Patent Publication Number: US-2022219381-A1

Title: Building an object with a three-dimensional printer using vibrational energy

Description:
TECHNICAL FIELD 
     The present teachings relate generally to three-dimensional (3D) printing and, more particularly, to systems and methods for building (e.g., printing) an object with a 3D printer using vibrational energy. 
     BACKGROUND 
     A 3D printer builds (e.g., prints) a 3D object from a computer-aided design (CAD) model, usually by successively depositing material layer upon layer. For example, a first layer may be deposited upon a substrate, and then a second layer may be deposited upon the first layer. One particular type of 3D printer is a magnetohydrodynamic (MHD) printer, which is suitable for jetting liquid metal layer upon layer to form a 3D metallic object. Magnetohydrodynamic refers to the study of the magnetic properties and the behavior of electrically conducting fluids. 
     An MHD printer causes an electrical current to flow through a metal coil, which produces time-varying magnetic fields that induce eddy currents within a reservoir of liquid metal compositions. Coupling between magnetic and electric fields within the liquid metal results in Lorentz forces that cause ejection of drops of the liquid metal through a nozzle of the printer. The nozzle may be controlled to select the size and shape of the drops. The drops land upon the substrate and/or the previously deposited drops to cause the object to grow in size. However, objects produced in this manner oftentimes have cold joints between deposited drops caused by incomplete drop coalescence due to inter-droplet surface tension which leads to insufficiencies in 3D object microstructures and mechanical properties. 
     SUMMARY 
     The following presents a simplified summary in order to provide a basic understanding of some aspects of one or more embodiments of the present teachings. This summary is not an extensive overview, nor is it intended to identify key or critical elements of the present teachings, nor to delineate the scope of the disclosure. Rather, its primary purpose is merely to present one or more concepts in simplified form as a prelude to the detailed description presented later. 
     A three-dimensional (3D) printer is disclosed. The 3D printer also includes an ejector having a nozzle, a coil wrapped at least partially around the ejector, and a power source configured to transmit voltage pulses to the coil and configured to supply one or more pulses of power to the coil, which causes one or more drops of a printing material to be jetted out of the nozzle. The 3D printer also includes a vibrational source configured to transmit vibrational energy towards the one or more drops of printing material. 
     In another embodiment, the 3D printer transmits vibrational energy having an amplitude that is less than or equal to 75% of a diameter of the one or more drops of printing material and a frequency that ranges from 100 Hz to 20 kHz and wherein the frequency of the vibrational energy may be dynamically modulated as a 3D object is formed by the 3D printer. The 3D printer may include a heating element configured to heat the printing material in the ejector, thereby causing the printing material to change from a solid state to a liquid state within the ejector, a substrate positioned below the nozzle and configured to receive the drops of the printing material after the drops of the printing material are jetted through the nozzle, and a substrate control motor configured to move the substrate after the drops of the printing material are jetted through the nozzle. 
     In another embodiment, the vibrational source may be directly or indirectly applied to the substrate. The vibrational energy may be directly applied to the substrate in a direction parallel to the substrate, in an oblique direction, in an orbital direction, intermittently or a combination thereof. The vibrational source may transmit vibrational energy towards the drops of the printing material after the substrate receives the drops of the printing material. 
     In another embodiment, the 3D printer includes a vibrational source that may be a piezoelectric source, ultrasonic source, a focused acoustic energy source, a laser vibrational source, or combinations thereof. 
     Also disclosed is a method for printing a three-dimensional (3D) object using a 3D printer. The method may include jetting a first plurality of drops of a printing material through a nozzle and directing a vibrational energy towards the first plurality of drops of printing material. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments of the present teachings and together with the description, serve to explain the principles of the disclosure. In the figures: 
         FIG. 1  depicts a schematic cross-sectional view of a 3D printer (e.g., a MHD printer and/or multi-jet printer), according to an embodiment. 
         FIG. 2  illustrates a schematic side view of a first example of the 3D object on the substrate, according to an embodiment. 
         FIG. 3  illustrates a photograph of the first example of the 3D object from  FIG. 2 , according to an embodiment. 
         FIG. 4  illustrates schematic side views of a second example of the 3D object on the substrate that is formed when the 3D printer operates with vibrational energy, according to an embodiment. 
