Using an Inverse Cutting Simulation-Based Method to Determine the Johnson-Cook Material Constants of Heat-Treated Steel

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Procedia CIRP 00 (2017) Procedia CIRP 000–000 77 (2018) 26–29 www.elsevier.com/locate/procedia

8th CIRP Conference on High Performance Cutting (HPC 2018) 8th CIRP Conference on High Performance Cutting (HPC 2018)

Using an Inverse Cutting Simulation-Based Method to Determine the Using an Inverse Simulation-Based to Determine the 28th Cutting CIRP Design Conference, May 2018,Method Nantes, France Johnson-Cook Material Constants of Heat-Treated Steel Johnson-Cook Material Constants of Heat-Treated Steel A Rocco new methodology to analyze the functional and physical architecture of Eisselera,a,*, Konstantin Drewleaa, Karl Christoph Grötzingeraa, Hans-Christian Möhringaa Rocco Eisseler *, Konstantin , Karloriented Christoph Grötzinger , Hans-Christian Möhring existing products for anDrewle assembly product family identification University of Stutttgart, Institute for Machine Tools, Holzgartenstr. 17, 70327 Stuttgart, Germany University of Stutttgart, Institute for Machine Tools, Holzgartenstr. 17, 70327 Stuttgart, Germany

a a

Paul Stief *, Jean-Yves Dantan, Alain Etienne, Ali Siadat

* Corresponding Tel.:Supérieure +4971168583876; +497117858376. E-mail address:LCFC [email protected] Écoleauthor. Nationale d’Arts etfax: Métiers, Arts et Métiers ParisTech, EA 4495, 4 Rue Augustin Fresnel, Metz 57078, France * Corresponding author. Tel.: +4971168583876; fax: +497117858376. E-mail address: [email protected]

* Corresponding author. Tel.: +33 3 87 37 54 30; E-mail address: [email protected]

Abstract Abstract The Johnson-Cook approach is a common model used for machining simulations which represents the material behavior by taking 5 material Abstract The Johnson-Cook approach Johnson-Cook is a common model usedare foravailable machining which thethe material behavior bywith taking 5 material constants into consideration. constants forsimulations a large number of represents materials, in majority for such a widespread constants consideration. constants are available a large of materials, thehardly majority for such a widespread applicationinto or which are in theJohnson-Cook focus of research activities. Material for models for number e.g. heat-treated steelsinare to find. The with material constants In today’s business environment, the trend towards more product variety and customization is unbroken. Due to this development, the need of application or whichbyare in theoffocus of research activities. Materialtomodels for e.g. heat-treated steels are hardly to find. The characteristics. material constants can be determined means material tests with the objective get information about the thermo-mechanical material To agile and reconfigurable production systems emerged to cope with various products and product families. To design and optimize production can be determined bycutting means conditions of materialwith teststheir withlarge the objective to and get information about thecontact thermo-mechanical material characteristics. consider the complex temperature time gradients in the zone, expensive technical equipment isToa systems as well as to choose the optimal product matches, product analysis methods are needed. Indeed, most of the known methods aim to consider theAn complex cutting conditions their large temperature and time gradients in the contact zone, expensive technical equipment is a perquisite. alternative to this practicewith is the determination of material constants by means of inverse simulation based methods. Therefore analyze a product or one product family on the physical level. Different product families, however, may differ largely in terms of the number and perquisite. Andesigns alternative this practice the determination of material constants by means inverse simulation based methods.InTherefore experimental with to varied material is constants are being prepared within predefined value of ranges by means of DoE approaches. addition nature of components. This fact impedes an efficient comparison and choice of appropriate product family combinations for the production experimental designs with varied arecriteria being prepared within predefined value ranges by means of DoE approaches. In addition cutting tests are performed to get material relevant constants comparison e.g. forces or chip shape characteristics with the objective to fit and validate the system. A new methodology is proposed to analyze existing products in view of their functional and physical architecture. The aim is to cluster cutting testsresults are performed relevant comparison criteria forces or with chip the shape characteristics the objective to fit and validate the simulation regardingtotoget realistic material constants. Thise.g. article deals inverse procedurewith to determine the Johnson-Cook material these products in new assembly oriented product families for the optimization of existing assembly lines and the creation of future reconfigurable simulationofresults regarding to realistic material This article deals with the inverse procedure determine thetechniques Johnson-Cook material constants the heat treatable steel SAE 4142 constants. with the hardness 42 HRC. It describes simulation andto experimental regarding to assembly systems. Based on Datum Flow Chain, the physical structure of the products is analyzed. Functional subassemblies are identified, and constants ofcutting the heat treatable steel and SAEthe 4142 with the hardness 42 HRC. It describes simulation andmodels experimental techniques regarding to orthogonal in groove turning valuation of using the gained material constants in material for cutting simulations. a functional analysis is performed. Moreover, a hybrid functional and physical architecture graph (HyFPAG) is the output which depicts the orthogonal cutting in groove turning and the valuation of using the gained material constants in material models for cutting simulations. similarity between product families by providing design support to both, production system planners and product designers. An illustrative © 2018 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license example nail-clipper is used by to explain proposed methodology. An industrial case study on two product families of steering columns of © 2018 2018 of Thea Authors. Elsevierthe Ltd. © The Authors. Published Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/) thyssenkrupp Presta France is then to give a first industrial evaluation of the proposed approach. This is an open access article undercarried the CCout BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) (http://creativecommons.org/licenses/by-nc-nd/3.0/) Peer-review under responsibility of the International Scientific Committee of the 8th CIRP Conference on High Performance Cutting (HPC peer-review under ©Selection 2017 Theand Authors. Published by responsibility Elsevier B.V. of the International Scientific Committee of the 8th CIRP Conference on High Performance Peer-review under responsibility of the International Scientific Committee of the 8th CIRP Conference on High Performance Cutting (HPC 2018). Cutting (HPC 2018). Peer-review under responsibility of the scientific committee of the 28th CIRP Design Conference 2018. 2018). Keywords: Cutting; Steel; Simulation; Heat treatment; Material Keywords: Assembly; Design method; Family identification Keywords: Cutting; Steel; Simulation; Heat treatment; Material

