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Linear advance calibration pattern [WWW document]. marlin firmware
(2019)
Another acceleration - extrusion compensation for repraps [ WWW document ] ”
(2019)
Slic3r manual-flow math [WWW document]
O.C. Kevin (2018)
Klipper firmware [WWW document]
P. Pandey, N. Reddy, S. Dhande (2003)
Improvement of surface finish by staircase machining in fused deposition modelingJournal of Materials Processing Technology, 132
S. Sineos (2018)
Linear advance [WWW document]. marlin firmware
T. Coogan, D. Kazmer (2017)
Bond and part strength in fused deposition modelingRapid Prototyping Journal, 23
(2014)
Drawing of E 3 Dv 6 nozzle series rev . 8 . [ WWW document ] ”
A. Bellini, S. Güçeri, M. Bertoldi (2004)
Liquefier Dynamics in Fused DepositionJournal of Manufacturing Science and Engineering-transactions of The Asme, 126
Daekeon Ahn, J. Kweon, Soon-man Kwon, Jung‐il Song, Seok-Hee Lee (2009)
Representation of surface roughness in fused deposition modelingJournal of Materials Processing Technology, 209
Huajun Zhou, T. Green, Y. Joo (2006)
The thermal effects on electrospinning of polylactic acid meltsPolymer, 47
Purpose – This paper aims to present the mathematical foundation of so-called advance algorithms, developed to compensate for defects during acceleration and deacceleration of the print head in filament-based melt extrusion additive processes. It then investigates the validity of the mathematical foundation, its performance on a low-cost system and the effect of changing layer height on the algorithm’s associated process parameter. Design/methodology/approach – This study starts with a compilation and review of literature associated with advance algorithms, then elaborates on its mathematical foundation and methods of implementation. Then an experiment displaying the performance of the algorithm implemented in Marlin machine firmware, Linear Advance 1.0, is performed using three different layer heights. The results are then compared with simulations of the system using Simulink. Findings – Findings suggests that advance algorithms following the presented approach is capable of eliminating defects because of acceleration and deacceleration of the print head. The results indicate a layer height dependency on the associated process parameter, requiring higher compensationvalues for lower layer heights. It also shows higher compensation values for acceleration than deacceleration. Results from the simulated mathematical model correspond well with the experimental results but predict some rapid variations in flow rate that is not reflected in the experimental results. Research limitations/implications – As there are large variations in printer design and materials, deviation between different setups must be expected. Originality/value – To the best of authors’ knowledge, this study is the first to describe and investigate advance algorithms in academic literature. Keywords Fused deposition modelling, Advance, Flow control, FDM, Melt extrusion additive manufacturing Paper type Research paper H = transfer function of input to output speed; Nomenclature k = compliance of system; A = cross section of filament; in K = lag factor of system; A = cross section of annular section of nozzle; out K = correction parameter for linear advance; LA A = cross section of deposited material; print l = length of filament inside extruder; d = diameter of annular section of nozzle; out L = length of nozzle outlet; d = diameter of filament; in F = forces exerted on the filament by the drive wheels; dw F = forces exerted on the filament by pressure loss in © Sigmund Arntsønn Tronvoll, Sebastian Popp, Christer Westum Elverum and Torgeir Welo. Published by Emerald Publishing Limited. the nozzle; This article is published under the Creative Commons Attribution F = forces because of pressure loss caused by friction; (CC BY 4.0) licence. Anyone may reproduce, distribute, translate and F = forces because of pressure loss caused by create derivative works of this article (for both commercial and non- acceleration of material; commercial purposes), subject to full attribution to the original h = layer height; publication and authors. The full terms of this licence may be seen at http://creativecommons.org/licences/by/4.0/legalcode The authors would like to thank Bernhard Kubicek for his valuable input to The current issue and full text archive of this journal is available on this paper. They would also