         FIG. 5  illustrates a flowchart of a method for printing the object using the 3D printer, according to an embodiment. 
     
    
    
     DETAILED DESCRIPTION 
     Reference will now be made in detail to exemplary embodiments of the present teachings, examples of which are illustrated in the accompanying drawings. Wherever possible, the same reference numbers will be used throughout the drawings to refer to the same, similar, or like parts. 
       FIG. 1  depicts a schematic cross-sectional view of a 3D printer  100 , according to an embodiment. The 3D printer  100  may include an ejector (also referred to as a body or pump chamber)  120 . The ejector  120  may define an inner volume (also referred to as a cavity). A printing material  130  may be introduced into the inner volume of the ejector  120 . The printing material  130  may be or include a metal, a polymer, composite, or the like. For example, the printing material  130  may be or include aluminum or aluminum alloy (e.g., a spool of aluminum wire). 
     The 3D printer  100  may also include one or more heating elements  140 . The heating elements  140  are configured to melt the printing material  130 , thereby converting the printing material  130  from a solid state to a liquid state (e.g., liquid metal  132 ) within the inner volume of the ejector  120 . 
     The 3D printer  100  may also include a power source  150  and one or more metallic coils  152  that are wrapped at least partially around the ejector  120 . The power source  150  may be coupled to the coils  152  and configured to provide an electrical current to the coils  152 . In one embodiment, the power source  150  may be configured to provide a step function direct current (DC) voltage profile (e.g., voltage pulses) to the coils  152 , which may create an increasing magnetic field. The increasing magnetic field may cause an electromotive force within the ejector  120 , that in turn causes an induced electrical current in the liquid metal  132 . The magnetic field and the induced electrical current in the liquid metal  132  may create a radially inward force on the liquid metal  132 , known as a Lorenz force. The Lorenz force creates a pressure at an inlet of a nozzle  122  of the ejector  120 . The pressure causes the liquid metal  132  to be jetted through the nozzle  122  in the form of one or more liquid drops  134 . 
     The 3D printer  100  may also include a substrate  160  that is positioned proximate to (e.g., below) the nozzle  122 . The drops  134  may land on the substrate  160  and solidify to produce a 3D object  136 . In one example, the 3D object  136  may be or include a strut, which may be part of a lattice structure. A 3D object  136  may be considered to be comprised of one or more drops  134  of a printing material  130  jetted by the 3D printer  100 . 
     The 3D printer  100  may also include a substrate control motor  162  that is configured to move the substrate  160  while the drops  134  are being jetted through the nozzle  122 , or during pauses between when the drops  134  are being jetted through the nozzle  122 , to cause the 3D object  136  to have the desired shape and size. The substrate control motor  162  may be configured to move the substrate  160  in one dimension (e.g., along an X axis), in two dimensions (e.g., along the X axis and a Y axis), or in three dimensions (e.g., along the X axis, the Y axis, and a Z axis). In another embodiment, the ejector  120  and/or the nozzle  122  may be also or instead be configured to move in one, two, or three dimensions. In other words, the substrate  160  may be moved under a stationary nozzle  122 , or the nozzle  122  may be moved above a stationary substrate  160 . In yet another embodiment, there may be relative rotation between the nozzle  122  and the substrate  160  around one or two additional axes, such that there is four or five axis position control. 
     The 3D printer  100  may also include one or more gas-controlling devices, which may be or include gas sources (two are shown:  170 ,  172 ). The first gas source  170  may be configured to introduce a first gas. The first gas may be or include an inert gas, such as helium, neon, argon, krypton, and/or xenon. In another embodiment, the first gas may be or include nitrogen. The first gas may include less than about 10% oxygen, less than about 5% oxygen, or less than about 1% oxygen. 
     In at least one embodiment, the first gas may be introduced at a location that is above where the second gas is introduced. For example, the first gas may be introduced at a location that is above the nozzle  122  and/or the coils  152 . This may allow the first gas (e.g., argon) to form a shroud/sheath around the nozzle  122 , the drops  134 , the 3D object  136 , and/or the substrate  160  to reduce/prevent the formation of oxide (e.g., aluminum oxide). Controlling the temperature of the first gas may also or instead help to control (e.g., minimize) the rate that the oxide formation. 
