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Experimental dynamical analysis of specimens’ material properties manufactured by additive technologies
Available online at www.sciencedirect.com
ScienceDirect Materials Today: Proceedings 12 (2019) 352–357
www.materialstoday.com/proceedings
DAS35
Experimental dynamical analysis of specimens’ material properties manufactured by additive technologies Peter Ficzerea, Lajos Borbásb,* a
Budapest University of Technology and Economics, Department of Vehicle Parts and Structures Analysis, H-1111 Budapest, Stoczek u. 2 b Budapest University of Technology and Economics, Department of Vehicle Parts and Structures Analysis; and EDUTUS University, Technical Institution, H-2800 Tatabánya, Stúdium tér.
Abstract In the recent years 3D printing has become a hot topic, however it is hard to design parts without a deep understanding of the material properties. The aim of this study is to estimate the modal parameters and the damping properties via experimental dynamic analysis of a part made from PLA. We will study the effects of the different directions of printing. With the results data for the FEM software’s input can be provided. © 2019 Elsevier Ltd. All rights reserved. Selection and peer-review under responsibility of 35th Danubia Adria Symposium on Advances in Experimental Mechanics. Keywords: experimental modal analysis, additive manufacturing, eigenfrequency, mode shapes, polymers, material law
1. Introduction In the recent years 3D printing has attracted great attention thanks to the rapid development of the technologies. At the same time the need for a good alternative of the currently popular non-biodegradable plastics also arise. Polylactic acid (PLA) seems to be a good option replacing other plastics. With additive manufacturing technologies using biodegradable plastics, which become a viable option for rapid prototyping or custom manufacturing, we need a deep understanding of the material properties [1] [2] [3] [4]. We looked at the available papers on PLA’s material properties. There are only a few about modeling the material properties and the results show big deviation regarding the same properties [5] [6] [7].
* Corresponding author. Tel.: +36-1-463-1111/5821 E-mail address: [email protected] 2214-7853 © 2019 Elsevier Ltd. All rights reserved. Selection and peer-review under responsibility of 35th Danubia Adria Symposium on Advances in Experimental Mechanics.
P. Ficzere, L. Borbas / Materials Today: Proceedings 12 (2019) 352–357
353
Fig. 1 Stress-strain curves of PLA with FDM technology
The results of the tensile test can be seen in Fig 1 and Table 1. Table 1. Classification of the mode shapes Ultimate strength Rm [MPa]
Young modulus E [MPa]
Laying (x-y)
54.619±0.33
3019.817±67.909
Standing (z)
27.464±2.928
2891.227±6.695
Our goal is to better know these parts’ damping properties and the effects of the printing parameters on material properties, more precisely the printing direction. 2. Materials and methodology After studying the available literature, we were certain that the positioning of the part in the printer has a massive impact on the material properties. We found that the tensile strength in the printing direction was 50% less than in the other two directions [5] [6]. This coincides with our assumption: parts made by this method show orthotropic properties [7] [8] [9]. It is clear that the main factor is the printing direction therefore we focus on that printing property. To keep our model simple, we print our specimens as prismatic columns.
Fig. 2. Printing directions of the specimen. (A, B and C)
354
P. Ficzere, L. Borbas ./ Materials Today: Proceedings 12 (2019) 352–357
For every direction, we printed 3 specimens to check the reproducibility and eliminate errors of the printer. So far, the two laying positions have been tested. We tested the parts as cantilevers. For excitation we used an impact hammer, and measured the response using accelerometers. The theoretical measurement set-up can be seen in Fig 3.
