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A robust ink deposition system for binder jetting and material jetting
Accepted Manuscript Title: A Robust Ink Deposition System for Binder Jetting and Material Jetting Authors: Xuechen Shen, Hani E. Naguib PII: DOI: Article Number:
S2214-8604(19)30169-1 https://doi.org/10.1016/j.addma.2019.100820 100820
Reference:
ADDMA 100820
To appear in: Received date: Revised date: Accepted date:
11 February 2019 16 July 2019 28 July 2019
Please cite this article as: Shen X, Naguib HE, A Robust Ink Deposition System for Binder Jetting and Material Jetting, Additive Manufacturing (2019), https://doi.org/10.1016/j.addma.2019.100820 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
A Robust Ink Deposition System for Binder Jetting and Material Jetting Xuechen Shena, Hani E. Naguiba (corresponding author [email protected],ca)
Department of Mechanical and Industrial Engineering, University of Toronto, 5 Kingβs College Rd. Toronto, ON, Canada, M5S 3G8 a
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Abstract
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The adaptation of inkjet technology for additive manufacturing (AM) enabled the highest standards of print speed and print resolution in the industry. However, inkjet printheads impose strict limitations on ink properties. Ink compositions exhibiting volatility, rehydration, surface tension, chemical stability, abrasiveness, and electrical properties that deviate from printhead specifications shorten its service life. Frequent and complex maintenance procedures are necessary, but replacement is the only solution to declining print quality, accruing heavy maintenance costs. This is especially limiting for AM as part quality and properties are closely dependent on ink composition. We propose an ink deposition system designed for robustness by implementing modular and dedicated components. The system deposits ink in a continuous jet. We find optimal process parameters and evaluate system performance in comparison to inkjet and material extrusion (ME). The system produces line widths between 0.3 β 0.5mm, indicating print resolution capabilities are comparable to commercial ME systems.
1. Introduction
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Keywords: inkjet, binder jetting, material jetting, process enhancement, performance optimization, print resolution
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Inkjet is a pervasive printing technology in the modern world, and more recently it has become a platform for additive manufacturing (AM). Binder jetting (BJ) uses inkjet technology to deposit liquid bonding agents (binder) onto a powder bed [1]. Material jetting (MJ) uses inkjet to deposit photopolymers or wax onto a build platform.
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There are 2 main categories of state-of-the-art inkjet technology: drop-on-demand (DOD) and continuous inkjet (CIJ). In DOD (Figure 1aFigure), a heater or piezoelectric transducer effects a rapid volume change in the ink reservoir, which causes ejection of ink under pressure [2]. In CIJ (Figure 1b), a flowing jet is formed at the nozzle outlet under pressure. The jet is broken into distinct drops by applying a disturbance through a piezoelectric element. As they descend, the drops are inductively charged by an electrode, then selectively deflected on a trajectory by deflector plates towards a target position on the substrate. Undeflected drops are collected and recycled into the ink reservoir [2]. These technologies are wellestablished for graphical printing, but new challenges arise when they are adapted for AM. For BJ, ink (binder) formulation needs to accommodate binder-powder interactions including binding mechanism, spreading, and absorption [3]. For MJ, ink formulation needs to accommodate photoinitiation, photocrosslinking, and heat and UV degradation properties [4]. There may also be application-specific ink formulation considerations regarding mechanical, thermal and electrical properties. All of these considerations factor into volatility, rehydration, surface tension, chemical stability, abrasiveness, and electrical properties of ink formulations that cause issues for inkjet. For example, high volatility inks tend 1
to dry on the nozzle and cause clogs [2]. Clogs could become persistent if the material fails to rehydrate [3]. Abrasive nanoparticles are known to scratch nozzles through slurry erosion, causing considerable wear [5], [6]. Increasing nanoparticle loading destabilizes the jetting process, leading to clogging [7]. Caustic chemicals may etch and thus damage wetted components. For CIJ, precise knowledge of ink charging properties and deflection voltage is necessary to determine droplet trajectories [8]; inadvertent deflection events may also lead to charge accumulation on deflection plates resulting in electrical breakdown [2]. When improperly addressed, these issues result in printhead failure, necessitating heavy investments in maintenance. Furthermore, these issues impart strict requirements on ink composition and may be limiting innovation in the development of BJ and MJ materials, processes, and applications.
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Inkjet AM is one of the fastest AM processes owing to the line-sweep printing method enabled by individual control of multiple nozzles. However, the limitations of inkjet position the technology against manufacturability and material variation, making it less favorable for adoption by industry. Comparatively, material extrusion (ME) processes are widely adopted in industry despite lower printing speed and resolution [9]. Inkjet AM and ME are both pressure-driven material deposition techniques in principle. Thermoplastic ME, also known as Fused Filament Fabrication (FFF), involves melting a thermoplastic polymer and extruding it through a nozzle under roller-induced torque [10]. Upon leaving the nozzle, rapid cooling fixes extruded material in its printed shape. Viscoelastic slurries and gels are extrudable under piston-induced pressure at room temperature; this process is known as Direct Ink Writing (DIW) [11]. In ME processes, components are highly modular and dedicated. The ability to modify the components for increased compatibility with the ink formulation decreases its failure rate. The low cost and difficulty of replacing individual components decreases the severity of failure. The flexibility of operation simplifies material flushing and other maintenance procedures. Overall, the lower frequency of failure, ease of maintenance, and low-cost operation enabled by modular and dedicated components makes ME a more robust process for industrial application.
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We propose an ink dispensing system implementing modular and dedicated design. The system trades decreased print speed and resolution for improved robustness, which should facilitate material development and routine operation. These characteristics are intended to encourage industrial adoption of BJ and MJ processes. The proposed system explores a process to deposit low-viscosity inks using a pressure-induced jet. Pressure-induced jetting is used in abrasive water jet cutting [12]. The width of such water jets is comparable to the nozzle diameter and converges well below nozzle diameter at high traverse speed [13]. In the proposed system, a low-pressure pump forms a jet of ink at the nozzle outlet, which is applied over the substrate. The jet is controlled to form a highly stable continuous stream through gearing-enhanced peristaltic pumping and ejecting from industrially available dispensing needles.
2. Theoretical Basis
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A rationalization of the proposed system for ink jetting AM is presented from the assessment of drop volume and line width, parameters that define print resolution capabilities in AM. Drop volume measures the quantity of ink in each distinct drop. Drop volume enables quantitative comparison to inkjet technology. Line width is the minimum width of an extruded line. Line width enables quantitative comparison to ME. Without considering spreading effects after deposition, the two parameters are approximately related by modelling line width as the diameter of a spherical drop. Two distinct behavior regimes are observed when pumping through a vertically suspended nozzle outlet; 1) pendant drop dispensing at low fluid velocity produces unsuitable parameters for AM. 2) Jetting at high fluid velocity prints with resolution comparable to ME.
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2.1 Pendant drop regime Pendant drop dispensing occurs at low fluid velocity because the flow is dominated by contention between gravity and surface tension. Surface tension causes pumped fluid to accumulate at the nozzle outlet, producing a pendant drop. The drop only detaches when surface tension is overcome by gravity as the drop reaches sufficient mass. Surface tension πΎ at the liquid-air interface mediates adhesion to the nozzle outlet with a force proportional to the length of the liquid-nozzle boundary πππ (circumference of nozzle outer diameter ππ ). At the moment of drop detachment, adhesion equals gravitational pull on the drop πΉπ (Eq.1.). Fg = Οdo Ξ³
(1)
ΟVd g = Οdo Ξ³
(2)
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Modelling the pendant drop of water at a water-air interface, the surface tension is 72Jmβ2 and density π of water is 1000kgmβ3 , allowing us to predict its drop volume with Eq.3.
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πππ πΎ ππ
πππ =
(3)
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Plotting predicted drop volumes against nozzle outer diameter in Figure 3a, we determine whether a suitably small nozzle size could produce pendant drops comparable to inkjet. The predicted drop volumes range from 102ΞΌL at ππ = 4.57mm to 4ΞΌL at ππ = 0.18mm. Even with the smallest commercially available nozzles, the drop volumes exceed benchmark inkjet drop volumes (~10pL) by 6 orders of magnitude [2].
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This large disparity between inkjet and pendant drop volumes found by modelling is reflected in experimental data from literature. Murphy et al measured the drop volume of a balanced salt solution ejected from nozzle sizes ππ = 0.72, 0.64, 0.51, 0.41, and 0.31 (mm) [14]. The data are comparable because the salt solution has nearly identical surface tension and density to water. For these nozzles, the model consistently underestimates drop volumes, as shown in Figure 3a [14]. This indicates that experimental pendant drop volumes are strictly >6 orders of magnitude higher than benchmark inkjet drop volumes. For further evidence of the ineffectiveness of pendant drop to provide the print resolution needed for AM, drop diameter π·π is predicted using Eq. 4 as a measure of line width. 3
Dd = β
6do Ξ³ Οg
(4)
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Plotting predicted drop diameters against nozzle outer diameter in Figure 3b, we find that the minimum drop diameter achievable with a ππ = 0.18mm nozzle is 2mm, even though the nominal outer diameter of the nozzle is significantly smaller. Compared to benchmark line widths of ME printers between 0.1 β 0.5mm, line widths >> 2mm are evidently insufficient for AM. Our analysis suggests that the pendant drop regime of flow yields drop volumes strictly >6 orders of magnitude higher than inkjet, and line widths 1 order of magnitude higher than ME. Empirical data from literature and our own work support the derived conclusion. Furthermore, we observed that long accumulation times between drops resulted in drop spacings that are too long to be visually interpreted as a continuous line.
