NOVEL APPLICATIONS OF EXPERIMENTAL MECHANICS ON THE DESIGN
OF ULTRASONIC HORNS
Wei-Chung Wang1, Ying-Huang Tsai2 and Chun-Yao Ni3
1 Professor, Department of Power Mechanical Engineering, National Tsing Hua University, 101, Section
2, Kuang Fu Road, Hsinchu, Taiwan 30013, Republic of China, [email protected]
2 Graduate Assistant, Department of Power Mechanical Engineering, National Tsing Hua University, 101,
Section 2, Kuang Fu Road, Hsinchu, Taiwan 30013, Republic of China, [email protected]
3 Graduate Assistant, Department of Power Mechanical Engineering, National Tsing Hua University, 101,
Section 2, Kuang Fu Road, Hsinchu, Taiwan 30013, Republic of China, [email protected]
ABSTRACT
In this paper, two novel applications of experimental mechanics on the design of two ultrasonic horns, i.e. horn I and horn II, for
ultrasonic welding and flip-chip bonding are reported. Three photomechanics methods, e.g. transmitted photoelasticity,
amplitude-fluctuation electronic speckle pattern interferometry (AF-ESPI) and laser Doppler vibrometer were employed to
measure the state of stress and deformation of the two ultrasonic horns.
Introduction
The frequency of sound that can be heard by human ears ranges from 16Hz to 20 kHz. The waves whose frequencies above
20 kHz are usually called the ultrasonic waves. Ultrasonic waves have been employed in many industrial applications, e.g.
ultrasonic cutting, ultrasonic welding, etc. In general, the ultrasonic energy is transmitted from the transducer by the horn in
the ultrasonic machine. The ultrasonic horn is therefore the key component of the ultrasonic equipment. Because of its
complicated geometry, exact solutions cannot be easily obtained for the ultrasonic horn. Numerical technique such as finite
element method (FEM) can be used; however, the validity of its results must be verified. Methods of experimental mechanics
thus become indispensable not only for solving problems but also for verification purpose.
Because of their whole-field, real-time and non-contact advantages, photomechanics methods have been applied in many fields.
In this paper, the design of two ultrasonic horns were investigated by three photomechanics methods including transmitted
photoelasticity, amplitude-fluctuation electronic speckle pattern interferometry (AF-ESPI) [1] and laser Doppler vibrometer.
Stresses generated by ultrasonic wave in the horn, either thermal stress and/or mechanical stresses may deteriorate the horn’s
performance or even cause damage to the horn itself. Therefore, it is important to investigate not only the wave propagation
but also mechanics characteristics in the horn of the ultrasonic machine. To simulate a horn for ultrasonic welding, a strip
model (horn I) incident by an ultrasonic wave was investigated by the transmitted photoelastic method. Wang and Tsai [2, 3]
proposed the complete theory and calibration procedures of time-averaged photoelasticity, i.e. a symbiosis of the digital
photoelastic technique and time-averaged method. By using the time-averaged photoelasticity, stress characteristics
generated by ultrasonic wave can be readily obtained and the experimental procedures are much simplified.
In the manufacturing process of flip-chips, ultrasonic bonding has been widely used. To achieve best quality of flip-chip
bonding and satisfy the requirements of environmental protection and low temperature, an ultrasonic horn must possess three
features: (1) corresponding resonant mode is purely longitudinal; (2) no non-coplanar phenomenon between the horn and the
substrate and (3) no slip phenomenon occurred during bonding between the ultrasonic horn and the wafer. By considering the
aforementioned three features and other factors (e.g. stress concentration, accommodation of the tightening screw, etc.); a
series of modifications of the design of the horn II was performed by using the commercially available FEM software ANSYS [4].
Both the AF-ESPI and laser Doppler vibrometer were used to verify the correctness of the FEM results.
Test Specimen
Horn I
The photoelastic test specimen was made from PSM-1 (Measurements Group Inc., U. S. A.). The material properties of the
3
PSM-1 are Young’s modulus E=2.39GPa, Poisson’s ratio ν =0.38, density ρ=1235Kg/m . The P-wave velocity of the PSM-1
can be calculated from [5]
v=
E
1− ν
= 1903.34m / sec
ρ (1 + ν )(1 − 2ν )
(1)
Since wave speed v = fη , where f is the frequency of the wave and η is the wavelength. The wavelength of the P-wave is
9.51cm for the PSM-1 under 20 kHz impinging wave. So the length of the strip specimen was designed according to this
length as depicted in Fig. 1. While the ultrasonic waves were impinging, resonance would be occurred and generated
standing wave synchronously.
