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Hydrodynamic response model of a piezoelectric inkjet print-head
Accepted Manuscript Title: Hydrodynamic response model of a piezoelectric inkjet print-head Authors: Wang Jianjun, Huang Jin, Peng Ju PII: DOI: Reference:
S0924-4247(18)30963-4 https://doi.org/10.1016/j.sna.2018.11.001 SNA 11096
To appear in:
Sensors and Actuators A
Received date: Revised date: Accepted date:
7 June 2018 10 October 2018 1 November 2018
Please cite this article as: Wang J, Huang J, Peng J, Hydrodynamic response model of a piezoelectric inkjet print-head, Sensors and amp; Actuators: A. Physical (2018), https://doi.org/10.1016/j.sna.2018.11.001 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.
Hydrodynamic response model of a piezoelectric inkjet print-head
Wang Jianjun 1, Huang Jin *, Peng Ju
Key Laboratory of Electronic Equipment Structure Design, Ministry of Education, Xidian University, Xi’an 710071,
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China
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Highlights: There are the following highlights in this article: 1. A new equivalent circuit model based on radial displacement is presented that can predict the flow state in the channel through the variation of the pipe diameter. 2. An effective parameter equivalent method is proposed to precisely estimate energy attenuation due to the viscous force. 3. Experimental results confirm that the method is attracting.
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Abstract: The concentric squeeze-mode piezoelectric print-head (PPH) has been applied to the field of additive manufacturing, which requires a high deposition precision of droplets. To combine the
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self-sensing technique of a PPH, this paper presents a linear time-varying system equivalent circuit model based on radial displacement. This system is able to predict the flow state in the channel
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according to the variation of the pipe diameter. Compared with current models, this equivalent circuit model is more accurate in regard to energy attenuation. The equivalent thickness of the boundary layer is presented using a combination of boundary layer theory and oscillating plate flow to calculate the
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equivalent resistance of the viscous force. The experimental results show that the proposed method is more precise than the previous equivalent methods. To verify the model, a single trapezoidal pulse waveform and double trapezoidal pulse waveform were designed to realize the superposition of
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pressure and suppression of residual oscillation, respectively. The experimental results showed that the single trapezoidal pulse waveform based on the modelled pressure response was able to exactly realize the superposition of pressure and that the double trapezoidal pulse waveform based on the modelled
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pressure response was able to suppress the residual oscillation. The pressure and volume flow rate responses of the model are highly consistent with the experimental results in the time domain.
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Keywords: piezoelectric print-head, time-varying system, equivalent circuit
1. Introduction PPHs have been applied to such fields as printed electronics [1] and additive manufacturing [2] as an alternative to traditional printing applications. A PPH can produce tiny droplets of less than 17 pL on demand [3]. With the advantages of a high deposition precision and good control of the size and speed of droplets, the PPH has become an effective device for accurate material deposition in additive manufacturing, which not only simplifies the present technological processes but also reduces the scrap rate caused by multiple process steps.
The structure of a concentric squeeze-mode PPH consists of glass tube surrounded by a piezoelectric tube. When an external voltage is applied, the piezoelectric material drives the glass tube to shrink or expand radially, which also causes the fluid inside the PPH channel to flow and produce droplets at the nozzle. It is difficult to monitor the process through sensors. Due to the piezoelectric effect, piezoelectric material can act as not only a sensor (direct piezoelectric effect) but also as an actuator (inverse piezoelectric effect). In fact, piezoelectric material plays the two roles when it is working, which is called the self-sensing of piezoelectric material. The detailed description of the self-sensing can be found in the references [4, 5]. During the jetting process, the self-sensing of the piezoelectric material was used to measure the radial displacement of the glass tube. Kwon has achieved the
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measurement of the self-sensing signal through a differential amplifier and a matching capacitor [6]. The signal represents the deformation of piezoelectric material. For the concentric squeeze-mode PPH, the signal means the radial displacement of piezoelectric material, which cannot represent the flow
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state (pressure, flow velocity) inside the PPH channel. Therefore, it cannot be used to predict the flow state at the nozzle. Therefore, a great need exists to create a model to predict the flow state inside the PPH channel based on radial displacement.
To create the jetting model, Quentin Gallas [7] and Chiatto M [8] et al. proposed an equivalent circuit model for piezoelectric-driven synthetic jet actuators according to the lumped element method
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(LEM), and provided the parameter evaluation method of circuit components. Byung-Hun Kim [9] et al. designed a PPH with a shrinking structure at both ends of the channel and established a corresponding
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LEM. It was proven that LEM could be used to study the action mechanism of PPH effectively. For these studies, the pressure change caused by the excitation voltage is equivalent to the energy
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conversion of an ideal transformer. The voltage is converted to the pressure acting on the surface of the
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piezoelectric material. However, a large number of experimental measurements are required to determine the relevant equivalent parameters related to the structure and material, including the elastic force, damping force, and inertial force of the piezoelectric materials. Moreover, the pressure loss
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predicted by Darcy’s law [7, 9] regarding the equivalent fluid viscosity introduces large errors, as the Darcy formula is derived based on steady-state conditions, whereas the liquid response in the PPH channel is transient, among which the pressure loss predicted by the viscosity is larger than that under
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steady-state conditions. Despite their high accuracy in time consistency, these models are inaccurate in regard to energy attenuation and are less practical because of the cumbersome measurement parameters. In this paper, a novel equivalent circuit model is proposed that has more accurate equivalence to the
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flow resistance. The proposed model is practical and is able to predict the flow state in the channel according to a real-time measurement of the radial displacement of the piezoelectric material. The model in this paper is based on a more realistic physical mechanism to simulate the droplet
formation process. Because the behaviour of the tube flow can be simulated by circuits [10], the pressure and volume flow rate in a fluid are similar to the voltage and currents in the circuit,
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respectively; thus, the fluid’s inertial, viscous and elastic behaviours are equivalent to the behaviours of an inductor, a resistor and a capacitor, respectively. The equivalent parameter estimation method of the inertial force is derived from Navier-Stokes equations. The displacement of the fluid during ink jetting is so small that the boundary layer is far from being fully developed [11]. A viscous force is assumed to act in a thin layer (thickness of less than 10 µm) near the tube wall. The calculation method to determine the equivalent thickness of the boundary layer uses the combination of boundary layer theory and oscillating plate flow. Based on the thickness of the boundary layer, an equivalent parameter estimation method for the viscous force is given. To determine the nonlinear behaviour of the viscous
force at the nozzle caused by the contraction of the pipe diameter, the linear superposition method is applied to calculate the total viscous force. The expansion of the pressure chamber wall decreases the interior pressure, and the resulting low pressure causes the liquid from both sides of the chamber to flow into the pressure chamber. The process is the same as that in the circuit, i.e., the increase of a time-varying capacitor decreases the voltage at both ends. The low voltage makes charges flow into the capacitor from the connected circuits. Therefore, the change of the time-varying capacitor is equivalent to the change of the pressure chamber radius. Moreover, the ink jetting process of a single droplet is short enough to be assumed to be an adiabatic process. A method is derived to estimate the equivalent
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variable capacitance in a pressure chamber with a variable diameter using the state equation [10] (dp=c2dρ) under the adiabatic conditions. The aim of this paper is to provide an accurate equivalent circuit model based on radial displacement
to predict the flow state in a pipe to help improve the theoretical ink jetting capability and waveform
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adaptation of a PPH. Moreover, this model provides a means to realize semi-closed-loop control of the
flow state via the piezoelectric material’s self-sensing. In section 2, the schematic of the experimental system is introduced. In section 3, an equivalent circuit model and parameter estimation method are presented. In section 4, a recursive solution method of the model is presented that is used to calculate the dynamic response of the ramp step driving the waveform; comparisons with the experimental
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results show that the model is highly accurate in regard to time consistency and energy attenuation. In section 5, an analysis of the pressure and volume flow rate response in the channel based on the model
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is performed for a single trapezoidal pulse waveform and a double trapezoidal pulse waveform. The
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model is shown to be accurate according to the experimental results.
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2. Experimental setup The schematic of the experimental system is shown in Fig 1 [12-14]; this system consists of a CCD Camera, an LED strobe, a PPH, a controller, a pressure controller and a data processor. The oscilloscope (MSO4104B) is applied to monitor the dependability of the output signal of controller.
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The pressure controller generates negative pressure inside the PPH to balance the gravity of the liquid. The data processor is used to analyse photos captured by the CCD camera. The controller consists of an embedded system (STM32F103ZET6), an FPGA (EP1C3T144C8N), high-speed DA converters
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(AD9708), an LED driver (PT4115) and a high power amplifier (PA84). The embedded system is applied to create a trigger signal for jetting at specified frequencies. When the FPGA detects the trigger signal for jetting, it drives the DA convertor (output range: ± 5 V) to generate the low voltage driving
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waveform. The low voltage driving waveform is magnified (output range: ± 100 V) by the high power amplifier to drive the PPH. Moreover, when the FPGA detects the trigger signal for jetting and waits for a delay, the FPGA also generates an LED trigger signal and a camera trigger signal. There is a delay time between the LED trigger signals and the trigger signal for jetting. The image of a droplet at different times is captured by adjusting the delay time. These captured images are sent to the data
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processor sequentially via a USB. The resolution of the droplet edge in the captured image is controlled by adjusting the pulse width of the LED trigger signal. To improve the resolution ratio of the droplet edge in the captured image, the pulse width of the LED trigger should be as small as possible without lowering the image brightness. The detailed experimental theory can be found in the reference [15].
