MODELING USING THE FINITE ELEMENT METHOD OF AN ULTRASONIC STACK USED FOR ULTRASONIC WELDING STAKING PROCESS

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1 SISOM 2011 and Session of the Commission of Acoustics, Bucharest May MODELING USING THE FINITE ELEMENT METHOD OF AN ULTRASONIC STACK USED FOR ULTRASONIC WELDING STAKING PROCESS Doru Virgil PĂUŞAN 1, Victor POPOVICI 1, 1 University Politehnica, Bucharest, popovici_victor@yahoo.com. The paper presents the modeling of an ultrasonic stack used for ultrasonic welding-staking joint using the finite element method(fem). The ultrasonic stack is formed of a piezoceramic transducer, a booster, a conical horn and a horn tip. The joint procedure of ultrasonic welding-staking stands as a complex operation which involves three elements: the two components which need to be jointed and a bolt. The three parts which contributes to the joint can be made of different materials. The paper contains the scheme of the procedure, samples of joints and a partial view of the stand. By using FEM we can obtain strain and deformation states along the ultrasonic stack, and we can also obtain particle amplitude speed value, essential elements only for dimensioning but also for determining the system efficiency. Keywords: FEM, welding-staking, ultrasonic stack, piezoceramic transducer, ultrasonic horn, booster. 1. INTRODUCTION Ultrasonic welding - staking is an original technique that allows joining by overlapping the two upper and lower components using a bolt with a specific configuration. In the area of contact with the lower part, the bolt (fig.1) is provided with a sharp conical area which serves as acoustic energy director. Its primary function is to concentrate the energy in order to rapidly initiate the softening and melting of the parts in the joining area. Usually the apex angle cone 2α amounts to 90 0 for the amorphous resins and to 60 0 for the semicrystalline resins. Figure 1: Bolt used for joining by ultrasonic welding-staking. The diameter d of bolts is determined depending on the thickness of the upper component. Bolt length l is determined so that to be mm greater than that resulting from the calculation by geometric volume matching of the bolt with the head of the formed bolt head (horn tip shape) plus the volume of the upper component hole.

2 421 Modeling using the finite element method of an ultrasonic stack used for ultrasonic welding-staking process Figure 2 is shown the principle scheme of the assembly by ultrasonic welding-staking. The upper part is a passive part that practically is not involved in the joining process and consequently it may be made of any metallic or nonmetallic material. a b Figure 2: The scheme for the welding-staking assembling procedure a - before welding-staking; b - after welding-staking; 1 - bolt; 2 - upper part; 3 - lower part; 4 horn tip; 5 - weld; A - amplitude of the horn tip oscillation; P s - contact pressure. The most used materials for the bolt and the lower component are amorphous and semicrystalline thermoplastic polymers. The acoustic energy introduced by the horn tip into the bolt will be concentrated in a first stage in its contact area with the lower part, producing the softening and then the melting of this area, thus leading to their welding. In the next stage of the joining process the bolt will reach the softening temperature in the contact area with the horn tip as well, so that it will take the shape of the active area of the horn tip, thus joining the two parts. As the distance between the contact area of the horn tip with the bolt and the contact area of the bolt with the lower part has values that lead to the execution of the welding process in a far field, the bolt material should permit welding by this method. Examples of polymers that can be welded in a far field : PS, ABS, PMMA, PC, PSU, PA. Furthermore, in order that the bolt to take the shape of the cavity in the horn tip, its material should have good workability by thermoforming. The above mentioned materials comply with this requirement. For welding different polymers, in order to obtain quality joints their melting temperatures should be as close as possible. Furthermore, in order to weld different plastic materials, they should have similar molecular structure (i.e. they should be chemically compatible). Examples of material combinations bolt - lower part that can be joined by welding-staking: ABS+PMMA; PMMA+ABS; ABS+PC; PC+ABS; ABS+PVC; PC+PEI; PMMA+PC; PC+PMMA; PC+PSU;PSU+PC. The experiments regarding ultrasonic welding-staking process of different materials combinations was made using an ultrasonic welding stand. Figure 3 shows a partial view of this stand. This stand allows setup, maintenance and control of the main parameters of the joint process in order to establish the optimal regimes. The positioning system assures the correct positioning of the ultrasonic stack in relation to the jointed components and allows the motion to be transmitted from the setup system of the pressing force to the ultrasonic stack during the joint process. Monitoring the amplitude of oscillation is done using an accelerometer mounted on the reflector of ultrasonic stack. This is possible due to the existence of a dependency between the amplitudes oscillations in different areas of the ultrasonic stack. The strain gauge transducer and the measuring chain serve for the monitoring of the statically pressing force.

