Journal o[ Materials Processing Technology, 24 (1990) 485--494 485 Elsevier

DEVELOPMENT OF TUBE DRAWING SCHEDULES IN A COLD DRAWING

PLANT USING EXPERT SYSTEM TECHNIQUE

M. SIDDIQUE and I. M. COLE

Department of Mechanical and Production Engineering, Aston University, Birmingham, U. K.

SUMMARY Seamless tubes have gained wider applications and are being used extensively in nuclear

and conventional power plants, refinexies, machine tools and hydraulic equipment and pipelines for conveying oil and gases and are manufactured by the use of rotary or non-rotary processes to produce hollows, followed by cold drawing operations. These hollows are then cold drawn to attain high dimensional accuracy and required surface f'mish by any of the cold drawing processes such as sinking, mandrel drawing, fixed plug drawing or floating plug drawing. In order to achieve the required dimensions of the finished tube, it is common practice to carry out one or more passes depending upon many factors such as drawing capacity of the bench in terms of maximum safe load, stress/swain characteristics of material being used, prior work hardening and availability of tools. Traditionally, the tube drawing schedules are prepared by making use of personal shop floor experience, judgment and expertise in the field without giving much attention to the aforementioned process parameters.

A prototype expert system is being developed for process planning in a seamless steel tube plant. Expert systems are computer programmes using domain-specific knowledge to achieve a high level of performance in a field which would otherwise require a human expert. This paper discusses the part of the process planning system which deals with the generation of tube drawing schedules. In the fLrSt section the theoretical approach for determining process parameters for fixed plug drawing such as stress/strain and hence the drawing loads is described. In the second section of the paper, the generation of aitemative tube drawing schedules, selection of optimum schedule by the use of heuristic rules, selection of other secondary operations and operation sequence are discussed. The system is implemented in Turbo-Prolog language and has been tested on the actual data of the plant with satisfactory results. An operation sequence sheet for an example part is included at the end.

INTRODUCTION

The manufacture of cold drawn seamless tubes is a multi-stage production process.

Initially, the semi-finished hollows (shells) are produced from a solid billet by either rotary

processes (e.g. cross and longitudinal rolling) or a non-rotary process such as punch piercing. The

semi-finished hollows are then cold drawn to required sizes by any of the cold drawing processes

of sinking, mandrel drawing, fixed plug drawing or floating plug drawing. The required reduction

of area (i.e. from initial dimensions of hollow to the required dimensions of the tube) can be

achieved by one or a repetition of the cold drawing process, each being called a "pass". The

standard procedure for determining the number of passes is to divide the total reduction by the

allowable reduction per pass (reL 1). This requires the computation of the allowable reduction per

pass by taking into consideration many factors such as the stress/strain characteristics of the

material, the capability of drawbench in terms of length and power, tool geometry, frictional

condition and the properties required in the finished tube (ref. 2). Once the number of passes is

0924-0136/90/$03.50 © 1990---Elsevier Science Publishers B.V.

486

determined, a tube drawing schedule should be drawn up which determines what tools (die and

plug) sizes should be selected and what dimensions should be achieved in the intermediary passes

in order to obtain the required dimensions in the final pass. A method has been suggested in ref. 2

to select the ideal sizes of the tools by the use of a graph (called Iso-graph) consisting of constant

area lines relating the different outside and inside diameters. The suggested approach is based

upon the zero residual stress concept and assumes the availability of an infinite number of

semi-finished hollow, plug and die sizes. It has been said that available tool sizes can be selected

by deviating from the required ideal sizes by allowing a certain amount of residual stress which can

be tolerated in the drawn tube, but the level of which cannot be determined.

