Annalsăofătheă„ConstantinăBrâncuși”ăUniversity ofăTârgu-Jiu,Engineering Series, Issue 3/2015

SIMULATION STUDY WITH SOLIDWORKS SOFTWARE OF AN

ULTRASONIC HORN OF DIFFERENT MATERIALS AND DIMENSIONS
TO OBTAIN THE NATURAL FREQUENCY OF 20 kHz

CornelăHa iegan, Eftimie Murgu University of Resita, Resita, ROMANIA

Marian-Dumitru Nedeloni, Eftimie Murgu University of Resita, Resita, ROMANIA
Diana Micliuc, Eftimie Murgu University of Resita, Resita, ROMANIA
Adrian Pellac, Eftimie Murgu University of Resita, Resita, ROMANIA
SorinăLauren iuăBogdan, Eftimie Murgu University of Resita, Resita, ROMANIA
Ionela Mariana Pelea, Eftimie Murgu University of Resita, Resita, ROMANIA

ABSTRACT: This paper present a study regarding especially the simulation results of an
ultrasonic horn of different materials, especially Titanium (Ti). Such an ultrasonic horn can be used
within a vibratory apparatus for experimental research regarding the cavitation erosion of materials.
By simulating this ultrasonic horn using the SolidWorks software, there will be determined the
natural frequencies according to the mode shapes for different materials as well as the various
dimensions imposed on the Titanium ultrasonic horn. After the proper simulation of this ultrasonic
horn, the final results, around the value of 20 kHz appear values at which the vibratory apparatus
for cavitation erosion researches may correctly function.

KEY WORDS: Simulation, ultrasonic horn, materials, natural frequency.

1. INTRODUCTION Currently, this vibratory apparatus is used

The ultrasonic horn or sonotrode that will in experimental research through the indirect
be simulated is a part of a vibratory apparatus cavitation method for different materials yields,
used for experimental research cavitation with different results that were disseminated [6]
erosion of materials. - [9].
In this case, the vibratory apparatus, in All the while an ultrasonic horn fails,
addition to the ultrasonic horn further comprises requiring reaching others ultrasonic horns for
a DG 2000 type ultrasonic generator, a piece- further experimental research [10] - [12].
electric acoustic transducer and a mechanical In this paper, through the SolidWorks
transformer [1] - [4]. software, the study that will be made is a
For an ultrasonic horn to operate properly Frequency type study.
in the composition of this vibratory apparatus, it For the 3D designed ultrasonic horn, its
is necessary that the natural frequency to be frequency will be determined according to the
aroundΝβ0Ν±0.5 kHz. vibration modes in the area aroundΝβ0Ν±Ν0.5ΝkHzΝ
Also, this vibratory apparatus has been for different materials and different sizes for the
equipped by the manufacturers [5], with two Titanium material.
Titanium ultrasonic horns (Ti-6Al-4V) Based on results from other citations of
especially calibrated for Steel and Aluminum authors [3], [13], [14], ultrasonic horns have
materials, for the direct cavitation method. been achieved in practical lengths between 154
÷ 155 mm.

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At these lengths, the ultrasonic horns 2.1. The simulating on different

functioned correctly for the vibratory apparatus. materials
Such an ultrasonic horn is shown in Figure 1. This simulation that includes 20 vibration
modes for the ultrasonic horn with the length of
154 mm, will be made on 8 materials with
different mechanical properties chosen by the in
SolidWorks, namely: Alloy Steel, Cobalt,
Molybdenum, Nickel, pure Gold, pure Silver,
Titanium and Vanadium.
The selection of some of the 8 materials
Figure 1. A practicably realized described above is shown in Figure 3.
ultrasonic horn

For the proper simulation it will be chosen

the 3D projection of the assembly: mechanic
transformer (booster) – ultrasonic horn.

2. THE SIMULATION STUDY

OF THE ULTRASONIC HORN
For going through the simulation with the Selecting the Cobalt material
SolidWorks on the Frequency type study
several stages are covered [15] - [17], of which
we remind:
- design the 3D geometries of the
mechanic transformers (booster) and of the
ultrasonic horn components (fig. 2);
- attributing the material from the
SolidWorks library; Selecting the Molybdenum material
- meshing in finite elements;
- running the study;
- visualizing the results that include, in
principle, the vibration mode shapes and the
values of the natural frequencies, respectively
the mass participation coefficients.

