ULTRASONIC WELDING OF COMPOSITE MATERAILS. ULTRASONIC BOOSTER DESIGN AND FEM SIMULATION

Transcription

1 ULTRASONIC WELDING OF COMPOSITE MATERAILS. ULTRASONIC BOOSTER DESIGN AND FEM SIMULATION Gh. AMZA, Zoia Apostolescu, Dan NITOI University Politehnica fro Bucharest, Keywords: ultrasonic, welding, FEM, siulation Abstract: The paper proposes a new research point of view about the ultrasonic welding which uses the finite eleent odeling. In the first there are presented soe analytical aspects for the booster design and the second part presents the ANSS odal analyze that offers good inforation about the ultrasonic syste vibration odes and frequency that are used forward to optiize the welding process. 1. THEORETICAL ASPECTS The paper presents soe analytical aspects regarding the design of the active part of the ultrasonic welding syste that covers the piezoceraic active eleents and the ultrasonic booster. In the case of a syetrical (fig.1) copound piezoceraic transducer fored by two piezoceraic disks with the diaeter a 1 and high h p, acoustic characteristic ipedance ρ v, two identical etallic eleents h with the diaeter a and acoustic ipedance ρ 1 1 s1 v s, the elasticity odulus for the etallic parts z and r have the relations: 1 1 ν z = 1 + (1) n1 1 1 r = ( 1 ν ) + ν( 1 + ν) n1 () Where: is the oung odulus; ν - Poisson coefficient and n 1 is given by the relation: θ Tz Tz n1 = = (3) T T r ϕ v s ϕ v s a 1 h p h a Fig. 1 Sietrical copound piezoceraic transducer 1181

2 For the piezoceraic disks we get: 1 E ν31 z = s (4) E { s ( 1 ν ) + ν ( + ν ) } 1 n r = n (5) Were ν1 is the Poisson coefficient and has the relation: E s1 ν 1 = (6) E s11 and E E s13 s13 Tz Tz ν13 = ; ν = ; n = = E 31 E (7) s11 s33 Tr Tθ The resonance condition for the passive eleents is : kr aj 0 ( kr a ) = ( 1 ν) J1( kr a ) (8) Were: kr = ω0 ρ / r ; ω0 = πf0 (9) Considering the relation (8) the following relation is available: ρ 1 ω ( ) ( ) 0a = R1 1 ν + n1ν 1 + ν (10) Where R 1 is the first solution of the equation (8). The resonance condition for the piezoceraic eleents has the for: ( k a ) ( ν ) J ( k ) kra1j 0 r 1 = ra1 (11) Were: ρ1 k r = ω0 (1) Fro the relation (11) it follows: ω {( 1 ν ) + n ν ( + ν )} E 0a1 ρ1s11 = R (13) The resonance condition for the copound transducer becoes: tg ( k l ) tg( k l ) 1 1 ρ v S = (14) ρvs Were: ω0 z ω0 k1 = ; v1 = ; k = ; v = (15) v1 ρ1 v ρ and l 1, l S 1 and S are the piezoceraic aterial diensions respective passive eleents. The resonance condition (14) ay be written as: 118