In the present work, a different technique has been used for developing the tube-drawing

schedules which takes into account the expertise and experience of the expert, shop practice and the

availability of hollow and tool sizes. Knowing the initial dimensions of the hollow, final required

size of the tube and the available tool sizes in the range, all possible alternatives schedules are

generated by the computer programmes. The selection of best amongst the alternatives is achieved

by using a group of rules compiled from human expertise and shop practice. This schedule can

then be validated or rejected by computing the process parameters such as stress/strain and drawing

load and comparing with the drawing capability of the selected drawbench. The computation of

process parameters is based upon the mathematical model given in ref. 3 which has been extended

for predicting certain parameters analytically so that it can be used in a computer programme, as

discussed below. This gives an extra safeguard to check the validity of a best schedule which is

based on expertise and shop practice.

The technique used is that of expert systems or knowledge-based systems.

Knowledge-based systems are computer programmes which use domain-specific knowledge to

achieve a high level of performance in a field which otherwise requires a human expert. In a

knowledge-based system the knowledge is organised in a way that separates the domain-specific

knowledge from the problem solving knowledge. The collection of domain-specific knowledge is

called the "knowledge base" while the problem solving knowledge is termed the "inference

engine" (ref. 4). The systems are best suited for problems which have human expertise as an

important constituent factor.

A prototype knowledge-based system is being developed for process planning in a

seamless tube plant (ref. 5). In this paper, after giving the theory of timed plug tube drawing, those

modules of process planning system which deal with determining the number of passes, generation

of alternatives schedules, selecting and validating the best schedule and selection of secondary

processes will be discussed. A detailed operations sequence sheet as planned by the system is

presented for the manufacture of an example tube.

THEORY OF PLUG DRAWING

Expressions for computing the total drawing load and load of deformation in plug drawing

have been given as follows (ref. 3):

I-~/e= ° l c ' a (I)

O 2 c - a

487

a 2 = a 1 + a o On h ) (2)

where <~2 = drawing stress at the exit from the die; c 1 = back pull stress; % = true mean yield

stress; c = 2p./tana; a = a0(l+c), t I and t 2 are initial and final tube thickness respectively; a = die

semi-angle and Ix = coefficient of friction.

The frictional component of drawing load then can be obtained by taking the difference

between total drawing load and deformation load computed by equations (1) and (2) respectively.

Values of a 1 and a 0 are required in order to be able to determine the load components. In

industrial practice, tubes are commonly drawn by a combination of sink and draft reduction in a

single pass. Unless the tube is drawn in a pure draft condition ( i.e. no reduction in the inside

diameter, in which case at=0), the value of back pull (Gt) for the sinking condition where both

outside and inside diameters are reduced and the wail tends to thicken because of the lack of

internal support, can be obtained by the empirical relations for different die geometry as quoted in

ref.3.

In order to determine the true mean yield stress, knowledge of initial strain before drawing

and final strain imparted in the drawing operation are necessary. In case of annealed material, the

initial strain can be taken as zero and the total strain imparted to the tube can be obtained by:

~=~Ao+~ (3) 2 A 1 t 2

where ~ = total strain; A 0 and A t = cross-sectional areas of tube before and after the sinking

portion; t o and t 1 tube thickness before and after sinking ( t o = t t, assuming the thickening to be

negligible)

Assuming that the basic stress-strain curve for the material and the true stress-strain curve

for the drawn tube obtained experimentally coincide with each other ( which is not the case as

mentioned later) and using the approximate relation a= C~ , where C is a constant and n is strain

hardening exponent, the mean yield stress (%) then can be determined by:

/ . er n 1

I c ~ de (4) a 0 -- m+- vs,,

Equations (3) and (4) can then be used to determine the mean yield stress for the solution of

equations (1) and (2) for total drawing load and load of deformation.

However, as discussed in ref.3, the experimentally obtained basic stress-strain curve for

the material and the true stress-strain curve for the drawn tube do not coincide and the value of the

true mean yield stress is higher than that given in the basic curve for a given amount of

deformation. The difference between two values of yield stress is due to the additional strain

hardening and related to redundant work. The higher value of the true mean yield stress can be

found by the use of "equivalent strain" concept as defined by Hill and Tupper (ref. 6)which

488

can be determined experimentally as in the initial investigation. In order to simulate the model in a

computer programme, a provision must be made to f'md the equivalent strain analytically which can

then be used for the determination of true true mean yield stress and the actual drawing load.

