<figure><img src="image_2519.png" /><figcaption>Figure 1. Bragg wavelength versus time (a) and correlation of Bragg wavelength shift versus temperature (b)</figcaption></figure>

Based on the accumulation of data for the isotherms, the responses of the sensors recorded as changes in wavelength with increasing temperature are shown in **Figure 3.b**. The FBG shows a linear response to temperature over the ranges from 25 °C to 350 °C. All four isotherms exhibited very similar performance characteristics. The results show a linear relationship between Bragg wavelength shift and temperature: all gratings shifted approximately 1.5 nm per 100 °C. A correlation factor of 1 indicates there is no stress during this experiment, as wavelength shift is only affected by temperature. The linear fit which represents the calibration of the optical fibre sensors can be given by the following equation:

$$ \Delta\lambda_{Bragg} = 0.0145 * T + 0.39 \quad (4) $$

where $\Delta\lambda_{Bragg}$ is the wavelength shift of the initial peak at 25 °C and T is the temperature [°C], at which the measurement is taken. From this formula, the parameter, $d\Delta\lambda/dT$, can be calculated and hence for this FBG the temperature sensitivity can be determined to be 0.0145 nm·°C⁻¹ over the temperature range of 25-350 °C. Then, the temperature gradient for all measurements can be calculated from the following equation:

$$ T = 69.081 * \Delta\lambda_{Bragg} + T_0 \quad (5) $$

where $T_0$ is the beginning temperature during the measurements [°C].

Typical uncertainty in the temperature measurements was ± 5 °C [10].

## Experimental results and validation

As mentioned before, two optical fibre temperature measurements were examined: the response of the FBG as a function of temperature in static mode and subject to mechanical stresses. Moreover, the influence of PEI and FBG left loose on top of CF/PEEK, as well as, PEI and FBG integrated on CF/PEEK surface were studied. The results combining gradient temperature from FBG sensors and thermocouples are presented in **Figure 4** and **Figure 5**. The measurements were taken from ambient temperature up to 350 °C with an isotherm for 15 min to ensure thermal stabilization. The chosen temperature did not affect the $T_m$ of PEEK noticeably, however, overcame the $T_g$ of both, PEEK and PEI. Then, the cooling rate was registered for 10 min. The temperature results were taken by a thermocouple during assembly with a measurement interval of 1.00 s, while the shift of Bragg wavelength may be more accurate with 0.04 s.

Comparing the experimental temperature profiles from FBG sensors and thermocouples, a slight mismatch can be highlighted. It was expected, as the results of fibre Bragg gratings were
<figure><img src="image_2512.png" /><figcaption>Figure 1. Bragg wavelength versus time (a) and correlation of Bragg wavelength shift versus temperature (b)</figcaption></figure>

Based on the accumulation of data for the isotherms, the responses of the sensors recorded as changes in wavelength with increasing temperature are shown in **Figure 3.b**. The FBG shows a linear response to temperature over the ranges from 25 °C to 350 °C. All four isotherms exhibited very similar performance characteristics. The results show a linear relationship between Bragg wavelength shift and temperature: all gratings shifted approximately 1.5 nm per 100 °C. A correlation factor of 1 indicates there is no stress during this experiment, as wavelength shift is only affected by temperature. The linear fit which represents the calibration of the optical fibre sensors can be given by the following equation:

$$ \Delta\lambda_{Bragg} = 0.0145 * T + 0.39 \quad (4) $$

where $\Delta\lambda_{Bragg}$ is the wavelength shift of the initial peak at 25 °C and T is the temperature [°C], at which the measurement is taken. From this formula, the parameter, $d\Delta\lambda/dT$, can be calculated and hence for this FBG the temperature sensitivity can be determined to be 0.0145 nm·°C⁻¹ over the temperature range of 25-350 °C. Then, the temperature gradient for all measurements can be calculated from the following equation:

$$ T = 69.081 * \Delta\lambda_{Bragg} + T_0 \quad (5) $$

where $T_0$ is the beginning temperature during the measurements [°C].

Typical uncertainty in the temperature measurements was ± 5 °C [10].

## Experimental results and validation

As mentioned before, two optical fibre temperature measurements were examined: the response of the FBG as a function of temperature in static mode and subject to mechanical stresses. Moreover, the influence of PEI and FBG left loose on top of CF/PEEK, as well as, PEI and FBG integrated on CF/PEEK surface were studied. The results combining gradient temperature from FBG sensors and thermocouples are presented in **Figure 4** and **Figure 5**. The measurements were taken from ambient temperature up to 350 °C with an isotherm for 15 min to ensure thermal stabilization. The chosen temperature did not affect the $T_m$ of PEEK noticeably, however, overcame the $T_g$ of both, PEEK and PEI. Then, the cooling rate was registered for 10 min. The temperature results were taken by a thermocouple during assembly with a measurement interval of 1.00 s, while the shift of Bragg wavelength may be more accurate with 0.04 s.

Comparing the experimental temperature profiles from FBG sensors and thermocouples, a slight mismatch can be highlighted. It was expected, as the results of fibre Bragg gratings were
recorded at the interface of PEI while the thermocouple was located under the bottom plate of the experimental set-up. Despite this, the curves are well correlated. The faster heating and cooling rates are observed for TC as the temperature in the oven affects them directly. Temperature stabilization around 350 °C in the oven still takes at least 5 min. During this time, no specific changes are observed on TC curves.

<figure><img src="image_2520.png" /></figure>

<figure><img src="image_2521.png" /></figure>

In the case of fibre Bragg gratings, a regular disconnection is apparent during thermal transitions (vertical red lines), whereas none is observed when the temperature is stabilized. This is attributed to the vertical mechanical action of the rheometer to maintain the assembly under constant pressure during its thermal expansion. We remind that an excess of curvature or micro-curvatures may reduce the light power inside the optical fibre and then the reflected peak is no longer recognized. This also indicates that the vertical loads have a greater impact on the wavelength intensity than the shear loads applied by the rheometer. While heating, PEI begins to flow as a result of nucleation (viscoelastic heating mechanism controlled by surface heating) and the growth of hot spots. The flow of the energy director after reaching its Tg of 220 °C causes a peak registered by FBG sensors. For loose PEI the peak reached 273 °C at 1.7 min while for integrated PEI it was 261 °C at 1.6
recorded at the interface of PEI while the thermocouple was located under the bottom plate of the experimental set-up. Despite this, the curves are well correlated. The faster heating and cooling rates are observed for TC as the temperature in the oven affects them directly. Temperature stabilization around 350 °C in the oven still takes at least 5 min. During this time, no specific changes are observed on TC curves.

<figure><img src="image_2513.png" /></figure>

<figure><img src="image_2514.png" /></figure>

In the case of fibre Bragg gratings, a regular disconnection is apparent during thermal transitions (vertical red lines), whereas none is observed when the temperature is stabilized. This is attributed to the vertical mechanical action of the rheometer to maintain the assembly under constant pressure during its thermal expansion. We remind that an excess of curvature or micro-curvatures may reduce the light power inside the optical fibre and then the reflected peak is no longer recognized. This also indicates that the vertical loads have a greater impact on the wavelength intensity than the shear loads applied by the rheometer. While heating, PEI begins to flow as a result of nucleation (viscoelastic heating mechanism controlled by surface heating) and the growth of hot spots. The flow of the energy director after reaching its Tg of 220 °C causes a peak registered by FBG sensors. For loose PEI the peak reached 273 °C at 1.7 min while for integrated PEI it was 261 °C at 1.6
min. The cooling rate of FBG is slower than TC. Indeed, the welding interphase takes more time to cool down than the aluminium set-up.

The FBG responses to mechanical stresses show small differences compared to static mode. The thermal profiles obtained by optical fibre sensors and thermocouples are almost identical. However, Bragg wavelength disconnections are more pronounced for loose ED configurations. In dynamic mode, the flowing of PEI after reaching its Tg causes a less intense peak registered by FBG sensors, but closer to the glass transition temperature of material. Thus, for loose PEI and integrated PEI at 1.7 min, the peak reached 235 °C and 240 °C, respectively. The cooling rate seems to be similar for both methods (FBG and TC). It means that material after the application of mechanical stresses organizes the chemical structure to be cooled down about 5 °C·min⁻¹ faster than material in static mode.

After the first temperature measurements by fibre Bragg gratins, the samples in static and dynamic mode were subjected to a second measurement, as presented in **Figure 6**. In this case, CF/PEEK composite samples are already assembled by a unified PEI interphase and the FBG is embedded inside. In each case, the first experiment caused partial deconsolidation of the composite, reducing its conductive properties, which led to a reduction in the heating and cooling rates recorded by the optical fibre sensors in the second measurement. Also, the peak previously recorded after Tg of PEI is not apparent during the second experiment. It could suggest an optical change in the fibre due to the environmental transition from the glassy to the rubbery state, but fully embedded fibres should be affected. Therefore, a stress release on the fibre is more likely: the slight pressure of the rheometer set-up squeezes the optical fibre, but when the Tg of PEI is reached, it softens, and the fibre returns to its original shape.

<figure><img src="image_2522.png" /><figcaption>Figure 4. Second temperature measurement passes (a) static mode and (b) dynamic mode</figcaption></figure>

The fibre Bragg grating wavelength is affected by different environmental conditions such as temperature, strain, and coupling with the host material. The agreement between the results from optical fibre sensors and thermocouples demonstrated the FBG method's validity.

## Summary

This study focused on the temperature profiles during the assembly of CF/PEEK specimens. CF/PEEK parts with 250 µm PEI layers were joined together to obtain the response of the FBG sensors as a function of temperature in static mode and subject to mechanical stresses. Both configurations with loose and integrated PEI layers on top of the composite sample were studied. The FBG considered as temperature sensors up to 350 °C showed linear Bragg wavelength shift with temperature. The optical fibre sensors are then able to monitor high temperatures in the
min. The cooling rate of FBG is slower than TC. Indeed, the welding interphase takes more time to cool down than the aluminium set-up.

The FBG responses to mechanical stresses show small differences compared to static mode. The thermal profiles obtained by optical fibre sensors and thermocouples are almost identical. However, Bragg wavelength disconnections are more pronounced for loose ED configurations. In dynamic mode, the flowing of PEI after reaching its Tg causes a less intense peak registered by FBG sensors, but closer to the glass transition temperature of material. Thus, for loose PEI and integrated PEI at 1.7 min, the peak reached 235 °C and 240 °C, respectively. The cooling rate seems to be similar for both methods (FBG and TC). It means that material after the application of mechanical stresses organizes the chemical structure to be cooled down about 5 °C·min⁻¹ faster than material in static mode.

After the first temperature measurements by fibre Bragg gratins, the samples in static and dynamic mode were subjected to a second measurement, as presented in **Figure 6**. In this case, CF/PEEK composite samples are already assembled by a unified PEI interphase and the FBG is embedded inside. In each case, the first experiment caused partial deconsolidation of the composite, reducing its conductive properties, which led to a reduction in the heating and cooling rates recorded by the optical fibre sensors in the second measurement. Also, the peak previously recorded after Tg of PEI is not apparent during the second experiment. It could suggest an optical change in the fibre due to the environmental transition from the glassy to the rubbery state, but fully embedded fibres should be affected. Therefore, a stress release on the fibre is more likely: the slight pressure of the rheometer set-up squeezes the optical fibre, but when the Tg of PEI is reached, it softens, and the fibre returns to its original shape.

<figure><img src="image_2515.png" /><figcaption>Figure 4. Second temperature measurement passes (a) static mode and (b) dynamic mode</figcaption></figure>

The fibre Bragg grating wavelength is affected by different environmental conditions such as temperature, strain, and coupling with the host material. The agreement between the results from optical fibre sensors and thermocouples demonstrated the FBG method's validity.

## Summary

This study focused on the temperature profiles during the assembly of CF/PEEK specimens. CF/PEEK parts with 250 µm PEI layers were joined together to obtain the response of the FBG sensors as a function of temperature in static mode and subject to mechanical stresses. Both configurations with loose and integrated PEI layers on top of the composite sample were studied. The FBG considered as temperature sensors up to 350 °C showed linear Bragg wavelength shift with temperature. The optical fibre sensors are then able to monitor high temperatures in the
assembly interphase, as correlated to thermocouples. Temperatures above the Tg of the materials reduced fibre strain, and therefore its impact on wavelength shift.

It is a promising technique to quantify temperature distribution inside molten polymers. This measurement would lead to an accurate characterization of thermal or even mechanical behaviour where classical techniques are only able to provide surface measurements.

The method has been validated and can be applied for CF/PEEK composite joining processes such as welding. FBG method has great potential for temperature gradient measurement and could be less intrusive than incorporated thermocouples. Further work will focus on using FBG sensors during ultrasonic welding of CF/PEEK parts with PEI as energy director.

## Acknowledgements

This work received financial support from ANR through France Relance plan of the French government in collaboration with the company Lauak Group (France).

## References

[1] A. Korycki, F. Carassus, C. Garnier, F. Chabert, T. Djilali, *Effect of energy director thickness on thermal diffusion and joint quality during ultrasonic welding of CF/PEEK composites*, in: Material Research Proceedings, Krakow, Poland, 1819-1828, 2023.
https://doi.org/10.21741/9781644902479-197

[2] Y.J. Rao, *Recent progress in applications of in-fibre Bragg grating sensors*, Optics and Lasers in Engineering, 31(1), 297-324, 1999. https://doi.org/10.1016/S0143-8166(99)00025-1

[3] L. Hoffmann, M.S. Müller, S. Krämer, M. Giebel, G. Schwotzer, T. Wieduwilt, *Applications of fibre optic temperature measurement*, Estonian Journal of Engineering, 13(4), 363, 2007.
https://doi.org/10.3176/eng.2007.4.09

[4] A.J. Rogers, *Distributed optical-fibre sensors for the measurement of pressure, strain and temperature*, Physics Reports, 169(2), 99-143, 1988. https://doi.org/10.1016/0370-1573(88)90110-X

[5] Jirapong Lim, Qingping Yang, B.E. Jones, P.R. Jackson, *Strain and temperature sensors using multimode optical fiber Bragg gratings and correlation signal processing*, IEEE Transactions on Instrumentation and Measurement, 51(4), 622-627, 2002.
https://doi.org/10.1109/TIM.2002.802253

[6] J. Juergens, G. Adamovsky, R. Bhatt, G. Morscher, B. Floyd, *Thermal evaluation of fiber Bragg gratings at extreme temperatures*, in: 43rd AIAA Aerospace Sciences Meeting and Exhibit, American Institute of Aeronautics and Astronautics, Reno, Nevada, 2005.
https://doi.org/10.2514/6.2005-1214

[7] T. Habisreuther, T. Elsmann, Z. Pan, A. Graf, R. Willsch, M.A. Schmidt, *Sapphire fiber Bragg gratings for high temperature and dynamic temperature diagnostics*, Applied Thermal Engineering, 91 860-865, 2015. https://doi.org/10.1016/j.applthermaleng.2015.08.096

[8] X. Chapeleau, P. Casari, D. Leduc, Y. Scudeller, C. Lupi, R.L. Ny, C. Boisrobert, *Determination of strain distribution and temperature gradient profiles from phase measurements of embedded fibre Bragg gratings*, Journal of Optics A: Pure and Applied Optics, 8(9), 775-781, 2006. https://doi.org/10.1088/1464-4258/8/9/011

[9] G. Pereira, M. McGugan, L.P. Mikkelsen, *Method for independent strain and temperature measurement in polymeric tensile test specimen using embedded FBG sensors*, Polymer Testing, 50(1), 125-134, 2016. https://doi.org/10.1016/j.polymertesting.2016.01.005

[10] T. Venugopalan, T. Sun, K.T.V. Grattan, *Temperature characterization of long period gratings written in three different types of optical fibre for potential high temperature measurements*, Sensors and Actuators A: Physical, 160(1-2), 29-34, 2010.
https://doi.org/10.1016/j.sna.2010.03.016
assembly interphase, as correlated to thermocouples. Temperatures above the Tg of the materials reduced fibre strain, and therefore its impact on wavelength shift.

It is a promising technique to quantify temperature distribution inside molten polymers. This measurement would lead to an accurate characterization of thermal or even mechanical behaviour where classical techniques are only able to provide surface measurements.

The method has been validated and can be applied for CF/PEEK composite joining processes such as welding. FBG method has great potential for temperature gradient measurement and could be less intrusive than incorporated thermocouples. Further work will focus on using FBG sensors during ultrasonic welding of CF/PEEK parts with PEI as energy director.

## Acknowledgements

This work received financial support from ANR through France Relance plan of the French government in collaboration with the company Lauak Group (France).

## References

[1] A. Korycki, F. Carassus, C. Garnier, F. Chabert, T. Djilali, *Effect of energy director thickness on thermal diffusion and joint quality during ultrasonic welding of CF/PEEK composites*, in: Material Research Proceedings, Krakow, Poland, 1819–1828, 2023.
https://doi.org/10.21741/9781644902479-197

[2] Y.J. Rao, *Recent progress in applications of in-fibre Bragg grating sensors*, Optics and Lasers in Engineering, 31(1), 297–324, 1999. https://doi.org/10.1016/S0143-8166(99)00025-1

[3] L. Hoffmann, M.S. Müller, S. Krämer, M. Giebel, G. Schwotzer, T. Wieduwilt, *Applications of fibre optic temperature measurement*, Estonian Journal of Engineering, 13(4), 363, 2007.
https://doi.org/10.3176/eng.2007.4.09

[4] A.J. Rogers, *Distributed optical-fibre sensors for the measurement of pressure, strain and temperature*, Physics Reports, 169(2), 99–143, 1988. https://doi.org/10.1016/0370-1573(88)90110-X

[5] Jirapong Lim, Qingping Yang, B.E. Jones, P.R. Jackson, *Strain and temperature sensors using multimode optical fiber Bragg gratings and correlation signal processing*, IEEE Transactions on Instrumentation and Measurement, 51(4), 622–627, 2002.
https://doi.org/10.1109/TIM.2002.802253

[6] J. Juergens, G. Adamovsky, R. Bhatt, G. Morscher, B. Floyd, *Thermal evaluation of fiber Bragg gratings at extreme temperatures*, in: 43rd AIAA Aerospace Sciences Meeting and Exhibit, American Institute of Aeronautics and Astronautics, Reno, Nevada, 2005.
https://doi.org/10.2514/6.2005-1214

[7] T. Habisreuther, T. Elsmann, Z. Pan, A. Graf, R. Willsch, M.A. Schmidt, *Sapphire fiber Bragg gratings for high temperature and dynamic temperature diagnostics*, Applied Thermal Engineering, 91 860–865, 2015. https://doi.org/10.1016/j.applthermaleng.2015.08.096

[8] X. Chapeleau, P. Casari, D. Leduc, Y. Scudeller, C. Lupi, R.L. Ny, C. Boisrobert, *Determination of strain distribution and temperature gradient profiles from phase measurements of embedded fibre Bragg gratings*, Journal of Optics A: Pure and Applied Optics, 8(9), 775–781, 2006. https://doi.org/10.1088/1464-4258/8/9/011

[9] G. Pereira, M. McGugan, L.P. Mikkelsen, *Method for independent strain and temperature measurement in polymeric tensile test specimen using embedded FBG sensors*, Polymer Testing, 50(1), 125–134, 2016. https://doi.org/10.1016/j.polymertesting.2016.01.005

[10] T. Venugopalan, T. Sun, K.T.V. Grattan, *Temperature characterization of long period gratings written in three different types of optical fibre for potential high temperature measurements*, Sensors and Actuators A: Physical, 160(1–2), 29–34, 2010.
https://doi.org/10.1016/j.sna.2010.03.016
# Analysis of the effect of draft angle and surface roughness on ejection forces in micro injection molding

MACIARIELLO Francesco¹,ᵃ*, LUCCHETTA Giovanni¹,ᵇ and SORGATO Marco¹,ᶜ

¹Department of Industrial Engineering, University of Padova, via Venezia 1, 35010, Padova, Italy

ᵃmaciariello.francesco@gmail.com, ᵇgiovanni.lucchetta@unipd.it, ᶜmarco.sorgato@unipd.it

**Keywords:** Micro Injection Molding, Draft Angle, Surface Roughness, Ejection Force, Demolding

**Abstract.** Minimizing ejection forces is a crucial challenge in micro injection molding to prevent component damage during demolding. This research investigates the effects and interactions of draft angle, surface roughness, mold temperature, and holding pressure on the ejection force in a small, box-shaped component made from polypropylene (PP) and cyclic olefin copolymer (COC). A piezoelectric force sensor, integrated into the ejection tray of the mold, was used to measure the peak ejection force. The results indicate a significant influence of polymer type on ejection force, with PP exhibiting a 26% lower peak ejection force than COC. The draft angle consistently reduced demolding forces. Strong interactions were observed between mold temperature, surface roughness, and polymer type. Specifically, an increase in mold temperature led to an 88% increase in ejection force for COC, while resulting in a 63% decrease for PP. For PP, the optimal ejection force was measured at a surface roughness (Sa) of 0.095 µm, while for COC, a continuous decrease in ejection force was measured with decreasing surface roughness.

**Introduction**

Micro injection molding (µIM) is a key technology in the production of small, high-precision thermoplastic components for applications in the biomedical, microelectronics and automotive industries. From the miniaturization of components and molds arises the necessity for better understanding of the µIM process, especially regarding the demolding phase. During separation of the part from the mold, ejector pins can produce concentrated stresses that lead to deformation and surface defects in the component [1], [2]. Management of ejection forces is therefore critical to ensure defect-free production [3].

The correct replication of the mold cavity is influenced by many process parameters and by the correct design and fabrication of the injection mold itself [4], [5]. Of the variables that have an impact on the molding process, mold temperature (Tm), holding pressure (Ph), draft angle and surface roughness have been shown to have the greatest effect on the ejection forces [6]-[10]. A draft angle between 1° and 3° is commonly used to facilitate demolding. A core surface roughness between 0.092 µmRa and 0.212 µmRa has also been shown to result minimal ejection forces in cylindrical components [11]. As it is often the case in micro injection molding, the geometrical properties of the mold are constrained by aesthetical and functional requirements of the molded component. When geometrical parameters cannot be altered, ejection forces can be mitigated via the correct selection of process parameters. While holding pressure and mold temperature have been shown to influence the ejection force, their effect is not easily predictable and seems to be dependent on polymer selection. Pontes et al. [8] found a reduction in ejection forces with the increase of Tm for PP and PS. They also found a value of Ph that maximizes ejection forces. Griffiths et al. [12] found an increase in ejection forces when increasing Tm and Ph in COC. Bhagavatula et al. [13] found on the other hand a decrease in force with pressure when molding HDPE and HIPS.

<figure><img src="image_2523.png" /></figure>
# Analysis of the effect of draft angle and surface roughness on ejection forces in micro injection molding

MACIARIELLO Francesco¹,ᵃ*, LUCCHETTA Giovanni¹,ᵇ and SORGATO Marco¹,ᶜ

¹Department of Industrial Engineering, University of Padova, via Venezia 1, 35010, Padova, Italy

ᵃmaciariello.francesco@gmail.com, ᵇgiovanni.lucchetta@unipd.it, ᶜmarco.sorgato@unipd.it

**Keywords:** Micro Injection Molding, Draft Angle, Surface Roughness, Ejection Force, Demolding

**Abstract.** Minimizing ejection forces is a crucial challenge in micro injection molding to prevent component damage during demolding. This research investigates the effects and interactions of draft angle, surface roughness, mold temperature, and holding pressure on the ejection force in a small, box-shaped component made from polypropylene (PP) and cyclic olefin copolymer (COC). A piezoelectric force sensor, integrated into the ejection tray of the mold, was used to measure the peak ejection force. The results indicate a significant influence of polymer type on ejection force, with PP exhibiting a 26% lower peak ejection force than COC. The draft angle consistently reduced demolding forces. Strong interactions were observed between mold temperature, surface roughness, and polymer type. Specifically, an increase in mold temperature led to an 88% increase in ejection force for COC, while resulting in a 63% decrease for PP. For PP, the optimal ejection force was measured at a surface roughness (Sa) of 0.095 µm, while for COC, a continuous decrease in ejection force was measured with decreasing surface roughness.

