Abstract of mathematical model is needed for the optimization

Abstract

 

            Use
of plastics in structural and non- structural applications is increasing
rapidly. The material used for manufacturing horn should have high fatigue
strength and low acoustic losses. The horn is the only part of the ultrasonic
insertion system which is unique to each process. The resonant frequency of
horn is usually determined numerically using Finite Element Method (FEM). Block
horns used in ultrasonic insertion process have more weight and the amplitude
of vibrations transmitted is uneven. Slotted block horns provide an advantage
by having less weight and the longitudinal direction. The required slots can
introduce additional problems, although these can be reduced through careful
design. Also, the temperature at the interface of the thermoplastic component
and the metal insert is very important in order to obtain the rigid parts. In
this work, the ultrasonic horn will be fabricated for the optimized results
using Aluminium for multiple insertions at a time. Modal and harmonic analysis
of the horn is done using CAE software. Optimization is done by RSM method. The
temperature at the interface of the thermoplastic component and the metal
insert will be calculated by using the numerical calculations. This will be
compared with the results of thermal analysis done using ANSYS software.
Finally, the components will be fabricated and the experiment is carried out in
the ultrasonic plastic welding machine using the fabricated horn.

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Keywords

            Ultrasonic
Welding, Thermal Analysis, Metal Insertion, Slotted Horn, Finite Element
Method.

 

1. INTRODUCTION

Ultrasonic insertion is the process of embedding or
encapsulating a small metal component into a thermoplastic part. This process
replaces the costly, time consuming, conventional method of injection molding
plastic around the metal component known as insert molding. An endless variety
of part configurations can be inserted through this process like flat, round,
etc.; the most common configuration is round, threaded inserts. In ultrasonic
insertion, a hole slightly smaller than the insert diameter is either molded or
drilled into the plastic part. This hole provides a certain degree of
interference and guides the insert into place. The metal insert is usually designed
with exterior knurls, undercuts, or threads to resist loads imposed on the
finished assembly. Ultrasonic insertion can be accomplished by two methods, one
method is about the horn can touch the insert, driving it into the plastic part
and in the another method the horn can touch the plastic part, driving it over
the insert.

 

 

2. LITERATURE REVIEW

 

Several types of ultrasonic horns were developed so
far. Models based on different approaches and techniques have been constructed
to enhance the process performance and efficiency. In order to find out the
optimized set of input parameters and also to identify the effect of each
towards a particular output, researchers have been trying for years together. A
brief review on literature on ultrasonic horn designing and modal, harmonic
simulation by ANSYS also development of mathematical model is needed for the
optimization of the ultrasonic horns for insertion process. Anand and Elangovan 1have tried to
optimize the ultrasonic inserting parameters to achieve maximum pull out
strength of ultrasonic insertion process. Cardoni et al 2investigated the design requirements of block
horns which operate as intermediate components in ultrasonic systems. Patrick et al 3investigated the effect of manual and ultrasonic
insertion of standardized class I inlays using three composite resin materials
of different viscosity. Roopa Rani et al 4
have developed different ultrasonic horns from materials a made a study on
thermo-elastic heating of the horns used in ultrasonic plastic welding. Safe
stress levels were predicted by modal and harmonic analysis followed by stress analysis
using ANSYS software. Roopa Rani
and Rudramoorthy 5 have tried computational modeling and experimental
studies of the dynamic performance of ultrasonic horns. Suresh et al 6 have done the modeling and of temperature
distribution in ultrasonic welding of thermoplastics for various joint designs.
Lin 7derived an equation for
the resonance frequency for the design of the longitudinal-torsional composite
ultrasonic exponential horns. Ganeshamoorthi
et al 8 have studied about the optimizing technique used in ultrasonic
metal welding of copper sheet and copper wire. 
Ioan-Calin et
al 9 have developed the design and characterization of an axisymmetric
ultrasonic horn held by its circumference, with specified working frequency,
amplification factor and nodal point position. Siddiq and Ghassemieh 10 have
attempted to simulate the ultrasonic welding of metals by taking into account
of effects of surface and volume. Elangovan et al 11 have developed a model
for the temperature distribution during welding and stress distribution in the
horn and welded joints. Arthur et al 12
have developed a model for the mechanics (oscillating deformation), heat
transfer including viscoelastic heat generation and friction dissipation, and
degree of adhesion (intimate contact and healing) for the initial transient
heating phase. Numerical resolution was performed using a multi-physical finite
element code. Kaifeng et al 13 have made a study on Effect of interfacial
preheating on welded joints during ultrasonic composite welding. Mantra et al 14 have made a
study on the control parameters like vibration amplitude, weld pressure and
weld time are considered for the welding of dissimilar metals like aluminum
(AA1100) and brass (UNS C27000) sheet of 0.3 mm thickness. Chen and Zhang 15
have developed a three-dimensional finite element model to study the
temperature distribution and heat generation in ultrasonic welding process.
Chunbo and Li 16 have been developed a three-dimensional (3-D) finite element
model to simulate the coupled thermal-mechanical fields in ultrasonic welding
of aluminum foils. Roopa et al 17 have made study on the far field welding of
semi crystalline polymer/high-density polyethylene. Volkov 18 has developed a
hypothesis for the mechanism of heat generation in the ultrasonic welding of
plastics. Volkov 19 has made an investigation on the special features of
joining metallic components with thermoplastics. Kamaleash and Elangovan 20
have studied about the temperature distribution between the metal and the
plastic component during ultrasonic insertion process. Tsujino et al 21 have made a study on the joint
structure of a transducer horn-holder assembly for a wire bonder. Cretu 22
has made an investigation on the behavior of the finite cylindrical rods with
harmonic variation of the cross section. Himanshu and Harshit 23have
considered weld strength as an effective attribute to identify the quality of
ultrasonically welded joints. Volkov and Bigus 24 have developed a specialized welding
machine for the ultrasonic contour welding of ABS plastics.Jingzhou et al 25 investigated the thermal phenomena and to realize production level in-situ
temperature measurement by using micro thin-film thermocouples and thin-film
thermopile arrays at the very vicinity of the ultrasonic welding spot during
joining of three-layered battery tabs and Cu bus bars (i.e., battery
interconnect) as in General Motors Chevy Volt. Micro sensors were first
fabricated on the bus bars. Kaifeng et al
26 have tested the ultrasonic welding of an injection molded short carbon
fiber reinforced composite is to investigate three important weld attributes,
bonding efficiency, weld area, and horn indentation. From the above research
papers, various design and performance of different types of horns, material
vibrational characteristics, welding of thermoplastics, techniques to evaluate
the parameters were studied and understood. Modal, harmonic analyses for the
different horn profiles were done by using ANSYS software are studied. The
finite element method for calculating the interface temperature and the
derivations of thermo-mechanical problem has been studied. In this project, for
the optimized dimensions the horn will be fabricated and the thermal analysis
will be carried out to find the interface temperature thus, the literatures
from the finite element methods are helpful in doing the simulations as well as
compare it with the experimental results. 