Nomenclature Tr Reference melt temperature [K] Nomenclature 1. Introduction of the product range and characteristics T Reference melt temperature r T* Temperature Quotient [K] [K] manufactured and/or A Material constant [MPa] assembled in this system. In this T* Temperature f feed [mm/rev]Quotient [K]context, the main challenge in A Material constant [MPa] B Due to the fast development in the domain of modelling and analysis is now frb feed [mm/rev] Cutting edge radius [mm]not only to cope with single B Material constant [MPa] C communication and an ongoing trend of digitization and products, a limited product range rt b Cutting Time [s]edge radius [mm] or existing product families, C DoE Material Design ofconstant Experiments digitalization, manufacturing enterprises are facing important but also to be able to analyze and to compare products to define tvc Time [s]speed Cutting [m/min] DoE of hardness Experiments HRC Design Rockwell challenges in today’s market environments: a continuing new product families. It can be observed that classical existing v Cutting speed [m/min] c Clearance angle [°] HRC Rockwellconstant hardness n Material tendency towards reduction of product development times and product families are regrouped in function of clients or features.  Clearance angle [°]  Rake angle n Material constant m shortened product lifecycles. In addition, there is an increasing However, assembly oriented product families are hardly to find. ∗  Rake 𝜀𝜀̇ Plasticangle strain-rate m Materialforce constant Fc Cutting [N] ∗ On the product family level, products differ mainly in two demand of customization, being at the same time in a global 𝜀𝜀̇ Plastic strain-rate Equivalent plastic strain Fcf Cutting force Feed force [N][N] competition with competitors all over the world. This trend, main characteristics: (i) the number  Equivalent plastic strain  Effective plastic strain rate of components and (ii) the Ffp Feed force [N]  Passive force [N] which is inducing the development from macro to micro type of components (e.g. mechanical,  Effective plastic strain rate electrical, electronical). Stress [MPa] F Passive force [N] Tpm Reference temperature [K] markets, results in diminished lot sizes due to augmenting Classical methodologies considering mainly single products  Stress [MPa] Tm Reference temperature [K] product varieties (high-volume to low-volume production) [1]. or solitary, already existing product families analyze the To cope with this variety as wellLtd. asThis to be structure on a physical level (components level) which 2212-8271 © 2018 Theaugmenting Authors. Published by Elsevier is anable opento access product article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/) 2212-8271 © 2018 The optimization Authors. Publishedpotentials by Elsevier Ltd. an open access causes article under the CC BY-NC-ND license an efficient definition and identify possible in This the is existing difficulties regarding Peer-review under responsibility of the International of the 8th CIRP Conference High Performance (HPC 2018).. (http://creativecommons.org/licenses/by-nc-nd/3.0/) production system, it is important to have aScientific preciseCommittee knowledge comparison of on different productCutting families. Addressing this Peer-review of the International Scientific Committee of the 8th CIRP Conference on High Performance Cutting (HPC 2018).. 2212-8271 ©under 2018responsibility The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Selection © and peer-review under responsibility of the International Scientific Committee of the 8th CIRP Conference on High Performance Cutting 2212-8271 2017 The Authors. Published by Elsevier B.V. (HPC 2018). Peer-review under responsibility of the scientific committee of the 28th CIRP Design Conference 2018. 10.1016/j.procir.2018.08.198