like to thank the whole open source additive Emerald Insight at: www.emeraldinsight.com/1355-2546.htm manufacturing community for designing quality software and hardware for free. This research is supported by The Research Council of Norway through Project No. 235410. The authors greatly acknowledge this support. Rapid Prototyping Journal Received 21 October 2018 25/5 (2019) 830–839 Revised 10 December 2018 Emerald Publishing Limited [ISSN 1355-2546] [DOI 10.1108/RPJ-10-2018-0275] Accepted 22 January 2019 830 Pressure advance algorithms Rapid Prototyping Journal Sigmund Arntsønn Tronvoll et al. Volume 25 · Number 5 · 2019 · 830–839 m = friction coefficient; Figure 1 Over-extrusion in corners because of deacceleration DP = pressure loss in nozzle caused by acceleration of material; DP = pressure loss in nozzle outlet caused by friction; Q = ingoing material volume flow; in Q = outgoing material volume flow; out R = flow rate (v =v ); out in s = complex domain variable for Laplace transforms; v = ingoing extrusion speed; in v = ingoing prescribed extrusion speed; in V = Laplace transform of v ; in in v = outgoing extrusion speed; out v = Q /A ; out in out Generally, the extruder tends to extrude too much material V = Laplace transform of v ; out out while deaccelerating and too little while accelerating (referred v = printing speed; print to as over-extrusion and under-extrusion, respectively) as w = line width; and illustrated in Figure 2. v = rotational speed of the drive wheels. dw As these defects will severely impact the tolerances at corners, manufacturing fine tolerance clearances or press fits Introduction would often require post-processing of the parts by sanding or For the development of filament-based melt extrusion additive machining, for removing excess material. manufacturing, the activity level of the open source and There is a shortage of academic work on extrusion dynamics practitioner community has resulted in a multitude of practical related to FDM, with the exception of Bellini et al. (2004) who techniques and tools being available before they are described made a thorough exploration of extrusion dynamics using and analyzed in academic research. One such widely used Stratasys equipment, working toward strategies for flow aspect, yet less described, is the compensation of defects control. They did however have a focus on the electronic because of undesirable extrusion dynamics occurring while circuit, assuming the heat transfer, rate and temperature accelerating and deaccelerating the print head – known as dependent characteristics to be the root cause of the dynamics. advance algorithms. These algorithms have the potential to The first applied open source algorithm attempting to substantially enhance the print quality, but they can also impact calibrate for the defects, as shown in Figure 1, was through an the performance negatively if they are not correctly configured. algorithm called Advance, developed by Matt Roberts (2019). There is also uncertainty about how these algorithms are This was later implemented in the widely used Marlin affected by different process characteristics, such as layer firmware. The algorithm assumed that the root cause of the height, material, temperature and nozzle geometry. error was the compression of filament in the extruder combined To be able to investigate these aspects thoroughly, we will with the pressure loss in the nozzle due to acceleration of first present the algorithms’ background and develop its material. Influenced by this work, Bernard Kubicek pointed theoretical foundation, both in terms of mathematical out that the pressure loss in the nozzle was dominated by description and graphical block-system design. This would friction forces rather than forces due to acceleration (Kubicek, hopefully aid further research on the matter and ease the 2019). An algorithm incorporating these ideas was then understanding of the algorithms for practitioners. As most of implemented in the Sailfish firmware by Jetty, Kubiceck and the work on this subject is conducted by the open source Newman, hence called JKN-advance (Jetty Firmware Manual, community, the previous work is rarely published and therefore 2019). This progress led many firmware developers to develop consists of sources outside of the academic sphere. their own version of this algorithm, and different versions are As a start of investigating the algorithm’s dependency of now implemented in many other