optimization of oval-round pass design using genetic algorithm
TRANSCRIPT
Robotics and Computer-Integrated Manufacturing 28 (2012) 493–499
Contents lists available at SciVerse ScienceDirect
Robotics and Computer-Integrated Manufacturing
0736-58
doi:10.1
n Corr
E-m
huaby0
Kazem.A
journal homepage: www.elsevier.com/locate/rcim
Optimization of oval–round pass design using genetic algorithm
Bin Huang n, Ke Xing, Kazem Abhary, Sead Spuzic
School of Advanced Manufacturing and Mechanical Engineering, University of South Australia,Adelaide 5095, SA, Australia
a r t i c l e i n f o
Article history:
Received 14 January 2011
Received in revised form
1 February 2012
Accepted 13 February 2012Available online 7 March 2012
Keywords:
Oval–round pass
Rod rolling
Hybrid model
Roll pass optimal design
Genetic algorithm
45/$ - see front matter & 2012 Elsevier Ltd. A
016/j.rcim.2012.02.004
esponding author. Tel.: þ61 8 8302 5561.
ail addresses: [email protected]
[email protected] (B. Huang), Ke.Xing@
[email protected] (K. Abhary), Sead.Spuzic
a b s t r a c t
The primary purpose of this paper is to propose a computer aided optimal design system to support a
generalized oval–round pass design, which is widely used as both intermediate and final passes in the
process of rod rolling. This system, which is based on a hybrid model and the genetic algorithm, is
developed to improve the efficiency, to reduce the manufacturing errors, as well as to extend the useful
life of rolls through uniform wear design. Generalized parametric equations are established for
geometrical modeling, graphic plotting of oval–round passes, as well as calculation of the cross section
area, contact area and the lengths of contact arcs along the cross section of round groove in the MATLAB
programming environment. Moreover, these equations can also realize the parametric transformation
between roll profile and mathematical models for the oval–round pass design and optimization. The
genetic algorithm is employed for the optimal design of oval–round passes in this paper. The objective
functions are formulated for minimization of power consumption in the rolling process, variances
between ideal dimensions and design dimensions, as well as variances between the lengths of contact
arcs. To reduce the complexity and computational burden of the system, some reliable empirical
formulas for the calculations of contact area and contact arc length are applied. Finally, the proposed
approach is applied to an oval–round pass design. Through simulation and comparison of results
against experimental data acquired from literature, it is found that this system is reliable, effective and
easier to use.
& 2012 Elsevier Ltd. All rights reserved.
1. Introduction
As a most important metal processing technique, rolling isemployed to reduce the thickness or change the profile of a longwork piece through plastic forces provided by a set of rolls. It iswidely used due to the good mechanical properties of rolledproducts, high ratio of length to thickness allowed for work piece,as well as high productivity of rolling system [1,2]. Rolling can beroughly classified into flat rolling and shape (or profile) rollingaccording to the cross sections of the final products. Roll pass design(RPD), which is the most important part in the process of shaperolling operation, generally means to design a series of embeddedgrooves and passes through which the rolled work piece can bedeformed sequentially to get the desired contour, size and mechan-ical attributes [3,4]. It is commonly believed that the acceleration ofindustrialization has led to a rapid increase of demand for steelproducts, which will place both opportunities and heavy burdens onsteel manufacturers. To satisfy the ever-increasing demand andcompetition in the steel industry, steel manufacturers are forced
ll rights reserved.
.au,
unisa.edu.au (K. Xing),
@unisa.edu.au (S. Spuzic).
to put more emphasis on technological innovation to improve theyield and quality of their rolling systems, as well as to improve theproduct diversity though developing flexible and reliableapproaches for RPD [5]. However, with the spread and elongationtaking place simultaneously in the deformation zone, numerouscombinations of system parameters must be analyzed. The intricaterelationships between parameters greatly increase the complexity ofRPD models, and place heavy computational burdens on designersas well as computer-aided systems. Thus, how to get an efficientsolution without losing its accuracy becomes the application bottle-neck of the RPD problem [6,7].