3 ρ1v1a1 tg( k1y0h) tg[ k( 1 y0 ) h] = (16) ρva Fro the experients it resulted that in the assebly ceraic aterial reflector longitudinal and transversal oscillations appeared instead the longitudinal oscillations transitted by the ceraic to the radiant eleent. These oscillations are independently transitted (according to Hooke law) and the characteristic ipedance of the radiant eleent is a total of the characteristic ipedances of each generated radiations type.. FINITE ELEMENT ANALIZE OF THE ULTRACOUSTIC SSTEM USED IN COMPOSITE MATERIAL WELDING.1 THEORETICAL CONSIDERATIONS The ultraacoustic syste is the ost iportant asssebly of an ultraacoustic welding achine because it offers the acoustical paraeters ( acoustic intensity, acoustic energy density, oscillation aplitude, oscillation frequency, vibration type) and the echanical paraeters (static pression and pression force). The ultra acoustic syste used at the ultrasonic welding consists in the piezoceraic assebly, booster and concentrator (fig.) Fig. Ultrasonic syste 1. - Reflector;. -Piezoceraic eleents; 3. -Radiant eleent; 4. Booster; 5. Concentrator. The piezoceraic assebly is set to frequency f = 0 KHz, and generates the ultrasonic waves (usually longitudinal waves). The ultrasonic energy concentrator (5) is coupled to the piezoceraic assebly by the booster eleent (4). The booster is an ultrasonic syste eleent, which is an interface eleent between the transducer and concentrator and has the role to increase the transitted concentrator vibration aplitude up to the superior liit of the transducer. The ultrasonic concentrator eleent is designed as a function of its aterial properties in such a way that its length is equal to a wave half-length and has to work in resonance condition. Its role is to aplify the oscillations and to transit the ultrasonic energy in the working zone. For a axiu efficacy the concentrator ust be accorded with an approxiation of a few periods with the calculated frequency of the ultrasonic transducer. In this condition the whole oscillating syste has to work in the resonance condition for axiu vibration aplitude at the tool peak zone as a result of a high acoustic intensity. The ultra acoustic syste geoetrical diensions for the welding achine are presented in the fig

4 51 R30 41 R1 R16 Ø53 Ø50 Ø53 Ø51 Ø53 Ø40 Ø80 Ø Fig. 3. The ultra acoustic syste geoetrical diensions An isoetric view of the ultrasonic syste is presented in the figure 4. Fig. 4 Welding achine ultrasonic syste Syste analytical calculus and design is done in such a way that this has to work in resonance regie, but this proble is very difficult to be resolved and the finite eleent odel ethod is a good ethod to be used. Because the odal analyze for this syste is very coplex, the ethod will be applied for each ultrasonic syste acoustic eleent. The piezoceraic eleent odal vibrations results will be input data for the concentrator eleent odal analyze. 3. FEM OF THE PIEZOCERAMIC MATERIALS The ultraacoustic active eleents are the piezoceraic disks ade fro PZT 4 aterial. The geoetrical diensions are presented in the figure 5. 5 Ø 0 Ø 5 0 Fig. 5 Geoetrical diensions of the piezoceraic plates In the figure 6 there are presented the piezoceraic plates geoetry and the eshed structure. 1184

5 Fig.6 Piezoceraic plates geoetry and the eshed structure. With the repect of reality the coon nodes in the coon areas are set to zero displaceents (fig. 7) and on the free areas and coon area of the piezoceraic plates is U = 000 V. The two corrresponding iages are presented in the figure 7 and 8. Fig. 7 Zero displaceent on the coon area Fig. 8 Applied of the electrical voltage an piezoceraic disks areas For this analyse type the ost iportant result is the displaceent of piezoceraic plates free surfaces For the case of positive electrical voltage on the exterior surfaces, the result is presented in the figure 9. Fig. 9 Piezoceraic disks displaceents at applied positive voltage on exterior surfaces In the case of negative electrical voltage on the external surfaces the displaceents of the piezoceraic disks are presented in the figure 10. Fig. 10 Piezoceraic disks displaceents at applied negative voltage on exterior surfaces 1185

6 Perforing an aronic analise for the frequency f = 0 khz the result is the nodal displaceent that represents the input attac value for ultrasonic concentrator. The results of this anlize in the case of different voltages applied on the piezoceraic surfaces are presented in the table 1. Tabelul 1. The dependence of the oscilating aplitude as a function of the applied voltage. Applied voltage on the piezoceraic surfaces [V] Oscillation aplitude [µ] The grafic presentation of the displaceent values is presented in the figure 11. Aplitudine oscilatie [icroetrii] Tensiune de atac eleente piezo [V] Fig. 11 Linear variation of the oscillations aplitude as a function of applied voltage. 3. FEM OF THE PIEZOCERAMIC ASSEMBL The active eleent of the syste is the piezoceraic transducer that transfors the electrical oscillations in to echanical displaceents. 1186