Selecting the pure Silver material

Figure 2. The 3D design assembly in Selecting the Vanadium material

SolidWorks: mechanic transformer – ultrasonic Figure 3. Selecting and choosing of some
horn materials from the SolidWorks software

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These materials are different for the The amount of approximately 20 kHz for
ultrasonic horn, while the mechanical the Titanium material, which in Table 2 are
transformer was awarded only the Alloy Steel intended to show the 20 mode shapes of mass
material. participation coefficients, and in Figure 4,
The obtained results for these materials, several vibration modes.
we were interested in only their frequencies Table 2. Natural frequencies and the mass
around 20 kHz. These values are the only mode participation coefficients for the Ti material
of vibration corresponding to the mode number Frequency Mass participation coefficients
Mode
19, as shown in Table 1, wherein the density of [kHz] X direction Y direction Z direction
each material is shown. 1 1,3985 0.16798 0.0000185 0.6233800
2 1,4041 0.6241400 0.0000022 0.16868
Table 1. Natural frequencies - mode 19 and the 3 3,5073 0.056183 0.0000699 0.0090681
density for each material 4 3,5093 0.0092024 0.0000114 0.055624
Natural Density 5 6,4969 0.032453 0.0001436 0.1834800
No. Name of 6 6,5244 0.1168700 0.0006552 0.031177
frequencies [kg/m3]
Crt. material 7 6,7909 0.0001462 0.0001686 0.0001212
[kHz]
8 7,953 0.021427 0.0012750 0.41268
1 Alloy steel 20,507 7700 9 7,9554 0.41101 0.0013526 0.02143
2 Cobalt 19,615 8900 10 8,5358 0.0021665 0.49567 0.0045818
3 Molybdenum 21,595 10000 11 12,594 0.08347 0.0001203 0.00066715
4 Nickel 19,896 8500 12 12,598 0.00068585 0.0006022 0.082096
5 Pure Gold 12,444 19000 13 12,888 0.0013761 0.0002206 0.0000667
6 Pure Silver 14,345 11000 14 13,602 0.0004599 0.0001296 0.0000100
7 Titanium 20,041 4600 15 14,797 0.0000010 0.0420910 0.0000010
8 Vanadium 19,649 6100 16 15,370 1.59e-008 0.44979 0.0000586
17 17,571 0.051019 0.0037638 0.00022043
18 17,606 0.00020626 0.0000003 0.052381
Among these materials, the lower 19 20,041 0.0002698 0.022648 0.0104810
frequencies were recorded in pure Gold and 20 21,258 0.00011087 0.0000888 0.10728
pure Silver, materials which in reality are very Sum X = Sum Y = Sum Z =
expensive and which do not achieve the level at - -
0.83382 0.96812 0.94138
which an ultrasonic horn pays off.
The results are closest to the value of 20
kHz for the materials: Alloy Steel, Nickel,
Titanium and Vanadium. Figure 3 presents these
results in graphic form for all 20 of the mode
shapes.

25

Frequency a) Mode 1 b) Mode 5

20 [kHz] Alloy Steel
Nickel (Ni)
15 Titanium (Ti)
Vanadium (V)
10

5
Mode [-]
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Figure 3. The graphic of the values close c) Mode 15 d) Mode 19

to 20 kHz Figure 4. Some vibration mode shapes for the
Titanium material

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As there can be seen from Table 2, the

mass participation coefficient in the Y direction For the 9 dimensions chosen for the
is greater in value than those in the X and Z acoustic concentrator, the results thus obtained
direction, respectively, as can be seen in Figure were around 20 kHz for the same vibration
4 d), where the ultrasonic horn at mode 19 has mode of number 19 (Table 3).
an axial displacement. Table 3. The natural frequencies of the
Because the nearest to 20 kHz is the Titanium material - mode 19
20.041 kHz value, it belongs to the Titanium Dimension of the Natural
material. Thus, a simulation will now be made No.
upper cylindrical frequencies
only on the material for the ultrasonic horn of Crt.
part [kHz]
154 mm length, but also for the different 1 83 mm 19,456
dimensions of the upper cylindrical part. 2 84 mm 19,574
3 85 mm 19,697
2.2. Simulating on the Titanium 4 86 mm 19,820
material for different dimensions 5 87 mm 19,944
These dimensions of the upper cylindrical 6 87,5 mm 20,006
part of the ultrasonic horn with an overall length 7 88 mm 20,068
of 154 mm are given next in Figure 5.
8 89 mm 20,190
9 90 mm 20,312