     The second gas source  172  may be configured to introduce a second gas. The second gas may be different than the first gas. The second gas may be or include oxygen, water vapor, carbon dioxide, nitrous oxide, ozone, methanol, ethanol, propanol, or a combination thereof. The second gas may include less than about 10% inert gas and/or nitrogen, less than about 5% inert gas and/or nitrogen, or less than about 1% inert gas and/or nitrogen. The second gas may be introduced at a location that is below the nozzle  122  and/or the coils  152 . For example, the second gas may be introduced at a level that is between the nozzle  122  and the substrate  160 . The second gas may be directed toward the nozzle  122 , the falling drops  134 , the 3D object  136 , the substrate  160 , or a combination thereof. This may help to control the properties (e.g., contact angle, flow, coalescence, and/or solidification) of the drops  134  and/or the 3D object  136 . 
     The 3D printer  100  may also include another gas-controlling device, which may be or include a gas sensor  174 . The gas sensor  174  may be configured to measure a concentration of the first gas, the second gas, or both. More particularly, the gas sensor  174  may be configured to measure the concentration proximate to the nozzle  122 , the falling drops  134 , the 3D object  136 , the substrate  160 , or a combination thereof. As used herein, “proximate to” refers to within about 10 cm, within about 5 cm, or within about 1 cm. 
     The 3D printer  100  may also include a computing system  180 . The computing system  180  may be configured to control the printing of the 3D object  136 . More particularly, the computing system  180  may be configured to control the introduction of the printing material  130  into the ejector  120 , the heating elements  140 , the power source  150 , the substrate control motor  162 , the first gas source  170 , the second gas source  172 , the gas sensor  174 , or a combination thereof. As discussed in greater detail below, in one embodiment, the computing system  180  may control the rate at which the voltage pulses are provided from the power source  150  to the coils  152 , and thus the corresponding rate at which the drops  134  are jetted through the nozzle  122 . These two rates may be substantially the same. 
     In another embodiment, the computing system  180  may be configured to receive the measurements from the gas sensor  174 , and also configured to control the first gas source  170  and/or the second gas source  172 , based at least partially upon the measurements from the gas sensor  174 , to obtain the desired gas concentration around the drops  134  and/or the object  136 . In at least one embodiment, the concentration of the first gas (e.g., nitrogen) may be maintained between about 65% and about 99.999%, between about 65% and about 75%, between about 75% and about 85%, between about 85% and about 95%, or between about 95% and about 99.999%. In at least one embodiment, the concentration of the second gas (e.g., oxygen) may be maintained between about 0.000006% and about 35%, between about 0.000006% and about 0.00001%, between about 0.00001% and about 0.0001%, between about 0.0001% and about 0.001%, between about 0.001% and about 0.01%, between about 0.01% and about 0.1%, between about 0.1% and about 1%, between about 1% and about 10%, or between about 10% and about 35%. 
     The 3D printer  100  may also include an enclosure  190  that defines an inner volume (also referred to as an atmosphere). In one embodiment, the enclosure  110  may be hermetically sealed. In another embodiment, the enclosure  110  may not be hermetically sealed. In one embodiment, the ejector  120 , the heating elements  140 , the power source  150 , the coils  152 , the substrate  160 , the computing system  170 , the first gas source  180 , the second gas source  182 , the gas sensor  184 , or a combination thereof may be positioned at least partially within the enclosure  190 . In another embodiment, the ejector  120 , the heating elements  140 , the power source  150 , the coils  152 , the substrate  160 , the computing system  170 , the first gas source  180 , the second gas source  182 , the gas sensor  184 , or a combination thereof may be positioned at least partially outside of the enclosure  190 . 
