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Natural Frequency prediction of FDM manufactured parts using ANN approach
9th IFAC Conference on Manufacturing Modelling, Management and 9th IFAC Conference on Manufacturing Modelling, Management and Control 9th IFAC Conference on Manufacturing Modelling, Management and Control Berlin, Germany, August 28-30, 2019 Available online at www.sciencedirect.com 9th IFAC Conference Conference on on Manufacturing Manufacturing Modelling, Management and Control 9th IFAC Modelling, Management and Berlin, Germany, August 28-30, 2019 Control Berlin, Germany, August 28-30, 2019 Control Berlin, Berlin, Germany, Germany, August August 28-30, 28-30, 2019 2019
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IFAC PapersOnLine 52-13 (2019) 403–408 Natural Frequency prediction of FDM manufactured parts Natural Frequency prediction of FDM manufactured parts Natural Frequencyusing prediction of FDM manufactured parts ANN approach Natural prediction of ANN approach Natural Frequency Frequencyusing prediction of FDM FDM manufactured manufactured parts parts using ANN approach using ANN approach Fahraz Ali* Boppana V. Chowdary* using ANN approach Fahraz Ali* Boppana V. Chowdary*
Fahraz Ali* Boppana V. Chowdary* Fahraz Ali* Boppana V. Fahraz Ali* Boppana V. Chowdary* Chowdary* *Department of Mechanical and Manufacturing Engineering, *Department of Mechanical and Manufacturing Engineering, The University of the West Indies,and St. Augustine, Trinidad and Tobago, *Department of Mechanical Manufacturing Engineering, The University of the West Indies, St. Augustine, Trinidad and Tobago, (e-mail:[email protected], [email protected]) *Department of Mechanical and Manufacturing Engineering, *Department of Mechanical Manufacturing Engineering, The University of the West Indies,and St. Augustine, Trinidad and Tobago, (e-mail:[email protected], [email protected]) The University Augustine, The University of of the the West West Indies, Indies, St. St. Augustine, Trinidad Trinidad and and Tobago, Tobago, (e-mail:[email protected], [email protected]) __________________________________________________________________________________________________________ (e-mail:[email protected], [email protected]) (e-mail:[email protected], [email protected]) __________________________________________________________________________________________________________ __________________________________________________________________________________________________________ Abstract: This research study demonstrates the use of machine learning tools for the prediction of __________________________________________________________________________________________________________ __________________________________________________________________________________________________________ Abstract: This research study demonstrates the usebyofthe machine learning tools for the prediction of dynamic mechanical characteristics of parts produced Fused Deposition Modeling (FDM) process. Abstract: This research study demonstrates the usebyofthe machine learning tools for the prediction of dynamic mechanical characteristics of parts produced Fused Deposition Modeling (FDM) process. In this regard, I-optimal design of experiments wasuse followed with raster angle, air for gap,the build orientation Abstract: This research study demonstrates the of machine learning tools prediction of Abstract: This research study demonstrates the use of machine learning tools for the prediction of dynamic mechanical characteristics of parts produced by the Fused Deposition Modeling (FDM) process. In this regard, I-optimal design of experiments was followed with raster angle,Modeling airasgap, build orientation and number of contours as independent variables together with natural frequency the mechanical part dynamic mechanical characteristics of parts produced by the Fused Deposition (FDM) process. dynamic mechanical characteristics of parts produced by the Fused Deposition Modeling (FDM) process. In this regard, I-optimal design of experiments was followed with raster angle, air gap, build orientation and number offor contours as independent variables together with natural frequency asgap, thewas mechanical part characteristic investigation. Accordingly, a Artificial Neural Network (ANN) model trained using In this regard, I-optimal design of was followed with raster angle, build orientation In this regard, I-optimal design of experiments experiments was followed with rasterfrequency angle, air air build orientation and number offor contours as independent variables together with natural asgap, thewas mechanical part characteristic investigation. Accordingly, a Artificial Neural Network (ANN) model trained using the Bayesian regularization function. Finally, the trained ANN model was validated bytrained performing and number of contours as independent variables together with natural frequency as the mechanical part and number of contours as independent variables together with natural frequency as the mechanical part characteristic for investigation. Accordingly, a Artificial Neural Network (ANN) model was using the Bayesian regularization function. Finally, the trained ANN model was validated bytrained performing multiple confirmation runs which provided predictions generally within 5% accuracy. characteristic for investigation. Accordingly, a Artificial Neural Network (ANN) model was using characteristic for investigation. Accordingly, a Artificial Neural Network (ANN) model was trained using the Bayesian regularization function. Finally, the trained ANN model was validated by performing multiple confirmation runs which provided predictions generally within 5%was accuracy. the Bayesian Bayesian regularization function. Finally, the trained trained ANN model validated by by performing performing the regularization function. Finally, the ANN model validated multiple confirmation runs which provided predictions generally within 5%was accuracy. Copyright © 2019 IFAC multiple confirmation runs which provided predictions generally within 5% accuracy. © 2019, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. multiple confirmation runs which provided predictions generally within 5% accuracy. Copyright © 2019 IFAC Copyright ©Fused 2019Deposition IFAC Keywords: Modeling, Artificial Neural Network, Machine Learning, Natural Frequency Copyright © 2019 IFAC Copyright © 2019 IFAC Keywords: Fused Deposition Modeling, Artificial Neural Network, Machine Learning, Natural Frequency __________________________________________________________________________________________________________ Keywords: Fused Deposition Modeling, Artificial Neural Network, Machine Learning, Natural Frequency __________________________________________________________________________________________________________ Keywords: Fused Deposition Network, Machine Learning, Natural __________________________________________________________________________________________________________ Keywords: Fused Deposition Modeling, Modeling, Artificial Artificial Neural Neural Network, Machine Learning,experimental Natural Frequency Frequency Sood et al. (2009) performed investigations on __________________________________________________________________________________________________________ 1. INTRODUCTION __________________________________________________________________________________________________________ Sood et al. (2009) performed experimental investigations on the effect of FDM process parameters such as layer thickness, 1. INTRODUCTION Sood et al.of(2009) performed experimental investigations on the effect FDM process parameters such as layer thickness, 1. INTRODUCTION build orientation, rasterparameters angle, raster toas raster air gap and Fused Deposition Modeling (FDM) is an additive part Sood et al. (2009) performed experimental investigations on the effect of FDM process such layer thickness, Sood et al. (2009) performed experimental investigations on 1. INTRODUCTION build orientation, raster angle, raster toas raster air gap and Fused Deposition (FDM) three is an additive part 1.Modeling INTRODUCTION raster width on the dimensional accuracy of a standard the effect of FDM process parameters such layer thickness, manufacturing technology that produces dimensional the effect of FDM process parameters such as layer thickness, part build orientation, raster angle, raster to raster air gap and Fused Deposition Modeling (FDM) is an additive raster width on the raster dimensional accuracy of air aspecimen. standard manufacturing technology that produces three dimensional acrylonitrile styrene butadiene (ABS) test part build orientation, angle, raster raster to raster raster gap and and parts by Deposition vertically stacking layers of extruded semi-molten Fused Modeling (FDM) is additive build orientation, angle, to gap raster width on the raster dimensional accuracy of air aspecimen. standard Fused Deposition Modeling (FDM) is an an additive part manufacturing technology that produces three dimensional acrylonitrile styrene butadiene (ABS) test parts by vertically stacking layers of extruded semi-molten Furthermore, the authors implemented grey Taguchi method raster width