Design and experiment of a needle-type Piezostack Driven Jetting Dispenser

This article was downloaded by: [Harbin Institute of Technology]On: 10 February 2015, At: 19:15Publisher: Taylor & FrancisInforma Ltd Registered in England and Wales Registered Number: 1072954 Registeredoffice: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UKClick for updatesJournal of Adhesion Science and TechnologyPublication details, including instructions for authors and subscription information:/loi/tast20Design and experiment of a needle-type piezostack-driven jettingdispenser based on lumped parameter methodShizhou Lu a, Yufeng Yao a, Yaxin Liu a& Yatao ZhaoaaState Key Laboratory of Robotics and System, Harbin Institute of T echnology , 150001 Harbin, China Published online: 29 Jan 2015.PLEASE SCROLL DOWN FOR ARTICLETaylor & Francis makes every effort to ensure the accuracy of all the information (the “Content”) contained in the publications on our platform. However , Taylor & Francis,our agents, and our licensors make no representations or warranties whatsoever as to the accuracy, completeness, or suitability for any purpose of the Content. Any opinions and views expressed in this publication are the opinions and views of the authors,and are not the views of or endorsed by Taylor & Francis. The accuracy of the Content should not be relied upon and should be independently verified with primary sources of information. Taylor and Francis shall not be liable for any losses, actions, claims,proceedings, demands, costs, expenses, damages, and other liabilities whatsoever or howsoever caused arising directly or indirectly in connection with, in relation to or arising out of the use of the Content.This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing,systematic supply, or distribution in any form to anyone is expressly forbidden. Terms &D o w n l o a d e d b y [H a r b i n I n s t i t u t e o f T e c h n o l o g y ] a t 19:15 10 F e b r u a r y 2015Design and experiment of a needle-type piezostack-driven jettingdispenser based on lumped parameter methodShizhou Lu,Yufeng Yao *,Yaxin Liu and Yatao ZhaoState Key Laboratory of Robotics and System,Harbin Institute of Technology,150001Harbin,China(Received 15September 2014;final version received 14November 2014;accepted 18December 2014)Micro liquid dispensing technology is widely used in the field of electronic packaging.This study presents a lumped parameter model of a needle-type piezostack-driven jetting dispenser,which can produce small high viscosity adhesive droplets with a high driving frequency.After describing the structural components and operating principles of the dispenser,a lumped parameter model for the system is derived by integrating the sub-models of the structural and fluid parts.According to the lumped parameter method,the fluid channels of the dispenser have been divided into several lumps to obtain a more accurate performance.Based on the proposed model,the jetting dispenser is designed and manufactured,and its performance is then evaluated through both computer simulations and experiments.Further experimental studies about its working properties based on the proposed dis-penser are carried out.The results are used to guide the design and control works about the proposed dispenser.Keywords:jetting dispenser;piezostack actuator;lumped parameter method;high viscosity1.IntroductionIn microelectronic packaging field,many types of adhesive materials with different viscosities and desired volumes need to be dispensed accurately and quickly.[1,2]In particular with the rapid development of integrated circuit packaging technologies,many new types of high viscosity adhesives have been applied for realizing high density assembly.[3,4]This trend requires that the dispensing methods,which are used to transfer liquid,can transfer small volume of adhesives more accurately,rapidly,and flexibly.So far,numerous types of dispensing approaches have been developed and success-fully implemented in semiconductor applications.And these methods can be classi fied into two types:contact dispensing and non-contact dispensing.[5–7]The former method is suitable for some high viscosity adhesive dispensing because of its high-driven char-acteristic.[6,7]But this method requires its dispenser nozzle to contact with the sub-strate or printed circuit board (PCB)via dispensed adhesive during the dispensing process,which increases cycle time and complicates the process.