Indian Journal of Engineering & Materials Sciences Vol.6,June 1999, pp. III-118

Neural network modelling and simulation of hot upsetting

K Hans Raj, Rahul S Sharma, S K Srivastava & C Patvardhan Faculty of Engineering, Dayalbagh Educational Institute, Dayalbagh, Agra 282 005, India

Received 4 May 1998; accepted 5 January 1999

Modern metal forming often caters to rapidly changing product specifications determined by the continuously increasing productivity, flexibility and quality demands. Automatic selection of press tools and accessories heavily relies on the forging force estimation. There is a complex relationship between process parameters like die velocity, temperature of the billet, co­efficient of friction at the interface of die and workpiece, tool geometry 1!nd forging forces. Models are needed to enable fast "eomputation of the forging forces based on these factors . However, it is not easy to develop mathematical formulations for thi s purpose. Finite element methods (FEM) now offer reliable means of modelling metal forming processes. The main limitation of these methods is the req.uirement of lot of man-hours of code development time, and CPU time for simulation and computer resources. This is because a small change in one parameter requires a fresh simulation run to predict the forging force and combinatori al explosion takes over. Computational paradigms like the artificial neural networks (ANNs) oFter an approach to this problem. In the present work , the applicability and relative effectiveness of the artificial neural networks based model s fo r rapid estimation of the forging force by invoking the function approximation capabilities of these models have been investigated . Neural network models are developed that can predict forging force given the initial temperatures of billet and die, friction co-efficient at die-billet interface and die velocity. The results obtained by these models correlate well with the finite element modelling results. This work has implications in the real time monitoring and control of the forming process and design of dies, computation of optimal parameters like punch velocity, billet and die temperatures .

Hot upset forging! is a metal forming process for enlarging and reshaping some of the cross-section of a bar, tube or other product form of uniform section. The process is widely used for producing finished forgings ranging in complexity from simple bolts or flanged shafts to wrench sockets that require si multaneous upsetting and piercing. Hot upsetting is also occasionally used as a finishing operation following hammer or press forging, such as in making crankshafts. A wide variety of shapes can be' fo rged in hot upsetting.

The traditional build and test methods of developing a complete manufacturing process in hot forging domai n are heavily experience based, because the analytical approach to process design was inadequately developed! . The advent of numerical methods such as general purpose finite element method (FEM) codes to handle large deformation plasticity has made accurate analysis possible. Many researchers have attempted the modelling of upsetting2

.4 and thermoplastic analysis for plane strain

and ax i-symmetrical deformations5•7

• The generation of solution adaptive grids for FEM has received a great deal of interest. In simulation of hot forging by an updated Lagrangian approach8

.JO the remeshing

problem becomes crucial to allow large deformations . The recent publications clearly demonstrate the advantage of using this approach to hot metal forming problems. FORGE2 is an FEM environment used to perform simulation of hot upsetting process on steel billets. A detailed pres~tation of capabilities of FORGE2 is given by Hans Raj et al. JO FORGE2 can be used to estimate the forging force for any given set of process parameters .

The finite element modelling techniques still have several limitations and are quite expensive to use in terms of required computer time and facilities. Because the potentially viable processing routes are numerous, many FEM process simulations are necessary to identify optimal processing methods. The problem of large design solution spaces is not restricted to the design of the deformation process, but also applies to the selection of correct combinations of processing temperatures, die profiles, friction conditions and strain rates etc. Though the finite element modelling is capable of giving detailed analysis of the problem at hand, the pre-processing and program execution consume a lot of time. A small change in a single process parameter requires a new simulation run to predict its effect on forging

112 INDIAN J. ENG. MATER. SCI. , JUNE 1999

force. Therefore, a need is felt to develop a much more generalized model, which can predict the forging force fo r a wide variation in process parameters quickly without extensive numerical modelling and give assistance to a production engineer on factory floor in real time. .

