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Technical Assessment of Fini te ElementSoftware for modelling manufacturing processes

Rushabh J Vora a, Mohammed A Sheikh b

a Wolfson School of Mechanical & Manufacturing Engineering, Loughborough University,Loughborough, Leicestershire, LE11 3TU, UK. Email: - [email protected]

bDepartment of Mechanical, Aerospace & Manufacturing Engineering, UMIST, P.O. Box 88,Manchester M60 1QD, UK

Abstract: Finite element analysis is a technique where a complex region defining acontinuum is discretised into finite elements. The behavior of each element is predicted bymathematical equation whose summation approximately simulates the actual response of thePart. Finite element method has steadily increased its importance in simulation ofmanufacturing processes as the benefits of determining the effects of various process

parameters on computer has decreased the shop floor trials. The objective of the paper is todo technical assessment of finite element software’s like DEFORM for modellingmanufacturing processes. DEFORM is a simulation system whose application ranges fromvarious forming and heat treatment processes used in metal forming industry. Factors likesoftware’s capability in handling object geometries, range of material available in thedatabase, its control over process parameters and simulation were investigated. Theassessment was made on the basis of the efficacy of the software for particular process andresults obtained. Accuracy was checked directly by comparing the results with the shop floortrials.

1. Introduction

In the late 1970s and early 1980s the use of computer-aided techniques (Computeraided engineering, design and manufacturing) in metal forming industry hasincreased considerably [1]. However, accurate determination of various process

parameters became possible only when finite element method was developed [2].

Finite Element Formulation for deformation analysis of metal forming processes

Discretization of a finite element problem consists of the following steps: -

Description of the finite element: The geometry of an element, in general, isuniquely defined by a finite number of nodal points. The shape and the order ofshape functions characterize the element to produce an element strain-rate matrixand an element stiffness equation.A set of nodal point velocities in vector form is represented as:

{ }n21T

, , ,v ν ν ν ⋅⋅⋅= (1)where n = total number of freedoms in the model.The shape functions for the element defines an admissible velocity field locally interms of velocities of associated nodes. For example, for a two-dimensional 4-



Solution of the global system of equations: From a variation formulation, andarbitrariness of I δν

0) j( j I I

=⎟⎟

⎠ ⎞

⎜⎜

⎝ ⎛ ∂∂=

∂∂ ∑

ν π

ν π (8)

ν , I δν are the nodal velocities and their variations respectively; (j): the j th element.

The above stiffness equation is generally nonlinear and the solution is obtained byemploying an iterative procedure such as the Newton-Raphson method. Here, onlinearization by Taylor expansion

0 J

J I

2

I 00

=⎥

⎦

⎤⎢

⎣

⎡

∂∂

∂+⎥

⎦

⎤⎢

⎣

⎡

∂

∂

==

ν ∆

ν ν

π

ν

π

υ υ υ υ

Or f vK =∆ (9)

where 0v is the Assumed velocity (updated according to vv ∆+α 0 ); K: Stiffness

matrix; f: residual of the nodal force vector.

Time increment and geometry updating: The deformed geometry of the work-piecein the case of two dimensions is obtained by updating the co-ordinates of the nodes(Lagrangian mesh system) by:

t ut yt t y

t ut xt t xi yii

i xii

∆++=∆+∆++=∆+

)()(

)()(

00

00 (10)

where, ( i x , i y ): Co-ordinates of node i ,

0t = Time at current configuration and

t ∆ = Time increment.The strains are updated in a similar manner from the strain-rate solution [2].

2. Software - DEFORM

DEFORM ( Design Environment for Form ing) is an engineering software thatenables designers to analyse metal forming processes [3]. It is an implicit softwarecode and follows a Lagrangian approach for updating the algorithm.

DEFORM 3D (Version 4.0) is used for three-dimensional simulations; DEFORM2D models axi-symmetric and plain strain problems; DEFORM PC-PRO andDEFORM PC are variants for simulations on personal computers, DEFORM HT

provides heat treatment process simulation capability, and DEFORM TOOLS addsto the overall presentation capability of the DEFORM system.



DEFORM 2D and 3D are available on all popular UNIX platforms (HP, SGI, SUN,DEC and IBM), as well as, on PCs running Windows NT.

3. Applications

Non-isothermal spike forging

A benchmark problem of non-isothermal spike forging is analysed for determiningthe stresses in the dies. It is selected here to explore the capability of DEFORM-3Din forging and die stress analysis [3].

The height of the billet is taken as 2.25 inch and the top die velocity is set at of 2in/sec. The top die and the bottom pad are meshed and imported from IDEAS. The

billet, on the other hand, has been meshed in DEFORM itself.