Since the design and implementation of RPD has been inves-tigated for centuries and quite a great deal of theoretical andexperimental data was accumulated, traditional approaches forRPD are always based on the experience of designers andempirical formulae [8,9]. This kind of method was popular forits ease of use in the early years. However, due to overlookingsome influencing factors as well as large approximations betweentheoretical models and practical operations, the traditional meth-ods are not able to establish mathematical models with enoughprecision for RPD, which greatly limited its application [10].
The development of finite element analysis (FEA) technology haspromoted its application in RPD. Currently, FEA has been widelyusing to simulate the deformation behavior of rolled material, and
B. Huang et al. / Robotics and Computer-Integrated Manufacturing 28 (2012) 493–499494
predict quite accurate procedure parameters such as rolling load,contact stress, rolling torque, and power consumption [11,12].Although these FEA-based methods can provide precise and detailedinformation about plastic deformation as well as an extensivedescription of the material flow in the deformation zone, theirdemand on computational resources remains a huge challenge [13].
In recent years, expert system technology using optimal algo-rithms and artificial intelligence has found a wide range of applica-tions in RPD and its optimization. Perotti and Kapai made the firstattempt to design an expert system to deliver solutions for roundbar rolling [14]. Kim and Im developed another expert system basedon the backward chaining algorithm for round and square barsrolling [15]. Kwon and Im proposed a computer-aided-designsystem for roll pass and roll profile design to minimize trials anderrors in industry [1]. Lambiase and Langella developed an auto-matic RPD method, which permitted a geometrical optimization ofroll passes while allowing for automation of the RPD process [16].In these systems, artificial intelligent strategies, such as geneticalgorithm, neural networks, particle swarm algorithm and antcolony algorithm are always employed for optimal calculation andoptimal design. These algorithms use some natural mechanismsinspired by biological evolution as their search engine, which canmake a strategic decision automatically, as well as guarantee theefficiency and enhance the flexibility of RPD.
The oval–round pass is the most commonly pass applied inintermediate and final stands, due to its simple profile, uniformdeformation, good surface quality and easy design [17]. This studyaims to present a parameterized and generalized strategy foroval–round pass optimal design, which is based on the geneticalgorithm. The analysis uses comparative analysis skills, and somesimple combined thermo-mechanical effects are taken intoaccount. The optimal solutions obtained from this research arecompared with some results from other publications. Somesimulations and lab-scale experiments will be carried out forfurther validation and modification. Solutions will be applied toindustrial production of round bars. This paper is organized asfollows. Section 2 presents a three-arc strategy for parameterizedgeometrical modeling, as well as an approach for the calculationof cross section area. Section 3 gives parametric equation basedapproaches for contact area and contact arc length calculation.The genetic algorithm employed for oval–round pass optimaldesign was introduced in Section 4. Section 5 is about case studyand comparative analysis between optimal solution achieved bythis research and result from other publication. The summary andconclusions were proposed in Section 6. A GA-based MATLABprogram was designed for oval–round pass optimal design andgraphic plotting.
Fig. 1
2. Parameterized geometrical modeling and cross sectionarea calculation
To apply the optimal algorithms and graphical output con-veniently, as well as improve the commonality of this methodol-ogy, it is first necessary to build parameterized geometricalmodels to realize the translation of roll pass profiles into designvectors [18]. According to statistical analysis of published data anddesign solutions, there are five kinds of grooves widely applied inrod rolling systems: round, rectangle (box), oval, edge oval, anddiamond (square) [1,14–19]. For brief models, the profiles of thesegrooves can be described using serials of arcs and sloping lines.In this part, a generalized three-arc method was proposed todescribe the profile of oval–round pass, and piecewise parametricequations were employed to translate cross sections into designvectors.
