitating entry and spread of lubricant into the thin gap between the two. Using LI to denote lubrication index, it follows that one of the tasks of optimization is to maximize LI.

Likewise one may denote peak friction and depth of oscillation marks as PF and OM respectively. As discussed, these are the two undesirable side effects of oscillation and obviously they are sought to be minimized.
From above considerations one may define a performance metric PM1 for maximization as

For the purpose of optimization a fitness function needs to be defined that can be expressed in terms of the free parameters v, s, f and x denoting casting speed, stroke, frequency and deviation from sinusoid, respectively. This function would provide the performance 'fitness' of any selected parameter set {v, s, /, x}. It is shown in the next section that the effect LI can be explicitly defined in terms of these parameters. However, PF and OM are dependent on many lateral conditions and a reliable mapping between the parameter set and these effects cannot be easily extracted, thus ruling out direct use of metric PM1 within a fitness function for simulated optimization.

Figure 4 provides a view of the physical relationship between the free parameters and the three effects. Each effect is shown as a circle, with a '+' or '-' at the top denoting desirability or otherwise. The arrows represent the four free parameters, with a'+', a'-' or a '0' next to the arrow denoting direct, indirect or no relationship with the effect shown in the corresponding circle, when other parameters are held constant. If the product of the sign shown near an arrow and the sign within the circle is a plus, the parameter is desirable from the viewpoint of that effect, else it is undesirable. Thus, if a circle is negative, and a parameter varies inversely with the effect shown in that circle, then it is desirable to increase this parameter.
The Figures themselves need a physical explanation. As stated in the introduction, also [3], [4], increasing x reduces peak friction as also the depth of oscillation marks. Thus x contributes negatively to these circles. From detailed analysis of the mechanism of formation of oscillation marks, as in [5] or [2], it is known that higher frequency damps oscillation mark depth while stroke increases it. The signs are shown accordingly. Considering peak friction, both frequency and stroke increase mold upward velocity and hence amplify PF. As for lubrication, it is understood that higher stroke has a beneficial effect while frequency tends to mildly damp it ([2], [4]), the figures reflect accordingly.

From an analysis of the above figures, and the physics behind these figures, one can generate a substitute for PM1 bypassing the need for explicit mathematical relationship between PF and OM, and the parameter set {v, s, ƒ,τ}. Since LI can be expressed mathematically, the focus is on PF and OM. From Figure 4, one may see that stroke s is undesirable for both. Frequency / is undesirable from the viewpoint of PF, but desirable for OM. IF one considers OM as more critical, then it is desirable to increase / but the relationship is not as explicit as in case of stroke. Accordingly, a new performance metric PM2 may be crated for maximization as

Although PM2, unlike PM1, is numerically tractable in the sense that given a parameter set { v, s, ƒ,τ} the performance metric can be numerically evaluated thus making it usable within an evolutionary optimization algorithm, it is somewhat simplistic in that it short-circuits the design parameters directly into the metric (the last two terms).

Optimization results using PM2 (i.e. equation (2)) as a cost function have been carried out and reported in [8], steep variation in frequency with casting speeds have been observed and the benefits in LI seem to be sub-optimal, primarily because forced reduction in stroke is enforced in this metric - and stroke, as just discussed, contributes positively to lubrication. Thus a more realistic, numerically tractable representation of PM1 is sought.
In the following sections, it is shown (equation 56) that the peak friction PF can be approximated by a term called peak-friction-factor or PFF, which can be numerically calculated from a given parameter set. Also, the depth of oscillation mark or OM can be replaced by the negative strip time or NST that is numerically deducible from the given parameter set. Accordingly, one may express PM1 as

where the metric PM3 is sought to be maximized. Different selections of positive weights wl, w2 and w3 (based on domain-heuristic considerations) on PM3 as a scalar objective function are expected to provide specific optimal solutions using a GA, that would

otherwise be identified (again using domain heuristics) as specific points on the pareto-optimal solution surface in the parameter space resulting from evolutionary optimization of the multiple conflicting objectives LI, PFF and NST. In other words, the direct fusion of domain heuristics with evolutionary optimization can effectively bypass the need to first generate a pareto-optimal front, and then seek solutions on that front.
Expressions for the displacement of the mold
To start with, the expressions for the displacement of the mold as the function of time were derived and can be represented by a set of equations over a single cyclic divided into four zones as given below.