     The 3D printer  100  may also include an integrated vibrational energy source  200  coupled to the substrate  160 , which introduces vibrational energy to drops  134  of the printing material  130  forming the 3D object  136  after the drops  134  are ejected from the nozzle  122  and after the drops  134  land onto the substrate  160 . In one embodiment, the integrated vibrational energy source  200  is mechanically coupled to the substrate  160  and introduces a vibrational energy prior to one or more drops  134  landing on the substrate  160 . In one embodiment, the integrated vibrational energy source  200  introduces a vibrational energy to the substrate  160  as the drops  134  land on the substrate  160 , In one embodiment, the integrated vibrational energy source  200  introduces a vibrational energy to the substrate  160  prior to one or more drops  134  landing on the substrate  160 , while the drops  134  are solidifying, or after multiple drops  134  land on the substrate  160 , or combinations thereof. The integrated vibrational energy source  200  may have an internal control system. In some embodiments, the integrated vibrational energy source  200  may be independently controlled with the substrate control motor  162 , the computing system  180 , or a combination thereof. In one embodiment, the computing system  180  may interface with and directly control the internal control system of the integrated vibrational energy source  200 . Examples of integrated, contacting, or coupled vibrational energy sources include eccentric rotating mass vibration motors (ERM), electromagnetic-driven vibration motors, contacting ultrasonic vibrational sources, piezoelectric vibrational sources, a vibration platform coupled to the substrate  160 , and combinations thereof. 
     The 3D printer  100  may also include an external non-contact vibrational energy source  202 , which is directed towards and subjects drops  134  of the printing material  130  to vibrational energy after the drops  134  are ejected from the nozzle  122 . In one embodiment, the non-contact vibrational energy source  202  is aimed at a location between the nozzle  122  and the substrate  160  and the vibrational energy is directed towards drops  134  of the printing material  130  before the drops  134  land on the substrate  160 . In another embodiment having an external vibrational energy source  202 , the external vibrational energy source  202  is aimed at a location on the substrate  160  and the vibrational energy is directed towards drops  134  of the printing material  130  after the drops  134  land on the substrate  160 , forming a 3D object  136 . The non-contact vibrational energy source  202  may have an internal control system. In some embodiments, the non-contact vibrational energy source  202  may be independently controlled with the substrate control motor  162 , the computing system  180 , or a combination thereof. In one embodiment, the computing system  180  may interface with and directly control the internal control system of the non-contact vibrational energy source  202 . In one embodiment, there may be multiple external vibrational energy sources that introduce vibrational energy to drops  134  of printing material  130  before and after the drops  134  are deposited onto the substrate  160 . Examples of external non-contact vibrational energy sources include laser doppler vibrometer (LDV), vibrational photo acoustic (VPA) sources, focused sound waves utilizing an acoustic lens, non-contact ultrasonic vibration sources, and combinations thereof. Focused or unfocused acoustic sound or acoustic vibrational energy sources of any type may have a frequency from about 40 Hz to about 20 KHz. Focused or unfocused ultrasonic vibrational energy sources of any type may have a frequency from about 8 kHz to about 24 KHz. 
     In one embodiment, the vibrational source may be powered on or operational in a consistent or continuous manner during jetting. Alternatively, in an embodiment, the vibrational source may be intermittently powered on or operational in a non-continuous manner during jetting. In one embodiment, vibrational energy may be applied with the 3D printer parallel to a plane defined by the substrate  160  in an oscillating or back-and-forth manner. Alternatively, the motion of the vibrational energy source may be orbital or elliptical yet parallel with respect to a plane defined by the substrate  160  or directed in such a way that the contact vibrational energy source is specifically directed towards a localized area on the substrate  160  where the droplets of printing material  130  are cooling or solidifying. 
     The vibrational energy may be applied, in one embodiment, in a direction perpendicular to a plane defined by the substrate  160 , or in an oblique direction compared to a plane defined by the substrate  160 . In an embodiment utilizing a non-contact or external vibrational energy source, the vibrational energy may be focused, with either an adjustable focus or a fixed focus, the focus being directed at drops of printing material  130  on the substrate  160  or towards the substrate  160  in proximity to drops of printing material  130 . Alternatively, in an embodiment, the non-contact vibrational energy source may be non-focused. In some embodiments, combinations of one or more of the contacting, non-contacting or directional applications or directional motions as described herein may be used. 