firmware, for example, process parameters, we will perform an experimental procedure Marlin, RepRap and Klipper (“G-code,” 2019; Kevin, 2018; focusing on the dependency of layer height and whether the Sineos, 2018). Building on the same physical principles of JKN-advance, acceleration is positive or negative. These results will then be the developers of Marlin created an algorithm named linear compared with simulation results of the process using Simulink, advance, which because of Marlin’s popularity is now possibly which can determine the model validity. Although trademarked by Stratasys Inc., filament-based melt extrusion additive manufacturing is commonly referred to as Figure 2 Typical printed shape while print acceleration/deacceleration. fused deposition modeling (FDM), which will be used throughout 1 – uniform extrusion at consistent slow speed, 2 – defects start during the article. acceleration, 3 – returning to uniform extrusion at consistent high speed, 4 – defects start during deacceleration and 5 – returning to uniform extrusion at slow speed Background and objectives A typical area for defects is in regions of high acceleration or deacceleration of the print head. The most common display of these effects is shown in terms of over-extrusions on corners when printing with a fast pace, as seen in Figure 1. 831 Pressure advance algorithms Rapid Prototyping Journal Sigmund Arntsønn Tronvoll et al. Volume 25 · Number 5 · 2019 · 830–839 the most adopted version. The algorithm was developed and wheel are equal to those arising from the pressure drop in the implemented by Sebastian Popp, improved by multiple nozzle: GitHub users including Scott Latheine and documented by F ¼ F (1) dw n Sineos (2018). As there might be slight differences in the implementational details for different firmware, we will be Explanation for the symbols are shown in Figure 3. Moreover, referring to the Marlin implementation, if not stated the compression or possibly buckling deformations of the otherwise. filament inside the extruder is assumed to be linearly dependent on the forces in the following way: Mathematical formulation Dl ¼ kF (2) Some of the most promising explanations for potential contributions to these deformities are: where k is a constant and Dl = l l , where l is the initial 0 0 deflection of the drive wheel position relative to the nozzle; (unloaded) length of the filament section between the nozzle compression/deformation of the filament between the and drive wheel. The counteracting forces are assumed to be drive wheels and nozzle; caused by pressure loss in the nozzle or nozzle outlet. There deflection/elongation of the guide tube (in case of might also be friction stemming from along the rest of the path Bowden-type extruders, using extruder drive wheel from drive wheel to nozzle, but as the filament normally has a diametral clearance of 0.15-0.25 mm to the walls that are mechanism placed apart from the heating assembly, mostly covered with low-friction Teflon or nylon tubing, this connected by a polymer tube); and contribution is assumed low. The remaining question is then load-dependent phase lag in the extruder stepper motor. the relation between velocity and forces in the nozzle, where we Together with a pressure loss in the molten plastic have both contribution from the acceleration of material, for throughout the nozzle, which increases with material which the contribution can be found through the Bernoulli velocity, any of these causes could possibly reproduce the equation, and frictional forces. same phenomena. As a rough estimate of magnitude of these forces, we would In the compensation procedure to be described here, the use an example of a standard E3D nozzle (Younge, 2014), with assumed root causes are all modeled as linearly dependent on 0.4 mm diameter nozzle (d ), 0.6-mm outlet length (L), used out therateof the filament extrusion, and hence pooled into for 1.75 mm filament diameter (d ) and at an relatively high in single system. The easiest way to describe the mechanism extrusion speed of 100 mm/s (v ). We would choose to use out would be using the compression of filament analogy, as seen polylactic acid (PLA) data as it is the most common material in Figure 3. for FDM. PLA is found to exhibit low shear thinning and is Based on Sineos (2018) and Kubicek (2019), the following therefore assumed to be Newtonian. We assume a density of procedure could describe a compensation procedure for this 1,250 kg/m r and a viscosity of approximately 200 to type of system. The system is assumed to be quasistatic, so that 1000 Pa.