3 Doru Virgil PĂUŞAN, Victor POPOVICI 422 Figure 3. Ultrasonic welding stand 1-transducer; 2-booster; 3-horn; 4-upper part; 5-lower part; 6-anvil; 7- accelerometer; 8- strain gauge transducer. 2. THE MODELING USING THE FINITE ELEMENT METHOD OF THE PIEZOCERAMIC TRANSDUCER BOOSTER CONICAL HORN HORN TIP The modeling of the piezoceramic transducer booster - conical horn horn tip using the finite element method aims to determine the variation of the amplitude along the ultrasonic stack and in the active zone of the horn tip depending of the electrical tension applied to the piezoceramic elements. Because of the high complexity of such assemble, the finite element analyze will be applied consecutive for each component. This way, the results of the piezoceramic transducer analyze will constitute the input data for piezoceramic transducer coupled with the booster analyze and continues for the entire ultrasonic stack including the conical horn and the horn tip. From the main menu of the ANSYS software, the structural analyze which conditions the library with discretization elements is chosen. The discretization elements, shown in figure 4, chosen from the ANSYS library are SOLID 92 and SOLID 98 which are 3D elements with 10 solid tetrahedral nodes. The elements are alike but to the SOLID 98 element electric and magnetic properties can be attached. Fig. 4. SOLID 92 element

4 423 Modeling using the finite element method of an ultrasonic stack used for ultrasonic welding-staking process The harmonic analyze is chosen because it gives the possibility to predict the sustained dynamic behavior of the structures. Also gives the possibility to check if the system reaches resonance, fatigue and other harmonic effects of the vibration forces. The harmonic analyze stands as a method used to determine the stationary linear response of the structure when the load varies sinusoidal (harmonic). The idea is to calculate the response of the structure for few frequencies and to determine the graphical representation of the response in frequency of some measures (usually displacements). Using this type of analyze only the stationary vibration forces of the structure can be determined. The transitional vibrations which take place at the beginning of the excitation are not taken into consideration by the harmonic analyze. The analyze of the harmonic answer is a linear analyze. Any non-linearity like the plasticity and the interspaces between the elements will be ignored even if they have been already defined. The harmonic analyze can be done also for a pre-tensioned structure. The analyze was made for the 20 KHz frequency which corresponds to the resonance frequency both of the piezoceramic transducer and the entire ultrasonic stack. The ultrasonic stack which was analyzed and it s components are shown in figure 5. 1 piezoceramic transducer; 2 booster; 3 conical horn; 4 horn tip Fig. 5. Ultrasonic stack used for welding-staking The active area of the horn tip is shaped having the desired shape of the free end of the bolt. The mounting area is threaded, the conical horn having a threaded hole. Figure 6 contains the construction stages of the piezoceramic transducer model coupled with the booster and the conical horn: defining the volumes, finite elements discretization, and application of loads. For the piezoceramic elements of the piezoceramic transducer the loads are tension type having values from 0 to 2000 V. The booster receives as input data the displacements resulted at the piezoceramic transducer exit. The displacements at the booster exit are input data for the welding horn analyze. Defining the volumes Finite elements discretization Applying the loads Fig. 6. Construction stages of the piezoceramic transducer model coupled with the booster and the conical horn Figure 7 contains the deformation stages resulted from the harmonic analyze - for a 20 khz frequency.

5 Doru Virgil PĂUŞAN, Victor POPOVICI 424 Fig. 7. The deformation stages of the piezoceramic transducer coupled with the booster and the conical horn Table 1 contains the values of the amplitude in the exit section of the conical horn(outhorn) depending of the tension applied to the piezoceramic elements, the amplitudes in the contact areas of the piezoceramic elements with the reflector(enreflector) and the radiant(enradiant) and also the exit section of the radiant (enbooster) and the booster (enhorn). Table 1 Voltage [V] Enreflector Enradiant Enbooster Enhorn - Outhorn Figure 8 contains the graphical representation of the amplitude variation at the booster entrance (enbooster), the conical horn (enhorn) and the horn tip (outhorn) depending of the voltage applied to the piezoceramic elements. Amplitude Voltage [V] Enbooster Enhorn Outhorh Fig. 8. The amplitude in the outhorn depending of the voltage applied to the piezoceramic elements.