A mathematical model has been proposed for programming in the software which predicts

values of equivalent strain which are in close agreement with the experimental values published in

ref.3. The model is based on similar analysis as presented by Bramely and Smith (ref. 7) for

floating plug drawing and has been modified for fLxed plug drawing as discussed below.

----T-t2

Ro:

Ri:

DIE

II Xmax

Plug

plug bar

¢ t 1

Ril Rol

Fig. 1: Pass geometry and assumed pattern of velocity discontinuities for fixed plug drawing

Reffering to Figure 1, AB and CD being the discontinuity lines where the material changes course

during the operation. At any discontinuity, plastic work is done causing strain hardening of the

material from a initial value e I tO a next higher value e. 2. The change in the strain can be obtained by

the equation : Ad Ud

e2 - el = ~ A. U (see appendix for derivation) (5)

where A,i = area of discontinuity; U d = velocity of material at discontinuity; U = velocity of material

after discontinuity and A -- area of material after discontinuity. The various parameters in equation

(5) as applied to discontinuity AB are:

U d = UAB; A a = AAB; U= Ur2; A = Ar2; e 1 = el; e. 2 = eAS where subscript rl and r2 denote regions

1 and 2 (Figl). Assuming that there is no thickness change between region 1 and region 2, i.e.,

Url = Ur2 and Arl = Ar 2 and considering the velocity diagram for discontinuity AB in Fig. 2.

Ur2 sin a At2 UA8 = - - and AAB =

~X (X COS ~ COS -~-

489

a/2

A 7 Url

B

Fig.2: velocity diagram for discontinuity AB

putting these values in equation (5) we have sin~

~AS = ~1 ÷ (6) 2

2

For discontinuity CD, the parameters in equation (5) are

~1 = ~2CD = E2AB+~2; Ud = UCD; Ad = ACD; U= Ur3; A = Ar3 and ~2 =~f where E2AB= eAB and

E 2 is the equivalent strain in the region 2. In case of no thickness straining in the region 2 (er = 0)

and the average value of e 2 can be computed by (ref. 6):

_ 1 _ 1 , Zo, Ril e2= ~ - e 0 = ~f~ -. Ro 2 Ri 2 (7)

where Rol; Ro2; Ril; Ri2 are outside and inside diameters of the tube before and after drawing.

Considering the velocity diagram for discontinuity CD in fig. 3:

B Ur3 D

C

Fig.3: velocity diagram for discontinuity CD

A

U r3 sin a Ar3 UCD = and A C D = - -

sin (or+y) sin a

putting these values in equation (5) we get sin ct

~f= [3CD = E2CD q ,¢r~sin 7 sin(a+ 7) (8)

and the value of angle "/can be determined by referring to fig.1 and triangles CFN and CDE i.e., t2 tl t2

T = tan-1 [ ~ ] where Xm~x = - - sin a tan a

Table 1 gives the initial and final dimensions of the tubes with total reduction of area.The

490

values of equivalent strain, mean yield stress, total drawing load, total deformation load and useful

deformation load (using lower value of mean yield stress obtained by equations (4) and (5))

obtained by the means of equations (8), (4), (1) and (2) respectively have been compared in Table

2 with the experimental values published in ref. 3. For the computation of these values, the

coefficient of friction was taken as 0.05. Figure 4 shows that the computed values of total drawing

load are an over-estimate compared with experimental values, which is desirable for safe validation

of the drawing schedules. Thus the model can be used safely to validate or reject the tube drawing

schedules in the computer programme.