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Fig 1. Schematic of experimental system
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3. Lumped parameter model 3.1 Equivalent circuit model The structure of a circle squeeze-mode PPH MJ-AL-80 (a type of PPH fabricated by MicroFab, where “MJ-AL” is the name of a series of PPH, and “80” means the diameter of the nozzle is 80 µm) is
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shown in Figure 2. Because of the radial expansion of the chamber wall caused by the positive voltage acting on the piezoelectric surrounding [16], a negative pressure is built-up in the interior of the
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chamber because of the sudden volume change, which causes the liquid from both ends of the chamber to flow into the pressure chamber. The pressure inside the pressure chamber reduces to the ambient
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pressure when the chamber is filled by the liquid that has not been compressed. The chamber is further filled via the inertial force. When the liquid flow rate falls to zero, the positive pressure (elastic potential energy) inside the pressure chamber reaches the maximum. Next, the liquid in the pressure chamber flows to both sides of the chamber to release the pressure. The process repeats until all of the
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energy is consumed.
Fig 2. Structure of the MJ-AL-80 print-head The size of the piezoelectric print-head is small enough that the effects of gravity can be ignored [17]. The pressure at the exit of the nozzle chamber and left flow channel is standard atmospheric pressure (1[atm]). Figure 3 presents an equivalent circuit diagram of the squeeze-mode PPH. Because the
pressure in the liquid is equivalent to the voltage and the volumetric flow rate is equivalent to the current, the atmospheric pressure at the exit of the nozzle chamber and that at the left flow channel are equivalent to the power source Us. The radial displacement of the pressure chamber wall results in a change of the pressure inside the chamber, leading to flow-out/in of the liquid. This process is similar to the charge and discharge of a capacitor, as indicated by the equivalent time-varying capacitor C1 located in the middle of the pressure chamber. Because there is no obvious change in the size of the left flow channel and the left part of the pressure chamber connected during ink jetting, the liquid inside these parts can be assumed to be incompressible, and only the corresponding flow resistance and inertia force should be taken into account; the flow resistance and inertia force are equivalent to the resistance
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R1 and inductance L1, respectively. Because of the shrinkage of the diameter of the nozzle, it is difficult
for liquid to flow in the right parts. The compressibility of the liquid in the right flow channel and the
nozzle should be taken into account; this compressibility is equivalent to the capacitor C2 located in the
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connection between the pressure chamber and right flow channel, of which the flow resistance and
inertia force are equivalent to the resistance R2 and inductance L2, respectively. Similarly, the flow resistance and inertia force inside the nozzle are equivalent to the resistance R3 and inductance L3, respectively. The Laplace pressure characteristics caused by surface tension are equivalent to those of the capacitor C3. The power source Ud is used to ensure that the mathematical description of the
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relationship of voltages u1 and u2 with respect to their corresponding position is the same as that
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observed in the parameter equivalence.
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Fig 3. Equivalent circuit model of the inkjet print-head 3.2 Parameter estimation The estimations of the viscous force and inertia force inside the pipe are derived from the Navier-Stokes equation, which provides estimations of the equivalent resistance and equivalent inductance. The size of the structure of the PPH channel and the displacement of the liquid inside the
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channel are so small that the body force and convective acceleration can be neglected; thus, the corresponding incompressible Navier-Stokes equation is simplified as [18]:
u p 2u t
(1)
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Where ρ is the density, μ is the viscosity, u is the flow velocity, and p is the pressure. Because the
volume flow rate q is equivalent to the current in an equivalent circuit, the flow velocity u is transformed to the volume flow rate q by the expression q=πr2u. Similarly, because the pressure inside the pipe is equivalent to the voltage in an equivalent circuit, the pressure gradient ∇p is transformed to the pressure increase Δp multiplied the length of tube l:
p
l dq l 2 q r 2 dt r 2
(2)
Where r is the inner radius of PPH channel. Typically, the following approach is used to calculate pressure drops due to inertia and viscous forces. The pressure drop caused by an inertia force is
recorded as Δpi , and the pressure drop caused by the viscous force is recorded as Δpv:
l dq r 2 dt l pv 2 2 q r pi
(3) (4)
Because the viscous force is equivalent to a resistance, there should be a relationship similar to Δpv=Rq. It is obvious that equation (4) does not meet the requirements due to the term ∇2q. The viscous force affects the liquid in the channel within a small boundary layer. The viscous force can be viewed as the shear stress on the wall that consumes the liquid momentum. Therefore, the
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momentum-consumed boundary thickness δE is used to approximately calculate the shear stress on the wall [11]. E
0
u u 1 dr U U
(5)
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T
(6)
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u e k ( rt r ) , k U
U
where u is the velocity in the boundary layer, U is the velocity that is not influenced by the boundary layer, and δ is the thickness of the boundary layer on the condition of u/U=0.99. The two thicknesses of the boundary layer are shown in Figure 4a. To obtain the expression of the momentum-consumed boundary thickness δE, combined with the method of Stokes second problem [11], the expression of u/U is presented:
where T is the oscillating period of the liquid inside the channel, and rt is the position of the tube
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wall. Combining equation (5) and equation (6), the expression of the momentum-consumed boundary thickness δE is given as:
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E
1 2k
(7)
In Figure 4b, as shown by the red short dotted line, the velocity of the liquid in the momentum-consumed boundary thickness δE is zero, and the velocity of the liquid beyond δE
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becomes the ideal velocity U, i.e., the velocity gradient at δE from the wall is infinite, and the situation is not reasonable. The approximate velocity profile is shown as a blue short dotted line with a boundary thickness δV , which is the twice the value of δE , in which the velocity gradient is equal to U/δV. The
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period lag caused by surface tension has a slight effect on δE ; thus, the liquid oscillating period T inside the channel can be calculated using sound reflection theory [19].
T
2lT c
(8)
To obtain the expression of the resistance estimation, with the approximate substitution of U/δV for
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the shear rate at the boundary layer, equation (4) is substituted in the form of equation (9):
pv
2 rl U 2lq 3 2 r V r V
(9)
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(a)
(b)
Fig 4. (a) Distribution of u/U, (1-u/U) and (1-u/U)u/U within the boundary layer [11]; (b) the velocity distribution within the pipe
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To realize the accurate equivalence to the nonlinear flow resistance in the nozzle, as shown in Figure 5, the structure of the nozzle is divided into N equal parts along the axis. These divided parts are all
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viewed as straight pipes, and the pressure drop of every part is calculated using equation (9). The total pressure drop can be expressed as:
2lq N ri3V
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po
(10)
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i 1
Fig 5. Nozzle segmentation schematic diagram
Assuming that there is a straight pipe with an equivalent radius re and length L, which have the same
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pressure drop as the nozzle, the equivalent radius is described by the following equation:
re
1 3
N
1 3 i 1 Nri
(11)
where N is the number of the segments of the nozzle. Equation (11) is used to calculate the equivalent radius of the nozzle. To understand the effect of the section number on the accuracy of re , the variation relationship between N and re for the MJ-AL-80 PPH is shown in Figure 6. re converges to
a fixed value with the increase of the section number. For MJ-AL-80 PPH, the nozzle radius is 40 µm,
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re is approximately 86.5 µm.
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Fig 6. Convergence of the equivalent radius with the increase in the number of segments
The ink jetting process of a single droplet is transient enough to be assumed to be adiabatic. The liquid obeys the state equation dp=c2dρ [10], where dp is the pressure increase, dρ is the density increase, and c is the sound speed of fluid material. The density increase in the pressure chamber can be expressed as:
t
t
U
t0
t0
V (t )
(12)
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d (t0 )
(t0 ) V (t0 ) q1 (t )dt q2 (t )dt
In equation (6), ρ(t0) and V(t0) represent the density of the liquid and volume of the pipe at the initial
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moment, respectively. q1(t) is the liquid volumetric flow rate in the left pipe, q2(t) is the liquid
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volumetric flow rate in the right pipe, and V(t) is the volume of the piezoelectric section. The combination of equation (12) and the state equation is
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dp c 2 (t0 )
t
t
t0
t0
V (t0 ) q1 (t )dt q2 (t )dt V (t ) 2 c (t0 )
(13)
t
U (t )
Q(t0 ) idt
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In equation (13), c2ρ(t0) is a constant with a dimension of [Pa]. For a variable capacity, its voltage, charge and capacitance meet the following relationship: t0
C (t )
(14)
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where Q(t0) is the initial charge number of the capacitor, i is the current through the capacitor, C(t) is the capacitance of the capacitor, and U(t) is the voltage acted on the capacitor. To express equation (14) in the same form as equation (13), a power source Ud is connected oppositely in front of the capacitor. The voltages at both ends of the capacitor branch after the connection of the power source can be expressed as: t
u (t ) Ud
Q(t0 ) idt t0
C (t )
(15)
Equations (15) and (13) are consistent in terms of the mathematical expression. The combined system composed of a power source Ud and the corresponding capacitor is equivalent to the pressure response inside the channel; the position of the power source Ud is shown in Figure 3. A certain capacitor is equivalent to the Laplace pressure caused by surface tension. To estimate the
expression of the capacitor parameter, the average values of the flow-out/in volumes at the nozzle are roof-shaped [9]. The equivalent capacitance of the surface tension can be described as:
C
Q Vmen ro4 U pmen 3
(16)
Where Vmen is the roof-shaped volume of the fluid with the nozzle radius ro , pmen is the Laplace pressure, and σ is the coefficient of surface tension. Combining equations (3), (10), (11), (14) and (15), the calculation relationships of all of the Table 1. Parameter mapping relation
Equivalent circuit components
Mapping expression
r 2 L3 ro4 , c 2 (t0 ) 3
C1 (t )
r (t ) 2 L2 c 2 (t0 )
Voltage source Ud
c 2 (t0 )
R1 , R2 , R3
Inductance
L1 , L2 , L3
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2 L1 L2 2 2 L3 L2 2 2 Lo , , V r 3 V r 3 V re3
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Resistance
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Capacitance
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C2 , C3
Capacitance
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component parameters in the equivalent circuit in Figure 3 are listed in Table 1.
