Experimentally validated calculation of the cutting edge temperature during dry milling of Ti6Al4V

Journal Pre-proof Experimentally validated calculation of the cutting edge temperature during dry milling of Ti6Al4V A.W. Nemetz, W. Daves, T. Klunsner, ¨ C. Praetzas, W. Liu, T. ¨ Teppernegg, C. Czettl, F. Haas, C. B¨olling, J. Schafer

PII:

S0924-0136(19)30517-5

DOI:

https://doi.org/10.1016/j.jmatprotec.2019.116544

Reference:

PROTEC 116544

To appear in:

Journal of Materials Processing Tech.

Received Date:

9 September 2019

Revised Date:

24 October 2019

Accepted Date:

3 December 2019

Please cite this article as: Nemetz AW, Daves W, Klunsner ¨ T, Praetzas C, Liu W, Teppernegg ¨ T, Czettl C, Haas F, B¨olling C, Schafer J, Experimentally validated calculation of the cutting edge temperature during dry milling of Ti6Al4V, Journal of Materials Processing Tech. (2019), doi: https://doi.org/10.1016/j.jmatprotec.2019.116544

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Experimentally validated calculation of the cutting edge temperature during dry milling of Ti6Al4V A.W. Nemetza*[email protected], W. Davesa,e, T. Klünsnera, C. Praetzasb, W. Liuc, T. Tepperneggd, C. Czettld, F. Haasc, C. Böllingb, J. Schäferd a

Materials Center Leoben Forschung GmbH, Roseggerstraße 12, 8700 Leoben, Austria Institute of Production Management, Technology and Machine Tools (PTW), 64287 Darmstadt,

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Germany c

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Institute of Production Engineering (IFT), Graz University of Technology,

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CERATIZIT Austria GmbH, 6600 Reutte, Austria

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Kopernikusgasse 24/1, 8010 Graz, Austria

*Corresponding author: (A.W. Nemetz)

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Institute of Mechanics, Montanuniversität Leoben, Franz-Josef-Straße 18, 8700 Leoben, Austria

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[email protected] (W. Daves), [email protected] (T. Klünsner), [email protected] (C.Praetzas), [email protected] (W. Liu),

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[email protected] (T. Teppernegg), [email protected] (C. Czettl), [email protected] (F. Haas), [email protected] (C. Bölling)

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[email protected] (J. Sc

Graphical abstract

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Highlights:

Experimentally validated calculation of cutting edge temperature

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Realistic prediction of tool heat-up during dry milling with a coated end mill

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Simulation of an unprecedented high number of milling cycles

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Validation via milling experiments with instrumented tool and workpiece

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Abstract

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In service, milling tools have to cope with severe levels of thermal and mechanical load. Especially temperature influences the damage behavior of a tool’s cutting edge by influencing

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material properties and thermally induced stresses. It is therefore of relevance to gain quantitative information on the thermal tool load situation. Information on temperatures in milling tools is not readily available today. Therefore, extensive experimental effort was necessary to determine temperatures in-situ during milling in the axial center of a rotating end mill and in a Ti6Al4V workpiece near the milled surface. The used end mill was a WC-Co hard metal tool protected by a TiAlN coating. Since the damage-relevant cutting edge temperature is not directly accessible by 2

experimental means, a simulation was employed. The transient temperature field in the tool was calculated by an iterative and synergetic use of two-dimensional finite element cutting models, three-dimensional finite element end mill models and two-dimensional workpiece models. The simulation allows for the description of the time-dependent temperature distribution from the chip formation site at the cutting edge to the axial tool center and into the workpiece, where thermocouples were placed in experiments. Validation of the calculated cutting edge

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temperatures was performed for 5000 individual consecutive cuts via comparison of results for

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tool core temperature in experiment and simulation. The model yields a very pronounced

concentration of the thermal load maximum of T>650°C near the cutting edges in a very small

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volume of only 1 ppm of the tool’s volume. In particular, the model’s spatial discretization is able

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to resolve the gradient of temperature in the hard coating towards the coating/substrate interface,

Keywords:

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showing temperature shielding effects of the hard coating.

Cutting edge temperature; Instrumented milling tool; Finite element model; Metal cutting;

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Heat transfer

1. Introduction

A milling tool’s cutting edges have to cope with severe loading conditions. Among other factors

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that affect their damage behavior, temperature is a very important one, as already investigated in Nemetz et al. (2018). Sufficiently high levels of temperature may cause a significant drop of the yield strength of the used tool materials, which can in turn lead to localized plastic deformation and crack formation, as evidenced experimentally in Teppernegg et al. (2014). To avoid premature tool failure, quantitative information on cutting edge temperature is therefore very relevant. The reliable determination of a milling tool’s cutting edge temperature is still a major 3

metrological challenge. The pronounced localization of the temperature maximum directly at the surface of the cutting edge (Nemetz et al. (2019)) makes it difficult to quantitatively determine this maximum experimentally. In recent work from Biermann et al. (2013), Kryzhanivskyy et al. (2018) and Li et al. (2018), attempts to determine cutting edge temperature were made for turning tools by placement of thermocouples as close as possible to the cutting edge. For interrupted cutting (Li et al. (2018)) and milling processes (Le Coz et al. (2012),

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Karaguzel and Budak (2018)), the usually complex tool movement makes their temperature

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instrumentation far more elaborate. In any case, thermocouples cannot be placed arbitrarily close to the cutting edge because the necessary holes may i) reduce the stability of the cutting edge, and

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ii) influence the transport of heat away from the thermal hotspot in the tool and therefore

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significantly alter the temperature field of interest. As an alternative, thermography may be used to measure temperatures at the rake face of the cutting tool, as documented in Soler et al. (2018).

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A disadvantage of this technique is the need for visual contact during the measurement process. Therefore, the determination of the temperature is possible only after the tool has been

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disengaged and not during the chip formation process. The use of transparent cutting tools (Garcia-Gonzalez et al. (2016)) is one viable option to overcome this drawback. However, this approach necessitates a change of the tool material and of the process itself.