95.1
THICKNESS : 6
30
UNIT:mm
Fig. 1 Dimensions of the strip specimen [2, 3]
Horn II [6, 7]
SUS-304 was selected as the material of the horn II. The material properties of the SUS-304 are Young’s modulus 198.73GPa,
Poisson’s ratio 0.28 and density 7930Kg/m3. Based on the one-dimensional longitudinal wave equation of a uniform bar, an
initial length of the horn for the first natural frequency at 20 kHz can be calculated as 133.25 mm. This initial length was then
used in the FEM calculations. The final length of the real ultrasonic horn was determined by considering the aforementioned
three features and other factors (e.g. stress concentration, accommodation of the tightening screw, etc.). After a series of
attempts on design, the final geometry of the ultrasonic horn was obtained and depicted in Fig. 2. Its dimensions are shown in
Fig. 3. End faces A and B are the input and output end faces of the ultrasonic wave, respectively. While meeting the
requirements of a frequency of 20 kHz and the smallest possible degree of planarity at the same time, the length of X shown in
Fig. 3 was determined by trial and error. Since the proposed ultrasonic horn is designed for bonding chips of two inches, the
shape of end face B was selected as circular with a diameter of 50 mm.
A
B
unit: mm
Fig. 2 The final geometry of the horn
Fig. 3 Dimensions of ultrasonic horn
Experimental Setup and Theory
Time-Averaged Photoelasticity [2, 3]
The schematic diagram of the experimental setup is shown in Fig. 4, including a polariscope, a digital video camera and a
personal computer. An industrial type ultrasonic generator, including a control box and a transducer, was used to generate a
20 kHz P-wave. The photograph of the ultrasonic generator and polariscope is shown in Fig. 5.
1
2
3
4
5
6
7
8
1. LIGHT SOURCE
5. ANALYZER
2. POLARIZER
6. SPECIMEN
3. QUARTER WAVE PLATE
7. DIGITAL VIDEO CAMERA
4. QUARTER WAVE PLATE
8. PERSONAL COMPUTER
Fig. 4 The schematic of the polariscope [3]
Fig. 5 Photograph of the ultrasonic generator and polariscope [8]
For two-dimensional plane-stress problems, in a dark field circular polariscope setup, the intensity of the transmitted light
emerging from the analyzer is given by [9]
I = I 0 sin 2
where I0 is a constant; ∆ =
∆
2
(2)
2πhc
(σ1 − σ 2 ) ; σ1 and σ2 are the in-plane maximum and minimum principal stresses; h is
λ
the thickness of the model; λ is the wavelength of the monochromatic light traversing the model; c is the relative stress optical
coefficient.
Considering a harmonic wave motion in an infinite photoelastic model, the variation of maximum and minimum principal
stresses can be assumed as a function of cosωt, where ω is the frequency of the wave. Therefore the principal stress
difference can be expressed as (σ1 −σ2 )cos ωt . If the recorded time of an image is τ , the incoming light intensity ought to be
accumulated from t 1 to t 1 + τ ; the light intensity becomes [2, 3]
I = αI 0 [1 − J 0 ( ∆ )]
(3)
where α is a constant.
Because an image can only display positive value of the gray level, so the local minimum values in the absolute value of
equation (3) give the corresponding dark fringes in an interference fringe pattern. Therefore, the dark fringes obtained by the
time-averaged photoelastic method give the in-plane maximum shear stress.
AF-ESPI
The schematic diagram of the in-plane AF-ESPI experimental setup is shown in Fig. 6. As for the optical setup, a 35 mW He-Ne
laser of wavelength 632.8 nm was used as light source. An integration CCD (Plunix Co. of U.S.A.) camera was used to
conjoint the optical setup with the image processing system. The photograph of optical setup is shown in Fig. 7. To perform
the real-time image operation, computer programs were developed.