In equations (5)-(8), x is the oscillation mode and is given by, Maximum amplitude location (in T)
" (9)
Further, in equations (5)-(9), T is defined as T= tf. Two new zones can further be created and are given by zone-AB and Zone-CD.
Zone AB:

Expressions for the velocity of the mold
It is easy to obtain the expressions for the velocity at different zones by differentiating the displacement expressions given by equations (8)-(ll) with respect to T as given below.
Zone A: (Displacement is positive and the mold moves upwards)

Zone B: (Displacement is positive and the mold moves downwards)


Zone C: (Displacement is negative and the mould moves downwards)

Similarly, the expressions for the velocity in Zone: AB and Zone-CD can also he calculated as given below. Zone AB:

Expressions for the acceleration of the mould
The expressions for the acceleration of the mould in the four zones can be obtained by differentiating eqns.(i6)-(21) with respect to T.

Zone B: (Displacement is positive and the mould moves downwards)

Zone C: (Displacement is negative and the mould moves downwards)


where a = s/ 2 , a is the amplitude.
Similarly, the expressions for the acceleration in Zone-AB and Zone-CD can also be calculated as given below.

Constrained equation far mould velocity
In order to obtain the constrained equation of mould velocity, the time derivative of the mould velocity was obtained and the maximum mould velocity was found out by equating the time derivative to zero. The expression for the velocity of the mould in zone-B is given by eqn.(17).


In order to obtain the maximum mould velocity, the expression given in eqn.(28) is
differentiated with reapecl to and equated to zero, i.e.,
Alter differentiating and equaling to zero, one can obtain the expression as.

Further, the expression for / can be calculated from eqn.(29) and given m,

Different values of n correspond to the instant of maximum velocity for successive waves. Now, by substituting the value of t into eqn.(28), the maximum velocity v'is obtained and given by,

Substituting n = 1 in eqn.(30), the value of r is obtained as,

Now, the machine generic constrained equation for (he vehocity can be obtained by substituting eqn.(32) into eqn.(31) and this is given by,

fn order to obtain the constraint for the machine specific maximum possible velocity, the machine limit of velocity given by the Original Equipment Manufacturer (OEM) and denoted as Vmax is multiplied by a constant, say 0.9.

Constrained equation for mould acceleration
In order to obtain the constrained equation of mould acceleration the time derivative of mould acceleration was obtained and the maximum mould acceleration was found out. The expression for the velocity of the mould in zone-B is given by eqn.(17).
Now, it is known that Hence, the mould acceleration can be expressed as.

In order to obtain the maximum mould velocity, the expression given in eqn.(34) is differentiated with respect to f and equated to zero, Thus, one can obtain the expression as,

Further, the expression for t can be calculated from eqn.(35) and given as,

Different values of n correspond to the instant of maximum velocity for successive waves. Now, by substituting the value of t into eqn.(34), the maximum velocity A* is obtained and given by,

However, this point lies in Zone-CD which is a weighted combination of zones-C and D, with much heavier weight towards zone:D. Hence, at the above value of t, the acceleration is significantly damped and the maximum value is not obtained. The start
and end points of different Zones when perturbation =
are given as below.