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L1 L2 2 L3 L2 2 Lo , , r2 r2 re2
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3.3 Circuit model Several equations are derived from Kirchhoff's voltage law and Kirchhoff’s current law to solve the equivalent circuit model shown in Figure 3[20]:
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duc1 (t ) 1 dC1 (t ) 1 1 uc1 (t ) i1 (t ) i2 (t ) dt C1 (t ) dt C1 (t ) C1 (t ) duc 2 (t ) 1 1 i2 (t ) i3 (t ) dt C2 C2 (t )
(17)
(18)
duc 3 (t ) 1 i3 (t ) dt C3
(19)
di1 (t ) R 1 1 uc1 (t ) 1 i1 (t ) Us Ud dt L1 L1 L1
(20)
di2 (t ) 1 R 1 uc1 (t ) uc 2 (t ) 2 i2 (t ) dt L2 L2 L2
(21)
di3 (t ) 1 R 1 1 uc 2 (t ) uc 3 (t ) 3 i3 (t ) Us Ud dt L3 L3 L3 L3
(22)
In the above equations, uc1(t), uc2(t), and uc3(t) represent the terminal voltages of the capacitor C1, C2 and C3, respectively. Choosing uc1(t), uc2(t), uc3(t), i1(t), i2(t), and i3(t) as state variables, equations (17)-(22) can be expressed as state equations of a linear time-varying system[21]:
x(t ) A(t )x(t ) Bu
(23)
du (t ) x c1 dt
duc 2 (t ) dt
duc 3 (t ) dt
di1 (t ) dt
T
di3 (t ) , dt
di2 (t ) dt
u Us Ud
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0
0
0
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0
0
1 C2
0
0
R1 L1
0
0
1 L2
0
0
1 L3
0
0
0
1 L3
1 C1 (t )
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1 C1 (t )
0
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1 dC1 (t ) C (t ) dt 1 0 0 A(t ) 1 L1 1 L2 0
1 L1
T
1 0 , L3
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x uc1 (t ) uc 2 (t ) uc3 (t ) i1 (t ) i2 (t ) i3 (t ) , B 0 0 0 T
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In equation (23),
R2 L2 0
0 1 C2 0 0 0 R3 L3
For the PPH, it is significant to obtain the pressure and volume flow in the channel. Three equivalent
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voltages u1(t), u2(t), u3(t) and the corresponding currents i1(t), i2(t), and i3(t) are chosen as the output variables. The output equation can be expressed as:
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u1 (t ) 1 u (t ) 0 2 u3 (t ) 0 where y (t ) ,C i1 (t ) 0 i2 (t ) 0 0 i3 (t )
y(t ) Cx(t ) D
(24)
Ud 0 0 0 0 0 Ud 1 0 0 0 0 0 0 1 0 0 0 and D 0 . 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1 0
Equations (23) and (24) describe a state-space model of the PPH, which is a linear time-varying
system; there is no exact analytical solution of the model. 4. Solution of the model 4.1 Recursive solution In fact, it is difficult to obtain the analytical solution of equation (23). To solve the linear time-varying system, the block pulse function method shown in equation (25) is used to solve equation (23). As the ink jetting of a single droplet is transient, it is not necessary to use a long-time recursion to solve the model. The ink jetting of each droplet starts from the same initial condition to avoid the drift
—
(25)
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1 2 2 x I A x(t0 ) B1u1 1 1 t t 1 2 2 xk 1 t I Ak 1 t I Ak xk Bk uk Bk 1uk 1
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problems caused by the accumulation of long-time recursion errors.
—
—
—
where x k is the average value of the state variables, Ak is the state matrix, Bk is the input matrix, uk is the average value of the system input during the kth sampling period, I is the unit matrix, and Δt is the —
sampling time step length. The state variable x k+1 during the k+1th sampling period is obtained by the —
—
—
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recursion of Ak , Bk and uk during the kth sampling period, and the corresponding pressure response to
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equation (23) is given. 4.2 Results of LEM To verify the model and accuracy of the calculation method, the parameters of an ethanol solution
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shown in Table 2 are applied to the model to determine the system response inside the pressure chamber under the excitation of the ramp step signal. The response of the piezoelectric tube wall to the
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excitation is dynamic, during which shock, oscillation and other phenomena occur. With an accurate self-sensing measurement of the tube, the radial displacement of the tube wall is assumed to be a linear
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function of the excitation voltage given by:
dr V
(26)
Table 2. Ethanol material parameters
Ethanol solution
Speed of sound (m/s)
Density (kg/m3)
Viscosity (Pa·s)
Surface tension (N/m)
1120
807.73
0.0011933
0.02255
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Material
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where dr is the radial displacement of the pressure chamber wall under the excitation of the
impressed voltage, V is the voltage across the piezoelectric tube, and α(For MJ-AL-80 PPH, α≈0.32×10-9[m/V]) is the conversion coefficient corresponding to the transformation between the electrical signal and displacement and has dimensions of [m/V]. The response of the relevant state variables in the PPH channel over 200 µs under the excitation of the ramp step signal is shown in
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Figure 7.
(b)
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(a)
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Fig 7. (a) Transient pressure response and (b) transient volume flow rate response
Analysing the solution of the model shown in Figure 7a, it takes 3 µs for the pressure chamber wall to expand to the expected size. Meanwhile, the pressure inside the chamber wall reaches the minimum, followed by a pressure oscillation. When the pressure inside the chamber wall reaches the maximum, the lowest Laplace pressure and largest meniscus concave surface are found at the nozzle. When the
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pressure inside the chamber wall reaches the minimum, the highest Laplace pressure and largest meniscus convex surface are found at the nozzle. The four moments corresponding to the largest
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meniscus convex surface are 60.5 µs, 106.8 µs, 151.3 µs, and 196 µs. The transient pressure response of the pressure chamber is applied to realize the pressure superposition to enhance the ink jetting
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capacity. Therefore, the pressure inside the chamber wall is higher when a squeeze voltage is applied at
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36.75 µs in the ethanol solution. In the case of a standard trapezoidal pulse, the optimum pulse width is 23.75 µs (13 µs to 36.75 µs). Pressure superposition occurs when a squeeze voltage is applied at 83.5 µs, 129 µs, and 173.5 µs, with the effect weakening via viscous attenuation. The transient response of
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the volumetric flow rate inside the tube is shown in Figure 7b. The liquid in the left tube and right tube starts to flow after excitation to counteract the negative pressure and then flows back at the moment that the pressure in the chamber reaches the maximum. With an oscillating pressure, the volumetric
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flow rates in the left tube and in the right tube oscillate at the same frequency. There is a phase difference of pi between the two oscillations. According to the volumetric flow rate at the nozzle, the meniscus surface oscillates. Consistent with the former results, the moments corresponding to the four
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peaking values of the meniscus convex surface are 60.5 µs, 106.8 µs, 151.3 µs and 196 µs, which are in very good agreement with the experimental results based on the photogrammetric method. The photogrammetric experimental results at 10 µs are shown in Figure 8, with an actual sampling period
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of 1 µs, in good agreement with the theoretical solutions in regard to accuracy.
Fig 8. Experimental results of the ramp step drive waveform Compared with the current models, the model in this paper performs well in regard to energy attenuation and time accuracy. The shape of the meniscus at the peaking value under an excitation of a -36 V ramp step signal is shown in Figure 9a. The pixel distances between the meniscus and nozzle are measured according to image binarization using the same threshold of 20, 17, 14, and 11 pixels (1.1
µm/pixel). There is a direct correspondence relationship between the volumetric flow rate and shape of the meniscus at the nozzle. The experimental data and model data are divided by the peak values of the
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corresponding volume flow rate; the result is shown in Figure 9b.
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(b)
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(a)
Fig 9. (a) Shape of the meniscus at the peaking value under an excitation of a -36 V ramp step signal;
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(b) The normalized energy decays are compared between the two models and experimental results
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Based on the above analysis, the results of this model exhibit higher consistency with the experimental results compared with current models. This model realizes semi-closed-loop control of the flow state in the pipe using the combination of piezoelectric material displacement self-sensing
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technique, making it more practical than current models. 5. Results and discussion 5.1 Model results To further verify the accuracy of the proposed model, the standard single trapezoidal pulse waveform
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[4, 13] and double trapezoidal pulse waveform [22-25] are applied to drive an ethanol solution to form droplets. The standard single trapezoidal pulse waveforms cannot suppress the subsequent oscillation
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of the liquid, and normally, there are still strong oscillations at the meniscus after the formation of the main droplets. The satellite droplets come out of solution if the residual energy is high enough (one of the ways in which satellite droplets are formed). A double trapezoidal pulse waveform is designed to suppress the residual oscillation of the meniscus after the formation of the main droplets. The two
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driving waveforms are shown in Figure 10:
(a)
(b)
Fig 10. (a) Signal trapezoidal pulse waveform; (b) Double trapezoidal pulse waveform For the MJ-AL series PPHs, the wall of the pressure chamber expands when a positive voltage is applied, whereas the wall shrinks when a negative voltage is applied. In the case of a single trapezoidal pulse waveform, with the application of voltage with an amplitude of V1 during the time period t1, the pressure chamber expands. The delay time t2 is designed to wait for the pressure to reach the maximum to realize pressure superposition. Based on the analysis mentioned above, t2 is set to 24 µs for an ethanol solution. During the time period t3, the voltage is reduced to zero. Normally, t1 and t3 are set to 3 µs. The shrinking of the pressure chamber wall leads to a further increase of the pressure in the chamber, and the liquid at the nozzle is ejected to form droplets under the excitation of high pressure.