4
5
1
6
θO
2
3
8
1. He-Ne LASER
2. BEAM STEERING DEVICE
3. BEAM SPLITTER
4. MIRROR
5. SPATIAL FILTER
6. SPECIMEN
7. CAMERA
8. IMAGE PROCESSING SYSTEM
θr
7
Y
5
4
Z
Fig. 6 The schematic of the AF-ESPI [10]
X
Fig. 7 Photograph of the AF-ESPI setup [7]
The AF-ESPI method for vibration measurement is based on the video signal subtraction method which has been widely used
to evaluate the steady state displacement field. However, the reference image in the AF-ESPI method is no longer being taken
from the stress-free state but a vibrating state instead. Note that even for a periodic vibrating motion, the vibration amplitude
would be slightly changed during each cycle because of the environmental or electronic noises of the vibration system. The
AF-ESPI can provide better image resolution and narrower fringe width, hence better contrast and higher sensitivity.
Laser Doppler vibrometer
The photograph of a laser Doppler vibrometer (Ahead Optoelectronics, Inc., R. O. C.) is shown in Fig. 8. The light source is a
He-Ne laser. Working distance is from 40mm to 10m. The lowest resolution is 0.1nm and the bandwidth is DC 20 MHz.
Fig. 8 Photograph of the laser Doppler vibrometer [7]
Experimental Procedures
Transmitted Photoelasticity
Since the photoelastic test specimen itself is too soft to fix directly to the transducer, a connecting rod was prepared and placed
between the test specimen and the transducer to propagate the P-wave from the transducer to the test specimen. When the
specimen was incident by the ultrasonic wave, the standing wave was occurred almost immediately and the photoelastic fringe
patterns were taken by the digital video camera simultaneously. Because the fringe patterns shift rapidly under the induced
thermal stress, the digital video camera has to record all the variations of fringe patterns before the incidence of the ultrasonic
wave until experiment was finished. These video signals were converted into a series of digital images by the image grabber
card and image editing software stored in the personal computer.
AF-ESPI
The horn II was fixed on the transducer with screws and placed on the vibration-isolated optical table. Three different AF-ESPI
views as shown in Fig. 9 were observed. When the horn II was incident by the ultrasonic wave, an image was first captured
and stored into the RAM of image processing board as a reference image. Then CCD will capture the second image, and then
the second image will be subtracted from the reference image by the image processing system. The result of the output signal
will be modified by the look up table (LUT) and converted into gray level, and then the result will be displayed on the screen
continuously.
(a) Side view
(b) Tilt view
(c) End View
Fig. 9 Three different AF-ESPI views [7]
Laser Doppler Vibrometer
The laser Doppler vibrometer was used to measure the out-of-plane displacement along a diameter of the end face B. There
are 21 data points along the diameter; the distance between each data points is 2.5mm. When the horn II was incident by the
ultrasonic wave, the vibrating out-of-plane displacement at each data points were measured by using laser Doppler vibrometer
one by one.
Results and Discussions
Horn I
The ultrasonic wave was impinged on the right end of the specimen (Fig. 1). At room temperature and in a dark field circular
polariscope setup, the photoelastic fringe pattern after less than 0.1 sec incidence of the ultrasonic wave is shown in Fig. 10 (a).
This fringe pattern was produced by the standing wave only. As shown in Fig. 10 (a), except the fringes near the right end,
fringes of order zero were located at the top and bottom edges as well as the left end. The fringe orders at left and central
contours were one order higher than those of the right contour. For all those three fringe contours, the order of fringe
increases from the edge to the contour center. The highest order of fringe 5 occurs near the center of the right and central
parts of the fringe pattern.
Figures 10 (b)~10(d) depict photoelastic fringe patterns obtained after ultrasonic wave incident 2 seconds, 4 seconds and 6
seconds, respectively. In fact, photoelastic fringe patterns shown in Figs. 10 (b) ~10(d) were produced by both the standing
wave and thermal stress induced. Distinguishable difference can be found among Figs. 10 (a) and 10(b) ~10(d), in particular,
the increasing influence of the thermal stress on the fringe patterns shown in Figs. 10 (b) ~10(d). The generation of the
induced thermal stress can be realized in the following explanations. First of all, as long as the power of the ultrasonic wave
was on, the standing wave remains in the fringe pattern. To eliminate the effect of the standing wave on the photoelastic fringe
patterns, the power of the ultrasonic wave should be shut down. Whatever remains was due to the temperature changes, i.e.
the thermal-stress induced photoelastic fringe patterns. Fig. 11 depicts the photoelastic fringe pattern when the power of the
ultrasonic wave was shut down after 7 seconds incidence. In contrast to the blurring fringe patterns shown in Fig. 10 (b) ~ (d),
very sharp fringe pattern is obtained in Fig. 11. By using an infrared thermometer, temperatures at points G and H in Fig. 11
were measured [11] and found as 46 and 43 degrees Celsius, respectively. Indeed, the highest order of fringe 2 occurs at
points G and H. The photoelastic fringe pattern shown in Fig. 11 gradually disappeared after about 5 minutes from shutting
down the power of the ultrasonic wave. Therefore, it can be concluded that the photoelastic fringe pattern shown in Fig. 11
was produced by thermal stress only.
