Analysis of Different Shaped Sonotrodes used for Plastic Welding

INSTITUTE OF TECHNOLOGY, NIRMA UNIVERSITY, AHMEDABAD – 382 481, 08-10 DECEMBER, 2011
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Analysis of Different Shaped Sonotrodes used for
Plastic Welding
A. Dipal M. Patel, B. Avadhoot U. Rajurkar
A & B. Department of Mechanical Engineering, Faculty of Technology and Engineering, Charotar University of
Science and Technology, Changa, Anand - 388 421, Gujarat, INDIA
Abstract-- For proper concentration of ultrasonic energy
across work piece surface during welding, geometry of
horn plays a vital role. The issues involved in the study of
design are horn material and shape, frequency and
amplitude of vibration. This paper discusses on design of
different shaped acoustic horns like conical, stepped and
exponential for ultrasonic welding of plastics. First, the
theoretical dimensions of different shaped horn are
calculated and compared with the dimensions obtained
through commercial horn design software CARD®.
Correspondingly, the magnification factors attainable for
both cases for all horn shapes have been compared. The
said discussion is a part of research work intended to
study the joint strength of Acrylic and Polycarbonate
joints under various welding parameters.
Keyword-- Ultrasonic plastic welding, Horn, Frequency,
Amplitude
I. INTRODUCTION
ltrasonic welding, one of the most widely used
Uwelding methods for joining thermoplastics, uses
ultrasonic energy at high frequencies (20 – 40 kHz) to
produce low amplitude (1 – 25 µm) mechanical
vibrations. The vibrations generate heat at the joint
interface of the parts being welded, resulting in melting
of the thermoplastic materials and weld formation after
cooling. Ultrasonic welding is the fastest known
welding technique, with weld times typically between
0.1 and 1.0 seconds.
In addition to welding, ultrasonic energy is
commonly used for processes such as inserting metal
parts into plastic or reforming thermoplastic parts to
mechanically fasten components made from dissimilar
materials.
When a thermoplastic material is subjected to
ultrasonic vibrations, sinusoidal standing waves are
generated in the material. Part of this energy is
dissipated through intermolecular friction, resulting in
a build-up of heat in the bulk material, and part is
transmitted to the joint interface where boundary
friction causes local heating. Optimal transmission of
ultrasonic energy to the joint and subsequent melting
behavior is therefore dependent on the geometry of the
part and also on the ultrasonic absorption
characteristics of the material.
In Ultrasonic plastic welding, function of the
acoustic horn is to magnify the amplitude of
mechanical vibrations or to accumulate the energy on
the smaller cross section. In general, the amplitude
produced by an ultrasonic vibrator is 4 – 10 µm.
However, the amplitude required for effective
ultrasonic machining has to be more than 10-100 µm
(Amin et al. 1995). The amplitude of a vibrator has to
be magnified by an acoustic horn. The principle of
amplification of the acoustic horn is that the vibration
energy through a cross section remains unchanged,
therefore the smaller the cross section, the larger the
energy density. The amplitude through the small
section is magnified neglecting the losses during
energy transfer (Kremer D et. al. 1981).
II. HORN DESIGN FOR ULTRASONIC PLASTIC
WELDING
A welding horn, also known as a Sonotrode is an
acoustical tool that transfers the mechanical vibrations
to the work piece and is custom-made to suit the
requirements of the application. The molecules of a
horn expand and contract longitudinally along its
length so the horn expands and contracts at the
frequency of vibration.
The amplitude of the horn is determined by the
movement from the longest value to the shortest value
of the horn face in contact with the part (i.e. peak-topeak movement). Horns are designed as long resonant
bars with a half wavelength. By changing the cross
sectional shape of a horn, it is possible to give it a gain
factor increasing the amplitude of the vibration it
receives from the transducer – booster combination.
Three common horn shapes are the stepped,
exponential and conical in plastic welding industry.
INSTITUTE OF TECHNOLOGY, NIRMA UNIVERSITY, AHMEDABAD – 382 481, 08-10 DECEMBER, 2011
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Stepped horns consist of two sections with different
but uniform cross-sectional areas. The transition
between the sections is located near the nodal point.