TABLE 1

Tube dimensions before and after drawing (ref. 3)

Initial dimensions Final dimensions Reduction outside l'hicknes outside Th/cknes~ Total diameter diame~ percent (mm) ( m m ) ( r am) (mm)

1 54.91 3.66 50.34 4.22 25.50 2 55.50 3.94 50.34 4.22 31.50 3 56.00 4.22 50.32 4.22 35.90 4 56.75 4.52 50.29 4.22 41.10 5 57.33 4.83 50.29 4.22 45.00 6 58.24 5.31 50.27 4.22 50.40

TABLE 2

Comparision of stess/strain and load components (experimental from ref. 3 and computed)

No. Equivalent strain True mean yield stress Total drawin~ load Total deformation load Useful deformation load[ Rof. 3 [Cemput i Ref. 3 Computed ] Ref. 3 IComlmtl Ref.3 [ C o m ~ d I Ref. 3 ]Comput.[

/ I~/mm2 ~/n~2) l ~N) I~d '~ / ~ I ~'~ I ~ l (~ '~1 1 0.53 10.47 1628-56 615.13 I 116.58 1122.161 86.29 I 82.32 I 76.12 77.12 2 0.66 /0 .63 I 652.19 647.86 I 145.47 1150.851 109.90 I 106.22 I 97.55 98.15 3 0.80 /0 .80 | 676.74 673.03 [ 165.40 1177.76[ 130.33 [ 129.73 I 116.58 118.67 4 0.97 10.97 [ 700.36 696.34 I 188.32 1204.06[ 156.04 [ 154.34 I 140.79 139.69 5 1.03 /1 .15 1 706.53 715.64 I 214.23 1229.671 177.16 I 178.65 I 161.62 158.13 6 1.19 11.41 [ 726.45 742.36 I 246.11 1266.341 209.04 I 214.62 I 191.41 190.71

300

~,~ 250

o 200

150

100 20

/ - J £

30 40 50 Reduction of area (percent)

. / /

Fig. 4: Comparison of total drawing load

B Ref. 3 • Model

60

491

EXPERT SYSTEM

The Expert or Knowledge-based system for the development of tube-drawing schedules

consists of different modules such as selection of number of passes, alternative and best

manufacturing schedule, selection of secondary processes, validation of the best schedule and

operation sequence. The methods used for the development of these modules are briefly discussed

below:

Sdection of number of passes

Determination of the number of passes for a given reduction of area on the basis of an

allowable reduction per pass may not correspond with the practice in the plant because of different

actual dimensions of hollows, frictional condition and non-standard tooling. In order to overcome

this, the manufacturing records of the plant have been analysed and it has been observed that the

factors such as total reduction, selected drawbench, material composition and the tube finish are

taken into consideration and there exists a pattern by which the number of passes can be decided.

This pattern has been reduced to a set of heuristic rules which which has been represented in the

knowledge base. The decision about the number of passes by these rules is thus in agreement with

actual shop practice. An example of such rules is as follows:,

Select_number_of_passes(TOTAL_RED, BENCH, MATERIAL, _, NPASSES):-

TOTAL_RED<= 36.0,

BENCH="Bench 1",

Material_Properties(MATERIAL, PROPLIST),

head(PROPLIST, Carbon),

Carbon > 0.4,

NPASSES=2,!.

The above rule says that if the total reduction of area is less than or equal to 36.0 % and the

selected bench is bench 1 and the carbon content of the material (given the material grade, carbon

content can be found from the material properties and composition stored in the knowledge-base) is

greater than 0.4 then select two passes for this job.

Alternatives and best drawing schedule

To generate alternative manufacturing schedules, the system requires the knowledge of

available plug and die sizes. The available tool sizes are represented in the knowledge base in the

form of facts as shown below and can be modified to include new tool sizes:

infCdie_sizes", [size 1, size 2 ............ size n]).

inf("plug_sizes", [size 1, size 2 ............ size n]).