Substituting n = i (as the instant at which the maximum acceleration occurs in a wave will not change across successive waves) in eqn.(36), the value of / where the maximum acceleration occurs, is obtained as,

Similarly, the machine generic constrained equation for the acceleration can be obtained by substituting n=l in eqn.(37) and is given by,

Further, in order to obtain the constraint for'the machine specific maximum possible acceleration, the machine limit of acceleration as provided by the Original Equipment Manufacturer (OEM) and denoted as amax, is multiplied by a constant, say 0.9.
Expressions for the objective functions
Araki and Ikeda [4] have proposed a relationship between LI and other intermediate casting variables, which in turn may be related to parameter set S. This relationship has been shown to be working well on comparing computed LI with rate of powder (lubricant) consumption, which is an indication of the effectiveness of oscillation in enhancing lubrication. The authors have independently verified this relationship by performing simulations on the ilSI website 11 J. The relation stales


with Nd the negative strip distance, i.e. distance covered in negative strip in one cycle, Vc .= v, and tp is the positive strip time.
Further, the negative strip distance Nd may be expressed as

The time-dependent velocity of the mould, Vm is given by.

By substituting eqn.(43) in eqn.(42) and integrating, the expression for tlie negative strip distance is obtained as,

(Eqa.(44) is similar to the expression for S (ie. Nd) under non-sinusoidal conditions as
*
provided in [4].)
where tneg is the negative strip time expressed as

Equations (8) and (9) for non-sinusoidal oscillations are according to [6], under sinusoidal conditions, i.e. x = 0-5, they reduce to standard equations for negative strip found in open literature, i.e.

with positive strip time tp defined as


Substituting eq. (45) in eqs. (44) and (47), eq. (44) in eq. (41), and eqs. (41.) and (47) in eq. (40), one may write the expression for Li a,s

The fitness function is obtained by substituting eq. (48) in eq. (B) for PM2, thus providing a performance measure for any selected parameter set S.
Constraints are defined in terms of the following

While relations (49-53) are generally taken as standard limits lor mold oscillation and considered here accordingly (note than ƒis expressed in cycles per minute), the LBS of relations (52-53) are derived from equations describing non-sinusoidal waveforms and correspond to the maximum attainable values of velocity and acceleration for a selected waveform. These are set to he less than 80% of the machine limits, expressed as Vmax and

At a given value of v (=VC), the peak friction PF may be expressed as

where Vupmsx is the maximum upward speed in a cycle, is the viscosity of lubricant and a, tile thickness of lubricant film in the gap between strand and mould. The latter two being extraneous factors to an oscillation schedule, a Peak friction Factor PFF may be defined such drat

A GA is used to derive that parameter set S, which maximizes the fitness function, defined by performance metric PM2. In this process the casting speed v is fixed, and s, f, and r are evaluated as a function of v. Different values of v are fed. as input, the GA generates corresponding output sets of s, /and c
A baseline GA process is well known and not described here. The parameters to be optimized, namely s. f, and %, are binary coded and concatenated to form bit strings (chromosomes) mat constitute the population members that are operated upon in parallel. In each generation the fitness of a population member is evaluated by calling the fitness function, expressed inetjs. (2) & (47).
Genetic algorithms 6end to slow down after nearing an optimum solution point in the n-dimensional (here n = 3) solution space, and some means are usually implemented for accelerating the GA process. The acceleration methods used here are, first, elitism [7] where the best solution obtained in a certain generation is preserved in succeeding generations until a better one is found, second, cyclical variation of mutation rate across generations [8], and third, differential mutation of bits according to significance in good and bad schema in solution strings [9][10].