[6,7]These limitations have restricted its application in the field of microelectronic packaging.Thus,the*Corresponding author.Email:hitwhyyf@©2015Taylor &FrancisJournal of Adhesion Science and Technology ,2015V ol.29,No.8,716–730,/10.1080/01694243.2014.1001962D o w n l o a d e d b y [H a r b i n I n s t i t u t e o f T e c h n o l o g y ] a t 19:15 10 F e b r u a r y 2015non-contact method has been adopted due to its characteristics of high accuracy,ef ficiency,and reliability.[8]The needle-type jetting method,which utilizes a closed-loop,positive striking needle to dispense adhesive,is one of the main non-contact methods applied in produc-tion.[9,10]The adhesive is pressured in the syringe to ensure a continued flow through the channels of the dispenser.The proposed needle is used to hit and break the stream of adhesive,which jets out from the nozzle and forms droplets.The volumes and shapes of droplets will not be affected by the surface qualities of the substrate or PCB since there is no contact between the needle and the board.Furthermore,a quite smaller droplet is available by this method.[11]Many existing needle-type dispensers employ high-pressure pulses to drive the nee-dle,[11–13]but they face a limited potential for motion accuracy and frequency improvements due to the compressibility of the gases and valve hysteresis.Then,piezoelectric actuator is applied by some institutes and companies due to its high driving frequency and accurate output.For example,Nguyen uses a piezoelectric to drive the needle.[9,10]The companies of Asymetk and EFD have also produced many piezo-driven microjet valves.[4,7]Consequently,the main contribution of this work is to develop a new needle-type jetting dispenser driven by a piezostack actuator,which can overcome the above-mentioned limitations.Besides,an amplifying mechanism is employed to magnify the displacement of piezostack so that the amplitude of the needle motion can reach such a value that is suitable for high viscosity adhesive dispensing.When a voltage is applied to the piezostack,the displacement of the piezostack causes a reciprocating motion of the needle,which initiates the droplet jetting.After describing the structural compo-nents and the operating principles of the dispenser,the dynamic model of the dispenser is established based on the lumped parameter method.The governing equation is obtained by integrating the fluid model with the structural model of the dispenser.Then,an experimental platform including the dispenser is constructed,and the dynamic behaviors of the dispenser (such as needle displacement and dispensing amount)are investigated through both computer simulations andexperiments.Figure 1.Schematic con figuration of the dispenser:(a)structural part and (b)fluid part.Journal of Adhesion Science and Technology 717D o w n l o a d e d b y [H a r b i n I n s t i t u t e o f T e c h n o l o g y ] a t 19:15 10 F e b r u a r y 20152.Con figuration of the dispenserAs demonstrated in Figure 1,the jetting dispenser is composed of structural part and fluid part.In the structural part,the piezostack is fixed horizontally in the internal part of the amplifying mechanism and functions as the needle actuator.As is well known,the displacement of the piezostack is too small to dispense the liquid materials,espe-cially for some high viscosity adhesives.[14]Thus,an amplifying mechanism is employed to magnify the displacement.A syringe containing the adhesive connects to the gas source,which can push the adhesives into the fluid part.A needle,whose top is connected with the amplifying mechanism after passing through the spring and spring adjuster,is adopted to hit the adhesive.When a voltage is applied to the piezo-stack,the piezoelectric material deforms,causing a horizontal displacement of the amplifying mechanism.Then,the needle is lifted and the spring is compressed due to the amplifying mechanism.With the attenuation of the voltage,the needle will fall down rapidly due to the spring and piezostack forces.Thus,when a periodic voltage is applied,reciprocating motion of the needle is obtained.As Figure 1(b)shows,the fluid part is divided into five parts,which are named by f 0–f 4,respectively.The motion of the needle increases the pressure in f 0and drives adhesive flow out of the nozzle.As the