 

3. PROBLEM DEFINITION

                        

The process of joining the metals with the plastics
using mechanical fastening method gives low tensile strength and less torsional
resistance, which leads to distortion of the component used. By placing a metal
insert inside thermoplastic component through ultrasonic insertion process,
complexity can be reduced. Block horns, which are used in the ultrasonic
insertion process having more weight and provide uneven vibration transmission.
Slotted block horns will produce high amplitude of vibrations, having less
weight and reduce the transverse coupling. Usually, only one metal insert could
be inserted in the thermoplastic component. To increase the productivity, a
horn is to be designed multiple insertions at a time. Finding out the interface
temperature between the thermoplastic component and metal insert is important
for the insertion process. This will be finding out by thermal analysis using
ANSYS software.

 

3.1.Objectives

 

This work consists of several objectives in order to
achieve the temperature developed in the ultrasonic insertion process.

a.      
To
understand the mechanism, working and applications of the ultrasonic insertion
process.

b.     
To
design and manufacture the thermoplastic component in which the metal insertion
can be done.

c.      
To
design a slotted block horn and fabricate it according to the optimized
conditions for ultrasonic insertion of metal inserts into the thermoplastic
components,

d.     
To
carry out the thermal analysis for the assembly of metal insert and
thermoplastic component in order to obtain the interface temperature,

e.      
To
derive the mathematical equations for the measurement of interface temperature.

f.      
To
compare the simulation results with the mathematical results.

4. METHODOLOGY

 

The metal insert to be inserted is selected first and
the modeling of slotted horn and thermoplastics are done in CREO software. The
simulation is carried out to find out the intermediate temperature between the
plastics and insert. This will be compared with mathematical results. Then the
thermoplastic component and the horn will be manufactured and tuned to machine
frequency and test by the inserting the metal insert into the plastic
component. Based on the objectives, the methodology has been adopted to carry
out the work shown in Fig 4.1.

 

 

 

Fig. 4.1. Flow chart

 

5. DESIGNING OF HORN

The actual slotted horn will be designed
after the thorough study on the existing horn profiles. The energy of
vibrations is non-uniformly distributed along the length of the horn with
velocity/amplitude being greater at the tip of the horn than at the booster
end. The commonly used horn profiles in the industry are Stepped and
Catenoidal. Along with these horns the Cylindrical, Gaussian and Bezier horn
profiles are considered for the present study. The Cylindrical horn was
included so as to have comparison with low amplitude horns. The performance of
a horn is usually assessed by the amplification factor or ‘gain’ that can be
achieved at the horn face/end. The gain ‘?’ is defined by the ratio of output
amplitude (A2) to input amplitude (A1). The basic requirement for a gain is
when the amplitude factor ‘?’ > 1. Different horn shapes give different gain
depending on the variation of their cross sections. For a cylindrical horn the
gain in amplitude is ‘1’ as it is of uniform cross section. The length of the horns
is measured from the horns available in the laboratory. Usual horn profiles
include cylindrical, Bezier, catenoidal, stepped and block. When a sonotrode or
horn is made for an existing facility, its frequency should be matched. The
length of the sonotrode should be half the wavelength of vibrations through the
material. The end diameters of all horn profiles are taken as 57 mm and 38 mm
at the top and bottom respectively, to suit the machine and the component. The
cylindrical horn has a uniform diameter of 57 mm. Different horn Profiles are
shown from Fig 5.1 – 5.4.

