NUMERICAL MODELLING OF HOT FORMING AND HEAT … · Gear Solutions, July 2014. pp. 37-50. NUMERICAL MODELLING OF HOT FORMING AND HEAT-TREATMENT OF ANNULAR GEARS …

Gear Solutions, July 2014. pp. 37-50.

NUMERICAL MODELLING OF HOT FORMING AND

HEAT-TREATMENT OF ANNULAR GEARS

Prof. Dr. Miklós Tisza1 – Zsolt Lukács

2 – Gaszton Gál

3

1Professor, Head of Department, e-mail: [email protected]

2senior lecturer, e-mail: [email protected]

3senior lecturer, e-mail: [email protected]

Department of Mechanical Engineering, The University of Miskolc

3515 Miskolc, Miskolc - Egyetemváros

Abstract:

In this paper, first, the state-of-the-art of numerical modelling in hot forming processes will

be shortly overviewed. Then the paper briefly reviews the theoretical background of metal

forming simulation including the basic constitutive equations, and the information flow in

process modelling. The important process variables and the main characteristics of various

hot forming processes will also be discussed. Finally, some industrial examples will be

shown. An integrated approach of forging and heat-treatment will also be illustrated.

Keywords: hot forming, modelling, numerical simulation

1. Introduction

During the last two decades, there has been a very intense research activity in the field

of finite element simulation in metal forming processes; among them, hot forming has

gained a special attention. It is mainly due to the high importance of the process on the one

hand, and also to the rather challenging nature of this process since simulation of hot

forging processes implies most of the numerical difficulties what usually we can meet in

finite element simulation, i.e.:

- Complicated temperature evolution is characteristic for these processes, therefore,

thermal and mechanical coupling should be considered.

- Usually, severe, large deformations occur.

- Contact phenomena and friction play a significant role.

- Significant microstructure changes of the parts occur, which have significant effects

on the final properties (e.g. the mechanical properties, etc.).

The main objectives of finite element modelling in bulk forming processes can be

summarised as follows:

- Development of adequate process sequence and die design by process simulation of

die cavity filling, predicting temperature distribution so that part properties, friction

conditions, and die wear can be controlled.

- Increasing part complexity and process economy by maintaining or reducing

manufacturing costs, reducing die try-outs and lead times, and reducing rejects, etc.

mailto:[email protected]



Miklós Tisza, Zsolt Lukács, Gaszton Gál

2

- Improving part quality by predicting process limits that should not be exceeded in

order to avoid internal and surface defects and improving material flow, grain flow

and microstructure changes.

- Predicting forging load and energy, as well as tool stresses so that premature tool

failure can be avoided, and finally

- Selecting the appropriate forging machines for the given applications.

2. Short overview of FEM applications in hot forming processes

2.1. The early days in metal forming simulation

While forging is a process with many centuries of history, its theoretical basis is a

relatively young science; however, it is of utmost importance to the understanding of the

process itself and to the development and application of finite element modelling. Various

useful methods and techniques were developed to analyse metal forming processes: the slab

method, the slip-line technique, the various upper bound methods are very useful for

predicting forming loads, overall geometry changes, etc. [1] but accurate determination of

the effects of various process parameters and detailed material flow analysis have also

become possible by developing finite element procedures to metal forming processes.

Although, linear-elastic FEM analysis was already successfully used as a powerful

structural analysis tool many decades ago, non-linear finite element analysis had serious

problems at the beginning due to its heavy computing need and the lack of sufficient

computer power. The application of finite element method to metal forming problems

began as an extension of structural analysis technique to the plastic deformation [2]. Since

in metal forming processes, the plastic strain significantly outweigh the elastic strain, in

many cases the rigid-plastic, or rigid-viscoplastic material behaviour is acceptable. The

resulting analysis based on this assumption is known as the flow formulation [3]. However,

in many applications, elastic strains cannot be neglected: therefore, in these applications,

the so-called solid formulation based plastic stress-strain matrix developed from the

Prandtl-Reuss equations was used [4]. In this analysis, the material is considered as elastic-

plastic, or elastic-viscoplastic.