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2.2 Jet Regime The pendant drop regime is characterized by slow development of large drops due to the mass-driven detachment mechanism. The force balance between surface tension and gravity is illustrated in Figure 4a. In DOD inkjet technology, a pulse-driven actuator imparts a momentum that instantaneously overcomes surface tension forces, terminating drop growth and limiting the drop volume [2]. When fluid is accelerated to a high velocity before ejection, momentum from sustained velocity overcomes surface tension at the nozzle outlet, forming a column of fluid. This is the jet flow regime. In the same principle as DOD, jet formation terminates drop growth and constrains the profile of the jet column. This is illustrated in Figure 4b.
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The momentum-driven fluid ejects from the narrow orifice of the nozzle and intrudes into the ambient air, forming a jet. An empirical model of jet spread describes the jet radius π at distance π away from a nozzle with inner diameter ππ as: (5)
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π = πΎπ’ (π β πΆπ’ ππ )
Where πΎπ’ is the spread rate and πΆπ’ is a constant that describes the position of the jetβs virtual source, which models the implications of ππ [15]. The model is illustrated in Figure 5.
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Since the model predicts a linear jet spread, as π β 0, the jet diameter approaches ππ , as intuition might suggest. However, nozzle placement at the same height as the substrate is prone to cause issues of clogging and mobilization of uncured material in MJ or powder clusters in BJ, practical π must be limited in proximity to 0.
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Values of the spread rate πΎπ’ are quoted between 0.11 for a high Reynolds number turbulent jet and 0.4 for a laminar jet. Flows intruding into ambient fluid (air) tend to be partly turbulent due to local interactions between the jet and the ambient fluid. Empirical data suggests the subtended spread angle is 5
11.8Β°. This results in πΎπ’ β , and πΆπ’ β β [16]. Thus, Eq. 5 becomes: 5
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π =
1 5 (π + ππ ) 5 2
(6)
If we impose a line width requirement ππ€ on π to match benchmark ME line widths of 0.1 β 0.5mm, we can rewrite the relation to solve for maximum separation ππππ₯ between nozzle and substrate; between separation 0 and ππππ₯ from the nozzle, jet diameter is restricted to produce the target line width, such that 2π β€ ππ€ .
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5 (7) ππππ₯ β€ (ππ€ β ππ ) 2 Plotting this relation for all positive ππππ₯ in Figure 6b, we find all nozzles with which the target line width benchmark can be upheld, as well as the maximum separation it can be upheld at. From Figure 6b, we can discern that there is only a single solution for upholding a 0.1mm line width; it is achieved with a ππ = 0.08mm nozzle at separation < 0.0435mm. As such, 0.1mm is approximately the minimum line width achievable using this jetting method. This result makes sense, as the nozzle has ππ = 0.08mm (ππ < 0.1mm). Under the idealized conditions that the jet traverses fast enough in the X-Y plane and ink spreading is insignificant, the line width can be interpreted as the diameter of a spherical drop. A calculation of drop volume using a spherical model is shown in Figure 6a. The model suggests that the lowest achievable 4
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drop volume is 524pL from 0.1mm line width. The relation between drop volume and line width is governed by a trinomial function, rapidly rising to 4.19nL for a 0.2mm line width and 65.5nL for a 0.5ππ line width. At the minimum drop volume of 524pL, the jet achieves a drop volume 1.7 magnitudes higher than the 10pL inkjet benchmark. Between 0.2ππ and 0.5ππ line widths, drop volume increases to 2.5 and 4 magnitudes higher than inkjet. Compared to the 6-magnitude difference found in the pendant drop regime, these values indicate projected print resolution approaching inkjet. From the model analysis, we find that the jet flow regime can approach a drop volume benchmark for inkjet, achieving a minimum value of 524pL. Although the 1.7 magnitude difference indicates inability to compare competitively to commercial inkjet technologies, it can uphold common ME line width benchmarks between 0.1~0.5mm. Coupled with the advantages of robustness and low-maintenance operation, we believe that an ink jetting system applying jet flow offers an approach to facilitate AM of a diverse range of materials while meeting industrial AM benchmarks.
3. Methods and Materials
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3.1 System Design
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Building upon the analysis in section 2, we propose an ink jetting system that operates by pumping ink to manifest jet flow. Upon reaching the jet flow regime, surface tension is continuously overcome by momentum derived from fluid velocity, resulting in minimal drop growth. Thus, ink needs to be accelerated above an escape velocity, which enables jet flow at the nozzle outlet. Mechanically, this can be accomplished using a variety of positive displacement pumps.
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3.1.1 Pump A peristaltic pump design is chosen over alternatives such as diaphragm and piston pumps for its lack of wetted mechanical components and elimination of fluid slip. Furthermore, peristaltic pumping is already used in the industry for transporting ink from reservoirs to inkjet printheads in both graphical and 3D printing [17], [18], [19].
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A peristaltic pump operates by sequentially compressing a fluid-carrying tube between a set of rollers mounted around a rotor stage and the pump casing. At any point along the tube, the volume of the cavity holding the tube changes sinusoidally as a roller approaches and distances from that point. When the cavity volume minimizes, the corresponding section of the tube is pinched closed, forming an occlusion. The occlusion is transported by the roller as it travels. Fluid trapped before the occlusion is pushed by it, and fluid behind is drawn by suction from the vacuum formed at the occlusionβs previous position. The suction prevents fluid slip, and the overall motion results in transportation of fluid along the tube. A diagram of peristaltic pump components and operation is shown in Figure 7.
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3.1.2 Tubing In the peristaltic pump, the tubing is the only wetted component. This is advantageous over other pumping methods because tubing exists in many varieties, is expendable and readily available compared to diaphragms or valves. Tubing can be selected or coated to accommodate abrasiveness, chemical stability, and viscosity of the transported fluid [20]. Blockage and wear can also be assuaged by choosing appropriate tubing material to mediate desirable surface interactions with the fluid. However, tubing used for peristalsis must be compressible, narrowing the selection of base material to flexible polymers such as silicones, vinyls, and fluoropolymers. A long length of tubing extends from the peristaltic pump outlet to the carriage. This length of tubing allows the pump and ink reservoir to be detached from the carriage, decreasing the carried load and thus
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reducing the risk of step loss in gantry motors. Furthermore, pulsation from pump operation is reduced along the tubing. 3.1.3 Nozzle Fluid is ejected from an industrially available dispensing needle. Inkjet nozzles are complex and thus prone to failure through clogging or actuator malfunction; maintenance difficulty also increases with complexity. Dispensing needles are more expendable due to their low cost. The selection of mechanically and chemically resistant constituent materials such as stainless-steel and PTFE make dispensing needles more robust and thus compatible with a large range of ink compositions.
ππ΅ ππ΅ ππ΄ = = ππ΄ ππ΄ ππ΅
(8)
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π. π΄. =
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3.1.4 Gear train To ensure that the pumped fluid reaches escape velocity, gears are implemented in the system design. This allows manipulation of mechanical advantage to raise pump rate limits as required. For a two-gear gear train composed of input gear A and output gear B, mechanical advantage (π. π΄. ) is
Where π refers to the radius of the gear, π refers to its teeth quantity, and π refers to its angular velocity. When the input gear has more teeth than the output gear, such that ππ΄ > ππ΅ , the angular velocity of the ππ΄
ππ΅
that of the input gear. Since
ππ΄
ππ΅
> 1, this gear train increases the output angular velocity
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output gear is
of the pump. A diagram of the gearing system is shown in Figure 8.
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3.1.5 Integration of components The system described in section 3.1 is designed to pump fluid from a reservoir along a length of tubing to a dispensing needle, where it is ejected in the form of a jet. Jet formation is controlled by increasing pump speed using a gear train system. Pump speed is controlled electronically by adjusting the input motorβs angular velocity in rotations per minute (RPM). This system should be mountable on the carriage of any BJ or MJ printer with a computer numerical controlled (CNC) gantry. When mounted and operated, it forms a jet of ink, which performs the ink jetting task akin to an inkjet printhead. A rendering of the design is highlighted in Figure 9b, c, d. The printer we use to evaluate the proposed ink jetting system is a BJ printer that uses a printer body designed by Yvo de Haas, which we use under the CC BY-SA 4.0 License. A rendering of the printer mounted with the ink jetting system is depicted in Figure 9a.