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Rocco Eisseler et al. / Procedia CIRP 77 (2018) 26–29 Eisseler, R. et al./ Procedia CIRP 00 (2018) 000–000

1. Introduction The efficient machining of heat-treated steel with geometrical defined cutting edges assume a more and more important role in the field of production engineering. Production becomes leaner by moving heat-treatment processes to the beginning of the manufacturing chain and ceasing finishing processes. For this purpose each individual step in the chain has to be suitable for the machining of hard materials. This has been implemented well for processes such as milling, turning and partially for drilling. By comparison, deep-hole drilling has a further potential for optimization, in particular the tool lifetime. Numerical based models provide a good opportunity to support the optimization of machining processes. Simulating the machining of steels in their initial state is an intensively examined field resulting in a variety of relevant material models. Scant attention has been paid to the simulation of machining processes in the context of heat-treated steels. This paper presents an inverse parameter identification approach to get the Johnson-Cook material model for heattreatable steel SAE 4142 with a hardness of 42 HRC. The parameters were gained by means of modeling an orthogonal machining process using the DEFORM®-3D V11.0 engineering software. Therefore required parameter fields were generated by Design of Experiments capabilities. Cutting tests in groove turning performed on a DMG CTX 420 linear turning machine conducted to validate the model. 2. State of the art 2.1. Material models for use in machining simulation The lifelike simulation of a machining process requires accurate material models describing the material behavior under appropriate thermal and mechanical conditions. With respect to machining simulation applications the following material model approaches are among the most widely used ones:      

Johnson-Cook approach (1983) Bammann-Chiesa-Johnson (1996) Zerilli und Armstrong (1987) Obikawa und Usui (1996) Marusich et al. Rhim und Oh (2006)

In contrast to phenomenological material models recent approaches just as presented by Storchak and Kushner deal with describing the material behavior by mathematical correlations. Based on a mathematical model the authors describe flow curves and yield point depending on rising temperatures due to adiabatic and isothermal deformations. The approach ensures the reproduction accuracy of machining simulations [1]. Among the above-mentioned approaches the Johnson-Cook material model is characterized by depending on only 5 unknown parameters A, B, C, m and n have to be

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determined regarding to the respective applications, see Eq. 1. This ease of use gives the reason for the wide dissemination of the model in the field of machining simulation. 𝜎𝜎 = [𝐴𝐴 + 𝐵𝐵 ∙ 𝜀𝜀 𝑛𝑛 ] ∙ [1 + 𝐶𝐶 ∙ 𝑙𝑙𝑙𝑙𝜀𝜀̇∗ ] ∙ [1 − 𝑇𝑇 ∗𝑚𝑚 ]

(1)

A variety of research work was done to get the parameters for most diverse materials. As an example the required parameters according to Molinari et al. for initial state steel SAE 4142 are specified in Table 1 [2, 3]. Table 1. Johnson-Cook parameters for initial state steel 4142 [2, 3]. A [MPa]

B [MPa]

C

n

0 [s-1]

m

Tr [K]

Tm [K]