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The practical problems of measuring the cutting edge temperatures make it necessary to resort to alternative approaches. Knowledge-based determinations of the heat flux and the temperature at the tool/workpiece interface were developed. A numerical approach to estimate the heat flux into the tool is used in Lazoglu and Altintas (2002). The applied finite difference method considers the frictional heat generated at the interface between tool and workpiece and the rise of temperature on the shear plane due to plastic deformation as the source of the occurring heat flow. More recently, Islam et al. (2016) presented an advanced application of the finite difference 4

method in which the generated heat is transmitted to the tool and the workpiece to calculate transient and steady state temperatures. The thermal model of Islam and Altintas (2019) additionally features the investigation of coated tools and varying tool and workpiece material properties. Carefully designed finite element (FE) cutting models can reproduce both relevant heat sources, namely the frictional heat and the heat due to plastic deformation, and are widely used in many different variants and grades of complexity. For example, the models differ in their

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handling of the extremely high deformation and strain rates in the chip. In addition to re-meshing

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models (Umbrello (2008), Kone et al. (2011)), mixed forms of Lagrange and Euler models, socalled Arbitrary Lagrangian-Eulerian (ALE) models exist (Miguélez et al. (2009)). However, the

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majority of the FE-models in the literature depict the turning process, e.g. see

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Ceretti et al. (2000). The complex milling process, in which the tool and the workpiece engage cyclically and the cutting kinematics are more complex, is only dealt with in a small number of

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publications, e.g. Nemetz et al. (2018), Nemetz et al. (2019). For a holistic view on the temperature evolution at the cutting edges of milling tools, it is also necessary to realistically

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depict the complete sequence of heating and subsequent cooling stages that occur in milling processes, with a recent first attempt described in Nemetz et al. (2019). The setup of the milling experiments studied in the current work is based on instrumented milling

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experiments that have been carried out to shed light on the influence of coolants and lubricants on the tool core temperature during milling (Praetzas et al. (2018a), Praetzas et al. (2018b)). Although the temperature is measured at the tool’s axial center, i.e. relatively far away from the cutting edge, the results of the experiments represent a valuable insight into the temperature evolution in the tool. It is desirable to determine the entire temperature field in the milling tool to correlate the temperatures of tool core and cutting edge. In particular, knowledge of the

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temperature profile at, and the gradient of temperature near the cutting edge is useful in optimizing both milling tool design and milling process parameters. Within the current work, a knowledge-based numerical methodology including experimentally parameterized material models is presented to quantify the evolving temperature field in a hard coated milling tool including the temperature hotspot at the cutting edge. The current modeling

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approach is holistic due to consideration of the cyclic heat-up of both tool and workpiece. The model’s results regarding temperature were validated by instrumented dry milling experiments.

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For this purpose, in-situ measurements of the tool core temperature and the workpiece

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temperature were performed during milling of a material segment of 250 mm in length corresponding to 1250 tool revolutions or 5000 individual cuts. The description of the

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temperature evolution in the entire tool for this large number of cuts is unprecedented in the literature and deemed very significant due to the unequaled grade of underlying experimental

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model parameterization and validation. The current paper intends to provide modelers, tool designers, milling technologist and materials scientists with a knowledge-base regarding the

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thermal load situation of milling tools to improve e.g. thermal management, cooling strategies and substrate/coating architectures for milling tools.

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2. Examined milling setup and numerical evaluation 2.1 Dry milling setup The milling experiments were conducted on a GROB G350 machining center, able to realize linear multipass shoulder milling in a climb milling process (Fig. 1). The applied cutting speeds 𝑣𝑐 were 45 m/min and 60 m/min, at a constant feed per tooth 𝑓𝑧 = 0.05 mm. The chosen width of cut 𝑎𝑒 was 3 mm, the depth of cut 𝑎𝑝 was 10 mm. The used tool was an end mill with four 6

cutting edges, made of WC-Co hard metal with 10 wt. % cobalt binder and an average WC grain size of 0.7 µm, with a 6 µm thick TiAlN-based hard coating on top. The tool geometry was characterized by a diameter of 10 mm, a cutting edge radius of 12 µm and a cutting edge helix angle of 45°. The workpiece material was Ti6Al4V in an annealed condition. The length of the machined workpiece segment was 250 mm, resulting in 5000 individual cuts and a removed material volume of approximately 7500 mm³. The milling process was dry, no cooling agent or

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lubricant were used. To perform in-situ measurement of the tool core temperature at two

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positions on the rotational axis of the end mill, a blind hole was introduced at the rotational axis of the tool, see Fig. 1a. Two thermocouples of type K with a diameter of 0.25 mm were placed in

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this blind hole and the remaining cavity was filled with conductive silver paste to ensure

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continuous thermal connection between the hard metal and the thermocouples, as it was also done in Praetzas et al. (2018a), Praetzas et al. (2018b). The first thermocouple (TTool1) was positioned

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at the bottom of the blind hole at a distance of 5 mm, and the second (TTool2) at a distance of 10 mm from the tool center point (TCP), see Fig. 1a. To obtain the whole picture of the heat

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production and heat transfer during the dry milling process, seven thermocouples (TWorkpiece) of type K with a diameter of 1 mm were applied in the workpiece, also ensuring continuous thermal connection. They were embedded in blind holes at a depth of 𝑎𝑝 ⁄2 = 5 mm. The minimum distance between the holes’ center and the axis of the end mill during the process was 5.8 mm. In

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the feed direction, the respective distances of the seven thermocouples (TWorkpiece) from the side surface of the titanium block were 4.6 mm, 9.6 mm, 19.6 mm, 39.6 mm, 79.6 mm, 159.6 mm and 239.6 mm. The thermocouple-equipped tools were used with a modified instrumented tool holder with integrated data processing electronics (Praetzas et al. (2018a), Praetzas et al. (2018b)). At a sampling rate of 1.6 kHz, the collected temperature data of the two thermocouples in the tool was transmitted immediately to a measuring computer by Wifi during the milling process. The 7

thermocouples positioned in the workpiece were connected to LKM Type 102 measuring transducers, which themselves were connected to a NI BNC 2090 device. From this device, data was collected in parallel to the process with a sample rate of 1 kHz via Matlab, running on a measuring computer. The measuring transducers have a linearity error of less than 1% full scale

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and an error at the reference junction of ±0.5°C.

Fig. 1: Schematic representation of the milling setup and thermocouple locations in a) end mill and b) workpiece.

2.2 Simulation strategy

A fully thermo-mechanical simulation of the heating of the milling tool and the workpiece during

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5000 cuts is practically impossible, even using the fastest available computers. Hence, the simulation of the milling process is split into three models. A two-dimensional (2D) thermomechanical cutting model (Module 1) simulates the cutting stage and calculates the occurring cutting edge temperature. A three-dimensional (3D) thermal model of the end mill (Module 2) determines the heating of the tool and a 2D thermal model of the workpiece (Module 3) estimates its heating during the dry milling process. The evolution of the temperature in the tool and at its 8

cutting edges can be calculated in a reasonable time by applying these three modules, mutually complementing. The modules are described below in detail. 2.3 Simulation of the cutting stage - Module 1 To model the cutting stage of the investigated climb milling process (Fig. 1), a 2D explicit FEALE-model was developed. It is based on the 2D cutting model presented in

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Nemetz et al. (2018), using a moving tool and ALE-constraints of the mesh of the workpiece. However, for reasons of mesh-stability and reduction of computational costs, the chip is not

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reproduced entirely. This strategy is also common in established cutting models, as e.g.

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Madhavan and Adibi-Sedeh (2005), dealing with constant uncut chip thickness,

Avevor et al. (2017), simulating the conventional milling process, and Kubin et al. (2019),

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modeling the climb milling process. The current model is referred to below as Module 1 and is

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divided into two submodels, referred to as Sub-Module 1* and Sub-Module 1**, see Fig. 2.