3.2 Materials
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For the current study, system components and process parameters are: a printed polylactic acid (PLA) gear train of π. π΄. = 0.5 with ππ΄ = 30 and ππ΅ = 15 is used. A NEMA17 stepper motor with step angle 0.9Β° drives the input gear. A stepper motor precisely tracks ejected volume and resists friction loss. An INTLLAB DIY peristaltic pump for 3mm ID x 5mm OD silicone tubing is driven by the output gear.
3.3 Printing
Printing of each layer begins by accelerating the pump to the input RPM using the function in Eq. 9 π (9) RPMn = ( + 1) Γ RPMinput π π is the number of rotations since activation, and π is a parameter used to control the acceleration rate. When the layer is complete, printing is terminated by stopping the pump. Using smaller nozzles, pump termination has a delayed effect. An electrical valve is required to terminate dispensing in short time scales. 6
4. Results and Discussion 4.1 System Validation The system described in section 3 is designed to jet ink by accelerating fluid above escape velocity to manifest a thin, stable jet from a nozzle outlet. Through a mathematical analysis, we predicted that jet flow profiles with 0.1 β 0.5mm diameter can be achieved using dispensing needles of sizes ππ = 0.08 β 0.41mm; jetting fluid along a line enables printing at a line width equal to the jet diameter. The line width of the system is predicted to be controllable as it is linearly dependent on needle diameter and separation from the build platform. An experiment is devised to validate the systemβs performance. This study measures system parameters using deionized water as ink and a stainless-steel dispensing needle.
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4.1.1 Jet Diameter The pumpβs output speed is set to 500RPM for a short duration (3-5s) to establish a stable jet. An image is captured and processed to highlight the edges. The highlighted pixels are counted as an estimate of the jet diameter at discrete separations from the needle outlet. A captured image and the processed image are shown in Figure 10. It should be noted that there are 2 major limitations to the method: it is improbable for long sections of the jet to be entirely in focus, and pixel counting is an inherently subjective process due to difficulties assigning pixels to define jet boundaries. To improve reliability, sections of the jet with bright post-processed pixels indicating a more distinguished boundary are preferentially used for counting. Jet diameter is plotted against distance from the nozzle in Figure 11Figure .
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Jet diameters increase with distance from nozzle outlet, but spread angles are significantly smaller than the predicted 11.8Β°. Experimentally determined spread angles are between 1-3Β°. The weak dependence of jet diameter on nozzle-build plate separation suggests that using separation to control jet diameter as predicted is unfeasible.
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However, this implies that a wide range of nozzle-build plate separations can be used without detracting from line width or jet stability. Jet diameter and stability do not change significantly between 0-30mm nozzle-build plate separations. Based on these results, the most viable method of controlling jet diameter is changing nozzle diameters; the line widths achievable are still between 0.1 β 0.5mm.
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The study of jet profile suggests that nozzle inner diameter is the main factor defining jet profile. Jet diameter varies approximately linearly with nozzle-build plate separation, but within a small range due to the small spread angle. These flow characteristics form the basis of fine control over line width by exchanging nozzles of appropriate size and minimizing separation.
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However, in experimental prints, we found large discrepancies between jet diameter and practical line width. Figure 12aFigure depicts a single-layer outline of an ASTM D638 Type V Test Specimen printed using a the ππ = 0.18mm nozzle, water as binder, and Sekisui Celvol 203S polyvinyl alcohol (PVOH) as powder. The line width of the print is measured using a digital caliper to be~0.7mm, while jet diameter is bound between 0.13mm and 0.19mm as determined in Figure 11. It is evident that jet diameter is not the sole factor determining line width. The line width discrepancy contributes to dimensional inaccuracies in the completed print in Figure 12b: 1) Overall width: 5.48Β±4.75% 2) Overall length: 4.60Β±0.41% 3) Height: 5.45Β±4.51% 4) Width of narrow section: 75.7Β±9.73%. Other factors for dimensional inaccuracies are gantry traversing speed and ink spreading and penetration, layer shift, shrinkage, warping, and adhesion issues. Jet diameter is only equivalent to line width in the idealized scenario of sufficiently fast gantry traversing speed and absence of ink spreading. Ink spreading is essentially determined by material properties. It is a product of ink-substrate interactions including surface wetting dynamics, absorption, and wicking [21], [22]. Gantry traversing speed is a process parameter. The gantry needs to move a target line width away from its initial position in the time the equivalent drop volume is 7
jetted; this upholds the target line width in all directions of the X-Y plane. Otherwise, a thicker line is drawn as the larger drop spreads to occupy a bigger space due to surface tension as the jet stalls. Since gantry traversing speed is related to drop volume over time (volumetric flow rate), and its optimization is expected to rectify the discrepancy between jet diameter and actual line width, it is important to characterize the relation. 4.1.2 Volumetric Flow Rate To further characterize practical system capabilities and validate printability, volumetric flow rate from the jet is measured. Flow rate π is measured by setting pump speed to a discreet RPM and collecting pumped fluid of volume π for duration π‘ according to Eq. 10. V (10) t Flow rate is plotted against pump output speed in Figure 13. A general pattern is observed: flow rate increases nonlinearly with increased pump output and decreasing nozzle diameter. It can be categorized into three stages: 1) Pendant drop at low output; 2) Turbulent jet with intermittent collapse to pendant drop at medium output; and 3) Highly stable jet at high output. The relation between nozzle inner diameter, pump output, and flow characteristics is summarized in Table 1.
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The highly stable jet stage is suitable for ink deposition. It is characterized by a threshold in flow rate. Beyond the threshold, further increasing pump output speed results in diminishing increases in flow rate. This threshold coincides with the development of a highly stable jet characterized by absence of significant turbulent effects.
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Fluid velocity at the nozzle outlet π£π can be calculated from flow rate and jet diameter ππ using Eq.11. π£π =
4π πππ2
(11)
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Although fluid velocity is limited by the same threshold as flow rate, very high fluid velocity should be avoided to prevent elastic collision with the powder substrate or build plate.
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4.1.3 Gantry Traversing Speed The gantry traversing speed is a process parameter that should meet requirements set by the volumetric flow rate. The time to reach the drop volume corresponding to a target line width is the allotted time for the gantry to move a line width away from its original position; this upholds the target line width in all directions of the X-Y plane. Thus, the minimum traversing speed can be determined: πππ€ ππ€ = π π£π
(12)
6 π (13) π ππ€ 2 Where π£π is the gantry traversing speed, π is the volumetric flow rate, ππ€ is the line width and πππ€ is the drop volume of a sphere with the line width as its diameter. The gantry traversing speed is expressed in mms β1 . Assuming the gantry is operated at its maximum step size of 5 stepsmmβ1 , the step size can be integrated into a final expression of minimum motor RPM. Motor RPM enables comparison to practical limits of motor function. Traversing speed further incorporates belt and electronic control parameters but enables comparison to industry benchmarks. Figure π£π =
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14 shows the minimum gantry motor RPM and traversing speed for each nozzle to uphold a target line width. In Figure 14, minimum motor RPM and gantry traversing speed are shown on a logarithmic scale, as they increase drastically with finer line width targets and smaller nozzles. Most stepper motors can operate just above 1000 RPM (667 mms β1 for the present design) with the appropriate driver parameters. Thus, 1000 RPM can be used as a benchmark for the gantry motors to uphold the target line width. This imposes a further restriction on the nozzle sizes that would be suitable for ink jetting.
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Table 2 summarizes the nozzle sizes and motor RPMs needed to uphold each target line width. Only the di = 0.08 β 0.16mm nozzles produce line widths below 0.5mm. Line widths between 0.3-0.5mm are achievable under 1000 RPM.
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ME of thermoplastic filaments operates optimally at maximum traversing speeds of approximately 150 mms β1 . As a direct comparison, only the πi = 0.08 nozzle upholding a 0.5mm line width can traverse below 150 mms β1 . However, this comparison only holds superficial value, as ME of thermoplastics fails above 150 mms β1 due to thermal conduction issues, which are not applicable in BJ and MJ. Particle inertia and motor acceleration issues may arise at higher traversing speeds instead.
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This analysis suggests that the maximum hardware capabilities of the proposed ink jetting system is further limited by gantry traversing speeds. According to the analysis, the πi = 0.08mm nozzle produces a line width of 0.5mm while traversing at 142 mms β1 . This result is validated experimentally. Deionized water is printed onto a Polymethyl Methacrylate (PMMA) surface. PMMA is a hydrophobic surface, which minimizes the impact of spreading effects on line width at short time scales [23]. The results are shown in Figure 15. Printing at 150 mms β1 traversing speed, a line width of 0.506mm is produced. The experimentally determined line width agrees well with the analysis. At lower traversing speeds, the analysis overestimates line widths compared to the experimental results.