Fig. 3. Measurement set-up
We located the specimen’s natural frequencies (bending and torsion), damping ratios and mode shapes in the f=0-1000 Hz range. For every mode we checked if the mode shape is classical normal mode or not. As it is known classical normal modes’ mode shapes show standing wave nature, equivalent to the undamped system’s mode shapes. Thus, the mathematical model is significantly simpler. We also separated the detected mode shapes into two groups depending on the nature of the mode shape: bending and torsion. To avoid false results, to detect natural frequencies, we also measured the base’s natural frequencies. To identify the damping mechanism, we will define regression functions, which express the damping factor’s frequency dependence [6]. These functions have a direct connection to the damping factor’s function. For the measured Frequency Response Function’s (FRF from now) analytic approximation we used the partial fraction form: n Pi Pi H ( j ) j i i 1 j i
i i j d ,i
(1)
(2)
P. Ficzere, L. Borbas / Materials Today: Proceedings 12 (2019) 352–357
355
where: Pi is residuum of mode i [m/sec/N], λi is the complex eigenvalue of mode i [rad/s], σi is modal damping of mode i, ωd,i is damped natural frequency of mode i, and j is the imaginary part. 3. Results Fig. 4 shows the FRF of a part printed with method “B”, the laying case in the middle of Figure 2. The frequency values belonging to the peaks of the curve indicate the own frequency.
Fig. 4. . FRF of part B1
We excite in a fixed point, and the response is measured also in locations 1 and 2 of the specimen (Fig. 3.) The points belonging to peak FRF on the identical own frequency, the Nyquist plots belonging to the two response measurement locations indicate whether the two points reach the extreme position in phase or counterphase. The cursor in both cases is on the same point belonging to the own frequency. It is clear that the two points are approximately in counterphase, so the vibration image is of torsion character, otherwise we could have assumed bending vibration. In Fig. 5 the dominant modal circles can be seen. Further analysis has to be made to estimate the modes with smaller amplitude (near the origin).
Fig. 5. Vibration image classification with Nyquist plots
356
P. Ficzere, L. Borbas ./ Materials Today: Proceedings 12 (2019) 352–357
Using this method, we could detect 4 natural frequencies frequency value belonging to the 4 peaks (Table 2) . For the classification we use the Nyquist-plot of the FRF. (B – Bend, T – Torsion) Table 2. Classification of the mode shapes Mode i
1
2
3
4
fi [Hz]
116.87
304.58
692.03
762.96
ξi [%]
2.61
9.14
1.49
0.93
Type
B
T
T
B
4. Conclusions
The results show little to no difference between the two laying parts (B and C). With the last measurements done we will be able to compare the different orientations. When processing the data, we suspected nonlinearity of the material properties. We can state the material model of elements produced by FDM technology in case of PLA materials follows fluid-type behavior (viscous-elastic behavior). Jeffrey-body, the construction is a serial connection of a Kelvin-Voight and a Newton body, so it is a fluid-type model. Sometimes it is called Fluid II. Model [10]. The Jeffrey-body can be seen in Fig. 6. We found that this model realizes a Rayleigh-shape with proportional damping behaviour.
Fig. 6. . Jeffrey-body material model
Based on the experimental results the PLA material shows anisotropic behaviour, the damping parameters are changing in the function of the printing directions. Based on our investigation we can state that the standard deviation of damping parameters of FRF functions determined by analytical approximation is in a great range. Probably the clamping conditions must be changed. One of the possible solutions is the free hanging of the test specimens. The experimental results must be verified by numerical simulation. Generally, the Hooks Law is applied, where to describe the behavior of the material, the determination of the Young Modulus is enough (σ = Eε). In orthotropic case, stiffness constant in the 3 printing directions is different. Based on our investigation the “Jeffrey-body” describes the behaviour of the material more exactly, where the determination of the damping parameters is necessary. From the creeping model of the “Jeffrey-body” it can be established that the material behavior could be characterized with a hysteresis curve, which is proportional to the damping parameters of the material. The curve – generated from the peak-points of the hysteresis loops – could describe the fatigue behavior of the material. The determination of the model parameters, fatigue investigation will be carried out.