       FIG. 2  illustrates a schematic side view of a first example of the 3D object  136  on the substrate  160  that is formed when the 3D printer  100  operates without the introduction of vibrational energy, according to an embodiment. To form the 3D object  136 , the power source  150  may transmit a plurality of voltage pulses to the coils  152 , which may cause a corresponding plurality of drops (twelve are shown:  134 A- 134 M, note that 1341 is skipped to avoid confusion with the number  1341 ) to jet through the nozzle  122 . The drops,  134 A- 134 M, may be jetted at a predetermined frequency and allows each drop for example (e.g. drop  134 A) to begin cooling before the next drop (e.g. drop  134 B) is jetted through the nozzle  122  and deposited onto the previous drop or the substrate  160 . The predetermined frequency may be from about 10 Hz to about 1000 Hz, which may cause from about 10 drops to about 1000 drops to be jetted through the nozzle  122  per second. Forming the 3D object  136  in this manner may also cause the 3D object  136  to have internal micro voids, cold weld joints between drops, or other structural defects, such as a bumpy (not smooth) surface morphology, as shown in  FIG. 3 . 
     In the embodiment shown, the first layer  135 A of drops may be deposited onto the substrate  160 , the second layer  135 B of drops may be deposited onto the first layer, and so on with respect to successive layers of drops ( 135 C- 135 F). Each drop (e.g., drop  134 B) is horizontally offset from the previously jetted drop (e.g., drop  134 A) by less than a width of the previously jetted drop (e.g., drop  134 A). In the embodiment shown, the resulting diameter of drops  134 A- 134 M may be from about 0.05 mm to about 1 mm, from about 0.1 mm to about 0.5 mm, or from about 0.25 mm to about 0.5 mm. Other embodiments may result in drops having a diameter larger or smaller than those mentioned herein. While the drops ( 134 A- 134 M) shown in each of the respective layers  135 A- 135 F, in  FIG. 2  are shown in proximity to one another, they may not be completely coalesced and they may not form a cohesive and completely welded structure with respect to the boundary layers between each of the individual drops ( 134 A- 134 M). This incomplete melding of neighboring drops may cause the 3D object  136  to be bumpy (e.g., not smooth), as shown in  FIG. 3 . 
       FIG. 4  illustrates a schematic side view of a second example of the 3D object  136  on the substrate  160  that is formed when the 3D printer  100  operates with the introduction of vibrational energy, according to an embodiment. To form the 3D object  136  according to one embodiment, the power source  150  may transmit a plurality of voltage pulses to the coils  152 , similarly as to the process described in regard to  FIGS. 2 and 3 . According to one embodiment, as shown in  FIG. 4 , when the drops  134 A- 134 M are subjected to vibrational energy after they land onto the substrate  160 , the surface tension of the outer layer of each drop may be disrupted by vibrational energy. As used herein, vibrational energy refers to energy that is directed towards a jetted drop prior to landing onto a substrate  160  and/or after a jetted drop lands onto a substrate  160 . As discussed in greater detail below, the vibration frequency and vibration amplitude at which the vibrational energy is applied to the drop or drops, is sufficient to disrupt the surface tension of the outer layer of each drop, yet below a threshold value that would distort or otherwise compromise the overall structure of a formed 3D object  136 . 
     As shown in  FIG. 4 , a first plurality of drops (two are shown:  134 A- 134 B) may be jetted through the nozzle  122  to form a first layer  135 A on the substrate  160 . The first plurality of drops  134 A- 134 B may be jetted at a frequency that substantially allows each drop (e.g., drop  134 A) in a particular layer (e.g., layer  135 A) or adjacent to one another to cool and solidify before the next drop (e.g., drop  134 B) in that layer  135 A is jetted through the nozzle  122  and/or deposited on the previous drop (e.g., drop  134 A). In certain embodiments, a droplet may land on and/or overlap a previously jetted droplet before it has cooled enough to begin solidification. While rate of jetting and cooling of the drops is one mechanism that contributes to the coalescence of adjacent drops or layers, the surface tension formed when a drops lands may also be a contributing factor. Thus, the introduction of vibrational energy towards the substrate  160  in one embodiment may disrupt the surface tension between adjacent cooling drops or layers to allow the second drop  134 B to contact and/or at least partially combine with the first drop  134 A while the first drop  134 A is still partially or fully in a liquid state. As a result, the drops  134 A- 134 B may form a puddle of liquid metal, which may subsequently solidify to form the first layer  135 A. 