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Fig. 2: Illustration of Module 1, built from a) a database including the temperature field of the tool and the workpiece at an initial status, b) the start model Sub-Module 1* and c) the cutting model Sub-Module 1**. The magnifying glass indicates the enlarged detail area. d) Saving of cutting edge temperature and moving heat source as a function of time for the simulated cutting stage for later use as input for Module 2 and Module 3 described in the main text.

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Before running the cutting model, a pre-defined temperature field in the tool and the workpiece is needed to define the initial thermal status (Fig. 2a). Sub-Module 1* (Fig. 2b), a start model to simulate the initial sequence of the cut, where the chip root is forming, uses the initial thermal status. After this short time period, the current geometry and thermo-physical state of the workpiece as well as the tool are transferred to the main cutting model, called Sub-Module 1** (Fig. 2c). This thermo-mechanical model then simulates approximately 70 % of the entire cut. 10

The selected model type is suitable for simulating the high plastic deformation and strain rate within the workpiece which results in heat production and in the formation of a chip. Friction between the chip and the tool, an important physical phenomenon associated with the production of heat during the machining process, is considered within the model. The used friction coefficient is 0.5 and no artificial shear stress limit is used whose influence on temperature evolution is discussed in Arrazola and Özel (2010). In accordance to Iqbal et al. (2009), the heat

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transfer coefficient between the workpiece and the cutting edge is assumed to be 100 kW/m²K.

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The partition of the heat, caused by friction between tool and workpiece was modeled using the default parameter 0.5. As a result, this generated heat is equally divided between the two

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contacting surfaces. The 2D model consists of the Ti6Al4V workpiece and the coated end mill

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penetrating into it. The deformation behavior of the workpiece depends on temperature, strain and strain rate, and is described by a Johnson-Cook material law. The end mill consists of the

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hard metal substrate and the 6 µm thick TiAlN coating deposited on the tool surface, assuming elasto-plastic and purely elastic material behavior, respectively.

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The output of Module 1 is the time-dependent contact temperatures at the cutting edge during a single cut. At every node located at the 2D tool contour contacting the workpiece, a timedependent temperature value is recorded for the first 70 % of the cutting time. The temperature

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values during the missing 30 % of cutting time were extrapolated linearly, in analogy to Nemetz et al. (2019). The extrapolation is based on the averaged slope during the last six recorded temperature values. If the slope is positive, it is set to zero to avoid the development of artificial hotspots at the cutting edge. Otherwise the linear extrapolation is carried out using the identified slope. The temperature signals extracted in this way then quantify the heat input into the tool during one cut. The temperature at the milled surface of the workpiece is recorded at a distance of 100 µm behind the point of contact loss between the tool’s flank face and the 11

workpiece surface. This data is used to parameterize a moving heat source, which quantifies the heat input into the workpiece in a first approximation. Both, the cutting edge temperature and the moving heat source are stored in a database (Fig. 2d) for later use in Module 2 and Module 3 as described later on. The used FE-software package for all developed models within this work is Abaqus 6.14-2. In Module 1, elements of type CPE4RT were used for the explicit 2D ALE

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models. 2.4 Predicting temperature fields – Module 2 and Module 3

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In addition to the simulation of the cutting stage, done in Module 1 (Fig. 2), further models were

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built to facilitate the prediction of the temperature fields that evolve in the end mill and in the workpiece during a relatively large number of individual cuts. To reduce the associated

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computational cost, the deformations of tool and workpiece included in Module 1 were excluded in a 3D model of the end mill and a 2D model of the workpiece, referred to as Module 2 and

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Module 3, respectively. These two modules shall hence also be referred to as thermal models,

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since they exclusively reproduce the propagation of heat without considering deformations. The suggested method to attain information on the evolving temperature field in the end mill during the dry milling process, the cutting edge temperatures, calculated in Module 1, are used as thermal load for the cutting edges in a first thermal 3D model, referred to as Module 2*, see Fig.

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3a-c. The transient contact temperatures corresponding to one chip formation process provided by

Module 1 for the milling parameters 𝑎𝑒 , 𝑎𝑝 , 𝑓𝑧 and 𝑣𝑐 is retrieved from the database (Fig. 3a) and is applied as a time-dependent Dirichlet temperature boundary at each of the four cutting edges of the end mill, see Fig. 3b. In the physical milling process, the initiation and end of contact between the cutting edge and the workpiece depend on the orientation of a respective cutting edge towards the workpiece and the axial position on the helix-shaped cutting edge. Therefore, the time12

dependent Dirichlet temperature boundary provided by Module 1 is applied to Module 2 in a sequential manner depending on the two mentioned factors. In this way, the evolving temperature field is calculated in a first approximation for a certain number of tool revolutions. The output of Module 2* saved in the database represents the transient 3D temperature field inside the tool

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(Fig. 3c). Note, that Module 2* only uses input from one prior Module 1 simulation (Fig. 3a).

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Fig. 3: a) The cutting edge temperature is recorded during the run of Module 1 and saved in a database. The cutting edge temperature is applied cyclically on a b) thermal 3D model to predict the transient temperature field in a first approximation. c) The calculated temperature field in the tool is stored in a database. The combination of a), b) and c) represents Module 2*. d) The cutting edge temperatures are recorded during the run of two Module 1 models

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representing consecutive states of the tool heat-up process. d) Contact temperatures interpolated between the two consecutive thermal states are applied cyclically on a e) thermal 3D model to predict the transient temperature field in a second approximation. f) The calculated transient temperature field is stored in a database and represents the outcome of the model. The combination of d), e) and f) represents Module 2**.

The end mill’s part containing the helix-shaped cutting edge is coated with a 6 µm thick TiAlN layer, see Fig. 3b. Radiation and convection are included in the model. The applied emissivity

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and heat transfer coefficient were adjusted to respective values of ε = 0.75 and ℎ = 75 W/m²K based on a comparison of the cooling of the heated-up Module 2 with an end mill heated during a dry milling experiment, see Fig. 9b,c in section 4.1. The tool holder is modeled as a heat sink, forcing all nodes of Module 2 sitting on the vertical red line indicated in Fig. 3b and Fig. 3e to have a constant temperature of 20°C. In Module 2, elements of type DC3D8 were used.

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To quantify the evolving temperature field in the workpiece during a certain number of tool revolutions, a 2D model of the machined Ti6Al4V block (Fig. 4) was built. A moving one-

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dimensional heat source (Fig. 4a), parameterized by output of Module 1 as described above (Fig.

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2d), simulates the heating-up of the Ti6Al4V block due to the passing of the milling tool. The

moving heat source sequentially restricts one node after the other on the newly created milled

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surface by a Dirichlet temperature boundary during the corresponding cut. Using this approach, named Module 3 (Fig. 4), the developing temperature field in the Ti6Al4V block during several

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cuts is calculated in a first approximation. Additionally, the temperature field present within the workpiece is stored in a database (Fig. 4c). At the free surfaces, the emissivity and convection

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parameters, which have already been used in Module 2, are applied for thermal interaction with

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the environment. In Module 3, elements of type DC2D4 were used for the thermal 2D models.