Fig. 1 shows a quart profile curve for the round and ovalgrooves, which can transform into each other through changingthe central points and radii of the three arcs. The dotted arc is theideal outline of products. This curve is composed of five parts:arcs AO1B, BO2C and CO3D , sloping line DE , as well as inner roundEO4F, where O1, O2, O3 and O4 are the center points of related arcs.D is the separating point, thus, in the rolling process, arcs AO1B,BO2C and CO3D play a dominant role in the deformation behavior,and only these three arcs are taken into account in the oval–roundpass design process.
Assuming the cross section curve is located in the y–z plane,and the x-axis is paralleled to the central axis of rolls and throughthe center of the roll gap. According to the definition andpreliminary properties of derivative, to avoid sharp points andensure the smooth of curve, the whole curve should be continu-ously derivable. Namely, B and C, which are the intersectionpoints of the three arcs, must have unique derivative values. Thus,central points O2 and O3 should be located on the straight linesO1B and O2C respectively. The whole cross section curve issymmetrical to z-axis, to ensure the intersection point A hasunique derivative value; central point O1 should be located on thez-axis. The piecewise functions for the oval and round grooves canbe described as
y¼
r1 sina aE½0,y1�
d1 siny1þr2 sina aE½y1,y12�
d1 siny1þd2 siny12þr3 sina aE½y12,y123�
8><>: ð1Þ
z¼ z0þ
r1 cosa aE½0,y1�
d1 cosy1þr2 cosa aE½y1,y12�
d1 cosy1þd2 cosy12þr3 cosa aE½y12,y123�
8><>: ð2Þ
where, r1 through r3 mark the radii of arcs AO1B, BO2C and CO3D
respectively; y1, y2 and y3 are the angles of arcs AO1B, BO2C andCO3D respectively; d1¼r1�r2, d2¼r2�r3, y12¼y1þy2, y123¼y12þ
y3, z0 is the vertical coordinate value of central point O1.Assuming B is also the intersection point of ideal outline and
design groove profile, and then y1 can be solved from Eq. (3). For agiven value c, which is the horizontal coordinate value of separating
Fig. 2
B. Huang et al. / Robotics and Computer-Integrated Manufacturing 28 (2012) 493–499 495
point D, find the value of y3 as Eq. (4).
r1 siny1 ¼ rk sin+AOB
z0þr1 cosy1 ¼ rk cos+AOB
(ð3Þ
y3 ¼ sin�1½ðc�d1 siny1�d2 siny12Þ=r3� ð4Þ
where, rk is the radium of ideal outline, which is a given parameter.As shown in Fig. 1, the one quart cross section can be divided
into four parts, ABJO1, BCIJ, CDHI and DFGH. The whole area of thegroove can be calculated from
S¼ 4� ðSABJO1þSBCIJþSCDHIþSDFGHÞ ð5Þ
Trapezium and sector formulas were employed to calculatethe areas of these four parts, and SABJO1
,SBCIJ, SCDHI as well as SDFGH
were solved from Eqs. (6)–(9) respectively.
SABJO1¼ 0:25r2
1ð2y1þsin2y1Þþz0r1 siny1 ð6Þ
SBCIJ ¼ 0:5r22ðy2�siny2Þ
þ0:5r2ðsiny12�siny1Þ½2z0þðr1þd1Þcosy1þr2 cosy12� ð7Þ
SCDHI ¼ 0:5r23ðy3�siny3Þ
þ0:5r3ðsiny123�siny12Þ½2z0þ2d1 cosy1
þðr2þd2Þcosy12þr3 cosy123� ð8Þ
SDFGH ¼ 0:5ð0:5bk�cÞð0:5sþz0þd1 cosy1þd2 cosy12þr3 cosy123Þ
þ0:125r22½4tanð0:25p�0:5y4Þ�pþy4� ð9Þ
where, s is the value of roll gap, bk is the half width of grooveprofile, y4 is the angle between sloping line O3D and y-axis.