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The wall no longer moves during the subsequent periods as there is no excitation voltage
(fluid-structure interaction is neglected as the liquid is weakly coupled to the wall). The model responses of the pressure in the chamber and volume flow rate under the excitation of the single
trapezoidal pulse waveform are shown in Figure 11. It is obvious that a pulse width of 24 µs was able
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to realize pressure superposition; meanwhile, the volume flow rate at the nozzle increased, except for
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some residual oscillations during the subsequent time periods.
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Fig 11. Model response of the pressure in the chamber and the volume flow rate under the excitation of the single trapezoidal pulse waveform To suppress residual oscillations following the main droplets, the first trapezoidal pulse in the double trapezoidal pulse waveform plays the same role as the single trapezoidal pulse waveform, which is also applied to eject the liquid to form the main droplets, and the second trapezoidal pulse is applied to
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eliminate the residual pressure oscillations [4]. The delay time t4 is designed to allow the pressure to reach the minimum (the main droplets have been formed) because during the time period t5, a positive pressure increase occurs in the chamber. According to the transient response of the single trapezoidal pulse waveform, t4 should be set to 17 µs. In the same manner, a negative pressure increase in the
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chamber is found during the time period t7. The delay time t6 is designed to allow the pressure to reach the maximum (the compression of liquid in the chamber reaches the maximum); similarly, t6 is set to 24 µs while t5 and t7 are set to 3 µs. During time period t7, there is a further pressure decrease in the chamber, resulting in suppression of the pressure in the chamber and the oscillation of the meniscus surface. The model response of the pressure in the chamber and volume flow rate under the excitation of a double trapezoidal pulse waveform is shown in Figure 12.
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Fig 12. Model response of the pressure in the chamber and the volume flow rate under the excitation of a double trapezoidal pulse waveform 5.2 Experimental results Regarding the two driving waveforms mentioned in section 4.1, the photogrammetric method is applied during the experiment to record the suppression of the residual oscillation. The experimental
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results of the two driving waveforms are shown in Figure 13a and b.
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(a)
(b)
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Fig 13. (a) Experimental results of the single trapezoidal pulse waveform; (b) Experimental results of the double trapezoidal pulse waveform Through analysis of the experimental results, in the case of a single trapezoidal pulse waveform,
more liquid is ejected via the pressure residual oscillation following the main droplets, consistent with the theoretical results in the time domain. In the case of a double trapezoidal pulse waveform, there is no obvious meniscus residual oscillation during the experiment. Based on the analysis, the model is shown to be accurate based on the good agreement with the experimental results. 6. Conclusions The equivalent circuit model proposed in this paper, in keeping with the PPH in the physical
mechanism, is more accurate compared with the traditional equivalent circuit models regarding equivalent parameters. The nonlinear flow resistance at the nozzle calculated by utilizing an effective radius was shown to be convergent. Combined with the characteristics of the PPH, the recursive solution method of the system model not only makes the model more practical but also avoids the errors caused by long-time recursion. The response of the ramp step signal was analysed through experiments, revealing that the solution to the model was highly consistent with the experimental results in the time domain regarding the energy attenuation. To further verify the accuracy of the model, a single trapezoidal pulse waveform and a double trapezoidal pulse waveform were designed to suppress the residual oscillation, and the model was shown to be accurate according to the
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experimental results. Acknowledgments
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This work was supported by the Natural Science Foundation of China (Grant No.51575419) and the 111 Project (Grant No.B14042); The authors kindly acknowledge these supports.
References [1] J. Roh, H. Kim, M. Park, J. Kwak, C. Lee, Improved electron injection in all-solution-processed
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n-type organic field-effect transistors with an inkjet-printed ZnO electron injection layer, Applied Surface Science, 420 (2017) 100-104.
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[2] M. Kyobula, A. Adedeji, M.R. Alexander, E. Saleh, R. Wildman, I. Ashcroft, P.R. Gellert, C.J. Roberts, 3D inkjet printing of tablets exploiting bespoke complex geometries for controlled and
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tuneable drug release, J Control Release, 261 (2017) 207-215.
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[3] A.U. Chen, O.A. Basaran, A new method for significantly reducing drop radius without reducing nozzle radius in drop-on-demand drop production, Physics of Fluids, 14 (2002) L1-L4. [4] K.-S. Kwon, W. Kim, A waveform design method for high-speed inkjet printing based on
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self-sensing measurement, Sensors and Actuators A: Physical, 140 (2007) 75-83. [5] K.-S. Kwon, Methods for detecting air bubble in piezo inkjet dispensers, Sensors and Actuators A: Physical, 153 (2009) 50-56.
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[6] K.-S. Kwon, Y.-S. Choi, J.-K. Go, Inkjet jet failures and their detection using piezo self-sensing, Sensors and Actuators A: Physical, 201 (2013) 335-341. [7] Q. Gallas, R. Holman, T. Nishida, B. Carroll, M. Sheplak, L. Cattafesta, Lumped Element Modeling
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of Piezoelectric-Driven Synthetic Jet Actuators, AIAA Journal, 41 (2003) 240-247. [8] M. Chiatto, F. Capuano, G. Coppola, L. de Luca, LEM Characterization of Synthetic Jet Actuators Driven by Piezoelectric Element: A Review, Sensors (Basel), 17 (2017). [9] B.-H. Kim, H.-S. Lee, S.-W. Kim, P. Kang, Y.-S. Park, Hydrodynamic responses of a piezoelectric driven MEMS inkjet print-head, Sensors and Actuators A: Physical, 210 (2014) 131-140.
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[10] Z.Z. DU Gong huan, Theory of Acoustics, 3 ed., Nanjing University Press, Nanjing, 2012. [11] D.C. ZHANG Zixiong, Viscous Fluid Mechanics, 2 ed., Peking University Press, Beijing, 2011. [12] K.S. Kwon, M.H. Jang, H.Y. Park, H.S. Ko, An inkjet vision measurement technique for high-frequency jetting, Rev Sci Instrum, 85 (2014) 065101. [13] K. Kye-Si, Waveform Design Methods for Piezo Inkjet Dispensers Based on Measured Meniscus Motion, Journal of Microelectromechanical Systems, 18 (2009) 1118-1125. [14] H. Dong, W.W. Carr, J.F. Morris, Visualization of drop-on-demand inkjet: Drop formation and deposition, Review of Scientific Instruments, 77 (2006).
[15] K.-S. Kwon, Experimental analysis of waveform effects on satellite and ligament behavior viain situmeasurement of the drop-on-demand drop formation curve and the instantaneous jetting speed curve, Journal of Micromechanics and Microengineering, 20 (2010). [16] MicroFab, Drive Waveform Effects, 1999. [17] S. Poozesh, N. Akafuah, K. Saito, New criteria for filament breakup in droplet-on-demand inkjet printing using volume of fluid (VOF) method, Korean Journal of Chemical Engineering, 33 (2016) 775-781. [18] Z.X. Zhu Baoshan, Fluid Mechanics, 1 ed., Peking University Press, Beijing, 2013. [19] D.B. Bogy, F.E. Talke, Experimental and Theoretical Study of Wave Propagation Phenomena in [20] B.R. L, Introductory Circuit Analysis, 9 ed., Hall,Inc, Prentice, 2000.
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Drop-on-Demand Ink Jet Devices, IBM Journal of Research and Development, 28 (1984) 314-321.
[21] W. Jiwei, Modern Control Theory and Engineering, 2 ed., Higher Education Press, Beijing, 2010.
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[22] M.-w. He, L.-l. Sun, K.-y. Hu, Y.-l. Zhu, H.-n. Chen, Analysis of DoD inkjet printhead performance for printable electronics fabrication using dynamic lumped element modeling and swarm intelligence based optimal prediction, Journal of Central South University, 22 (2015) 3925-3934. [23] P. Shin, J. Sung, M.H. Lee, Control of droplet formation for low viscosity fluid by double waveforms applied to a piezoelectric inkjet nozzle, Microelectronics Reliability, 51 (2011) 797-804.
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[24] A.A. Khalate, X. Bombois, R. Babuška, H. Wijshoff, R. Waarsing, Performance improvement of a drop-on-demand inkjet printhead using an optimization-based feedforward control method, Control
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Engineering Practice, 19 (2011) 771-781.
[25] A.A. Khalate, X. Bombois, G. Scorletti, R. Babuska, S. Koekebakker, W. de Zeeuw, A Waveform
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Design Method for a Piezo Inkjet Printhead Based on Robust Feedforward Control, Journal of
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Microelectromechanical Systems, 21 (2012) 1365-1374.