**Introduction**

Micro injection molding (µIM) is a key technology in the production of small, high-precision thermoplastic components for applications in the biomedical, microelectronics and automotive industries. From the miniaturization of components and molds arises the necessity for better understanding of the µIM process, especially regarding the demolding phase. During separation of the part from the mold, ejector pins can produce concentrated stresses that lead to deformation and surface defects in the component [1], [2]. Management of ejection forces is therefore critical to ensure defect-free production [3].

The correct replication of the mold cavity is influenced by many process parameters and by the correct design and fabrication of the injection mold itself [4], [5]. Of the variables that have an impact on the molding process, mold temperature (Tm), holding pressure (Ph), draft angle and surface roughness have been shown to have the greatest effect on the ejection forces [6]-[10]. A draft angle between 1° and 3° is commonly used to facilitate demolding. A core surface roughness between 0.092 µmRa and 0.212 µmRa has also been shown to result minimal ejection forces in cylindrical components [11]. As it is often the case in micro injection molding, the geometrical properties of the mold are constrained by aesthetical and functional requirements of the molded component. When geometrical parameters cannot be altered, ejection forces can be mitigated via the correct selection of process parameters. While holding pressure and mold temperature have been shown to influence the ejection force, their effect is not easily predictable and seems to be dependent on polymer selection. Pontes et al. [8] found a reduction in ejection forces with the increase of Tm for PP and PS. They also found a value of Ph that maximizes ejection forces. Griffiths et al. [12] found an increase in ejection forces when increasing Tm and Ph in COC. Bhagavatula et al. [13] found on the other hand a decrease in force with pressure when molding HDPE and HIPS.

<figure><img src="image_2516.png" /></figure>
A deeper understanding of the effect of process and geometrical parameters on ejection forces is needed, especially for the accurate reproduction of micro-components. Beyond considering the main effects of the studied variables, it is essential to understand their interactions, as these can significantly affect peak ejection forces.

## Materials and Methods

Two distinct thermoplastic materials were used in this analysis: TOPAS 5013-10L cyclic olefin polymer (COC) and ISOPLEN A H F polypropylene (PP) by Sirmax. Both polymers are widely used in biomedical and mechanical applications [14]. The materials' thermal properties were evaluated using Differential Scanning Calorimetry (DSC) on a TA Instruments DSC Q200. Rheological properties were evaluated on an oscillatory rheometer TA Instruments ARES. The DSC tests for PP spanned a temperature between -40°C and 250°C, with a heating rate of 10°C/min, whereas for COC the range was 0°C to 360°C, also with a heating rate of 10°C/min. Rotary rheometer tests were conducted at 185°C, 200°C and 215°C for PP and 220°C, 240°C and 260°C for COC.

<figure><img src="image_2524.png" /><figcaption>Figure 1: technical drawing of the molded component, where α represents the variable draft angle.</figcaption></figure>

A small box-shaped component was designed for the experiments, measuring 14.4 x 11.6 x 10.7 mm with a wall thickness of 1.2 mm. Of the four lateral faces of the mold core, only two underwent surface treatment and had variable draft angle ranging between 0.25°, 1°, 2°. The non-treated faces had an 8° draft angle and a smaller surface area to minimize their impact on ejection forces. A technical drawing of the component is shown in Fig. 1, where α indicates the variable draft angle.

The samples were injected from the center of the upper face to ensure optimal and symmetrical filling of the cavity. This design prevents the formation of weld lines and air inclusions. It also minimizes the pressure loss during packing and holding, thereby reducing deformation due to
A deeper understanding of the effect of process and geometrical parameters on ejection forces is needed, especially for the accurate reproduction of micro-components. Beyond considering the main effects of the studied variables, it is essential to understand their interactions, as these can significantly affect peak ejection forces.

## Materials and Methods

Two distinct thermoplastic materials were used in this analysis: TOPAS 5013-10L cyclic olefin polymer (COC) and ISOPLEN A H F polypropylene (PP) by Sirmax. Both polymers are widely used in biomedical and mechanical applications [14]. The materials' thermal properties were evaluated using Differential Scanning Calorimetry (DSC) on a TA Instruments DSC Q200. Rheological properties were evaluated on an oscillatory rheometer TA Instruments ARES. The DSC tests for PP spanned a temperature between -40°C and 250°C, with a heating rate of 10°C/min, whereas for COC the range was 0°C to 360°C, also with a heating rate of 10°C/min. Rotary rheometer tests were conducted at 185°C, 200°C and 215°C for PP and 220°C, 240°C and 260°C for COC.

<figure><img src="image_2517.png" /><figcaption>Figure 1: technical drawing of the molded component, where α represents the variable draft angle.</figcaption></figure>

A small box-shaped component was designed for the experiments, measuring 14.4 x 11.6 x 10.7 mm with a wall thickness of 1.2 mm. Of the four lateral faces of the mold core, only two underwent surface treatment and had variable draft angle ranging between 0.25°, 1°, 2°. The non-treated faces had an 8° draft angle and a smaller surface area to minimize their impact on ejection forces. A technical drawing of the component is shown in Fig. 1, where α indicates the variable draft angle.

The samples were injected from the center of the upper face to ensure optimal and symmetrical filling of the cavity. This design prevents the formation of weld lines and air inclusions. It also minimizes the pressure loss during packing and holding, thereby reducing deformation due to
uneven shrinkage. These design assumptions were validated through process simulations using Moldflow Insight 2019.

The mold used for the experiments was based on a Hasco modular system. Special attention was placed on the design of the cooling system to obtain a uniform temperature in the cavity. Six cylindrical ejector pins, each with a 1 mm tip diameter (Hasco code Z441), were placed symmetrically around the component's perimeter to balance the ejection force. The even distribution of the ejectors is chosen to limit part deformation during the demolding phase [15], [16]. The ejectors' base was placed on a distribution plate to transfer the total ejection force to the piezoelectric sensor in the ejection tray, as shown in Fig. 2.

Molding was performed on a Wittmann Battenfeld Micropower 15, a state-of-the-art micro injection molding machine equipped with a 15-ton clamping unit and an advanced control system that enables precise adjustment of process parameters. Ejection forces were measured using a Kistler 9223A piezoelectric force sensor, interfaced to a Kistler 5865A10 measuring and control unit with a sampling frequency of 60 kHz.

<figure><img src="image_2525.png" /><figcaption>Fig. 2: mold design details: (a) cooling system, (b) ejection system.</figcaption></figure>

The different roughness profiles of the mold core inserts were achieved through manual polishing, resulting in three finishes (fine, medium, coarse), ranging between 0.01 µmRa and 0.3 µmRa. In this range, minimum ejection forces should be measured according to previous research [10], [11], [17]. The manual polishing procedure was performed by a trained operator to reduce process variability.

Surface roughness of the treated faces was then measured with a Sensofar optical profilometer equipped with Nikon TU Plan Flour 20x lenses. The scanned area consists of two rectangular sections measuring 1.5 x 5 mm, located on the top left corner of the insert's face. Both polished faces of each mold insert were scanned. A 3D printed support was used to facilitate the horizontal positioning of the faces during analysis. The data was processed in the SensoVIEW 1.9.2 software. A plane form removal filter was applied in accordance with ISO 25178 to eliminate any error due to uneven placement of the component. A short filter ($\lambda_s$) of 2.5 µm was applied to all scanned surfaces. A long filter ($\lambda_c$) of 80 µm was applied to the coarse and medium finished surfaces, while a 25 µm filter was applied to the fine finished surfaces before measuring the areal surface
uneven shrinkage. These design assumptions were validated through process simulations using Moldflow Insight 2019.

The mold used for the experiments was based on a Hasco modular system. Special attention was placed on the design of the cooling system to obtain a uniform temperature in the cavity. Six cylindrical ejector pins, each with a 1 mm tip diameter (Hasco code Z441), were placed symmetrically around the component's perimeter to balance the ejection force. The even distribution of the ejectors is chosen to limit part deformation during the demolding phase [15], [16]. The ejectors' base was placed on a distribution plate to transfer the total ejection force to the piezoelectric sensor in the ejection tray, as shown in Fig. 2.

Molding was performed on a Wittmann Battenfeld Micropower 15, a state-of-the-art micro injection molding machine equipped with a 15-ton clamping unit and an advanced control system that enables precise adjustment of process parameters. Ejection forces were measured using a Kistler 9223A piezoelectric force sensor, interfaced to a Kistler 5865A10 measuring and control unit with a sampling frequency of 60 kHz.

<figure><img src="image_2518.png" /><figcaption>Fig. 2: mold design details: (a) cooling system, (b) ejection system.</figcaption></figure>

The different roughness profiles of the mold core inserts were achieved through manual polishing, resulting in three finishes (fine, medium, coarse), ranging between 0.01 µmRa and 0.3 µmRa. In this range, minimum ejection forces should be measured according to previous research [10], [11], [17]. The manual polishing procedure was performed by a trained operator to reduce process variability.

Surface roughness of the treated faces was then measured with a Sensofar optical profilometer equipped with Nikon TU Plan Flour 20x lenses. The scanned area consists of two rectangular sections measuring 1.5 x 5 mm, located on the top left corner of the insert's face. Both polished faces of each mold insert were scanned. A 3D printed support was used to facilitate the horizontal positioning of the faces during analysis. The data was processed in the SensoVIEW 1.9.2 software. A plane form removal filter was applied in accordance with ISO 25178 to eliminate any error due to uneven placement of the component. A short filter ($\lambda_s$) of 2.5 µm was applied to all scanned surfaces. A long filter ($\lambda_c$) of 80 µm was applied to the coarse and medium finished surfaces, while a 25 µm filter was applied to the fine finished surfaces before measuring the areal surface
roughness. Ra values were determined in accordance with ISO 4288, ISO 4287, and ISO 13565-2.

In addition to studying surface finish and draft angle, the research also examined the effects of holding pressure (Ph) and mold temperature (Tm) on ejection forces. For each polymer, two levels of packing pressure and mold temperature were chosen, covering the recommended processing window for each material, as shown in Table 1. All other process parameters, except for melt temperature (T_b), were standardized for both polymers, as detailed in Table 2.

For every combination of the four study parameters, the peak force was measured. The data was then analyzed to find main effect and first-order interaction of the variables.

<table><caption>Table 1: Variables and levels tested in the study for PP and COC.</caption><thead><tr><th>Variable Level</th><th>Draft angle [°]</th><th>Roughness Sa [µm]</th><th>Tm COC [°C]</th><th>Tm PP [°C]</th><th>Ph [bar]</th></tr></thead><tbody><tr><td>1</td><td>0.25</td><td>0.015</td><td>105</td><td>35</td><td>50</td></tr><tr><td>2 | 1</td><td>1</td><td>0.095</td><td>125</td><td>60</td><td>100</td></tr><tr><td>3</td><td>2</td><td>0.278</td><td>\</td><td>\</td><td>\</td></tr></tbody></table>

<table><caption>Table 2: Melt temperature, injection speed, packing time and cooling time for the µIM experiments.</caption><thead><tr><th>Parameter</th><th>Melt temperature [°C]</th><th>Injection speed [mm/s]</th><th>Packing time [s]</th><th>Cooling time [s]</th></tr></thead><tbody><tr><td>PP</td><td>240</td><td>100</td><td>5</td><td>12</td></tr><tr><td>COC</td><td>320</td><td>100</td><td>5</td><td>12</td></tr></tbody></table>

## Results and discussion

Polymer analysis: The thermal properties of the studied materials, and the fitted Cross-WLF constants (Eq. 1 and Eq. 2) are shown in Table 3.

$$ \eta = \frac{\eta_0}{1 + \left(\frac{\eta_0}{\tau^*} \dot{\gamma}\right)^{1-n}} \quad (1) $$

$$ \eta_0 = D_1 \exp \left( \frac{-A_1 (T - T^*)}{A_2 + (T - T^*)} \right) \quad (2) $$

The two polymers present markedly different flow behavior. The Melt Flow Index (MFI) of COC is almost four times greater than that of PP.
roughness. Ra values were determined in accordance with ISO 4288, ISO 4287, and ISO 13565-2.

In addition to studying surface finish and draft angle, the research also examined the effects of holding pressure (Ph) and mold temperature (Tm) on ejection forces. For each polymer, two levels of packing pressure and mold temperature were chosen, covering the recommended processing window for each material, as shown in Table 1. All other process parameters, except for melt temperature (T_b), were standardized for both polymers, as detailed in Table 2.

For every combination of the four study parameters, the peak force was measured. The data was then analyzed to find main effect and first-order interaction of the variables.

<table><caption>Table 1: Variables and levels tested in the study for PP and COC.</caption><thead><tr><th>Variable Level</th><th>Draft angle [°]</th><th>Roughness Sa [µm]</th><th>Tm COC [°C]</th><th>Tm PP [°C]</th><th>Ph [bar]</th></tr></thead><tbody><tr><td>1</td><td>0.25</td><td>0.015</td><td>105</td><td>35</td><td>50</td></tr><tr><td>2 | 1</td><td></td><td>0.095</td><td>125</td><td>60</td><td>100</td></tr><tr><td>3 | 2</td><td></td><td>0.278</td><td>\</td><td>\</td><td>\</td></tr></tbody></table>

<table><caption>Table 2: Melt temperature, injection speed, packing time and cooling time for the µIM experiments.</caption><thead><tr><th>Parameter</th><th>Melt temperature [°C]</th><th>Injection speed [mm/s]</th><th>Packing time [s]</th><th>Cooling time [s]</th></tr></thead><tbody><tr><td>PP</td><td>240</td><td>100</td><td>5</td><td>12</td></tr><tr><td>COC</td><td>320</td><td>100</td><td>5</td><td>12</td></tr></tbody></table>

## Results and discussion

Polymer analysis: The thermal properties of the studied materials, and the fitted Cross-WLF constants (Eq. 1 and Eq. 2) are shown in Table 3.

$$ \eta = \frac{\eta_0}{1 + \left(\frac{\eta_0}{\tau^*} \dot{\gamma}\right)^{1-n}} \quad (1) $$

$$ \eta_0 = D_1 \exp \left( \frac{-A_1 (T - T^*)}{A_2 + (T - T^*)} \right) \quad (2) $$

The two polymers present markedly different flow behavior. The Melt Flow Index (MFI) of COC is almost four times greater than that of PP.
<table><caption>Table 3: thermal properties of the studied polymers and Cross-WLF model constants.</caption><thead><tr><th>Property</th><th>PP</th><th>COC</th></tr></thead><tbody><tr><td>Melt temperature [°C]</td><td>168</td><td>//</td></tr><tr><td>Crystallization temperature [°C]</td><td>120</td><td>//</td></tr><tr><td>Glass transition temperature (T<sub>g</sub>) [°C]</td><td>-13</td><td>137</td></tr><tr><td>MFI (ISO 1133) [g/10 min]</td><td>12 (230°C, 2.16kg)</td><td>47 (260°C, 2.16kg)</td></tr><tr><td>n []</td><td>0.269</td><td>0.329</td></tr><tr><td>τ* [Pa]</td><td>11700</td><td>50900</td></tr><tr><td>T* [K]</td><td>260</td><td>410</td></tr><tr><td>D1 [Pa·s]</td><td>331777</td><td>96633</td></tr><tr><td>A1 []</td><td>1072</td><td>2491</td></tr><tr><td>A2 [K]</td><td>41220</td><td>50111</td></tr></tbody></table>

Roughness analysis: Surface roughness measurements of the mold's core show good repeatability of the manual polishing procedure. The three surface finishes range between 0.015 µmRa and 0.275 µmRa. Surface roughness measures expressed as S<sub>a</sub>, S<sub>pk</sub>, S<sub>vk</sub>, and R<sub>a</sub> are shown in Table 4. For the remainder of the paper, roughness values will be indicated in terms of S<sub>a</sub> [µm].

<table><caption>Table 4: Roughness of the polished core faces.</caption><thead><tr><th>Roughness level</th><th>R1 (smooth)</th><th>R2 (medium)</th><th>R3 (coarse)</th></tr></thead><tbody><tr><td>S<sub>a</sub> [µm]</td><td>0.015</td><td>0.095</td><td>0.275</td></tr><tr><td>S<sub>pk</sub> [µm]</td><td>0.020</td><td>0.100</td><td>0.285</td></tr><tr><td>S<sub>vk</sub> [µm]</td><td>0.025</td><td>0.115</td><td>0.350</td></tr><tr><td>R<sub>a</sub> [µm]</td><td>0.016</td><td>0.098</td><td>0.270</td></tr></tbody></table>

<figure><img src="image_2526.png" /><figcaption>Figure 3: Image of the mold's core surface (a) R1 (b) R2 (c) R3.</figcaption></figure>

Micro injection molding results: The results from the Analysis of Variance (ANOVA) applied to the µIM experiments show that all the main factors investigated have a significant impact on peak ejection force (Table 5). Many of the first-order interactions of the studied variables are also statistically significant. Plots showing the effect of the studied parameters on peak ejection force for PP and COC are shown in Fig. 3.
<table><caption>Table 3: thermal properties of the studied polymers and Cross-WLF model constants.</caption><thead><tr><th>Property</th><th>PP</th><th>COC</th></tr></thead><tbody><tr><td>Melt temperature [°C]</td><td>168</td><td>//</td></tr><tr><td>Crystallization temperature [°C]</td><td>120</td><td>//</td></tr><tr><td>Glass transition temperature (T<sub>g</sub>) [°C]</td><td>-13</td><td>137</td></tr><tr><td>MFI (ISO 1133) [g/10 min]</td><td>12 (230°C, 2.16kg)</td><td>47 (260°C, 2.16kg)</td></tr><tr><td>n []</td><td>0.269</td><td>0.329</td></tr><tr><td>τ* [Pa]</td><td>11700</td><td>50900</td></tr><tr><td>T* [K]</td><td>260</td><td>410</td></tr><tr><td>D1 [Pa·s]</td><td>331777</td><td>96633</td></tr><tr><td>A1 []</td><td>1072</td><td>2491</td></tr><tr><td>A2 [K]</td><td>41220</td><td>50111</td></tr></tbody></table>

Roughness analysis: Surface roughness measurements of the mold's core show good repeatability of the manual polishing procedure. The three surface finishes range between 0.015 µmRa and 0.275 µmRa. Surface roughness measures expressed as S<sub>a</sub>, S<sub>pk</sub>, S<sub>vk</sub>, and R<sub>a</sub> are shown in Table 4. For the remainder of the paper, roughness values will be indicated in terms of S<sub>a</sub> [µm].

<table><caption>Table 4: Roughness of the polished core faces.</caption><thead><tr><th>Roughness level</th><th>R1 (smooth)</th><th>R2 (medium)</th><th>R3 (coarse)</th></tr></thead><tbody><tr><td>S<sub>a</sub> [µm]</td><td>0.015</td><td>0.095</td><td>0.275</td></tr><tr><td>S<sub>pk</sub> [µm]</td><td>0.020</td><td>0.100</td><td>0.285</td></tr><tr><td>S<sub>vk</sub> [µm]</td><td>0.025</td><td>0.115</td><td>0.350</td></tr><tr><td>R<sub>a</sub> [µm]</td><td>0.016</td><td>0.098</td><td>0.270</td></tr></tbody></table>

<figure><img src="image_2519.png" /><figcaption>Figure 3: Image of the mold's core surface (a) R1 (b) R2 (c) R3.</figcaption></figure>

Micro injection molding results: The results from the Analysis of Variance (ANOVA) applied to the µIM experiments show that all the main factors investigated have a significant impact on peak ejection force (Table 5). Many of the first-order interactions of the studied variables are also statistically significant. Plots showing the effect of the studied parameters on peak ejection force for PP and COC are shown in Fig. 3.
<table><caption>Table 5: effect of the studied variables on peak ejection force, ANOVA results.</caption><thead><tr><th>Source</th><th>DF</th><th>Adj MS</th><th>F-Value</th><th>P-Value</th></tr></thead><tbody><tr><td>Draft angle</td><td>2</td><td>3005.4</td><td>107.96</td><td>0.000</td></tr><tr><td>Roughness</td><td>2</td><td>2404.3</td><td>86.36</td><td>0.000</td></tr><tr><td>Tm</td><td>1</td><td>500.8</td><td>17.99</td><td>0.000</td></tr><tr><td>Ph</td><td>1</td><td>1586.5</td><td>56.99</td><td>0.000</td></tr><tr><td>Polymer</td><td>1</td><td>10720.4</td><td>385.08</td><td>0.000</td></tr><tr><td>Draft angle * Roughness</td><td>4</td><td>195.8</td><td>7.03</td><td>0.000</td></tr><tr><td>Draft angle * Tm</td><td>2</td><td>859.6</td><td>30.88</td><td>0.000</td></tr><tr><td>Draft angle * Ph</td><td>2</td><td>194.3</td><td>6.98</td><td>0.001</td></tr><tr><td>Draft angle * Polymer</td><td>2</td><td>34.5</td><td>1.24</td><td>0.291</td></tr><tr><td>Roughness * Tm</td><td>2</td><td>1164.7</td><td>41.84</td><td>0.000</td></tr><tr><td>Roughness * Ph</td><td>2</td><td>132.9</td><td>4.77</td><td>0.009</td></tr><tr><td>Roughness * Polymer</td><td>2</td><td>5307.5</td><td>190.65</td><td>0.000</td></tr><tr><td>Tm * Ph</td><td>1</td><td>4.7</td><td>0.17</td><td>0.683</td></tr><tr><td>Tm * Polymer</td><td>1</td><td>68640.1</td><td>2465.59</td><td>0.000</td></tr><tr><td>Ph * Polymer</td><td>1</td><td>17.2</td><td>0.62</td><td>0.432</td></tr><tr><td>Total</td><td>359</td><td></td><td></td><td></td></tr></tbody></table>

Effects of polymer selection: The experimental data underscores the critical role of polymer selection in determining the ejection force. In COC, a 11.5 N higher mean peak ejection force was measured compared to PP. The two polymers also exhibit a different response to some of the other variables. Consequently, the following results are presented separately for cyclic olefins and polypropylene.

Effects of draft angle and packing pressure: Both materials exhibited a similar response to draft angle and packing pressure variations. Increasing packing pressure from 50 bar to 100 bar produced an increase in peak ejection force of 13.0 N in COC and 4.6 N in PP. An increase in packing pressure can result in a reduction of through-thickness shrinkage [8], and therefore in an increase in contact pressure between component and mold core. The higher contact pressure increases the frictional forces during separation and ejection forces increase. An increase in draft angle systematically reduced the ejection force for both polymers. This reduction is greater at lower draft values. An increment from 0.25° to 1° resulted in the reduction in ejection force by 6.7 N in COC and 6.9 N in PP. The further increase of draft angle to 2° only produced a decrease in peak ejection force of 2 N in COC and 1.9 N in PP.