Fig. 3
3. Computational model for contact area and lengthsof contact arc
To analyze the deformation behavior as well as calculate somephysical parameters, the basic but most important step is todetermine the contact area. The uniform wear of rolls is subject tothe uniform distribution of contact arc lengths. Here, contact arclength is defined as, for every point located on the ingot surface,its contact arc length equals to the arc length from the start pointof deformation to the end point of deformation. To facilitate thecalculation and analysis, the following assumptions have beenmade: (i) ignore the effect from the spread of work piece, whichmay change the location of contact point on the groove surface;(ii) the work piece is deformed uniformly in the deformationzone; (iii) overlook the effect from thermal expansion, which mayaffect the dimensions of outgoing work piece; (iv) rolls are rigidbodies, and the rolling load is distributed uniformly along thecontact surface.
3.1. Computational model for contact area
According to the descriptive geometry method proposed byRagab and Samy [20], in the process of symmetrical rolling,namely the symmetry axis of work piece is superimposed on thatof roll gap; the contact area can be presented by
At ¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiA2
xþA2y
qð10Þ
where, Ax and Ay are the project areas of contact in the horizontal(x–y) plane and the vertical (y–z) plane respectively.
As shown in Fig. 2, for a given point is (b cosj, a sinj) locatedon the surface of oval bar, the projected coordinates in the
horizontal plane can be calculated from
y¼ ðasinj�zÞcotðb=2Þ
z¼ bcosj
(ð11Þ
where, b is the half minor axis, a is the half major axis, and j isthe eccentric angle. Value of z can be calculated from Eq. (2) andvalue of b can be obtained from
b¼ cos�1½ðR0þ0:5hk�asinjÞ=ðR0þ0:5hk�asinjÞ� ð12Þ
where, R0 is the minimum radius of rolls, hk is the height ofgroove. The projected area of horizontal plane Ax can be calcu-lated using numerical integration method.
Fig. 3 shows the outline of round groove drawn superimposedon the cross section of an oval work piece. It is easy to get theintersections of the oval curve and the round groove profile curve,and then the project areas of contact in the vertical plan Ay can becalculated through integral operation for the blank area in thecenter of Fig. 3. After that the value of contact area can beobtained through solving Eq. (10). Contact area calculation forother roll passes can use the same approach.
3.2. Model for calculating the length of contact arc
For a given point C located in the deformation zone, Fig. 2shows the start point of deformation C1, Fig. 3 gives the end pointof deformation C2, thus, the length of contact arc related to point
B. Huang et al. / Robotics and Computer-Integrated Manufacturing 28 (2012) 493–499496
C can be presented by
x¼ asinjy¼ bðR0þhk=2�zÞ
(ð13Þ
For any point located on the surface of deformation zone, thelengths of contact arc and sliding distance have a leading role inits rate of wear. For example, assuming the load is distributeduniformly along the deformation zone, in the flat rolling process,due to the contact arc length as well as the sliding distance ofevery deformation point equals those of other deformation points,rolls can achieve a uniform wear, and the useful life of roll can beextended.
Fig. 4
4. Optimal design method based on genetic algorithm
This section introduces the genetic algorithm (GA) that manip-ulates the genome pool (termed population) to find an optimalsolution for the oval–round pass design problem. GA, whichcombines iterative search method with simple random searchstrategy, is an optimization and search strategy based on biolo-gical evolution inspired natural mechanisms. This method hasmany advantages in the field of multi-objective optimization,such as little initial knowledge needed, suited for both continuousand discrete optimizations of variables, does not require deriva-tive information, has a capacity to deal with a large number ofvariables, less susceptible to the shape or continuity of the Paretofront, easy to implement, robust, and could be carried out in aparallel environment [21–23]. Besides, GA combines directed andstochastic searches, which ensures a remarkable balance betweenexploration and exploitation of the search space. Through geneticand evolution operations, this algorithm can converge to theoptimal solution effectively [24,25]. Reference 24, 25 also presentmany case studies of GA-based optimization in industrial applica-tions. The optimization of RPD is a typical multi-objective, multi-process and multi-constraint problem. In the design process,many constraints should be considered. Thus, GA is an appro-priate choice for the optimal design of roll passes.