on the dimensional accuracy of a standard materials. Since its inception in the 1980s, FDM has manufacturing technology that produces three dimensional raster width on the dimensional accuracy of a standard acrylonitrile styrene butadiene (ABS) test specimen. manufacturing technology that produces three dimensional parts by vertically stacking layersin ofthe extruded semi-molten Furthermore, the authors implemented grey Taguchi method materials. Since its inception 1980s,like FDM has acrylonitrile order to generate a single response from the styrene butadiene (ABS) test specimen. stimulated great interest due to inkey drivers product parts by vertically stacking layers of extruded semi-molten acrylonitrile styrene butadiene (ABS) test dimensional specimen. Furthermore, the authors implemented grey Taguchi method parts by vertically stacking layers of extruded semi-molten materials. Since its inception the 1980s, FDM has in in order to generate a single response from the dimensional stimulated Since greatlow interest due to in keythedrivers like product performance characteristics: percentage change in length, Furthermore, the authors implemented grey Taguchi method customization, cost and complex functional part materials. its inception 1980s, FDM has Furthermore, the authors implemented grey Taguchi in order to generate a single response from the dimensional materials. Since its inception in the 1980s, FDM has stimulated great interest due to key drivers like product characteristics: percentage change in method length, customization, low cost due and complex functional part performance width and thickness. Finally, ANN model was developed for in order to generate a single response from the dimensional manufacture without tooling (Mohamed et al. (2015); Mishra stimulated great interest to key drivers like product in order tothickness. generate aFinally, single ANN response from thedeveloped dimensional characteristics: percentage change in length, stimulated great interest to complex key drivers like product customization, low cost due and functional part performance width and model was for manufacture without tooling (Mohamed et al. (2015); Mishra prediction of the dimensional performance characteristics. performance characteristics: percentage change in length, and Mahapatra (2018)). Despite these benefits, there are customization, low cost and complex functional part performance characteristics: percentage in length, width and thickness. Finally, ANN model change wascharacteristics. developed for customization, low costDespite and complex part manufacture without tooling (Mohamed etbenefits, al.functional (2015); Mishra prediction of the dimensional performance and Mahapatra (2018)). these there are The proposed model proved ANN its performance suitability forcharacteristics. use due tofor a width and thickness. Finally, model was developed challenges with FDM technology such as (2015); lack there ofMishra high manufacture without tooling (Mohamed et al. width and thickness. Finally, ANN model was developed prediction of the dimensional manufacture without tooling (Mohamed et al. (2015); Mishra and Mahapatra (2018)). Despite these benefits, are The proposed model proved its performance suitability forcharacteristics. use due tofora challenges with FDMmechanical technology suchbenefits, as as lack of ashigh small percentage of error between predicted and experimental prediction of the dimensional accuracy and desired properties well its and Mahapatra (2018)). Despite these there are prediction of the proposed model proved its performance suitability forcharacteristics. use due to a and Mahapatra (2018)). Despite these there are challenges with FDMmechanical technology suchbenefits, as as lack of ashigh small percentage ofdimensional error between predicted and experimental accuracy and desired well its The data. The proposed model proved its suitability for use due heavy reliance onFDM themechanical adjustmentproperties of process parameters challenges with technology such as lack of high The proposed model proved its suitability for use due to to aa small percentage of error between predicted and experimental challenges with FDM technology such as lack of high accuracy and desired properties as well as its data. heavy reliance on (2016)). themechanical adjustment of process parameters (Mohamed et al. In this regard, many research small percentage of error between predicted and experimental accuracy and desired properties as well as its data. small percentage of error between predicted and experimental accuracy and desired as well as its Rodríguez-Panes et al. (2018) present a comparative study of heavy reliance themechanical adjustment of process parameters (Mohamed al.on In thisproperties regard, many research studies haveet focused on understanding optimizing FDM data. heavy reliance reliance on (2016)). the adjustment ofand process parameters Rodríguez-Panes et al. of (2018) a comparative study of data. (Mohamed et al. (2016)). In this regard, many research heavy on the adjustment of process parameters the tensile strength test present specimens produced by FDM studies have focused onforunderstanding and optimizing FDM Rodríguez-Panes et al. of (2018) present a comparative study of process parameters the enhancement of various (Mohamed et al. (2016)). In this regard, many research the tensile strength test specimens produced by FDM (Mohamed et al. (2016)). In this regard, many research studies have focused on understanding and optimizing FDM technology using two common polymer materials: ABS and Rodríguez-Panes et al. (2018) present aa comparative study of process parameters forunderstanding thelike enhancement of quality, various Rodríguez-Panes et al. (2018) present comparative study of the tensile strength of test specimens produced by FDM performance characteristics part surface studies have focused on and optimizing FDM using two common polymer materials: ABS and studies have focused onforunderstanding and surface optimizing FDM technology process parameters thelike enhancement of quality, various polyactic acid (PLA). The effect of process parameters such the tensile strength of test specimens produced by FDM performance characteristics part the tensile strength of test specimens produced by FDM technology using two common polymer materials: ABS and dimensional accuracy as well as mechanical properties in process parameters for the enhancement of various polyactic acid (PLA). The effect ofmanufacturing process parameters process parameters for thelike of quality, various performance characteristics part surface layer height, infill and orientation technology using two density common polymer materials: ABSsuch and dimensional accuracy as well asenhancement mechanical properties in as technology using two common polymer materials: ABS and polyactic acid (PLA). The effect ofmanufacturing process parameters such order to extend the application areas of FDM technology performance characteristics like part surface quality, as layer height, infill density and orientation performance characteristics like part surface quality, dimensional accuracy as well as mechanical properties in on tensile yield stress, tensile strength, nominal strain at polyactic acid (PLA). The effect of process parameters such order to extend the application areas of FDM technology polyactic acid (PLA). The effect of process parameters such as layer height, infill density and manufacturing orientation (Mohamed et accuracy al. (2016); Wu et al. (2018)). dimensional as well as mechanical properties in on tensile yield stress, tensile strength, nominalorientation strain at dimensional accuracy as well as mechanical properties in order to extend the application areas of FDM technology break and the modulus of elasticity were investigated for each as layer height, infill density and manufacturing (Mohamed et al. (2016); Wu et al. areas (2018)). as layer height, infill density andstrength, manufacturing on tensile yield stress, tensile nominalorientation strain at order to extend the application of FDM technology break and the modulus of elasticity were investigated for each order extend the application technology (Mohamed etundertaken al. (2016); Wu et al. areas (2018)). Itthe was observed that thestrength, adjustment of layer height on tensile yield stress, tensile nominal strain at In the to study by Boschetto etofal.FDM (2013), a FDM material. on tensile yield stress, tensile strength, nominal strain at break and modulus of elasticity were investigated for each (Mohamed et al. Wu et al. material. It was observed that the adjustment of layer height In the study by Boschetto et al. (2013), afor FDM (Mohamed etundertaken al. (2016); (2016); Wu et model al. (2018)). (2018)). had little effect on mechanical strength for ABS whereas for break and the modulus of elasticity were investigated for each surface roughness prediction was developed all break and the modulus of elasticity were investigated for each material. It was observed that the adjustment of layer height In the study undertaken by Boschetto et al. (2013), a FDM little effect on mechanical strength for in ABS whereas for surface roughness prediction model Multiple was