One of the most important steps in the simulation of metal forming processes was the

inclusion of the effects of strain-rate and temperature in material properties and the thermal

coupling in forming solution [5]. This was that development which made possible the

extension of finite element analysis towards warm and hot forming processes [6]. A further

important step was the development of process-oriented special purpose FEM codes [7] that

are nowadays widely available in the market.

2.2. Forging simulation today – The need of the industry

By the 1990s with the enhancement of computing power, plasticity based finite element

methods had gained sufficient ground to result in the emergence of several forging specific

simulation packages. The user interface of these packages is continuously improved to

make their industrial application more user-friendly. The sophistication of commercially

available simulation tools is such that by modelling the elastic and thermal dimensional

changes of both the part and the tools, it is possible to improve the precision of the forging

Numerical modelling of hot forming

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process leading to near net shape products and a reduction in wastage of workpiece

material. The ability to achieve close proximity to net shape so as to enable single pass

machining or even grinding is currently quite realistic for parts that can be simulated. Also,

powerful as they are, simulation tools do not displace the need for a traditional tool design

capability. Simulation can only simulate a pre-conceived tool design.

Nowadays, various commercial forging simulation packages are available. Among them

the most widely applied are the following ones: DEFORM, MARC AutoForge, MSC

SuperForge, Forge 2 and 3, QForm, etc. They variously enable the simulation of cogging,

rolling, forging, ring rolling, extrusion, piercing and many of them are associated with

heating and cooling processes. The forging equipment definitions incorporated within the

packages include hydraulic presses, mechanical presses, screw presses, drop hammers or

any other machine characteristics that can be defined by the user.

Considering the industrial application of FEM simulation, from the point of view of an

industrialist, two important questions should be asked:

What effect could the development of simulation tools have on the forging industry?

How realistic and effective is their implementation under industrial circumstances?

A typical response is that the application of simulation tools will result in a reduction in

lead-time. Lead-time is often dominated by tool manufacture and set-up time. The real

benefit in production terms is more likely to come from the enhanced speed of quotation

preparation, reductions in tool trials and hence lead-times or, in product development terms

by increasing confidence in the ability to extend the product range. A further "business

benefit" arises from the enablement of a quality assurance aspect of simulation. A potential

supplier can now offer simulation output as evidence that the proposed die design is

feasible and then gives assurance of anticipated satisfactory delivery.

3. Theoretical background of Finite Element Analysis

For accurate finite element prediction of the material flow during bulk metal forming,

the formulation must take into account the large plastic deformation, incompressibility,

component–tool contact, and temperature coupling. The basic equations to be satisfied are

the equilibrium equation, the incompressibility condition, and the stress-strain relationships.

When applying the penalty method, the velocity is the primary solution variable. The

variation equation is in the form

( ) 0v i i

V V S

v dV dV F v dS . (1)

In the mixed formulation, both velocity and pressure are solution variables. They are

solved by the variation equation

( , ) 0v v i i

V V V S

v p dV p dV p F v dS , (2)

where v is the volumetric strain rate, is the effective stress, is effective strain and

is the effective strain rate, p is the pressure, V is the volume and S is the surface of the

deforming workpiece, respectively.