Given the initial and final dimensions of the tube, the system first processes the lists of

available tools in order to find those sizes which lie within the range and can be selected. It then

generates all possible alternative drawing schedules by taking into account the selected number of

passes and the different combination of dies and plugs which can be used. The number of

492

alternative schedules can be restrained by discarding those which lie outside the actual production

criteria. For example, a schedule having 50 % or 5 % reduction of area per pass is obviously not

desirable. The best schedule, which has a minimum variation in reduction of area over the selected

number of passes, with the exception of cold drawn/soft finish tube where a light reduction of area

is required in the final pass, can be selected amongst the alternatives. The alternative tube drawing

schedules for the manufacture of an example tube, as generated by the system, are shown in Fig 5.

HOLLOW ist PASS 2nd PASS

OD Thick. OD Thick. Red % OD Thick. Red % (mm) (mm) (mm) (mm) (~) (mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

44.45 4.88 42.40 4.67 8.7 38.10 4.06 21.5

44.45 4.88 42.40 4.47 12.2 38.10 4.06 18.4

44.45 4.88 41.28 4.67 11.4 38.10 4.06 19.1

44.45 4.88 41.28 4.47 14.7 38.10 4.06 15.9

44.45 4.88 41.28 4.26 18.2 38.10 4.06 12.4

44.45 4.88 39.67 4.47 18.5 38.10 4.06 12.1

44.45 4.88 39.67 4.26 21.7 38.10 4.06 8.5

Fig. 5. The alternative tube drawing schedules for the manufacture of example tube

Selection of secondarv orocesses

The selection of secondary processes may include hollow preparation processes (tagging,

pickling, lubricating), heat treatment processes such as inter-pass annealing, finish annealing,

normalising, tempering and other tube finishing processes. Prior to the first pass, hollow

preparation processes are always selected but subsequent selection depends upon inter-pass

annealing, which is mainly decided on the basis of material composition. The selection of other

finishing processes depends the tube specification or on special requirements specified by the

customer. The system is capable of selecting these processes when and where necessary based on

the knowledge it possesses.

Validation of schedule

Once the inter-pass annealing is decided, it is possible to compute the process parameters

such as stress/strain and hence the drawing load for every pass by the use of a model, as

discussed in the theory section. The drawing load can then be used together with the knowledge of

speed of the selected drawbench for estimation of the power requirement. The schedule can be

validated or rejected by comparing the computed required power with the design power capability

of the selected drawbench. The chances of rejection of such a schedule are minimal because it is

based upon actual shop practice. The procedure has been incorporated as an extra safeguard to

check the validity of a given schedule.

OPeration seouence

The selected processes must be arranged in succession depending upon the precedence

relationships of operations to form an operation sequence sheet which gives the operations

sequence for the manufacture of finished tube. Such an operation sequence sheet, generated by the

493

system for an example part together with the selected tool sizes and process parameters, is shown

in figure 6. The sequencing of operations is achieved by checking the present state of the tube

(initially semi-finished hollows) iterativdy and selecting the necessary operations to convert it from

the present state to next state until the required state is reached.

EXPERT SYSTEM FOR PROCESS PLANNING IN A SEAMLESS TUBE PLANT

PLANNER NAME: SIDDIQUE,M. date: 30/3/1990 at: 11:10:47 ............................................................................

OPERATION SEQUENCE IN COLD DRAWING MILL .......................................

PLEASE NOTE: ALL DIMENSIONS ARE IN rmn .....................................

*OPER NO: OPER NAME : OPERATION DETAIL ............................................................................

* OPER #i : TAG THE HOLLOWS

#2 : PICKLE

#3 :

* OPER

* OPER

* OPER

* OPER

* OPER

* OPER

* OPER

* OPER

LUBRICATE

OD WALL X-AREA OD WALL %R ........................................................

14.7 #4 : PASS i: 44.45 4.88 606.34 ::> 41.28 4.47

#5 : ANNEAL AT 660 - 720 deg C

#6 : PICKLE

#7 : LUBRICATE

#8 : PASS 2:41.28 4.47 516.58 ::> 38.10 4.06 15.9 #9 : REEL

* OPER #10: CUT TO LENGTH

* PLEASE NOTE: LEAVE 0.025 mm STOCK ON BORE FOR HONING OPERATION ............................................................................