developed all had PLA, an It increase in layerthat height resulted a reduction of was observed the adjustment of layer height ranges of the deposition angle. feed-forward In undertaken by et (2013), aafor FDM material. It was on observed that the adjustment of layer height had little effect mechanical strength for in ABS whereas for In the the study study undertaken by Boschetto Boschetto et al. al. (2013), FDM surface roughness prediction model Multiple was developed for all material. PLA, an increase in layer height resulted a reduction of ranges of the deposition angle. feed-forward tensile strength by 11%. Generally, infill density had the had little effect on mechanical strength for ABS whereas for Artificial Neural Network (ANN) structures were generated surface roughness prediction model was developed for all little effect on mechanical strength for in ABS whereas for PLA, anstrength increase in layer Generally, height resulted a reduction of surface roughness prediction model was developed for all had ranges ofNeural the deposition angle. Multiple feed-forward tensile by 11%. infill density had the Artificial Network (ANN) structures were generated greatest influence on the results, with ainfill more apparent effect an increase in layer height resulted in aa reduction of to fit experimental data by(ANN) varying the number ofgenerated neurons PLA, ranges of the deposition angle. Multiple feed-forward PLA, an increase in layer height resulted in reduction of tensile strength by 11%. Generally, density had the ranges of the deposition angle. Multiple feed-forward Artificial Neural Network structures were greatest influence on11%. the results, with ainfill more apparent effect to fitactivation experimental data type. by(ANN) varying the number of neurons on PLA. In essence, the test specimens manufactured with and function Following this, an evaluation tensile strength by Generally, density had the Artificial Neural Network structures were generated greatest influence on the results, with a more apparent effect tensile strength by 11%. Generally, infill density had the Artificial Neural Network (ANN) structures were generated to fit experimental data by varying the number of neurons on PLA. In essence, the results, test specimens manufactured with and function type. Following this,model an of evaluation PLA demonstrated rigidity and aahigher tensile strength influence on the with more apparent effect function was utilized to select the bestthe ANN based on greatest to fitactivation experimental data by varying varying the number neurons greatest influence onmore the with more apparent effect PLA. In essence, the results, test specimens manufactured with and activation function type. Following this,model an of evaluation to fit experimental data by number neurons PLA demonstrated more rigidity and higher tensile strength function was criteria. utilized to select the best ANN based on on than ABS. on PLA. In essence, the test specimens manufactured with performance Accordingly, validation of the proposed and activation function type. Following this, an evaluation on PLA. In essence, the test specimens manufactured with PLA demonstrated more rigidity and higher tensile strength and activation function type. Following this, an evaluation function was utilized to select the best ANN model based on than ABS. performance criteria. Accordingly, validation of the proposed PLA demonstrated more rigidity and higher tensile strength surface roughness model was achieved using various function was utilized to select the best ANN model based on PLA demonstrated more rigidity and higher tensile strength than ABS. function was utilized to select the best ANN model based on performance criteria. Accordingly, validation of the proposed common trend from the existing literature, however, surface roughness model achieved using various A ABS. materials andcriteria. different FDMwas machines, thusof demonstrating performance Accordingly, validation the A common trend mainly from the existing literature, however, than ABS. performance criteria. Accordingly, validation of the proposed proposed surface roughness model was achieved using various than reveals that studies focused on the static mechanical materials and different FDM machines, thus demonstrating A common trend mainly from the existing literature, however, ANN suitability for surface quality prediction in FDM surface roughness model was achieved using various reveals thatwhereas studies focused on the static mechanical surface roughness model was achieved using various materials and different FDM machines, thus demonstrating properties practical applications of FDM parts in A common trend from the existing literature, however, ANN suitability for surface quality prediction in FDM A common trend from the existing literature, however, reveals that studies mainly focused on the static mechanical fabrication. materials and different FDM machines, thus demonstrating properties whereas practicalfocused applications of FDM partsand in materials and different FDM machines, thus demonstrating ANN suitability for surface quality prediction in FDM machinery and transportation like gears, propellers reveals that studies mainly on the static mechanical fabrication. reveals thatwhereas studies mainly ongears, the of static mechanical properties practicalfocused applications FDM partsand in ANN suitability for surface quality prediction in FDM machinery and transportation like propellers ANN suitability for surface quality prediction in FDM properties whereas practical applications of FDM parts in fabrication. properties whereas practical applications of FDM parts in machinery and transportation like gears, propellers and fabrication. fabrication. machinery machinery and and transportation transportation like like gears, gears, propellers propellers and and
Copyright © 2019, 2019 IFAC 408Hosting by Elsevier Ltd. All rights reserved. 2405-8963 © IFAC (International Federation of Automatic Control) Copyright ©under 2019 responsibility IFAC 408Control. Peer review of International Federation of Automatic Copyright © 2019 IFAC 408 10.1016/j.ifacol.2019.11.083 Copyright 408 Copyright © © 2019 2019 IFAC IFAC 408
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bearings usually undergo dynamic mechanical loading and vibration (Domingo-Espin et al. (2014); Mohamed et al. (2017); Balderrama-Armendariz et al. (2018)). Moreover, one of the major drawbacks when using parts under dynamic loading is the appearance of resonance (Domingo-Espin et al. (2014)). Therefore, this research study focuses on the prediction of the natural frequency of FDM processed polycarbonate (PC) part in order to mitigate the effect of resonance under dynamic conditions. 2.
Table 1. Process Parameters and Levels Process Parameters
Units
Raster Angle Air Gap Build Orientation Number of Contours
degree mm degree -
1 0 0 0 0
Levels 2 45 0.008 9 4
3 90 0.016 12 8
In continuation, the I-optimal design of experiments was followed due to its suitability for development of prediction models associated with non-linear systems such as FDM, in addition to its efficient use of resources through minimal experimental runs (Mohamed et al. (2017)). Hence, the experimental plan used for this study is shown in Table 2.
MATERIAL AND METHODS
The steps illustrated in Fig. 1 were conducted for this research study.
Fig. 3. FDM process parameters. Table 2. I-optimal design of experiments Experiment Number 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Fig. 1. Research methodology. 2.1 Design of test specimen A cantilever beam was selected as the test specimen for investigation of the natural frequency. Accordingly, a Computer Aided Design (CAD) model of the cantilever beam was created in SolidWorks as shown in Fig. 2. The CAD model was later converted into Stereolithography (STL) file format for further processing according to the experimental plan.
Fig. 2. Test specimen (all dimensions in mm). 2.2 Experimental plan Subsequently, the number of experimental runs required for this study was determined from the FDM process parameters and their levels presented in Table 1. Graphical representations of these process parameters are shown in Fig. 3.
Raster Angle 45 0 90 0 0 0 45 45 90 45 0 45 45 90 90 90 0 0 45 0 45 0 45 45 90
Air Gap 0 0.008 0.008 0.016 0.008 0.008 0 0.008 0.008 0.016 0.008 0.016 0.008 0.008 0 0.008 0 0.016 0.008 0.016 0 0.016 0.008 0.016 0.016
Build Orientation 9 0 0 0 9 0 0 9 9 0 12 12 0 9 12 0 9 12 9 9 12 9 9 0 12
Number of Contours 8 8 0 0 8 4 4 0 4 4 4 8 0 4 0 8 0 0 0 4 4 4 0 4 0
2.3 Build test specimens Following this, the job files for each experimental run were prepared within Insight® programme using the STL file format of the selected test specimen. In addition, PC material 409
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was chosen for fabrication of the test specimens because of its growing use in many applications and also due to less focus given to this material concerning experimental FDM studies (Mohamed et al. (2015)). Hence, all test specimens were built on a Stratasys FortusTM 400mc machine with a fixed layer thickness of 0.1778 mm as well as constant raster and contour widths of 0.3556 mm.