Effects of mold temperature: Increasing the mold temperature has opposite effects on the two materials. The increase in Tm to 60°C results in a 29.8 N reduction in ejection force for PP, when compared to the ejection force at 35°C. If cycle time is kept constant, an increase in mold temperature leads to an increase in part surface temperature. Higher temperatures lead to a reduction in component's stiffness and therefore to a reduction in ejection force [8]. In the case of COC, increasing mold temperature from 105°C to 125°C produces a 26.8 N increase in peak ejection force. Similar results were obtained by Griffiths et. Al. [12] when printing Topas 5013 COC at 70°C and 130°C. The increase in ejection force at higher Tm may be the result of better mold core replication. The different response of the two materials to changes in mold temperature is the result of the different thermal and rheological properties of the polymers. Topas 5013 have a high heat deflection temperature (HDT) of 130°C and a high shear modulus that does not decrease until 10°C below Tg. Therefore, the increase in ejection force with mold temperature is the consequence of better tool replication and high stiffness of the polymer. In the case of PP, the effect of better replication is compensated by the reduction in material rigidity at higher mold
<table><caption>Table 5: effect of the studied variables on peak ejection force, ANOVA results.</caption><thead><tr><th>Source</th><th>DF</th><th>Adj MS</th><th>F-Value</th><th>P-Value</th></tr></thead><tbody><tr><td>Draft angle</td><td>2</td><td>3005.4</td><td>107.96</td><td>0.000</td></tr><tr><td>Roughness</td><td>2</td><td>2404.3</td><td>86.36</td><td>0.000</td></tr><tr><td>Tm</td><td>1</td><td>500.8</td><td>17.99</td><td>0.000</td></tr><tr><td>Ph</td><td>1</td><td>1586.5</td><td>56.99</td><td>0.000</td></tr><tr><td>Polymer</td><td>1</td><td>10720.4</td><td>385.08</td><td>0.000</td></tr><tr><td>Draft angle * Roughness</td><td>4</td><td>195.8</td><td>7.03</td><td>0.000</td></tr><tr><td>Draft angle * Tm</td><td>2</td><td>859.6</td><td>30.88</td><td>0.000</td></tr><tr><td>Draft angle * Ph</td><td>2</td><td>194.3</td><td>6.98</td><td>0.001</td></tr><tr><td>Draft angle * Polymer</td><td>2</td><td>34.5</td><td>1.24</td><td>0.291</td></tr><tr><td>Roughness * Tm</td><td>2</td><td>1164.7</td><td>41.84</td><td>0.000</td></tr><tr><td>Roughness * Ph</td><td>2</td><td>132.9</td><td>4.77</td><td>0.009</td></tr><tr><td>Roughness * Polymer</td><td>2</td><td>5307.5</td><td>190.65</td><td>0.000</td></tr><tr><td>Tm * Ph</td><td>1</td><td>4.7</td><td>0.17</td><td>0.683</td></tr><tr><td>Tm * Polymer</td><td>1</td><td>68640.1</td><td>2465.59</td><td>0.000</td></tr><tr><td>Ph * Polymer</td><td>1</td><td>17.2</td><td>0.62</td><td>0.432</td></tr><tr><td>Total</td><td>359</td><td></td><td></td><td></td></tr></tbody></table>

Effects of polymer selection: The experimental data underscores the critical role of polymer selection in determining the ejection force. In COC, a 11.5 N higher mean peak ejection force was measured compared to PP. The two polymers also exhibit a different response to some of the other variables. Consequently, the following results are presented separately for cyclic olefins and polypropylene.

Effects of draft angle and packing pressure: Both materials exhibited a similar response to draft angle and packing pressure variations. Increasing packing pressure from 50 bar to 100 bar produced an increase in peak ejection force of 13.0 N in COC and 4.6 N in PP. An increase in packing pressure can result in a reduction of through-thickness shrinkage [8], and therefore in an increase in contact pressure between component and mold core. The higher contact pressure increases the frictional forces during separation and ejection forces increase. An increase in draft angle systematically reduced the ejection force for both polymers. This reduction is greater at lower draft values. An increment from 0.25° to 1° resulted in the reduction in ejection force by 6.7 N in COC and 6.9 N in PP. The further increase of draft angle to 2° only produced a decrease in peak ejection force of 2 N in COC and 1.9 N in PP.

Effects of mold temperature: Increasing the mold temperature has opposite effects on the two materials. The increase in Tm to 60°C results in a 29.8 N reduction in ejection force for PP, when compared to the ejection force at 35°C. If cycle time is kept constant, an increase in mold temperature leads to an increase in part surface temperature. Higher temperatures lead to a reduction in component's stiffness and therefore to a reduction in ejection force [8]. In the case of COC, increasing mold temperature from 105°C to 125°C produces a 26.8 N increase in peak ejection force. Similar results were obtained by Griffiths et. Al. [12] when printing Topas 5013 COC at 70°C and 130°C. The increase in ejection force at higher Tm may be the result of better mold core replication. The different response of the two materials to changes in mold temperature is the result of the different thermal and rheological properties of the polymers. Topas 5013 have a high heat deflection temperature (HDT) of 130°C and a high shear modulus that does not decrease until 10°C below Tg. Therefore, the increase in ejection force with mold temperature is the consequence of better tool replication and high stiffness of the polymer. In the case of PP, the effect of better replication is compensated by the reduction in material rigidity at higher mold
temperatures. A higher Tm could then be useful to ensure correct replication of the mold, lower ejection forces, and increase crystallinity and tensile properties in PP components [18].

<figure><img src="image_2527.png" /><figcaption>Fig. 4: main effect plot for the studied parameters.</figcaption></figure>

Effects of surface roughness: PP and COC responded differently to variations in surface roughness. COC showed a consistent increase in ejection force with the increase of Sa. The minimum peak force was measured at 0.015 µmSa with a value of 31.6 N. Increasing Sa to 0.095 µm resulted in an increase in force by 12.9 N, and further increasing Sa to 0.275 µm produced an additional 10.9 N increase in peak ejection force. This trend contradicts previous studies in which a minimum in ejection force was observed within the roughness range studied. In the case of Polypropylene, the minimum ejection force of 30.6 N was measured for a surface roughness of 0.095 µmSa. The maximum ejection force of 35.2 N was measured at the minimum core roughness value, while a force of 31.5 N was measured when molding on the roughest core. This data is consistent with previous studies [11] and shows the existence of an optimal surface roughness for minimizing ejection forces in PP.

As surface roughness decreases, the frictional forces due to mechanical interlocking between the mold and the plastic component decrease, while adhesion forces increase. This was found to lead to an optimal surface roughness where ejection forces are minimized [11]. In the case of COC, the steady decrease in peak ejection force even at very low surface roughness suggests the dominance of mechanical interlocking forces over adhesion forces. To reduce ejection forces for COC components molded on uncoated steel molds, it is then recommended to reduce surface roughness to values between 0.015 µmSa and 0.1 µmSa.

## Summary

This study provided a comprehensive analysis of the impact of draft angle, surface roughness, mold temperature, and packing pressure on ejection forces in micro injection molding, utilizing polypropylene (PP) and cyclic olefin copolymer (COC). Key findings demonstrate that polymer selection significantly affects ejection forces, with PP exhibiting a 26% lower peak ejection force compared to COC. Additionally, an increase in mold temperature resulted in an 88% increase in ejection force for COC, and a 63% decrease for PP. Surface roughness also had a key role, with the ejection force for PP reaching a minimum at a roughness value (Sa) of 0.095 µm, while COC showed a continual decrease in ejection force with decreasing surface roughness, without an optimum point. These findings underline the complex interactions that exist between polymer selection, geometrical and process parameters, showing the importance of considering material-specific responses when optimizing the injection molding process.
temperatures. A higher Tm could then be useful to ensure correct replication of the mold, lower ejection forces, and increase crystallinity and tensile properties in PP components [18].

<figure><img src="image_2520.png" /><figcaption>Fig. 4: main effect plot for the studied parameters.</figcaption></figure>

Effects of surface roughness: PP and COC responded differently to variations in surface roughness. COC showed a consistent increase in ejection force with the increase of Sa. The minimum peak force was measured at 0.015 µmSa with a value of 31.6 N. Increasing Sa to 0.095 µm resulted in an increase in force by 12.9 N, and further increasing Sa to 0.275 µm produced an additional 10.9 N increase in peak ejection force. This trend contradicts previous studies in which a minimum in ejection force was observed within the roughness range studied. In the case of Polypropylene, the minimum ejection force of 30.6 N was measured for a surface roughness of 0.095 µmSa. The maximum ejection force of 35.2 N was measured at the minimum core roughness value, while a force of 31.5 N was measured when molding on the roughest core. This data is consistent with previous studies [11] and shows the existence of an optimal surface roughness for minimizing ejection forces in PP.

As surface roughness decreases, the frictional forces due to mechanical interlocking between the mold and the plastic component decrease, while adhesion forces increase. This was found to lead to an optimal surface roughness where ejection forces are minimized [11]. In the case of COC, the steady decrease in peak ejection force even at very low surface roughness suggests the dominance of mechanical interlocking forces over adhesion forces. To reduce ejection forces for COC components molded on uncoated steel molds, it is then recommended to reduce surface roughness to values between 0.015 µmSa and 0.1 µmSa.

## Summary

This study provided a comprehensive analysis of the impact of draft angle, surface roughness, mold temperature, and packing pressure on ejection forces in micro injection molding, utilizing polypropylene (PP) and cyclic olefin copolymer (COC). Key findings demonstrate that polymer selection significantly affects ejection forces, with PP exhibiting a 26% lower peak ejection force compared to COC. Additionally, an increase in mold temperature resulted in an 88% increase in ejection force for COC, and a 63% decrease for PP. Surface roughness also had a key role, with the ejection force for PP reaching a minimum at a roughness value (Sa) of 0.095 µm, while COC showed a continual decrease in ejection force with decreasing surface roughness, without an optimum point. These findings underline the complex interactions that exist between polymer selection, geometrical and process parameters, showing the importance of considering material-specific responses when optimizing the injection molding process.
In conclusion, this research contributes to a deeper understanding of the µIM process, particularly in terms of managing ejection forces. These findings can be helpful in guiding future mold designs and process optimizations, especially in micro injection molding.

## References

[1] K. D. Delaney, G. Bissacco, D. Kennedy, A Structured Review and Classification of Demolding Issues and Proven Solutions, Int. Polym. Process. 27 (2012) 77-90.
https://doi.org/10.3139/217.2514

[2] C. A. Griffiths, S. S. Dimov, E. B. Brousseau, C. Chouquet, J. Gavillet, and S. Bigot, Investigation of surface treatment effects in micro-injection-moulding, Int. J. Adv. Manuf. Technol. 47 (2010) 99-110. https://doi.org/10.1007/s00170-009-2000-4

[3] O. M. Bataineh, B. E. Klamecki, Prediction of local part-mold and ejection force in injection molding, J. Manuf. Sci. Eng. 127 (2005) 598-604. https://doi.org/10.1115/1.1951785

[4] J. Zhao, R. H. Mayes, G. Chen, P. S. Chan, Z. J. Xiong, Polymer micromould design and micromoulding process, Plast. Rubber Compos. 32 (2003) 240-247.
https://doi.org/10.1179/146580103225002614

[5] J. Giboz, T. Copponnex, P. Mélé, Microinjection molding of thermoplastic polymers: A review, J. Micromech. Microeng. 17 (2007) R96. https://doi.org/10.1088/0960-1317/17/6/R02

[6] M. Sorgato, D. Masato, G. Lucchetta, Effects of machined cavity texture on ejection force in micro injection molding, Precis. Eng. 50 (2017) 440-448.
https://doi.org/10.1016/j.precisioneng.2017.06.019

[7] P. Parenti, D. Masato, M. Sorgato, G. Lucchetta, M. Annoni, Surface footprint in molds micromilling and effect on part demoldability in micro injection molding, J. Manuf. Process. 29 (2017) 160-174. https://doi.org/10.1016/j.jmapro.2017.05.024

[8] A. J. Pontes, A. S. Pouzada, Ejection force in tubular injection moldings. Part I: Effect of processing conditions, Polym. Eng. Sci. 44 (2004) 891-897. https://doi.org/10.1002/pen.20080

[9] K. Shen, L.-M. Chen, L. Jiang, Calculation of ejection force of hollow, thin walled, and injection moulded cones, Plast. Rubber Compos. 28 (1999) 341-345.
https://doi.org/10.1179/146580199101540493

[10] M. S. Correia, A. S. Miranda, M. C. Oliveira, C. A. Capela, A. S. Pouzada, Analysis of friction in the ejection of thermoplastic mouldings, Int. J. Adv. Manuf. Technol. 59 (2012) 977-986.
https://doi.org/10.1007/s00170-011-3573-2

[11] T. Sasaki, N. Koga, K. Shirai, Y. Kobayashi, A. Toyoshima, An experimental study on ejection forces of injection molding, Prec. Eng. 24 (2000) 270-273. https://doi.org/10.1016/S0141-6359(99)00039-2

[12] C. A. Griffiths, S. S. Dimov, S. G. Scholz, G. Tosello, A. Rees, Influence of injection and cavity pressure on the demoulding force in micro-injection moulding, J. Manuf. Sci. Eng. 136 (2014) 1087-1357. https://doi.org/10.1115/1.4026983

[13] N. Bhagavatula, D. Michalski, B. Lilly, and G. Glozer, Modelling and verification of ejection forces in thermoplastic injection moulding, Model. Simul. Mat. Sci. Eng. 12 (2004) S239.
https://doi.org/10.1088/0965-0393/12/3/S12

[14] A. Gopanna, S. P. Thomas, K. P. Rajan, R. Rajan, E. Rainosalo, J. Zavašnik, M. Chavali, Investigation of mechanical, dynamic mechanical, rheological and morphological properties of
In conclusion, this research contributes to a deeper understanding of the µIM process, particularly in terms of managing ejection forces. These findings can be helpful in guiding future mold designs and process optimizations, especially in micro injection molding.

## References

[1] K. D. Delaney, G. Bissacco, D. Kennedy, A Structured Review and Classification of Demolding Issues and Proven Solutions, Int. Polym. Process. 27 (2012) 77-90.
https://doi.org/10.3139/217.2514

[2] C. A. Griffiths, S. S. Dimov, E. B. Brousseau, C. Chouquet, J. Gavillet, and S. Bigot, Investigation of surface treatment effects in micro-injection-moulding, Int. J. Adv. Manuf. Technol. 47 (2010) 99-110. https://doi.org/10.1007/s00170-009-2000-4

[3] O. M. Bataineh, B. E. Klamecki, Prediction of local part-mold and ejection force in injection molding, J. Manuf. Sci. Eng. 127 (2005) 598-604. https://doi.org/10.1115/1.1951785

[4] J. Zhao, R. H. Mayes, G. Chen, P. S. Chan, Z. J. Xiong, Polymer micromould design and micromoulding process, Plast. Rubber Compos. 32 (2003) 240-247.
https://doi.org/10.1179/146580103225002614

[5] J. Giboz, T. Copponnex, P. Mélé, Microinjection molding of thermoplastic polymers: A review, J. Micromech. Microeng. 17 (2007) R96. https://doi.org/10.1088/0960-1317/17/6/R02

[6] M. Sorgato, D. Masato, G. Lucchetta, Effects of machined cavity texture on ejection force in micro injection molding, Precis. Eng. 50 (2017) 440-448.
https://doi.org/10.1016/j.precisioneng.2017.06.019

[7] P. Parenti, D. Masato, M. Sorgato, G. Lucchetta, M. Annoni, Surface footprint in molds micromilling and effect on part demoldability in micro injection molding, J. Manuf. Process. 29 (2017) 160-174. https://doi.org/10.1016/j.jmapro.2017.05.024

[8] A. J. Pontes, A. S. Pouzada, Ejection force in tubular injection moldings. Part I: Effect of processing conditions, Polym. Eng. Sci. 44 (2004) 891-897. https://doi.org/10.1002/pen.20080

[9] K. Shen, L.-M. Chen, L. Jiang, Calculation of ejection force of hollow, thin walled, and injection moulded cones, Plast. Rubber Compos. 28 (1999) 341-345.
https://doi.org/10.1179/146580199101540493

[10] M. S. Correia, A. S. Miranda, M. C. Oliveira, C. A. Capela, A. S. Pouzada, Analysis of friction in the ejection of thermoplastic mouldings, Int. J. Adv. Manuf. Technol. 59 (2012) 977-986.
https://doi.org/10.1007/s00170-011-3573-2

[11] T. Sasaki, N. Koga, K. Shirai, Y. Kobayashi, A. Toyoshima, An experimental study on ejection forces of injection molding, Prec. Eng. 24 (2000) 270-273. https://doi.org/10.1016/S0141-6359(99)00039-2

[12] C. A. Griffiths, S. S. Dimov, S. G. Scholz, G. Tosello, A. Rees, Influence of injection and cavity pressure on the demoulding force in micro-injection moulding, J. Manuf. Sci. Eng. 136 (2014) 1087-1357. https://doi.org/10.1115/1.4026983

[13] N. Bhagavatula, D. Michalski, B. Lilly, and G. Glozer, Modelling and verification of ejection forces in thermoplastic injection moulding, Model. Simul. Mat. Sci. Eng. 12 (2004) S239.
https://doi.org/10.1088/0965-0393/12/3/S12

[14] A. Gopanna, S. P. Thomas, K. P. Rajan, R. Rajan, E. Rainosalo, J. Zavašnik, M. Chavali, Investigation of mechanical, dynamic mechanical, rheological and morphological properties of
blends based on polypropylene (PP) and cyclic olefin copolymer (COC), Eur. Polym. J. 108 (2018) 439-451. https://doi.org/10.1016/j.eurpolymj.2018.09.030

[15] S. Kwak, T. Kim, S. Park, and K. Lee, Layout and sizing of ejector pins for injection mould design using the wavelet transform, Proc. Inst. Mech. Eng., Part B 217 (2003) 463-473. https://doi.org/10.1243/095440503321628143

[16] Z. Wang, K.S. Lee, J.Y.H. Fuh, Z. Li, Y.F. Zhang, A.Y.C. Nee, D.C.H. Yang, Optimum ejector system design for plastic injection mould, Int. J. Comput. Appl. Technol. 9 (1996) 211-218. https://doi.org/10.1504/IJMPT.1996.036339

[17] A. S. Pouzada, E. C. Ferreira, and A. J. Pontes, Friction properties of moulding thermoplastics, Polym. Test. 25 (2006) 1017-1023 https://doi.org/10.1016/j.polymertesting.2006.06.009

[18] S. J. A. Rizvi, Effect of injection molding parameters on crystallinity and mechanical properties of isotactic polypropylene, International Journal of Plastics Technology, 21 (2017) 404-426. https://doi.org/10.1007/s12588-017-9194-3
blends based on polypropylene (PP) and cyclic olefin copolymer (COC), Eur. Polym. J. 108 (2018) 439-451. https://doi.org/10.1016/j.eurpolymj.2018.09.030

[15] S. Kwak, T. Kim, S. Park, and K. Lee, Layout and sizing of ejector pins for injection mould design using the wavelet transform, Proc. Inst. Mech. Eng., Part B 217 (2003) 463-473. https://doi.org/10.1243/095440503321628143

[16] Z. Wang, K.S. Lee, J.Y.H. Fuh, Z. Li, Y.F. Zhang, A.Y.C. Nee, D.C.H. Yang, Optimum ejector system design for plastic injection mould, Int. J. Comput. Appl. Technol. 9 (1996) 211-218. https://doi.org/10.1504/IJMPT.1996.036339

[17] A. S. Pouzada, E. C. Ferreira, and A. J. Pontes, Friction properties of moulding thermoplastics, Polym. Test. 25 (2006) 1017-1023 https://doi.org/10.1016/j.polymertesting.2006.06.009

[18] S. J. A. Rizvi, Effect of injection molding parameters on crystallinity and mechanical properties of isotactic polypropylene, International Journal of Plastics Technology, 21 (2017) 404-426. https://doi.org/10.1007/s12588-017-9194-3
# Evaluation of thermal properties of PEEK samples made by MEX

SPINA Roberto<fnref n="1" />,<fnref n="2" />,<fnref n="3" />,a* and GURRADO Nicola<fnref n="1" />,b

**Keywords:** Material Extrusion, PEEK, Thermal Properties

**Abstract.** The work studies the Polyether ether ketone (PEEK) specimens realized with the material extrusion (MEX) process, evaluating thermal material properties for potential application for polymer heat exchangers. The research investigates the influence of infill density on the thermal properties of PEEK components. A specific instrument measured PEEK specimens' thermal conductivity, thermal diffusivity, and specific heat. The procedure initially required a two-point calibration with references in the investigated ranges, followed by measurement with variable-filled specimens from sparse (20% infill) to full (100% infill). The results indicate that a decrease in the infill value causes a positive reduction in the thermal conductivity and specific heat. In contrast, the diffusivity remains stable with the infill variation.

**Introduction**

Heat exchangers (HXs) are indispensable in several industrial and engineering applications to eliminate the excessive heat generated during a process or operation by transferring heat between fluids in motion. The HX design results from the complex balance between maximizing the part's surface area and minimizing the pressure drop within the part. A large amount of heat exchange surface per unit of volume characterizes a compact HX. For this reason, maximizing heat transfer by reducing the total volume of the component can lead to a successful design. The combination of topological optimization in the design phase and Additive Manufacturing (AM) in the construction phase improves the expansion of the production space of HXs [1].

Polymer HXs, a particular class among HXs, are a promising alternative to metal HXs for critical applications requiring low weight, low surface energy, antifouling, and anti-corrosion properties. Despite these advantages, polymer HXs are limited by their low inherent thermal conductivity compared to metal HXs, usually two or three orders lower than metals such as stainless steel and aluminum. In heat transfer applications, where the wall thermal resistance has an appreciable impact on the overall thermal resistance, substituting polymers for metals can require significantly more area to achieve the same total heat transfer. The main strategies to reduce the impact of wall thermal resistance are using extremely thin wall thicknesses, lower than <100 µm, or adding a high thermal conductivity filler to the polymer to form a composite [2]. Advanced design topologies can also improve the low thermal conductivity of PHXs. The low conductivity of polymeric materials could be compensated by optimizing geometric parameters, reaching the performances of compact metallic HXs [3]. Heat exchanger geometry is a critical factor in its performance. Conventional manufacturing techniques cannot make these complex geometries. Additive manufacturing (AM) enables the fabrication of complex heat transfer features for next-generation polymer HXs. This is particularly relevant for PHXs due to their low processing temperatures and, thus, cost-effective manufacturing. The fabrication of a physical model allows the design evaluation and then the physical model testing. This would give further data to compare

<figure><img src="image_2528.png" /></figure>

<footnote n="1">¹Dip. di Meccanica, Matematica e Management, Politecnico di Bari, Italy</footnote>

<footnote n="2">²Istituto Nazionale di Fisica Nucleare (INFN) - Sezione di Bari, Italy</footnote>

<footnote n="3">³Consiglio Nazionale delle Ricerche - Istituto di Fotonica e Nanotecnologie (CNR-IFN), Italy</footnote>

<footnote>aroberto.spina@poliba.it, bnicola.gurrado@poliba.it</footnote>
# Evaluation of thermal properties of PEEK samples made by MEX

SPINA Roberto¹,²,³,a* and GURRADO Nicola¹,ᵇ

¹Dip. di Meccanica, Matematica e Management, Politecnico di Bari, Italy

²Istituto Nazionale di Fisica Nucleare (INFN) - Sezione di Bari, Italy

³Consiglio Nazionale delle Ricerche - Istituto di Fotonica e Nanotecnologie (CNR-IFN), Italy

aroberto.spina@poliba.it, bnicola.gurrado@poliba.it

**Keywords:** Material Extrusion, PEEK, Thermal Properties

**Abstract.** The work studies the Polyether ether ketone (PEEK) specimens realized with the material extrusion (MEX) process, evaluating thermal material properties for potential application for polymer heat exchangers. The research investigates the influence of infill density on the thermal properties of PEEK components. A specific instrument measured PEEK specimens' thermal conductivity, thermal diffusivity, and specific heat. The procedure initially required a two-point calibration with references in the investigated ranges, followed by measurement with variable-filled specimens from sparse (20% infill) to full (100% infill). The results indicate that a decrease in the infill value causes a positive reduction in the thermal conductivity and specific heat. In contrast, the diffusivity remains stable with the infill variation.

**Introduction**

Heat exchangers (HXs) are indispensable in several industrial and engineering applications to eliminate the excessive heat generated during a process or operation by transferring heat between fluids in motion. The HX design results from the complex balance between maximizing the part's surface area and minimizing the pressure drop within the part. A large amount of heat exchange surface per unit of volume characterizes a compact HX. For this reason, maximizing heat transfer by reducing the total volume of the component can lead to a successful design. The combination of topological optimization in the design phase and Additive Manufacturing (AM) in the construction phase improves the expansion of the production space of HXs [1].