Recently , artificial neural networks (ANNs) are gaining wide popularity in the intelligent manu­facturing field . ANN's are massively interconnected networks of simple elements and their hierarchical organizations. The ANN approach is an inductive approach driven by data. The data driven approach of the ANNs enables them to be/lave as model free estimators, i.e., they can capture and model complex input-output relationships even without the help of a mathematical model il

. Some attempts l2•13 have been

made to apply this technique as an opportunity to shorten the reaction time of the manufacturing sy ·tems, increase the product quality, make systems more reliable and enhance the system's intelligence by the leaming capabilities of neural networks. Excel lent surveys of these attempts are found in Monostori 14 and Zhang and Huang l 5

. As per these surveys the most promising application fields of ANNs in manufacturing include leaming of process models and monitoring and diagnosticsI 6

. 17

.

In this paper, initial investigations are carried out using FEM with upsetting of ck-45 steel billet (whose height versus diameter ratio is 1/2) under varying friction conditions, temperatures and die velocities. These investigations provide valuable data for est imation of forging force required under various parameter conditions. An ANN is trained with the data obtained from FEM simulation . This uses Levenberg-Maquardt rule for leaming. The ANN model is validated by comparing its predicted values of the forging force for untrained data with those of FEM. Thi s generalization capability of the ANN model demonstrated the necessity to simulate the process for each selection of process parameters and can be used by the process engineer to determine the force required for any combination thus saving enormous time . The idea is being extended to other metal forming processes for the formation of a metal forming advisor to be used in factory environments.

Finite Element Modelling Methodology

A domain specific software FORGE2 is used to model the hot upsetting. The material is' assumed to

be homogeneous, isotropic and incompressible. The elastic strains in comparison to viscoplastic ones are considered to be negligible. The material behaviour is assumed to follow Norton Hoff law 10. The friction law between die and workpiece is similar to the constitutive law. Using the penalty approach to enforce approximate incompressibility the variational principle states that the velocity field soluti on of the problem minimizes the functional

[k )r;; 'l>l+' </>(v)=f -+I . v3EJ dQ+ff ·VdS

f n m Sf

+ f (aK I p+ 1) II f1 VtII P+

1 dS, n

... (1)

Where k is t~e material consistency, £ is the strain rate tensor, E is the equivalent strain rate, m is the strain rate sensitivity, n is the work piece domain, v is the velocity field , Sf is the surface on which stress vector is prescribed, and r is the large positive constant (10\

A fully automated remeshing procedure is incorporated into the analysis . Six noded triangular elements are used to model the part. The remesh ing procedure uses trigger values to decide the generation of a new mesh (for instance when any element of the existing mesh degenerates). Then a new boundary suitable to the problem at this increment of time is built. Intemal nodes are added according to the prescribed level of refinement and triangulation is obtained through a Delaunay type algorithm. This new mesh is regularized and its topology improved. Middle points are added on the sides of the triangles to build 6 node elements. At the end state parameters of the previous mesh are interpolated on the new one.

Simulatioas A number of FEM simulations are performed for

hot upsetting of a ck-45 steel preform at temperatures varying from 350 to 1300 DC under different punch velocities (I to 5mm/s) and friction conditions (where 11, the friction co-efficient is 0.1 to 0.8) using the model described above. The dies are kept at 350 DC. The material parameters chosen are m = 0.02 It = 0.1 a = 0.2 s p·m. lTlJlLp

The geometry is ax i-symmetric in nature so only one half of the section is simulated. The billet height is initially kept at 10 mm and the final height is 5 mm. The diameter of the billet is 20 mm. The forging force

HANS RAJ el at.: NEURAL NETWORK MODELLING AND SIMULATION OF HOT UPSEmNG 113

Table I-Forging load (Tonnes) required in hot upsetting for 50% deformation at different input conditions

Coefficient Velocity Forging load (Tonnes) for following initial temperatures (UC) of the ck-45 steel billet at 50% deformation . of friction mmls 350 400 500 600 700 800 900 1000 I 100 1200 1300