needle hits the bottom of f 0,the flow is cut off and an adhesive droplet falls to the substrate due to its inertia.When the needle retracts vertically,the pressurized fluid in the syringe fills the void.Thus,the reciprocating motion of the needle drives the adhesive out from the nozzle in the form of jetting droplets.During the jetting process,the jetting speed,volume,and many other impor-tant indicators will be signi ficantly affected by the voltage,pressure,structural and other system parameters.To study the jetting effect and show support for the design and operation of the dispenser,this study has constructed the mathematical model of the proposed dispenser as the basis for simulation.3.Dynamic model and governing equationsAs depicted in Figure 1,the proposed jetting dispenser integrates electromechanical and hydraulic sub-systems,the variables from either energy domain should be re flected in its mathematical model.Thus,the modeling method must be able to convert these variables to the ones that can ful fill some mathematical operations.In this study,the lumped parameter method is proposed to model the dispenser.This method was first proposed by Doebelin [15]for a Newtonian fluid in a pipe.Masato [16],Pietrabissa et al.[17],and Khalil and Leo [18]developed lumped parameter mod-els for Bingham fluid flow in a circular pipe and axial Couette flow in an annular duct,and successfully applied in modeling a jetting dispensing process.The lumped parameter method,which is quite suitable for dynamic analysis of some complex multi-systems,focuses on the effects of multi-variables from different energy fields on flow behaviors by neglecting the internal space distribution of fluid characteristics.In the lumped parameter model,the fluid system is divided into lumps with lumped masses and average parameters such as velocity and pressure.The system elements are obtained by applying conservation of mass and Newton ’s law to the lumps of the fluid.[15,18]In this study,an equivalent electrical model is proposed to simulate the fluid performance.During the modeling,the fluid compressibility is represented via capacitance,the fluid inertia effect is represented via inductance,the viscous shear force is represented via resistance,and the pressure drop is represented by voltage source.718S.Lu et al.D o w n l o a d e d b y [H a r b i n I n s t i t u t e o f T e c h n o l o g y ] a t 19:15 10 F e b r u a r y 2015In this part,the mathematical models of different fluid channels are firstly studied.Then,after building the dynamic models of the structural and fluid parts,the whole model and governing equations of the dispenser are obtained.3.1.Mathematical models of fluid channelsIt can be observed from Figure 1(b)that the five chambers of fluid part have two struc-tural types:circular channels (as f 0,f 1,and f 4)and annular channels (as f 2and f 3).Note that the flow mechanism and variables ’calculating method differ greatly at different channels.Thus,the models of different fluid channels are firstly constructed.As Figure 2(a)shows,the circular channel is divided into several lumps according to the lumped parameter method.The flow of adhesive in the i th lump can be described by the elements of resistance (R c,i ),inductance (L c,i ),and capacitance (C c,i ),given by Equation (1).The analogous electrical model of the circular channel is shown in Figure 2(b).In Figure 2,q i ,l i ,and P i are the flow rate,length,and pressure in the i thlump,respectively._Qi is the equivalent current for the i th circuit branch.R c ;i ¼8l b l ip r 4i L c ;i ¼q b l i A i C c ;i ¼A i l iB b 8><>:(1)It is well known that the adhesive used in the jetting system exhibits non-Newtonianbehavior.The Bingham fluid model is widely used to describe the dynamic behavior of adhesive flows.[19]The shearing force of a Bingham fluid is as follows:s =s y þK _c(2)In Equations (1)and (2),l b ,q b ,and B b are the viscosity,density,and bulk modulus ofthe Bingham fluid,respectively.r i and A i are the radius and cross-section area of thei th lump,respectively.s y ,_c,and K are the yield stress,shearing rate,and apparent viscosity of the Bingham fluid,respectively.The pressure drop due to the yield stress of a Bingham fluid in a circular channel is calculated from Equation (3).V s ;i represents the pressure drop mentioned above.The negative signi fies that the pressure is consumed.V s ;i ¼À8l i s y =3r i(3)As depicted in Figure 1,the flows in chambers f 2and f 3can be considered as axial Couette flows in annular channels.