sensors
Article A Simplified Analysis Method for the Piezo Jet Dispenser with a Diamond Amplifier
Guiling Deng 1, Na Wang 1, Can Zhou 1,2,* ID and Junhui Li 1
1 The State Key Laboratory of High Performance Complex Manufacturing and School of Mechanical and Electrical Engineering, Central South University, Changsha 410083, China; [email protected] (G.D.); [email protected] (N.W.); [email protected] (J.L.) 2 School of Information Science and Engineering, Central South University, Changsha 410083, China * Correspondence: [email protected]
Received: 24 May 2018; Accepted: 29 June 2018; Published: 2 July 2018
Abstract: Diamond amplifiers have been widely applied in Nano actuators and Robots. In order to study the dynamic characteristics of the diamond amplifier system which is used in the piezo jet dispenser, it is simplified as a spring-mass-damper system. The dynamic characteristics of the jet dispenser system are analyzed with the simplified method. The characteristics are also tested. The results agree with the simulation, which proves the method is feasible. It will provide a simplified and intuitive representation of the movement of the amplifier, and also provide reliable simulation and experimental platforms for jet dispensing analysis.
Keywords: piezo jet dispenser; simulation; diamond amplifier; simplified method
1. Introduction Dispensing is a significant technology in the microelectronics packaging industry [1–8]. Piezo jet dispensers have the advantages of small size, high resolution, high frequency, and low-energy consumption, so they have been widely applied [9–12]. The needle requires 200–300 µm or even greater displacement to achieve better jet performance [13]. The elongation rate of the piezoelectric material is about 0.1–0.15% [14]. The output displacement of the piezo stacks is not large enough for the jet dispenser. A mechanical amplifier is usually applied to improve dynamic characteristics of piezo jet dispenser [15–17]. Most designs use flexible hinges. When the jet dispenser works, high stresses in the hinges usually cause damage. To tackle the motion interference issue, a diamond amplifier is proposed [18–20]. The mechanical amplifier is an important part of the piezo jet dispenser. Performance of the piezo jet dispenser is determined by the amplifier. It is essential to study the dynamic characteristics of the diamond amplifier for jet dispenser design. Previous research mainly focused on the maximum displacement [21–23]. The lumped parameter method was used to analyze the dynamic characteristics of the piezo jet dispenser [16,20], but this method involves a heavy calculation burden. A spring-mass-damper system simplified method is proposed in this paper, where the diamond amplifier system is simplified as a single or double degree spring-mass-damper system with only a little calculation. The mathematical models and simulation models are established, and the dynamic characteristics are also tested. The tested results agree with the simulation, which proves that the simplified method is reliable. This study will provide a simple approach to designing or assessing a diamond amplifier-based system.
Sensors 2018, 18, 2115; doi:10.3390/s18072115 www.mdpi.com/journal/sensors Sensors 2018, 18, 2115 2 of 13
Sensors 2018, 18, x FOR PEER REVIEW 2 of 13 2. Experimental System Sensors2. Experimental 2018, 18, x FOR System PEER REVIEW 2 of 13 TheSensors operating 2018, 18, x FOR principle PEER REVIEW of the piezo jet dispenser with a diamond amplifier is the following:2 of 13 adjust2. theExperimentalThe needle operating to S makeystem principle it come of the into piezo contact jet dispenser with the with nozzle a diamond and form amplifier a closed is the chamber. following: Then, applya2djust. pneumatic Experimental the needle pressure S ystemto make to the it come fluid into and contact makeit with flow the into nozzle the chamber. and form Aa pulseclosed voltagechamber. is Then, applied to The operating principle of the piezo jet dispenser with a diamond amplifier is the following: the piezoapply stack pneumatic to cause pressure a vertical to the stretching fluid and make motion it flow of the into amplifier. the chamber. Consequently, A pulse voltage the needle is applied and the atodjust theT phetheiezo operating needle stack toto principle causemake a it ve comeofrtical the into stretchingpiezo contact jet dispensermotion with theof withthe nozzle amplifier a diamond and .form Consequently, amplifier a closed ischamber. thethe needle following Then, and: amplifier obtain an up-and down motion. The fluid, driven by the pneumatic pressure, flows into the applytheadjust amplifier pneumaticthe needle obtain pressure to an make up- and toit thecome down fluid into motion. and contact make The withit fluid, flow the driveninto nozzle the by chamber. and the pneumaticform A a pulse closed pressure, voltage chamber. flowis applied Then,s into apply pneumatic pressure to the fluid and make it flow into the chamber. A pulse voltage is applied nozzle.tothe the Whennozzle. piezo theWhen stack needle tothe cause needle hits a ve thehitrticals nozzle,the stretchingnozzle the, the fluid motion fluid is is rapidlyof rapidly the amplifier ejected . throughConsequently, through the the nozzle nozzlethe needleand andbreak and breakss to the piezo stack to cause a vertical stretching motion of the amplifier. Consequently, the needle and fromthefrom it with amplifier it with fluid fluid obtain momentum. momentum. an up-and The T downhe system system motion. mainlymainly The includes includesfluid, driven Excitation Excitation by the voltage pneumatic voltage,, PZT, PZT,pressure, Wedge, Wedge, flowAmplifier,s Amplifier, into the amplifier obtain an up-and down motion. The fluid, driven by the pneumatic pressure, flows into GuidingtheGu inozzle.ding Part, Part, Needle, When Needle, the Filling needle Filling Pressure, hit Pressure,s the nozzle Adhesives, Adhesives,, the fluid and is rapidly No Nozzlezzle ejectedExit, Exit, as asthrough shown shown in the Figure in nozzle Figure 1. and 1. breaks fromthe nozzle. it with When fluid momentum.the needle hit Tshe the system nozzle mainly, the fluid includes is rapidly Excitation ejected voltage through, PZT, the Wedge,nozzle and Amplifier, breaks Gufromiding it with Part, fluid Needle, momentum. Filling Pressure, The system Adhesives, mainly includes and No Excitationzzle Exit, as voltage shown, PZT, in Figure Wedge, 1. Amplifier, Guiding Part, Needle, Filling Pressure, Adhesives, and Nozzle Exit, as shown in Figure 1.