612

436

0.008

0.15

5.77E-4

1.46

293

1793

2.2. Inverse parameter identification The literature recommends the inverse parameter identification due to various process influencing factors and the inadequate suitability of usual curve fitting methods [6]. Both cutting parameters and material properties are influencing several process characteristics such as machining forces and the chip shape. Here the mean cutting force reacts less to an inaccurate material model than the chip shape [5]. The underlying principle is to vary, for instance, a set of JohnsonCook parameters within a predefined parameter domain and to compare the calculated results with process characteristics determined in cutting analyses before. However, the cutting parameters are kept constant. This procedure is to be repeated iteratively until the calculated results correspond with those measured within the chip removal analyses. It has to be said that the determined material model parameters are only valid in the range of the provided cutting conditions [6]. Shrot and Baker present an inverse parameter identification to find Johnson-Cook parameters using the LevenbergMarquardt algorithm. The underlying minimization algorithm helps to diminish the divergence between the experimental and simulative determined criteria for example chip shape or cutting force. The identification was limited to three (A, B, n) of five Johnson-Cook parameters. This was done with respect to the fact that identifying all five parameters causes various parameter combinations which lead to the same criteria. A clear allocation would not possible then [6]. 2.3. Material models for hard materials Elbestawi et al. focuses the most realistic reproduction of chip breakage occurrences in machining heat-treated steel. A Johnson-Cook model within the machining simulation of heat treatable steel AISI 4340 with the hardness 52 HRC is presented. The authors predict that influence of the material hardness on the chip formation is considered too low in recently available commercial finite element based simulation software. Due to this matter Elbestawi et al. use an additional damage factor to reproduce chip formation and chip breakage in a more

Rocco Eisseler et al. / Procedia CIRP 77 (2018) 26–29 Author name / Procedia CIRP 00 (2018) 000–000

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accurate way. Orthogonal cutting with tools having a rake angles of 0° and a clearance angle of 11° was taken as an example machining case to perform corresponding experiments. The Johnson-Cook model is also used within examinations in hard milling heat-treated steels by Knodt. According to [7]. Detailed parameter identifications for Johnson-Cook models within simulating the machining of SAE 52100 with a hardness of 62 HRC have also been conducted by Shrot and Baeker [6].

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depicts the determined machining force components Fc, Ff and Fp during the measuring time t for one run with the parameter definition example cutting speed vc = 100 m/min and feed f = 0.005 mm.

3. Cutting experiments In a first step cutting tests were conducted in groove turning of heat-treated steel SAE 4142 with the hardness 42 HRC to get target data for a subsequent inverse parameter identification. Therefore a turning tool holder was used together with changeable square shaped carbide inserts. The inserts do not have any surface structures such as chip breakers, see Fig. 1. The clearance and rake angle were chosen with  = 8° and = 0°. Fc

4. Simulation

3 2

Ff

Fig. 2. Machining force components occurred in an exemplary cutting test.

4.1. Creation of the model In a second step the inverse parameter identification was prepared by means of a finite-element simulation. The twodimensional simulation-underlying model was developed by using DEFORM 3D™ V11.01. The tool shape has been taken into account by the above mentioned angles  und  as well as the cutting edge radius rb = 6 µm. The part’s mesh generation occurred with a local refining and a maximum element amount of 5000 to reduce computation time, see Fig 3.

Fp

Fig. 1. Test setup for groove turning experiments.

The cutting tests were conducted in a full factorial way with 15 sets of cutting parameters consisting the cutting speed vc and the feed f according to Table 2. With a view to an adequate statistical basis of the results, tests with individual parameter sets were performed three times in total. Table 2. Sets with varied cutting data. cutting speed vc [m/min]

feed f [mm] 0.01

0.02

0.05

25

1

2

3

50

4

5

6

75

7

8

9

100

10

11

12

125

13

14

15

Curves of the components of the machining force were captured by means of a 3-component piezoelectric dynamometer. As a result, cutting force mean values were determined depending on the varied cutting parameters. Fig. 2

Fig. 3. Part-specific mesh and mesh refining.

The inverse parameter identification described below is based on an approach referring to design of experiment (DoE) methods using the Latin Hypercube. The parameter variation takes into account all five Johnson-Cook parameters (A, B, C, m and n).