Polymer HXs, a particular class among HXs, are a promising alternative to metal HXs for critical applications requiring low weight, low surface energy, antifouling, and anti-corrosion properties. Despite these advantages, polymer HXs are limited by their low inherent thermal conductivity compared to metal HXs, usually two or three orders lower than metals such as stainless steel and aluminum. In heat transfer applications, where the wall thermal resistance has an appreciable impact on the overall thermal resistance, substituting polymers for metals can require significantly more area to achieve the same total heat transfer. The main strategies to reduce the impact of wall thermal resistance are using extremely thin wall thicknesses, lower than <100 µm, or adding a high thermal conductivity filler to the polymer to form a composite [2]. Advanced design topologies can also improve the low thermal conductivity of PHXs. The low conductivity of polymeric materials could be compensated by optimizing geometric parameters, reaching the performances of compact metallic HXs [3]. Heat exchanger geometry is a critical factor in its performance. Conventional manufacturing techniques cannot make these complex geometries. Additive manufacturing (AM) enables the fabrication of complex heat transfer features for next-generation polymer HXs. This is particularly relevant for PHXs due to their low processing temperatures and, thus, cost-effective manufacturing. The fabrication of a physical model allows the design evaluation and then the physical model testing. This would give further data to compare

<figure><img src="image_2521.png" /></figure>
to the analytical and numerical results gained and further evidence of the design's practical use for the given application [4].

This work investigates the thermal properties of PEEK specimens realized with the Material Extrusion (MEX) process. PEEK has excellent potential in HXs application due to its chemical resistance and mechanical and thermal properties. For this reason, it is crucial to investigate the influence of infill density on the thermal properties of PEEK components by using an instrumented measuring system to determine the thermal conductivity, thermal diffusivity, and specific heat.

## Materials and Methods

Polyether ether ketone (PEEK), a semicrystalline thermoplastic, is among the world's highest-performing functional materials due to its excellent biocompatibility, chemical resistance, and mechanical and thermal properties, which are retained at high temperatures. 1.75 mm diameter filaments were used for PEEK (naturally unfilled - code KT-820-NT) and PEEK CF (filled with 30% carbon fibers - code KT-820-CF30). The two materials were characterized by a different color, a variable not considered during this analysis [5]. The primary material data supplied by Solvay Group (Bruxelles, Belgium) are reported in Table 1.

The specimens were realized using the FUNMAT HT, a Fused Filament Fabrication (FFF) printer produced by Intamsys Technology Co., Ltd. (Shanghai, China). This printer had a build volume of 260×260×260 mm³. All samples with dimensions 100×10×5 mm³ were printed with a layer height of 200 µm, an infill of 20%, 60%, and 100% with an internal grid pattern, three bottom and three top layers, and three walls (Fig. 1). The printer nozzle was 600 µm diameter. Specimens were printed flat on the build platform (XY plane) with a printing speed of 25 mm/s, a nozzle temperature of 410°C, a build plate of 120°C, and a heating chamber of 90°C. Three specimens per time were simultaneously printed, keeping the printing parameters constant after the initial tuning to evaluate the thermal properties, not the AM process.

<table><caption>Table 1: Material data [6]</caption><thead><tr><th>Physical property</th><th>PEEK (KT-820-NT)</th><th>PEEK CF (KT-820-CF30)</th></tr></thead><tbody><tr><td>Density ρ</td><td>1.30 [g/cm³]</td><td>1.41 [g/cm³]</td></tr><tr><td>Glass transition temperature T<sub>g</sub></td><td>150 [°C]</td><td>150 [°C]</td></tr><tr><td>Melt temperature T<sub>m</sub></td><td>340 [°C]</td><td>340 [°C]</td></tr><tr><td>Thermal conductivity λ</td><td>0.24 [W/m×°C]</td><td>0.37 [W/m×°C]</td></tr><tr><td>Specific heat capacity c<sub>p</sub></td><td>2.15 [kJ/Kg×°C]</td><td>1.62 [kJ/Kg×°C]</td></tr><tr><td>Tensile Strength σ<sub>R</sub></td><td>96 [MPa]</td><td>217 [MPa]</td></tr><tr><td>Young's modulus E</td><td>3.5 [GPa]</td><td>19.7 [GPa]</td></tr><tr><td>Elongation at break</td><td>20-30 [%]</td><td>2 [%]</td></tr></tbody></table>
to the analytical and numerical results gained and further evidence of the design's practical use for the given application [4].

This work investigates the thermal properties of PEEK specimens realized with the Material Extrusion (MEX) process. PEEK has excellent potential in HXs application due to its chemical resistance and mechanical and thermal properties. For this reason, it is crucial to investigate the influence of infill density on the thermal properties of PEEK components by using an instrumented measuring system to determine the thermal conductivity, thermal diffusivity, and specific heat.

## Materials and Methods

Polyether ether ketone (PEEK), a semicrystalline thermoplastic, is among the world's highest-performing functional materials due to its excellent biocompatibility, chemical resistance, and mechanical and thermal properties, which are retained at high temperatures. 1.75 mm diameter filaments were used for PEEK (naturally unfilled - code KT-820-NT) and PEEK CF (filled with 30% carbon fibers - code KT-820-CF30). The two materials were characterized by a different color, a variable not considered during this analysis [5]. The primary material data supplied by Solvay Group (Bruxelles, Belgium) are reported in Table 1.

The specimens were realized using the FUNMAT HT, a Fused Filament Fabrication (FFF) printer produced by Intamsys Technology Co., Ltd. (Shanghai, China). This printer had a build volume of 260×260×260 mm³. All samples with dimensions 100×10×5 mm³ were printed with a layer height of 200 µm, an infill of 20%, 60%, and 100% with an internal grid pattern, three bottom and three top layers, and three walls (Fig. 1). The printer nozzle was 600 µm diameter. Specimens were printed flat on the build platform (XY plane) with a printing speed of 25 mm/s, a nozzle temperature of 410°C, a build plate of 120°C, and a heating chamber of 90°C. Three specimens per time were simultaneously printed, keeping the printing parameters constant after the initial tuning to evaluate the thermal properties, not the AM process.

<table><caption>Table 1: Material data [6]</caption><thead><tr><th>Physical property</th><th>PEEK (KT-820-NT)</th><th>PEEK CF (KT-820-CF30)</th></tr></thead><tbody><tr><td>Density ρ</td><td>1.30 [g/cm³]</td><td>1.41 [g/cm³]</td></tr><tr><td>Glass transition temperature T<sub>g</sub></td><td>150 [°C]</td><td>150 [°C]</td></tr><tr><td>Melt temperature T<sub>m</sub></td><td>340 [°C]</td><td>340 [°C]</td></tr><tr><td>Thermal conductivity λ</td><td>0.24 [W/m×°C]</td><td>0.37 [W/m×°C]</td></tr><tr><td>Specific heat capacity c<sub>p</sub></td><td>2.15 [kJ/Kg×°C]</td><td>1.62 [kJ/Kg×°C]</td></tr><tr><td>Tensile Strength σ<sub>R</sub></td><td>96 [MPa]</td><td>217 [MPa]</td></tr><tr><td>Young's modulus E</td><td>3.5 [GPa]</td><td>19.7 [GPa]</td></tr><tr><td>Elongation at break</td><td>20-30 [%]</td><td>2 [%]</td></tr></tbody></table>
<figure><img src="image_2529.png" /><figcaption>Fig. 1. Specimens in (a) isometric view and (b) top view (all dimensions in mm).</figcaption></figure>

The thermal conductivity of all specimens was then measured using an instrument supplied by Linseis Messgeraete GmbH (Selb, Germany) based on the Transient Hot-Point (THP) method. This instrumentation needed any sample preparation. The THP method estimated the thermal signal's propagation time t through a material sample by applying a short-duration heat pulse to the thermal sensor. Due to the specific layout, the constant electric current flowing through the sensor generated an inhomogeneous temperature profile within the specimens. The THP sensor, an evolution of the transient hot-strip technique, was developed to measure small or anisotropic samples by arranging nickel (laminated version) in a printed circuit foil between two insulating polyimide layers. The sensor, with an overall size of 65×5×0.06 mm³, was able to measure thermal conductivity in the range of 0.1÷2 W/m×K between -150 and 200°C. The bridge was inherently balanced at a uniform temperature, and no nulling was required before running a test. An electric current through the unequally spaced strips established an inhomogeneous temperature profile, resulting in an unbalanced condition. The sensor produced an offset-free output signal of high sensitivity as a measure of the thermal conductivity of the surrounding specimen [7].

The theory behind the hot point sensor was based on a small-point heat source. The thermal conductivity $\lambda$ and the thermal diffusivity $\alpha$ were determined from a single curve by plotting the temperature rise $\Delta T$ on a $t^{1/2}$ time scale and locating the linear part of the curve for long measurement times. $\lambda$ and $\alpha$ were computed as

$$ \lambda = \frac{\phi}{4\pi \times r \times n} \qquad (1) $$

$$ \alpha = \frac{1}{\pi} \times \left( \frac{n \times r}{m} \right)^2 \qquad (2) $$

where $\phi$ was the sensor heat flow rate, $r$ was the effective radius of the sensor (constant), and $n$ and $m$ were the intercept and the slope of the temperature signal $\Delta T$ versus the inverse square of time $t^{1/2}$. The specific heat capacity $c_p$ and the thermal effusivity $e$ were determined using the following equations, give the density $\rho$:

$$ c_p = \frac{\lambda}{\alpha \times \rho} \qquad (3) $$
<figure><img src="image_2522.png" /><figcaption>Fig. 1. Specimens in (a) isometric view and (b) top view (all dimensions in mm).</figcaption></figure>

The thermal conductivity of all specimens was then measured using an instrument supplied by Linseis Messgeraete GmbH (Selb, Germany) based on the Transient Hot-Point (THP) method. This instrumentation needed any sample preparation. The THP method estimated the thermal signal's propagation time t through a material sample by applying a short-duration heat pulse to the thermal sensor. Due to the specific layout, the constant electric current flowing through the sensor generated an inhomogeneous temperature profile within the specimens. The THP sensor, an evolution of the transient hot-strip technique, was developed to measure small or anisotropic samples by arranging nickel (laminated version) in a printed circuit foil between two insulating polyimide layers. The sensor, with an overall size of 65×5×0.06 mm³, was able to measure thermal conductivity in the range of 0.1÷2 W/m×K between -150 and 200°C. The bridge was inherently balanced at a uniform temperature, and no nulling was required before running a test. An electric current through the unequally spaced strips established an inhomogeneous temperature profile, resulting in an unbalanced condition. The sensor produced an offset-free output signal of high sensitivity as a measure of the thermal conductivity of the surrounding specimen [7].

The theory behind the hot point sensor was based on a small-point heat source. The thermal conductivity λ and the thermal diffusivity α were determined from a single curve by plotting the temperature rise ΔT on a t¹/² time scale and locating the linear part of the curve for long measurement times. λ and α were computed as

$$ \lambda = \frac{\phi}{4\pi \times r \times n} \qquad (1) $$

$$ \alpha = \frac{1}{\pi} \times \left( \frac{n \times r}{m} \right)^2 \qquad (2) $$

where φ was the sensor heat flow rate, r was the effective radius of the sensor (constant), and n and m were the intercept and the slope of the temperature signal ΔT versus the inverse square of time t¹/². The specific heat capacity cₚ and the thermal effusivity e were determined using the following equations, give the density ρ:

$$ c_p = \frac{\lambda}{\alpha \times \rho} \qquad (3) $$
$$e = \frac{\lambda}{\sqrt{\alpha}} = \sqrt{\lambda \times \rho \times c_p} \qquad (4)$$

## Results and Discussion

Before testing the two PEEK grades, the sensor was calibrated with some standards as reference materials, such as Polymethylmethacrylate (PMMA) and Polyacetal (POM-C), the data of which are reported in Table 2. A two-point calibration was used by re-scaling the sensor output, correcting both slope and offset errors of the sensor response. This calibration was employed because the sensor output was reasonably linear over the measurement range. The PMMA conductivity was near the low end of the measurement range, whereas the POM-C was near the high end.

The thermal conductivities of unfilled and filled PEEK materials were within the range of the reference materials. The tests were conducted at room temperature according to UNI-EN ISO 22007 standard, with a maximum execution time $t_{max}$ of 60 s and a pulse supply current of 50 mA. The calibration procedure allowed the sensor flow rate $\phi$ correlation with the thermal conductivity $\lambda$ and diffusivity $e$ for these reference materials, identifying constants from the interpolation of the calibration curve [8].

<table><caption>Table 2: Material data of the reference materials.</caption><thead><tr><th>Physical property</th><th>PMMA</th><th>POM-C</th></tr></thead><tbody><tr><td>Density ρ</td><td>1.19 [g/cm<sup>3</sup>]</td><td>1.41 [g/cm<sup>3</sup>]</td></tr><tr><td>Glass transition temperature T<sub>g</sub></td><td>117 [°C]</td><td>-60 [°C]</td></tr><tr><td>Melt temperature T<sub>m</sub></td><td>- [°C]</td><td>166 [°C]</td></tr><tr><td>Thermal conductivity λ</td><td>0.19 [W/m×°C]</td><td>0.39 [W/m×°C]</td></tr><tr><td>Specific heat capacity c<sub>p</sub></td><td>2.15 [kJ/Kg×°C]</td><td>1.40 [kJ/Kg×°C]</td></tr><tr><td>Tensile Strength σ<sub>R</sub></td><td>77 [MPa]</td><td>67 [MPa]</td></tr><tr><td>Young's modulus E</td><td>3.3 [GPa]</td><td>2.8 [GPa]</td></tr><tr><td>Elongation at break</td><td>5.5 [%]</td><td>32 [%]</td></tr></tbody></table>

The test of the unfilled PEEK and filled PEEK specimens with different infill was reported in Fig.2. The infill variable was crucial, as previous research revealed [9]. The temperature rise $\Delta T$ rapidly increased in the first time steps, and it became stable after 16 seconds, remaining constant. The maximum time $t_{max}$ was sufficient for reliable results. The maximum temperature variation $\Delta T_{max}$ recorded during the test was below 5°C. The initial temperature was equal to the room temperature for studying the air conditioning case. The higher the temperature rise, the lower the infill value. Identical results were identified by plotting the gradient $\Delta T/\Delta t$ vs. $t^{-1/2}$ (Fig.3), where the $t^{-1/2}$ equal to 0.25 s$^{-1/2}$ corresponded to t of 16 s. Using the inverse square of time $t^{-1/2}$ instead of the logarithm of time $\log(t)$ was functional to represent the graph abscissa between 0 and 1 for t greater than 1 s. The maximum gradient $\Delta T/\Delta t$ slightly changed with the infill value, remaining in the same interval for both materials. The maximum value of the $\Delta T/\Delta t$ was inverse to the infill, pointing out that the same heat flux generated a higher temperature rise.
$$e = \frac{\lambda}{\sqrt{\alpha}} = \sqrt{\lambda \times \rho \times c_p} \qquad (4)$$

## Results and Discussion

Before testing the two PEEK grades, the sensor was calibrated with some standards as reference materials, such as Polymethylmethacrylate (PMMA) and Polyacetal (POM-C), the data of which are reported in Table 2. A two-point calibration was used by re-scaling the sensor output, correcting both slope and offset errors of the sensor response. This calibration was employed because the sensor output was reasonably linear over the measurement range. The PMMA conductivity was near the low end of the measurement range, whereas the POM-C was near the high end.

The thermal conductivities of unfilled and filled PEEK materials were within the range of the reference materials. The tests were conducted at room temperature according to UNI-EN ISO 22007 standard, with a maximum execution time $t_{max}$ of 60 s and a pulse supply current of 50 mA. The calibration procedure allowed the sensor flow rate $\phi$ correlation with the thermal conductivity $\lambda$ and diffusivity $e$ for these reference materials, identifying constants from the interpolation of the calibration curve [8].

<table><caption>Table 2: Material data of the reference materials.</caption><thead><tr><th>Physical property</th><th>PMMA</th><th>POM-C</th></tr></thead><tbody><tr><td>Density ρ</td><td>1.19 [g/cm<sup>3</sup>]</td><td>1.41 [g/cm<sup>3</sup>]</td></tr><tr><td>Glass transition temperature T<sub>g</sub></td><td>117 [°C]</td><td>-60 [°C]</td></tr><tr><td>Melt temperature T<sub>m</sub></td><td>- [°C]</td><td>166 [°C]</td></tr><tr><td>Thermal conductivity λ</td><td>0.19 [W/m×°C]</td><td>0.39 [W/m×°C]</td></tr><tr><td>Specific heat capacity c<sub>p</sub></td><td>2.15 [kJ/Kg×°C]</td><td>1.40 [kJ/Kg×°C]</td></tr><tr><td>Tensile Strength σ<sub>R</sub></td><td>77 [MPa]</td><td>67 [MPa]</td></tr><tr><td>Young's modulus E</td><td>3.3 [GPa]</td><td>2.8 [GPa]</td></tr><tr><td>Elongation at break</td><td>5.5 [%]</td><td>32 [%]</td></tr></tbody></table>

The test of the unfilled PEEK and filled PEEK specimens with different infill was reported in Fig.2. The infill variable was crucial, as previous research revealed [9]. The temperature rise $\Delta T$ rapidly increased in the first time steps, and it became stable after 16 seconds, remaining constant. The maximum time $t_{max}$ was sufficient for reliable results. The maximum temperature variation $\Delta T_{max}$ recorded during the test was below 5°C. The initial temperature was equal to the room temperature for studying the air conditioning case. The higher the temperature rise, the lower the infill value. Identical results were identified by plotting the gradient $\Delta T/\Delta t$ vs. $t^{-1/2}$ (Fig.3), where the $t^{-1/2}$ equal to 0.25 s$^{-1/2}$ corresponded to $t$ of 16 s. Using the inverse square of time $t^{-1/2}$ instead of the logarithm of time $\log(t)$ was functional to represent the graph abscissa between 0 and 1 for $t$ greater than 1 s. The maximum gradient $\Delta T/\Delta t$ slightly changed with the infill value, remaining in the same interval for both materials. The maximum value of the $\Delta T/\Delta t$ was inverse to the infill, pointing out that the same heat flux generated a higher temperature rise.
<figure><img src="image_2530.png" /><figcaption>Figure 2. Temperature rise $\Delta T$ vs. time $t$ for PEEK (a) and PEEK CF (b) specimens.</figcaption></figure>

<figure><img src="image_2531.png" /><figcaption>Figure 3. Gradient $\Delta T/\Delta t$ vs. time $t^{-1/2}$ for PEEK (a) and PEEK CF (b) specimens.</figcaption></figure>

<figure><img src="image_2532.png" /><figcaption>Figure 4. Thermal conductivity $\lambda$ (a) and diffusivity $\alpha$ (b) vs. infill.</figcaption></figure>

Once the measurement process was analyzed in terms of the THP signal, the following step was the analysis of the thermal properties. Figure 4 reports the variation of the thermal conductivity $\lambda$ (a) and diffusivity $\alpha$ (b) with infill. A decrease in the infill value caused a positive reduction in the thermal conductivity $\lambda$. For the lowest value of the infill, the thermal conductivity was quite the same for both PEEK materials. In contrast, for the highest value of the infill, the contribution of
<figure><img src="image_2523.png" /><figcaption>Figure 2. Temperature rise $\Delta T$ vs. time $t$ for PEEK (a) and PEEK CF (b) specimens.</figcaption></figure>

<figure><img src="image_2524.png" /><figcaption>Figure 3. Gradient $\Delta T/\Delta t$ vs. time $t^{-1/2}$ for PEEK (a) and PEEK CF (b) specimens.</figcaption></figure>

<figure><img src="image_2525.png" /><figcaption>Figure 4. Thermal conductivity $\lambda$ (a) and diffusivity $\alpha$ (b) vs. infill.</figcaption></figure>

Once the measurement process was analyzed in terms of the THP signal, the following step was the analysis of the thermal properties. Figure 4 reports the variation of the thermal conductivity $\lambda$ (a) and diffusivity $\alpha$ (b) with infill. A decrease in the infill value caused a positive reduction in the thermal conductivity $\lambda$. For the lowest value of the infill, the thermal conductivity was quite the same for both PEEK materials. In contrast, for the highest value of the infill, the contribution of
the carbon fiber fillers was more evident. The behavior of the thermal diffusivity $\alpha$ was different because it remained pretty stable with the infill variation for both materials and different infill.

Figure 5 reports the change of the specific heat $c_p$ (a) and thermal effusivity $e$ (b) with infill. The tendency of the specific heat $c_p$ differed between the two PEEK materials. The unfilled PEEK had a linear correlation with the infill, with a $c_p$ reduction with an infill decrease. The behavior of filled PEEK presented a significant variation with an infill of 60%, remaining stable below this value. For the lowest infill, the specific heat $c_p$ was quite the same, with a small contribution of the carbon fiber. The behavior of the thermal effusivity $e$ also differed in the two PEEK materials. It positively increased with infill in the filled PEEK. In the case of unfilled PEEK, $e$ was relatively stable until the 60% infill and rapidly decreased for lower infill values.

<figure><img src="image_2533.png" /><figcaption>Figure 5. Specific heat $c_p$ (a) and thermal effusivity $e$ (b) vs. infill.</figcaption></figure>

## Conclusions

This work investigated the variation of the thermal properties of additively manufactured PEEK with different infill and carbon fiber content. In particular, PEEK specimens were examined using the transient hot point (THP) method after being produced with an additive material extraction (MEX) process with different infill values.

The following conclusions can be drawn from the experimental results. A short time was needed with THP to reach the stationary conditions for the thermal analysis, independently from the material, fiber content, and infill values. The following data analysis pointed out that a decrease in the infill value caused a positive reduction in the thermal conductivity $\lambda$. At the same time, effusivity $e$ was not influenced by the infill variation.

To be adopted in polymer exchangers made with MEX, further analysis is required to improve these results to composite materials with high carbon fiber content.

## Acknowledgments

The authors wish to thank Prof Luigi Galantucci, Prof Fulvio Lavecchia, and Luigi Morfini of Politecnico di Bari for their suggestions, Claudio Filippo of M. Penati srl and Erika Hahn of Linseis Messgeraete GmbH for the technical support.

The Project was funded under the program Department of Excellence - Law number 232/2016 (Grant No. CUP - D93C23000100001), the National Recovery and Resilience Plan (NRRP), Mission 4 Component 2 Investment 1.3 - Call for tender No. 341 of 15/03/2022 of the Italian Ministry of University and Research (MUR), funded by the European Union - NextGenerationEU, and the RIPARTI funding (assegni di Ricerca per ripartire con le Imprese) of the Apulia Region.
the carbon fiber fillers was more evident. The behavior of the thermal diffusivity $\alpha$ was different because it remained pretty stable with the infill variation for both materials and different infill.

Figure 5 reports the change of the specific heat $c_p$ (a) and thermal effusivity $e$ (b) with infill. The tendency of the specific heat $c_p$ differed between the two PEEK materials. The unfilled PEEK had a linear correlation with the infill, with a $c_p$ reduction with an infill decrease. The behavior of filled PEEK presented a significant variation with an infill of 60%, remaining stable below this value. For the lowest infill, the specific heat $c_p$ was quite the same, with a small contribution of the carbon fiber. The behavior of the thermal effusivity $e$ also differed in the two PEEK materials. It positively increased with infill in the filled PEEK. In the case of unfilled PEEK, $e$ was relatively stable until the 60% infill and rapidly decreased for lower infill values.

<figure><img src="image_2526.png" /><figcaption>Figure 5. Specific heat $c_p$ (a) and thermal effusivity $e$ (b) vs. infill.</figcaption></figure>

## Conclusions

This work investigated the variation of the thermal properties of additively manufactured PEEK with different infill and carbon fiber content. In particular, PEEK specimens were examined using the transient hot point (THP) method after being produced with an additive material extraction (MEX) process with different infill values.