Conclusions
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Based on mathematical predictions, we identified the suitability of jet flow from a dispensing needle for ink jetting AM. A geared peristaltic pump design is proposed for acceleration of fluid to achieve jet flow. Jet flow profiles are studied for jetting water from a set of needles, confirming that jet diameters between 0.1 β 0.5mm are achievable. Jet profiles suggested that line width could be controlled by nozzle inner diameter. Separation between nozzle and build plate between 0~30mm did not significantly affect line width due to low spread. However, experimental prints indicated that line width is influenced by jet diameter and other factors such as ink spreading and penetration. Gantry traversing speed further limits the achievable line widths, as constrained by motor RPM limits. Limiting gantry motor operation to 1000RPM (667 mms β1 ), only nozzles of size πi = 0.08~0.16mm uphold a line width below 0.5mm. Line widths between 0.3 β 0.5mm are feasible. The capabilities of the proposed ink jetting system are comparable to commercial ME systems. The modular design empowers robustness through the exchangeability, customizability and expendability of wetted components. The system may be particularly useful for material development and characterization.
Declaration of interest 9
None
Acknowledgments The authors would like to acknowledge the financial support of the Natural Science and Engineering Research Council of Canada (NSERC) and the NSERC Network for Holistic Innovation in Additive Manufacturing (HI-AM).
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[9] T. Li, J. Aspler, A. Kingsland, L. Cormier and X. Zou, "3d Printing β A Review Of Technologies, Markets, And Opportunities For The Forest Industry," Journal of Science & Technology for Forest Products and Processes, vol. 5, no. 2, 2016. [10] M. Sireesha, J. Lee, B. V. Kiran SKA, B. Keee and S. Ramakrishna, "A review on additive manufacturing and its way into the oil and gas industry," RSC advances, vol. 40, pp. 22460-22468, 2018. [11] H. Yuk and X. Zhao, "A New 3D Printing Strategy by Harnessing Deformation, Instability, and Fracture of Viscoelastic Inks," Advanced Materials, vol. 30, no. 6, 2018.
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[12] D. Krajcarz, "Comparison Metal Water Jet Cutting with Laser and Plasma Cutting," Procedia Engineering, vol. 69, pp. 834-843, 2014. [13] C. Ma and R. Deam, "A correlation for predicting the kerf profile from abrasive water jet cutting," Experimental Thermal and Fluid Science, vol. 30, no. 4, pp. 337-343, 2006. [14] G. K. Tripp, K. L. Good, M. J. Motta, P. H. Kass and C. J. Murphy, "The effect of needle gauge, needle type, and needle orientation on the volume of a drop," Vet Ophthalmol, vol. 19, no. 1, pp. 38-42, 2015. [15] R. Premnath, "Qualitative air flow modelling and analysis of data centre air conditioning as multiple jet array," Cochin University of Science and Technology, Cochin, 2011.
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[16] B. Cushman-Roisin, "Turbulent Jets," in Environmental Fluid Mechanics, Hanover, Dartmouth Thayer School of Engineering, 2018, pp. 153-161.
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[17] M. J. Diggins, "Disposable peristaltic pump assembly for facsimile printer". US Patent US4333088A, 03 11 1980.
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[18] W. Salmre, "Ink jet printer with peristaltic pump". US Patent US4359744A, 16 11 1982. [19] Y. Sheinman, "System and method for direct inkjet printing of 3d objects". US Patent US20150298394A1, 22 10 2015.
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[20] K. L. Hoffmeier, D. Hoffmann and F. Karl-Heinz, "A First Inherently Pulsation Free Peristaltic Pump.," 58th ilmenau scientific colloquium, pp. 1-11, 2014.
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[21] R. Daniel and J. Berg, "Spreading on and penetration into thin, permeable print media: Application to ink-jet printing," Advances in Colloid and Interface Science, Vols. 123-126, pp. 439-469, 2006.
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[22] H. Hamada, D. Bousfield and W. Luu, "Absorption Mechanism of Aqueous and Solvent Inks into Synthetic Nonwoven Fabrics," Journal of Imaging Science and Technology, vol. 53, no. 5, pp. 050201β 050201-6, 2009.
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[23] S. Semenova, V. Starova, R. Rubio, H. Agogob and V. MG, "Evaporation of sessile water droplets: Universal behaviour in presence of contact angle hysteresis," Colloids and Surfaces A: Physicochemical and Engineering Aspects, vol. 391, no. 1-3, pp. 135-144, 2011.
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Figure captions
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Figure 1: a) DOD actuator rapidly decreases the ink reservoir volume and ejects a drop. b) CIJ produces a pressure-induced jet that is broken into droplets; droplets are charged and deflected on a trajectory towards the printed surface.
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Figure 2: a) FFF drives melted thermoplastics out of a nozzle by pressure built-up from continuously feeding filament. b) DIW feeds viscoelastic inks from a syringe using a piston mechanism or a pump. ME printers typically use modular and dedicated components for the feeding mechanism, ink storage, and nozzle.
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Figure 3: a) Drop volumes from nozzle sizes of ππ = 0.18~4.57ππ are predicted using Eq. 3. b) Drop diameters are predicted by modelling the deposited drop as a sphere, as in Eq. 4.
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Figure 4: a) The force due to gravity is initially small compared to surface tension forces, but growth of the drop increases the force due to gravity. The drop is only ejected when the forces balance. b) When fluid is accelerated above escape velocity before ejection, for a differential volume βπ, momentum is large compared to surface tension and gravity.
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Figure 5: The linear model of jet flow depicted in a cross-sectional view. Spread rate K u is the slope of the jet cone outline. Setting the nozzle outlet at the origin, a virtual origin Cu depicts a virtual source that accounts for di . Using these parameters, jet radius R is a linear function of position along the jet centerline X.
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Figure 6: a) Predicted drop volume corresponding to a target line width. The drop volume is derived from approximating the line width as the diameter of a spherical drop. b) Predicted maximum separation between nozzle and substrate for each nozzle to produce a target line width between 0.1~0.5ππ.
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Figure 7: A peristaltic pump forms occlusions of trapped fluid by squeezing tubing between a set of rollers and the pump casing. Rotor stage rotation and fluid flow paths are traced with blue arrows.
Figure 8: A gear train raises pump speed limits applicable by the driving motor. Mechanical advantage is determined by the ratio of the gearsβ teeth.
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Figure 9: a) 3D model rendering of the printer body design by Yvo de Haas mounted with our proposed pump design. The ink jetting system is highlighted in purple. b) Isometric c) back d) front e) side views of a 3D rendering of the pump design.
Figure 10: a) Captured image of a jet formed at the outlet of a ππ = 0.41ππ/ππ = 0.72ππ needle. b) Captured image is processed to highlight edges.
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Figure 11: Jet diameter is measured by pixel counting and plotted against distance from the nozzle outlet. A line is fitted using the least-squares method with outliers removed to satisfy p<0.05 to characterize the jet profile of each needle size.
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Figure 12: a) Thus far, we have used jet diameter as a proxy for ideal line width. Experimental prints demonstrate large discrepancies between practical and ideal line widths. The measured line width is ~0.7ππ, while the range of jet diameters for this nozzle lies between 0.13ππ and 0.19ππ. b) A completed print using the same parameters.
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Figure 13: Flow rate is determined from volume of fluid collected at the nozzle outlet and collection duration. Flow rate reaches a threshold for sizes ππ = 0.08~0.21ππ. Flow rate thresholds for sizes ππ = 0.26~0.41ππ are not reached.
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Figure 14: Gantry motor speed required to uphold a target line width expressed as a) RPM as a measure of hardware limitations and b) expressed as speed for comparison with ME operation limits. The dotted lines show 1000RPM and 150 mms β1 respectively as guidelines for hardware and operation benchmarks.
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Figure 15: a) Printed lines from a ππ = 0.08mm nozzle at various gantry traversing speeds. b) The actual printed line widths plotted against the gantry traversing speed they were printed at. Theoretical values derived in Figure 14b are plotted on the same graph for comparison.
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Table
Nozzle inner diameter di 0.08mm 0.11~0.21mm 0.26~0.41mm
Pump Output (RPM) Turbulence and Pendant drop intermittent collapse to pendant drop 25 50-300 50 100-300 100 200-500
Highly stable jet (Threshold) 325-500 400-500 >500
Motor RPM to Uphold Line width 0.3mm
1327 >>1000 >>1000
590 965 >>1000
0.4mm
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0.2mm
332 543 993
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Nozzle inner diameter di 0.08mm 0.11 0.16
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Table 1: The three stages of flow in relation to nozzle inner diameter and pump output.