Due to the abrupt change in cross-section in the nodal
plane, step horns have a very high stress concentration
in this area and can fail if driven at excessive
amplitude. Gain factors up to 9:1 can be attained with
step horns.
And its amplitude magnification M is calculated by:
Conical horns have a cross-sectional area that
changes conically with length. The smooth transition
distributes the stress over a greater length thus offering
lower stress concentrations than that found in step
horns. They generally have lower gain factors so are
used for applications requiring low forces and low
amplitudes.
Exponential horns have a cross-sectional area that
changes exponentially with length. It is same as conical
horn but produced more gain than conical horn
Figure 1. Stepped Shaped horn
III. THEORETICAL LENGTH OF DIFFERENT
SHAPED HORN
Basic horn design equations are represented as
equation 1 and equation 2 in terms of particle
displacement ξ
1 ∂ 2ξ 1 ∂s∂ξ ∂ 2ξ
−
−
=0
c 2 ∂t 2 s ∂x∂x ∂x 2
(1)
FIGURE 2. Length of stepped shape horn by using
CARD software
And in terms of particles velocity v , and implying
harmonic motion,
∂ 2 v 1 ∂s∂v ω 2
+
+
v=0
∂x 2 s ∂x∂x c 2
A D 
M = 1 = 1 
A2  D2 
(2)
Where x is the distance from one end of horn to the
reference position, in meters; s the cross section area
of the horn at distance x , in square meters; ω the
angular frequency; and c the velocity of sound in the
medium of horn in meters per second
3.1 Calculation for stepped horn
By solving Equation 1 and getting the length of horn
from equation 3; where value of l1=70mm
l = l1 +
c
4f
(3)
c is the sound propagation velocity through horn
materials. f is frequency at input diameter D1
2
(4)
3. 2 Calculation for Exponential horn
By solving Equation 1 and getting the length of horn
from equation 5;
c
l=
2f
 ln( D1 / D2 ) 
1+ 

π


2
(5)
Where D1 and D2 are the diameters of the input end
and output end, respectively; f is frequency at input
diameter D1; c is the sound propagation velocity
through horn materials.
And its amplitude magnification M is calculated by:
D 
M = 1 
 D2 
(6)
INSTITUTE OF TECHNOLOGY, NIRMA UNIVERSITY, AHMEDABAD – 382 481, 08-10 DECEMBER, 2011
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M=
D1
ωl c ( D1 − D2 ) ωl
cos −
sin
D2
c
ωlD2
c
(8)
Figure 2 show horn dimension obtained from CARD
software
FIGURE 3. Length of exponential shape horn by using
CARD software
3.3 Calculation for conical horn
FIGURE 5. Length of conical shape horn by using
CARD software
Figure 6 shows the actual image of
manufactured in workshop for plastic welding.
horn
Figure 4. Conically tapered horn
Design equations are given for conically tapered
horns in which the area decreases with increasing x
(Figure 4.)
3.3.1 Area Decreasing with Increasing
x
Figure 1 depicts the profile of a conical horn with
area decreasing with increasing x . By solving Equation
1 and getting the length of horn from equation 7;
ωl
ωcl(D1 − D2 )2
= 2
tan
c c (D1 − D2 )2 + ω2 l 2 D1 D2
(7)
Where D1 and D2 are the diameters of the input end
and output end, respectively; ω (Resonance frequency)
=2πf; c is the sound propagation velocity through horn
materials.
And its amplitude magnification M is calculated by:
FIGURE 6. Actual image of horn
3.3.2 Horn materials
Due to high strength and stability in properties,
A2024 –T3 aluminum alloy is used as the horn
material. Its properties are: elastic modulus E = 71.7
GPa, Poisson ratio is µ0=0.33, mass density is ρ= 2810
kg/m3, Ultimate strength = 483 MPa.