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Fig. 4: a) The moving heat source is parameterized during a single run of Module 1. The b) moving heat source is applied cyclically on a b) thermal 2D model of the titanium workpiece to approximately predict the evolution of the

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temperature field during dry milling. c) The temperature field in the workpiece is stored in a database. The

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combination of a), b) and c) represents Module 3.

2.5 Iterative modeling strategy for cyclic thermal loading

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Module 2* (Fig. 3b) uses the contact temperatures obtained by only one run of Module 1 (Fig. 2d and Fig. 3a) to predict the evolving temperature field inside the end mill in a first

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approximation (Fig. 3c). To capture the cyclic heat-up of the end mill during the dry milling process in a more realistic way, an iterative modeling strategy has been developed based on a strategy documented in Nemetz et al. (2019). The present scheme of interaction of the individual modules (Fig. 2a-d, Fig. 3a-c, Fig. 3d-f and Fig. 4a-c), communicating in a synergetic way, is

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outlined below and is graphically depicted in Fig. 5:

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Fig. 5: Iterative modeling strategy of the cyclic heat-up of an end mill during a dry milling process. Interaction of a) Module 1, b) Module 2*, c) Module 3 and d) computation of Module 1 at a later stage in the tool heat-up process and

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e) Module 2**. The modules are connected by the in- and output cutting edge temperature, moving heat source and temperature field.

1. Fig. 5a – Module 1: At the beginning of the milling process, the tool and the workpiece

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have room temperature and therefore the initially applied temperatures of the tool and the workpiece (Fig. 2a) are both 20°C. The first cut of the milling process is simulated using Module 1 (Fig. 2b,c) and the calculated contact temperatures at the cutting edge are saved in a database (Fig. 2d) for later use. Also, the time-dependent temperature values at the milled surface of the workpiece, later used to define a moving heat source, are saved (Fig. 2d).

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2. Fig. 5b – Module 2*: The saved contact temperatures provided after the initial run of Module 1 are now loaded from the database (Fig. 2d and Fig. 3a). These contact temperatures are used as input in Module 2* (Fig. 3b) to calculate a first approximation of the temperature field in the end mill at a later stage of the milling process, i.e. after several tool revolutions. The temperature field after the last considered tool revolution is stored in a database (Fig. 3c) for later use.

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3. Fig. 5c – Module 3: The previous provided moving heat source, parameterized by the first

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calculation of Module 1, is now loaded from the database (Fig. 2d and Fig. 4a). This heat source is used in Module 3 (Fig. 4b) to cyclically calculate the temperature field in the

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machined workpiece at a later stage of the milling process, i.e. after several tool

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revolutions, in a first approximation. The temperature field for the last considered individual cut is stored in a database (Fig. 4c) for later use.

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4. Fig. 5d – Module 1: Within the next step in the simulation strategy, the previous saved temperature fields of the end mill (Fig. 2a and Fig. 3c) and the workpiece (Fig. 2a and Fig.

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4c) at a later stage of the milling process, i.e. after several tool revolutions, are loaded.

These initial temperature fields are used in Sub-Module 1* (Fig. 2b,c) and the simulation of a single cut is repeated with heated-up arrangement associated with the actualized stage of the milling process. This second Module 1 simulation brings out updated contact

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temperatures at the engaging cutting edge, associated to the heated-up and actual stage of the milling process. These actual cutting edge temperatures are saved in a database (Fig. 2d). At this stage of the simulation, contact temperatures at the cutting edge are available at two stages of the milling process, the initial cut and a cut at a later stage of the milling process, i.e. after several tool revolutions. Using a linear interpolation, contact temperature input for the cuts between the two simulated cuts are calculated and saved in 18

the database. Now contact temperatures at the engaging cutting edge for every individual cut are available in the model database (Fig. 2d). 5. Fig. 5e – Module 2**: These evaluated contact temperatures are loaded from the model database (Fig. 2d and Fig. 3d) and are used as input in the execution of Module 2** (Fig. 3e) simulation to calculate the more accurate and iterative approximated time-dependent

temperature field inside the end mill during a certain period of the milling process. The

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obtained transient temperature field represents the outcome of the model for the

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considered time interval of the milling process. It is saved in the database for later

validation by comparison with the experimentally determined tool core temperature (Fig.

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This iterative procedure is repeated in order to simulate the whole milling process, see Fig. 6a. It should be made sure that the chosen interval (Fig. 6b) of tool revolutions between the performed

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Module 1 simulations of cutting stages is not excessively long. Otherwise, the calculated and the

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real temperature field diverges because of the increasing underestimation of contact temperatures.

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Fig. 6: a) Schematic representation of the iterative and modular simulation strategy of the cyclic heat-up of an end

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mill during a dry milling process. b) Calculated core temperature of the end mill and maximum temperature in the workpiece at a distance of 0.8 mm from the straight section of the milled surface.

The used intervals of milling time, which in sum represent the whole milling process, are short

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close to the beginning of the milling process but increase in length progressively towards its end. This is motivated by the fact that the error committed when computing temperatures without updating the thermal boundary conditions scales with the occurring temperature gradients. When thermal gradients are steep at the beginning of the milling process, hence the tool still heats up at a rapid rate, a shorter time interval between executions of Modules 1 is necessary. With increasing milling time, the tool core temperature shows a tendency to converge towards a 20

stationary value, i.e. smaller thermal gradients, see Fig. 6b. Therefore, the interval length between the executions of Modules 1 can be increased in order to save calculation time. Specifically, the total of 1250 tool revolutions, or 5000 individual cuts needed to mill the 250 mm long distance within the workpiece, were approximated using seven executions of Module 1, at the 1st, 5th, 17th, 65th, 257th, 751th and 1251th rotation of the end mill, see Fig. 6. This pattern is in principle arbitrary, but fulfills the required bias in the relative distance between the performed Module 1

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simulations.

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Note that the neglect of the effect of the tool heat-up on the contact temperature, as it is done in

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Module 2*, leads to an underestimation of the tool core temperature and the whole temperature field in the milling tool, see Fig. 6b. Therefore, the suggested iterative simulation strategy is

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beneficial when trying to predict a realistic evolution of the temperature field within the tool during dry milling. Also, the influence of the heated-up workpiece on the contact temperature is

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3. Material data

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taken into account, at least in a first approximation.