[10]The Bingham fluid flows in the annular channel are modeled similarly to the flows in circular channels.The equivalent section and corresponding lumped model are shown in Figure 3(a)and (b),respectively.Figure 2.(a)Circular channel and (b)its analogous electrical model.Journal of Adhesion Science and Technology 719D o w n l o a d e d b y [H a r b i n I n s t i t u t e o f T e c h n o l o g y ] a t 19:15 10 F e b r u a r y 2015For the axial Couette flow in an annular channel,the resistance,inductance,and capacitance of the i th lump can be calculated asR a ;i ¼8l b l i ln ðr a ;i =r n Þp ðr 4a ;i Àr 4n Þln ðr a ;i =r n ÞÀðr 2a ;iÀr 2n Þ2C a ;i ¼A a ;i l ibI a ;i¼q b l iA a ;i8>><>>:(4)In Equation (4),R a ;i ,L a ;i ,and C a ;i are the resistance,inductance,and capacitance of thei th lump,respectively.r a ;i and A a ;i are the radius and cross-section area of the i th lump in annular channel,respectively.r n is the cross-section area of the needle.During the dispensing process,the pressure drop due to the yield stress is calculated by Equation (5),where C is a damping coef ficient between 2.0and 3.07.[10]V s a ;i ¼ÀC s yl i r a ;i Àr n(5)In addition,the needle can also cause pressure loss due to the friction from motion through the adhesive;this pressure drop is de fined asV va ;i ¼À4l b l i r 2a ;i Àr 2n À2r 2n ln ðr a ;i =r n Þh i v nðr 4a ;i Àr 4n Þln ðr a ;i =r n ÞÀðr 2a ;i Àr 2n Þ(6)In Equation (6),v n is the moving speed of the needle.3.2.Dynamic model of the dispenserAs Figure 1shows,the proposed dispenser is a multi-physics system of interactingfluids and structures.In this study,a lumped parameter method is adopted to describe the dynamic behavior of the structural part as well as the fluid part.After getting the dynamic model of each part,the governing equations of the disperser are obtained.Firstly,the sub-model is constructed to describe the dynamic behaviors of the struc-tural part (the piezostack,the amplifying mechanism,the needle,and the spring).As Figure 4(b)shows,the piezostack produces a displacement,whosemathematicalFigure 3.(a)Annular channel and (b)its analogous electrical model.720S.Lu et al.D o w n l o a d e d b y [H a r b i n I n s t i t u t e o f T e c h n o l o g y ] a t 19:15 10 F e b r u a r y 2015description can be expressed as Equation (7).Then,the amplifying mechanism,whose effect is presented by the transformer K in Figure 4(b),magni fies the proposed dis-placement and drives the needle.This action is de fined as Equation (8).In the next step,the needle moves and pushes the liquid in the fluid part,the process is shown by Equation (9).Thus,the analogous electrical model of the structural part is shown in Figure 4(b).L p €Q p þB p _Q p þ1C p Q p ¼V p ÀV pn (7)In Equation (7),L p ¼m p0,B p ¼b p ,and C p ¼1=K p are the equipotent inductance,resistance,and capacitance of the piezostack,respectively.m p0¼m p =3is the dynamic effective mass of the piezostack,where m p is the actual mass of the piezostack.b p and K p are the damping coef ficient and stiffness of the piezostack,respectively.V p ¼K p x p0V is a voltage source to simulate the force generated by the piezostack.x p0is the free displacement of the piezostack due to a unit of applied voltage.V is the volt-age applied to the piezostack.V pn is the force action on the amplifying mechanism.Q p is the electric charge flows in the circuit branch to simulate the displacement of the piezostack.V n ¼V pn KQ n ¼Q p =K(8)L n €Qn þB n _Q n þ1C nQ n ¼V n ÀV s (9)In Equations (8)and (9),L n ¼m n ,B n ¼b n ,and C n ¼1=K s are the equipotent induc-tance,resistance,and capacitance of the needle,respectively.m n and b n are the actual mass and damping coef ficient of the piezostack,respectively.K s is the stiffness of the spring.V n and V s are the force of the needle action on the adhesive and the pre-stressed force of the spring,respectively.Q n is the electric charge flows in the circuit branch to simulate the displacement of the needle.K =tan θis the conversion coef ficient of the transformer,[20]where θis the angle of the beam of the amplifying mechanism.As Figure 1(b)shows,the part of the needle threading into the chamber separates the fluid channel into five parts.In the model,due to very small volume of chamber f 0,only one lump is used for this chamber.Each of other channels (f 1–f 4)is divided into several lumps according to the lumped parameter method.The fluid behavior in each lump is expressed by the appropriate equipotent elements as shown in Figure 5.Figure 4.