I

2

. .3

4

5

I

2

3

4

5

32.14 29.74 25.79 22.31 19.63 16.85 14.87

2.89

1.42

0.93

0.63

15.82

12.49 10.88 9.72 8.38

1.32 0.6 1

0.38

0.25

8.84

1.36 0.63

0.4

0.26

9.4 1.39 0.65

0.41

0.27

9.48

1.41

0.66

0.42

0.27

10.34

1.39 0.67

0.42

0.28

10.86

1.51

0.67

0.43

0.28

11.1

1.52

0.67

0.43

0.3 1

8.54 7.75 6.37 5.23 4 .3 3.53 2.37 1.95 1.6

0.75

0.48

0.32

10.38

0.2

0.3

0.4

0.5

0.6

0.7

0.8

2

3

4

5

I

2

3

4

5

I

2 3

4

5

I

2

3

4

5

I

2

3

4

5

4.65 4.18 3.37

3. 16 2.83 2.27

2.25

33.57

8.87

4.82

3.27

2.33

36.53

9.12

4.96

3.36

2.39

37.92

9.42

5.07

3.44

2.44

39.08

9.63

5.25

3.5

2.49

40.86

9.69

5.2

3.55

2.53

44.22

9.89

5.15

3.57

2.71

2.01 1.59

31.44 29.93

8.05 6.61

4.33 3.49

2.93 2.34

2.08 1.65

34.33 29.61

8.27 6.8

4.45 3.59

3.01 2.41

2.13 1.69

35.06 31.08

8.54 7.01

4.56 3.67

3.08 2.46

2. I 8 1.73

37.49 33.56

8.74 7.18

4.63

3.13

2.22

39.23

8.78

4.67

3. 18

2.25

41.45

8.96

4.63

3.2

2.42

3.73

2.51

1.76

34.33

7.19

3.76

2.54

1.79

36.32

7.34

3.73

2.56

1.93

2.72

1.81

1.26

24.17

5.43

2.82

1.88

1.31 25.18

5.58

2.9

1.93

1.34 26.67

5.75

2.96

1.97

1.38 27.91

5.89

3.01

2.01

1.4

30.29

6.09

3.03

2.03

1.42

30.93

6. 13

3.01

2.04

1.53

2.19

1.45

21.08

4.46 2.27

1.5

1.04

21.79

4.57

2.34

1.57

1.06

23 .76

4.7

2.39

1.58

1.09

24.93

4 .83

2.42

1.6

1.11

25.21

4.99

2.44

1.62

1.1 2

26.84

5.06

2.42

1.63

1.22

required for 50% reduction at different punch ve locit ies. at temperatures varying from 350 to 1300 0 e under varying friction conditions is obtained (Tab le I ). Results of radial stress contours with evo lving mes h, equivalent strain contours, equivalent stress contours and the temperature contours at 50% deformation for a sample s imulation are presented (Figs 1-6). In thi s simulation , the initial billet is kept at 1200 "e and upset between rigid dies is kept at 350 "e with a press ve loc ity of 3 mmls and a friction coeffic ie nt of 0.6 . The variation of forging force with

1.77

1.16

0.8

17.84

3.65

1.83

1.2

0.83

19.54

3.75

1.88

1.23

0.85

20.5

3.85

1.92

1.26

0.87

21.22

3.96

1.95

1.28

0.89

22.63

4.08

1.92

1.3 0.89

23.85

4. 14

1.88

1.3 0.97

3

1.48

0.96

0.66

16.63

3.07

1.52

0.99

0.67

17.74

3.15

1.53

1.01

0.69

18.19

3.25

1.57

1.02

0.78

19.63

3.34

1.58

1.04

0.7 1

20.4

3.33

1.57

1.04

0.78

1.15

0.75

0.5

13 .98

2.46

1.19

0.77

0.52

14.7

2.52

1.22

0.79

0.54

15 .2

2.57

1.25

0.81

0.55

16.02

2.57

1.27

0.82

0.56

17.33

2.71

1.27

0.83

0.56

17.6

2.73

1.27

0.84

0.62

0.93

0.6

0.4

12.08

2.02

0.96

0.62

0.41

12.4

2.07

0.99

0.64

0.44

13.02

2.11

1.01

0.65

0.43

13 .75

2.09

1.02

0.66

0.44

14.57

2.23

1.03

0.67

0.45

15 .18

2.24

1.02

0.67

0.49

1.6

0.78

0.5

0.33

10.71

1.7

0.8

0.51

0.34

11 .56

1.73

0.82

0.52

0.35

11.91

1.7

0.83

0.53

0.35

12.55

1.83

0.83

0.53

0.36

12.89 1.84

0.82

0.53

0.39

change in temperature (Fig. 7), the effect of friction co-efficient on forging force (Fig. 8) and the influence of variation in die velocity on forging force (Fig. 9) are plotted.