3.1 Workpiece material – Ti6Al4V

The Johnson-Cook material law describes the flow stress 𝜎𝑒𝑞 of the Ti6Al4V workpiece material,

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used in Module 1. It is represented by

𝜎𝑒𝑞

= [𝐴 + 𝐵𝜀 𝑛 ] [1 + 𝐶 ln

𝜀̇ 𝑇 − 𝑇0 𝑚 ] [1 − ( ) ]. 𝜀0̇ 𝑇𝑚𝑒𝑙𝑡 − 𝑇0

(1)

This material model is suitable for simulating large deformations occurring in the milling process, since hardening, strain rate dependency and thermal softening effects are included. The 21

values of the material parameters used in the Johnson-Cook constitutive law (1) were adopted from Lee and Lin (1998) and information about their physical interpretation are documented in Table 1. Table 1: Material properties of Ti6Al4V used in Johnson-Cook (J-C) material constitutive equation adopted from Lee and Lin (1998).

Physical unit Physical meaning

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J-C parameters Value 782.7

[MPa]

Yield stress

𝐵

498.4

[MPa]

Hardening modulus

𝐶

0.028

𝑚

1

𝑛

0.28

𝜀0̇

0.00001 [s-1]

-p

Thermal softening coefficient

re

Hardening coefficient Reference plastic strain rate

1605

[°C]

Melting temperature

25

[°C]

Room temperature

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𝑇0

Strain rate coefficient

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𝑇𝑚𝑒𝑙𝑡

ro

𝐴

The density 𝜌 = 4 430 kg/m³, the Poisson´s ratio 𝜈 = 0.342, the Young´s modulus 𝐸 = 113.8 GPa and the thermal expansion coefficient 𝛼𝑡ℎ = 0.000086 1/°C were assumed to be temperature-

Jo

independent. In addition to the mentioned material properties, needed in Module 1, the thermal properties, namely thermal conductivity 𝜆 = 7.3 W/mK and specific heat 𝑐𝑝 = 580 J/kgK also used in Module 3, were both assumed to be constant within the regarded temperature range. An inelastic heat fraction of 0.9, quantifying the heat production caused by plastic deformation, is used. The mentioned material data was adopted from the established FE-Models Ducobu et al. (2014) and Ducobu et al. (2017) from titanium cutting. 22

3.2 Substrate material – WC-Co hard metal The mechanical and thermo-physical material properties of the hard metal substrate with 10 wt. % Co-binder and an average WC grain size of 0.7 µm used in the FE-material-models were found experimentally as a function of temperature. The stress-strain curves and the yield strength 𝑅𝑝 (𝑇) were recorded in a servo-hydraulic testing machine (Instrone 8803). The thermal diffusivity 𝑎(𝑇) determined by a laser flash method was converted to thermal conductivity 𝜆(𝑇)

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using the specific heat capacity 𝑐𝑝 (𝑇), see (2), also determined by means of the laser flash

ro

method. The Young´s modulus 𝐸(𝑇) and the Poisson´s ratio 𝜈(𝑇) were determined in a vacuum furnace by a resonant beam technique. The thermal expansion coefficient 𝛼𝑡ℎ (𝑇) was measured

-p

with a dilatometer. All mentioned material data is documented in graphical form in Fig. 7. The

re

density 𝜌 = 14 330 kg/m³ of the hard metal substrate is assumed to be constant within the

(2)

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ur na

𝜆(𝑇) = 𝑐𝑝 (𝑇) ∙ 𝑎(𝑇) ∙ 𝜌

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temperature range of the simulation of the milling process.

23

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Fig. 7: Experimentally determined a) stress-strain curves, b) specific heat capacity and thermal conductivity and c)

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Young´s modulus and Poisson´s ratio for the investigated WC-Co hard metal as a function of temperature. d) Thermal expansion coefficient, experimentally determined for the investigated WC-Co hard metal and adopted from

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literature for TiAlN coating (Krajinović et al. (2016), Chang and Wu (2013)) as a function of temperature.

Since Module 1 (Fig. 2b,c) is a thermo-mechanical model, all mentioned material properties are used there. In contrast, only the thermo-physical material properties are used in the pure thermal

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models of Module 2 (Fig. 3b,e). 3.3 Coating system – TiAlN

An elastic material behavior was assumed for the TiAlN coating. Its material parameters are modeled temperature-dependent or independent, depending on availability in the literature. Temperature-dependent modeled parameters are: thermal expansion coefficient 𝛼𝑡ℎ (𝑇) and specific heat capacity 𝑐𝑝 (𝑇), see Fig. 7d and Fig. 7b, respectively. The following properties were 24

modeled as temperature-independent parameters: thermal conductivity 𝜆 = 5.6 W/mK, density 𝜌 = 5 400 kg/m³, Young´s modulus 𝐸 = 557 GPa and Poisson´s ratio 𝜈 = 0.25. All values were adopted from Krajinović et al. (2016) with exception of the Poisson’s ration which was taken from Chang and Wu (2013). As in the case of the substrate material, all mentioned material properties are used in Module 1 (Fig. 2b,c), but only the thermo-physical material properties are

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used in Module 2 (Fig. 3b,e).

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4. Experimental model validation and discussion

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4.1 Validation - Tool core temperature

To provide means of validation for the presented iterative modeling strategy, in-situ

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measurements of tool core temperature were performed in instrumented dry milling experiments

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with process parameters identical to the ones investigated in the simulations, compare section 2.1. When milling a straight segment, the chips’ length usually rises from short to long to reach a constant value at a certain point in time, depending on the milling parameters and the tool

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geometry. To avoid excessive model complexity, this initial phase of non-constant chip length is neglected in the current modeling approach. It simplifies the initial tool/workpiece engagement situation by considering only a constant chip length throughout all considered cuts. To this end,

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material was removed at the position of first contact between the end mill and the workpiece before the milling experiment and the associated simulation started, see Fig. 8.

25

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Fig. 8: a) Instrumented milling arrangement with b) detail of workpiece geometry prior to start of validation

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experiment. The workpiece geometry exhibits initially removed material to ensure the same initial conditions, i.e. constant chip length in the milling experiment and the simulation. c) Schematic illustration of the chips of non-

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constant length removed prior to the investigated milling experiment.

re

Since an experimental validation of the cutting edge temperature directly at the cutting edge is not feasible for reasons mentioned in the discussion section, an alternative validation strategy is

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followed: If the time-dependent evolutions of the tool core temperatures determined experimentally and via simulation are similar, it can be concluded that this is caused by a similar

Jo

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input of thermal energy in form of heat flux at the cutting edges, see Fig. 9a.

26

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Fig. 9: a) Schematic of the experimental validation strategy for the applied simulation model using results of tool

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core temperature determined at two axial positions (TTool1 and TTool2) by instrumented milling experiments and

re

simulation for b) 𝒗𝒄 = 45 m/min and c) 𝒗𝒄 = 60 m/min.

The validation was performed using two experimental dry milling setups with two different

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cutting speeds. However, to enhance the model’s predictive power, more experiments with different milling process parameters would be beneficial to investigate the influence of e.g. the

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friction model, the material law parameters used for the Ti6Al4V, the cutting edge wear state, etc. on the temperature results.