5
4
5
3
2
1
0
4
3
2
1
0
1
(a) less than 0.1 second
2
3
4
1
(b) 2 seconds
Fig. 10 Photoelastic fringe pattern after incidence of ultrasonic wave [2, 3]
(c) 4 seconds
(d) 6 seconds
Fig. 10 (Continued)
Fig. 11 Photoelastic fringe pattern obtained after ultrasonic wave stops incidence [2, 3]
Horn II
The AF-ESPI fringe patterns of Fig. 9 (a) and 9(b) are shown in Figs. 12 and 13, respectively. Since the shape of the horn II is
essentially cylindrical, the fringe patterns shown in Figs. 9(a) and 9(b) look circular. Fringes depicted in Fig. 12 are nearly
perpendicular and they are parallel to each other, i.e. the displacement is almost purely longitudinal. Fringe of order zero, i.e.
the nodal point, is located at 43mm from the end face (Fig. 13). This experimental result was confirmed by the FEM result [7].
Fig. 12 AF-ESPI fringe pattern of Fig. 9(a) [7]
Fig. 13 AF-ESPI fringe pattern of Fig. 9(b) [7]
The AF-ESPI fringe pattern of Fig. 9(c) is shown in Fig. 14. No fringes are present, i.e. no in-plane displacements. In other
words, the degree of coplanarity is very high. In comparison, Fig. 15 shows the AF-ESPI fringe pattern of a typical industrial
horn under the same working condition as the horn II. Order of fringe reaches 5 in Fig. 15, i.e. the corresponding displacement
is 0.84µm [1]. Significant improvement of the slip phenomenon by using horn II is very clear.
Fig. 14 AF-ESPI fringe pattern of Fig. 9(c) [7]
Fig. 15 AF-ESPI fringe pattern of a typical horn [7]
As shown in Fig. 16, the largest and smallest displacements along a diameter of the end face are 3.873µm and 3.735µm,
respectively. The difference 0.138µm between the largest and smallest displacements is much lower than the 2µm required by
industry.
Define coplanarity as (1 −
D−d
d
) × 100% , where D and d are the largest and smallest displacements, respectively.
The coplanarity achieved by the horn II is 96.5% by laser Doppler measurements. The ANSYS calculations give the
coplanarity as 98.92%. The difference between the experimental and numerical results may be due to the manufacturing
allowance, environmental influence on the measurement and the accuracy of the vibrometer itself, etc. Nevertheless, the horn
II has reached the goal of improving the non-coplanarity exists in the typical industrial horn.
It should be pointed out here that the out-of-plane AF-ESPI setup was attempted to measure the coplanarity of the end face.
However, the displacement caused by the rigid body motion of the horn itself is much higher than the resolution of the AF-ESPI.
Furthermore, the difference 0.138µm between the largest and smallest displacements of the end face is lower than 0.195µm
required for the appearance of the first order of AF-ESPI fringe [1]. Therefore, an alternative measurement technique such as
the laser Doppler vibrometer was used instead.
Fig. 16 Displacement distribution on the end face [7]
Conclusions
The stress characteristics of horn I simulated by a strip incident by an ultrasonic wave were observed by the digital dynamic
photoelastic system. By using the time-averaged photoelastic technique, a series of photoelastic fringe patterns were
obtained for (1) standing wave only; (2) mixed standing wave and thermal stress induced and (3) thermal stress induced only.
Locations of highest orders of fringes were found for cases of standing wave only and thermal stress induced only. In addition,
with the consideration of producing the resonant mode of the horn purely longitudinal, a new ultrasonic horn, horn II, for flip-chip
bonding was first designed by computer simulation. Both the AF-ESPI and laser Doppler vibrometer were then used to
measure both the in-plane and out-of-plane displacements of the prototype of the horn and verify the FEM results.
Acknowledgments
This paper was supported in part by the National Science Council (grant nos. NSC 93-2212-E007-013 and NSC
94-2212-E007-007), Taiwan, Republic of China.
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