     The vibrational energy applied to the substrate  160  may be characterized as having a vibrational frequency, or number of cycles that a vibrating object completes in one second, in a subsonic range, or less than 20 Hz, a sonic range, or from about 20 Hz to about 20,000 Hz, or in an ultrasonic range, or from about 8 kHz to greater than 20 kHz. In some embodiments, the vibrational energy may operate in a frequency that may be proportional to the mass of a 3D object  136  formed by the 3D printer. Furthermore, the frequency may be dynamically modulated or adjusted as the mass of the 3D object  136  changes during material printing. While dependent on the inherent properties of the printing material, the resonant frequencies of a part and an associated build plate may change as the amount of material and resulting mass of the printed object increase during the printing of a 3D object. Thus, the frequency of vibration in some embodiments may be dynamically changed during printing to target a dynamically changing resonant frequency of a 3D object as it is printed. 
     The vibration amplitude, intensity, or distance from the stationary position to the extreme position on either side of a vibration oscillation cycle, applied to the substrate  160  may be from about 0.001 mm to about 0.75 mm, from about 0.01 mm to about 0.40 mm, or from about 0.15 mm to about 0.4 mm. In some embodiments, the vibrational energy may have an amplitude that is less than or equal to 75% of a diameter of the one or more drops  134  of printing material  130 . 
     The vibration frequency, vibration amplitude, and oscillation may be selected/varied based at least partially upon the volume and/or mass of each drop  134 A- 134 B. In addition to drop size and 3D object  136  mass, frequency and amplitude selection may also be influenced by the printing material  130 , inherent resonance of the printing material  130 , or temperature in certain embodiments. The vibration energy may be directed towards the drops  134  or the 3D printed object in a direction that may be perpendicular, parallel, at an angle relative to the substrate  160  or 3D object  136 , or combinations thereof when multiple vibrational sources are used in particular embodiments. 
     After the first layer  135 A is jetted, the 3D printer  100  may then jet a second layer  135 B of drops (two additional drops are shown:  134 C- 134 D) onto the first layer  135 A. The second layer  135 B of drops  134 C- 134 D may be jetted in concert with a vibrational energy to disrupt the surface tension of each drop and assist the liquid to spread out and merge with surrounding printing material to avoid the formation of voids or pores in the printed material. prevent each drop (e.g., drop  134 C) in a particular layer (e.g., layer  135 B) from cooling and solidifying before the next drop (e.g., drop  134 D) in that layer  135 B is jetted through the nozzle  122  and/or deposited on the previous drop (e.g., drop  134 C). This may allow the second drop  134 D to contact and/or at least partially combine with the first drop  134 C while the first drop  134 C is still partially or fully in a liquid state. As a result, the drops  134 C- 134 D may form a puddle of liquid metal, which may subsequently solidify to form the second layer  135 B. 
     The second layer  135 B of drops  134 C- 134 D may at least partially re-melt the previously deposited layer (e.g., layer  135 A). For example, the second layer  135 B of drops  134 C- 134 D may have enough heat to at least partially re-melt and combine with an upper portion (e.g., the top surface)  138  of the previously deposited layer  135 A without causing the 3D object  136  to slump over or otherwise distort from the desired shape and/or angle. Vibrational energy applied to either the drops  134 A- 134 D or 3D object  136  via coupling to the substrate  160  or an external vibration energy source may provide disruption of the interfacial surface tension of the drops  134 A- 134 D or the upper portion  138  such that the vibrational energy interferes with the crystallization and solidification of the first deposited layer  135 A or second deposited layer  135 B. After the second layer of drops  134 C- 134 D has been jetted, the process may repeat to form a plurality of additional layers  135 C- 135 G, as shown in  FIG. 4 . 