0.5mm 212 347 636
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Table 2: Achievable line widths as determined by nozzle inner diameter and motor RPM
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S2214-8604(19)30169-1 https://doi.org/10.1016/j.addma.2019.100820 100820
Reference:
ADDMA 100820
To appear in: Received date: Revised date: Accepted date:
11 February 2019 16 July 2019 28 July 2019
Please cite this article as: Shen X, Naguib HE, A Robust Ink Deposition System for Binder Jetting and Material Jetting, Additive Manufacturing (2019), https://doi.org/10.1016/j.addma.2019.100820 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
A Robust Ink Deposition System for Binder Jetting and Material Jetting Xuechen Shena, Hani E. Naguiba (corresponding author [email protected],ca)
Department of Mechanical and Industrial Engineering, University of Toronto, 5 Kingβs College Rd. Toronto, ON, Canada, M5S 3G8 a
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Abstract
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The adaptation of inkjet technology for additive manufacturing (AM) enabled the highest standards of print speed and print resolution in the industry. However, inkjet printheads impose strict limitations on ink properties. Ink compositions exhibiting volatility, rehydration, surface tension, chemical stability, abrasiveness, and electrical properties that deviate from printhead specifications shorten its service life. Frequent and complex maintenance procedures are necessary, but replacement is the only solution to declining print quality, accruing heavy maintenance costs. This is especially limiting for AM as part quality and properties are closely dependent on ink composition. We propose an ink deposition system designed for robustness by implementing modular and dedicated components. The system deposits ink in a continuous jet. We find optimal process parameters and evaluate system performance in comparison to inkjet and material extrusion (ME). The system produces line widths between 0.3 β 0.5mm, indicating print resolution capabilities are comparable to commercial ME systems.
1. Introduction
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Keywords: inkjet, binder jetting, material jetting, process enhancement, performance optimization, print resolution
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Inkjet is a pervasive printing technology in the modern world, and more recently it has become a platform for additive manufacturing (AM). Binder jetting (BJ) uses inkjet technology to deposit liquid bonding agents (binder) onto a powder bed [1]. Material jetting (MJ) uses inkjet to deposit photopolymers or wax onto a build platform.
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There are 2 main categories of state-of-the-art inkjet technology: drop-on-demand (DOD) and continuous inkjet (CIJ). In DOD (Figure 1aFigure), a heater or piezoelectric transducer effects a rapid volume change in the ink reservoir, which causes ejection of ink under pressure [2]. In CIJ (Figure 1b), a flowing jet is formed at the nozzle outlet under pressure. The jet is broken into distinct drops by applying a disturbance through a piezoelectric element. As they descend, the drops are inductively charged by an electrode, then selectively deflected on a trajectory by deflector plates towards a target position on the substrate. Undeflected drops are collected and recycled into the ink reservoir [2]. These technologies are wellestablished for graphical printing, but new challenges arise when they are adapted for AM. For BJ, ink (binder) formulation needs to accommodate binder-powder interactions including binding mechanism, spreading, and absorption [3]. For MJ, ink formulation needs to accommodate photoinitiation, photocrosslinking, and heat and UV degradation properties [4]. There may also be application-specific ink formulation considerations regarding mechanical, thermal and electrical properties. All of these considerations factor into volatility, rehydration, surface tension, chemical stability, abrasiveness, and electrical properties of ink formulations that cause issues for inkjet. For example, high volatility inks tend 1
to dry on the nozzle and cause clogs [2]. Clogs could become persistent if the material fails to rehydrate [3]. Abrasive nanoparticles are known to scratch nozzles through slurry erosion, causing considerable wear [5], [6]. Increasing nanoparticle loading destabilizes the jetting process, leading to clogging [7]. Caustic chemicals may etch and thus damage wetted components. For CIJ, precise knowledge of ink charging properties and deflection voltage is necessary to determine droplet trajectories [8]; inadvertent deflection events may also lead to charge accumulation on deflection plates resulting in electrical breakdown [2]. When improperly addressed, these issues result in printhead failure, necessitating heavy investments in maintenance. Furthermore, these issues impart strict requirements on ink composition and may be limiting innovation in the development of BJ and MJ materials, processes, and applications.
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Inkjet AM is one of the fastest AM processes owing to the line-sweep printing method enabled by individual control of multiple nozzles. However, the limitations of inkjet position the technology against manufacturability and material variation, making it less favorable for adoption by industry. Comparatively, material extrusion (ME) processes are widely adopted in industry despite lower printing speed and resolution [9]. Inkjet AM and ME are both pressure-driven material deposition techniques in principle. Thermoplastic ME, also known as Fused Filament Fabrication (FFF), involves melting a thermoplastic polymer and extruding it through a nozzle under roller-induced torque [10]. Upon leaving the nozzle, rapid cooling fixes extruded material in its printed shape. Viscoelastic slurries and gels are extrudable under piston-induced pressure at room temperature; this process is known as Direct Ink Writing (DIW) [11]. In ME processes, components are highly modular and dedicated. The ability to modify the components for increased compatibility with the ink formulation decreases its failure rate. The low cost and difficulty of replacing individual components decreases the severity of failure. The flexibility of operation simplifies material flushing and other maintenance procedures. Overall, the lower frequency of failure, ease of maintenance, and low-cost operation enabled by modular and dedicated components makes ME a more robust process for industrial application.
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We propose an ink dispensing system implementing modular and dedicated design. The system trades decreased print speed and resolution for improved robustness, which should facilitate material development and routine operation. These characteristics are intended to encourage industrial adoption of BJ and MJ processes. The proposed system explores a process to deposit low-viscosity inks using a pressure-induced jet. Pressure-induced jetting is used in abrasive water jet cutting [12]. The width of such water jets is comparable to the nozzle diameter and converges well below nozzle diameter at high traverse speed [13]. In the proposed system, a low-pressure pump forms a jet of ink at the nozzle outlet, which is applied over the substrate. The jet is controlled to form a highly stable continuous stream through gearing-enhanced peristaltic pumping and ejecting from industrially available dispensing needles.
2. Theoretical Basis
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A rationalization of the proposed system for ink jetting AM is presented from the assessment of drop volume and line width, parameters that define print resolution capabilities in AM. Drop volume measures the quantity of ink in each distinct drop. Drop volume enables quantitative comparison to inkjet technology. Line width is the minimum width of an extruded line. Line width enables quantitative comparison to ME. Without considering spreading effects after deposition, the two parameters are approximately related by modelling line width as the diameter of a spherical drop. Two distinct behavior regimes are observed when pumping through a vertically suspended nozzle outlet; 1) pendant drop dispensing at low fluid velocity produces unsuitable parameters for AM. 2) Jetting at high fluid velocity prints with resolution comparable to ME.
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2.1 Pendant drop regime Pendant drop dispensing occurs at low fluid velocity because the flow is dominated by contention between gravity and surface tension. Surface tension causes pumped fluid to accumulate at the nozzle outlet, producing a pendant drop. The drop only detaches when surface tension is overcome by gravity as the drop reaches sufficient mass. Surface tension πΎ at the liquid-air interface mediates adhesion to the nozzle outlet with a force proportional to the length of the liquid-nozzle boundary πππ (circumference of nozzle outer diameter ππ ). At the moment of drop detachment, adhesion equals gravitational pull on the drop πΉπ (Eq.1.). Fg = Οdo Ξ³
(1)
ΟVd g = Οdo Ξ³
(2)
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Modelling the pendant drop of water at a water-air interface, the surface tension is 72Jmβ2 and density π of water is 1000kgmβ3 , allowing us to predict its drop volume with Eq.3.
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πππ πΎ ππ
πππ =
(3)
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Plotting predicted drop volumes against nozzle outer diameter in Figure 3a, we determine whether a suitably small nozzle size could produce pendant drops comparable to inkjet. The predicted drop volumes range from 102ΞΌL at ππ = 4.57mm to 4ΞΌL at ππ = 0.18mm. Even with the smallest commercially available nozzles, the drop volumes exceed benchmark inkjet drop volumes (~10pL) by 6 orders of magnitude [2].
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This large disparity between inkjet and pendant drop volumes found by modelling is reflected in experimental data from literature. Murphy et al measured the drop volume of a balanced salt solution ejected from nozzle sizes ππ = 0.72, 0.64, 0.51, 0.41, and 0.31 (mm) [14]. The data are comparable because the salt solution has nearly identical surface tension and density to water. For these nozzles, the model consistently underestimates drop volumes, as shown in Figure 3a [14]. This indicates that experimental pendant drop volumes are strictly >6 orders of magnitude higher than benchmark inkjet drop volumes. For further evidence of the ineffectiveness of pendant drop to provide the print resolution needed for AM, drop diameter π·π is predicted using Eq. 4 as a measure of line width. 3
Dd = β
6do Ξ³ Οg
(4)
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Plotting predicted drop diameters against nozzle outer diameter in Figure 3b, we find that the minimum drop diameter achievable with a ππ = 0.18mm nozzle is 2mm, even though the nominal outer diameter of the nozzle is significantly smaller. Compared to benchmark line widths of ME printers between 0.1 β 0.5mm, line widths >> 2mm are evidently insufficient for AM. Our analysis suggests that the pendant drop regime of flow yields drop volumes strictly >6 orders of magnitude higher than inkjet, and line widths 1 order of magnitude higher than ME. Empirical data from literature and our own work support the derived conclusion. Furthermore, we observed that long accumulation times between drops resulted in drop spacings that are too long to be visually interpreted as a continuous line.
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2.2 Jet Regime The pendant drop regime is characterized by slow development of large drops due to the mass-driven detachment mechanism. The force balance between surface tension and gravity is illustrated in Figure 4a. In DOD inkjet technology, a pulse-driven actuator imparts a momentum that instantaneously overcomes surface tension forces, terminating drop growth and limiting the drop volume [2]. When fluid is accelerated to a high velocity before ejection, momentum from sustained velocity overcomes surface tension at the nozzle outlet, forming a column of fluid. This is the jet flow regime. In the same principle as DOD, jet formation terminates drop growth and constrains the profile of the jet column. This is illustrated in Figure 4b.