(a)Structural part of the dispenser and (b)its analogous electrical model.Journal of Adhesion Science and Technology 721D o w n l o a d e d b y [H a r b i n I n s t i t u t e o f T e c h n o l o g y ] a t 19:15 10 F e b r u a r y 2015The dynamic equation of the adhesive flows in f 0can be depicted as Equation (10).By integrating Equations (9)and (10),the dynamic behavior of the needle and the adhesive under the bottom of the needle is derived as Equation (11).L 0€Q0þ1C 0ðQ 0ÀQ ef0Þ¼0(10)L n €Qn þL 0€Q 0þB n _Q n þ1C n Q n þ1C 0ðQ 0ÀQ ef0Þ¼V n ÀV s (11)The dynamic equation of the adhesive flows in f 1–f 4can also be expressed as Equations(12)–(15).L 11€Q 11þR 11_Q 11þ1C 11ðQ 11ÀQ 12ÞÀ1C 0ðQ 0ÀQ ef0Þ¼ÀV s 11L 1i €Q 1i þR 1i _Q 1i þ1C 1i ðQ 1i ÀQ 1i þ1ÞÀ1C 1i À1ðQ 1i À1ÀQ 1i Þ¼ÀV s 1i L 1n €Q 1n þR 1n _Q 1n À1C 1n À1ðQ 1n À1ÀQ 1n Þ¼ÀV s 1n 8><>:(12)L 21€Q 21þR 21_Q 21þ1C 21ðQ 21ÀQ 22ÞÀ1C 0ðQ 0ÀQ ef0ÞþV v21¼ÀV s 21L 2i €Q 2i þR 2i _Q 2i þ1C 2i ðQ 2i ÀQ 2i þ1ÞÀ1C 2i À1ðQ 2i À1ÀQ 2i ÞþV v2i ¼ÀV s 2i L 2n €Q 2n þR 2n _Q 2n þ1C 2n ðQ 2n ÀQ ef2ÞÀ1C 2n À1ðQ 2n À1ÀQ 2n ÞþV v2n ¼ÀV s 2n8><>:(13)L 31€Q 31þR 31_Q 31þ1C 31ðQ 31ÀQ 32ÞÀ1C 2n ðQ 2n ÀQ ef2ÞþV v31¼ÀV s 31L 3i €Q 3i þR 3i _Q 3i þ1C 3i ðQ 3i ÀQ 3i þ1ÞÀ1C 3i À1ðQ 3i À1ÀQ 3i ÞþV v3i ¼ÀV s 3i L 3n €Q 3n þR 3n _Q 3n þ1C 3nðQ 3n ÀQ ef3ÞÀ1C 3n À1ðQ 3n À1ÀQ 3n ÞþV v3n ¼ÀV s 3n8><>:(14)L 41€Q 41þR 41_Q 41þ1C 41ðQ 41ÀQ 42ÞÀ1C 3n ðQ 3n ÀQ ef3Þ¼ÀV s 41L 4i €Q 4i þR 4i _Q 4i þ14i ðQ 4i ÀQ 4i þ1ÞÀ14i À1ðQ 4i À1ÀQ 4i Þ¼ÀV s 4i L 4n €Q 4n þR 4n _Q 4n À1C 4n À1ðQ 4n À1ÀQ 4n Þ¼ÀV s 4n ÀV psy8><>:(15)Figure 5.Analogous electrical model of the fluid part according to lumped parameter method.722S.Lu et al.D o w n l o a d e d b y [H a r b i n I n s t i t u t e o f T e c h n o l o g y ] a t 19:15 10 F e b r u a r y 2015In Equations (10)–(15),L 0and C 0,whose values can be calculated by Equation (1),are the analogous inductance and capacitance of the adhesive in chamber f 0,respectively.L 1i ,R 1i ,C 1i ,L 2i ,R 2i ,C 2i ,L 3i ,R 3i ,C 3i and L 4i ,R 4i ,and C 4i ,whose values can be calculated by Equations (1)and (4),are the analogous inductance,resistance,and capacitance of chambers f 1–f 4,respectively.Q 0,Q 1i ,Q 2i ,Q 3i ,and Q 4i are the electric charges flowing in the circuit branch to simulate the flow rates of the adhesives in chambers f 0–f 4,respectively.Q ef0,Q ef2,and Q ef3are the additional equilibrium electric charges.V s 1i ,V s 2i ,V s 3i ,and V s 4i ,whose values can be calculated by Equations (3)and (5),are the analogous voltages to simulate the consumed pressure drops due to the yield stress of the adhesives,respectively.V v2i and V v3i ,whose values can be calculated by Equation (6),are the analogous voltages to simulate the consumed pressure drops due to the needle motion,respectively.V psy is the analogous voltage to simulate the applied pressure from the syringe.Equations (11)–(15)can be rewritten in matrix form asL €XþR _X þCX ¼V (16)In order to reduce the size of the state vector X ,some geometric constraints are mathe-matically expressed as:Q 0¼Q n A n Q ef0¼Q 11þQ 21Q ef2¼Q 31Q ef3¼Q 418>><>>:(17)Equation (17)can be expressed in matrix form as:X ¼T X (18)Using this matrix,Equation (16)can be rewritten in terms of the transformed states as:L€ X þ R _ X þ C X ¼V (19)Then,the second-order Equation (19)can be rewritten in first-order form as:_Z¼^AZ þ^BF (20)In the above equations,A n is the cross-section area of the needle,andX ¼½Q n Q 0Q ef0Q 1l ...Q 1n Q 2l ...Q 2n Q ef2Q 3l ...Q 3n Q ef3Q 4l ...Q 4n T and X¼½Q n Q 1l ...Q 1n Q 2l ...Q 2n Q 3l ...Q 3n Q 4l ...Q 4n T are the original and new state vectors,respectively.T is the geometric constraint matrix. L¼LT , R ¼RT , C ¼CT ,Z ¼½ X _ X T ,B ¼½0 L À1 T ,and A ¼½0I À L À1 C À L À1 RT .The dynamic behavior of the whole dispenser can be obtained by combining Equations (7),(8),and (20).Figure 6shows the block diagram of the simulation code for the proposed dispenser.The simulation code consists of the dynamic model of the piezostack,the behavior of the amplifying mechanism,and the integrated model of the needle and the fluid part.From the input