Author Biography Jianjun Wang received the B.E. degrees from Kun Ming University of Science and Technology, Kun’ming, China, in 2015 and he is currently working toward the Ph.D. degree at the School of Electro-Mechanical Engineering, Xidian University. He has been a Member at the Key Laboratory of Electronic Equipment Structure Design, Xidian University, since 2015. His research interests include inkjet printing, additive manufacturing etc. Jin Huang received the M.S. and Ph.D. degrees in mechanical engineering from Xidian University, Xi’an, China, in 1995 and 1999,respectively.He was with the Department of Mechanical Engineering,
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University of British Columbia, Canada, as a Visiting Researcher, from 2001 to 2002. In 1995, he
joined the School of Electro-Mechanical Engineering, Xidian University, where he is currently a Professor and Director at the Key Laboratory of Electronic Equipment Structure Design, Ministry of
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Education. He has published more than 80 papers in journals and conference proceedings, and he has
12 patents issued and ten patents pending. His research interests include electronic equipment modeling and control.Dr. Huang received the Chinese National Science and Technology Progress Prize in 2008 and 2013, respectively.
Ju Peng received the B.E. degrees from China University of Mining Technology, Xu’zhou, China, in
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2015 and he is currently working toward the Ph.D. degree at the School of Electro-Mechanical Engineering, Xidian University. He has been a Member at the Key Laboratory of Electronic Equipment
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Structure Design, Xidian University, since 2015. His research interests include inkjet printing, additive
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manufacturing etc.
S0924-4247(18)30963-4 https://doi.org/10.1016/j.sna.2018.11.001 SNA 11096
To appear in:
Sensors and Actuators A
Received date: Revised date: Accepted date:
7 June 2018 10 October 2018 1 November 2018
Please cite this article as: Wang J, Huang J, Peng J, Hydrodynamic response model of a piezoelectric inkjet print-head, Sensors and amp; Actuators: A. Physical (2018), https://doi.org/10.1016/j.sna.2018.11.001 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.
Hydrodynamic response model of a piezoelectric inkjet print-head
Wang Jianjun 1, Huang Jin *, Peng Ju
Key Laboratory of Electronic Equipment Structure Design, Ministry of Education, Xidian University, Xi’an 710071,
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China
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Highlights: There are the following highlights in this article: 1. A new equivalent circuit model based on radial displacement is presented that can predict the flow state in the channel through the variation of the pipe diameter. 2. An effective parameter equivalent method is proposed to precisely estimate energy attenuation due to the viscous force. 3. Experimental results confirm that the method is attracting.
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Abstract: The concentric squeeze-mode piezoelectric print-head (PPH) has been applied to the field of additive manufacturing, which requires a high deposition precision of droplets. To combine the
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self-sensing technique of a PPH, this paper presents a linear time-varying system equivalent circuit model based on radial displacement. This system is able to predict the flow state in the channel
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according to the variation of the pipe diameter. Compared with current models, this equivalent circuit model is more accurate in regard to energy attenuation. The equivalent thickness of the boundary layer is presented using a combination of boundary layer theory and oscillating plate flow to calculate the
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equivalent resistance of the viscous force. The experimental results show that the proposed method is more precise than the previous equivalent methods. To verify the model, a single trapezoidal pulse waveform and double trapezoidal pulse waveform were designed to realize the superposition of
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pressure and suppression of residual oscillation, respectively. The experimental results showed that the single trapezoidal pulse waveform based on the modelled pressure response was able to exactly realize the superposition of pressure and that the double trapezoidal pulse waveform based on the modelled
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pressure response was able to suppress the residual oscillation. The pressure and volume flow rate responses of the model are highly consistent with the experimental results in the time domain.
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Keywords: piezoelectric print-head, time-varying system, equivalent circuit
1. Introduction PPHs have been applied to such fields as printed electronics [1] and additive manufacturing [2] as an alternative to traditional printing applications. A PPH can produce tiny droplets of less than 17 pL on demand [3]. With the advantages of a high deposition precision and good control of the size and speed of droplets, the PPH has become an effective device for accurate material deposition in additive manufacturing, which not only simplifies the present technological processes but also reduces the scrap rate caused by multiple process steps.
The structure of a concentric squeeze-mode PPH consists of glass tube surrounded by a piezoelectric tube. When an external voltage is applied, the piezoelectric material drives the glass tube to shrink or expand radially, which also causes the fluid inside the PPH channel to flow and produce droplets at the nozzle. It is difficult to monitor the process through sensors. Due to the piezoelectric effect, piezoelectric material can act as not only a sensor (direct piezoelectric effect) but also as an actuator (inverse piezoelectric effect). In fact, piezoelectric material plays the two roles when it is working, which is called the self-sensing of piezoelectric material. The detailed description of the self-sensing can be found in the references [4, 5]. During the jetting process, the self-sensing of the piezoelectric material was used to measure the radial displacement of the glass tube. Kwon has achieved the
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measurement of the self-sensing signal through a differential amplifier and a matching capacitor [6]. The signal represents the deformation of piezoelectric material. For the concentric squeeze-mode PPH, the signal means the radial displacement of piezoelectric material, which cannot represent the flow
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state (pressure, flow velocity) inside the PPH channel. Therefore, it cannot be used to predict the flow state at the nozzle. Therefore, a great need exists to create a model to predict the flow state inside the PPH channel based on radial displacement.
To create the jetting model, Quentin Gallas [7] and Chiatto M [8] et al. proposed an equivalent circuit model for piezoelectric-driven synthetic jet actuators according to the lumped element method
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(LEM), and provided the parameter evaluation method of circuit components. Byung-Hun Kim [9] et al. designed a PPH with a shrinking structure at both ends of the channel and established a corresponding
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LEM. It was proven that LEM could be used to study the action mechanism of PPH effectively. For these studies, the pressure change caused by the excitation voltage is equivalent to the energy
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conversion of an ideal transformer. The voltage is converted to the pressure acting on the surface of the
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piezoelectric material. However, a large number of experimental measurements are required to determine the relevant equivalent parameters related to the structure and material, including the elastic force, damping force, and inertial force of the piezoelectric materials. Moreover, the pressure loss
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predicted by Darcy’s law [7, 9] regarding the equivalent fluid viscosity introduces large errors, as the Darcy formula is derived based on steady-state conditions, whereas the liquid response in the PPH channel is transient, among which the pressure loss predicted by the viscosity is larger than that under
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steady-state conditions. Despite their high accuracy in time consistency, these models are inaccurate in regard to energy attenuation and are less practical because of the cumbersome measurement parameters. In this paper, a novel equivalent circuit model is proposed that has more accurate equivalence to the
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flow resistance. The proposed model is practical and is able to predict the flow state in the channel according to a real-time measurement of the radial displacement of the piezoelectric material. The model in this paper is based on a more realistic physical mechanism to simulate the droplet
formation process. Because the behaviour of the tube flow can be simulated by circuits [10], the pressure and volume flow rate in a fluid are similar to the voltage and currents in the circuit,
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respectively; thus, the fluid’s inertial, viscous and elastic behaviours are equivalent to the behaviours of an inductor, a resistor and a capacitor, respectively. The equivalent parameter estimation method of the inertial force is derived from Navier-Stokes equations. The displacement of the fluid during ink jetting is so small that the boundary layer is far from being fully developed [11]. A viscous force is assumed to act in a thin layer (thickness of less than 10 µm) near the tube wall. The calculation method to determine the equivalent thickness of the boundary layer uses the combination of boundary layer theory and oscillating plate flow. Based on the thickness of the boundary layer, an equivalent parameter estimation method for the viscous force is given. To determine the nonlinear behaviour of the viscous
force at the nozzle caused by the contraction of the pipe diameter, the linear superposition method is applied to calculate the total viscous force. The expansion of the pressure chamber wall decreases the interior pressure, and the resulting low pressure causes the liquid from both sides of the chamber to flow into the pressure chamber. The process is the same as that in the circuit, i.e., the increase of a time-varying capacitor decreases the voltage at both ends. The low voltage makes charges flow into the capacitor from the connected circuits. Therefore, the change of the time-varying capacitor is equivalent to the change of the pressure chamber radius. Moreover, the ink jetting process of a single droplet is short enough to be assumed to be an adiabatic process. A method is derived to estimate the equivalent
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variable capacitance in a pressure chamber with a variable diameter using the state equation [10] (dp=c2dρ) under the adiabatic conditions. The aim of this paper is to provide an accurate equivalent circuit model based on radial displacement
to predict the flow state in a pipe to help improve the theoretical ink jetting capability and waveform
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adaptation of a PPH. Moreover, this model provides a means to realize semi-closed-loop control of the
flow state via the piezoelectric material’s self-sensing. In section 2, the schematic of the experimental system is introduced. In section 3, an equivalent circuit model and parameter estimation method are presented. In section 4, a recursive solution method of the model is presented that is used to calculate the dynamic response of the ramp step driving the waveform; comparisons with the experimental
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results show that the model is highly accurate in regard to time consistency and energy attenuation. In section 5, an analysis of the pressure and volume flow rate response in the channel based on the model
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is performed for a single trapezoidal pulse waveform and a double trapezoidal pulse waveform. The
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model is shown to be accurate according to the experimental results.
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2. Experimental setup The schematic of the experimental system is shown in Fig 1 [12-14]; this system consists of a CCD Camera, an LED strobe, a PPH, a controller, a pressure controller and a data processor. The oscilloscope (MSO4104B) is applied to monitor the dependability of the output signal of controller.