Results and discussions
The. genetic algorithm as described above Ls used to optimise the oscillation paraimu-rs stroke, frequency and deviation from sinusoid, with the objective of maximizing lubrication and minimizing peat friction and oscillation marks. This is achieved by optimizing the fitness function according to eqs. (4) and (48), under the constraints expressed in relations (49-53).
The GA is tested with different population sizes and a size, of 20 is selected for performing downstream executions. A test case with WI = 0.85, w2 = 0.13 and w3 = 0.02 (refer eq. 2) is taken at v - 1.4, and the variation of convergence history and final converged solution with arbitrary changes in initial population is observed. The objective function PM2 (eq. (2)) is used, and the solution is stopped after 5000 generations, a stage when it is assumed to have fully converged. Variations in convergence are seen only within the first 1000 generations; the final solution is always same with practically no variation. In these test cases frequency is allowed to vary between 80 to 200, which is a wider range than that specified in eq. (49). This case takes less than a minute of computation time on a Pentium D 2.6 GHz desktop.
Production runs are executed to cover the entire range of casting speed, from 0.05 meters/min to 1.95 m/min, at intervals of 0.05 m/min. The performance metric PM3 is used as cost function (weight selection details are explained below), and the constraints are exactly as specified in eqs. (49-53). The resultant values of s, f, and x for each case were tabulated, with the objective of generating a schedule for the oscillation parameters against casting speed, In each speed case the complete GA solution over 5000 solutions was executed. The net computation time is approximately 30 mins. on the mentioned desktop.
Referring back to the discussion on Oscillation Performance Metric 3 (PM3, eq. (4)), the oscillation schedule designer would like to arrange the weights wl, w2 & w3 given lo 1.1, NST and PFF in a manner consistent with his understanding /interpretation of domain

heuristics. The three weights should preferably add up to one to normalize different weight allocation strategies.
Facilitating lubrication beiag the prime purpose of oscillations, prima-facie the major share of weight should be allocated to LI (i.e. wl). Between NST and PFF, one may say that NST is more important as it can directly affect product quality while the latter can be somewhat compensated with higher LI. Thus, one may broadly set an inequality of the form

Now, for peritectic steel grades, oscillation marks and their consequential effects are of greater concern than in case of low or medium carbon grades Correspondingly, the LI is of a slightly lower concern in peritectic grades. Figures (7j!$sho*v'ing variation of LI and NST with casting speed as calculated from oscillation schedules provided by an OEM, for peritectic and low/mid-C grades, corroborate this relative prioritization of oscillation performance objectives across steel grades. These figures show GA results also, to which we will return later for discussion. Thus, between wl and w2 (weights of LI.and NST), the designer's preference is for higher difference (wl - w2) for low/mid Carbon steels as compared to peritectic. Also, this difference should increase with casting speeds, to offset lower LI at higher speeds and deeper oscillation marks at lower speeds.
From the above discussions ihe following requirements can be defined on the selection of weights wl, w2 & w3. First,

Second, difference D = (wl - w2) should be greater in the case of low/mid-C as compared to periteetie grades. Third, D should be gradually increasing with casting
speeds.
Based on the above requirements, the following pattern of variation of weights was
implemented:
For peritectic grades:

Case (a) wl = 0.6, w2 = 0.3, w3 = 0.1; for cs < 0.8 m/min.
Case (b) w f = 0.7, w2 = 0.2, w3 = 0. j; for cs > ! A ami
Case (c) wi and w2 vary linearly from case (a) to (l>) for
0.8 1.5, and
Case (c) wl, w2 and w3 vary linearly from case (a) io (b)
for 0.8 < cs < 1.4.
Figures 5 and 6 show variation of stroke and frequency, respectively, with casting speed for ine two GA solutions against the schedules provided by the Original Equipment Manufacturer (OEM) for the same two grade cases. The value of deviation-from-sinusoid x quickly converges to the maximum (0.7) and hardly moves from there across the speed range, and hence this is not plotted. Recall from fig. 4 that increased T was desirable from the perspective of all 3 effects, and the GA solutions strongly confirm this. One needs to keep in mind that both OEM schedules are provided at sinusoidal waveform, i.e. x ~ O.S.
In the GA solutions the value of stroke remains at 10 (the maximum limit) throughout the speed range, ft is seen in Rg. 4. that large stroke is desirable from the viewpoint of increasing lubrication, but undesirable tor NST and PFF. However, as the allocated weight to LI makes it dominant, the value of stroke is driven towards its maximum.
Increasing frequency has only a weakly detrimental effect on LI, but is desirable from the viewpoint of reducing NST. These effects also vary with casting speed, and moreover the objective function weights are also scheduled across casting speed. Relative higher weights given to Li compared to NST, as in case of low/mid-C mode, tends to keep frequency on the lower side. For peritectic mode where relative weight to NST is higher, there are conflicting pulls on frequency across the speed range, making it tend to converge to higher values.