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equations (Sood et al. (2009)). Therefore, ANN modeling technique was selected in this study for development of the prediction model. A feed-forward back propagation network comprising an input layer, a hidden layer and an output layer was trained using the Bayesian regularization function within MATLAB®. After training of the experimental data, the network structure 4-10-2 with minimal error was found. Here, 4 neurons represent the process parameters in the input layer, 10 neurons in the hidden layer and 2 neurons (matching natural frequency modes 1 and 2) in the output layer.
2.4 Testing The setup illustrated in Fig. 4 was implemented for testing.
Thereafter, the trained ANN model was validated by conducting confirmation runs to compare the predicted and actual natural frequency values for modes 1 and 2. 3.
RESULTS AND DISCUSSION
From the experimental results, the main effects of the process parameters on natural frequency were analyzed. Similar trends were observed for modes 1 and 2 as depicted in Fig. 6 and 7.
Fig. 4. Natural frequency testing setup. Each test specimen was fixed at one end as well as secured to a leveled surface table with the use of clamps and a fixture. An accelerometer was positioned on the test specimen while a striking instrument was used to excite the test specimen. The signal conditioner, data acquisition unit and Lab View software were integrated to obtain the natural frequency readings. All of the test specimens were hit with the accelerometer at various marked points which revealed vibration modes 1 and 2 to be consistently excited (see Fig. 5). Hence, the natural frequencies at these modes were recorded for this study.
Fig. 6. Effect of process parameters on natural frequency mode 1.
Fig. 7. Effect of process parameters on natural frequency mode 2. It is noticed that the raster angle has the greatest impact on natural frequency. A decrease in raster angle results in higher natural frequency with an apparent increase occurring from 45 degrees to 0 degrees. This observation can be attributed to an increase in the stiffness of the specimens with a lower raster angle thus resulting in greater natural frequency. The specimens built with 0 degrees raster angle have all rasters
Fig. 5. Vibration modes 1 and 2. 2.5 Development and validation of prediction model As FDM process involves large number of conflicting factors and complex phenomena for part build, accurate prediction of the output characteristics is very difficult using mathematical 410
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perpendicularly aligned to the bending axis hence offering more resistance and therefore characterized with having greater stiffness.
Moreover, Fig. 9 shows a physical comparison of the surfaces for two specimens with build orientations of 0 and 9 degrees about the Y-axis as well as similar raster angle (45 degrees), air gap (0.016 mm) and no contours. It is evident that the structure has been altered, with a single continuous pattern noticed for the rasters in the specimen built at 0 degrees, whereas an overlapped continuous pattern was observed for the specimen built at 9 degrees.
In addition, it can be seen from Fig. 6 and 7, an increase in air gap leads to minimal reduction in natural frequency. A less dense structure is created with the inclusion of air gap thereby reducing its resistance to deformation and accordingly lower natural frequency. Interestingly, building the specimen oriented about the Y-axis resulted in a subtle increase in its natural frequency. This may be due to an improvement in the density of the specimen’s structure through interaction with the laid rasters. Fig. 8 (a) and (b) support this with surface plots of interaction effects between raster angle and build orientation for natural frequency modes 1 and 2.
(a)
(a)
(b) (b)
Fig. 9. Surface examination of specimens built using build orientation (a) 0 degrees and (b) 9 degrees.
Fig. 8. Surface plots of interaction effects between raster angle and build orientation for natural frequency (a) Mode 1 and (b) Mode 2.
Also, from Fig. 6 and 7, the number of contours is seen to have a minor impact on the natural frequency. Nonetheless, the natural frequency can be increased with addition of 411
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contours since these outlines help to distribute applied loads and thus improve the stiffness of the part for a higher natural frequency.
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technique. The trained ANN prediction model has been validated through various confirmation runs ranging from 0.42 to 5.63% prediction error. Thus, the trained ANN model can be used to determine the desired natural frequencies for modes 1 and 2 through adjustment of the FDM process parameters. In this regard, lower raster angle and air gap together with higher build orientation about the Y-axis and additional contours have been seen from this study to produce parts with greater natural frequencies. This type of control offered by the prediction model provides an offline means to ensure that the natural frequency of the FDM built part is outside the range of operating frequency which helps to mitigate resonance in dynamic conditions. Hence, greater design flexibility can be afforded to industries that utilize composite thermoplastic materials for the production of functional parts, particularly in applications such as aerospace, automotive, biomedical and customer product manufacturing (Turner and Gold (2015); Boschetto and Bottini (2015)).
In following, the performance of the trained ANN model is represented in Fig. 10. The goodness of fit between the predicted values obtained from the ANN model and the experimental values are seen for the training and testing samples with an overall R2 value of 99.96%.
Furthermore, this research work is in alignment with the contemporary shift towards the use of sustainable processes to produce parts with near-zero material waste as well as compatibility with tailored materials for reduced weight while maintaining desired mechanical characteristics such as natural frequency (Bikas et al. (2016); Gardan (2016)). In closing, our future research agenda includes multiobjective optimization studies of other mechanical characteristics like tensile strength and surface roughness in conjunction with natural frequency. The simultaneous satisfaction of all responses will be focused to determine trade off solutions for real life scenarios that require conflicting process settings in FDM.
Fig. 10. Regression plots for trained ANN model.
REFERENCES
Furthermore, three confirmation runs were conducted to validate the use of the trained ANN model for prediction. Table 3 shows these results. The ANN model performed quite satisfactory with all predictions generally within 5% error, hence proving its suitability for future application.
Balderrama-Armendariz, C.O., MacDonald, E., Espalin, D., Cortes-Saenz, D., Wicker, R., and Maldonado-Macias, A. (2018). Torsion analysis of the anisotropic behavior of fdm technology. The International Journal of Advanced Manufacturing Technology, 96, 307-317. Bikas, H., Stavropoulos, P., and Chryssolouris, G. (2016). Additive manufacturing methods and modelling approaches: a critical review. The International Journal of Advanced Manufacturing Technology, 83(1-4), 389-405. Boschetto, A., Giordano, V., and Veniali, F. (2013). Surface roughness prediction in fused deposition modelling by neural networks. International Journal of Advanced Manufacturing Technology, 67, 2727-2742. Boschetto, A. and Bottini, L. (2015). Roughness prediction in coupled operations of fused deposition modeling and barrel finishing. Journal of Materials Processing Technology, 219, 181-192. Domingo-Espin, M., Borros, S., Agullo, N., Garcia-Granada, A-A., and Reyes, G. (2014). Influence of building parameters on the dynamic mechanical properties of polycarbonate fused deposition modeling parts. 3D Printing and Additive Manufacturing, 1(2). Gardan, J. (2016). Additive manufacturing technologies: state of the art and trends. International Journal of Production Research, 54(10), 3118-3132.
Table 3. Results of confirmation runs
4.