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The momentum-driven fluid ejects from the narrow orifice of the nozzle and intrudes into the ambient air, forming a jet. An empirical model of jet spread describes the jet radius π at distance π away from a nozzle with inner diameter ππ as: (5)
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π = πΎπ’ (π β πΆπ’ ππ )
Where πΎπ’ is the spread rate and πΆπ’ is a constant that describes the position of the jetβs virtual source, which models the implications of ππ [15]. The model is illustrated in Figure 5.
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Since the model predicts a linear jet spread, as π β 0, the jet diameter approaches ππ , as intuition might suggest. However, nozzle placement at the same height as the substrate is prone to cause issues of clogging and mobilization of uncured material in MJ or powder clusters in BJ, practical π must be limited in proximity to 0.
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Values of the spread rate πΎπ’ are quoted between 0.11 for a high Reynolds number turbulent jet and 0.4 for a laminar jet. Flows intruding into ambient fluid (air) tend to be partly turbulent due to local interactions between the jet and the ambient fluid. Empirical data suggests the subtended spread angle is 5
11.8Β°. This results in πΎπ’ β , and πΆπ’ β β [16]. Thus, Eq. 5 becomes: 5
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π =
1 5 (π + ππ ) 5 2
(6)
If we impose a line width requirement ππ€ on π to match benchmark ME line widths of 0.1 β 0.5mm, we can rewrite the relation to solve for maximum separation ππππ₯ between nozzle and substrate; between separation 0 and ππππ₯ from the nozzle, jet diameter is restricted to produce the target line width, such that 2π β€ ππ€ .
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5 (7) ππππ₯ β€ (ππ€ β ππ ) 2 Plotting this relation for all positive ππππ₯ in Figure 6b, we find all nozzles with which the target line width benchmark can be upheld, as well as the maximum separation it can be upheld at. From Figure 6b, we can discern that there is only a single solution for upholding a 0.1mm line width; it is achieved with a ππ = 0.08mm nozzle at separation < 0.0435mm. As such, 0.1mm is approximately the minimum line width achievable using this jetting method. This result makes sense, as the nozzle has ππ = 0.08mm (ππ < 0.1mm). Under the idealized conditions that the jet traverses fast enough in the X-Y plane and ink spreading is insignificant, the line width can be interpreted as the diameter of a spherical drop. A calculation of drop volume using a spherical model is shown in Figure 6a. The model suggests that the lowest achievable 4
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drop volume is 524pL from 0.1mm line width. The relation between drop volume and line width is governed by a trinomial function, rapidly rising to 4.19nL for a 0.2mm line width and 65.5nL for a 0.5ππ line width. At the minimum drop volume of 524pL, the jet achieves a drop volume 1.7 magnitudes higher than the 10pL inkjet benchmark. Between 0.2ππ and 0.5ππ line widths, drop volume increases to 2.5 and 4 magnitudes higher than inkjet. Compared to the 6-magnitude difference found in the pendant drop regime, these values indicate projected print resolution approaching inkjet. From the model analysis, we find that the jet flow regime can approach a drop volume benchmark for inkjet, achieving a minimum value of 524pL. Although the 1.7 magnitude difference indicates inability to compare competitively to commercial inkjet technologies, it can uphold common ME line width benchmarks between 0.1~0.5mm. Coupled with the advantages of robustness and low-maintenance operation, we believe that an ink jetting system applying jet flow offers an approach to facilitate AM of a diverse range of materials while meeting industrial AM benchmarks.
3. Methods and Materials
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3.1 System Design
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Building upon the analysis in section 2, we propose an ink jetting system that operates by pumping ink to manifest jet flow. Upon reaching the jet flow regime, surface tension is continuously overcome by momentum derived from fluid velocity, resulting in minimal drop growth. Thus, ink needs to be accelerated above an escape velocity, which enables jet flow at the nozzle outlet. Mechanically, this can be accomplished using a variety of positive displacement pumps.
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3.1.1 Pump A peristaltic pump design is chosen over alternatives such as diaphragm and piston pumps for its lack of wetted mechanical components and elimination of fluid slip. Furthermore, peristaltic pumping is already used in the industry for transporting ink from reservoirs to inkjet printheads in both graphical and 3D printing [17], [18], [19].
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A peristaltic pump operates by sequentially compressing a fluid-carrying tube between a set of rollers mounted around a rotor stage and the pump casing. At any point along the tube, the volume of the cavity holding the tube changes sinusoidally as a roller approaches and distances from that point. When the cavity volume minimizes, the corresponding section of the tube is pinched closed, forming an occlusion. The occlusion is transported by the roller as it travels. Fluid trapped before the occlusion is pushed by it, and fluid behind is drawn by suction from the vacuum formed at the occlusionβs previous position. The suction prevents fluid slip, and the overall motion results in transportation of fluid along the tube. A diagram of peristaltic pump components and operation is shown in Figure 7.
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3.1.2 Tubing In the peristaltic pump, the tubing is the only wetted component. This is advantageous over other pumping methods because tubing exists in many varieties, is expendable and readily available compared to diaphragms or valves. Tubing can be selected or coated to accommodate abrasiveness, chemical stability, and viscosity of the transported fluid [20]. Blockage and wear can also be assuaged by choosing appropriate tubing material to mediate desirable surface interactions with the fluid. However, tubing used for peristalsis must be compressible, narrowing the selection of base material to flexible polymers such as silicones, vinyls, and fluoropolymers. A long length of tubing extends from the peristaltic pump outlet to the carriage. This length of tubing allows the pump and ink reservoir to be detached from the carriage, decreasing the carried load and thus
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reducing the risk of step loss in gantry motors. Furthermore, pulsation from pump operation is reduced along the tubing. 3.1.3 Nozzle Fluid is ejected from an industrially available dispensing needle. Inkjet nozzles are complex and thus prone to failure through clogging or actuator malfunction; maintenance difficulty also increases with complexity. Dispensing needles are more expendable due to their low cost. The selection of mechanically and chemically resistant constituent materials such as stainless-steel and PTFE make dispensing needles more robust and thus compatible with a large range of ink compositions.
ππ΅ ππ΅ ππ΄ = = ππ΄ ππ΄ ππ΅
(8)
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3.1.4 Gear train To ensure that the pumped fluid reaches escape velocity, gears are implemented in the system design. This allows manipulation of mechanical advantage to raise pump rate limits as required. For a two-gear gear train composed of input gear A and output gear B, mechanical advantage (π. π΄. ) is
Where π refers to the radius of the gear, π refers to its teeth quantity, and π refers to its angular velocity. When the input gear has more teeth than the output gear, such that ππ΄ > ππ΅ , the angular velocity of the ππ΄
ππ΅
that of the input gear. Since
ππ΄
ππ΅
> 1, this gear train increases the output angular velocity
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output gear is
of the pump. A diagram of the gearing system is shown in Figure 8.
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3.1.5 Integration of components The system described in section 3.1 is designed to pump fluid from a reservoir along a length of tubing to a dispensing needle, where it is ejected in the form of a jet. Jet formation is controlled by increasing pump speed using a gear train system. Pump speed is controlled electronically by adjusting the input motorβs angular velocity in rotations per minute (RPM). This system should be mountable on the carriage of any BJ or MJ printer with a computer numerical controlled (CNC) gantry. When mounted and operated, it forms a jet of ink, which performs the ink jetting task akin to an inkjet printhead. A rendering of the design is highlighted in Figure 9b, c, d. The printer we use to evaluate the proposed ink jetting system is a BJ printer that uses a printer body designed by Yvo de Haas, which we use under the CC BY-SA 4.0 License. A rendering of the printer mounted with the ink jetting system is depicted in Figure 9a.
3.2 Materials
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For the current study, system components and process parameters are: a printed polylactic acid (PLA) gear train of π. π΄. = 0.5 with ππ΄ = 30 and ππ΅ = 15 is used. A NEMA17 stepper motor with step angle 0.9Β° drives the input gear. A stepper motor precisely tracks ejected volume and resists friction loss. An INTLLAB DIY peristaltic pump for 3mm ID x 5mm OD silicone tubing is driven by the output gear.
3.3 Printing
Printing of each layer begins by accelerating the pump to the input RPM using the function in Eq. 9 π (9) RPMn = ( + 1) Γ RPMinput π π is the number of rotations since activation, and π is a parameter used to control the acceleration rate. When the layer is complete, printing is terminated by stopping the pump. Using smaller nozzles, pump termination has a delayed effect. An electrical valve is required to terminate dispensing in short time scales. 6
4. Results and Discussion 4.1 System Validation The system described in section 3 is designed to jet ink by accelerating fluid above escape velocity to manifest a thin, stable jet from a nozzle outlet. Through a mathematical analysis, we predicted that jet flow profiles with 0.1 β 0.5mm diameter can be achieved using dispensing needles of sizes ππ = 0.08 β 0.41mm; jetting fluid along a line enables printing at a line width equal to the jet diameter. The line width of the system is predicted to be controllable as it is linearly dependent on needle diameter and separation from the build platform. An experiment is devised to validate the systemβs performance. This study measures system parameters using deionized water as ink and a stainless-steel dispensing needle.