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Rocco Eisseler et al. / Procedia CIRP 77 (2018) 26–29 Eisseler, R. et al./ Procedia CIRP 00 (2018) 000–000

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4.2. Simulation experiments For an initial parameter field literature values according to Molinari et al. have been adopted, see Table 3. To set an adequate parameter field an upper as well as a lower value limit was set, each with a difference of 30% to the basic values. The required tool to prepare the DoE is already implemented within the DEFORM 3D™ platform. Table 3. Initial parameter field.

Thereby the calculated cutting force could be approximated in a further way to the measured value. Completing the third iteration’s data points 1 and 2 show the closest approximation to the measured cutting force value. The resulting Johnson-Cook parameter sets as well as the remaining deviation between the individual parameters of each set are listed in Table 4. Table 4. Resulting Johnson-Cook parameters for vc = 100 m/min and f = 0.05 mm after three inverse parameter identification iterations

A [MPa]

B [MPa]

Basic value

612

436

0.008

1.46

0.15

Upper limit

800

900

0.0104

1.898

0.195

Johnson-Cook parameter A [MPa]

Lower limit

500

400

0.0056

0.195

0.105

B [MPa]

483.5

483.7

0.0%

C

0.00908

0.00925

1.9%

C

m

n

4.3. Results of the inverse parameter identification The following are the simulation results of inverse parameter identifications performed with two exemplary cutting parameters either cutting speed vc = 100 m/min and feed f = 0.05. Fig. 4 shows the calculated cutting force values (circular data points) for 50 parameter sets consisting of varied A, B, C, m and n prepared by means of the Latin Hypercube. The simulated cutting force resulting from the basic values is depicted as a solid at Fc = 241 N line. It can be seen that only two parameter sets (data points 20 and 43) lead to results approximating close to the measured value (dashed line) at Fc = 295 N.

Parameter set 1 2 791.1 792.0

Difference 1→2 0.1%

m

1.5598

1.5173

-2.7%

n

0.1797

0.1756

-2.2%

5. Conclusions Parameters for Johnson-Cook material models are available for a large number of steels in their initial state. In the field of heat-treated steels this only applies in a limited extend. By means of inverse parameter identifications Johnson-Cook parameters were determined for steel SAE 4142 with a hardness of 42 HRC. The identification was occurred with all five Johnson-Cook material model parameters. Cutting forces determined by means of cutting tests served as evaluation criterion which had to be approximated by the simulation results. The parameter sets intended to be varied were determined with the help of the Latin Hypercube sampling. During iterative done simulation procedures suitable parameter sets could be identified for individual predefined cutting parameters. References

Fig. 4. Part-specific mesh and mesh refining.

Due to these two points, two more iterations were performed with tighter limits based on the minimum and maximum values of the individual Johnson-Cook parameters determined in the first simulation. With an increasing accuracy the second (square data points) and third (triangular data points) iteration was each done with a reduced number of datasets to reduce required calculation time.

[1] Kushner, V. and Storchak, M. 2017. Modelling the material resistance to cutting. Interna-tional Journal of Mechanical Sciences 126, 44–54. [2] Molinari, A., Cheriguene, R., and Miguelez, H. 2012. Contact variables and thermal ef-fects at the tool-Chip interface in orthogonal cutting. International Journal of Solids and Structures 49, 26, 3774–3796. [3] Molinari, A., Moufki, A., and Dudzinski, D. 1997. Analysis of the Behaviour of 42CrMo4 Steel. Final Technical Report, Université de MetzCREAS Ascometal. [5] Bäker, M.: Finite element simulation of chip formation. Zugl.: Braunschweig, Techn. Univ., Habil.-Schr., 2004. Berichte aus der Materialwissenschaft. Shaker, Aachen. [6] Shrot, A. and Bäker, M.: Determination of Johnson-Cook parameters from machin-ing simulations. Computational Materials Science 52, 1,2012, 298–304. [7] Knodt, S.: Hartfräsen pulvermetallurgisch erzeugter ledeburitischer Werkzeugstähle. Berichte aus der Produktionstechnik Bd. 2004,22. Shaker, Aachen.