The following conclusions can be drawn from the experimental results. A short time was needed with THP to reach the stationary conditions for the thermal analysis, independently from the material, fiber content, and infill values. The following data analysis pointed out that a decrease in the infill value caused a positive reduction in the thermal conductivity $\lambda$. At the same time, effusivity $e$ was not influenced by the infill variation.

To be adopted in polymer exchangers made with MEX, further analysis is required to improve these results to composite materials with high carbon fiber content.

## Acknowledgments

The authors wish to thank Prof Luigi Galantucci, Prof Fulvio Lavecchia, and Luigi Morfini of Politecnico di Bari for their suggestions, Claudio Filippo of M. Penati srl and Erika Hahn of Linseis Messeraete GmbH for the technical support.

The Project was funded under the program Department of Excellence - Law number 232/2016 (Grant No. CUP - D93C23000100001), the National Recovery and Resilience Plan (NRRP), Mission 4 Component 2 Investment 1.3 - Call for tender No. 341 of 15/03/2022 of the Italian Ministry of University and Research (MUR), funded by the European Union - NextGenerationEU, and the RIPARTI funding (assegni di Ricerca per ripartire con le Imprese) of the Apulia Region.
References

[1] F. Careri et al. Additive manufacturing of heat exchangers in aerospace applications: A review. Applied Thermal Engineering 235 (2023) 121387. https://doi.org/10.1016/j.applthermaleng.2023.121387

[2] X. Chen et al. Recent research developments in polymer heat exchangers - A review. Renewable and Sustainable Energy Reviews 60 (2016) 1367-1386. https://doi.org/10.1016/j.rser.2016.03.024

[3] B. Ahmadi, S. Bigham. Performance Evaluation of hi-k Lung-inspired 3D-printed Polymer Heat Exchangers. Applied Thermal Engineering 204 (2022) 117993. https://doi.org/10.1016/j.applthermaleng.2021.117993

[4] O. Bonner-Hutton et al. Analysis of gyroid heat exchangers for superconducting electric motors. Materials Today: Proceedings. in Press. https://doi.org/10.1016/j.matpr.2023.03.780

[5] R. Spina, Performance analysis of colored PLA products with a fused filament fabrication process. Polymers 11 (2019) 1984. https://doi.org/10.3390/polym11121984

[6] KetaSpire® PEEK Design and Processing Guide. Information on: https://www.solvay.com/.

[7] R. Model, R. Stosch, U. Hammerschmidt. Virtual experiment design for the Transient Hot-Bridge sensor. International Journal of Thermophysics, 28 (2007) 1447-1460. https://doi.org/10.1007/s10765-007-0152-8

[8] K.D. Antoniadis et al. Reference Correlations for the Thermal Conductivity of Solid BK7, PMMA, Pyrex 7740, Pyroceram 9606 and SS304. International Journal of Thermophysics (2020) 41:98. https://doi.org/10.1007/s10765-020-02678-9

[9] L. Morfini, N. Gurrado, R. Spina. Effect of process parameters on the thermal properties of material extruded AM parts. Materials Research Proceedings. 35 (2023) 225-231. https://doi.org/10.21741/9781644902714-27
## References

[1] F. Careri et al. Additive manufacturing of heat exchangers in aerospace applications: A review. Applied Thermal Engineering 235 (2023) 121387. https://doi.org/10.1016/j.applthermaleng.2023.121387

[2] X. Chen et al. Recent research developments in polymer heat exchangers - A review. Renewable and Sustainable Energy Reviews 60 (2016) 1367-1386. https://doi.org/10.1016/j.rser.2016.03.024

[3] B. Ahmadi, S. Bigham. Performance Evaluation of hi-k Lung-inspired 3D-printed Polymer Heat Exchangers. Applied Thermal Engineering 204 (2022) 117993. https://doi.org/10.1016/j.applthermaleng.2021.117993

[4] O. Bonner-Hutton et al. Analysis of gyroid heat exchangers for superconducting electric motors. Materials Today: Proceedings. in Press. https://doi.org/10.1016/j.matpr.2023.03.780

[5] R. Spina, Performance analysis of colored PLA products with a fused filament fabrication process. Polymers 11 (2019) 1984. https://doi.org/10.3390/polym11121984

[6] KetaSpire® PEEK Design and Processing Guide. Information on: https://www.solvay.com/.

[7] R. Model, R. Stosch, U. Hammerschmidt. Virtual experiment design for the Transient Hot-Bridge sensor. International Journal of Thermophysics, 28 (2007) 1447-1460. https://doi.org/10.1007/s10765-007-0152-8

[8] K.D. Antoniadis et al. Reference Correlations for the Thermal Conductivity of Solid BK7, PMMA, Pyrex 7740, Pyroceram 9606 and SS304. International Journal of Thermophysics (2020) 41:98. https://doi.org/10.1007/s10765-020-02678-9

[9] L. Morfini, N. Gurrado, R. Spina. Effect of process parameters on the thermal properties of material extruded AM parts. Materials Research Proceedings. 35 (2023) 225-231. https://doi.org/10.21741/9781644902714-27
# Study of surface grinding of PEEK parts

SPINA Roberto<fnref n="1" />,<fnref n="2" />,<fnref n="3" />,a* and GURRADO Nicola<fnref n="1" />,ᵇ

**Keywords:** Surface Grinding, PEEK, Statistical Analysis

**Abstract.** The work studies the surface grinding of polyether ether ketone (PEEK) specimens, evaluating material properties and the machining process. An experimental procedure was implemented to collect data during machining to support statistical analysis. Statistical analysis was implemented, mainly based on material properties, which computes roughness achieved after machining by varying cutting speed, feed velocity, and cutting depth, giving helpful information to apply different configurations and strategies.

**Introduction**

Precision grinding is one of the primary manufacturing methods for removing materials for finishing surfaces on high-accuracy components, thanks to abrasive grits with different shapes randomly distributed on the grinding wheel. Compared to other machining operations, the material removal mechanism and relative interactions between grits and the workpiece are more complex [1]. The tool consists of randomly oriented, positioned, and shaped grits, acting as cutting edges and individually removing material from the workpiece to produce the final surface. Considering the stochastic nature of the abrasive wheel topography and the high number of process variables, achieving optimum conditions in a repeatable manner based only on experience is very low. Therefore, the process modeling is crucial to design a successful strategy. Once the abrasive wheel topography and grain properties are determined, chip thickness analysis makes force prediction possible. They established force equations for the ploughing and cutting phases, which need experimental calibration. Single grit tests were performed to understand the ploughing mechanism where the measured values are used to calculate the total process forces [2]. Grinding tools are realized in several shapes, sizes, and materials to be adapted to the functional properties of work surfaces for the specific application. The support structure, binder material, and abrasive grits remained the fundamental elements of a grinding tool through the years [3].

Grinding is a significant secondary process applied to parts made with additive manufacturing (AM) to improve the low surface quality resulting at the end of the deposition process. A strict correlation between the process parameters and surface roughness exists, in which the variation of the nozzle and chamber temperatures mainly influenced the roughness values. Poor-quality AM surfaces are obtained with high relative roughness values [4, 5]. Grinding can be combined with AM for improving, repairing, and remanufacturing AM components. This combination allows the full use of individual processes' capabilities while overcoming shortcomings. Because grinding is commonly used at pre- and post-processing stages, improvements are still needed to propose a stable hybrid technology combining additive and subtractive processes in a single system [6]. The non-homogeneous cooling conditions inherent to deposition may vary mechanical properties, leading to a different machining response regarding forces and power consumption, chip morphology, machined surface finish, and integrity. Moreover, residual stresses generated during grinding can lower the performance of the final ground component, with a significant reduction in

<figure><img src="image_2534.png" /></figure>

<footnote n="1">¹Dip. di Meccanica, Matematica e Management, Politecnico di Bari, Italy</footnote>

<footnote n="2">²Istituto Nazionale di Fisica Nucleare (INFN) - Sezione di Bari, Italy</footnote>

<footnote n="3">³Consiglio Nazionale delle Ricerche - Istituto di Fotonica e Nanotecnologie (CNR-IFN), Italy</footnote>

<footnote>aroberto.spina@poliba.it, bnicola.gurrado@poliba.it</footnote>
# Study of surface grinding of PEEK parts

SPINA Roberto<fnref n="1" />,<fnref n="2" />,<fnref n="3" />,a* and GURRADO Nicola<fnref n="1" />,ᵇ

**Keywords:** Surface Grinding, PEEK, Statistical Analysis

**Abstract.** The work studies the surface grinding of polyether ether ketone (PEEK) specimens, evaluating material properties and the machining process. An experimental procedure was implemented to collect data during machining to support statistical analysis. Statistical analysis was implemented, mainly based on material properties, which computes roughness achieved after machining by varying cutting speed, feed velocity, and cutting depth, giving helpful information to apply different configurations and strategies.

**Introduction**

Precision grinding is one of the primary manufacturing methods for removing materials for finishing surfaces on high-accuracy components, thanks to abrasive grits with different shapes randomly distributed on the grinding wheel. Compared to other machining operations, the material removal mechanism and relative interactions between grits and the workpiece are more complex [1]. The tool consists of randomly oriented, positioned, and shaped grits, acting as cutting edges and individually removing material from the workpiece to produce the final surface. Considering the stochastic nature of the abrasive wheel topography and the high number of process variables, achieving optimum conditions in a repeatable manner based only on experience is very low. Therefore, the process modeling is crucial to design a successful strategy. Once the abrasive wheel topography and grain properties are determined, chip thickness analysis makes force prediction possible. They established force equations for the ploughing and cutting phases, which need experimental calibration. Single grit tests were performed to understand the ploughing mechanism where the measured values are used to calculate the total process forces [2]. Grinding tools are realized in several shapes, sizes, and materials to be adapted to the functional properties of work surfaces for the specific application. The support structure, binder material, and abrasive grits remained the fundamental elements of a grinding tool through the years [3].

Grinding is a significant secondary process applied to parts made with additive manufacturing (AM) to improve the low surface quality resulting at the end of the deposition process. A strict correlation between the process parameters and surface roughness exists, in which the variation of the nozzle and chamber temperatures mainly influenced the roughness values. Poor-quality AM surfaces are obtained with high relative roughness values [4, 5]. Grinding can be combined with AM for improving, repairing, and remanufacturing AM components. This combination allows the full use of individual processes' capabilities while overcoming shortcomings. Because grinding is commonly used at pre- and post-processing stages, improvements are still needed to propose a stable hybrid technology combining additive and subtractive processes in a single system [6]. The non-homogeneous cooling conditions inherent to deposition may vary mechanical properties, leading to a different machining response regarding forces and power consumption, chip morphology, machined surface finish, and integrity. Moreover, residual stresses generated during grinding can lower the performance of the final ground component, with a significant reduction in

<figure><img src="image_2527.png" /></figure>

<footnote n="1">¹Dip. di Meccanica, Matematica e Management, Politecnico di Bari, Italy</footnote>

<footnote n="2">²Istituto Nazionale di Fisica Nucleare (INFN) - Sezione di Bari, Italy</footnote>

<footnote n="3">³Consiglio Nazionale delle Ricerche - Istituto di Fotonica e Nanotecnologie (CNR-IFN), Italy</footnote>

<footnote>aroberto.spina@poliba.it, bnicola.gurrado@poliba.it</footnote>
fatigue life and the development of subsurface cracking if the grinding process is not accurately controlled [7].

The work aim is to investigate the surface grinding of polyether ether ketone (PEEK) specimens, evaluating material properties and the machining process. The paper initially investigated the setup of the experimental procedure to collect data during grinding. Statistical analysis was then implemented, mainly based on material properties, to compute roughness achieved after grinding by varying cutting speed, feed velocity, and cutting depth. As a result, the process know-how was implemented, providing helpful information for applying different configurations and strategies.

## Materials and Methods

Polyether ether ketone (PEEK), a semicrystalline thermoplastic, is among the world's highest-performing functional materials due to its excellent biocompatibility, chemical resistance, and mechanical and thermal properties, which are retained at high temperatures. This polymer is often used in demanding aerospace, automotive, chemical, and medical applications. A 1.75 mm filament diameter was used. The primary data are reported in Table 1.

The specimens were realized using the FUNMAT HT, a Fused Filament Fabrication (FFF) printer produced by Intamsys Technology Co., Ltd. (Shanghai, China). This printer had a build volume of 260×260×260 mm³. All samples with dimensions 30×60×5 mm³ were printed with a layer height of 300 µm, an infill of 20% with an internal grid pattern, three bottom and three top layers, and five walls (Fig. 1). The selected numbers of walls and layers were chosen to sufficiently resist to the grinding loads whereas reducing the final cost of the AM specimens. The printer nozzle was 600 µm diameter. All specimens were printed flat on the build platform (XY plane) with a printing speed of 25 mm/s, the nozzle temperature of 410°C, the build plate, and the heating chamber equal to 120°C and 90°C, respectively. For this study, the printing parameters were kept constant after the initial tuning to evaluate the grinding process, not the AM process.

<figure><img src="image_2535.png" /><figcaption>Fig. 1. Specimen with internal structure (a) and final configuration (b) (all dimensions in mm).</figcaption></figure>

<table><caption>Table 1: Material data [8]</caption><thead><tr><td>Physical property</td><td>Value</td><td>Physical property</td><td>Value</td></tr></thead><tbody><tr><td>Density ρ</td><td>1.30 [g/cm³]</td><td>Tensile Strength σ<sub>R</sub></td><td>99.9 [MPa]</td></tr><tr><td>Glass transition temperature T<sub>g</sub></td><td>143 [°C]</td><td>Young's modulus E</td><td>3.74 [GPa]</td></tr><tr><td>Melt temperature T<sub>m</sub></td><td>343 [°C]</td><td>Elongation at break</td><td>9.1 [%]</td></tr><tr><td>Thermal conductivity λ</td><td>0.29 [W/m×K]</td><td>Impact strength</td><td>7.1 [kJ/m²]</td></tr></tbody></table>

The specimens were then processed on an instrumented grinding machine, a Planomat 408 CNC machine (Blohm Jung GmbH, Hamburg, Germany), designed and implemented in previous
fatigue life and the development of subsurface cracking if the grinding process is not accurately controlled [7].

The work aim is to investigate the surface grinding of polyether ether ketone (PEEK) specimens, evaluating material properties and the machining process. The paper initially investigated the setup of the experimental procedure to collect data during grinding. Statistical analysis was then implemented, mainly based on material properties, to compute roughness achieved after grinding by varying cutting speed, feed velocity, and cutting depth. As a result, the process know-how was implemented, providing helpful information for applying different configurations and strategies.

## Materials and Methods

Polyether ether ketone (PEEK), a semicrystalline thermoplastic, is among the world's highest-performing functional materials due to its excellent biocompatibility, chemical resistance, and mechanical and thermal properties, which are retained at high temperatures. This polymer is often used in demanding aerospace, automotive, chemical, and medical applications. A 1.75 mm filament diameter was used. The primary data are reported in Table 1.

The specimens were realized using the FUNMAT HT, a Fused Filament Fabrication (FFF) printer produced by Intamsys Technology Co., Ltd. (Shanghai, China). This printer had a build volume of 260×260×260 mm³. All samples with dimensions 30×60×5 mm³ were printed with a layer height of 300 µm, an infill of 20% with an internal grid pattern, three bottom and three top layers, and five walls (Fig. 1). The selected numbers of walls and layers were chosen to sufficiently resist to the grinding loads whereas reducing the final cost of the AM specimens. The printer nozzle was 600 µm diameter. All specimens were printed flat on the build platform (XY plane) with a printing speed of 25 mm/s, the nozzle temperature of 410°C, the build plate, and the heating chamber equal to 120°C and 90°C, respectively. For this study, the printing parameters were kept constant after the initial tuning to evaluate the grinding process, not the AM process.

<figure><img src="image_2528.png" /><figcaption>Fig. 1. Specimen with internal structure (a) and final configuration (b) (all dimensions in mm).</figcaption></figure>

<table><caption>Table 1: Material data [8]</caption><thead><tr><td>Physical property</td><td>Value</td><td>Physical property</td><td>Value</td></tr></thead><tbody><tr><td>Density ρ</td><td>1.30 [g/cm³]</td><td>Tensile Strength σ<sub>R</sub></td><td>99.9 [MPa]</td></tr><tr><td>Glass transition temperature T<sub>g</sub></td><td>143 [°C]</td><td>Young's modulus E</td><td>3.74 [GPa]</td></tr><tr><td>Melt temperature T<sub>m</sub></td><td>343 [°C]</td><td>Elongation at break</td><td>9.1 [%]</td></tr><tr><td>Thermal conductivity λ</td><td>0.29 [W/m×K]</td><td>Impact strength</td><td>7.1 [kJ/m²]</td></tr></tbody></table>

The specimens were then processed on an instrumented grinding machine, a Planomat 408 CNC machine (Blohm Jung GmbH, Hamburg, Germany), designed and implemented in previous
experiences [9-11]. Based on the Box-Behnken design, a Design of Experiment (DoE) plan was used to conduct, analyze, and interpret controlled tests to evaluate the influence of grinding process parameters on the AM part surface quality. The Box-Behnken design was a very efficient response surface design, giving information on the effect of experiment variables and overall experimental error with a minimum run number [12]. The following characterized it: each factor had three levels, the design focused on fitting a quadratic model with interaction effects, and the ratio of experimental points to the coefficient number was as low as possible. As a response surface design, the design factors (input parameters) were the cutting speed $v_c$, the feed velocity $v_f$, and the depth of cut $a_e$, each with three coded levels (-1, 0, +1) generating 15 runs. The uncoded values are reported in Table 2. The uncoded value ranges were chosen following previous experiments [9-11], focusing on high cutting and feed speed with low depths of cut.

<table><caption>Table 2: Material data.</caption><thead><tr><td>Design factor</td><td>Coded values</td><td>Uncoded values</td></tr></thead><tbody><tr><td>cutting speed v<sub>c</sub></td><td>-1, 0, +1</td><td>25, 50, 75 [m/s]</td></tr><tr><td>feed velocity v<sub>f</sub></td><td>-1, 0, +1</td><td>900, 1350, 1800 [mm/min]</td></tr><tr><td>depth of cut a<sub>e</sub></td><td>-1, 0, +1</td><td>0.10, 0.15, 0.20 [mm]</td></tr></tbody></table>

The grinding machine used a SINUMERIK 840d sl control (Siemens AG, Munich, Germany) with a Data Acquisition (DAQ) system to register spindle power at a sampling of 0.002 s. The maximum machine spindle limits were 1,450 rpm and 7.5 kW. The wheel was coded as 45A120-5G11RM-LV233/35 (ELBE Schleifmittelwerk GmBh & Co KG, Sachsenheim, Germany) and had an initial diameter of 400 mm and a thickness of 30 mm. Two Slimline cells (Kistler Group AG, Winterthur, Switzerland) were interfaced to measure the normal and tangential forces. A MAXYMOS TYP5877A/B (Kistler Group AG, Winterthur, Switzerland) acquired the cell signals, working as an amplifier and monitoring system, with a sampling of 0.001 s. A type J thermocouple (1.0 mm diameter and 500 mm length), measuring up to 760°C, was also available to measure workpiece temperature. The temperature sensor's tip was 29.5 mm from the pressure plate top, and the hole was filled with epoxy to fix it. The temperature had to be filtered as the power after the data acquisition in the post-processing. All cell signals were acquired, filtered, and post-processed for the following analyses. In particular, the normal $F_n$ and the tangential $F_t$ forces were used as two main response variables of the DoE design. The normal force $F_n$ was usually lower than the tangential force $F_t$. The other response variables were the average roughness $R_a$ and the mean roughness depth $R_z$, determined transversally to the specimen length. The roughness was measured offline using a Conoscan 3000 (Oproprint srl, Rome, Italy), a laser-based conoscopic holographic sensor with a 50 mm lens and an optical resolution of 10 µm. The laser sensor acquisition was performed on a surface patch of 3×50 mm², then extracting the roughness profiles, according to definitions of ISO 21920-2:2021. $R_z$ was almost always greater than $R_a$ because $R_a$ represented the average values, and $R_z$ was based on maximum values. The difference between the two parameters also depended on the roughness profile uniformity. Figure 2 shows the flowchart of the data acquisition system.
experiences [9-11]. Based on the Box-Behnken design, a Design of Experiment (DoE) plan was used to conduct, analyze, and interpret controlled tests to evaluate the influence of grinding process parameters on the AM part surface quality. The Box-Behnken design was a very efficient response surface design, giving information on the effect of experiment variables and overall experimental error with a minimum run number [12]. The following characterized it: each factor had three levels, the design focused on fitting a quadratic model with interaction effects, and the ratio of experimental points to the coefficient number was as low as possible. As a response surface design, the design factors (input parameters) were the cutting speed $v_c$, the feed velocity $v_f$, and the depth of cut $a_e$, each with three coded levels (-1, 0, +1) generating 15 runs. The uncoded values are reported in Table 2. The uncoded value ranges were chosen following previous experiments [9-11], focusing on high cutting and feed speed with low depths of cut.

<table><caption>Table 2: Material data.</caption><thead><tr><td>Design factor</td><td>Coded values</td><td>Uncoded values</td></tr></thead><tbody><tr><td>cutting speed v<sub>c</sub></td><td>-1, 0, +1</td><td>25, 50, 75 [m/s]</td></tr><tr><td>feed velocity v<sub>f</sub></td><td>-1, 0, +1</td><td>900, 1350, 1800 [mm/min]</td></tr><tr><td>depth of cut a<sub>e</sub></td><td>-1, 0, +1</td><td>0.10, 0.15, 0.20 [mm]</td></tr></tbody></table>

The grinding machine used a SINUMERIK 840d sl control (Siemens AG, Munich, Germany) with a Data Acquisition (DAQ) system to register spindle power at a sampling of 0.002 s. The maximum machine spindle limits were 1,450 rpm and 7.5 kW. The wheel was coded as 45A120-5G11RM-LV233/35 (ELBE Schleifmittelwerk GmBh & Co KG, Sachsenheim, Germany) and had an initial diameter of 400 mm and a thickness of 30 mm. Two Slimline cells (Kistler Group AG, Winterthur, Switzerland) were interfaced to measure the normal and tangential forces. A MAXYMOS TYP5877A/B (Kistler Group AG, Winterthur, Switzerland) acquired the cell signals, working as an amplifier and monitoring system, with a sampling of 0.001 s. A type J thermocouple (1.0 mm diameter and 500 mm length), measuring up to 760°C, was also available to measure workpiece temperature. The temperature sensor's tip was 29.5 mm from the pressure plate top, and the hole was filled with epoxy to fix it. The temperature had to be filtered as the power after the data acquisition in the post-processing. All cell signals were acquired, filtered, and post-processed for the following analyses. In particular, the normal $F_n$ and the tangential $F_t$ forces were used as two main response variables of the DoE design. The normal force $F_n$ was usually lower than the tangential force $F_t$. The other response variables were the average roughness $R_a$ and the mean roughness depth $R_z$, determined transversally to the specimen length. The roughness was measured offline using a Conoscan 3000 (Oproprint srl, Rome, Italy), a laser-based conoscopic holographic sensor with a 50 mm lens and an optical resolution of 10 µm. The laser sensor acquisition was performed on a surface patch of 3×50 mm², then extracting the roughness profiles, according to definitions of ISO 21920-2:2021. $R_z$ was almost always greater than $R_a$ because $R_a$ represented the average values, and $R_z$ was based on maximum values. The difference between the two parameters also depended on the roughness profile uniformity. Figure 2 shows the flowchart of the data acquisition system.
<figure><img src="image_2536.png" /><figcaption>Fig. 2. Data acquisition flow chart.</figcaption></figure>

## Results and Discussion

The measures with the thermocouple indicated temperatures below the glass transition in all process conditions. This outcome was associated with a high lubricant flow rate and a low friction coefficient of the PEEK. Reducing temperatures was also crucial to avoid burns on the machined parts and kneading on the grinding wheel [9]. These latter problems were eliminated by adopting a high liquid coolant flow rate and performing an appropriate dressing before use.