Figure 1. Piezo jet dispenser. Figure 1. Piezo jet dispenser.
The experimental system consistsFig ofure four 1. Piezo parts: jet a dispenser piezo jet. dispenser, a signal generator, a glue Thesupply experimental system, and systema laser displacement consistsFig ofure four sensor 1. Piezo parts: system jet adispenser piezo. The experiment jet. dispenser, facilities a signal used generator, to measure a glue supplythesystem, dynamicThe experimental and characteristics a laser system displacement of theconsists amplifier of sensorfour are parts: shown system. a inpiezo Fig The urejet experiment dispenser,2; the structure a signal facilities diagram generator used is shown, toa glue measure in supplyThe system experimental, and a laser system displacement consists of foursensor parts: system a piezo. The jet experiment dispenser, facilitiesa signal generatorused to measure, a glue the dynamicFigure 3. characteristics of the amplifier are shown in Figure2; the structure diagram is shown in thesupply dynamic system characteristics, and a laser ofdisplacement the amplifier sensor are shown system in. FigTheure experiment 2; the structure facilities diagram used isto shown measure in FigureFigurethe3. dynamic 3. characteristics of the amplifier are shown in Figure 2; the structure diagram is shown in Figure 3.
Figure 2. Experimental facilities used to measure the amplifier.
Figure 2. Experimental facilities used to measure the amplifier. Figure 2. Figure Experimental2. Experimental facilitiesfacilities used to to measure measure the the amplifier. amplifier.
Figure 3. Structure diagram for the amplifier’s experimental facilities.
Figure 3. Structure diagram for the amplifier’s experimental facilities.
Figure 3. Structure diagram for the amplifier’s experimental facilities. Figure 3. Structure diagram for the amplifier’s experimental facilities.
Sensors 2018, 18, 2115 3 of 13 Sensors 2018, 18, x FOR PEER REVIEW 3 of 13
The needle’s displacement is measured by the KEYENCE LK LK-G-G laser sensor sensor,, whose sampling frequency is 2 200 K KHz.Hz. The The control control signal signal,, generated generated by by an an AFG AFG-3102-3102 signal signal generator generator from from Tektronix, Tektronix, Inc ( (Beaverton,Beaverton, ON ON,, USA USA),), is amplified amplified by XE XE-500-500 power amplifier. amplifier. As the pulse voltage is supplied to the piezo stacks stacks,, t thehe diamond amplifier amplifier with the needle is fixed fixed on the table table,, and a laser sensor is fixedfixed on the top of the the needle. needle. When When the the experimental experimental system works, a laser beam shoots at the needle vertically, andand thethe real-timereal-time displacementdisplacement isis testedtested andand recorded.recorded.
3. Dynamic Models of the Jet Dispenser 3. Dynamic Models of the Jet Dispenser The jet jet dispenser dispenser consists consists of of the the piezo piezo stacks, stacks, a diamond a diamond amplifier amplifier,, and and a special a special injector. injector. To simplifyTo simplify the themotion motion process process of the of the system, system, a dynamic a dynamic analysis analysis of the of the system system is carried is carried out. out. 3.1. Mathematical Model of the PZT 3.1. Mathematical Model of the PZT Output characteristics of the piezo stacks are mainly determined by input parameters and preload. Output characteristics of the piezo stacks are mainly determined by input parameters and Performance of piezo stacks are analyzed with different technical parameters. Combined with the preload. Performance of piezo stacks are analyzed with different technical parameters. Combined knowledge of spring-mass-damper system dynamics analysis, the dynamics analysis of piezo stacks with the knowledge of spring-mass-damper system dynamics analysis, the dynamics analysis of can be carried out. piezo stacks can be carried out. The material of piezo stacks used in this experiment is PZT5. Material properties are density The material of piezo stacks used in this experiment is PZT5. Material properties are density 7500 kg/m3, elastic modulus 36.7 Gpa, Poisson’s ratio 0.32. The technical parameters of each of the 7500 kg/m3, elastic modulus 36.7 Gpa, Poisson’s ratio 0.32. The technical parameters of each of the piezo stacks are listed in Table1. piezo stacks are listed in Table 1. Table 1. Piezo stacks technical parameters. Table 1. Piezo stacks technical parameters. × × × × µ µ SSizeize A × BB × LL (mm (mm × mmmm × mm)mm) Maximum Maximum D Displacementisplacement (μm/v) ( m/v) Stiffness Stiffness (N/μm) (N/ m) × × 77 × 88 × 1818 0.1044 0.1044 114 114
TThehe relationship between the force and displacement under different working voltages is shown in Fig Figureure 44..