Eq. (1) and (2) can be converted into a set of algebraic equations by utilizing the

standard FEM discretization procedures. Due to the non-linearity involved in the material


4

properties and frictional contact conditions, the solution is obtained iteratively. The

temperature distribution of the workpiece and/or dies can be obtained readily by solving the

energy balance equation rewritten, by using the weighted residual method, as

, ,j j v n

V V V S

kT T dV cT TdV TdV q TdS , (3)

where k is the thermal conductivity, T is the temperature, ρ is the density, c is the specific

heat, α is the fraction of deformation energy that converts into heat, and qn is the heat flux

normal to the boundary, including heat loss to the environment and friction heat between

two contacting objects. By applying the FEM discretization procedure, Eq. (3) can also be

converted to a system of algebraic equations and solved by a standard method. In practice,

the solutions of mechanical and thermal problems are coupled in a staggered manner. After

the nodal velocities are solved at a given time step, the deformed configuration can be

obtained by updating the nodal coordinates [8].

3.1. Some important considerations in bulk metal forming simulation

Obviously, it is of primary importance to have an accurate and robust computer system

for the simulation of various 3D bulk forming processes. To meet these objectives, many

important issues have been considered in the development of simulation methodology, for

example:

How to discretize the deforming workpiece?

What is the most efficient solving method available?

How to reduce the memory requirement in solving equations?

Many considerations are arising and many selections are changing as both the

computational methodology and the computing technology evolves. Some of the most

important issues will be shortly summarized here.

3.1.1. Materials characterization – Tool and workpiece properties

In finite element modelling, the real material behaviour is of utmost importance to

facilitate the analysis. In order to accurately predict the metal flow and forming loads, it is

necessary to have reliable input data. For many bulk forming problems, especially at

elevated temperatures, which is the case in hot forming processes, the elastic deformation is

often insignificant and therefore can be neglected, rigid–plastic material model (the flow

stress is a function of strain and temperature) and rigid–viscoplastic material model (the

flow stress is a function of strain, strain rate and temperature) are used widely due to their

simplicity and fast convergence in iteration. If residual stresses and/or spring-back are a

primary concern, the elasto-plastic material model, which is generally characterized by an

initial yield and strain hardening, is a better choice. The grain size is also an important

parameter that governs the material behaviour.

3.1.2. Lagrangian or Eulerian formulation

In order to represent the evolution of workpiece geometry, the updated Lagrangian

method is often used. As a drawback of this method, however, that the elements degenerate


5

easily when large deformation and drastic change in shape occur during the bulk forming

process. In order to continue the analysis, a new mesh must be created out of the surface of

the old mesh, known as remeshing or rezoning. It may be needed to perform many times

before a complete forming process is simulated and hence has to be automated. The

Eulerian formulation is more suitable for the steady-state processes such as extrusion and

rolling. For a more efficient modelling of these processes, the code is being further

developed to include the Arbitrary Lagrangian Eulerian (ALE) formulation.

4. Process modelling

Once the part is designed for a specific process, the following steps lead to a rational

process design:

1. Establishment of a preliminary die design and selection of process parameters by

using experience based knowledge.

2. Verification of the initial design and process conditions using process modelling.

3. Modification of the die design and initial selection of process variables, as needed,

based on the results of process simulation.

4. Completion of the die design phase and manufacturing of the dies.

5. Performing die try-outs on production equipment.

6. Modification of die design and process conditions, if necessary, to produce quality

parts.

The information flow corresponding to the above steps in process modelling is shown in

Figure 1.

Geometric parameters Process parameters Material parameters

Process Model

Metal Flow of Part

Die filling

defect formation, etc.

Thermomechanical history

Stress, strain, strain-rate

Temperature, etc.

Equipment control

Load - stroke/time

Ram velocity - stroke/time

Microstructural Model

Grain size, fraction of recrys-

tallization, Precipitation, etc.

Optimum Process Parameters

and Control Limits

Figure 1. Flow chart of process modelling in forging simulation

The input of the geometric parameters process parameters, and material parameters set

up a unique case of a closed-die forging. Modelling is then performed to provide


6

information on the metal flow and thermo-mechanical history of the forging, the

distribution of the state variables at any stage of the forging, and the equipment response

during forging. The histories of the state variables, such as strain, strain rate, temperature,

etc., are then input to the microstructure model for microstructural feature prediction. All of

the information generated used for judging the forging operation. The non-satisfaction in

any of these areas will require a new model with a set of modified process parameters until

the satisfied results are obtained. Then, the optimum process is selected for shop practice.