Figures 7-9 show variation of LI, NST and PFF respectively against casting speed. Values obtained from GA optimization using weights corresponding to peritectic mode, and low/mid-C mode, are shown and compared against values provided by OEM for the same two grade-classes and currently installed in the casters of Tata Steel Jamshedpur. The following explicit observations can be made:
1) The values of Lubrication Index LI obtained from GA are higher than those obtained from OEM all across the casting speed range. This value is about 55% higher than the higher OEM value (for low/mid-C) at a speed of 0.8 meters/min, and about 25% higher at a speed of 1.95. This is significant, since insufficient lubrication is assumed to be one reason why casting becomes difficult at high speeds. In particular, the value of LI of 1.78 at me maximum speed of 1.95 is touched by the higher OEM curve at a low speed of 0.45, and continues to fall thereafter.
2) Between the OEM-provided values, LI for low/mid-C is consistently higher than that for peritectic-C
3) Somewhat unexpectedly, the LI generated by GA from bom the modes of weight selection are practically identical The reason behind this is explained later
4) All through the range of production speeds, me NST and consequently the depth of oscillation marks, arc lower for peritectic-C as compared to low/mid-C, bom for the two OEM curves when mutually compared, as well as for the two GA curves. This is exactly as expected
5) When comparing NST between low/mdrC from OEM versus low/mid-C from GA, the GA values are lower (equaling OEM at a few points), while comparing NST for peritectic-C from OEM against mat from GA shows that mey are more or less similar across the range of production speeds
6) Looking at peak friction factor (Fig. 9% it is seen that throughout the operating speed range, both GA from low/mid-C mode and peritectic-C mode produce lower PFF as compared to OEM for low/mid-C grades; however, OEM values from peritectic grades, with lower PFF, are at par with GA solutions for mese grades.

Figures 10 and 11 compare Negative Strip distance or NSD (this may be defined as the distance traversed by the mold within the part of one oscillation cycle when it is moving downwards faster than the strand), and positive .Strip time or PST, between GA from the two modes, and OEM schedules provided for the two grade types. This comparison is necessary as there is a perception that low NST leads to lower lubrication. This perception is tiue for a sinusoidal waveform, but wrong for non-sinusoidal waveforms. It is not NST, but NSD, which facilitates penetration of lubricant into the mold-strand gap. When waveform is sinusoidal, NST and NSD vary directly, while lor non-sinusoidal waveform this variation becomes inverse. Thus lower NST may be associated with lower lubrication for sinusoidal waveforms (as, e.g., provided by OEM schedules), but not all so for non-sinusoidal waveforms, as provided by the GA solutions.
Looking at figs, 8 and 10 together, it may be observed that between the OEM values, NST is higher for low/mid-C, while NSD is also higher for the same grades, as compared to peritectic-C. ft has to be kept in mind that OEM values are on sinusoidal waveforms. For the GA solutions, it is seen that peritectic-C provides lower NST as compared to low/mid-C, but it also provides higher NSD. The waveform of GA solutions converges to a t-faetor (degree of deviation from sinusoid, 0.5 corresponds to sinusoid) of 0 7. This demonstrates that lower NST is associated with higher NSD, and actually better lubrication, for these conditions. Figure 3 explains the physics behind this variation. It shows that as the deviation from sinusoidal waveform increases, the NST (represented by intercept on the x-axis) reduces, while the NSD (shaded area between mold velocity and strand velocity (i.e. casting speed)) increases.
Figure 1.1 Shows variation of PST for the four cases. The only point of observation in these curves is that PST from peritectic-C GA solution is lower than from low/mid-C GA. It is a combination of NSD and PST that facilitate lubrication; between the two GA modes peritectic-C provides higher NSD but lower PST, which combine to provide net LI at similar levels as from low/mid-C GA solution. This explains the unexpected observed similarity in LI values between these two GA modes.