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The pressure controller generates negative pressure inside the PPH to balance the gravity of the liquid. The data processor is used to analyse photos captured by the CCD camera. The controller consists of an embedded system (STM32F103ZET6), an FPGA (EP1C3T144C8N), high-speed DA converters
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(AD9708), an LED driver (PT4115) and a high power amplifier (PA84). The embedded system is applied to create a trigger signal for jetting at specified frequencies. When the FPGA detects the trigger signal for jetting, it drives the DA convertor (output range: ± 5 V) to generate the low voltage driving
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waveform. The low voltage driving waveform is magnified (output range: ± 100 V) by the high power amplifier to drive the PPH. Moreover, when the FPGA detects the trigger signal for jetting and waits for a delay, the FPGA also generates an LED trigger signal and a camera trigger signal. There is a delay time between the LED trigger signals and the trigger signal for jetting. The image of a droplet at different times is captured by adjusting the delay time. These captured images are sent to the data
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processor sequentially via a USB. The resolution of the droplet edge in the captured image is controlled by adjusting the pulse width of the LED trigger signal. To improve the resolution ratio of the droplet edge in the captured image, the pulse width of the LED trigger should be as small as possible without lowering the image brightness. The detailed experimental theory can be found in the reference [15].
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Fig 1. Schematic of experimental system
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3. Lumped parameter model 3.1 Equivalent circuit model The structure of a circle squeeze-mode PPH MJ-AL-80 (a type of PPH fabricated by MicroFab, where “MJ-AL” is the name of a series of PPH, and “80” means the diameter of the nozzle is 80 µm) is
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shown in Figure 2. Because of the radial expansion of the chamber wall caused by the positive voltage acting on the piezoelectric surrounding [16], a negative pressure is built-up in the interior of the
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chamber because of the sudden volume change, which causes the liquid from both ends of the chamber to flow into the pressure chamber. The pressure inside the pressure chamber reduces to the ambient
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pressure when the chamber is filled by the liquid that has not been compressed. The chamber is further filled via the inertial force. When the liquid flow rate falls to zero, the positive pressure (elastic potential energy) inside the pressure chamber reaches the maximum. Next, the liquid in the pressure chamber flows to both sides of the chamber to release the pressure. The process repeats until all of the
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energy is consumed.
Fig 2. Structure of the MJ-AL-80 print-head The size of the piezoelectric print-head is small enough that the effects of gravity can be ignored [17]. The pressure at the exit of the nozzle chamber and left flow channel is standard atmospheric pressure (1[atm]). Figure 3 presents an equivalent circuit diagram of the squeeze-mode PPH. Because the
pressure in the liquid is equivalent to the voltage and the volumetric flow rate is equivalent to the current, the atmospheric pressure at the exit of the nozzle chamber and that at the left flow channel are equivalent to the power source Us. The radial displacement of the pressure chamber wall results in a change of the pressure inside the chamber, leading to flow-out/in of the liquid. This process is similar to the charge and discharge of a capacitor, as indicated by the equivalent time-varying capacitor C1 located in the middle of the pressure chamber. Because there is no obvious change in the size of the left flow channel and the left part of the pressure chamber connected during ink jetting, the liquid inside these parts can be assumed to be incompressible, and only the corresponding flow resistance and inertia force should be taken into account; the flow resistance and inertia force are equivalent to the resistance
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R1 and inductance L1, respectively. Because of the shrinkage of the diameter of the nozzle, it is difficult
for liquid to flow in the right parts. The compressibility of the liquid in the right flow channel and the
nozzle should be taken into account; this compressibility is equivalent to the capacitor C2 located in the
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connection between the pressure chamber and right flow channel, of which the flow resistance and
inertia force are equivalent to the resistance R2 and inductance L2, respectively. Similarly, the flow resistance and inertia force inside the nozzle are equivalent to the resistance R3 and inductance L3, respectively. The Laplace pressure characteristics caused by surface tension are equivalent to those of the capacitor C3. The power source Ud is used to ensure that the mathematical description of the
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relationship of voltages u1 and u2 with respect to their corresponding position is the same as that
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observed in the parameter equivalence.
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Fig 3. Equivalent circuit model of the inkjet print-head 3.2 Parameter estimation The estimations of the viscous force and inertia force inside the pipe are derived from the Navier-Stokes equation, which provides estimations of the equivalent resistance and equivalent inductance. The size of the structure of the PPH channel and the displacement of the liquid inside the
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channel are so small that the body force and convective acceleration can be neglected; thus, the corresponding incompressible Navier-Stokes equation is simplified as [18]:
u p 2u t
(1)
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Where ρ is the density, μ is the viscosity, u is the flow velocity, and p is the pressure. Because the
volume flow rate q is equivalent to the current in an equivalent circuit, the flow velocity u is transformed to the volume flow rate q by the expression q=πr2u. Similarly, because the pressure inside the pipe is equivalent to the voltage in an equivalent circuit, the pressure gradient ∇p is transformed to the pressure increase Δp multiplied the length of tube l:
p
l dq l 2 q r 2 dt r 2
(2)
Where r is the inner radius of PPH channel. Typically, the following approach is used to calculate pressure drops due to inertia and viscous forces. The pressure drop caused by an inertia force is
recorded as Δpi , and the pressure drop caused by the viscous force is recorded as Δpv:
l dq r 2 dt l pv 2 2 q r pi
(3) (4)
Because the viscous force is equivalent to a resistance, there should be a relationship similar to Δpv=Rq. It is obvious that equation (4) does not meet the requirements due to the term ∇2q. The viscous force affects the liquid in the channel within a small boundary layer. The viscous force can be viewed as the shear stress on the wall that consumes the liquid momentum. Therefore, the
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momentum-consumed boundary thickness δE is used to approximately calculate the shear stress on the wall [11]. E
0
u u 1 dr U U
(5)
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T
(6)
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u e k ( rt r ) , k U
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where u is the velocity in the boundary layer, U is the velocity that is not influenced by the boundary layer, and δ is the thickness of the boundary layer on the condition of u/U=0.99. The two thicknesses of the boundary layer are shown in Figure 4a. To obtain the expression of the momentum-consumed boundary thickness δE, combined with the method of Stokes second problem [11], the expression of u/U is presented:
where T is the oscillating period of the liquid inside the channel, and rt is the position of the tube
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wall. Combining equation (5) and equation (6), the expression of the momentum-consumed boundary thickness δE is given as:
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1 2k
(7)
In Figure 4b, as shown by the red short dotted line, the velocity of the liquid in the momentum-consumed boundary thickness δE is zero, and the velocity of the liquid beyond δE
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becomes the ideal velocity U, i.e., the velocity gradient at δE from the wall is infinite, and the situation is not reasonable. The approximate velocity profile is shown as a blue short dotted line with a boundary thickness δV , which is the twice the value of δE , in which the velocity gradient is equal to U/δV. The
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period lag caused by surface tension has a slight effect on δE ; thus, the liquid oscillating period T inside the channel can be calculated using sound reflection theory [19].
T
2lT c
(8)
To obtain the expression of the resistance estimation, with the approximate substitution of U/δV for
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the shear rate at the boundary layer, equation (4) is substituted in the form of equation (9):
pv
2 rl U 2lq 3 2 r V r V
(9)
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(a)
(b)
Fig 4. (a) Distribution of u/U, (1-u/U) and (1-u/U)u/U within the boundary layer [11]; (b) the velocity distribution within the pipe
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To realize the accurate equivalence to the nonlinear flow resistance in the nozzle, as shown in Figure 5, the structure of the nozzle is divided into N equal parts along the axis. These divided parts are all
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viewed as straight pipes, and the pressure drop of every part is calculated using equation (9). The total pressure drop can be expressed as:
2lq N ri3V
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po
(10)
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i 1
Fig 5. Nozzle segmentation schematic diagram
Assuming that there is a straight pipe with an equivalent radius re and length L, which have the same
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pressure drop as the nozzle, the equivalent radius is described by the following equation:
re
1 3
N
1 3 i 1 Nri
(11)
where N is the number of the segments of the nozzle. Equation (11) is used to calculate the equivalent radius of the nozzle. To understand the effect of the section number on the accuracy of re , the variation relationship between N and re for the MJ-AL-80 PPH is shown in Figure 6. re converges to
a fixed value with the increase of the section number. For MJ-AL-80 PPH, the nozzle radius is 40 µm,
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re is approximately 86.5 µm.