4.1. Process modelling parameters

The most important input parameters for forging process modelling are the geometric,

the materials and process parameters. In the following, the types and importance of these

input parameters are shortly discussed.

Geometric parameters: The starting workpiece geometry and the die geometry need to

be defined in a closed-die forging modelling. Depending on its complexity, a forging

process can be simulated either as a two-dimensional, axisymmetric or plane-strain, or a

three-dimensional problem. If the process involves multiple stations, the die geometry of

each station needs to be provided.

Material properties: In order to accurately predict the material flow and forming loads,

it is necessary to use reliable input data. The stress-strain relation or flow curve is generally

obtained from a compression test. In most simulations, the tools are considered rigid; thus,

die deformation and stresses are neglected. However, in precision forging operations, the

relatively small elastic deformations of the dies may influence the thermal and mechanical

loading conditions and the contact stress distribution at the die/workpiece interface. Thus,

die stress analysis is a crucial part of process simulation to verify the die design and the

forging process parameters.

Interface conditions: The friction and heat-transfer conditions at the interface between

the die and the billet have a significant effect on the metal flow and the loads required to

produce the part. In forging simulations, due to the high contact stresses at the interface

between the workpiece and the die, the constant shear friction factor gives better results

than the Coulomb friction coefficient. The most common way to determine the constant

shear friction factor in forging is the well-known ring compression test.

Process parameters: The typical process parameters to be considered in a closed-die

forging include: the environment, the workpiece and the die temperatures, the coefficients

of heat transfer between dies and the billet and the atmosphere, the time used to transfer the

workpiece from the furnace to the dies, the time needed to have the workpiece resting on

the bottom die, the workpiece and die interface heat-transfer coefficient during free resting,

the workpiece and die interface heat-transfer coefficient during deformation, the workpiece

and die interface friction, etc. The die velocity is also a very important parameter to be

defined in the modelling of a closed-die forging.

5. Industrial application examples

Process modelling of closed-die forging using finite-element modelling has been

applied in forging industry for a couple of decades. The goal of using computer modelling

in closed-die forging is the rapid development of right-the-first-time processes and to

enhance the performance of components through better process understanding and control.


7

In its earlier application, process modelling helped die design engineers to preview the

metal flow and possible defect formation in a forging. After the forging simulation is done,

the contours of state variables, such as effective strain, effective strain rate, and temperature

at any instant of time during a forging, can be generated. The thermo-mechanical histories

of selected individual locations within a forging can also be tracked. These functions of

process modelling provided an insight into the forging process that was not available in the

old days. Integrated with the process modelling, microstructure modelling is a new area that

has a bright future [9], [10]. Microstructure modelling allows the optimum metallurgical

features of the forging to be previewed on the computer. Metallurgical aspects of forging,

such as grain size and precipitation can be predicted with reasonable accuracy. Some

proven practical applications will be shortly described in the following parts. One of the

main industrial application fields of forging simulation is the design of forging sequences in

cold, warm, and hot forging, including the determination of preform shapes and dimensions

with the prediction of material flow, the forming forces, die stresses, etc.

In Figure 2, the final shape and dimensions of an annular gear to be produced by hot

forging can be seen. Due to its complicated shape and strongly changing cross-sections, it is

an excellent example for multi-stage hot forging simulations. Furthermore, due to its de-

signation, it should be also heat-treated, which provides a further possibility to illustrate the

integrated simulation of multi-stage hot forging and heat-treatment processes.

The dimensions of the starting billet are calculated from the final shape and dimensions

of the forged component using the volume constancy rule. The billet is made of plain

carbon steel (C = 0.45 %) from a cylindrical bar with the dimensions: Ø 75 x 120 mm.