·s (m) at 220°C-190°C (Zhou et al.,2006). The forces forces due to acceleration of solid material are assumed on the filament due to acceleration of material, named F , negligible. This means that the forces exerted by the drive would be calculated as: Figure 3 Direct drive extruder assembly, together with simplified physical model. Forces at nozzle F , the length of the filament section inside extruder l, drive wheel forces F and incoming/outgouing material volume flow, Q and Q , together with incoming/outgoing extrusion speed v and v , dw in out in out printing speed v and rotational speed of the extruder drive wheel v print dw 832 Pressure advance algorithms Rapid Prototyping Journal Sigmund Arntsønn Tronvoll et al. Volume 25 · Number 5 · 2019 · 830–839 2 2 r v v process parameters to surface roughness. Most notable is the out in 2 F ¼ DP A ¼ pd a a in in elliptical cross-sections model by Ahn et al. (2009), and the ! parabolic model by Pandey et al. (2003). These have limitations out in practical implementations, as these are based on rv 1 out 4 experimental observations. in 2 5 ¼ pd 1:37 10 N (3) in Relating the geometric measures to the output geometry gives (Gary et al., 2019): where DP is the pressure loss in the nozzle. Using the Hagen– Poiseuille equation, assuming laminar flow, the friction A ¼ wh 1 h (7) print contribution of the force from the nozzle outlet only, named F , can be found as: For accelerating/deaccelerating, equation (4) gives: F ¼ DP A ¼ p8mLv 0:28 to 1:4 N (4) f f out out d d Q out Dl ¼ K (8) dt dt A in where DP is the pressure loss due to friction. The friction forces from the conical section are harder to assess, as this is a region where the material goes from solid to melt, and its rheological Q Q Q in out out (9) ¼ K properties would therefore be very difficult to include. A A in in However, the friction forces from the nozzle outlet only, are larger than the acceleration contribution by a magnitude of 4 Q Q out out 3.5 10 , and hence clearly the dominating force. The relation (10) v ¼ K 1 in A A in in between velocity and forces from the nozzle is therefore assumed linear. This leads to a relation between the velocity out Solving for gives: and the compression of the filament that is also linear, related in by a constant K, which we call the lag factor, by the following Q Q out out (11) convention: v K ¼ in A A in in out Dl ¼ K (5) In the advance algorithms, one simply corrects v to be equal to in in 0 0 K v _ 1 v , where v is the required extrusion speed, as LA in in in defined by the G-code. This gives: The older advance created by Matt Roberts assumed the Bernoulli pressure drop to be the dominant term, and hence Q Q out defined: 0 0 out v 1 K v _ K ¼ LA in in A A in in (6) Dd ¼ KQ out As shown, there are many factors influencing the pressure _ _ Q Q Q out 0 out out v 1 K K ¼ LA loss, and results from one FDM printer setup (machine, in A A A in in in material, temperature), might therefore not be the same in another setup. which for K = K would give Q =A ¼ v , as required for LA out in in The ratio between the extruder speed and printing speed is a correct extrusion width. The reason for having the 1/A factor in dictated by the slicer, based on the assumed geometry of the is because of G-code conventions for most FDM firmware. For printed filament. To prescribe toolpaths, trying to match a a printing move the G-code prescribes the required length of sampled geometry outline, slicer software assumes that the raw-filament needed to extract the correct amount of material cross section of the extruded filament is rectangular with as prescribed by the computer-aided manufacturing software, semicircular ends, as seen in Figure 4, which is however only as illustrated in Figure 5. defined for width less than the layer height. Much work has As FDM printers are most often driven by stepper motors, been done on microgeometry of FDM parts, for relating the which are advancing in discrete time/length intervals, this could be implemented in each of these intervals. Calculating the required length of filament at interval n, DD , with time step Figure 4 Assumed geometry of extruded filament for slicer Dt , as a function of the requested extruded filament segment implementation. Out-of-plane printing movement DD in each time step, can be done as follows: Figure 