The measures of the grinding forces were crucial to evaluate the material machinability. The normal force had a similar trend to the tangential force. Figure 3 presents the experimental results of the Box-Behnken design of the maximum normal $F_n$ and tangential $F_t$ forces. The experiment number identified the triplet of the process parameters $v_c$, $v_f$, and $a_e$ in the side table.

<figure><img src="image_2537.png" /><figcaption>Fig. 3. Experimental data results of the maximum $F_n$ and $F_t$.</figcaption></figure>

<table><thead><tr><th>Experiment</th><th>v<sub>c</sub> (m/s)</th><th>v<sub>f</sub> (mm/min)</th><th>a<sub>e</sub> (mm)</th></tr></thead><tbody><tr><td>1</td><td>75</td><td>1800</td><td>0.15</td></tr><tr><td>2</td><td>25</td><td>1800</td><td>0.15</td></tr><tr><td>3</td><td>50</td><td>1350</td><td>0.15</td></tr><tr><td>4</td><td>25</td><td>900</td><td>0.15</td></tr><tr><td>5</td><td>50</td><td>900</td><td>0.1</td></tr><tr><td>6</td><td>75</td><td>900</td><td>0.15</td></tr><tr><td>7</td><td>50</td><td>1350</td><td>0.15</td></tr><tr><td>8</td><td>75</td><td>1350</td><td>0.2</td></tr><tr><td>9</td><td>75</td><td>1350</td><td>0.1</td></tr><tr><td>10</td><td>50</td><td>1350</td><td>0.15</td></tr><tr><td>11</td><td>25</td><td>1350</td><td>0.1</td></tr><tr><td>12</td><td>50</td><td>1800</td><td>0.1</td></tr><tr><td>13</td><td>50</td><td>1800</td><td>0.2</td></tr><tr><td>14</td><td>50</td><td>900</td><td>0.2</td></tr><tr><td>15</td><td>25</td><td>1350</td><td>0.2</td></tr></tbody></table>

The Analysis of Variance (ANOVA) was employed to estimate the impact of the grinding process parameters and their interactions on the selected response variables, computing suitable regression models. From the first data analysis, both forces were reduced with a decrease of the cutting depth $a_e$ and an increase of the cutting speed $v_c$. The feed speed $v_f$ had a slight effect on force variations. Response surfaces of the maximum measured normal force $F_n$ (Figure 4) and tangential force $F_t$ (Figure 5) corroborated the above analysis. The coefficient of determination $R^2$ of both responses was greater than 97%, confirming the excellent prediction of the statistical model.
<figure><img src="image_2529.png" /><figcaption>Fig. 2. Data acquisition flow chart.</figcaption></figure>

## Results and Discussion

The measures with the thermocouple indicated temperatures below the glass transition in all process conditions. This outcome was associated with a high lubricant flow rate and a low friction coefficient of the PEEK. Reducing temperatures was also crucial to avoid burns on the machined parts and kneading on the grinding wheel [9]. These latter problems were eliminated by adopting a high liquid coolant flow rate and performing an appropriate dressing before use.

The measures of the grinding forces were crucial to evaluate the material machinability. The normal force had a similar trend to the tangential force. Figure 3 presents the experimental results of the Box-Behnken design of the maximum normal $F_n$ and tangential $F_t$ forces. The experiment number identified the triplet of the process parameters $v_c$, $v_f$, and $a_e$ in the side table.

<figure><img src="image_2530.png" /><figcaption>Fig. 3. Experimental data results of the maximum $F_n$ and $F_t$.</figcaption></figure>

<table><thead><tr><th>Experiment</th><th>v<sub>c</sub> (m/s)</th><th>v<sub>f</sub> (mm/min)</th><th>a<sub>e</sub> (mm)</th></tr></thead><tbody><tr><td>1</td><td>75</td><td>1800</td><td>0.15</td></tr><tr><td>2</td><td>25</td><td>1800</td><td>0.15</td></tr><tr><td>3</td><td>50</td><td>1350</td><td>0.15</td></tr><tr><td>4</td><td>25</td><td>900</td><td>0.15</td></tr><tr><td>5</td><td>50</td><td>900</td><td>0.1</td></tr><tr><td>6</td><td>75</td><td>900</td><td>0.15</td></tr><tr><td>7</td><td>50</td><td>1350</td><td>0.15</td></tr><tr><td>8</td><td>75</td><td>1350</td><td>0.2</td></tr><tr><td>9</td><td>75</td><td>1350</td><td>0.1</td></tr><tr><td>10</td><td>50</td><td>1350</td><td>0.15</td></tr><tr><td>11</td><td>25</td><td>1350</td><td>0.1</td></tr><tr><td>12</td><td>50</td><td>1800</td><td>0.1</td></tr><tr><td>13</td><td>50</td><td>1800</td><td>0.2</td></tr><tr><td>14</td><td>50</td><td>900</td><td>0.2</td></tr><tr><td>15</td><td>25</td><td>1350</td><td>0.2</td></tr></tbody></table>

The Analysis of Variance (ANOVA) was employed to estimate the impact of the grinding process parameters and their interactions on the selected response variables, computing suitable regression models. From the first data analysis, both forces were reduced with a decrease of the cutting depth $a_e$ and an increase of the cutting speed $v_c$. The feed speed $v_f$ had a slight effect on force variations. Response surfaces of the maximum measured normal force $F_n$ (Figure 4) and tangential force $F_t$ (Figure 5) corroborated the above analysis. The coefficient of determination $R^2$ of both responses was greater than 97%, confirming the excellent prediction of the statistical model.
<figure><img src="image_2538.png" /><figcaption>Fig. 4. Maximum normal force $F_n$ graphs.</figcaption></figure>

<figure><img src="image_2539.png" /><figcaption>Fig. 5. Maximum tangential force $F_t$ graphs.</figcaption></figure>

The lowest values of the normal and tangential forces were achieved for high $v_c$ and low $v_f$ and $a_e$. Low force values reduced wheel abrasive shedding, pore blockage, and machined surface damages. These results were coherent with the analysis of the maximum cutting depth $h_{max}$, correlated to the process parameters with the following equation:

$$h_{max} = \sqrt{\frac{6}{C \times r} \times \frac{v_f}{v_c} \times \sqrt{\frac{a_e}{d_e}}} \quad (1)$$

where C is the number of cutting points per unit area, r is the average effective chip width to undeformed chip thickness ratio, and $d_e$ is the equivalent wheel diameter. $h_{max}$ increased with an increase of $a_e$ and $v_f$, and decreased with $v_c$ increase. The greater the value of $h_{max}$ was, the larger the volume of material removed and the greater the grinding force was.

The measures of the surface roughness allowed the assessment of the surface quality of the final components. Figure 6 presents the experimental results of the Box-Behnken design in terms of the average roughness $R_a$ and the mean roughness depth $R_z$. The experiment number identified the triplet of the process parameters $v_c$, $v_f$, and $a_e$ in the side table. The roughness values were one order lower than the rough components. The ANOVA results showed that $R_a$ increased with low $v_c$, $a_e$, and high $v_f$. The same trend was also evident for $R_z$. The surface roughness was closely related to the maximum cutting depth [13], as reported from the following relation:

$$R_t \propto \sqrt[3]{\frac{h_{max}}{a_e}} \approx \sqrt[3]{\left(\frac{v_f}{v_c} \times \frac{1}{C \times r \times \sqrt{d_e}}\right)^2} \quad (2)$$
<figure><img src="image_2531.png" /><figcaption>Fig. 4. Maximum normal force $F_n$ graphs.</figcaption></figure>

<figure><img src="image_2532.png" /><figcaption>Fig. 5. Maximum tangential force $F_t$ graphs.</figcaption></figure>

The lowest values of the normal and tangential forces were achieved for high $v_c$ and low $v_f$ and $a_e$. Low force values reduced wheel abrasive shedding, pore blockage, and machined surface damages. These results were coherent with the analysis of the maximum cutting depth $h_{max}$, correlated to the process parameters with the following equation:

$$h_{max} = \sqrt{\frac{6}{C \times r} \times \frac{v_f}{v_c} \times \sqrt{\frac{a_e}{d_e}}} \quad (1)$$

where C is the number of cutting points per unit area, r is the average effective chip width to undeformed chip thickness ratio, and $d_e$ is the equivalent wheel diameter. $h_{max}$ increased with an increase of $a_e$ and $v_f$, and decreased with $v_c$ increase. The greater the value of $h_{max}$ was, the larger the volume of material removed and the greater the grinding force was.

The measures of the surface roughness allowed the assessment of the surface quality of the final components. Figure 6 presents the experimental results of the Box-Behnken design in terms of the average roughness $R_a$ and the mean roughness depth $R_z$. The experiment number identified the triplet of the process parameters $v_c$, $v_f$, and $a_e$ in the side table. The roughness values were one order lower than the rough components. The ANOVA results showed that $R_a$ increased with low $v_c$, $a_e$, and high $v_f$. The same trend was also evident for $R_z$. The surface roughness was closely related to the maximum cutting depth [13], as reported from the following relation:

$$R_t \propto \sqrt[3]{\frac{h_{max}}{a_e}} \approx \sqrt[3]{\left(\frac{v_f}{v_c} \times \frac{1}{C \times r \times \sqrt{d_e}}\right)^2} \quad (2)$$
<figure><img src="image_2540.png" /><figcaption>Fig. 6. Experimental data results of $R_a$ and $R_z$.</figcaption></figure>

<table><thead><tr><th>Experiment</th><th>v<sub>c</sub> (m/s)</th><th>v<sub>f</sub> (mm/min)</th><th>a<sub>e</sub> (mm)</th></tr></thead><tbody><tr><td>1</td><td>75</td><td>1800</td><td>0.15</td></tr><tr><td>2</td><td>25</td><td>1800</td><td>0.15</td></tr><tr><td>3</td><td>50</td><td>1350</td><td>0.15</td></tr><tr><td>4</td><td>25</td><td>900</td><td>0.15</td></tr><tr><td>5</td><td>50</td><td>900</td><td>0.1</td></tr><tr><td>6</td><td>75</td><td>900</td><td>0.15</td></tr><tr><td>7</td><td>50</td><td>1350</td><td>0.15</td></tr><tr><td>8</td><td>75</td><td>1350</td><td>0.2</td></tr><tr><td>9</td><td>75</td><td>1350</td><td>0.1</td></tr><tr><td>10</td><td>50</td><td>1350</td><td>0.15</td></tr><tr><td>11</td><td>25</td><td>1350</td><td>0.1</td></tr><tr><td>12</td><td>50</td><td>1800</td><td>0.1</td></tr><tr><td>13</td><td>50</td><td>1800</td><td>0.2</td></tr><tr><td>14</td><td>50</td><td>900</td><td>0.2</td></tr><tr><td>15</td><td>25</td><td>1350</td><td>0.2</td></tr></tbody></table>

where $R_t$ was the total height of the roughness profile. $R_z$ was computed by averaging successive values of $R_t$ calculated over the evaluation length. The most influencing factors on $R_a$ and $R_z$ variations were $a_e$ and $v_c$. Increasing the $a_e$ while reducing $v_c$ produced a greater chip thickness and higher $R_a$ and $R_z$. The interactions between $a_e$ and $v_c$ resulted in increased force, causing more wheel vibration and increased surface roughness. Response surfaces of the transversal average roughness $R_a$ (Figure 7) and the transversal mean roughness depth $R_z$ (Figure 8) supported the above analysis. The coefficient of determination $R^2$ of both responses was greater than 93%, confirming the excellent prediction of the statistical model.

<figure><img src="image_2541.png" /><figcaption>Fig. 7. Average roughness $R_a$ graphs.</figcaption></figure>

<figure><img src="image_2542.png" /><figcaption>Fig. 8. Mean roughness depth $R_z$ graphs.</figcaption></figure>
<figure><img src="image_2533.png" /><figcaption>Fig. 6. Experimental data results of $R_a$ and $R_z$.</figcaption></figure>

<table><thead><tr><th>Experiment</th><th>v<sub>c</sub> (m/s)</th><th>v<sub>f</sub> (mm/min)</th><th>a<sub>e</sub> (mm)</th></tr></thead><tbody><tr><td>1</td><td>75</td><td>1800</td><td>0.15</td></tr><tr><td>2</td><td>25</td><td>1800</td><td>0.15</td></tr><tr><td>3</td><td>50</td><td>1350</td><td>0.15</td></tr><tr><td>4</td><td>25</td><td>900</td><td>0.15</td></tr><tr><td>5</td><td>50</td><td>900</td><td>0.1</td></tr><tr><td>6</td><td>75</td><td>900</td><td>0.15</td></tr><tr><td>7</td><td>50</td><td>1350</td><td>0.15</td></tr><tr><td>8</td><td>75</td><td>1350</td><td>0.2</td></tr><tr><td>9</td><td>75</td><td>1350</td><td>0.1</td></tr><tr><td>10</td><td>50</td><td>1350</td><td>0.15</td></tr><tr><td>11</td><td>25</td><td>1350</td><td>0.1</td></tr><tr><td>12</td><td>50</td><td>1800</td><td>0.1</td></tr><tr><td>13</td><td>50</td><td>1800</td><td>0.2</td></tr><tr><td>14</td><td>50</td><td>900</td><td>0.2</td></tr><tr><td>15</td><td>25</td><td>1350</td><td>0.2</td></tr></tbody></table>

where $R_t$ was the total height of the roughness profile. $R_z$ was computed by averaging successive values of $R_t$ calculated over the evaluation length. The most influencing factors on $R_a$ and $R_z$ variations were $a_e$ and $v_c$. Increasing the $a_e$ while reducing $v_c$ produced a greater chip thickness and higher $R_a$ and $R_z$. The interactions between $a_e$ and $v_c$ resulted in increased force, causing more wheel vibration and increased surface roughness. Response surfaces of the transversal average roughness $R_a$ (Figure 7) and the transversal mean roughness depth $R_z$ (Figure 8) supported the above analysis. The coefficient of determination $R^2$ of both responses was greater than 93%, confirming the excellent prediction of the statistical model.

<figure><img src="image_2534.png" /><figcaption>Fig. 7. Average roughness $R_a$ graphs.</figcaption></figure>

<figure><img src="image_2535.png" /><figcaption>Fig. 8. Mean roughness depth $R_z$ graphs.</figcaption></figure>
## Conclusions

This work investigated the performance of additively manufactured PEEK regarding grinding forces and surface roughness. In particular, PEEK specimens were examined using several process parameters according to the Design of the Experiment plan. The grinding forces were monitored in real time while profile roughness was computed offline.

The following conclusions can be drawn from the experimental results. The grinding forces were positively correlated with the depth of cut $a_e$ and feed speed $v_f$, and negatively associated with the cut speed $v_c$. The lowest values of the normal $F_n$ and tangential $F_t$ forces were achieved for high $v_c$ and low $v_f$ and $a_e$. The surface quality of the ground parts was significantly better than the rough parts, approximately one order of magnitude lower. The most influencing factors on the average roughness $R_a$ and the mean roughness depth $R_z$ were the depth of cut $a_e$ and the cut speed $v_c$. The surface quality was effectively improved by reducing the depth $a_e$ and the feed speed $v_f$, increasing the cut speed $v_c$.

## Acknowledgments

The authors thank Prof Luigi Galantucci and Prof Fulvio Lavecchia of Politecnico di Bari for their suggestions, Marco Massari and Giuseppe Glionna of Tecnologie Diesel S.p.A for the experimental support.

The Project was funded under the program Department of Excellence - Law number 232/2016 (Grant No. CUP - D93C23000100001), the National Recovery and Resilience Plan (NRRP), Mission 4 Component 2 Investment 1.3 - Call for tender No. 341 of 15/03/2022 of the Italian Ministry of University and Research (MUR), funded by the European Union – NextGenerationEU, and the RIPARTI funding (assegni di Ricerca per ripartire con le Imprese) of the Apulia Region.

## References

[1] Y. Chen et al. Study the dynamic influence of the distribution of cutting depth on the ground surface quality in a precision grinding process. Journal of Manufacturing Processes 107 (2023) 134-143. https://doi.org/10.1016/j.jmapro.2023.10.028

[2] K. Kanishka, B. Acherjee. A systematic review of additive manufacturing-based remanufacturing techniques for component repair and restoration. Journal of Manufacturing Processes 89 (2023) 220-283. https://doi.org/10.1016/j.jmapro.2023.01.034

[3] A. Beaucamp, B. Kirsch, W. Zhu. Advances in grinding tools and abrasives. CIRP Annals - Manufacturing Technology 71 (2022) 623646. https://doi.org/10.1016/j.cirp.2022.05.003

[4] D. Aslan, E. Budak. Surface roughness and thermo-mechanical force modeling for grinding operations with regular and circumferentially grooved wheels. Journal of Materials Processing Technology 223 (2015) 75-90. https://doi.org/10.1016/j.jmatprotec.2015.03.023

[5] A. Bell, T. Jin, D.J. Stephenson. Burn threshold prediction for High Efficiency Deep Grinding. International Journal of Machine Tools & Manufacture 51 (2011) 433-438. https://doi.org/10.1016/j.ijmachtools.2011.01.006

[6] P. Wang, B. Zou, S. Ding. Modeling of surface roughness based on heat transfer considering diffusion among deposition filaments for FDM 3D printing heat-resistant resin. Applied Thermal Engineering 161 (2019) 114064. https://doi.org/10.1016/j.applthermaleng.2019.114064

[7] A. Pulipaka et al. Effect of 3D printing process parameters on surface and mechanical properties of FFF-printed PEEK. Journal of Manufacturing Processes 85 (2023) 368-386. https://doi.org/10.1016/j.jmapro.2022.11.057

[8] Information on https://www.intamsys.com/
## Conclusions

This work investigated the performance of additively manufactured PEEK regarding grinding forces and surface roughness. In particular, PEEK specimens were examined using several process parameters according to the Design of the Experiment plan. The grinding forces were monitored in real time while profile roughness was computed offline.

The following conclusions can be drawn from the experimental results. The grinding forces were positively correlated with the depth of cut $a_e$ and feed speed $v_f$, and negatively associated with the cut speed $v_c$. The lowest values of the normal $F_n$ and tangential $F_t$ forces were achieved for high $v_c$ and low $v_f$ and $a_e$. The surface quality of the ground parts was significantly better than the rough parts, approximately one order of magnitude lower. The most influencing factors on the average roughness $R_a$ and the mean roughness depth $R_z$ were the depth of cut $a_e$ and the cut speed $v_c$. The surface quality was effectively improved by reducing the depth $a_e$ and the feed speed $v_f$, increasing the cut speed $v_c$.

## Acknowledgments

The authors thank Prof Luigi Galantucci and Prof Fulvio Lavecchia of Politecnico di Bari for their suggestions, Marco Massari and Giuseppe Glionna of Tecnologie Diesel S.p.A for the experimental support.

The Project was funded under the program Department of Excellence - Law number 232/2016 (Grant No. CUP - D93C23000100001), the National Recovery and Resilience Plan (NRRP), Mission 4 Component 2 Investment 1.3 - Call for tender No. 341 of 15/03/2022 of the Italian Ministry of University and Research (MUR), funded by the European Union – NextGenerationEU, and the RIPARTI funding (assegni di Ricerca per ripartire con le Imprese) of the Apulia Region.

## References

[1] Y. Chen et al. Study the dynamic influence of the distribution of cutting depth on the ground surface quality in a precision grinding process. Journal of Manufacturing Processes 107 (2023) 134-143. https://doi.org/10.1016/j.jmapro.2023.10.028

[2] K. Kanishka, B. Acherjee. A systematic review of additive manufacturing-based remanufacturing techniques for component repair and restoration. Journal of Manufacturing Processes 89 (2023) 220-283. https://doi.org/10.1016/j.jmapro.2023.01.034

[3] A. Beaucamp, B. Kirsch, W. Zhu. Advances in grinding tools and abrasives. CIRP Annals - Manufacturing Technology 71 (2022) 623646. https://doi.org/10.1016/j.cirp.2022.05.003

[4] D. Aslan, E. Budak. Surface roughness and thermo-mechanical force modeling for grinding operations with regular and circumferentially grooved wheels. Journal of Materials Processing Technology 223 (2015) 75-90. https://doi.org/10.1016/j.jmatprotec.2015.03.023

[5] A. Bell, T. Jin, D.J. Stephenson. Burn threshold prediction for High Efficiency Deep Grinding. International Journal of Machine Tools & Manufacture 51 (2011) 433-438. https://doi.org/10.1016/j.ijmachtools.2011.01.006

[6] P. Wang, B. Zou, S. Ding. Modeling of surface roughness based on heat transfer considering diffusion among deposition filaments for FDM 3D printing heat-resistant resin. Applied Thermal Engineering 161 (2019) 114064. https://doi.org/10.1016/j.applthermaleng.2019.114064

[7] A. Pulipaka et al. Effect of 3D printing process parameters on surface and mechanical properties of FFF-printed PEEK. Journal of Manufacturing Processes 85 (2023) 368-386. https://doi.org/10.1016/j.jmapro.2022.11.057

[8] Information on https://www.intamsys.com/
[9] R. Spina, B. Cavalcante. Evaluation of grinding of unfilled and glass fiber reinforced polyamide 6,6. Polymers, 12 (2020) 1-11. https://doi.org/10.3390/polym12102288

[10] R. Spina et al. Forces and specific energy of polyamide grinding. Materials, 14 (2021) 5041. https://doi.org/10.3390/ma14175041

[11] R. Spina et al. Analysis of surface grinding of thermoplastics specimens with inline measurements. Journal of Manufacturing and Materials Processing, 6 (2022) 81. https://doi.org/10.3390/jmmp6040081

[12] NIST/SEMATECH e-Handbook of Statistical Methods. Information on https://www.itl.nist.gov/div898/handbook/pri/section3/pri3362.htm.

[13] I.D. Marinescu et al. Handbook of machining with grinding wheels. CRC Press. https://doi.org/10.1201/b19462
[9] R. Spina, B. Cavalcante. Evaluation of grinding of unfilled and glass fiber reinforced polyamide 6,6. Polymers, 12 (2020) 1-11. https://doi.org/10.3390/polym12102288

[10] R. Spina et al. Forces and specific energy of polyamide grinding. Materials, 14 (2021) 5041. https://doi.org/10.3390/ma14175041

[11] R. Spina et al. Analysis of surface grinding of thermoplastics specimens with inline measurements. Journal of Manufacturing and Materials Processing, 6 (2022) 81. https://doi.org/10.3390/jmmp6040081

[12] NIST/SEMATECH e-Handbook of Statistical Methods. Information on https://www.itl.nist.gov/div898/handbook/pri/section3/pri3362.htm.

[13] I.D. Marinescu et al. Handbook of machining with grinding wheels. CRC Press. https://doi.org/10.1201/b19462
# Multi-material topology optimization of additively manufactured thermoplastic molds for heat transfer enhancement

STORTI Bruno A.¹,ᵃ*, SOBOTKA Vincent¹,ᵇ, ÁLVAREZ HOSTOS Juan C.²,ᶜ, LEFEVRE Nicolás¹,ᵈ, LE CORRE Steven¹,ᵉ, FACHINOTTI Victor²,*f

¹Nantes Université, CNRS, Laboratoire de Thermique et Énergie de Nantes, LTeN, UMR 6607, Rue Christian Pauc, Nantes, 44300, Pays de la Loire, France

²Centro de Investigación de Métodos Computacionales (CIMEC), Universidad Nacional del Litoral (UNL)/Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Colectora Ruta Nac. N° 168 Km 0, Santa Fe, 3000, Argentina

ᵃbruno.storti@univ-nantes.fr, ᵇvincent.sobotka@univ-nantes.fr, ᶜjchostos@cimec.unl.edu.ar,

ᵈnicolas.lefevre@univ-nantes.fr, ᶜsteven.lecorre@univ-nantes.fr,

ᶜvfachinotti@santafe-conicet.gov.ar

**Keywords:** Injection Molding, Topology Optimization, Metadevices, Additive Manufacturing, FEM

**Abstract.** For low-volume scale manufacturing of plastic parts, thermoplastic molds made of polymers and printed by additive manufacturing (AM) technology have proved to be a viable alternative to replace expensive and time-consuming steel molds. Nevertheless, due to the relatively low thermal conductivity of the polymers employed for their manufacture, not only the cycle times are increased, but also the surface temperature homogeneity is affected during the cooling of the part, potentially impacting its final quality. On the other hand, the latest advances in AM technology allow the 3D printing of parts with two polymers of different thermophysical properties, opening the possibility for heat flux manipulation within the thermoplastic mold. This work is devoted to the numerical implementation of a topology optimization (TO) methodology to enhance the temperature homogeneity of an injected part during the cooling phase. The proposed scheme relies on the usage of the gradient-free particle swarm optimizer (PSO) in conjunction with filtering techniques to obtain a feasible-to-manufacture multi-material thermoplastic mold. The TO strategy is thoroughly validated against gradient-based techniques found in the related literature conceived for heat flux manipulation in the transient regime. The results show outstanding improvements in the temperature homogeneity of the part when strategically placing the low-conductivity polymer in easy-to-cool regions and the high-conductivity polymer in regions that cool down slower. We further report in this work the possibility of achieving standard deviation values like those obtained by a steel counterpart.