The radial compressive stress contours and equivalent stress contours indicate that radial stress is maximum at the axis of symmetry and equivalent stress is maxi mum at the comers indicating folding tendency of upset. The hydrostatic pressure contours also depict that the maximum hydrostatic pressure occurs at centre of the specimen along its axis of

114 INDIAN 1. ENG. M ATER. SCI. , JUNE 1999

Fi ~ . 1 - 1~ :lJi :l1 ~ l rt: ~ ~ ' cO Il\() u r~ (MPa) wilh aUlo-generated li nal Il1c ~ h :II ) 0'; ddurll1;l 1 ion

FJ ~. 2- Equi\ ;ill'nl ~ l ra in Cl!nIIlUr, at 500/, deformation

Fi g. . ."I-Equi valenl , I n:~~ contours U,,1Pa) at 50% deformat ion

HANS RAJ et af. : NEURAL NETWORK MODELLING AND SIMULATION OF HOT UPSETIlNG 115

F i ~ . ~- l-I ydros t ; lIi c p rc~surc contours (MPa) at 50% deformation

Fi~ . ) - Tcmperature: COll t,,· 'rs ("C) at )0% ddonnati on

Fig . 6-Princ ip;iI stress con t ou4~, (MPa) at 50% deformation

116 INDIAN J. ENG. MATER. SCI. , JUNE 1999

h g. 7- 1' lll'c t ()f hilkt tl' lnpC rallire ()n the evo luti o n o f fo rg ing f() rce during ho t up'l'lIing.

Temperature of btllet=350 oC

O ~~-L.....-..-------J~_~--.l.....-_ J _ . _ _ _ ---I....-._..............I __ _ _ ---L _~_

5 55 6 65 7 75 8 85 9 9.5 10 Displacement, mm

Fig. R-Elkct nf fr ict ion c(l-cfi ic il' nt on the evo lution of forg ing force du ring hot upsl'lIing with die ve loc it y o f Im m/s at 350 "c

~ y lllill e try and at edges <Ind minimum :1long the bulge uf the upse t. The temperature contours indicate that th l' max imum temperature is at the central region of the work pi ece away from the dies and free surface. It is mini mum nca r the di es due to the heat loses ()cc urrin g ,It the di e interface. The results of thi s an, ti ys is al s() confirm that at hi gh temperature the l' fkc t o f heat conducti on is large ly more important than th osl' relat ed to heat ge neration due to cO llvers illn of plasti c work. The temperature and equi valent str,lin co nt ours are very significant in bulk forming ,tS they ca n be used to predi ct the phase changes inside the bilkt. The processing maps inJ icltl' the proble m regions in the billet as the defects may deve lop at un stable regions and hence,

, 2: V:;2mm/sec r - ---I I . --. ~ V=~fj1If\/S~_

Oi _-=-_y.=.~m_r!l7s~c -5 55 6

V=3mm/ssc -......... -. ,

.. -:~- -~~~'~=---~~---'-: -~ 85 <, 95 10

Fig. 9- E tlect o f di c ve loc it y on evo lut ion o f fo rg ing fo rce during hot upsettin g upto 501y~ deformati on a t 1200 "c

t he need for correc t i ve measures in choos ing process p,trailleters. Principal stress contours depi ct that maximum princ ipal stress is compress ive in nature as is ex pected in upse ttin g and occurs at the bul ge.

