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ScienceDirect Procedia CIRP 46 (2016) 119 – 122

7th HPC 2016 – CIRP Conference on High Performance Cutting

Experimental Investigation of Thermal Boundary Conditions during Metal Cutting T. Augspurgera, M. Brockmanna*, Y. Frekersb, F. Klockea, R. Kneerb a b

WZL RWTH Aachen, RWTH Aachen University, Steinbachstr. 19, 52074 Aachen, Germany WSA RWTH Aachen, RWTH Aachen University, Augustinerbach 6, 52056 Aachen, Germany

* Corresponding author. Tel.: +49-241-80-20255; fax: +49-241-80-22293. E-mail address: [email protected]

Abstract Thermal boundary conditions in metal cutting are of major significance for the credibility of thermal models. Relevant boundary conditions need to be defined at the characteristic regions of metal cutting: the shear zone, the contact zone of chip and tool, the clearance face and the work piece surface. In this contribution, the experimental investigation of the thermal boundary conditions at these characteristic regions is presented. The boundary conditions were investigated by detailed analysis of infrared thermal images. Different materials and cutting parameters were investigated. From the investigation heat source strengths and heat partition ratios were yielded. ©©2016 Authors. Published by Elsevier B.V This is an open access article under the CC BY-NC-ND license 2016The The Authors. Published by Elsevier B.V. (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the International Scientific Committee of 7th HPC 2016 in the person of the Conference Chair Prof. MatPeer-review under responsibility of the International Scientific Committee of 7th HPC 2016 in the person of the Conference Chair thias Putz. Prof. Matthias Putz Keywords: Cutting, Thermal Effects, Boundary Conditions

1. Temperatures and Heat in Metal Cutting Temperatures evolving during metal cutting are of major importance for the efficiency of the cutting process. Increased temperatures can result in excessive wear the tool, i.e. costs, or cause thermal deflection of the work piece geometry [1]. The understanding of temperature fields and the resulting heat flux distribution is therefore a key enabler for optimized design and operation of cutting processes [2]. Despite the importance of the knowledge of thermal issues in metal cutting, temperature measurements require high experimental effort and are prone to errors. Therefore, computational models of thermal issues in metal cutting are of major significance. While empirical models are by nature sensible concerning their numerical values, these type of models are mostly only valid for the regarded case. Models which are based on the fundamental physics, i.e. the partial differential equation of heat conduction, are transferable if a sound validation was conducted. The equation can be either solved by means of

analytical computational models or numerical, i.e. simulative approaches. For both types, the thermal boundary conditions, i.e. Neumann (i.e. prescribed gradient) or Dirichlet Condition (i.e. prescribed temperature value), at the characteristic regions of interest in metal cutting are of major importance. In particular the shear zone, friction zone and clearance face are regions of interest. 2. Experimental Investigation of Thermal Boundary Conditions For the experimental investigation of typical thermal boundary conditions in metal cutting, cutting experiments on a broaching machine were conducted. The tests were carried out with an HSS broaching tool featuring a rake angle γ = 10 °and a cutting edge radius rβ = 5 µm. As cutting parameters, a cutting depth ap = 40 µm and a cutting speed of vc = 4 m/min was chosen. The test setup is shown in Fig.1. The temperature field was measured with an infrared camera and

2212-8271 © 2016 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the International Scientific Committee of 7th HPC 2016 in the person of the Conference Chair Prof. Matthias Putz doi:10.1016/j.procir.2016.03.190

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T. Augspurger et al. / Procedia CIRP 46 (2016) 119 – 122

an additional two-color pyrometer focused on the rake face with a bore hole inside the work piece. The test material was Inconel 718, the cutting was conducted with dry conditions. Further details on the measurement method can be found in [3].

in the infrared image is considerably high. The orthogonal horizon plot shows the temperature curve through the contact zone at three different, arbitrarily chosen planes. For the two planes in chip direction, a clear maximum value can be identified. The slope of the curve on both sides of this local maximum is corresponding to the heat partition ratio in chip and tool. An analysis of the ratio reveals that around 10% of the heat flows into the chip (assuming a heat conductivity of λchip = 45 W/mK for the chip and λtool = 88 W/mK for the tool). Parallel Horizon