Figure 4. Relationship between the force and displacement under different working voltages. Figure 4. Relationship between the force and displacement under different working voltages.
When the load is constant, the larger the operating voltage, the larger the output displacement of theWhen piezo the stack loads. When is constant, the displ theacement larger the is operating constant, voltage,the output the of larger the piezo the output stacks displacement is positively correlatedof the piezo with stacks. the operating When the voltage. displacement When the is constant, operating the voltage output of ofthe the piezo piezo stack stackss is constant, is positively the outputcorrelated displacement with the operating of the piezo voltage. stacks Whenis negatively the operating correlated voltage with the of the load. piezo As the stacks load is increases, constant, the output output displacement displacement decreases. of the piezo The piezo stacks stack is negativelys have the same correlated stiffness with under the different load. As operating the load voltages.increases, the output displacement decreases. The piezo stacks have the same stiffness under different operatingWhen voltages. the working voltage of the piezo stacks is 130 V, the relationship between the displacement S (μm) and the force F (N) is shown in the Equation (1),
SF 0.0088 13.57 , (1)
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When the working voltage of the piezo stacks is 130 V, the relationship between the displacement S (µm) and the force F (N) is shown in the Equation (1),
S = −0.0088F + 13.57, (1)
Since the motion of piezo stacks is equivalent to the forced vibration of a damped single degree of freedom system, its dynamic analysis can be carried out according to that of the forced vibration of a damped single degree of freedom system. In this paper, three piezo stacks are connected in series, whose total length is 54 mm. Since it is symmetrical, only half of the structure is needed to establish the static models. Then, the following Equation (2) can be obtained for piezo stacks,
.. . me1x + c1x + KV x = KV x0U − F0 − F1, (2) where me1 = m1/2 is the dynamic equivalent mass of the piezo stack. m1 is the mass of the piezo stack. c1, KV, and x are the damping coefficient, the stiffness and the displacement of the piezo stack respectively. F1 and F0 are the blocked force and preload on the piezo stack U is the voltage applied and x0 is the free displacement of the piezo stacks under a voltage unit.
3.2. Mathematical Model of the Displacement Output System The diamond amplifier has two degrees of freedom in horizontal and vertical direction. First, the dynamic analysis of the jet dispenser is carried out only from the force analysis. It is simplified according to the analysis of double degree of freedom. Second, considering that there is a certain multiplier relationship between the horizontal and vertical displacement of the diamond amplifier, the force in the horizontal direction is equivalent to the force in the vertical direction; then, only the vertical motion needs to be analyzed. The analysis is simplified into a single degree of freedom system dynamics analysis.
3.2.1. Double Degree of Freedom Output System The displacement of the amplifier consists of two directions: horizontal and vertical. Through the amplifier, the input displacement in the horizontal direction is amplified and output in the vertical direction. Because the diamond amplifier is elastomer, it can be analyzed according to the spring-mass-damper system, then its dynamic equation can be obtained. The diamond amplifier is affected by FH horizontally and FV vertically. The output displacement is linear superposition of the displacement caused by FH and FV. The relationships between x, y and FH, FV are shown in Equations (3) and (4).
FH FV x = − 0 , (3) K1 K2
FH FV y = 0 − , (4) K1 K2 where K1 and K2 are the stiffness of the amplifier in the horizontal direction and vertical direction, 0 0 respectively. K 1 is the displacement coefficient affected by FH in vertical direction. K 2 is the displacement coefficient affected by FV in horizontal direction. Then, Equations (5) and (6) can be obtained:
FH = a1x − b1y, (5)
FV = a2x − b2y, (6) Sensors 2018, 18, 2115 5 of 13
When the mass of the amplifier cannot be neglected, the force analysis of the amplifier and the equivalent mass of the ejector elastic system can be used to obtain the dynamic Equation (7).
.. . me2y + c2y + K2y = FV, (7)
Because of the symmetry of the diamond amplifier, its vertical direction can be equivalent to a
Sensorsspring-mass 2018, 18, system,x FOR PEER as shownREVIEW in Figure5. 5 of 13 Sensors 2018, 18, x FOR PEER REVIEW 5 of 13
FigFigureure 5 5.. SSpring-masspring-mass diagram diagram of of the the amplifier amplifier.. Figure 5. Spring-mass diagram of the amplifier. From Figure 5 we can see that KH = KD = 2 × K2. From Figure5 we can see that KH = KD = 2 × K2. FromFrom EquationFigure 5 swe (2) can and see (5 )that–(8) KcanH = be KD obtained, = 2 × K2. From Equations (2) and (5)–(8) can be obtained, From Equations (2) and (5)–(8) can be obtained, mxcxKx KxU F F .. e1. 1VV 0 00 1 + + = − − me1xmmxcxKxe1yc1x c 1 y K KVVVx y KxU FKV 0x0 0U0 F0 F F0 1 F1 .. e2. 2 2 V , m y + c y + K y = F (8) e2Fame2y2x c 2 yby 2 K 2 y FVV V 2 2 , ,( (8)8) FV=FFaa2Kx −xx b2byy 11V 2 2 F1 = K1x F11 K x where c2 is damping coefficient of the displacement output system. The equivalent mass of the verticalwherewherec 2cspring2is is damping damping-mass- coefficientdamper coefficient system of theof the displacementincludes displacement the equivalent output output system. mass system. The of equivalentthe The diamond equivalent mass amplifier of mass the vertical in of the the verticalspring-mass-dampervertical directionspring-mass, the- massdamper system of theincludessystem piezo includes thestacks, equivalent the the mass equivalent mass of the of wedgemass the diamond of and the the diamond amplifiermass of amplifierthe in needle. the vertical in The the simplifieddirectionvertical direction, the spring mass-,mass the of the mass-damper piezo of the stacks, diagram piezo the stacks, massis shown ofthe the massin wedge Fig ofure the and 6. wedge the mass and of the the mass needle. of the The needle. simplified The spring-mass-dampersimplified spring-mass diagram-damper is showndiagram in is Figure shown6. in Figure 6.