6 425 Modeling using the finite element method of an ultrasonic stack used for ultrasonic welding-staking process Based on the results of assessments carried out curves can be drawn the variation of oscillation amplitude ultrasonic Z axis direction ultrasonic stack for different activation voltage of the transducer. Figure 9 is shown the variation of 2000 V. The curves also allow determination of nodal planes in the ultrasonic stack is mounted on the welding equipment. Amplitude [μm ] Coordinate Z [mm] Transducer Booster Conical horn Horn tip Fig. 9. Amplitude variation on the Z axis of the ultrasonic stack with conical horn and profiled horn tip. The horn tip modelling aims to determine the amplitude on it s active area generating line. Figure 10 contains the stages of construction of the horn tip model. The horn tip is loaded with displacements type loads having the values obtained at the outhorn section. Defining the volumes Finite elements discretization Applying the loads Fig. 10. The construction stages of the horn tip model 11. The deformed state of the horn tip coupled with the conical horn in isomeric view can be seen in figure Fig. 11. The deformed stages of the horn tip coupled with the conical horn Fig. 12. The generating line of the active zone of the horn tip

7 Doru Virgil PĂUŞAN, Victor POPOVICI 426 The active zone of the horn tip is the one which comes in contact with the material of the assembled part and introduces the ultrasonic oscillations into it. The generating line of this zone defined by the 37 line in figure 12. The results in table 2 contains the sizes of the amplitudes in the nodes located on the generating line of the active contact zone, depending of the Z coordinate after the harmonic analyze and figure 13 contains the graphical representation of this variation. Table 2 Amplitude Amplitude Amplitude Amplitude Coordinate Z [mm] A 400V A/2 800V A/ V A/ V Amplitude Coordinate Z [mm] 400 V (A) 800 V (A/2) 1200 V (A/2.88) 1600 V (A/3.97) Fig. 13. The value of the amplitude on the active zone of the horn tip depending of the Z coordinate

8 427 Modeling using the finite element method of an ultrasonic stack used for ultrasonic welding-staking process 3. CONCLUSIONS The modeling using the finite element method using the Ansys software package proves to be very important in order to highlight the behavior of the ultrasonic stack. This method relieves the researcher from doing difficult amplitude determination because of the high frequencies used for the ultrasonic transducer. Knowing the way every section of an ultrasonic stack vibrates is necessary for designing and it is possible using FEM from which we get the speed amplitude variation diagram of the particle movement along the section and type of vibration in the system. Diagrams are necessary not only for designing and determining the resistance elements but for building an ultrasonic stack with a pre-determined acousticmechanical efficiency. The input data for modeling using FEM have been obtained by measuring them, where in most cases it is necessary only an input value taken-up by measuring to scale the model in reality. A result obtained from a specific analyze is enough as input data for a later analyze. The results obtained by modeling are very much close to the results obtained analytically and experimentally. Knowing the value of the amplitude in each section of the ultrasonic stack permits to: precisely determine the position of the nodal plane for fastening the ultrasonic stack, setting the activation tension of the piezoceramic elements which can lead to obtaining in the active zone of the horn tip the necessary amplitude for the joint. REFERENCES 1. ANSYS. Analysis Guides, Ansys, Inc. 201 Johnson Road, Huston; 2. FREDERICK,J.R., Ultrasonic Engineering,John Wiley & Sons, Inc. New York, London, Sydney; 3. PĂUŞAN, D, V., Procedeu de sudare şi nituire cu ultrasunete, brevet de invenţie nr ; 4. PĂUŞAN, D, V., POPOVICI, V., Stand for parameters setting and monitoring the ultrasonic welding and inserting processes,, TEHNOMUS, New Technologies and Products in Machine Manufacturing Technologies, Journal no , Editura Universităţii Ştefan cel Mare din Suceava, 41-46; 5. PĂUŞAN, D, V., POPOVICI, V., Monitoring the static force and the amplitude of vibration of the sonotrode of an ultrasound welding stand, The Annual Symposium of the Institute of Solid Mechanics SISOM mai 2008, ; 6. PĂUŞAN, D, V., POPOVICI, V., Finite element modelling of the corresponding thermal field of ultrasonic welding staking process, Proceedings of The 3 rd International Conference INNOVATIVE TECHNOLOGIES FOR JOINING ADVANCED MATERIALS,Timişoara, ,