IV. RESULTS AND DISCUSSION
4.1 Analysis of conical shaped horns
In order to calculate the dimension of horn by CARD
software, the inputs required are diameter of horn D1
INSTITUTE OF TECHNOLOGY, NIRMA UNIVERSITY, AHMEDABAD – 382 481, 08-10 DECEMBER, 2011
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and D2 and material properties. Similar practice is
required for calculations using theoretical equations. In
either cases diameter D1 is assumed arbitrarily
considering the least size matching with booster on
machine setup. Diameter D2 is the required diameter of
the weld joint. However the diameter ratios are
according to the ratios used for commercial horns. The
input and Output parameters are listed in Table 1.
TABLE 1. Values of Different shaped Horn
Parameters
Dimension By
From
CARD
Theoretical
software(mm)
equation(mm)
Inputs
30
30
D1
10
10
D2
A2024 –T3
A2024 –T3
Material
aluminum alloy
aluminum alloy
3:1
3:1
D1/D2
20KHz
20KHz
Frequency
Outputs for Conical shaped horn
142
140
L
3.33
2.84
Magnification
Outputs for Stepped shaped horn
132
134
L
10
9
Magnification
Outputs for Exponential shaped horn
133
135
L
4
3
Magnification
Values of magnification calculated by using
Equation (4, 6, 8) and by using CARD software are
given in Table 1.
Figure 6, 7 & 8 give the values of amplifications by
taking the ratio of amplitude at diameter D1 to
amplitude at diameter D2 by using CARD software.
FIGURE 7. Amplitude distribution in exponential
horn
FIGURE 8. Amplitude distribution in conical horn
The stress distribution along the length of conical
shaped horn given by CARD softwares is shown in
Figure 9. Similarly, the stress distribution for stepped
horn and exponential horn are shown in Figure 10 and
Figure 11 respectively for comparison. All the figures
show that stresses generated in horn during ultrasonic
plastic welding are lesser than the ultimate strength of
material. Therefore the horn performance is safe for
plastic welding application. Stresses generated in
conical shaped horns are much lesser than stepped
horn.
FIGURE 6. Amplitude distribution in stepped horn
FIGURE 9. Stress distribution in conical horn
INSTITUTE OF TECHNOLOGY, NIRMA UNIVERSITY, AHMEDABAD – 382 481, 08-10 DECEMBER, 2011
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closer. Hence CARD software may be useful tool for
horn design.
VI. ACKNOWLEDGEMENTS
FIGURE 10. Stress distribution in stepped horn
The authors wish to thank Mr. Vijay Chaudhary,
Head, Department of Mechanical Engineering and Dr.
N. D. Shah, Principal, Faculty of Technology and
Engineering, Charotar University of Science and
Technology, Changa for their guidance, encouragement
and support in undertaking the research work. Special
thanks to the Management for their moral support and
continuous encouragement.
VII. REFERENCES
[1] S. G. Amin, H. M. M. Ahmed and H. A. Youssef.
(1995), Computer-aided design of acoustic horns for
ultrasonic machining using finite-element analysis.
Journal of Material Processing Technology., vol.
55, No. 3-4, pp. 254-260.
FIGURE 11. Stress distribution in exponential horn
V. CONCLUSIONS
From the above discussion it is evident that under the
condition of same area ratio between its’ two ends
cross sections the amplitude magnification of them is
in descending order for the stepped shape, exponential
shape and conical shape respectively. A stepped shape
horn produces larger amplitude, since it will have
larger vibration stress. Stress distribution results show
that for ultrasonic plastic welding, conical shaped horn
and exponential shaped horn are better than any other
shape of horn. Same as the computation for an
exponential shape horn is easiest among three different
shapes. Also the horn of exponential shape has better
amplitude than conical shaped horn. But due to
difficulty in machining it is rarely used in practice
where its machining cost is justified. Although the
computation for conical horn shape is most difficult, it
is easy to manufacture and also has almost same
amplitude as exponential shape horn. Therefore,
conical shaped horn is extensively used in industry.
However, it can be clearly observed that both values
calculated by CARD software are slightly exceeding
the values by theoretical equations. From above results
one can conclude that magnification of horn by using
CARD software and by using theoretical equation is
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[13] H.A. Youssef. (1971), Design of conical acoustic horns
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