P. Ficzere, L. Borbas / Materials Today: Proceedings 12 (2019) 352–357
357
5. Acknowledgements These project results have been realized with a subsidy of the National Research Development and Innovation Office from the fund of NKIH. The title of the project is “Development of the New Generation of Production Technology for Individual Medical-Biological Implantation and Tools”. Project identification No.: NVKP_16-12016-0022., and: Basic Research project in the field of Laser-beam - technologies …. (in Hungarian: Lézertechnológiai és energetikai alapkutatás megvalósítása az Edutus Főiskolán, tudástranszfer, továbbá a vállalati kapcsolatok és a társadalmi szerepvállalás erősítését célzó tevékenységekkel kiegészítve). Project identification No.: EFOP-3.6.1-16-2016-000 The elaborators express their thanks for the support. 6. References [1] P. Ficzere, L. Borbás, Á. Török, Int. J. Traffic Transp. Eng. 3(3) (2013) 344-350. [2] P. Ficzere, L. Borbás, Á. Török, Acta Mech. Slovaca 18. (2014) 14-24. [3] M. Győri, P. Ficzere, Period. Polytech. Transp. 45:(1) . (2017) 21-24 [4] M. Győri, P. Ficzere, Period. Polytech. Transp. 44:(3) (2016) 164-171. [5] P. Ficzere, GÉP 67:(5-6) (2016) 78-81 [6] M. Tisza, P.Z. Kovács, D. Tóth, In: XXIX. microCAD International Multidisciplinary Scientific Conference, University of Miskolc, 9-10 April, 2015. ISBN 978-963-358-061-5 (In Hungarian). [7] B.Á. Kovács, P. Ficzere, Á. Török, PLA anyagból készült próbadarab tulajdonságainak kísérleti dinamikai vizsgálata, Műszaki Tudományos Közlemények 9. (2018) 135-138. ISSN 2393-1280 (In Hungarian). [8] P. Ficzere, L. Borbás, Gy. Falk, Biomechanica Hungarica 10/2. (2017) 57-58 (In Hungarian). [9] P. Ficzere, L. Borbás, Biomechanica Hungarica 10/2 (2017) 22. (In Hungarian) [10] F. Pápai, In: XI. Magyar Mechanikai Konferencia, MaMeK, 2011, Miskolc, 29-31 Aug, 2011, 1-11 (In Hungarian).
ScienceDirect Materials Today: Proceedings 12 (2019) 352–357
www.materialstoday.com/proceedings
DAS35
Experimental dynamical analysis of specimens’ material properties manufactured by additive technologies Peter Ficzerea, Lajos Borbásb,* a
Budapest University of Technology and Economics, Department of Vehicle Parts and Structures Analysis, H-1111 Budapest, Stoczek u. 2 b Budapest University of Technology and Economics, Department of Vehicle Parts and Structures Analysis; and EDUTUS University, Technical Institution, H-2800 Tatabánya, Stúdium tér.
Abstract In the recent years 3D printing has become a hot topic, however it is hard to design parts without a deep understanding of the material properties. The aim of this study is to estimate the modal parameters and the damping properties via experimental dynamic analysis of a part made from PLA. We will study the effects of the different directions of printing. With the results data for the FEM software’s input can be provided. © 2019 Elsevier Ltd. All rights reserved. Selection and peer-review under responsibility of 35th Danubia Adria Symposium on Advances in Experimental Mechanics. Keywords: experimental modal analysis, additive manufacturing, eigenfrequency, mode shapes, polymers, material law
1. Introduction In the recent years 3D printing has attracted great attention thanks to the rapid development of the technologies. At the same time the need for a good alternative of the currently popular non-biodegradable plastics also arise. Polylactic acid (PLA) seems to be a good option replacing other plastics. With additive manufacturing technologies using biodegradable plastics, which become a viable option for rapid prototyping or custom manufacturing, we need a deep understanding of the material properties [1] [2] [3] [4]. We looked at the available papers on PLA’s material properties. There are only a few about modeling the material properties and the results show big deviation regarding the same properties [5] [6] [7].
* Corresponding author. Tel.: +36-1-463-1111/5821 E-mail address: [email protected] 2214-7853 © 2019 Elsevier Ltd. All rights reserved. Selection and peer-review under responsibility of 35th Danubia Adria Symposium on Advances in Experimental Mechanics.