5 General entries in a printing move, using the G1 G-code command 833 Pressure advance algorithms Rapid Prototyping Journal Sigmund Arntsønn Tronvoll et al. Volume 25 · Number 5 · 2019 · 830–839 0 1 0 0 link between the theoretical extrusion speed of the drive wheel DD DD n n1 B C and the real extrusion speed of the filament. These values DD @ A D (12) n Dt Dt n n1 n ¼ K 1 LA would have discrepancy because of the slip between the drive Dt Dt Dt n n n wheel and the filament and deformation in the filament. For printing applications, it is assumed constant and usually tuned 0 0 DD DD on the printer through the parameter extruder steps per millimetre n n1 0 (13) DD ¼ K 1 DD n LA and in the G-code through the parameter called flow rate, flow Dt Dt n n1 or extrusion multiplier. This is however omitted in this article, as these parameters are tuned in advance. The resulting system is The K -factor is in units of seconds, and its magnitude is LA the solution of the system as seen in Figure 7. found experimentally, typically seen in the range of 0.1-0.3 for Although less important for uncorrected flow, for special direct drive extruders, and in the range of 2.0-3.0 for Bowden- cases as, for example, overcompensation, v might become type extruders (Sineos, 2018). The presented framework out negative. This would empty the nozzle for material instead of represents most advance algorithms, but some have a scaling dragging material from the print bed into the nozzle again. factor for K , which for the Linear Advance 1.0 from the LA During negative v , the velocity-dependent friction is out Marlin Firmware is 512. assumed neglectable, as no material is moving through the It is debatable whether the volume flow is a valid nozzle and the correction of the system for negative speeds in independent variable for this compensation. The material from Figure 8 is therefore applied. the nozzle is deposited on a bed perpendicular to the extrusion The combined system of the extruder and the pre-processing direction, and there is contact between the nozzle and melt of the speeds using linear advance is as seen in Figure 9. both inside and outside of the nozzle, as seen in Figure 6. This All these models assume that the mechanical/mechatronic would create a layer height-dependent pressure drop, but the system is flawless and that the method of discretization is magnitude is difficult to assess because of a complex flow irrelevant, and will be used in the Simulink simulation pattern with combined open, moving and stationary software. boundaries. As lower layer heights are associated with a higher pressure loss (Coogan and Kazmer, 2017), it is expected that lower layer heights also require higher compensation parameters. Figure 7 Resulting extruder system from equation (14) For simulation purposes, the solution of equation (8) could be found using Laplace transformation, where the solution of this first-order ordinary differential equation is: V s ¼ V sðÞ Ks1 1 (14) ðÞ ðÞ in out And the transfer function H(S) would be written as: V s 1 ðÞ out Hs ¼ ¼ Figure 8 Corrected extruder system eliminating backflow of material ðÞ (15) V ðÞ s 11 Ks in where Q /A is called v for simplicity and its Laplace out in out transform is called V . This transfer function is very similar to out what Bellini et al. (2004) found in their research, where the only difference is a time-delay function and a gain. The gain is the Figure 6 Overview of the different boundary types in the nozzle. Stationary boundaries would increase the pressure drop, while the pressure drop because of open and moving boundaries has a more uncertain influence 834 Pressure advance algorithms Rapid Prototyping Journal Sigmund Arntsønn Tronvoll et al. Volume 25 · Number 5 · 2019 · 830–839 Figure 9 Model for processing the input speed using linear advance, altering the G-code input speed v based on the acceleration to calibrate the in extruder speed simulations by, e.g., finite element analysis using mixed Experimental setup Eulerian–Lagrangian formulation and hard-to-obtain Using an Original Prusa i3 MK2.5 desktop FDM printer, a rheological properties, and is in this study omitted because of controlled experimental test for different linear advance values complexity. The implications of displaying flow rate compared and different layer heights was performed. The test was to the cross-section model implemented in the slicers generated from the test template provided in the Marlin (Figure 