**Introduction**

Injection molding is a widely employed manufacturing process that is mainly based on injecting a melted polymer inside the cavity of a mold, and then quickly cooling it to have the manufactured plastic part [1]. Due to its high strength and thermal conductivity, steel molds are commonly employed for large batches of products. However, their manufacturing cost is high and the time to produce them is large since multiple complex machining processes are needed depending on the part complexity. Furthermore, when non-straight cooling channels (CCs) are needed within the mold, this becomes particularly hard to manufacture with common machining techniques. On the other hand, additive manufacturing (AM) technology emerged as a matured technology capable of manufacturing complex thermoplastic molds, saving costs while reducing the manufacturing time. Particularly in this work, molds for low batches of products are addressed, either for quick product development or prototyping, where steel molds are not suitable.

<figure><img src="image_2543.png" /></figure>

Content from this work may be used under the terms of the Creative Commons Attribution 3.0 license. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Published under license by Materials Research Forum LLC.
# Multi-material topology optimization of additively manufactured thermoplastic molds for heat transfer enhancement

STORTI Bruno A.¹,ᵃ*, SOBOTKA Vincent¹,ᵇ, ÁLVAREZ HOSTOS Juan C.²,ᶜ, LEFEVRE Nicolás¹,ᵈ, LE CORRE Steven¹,ᵉ, FACHINOTTI Victor²,*f

¹Nantes Université, CNRS, Laboratoire de Thermique et Énergie de Nantes, LTeN, UMR 6607, Rue Christian Pauc, Nantes, 44300, Pays de la Loire, France

²Centro de Investigación de Métodos Computacionales (CIMEC), Universidad Nacional del Litoral (UNL)/Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Colectora Ruta Nac. N° 168 Km 0, Santa Fe, 3000, Argentina

ᵃbruno.storti@univ-nantes.fr, ᵇvincent.sobotka@univ-nantes.fr, ᶜjchostos@cimec.unl.edu.ar,

ᵈnicolas.lefevre@univ-nantes.fr, ᶜsteven.lecorre@univ-nantes.fr,

ᶜvfachinotti@santafe-conicet.gov.ar

**Keywords:** Injection Molding, Topology Optimization, Metadevices, Additive Manufacturing, FEM

**Abstract.** For low-volume scale manufacturing of plastic parts, thermoplastic molds made of polymers and printed by additive manufacturing (AM) technology have proved to be a viable alternative to replace expensive and time-consuming steel molds. Nevertheless, due to the relatively low thermal conductivity of the polymers employed for their manufacture, not only the cycle times are increased, but also the surface temperature homogeneity is affected during the cooling of the part, potentially impacting its final quality. On the other hand, the latest advances in AM technology allow the 3D printing of parts with two polymers of different thermophysical properties, opening the possibility for heat flux manipulation within the thermoplastic mold. This work is devoted to the numerical implementation of a topology optimization (TO) methodology to enhance the temperature homogeneity of an injected part during the cooling phase. The proposed scheme relies on the usage of the gradient-free particle swarm optimizer (PSO) in conjunction with filtering techniques to obtain a feasible-to-manufacture multi-material thermoplastic mold. The TO strategy is thoroughly validated against gradient-based techniques found in the related literature conceived for heat flux manipulation in the transient regime. The results show outstanding improvements in the temperature homogeneity of the part when strategically placing the low-conductivity polymer in easy-to-cool regions and the high-conductivity polymer in regions that cool down slower. We further report in this work the possibility of achieving standard deviation values like those obtained by a steel counterpart.

**Introduction**

Injection molding is a widely employed manufacturing process that is mainly based on injecting a melted polymer inside the cavity of a mold, and then quickly cooling it to have the manufactured plastic part [1]. Due to its high strength and thermal conductivity, steel molds are commonly employed for large batches of products. However, their manufacturing cost is high and the time to produce them is large since multiple complex machining processes are needed depending on the part complexity. Furthermore, when non-straight cooling channels (CCs) are needed within the mold, this becomes particularly hard to manufacture with common machining techniques. On the other hand, additive manufacturing (AM) technology emerged as a matured technology capable of manufacturing complex thermoplastic molds, saving costs while reducing the manufacturing time. Particularly in this work, molds for low batches of products are addressed, either for quick product development or prototyping, where steel molds are not suitable.

<figure><img src="image_2536.png" /></figure>

Content from this work may be used under the terms of the Creative Commons Attribution 3.0 license. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Published under license by Materials Research Forum LLC.
The main limitation regarding the use of thermoplastic molds comes from the relatively low thermal conductivity of the polymers commonly employed in AM such as in the material extrusion (MEX) process, for instance. It was shown in recent experimental [2] and numerical [3, 4] works that, for a given manufacturing process setup featuring CCs, the cooling time needed to reach the ejection temperature of the part is highly sensitive to the mold's thermal conductivity. Emphasizing the aforementioned, a slight improvement from 0.21 W/(mK) to 0.33 W/(mK) led to a 30% reduction in the cycle time [3], for instance. Furthermore, the relatively low mold's thermal conductivity leads not only to extended cycle times but also to an increase of through-surface thermal gradients within the plastic part, which can eventually lead to defects of the final product [5]. In light of the aforementioned, common practices in the thermal optimization of metal injection molds, such as the optimization of the geometry and positioning of CCs, as well as the regulation of coolant flow rate and temperature, may assume a subordinate role in comparison to the proper selection of material for polymeric-based molds. Fortunately, as AM technology evolves, material sciences evolve as well by developing high-performance (filled or not) polymers specifically designed to improve their thermal conductivity [6]. Exploiting the sensitivity of the part cooling velocity to the mold material, this work delves into the feasibility of employing two polymers of different thermal conductivity to enhance the heat transfer within a thermoplastic mold.

It is known from the literature that heat flux manipulation within thermal devices can be achieved by optimizing the distribution of two or more materials with different thermophysical properties to accomplish a desired task [7]. Such devices are often referred to as metadevices, i.e., devices whose microstructure topology is artificially conceived to achieve a specific goal. These goals could include shielding [8,9], reversing [7], cloaking [7,9,10,11], or concentrating [10,11] the heat flux in either the stationary and transient heat transfer regime, with potential applications in the design of electronic, thermal characterization, and energy harvesting devices, among others. While commonly employed numerical approaches to perform the topology optimization (TO) task rely on gradient-based implementations, their rate of success in achieving the imposed task can often be linked to the contrast in thermophysical properties between materials, i.e., greater differences (as seen in materials like steel and polymer) enhance the likelihood of achieving optimal convergence.

In this work, a TO strategy is employed to find a suitable material distribution within a thermoplastic mold to improve the temperature homogeneity at the part surface. The TO scheme followed here is based on using the stochastic particle swarm optimization (PSO) method, where the properties of each element of the finite element mesh are defined by the optimizer. Filtering strategies are proposed in order to avoid checkerboard-type solutions, and to obtain a feasible-to-manufacture material distribution from the numerical results. Both the FEM model and the TO proposed here are first validated with previous results reported in the literature [1,8,12].

## Problem Statement and Governing Equations

Study Case: Ribbed Plate Part. We start studying the cooling of a T-shape ribbed plate geometry, as observed in Fig. 1a. This shape is of particular interest it presents hard-to-cool regions, such as the near-rib zone, and easy-to-cool ones, such as corners. The injected part is 3.75 mm thick, and the mold is originally conceived on steel featuring internal CCs whose positions were already optimized in [12] (see Fig. 1b). Due to the non-variation of the geometry in the z-axis, the problem can be modeled as two-dimensional symmetric case (see Fig. 1b).
The main limitation regarding the use of thermoplastic molds comes from the relatively low thermal conductivity of the polymers commonly employed in AM such as in the material extrusion (MEX) process, for instance. It was shown in recent experimental [2] and numerical [3, 4] works that, for a given manufacturing process setup featuring CCs, the cooling time needed to reach the ejection temperature of the part is highly sensitive to the mold's thermal conductivity. Emphasizing the aforementioned, a slight improvement from 0.21 W/(mK) to 0.33 W/(mK) led to a 30% reduction in the cycle time [3], for instance. Furthermore, the relatively low mold's thermal conductivity leads not only to extended cycle times but also to an increase of through-surface thermal gradients within the plastic part, which can eventually lead to defects of the final product [5]. In light of the aforementioned, common practices in the thermal optimization of metal injection molds, such as the optimization of the geometry and positioning of CCs, as well as the regulation of coolant flow rate and temperature, may assume a subordinate role in comparison to the proper selection of material for polymeric-based molds. Fortunately, as AM technology evolves, material sciences evolve as well by developing high-performance (filled or not) polymers specifically designed to improve their thermal conductivity [6]. Exploiting the sensitivity of the part cooling velocity to the mold material, this work delves into the feasibility of employing two polymers of different thermal conductivity to enhance the heat transfer within a thermoplastic mold.

It is known from the literature that heat flux manipulation within thermal devices can be achieved by optimizing the distribution of two or more materials with different thermophysical properties to accomplish a desired task [7]. Such devices are often referred to as metadevices, i.e., devices whose microstructure topology is artificially conceived to achieve a specific goal. These goals could include shielding [8,9], reversing [7], cloaking [7,9,10,11], or concentrating [10,11] the heat flux in either the stationary and transient heat transfer regime, with potential applications in the design of electronic, thermal characterization, and energy harvesting devices, among others. While commonly employed numerical approaches to perform the topology optimization (TO) task rely on gradient-based implementations, their rate of success in achieving the imposed task can often be linked to the contrast in thermophysical properties between materials, i.e., greater differences (as seen in materials like steel and polymer) enhance the likelihood of achieving optimal convergence.

In this work, a TO strategy is employed to find a suitable material distribution within a thermoplastic mold to improve the temperature homogeneity at the part surface. The TO scheme followed here is based on using the stochastic particle swarm optimization (PSO) method, where the properties of each element of the finite element mesh are defined by the optimizer. Filtering strategies are proposed in order to avoid checkerboard-type solutions, and to obtain a feasible-to-manufacture material distribution from the numerical results. Both the FEM model and the TO proposed here are first validated with previous results reported in the literature [1,8,12].

## Problem Statement and Governing Equations

Study Case: Ribbed Plate Part. We start studying the cooling of a T-shape ribbed plate geometry, as observed in Fig. 1a. This shape is of particular interest it presents hard-to-cool regions, such as the near-rib zone, and easy-to-cool ones, such as corners. The injected part is 3.75 mm thick, and the mold is originally conceived on steel featuring internal CCs whose positions were already optimized in [12] (see Fig. 1b). Due to the non-variation of the geometry in the z-axis, the problem can be modeled as two-dimensional symmetric case (see Fig. 1b).
<figure><img src="image_2544.png" /><figcaption>Figure 1: Geometry of a "T" shaped injected part and the mold to produce it considered from [1,12], and to be addressed in this work.</figcaption></figure>

Heat Transfer Governing Equations. The heat released by the melted polymer is transferred by conduction within the mold, and then exchanged through the coolant and the ambient by convection. Therefore, for the numerical heat transfer modeling, the equations to be solved are those of the 2D transient heat conduction problem with convective boundary conditions. The heat equations are to be solved on two domains (see Fig. 1b) accounting for the injected polymer $\Omega_p$, and the insert mold $\Omega_m$. Then, the heat equations yield:

$$ \rho_{p,m} C p_{p,m} \frac{\partial T_{p,m}}{\partial t} = \nabla \cdot (\lambda_{p,m} \nabla T_{p,m}) \quad \forall T_{p,m} \in \Omega_{p,m} \times [0, t_c], \quad (1) $$

where $\rho_{p,m}$, $C p_{p,m}$ and $\lambda_{p,m}$ stands for the density, heat capacity, and the thermal conductivity of the $\Omega_{p,m}$ domains, $T_{p,m}$ is the unknown temperature, and $t_c$ stands for the cycle time. The injection phase is modeled as an instantaneous non-perfect contact between the molten polymer at a temperature $T_{inj}$, and the insert at a temperature obtained from the previous cycle. Such an approach is allowed since the duration of the filling stage is negligible with respect to the cooling stage [5,13]. Then, the following initial conditions are employed:

$$ T_p(t = 0^+) = T_{inj} \quad \text{in } \Omega_p, \quad \text{and} \quad T_m(t = 0^+) = T_m(t = t_c^-) \quad \text{in } \Omega_m, \quad (2) $$

where $T_m(t = 0^+) = T_m(t = t_c^-)$ means that the temperature field $T_m$ of $\Omega_m$ at the beginning of a given cycle $t = 0^+$ is considered to be the same as the temperature field at the final time of the previous cycle $t = t_c^-$. The Eq. (2) is subject to the boundary conditions described next. The heat flux at the part-mold interface is modeled as a non-perfect contact condition as follows:

$$ -\lambda_p \frac{\partial T_p}{\partial n} = \frac{T_p - T_m}{TCR_{p-m}} \quad \text{at} \quad \Gamma_p \quad \forall t \in [0, t_c], \quad (3) $$

where $TCR_{p-m}$ stands for the thermal contact resistance (TCR) at the part-mold interface $\Gamma_p$ (see Fig. 1b), and $n$ stands for its outward normal vector. The heat flux exchanged between the mold and the CCs is modeled as:

$$ -\lambda_m \frac{\partial T_m}{\partial n} = h_c(T_m - T_c) \quad \text{at} \quad \Gamma_{m(cc)} \quad \forall t \in [0, t_c], \quad (4) $$

where $T_c$ is the coolant temperature, and $h_c$ is the convective coefficient. Finally, the heat transferred from the mold to the environment by convection and radiation is modeled with the following third-type boundary condition:
<figure><img src="image_2537.png" /><figcaption>Figure 1: Geometry of a "T" shaped injected part and the mold to produce it considered from [1,12], and to be addressed in this work.</figcaption></figure>

Heat Transfer Governing Equations. The heat released by the melted polymer is transferred by conduction within the mold, and then exchanged through the coolant and the ambient by convection. Therefore, for the numerical heat transfer modeling, the equations to be solved are those of the 2D transient heat conduction problem with convective boundary conditions. The heat equations are to be solved on two domains (see Fig. 1b) accounting for the injected polymer $\Omega_p$, and the insert mold $\Omega_m$. Then, the heat equations yield:

$$ \rho_{p,m} C p_{p,m} \frac{\partial T_{p,m}}{\partial t} = \nabla \cdot (\lambda_{p,m} \nabla T_{p,m}) \quad \forall T_{p,m} \in \Omega_{p,m} \times [0, t_c], \quad (1) $$

where $\rho_{p,m}$, $C p_{p,m}$ and $\lambda_{p,m}$ stands for the density, heat capacity, and the thermal conductivity of the $\Omega_{p,m}$ domains, $T_{p,m}$ is the unknown temperature, and $t_c$ stands for the cycle time. The injection phase is modeled as an instantaneous non-perfect contact between the molten polymer at a temperature $T_{inj}$, and the insert at a temperature obtained from the previous cycle. Such an approach is allowed since the duration of the filling stage is negligible with respect to the cooling stage [5,13]. Then, the following initial conditions are employed:

$$ T_p(t = 0^+) = T_{inj} \quad \text{in } \Omega_p, \quad \text{and} \quad T_m(t = 0^+) = T_m(t = t_c^-) \quad \text{in } \Omega_m, \quad (2) $$

where $T_m(t = 0^+) = T_m(t = t_c^-)$ means that the temperature field $T_m$ of $\Omega_m$ at the beginning of a given cycle $t = 0^+$ is considered to be the same as the temperature field at the final time of the previous cycle $t = t_c^-$. The Eq. (2) is subject to the boundary conditions described next. The heat flux at the part-mold interface is modeled as a non-perfect contact condition as follows:

$$ -\lambda_p \frac{\partial T_p}{\partial n} = \frac{T_p - T_m}{TCR_{p-m}} \quad \text{at} \quad \Gamma_p \quad \forall t \in [0, t_c], \quad (3) $$

where $TCR_{p-m}$ stands for the thermal contact resistance (TCR) at the part-mold interface $\Gamma_p$ (see Fig. 1b), and $n$ stands for its outward normal vector. The heat flux exchanged between the mold and the CCs is modeled as:

$$ -\lambda_m \frac{\partial T_m}{\partial n} = h_c(T_m - T_c) \quad \text{at} \quad \Gamma_{m(cc)} \quad \forall t \in [0, t_c], \quad (4) $$

where $T_c$ is the coolant temperature, and $h_c$ is the convective coefficient. Finally, the heat transferred from the mold to the environment by convection and radiation is modeled with the following third-type boundary condition:
$$ -\lambda_m \frac{\partial T_m}{\partial n} = h_{eq}(T_m - T_{env}), \quad \text{at } \Gamma_{m(ext)} \quad \forall t \in [0, t_c], \qquad (5) $$

where $\Gamma_{m(ext)}$ is the boundary of the domain in contact with the surrounding air, $T_{env}$ stands for the ambient temperature, and $h_{eq}$ is an effective exchange coefficient. An additional *erosion surface* $\Gamma_e$ (see Fig. 1b) internal to $\Omega_p$ is considered for analysis, which is basically obtained by rolling internally to $\Gamma_p$, a circular structuring element of 1.5mm diameter [1].

Thermophysical Properties and Process Parameters. The properties of the injected polymer and the mold material are depicted in Table 1. The mold material originally considered by [12] is steel, and the injected polymer ABS. Two polymers are considered for the thermoplastic mold design: one highly conductive (referred by the super-index c), and one less conductive or *insulating* (referred by the super-index i), envisaging the use of the commercially available PEKK TCPoly ICE 9 and the polycarbonate as potential candidates, respectively. Their thermophysical properties are depicted in Table 1 as well. The parameters of the injection molding process are those reported in [1, 12], and are depicted in Table 2. According to such parameters, a convective coefficient $h_c = 27810 \text{ W/(m}^2\text{K)}$ is estimated, and $h_{eq} = 10 \text{ W/(m}^2\text{K)}$ is adopted from [3,4]. Regarding TCR values, $1.10^{-4} \text{ m}^2\text{K/W}$ is employed for polymer-steel contact [1,5], and $1.10^{-2} \text{ m}^2\text{K/W}$ for polymer-polymer contact [3,4].

<table><caption>Table 1: Material properties of the steel and thermoplastic molds, and of the injected polymer.</caption><thead><tr><th>Steel mold</th><th>Injected polymer</th><th colspan="2">Thermoplastic mold</th></tr></thead><tbody><tr><td>λ<sub>m</sub><sup>s</sup>=36.5 [W/(mK)]</td><td>λ<sub>p</sub>=0.25 [W/(mK)]</td><td>λ<sub>m</sub><sup>i</sup>=0.20 [W/(mK)]</td><td>λ<sub>m</sub><sup>c</sup>=2.0 [W/(mK)]</td></tr><tr><td>ρ<sub>m</sub><sup>s</sup>=7820 [kg/m<sup>3</sup>]</td><td>ρ<sub>p</sub>=938 [kg/m<sup>3</sup>]</td><td>ρ<sub>m</sub><sup>i</sup>=1210 [kg/m<sup>3</sup>]</td><td>ρ<sub>m</sub><sup>c</sup>=1500 [kg/m<sup>3</sup>]</td></tr><tr><td>Cp<sub>m</sub><sup>s</sup>=460 [J/(kgK)]</td><td>Cp<sub>p</sub>=1800 [J/(kgK)]</td><td>Cp<sub>m</sub><sup>i</sup>=1300 [J/(kgK)]</td><td>Cp<sub>m</sub><sup>c</sup>=1300 [J/(kgK)]</td></tr></tbody></table>

<table><caption>Table 2: Injection molding parameters [12].</caption><thead><tr><th>Fluid temperature</th><th>Flow rate</th><th>Cycle time</th><th>Injection temperature</th></tr></thead><tbody><tr><td>T<sub>c</sub>= 303 [K]</td><td>Q̇= 364 [cm<sup>3</sup>/s]</td><td>t<sub>c</sub>= 23.5 [s]</td><td>T<sub>inj</sub>= 503 [K]</td></tr></tbody></table>

Steel vs. Thermoplastic Mold Thermal Performance. Prior to address the optimization stage, it is of interest to compare the thermal performance of the original steel insert with respect to the highly conductive thermoplastic one. Due to the lower heat diffusivity of the thermoplastic material, $t_c$ needs to be inevitably increased to reach the ejection temperature at the erosion surface. Hence, a parametric study was performed assessing the time needed for the plastic mold case to reach the ejection temperature at $\Gamma_e$, and to assess the temperature standard deviation at $\Gamma_p$. Then, the outputs to study are the mean temperature of the part ($\bar{T}_p$), mean temperature of the erosion ($\bar{T}_e$), and temperature standard deviation at the part surface ($\sigma_p$), all at the ejection time ($t_e$), and are computed as follows:

$$ \bar{T}_p(t_e) = \frac{1}{\Gamma_p} \int_{\Gamma_p} T_p(t_e) d\Gamma, \quad \sigma_p(t_e) = \left( \frac{1}{\Gamma_p} \int_{\Gamma_p} (T_p(t_e) - \bar{T}_p)^2 d\Gamma \right)^{1/2}, \qquad (6) $$

considering that $\bar{T}_e$ is computed analogously to $\bar{T}_p$ but at $\Gamma_e$.

The heat transfer problems were solved with the open-source code PETScFEM (PF) on an unstructured mesh of 13570 triangular elements with a time step of $\Delta t = 0.5 \text{ s}$ for the steel case, and with $\Delta t = 5 \text{ s}$ for the thermoplastic mold scenario. Both the spatial and time discretizations
$$-\lambda_m \frac{\partial T_m}{\partial n} = h_{eq}(T_m - T_{env}), \quad \text{at } \Gamma_{m(ext)} \quad \forall t \in [0, t_c], \qquad (5)$$

where $\Gamma_{m(ext)}$ is the boundary of the domain in contact with the surrounding air, $T_{env}$ stands for the ambient temperature, and $h_{eq}$ is an effective exchange coefficient. An additional *erosion surface* $\Gamma_e$ (see Fig. 1b) internal to $\Omega_p$ is considered for analysis, which is basically obtained by rolling internally to $\Gamma_p$, a circular structuring element of 1.5mm diameter [1].

Thermophysical Properties and Process Parameters. The properties of the injected polymer and the mold material are depicted in Table 1. The mold material originally considered by [12] is steel, and the injected polymer ABS. Two polymers are considered for the thermoplastic mold design: one highly conductive (referred by the super-index c), and one less conductive or *insulating* (referred by the super-index i), envisaging the use of the commercially available PEKK TCPoly ICE 9 and the polycarbonate as potential candidates, respectively. Their thermophysical properties are depicted in Table 1 as well. The parameters of the injection molding process are those reported in [1, 12], and are depicted in Table 2. According to such parameters, a convective coefficient $h_c = 27810 \text{ W/(m}^2\text{K)}$ is estimated, and $h_{eq} = 10 \text{ W/(m}^2\text{K)}$ is adopted from [3,4]. Regarding TCR values, $1.10^{-4} \text{ m}^2\text{K/W}$ is employed for polymer-steel contact [1,5], and $1.10^{-2} \text{ m}^2\text{K/W}$ for polymer-polymer contact [3,4].