CONCLUSION
The present work has made an attempt to predict the natural frequency for FDM processed PC part using ANN modeling 412
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Mishra, S.B. and Mahapatra, S.S. (2018). An experimental investigation on strain controlled fatigue behaviour of fdm build parts. International Journal of Productivity and Quality Management, 24(3), 323-345. Mohamed, O.A., Masood, S.H., and Bhowmik, J.L. (2015). Optimization of fused deposition modeling process parameters: a review of current research and future prospects. Advances in Manufacturing, 3, 42-53. Mohamed, O.A., Masood, S.H., Bhowmik, J.L., Nikzad, M., and Azadmanjiri, J. (2016). Effect of process parameters on dynamic mechanical performance of fdm pc/abs printed parts through design of experiment. Journal of Materials Engineering and Performance, 25(7), 29222935. Mohamed, O.A., Masood, S.H., and Bhowmik, J.L. (2017). Experimental investigation for dynamic stiffness and dimensional accuracy of fdm manufactured part using ivoptimal response surface design. Rapid Prototyping Journal, 23(4), 736-749. Rodríguez –Panes, A., Claver, J., and Camacho, A.M. (2018). The influence of manufacturing parameters on the mechanical behaviour of pla and abs pieces manufactured by fdm: a comparative analysis. Materials, 11(8). Sood, A.K., Ohdar, R.K., and Mahapatra, S.S. (2009). Improving dimensional accuracy of fused deposition modelling processed part using grey taguchi method. Materials and Design, 30, 4243-4252. Turner, B.N. and Gold, S.A. (2015). A review of melt extrusion additive manufacturing processes: II. Materials, dimensional accuracy, and surface roughness. Rapid Prototyping Journal, 21(3), 250-261. Wu, W., Jiang, J., Jiang, H., Liu, W., Li, G., Wang, B., Tang, M., and Zhao, J. (2018). Improving bending and dynamic mechanics performance of 3d printing through ultrasonic strengthening. Materials Letters, 220, 317-320.
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IFAC PapersOnLine 52-13 (2019) 403–408 Natural Frequency prediction of FDM manufactured parts Natural Frequency prediction of FDM manufactured parts Natural Frequencyusing prediction of FDM manufactured parts ANN approach Natural prediction of ANN approach Natural Frequency Frequencyusing prediction of FDM FDM manufactured manufactured parts parts using ANN approach using ANN approach Fahraz Ali* Boppana V. Chowdary* using ANN approach Fahraz Ali* Boppana V. Chowdary*
Fahraz Ali* Boppana V. Chowdary* Fahraz Ali* Boppana V. Fahraz Ali* Boppana V. Chowdary* Chowdary* *Department of Mechanical and Manufacturing Engineering, *Department of Mechanical and Manufacturing Engineering, The University of the West Indies,and St. Augustine, Trinidad and Tobago, *Department of Mechanical Manufacturing Engineering, The University of the West Indies, St. Augustine, Trinidad and Tobago, (e-mail:[email protected], [email protected]) *Department of Mechanical and Manufacturing Engineering, *Department of Mechanical Manufacturing Engineering, The University of the West Indies,and St. Augustine, Trinidad and Tobago, (e-mail:[email protected], [email protected]) The University Augustine, The University of of the the West West Indies, Indies, St. St. Augustine, Trinidad Trinidad and and Tobago, Tobago, (e-mail:[email protected], [email protected]) __________________________________________________________________________________________________________ (e-mail:[email protected], [email protected]) (e-mail:[email protected], [email protected]) __________________________________________________________________________________________________________ __________________________________________________________________________________________________________ Abstract: This research study demonstrates the use of machine learning tools for the prediction of __________________________________________________________________________________________________________ __________________________________________________________________________________________________________ Abstract: This research study demonstrates the usebyofthe machine learning tools for the prediction of dynamic mechanical characteristics of parts produced Fused Deposition Modeling (FDM) process. Abstract: This research study demonstrates the usebyofthe machine learning tools for the prediction of dynamic mechanical characteristics of parts produced Fused Deposition Modeling (FDM) process. In this regard, I-optimal design of experiments wasuse followed with raster angle, air for gap,the build orientation Abstract: This research study demonstrates the of machine learning tools prediction of Abstract: This research study demonstrates the use of machine learning tools for the prediction of dynamic mechanical characteristics of parts produced by the Fused Deposition Modeling (FDM) process. In this regard, I-optimal design of experiments was followed with raster angle,Modeling airasgap, build orientation and number of contours as independent variables together with natural frequency the mechanical part dynamic mechanical characteristics of parts produced by the Fused Deposition (FDM) process. dynamic mechanical characteristics of parts produced by the Fused Deposition Modeling (FDM) process. In this regard, I-optimal design of experiments was followed with raster angle, air gap, build orientation and number offor contours as independent variables together with natural frequency asgap, thewas mechanical part characteristic investigation. Accordingly, a Artificial Neural Network (ANN) model trained using In this regard, I-optimal design of was followed with raster angle, build orientation In this regard, I-optimal design of experiments experiments was followed with rasterfrequency angle, air air build orientation and number offor contours as independent variables together with natural asgap, thewas mechanical part characteristic investigation. Accordingly, a Artificial Neural Network (ANN) model trained using the Bayesian regularization function. Finally, the trained ANN model was validated bytrained performing and number of contours as independent variables together with natural frequency as the mechanical part and number of contours as independent variables together with natural frequency as the mechanical part characteristic for investigation. Accordingly, a Artificial Neural Network (ANN) model was using the Bayesian regularization function. Finally, the trained ANN model was validated bytrained performing multiple confirmation runs which provided predictions generally within 5% accuracy. characteristic for investigation. Accordingly, a Artificial Neural Network (ANN) model was using characteristic for investigation. Accordingly, a Artificial Neural Network (ANN) model was trained using the Bayesian regularization function. Finally, the trained ANN model was validated by performing multiple confirmation runs which provided predictions generally within 5%was accuracy. the Bayesian Bayesian regularization function. Finally, the trained trained ANN model validated by by performing performing the regularization function. Finally, the ANN model validated multiple confirmation runs which provided predictions generally within 5%was accuracy. Copyright © 2019 IFAC multiple confirmation runs which provided predictions generally within 5% accuracy. © 2019, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. multiple confirmation runs which provided predictions generally within 5% accuracy. Copyright © 2019 IFAC Copyright ©Fused 2019Deposition IFAC Keywords: Modeling, Artificial Neural Network, Machine Learning, Natural Frequency Copyright © 2019 IFAC Copyright © 2019 IFAC Keywords: Fused Deposition Modeling, Artificial Neural Network, Machine Learning, Natural Frequency __________________________________________________________________________________________________________ Keywords: Fused Deposition Modeling, Artificial Neural Network, Machine Learning, Natural Frequency __________________________________________________________________________________________________________ Keywords: Fused Deposition Network, Machine Learning, Natural __________________________________________________________________________________________________________ Keywords: Fused Deposition Modeling, Modeling, Artificial Artificial Neural Neural Network, Machine Learning,experimental Natural Frequency Frequency Sood et al. (2009) performed investigations on __________________________________________________________________________________________________________ 1. INTRODUCTION __________________________________________________________________________________________________________ Sood et al. (2009) performed experimental investigations on the effect of FDM process parameters such as layer thickness, 1. INTRODUCTION Sood et al.of(2009) performed experimental investigations on the effect FDM process parameters such as layer thickness, 1. INTRODUCTION build orientation, rasterparameters angle, raster toas raster air gap and Fused Deposition