In Figure 3. the process sequences of principal forging operations can be seen that are

needed to produce the above annular gear component.

Figure 2. CAD drawing of the hot forged annular gear

The preform shapes and dimensions are determined on the basis of theoretical and

practical considerations including a great amount of workshop experiences summarised in

the book Design of hot forming processes [11]. In each stage, the volume constancy rule is

applied, and the intermediate preform shapes are determined as to provide a smooth

material flow with a continuous approximation of the final shape of the component. The

third stage is followed by a burring operation removing the flash necessary during the

preform operations. Finally, the cutting operation of the central hole is performed and the


8

gearing is done by machining operation. The heat-treatment of the component is done by

hardening with subsequent tempering to get the prescribed hardness and other mechanical

properties. The forming of the part is done on a National type hot forming press with a

nominal capacity of 4000 tons and the stroke length of 250 mm.

Figure 3. Process sequence of multi-stage hot forming of annular gear

The feasibility of the above process sequence was simulated with the DEFORM 3D

package. Since this part is produced at elevated temperature, simulation has to be run in

non-isothermal conditions. The material is considered as a rigid-viscoplastic one

characterised by the well-known stress-strain-strain rate expression:

n mC y (4)

where is the effective true stress, is the effective true strain, is the effective strain-

rate, n is the strain-hardening exponent, m is the strain-rate exponent, C, n, m and y are

material constants.

The flow curves for the applied material at the most relevant temperature ranges

concerning the hot forming processes are shown in Figure 4.

For the forging simulation, the surface of the tools was preheated to 350 0C degrees.

During the simulations, the temperature distribution, the stress and strain state distribution

was analysed. Due to the symmetry of the component, only the forging of a quarter of the

part was modelled to reduce the time needed for the simulation.

In Figure 5, the temperature distribution is shown at the end of the 1st, 2

nd and 3

rd

forging stages, together with the temperature scale. In this Figure, so-called global

temperature scale is applied, i.e. the attached scale is valid for each forging stage. In these

pictures as it can be seen in Figure 5, the temperature increase due to the absorbed

deformation energy, as well as the cooling effect of the tools can be clearly observed.


9

Thus, for example, in the first forging

operation, the temperature maximum

inside the preform attains 1160 0C

degrees, as the highest temperature value

during the whole forging process. As the

contact surface of the part and the tool is

increasing, the cooling effect of the

forging tool is more significant. The

lowest temperature at the end of the third

forging stage is 6670C, which can be

measured at the outer surface of the

lower bush part of the annular gear.

In Figure 6, the effective strain

distribution of the forged annular gear at

the end of the third forging operation is

shown. As it can be seen, there are very

significant differences in the value of

effective strain: the lowest value is

=0.922, whilst the highest one is right

above =3.0, however, there is no any

critical deformation causing failure.

Figure 5. Temperature distribution at the end of the first three forging stages

150

225

300

375

450

Flow

Stress

(Mpa)

T = 900 oC

T = 1000 oC

T = 1100 oC

0,050 0,125 0,200 0,275 0,350 Strain

Figure 4. Flow curves at elevated

temperatures


10

Figure 6. The effective strain distribution at the end of the third forging stage

In Figure 7, the effective stress distribution of the forged annular gear at the end of the

third forging operation can be seen, which shows quite acceptable stress values.

Figure 7. The effective stress distribution at the end of the third forging stage


11

After the forging simulation, the gear geometry was modified to take into account the

flash removal and drilling operations. Then, the modified gear geometry was used to

simulate the heat-treatment operation. The gear was heated up to the austenitization

temperature (T = 850oC) and cooled down in 60 seconds with oil quench. A time-

temperature transformation diagram for the given material was used to follow the austenite

to pearlite/bainite/martensite transformation. In the simulation package, various expressions

are used to describe the phase transformations depending on the transformation kinetics. In

Figure 8, the distribution of martensite phase is shown at the end of quenching.