Overall, it can be observed that between the OEM values and the GA solutions, the latter is better in all the performance indicators of oscillation, namely, better Lubrication Index, lower NST (i.e. shallower oscillation marks), and lower PFF (i.e. lower friction overhead of oscillation). Further, it appears that both GA solutions, one for peritectic-C and the other for low/mid-C, have the same distribution of LI across casting speeds, while the former provides lower NST and the latter lower PFF. Since NST is a more important factor in casting than PFF, one may converge to the view that the GA solution for low/mid-C mode can be over-ridden by the GA solution for the peritectic mode, for casting all categories of steel grades.
The schedule for variation of s, f, and T with casting speed is presented in Table 1. This schedule is implemented in the PLC for controlling the running oscillation parameters as the casting speed varies.

WE CLAIM
1. A method for producing improved castings in a continuous casting process of steel manufacture, said method comprising the steps of:
- passing molten steel through a substantially vertically-aligned hydraulically
operated oscillating mold of rectangular section to emerge in the form of a
continuous strand comprising a solidified shell encapsulating molten
material;
imposing oscillation on the oscillating mold with a waveform having frequency less than 300 cycles / min and stroke below 10 mm for preventing sticking / attachment between downward moving strand and mold and for uniform penetration of lubricant film between said moving strand and said mold; and
- regulating the oscillation parameters based on casting speed wherein the
parametric variation of oscillation schedule is synthesized with the casting
speed with the aid of a genetic rule for maximizing lubrication benefits and
minimizing adverse effects of peak cyclical friction and depth of oscillation
mark.

2. The method as claimed in claim 1, wherein the oscillation schedule comprising stroke, frequency and waveform is synthesized with the casting speed with the aid of a genetic the rule or algorithm (GA) 'survival of the fittest'.
3. The method as claimed in claim 2, wherein fitness function for the GA is singularly constructed from synthesized prior knowledge of the oscillation using interrelationship of derived quantities.
4. The method as claimed in claim 1, wherein said oscillation schedule is run on a programmable logic controller (PLC) in the form of a control table.
5. The method as claimed in claim 4, wherein said control table receives real time inputs of the casting speed from sensors and controllers arranged at different points of the plant-wide network.
6. The method as claimed in the preceding claims, wherein said control table generates realtime outputs in the form of command signals from said PLC to actuators provided in the mold hydraulic oscillator for modifying the stroke and frequency appropriately.

7. A system for producing improved castings in a continuous casting process of steel manufacture, said system comprising:
a water-cooled hydraulically operated and substantially vertically-aligned oscillating mold of rectangular cross section for passing molten steel therethrough so as to emerge in the form of a continuous strand comprising solidified steel encapsulating molten material;
a processor for regulating the oscillation parameters based on casting speed, said processor provided with means for synthesizing the parametric variation of operation schedule with the casting speed, using a genetic rule; and
a programmable logic controller (PLC) for running the operation schedule in the form of a control table and generating command signals from said PLC to hydraulic actuators provided in said mold oscillator for modifying the oscillation parameters and outputting said signals to actuators provided in the hydraulically operated oscillating mold.

8. A method for producing improved castings in a continuous casting process of steel manufacture, substantially as herein described and illustrated in the figures of the accompanying drawings.

A method and a system for producing improved castings in a continuous casting process of steel manufacture comprising passing molten steel through a vertically-aligned hydraulically operated oscillating mold of rectangular section; imposing oscillation on the oscillating mold with a waveform having frequency less than 300 cycles / min and stroke below 10 mm for preventing sticking / attachment between downward moving strand and mold and for uniform penetration of lubricant film between said moving strand and said mold; and regulating the oscillation parameters based on casting speed wherein the parametric variation of oscillation schedule is synthesized with the casting speed with the aid of a genetic rule for maximizing lubrication benefits and minimizing adverse effects of peak cyclical friction and depth of oscillation mark.