Fig. 4 shows a flowchart of GA, in this flowchart, there are fouroperations (selection, reproduction, crossover and mutation)employed for the searching of optimal solutions. Here, selectionis used to pick out fit individuals from population. Reproduction isemployed to ensure good individuals can be transmitted to nextgeneration. Crossover, which is applied with high probability,allows information exchange between chromosomes. Mutation,as in the natural system, is a very low probability event.The mutation operator is employed to help the algorithm to jumpout of the traps of local minimum and diversify the searchdirections. Through these four basic operations, at each popula-tion high-fitness solutions have a high probability to be repro-duced, while bad solutions have a high probability to die [26].In the whole process of genetic optimization, fitness value is usedto evaluate the performance of an individual. Here, an individual,or a chromosome corresponds to a solution to the optimalproblem. Generations number (Gen) is applied to recordthe evolutionary number of population, or iterations. To applyGA in optimization, constrains and objective functions shouldbe established to guide the searching of optimal solutions.Simultaneously, appropriate GA parameters should be set foroptimization.
4.1. Constraints
In each engineering task there are some restrictions dictatedby the design, technological and manufacturing requirements,which must be satisfied in order to produce an acceptable
solution. In the oval–round optimal design example, there arefour constraints to be satisfied.
(i)
To avoid sharp points and ensure the smooth of the profilecurve, the whole profile curve should be continuously deri-vable. In other words, every intersection point must have aunique derivative value.(ii)
To ensure the monotonicity of arc AD, the following equationmust be satisfiedy1þy2þy3rp=2
y1Z0,y2Z0,y3Z0
(ð14Þ
(iii)
Assuming the tolerance of final products is D, then for everypoint (x,y,z) located on arc AD2ffiffiffiffiffiffiffiffiffiffiffiffiffiffiy2þz2
qAðr7DÞ ð15Þ
where, r is the ideal radius of final products.
(iv) Constraint from bite angle gr[g], where, [g] is the maximumallowable bite angle for oval–round pass.
4.2. Objective functions
In the process of selecting the best one from all feasiblesolutions (solutions which can satisfy all constraints), there mustbe some standards or criteria, which make these feasible solutionscomparable. In this research, the main objective is to build adecision support system for the (re)design of oval–round passes,which can improve the efficiency and quality of RPD, as well asreduce the dependence on design experience. The optimizationfocuses on decrease energy consumption and manufacturingerrors in the rolling process, as well as extends the useful life ofrolls. Three objective functions are assigned to these problems.
B. Huang et al. / Robotics and Computer-Integrated Manufacturing 28 (2012) 493–499 497
4.2.1. Minimum energy consumption
To improve the energy efficiency and phase down energydissipation, energy consumption should be taken into accountas an objective function in the process of optimization. Accordingto reference [20], the energy consumption for a multi-pass rollingsystem can be presented by
f 1 ¼min q¼minðMzVt=DkÞ ð16Þ
where, q, Mz, V, t and Dk are the energy consumption, rollingtorque, rolling velocity, rolling time, and working diameter of theoval–round pass respectively. The rolling torque can be deter-mined by the widely used Sims formula [18].
4.2.2. Minimum manufacturing errors
To improve the manufacturing accuracy of the rolling system,a variance function for the description of manufacturing errorsshould be brought into the process of optimization. For any givenpoint (x,y,z) on arc AD, whose horizontal and vertical ordinates arefunctions on variable y, the objective function is determined by
f 2 ¼minXy123
y ¼ 0
ðy2þz2�r2k Þ ð17Þ
4.2.3. Maximum useful life
It is commonly believed that, wear of rolls is always affected bythe length of contact arc, sliding distance, as well as the distributionof roll load. In this research, to simplify the optimization process, onlythe length of contact arc is taken into account. Because the useful lifeof rolls can be extended when a uniform wear of rolls is achieved,while the uniform wear of rolls is subject to the uniform distributionof contact arc lengths. Thus, a variance function was established foroptimization. According to Eq. (13), for any given point (xc, yc, zc)located on arc AD, the objective function can be presented by
f 3 ¼minXy123
y ¼ 0ðy2
c�L2Þ ¼min
Xy123
y ¼ 0½b2ðR0þhk=2�zcÞ
2�L
2� ð18Þ
where, L is the mean value of contact arc lengths for every pointlocated on arc AD.