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4.1.1 Jet Diameter The pumpβs output speed is set to 500RPM for a short duration (3-5s) to establish a stable jet. An image is captured and processed to highlight the edges. The highlighted pixels are counted as an estimate of the jet diameter at discrete separations from the needle outlet. A captured image and the processed image are shown in Figure 10. It should be noted that there are 2 major limitations to the method: it is improbable for long sections of the jet to be entirely in focus, and pixel counting is an inherently subjective process due to difficulties assigning pixels to define jet boundaries. To improve reliability, sections of the jet with bright post-processed pixels indicating a more distinguished boundary are preferentially used for counting. Jet diameter is plotted against distance from the nozzle in Figure 11Figure .
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Jet diameters increase with distance from nozzle outlet, but spread angles are significantly smaller than the predicted 11.8Β°. Experimentally determined spread angles are between 1-3Β°. The weak dependence of jet diameter on nozzle-build plate separation suggests that using separation to control jet diameter as predicted is unfeasible.
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However, this implies that a wide range of nozzle-build plate separations can be used without detracting from line width or jet stability. Jet diameter and stability do not change significantly between 0-30mm nozzle-build plate separations. Based on these results, the most viable method of controlling jet diameter is changing nozzle diameters; the line widths achievable are still between 0.1 β 0.5mm.
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The study of jet profile suggests that nozzle inner diameter is the main factor defining jet profile. Jet diameter varies approximately linearly with nozzle-build plate separation, but within a small range due to the small spread angle. These flow characteristics form the basis of fine control over line width by exchanging nozzles of appropriate size and minimizing separation.
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However, in experimental prints, we found large discrepancies between jet diameter and practical line width. Figure 12aFigure depicts a single-layer outline of an ASTM D638 Type V Test Specimen printed using a the ππ = 0.18mm nozzle, water as binder, and Sekisui Celvol 203S polyvinyl alcohol (PVOH) as powder. The line width of the print is measured using a digital caliper to be~0.7mm, while jet diameter is bound between 0.13mm and 0.19mm as determined in Figure 11. It is evident that jet diameter is not the sole factor determining line width. The line width discrepancy contributes to dimensional inaccuracies in the completed print in Figure 12b: 1) Overall width: 5.48Β±4.75% 2) Overall length: 4.60Β±0.41% 3) Height: 5.45Β±4.51% 4) Width of narrow section: 75.7Β±9.73%. Other factors for dimensional inaccuracies are gantry traversing speed and ink spreading and penetration, layer shift, shrinkage, warping, and adhesion issues. Jet diameter is only equivalent to line width in the idealized scenario of sufficiently fast gantry traversing speed and absence of ink spreading. Ink spreading is essentially determined by material properties. It is a product of ink-substrate interactions including surface wetting dynamics, absorption, and wicking [21], [22]. Gantry traversing speed is a process parameter. The gantry needs to move a target line width away from its initial position in the time the equivalent drop volume is 7
jetted; this upholds the target line width in all directions of the X-Y plane. Otherwise, a thicker line is drawn as the larger drop spreads to occupy a bigger space due to surface tension as the jet stalls. Since gantry traversing speed is related to drop volume over time (volumetric flow rate), and its optimization is expected to rectify the discrepancy between jet diameter and actual line width, it is important to characterize the relation. 4.1.2 Volumetric Flow Rate To further characterize practical system capabilities and validate printability, volumetric flow rate from the jet is measured. Flow rate π is measured by setting pump speed to a discreet RPM and collecting pumped fluid of volume π for duration π‘ according to Eq. 10. V (10) t Flow rate is plotted against pump output speed in Figure 13. A general pattern is observed: flow rate increases nonlinearly with increased pump output and decreasing nozzle diameter. It can be categorized into three stages: 1) Pendant drop at low output; 2) Turbulent jet with intermittent collapse to pendant drop at medium output; and 3) Highly stable jet at high output. The relation between nozzle inner diameter, pump output, and flow characteristics is summarized in Table 1.
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The highly stable jet stage is suitable for ink deposition. It is characterized by a threshold in flow rate. Beyond the threshold, further increasing pump output speed results in diminishing increases in flow rate. This threshold coincides with the development of a highly stable jet characterized by absence of significant turbulent effects.
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Fluid velocity at the nozzle outlet π£π can be calculated from flow rate and jet diameter ππ using Eq.11. π£π =
4π πππ2
(11)
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Although fluid velocity is limited by the same threshold as flow rate, very high fluid velocity should be avoided to prevent elastic collision with the powder substrate or build plate.
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4.1.3 Gantry Traversing Speed The gantry traversing speed is a process parameter that should meet requirements set by the volumetric flow rate. The time to reach the drop volume corresponding to a target line width is the allotted time for the gantry to move a line width away from its original position; this upholds the target line width in all directions of the X-Y plane. Thus, the minimum traversing speed can be determined: πππ€ ππ€ = π π£π
(12)
6 π (13) π ππ€ 2 Where π£π is the gantry traversing speed, π is the volumetric flow rate, ππ€ is the line width and πππ€ is the drop volume of a sphere with the line width as its diameter. The gantry traversing speed is expressed in mms β1 . Assuming the gantry is operated at its maximum step size of 5 stepsmmβ1 , the step size can be integrated into a final expression of minimum motor RPM. Motor RPM enables comparison to practical limits of motor function. Traversing speed further incorporates belt and electronic control parameters but enables comparison to industry benchmarks. Figure π£π =
8
14 shows the minimum gantry motor RPM and traversing speed for each nozzle to uphold a target line width. In Figure 14, minimum motor RPM and gantry traversing speed are shown on a logarithmic scale, as they increase drastically with finer line width targets and smaller nozzles. Most stepper motors can operate just above 1000 RPM (667 mms β1 for the present design) with the appropriate driver parameters. Thus, 1000 RPM can be used as a benchmark for the gantry motors to uphold the target line width. This imposes a further restriction on the nozzle sizes that would be suitable for ink jetting.
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Table 2 summarizes the nozzle sizes and motor RPMs needed to uphold each target line width. Only the di = 0.08 β 0.16mm nozzles produce line widths below 0.5mm. Line widths between 0.3-0.5mm are achievable under 1000 RPM.
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ME of thermoplastic filaments operates optimally at maximum traversing speeds of approximately 150 mms β1 . As a direct comparison, only the πi = 0.08 nozzle upholding a 0.5mm line width can traverse below 150 mms β1 . However, this comparison only holds superficial value, as ME of thermoplastics fails above 150 mms β1 due to thermal conduction issues, which are not applicable in BJ and MJ. Particle inertia and motor acceleration issues may arise at higher traversing speeds instead.
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This analysis suggests that the maximum hardware capabilities of the proposed ink jetting system is further limited by gantry traversing speeds. According to the analysis, the πi = 0.08mm nozzle produces a line width of 0.5mm while traversing at 142 mms β1 . This result is validated experimentally. Deionized water is printed onto a Polymethyl Methacrylate (PMMA) surface. PMMA is a hydrophobic surface, which minimizes the impact of spreading effects on line width at short time scales [23]. The results are shown in Figure 15. Printing at 150 mms β1 traversing speed, a line width of 0.506mm is produced. The experimentally determined line width agrees well with the analysis. At lower traversing speeds, the analysis overestimates line widths compared to the experimental results.
Conclusions
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Based on mathematical predictions, we identified the suitability of jet flow from a dispensing needle for ink jetting AM. A geared peristaltic pump design is proposed for acceleration of fluid to achieve jet flow. Jet flow profiles are studied for jetting water from a set of needles, confirming that jet diameters between 0.1 β 0.5mm are achievable. Jet profiles suggested that line width could be controlled by nozzle inner diameter. Separation between nozzle and build plate between 0~30mm did not significantly affect line width due to low spread. However, experimental prints indicated that line width is influenced by jet diameter and other factors such as ink spreading and penetration. Gantry traversing speed further limits the achievable line widths, as constrained by motor RPM limits. Limiting gantry motor operation to 1000RPM (667 mms β1 ), only nozzles of size πi = 0.08~0.16mm uphold a line width below 0.5mm. Line widths between 0.3 β 0.5mm are feasible. The capabilities of the proposed ink jetting system are comparable to commercial ME systems. The modular design empowers robustness through the exchangeability, customizability and expendability of wetted components. The system may be particularly useful for material development and characterization.
Declaration of interest 9
None
Acknowledgments The authors would like to acknowledge the financial support of the Natural Science and Engineering Research Council of Canada (NSERC) and the NSERC Network for Holistic Innovation in Additive Manufacturing (HI-AM).