P. Ficzere, L. Borbas / Materials Today: Proceedings 12 (2019) 352–357
353
Fig. 1 Stress-strain curves of PLA with FDM technology
The results of the tensile test can be seen in Fig 1 and Table 1. Table 1. Classification of the mode shapes Ultimate strength Rm [MPa]
Young modulus E [MPa]
Laying (x-y)
54.619±0.33
3019.817±67.909
Standing (z)
27.464±2.928
2891.227±6.695
Our goal is to better know these parts’ damping properties and the effects of the printing parameters on material properties, more precisely the printing direction. 2. Materials and methodology After studying the available literature, we were certain that the positioning of the part in the printer has a massive impact on the material properties. We found that the tensile strength in the printing direction was 50% less than in the other two directions [5] [6]. This coincides with our assumption: parts made by this method show orthotropic properties [7] [8] [9]. It is clear that the main factor is the printing direction therefore we focus on that printing property. To keep our model simple, we print our specimens as prismatic columns.
Fig. 2. Printing directions of the specimen. (A, B and C)
354
P. Ficzere, L. Borbas ./ Materials Today: Proceedings 12 (2019) 352–357
For every direction, we printed 3 specimens to check the reproducibility and eliminate errors of the printer. So far, the two laying positions have been tested. We tested the parts as cantilevers. For excitation we used an impact hammer, and measured the response using accelerometers. The theoretical measurement set-up can be seen in Fig 3.
Fig. 3. Measurement set-up
We located the specimen’s natural frequencies (bending and torsion), damping ratios and mode shapes in the f=0-1000 Hz range. For every mode we checked if the mode shape is classical normal mode or not. As it is known classical normal modes’ mode shapes show standing wave nature, equivalent to the undamped system’s mode shapes. Thus, the mathematical model is significantly simpler. We also separated the detected mode shapes into two groups depending on the nature of the mode shape: bending and torsion. To avoid false results, to detect natural frequencies, we also measured the base’s natural frequencies. To identify the damping mechanism, we will define regression functions, which express the damping factor’s frequency dependence [6]. These functions have a direct connection to the damping factor’s function. For the measured Frequency Response Function’s (FRF from now) analytic approximation we used the partial fraction form: n Pi Pi H ( j ) j i i 1 j i
i i j d ,i
(1)
(2)
P. Ficzere, L. Borbas / Materials Today: Proceedings 12 (2019) 352–357
355
where: Pi is residuum of mode i [m/sec/N], λi is the complex eigenvalue of mode i [rad/s], σi is modal damping of mode i, ωd,i is damped natural frequency of mode i, and j is the imaginary part. 3. Results Fig. 4 shows the FRF of a part printed with method “B”, the laying case in the middle of Figure 2. The frequency values belonging to the peaks of the curve indicate the own frequency.
Fig. 4. . FRF of part B1
We excite in a fixed point, and the response is measured also in locations 1 and 2 of the specimen (Fig. 3.) The points belonging to peak FRF on the identical own frequency, the Nyquist plots belonging to the two response measurement locations indicate whether the two points reach the extreme position in phase or counterphase. The cursor in both cases is on the same point belonging to the own frequency. It is clear that the two points are approximately in counterphase, so the vibration image is of torsion character, otherwise we could have assumed bending vibration. In Fig. 5 the dominant modal circles can be seen. Further analysis has to be made to estimate the modes with smaller amplitude (near the origin).