Figure 6. Spring-mass-damper diagram. FigureFigure 6.6. Spring-mass-damperSpring-mass-damper diagram.diagram. The equivalent mass of the vertical spring-mass-damper system is shown in the Equation (9). The equivalent mass of the vertical spring-mass-damper system is shown in the Equation (9). The equivalent mass of the vertical spring-mass-damper3mm1 0 m2 / 6 systemm2 is shown in the Equation (9). mme23 , (9) 3mm1 260 m2 / 6 m2 mme233m + m + m /6 m, (9) m = 1 0262 + m + 2 , (9) The equivalent mass of half ofe2 the piezo stacks2 is shown 3in the6 Equation (10). The equivalent mass of half of the piezo stacks is shown in the Equation (10). m m 1 , (10) e1 m2 m 1 , (10) e1 2 where m2, m3, m0 are the mass of the diamond amplifier, the mass of the needle and the mass of the wedgewhere respectively.m2, m3, m0 are the mass of the diamond amplifier, the mass of the needle and the mass of the wedge respectively. 3.2.2. Single Degree of Freedom Output System 3.2.2. Single Degree of Freedom Output System The material of diamond amplifier used in this experiment is 65 Mn. In this study, the key geometricThe materialand material of diamond parameters amplifier of the diamondused in thisamplifier experiment are listed is 6 in5 MTabn. leIn 2. this study, the key geometric and material parameters of the diamond amplifier are listed in Table 2.
Sensors 2018, 18, 2115 6 of 13
The equivalent mass of half of the piezo stacks is shown in the Equation (10). m m = 1 , (10) e1 2 where m2, m3, m0 are the mass of the diamond amplifier, the mass of the needle and the mass of the wedge respectively.
3.2.2. Single Degree of Freedom Output System The material of diamond amplifier used in this experiment is 65 Mn. In this study, the key geometric and material parameters of the diamond amplifier are listed in Table2. Sensors 2018, 18, x FOR PEER REVIEW 6 of 13 Sensors 2018, 18,Table x FOR PEER 2. Key REVIEW geometric and material parameters of the diamond amplifier. 6 of 13 Table 2. Key geometric and material parameters of the diamond amplifier. Table 2. Key geometricParameters and material parameters of the Values diamond amplifier. Parameters Values ◦ FlexureFlexure angleParameterθ angle( ) θs (°) Value8 8s FlexureFlexure thicknessFlexure thickness tangle(mm) θt (mm)(°) 1.48 1.4 Flexure breadth d (mm) 10 FlexureFlexure thicknessbreadth d t (mm) (mm) 1.410 Flexure length L (mm) 30 Flexure breadth d (mm) 10 FlexureE (Gpa) length L (mm) 30 211 DensityFlexureρ (kg/mE leng (G3pth)a) L (mm) 211307820 Poisson’sDensity ratioE (G ρbp (kg/ma) 3) 78202110.288 DensityPoisson ρ’s (kg/mratio b3 ) 0.2887820 Poisson’s ratio b 0.288 The diamondThe diamond amplifier amplifier can can be be considered considered asas aa singlesingle degree degree of of freedom freedom elastic elastic system. system. The diamondThe diamond amplifier amplifier is depictediscan depicted be considered in in Figure Figure as7 7.a. single degree of freedom elastic system. The diamond amplifier is depicted in Figure 7.
FigureFigure 7. 7.Diamond Diamond amplifier. amplifier. Figure 7. Diamond amplifier. Since the symmetrical of the diamond amplifier, only a quarter of the structure is needed to SinceestablishSince the the symmetricalthe static symmetrical model, ofas of theshown the diamond diamo in Figurend amplifier,amplifier 8. , only only a a quarter quarter of ofthe the structure structure is needed is needed to to establishestablish the static the static model, model, as shownas shown in in Figure Figure8 .8.
Figure 8. Force diagram of one arm of the diamond amplifier . Figure 8. Force diagram of one arm of the diamond amplifier. Figure 8. Force diagram of one arm of the diamond amplifier. Considering the force equilibrium along the x-axis and the moment equilibrium, the following relationsConsidering can be obtained: the force equilibrium along the x-axis and the moment equilibrium, the following relations can be obtained: fA f B f f PZT /4, (11)
fA f B f f PZT /4, (11) 2M fL sin , (12) 2M fL sin , (12) where M is a supplemented moment to ensure that the deflection angles at the both ends of link AB remainwhere M zero. is a Lsupplemented and θ are structural moment parameters to ensure ofthat the the amplifier deflection as shownangles inat Ftheigure both 7. ends of link AB remain zero. L and θ are structural parameters of the amplifier as shown in Figure 7.