Dies are made up of H-13 whilst the material of the billet is AISI – 1025. Thetemperature of the billet is 2000 0F and the temperatures of top and bottom dies are300 0F and 400 0F respectively.

After importing object geometries, meshing, and defining the boundary condition,the inter-object relationships are defined as per Table 1.

Object Relation Shear-friction

Heat-transferCoefficient

Billet-topdie

Slave-Master

0.3 0.004

BilletBottom die

Slave-Master

0.3 0.004

Table 1. Inter-object interface

The initial step for the spike forging problem is shown in Figure [1].

Figure 1. The Initial Step



Figure 2. Temperature Profile Figure 3. Load vs. Stroke

The results are obtained for various state variables such as strain, strain rate,effective stress and temperature. From the load/ stroke curve Figure [3], the totalload required at the top die to deform the billet was observed. The temperature

profile at the end of 10 steps (defined for the simulation) is shown in Figure [2]

Here, the maximum and minimum temperatures are 2000 0F and 1510 0Frespectively. The load/stroke graph of Figure [3] shows that the load gradually riseswith the maximum (19.4 klb) at the end of the last step. This represents themaximum force required for the deformation. Through a sensitivity study of variousother parameters it was found that the main factor, which affect the load of the press

is the coefficient of friction between the billet and the bottom die. A reduction inthe value of the friction coefficient from 0.3 to 0.1 would significantly change themaximum load.

On examining the temperature profile in Figure [2], greater chilling is seen at thecontacts between the dies and the billet. This effect should be minimized and inorder to lower the forging loads.The effective stress distribution for the billet is shown in Figure [4]. It can be seenthat maximum stress of 37.1 ksi occurs in region ‘A’ which is in direct contact withthe top die. For further examination of effective stress in this region the billet is alsosliced in a plane normal to the billet and oriented to view the cross-section of the

billet.

Die stress analysis

The stresses which are developed in the dies at the end of the above forging processare now analysed for the integrity assessment of the dies. The work-piece isremoved and the forces exerted on the dies by the work-piece are interpolated.



Figure 4. Effective stress

Figure 5. Die stress analysis

The effective stress distribution within the dies is shown in Figure [5], where theregions of high stress have been marked. The maximum stress in the die is 31.8 ksi(220 MPa). This is much lower than the yield stress value of 372 MPa for H-13 (diematerial) and is thus acceptable.

4. Discussion

DEFORM is a reliable software in metal forming industry. The forging and diestress analysis was performed effectively, where DEFORM was able to estimate theforging loads and the stresses in dies at the end of the simulation.

Application ranges from forging, extrusion, machining, die stress analysis, cogging,glass pressing, shape rolling, drilling to predicting phase transformation, ductilefracture, micro structural evolution, machining distortion & chip morphology.



DEFORM has separate templates for extrusion, cogging (DEFORM 3D) andHammer, machining, and rolling (DEFORM 2D), due to which process can besimulated very accurately and in less pre-processing time.

Advantages of the software are in its wide range of application and its user friendlygraphic user interface. Important features include its extensive material database,capability to create user defined material data input, good geometry handlingcapability, and good control over process parameters. DEFORM is capable to

produce accurate results which rages from stresses, strains, temperatures, Load-stroke information, point tracking as well die strain, grain flow, material flow, diefill, defect formation and ductile fracture.

The software is still being developed in the areas of rotary forming and extrusion processes. As DEFORM uses solid elements, it is hard to simulate thin surfacesmade up of shell elements. It is a straight forward application to the metal formingindustry and so not much suitable for solving structural and dynamic problem.

5. Conclusions

The areas of application of the Finite Element Method to model manufacturing processes are potentially broad. It can be used for the simulation of many complex processes where theoretical analysis of the process parameters would be difficult.DEFORM is an example of some effective finite element programs developed formetal forming, ring rolling and roll forming processes respectively. It can beinferred from the paper that DEFORM is capable to simulate metal forming

processes effectively.

References[1] Kalpakjian, S. Manufacturing processes for engineering materials, Addison-Wesley, NY,1991.

[2] Kobayashi. S, Soo-Ik Oh, and Altan, T. Metal forming and finite element method,Oxford University Press, NY, 1989.

[3] Scientific Forming Technologies Corporation, DEFORM-3D, V 4.0, Columbia, Ohio,1993.

[4] SHAPE-RR User Manual V 1.3, SHAPE Co. Ltd (Korea).

[5] www.imsteel.com/h13.htm, Sept. 2003.

[6] Zienkiewicz, O C. The Finite Element Method in Engineering science, McGraw-Hill,Maidenhead, 1971.

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