DIE AND PLUG SIZES ......................

DIE SIZES (mm) ist PASS : 41.28 2nd PASS : 38.10

PLUG SIZES (r~n) ist PASS : 32.33 2nd PASS : 29.97 .............................................................................

STRESS/LOAD/POWER .....................

DRAWING LOADS (kN) ist PASS : 56.46 2nd PASS : 51.39

DRAWING STRESSES (N/~n2) ist PASS : 109.29 2nd PASS : 118.32

POWER REQUIREMENT (kW) ist PASS : 8.60 2nd PASS : 7.83 .............................................................................

Fig. 6. Operation sequence sheet, selected tool sizes and process parameters

CONCLUSION

A prototype expert or knowledge-based system has been developed for generating the tube

drawing schedules in a cold drawing plant. The system is capable of generating the alternative tube

drawing schedules by taking into consideration the available tools, selecting the best schedule

amongst the alternatives and validating or rejecting it by computing the process parameters with the

design capabilities. The proposed model for predicting the values of equivalent strain to be used in

the computation of other parameters gives reasonably good results compared with the experimental

investigation in ref.3. The system, like other expert systems, is mostly based upon expertise,

experience and shop practice and thus, for actual orders, it produces the results which are valuable and consistent for the actual production.

494

In addition to tube drawing schedules, the system is also capable of preparing the operation

sequence sheet. The system is written in Turbo-prolog, a PC version of Prolog, and can be

implemented on IBM-PC and compatible machines. Expert system technology is being used

extensively in other fields but there is little evidence of such technology in the field of seamless

tube manufacture. The present work is an attempt to benefit from the established potentials of

expert systems technology in solving the problems associated with tube making.

REFERENCES

1 G.W. Rowe, An Introduction to Principles of Metal Working, Edward Arnold, London, 1965.

2 B.J. Meadows and A.G. Lawrence, Theoretical approach to the rationalisation of tube drawing schedules, J. Inst. Met., 98 (1970) 102-105.

3 T.Z. Blazynski and I.M. Cole, An Investigation of the Plug Drawing Process, Proc. Inst. Mech. Engrs. 174(28) (1960) 797-804.

4 D.A. Waterman, A Guide to Expert Systems, Addison-Wesley, USA, 1986. 5 M. Siddique and I.M. Cole, An Expert System for Process Planning in a Seamless Tube

Plant, 28th International MATADOR Conf. April 1990. 6 R. Hill and S. J. Tupper, A New Theory of Plastic Deformation in Wire Drawing, J. Iron St.

Inst., 159 (1948) 353-359. 7 A.N. Bramley, and D.J.Smith, Tube Drawing with a Floating Plug, Metals Technology,

July (1976) 322-331.

Avpendix : Derivation of equation (5)

The rate of energy dissipation, i.e. rate of plastic work across a velocity discontinuity line, is given

by (ref. 6):

dW = W = KdAdU d (a) dt

where K d = shear yield stess

At any discontinuity, plastic work is done which changes the equivalent strain of the material from

an initial value E l to a final value ~2- Thus the plastic work done per unit volume of material

crossing the discontinuity line is given by:

W J~f" f" - - =:! (r dR or W = o c~ A. U where V = A.U (b)

on integrating equation (b) we have W = cr (g2 - ~1 ) A.U (c)

Equation (c) gives the plastic work done per unit time.Using the von Mises yield criterion ;

~= ~/3-K d

Putting this value of true mean yield stress in equation (c)

W = ~ K d (~2 - 2 1 ) A.U

from equation (d) and

discontinuity as: _ _ A~ Ud ~-~I=~A.U

(d)

(a) we can find the increase in equivalent strain across a velocity

(5)