Fig. 5. Vibration image classification with Nyquist plots
356
P. Ficzere, L. Borbas ./ Materials Today: Proceedings 12 (2019) 352–357
Using this method, we could detect 4 natural frequencies frequency value belonging to the 4 peaks (Table 2) . For the classification we use the Nyquist-plot of the FRF. (B – Bend, T – Torsion) Table 2. Classification of the mode shapes Mode i
1
2
3
4
fi [Hz]
116.87
304.58
692.03
762.96
ξi [%]
2.61
9.14
1.49
0.93
Type
B
T
T
B
4. Conclusions
The results show little to no difference between the two laying parts (B and C). With the last measurements done we will be able to compare the different orientations. When processing the data, we suspected nonlinearity of the material properties. We can state the material model of elements produced by FDM technology in case of PLA materials follows fluid-type behavior (viscous-elastic behavior). Jeffrey-body, the construction is a serial connection of a Kelvin-Voight and a Newton body, so it is a fluid-type model. Sometimes it is called Fluid II. Model [10]. The Jeffrey-body can be seen in Fig. 6. We found that this model realizes a Rayleigh-shape with proportional damping behaviour.
Fig. 6. . Jeffrey-body material model
Based on the experimental results the PLA material shows anisotropic behaviour, the damping parameters are changing in the function of the printing directions. Based on our investigation we can state that the standard deviation of damping parameters of FRF functions determined by analytical approximation is in a great range. Probably the clamping conditions must be changed. One of the possible solutions is the free hanging of the test specimens. The experimental results must be verified by numerical simulation. Generally, the Hooks Law is applied, where to describe the behavior of the material, the determination of the Young Modulus is enough (σ = Eε). In orthotropic case, stiffness constant in the 3 printing directions is different. Based on our investigation the “Jeffrey-body” describes the behaviour of the material more exactly, where the determination of the damping parameters is necessary. From the creeping model of the “Jeffrey-body” it can be established that the material behavior could be characterized with a hysteresis curve, which is proportional to the damping parameters of the material. The curve – generated from the peak-points of the hysteresis loops – could describe the fatigue behavior of the material. The determination of the model parameters, fatigue investigation will be carried out.
P. Ficzere, L. Borbas / Materials Today: Proceedings 12 (2019) 352–357
357
5. Acknowledgements These project results have been realized with a subsidy of the National Research Development and Innovation Office from the fund of NKIH. The title of the project is “Development of the New Generation of Production Technology for Individual Medical-Biological Implantation and Tools”. Project identification No.: NVKP_16-12016-0022., and: Basic Research project in the field of Laser-beam - technologies …. (in Hungarian: Lézertechnológiai és energetikai alapkutatás megvalósítása az Edutus Főiskolán, tudástranszfer, továbbá a vállalati kapcsolatok és a társadalmi szerepvállalás erősítését célzó tevékenységekkel kiegészítve). Project identification No.: EFOP-3.6.1-16-2016-000 The elaborators express their thanks for the support. 6. References [1] P. Ficzere, L. Borbás, Á. Török, Int. J. Traffic Transp. Eng. 3(3) (2013) 344-350. [2] P. Ficzere, L. Borbás, Á. Török, Acta Mech. Slovaca 18. (2014) 14-24. [3] M. Győri, P. Ficzere, Period. Polytech. Transp. 45:(1) . (2017) 21-24 [4] M. Győri, P. Ficzere, Period. Polytech. Transp. 44:(3) (2016) 164-171. [5] P. Ficzere, GÉP 67:(5-6) (2016) 78-81 [6] M. Tisza, P.Z. Kovács, D. Tóth, In: XXIX. microCAD International Multidisciplinary Scientific Conference, University of Miskolc, 9-10 April, 2015. ISBN 978-963-358-061-5 (In Hungarian). [7] B.Á. Kovács, P. Ficzere, Á. Török, PLA anyagból készült próbadarab tulajdonságainak kísérleti dinamikai vizsgálata, Műszaki Tudományos Közlemények 9. (2018) 135-138. ISSN 2393-1280 (In Hungarian). [8] P. Ficzere, L. Borbás, Gy. Falk, Biomechanica Hungarica 10/2. (2017) 57-58 (In Hungarian). [9] P. Ficzere, L. Borbás, Biomechanica Hungarica 10/2 (2017) 22. (In Hungarian) [10] F. Pápai, In: XI. Magyar Mechanikai Konferencia, MaMeK, 2011, Miskolc, 29-31 Aug, 2011, 1-11 (In Hungarian).