Sensors 2018, 18, 2115 7 of 13
Considering the force equilibrium along the x-axis and the moment equilibrium, the following relations can be obtained: fA = fB = f = fPZT/4, (11) 2M = f L sin θ, (12) where M is a supplemented moment to ensure that the deflection angles at the both ends of link AB remain zero. L and θ are structural parameters of the amplifier as shown in Figure7. According to the principle of conservation of energy, work done by fPZT is transformed into the bending potential energy and the tensile deformation energy. Then, the following Equation (13) can be obtained for the amplifier.
1 Z L f 2(x) Z L M2(x) f ∆x = dx + dx, (13) 2 0 2EA(x) 0 2EI(x) where ∆x, M(x) and f (x) denote the input displacements, the moments in the elastic beam and the axial tension respectively. A(x) and I(x) are the area and moment of inertia of the corresponding cross-section about the neutral axis. E is Young’s modulus. Based on Hooke’s law, the following relation is obtained:
f (x) = f cos θ = Kl∆l, (14) where Kl and ∆l are, respectively, the translational stiffness and the axial tensile displacement of the amplifier. The moment in the elastic beam at the end point x changes along the neutral axis, and it can be obtained as: M(x) = M − f x sin θ = f sin θ(L/2 − x), (15)
In view of Equations (13)–(15), the strain energy produced by bending deformation in the amplifier can be obtained as: cos2θ L2 sin2 θ ∆x = ( + ) f , (16) Kl 12Kθ where Kθ is the rotational stiffness of the diamond amplifier. From the Euler–Bernoulli beam theory, the bending equation of a flexure element is:
d2η M(x) = , (17) dx2 EI(x)
Then, the output displacement in the amplifier can be deduced as:
M(x) L2 f sin θ cos θ ∆y = η cos θ = cos θ × x dx = , (18) EI(x) 12Kθ
In view of Equations (16) and (18), the displacement amplification ratio of the diamond amplifier can be obtained as: 2∆y K × L2 × sin θ × cos θ R = = L , (19) 2 2 2 2∆x 12Kθ cos θ + KL × L × sin θ According to the displacement amplification ratio of the amplifier, the parameters x and y can be connected by the Equation (20). y = 2H = x × 2R, (20)
The motion of the vertical direction corresponds to the force in horizontal direction. In the vertical direction, the amplifier and the needle form a spring-mass-damper system which is subjected to an external force of F = fPZT/R. Sensors 2018, 18, 2115 8 of 13
The single degree of freedom displacement output system mathematical model is shown in Equations (21) and (22). .. . mey + c2y + Ky = F, (20) Sensors 2018, 18, x FOR PEER REVIEW 8 of 13 .. . mey + c2y + K2y = (Kvx0U0 − F0 − K1y/2R)/R, (21) 3.3. Numerical Analysis Model 3.3. Numerical Analysis Model A pulse voltage is applied to the piezo stacks. The amplitude of the pulse voltage is 130 V, the highA-level pulse time voltage is 6 ms is appliedand the frequency to the piezo is 100 stacks. Hz. The The dynamic amplitude characteristics of the pulse simulation voltage is model 130 V, of thethe high-level piezo stack time is established is 6 ms and thewith frequency Simulink is model. 100 Hz. The The parameters dynamic characteristicsof the simulation simulation model are model listed ofin the Tab piezole 3. stack is established with Simulink model. The parameters of the simulation model are listed in Table3. Table 3. Parameters of the dynamic model. Table 3. Parameters of the dynamic model. Parameters Values Parametersm0 (g) Values8.6
m0 (g)m1 (g) 8.67.56 m1 (g)m2 (g) 7.5625 m (g) 25 2 m3 (g) 5.17 m3 (g) 5.17 C1 120 C1 120 2 C2 C 40.9640.96 F0 (N)F0 (N) 140140 µ KV (N/KV (m)N/μm) 114114
4.4 Results. Results and and Discussion Discussion
4.1.4.1 The. The Results Results of of the the Jet Jet Dispenser Dispenser for for the the Uper Uper Analysis Analysis StaticStatic analysis analysis of of the the amplifier amplifier was was carried carried out out by by ANSYS. ANSYS. The The magnifying magnifying mechanism mechanism is is fixed fixed at at thethe top top surface surface and and its its lower lower end end is freeis free in in the the vertical vertical direction. direction.FH FandH andFV FareV are applied applied in in the the horizontal horizontal andand vertical vertical directions directions respectively. respectively. The The deformations deformations of of the the amplifieramplifier areare shownshown inin FigureFigure9 9a,b.a,b.
(a) (b)
FigureFigure 9. 9Diamond. Diamond amplifier amplifier deformation: deformation: (a ()a Deformation) Deformation under under horizontal horizontal force; force; (b ()b Deformation) Deformation underunder vertical vertical force. force.
Relationship between the force and displacement of the diamond amplifier is shown in Figure 10. Relationship between the force and displacement of the diamond amplifier is shown in Figure 10. The K1, K’0 1 and K2, K’0 2 can be obtained. The results are listed in Table 4. The K1, K 1 and K2, K 2 can be obtained. The results are listed in Table4.