4) are shown in Figure 12. documentation (Marlin Firmware, 2018), which consists of an acceleration from low speed to high speed at values for K LA Results and discussion from 0 to 0.2. Key process parameters are listed in Table I and Figure 10, and simulated results are seen in Figures 11 and 12. First, we will present the combined results from the tests. Then The test is only performed for deposition onto the bed, and the the results from each layer height alongside a simulation will be geometry and stiffness of the substrate would possibly affect the presented. Figure 14 displays the results for all layer heights result. and all correction factors combined, along with a marking that Figure 11 shows the simulated output extrusion speed v out shows the lines that are estimated to have the smallest defects, for different K values of the system, when linear advance is not and hence the more optimal correction factor. applied. Dividing v(K)by v(K = 0) would give the flow rate for Table II summarizes the findings from the figure. The the different positions along the test line, as shown in Figure 13. identification of this correction factor is done by visual This would to some extent reflect the changes in extrusion estimation only, placing the ideal correction factor half way width but neglect the geometry of the filament line and between the test lines displaying visible defects. As a extrusion dynamics, after the melt leaves the nozzle. This quantitative result, an accuracy on ideal K of less than 0.01 s LA implies that, for example, the peaks in the flow rate will not be cannot be guaranteed. Owing to defects in the glued-on reflected in the extrusion width, as they will be smoothened out polyetherimide (PEI) print surface as well as tolerances of the by flow dynamics pushing material forward and backward from filament cross section of about 62 per cent, any higher the nozzle, establishing the path of least resistance. To include accuracy would anyways be difficult to achieve. these effects would possibly require highly non-linear As seen in Figure 14, the defects get smaller for increasing K until a value of around 0.04 to 0.95 for the different LA Table I Process parameters for experimental tests layer heights. Using a K value of more than twice the LA optimal one, will result in severe overcompensation to an Layer height (mm) 0.10, 0.20 and 0.30 extent that results in no extruded material when K -values 0-0.2 s in 0.01-s increments LA deaccelerating. The experimental study shows that there is Line width (mm) 0.48 mm approximately 0.01 s in difference between the optimal K- Nozzle size (mm) 0.40 values for acceleration and deacceleration. This is however Material Generic PLA within the range of the accuracy of our method. It must be Nozzle temperature 215°C emphasized that these values are only valid for our specific setup, as this will possibly be affected by many different parameters. As hypothesized, there is also evidence for a layer Figure 10 Test line speeds, accelerations and lengths dependency. The ideal compensation parameter is approximately twice as high for a layer height of 0.1 mm than for a layer height of 0.3 mm. This indicates that thin layers generate a significantly higher pressure-loss, which is suggested in literature (Coogan and Kazmer, 2017). However, because of the number of different nozzle geometries, it could be challenging to develop a universally valid layer height compensation function. As this test is quite easy to perform, the results could instead easily be implemented as tabular values in the slicer software. 835 Pressure advance algorithms Rapid Prototyping Journal Sigmund Arntsønn Tronvoll et al. Volume 25 · Number 5 · 2019 · 830–839 Figure 11 Simulated, non-calibrated output speed v from extruder for different K values, printing with 0.2-mm layer height along the test line out Figure 12 Difference in flow rate-to-line width relation between slicer Figure 13 Simulated non-calibrated flow rates R for different values of implemented model with circular ends and using a linear relation to the K, where R = v(K)/v(K = 0). Start width indicates the ideal flow rate flow rate as used for visualization of simulation results. Note that the (R = 100%) slicer implemented model is ill-defined for widths lower than layer height Figures 15-17 show the full test lines, alongside a simulation using the system shown in Figure 9, applying the identified length of the section with no extrusion