Figure 8. The distribution of martensite phase at the end of heat-treatment

Besides the above examples, prediction and optimization of flash dimensions,

prediction of die stresses, fracture, and die wear; improvement of process variables and die

design to reduce the risk of possible die failure, or simulation of microstructure and

properties, elastic recovery, and residual stresses are very important fields of industrial

applications.

6. Conclusion

In this paper, the numerical modelling of hot forging processes was overviewed. It was

shown that hot forging simulation has gained special attention in finite element modelling

of thermal processes due to its high importance among manufacturing processes, as well as

due to its complicated nature concerning the coupled thermal and mechanical modelling

and strongly non-linear physical and material behaviour during hot forging.

It was also shown that finite element simulation can successfully applied in modelling

of bulk forming processes to develop adequate process sequences and die design, die cavity


12

filling, for predicting process limits, to improve part quality by avoiding internal and

surface defects, and to increase part complexity.

In hot forging processes, material flow, grain size and microstructure changes can also

be simulated to reliably predict mechanical properties. Since hot forging processes are

performed at elevated temperatures, the integrated forging and heat-treatment simulation is

of special interest.

7. Acknowledgements

This research work was performed as part of the TÁMOP-4.2.1.B-10/2/KONV-2010-

0001 and TÁMOP-4.2.2.A-11/1/KONV-2012-0029 projects in the framework of the New

Hungarian Development Plan. The project is supported by the European Union, and co-

financed by the European Social Fund, which is gratefully acknowledged.

8. References

[1] Thomsen, E., Yang, O. and Kobayashi, S. (1983) “The Mechanics of Plastic

Deformation”

[2] Kobayashi, S., Oh, S. and Altan, T. (1989) “Metal Forming and the Finite Element

Method” Oxford University Press, Oxford-New York.

[3] Zienkiewicz, O. C. (1984) “Flow formulations for numerical solutions of forming

processes” John Wiley, New York.

[4] Pitman, J. F. T. (1984) “Numerical Analysis of Forming Processes” John Wiley, New

York.

[5] Boër, C. R., Rebelo, N., Rystad, H. and Schröder, G. (1986) “Process Modelling in

Metal Forming and Thermo-mechanical Treatment” Springer-Verlag, Berlin.

[6] Altan, T. and Vasquez, V. (1996) “Numerical process simulation for tool and process

design in bulk metal forming” Annals of the CIRP, Vol.45, No.2, pp. 599-610.

[7] Bramley, A. N. and Mynors, D. J. (1999) “The use of forging simulations tools”

Advanced Technology of Plasticity, v. 3. pp. 19-24.

[8] Wagoner, R. H. and Chenot, J.-L. (2001) “Metal Forming Analysis” Cambridge

University Press, Cambridge, UK.

[9] Li, G., Jinn, J. T. Wu, W. T. and Oh, S. I. (2001) „Recent development and

applications of three-dimensional finite element modelling in bulk forming processes“

Journal of Materials Processing Technology, v. 113. p. 40-45.

[10] Altan, T., Ngaile, G. and Shen, G. (2004) “Cold and hot forging” ASM Publisher,

Materials Park, Ohio.

[11] Brjuhanov, A. N. and Rebelski, A. V. (1972) “Design of Hot Forging Operations”

Masinostroenie, Moscow (in Russian)

[12] Tisza, M., Lukács, Zs., Hál, G.: “Numerical Modelling of Hot Forming Processes”, 3rd

International Conference on Thermal Process Modelling and Simulation, Budapest,

25-28. April 2006. Proceedings of IFHTS 2006. (2006) pp. 3-14.

Documents

NUMERICAL MODELLING OF HOT FORMING AND HEAT … · Gear Solutions, July 2014. pp. 37-50. NUMERICAL MODELLING OF HOT FORMING AND HEAT-TREATMENT OF ANNULAR GEARS …