Table 1Parameters of original solution.
Original
solution
Roll speed
(r/min)
Roll working
diameter (mm)
Height
(mm)
W
(m
Oval (billet) 14.00 24
Oval-round
pass
982.20 343.81 16.19 16
Temperature (1C) r1 (mm) y1 (1C) r2
900.00 8.10 69 0
* At is the contact area of roll pass; Ax is the projection of contact area in x–y plane; A
Table 2Parameters of optimal solution.
Optimal
solution
Roll
speed (r/min)
Roll working
diameter (mm)
Height
(mm)
W
(m
Oval (billet) 17.10 2
Oval-round
pass
982.20 305.00 15.81 1
Temperature (1C) r1 (mm) y1 (1C) r2
876.24 16.00 8.24 7
At (mm2) Ax (mm2)
534.92 415.52
According to Eqs. (16–18), the total objective function can bedescribed as
f ¼ w1 w2 w3� �
� f 1 f 2 f 3
h iTð19Þ
where, w1, w2 and w3 are weight coefficients, which can beadjusted as needed.
4.3. GA parameters
Parameter setting has a close bearing on the convergence speedand global astringency of GA. As stated previously, for givendefinitional domains of parameters, a longer chromosome canimprove the precision of optimization at the expense of decreasethe computation speed. Larger population size and high crossoverrate are good for the best solution searching but unfavorable toconvergence speed. A high mutation rate means the algorithm has ahigh probability to jump out of the traps of local minimum,however, the convergence and computation speed will be damagedat the same time. In this simulation, the following parameters areused. The length of the chromosome is 10 bit per one designvariable, while the total length of the chromosome is 80. Thepopulation size is 100 and the generational gap is 0.9. The crossoverrate and mutation rate are 0.7 and 0.013 respectively. Two-pointcrossover and ranking selection are used. The simulation is termi-nated when the generation is over 100.
5. Case study and discussion of results
A MATLAB program has been developed and applied to an oval–round pass optimal design to validate the proposed methodology.Computer analysis has been carried out, and results from the analysishave been compared with solution presented by Reference [27]. It hasbeen assumed that the billet is oval bar, and the final product is around bar with an ideal diameter of 16 mm and length of 10,000 mm.Material is 45 steel. Roll diameter is 360 mm. After 100 iterations, thebest solution is achieved. To compare with the original solution,
idth
m)
Area
(mm2)
Extension
rate
Power
consumption (kw)
Roll
gap (mm)
.82 250.00
.79 206.50 1.20 161.57 1.50
(mm) r3 (mm) At (mm2) Ax (mm2) Ay (mm2)
0 446.17 392.12 212.86
y is the projection of contact area in y–z plane.
idth
m)
Area
(mm2)
Extension
rate
Power
consumption (kw)
Roll
gap (mm)
0.85 280.00 1.50
7.45 233.35 1.20 142.43
(mm) y2 (1C) r3 (mm) y3 (1C)
.09 34.06 6.23 26.22
Ay (mm2)
336.87
B. Huang et al. / Robotics and Computer-Integrated Manufacturing 28 (2012) 493–499498
which are listed in Table 1, the best solution (listed in Table 2) wasused for comparative analysis.