Back Propagation Neural Networks The had propagati on neural network is a multiple

layn netwo rk with an input laye r. output layer and su me hidd en laye rs between input and ou tput layers l O

It s learning procedure is based on gradient search wi th least sum squared optimality criteri on. C tl culati on of the gradi ent is done by partial dcr i\'<ltiVt' of SUtll ~quared error with respect to weights. After the initial weights have been randoml y spec ified and the input has been prese nted to the neural network. eac h neuron currentl y outputs from all neu rons in the preceding layer. The sums and activation (output) values for each neuron in eac h layer are propagated forward through to entire network to compute an actual output and error of each neuron in the output laye r. The error for each neuron is computed as the di fference bet ween ac tu al output and its corresponding targe t output, and then the partial deri vati ve of sUIl1-squared errors of all the neurons in the output layer is propagated back through the entire network and the we ights are updated. In course of the back propagati on learnin g. a gradi ent sea rch procedure is used to find connecti on weights of the network, but it tends to trap it se lf into tl.e loca l minima. The loca l minima may be avoided by adjustin g value of the momentum. This algorithm can be ex pressed succinctly in the form of a pseudo­code.

..

HANS RAJ (' / ul.: NEURAL NETWORK MODELLING AND SIM ULATI ON OF HOT UPSETTING 117

Pick a rate parameter R. Until performance is sati sfactory For each sample input Compute the resultin g output Compute ~ for nodes in the output layer using

/3: = D: -0. . . . (2)

where D: represent s the desired out pu t and 0 : represents the ac tual output of the neuron Compute /3 for a ll ot her nodes using

/3J = I , WJ~' 0 , (1- 0 ,) /3, ... (3)

Compute weight changes for all we ights using

6w =rO O( I-O)/3 '--") I J ) J

... (4)

Add up the weight changes for all sample input s and change the weights.

Levenberg-Marquardt Approx ima tion

This algorithm uses Leve nberg-Marquardt learning mle, which uses an approximation of the Newton's method to get better performance l7. This tec hnique is relati vel y faster but requires more memory. The Levenberg-Marquardt (LM ) approxi mati on update rule is:

b.W=(l ' J +/J1) I J ' e ... (5)

which is used for updati ng weights of the network in stead of conventi onal back propagati on updati on ru le. Where .J is the Jacob ian matri x of derivatives of eac h error to eac h weight. is a scalar and e is an error \'eclO r. If the sca lar is very large, the above ex pression approx imates th e Gradient Descent method while if it is small the above expression becomes the Gauss-Newton method. The Gauss

ewtlln mcth od i:-- fa ster and more accurate near an crror minima. Hcnce. the aim is to shift towards the Gau ss- Ncwton as qui ck ly as poss ibl e. Thus, 11 is decreasL'd afkr c.lch successfu l step and increased onl y \\'hen SlL' p increases the error. Due to this advan tage th e LM rule was used in the network des igned.

;\Il'U r .. I Ill't \\ ork model of upsl:' ttin~

The :-- imulati on dat a obtained with the fini te element mode l. Table I is. used to train the feed forw.ml hack propagati on network (Fig. 10) with LM ru le dcscribed above. A three layer network is deve loped ,vith three input s. i.e .. temperature of hill et. co-cfli c icnt or fr icti on. ve loci ty of di e and one output. i.e .. forging load. The network predi ct ions

-0

!-'irs! Layer Second Laye r Th ird Layer

Fig. 10- Ncu ral nc twork archi tect ure used for mudel ling of hut upselling

Tahle 2~Compa ri sun uf forgi ng luad resul ts ohtained by FEM and NN models

S. l'\(] . Vel()c it y of Cll-eflicien t Temperature FEM resu lt s N results upper die of of hillet Forging luad Furging load

( 1l11llh. ) frict ion ("C) (Tonnes) (Tonncs)

2.5 0.75 950 2.0X 1. 89

2.5 0.55 1.250 1.02 0.97

2.5 0.4 1. 150 1.23 1.1 8

-l 2.5 0.2 1.450 0.63 0.6

.~ 3.5 0.65 850 1.41 1.38

:U 0.5 1.100 (l .X 0.79

7 3 ,) 0.3 950 1.06 106

-u 0.2 1. 150 O.-D 0.47 ') -u 0.3 700 1.24 1.28 i( ) -+'i 0.7 1.250 0.39 0.44

11 8 INDI AN J. ENG. MATER. SCI.. JUNE 1999

have de monstrated the ad vantage of such network in rea l time. The va li dati on is done by submitting raw, un tra ined data to the ne twork , evaluating the forging force and comparing the same with va lues obtained from finit e e lement mode l (Table 2). The close comparison o f va lues of forg ing force obtained using the neural ne twork c leJ rl y enumerates the accuracy of the mode l.