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Fig 6. Convergence of the equivalent radius with the increase in the number of segments
The ink jetting process of a single droplet is transient enough to be assumed to be adiabatic. The liquid obeys the state equation dp=c2dρ [10], where dp is the pressure increase, dρ is the density increase, and c is the sound speed of fluid material. The density increase in the pressure chamber can be expressed as:
t
t
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t0
t0
V (t )
(12)
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d (t0 )
(t0 ) V (t0 ) q1 (t )dt q2 (t )dt
In equation (6), ρ(t0) and V(t0) represent the density of the liquid and volume of the pipe at the initial
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moment, respectively. q1(t) is the liquid volumetric flow rate in the left pipe, q2(t) is the liquid
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volumetric flow rate in the right pipe, and V(t) is the volume of the piezoelectric section. The combination of equation (12) and the state equation is
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dp c 2 (t0 )
t
t
t0
t0
V (t0 ) q1 (t )dt q2 (t )dt V (t ) 2 c (t0 )
(13)
t
U (t )
Q(t0 ) idt
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In equation (13), c2ρ(t0) is a constant with a dimension of [Pa]. For a variable capacity, its voltage, charge and capacitance meet the following relationship: t0
C (t )
(14)
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where Q(t0) is the initial charge number of the capacitor, i is the current through the capacitor, C(t) is the capacitance of the capacitor, and U(t) is the voltage acted on the capacitor. To express equation (14) in the same form as equation (13), a power source Ud is connected oppositely in front of the capacitor. The voltages at both ends of the capacitor branch after the connection of the power source can be expressed as: t
u (t ) Ud
Q(t0 ) idt t0
C (t )
(15)
Equations (15) and (13) are consistent in terms of the mathematical expression. The combined system composed of a power source Ud and the corresponding capacitor is equivalent to the pressure response inside the channel; the position of the power source Ud is shown in Figure 3. A certain capacitor is equivalent to the Laplace pressure caused by surface tension. To estimate the
expression of the capacitor parameter, the average values of the flow-out/in volumes at the nozzle are roof-shaped [9]. The equivalent capacitance of the surface tension can be described as:
C
Q Vmen ro4 U pmen 3
(16)
Where Vmen is the roof-shaped volume of the fluid with the nozzle radius ro , pmen is the Laplace pressure, and σ is the coefficient of surface tension. Combining equations (3), (10), (11), (14) and (15), the calculation relationships of all of the Table 1. Parameter mapping relation
Equivalent circuit components
Mapping expression
r 2 L3 ro4 , c 2 (t0 ) 3
C1 (t )
r (t ) 2 L2 c 2 (t0 )
Voltage source Ud
c 2 (t0 )
R1 , R2 , R3
Inductance
L1 , L2 , L3
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2 L1 L2 2 2 L3 L2 2 2 Lo , , V r 3 V r 3 V re3
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Resistance
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Capacitance
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C2 , C3
Capacitance
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component parameters in the equivalent circuit in Figure 3 are listed in Table 1.
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L1 L2 2 L3 L2 2 Lo , , r2 r2 re2
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3.3 Circuit model Several equations are derived from Kirchhoff's voltage law and Kirchhoff’s current law to solve the equivalent circuit model shown in Figure 3[20]:
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duc1 (t ) 1 dC1 (t ) 1 1 uc1 (t ) i1 (t ) i2 (t ) dt C1 (t ) dt C1 (t ) C1 (t ) duc 2 (t ) 1 1 i2 (t ) i3 (t ) dt C2 C2 (t )
(17)
(18)
duc 3 (t ) 1 i3 (t ) dt C3
(19)
di1 (t ) R 1 1 uc1 (t ) 1 i1 (t ) Us Ud dt L1 L1 L1
(20)
di2 (t ) 1 R 1 uc1 (t ) uc 2 (t ) 2 i2 (t ) dt L2 L2 L2
(21)
di3 (t ) 1 R 1 1 uc 2 (t ) uc 3 (t ) 3 i3 (t ) Us Ud dt L3 L3 L3 L3
(22)
In the above equations, uc1(t), uc2(t), and uc3(t) represent the terminal voltages of the capacitor C1, C2 and C3, respectively. Choosing uc1(t), uc2(t), uc3(t), i1(t), i2(t), and i3(t) as state variables, equations (17)-(22) can be expressed as state equations of a linear time-varying system[21]:
x(t ) A(t )x(t ) Bu
(23)
du (t ) x c1 dt
duc 2 (t ) dt
duc 3 (t ) dt
di1 (t ) dt
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di3 (t ) , dt
di2 (t ) dt
u Us Ud
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0
0
0
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0
0
1 C2
0
0
R1 L1
0
0
1 L2
0
0
1 L3
0
0
0
1 L3
1 C1 (t )
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1 C1 (t )
0
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1 dC1 (t ) C (t ) dt 1 0 0 A(t ) 1 L1 1 L2 0
1 L1
T
1 0 , L3
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x uc1 (t ) uc 2 (t ) uc3 (t ) i1 (t ) i2 (t ) i3 (t ) , B 0 0 0 T
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In equation (23),
R2 L2 0
0 1 C2 0 0 0 R3 L3
For the PPH, it is significant to obtain the pressure and volume flow in the channel. Three equivalent
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voltages u1(t), u2(t), u3(t) and the corresponding currents i1(t), i2(t), and i3(t) are chosen as the output variables. The output equation can be expressed as:
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u1 (t ) 1 u (t ) 0 2 u3 (t ) 0 where y (t ) ,C i1 (t ) 0 i2 (t ) 0 0 i3 (t )
y(t ) Cx(t ) D
(24)
Ud 0 0 0 0 0 Ud 1 0 0 0 0 0 0 1 0 0 0 and D 0 . 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1 0
Equations (23) and (24) describe a state-space model of the PPH, which is a linear time-varying
system; there is no exact analytical solution of the model. 4. Solution of the model 4.1 Recursive solution In fact, it is difficult to obtain the analytical solution of equation (23). To solve the linear time-varying system, the block pulse function method shown in equation (25) is used to solve equation (23). As the ink jetting of a single droplet is transient, it is not necessary to use a long-time recursion to solve the model. The ink jetting of each droplet starts from the same initial condition to avoid the drift
—
(25)
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1 2 2 x I A x(t0 ) B1u1 1 1 t t 1 2 2 xk 1 t I Ak 1 t I Ak xk Bk uk Bk 1uk 1
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problems caused by the accumulation of long-time recursion errors.
—
—
—
where x k is the average value of the state variables, Ak is the state matrix, Bk is the input matrix, uk is the average value of the system input during the kth sampling period, I is the unit matrix, and Δt is the —
sampling time step length. The state variable x k+1 during the k+1th sampling period is obtained by the —
—
—
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recursion of Ak , Bk and uk during the kth sampling period, and the corresponding pressure response to
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equation (23) is given. 4.2 Results of LEM To verify the model and accuracy of the calculation method, the parameters of an ethanol solution
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shown in Table 2 are applied to the model to determine the system response inside the pressure chamber under the excitation of the ramp step signal. The response of the piezoelectric tube wall to the
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excitation is dynamic, during which shock, oscillation and other phenomena occur. With an accurate self-sensing measurement of the tube, the radial displacement of the tube wall is assumed to be a linear
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function of the excitation voltage given by:
dr V
(26)
Table 2. Ethanol material parameters
Ethanol solution
Speed of sound (m/s)
Density (kg/m3)
Viscosity (Pa·s)
Surface tension (N/m)
1120
807.73
0.0011933
0.02255
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Material
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where dr is the radial displacement of the pressure chamber wall under the excitation of the
impressed voltage, V is the voltage across the piezoelectric tube, and α(For MJ-AL-80 PPH, α≈0.32×10-9[m/V]) is the conversion coefficient corresponding to the transformation between the electrical signal and displacement and has dimensions of [m/V]. The response of the relevant state variables in the PPH channel over 200 µs under the excitation of the ramp step signal is shown in
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Figure 7.
(b)
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(a)
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Fig 7. (a) Transient pressure response and (b) transient volume flow rate response
Analysing the solution of the model shown in Figure 7a, it takes 3 µs for the pressure chamber wall to expand to the expected size. Meanwhile, the pressure inside the chamber wall reaches the minimum, followed by a pressure oscillation. When the pressure inside the chamber wall reaches the maximum, the lowest Laplace pressure and largest meniscus concave surface are found at the nozzle. When the
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pressure inside the chamber wall reaches the minimum, the highest Laplace pressure and largest meniscus convex surface are found at the nozzle. The four moments corresponding to the largest
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meniscus convex surface are 60.5 µs, 106.8 µs, 151.3 µs, and 196 µs. The transient pressure response of the pressure chamber is applied to realize the pressure superposition to enhance the ink jetting
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capacity. Therefore, the pressure inside the chamber wall is higher when a squeeze voltage is applied at
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36.75 µs in the ethanol solution. In the case of a standard trapezoidal pulse, the optimum pulse width is 23.75 µs (13 µs to 36.75 µs). Pressure superposition occurs when a squeeze voltage is applied at 83.5 µs, 129 µs, and 173.5 µs, with the effect weakening via viscous attenuation. The transient response of
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the volumetric flow rate inside the tube is shown in Figure 7b. The liquid in the left tube and right tube starts to flow after excitation to counteract the negative pressure and then flows back at the moment that the pressure in the chamber reaches the maximum. With an oscillating pressure, the volumetric
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flow rates in the left tube and in the right tube oscillate at the same frequency. There is a phase difference of pi between the two oscillations. According to the volumetric flow rate at the nozzle, the meniscus surface oscillates. Consistent with the former results, the moments corresponding to the four
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peaking values of the meniscus convex surface are 60.5 µs, 106.8 µs, 151.3 µs and 196 µs, which are in very good agreement with the experimental results based on the photogrammetric method. The photogrammetric experimental results at 10 µs are shown in Figure 8, with an actual sampling period
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of 1 µs, in good agreement with the theoretical solutions in regard to accuracy.
Fig 8. Experimental results of the ramp step drive waveform Compared with the current models, the model in this paper performs well in regard to energy attenuation and time accuracy. The shape of the meniscus at the peaking value under an excitation of a -36 V ramp step signal is shown in Figure 9a. The pixel distances between the meniscus and nozzle are measured according to image binarization using the same threshold of 20, 17, 14, and 11 pixels (1.1
µm/pixel). There is a direct correspondence relationship between the volumetric flow rate and shape of the meniscus at the nozzle. The experimental data and model data are divided by the peak values of the
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corresponding volume flow rate; the result is shown in Figure 9b.