Figure 10. Relationship between the force and displacement.
Sensors 2018, 18, x FOR PEER REVIEW 8 of 13
3.3. Numerical Analysis Model A pulse voltage is applied to the piezo stacks. The amplitude of the pulse voltage is 130 V, the high-level time is 6 ms and the frequency is 100 Hz. The dynamic characteristics simulation model of the piezo stack is established with Simulink model. The parameters of the simulation model are listed in Table 3.
Table 3. Parameters of the dynamic model.
Parameters Values m0 (g) 8.6 m1 (g) 7.56 m2 (g) 25 m3 (g) 5.17 C1 120 C2 40.96 F0 (N) 140 KV (N/μm) 114
4. Results and Discussion
4.1. The Results of the Jet Dispenser for the Uper Analysis Static analysis of the amplifier was carried out by ANSYS. The magnifying mechanism is fixed at the top surface and its lower end is free in the vertical direction. FH and FV are applied in the horizontal and vertical directions respectively. The deformations of the amplifier are shown in Figure 9a,b.
(a) (b)
Figure 9. Diamond amplifier deformation: (a) Deformation under horizontal force; (b) Deformation under vertical force.
SensorsRelationship2018, 18, 2115 between the force and displacement of the diamond amplifier is shown in Figure9 of10 13. The K1, K’1 and K2, K’2 can be obtained. The results are listed in Table 4.
FigFigureure 10 10.. RRelationshipelationship between between the the force force and and displacement. displacement. Sensors 2018, 18, x FOR PEER REVIEW 9 of 13 Table 4. Stiffness in the horizontal and vertical directions. Table 4. Stiffness in the horizontal and vertical directions. Direction K /N/µm K /N/µm Direction KHH/N/μm KV/N/μm V FH FH 13.0413.04 1.05 1.05 FV 2.04 0.15 FV 2.04 0.15
0 0 TheThe values values of of KK11, ,K’K1 1andand KK2,2 K’, K2 in2 in the the Equation Equationss (5 (5)) and and (6 (6)) can can be be obtained. obtained. AccordingAccording to to Equation Equationss (8 (8)) and and (22 (22),), Simulink Simulink is isused used to toobtain obtain the the vertical vertical displacement displacement curves curves of theof theneedle. needle. The The experimental experimental method method is used is used to toget get the the displacement displacement of of the the needle. needle. A A square square wave wave voltagevoltage is is applied applied.. The The voltage voltage amplitude amplitude is 130 is 130 V, the V, thetime time is 6 isms, 6 ms,and andthe frequency the frequency is 100 is Hz. 100 T Hz.he displacementThe displacement curves curves of the of needle the needle under under double double degree degree and single and single degree degree dynamic dynamic models models and andthe experimentalthe experimental system system in one in onecycle cycle are areshown shown in Fig in Figureure 11 11a, a,and and the the velocity velocity curves curves of of the the needle needle are are shownshown in in Figure Figure 11b 11b..
(a) (b)
FigureFigure 11 11.. DynamicDynamic characteristics characteristics of of the the needle: needle: (a (a) )The The vertical vertical displacement displacement graph; graph; ( (bb)) The The vertical vertical velocityvelocity graph. graph.
4.2. Another Piezo Jet Dispenser with New Diamond Amplifier Parameters 4.2. Another Piezo Jet Dispenser with New Diamond Amplifier Parameters
44.2.1..2.1. Numerical Numerical A Analysisnalysis M Modelodel InIn order order to to make make the the results results more more reliable, reliable, a a set set of of theoretical theoretical calculations calculations and and finite finite element element simulationssimulations comparation comparation under under the the changes changes of of the the amplifie amplifier’sr’s parameters parameters have have been been given given as as follows follows.. NewNew geometric geometric and and material material parameters parameters of of the the diamond diamond amplifier amplifier are are listed listed in Table 5 5..
Table 5. Key geometric and material parameters of the diamond amplifier.
Parameters Values Flexure angle θ (°) 11 Flexure thickness t (mm) 1.4 Flexure breadth d (mm) 10 Flexure length L (mm) 30 E (Gpa) 211 Density ρ (kg/m3) 7820 Poisson’s ratio b 0.288
Through the results and discussion in Section 3, the displacements of the new diamond amplifier under FH and FV are got and shown in Figure 12. The new K1, K’1 and K2, K’2 can be obtained. The results are listed in Table 6.
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Table 5. Key geometric and material parameters of the diamond amplifier.
Parameters Values Flexure angle θ (◦) 11 Flexure thickness t (mm) 1.4 Flexure breadth d (mm) 10 Flexure length L (mm) 30 E (Gpa) 211 Density ρ (kg/m3) 7820 Poisson’s ratio b 0.288
Through the results and discussion in Section3, the displacements of the new diamond amplifier 0 0 under FH and FV are got and shown in Figure 12. The new K1, K 1 and K2, K 2 can be obtained. TheSensors results 2018, 18 are, x FOR listed PEER in TableREVIEW6. 10 of 13
Figure 12. Relationship between the force and displacement. Figure 12. Relationship between the force and displacement.
Table 6. Stiffness in the horizontal and vertical directions. Table 6. Stiffness in the horizontal and vertical directions.