The tool core temperatures, measured at two positions in dry milling experiments (Fig. 1a) with

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cutting speeds 𝒗𝒄 = 45 m/min and 𝒗𝒄 = 60 m/min, show a rapid increase at the start of the milling process, see Fig. 9b,c. The tool core heat-up rate decreases with increasing milling time, see Fig. 9b,c. Hence, a nearly stationary core temperature is reached after 250 mm of cutting at the end of

one linear milling pass. The milling pass includes 1250 revolutions of the end mill with four cutting edges, corresponding to individual 5000 cuts.

27

In the case of cutting speed 𝒗𝒄 = 45 m/min, the difference between the tool core temperatures at the end of the process determined experimentally and via simulation is 30.5°C (7.0%) at measuring position TTool1 and 51.2°C (12.7%) at measuring position TTool2. The calculated tool core temperature evolution correlates well with the experimentally observed temperature evolution, see Fig. 9b. The maximum deviation of the tool core temperature is 55.4°C (17.7%) at measuring position TTool1 after 10 s of milling and 68.3°C (19.5%) at measuring position TTool2

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after 20 s of milling. In the case of cutting speed 𝒗𝒄 = 60 m/min, the deviation is more

ro

pronounced, see Fig. 9c and Table 2. The 20°C temperature constraint, depicted in Fig. 3b,e ensures that the role of the tool holder as a heat sink is considered, at least in a good

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approximation. Omitting the artificial temperature constraint or its displacement farther away

re

from the TCP (Fig. 1a) would lead to an overestimation of the slope of the tool core temperature

Jo

ur na

lP

at the end of the milling pass and thus to a delay in reaching a stationary core temperature.

28

Table 2: Tool core temperature data for experimental validation of the milling simulation model with cutting speeds 𝒗𝒄 = 45 m/min and 𝒗𝒄 = 60 m/min. Tabular overview of the differences between the measured and the calculated tool core temperatures ΔTTool1 and ΔTTool2.

𝑣𝑐 = 45 m/min

𝑣𝑐 = 60 m/min

Milling time ΔTTool1

ΔTTool2

ΔTTool1

ΔTTool2

[s]

[°C] [%]

[°C] [%]

[°C] [%]

[°C] [%]

Start

4.9

5

46.8 20.4 50.5 26.5 64.6 24.3 66.5 30.1

10

55.4 17.7 64.9 23.6 68.9 19.3 77.6 25.0

15

54.3 15.1 66.6 20.8 70.1 17.2 81.7 22.6

20

54.8 14.1 68.3 19.5 68.2 15.6 82.8 21.0

25

52.7 13.0 67.6 18.4 63.7 14.0 80.6 19.4

30

46.9 11.3 63.7 16.8 60.0 12.8 79.1 18.4

35

40.8 9.7

59.0 15.3 57.5 12.0 77.5 17.6

40

39.4 9.2

58.2 14.8 -

-

-

-

25.7 6.9

25.7

of

19.8 6.9

ur na

lP

re

-p

ro

19.6 4.9

35.5 8.2

55.1 13.9 -

-

-

-

50

31.0 7.1

51.4 12.9 -

-

-

-

End

30.5 7.0

51.2 12.7 53.7 11.0 75.0 16.8

Jo

45

4.2 Temperature field in the workpiece The temperature development in the workpiece influences the cutting edge temperature and thus the heat flow into the tool. This effect is considered qualitatively by the application of Module 3 (Fig. 4a-c) in the present iterative simulation strategy. Fig. 10a outlines the measurement setup including the special arrangement of the thermocouples in the workpiece. The measured 29

evolutions of temperature during one milling pass in the experiment and the outcome of Module 3 are compared in Fig. 10b. The temperature was measured and calculated at a minimum distance of 0.8 mm from the engaging cutting edge, since the distance of the centers of the seven applied thermocouples (Fig. 1b) from the straight part of the milled surface is 0.8 mm. Due to reasons analogue the ones that lead to the introduction of Module 2**, Module 3 (Fig. 4a-c) underestimates the measured temperature in the workpiece but fits the qualitative development,

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as can be concluded from Fig. 10b. The discontinuous update of the thermal input for Module 3

ro

at the 1st, 5th, 17th, 65th, 257th and 751th revolution leads to discontinuities of the simulated

workpiece temperature, see Fig. 6b and Fig. 10b. Thus, Module 3 potentially needs an extension

-p

in analogy to Module 2** to increase the prediction accuracy of the model. In any case, it does

Jo

ur na

lP

neglecting the heating of the workpiece.

re

offer an advantageous extension of the approach presented in Nemetz et al. (2019), which is

Fig. 10: a) Schematic representation of the spatial arrangement of the seven thermocouples applied in the workpiece. b) Measured temperature inside the Ti6Al4V workpiece during dry milling with cutting speed 𝒗𝒄 =45 m/min and comparison with calculated maximum temperatures in a distance of 0.8 mm from the surface for the thermocouple positions 1 to 7.

30

4.3 Temperature at the cutting edge Primarily, the experimentally validated numerical prediction of the tool core temperature enables to determine the heat transfer into the milling tool during the dry milling process. Furthermore, the time-dependent contact temperatures along the cutting edge are calculated, and Module 1 (Fig. 2) provides the local temperature profile at the cutting edge. On the one hand, the elevated

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temperature at the cutting edge influences the mechanical properties of the hard metal substrate, investigated in Teppernegg at al. (2016). On the other hand and in accordance to

ro

Nemetz et al. (2018), Teppernegg at al. (2014), Teppernegg at al. (2015), the cutting edge’s time-

-p

dependent and cyclic thermal history is of high relevance for the understanding of tool damage and the associated acting damage mechanisms. By currently available means it is not possible to

re

measure the temperature in-situ at the cutting edge. The described modeling approach including experimentally measured tool core temperatures for validation purposes, represents a valuable

lP

contribution to understand thermally driven tool failure mechanisms. Hence, the model provides an interpretation of the measured tool core temperature signals inside instrumented milling tools

ur na

in terms of cutting edge temperature.

In the following, the results of the simulated dry milling process (Fig. 1) with cutting speed 𝑣𝑐 = 45 m/min are presented and discussed. The temperature profile along a path A-B on the

Jo

outer surface of the cutting edge, marked with yellow arrows in Fig. 11a, during the initial cut shows an absolute temperature maximum of 551°C (see yellow line in Fig. 11b).The maximum is located at the tool tip and an additional local temperature maximum is located at the rake face. Between these two maxima, a local minimum of the temperature is present, in accordance to Krajinović et al. (2016), Nemetz et al. (2018), see Fig. 11b. This minimum is most probably caused by the flow behavior of the machined Ti6Al4V. During the cutting process, the workpiece 31

material flows in two directions: i) towards the rake face forming the chip, and ii) towards the flank face to form the new free surface. At a certain point in front of the tool tip, the strain rate is nearly zero and the speed of the material relative to the tool surface is zero, as depicted and marked by a black circle in Fig. 11c. At this area, no frictional heat is generated and the heat

ur na

lP

re

-p

ro

of

generated by plastic workpiece material deformation is strongly reduced.