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(b)
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(a)
Fig 9. (a) Shape of the meniscus at the peaking value under an excitation of a -36 V ramp step signal;
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(b) The normalized energy decays are compared between the two models and experimental results
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Based on the above analysis, the results of this model exhibit higher consistency with the experimental results compared with current models. This model realizes semi-closed-loop control of the flow state in the pipe using the combination of piezoelectric material displacement self-sensing
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technique, making it more practical than current models. 5. Results and discussion 5.1 Model results To further verify the accuracy of the proposed model, the standard single trapezoidal pulse waveform
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[4, 13] and double trapezoidal pulse waveform [22-25] are applied to drive an ethanol solution to form droplets. The standard single trapezoidal pulse waveforms cannot suppress the subsequent oscillation
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of the liquid, and normally, there are still strong oscillations at the meniscus after the formation of the main droplets. The satellite droplets come out of solution if the residual energy is high enough (one of the ways in which satellite droplets are formed). A double trapezoidal pulse waveform is designed to suppress the residual oscillation of the meniscus after the formation of the main droplets. The two
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driving waveforms are shown in Figure 10:
(a)
(b)
Fig 10. (a) Signal trapezoidal pulse waveform; (b) Double trapezoidal pulse waveform For the MJ-AL series PPHs, the wall of the pressure chamber expands when a positive voltage is applied, whereas the wall shrinks when a negative voltage is applied. In the case of a single trapezoidal pulse waveform, with the application of voltage with an amplitude of V1 during the time period t1, the pressure chamber expands. The delay time t2 is designed to wait for the pressure to reach the maximum to realize pressure superposition. Based on the analysis mentioned above, t2 is set to 24 µs for an ethanol solution. During the time period t3, the voltage is reduced to zero. Normally, t1 and t3 are set to 3 µs. The shrinking of the pressure chamber wall leads to a further increase of the pressure in the chamber, and the liquid at the nozzle is ejected to form droplets under the excitation of high pressure.
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The wall no longer moves during the subsequent periods as there is no excitation voltage
(fluid-structure interaction is neglected as the liquid is weakly coupled to the wall). The model responses of the pressure in the chamber and volume flow rate under the excitation of the single
trapezoidal pulse waveform are shown in Figure 11. It is obvious that a pulse width of 24 µs was able
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to realize pressure superposition; meanwhile, the volume flow rate at the nozzle increased, except for
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some residual oscillations during the subsequent time periods.
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Fig 11. Model response of the pressure in the chamber and the volume flow rate under the excitation of the single trapezoidal pulse waveform To suppress residual oscillations following the main droplets, the first trapezoidal pulse in the double trapezoidal pulse waveform plays the same role as the single trapezoidal pulse waveform, which is also applied to eject the liquid to form the main droplets, and the second trapezoidal pulse is applied to
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eliminate the residual pressure oscillations [4]. The delay time t4 is designed to allow the pressure to reach the minimum (the main droplets have been formed) because during the time period t5, a positive pressure increase occurs in the chamber. According to the transient response of the single trapezoidal pulse waveform, t4 should be set to 17 µs. In the same manner, a negative pressure increase in the
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chamber is found during the time period t7. The delay time t6 is designed to allow the pressure to reach the maximum (the compression of liquid in the chamber reaches the maximum); similarly, t6 is set to 24 µs while t5 and t7 are set to 3 µs. During time period t7, there is a further pressure decrease in the chamber, resulting in suppression of the pressure in the chamber and the oscillation of the meniscus surface. The model response of the pressure in the chamber and volume flow rate under the excitation of a double trapezoidal pulse waveform is shown in Figure 12.
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Fig 12. Model response of the pressure in the chamber and the volume flow rate under the excitation of a double trapezoidal pulse waveform 5.2 Experimental results Regarding the two driving waveforms mentioned in section 4.1, the photogrammetric method is applied during the experiment to record the suppression of the residual oscillation. The experimental
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results of the two driving waveforms are shown in Figure 13a and b.
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(a)
(b)
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Fig 13. (a) Experimental results of the single trapezoidal pulse waveform; (b) Experimental results of the double trapezoidal pulse waveform Through analysis of the experimental results, in the case of a single trapezoidal pulse waveform,
more liquid is ejected via the pressure residual oscillation following the main droplets, consistent with the theoretical results in the time domain. In the case of a double trapezoidal pulse waveform, there is no obvious meniscus residual oscillation during the experiment. Based on the analysis, the model is shown to be accurate based on the good agreement with the experimental results. 6. Conclusions The equivalent circuit model proposed in this paper, in keeping with the PPH in the physical
mechanism, is more accurate compared with the traditional equivalent circuit models regarding equivalent parameters. The nonlinear flow resistance at the nozzle calculated by utilizing an effective radius was shown to be convergent. Combined with the characteristics of the PPH, the recursive solution method of the system model not only makes the model more practical but also avoids the errors caused by long-time recursion. The response of the ramp step signal was analysed through experiments, revealing that the solution to the model was highly consistent with the experimental results in the time domain regarding the energy attenuation. To further verify the accuracy of the model, a single trapezoidal pulse waveform and a double trapezoidal pulse waveform were designed to suppress the residual oscillation, and the model was shown to be accurate according to the
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experimental results. Acknowledgments
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This work was supported by the Natural Science Foundation of China (Grant No.51575419) and the 111 Project (Grant No.B14042); The authors kindly acknowledge these supports.
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n-type organic field-effect transistors with an inkjet-printed ZnO electron injection layer, Applied Surface Science, 420 (2017) 100-104.
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[2] M. Kyobula, A. Adedeji, M.R. Alexander, E. Saleh, R. Wildman, I. Ashcroft, P.R. Gellert, C.J. Roberts, 3D inkjet printing of tablets exploiting bespoke complex geometries for controlled and
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of Piezoelectric-Driven Synthetic Jet Actuators, AIAA Journal, 41 (2003) 240-247. [8] M. Chiatto, F. Capuano, G. Coppola, L. de Luca, LEM Characterization of Synthetic Jet Actuators Driven by Piezoelectric Element: A Review, Sensors (Basel), 17 (2017). [9] B.-H. Kim, H.-S. Lee, S.-W. Kim, P. Kang, Y.-S. Park, Hydrodynamic responses of a piezoelectric driven MEMS inkjet print-head, Sensors and Actuators A: Physical, 210 (2014) 131-140.
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[10] Z.Z. DU Gong huan, Theory of Acoustics, 3 ed., Nanjing University Press, Nanjing, 2012. [11] D.C. ZHANG Zixiong, Viscous Fluid Mechanics, 2 ed., Peking University Press, Beijing, 2011. [12] K.S. Kwon, M.H. Jang, H.Y. Park, H.S. Ko, An inkjet vision measurement technique for high-frequency jetting, Rev Sci Instrum, 85 (2014) 065101. [13] K. Kye-Si, Waveform Design Methods for Piezo Inkjet Dispensers Based on Measured Meniscus Motion, Journal of Microelectromechanical Systems, 18 (2009) 1118-1125. [14] H. Dong, W.W. Carr, J.F. Morris, Visualization of drop-on-demand inkjet: Drop formation and deposition, Review of Scientific Instruments, 77 (2006).
[15] K.-S. Kwon, Experimental analysis of waveform effects on satellite and ligament behavior viain situmeasurement of the drop-on-demand drop formation curve and the instantaneous jetting speed curve, Journal of Micromechanics and Microengineering, 20 (2010). [16] MicroFab, Drive Waveform Effects, 1999. [17] S. Poozesh, N. Akafuah, K. Saito, New criteria for filament breakup in droplet-on-demand inkjet printing using volume of fluid (VOF) method, Korean Journal of Chemical Engineering, 33 (2016) 775-781. [18] Z.X. Zhu Baoshan, Fluid Mechanics, 1 ed., Peking University Press, Beijing, 2013. [19] D.B. Bogy, F.E. Talke, Experimental and Theoretical Study of Wave Propagation Phenomena in [20] B.R. L, Introductory Circuit Analysis, 9 ed., Hall,Inc, Prentice, 2000.
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[24] A.A. Khalate, X. Bombois, R. Babuška, H. Wijshoff, R. Waarsing, Performance improvement of a drop-on-demand inkjet printhead using an optimization-based feedforward control method, Control
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Author Biography Jianjun Wang received the B.E. degrees from Kun Ming University of Science and Technology, Kun’ming, China, in 2015 and he is currently working toward the Ph.D. degree at the School of Electro-Mechanical Engineering, Xidian University. He has been a Member at the Key Laboratory of Electronic Equipment Structure Design, Xidian University, since 2015. His research interests include inkjet printing, additive manufacturing etc. Jin Huang received the M.S. and Ph.D. degrees in mechanical engineering from Xidian University, Xi’an, China, in 1995 and 1999,respectively.He was with the Department of Mechanical Engineering,
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University of British Columbia, Canada, as a Visiting Researcher, from 2001 to 2002. In 1995, he
joined the School of Electro-Mechanical Engineering, Xidian University, where he is currently a Professor and Director at the Key Laboratory of Electronic Equipment Structure Design, Ministry of
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Education. He has published more than 80 papers in journals and conference proceedings, and he has
12 patents issued and ten patents pending. His research interests include electronic equipment modeling and control.Dr. Huang received the Chinese National Science and Technology Progress Prize in 2008 and 2013, respectively.
Ju Peng received the B.E. degrees from China University of Mining Technology, Xu’zhou, China, in
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2015 and he is currently working toward the Ph.D. degree at the School of Electro-Mechanical Engineering, Xidian University. He has been a Member at the Key Laboratory of Electronic Equipment
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Structure Design, Xidian University, since 2015. His research interests include inkjet printing, additive
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manufacturing etc.