Direction KH/N/μm KV/N/μm Direction K /N/µm K /N/µm FH H8.18 0.86 V FH FV 1.688.18 0.17 0.86 FV 1.68 0.17
As a result, the values of K1, K’1 and K2, K’2 can be obtained in Equations (5) and (6), respectively. 0 0 As a result, the values of K1, K 1 and K2, K 2 can be obtained in Equations (5) and (6), respectively. 4.2.2. Dynamic Simulation Analysis of Piezo Jet Dispenser with a Diamond Amplifier 4.2.2. Dynamic Simulation Analysis of Piezo Jet Dispenser with a Diamond Amplifier In the same experimental conditions as the previous example, the parameters of the new amplifierIn the and same the experimental values of the conditions obtained as variables the previous are example,substitute thed into parameters the Equation of thes new (8) amplifierand (22). andSimulink the values is used of to the obtain obtained the variablesvertical displacement are substituted curves into of the the Equations needle un (8)der and double (22). Simulinkdegree and is usedsingle to degree obtain dynamic the vertical models. displacement Then, the curves vertical of the displacement needle under curve double of degreethe piezoelectric and single driving degree dynamicdispenser models. is obtained Then, through the vertical finite element displacement analysis curve with Comsol. of the piezoelectric driving dispenser is obtainedThe throughmesh of the finite piezo element jet dispenser analysis with Comsol.a diamond amplifier is shown in the Figure 13. The mesh of the piezo jet dispenser with a diamond amplifier is shown in the Figure 13.
Figure 13. Mesh of the piezo jet dispenser with a diamond amplifier.
The multi physics field coupling simulation of the piezo jet dispenser with a diamond Amplifier is carried out by using the piezoelectric module of Comsol. With Comsol, the voltage function with time applied to piezoelectric ceramics in one cycle is approximate as the Equation (23). 0 (0t 0.001) 130000tt 130 (0.001 0.002) Vt() 130 (0.002t 0.008) , (22) 13000 (tt 0.008) 130 (0.008 0.009) 0 (0.009t 0.010)
Sensors 2018, 18, x FOR PEER REVIEW 10 of 13
Figure 12. Relationship between the force and displacement.
Table 6. Stiffness in the horizontal and vertical directions.
Direction KH/N/μm KV/N/μm FH 8.18 0.86 FV 1.68 0.17
As a result, the values of K1, K’1 and K2, K’2 can be obtained in Equations (5) and (6), respectively.
4.2.2. Dynamic Simulation Analysis of Piezo Jet Dispenser with a Diamond Amplifier In the same experimental conditions as the previous example, the parameters of the new amplifier and the values of the obtained variables are substituted into the Equations (8) and (22). Simulink is used to obtain the vertical displacement curves of the needle under double degree and single degree dynamic models. Then, the vertical displacement curve of the piezoelectric driving dispenserSensors 2018, is18 ,obtained 2115 through finite element analysis with Comsol. 11 of 13 The mesh of the piezo jet dispenser with a diamond amplifier is shown in the Figure 13.
Figure 13. Mesh of the piezo jet dispenser with a diamond amplifier. Figure 13. Mesh of the piezo jet dispenser with a diamond amplifier. The multi physics field coupling simulation of the piezo jet dispenser with a diamond Amplifier is carriedThe multiout by physics using fieldthe piezoelectric coupling simulation module of Comsol. the piezo With jet dispenser Comsol, withthe voltage a diamond function Amplifier with timeis carried applied out to by piezoelectric using the piezoelectric ceramics in moduleone cycle of is Comsol. approximate With Comsol,as the Equation the voltage (23). function with time applied to piezoelectric ceramics in one cycle is approximate as the Equation (23). 0 (0t 0.001) 0130000(0 ≤ t ThisThis isis aa pulsepulse wavewave withwith aa magnitudemagnitude ofof 130,130, aa high-levelhigh-level timetime ofof 66 ms,ms, andand aa riserise edgeedge andand fallfall edgeedge timetime ofof 11 ms.ms. ByBy monitoringmonitoring aa pointpoint onon thethe lowerlower endend ofof thethe amplifieramplifier withinwithin thethe waveform,waveform, thethe relationshiprelationship betweenbetween thethe displacementdisplacementand and speedspeed ofof thethe lowerlower endend faceface withwith the time can be obtained obtained.. TheThe displacementdisplacement curvescurves ofof thethe needleneedle underunder doubledouble degreedegree andand singlesingle degreedegree dynamicdynamic modelsmodels andand thethe finitefinite elementelement analysisanalysis inin oneone cyclecycle areare shownshown inin FigureFigure 14 14a.a. TheThe velocityvelocity curvescurves ofof thethe needleneedle underunder doubledouble degreedegree andand singlesingle degreedegree dynamicdynamic modelsmodels andand thethe finitefinite elementelement analysisanalysis inin oneone cyclecycle areare shownshown inin FigureFigure 14 14bb.. (a) (b) FigureFigure 14.14. DynamicDynamic characteristicscharacteristics ofof thethe needle:needle: ((aa)) TheThe verticalvertical displacementdisplacement graph;graph; ((bb)) TheThe verticalvertical velocityvelocity graph.graph. 