Modeling (FDM) is an additive part Sood et al. (2009) performed experimental investigations on the effect of FDM process such layer thickness, Sood et al. (2009) performed experimental investigations on 1. INTRODUCTION build orientation, raster angle, raster toas raster air gap and Fused Deposition (FDM) three is an additive part 1.Modeling INTRODUCTION raster width on the dimensional accuracy of a standard the effect of FDM process parameters such layer thickness, manufacturing technology that produces dimensional the effect of FDM process parameters such as layer thickness, part build orientation, raster angle, raster to raster air gap and Fused Deposition Modeling (FDM) is an additive raster width on the raster dimensional accuracy of air aspecimen. standard manufacturing technology that produces three dimensional acrylonitrile styrene butadiene (ABS) test part build orientation, angle, raster raster to raster raster gap and and parts by Deposition vertically stacking layers of extruded semi-molten Fused Modeling (FDM) is additive build orientation, angle, to gap raster width on the raster dimensional accuracy of air aspecimen. standard Fused Deposition Modeling (FDM) is an an additive part manufacturing technology that produces three dimensional acrylonitrile styrene butadiene (ABS) test parts by vertically stacking layers of extruded semi-molten Furthermore, the authors implemented grey Taguchi method raster width on the dimensional accuracy of a standard materials. Since its inception in the 1980s, FDM has manufacturing technology that produces three dimensional raster width on the dimensional accuracy of a standard acrylonitrile styrene butadiene (ABS) test specimen. manufacturing technology that produces three dimensional parts by vertically stacking layersin ofthe extruded semi-molten Furthermore, the authors implemented grey Taguchi method materials. Since its inception 1980s,like FDM has acrylonitrile order to generate a single response from the styrene butadiene (ABS) test specimen. stimulated great interest due to inkey drivers product parts by vertically stacking layers of extruded semi-molten acrylonitrile styrene butadiene (ABS) test dimensional specimen. Furthermore, the authors implemented grey Taguchi method parts by vertically stacking layers of extruded semi-molten materials. Since its inception the 1980s, FDM has in in order to generate a single response from the dimensional stimulated Since greatlow interest due to in keythedrivers like product performance characteristics: percentage change in length, Furthermore, the authors implemented grey Taguchi method customization, cost and complex functional part materials. its inception 1980s, FDM has Furthermore, the authors implemented grey Taguchi in order to generate a single response from the dimensional materials. Since its inception in the 1980s, FDM has stimulated great interest due to key drivers like product characteristics: percentage change in method length, customization, low cost due and complex functional part performance width and thickness. Finally, ANN model was developed for in order to generate a single response from the dimensional manufacture without tooling (Mohamed et al. (2015); Mishra stimulated great interest to key drivers like product in order tothickness. generate aFinally, single ANN response from thedeveloped dimensional characteristics: percentage change in length, stimulated great interest to complex key drivers like product customization, low cost due and functional part performance width and model was for manufacture without tooling (Mohamed et al. (2015); Mishra prediction of the dimensional performance characteristics. performance characteristics: percentage change in length, and Mahapatra (2018)). Despite these benefits, there are customization, low cost and complex functional part performance characteristics: percentage in length, width and thickness. Finally, ANN model change wascharacteristics. developed for customization, low costDespite and complex part manufacture without tooling (Mohamed etbenefits, al.functional (2015); Mishra prediction of the dimensional performance and Mahapatra (2018)). these there are The proposed model proved ANN its performance suitability forcharacteristics. use due tofor a width and thickness. Finally, model was developed challenges with FDM technology such as (2015); lack there ofMishra high manufacture without tooling (Mohamed et al. width and thickness. Finally, ANN model was developed prediction of the dimensional manufacture without tooling (Mohamed et al. (2015); Mishra and Mahapatra (2018)). Despite these benefits, are The proposed model proved its performance suitability forcharacteristics. use due tofora challenges with FDMmechanical technology suchbenefits, as as lack of ashigh small percentage of error between predicted and experimental prediction of the dimensional accuracy and desired properties well its and Mahapatra (2018)). Despite these there are prediction of the proposed model proved its performance suitability forcharacteristics. use due to a and Mahapatra (2018)). Despite these there are challenges with FDMmechanical technology suchbenefits, as as lack of ashigh small percentage ofdimensional error between predicted and experimental accuracy and desired well its The data. The proposed model proved its suitability for use due heavy reliance onFDM themechanical adjustmentproperties of process parameters challenges with technology such as lack of high The proposed model proved its suitability for use due to to aa small percentage of error between predicted and experimental challenges with FDM technology such as lack of high accuracy and desired properties as well as its data. heavy reliance on (2016)). themechanical adjustment of process parameters (Mohamed et al. In this regard, many research small percentage of error between predicted and experimental accuracy and desired properties as well as its data. small percentage of error between predicted and experimental accuracy and desired as well as its Rodríguez-Panes et al. (2018) present a comparative study of heavy reliance themechanical adjustment of process parameters (Mohamed al.on In thisproperties regard, many research studies haveet focused on understanding optimizing FDM data. heavy reliance reliance on (2016)). the adjustment ofand process parameters Rodríguez-Panes et al. of (2018) a comparative study of data. (Mohamed et al. (2016)). In this regard, many research heavy on the adjustment of process parameters the tensile strength test present specimens produced by FDM studies have focused onforunderstanding and optimizing FDM Rodríguez-Panes et al. of (2018) present a comparative study of process parameters the enhancement of various (Mohamed et al. (2016)). In this regard, many research the tensile strength test specimens produced by FDM (Mohamed et al. (2016)). In this regard, many research studies have focused on understanding and optimizing FDM technology using two common polymer materials: ABS and Rodríguez-Panes et al. (2018) present aa comparative study of process parameters forunderstanding thelike enhancement of quality, various Rodríguez-Panes et al. (2018) present comparative study of the tensile strength of test specimens produced by FDM performance characteristics part surface studies have focused on and optimizing FDM using two common polymer materials: ABS and studies have focused onforunderstanding and surface optimizing FDM technology process parameters thelike enhancement of quality, various polyactic acid (PLA). The effect of process parameters such the tensile strength of test specimens produced by FDM performance characteristics part the tensile strength of test specimens produced by FDM technology using two common polymer materials: ABS and dimensional accuracy as well as mechanical properties in process parameters for the enhancement of various polyactic acid (PLA). The effect ofmanufacturing process parameters process parameters for thelike of quality, various performance characteristics part surface layer height, infill and orientation technology using two density common polymer materials: ABSsuch and dimensional accuracy as well asenhancement mechanical properties in as technology using two common polymer materials: ABS and polyactic acid (PLA). The effect ofmanufacturing process parameters such order to extend the application areas of FDM technology performance characteristics like part surface quality, as layer height, infill density and orientation performance characteristics like part surface quality, dimensional accuracy as well as mechanical properties in on tensile yield stress, tensile strength, nominal strain at polyactic acid (PLA). The effect of process parameters such order to extend the application areas of FDM technology polyactic acid (PLA). The effect of process parameters such as layer height, infill density and manufacturing orientation (Mohamed et accuracy al. (2016); Wu et al. (2018)). dimensional as well as mechanical properties in on tensile