is less reflected in the average optimal K value of the system for each layer height to experimental data, as there seems to be a difficulty to make the LA display whether the proposed model can replicate the plastic stick to the print bed while restarting the extrusion. experimental results. The simulation results are only displayed Comparing the simulation results for flow rate with the in terms of extrusion flow rate, R ¼ v =v , and scaled so that experimental results for filament width, both are very similar out in the simulated flow rate is equal in width to the experimental when there are no large variations/spikes in flow rate. For large results sampled between the start of the line and start of the variations, the experimental results are smoothened out acceleration phase, which indicates ideal flow rate (R = 100 compared with the simulation results, as illustrated in per cent). Sample line for h = 0.2 and K = 0.06 is used as Figure 18. This discrepancy could be from dynamics of the LA reference. melt after it leaves the nozzle. It is also possible that this For 0.3-mm layer height, the model has a good fit to the discrepancy is because of high stepper motor load, resulting in experimental data with approximately the same variations in skipped steps, as this compensation uses large and discrete the acceleration zone and the same length of section where velocity jumps when it starts an acceleration. Another reason there is no extrusion of material. For the lower layer heights, the for the discrepancy could be deflection between the nozzle and 836 Pressure advance algorithms Rapid Prototyping Journal Sigmund Arntsønn Tronvoll et al. Volume 25 · Number 5 · 2019 · 830–839 Figure 14 Defects for different layer heights, and K values for linear advance calibration. X marks the line with least defects, or between if similar print bed because of higher volume flow and hence higher Table II Ideal correction factors for different layer heights pressure, increasing the layer height in those areas. K for K for Average LA LA When the flow rate is relatively low, the experimental Layer height acceleration[s] deacceleration[s] [s] samples are somewhat wider, as illustrated in Figure 19. This is expected, as in this region the assumed extrusion width is less 0.1 0.095 0.085 0.9 than the layer height. Having such a low flow rate would result 0.2 0.065 0.055 0.06 in an uncertain shape of the extruded line, as they will not be 0.3 0.05 0.04 0.045 sufficiently squeezed down onto the print bed. Figure 15 Experimental results for 0.1-mm layer height, alongside simulation results for ideal K =0.09 s 837 Pressure advance algorithms Rapid Prototyping Journal Sigmund Arntsønn Tronvoll et al. Volume 25 · Number 5 · 2019 · 830–839 Figure 16 Experimental results for 0.2-mm layer height alongside simulation results for ideal K = 0.06 s Figure 17 Experimental results for 0.3-mm layer height alongside simulation results for ideal K = 0.045 s Figure 18 Illustration of experimental width (top) and simulation of Figure 19 Illustration of experimental (top) width and simulation flow rate (bottom) results for 0.3 mm layer height and (a) acceleration (bottom) of flow rate from results for 0.3 mm layer height and (a) region for K = 0.2 and (b) deacceleration region for K = 0. Edges LA LA acceleration region for K = 0 and (b) deacceleration region for K = LA LA traced using the software Inkscape for image clarity 0.0. Edges traced using the software Inkscape for image clarity 838 Pressure advance algorithms Rapid Prototyping Journal Sigmund Arntsønn Tronvoll et al. Volume 25 · Number 5 · 2019 · 830–839 Jetty Firmware Manual [WWW Document] (2019), available at: Summary and further work http://makerbot.wikidot.com/jetty-firmware#toc46 (accessed The mathematical framework for the so-called advance 14 June 2018). algorithms is presented, and its effectiveness in compensating Kevin, O.C. (2018), “Klipper firmware [WWW document]”, for defects because of extrusion dynamics is demonstrated. available at: https://github.com/KevinOConnor/klipper The algorithm Linear Advance 1.0 from the Marlin Firmware (accessed 12 September 2018). is shown to effectively compensate for irregularities in Kubicek, B. (2019), “Another acceleration-extrusion extrusion widths during acceleration and deacceleration of compensation for repraps [WWW document]”, available at: the nozzle. As hypothesized, the required correction http://bernhardkubicek.soup.io/post/168776124/Another- parameters