Fig. 11: a) Temperature distribution in the tool and the chip at t = 5 ms in the first cut and representation of the paths

Jo

A-B on the outer contour of the tool (yellow arrows) and at the interface between the coating and the substrate (pink arrows). b) Temperature profiles along the two paths A-B as a function of milling time during the first cut; color code adopted from arrows in a). c) Distribution of the plastic strain rate in the chip at t = 5 ms in the first cut. d) Temperature distribution in the tool and the chip at t = 5 ms in the last cut of the investigated milling process. e) Temperature profiles along the two paths A-B as a function of milling time during the last cut of the investigated milling process, color code adopted from arrows in a). f) Distribution of the plastic strain rate in the chip at t = 5 ms during the last cut of the investigated milling process. Legends in a) and c) are also valid for d) and f), respectively.

32

Along a second path A-B, marked with magenta arrows in Fig. 11a and defined 6 µm below the tool surface at the interface between hard coating (Fig. 11c) and hard metal substrate, the thermal loading of the substrate is investigated. As depicted in Fig. 11b, the temperature at the interface does not show the pronounced maximum at the tool tip, but a smoother shape. The maximum temperature of the substrate during the first cut is 383°C. This result confirms the desired effect, also reported in Krajinović et al. (2016), Nemetz et al. (2019), of the hard coating as a thermal

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shield for the substrate.

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The temperature field, the temperature profiles along the two paths A-B (Fig. 11a) and the

-p

distribution of the plastic strain rate in the Ti6Al4V workpiece during the last cut are shown in Fig. 11d-f. The characteristic shapes of the temperature distributions (Fig. 11e) remain the same

re

during the milling process. The general temperature levels rise and the temperature differences between coating surface and coating/substrate interface diminishes throughout the course of the

lP

milling process, compare Fig. 11b and Fig. 11e. At the tool tip, a maximum temperature at the outer surface of the TiAlN coating of 788°C is reached and the maximum temperature of the

ur na

substrate is 652°C, also located at the tool tip (Fig. 11e). This outcome is valuable to assess the suitability of the applied coating depending on its thermal stability and oxidation resistance. Beside the calculation of the temperature profile along the cutting edge, a main benefit of the

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model is the possibility to represent the whole picture of the transient thermal field during the dry milling process, see Fig. 12a. Near the tool core, the temperature is constant over a broad range. Near the cutting edge a sharp increase of the temperature is found, Fig. 12b-d.

33

of ro -p

Fig. 12: a) Temperature field after 750 revolutions for dry milling setup with cutting speed 𝒗𝒄 = 45 m/min and

re

investigated slice in the middle of the thermally loaded zone at 𝒂𝒑 ⁄𝟐 shown in detail after b) 250 revolutions, c) 750

lP

revolutions and d) 1250 revolutions. e) Temperature distribution within the entire volume of the end mill at the end of the dry milling process at a cutting speed 𝒗𝒄 = 45 m/min.

ur na

The evaluation of the temperature distribution in the entire end mill (Fig. 12a) after the last cut of the investigated dry milling process illustrates that the volume of the highly thermally loaded zone is very small relative to the total tool volume, see Fig. 12e. The maximum temperatures (T>650°C) are concentrated in an extremely small fraction of only one part per million of the tool

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volume (see Fig. 12e), located in the vicinity of the cutting edge, see Fig. 12d.

5. Conclusions

The current work captures the cyclic evolution of tool temperature in a dry milling process consisting of thousands of individual cuts using an iterative multi-modular 2D/3D simulation model. Cutting edge temperatures are simulated on a knowledge-base of experimentally 34

parameterized material models and are experimentally validated via temperature instrumentation in tool core and workpiece. The time-dependent spatial distribution of temperature at the cutting edge is provided and the pronounced concentration of the maximum temperature is quantified. The developed milling model represents a virtual test-rig for milling applications and offers new opportunities for: Material developers and material testers

of



ro

by determining quantity and quality of the occurring thermal loading of milling tools. Materials testing techniques can be designed to mimic load situations relevant for milling

-p

tools based on the outcome of the current type of simulation. The observed material response can help to make material design processes knowledge-based. Hard coating developers

re



lP

by providing insight in the actually present load spectrum hard coatings have to cope with. Especially the effectiveness of coatings as a thermal barrier to thermally protect the



ur na

substrate can be investigated virtually. Tool technologists

to understand the effect of milling strategies and tool path variants within the workpiece on the associated thermal load peaks relevant to tool damage. Tool condition monitoring

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

by providing means to interpret measured tool core temperature signals far from the cutting edge and relate them to the cutting edge temperature relevant for tool damage.

In the future, the mechanical load of the end mill during dry milling may also be included in the model. The thermo-mechanical 2D models of the cut provide not only cutting edge temperatures,

35

but also contact pressures, which can be applied to calculate stresses and strains using a mechanical variant of the applied 3D thermal model of the end mill.

Acknowledgement The authors gratefully acknowledge the financial support under the scope of the COMET program within the K2 Center “Integrated Computational Material, Process and Product

of

Engineering (IC-MPPE)” (Project No 859480). This program is supported by the Austrian

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Federal Ministries for Transport, Innovation and Technology (BMVIT) and for Digital and

the federal states of Styria, Upper Austria and Tyrol.

-p

Economic Affairs (BMDW), represented by the Austrian research funding association (FFG), and

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This project (CHIP – COMPETENCE via HIGH INTELLIGENT PRODUCTION with a unique sensor integration for milling tools, 853474) is funded by the Austrian Federal Ministries for

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Transport, Innovation and Technology (BMVIT) and carried out under the program Production of

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the Future.

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Teppernegg, T., Klünsner, T., Kremsner, C., Tritremmel, C., Czettl, C., Puchegger, S., Marsoner, S., Pippan, R., Ebner, R., 2016. High temperature mechanical properties of WC-Co hard metals. Int. Journal of Refractory Metals and Hard Materials 56, 139-144. https://doi.org/10.1016/j.ijrmhm.2016.01.002. Umbrello, D., 2008. Finite Element simulation of conventional and high speed machining of

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re

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ro

https://doi.org/10.1016/j.jmatprotec.2007.05.007.