yield stress, tensile strength, nominalorientation strain at dimensional accuracy as well as mechanical properties in order to extend the application areas of FDM technology break and the modulus of elasticity were investigated for each as layer height, infill density and manufacturing (Mohamed et al. (2016); Wu et al. areas (2018)). as layer height, infill density andstrength, manufacturing on tensile yield stress, tensile nominalorientation strain at order to extend the application of FDM technology break and the modulus of elasticity were investigated for each order extend the application technology (Mohamed etundertaken al. (2016); Wu et al. areas (2018)). Itthe was observed that thestrength, adjustment of layer height on tensile yield stress, tensile nominal strain at In the to study by Boschetto etofal.FDM (2013), a FDM material. on tensile yield stress, tensile strength, nominal strain at break and modulus of elasticity were investigated for each (Mohamed et al. Wu et al. material. It was observed that the adjustment of layer height In the study by Boschetto et al. (2013), afor FDM (Mohamed etundertaken al. (2016); (2016); Wu et model al. (2018)). (2018)). had little effect on mechanical strength for ABS whereas for break and the modulus of elasticity were investigated for each surface roughness prediction was developed all break and the modulus of elasticity were investigated for each material. It was observed that the adjustment of layer height In the study undertaken by Boschetto et al. (2013), a FDM little effect on mechanical strength for in ABS whereas for surface roughness prediction model Multiple was developed all had PLA, an It increase in layerthat height resulted a reduction of was observed the adjustment of layer height ranges of the deposition angle. feed-forward In undertaken by et (2013), aafor FDM material. It was on observed that the adjustment of layer height had little effect mechanical strength for in ABS whereas for In the the study study undertaken by Boschetto Boschetto et al. al. (2013), FDM surface roughness prediction model Multiple was developed for all material. PLA, an increase in layer height resulted a reduction of ranges of the deposition angle. feed-forward tensile strength by 11%. Generally, infill density had the had little effect on mechanical strength for ABS whereas for Artificial Neural Network (ANN) structures were generated surface roughness prediction model was developed for all little effect on mechanical strength for in ABS whereas for PLA, anstrength increase in layer Generally, height resulted a reduction of surface roughness prediction model was developed for all had ranges ofNeural the deposition angle. Multiple feed-forward tensile by 11%. infill density had the Artificial Network (ANN) structures were generated greatest influence on the results, with ainfill more apparent effect an increase in layer height resulted in aa reduction of to fit experimental data by(ANN) varying the number ofgenerated neurons PLA, ranges of the deposition angle. Multiple feed-forward PLA, an increase in layer height resulted in reduction of tensile strength by 11%. Generally, density had the ranges of the deposition angle. Multiple feed-forward Artificial Neural Network structures were greatest influence on11%. the results, with ainfill more apparent effect to fitactivation experimental data type. by(ANN) varying the number of neurons on PLA. In essence, the test specimens manufactured with and function Following this, an evaluation tensile strength by Generally, density had the Artificial Neural Network structures were generated greatest influence on the results, with a more apparent effect tensile strength by 11%. Generally, infill density had the Artificial Neural Network (ANN) structures were generated to fit experimental data by varying the number of neurons on PLA. In essence, the results, test specimens manufactured with and function type. Following this,model an of evaluation PLA demonstrated rigidity and aahigher tensile strength influence on the with more apparent effect function was utilized to select the bestthe ANN based on greatest to fitactivation experimental data by varying varying the number neurons greatest influence onmore the with more apparent effect PLA. In essence, the results, test specimens manufactured with and activation function type. Following this,model an of evaluation to fit experimental data by number neurons PLA demonstrated more rigidity and higher tensile strength function was criteria. utilized to select the best ANN based on on than ABS. on PLA. In essence, the test specimens manufactured with performance Accordingly, validation of the proposed and activation function type. Following this, an evaluation on PLA. In essence, the test specimens manufactured with PLA demonstrated more rigidity and higher tensile strength and activation function type. Following this, an evaluation function was utilized to select the best ANN model based on than ABS. performance criteria. Accordingly, validation of the proposed PLA demonstrated more rigidity and higher tensile strength surface roughness model was achieved using various function was utilized to select the best ANN model based on PLA demonstrated more rigidity and higher tensile strength than ABS. function was utilized to select the best ANN model based on performance criteria. Accordingly, validation of the proposed common trend from the existing literature, however, surface roughness model achieved using various A ABS. materials andcriteria. different FDMwas machines, thusof demonstrating performance Accordingly, validation the A common trend mainly from the existing literature, however, than ABS. performance criteria. Accordingly, validation of the proposed proposed surface roughness model was achieved using various than reveals that studies focused on the static mechanical materials and different FDM machines, thus demonstrating A common trend mainly from the existing literature, however, ANN suitability for surface quality prediction in FDM surface roughness model was achieved using various reveals thatwhereas studies focused on the static mechanical surface roughness model was achieved using various materials and different FDM machines, thus demonstrating properties practical applications of FDM parts in A common trend from the existing literature, however, ANN suitability for surface quality prediction in FDM A common trend from the existing literature, however, reveals that studies mainly focused on the static mechanical fabrication. materials and different FDM machines, thus demonstrating properties whereas practicalfocused applications of FDM partsand in materials and different FDM machines, thus demonstrating ANN suitability for surface quality prediction in FDM machinery and transportation like gears, propellers reveals that studies mainly on the static mechanical fabrication. reveals thatwhereas studies mainly ongears, the of static mechanical properties practicalfocused applications FDM partsand in ANN suitability for surface quality prediction in FDM machinery and transportation like propellers ANN suitability for surface quality prediction in FDM properties whereas practical applications of FDM parts in fabrication. properties whereas practical applications of FDM parts in machinery and transportation like gears, propellers and fabrication. fabrication. machinery machinery and and transportation transportation like like gears, gears, propellers propellers and and
Copyright © 2019, 2019 IFAC 408Hosting by Elsevier Ltd. All rights reserved. 2405-8963 © IFAC (International Federation of Automatic Control) Copyright ©under 2019 responsibility IFAC 408Control. Peer review of International Federation of Automatic Copyright © 2019 IFAC 408 10.1016/j.ifacol.2019.11.083 Copyright 408 Copyright © © 2019 2019 IFAC IFAC 408
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bearings usually undergo dynamic mechanical loading and vibration (Domingo-Espin et al. (2014); Mohamed et al. (2017); Balderrama-Armendariz et al. (2018)). Moreover, one of the major drawbacks when using parts under dynamic loading is the appearance of resonance (Domingo-Espin et al. (2014)). Therefore, this research study focuses on the prediction of the natural frequency of FDM processed polycarbonate (PC) part in order to mitigate the effect of resonance under dynamic conditions. 2.
Table 1. Process Parameters and Levels Process Parameters
Units
Raster Angle Air Gap Build Orientation Number of Contours
degree mm degree -
1 0 0 0 0
Levels 2 45 0.008 9 4
3 90 0.016 12 8
In continuation, the I-optimal design of experiments was followed due to its suitability for development of prediction models associated with non-linear systems such as FDM, in addition to its efficient use of resources through minimal experimental runs (Mohamed et al. (2017)). Hence, the experimental plan used for this study is shown in Table 2.
MATERIAL AND METHODS
The steps illustrated in Fig. 1 were conducted for this research study.