are layer dependent and therefore will need to be acceleration-extrusion-compensation-for-repraps (accessed 7 tuned for each layer height used in a print. There is also June 2018). possibly a small difference in optimal correction parameter Marlin Firmware (2018), “Linear advance calibration pattern for whether the acceleration is positive or negative. The [WWW document]. marlin firmware”, available at: http:// mathematical model is, through simulations with Simulink marlinfw.org/tools/lin_advance/k-factor.html (accessed 4 and in comparison with the experimental data, shown to be July 2018). quite accurate for smooth variations in flow rate. When there Mattroberts’ Firmware - RepRap (2019), available at: https:// reprap.org/wiki/Mattroberts%27_Firmware (accessed 19 are rapid variations in flow rate, the extrusion width seems to July 2018). be smoothened out in the experimental results compared Pandey, P.M., Venkata Reddy, N. and Dhande, S.G. (2003), with the simulations. “Improvement of surface finish by staircase machining in As the algorithm enables printing a sufficiently uniform fused deposition modeling”, Journal of Materials Processing extrusion width for practical purposes, and the mathematical Technology, Vol. 132 Nos 1/3, pp. 323-331, available at: model can replicate that, we believe further work should focus https://doi.org/10.1016/S0924-0136(02)00953-6 on three areas: Sineos, S. (2018), “Linear advance [WWW document]. marlin 1 Investigate implications for printing 3D geometry: firmware”, available at: http://marlinfw.org//docs/features/ non-linear extruder movements; and lin_advance.html (accessed 7 March 2018). substrate stiffness and geometry. Younge, R. (2014), “Drawing of E3D-v6 nozzle series rev.8. 2 Investigate dependency of more process parameters, e.g.: [WWW document]”, available at: https://e3d-online.dozuki. material; com/Document/rWuaQCQsJTlRdB1k/.pdf (accessed 12 temperature; October 2018). specified extrusion width; and Zhou, H., Green, T.B. and Joo, Y.L. (2006), “The thermal nozzle diameter. effects on electrospinning of polylactic acid melts”, Polymer, 3 Develop solutions and standards for implementing the Vol. 47 No. 21, pp. 7497-7505. process parameter dependency in the printer firmware. About the authors References Sigmund Arntsønn Tronvoll has MSc in Industrial Mechanics Ahn, D., Kweon, J.-H., Kwon, S., Song, J. and Lee, S. (2009), and is a Postgraduate Student in additive manufacturing at “Representation of surface roughness in fused deposition NTNU. Sigmund Arntsønn Tronvoll is the corresponding author modeling”, Journal of Materials Processing Technology, and can be contacted at: sigmund.tronvoll@ntnu.no Vol. 209 Nos 15/16, pp. 5593-5600, available at: https://doi. Sebastian Popp volunteers as a software developer in the org/10.1016/j.jmatprotec.2009.05.016 Marlin Firmware community. Bellini, A., Güçeri, S. and Bertoldi, M. (2004), “Liquefier Christer Westum Elverum is an Associate Professor in dynamics in fused deposition”, Journal of Manufacturing Design and Manufacturing. Christer W. Elverum holds a PhD Science and Engineering, Vol. 126 No. 2, pp. 237. within prototyping and development strategies in the Coogan, T.J. and Kazmer, D.O. (2017), “Bond and part automotive industry, from the Department of Mechanical and strength in fused deposition modeling”, Rapid Prototyping Industrial Engineering at NTNU. Journal, Vol. 23 No. 2, pp. 414-422. Gary, H., Ranellucci, A. and Moe, J. (2019), “Slic3r Torgeir Welo is a Professor in Design and Manufacturing at manual-flow math [WWW document]”, available at: NTNU. Torgeir Welo holds a PhD in plastic bending http://manual.slic3r.org/advanced/flow-math (accessed behavior of aluminum alloy structures from the Department of 10 April 2018). Structural Engineering, NTH (now NTNU). Industry career G-code [WWW Document] (2019), available at: https:// includes SINTEF Production Engineering, SINTEF reprap.org/wiki/G-code (accessed 12 September 2018). Materials Technology and Hydro Automotive Structures. For instructions on how to order reprints of this article, please visit our website: www.emeraldgrouppublishing.com/licensing/reprints.htm Or contact us for further details: permissions@emeraldinsight.com
Rapid Prototyping Journal – Emerald Publishing
Published: Aug 21, 2019
Keywords: Fused deposition modelling; Advance; Flow control; FDM; Melt extrusion additive manufacturing
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