Under the assumption that the roll gap, extension rate, roll speedand rolling temperature of the original solution are totally equal tothose of the optimal solution, Tables 1 and 2 indicate that the powerconsumption of the optimal solution is smaller than that of theoriginal solution. At the same time, the required rolling temperatureis decreased. That means the energy efficiency is improved afteroptimization. Moreover, compared with the original solution, theroll working diameter is reduced after optimization, which meansthe cost of material for roll manufacturing is decreased. The contactarea of roll pass At, the projection of contact area in x–y plane Ax, aswell as the projection of contact area in y–z plane Ay are allincreased after optimization, which can improve the rolling forceon condition that the unit pressure is remain unchanged.
Fig. 5 shows the tracking performance of the total objectivefunction. It can be concluded that this algorithm has a goodsearching performance and fast convergence rate, the optimalsolution is achieved after 100 iterations.
Figs. 6 and 7 give the curves of contact arc lengths for originalsolution and optimal solution respectively. Through comparativeanalysis, it can be concluded that, due to the curvature of curve inFig. 7 is bigger than that of Fig. 6, the rolls employed in theoptimal solution can achieve a more uniform wear. Thus, theuseful life of rolls is extended after optimization.
The outline of oval–round pass for optimal solution is shownin Fig. 8, here, the dashed circle is the ideal cross section for the
Fig. 5
Fig. 6
final products. It was concluded that there are some dimensionalerrors between the design outline and ideal cross section, butthey are within the allowed range of rolling manufacturing.Besides, with the reduction of temperature after rolling, thosedimensional errors will decrease due to the rolled materialexpands with heat but contracts with cold.
6. Conclusions and future work
A generalized method based on GA has been proposed for theoptimal design of oval–round roll passes. The method employsnumerical approaches to optimize the energy consumption andwear equalization to improve the energy efficiency of the rollingsystem as well as extend the useful life of rolls.
Based on the comparison made between the results from theproposed system and solutions from other publication, thefollowing conclusions have been achieved:
�
The parameterized geometrical modeling method, which is thebase of hybrid model, is very easy to be applied to differentshapes and describe the profiles of roll passes accurately. Inother words it has a good flexibility, generality as well asprecision. Although the complexity of the optimization algo-rithm increased because more parameters are employed forgeometrical modeling, the computer system can afford thiscomputational burden easily. � The present method for the calculation of contact area is easyto be implemented with enough precision. The solutionsprovided by this method can be used for the calculation ofrolling force, torque and power consumption.
� Unlike other numerical strategy-based design approaches suchas FEM which is computational expensive and time consum-ing, the present method can deliver an optimal solution for theoval–round passes in few minutes.
� Software based on the hybrid model and MATLAB platformwas designed for the optimal design of oval–round passes.The software can also draw the profiles of roll passes, hor-izontal and vertical projections of contact area, as well ascurve of contact arc lengths, according to the geometri-cal models and parameters obtained through the GA-basedoptimization.
Future work will focus on:
�
More design data from succeed solutions will be collected toestablish an experiential database, and mathematical statisticsis employed for more accurate hybrid modeling and determi-nation of definitive ranges for parameters. � More parameterized geometrical models will be built for theoptimal design of other roll passes employed in the rod rollingsystems, and a new methodology will be proposed for theoptimization of the whole multi-pass rolling system, not onlythe optimization for single pass.
� Some improvements should be proposed to increase thesearching efficiency of the optimal algorithm. Because, withthe application of optimal design for the multi-pass systems,more and more parameters should be processed simulta-neously, which will place heavy computational burdens oncomputers, and increase (re)design cycles.
� Simulations based on FEM and small scale lab experiments arecarried out for model validation and modification, becausethey can give more accurate analysis results, although they arecomputational expensive and time consuming. At the stage ofmethodology validation, these proof techniques are necessary.
Fig. 7
B. Huang et al. / Robotics and Computer-Integrated Manufacturing 28 (2012) 493–499 499
References
[1] Kwon HC, Im YT. Interactive computer-aided-design system for roll pass andprofile design in bar rolling. Journal of Materials Processing Technology2002;123:399–405.
[2] Kalpakjian S, Schmid SR. Manufacturing processes for engineering materials.5th ed. New Jersey: Pearson Education, Inc.; 2003.