     In one embodiment, as one or more drops  134  solidify during the printing of a 3D object  136 , surface tension of a drop, drop surface oxidation, surface cooling, or combinations thereof can result in cold weld joints or incomplete drop coalescence between drops  134  leading to incomplete melting and flowing between drops  134  or between sets of drops  134 . Printed articles as described in regard to  FIGS. 2 and 3  may have decreased density, reduced physical properties, and microstructural voids or deformities. Vibrational energy introduced into these printed articles during or after drop deposition as described in  FIG. 4  may effectively interfere with the crystallization process during solidification. The application of vibratory energy during solidification of the melted printing material reduces the amount and size of pores, and reduces the columnar microstructure by disrupting nucleation and growth of long grains during solidification. Vibrational energy may also have an advantageous influence on providing vibration-driven wetting or disrupting inter-drop surface tension, thereby reducing or minimizing barriers to drop coalescence during solidification and/or cooling of neighboring drops  134  forming a 3D object  136 . In the embodiment shown, continuous vibrational energy may be applied to the printer  100  for the duration of jetting, solidification, subsequent layer formation, and substrate motion operations occurring during the operation of the 3D printer  100 . Alternatively, in one embodiment, intermittent vibrational energy is applied non-continuously during jetting, solidification, layer formation, and substrate motion during the operation of the 3D printer  100 . Forming the 3D object  136  using added vibrational energy may cause the 3D object  136  to be substantially smooth, which may improve the mechanical properties of the 3D object  136 . 
       FIG. 5  illustrates a flowchart of a method  500  for printing the 3D object  136  using the 3D printer  100 , according to an embodiment. An illustrative order of the method  500  is provided below. One or more steps of the method  500  may be performed in a different order, performed simultaneously, repeated, or omitted. 
     The method  500  may include jetting one or more drops such as  134 A- 134 B, as at  502 . This may include the computing system  180  causing the power source  170  to transmit a first number of voltage pulses to the coils  152 . In response, the coils  152  may cause the first jetting of one or more drops  134 A- 134 B to be jetted through the nozzle  122 . The first burst of drops  134 A- 134 C may be deposited onto the substrate  160 . The nozzle  122  and/or the substrate  160  may be/remain substantially stationary (e.g., with respect to one another) during step  502 . As mentioned above, each of the drops  134 A- 134 B may be deposited before the other drops  134 A- 134 B in that particular layer  135 A fully solidify. For example, the first drop  134 A may have a solid volume fraction that is less than about 90%, less than about 70%, less than about 50%, or less than about 30% before the second drop  134 B lands on the first drop  134 A. If the first drop  134 A has a solid volume fraction of 90%, this means that the first drop  134 A is 90% solid and 10% liquid. 
     The method  500  may also include directing vibrational energy towards drops  134 A- 134 B, towards the 3D object  136 , or towards the substrate  160 , as at  504 . Step  504  may be performed after step  502 . This step may include the computing system  180  causing the coupled vibrational energy source  200 , for example, a piezoelectric vibration source, to engage to introduce vibrational energy towards the substrate  160 . In response, the substrate  160  may transmit the vibrational energy to the drops  134 A- 134 B and/or towards the 3D object  136 . The first layer  135 A of drops  134 A- 134 B may cool and at least partially (or fully) solidify as the vibrational energy is applied. Step  502  may include continuous or intermittent vibrational energy. In some embodiments, the vibrational energy transmitted may have an amplitude equal to or less than 75% of a diameter of each drop  134  and a frequency that may be dynamically modulated or adjusted as the mass of the 3D object  136  increases during material printing. An example embodiment may alternatively include eccentric rotating mass vibration motors (ERM), electromagnetic-driven vibration motors, contacting ultrasonic vibrational sources, a vibration platform coupled to the substrate  160 , and combinations thereof. 
     The method  500  may also include generating relative movement between the nozzle  122  and the substrate  160 , as at  506 . Step  506  may be performed before, simultaneously with, or after step  502  and/or  504 . This step may include the computing system  180  causing the substrate control motor  162  to move the substrate  160  in one or more dimensions so that the drops  134 C- 134 D land in the desired location(s) to form the 3D object  136 . In one example, a (e.g., vertical) distance between the nozzle  122  and the substrate  160  may be increased. In another example, lateral (e.g., horizontal) movement between the nozzle  122  and the substrate  160  may be introduced so that the layers  135 A,  135 B are laterally offset from one another but at least partially overlapping. In yet another example, step  506  may be omitted. 