Fig. 3. FDM process parameters. Table 2. I-optimal design of experiments Experiment Number 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Fig. 1. Research methodology. 2.1 Design of test specimen A cantilever beam was selected as the test specimen for investigation of the natural frequency. Accordingly, a Computer Aided Design (CAD) model of the cantilever beam was created in SolidWorks as shown in Fig. 2. The CAD model was later converted into Stereolithography (STL) file format for further processing according to the experimental plan.
Fig. 2. Test specimen (all dimensions in mm). 2.2 Experimental plan Subsequently, the number of experimental runs required for this study was determined from the FDM process parameters and their levels presented in Table 1. Graphical representations of these process parameters are shown in Fig. 3.
Raster Angle 45 0 90 0 0 0 45 45 90 45 0 45 45 90 90 90 0 0 45 0 45 0 45 45 90
Air Gap 0 0.008 0.008 0.016 0.008 0.008 0 0.008 0.008 0.016 0.008 0.016 0.008 0.008 0 0.008 0 0.016 0.008 0.016 0 0.016 0.008 0.016 0.016
Build Orientation 9 0 0 0 9 0 0 9 9 0 12 12 0 9 12 0 9 12 9 9 12 9 9 0 12
Number of Contours 8 8 0 0 8 4 4 0 4 4 4 8 0 4 0 8 0 0 0 4 4 4 0 4 0
2.3 Build test specimens Following this, the job files for each experimental run were prepared within Insight® programme using the STL file format of the selected test specimen. In addition, PC material 409
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was chosen for fabrication of the test specimens because of its growing use in many applications and also due to less focus given to this material concerning experimental FDM studies (Mohamed et al. (2015)). Hence, all test specimens were built on a Stratasys FortusTM 400mc machine with a fixed layer thickness of 0.1778 mm as well as constant raster and contour widths of 0.3556 mm.
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equations (Sood et al. (2009)). Therefore, ANN modeling technique was selected in this study for development of the prediction model. A feed-forward back propagation network comprising an input layer, a hidden layer and an output layer was trained using the Bayesian regularization function within MATLAB®. After training of the experimental data, the network structure 4-10-2 with minimal error was found. Here, 4 neurons represent the process parameters in the input layer, 10 neurons in the hidden layer and 2 neurons (matching natural frequency modes 1 and 2) in the output layer.
2.4 Testing The setup illustrated in Fig. 4 was implemented for testing.
Thereafter, the trained ANN model was validated by conducting confirmation runs to compare the predicted and actual natural frequency values for modes 1 and 2. 3.
RESULTS AND DISCUSSION
From the experimental results, the main effects of the process parameters on natural frequency were analyzed. Similar trends were observed for modes 1 and 2 as depicted in Fig. 6 and 7.
Fig. 4. Natural frequency testing setup. Each test specimen was fixed at one end as well as secured to a leveled surface table with the use of clamps and a fixture. An accelerometer was positioned on the test specimen while a striking instrument was used to excite the test specimen. The signal conditioner, data acquisition unit and Lab View software were integrated to obtain the natural frequency readings. All of the test specimens were hit with the accelerometer at various marked points which revealed vibration modes 1 and 2 to be consistently excited (see Fig. 5). Hence, the natural frequencies at these modes were recorded for this study.
Fig. 6. Effect of process parameters on natural frequency mode 1.
Fig. 7. Effect of process parameters on natural frequency mode 2. It is noticed that the raster angle has the greatest impact on natural frequency. A decrease in raster angle results in higher natural frequency with an apparent increase occurring from 45 degrees to 0 degrees. This observation can be attributed to an increase in the stiffness of the specimens with a lower raster angle thus resulting in greater natural frequency. The specimens built with 0 degrees raster angle have all rasters
Fig. 5. Vibration modes 1 and 2. 2.5 Development and validation of prediction model As FDM process involves large number of conflicting factors and complex phenomena for part build, accurate prediction of the output characteristics is very difficult using mathematical 410
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perpendicularly aligned to the bending axis hence offering more resistance and therefore characterized with having greater stiffness.
Moreover, Fig. 9 shows a physical comparison of the surfaces for two specimens with build orientations of 0 and 9 degrees about the Y-axis as well as similar raster angle (45 degrees), air gap (0.016 mm) and no contours. It is evident that the structure has been altered, with a single continuous pattern noticed for the rasters in the specimen built at 0 degrees, whereas an overlapped continuous pattern was observed for the specimen built at 9 degrees.
In addition, it can be seen from Fig. 6 and 7, an increase in air gap leads to minimal reduction in natural frequency. A less dense structure is created with the inclusion of air gap thereby reducing its resistance to deformation and accordingly lower natural frequency. Interestingly, building the specimen oriented about the Y-axis resulted in a subtle increase in its natural frequency. This may be due to an improvement in the density of the specimen’s structure through interaction with the laid rasters. Fig. 8 (a) and (b) support this with surface plots of interaction effects between raster angle and build orientation for natural frequency modes 1 and 2.
(a)
(a)
(b) (b)
Fig. 9. Surface examination of specimens built using build orientation (a) 0 degrees and (b) 9 degrees.
Fig. 8. Surface plots of interaction effects between raster angle and build orientation for natural frequency (a) Mode 1 and (b) Mode 2.
Also, from Fig. 6 and 7, the number of contours is seen to have a minor impact on the natural frequency. Nonetheless, the natural frequency can be increased with addition of 411
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contours since these outlines help to distribute applied loads and thus improve the stiffness of the part for a higher natural frequency.
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technique. The trained ANN prediction model has been validated through various confirmation runs ranging from 0.42 to 5.63% prediction error. Thus, the trained ANN model can be used to determine the desired natural frequencies for modes 1 and 2 through adjustment of the FDM process parameters. In this regard, lower raster angle and air gap together with higher build orientation about the Y-axis and additional contours have been seen from this study to produce parts with greater natural frequencies. This type of control offered by the prediction model provides an offline means to ensure that the natural frequency of the FDM built part is outside the range of operating frequency which helps to mitigate resonance in dynamic conditions. Hence, greater design flexibility can be afforded to industries that utilize composite thermoplastic materials for the production of functional parts, particularly in applications such as aerospace, automotive, biomedical and customer product manufacturing (Turner and Gold (2015); Boschetto and Bottini (2015)).
In following, the performance of the trained ANN model is represented in Fig. 10. The goodness of fit between the predicted values obtained from the ANN model and the experimental values are seen for the training and testing samples with an overall R2 value of 99.96%.
Furthermore, this research work is in alignment with the contemporary shift towards the use of sustainable processes to produce parts with near-zero material waste as well as compatibility with tailored materials for reduced weight while maintaining desired mechanical characteristics such as natural frequency (Bikas et al. (2016); Gardan (2016)). In closing, our future research agenda includes multiobjective optimization studies of other mechanical characteristics like tensile strength and surface roughness in conjunction with natural frequency. The simultaneous satisfaction of all responses will be focused to determine trade off solutions for real life scenarios that require conflicting process settings in FDM.
Fig. 10. Regression plots for trained ANN model.
REFERENCES
Furthermore, three confirmation runs were conducted to validate the use of the trained ANN model for prediction. Table 3 shows these results. The ANN model performed quite satisfactory with all predictions generally within 5% error, hence proving its suitability for future application.
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Table 3. Results of confirmation runs
4.
CONCLUSION
The present work has made an attempt to predict the natural frequency for FDM processed PC part using ANN modeling 412
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