Conclusions A finite e le ment model is developed under

FORGE2 e nvironment for hot upsetting. A compre­hens ive database is developed by simul ating the FE mode l upto 50% deformati on of ck-45 steel specimen under va rying temperature, fr icti on and die ve locity conditions. A neural network model is deve loped and tra ined with LM rule lI s ing the data thus obtained . T he neura l ne twork models developed in thi s work cou ld effec ti ve ly es ti mate the forg ing fo rces based on temperature of the bille t, fri·c ti on conditions, die veloci ty for upsetting ck-45 steel specimen in a form ing press. It is va lidated by comparing the values of forg ing force obtained for untrained process variables with th ose o f finit e e lement mode l s imul atio ns.

ANN mode ls have e merged as a new alte rnati ve method fo r es timating fo rging forces in an inte lligent manu fact urin g environment. These techniques easily capture the intricate re lati onshi ps between vari ous

process parameters and can be easily integrated into exis ting manufacturing environment. These techniques open new avenues of parameter es timation , func tion approxi mati on, optimi zation and on-line control of complex manufacturing systems.

A brief review of the materia l mode lling used for hot upsetting a long with mathematical fo rmul ation used in the software was presented and its applicability to industry is depicted by an example of hot upsetting of a ck-45 preform with varying

temperatures, fri cti on conditions and d ie speeds. The example illu strated the ad vantage of Neural Network Simulation for producing parts wi th complex boundary conditi ons. The ad vantage of using Neural Networks fo r process mode lling in real time is reali zed .

Acknowledgement Partia l support fo r thi s research from the

Department of Sc ie nce and Technology under gran t number 111.5 (9 1)/96-ET (PRU) is gratefull y ackno wledged. The first author was introduced to FORGE2 environment and Finite E lement Modell ing of Metal forming by Prof. J .L. Chenot and Dr. L. Fourment at CEMEF Laboratory, France.

References I ASM Handbook: Fa n ning and Forging. ed it d by Semiat in S

L, VoL 14 (Metals Park , Ohio, USA), 1996. 2 Van der LUGT J & Huctink J, COIIIP Melh Appl Mech Eng,

54 ( 1986) 145 . 3 Alberti N, Cannizzaro L & Micari F, Anna ls CIRP, 39

( 1990) 231. 4 Carter Jr W T & Lee 0 , Trans ASME. 108 (1986) 198. 5 Rebelo N & Kobayashi S, Inl J Mech Sci , 22 ( 1980) 699. 6 Argyris J H & Doisin is J st, Camp Melh Appl Mech Eng, 23

( 198 1) 195 . 7 Kobayashi S. in Numerical Analysis of Forming Processes,

edited by Pitt man J F T (John Wil ey & Sons, Ch ichester), 1984, 45.

8 Zienkiewicz 0 C, in NU/llerical Analysis of Forming Processes, edited by Pittman J F T (John Wiley & Sons, Chi chester), 1984, I.

9 Abouf M, Chenot J L, Rai sson G & Bandui n P, In l J NII/n Melh Eng, 25 ( 1988) I.

10 Hans Raj K, Fourrnent L, Coupez T & Chenot J L, Inl J Eng Camp, 9 ( 1992) 575.

I I Fausett L, Fundamenlals of Neural Netwo rks (Prentice Hall , Eaglewood Cli ffs , N J), 1994.

12 Oskada K & Yang G, Annals CIRP, 40 ( 1990) 480. 13 Oskada K & Yang G. ln l J Mach Tool Mfg. 3 \ ( \ 99 \ ) 577. 14 Monostori L. Call/put Ill ig Mfg. 9 ( 1992) 42 1 . \ 5 Zhang H C & Haung S H, Camp Ind, 26 ( 1995) 107. 16 Monostori L, COlllpllld. 7 ( 1986) 53. 17 Monostori L, Allllais ClRP, 42 ( 1993) 485 .

.-