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References
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[1] E. M. Sachs, J. S. Haggerty, M. J. Cima and P. A. Williams, "Three-dimensional printing techniques". US Patent US5204055A, 22 04 1993. [2] G. D. Martin, S. D. Hoath and I. M. Hutchings, "Inkjet printing - the physics of manipulating liquid jets and drops," J. Phys. Conf. Ser, vol. 105, p. 012001, 2008.
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[3] B. Utela, D. Storti, R. Anderson and M. Ganter, "A review of process development steps for new material systems in three dimensional printing (3DP)," J Manuf Process, vol. 10, no. 2, pp. 96-104, 2008.
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[4] R. Pandey, "Photopolymers in 3D printing applications," Arcada University of Applied Sciences, 2014.
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[5] V. Javaheri, D. Porter and V.-T. Kuokkala, "Slurry erosion of steel β Review of tests, mechanisms and materials," Wear, Vols. 408-409, pp. 248-273, 2018.
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[6] M. R. Safaei, O. Mahian, F. Garoosi, A. Karimipour, S. N. Kazi and S. Gharehkhani, "Investigation of Micro- and Nanosized Particle Erosion in a 90Β° Pipe Bend Using a Two-Phase Discrete Phase Model," Sci. World J., pp. 1-12, 2014. [7] E. Sowade, T. Blaudeck and R. R. Baumann, "Inkjet Printing of Colloidal Nanospheres: Engineering the Evaporation-Driven Self-Assembly Process to Form Defined Layer Morphologies," Nanoscale Res Lett., vol. 10, no. 362, 2015. [8] S. Magdassi, "Ink Requirements and Formulations Guidelines," in The Chemistry of Inkjet Inks , Israel, The Hebrew University of Jerusalem, 2009, pp. 19-41.
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[9] T. Li, J. Aspler, A. Kingsland, L. Cormier and X. Zou, "3d Printing β A Review Of Technologies, Markets, And Opportunities For The Forest Industry," Journal of Science & Technology for Forest Products and Processes, vol. 5, no. 2, 2016. [10] M. Sireesha, J. Lee, B. V. Kiran SKA, B. Keee and S. Ramakrishna, "A review on additive manufacturing and its way into the oil and gas industry," RSC advances, vol. 40, pp. 22460-22468, 2018. [11] H. Yuk and X. Zhao, "A New 3D Printing Strategy by Harnessing Deformation, Instability, and Fracture of Viscoelastic Inks," Advanced Materials, vol. 30, no. 6, 2018.
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[12] D. Krajcarz, "Comparison Metal Water Jet Cutting with Laser and Plasma Cutting," Procedia Engineering, vol. 69, pp. 834-843, 2014. [13] C. Ma and R. Deam, "A correlation for predicting the kerf profile from abrasive water jet cutting," Experimental Thermal and Fluid Science, vol. 30, no. 4, pp. 337-343, 2006. [14] G. K. Tripp, K. L. Good, M. J. Motta, P. H. Kass and C. J. Murphy, "The effect of needle gauge, needle type, and needle orientation on the volume of a drop," Vet Ophthalmol, vol. 19, no. 1, pp. 38-42, 2015. [15] R. Premnath, "Qualitative air flow modelling and analysis of data centre air conditioning as multiple jet array," Cochin University of Science and Technology, Cochin, 2011.
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[16] B. Cushman-Roisin, "Turbulent Jets," in Environmental Fluid Mechanics, Hanover, Dartmouth Thayer School of Engineering, 2018, pp. 153-161.
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[17] M. J. Diggins, "Disposable peristaltic pump assembly for facsimile printer". US Patent US4333088A, 03 11 1980.
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[18] W. Salmre, "Ink jet printer with peristaltic pump". US Patent US4359744A, 16 11 1982. [19] Y. Sheinman, "System and method for direct inkjet printing of 3d objects". US Patent US20150298394A1, 22 10 2015.
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[20] K. L. Hoffmeier, D. Hoffmann and F. Karl-Heinz, "A First Inherently Pulsation Free Peristaltic Pump.," 58th ilmenau scientific colloquium, pp. 1-11, 2014.
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[21] R. Daniel and J. Berg, "Spreading on and penetration into thin, permeable print media: Application to ink-jet printing," Advances in Colloid and Interface Science, Vols. 123-126, pp. 439-469, 2006.
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[22] H. Hamada, D. Bousfield and W. Luu, "Absorption Mechanism of Aqueous and Solvent Inks into Synthetic Nonwoven Fabrics," Journal of Imaging Science and Technology, vol. 53, no. 5, pp. 050201β 050201-6, 2009.
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[23] S. Semenova, V. Starova, R. Rubio, H. Agogob and V. MG, "Evaporation of sessile water droplets: Universal behaviour in presence of contact angle hysteresis," Colloids and Surfaces A: Physicochemical and Engineering Aspects, vol. 391, no. 1-3, pp. 135-144, 2011.
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Figure captions
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Figure 1: a) DOD actuator rapidly decreases the ink reservoir volume and ejects a drop. b) CIJ produces a pressure-induced jet that is broken into droplets; droplets are charged and deflected on a trajectory towards the printed surface.
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Figure 2: a) FFF drives melted thermoplastics out of a nozzle by pressure built-up from continuously feeding filament. b) DIW feeds viscoelastic inks from a syringe using a piston mechanism or a pump. ME printers typically use modular and dedicated components for the feeding mechanism, ink storage, and nozzle.
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Figure 3: a) Drop volumes from nozzle sizes of ππ = 0.18~4.57ππ are predicted using Eq. 3. b) Drop diameters are predicted by modelling the deposited drop as a sphere, as in Eq. 4.
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Figure 4: a) The force due to gravity is initially small compared to surface tension forces, but growth of the drop increases the force due to gravity. The drop is only ejected when the forces balance. b) When fluid is accelerated above escape velocity before ejection, for a differential volume βπ, momentum is large compared to surface tension and gravity.
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Figure 5: The linear model of jet flow depicted in a cross-sectional view. Spread rate K u is the slope of the jet cone outline. Setting the nozzle outlet at the origin, a virtual origin Cu depicts a virtual source that accounts for di . Using these parameters, jet radius R is a linear function of position along the jet centerline X.
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Figure 6: a) Predicted drop volume corresponding to a target line width. The drop volume is derived from approximating the line width as the diameter of a spherical drop. b) Predicted maximum separation between nozzle and substrate for each nozzle to produce a target line width between 0.1~0.5ππ.
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Figure 7: A peristaltic pump forms occlusions of trapped fluid by squeezing tubing between a set of rollers and the pump casing. Rotor stage rotation and fluid flow paths are traced with blue arrows.
Figure 8: A gear train raises pump speed limits applicable by the driving motor. Mechanical advantage is determined by the ratio of the gearsβ teeth.
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Figure 9: a) 3D model rendering of the printer body design by Yvo de Haas mounted with our proposed pump design. The ink jetting system is highlighted in purple. b) Isometric c) back d) front e) side views of a 3D rendering of the pump design.
Figure 10: a) Captured image of a jet formed at the outlet of a ππ = 0.41ππ/ππ = 0.72ππ needle. b) Captured image is processed to highlight edges.
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Figure 11: Jet diameter is measured by pixel counting and plotted against distance from the nozzle outlet. A line is fitted using the least-squares method with outliers removed to satisfy p<0.05 to characterize the jet profile of each needle size.
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Figure 12: a) Thus far, we have used jet diameter as a proxy for ideal line width. Experimental prints demonstrate large discrepancies between practical and ideal line widths. The measured line width is ~0.7ππ, while the range of jet diameters for this nozzle lies between 0.13ππ and 0.19ππ. b) A completed print using the same parameters.
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Figure 13: Flow rate is determined from volume of fluid collected at the nozzle outlet and collection duration. Flow rate reaches a threshold for sizes ππ = 0.08~0.21ππ. Flow rate thresholds for sizes ππ = 0.26~0.41ππ are not reached.
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Figure 14: Gantry motor speed required to uphold a target line width expressed as a) RPM as a measure of hardware limitations and b) expressed as speed for comparison with ME operation limits. The dotted lines show 1000RPM and 150 mms β1 respectively as guidelines for hardware and operation benchmarks.
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Figure 15: a) Printed lines from a ππ = 0.08mm nozzle at various gantry traversing speeds. b) The actual printed line widths plotted against the gantry traversing speed they were printed at. Theoretical values derived in Figure 14b are plotted on the same graph for comparison.
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Table
Nozzle inner diameter di 0.08mm 0.11~0.21mm 0.26~0.41mm
Pump Output (RPM) Turbulence and Pendant drop intermittent collapse to pendant drop 25 50-300 50 100-300 100 200-500
Highly stable jet (Threshold) 325-500 400-500 >500
Motor RPM to Uphold Line width 0.3mm
1327 >>1000 >>1000
590 965 >>1000
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0.2mm
332 543 993
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Nozzle inner diameter di 0.08mm 0.11 0.16
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Table 1: The three stages of flow in relation to nozzle inner diameter and pump output.
0.5mm 212 347 636
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Table 2: Achievable line widths as determined by nozzle inner diameter and motor RPM
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