Orthogonal Horizon 650 650

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Fig. 1. Experimental Setup on Broaching Machine [3]

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A typical infrared image of the trials is shown in Fig. 2. On the upper left-hand side, a contour plot depicting the temperature distribution in chip, tool and work piece is shown with the isotherms marked in different colors. On the upper righthand side a mesh plot, i.e. the three-dimensional visualization of the temperature field can be found. As the thermal boundary conditions are defined by the gradient of the temperature along a space coordinate, the analysis of the mesh plot is a suitable tool for the analysis at the characteristic regions. Contour Plot

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Fig. 3. Parallel and Orthogonal Horizon Plot at the Rake Face [5]

The computation is only a rough value, however corresponds to conclusions from other authors for cutting with considerable cutting edge radius and decreased chip thickness [6]. In Fig. 4 the investigation of the shear zone is presented. The temperature slopes in the work piece, on the shear zone and in the chip show a similar behavior for all planes. For the shear zone, the temperature distribution is characterized more by a convex behavior. Parallel Horizon

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Fig. 2. Typical Infrared Image and Different Plot Types

For the analysis, the temperature slope was plotted against orthogonal and parallel planes of the mesh plot, as depicted in the lower part of the figure. The orthogonal horizon plot is thereby used for the investigation of the thermal boundary condition while the parallel horizon plot can be used for the temperature distribution at the appropriate characteristic region. For the rake face, i.e. the region were the chip is pushed out and heat due to friction is generated, the parallel and orthogonal horizon plot is shown in Fig. 3.The different curves belong to the appropriate planes shown in the figure, i.e. in the tool, on the contact zone and in the chip. All curves show a similar magnitude around 550 °C and a concave shape, which is not in line with theoretical assumed temperature distributions along the rake face [4]. However, the disturbance

Fig. 4. Parallel and Orthogonal Horizon Plot at the Shear Zone [5]

The temperature at the shear zone was found around 250 °C. Regarding the orthogonal horizon plot, a clear distinction of the shear zone is not possible. The temperature appears as a steady decreasing curve without any local maximum or minimum value. This fact shows that for the regarded broaching process, the shear zone should be interpreted rather as a bulk heat source than a thin ideal zone. 3. Numerical Investigation If the heat sources in a cutting process are known, the use of heat fluxes as boundary conditions is advantageous, since no temperature measurements are required for predicting the temperatures of the cutting tool. However, these heat sources are usually calculated through usage of parameters for friction, the output power of the machine, or the cutting force and

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cutting speed. Moreover, predicting how much heat is transported to tool, work piece and chip, is based on empirical models and on approximation. Calculating the temperature field of a machine tool through use of heat flux boundary conditions (Neumann Boundary), has been shown by [4] and [7] using the so called panel method. Due to the mentioned uncertainties, accurate modelling of the heat sources of a machine tool requires validation through temperature measurements. However, the temperatures within the machine tool, which are obtained through infrared thermography, also inherit uncertainties. As the tool surface is not a black body radiator, its surface brightness not only contains emitted radiation, but also reflected radiation from other heat sources within the tool’s vicinity (chip, shear zone and work piece). This leads to an increase of radiation intensity, which is recorded by the infrared camera and, wrongfully, interpreted as the tool’s own emitted radiation. As a result, measurement errors for the surface temperature can occur. These errors are insurmountable for optical temperature measurement principles based on thermal radiation. However, using infrared thermography has several distinct advantages, which ensures significantly more accurate results than measurements, which are conducted through common temperature sensors. For one, this is due to a high temporal and spatial resolution of the used FLIR SC7600 infrared camera (pixel pitch of 15µm/pixel and a frame rate of 860 Hz). Moreover, infrared imagery yields a two-dimensional temperature field, rather than just the temperature of one specified location. As the technique is also non-invasive, there is no thermal influence of the measuring device on the machine tool, as would be the case for sensors, which require contact to the tool.

Fig. 5. Detailed View of Single Cutting Edge of Broaching Tool

For the infrared measurement, errors especially need to be considered at the rake face, where a high amount of radiation is reflected from the significantly hotter chip, as well as at the clearance face, where the tool is chamfered, compare Fig. 5. Here, the observed tool surface is turned towards the work piece, making the area more prone for reflected radiation entering the camera. Unfortunately, the temperature information (and thus, the heat flux into the tool) at these regions is most important for the validation of the proposed thermal models.