voltage V and the piezostack displacement Q p obtained from the amplifying mechanism,the force V pn acting on the amplifying mech-anism from the piezostack is derived by solving the dynamic equation of the piezostack (Equation (7)).The inputs of the amplifying mechanism dynamics-block are V pn and the displacement of the amplifying mechanism which is equal to the displacement ofJournal of Adhesion Science and Technology 723D o w n l o a d e d b y [H a r b i n I n s t i t u t e o f T e c h n o l o g y ] a t 19:15 10 F e b r u a r y 2015the needle part (Q n ).From V pn and Q n ,by solving Equation (8),the force V n from the needle acting on the amplifying mechanism and the piezostack displacement Q p are obtained.V n is then considered as an input of the needle –fluid dynamics-block (Equation (20)).4.Results and discussionIn order to study the dynamic behavior and the jetting mechanism of the proposed jet-ting dispenser,computer simulation based on MATLAB-Simulink is carried out by adopting materials and dimensional speci fications according to Figure 6.In addition,due to the small volume of chamber f 0,only one lump is used for this region.Each of other channels (chambers f 1–f 4)is divided into five equal lumps according to the lump parameter method (where,n =5,in Figure 4).In this study,the signi ficant components of the dispenser such as the amplifying mechanism,housing,needle,and nozzle are designed and manufactured based on the proposed lumped parameter model in order to achieve operational requirements.The other components of the dispenser such as the spring,linear bearing,O-ring,syringe,and pipes are selected based on practical application of the conventional jetting dispensers widely used in industry.The purpose of the design requirement is that the needle motion amplitude can reach around 0.5mm during the high viscosity adhesive dispensing process.In order to meet these require-ments,a stack-type piezoelectric actuator (PST150/5/60,Piezomechanik)and a kind of silicone rubber (HT902T,Huitian)are used.The geometric dimensions of the proposed jetting dispenser and the mechanical properties of the components that are mentioned above are shown in Tables 1and 2,respectively.Furthermore,in order to validate the dynamic model,an experimental platform including the proposed jetting dispenser is adopted and experimental tests are under-taken.The experimental results are then compared with the simulated ones.Figure 7shows the experimental con figuration,which are used to test the dispensing perfor-mance of the dispenser.As demonstrated in Figure 7,under the control of PC,the sig-nal generator can create the desired voltage and control signals.The voltage signal is then applied to the piezostack of the dispenser after being magni fied by the power ampli fier.The control signal is sent to the electric proportionality valve to obtain a desired pressure at the syringe.The jetting mass of the adhesive and the displacement of the needle are measured by the electronic analytical balance (CPA225D)andLVDTFigure 6.Block diagram for computer simulation code.D o w n l o a d e d b y [H a r b i n I n s t i t u t e o f T e c h n o l o g y ] a t 19:15 10 F e b r u a r y 2015sensor of the micrometer,respectively.The data from the balance and the micrometer are sent to the PC and then processed.The jetting volume is then calculated by dividing the jetted mass by the fluid density.In the next step,some simulations and experiments are undertaken.The waveform of the voltage applied to the piezostack during simulation and experiment is shown in Figure 8,where V p is the amplitude of the voltage.T is the cycle of the voltage.T a ,whose value equals 0.5T,is the voltage width during one cycle.Then,the frequency Table 1.Dimensional parameters of the jetting dispenser (mm).Channel Needle radiusNeedle lengthHousing radiusHousing lengthf 0–– 1.50.5f 1––0.25 2.0f 216 1.56f 3225 2.525f 4––350Table 2.Parameters of the components.ComponentParameter Value Piezostack （PST150/5/60）M p 18gR p 1.5e –3Ns/mm K p 8e3N/mm x p00.4e –3mm/V Amplifying mechanism θ6°Needle q n 7800kg/m 3R n 6e –3Ns/m Spring K s 1.25e4N/m Adhesiveq b 1020kg/m 3l b 3000mPa s B b 1e9Pa s y 4.5Pa C2.2Figure 7.Experimental con figuration of piezostack-driven jetting dispenser.D o w n l o a d e d b y [H a r b i n I n s t i t u t e o f T e c h n o l o g y ] a t 19:15 10 F e b r u a r y 2015。