 

                    Fig 5.1 Bezier horn                                      Fig 5.2
Catenoidal horn

 

 

      Fig 5.3 Cylindrical horn                                    Fig 5.4
Stepped horn

 

Thermoplastic component and slotted horn were also designed and used to
predict the interface temperature using ANSYS software. Which will then compare
with the numerical results. Thermoplastic component and slotted horn are shown
in Fig 5.5 and 5.6.

 

      Fig 5.5 Slotted horn                                Fig 5.6
Thermoplastic component

 

5.1. Modal analysis

To determine
the mode shape and natural frequency of a horn, modal analysis could be used.
They are the important parameters in the design of the part for dynamic loading
conditions. Depend upon the applications, horn shape is modeled by using 3D
software package and imported to ANSYS software with parasolid file (.xt). The
model meshed by using Tetra 10 node 187 SOLID element with a fine mesh size of
3.  Material mode is then specified as
linear, elastic, isotropic and properties such as young’s modulus, poission’sraio
and density of the material were specified. Mode extraction is carried out in
the frequency range 19 – 21 KHz using Block-Lanchoz option.

 

5.1.1 Natural frequencies of horn
profiles

The natural frequency of the
longitudinal mode obtained in modal analysis for Stepped horn profile is 19697 Hz,
for Catenoidalhorn profile is 19605 Hz, for Bezier horn profile is 20401 Hz and
for Cylindrical horn profile is 19524 Hz and for slotted horn profile is 20476
Hz. Fig 5.7 – 5.10 represents modal analysis for various horn profiles.

 

Fig 5.7 Modal analysis of Catenoidal horn

Fig 5.8 Modal analysis of Bezier horn

Fig 5.9 Modal analysis of Cylindrical horn

Fig 5.10 Modal analysis of Stepped horn

 

Fig 5.11 Modal analysis of Slotted horn

 

5.2 Harmonic analysis

A harmonic analysis of the horn is carried out to find the displacement
and stresses experienced by the horn in the given frequency range. The
displacement amplitude produced by the machine 23.4 µm. The output is amplified
by the booster which is placed after the transducer. The displacement at the
booster end-23.4 µm is given as the input or the forcing function to the horn
for performing the harmonic analysis. The horn is constrained to longitudinal
movement by locking it to a nut.  This
analysis will show the displacement amplitude at the end of the horn which will
be used for insertion process.

 

5.2.1 Displacement of horn profiles

The maximum stress amplitude obtained
in harmonic analysis for cylindrical horn profile is horn profile is 0.255E-4,
for stepped horn profile is 0.541E-4, for catenoidal horn profile is 0.307E-4,
forbezier horn profile is 0.477E-4 and for slotted horn profile is 0.296E-4.
Fig 5.12 – 5.16 represents modal analysis for various horn profiles. 

 

Fig 5.12 Harmonic analysis of Catenoidal horn

Fig 5.13 Harmonic analysis of Bezier horn

 

Fig 5.14 Harmonic analysis of Cylindrical horn

 

Fig 5.15 Harmonic analysis of Stepped horn

 

Fig 5.16 Harmonic analysis of Slotted horn

 

5.3 Thermal analysis

            Thermal
analysis of the horn profiles was done in ANSYS software. The maximum
temperature obtained for cylindrical
horn profile is horn profile is 107.054°C, for stepped horn profile is196.163°C,
for catenoidal horn profile is 158.03°C, for bezier horn profile is 160.91°C
and for slotted horn profile is 122.36°C.The
simulation results are shown in Fig 5.17 to 5.21.

 

Fig 5.17 Thermal analysis of Catenoidal horn

Fig 5.18 Thermal analysis of Bezier horn

 

Fig 5.19 Thermal analysis of Cylindrical horn

 

Fig 5.20 Thermal analysis of Stepped horn

Fig 5.21 Thermal analysis of Slotted horn

6. CONCLUSION

From this work, the mechanism,
working and principle of ultrasonic insertion process have been studied.
Different horn profiles were designed and the modal and harmonic analysis of
the horns were done. The results of modal and harmonic analysis is shown in
Table 6.1.

Table 6.1
Results of modal and harmonic analysis

 
Profile

 
Frequency(Hz)

 
Displacement(m)

 
Temperature(°C)

Bezier

20401

0.477E-4

160.91°C

catenoidal

19605

0.307E-4

158.03°C

cylindrical

19524

0.255E-4

107.054°C

Stepped

19697

0.541E-4

196.163°C

 

Based on the above results the
various profiles of horn were validated successfully and then slotted block
horn profile is simulated through the ANSYS software and obtained natural
frequency of 20476 Hz, displacement of 0.296E-4 and the interfacial temperature
of 122.36°C. This will be then compared with the numerical results and finally
the experimentation will be done.