The measured temperature field of a cutting tool is shown in Fig. 6a, which incidentally shows significant increases in temperature towards the rake face (I) and the chamfered area (II), which are exposed to the highest amount of ambient radiation. The chamfered area is displayed located at frame II. This poses the question, how reliable the measured temperature data is. For the following investigations, the area in frame III is chosen as a reference zone, where less reflected radiation is presumed. In summary, both, values for Dirichlet-, as well as for Neumann-boundaries inherit sources of errors. Thus, different models and methods, using one of both boundary conditions, need to be compared and tested, so as to intensify the understanding of the thermal mechanism taking place and ultimately, to improve the accuracy of temperature and heat flux predictions for the machine tool.

Fig. 6. (a) Measured Temperature Field (b) Simulated Temperature Field

In order to investigate, whether the measured boundary temperatures are plausible, a two-dimensional finitedifference simulation of the tool has been conducted for the area close to the rake face and the reference zone (I and III, Fig. 6a). Within the used mesh, every element represents one measured temperature (camera pixel). The measured temperatures at the rake face and above the chamfered area, as well as the remaining two edges of the image (see red frame, Fig.6b) are used as boundary conditions (Dirichlet-boundary). The chamfered area itself is not part of included in the simulation; thermal losses through convection and radiation at the tool’s surface are disregarded. For a non-defective temperature measurement, the simulation should result the same temperature values as the infrared camera. In consequence, the computed temperature field can be used to determine, whether the measured temperatures at the rake face are plausible. The temperatures resulting from numerical simulation are shown in Fig.6b. The results of the simulation are fairly similar to the measured data. However, an increase in temperature towards the rake face, as indicated through the measurement, is not observed. As a measure for the magnitude of difference between simulated and measured temperatures, the standard deviation σ is used:

V=

1 (n x - 1)(n y - 1)

nx

ny

¦¦ (T ( x , y s

i

j

) Tm ( xi , y j )) 2

.

(1)

i 1 j 1

Here, nx and ny represent the number of temperature values in x and y direction, Ts represents the simulated and Tm the measured temperatures at each pixel, or finite element i, j. For

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the investigated machine tool, the standard deviation is calculated to 2.87 K. Assuming, as only the area above the chamfer (Zones I and II) is calculated, that the only temperature data, which is faulted through reflected radiation is close to the rake face, this boundary shall be examined further in detail. Using a non-linear regression analysis, an optimized temperature distribution at the rake face is attempted. For this, the rake face temperature distribution is iteratively altered, in order to match the resulting simulated temperatures to the measured temperatures within the reference zone (see frame III, Fig. 6a). The measured temperature distribution along the rake face, as well as the temperature distribution obtained through the described procedure is shown in Fig. 7.

4. Conclusion and Outlook In this paper, experimental and numerical methods for investigating thermal boundary conditions at characteristic regions of metal cutting were examined for a representative metal cutting process. A three dimensional mesh plot of the temperature field was used for investigation of the thermal boundaries at the rake face and the shear zone. Since temperature measurements at the considered areas can yield significant errors due to the constraints imposed by the experimental set up, a comprehensive analysis of the boundary conditions is conducted by means of numeric calculations. As basis for this investigation, undisturbed signals at the tool region were used. The presented results show the potential for the combination of both methods. In the future, a combination of both approaches should be evaluated for the validation of thermal models in metal cutting with higher cutting speeds. Acknowledgements The presented research results were achieved in the frame of the projects A02 and B02 of the collaborative research program SFB/TR 96: Thermo-energetic design of machine tools, funded by the German Science Foundation. References

Fig. 7. Measured and Optimized Temperature Distribution Rake Face

The results show, that the optimized rake face temperatures exceed the measured temperatures, contrary to the assumption, that the measurement overestimates the temperatures, due to reflected radiation. Similar results were obtained in [8]. However, the steep increase in temperature, as shown in the measurement (see frame I in Fig. 6a) is not shown in the second simulation result, which is given in Fig. 8.

Fig. 8. Simulated Temperature Field for Optimized Rake Face Temperatures

The improvement of the standard deviation of measurement to simulation for the optimized rake face temperature is not significant (2.74 K).

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