41

List of figure captions Fig. 1: Schematic representation of the milling setup and thermocouple locations in a) end mill and b) workpiece. Fig. 2: Illustration of Module 1, built from a) a database including the temperature field of the tool and the workpiece at an initial status, b) the start model Sub-Module 1* and c) the cutting model Sub-Module 1**. The magnifying glass indicates the enlarged detail area. d) Saving of cutting edge temperature and moving heat source as a function of time for the simulated cutting stage for later use as input for Module 2 and Module 3 described in the main text.

re

-p

ro

of

Fig. 3: a) The cutting edge temperature is recorded during the run of Module 1 and saved in a database. The cutting edge temperature is applied cyclically on a b) thermal 3D model to predict the transient temperature field in a first approximation. c) The calculated temperature field in the tool is stored in a database. The combination of a), b) and c) represents Module 2*. d) The cutting edge temperatures are recorded during the run of two Module 1 models representing consecutive states of the tool heat-up process. d) Contact temperatures interpolated between the two consecutive thermal states are applied cyclically on a e) thermal 3D model to predict the transient temperature field in a second approximation. f) The calculated transient temperature field is stored in a database and represents the outcome of the model. The combination of d), e) and f) represents Module 2**.

ur na

lP

Fig. 4: a) The moving heat source is parameterized during a single run of Module 1. The b) moving heat source is applied cyclically on a b) thermal 2D model of the titanium workpiece to approximately predict the evolution of the temperature field during dry milling. c) The temperature field in the workpiece is stored in a database. The combination of a), b) and c) represents Module 3. Fig. 5: Iterative modeling strategy of the cyclic heat-up of an end mill during a dry milling process. Interaction of a) Module 1, b) Module 2*, c) Module 3 and d) computation of Module 1 at a later stage in the tool heat-up process and e) Module 2**. The modules are connected by the in- and output cutting edge temperature, moving heat source and temperature field.

Jo

Fig. 6: a) Schematic representation of the iterative and modular simulation strategy of the cyclic heat-up of an end mill during a dry milling process. b) Calculated core temperature of the end mill and maximum temperature in the workpiece at a distance of 0.8 mm from the straight section of the milled surface. Fig. 7: Experimentally determined a) stress-strain curves, b) specific heat capacity and thermal conductivity and c) Young´s modulus and Poisson´s ratio for the investigated WC-Co hard metal as a function of temperature. d) Thermal expansion coefficient, experimentally determined for the investigated WC-Co hard metal and adopted from literature for TiAlN coating (Krajinović et al. (2016), Chang and Wu (2013)) as a function of temperature. 42

Fig. 8: a) Instrumented milling arrangement with b) detail of workpiece geometry prior to start of validation experiment. The workpiece geometry exhibits initially removed material to ensure the same initial conditions, i.e. constant chip length in the milling experiment and the simulation. c) Schematic illustration of the chips of non-constant length removed prior to the investigated milling experiment. Fig. 9: a) Schematic of the experimental validation strategy for the applied simulation model using results of tool core temperature determined at two axial positions (TTool1 and TTool2) by instrumented milling experiments and simulation for b) 𝒗𝒄 = 45 m/min and c) 𝒗𝒄 = 60 m/min.

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Fig. 10: a) Schematic representation of the spatial arrangement of the seven thermocouples applied in the workpiece. b) Measured temperature inside the Ti6Al4V workpiece during dry milling with cutting speed 𝒗𝒄 =45 m/min and comparison with calculated maximum temperatures in a distance of 0.8 mm from the surface for the thermocouple positions 1 to 7.

lP

re

-p

Fig. 11: a) Temperature distribution in the tool and the chip at t = 5 ms in the first cut and representation of the paths A-B on the outer contour of the tool (yellow arrows) and at the interface between the coating and the substrate (pink arrows). b) Temperature profiles along the two paths A-B as a function of milling time during the first cut; color code adopted from arrows in a). c) Distribution of the plastic strain rate in the chip at t = 5 ms in the first cut. d) Temperature distribution in the tool and the chip at t = 5 ms in the last cut of the investigated milling process. e) Temperature profiles along the two paths A-B as a function of milling time during the last cut of the investigated milling process, color code adopted from arrows in a). f) Distribution of the plastic strain rate in the chip at t = 5 ms during the last cut of the investigated milling process. Legends in a) and c) are also valid for d) and f), respectively.

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Fig. 12: a) Temperature field after 750 revolutions for dry milling setup with cutting speed 𝒗𝒄 = 45 m/min and investigated slice in the middle of the thermally loaded zone at 𝒂𝒑 ⁄𝟐 shown in detail after b) 250 revolutions, c) 750 revolutions and d) 1250 revolutions. e) Temperature distribution within the entire volume of the end mill at the end of the dry milling process at a cutting speed 𝒗𝒄 = 45 m/min.

43

List of table captions Table 1: Material properties of Ti6Al4V used in Johnson-Cook (J-C) material constitutive equation adopted from Lee and Lin (1998). Table 2: Tool core temperature data for experimental validation of the milling simulation model with cutting speeds 𝒗𝒄 = 45 m/min and 𝒗𝒄 = 60 m/min. Tabular overview of the differences between the measured and the calculated tool core temperatures ΔTTool1 and ΔTTool2.

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Table 3: Material properties of Ti6Al4V used in Johnson-Cook (J-C) material constitutive equation adopted from

J-C parameters Value

ro

Lee and Lin (1998).

Physical unit Physical meaning

𝐴

782.7

[MPa]

𝐵

498.4

[MPa]

𝐶

0.028

𝑚

1

𝑛

0.28

Hardening coefficient

𝜀0̇

0.00001 [s-1]

Reference plastic strain rate

-p

Hardening modulus

re

Strain rate coefficient

lP

Thermal softening coefficient

ur na

𝑇𝑚𝑒𝑙𝑡

Yield stress

[°C]

Melting temperature

25

[°C]

Room temperature

Jo

𝑇0

1605

44

Table 4: Tool core temperature data for experimental validation of the milling simulation model with cutting speeds 𝒗𝒄 = 45 m/min and 𝒗𝒄 = 60 m/min. Tabular overview of the differences between the measured and the calculated tool core temperatures ΔTTool1 and ΔTTool2.

𝑣𝑐 = 45 m/min

𝑣𝑐 = 60 m/min

Milling time ΔTTool1

ΔTTool2

ΔTTool1

ΔTTool2

[s]

[°C] [%]

[°C] [%]

[°C] [%]

[°C] [%]

Start

4.9

5

46.8 20.4 50.5 26.5 64.6 24.3 66.5 30.1

10

55.4 17.7 64.9 23.6 68.9 19.3 77.6 25.0

15

54.3 15.1 66.6 20.8 70.1 17.2 81.7 22.6

20

54.8 14.1 68.3 19.5 68.2 15.6 82.8 21.0

25

52.7 13.0 67.6 18.4 63.7 14.0 80.6 19.4

30

46.9 11.3 63.7 16.8 60.0 12.8 79.1 18.4

35

40.8 9.7

59.0 15.3 57.5 12.0 77.5 17.6

40

39.4 9.2

58.2 14.8 -

-

-

-

25.7 6.9

25.7

of

19.8 6.9

ur na

lP

re

-p

ro

19.6 4.9

35.5 8.2

55.1 13.9 -

-

-

-

50

31.0 7.1

51.4 12.9 -

-

-

-

End

30.5 7.0

51.2 12.7 53.7 11.0 75.0 16.8

Jo

45

45