4.3. The Discussion From Figure 11a, it can be seen that the dynamic analysis results of the double degree spring- mass-damper system are basically the same as those of the equivalent single degree spring-mass- damper system, and the maximum displacement can reach 300 μm. According to the experimental experience in the past, to obtain better jet performance, the needle needs to obtain a displacement of 200–300 μm [15]. Obviously, the diamond amplifier can meet the requirement because the maximum displacement under the experimental system is about 310 μm. The needle spends about 1.1 ms on single stroke, but the oscillation frequency of a curve obtained from experiments is not the same as the other two curves obtained from modeling. This is mainly due to the difference between the parameters of the piezo material, the thickness of the PZT, and the damping of the injection needle with the actual situation. However, the curves obtained from dynamic analysis are basically the same as those measured experimentally; this is reasonable and acceptable because the error between dynamic analysis and actual measurement is 5%. The experimental results agree with that from the simplified model, which proves that the simplified model is reliable. From the Figure 14a, it can be found that the dynamic analysis of the double degree spring-mass-damper system and the equivalent single degree spring-mass-damper system results are basically the same as those of the finite element analysis in one cycle, and the maximum displacement can reach 210 μm. From Figure 11b, it can be seen that the maximum velocity reaches 0.39 m/s, 0.40 m/s and 0.31 m/s under double degree and single degree dynamic models and the experiment system, respectively. When the needle moves downward, its velocity of colliding with the nozzle slightly decreases to 0.41 m/s, 0.4 m/s and 0.38 m/s respectively. From Figure 14b, it can be seen that the maximum velocity reaches 0.37 m/s, 0.38 m/s and 0.40 m/s under double degree and single degree dynamic models and the experiment system respectively. When the needle moves upward, its velocity of colliding with the nozzle slightly decreases to 0.40 m/s, 0.39 m/s and 0.42 m/s respectively. Sensors 2018, 18, 2115 12 of 13 4.3. The Discussion From Figure 11a, it can be seen that the dynamic analysis results of the double degree spring-mass-damper system are basically the same as those of the equivalent single degree spring-mass-damper system, and the maximum displacement can reach 300 µm. According to the experimental experience in the past, to obtain better jet performance, the needle needs to obtain a displacement of 200–300 µm [15]. Obviously, the diamond amplifier can meet the requirement because the maximum displacement under the experimental system is about 310 µm. The needle spends about 1.1 ms on single stroke, but the oscillation frequency of a curve obtained from experiments is not the same as the other two curves obtained from modeling. This is mainly due to the difference between the parameters of the piezo material, the thickness of the PZT, and the damping of the injection needle with the actual situation. However, the curves obtained from dynamic analysis are basically the same as those measured experimentally; this is reasonable and acceptable because the error between dynamic analysis and actual measurement is 5%. The experimental results agree with that from the simplified model, which proves that the simplified model is reliable. From the Figure 14a, it can be found that the dynamic analysis of the double degree spring-mass-damper system and the equivalent single degree spring-mass-damper system results are basically the same as those of the finite element analysis in one cycle, and the maximum displacement can reach 210 µm. From Figure 11b, it can be seen that the maximum velocity reaches 0.39 m/s, 0.40 m/s and 0.31 m/s under double degree and single degree dynamic models and the experiment system, respectively. When the needle moves downward, its velocity of colliding with the nozzle slightly decreases to 0.41 m/s, 0.4 m/s and 0.38 m/s respectively. From Figure 14b, it can be seen that the maximum velocity reaches 0.37 m/s, 0.38 m/s and 0.40 m/s under double degree and single degree dynamic models and the experiment system respectively. When the needle moves upward, its velocity of colliding with the nozzle slightly decreases to 0.40 m/s, 0.39 m/s and 0.42 m/s respectively. 5. Conclusions In summary, the mathematical models and simulation models have been established. The diamond amplifier is simplified as a single or double degree spring system while studying the dynamic characteristics. The tested results of the dynamic characteristics prove that the simplified method is reliable. The most important and difficult problem in designing concerns the amplifier. The study provides a simplified method to design or assess diamond amplifier-based system. Through a little calculation, the feasibility of the diamond amplifier design can be verified. The method is also available for other similar piezo dispenser applications. Author Contributions: G.D. and C.Z. conceived and designed the experiments; N.W. performed the experiments; J.L. and C.Z. analyzed the data; N.W. contributed reagents/materials/analysis tools; N.W. and C.Z. wrote the paper. Funding: This project is supported by the National Natural Science Foundation of China (Grant No. 51705538) and China Postdoctoral Science Foundation (Grant No. 2016M602422). Acknowledgments: The authors would like to express their gratitude to the reviewers and editors for their kind help. Conflicts of Interest: The authors declare no conflict of interest. The founding sponsors had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, and in the decision to publish the results. References 1. Zhou, C.; Deng, G. Giant Magnetostrictive Material Based Jetting Dispenser. Optik 2015, 126, 5859–5860. [CrossRef] 2. Zhou, C.; Duan, J.; Deng, G.; Li, J. Improved thermal characteristics of a novel magnetostrictive jet dispenser using water-cooling approach. Appl. Therm. Eng. 2017, 112, 1–6. [CrossRef] Sensors 2018, 18, 2115 13 of 13 3. Zuo, W.; Li, P.; Zhang, J.; Fang, Y. 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Enhanced mathematical modeling of the displacement amplification ratio for piezo compliant mechanisms. Smart Mater. Struct. 2016, 25, 075022. [CrossRef] © 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).