7 The transducer was coposed by two piezoceraic plates that are fixed between tow different blocks (like aterials and diensions) naed reflector and radiant (fig.1). Modeling using FEM offers inforation about structure deforations and stress. 1 3 Fig.1. Piezoceraic assebly 1 radiant; piezoceraice eleents; 3 reflector. In the figures 13 and 14 there are presented the steps in design and eshing the odel. Fig. 13 Piezoceraic assebly geoetry Fig. 14 Meshed odel The way to resolve the proble is to choose an haronic analyse that is able to predict the structure dinaic, fatigue behavior, to verify if the odel reach the resonance. In the sae tie, the haronic analize is used to find the structure liniar and stationary responce when the load varies in a sinusoidal for. The ideea is to calculate the structure responce for a few frequencies and to ake a grapf frequency displaceent. The analize was perfored at frequency f = 0 khz. That corresponds to resonance frequency of the both piezoceraic assebly and whole ultrasonic syste. In the figure 15 it is presented the defored shape of the piezoceraic at the vibration frequency f = 0 khz. Fig. 15 Defored shape of the piezoceraic at the vibration frequency f = 0 khz. 1187

8 The analyze results that presents the defored shape of the piezoceraic assebly are presented in the table.this contains the aplitude vibrations as a function of Z coordinate of the points on the syste axis. On the nodal plane between the piezoceraic plates the vibration aplitude is zero (Z = 50.) Table. Vibration aplitude for the points that belongs to syste axis. Z Coordinate [] Aplitude [µ] Z Coordinate [] [] Aplitude [µ] Graphic representation of the vibration aplitude on the Z-axis is presented in the figure 16. Aplitudinea [icroetrii] Coordonata in lungul axei [] Fig. 16 vibration aplitude on the Z axis 4. FEM OF THE ULTRASONIC SSTEM The ultrasonic syste consists in an assebly fored by an electroechanically transducer (usually piezoelectric transducer), booster and concentrator. It is the ost iportant assebly in an ultrasonic anufacturing achine because it controls the ultrasonic 1188

9 paraeters (acoustic intensity, density of the acoustic energy, vibration aplitude, wave type, vibration frequency) and echanical paraeters. The general schee of an ultrasonic device is presented in the figure 17. Fig. 17 Ultrasonic syste In the figure 18 it is presented the eshed geoetry of the syste and the applied loads (electric potential and displaceent). Fig. 18 Aplied loads on the ultrasonic syste; electric potential and displaceent Perforing a odal analyze, in the figure 19, 0, and 1 there are presented the ultrasonic syste defored shape and the frequency f = 0 khz. Fig. 19 The isoetric view of the ultrasonic syste at the frequency f = 0 khz. 1189

10 Fig. 0 The lateral view of the ultrasonic syste at the frequency f = 0 khz Fig The front view of the ultrasonic syste at the frequency f = 0 khz 4. CONCLUSIONS The article presents analytical and finite eleent analyze of an ultrasonic syste used in coposite aterials ultrasonic welding. Using the odal analyze it was found and is presented the vibration ode at f = 0 khz used in experients that offers axiu vibration aplitude a the lower consuption energy. 5. BBLIOGRAPH 1. Gheorghe Aza, Dănilă Barb; Florica Constantinescu,; Sistee Ultraacustice; Editura Tehnică, Bucureşti Jan Soderkvist; Electric Equivalent Circuit for Flexural Vibrations in Piezoelectric Materials; IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Controls, Nesbitt W, Andrew McFarland, Piezoelectric Materials for Ultrasonic Wave Applications, IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Controls, Qing Ming Wang, Eric Cross, Constitutive Equations of Syetrical Triple Layer Piezoelectric Benders,, IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Controls, 1999; 1190