     The method  500  may include jetting the second layer  135 B having one or more drops  134 C- 134 D, as at  508 . Step  508  may be performed before, simultaneously with, or after step  506 . This step may include the computing system  180  causing the power source  170  to transmit voltage pulses to the coils  152 . In response, the coils  152  may cause the second layer  135 B having one or more drops  134 C- 134 D to be jetted through the nozzle  122 . The second layer  135 B having one or more drops  134 C- 134 D may be deposited onto the substrate  160  and/or onto the first layer of drops  134 A- 134 B (e.g., the first layer  135 A), as shown in  FIG. 4 . The nozzle  122  and/or the substrate  160  may be/remain substantially stationary (e.g., with respect to one another) during step  508 . As mentioned above, each of the drops  134 C- 134 D may be deposited before the other drops  134 C- 134 D in that particular layer  135 B fully solidify. In one embodiment, the method  500  may loop back around to step  504  and repeat or continue directing vibrational energy towards the one or more drops on the substrate to form additional layers  135 C- 135 G of the 3D object  136 . 
     The method  500  may also include directing vibrational energy towards the one or more drops on the substrate from an external vibrational source  202 . This external vibrational energy source  202 , or non-contact vibrational energy source is not directly coupled to the substrate  160  but directs vibrational energy at or near the one or more drops  134  or the 3D object on the substrate  160  to influence the breaking of surface tension between drops  134  as they solidify during the printing of a 3D object  136 . This optional step may be performed before, simultaneously with, or after step  502 ,  504 ,  506 ,  508 , or a combination thereof. This step may include continuous or intermittent vibrational energy. In some embodiments, the vibrational energy transmitted may have an amplitude equal to or less than 75% of a diameter of each drop  134  and a frequency that may be dynamically changed as a 3D object is printed, based on the mass or resonant frequency of the 3D object. In an example embodiment, this step may include a non-contacting vibrational energy source, such as laser doppler vibrometer (LDV), vibrational photo acoustic (VPA) sources, non-contact ultrasonic vibration sources, or combinations thereof. In another example embodiment, this step may include both contacting and non-contacting methods of vibrational energy sources. 
     Notwithstanding that the numerical ranges and parameters setting forth the broad scope of the present teachings are approximations, the numerical values set forth in the specific examples are reported as precisely as possible. Any numerical value, however, inherently contains certain errors necessarily resulting from the standard deviation found in their respective testing measurements. Moreover, all ranges disclosed herein are to be understood to encompass any and all sub-ranges subsumed therein. For example, a range of “less than 10” may include any and all sub-ranges between (and including) the minimum value of zero and the maximum value of 10, that is, any and all sub-ranges having a minimum value of equal to or greater than zero and a maximum value of equal to or less than 10, e.g., 1 to 5. 
     While the present teachings have been illustrated with respect to one or more implementations, alterations and/or modifications may be made to the illustrated examples without departing from the spirit and scope of the appended claims. For example, it may be appreciated that while the process is described as a series of acts or events, the present teachings are not limited by the ordering of such acts or events. Some acts may occur in different orders and/or concurrently with other acts or events apart from those described herein. Also, not all process stages may be required to implement a methodology in accordance with one or more aspects or embodiments of the present teachings. It may be appreciated that structural objects and/or processing stages may be added, or existing structural objects and/or processing stages may be removed or modified. Further, one or more of the acts depicted herein may be carried out in one or more separate acts and/or phases. Furthermore, to the extent that the terms “including,” “includes,” “having,” “has,” “with,” or variants thereof are used in either the detailed description and the claims, such terms are intended to be inclusive in a manner similar to the term “comprising.” The term “at least one of” is used to mean one or more of the listed items may be selected. Further, in the discussion and claims herein, the term “on” used with respect to two materials, one “on” the other, means at least some contact between the materials, while “over” means the materials are in proximity, but possibly with one or more additional intervening materials such that contact is possible but not required. Neither “on” nor “over” implies any directionality as used herein. The term “conformal” describes a coating material in which angles of the underlying material are preserved by the conformal material. The term “about” indicates that the value listed may be somewhat altered, as long as the alteration does not result in nonconformance of the process or structure to the illustrated embodiment. The terms “couple,” “coupled,” “connect,” “connection,” “connected,” “in connection with,” and “connecting” refer to “in direct connection with” or “in connection with via one or more intermediate elements or members.” Finally, the terms “exemplary” or “illustrative” indicate the description is used as an example, rather than implying that it is an ideal. Other embodiments of the present teachings may be apparent to those skilled in the art from consideration of the specification and practice of the disclosure herein. It is intended that the specification and examples be considered as exemplary only, with a true scope and spirit of the present teachings being indicated by the following claims.