<table><caption>Table 1: Material properties of the steel and thermoplastic molds, and of the injected polymer.</caption><thead><tr><th>Steel mold</th><th>Injected polymer</th><th colspan="2">Thermoplastic mold</th></tr></thead><tbody><tr><td>λ<sub>m</sub><sup>s</sup>=36.5 [W/(mK)]</td><td>λ<sub>p</sub>=0.25 [W/(mK)]</td><td>λ<sub>m</sub><sup>i</sup>=0.20 [W/(mK)]</td><td>λ<sub>m</sub><sup>c</sup>=2.0 [W/(mK)]</td></tr><tr><td>ρ<sub>m</sub><sup>s</sup>=7820 [kg/m<sup>3</sup>]</td><td>ρ<sub>p</sub>=938 [kg/m<sup>3</sup>]</td><td>ρ<sub>m</sub><sup>i</sup>=1210 [kg/m<sup>3</sup>]</td><td>ρ<sub>m</sub><sup>c</sup>=1500 [kg/m<sup>3</sup>]</td></tr><tr><td>Cp<sub>m</sub><sup>s</sup>=460 [J/(kgK)]</td><td>Cp<sub>p</sub>=1800 [J/(kgK)]</td><td>Cp<sub>m</sub><sup>i</sup>=1300 [J/(kgK)]</td><td>Cp<sub>m</sub><sup>c</sup>=1300 [J/(kgK)]</td></tr></tbody></table>

<table><caption>Table 2: Injection molding parameters [12].</caption><thead><tr><th>Fluid temperature</th><th>Flow rate</th><th>Cycle time</th><th>Injection temperature</th></tr></thead><tbody><tr><td>T<sub>c</sub>= 303 [K]</td><td>Q̇= 364 [cm<sup>3</sup>/s]</td><td>t<sub>c</sub>= 23.5 [s]</td><td>T<sub>inj</sub>= 503 [K]</td></tr></tbody></table>

Steel vs. Thermoplastic Mold Thermal Performance. Prior to address the optimization stage, it is of interest to compare the thermal performance of the original steel insert with respect to the highly conductive thermoplastic one. Due to the lower heat diffusivity of the thermoplastic material, $t_c$ needs to be inevitably increased to reach the ejection temperature at the erosion surface. Hence, a parametric study was performed assessing the time needed for the plastic mold case to reach the ejection temperature at $\Gamma_e$, and to assess the temperature standard deviation at $\Gamma_p$. Then, the outputs to study are the mean temperature of the part ($\bar{T}_p$), mean temperature of the erosion ($\bar{T}_e$), and temperature standard deviation at the part surface ($\sigma_p$), all at the ejection time ($t_e$), and are computed as follows:

$$\bar{T}_p(t_e) = \frac{1}{\Gamma_p} \int_{\Gamma_p} T_p(t_e) d\Gamma, \quad \sigma_p(t_e) = \left( \frac{1}{\Gamma_p} \int_{\Gamma_p} (T_p(t_e) - \bar{T}_p)^2 d\Gamma \right)^{1/2}, \qquad (6)$$

considering that $\bar{T}_e$ is computed analogously to $\bar{T}_p$ but at $\Gamma_e$.

The heat transfer problems were solved with the open-source code PETScFEM (PF) on an unstructured mesh of 13570 triangular elements with a time step of $\Delta t = 0.5 \text{ s}$ for the steel case, and with $\Delta t = 5 \text{ s}$ for the thermoplastic mold scenario. Both the spatial and time discretizations
were derived from a convergence study, resulting in excellent agreement with the results reported in [1] performed in COMSOL (see Fig. 2a and Table 3). The results of the parametric study are presented in Table 3. It can be observed that for $\overline{T}_e$ to reach an ejection temperature below ≈ 335-336 °C (steel case), a $t_c$ = 140 s was needed by the thermoplastic mold. Despite of increasing $t_c$, it can be noticed that the temperature homogeneity at $\Gamma_p$ is severely affected, increasing $\sigma_p$ by ≈ 136 %. This can be also observed from Fig. 2a. While the maximum delta temperature $\Delta T$ = ($T_{\Gamma_p}^{max} - T_{\Gamma_p}^{min}$) is of roughly 7 °C for the steel case, such a delta increases to ≈ 23 °C for the thermoplastic case. It can be seen from Fig. 2b that due to the high heat diffusivity of steel, the through-thickness temperature gradients are high, and the through-surface gradients are reduced. In contrast, the opposite scenario is observed for the thermoplastic mold, where low through-thickness and high through-surface temperature gradients are observed. The thermal enhancement and optimization of the thermoplastic mold to improve $\sigma_p$ while reaching the ejection temperature at $\Gamma_e$ is the main concern of the next sections.

<table><caption>Table 3: Parametric study performed on the thermoplastic mold for different $t_c$.</caption><thead><tr><th></th><th>Steel [1]</th><th colspan="6">Steel (PF)</th><th colspan="2">Thermoplastic (PF)</th></tr></thead><tbody><tr><th>t<sub>c</sub> [s]</th><td>23.5</td><td colspan="6"></td><td colspan="2"></td></tr><tr><th>T&#773;<sub>e</sub> [K]</th><td>335.6</td><td>336.31</td><td>340.10</td><td>337.97</td><td>335.98</td><td>334.12</td><td colspan="2"></td></tr><tr><th>T&#773;<sub>p</sub> [K]</th><td>310.7</td><td>310.82</td><td>336.73</td><td>334.96</td><td>333.31</td><td>331.76</td><td colspan="2"></td></tr><tr><th>σ<sub>p</sub> [K]</th><td>1.43</td><td>1.42</td><td>3.81</td><td>3.65</td><td>3.50</td><td>3.37</td><td colspan="2">3.26</td></tr></tbody></table>

<figure><img src="image_2545.png" /><figcaption>Figure 2: Temperature fields obtained by the steel and thermoplastic injection molds at 23.5 s and 140 s, respectively, at (a) A-B arc of $\Gamma_p$ (Fig. 1b), and (b) within the mold and part.</figcaption></figure>

## Topology optimization for transient heat flux manipulation

TO-FEM Modeling. Let us consider the semi-discretized FEM form of Eq. (1):

$$C\dot{T} + KT = Q, \qquad (7)$$

where **C**, **K** and **Q** are the global capacitance matrix, conduction matrix, and heat load vector, respectively, which are defined as:

$$C = \int_{\Omega} N^T \rho C_p N \, d\Omega, \quad K = \int_{\Omega} B^T \lambda B \, d\Omega, \quad Q = - \int_{\Gamma} N^T q \, d\Gamma, \qquad (8)$$

being $B_{ij} = \partial N_i / \partial x_j$, such that $\nabla T \approx BT$, and the temperature field is approximated as $T(x, t) \approx N_j(x)T_j(t)$, where $N_j$ is the shape function associated to the node j of the
were derived from a convergence study, resulting in excellent agreement with the results reported in [1] performed in COMSOL (see Fig. 2a and Table 3). The results of the parametric study are presented in Table 3. It can be observed that for $\overline{T}_e$ to reach an ejection temperature below ≈ 335-336 °C (steel case), a $t_c$ = 140 s was needed by the thermoplastic mold. Despite of increasing $t_c$, it can be noticed that the temperature homogeneity at $\Gamma_p$ is severely affected, increasing $\sigma_p$ by ≈ 136 %. This can be also observed from Fig. 2a. While the maximum delta temperature $\Delta T$ = ($T_{\Gamma_p}^{max} - T_{\Gamma_p}^{min}$) is of roughly 7 °C for the steel case, such a delta increases to ≈ 23 °C for the thermoplastic case. It can be seen from Fig. 2b that due to the high heat diffusivity of steel, the through-thickness temperature gradients are high, and the through-surface gradients are reduced. In contrast, the opposite scenario is observed for the thermoplastic mold, where low through-thickness and high through-surface temperature gradients are observed. The thermal enhancement and optimization of the thermoplastic mold to improve $\sigma_p$ while reaching the ejection temperature at $\Gamma_e$ is the main concern of the next sections.

<table><caption>Table 3: Parametric study performed on the thermoplastic mold for different $t_c$.</caption><thead><tr><th></th><th>Steel [1]</th><th colspan="6">Steel (PF)</th><th colspan="2">Thermoplastic (PF)</th></tr></thead><tbody><tr><th>t<sub>c</sub> [s]</th><td>23.5</td><td colspan="6"></td><td colspan="2"></td></tr><tr><th>T&#773;<sub>e</sub> [K]</th><td>335.6</td><td>336.31</td><td>340.10</td><td>337.97</td><td>335.98</td><td>334.12</td><td colspan="2"></td></tr><tr><th>T&#773;<sub>p</sub> [K]</th><td>310.7</td><td>310.82</td><td>336.73</td><td>334.96</td><td>333.31</td><td>331.76</td><td colspan="2"></td></tr><tr><th>σ<sub>p</sub> [K]</th><td>1.43</td><td>1.42</td><td>3.81</td><td>3.65</td><td>3.50</td><td>3.37</td><td colspan="2">3.26</td></tr></tbody></table>

<figure><img src="image_2538.png" /><figcaption>Figure 2: Temperature fields obtained by the steel and thermoplastic injection molds at 23.5 s and 140 s, respectively, at (a) A-B arc of $\Gamma_p$ (Fig. 1b), and (b) within the mold and part.</figcaption></figure>

## Topology optimization for transient heat flux manipulation

TO-FEM Modeling. Let us consider the semi-discretized FEM form of Eq. (1):

$$C\dot{T} + KT = Q, \qquad (7)$$

where **C**, **K** and **Q** are the global capacitance matrix, conduction matrix, and heat load vector, respectively, which are defined as:

$$C = \int_{\Omega} N^T \rho C_p N \, d\Omega, \quad K = \int_{\Omega} B^T \lambda B \, d\Omega, \quad Q = - \int_{\Gamma} N^T q \, d\Gamma, \qquad (8)$$

being $B_{ij} = \partial N_i / \partial x_j$, such that $\nabla T \approx BT$, and the temperature field is approximated as $T(x, t) \approx N_j(x)T_j(t)$, where $N_j$ is the shape function associated to the node j of the
discretized finite element space of $\Omega$, and $T_j$ the unknown temperature of the node. For the time discretization we consider a backward Euler scheme throughout this work.

<figure><img src="image_2546.png" /><figcaption>Figure 3: Representative scheme of computational $\Omega_{dev}$: (a) a reference case reported in [8] and used here for validation, and (b) the actual injection mold domain to be optimized in this work.</figcaption></figure>

Now, let us consider a metadevice in a non-homogeneous region $\Omega_{dev} \subset \Omega$ (see Fig. 3) where a design variable vector $P$ of equal size of the finite element mesh of $\Omega_{dev}$ will define the type of material on each mesh element. Consequently, $C = C(P)$ and $K = K(P)$, with $P = [p_1, p_2, \dots, p_N]$, being $N$ the number of finite elements in $\Omega_{dev}$. Then, inevitably, the transient temperature field in the whole $\Omega$ will depend on $P$, i.e., $T = T(x, t, P) \forall x \in \Omega$. Then, our TO problem summarizes in finding the appropriate set of parameters $P$ in order to accomplish a desired behavior of the heat flux in a given $\Omega_{task}$ (Fig. 3a) or $\Gamma_{task}$ (Fig. 3b). Certainly, our main goal will be to improve temperature homogeneity at $\Gamma_{task} = \Gamma_p$, however, an additional case will be first addressed at $\Omega_{task}$ to validate our methodology.

**PSO and Filtering Algorithm.** The optimization procedure for material distribution in the TO followed here is based on the use of PSO along with density and topological filters, and it is briefly described as follows (please see Fig. 4a): 1) The PSO proposes a vector of parameters $P$ where each element in $\Omega_{dev}$ is defined as a continuous value in the [0,1] range; 2) the following density filter [14] is applied aiming to avoid checker-board patterns:

$$p^{(e)} = \frac{\sum_{i} r^{(e)} - \Delta_{ei}}{\sum_{i} r^{(e)} - \Delta_{ei}}, \qquad (9)$$

where $p^{(e)}$ is the design value of a given element $e$, $r^{(e)}$ is a predefined radius distance from the center of the element, $\Delta_{ei}$ is the distance between the i-th and e-th elements, and $p^{(i)}$ stands for the design variable of the i-th element; 3) a threshold is applied to either obtain a conductive/insulating polymer material on each element (threshold value of $w = 0.5$ [14]); 4) single isolated elements that do not share neighbors of the same species are converted into the alternative material; 5) the regions with the same type of material are grouped in sets; 6) those groups who do not accomplish a minimum size ($A \ge 63.6\text{mm}^2$, which is the CC area for reference) are converted in the alternative material. Steps 5) and 6) are performed for the sake of feasible-to-manufacture resulting designs, and two iterations may be needed.
discretized finite element space of $\Omega$, and $T_j$ the unknown temperature of the node. For the time discretization we consider a backward Euler scheme throughout this work.

<figure><img src="image_2539.png" /><figcaption>Figure 3: Representative scheme of computational $\Omega_{dev}$: (a) a reference case reported in [8] and used here for validation, and (b) the actual injection mold domain to be optimized in this work.</figcaption></figure>

Now, let us consider a metadevice in a non-homogeneous region $\Omega_{dev} \subset \Omega$ (see Fig. 3) where a design variable vector $P$ of equal size of the finite element mesh of $\Omega_{dev}$ will define the type of material on each mesh element. Consequently, $C = C(P)$ and $K = K(P)$, with $P = [p_1, p_2, \dots, p_N]$, being $N$ the number of finite elements in $\Omega_{dev}$. Then, inevitably, the transient temperature field in the whole $\Omega$ will depend on $P$, i.e., $T = T(x, t, P) \forall x \in \Omega$. Then, our TO problem summarizes in finding the appropriate set of parameters $P$ in order to accomplish a desired behavior of the heat flux in a given $\Omega_{task}$ (Fig. 3a) or $\Gamma_{task}$ (Fig. 3b). Certainly, our main goal will be to improve temperature homogeneity at $\Gamma_{task} = \Gamma_p$, however, an additional case will be first addressed at $\Omega_{task}$ to validate our methodology.

**PSO and Filtering Algorithm.** The optimization procedure for material distribution in the TO followed here is based on the use of PSO along with density and topological filters, and it is briefly described as follows (please see Fig. 4a): 1) The PSO proposes a vector of parameters $P$ where each element in $\Omega_{dev}$ is defined as a continuous value in the [0,1] range; 2) the following density filter [14] is applied aiming to avoid checker-board patterns:

$$p^{(e)} = \frac{\sum_i \langle r^{(e)} - \Delta_{ei} \rangle p^{(i)}}{\sum_i \langle r^{(e)} - \Delta_{ei} \rangle}, \quad (9)$$

where $p^{(e)}$ is the design value of a given element $e$, $r^{(e)}$ is a predefined radius distance from the center of the element, $\Delta_{ei}$ is the distance between the i-th and e-th elements, and $p^{(i)}$ stands for the design variable of the i-th element; 3) a threshold is applied to either obtain a conductive/insulating polymer material on each element (threshold value of $w = 0.5$ [14]); 4) single isolated elements that do not share neighbors of the same species are converted into the alternative material; 5) the regions with the same type of material are grouped in sets; 6) those groups who do not accomplish a minimum size ($A \ge 63.6 \text{mm}^2$, which is the CC area for reference) are converted in the alternative material. Steps 5) and 6) are performed for the sake of feasible-to-manufacture resulting designs, and two iterations may be needed.
<figure><img src="image_2547.png" /><figcaption>Figure 4: Filtering procedure in the PSO-based TO approach.</figcaption></figure>

Gradient-based and Gradient-free TO Approaches in the Transient Regime. Prior to apply the proposed gradient-free TO scheme to the injection mold design, it is convenient to assess its performance on a transient heat transfer scenario. Hence, the case reported in [8] of Fig. 3a is considered here, where the computational domains start at $T = 293$ K, and the right side temperature is fixed at $T_R = 293$ K. The left side temperature is first increased linearly with time until it reaches $T_L = 333$ K at 520 s and maintained until a first steady regime is reached at 10647 s, and it is subsequently subjected to a further linear increment to $T_L = 343$ K at $t = 10825$ s, and maintained until finishing the transient heat conduction analysis at $t = t_f = 19500$ s. The main goal is to minimize the function $f_{obj} = (1/t_f) \int_0^{t_f} g(\mathbf{P}, t)dt/f_0$, where $f_0$ is a constant, and $g(\mathbf{P}, t)$ being defined as:

$$g(\mathbf{P}, t) = \left[ \frac{1}{\Omega_{task}} \int_{\Omega_{task}} \left| \left| q(\mathbf{P}, \mathbf{x}, t) \right| \right|^2 d\Omega \right]^{1/2}, \quad (10)$$

which represents the total heat flux in $\Omega_{task}$. $\Omega_{out}$ is made of Gad Pad material, $\Omega_{task}$ is made of PMMA polymer, and $\Omega_{dev}$ can be either conformed by PMMA or copper. A symmetry case was considered where the upper half of $\Omega$ was meshed by 200x100 structured quadrangular elements, where 3614 finite elements (hence, variables) defined $\Omega_{dev}$. We refer the reader to [8] for detailed information of the materials properties and the numerical setup.

After 13500 $f_{obj}$ evaluations and roughly 8hs solving in parallel on 80 cores, the solution was converged. The results are presented and compared in Fig. 5. Despite of the dissimilarity in materials distribution obtained by the TO proposed in this work (see Fig. 5b) with respect to that reported in the literature (see Fig. 5a), it can be observed from Fig. 5c that the PSO-based solution successfully accomplished the heat flux shielding task. Furthermore, the PSO-based TO slightly outperformed the gradient-based one in the close-to-stationary state regimes.

## TO results on a 3D printed thermoplastic injection mold

Problem Definition. The PSO-based TO is applied to a mold design in this section. The two polymers considered as candidate materials for $\Omega_{dev}$ (see Fig. 3b) are those from Table 1. The objective function ($f_{obj}$) is to minimize $\sigma_p(t_e)$ subject to the constraint $\bar{T}_e < 336$ K. A total of 7733 variables were handled by PSO, corresponding to the number of elements at $\Omega_{dev}$. For each evaluation of $f_{obj}$, 8 injection cycles were performed using a $\Delta t = 5$ s, and each cycle with a total duration of $t_f = 140$ s. The $f_{obj}$ evaluations were solved in parallel in the HPC cluster of Pays de
<figure><img src="image_2540.png" /><figcaption>Figure 4: Filtering procedure in the PSO-based TO approach.</figcaption></figure>

Gradient-based and Gradient-free TO Approaches in the Transient Regime. Prior to apply the proposed gradient-free TO scheme to the injection mold design, it is convenient to assess its performance on a transient heat transfer scenario. Hence, the case reported in [8] of Fig. 3a is considered here, where the computational domains start at $T = 293$ K, and the right side temperature is fixed at $T_R = 293$ K. The left side temperature is first increased linearly with time until it reaches $T_L = 333$ K at 520 s and maintained until a first steady regime is reached at 10647 s, and it is subsequently subjected to a further linear increment to $T_L = 343$ K at $t = 10825$ s, and maintained until finishing the transient heat conduction analysis at $t = t_f = 19500$ s. The main goal is to minimize the function $f_{obj} = (1/t_f) \int_0^{t_f} g(\mathbf{P}, t)dt/f_0$, where $f_0$ is a constant, and $g(\mathbf{P}, t)$ being defined as:

$$g(\mathbf{P}, t) = \left[ \frac{1}{\Omega_{task}} \int_{\Omega_{task}} \left| \left| q(\mathbf{P}, \mathbf{x}, t) \right| \right|^2 d\Omega \right]^{1/2}, \quad (10)$$

which represents the total heat flux in $\Omega_{task}$. $\Omega_{out}$ is made of Gad Pad material, $\Omega_{task}$ is made of PMMA polymer, and $\Omega_{dev}$ can be either conformed by PMMA or copper. A symmetry case was considered where the upper half of $\Omega$ was meshed by 200x100 structured quadrangular elements, where 3614 finite elements (hence, variables) defined $\Omega_{dev}$. We refer the reader to [8] for detailed information of the materials properties and the numerical setup.

After 13500 $f_{obj}$ evaluations and roughly 8hs solving in parallel on 80 cores, the solution was converged. The results are presented and compared in Fig. 5. Despite of the dissimilarity in materials distribution obtained by the TO proposed in this work (see Fig. 5b) with respect to that reported in the literature (see Fig. 5a), it can be observed from Fig. 5c that the PSO-based solution successfully accomplished the heat flux shielding task. Furthermore, the PSO-based TO slightly outperformed the gradient-based one in the close-to-stationary state regimes.

## TO results on a 3D printed thermoplastic injection mold

Problem Definition. The PSO-based TO is applied to a mold design in this section. The two polymers considered as candidate materials for $\Omega_{dev}$ (see Fig. 3b) are those from Table 1. The objective function ($f_{obj}$) is to minimize $\sigma_p(t_e)$ subject to the constraint $\bar{T}_e < 336$ K. A total of 7733 variables were handled by PSO, corresponding to the number of elements at $\Omega_{dev}$. For each evaluation of $f_{obj}$, 8 injection cycles were performed using a $\Delta t = 5$ s, and each cycle with a total duration of $t_f = 140$ s. The $f_{obj}$ evaluations were solved in parallel in the HPC cluster of Pays de
la Loire (CCIPL), where each simulation took approximately 2 minutes in one single core, and the total optimization process took roughly 12 hours in 40 cores.

<figure><img src="image_2548.png" /><figcaption>Figure 5: TO solutions obtained by the gradient-based approach [8], and the gradient-free proposed in this work. In (a) and (b) blue regions represent copper material, while red zones represent PMMA material. In (c) the heat flux in $\Omega_{task}$ in time is compared.</figcaption></figure>

<figure><img src="image_2549.png" /><figcaption>Figure 6: Results obtained by the topologic optimization scheme: (a) convergence of the objective function, (b) constraint computation, (c) temperature at A-B in $\Gamma_p$ (see Fig. 1b).</figcaption></figure>

Results Obtained by the PSO-TO in the Injection Mold. The convergence tendency of $f_{obj}$ is evident from Fig. 6a, and the final best value was $\sigma_p = 1.62$ K after reaching 15000 $f_{obj}$ evaluations. The accomplishment of the maximum temperature constraint at $\Gamma_e$ can be observed in Fig. 6b, and the resulting $\bar{T}_e$ was 334.68 °C. The results are summarized in Table 4 where it can be deduced that, for the same cycle time ($t_f = 140$ s), a marked improvement is obtained in the temperature homogeneity by combining the two thermoplastics, reducing $\sigma_p$ by 52 %, and obtaining a similar value to that of steel.

<table><caption>Table 4: Results obtained by the mono-material and the optimized multi-material molds.</caption><thead><tr><th></th><th>Steel</th><th>Plastic (mono-material)</th><th>Plastic (multi-material)</th></tr></thead><tbody><tr><td>t<sub>f</sub> [s]</td><td>23.5</td><td>140</td><td>140</td></tr><tr><td>T&#773;<sub>e</sub> [K]</td><td>336.31</td><td>334.12</td><td>334.68</td></tr><tr><td>T&#773;<sub>p</sub> [K]</td><td>310.82</td><td>331.76</td><td>332.67</td></tr><tr><td>σ<sub>p</sub> [K]</td><td>1.42</td><td>3.37</td><td>1.62</td></tr><tr><td>ΔT<sub>Γ<sub>2</sub></sub> [K]</td><td>7,14</td><td>23.56</td><td>13.32</td></tr></tbody></table>