[3] Ginzburg VB. High-quality steel rolling: theory and practice. New York:Marcel Dekker, Inc.; 1993.
[4] Huang B, Xing K, Spuzic S, Abhary K. Development of parameterized roll passdesign based on a hybrid model. In: The 2010 International Conference onMechanical and Electrical Technology, ICMET 2010; September 2010, pp. 91–3.
[5] Tang L, Liu J, Rong A, Yang Z. A review of planning and scheduling systemsand methods for integrated steel production. European Journal of OperationalResearch 2001;133:1–20.
Fig. 8
[6] Hsiang SH, Lin SL. Modeling and optimization of caliber rolling process.
Journal of Manufacturing Science and Engineering 2007;129:77–83.[7] Abhary K, Garner K, Kovacic Z, Spuzic S, Uzunovic F, Xing K. A knowledge
based hybrid model for improving manufacturing system in rolling mills.In: The Nineth Asia-Pacific Conference on Materials Processing; in press.
[8] Said A, Lenard JG, Ragab AR, Elkhier MA. The temperature, roll force and rolltorque during hot bar rolling. Journal of Materials Processing Technology1999;88:147–53.
[9] Abhary K, Chan FTS, Luong LHS. A more accurate approach to mechanics ofcold rolling. In: Proceedings of the 32nd International MATADOR Conference;
July. 1997, p. 367–72.[10] Oduguwa V, Roy R. A review of rolling system design optimization. Interna-
tional Journal of Machine Tools & Manufacture 2006;46:912–28.[11] Zienkiewicz OC. The finite element method.3rd ed. New York: McGraw-Hill
Press; 1977.[12] Kobayashi S, Oh S, Altan T. Metal forming and the finite element. New York:
Oxford University Press, Inc.; 1989.[13] Abrinia K, Fazlirad A. Investigation of single pass shape rolling using an upper
bound method. Journal of Materials Engineering and Performance 2009;19:541–552.
[14] Perotti G, Kapai N. Roll pass design for round bars. CIRP Annals - Manufactur-ing Technology 1990;39:283–6.
[15] Kim SH, Im YT. A knowledge-based expert system for roll pass and profile
design for shape rolling of round and square bars. Journal of MaterialsProcessing Technology 1999;89:145–51.
[16] Lambiase F, Langella A. Automated procedure for roll pass design. Journal ofmaterials engineering and performance 2009;18:263–72.
[17] Bayoumi LS, Lee Y. Effect of interstand tension on roll load, torque andworkpiece deformation in the rod rolling process. Journal of MaterialProcessing Technology 2004;145:7–13.
[18] C. Xu, Q.S. Wang, C. Zhang, Xing Gang Kong Xing She Ji, Beijing: ChemicalIndustry Press, 2009.
[19] Beynon RE. Roll design and mill layout. Association of Iron & Steel Engineers1956.
[20] Ragab AR, Samy SN. Evaluation of estimates of roll separating force in barrolling. Journal of Manufacturing Science and Engineering 2006;128:34–45.
[21] Coello CAC. Comprehensive survey of evolutionary-based multiobjectiveoptimization techniques. International Journal of Knowledge and Informa-
tion Systems 1999;1:269–308.[22] Abraham A, Jain L, Goldberg R. Evolutionary multiobjective optimization:
theoretical advances and applications. London: Springer; 2005.[23] Haupt RL, Haupt SE. Practical genetic algorithms.2nd ed. New Jersey: John
Wiley & Sons, Inc.; 2004.[24] Gen M, Cheng R. Genetic algorithm and engineering design. New York: John
Wiley & Sons, Inc.; 1997.[25] Karr CL, Freeman LM. Industrial applications of genetic algorithms. Boca
Raton: CRC Press; 1999.[26] Osyczka A. Evolutionary algorithms for single and multicriteria design
optimization. Heidelberg: Physica-Verlag; 2002.[27] Zhang N. The multi-objective optimal pass design based on GA, Master
dissertation. The Yanshan University; 2006.