The value is close to 20 kHz for the

dimension of 87.5 mm, which in Table 4 are
shows the 20 mode shapes and the mass
participation coefficients.

Table 4. The Natural frequencies and the mass

participation coefficients for the dimension of
a) 83 mm b) 84 mm c) 85 mm 87,5 mm
Frequency Mass participation coefficients
Mode
[kHz] X direction Y direction Z direction
1 1,4071 0.16213 0.0000124 0.00015267
2 1,4129 0.00015342 0.0000023 0.1628
3 3,5064 0.064018 0.0000146 0.00081624
4 3508 0.00082799 0.0000853 0.063356
5 6,4843 0.0329 0.0000153 0.2451800
6 6,5116 0.2179600 0.0012789 0.031513
d) 86 mm e) 87 mm f) 87,5 mm 7 6,7843 0.0000023 0.0000656 0.0002790
8 7954 0.035667 0.0227150 0.4017
9 7,9567 0.39984 0.0074461 0.035739
10 8,5773 0.0081513 0.48675 0.0039792
11 12,529 0.08372 0.0002621 0.00066875
12 12,533 0.00068106 0.0000042 0.082093
13 12,811 0.0000181 0.0000284 0.0000795
14 13,577 0.0000480 0.0005851 0.0000204
15 14,722 0.0000090 0.0000461 0.0000354
g) 88 mm h) 89 mm i) 90 mm 16 15,323 0.0010692 0.45785 0.0012627
17 17,507 0.049897 0.0008617 0.00064843
Figure 5. The dimensions for the upper
18 17,543 0.0006041 0.0010291 0.051207
cylindrical part of the Titanium
19 20,006 0.0000834 0.02333 0.0070646
ultrasonic horn
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Frequency Mass participation coefficients 25

Mode Frequency
[kHz] X direction Y direction Z direction 20
[kHz] L = 87,4 mm
L = 87,45 mm
20 21,199 0.0465520 0.0004372 0.10942 L = 87,46 mm
15
Sum X = Sum Y = Sum Z = L = 87,47 mm
- - L = 87,48 mm
0.83046 0.96794 0.94013 10

Because the nearest 20 kHz size belongs to 5

Mode [-]
87,5 mm, next a simulation will carried out 0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
around this size.
Figure 6. The natural frequencies for the
2.3. Simulating on the Titanium 5 dimensions
material for the upper cylindrical part
around the dimension of 87, 5 mm From Table 5, it is noted in particular that
These dimensions around the 87,5 mm are the most appropriate value of 20 kHz for mode
shown numerically in Table 5 and also 19, is between the size of 87,46 and 87, 47 mm
graphically in Figure 6. respectively.
Based on the results of the simulation as
Table 5. Natural frequencies for the dimension well as on other results from the previous
of 87,5 mm research of authors [2] - [4] and [14], we can put
Length of the upper cylindrical part around in practice the realization of this ultrasonic horn.
Mode the dimension of 87,5 mm These dimensions will work correctly on the
87,4 87,45 87,46 87,47 87,48 vibratory apparatus used through the indirect
1 1407.7 1407.4 1407.2 1407.2 1407.2 method for experimental research on cavitation
2 1413.5 1413.1 1413.1 1413.1 1413.1 erosion of materials.
3 3500.2 3503.5 3503.8 3504.6 3504.9 3. CONCLUSION
4 3502.1 3504.9 3505.4 3505.9 3506.8
The conclusions that can be drawn from
5 6484.8 6485.8 6483.3 6484.3 6483.3
6
this paper are:
6512.6 6511.5 6511.4 6511.4 6511.8
7 6788.6 6785.9 6786.1 6786.2 6785.5
- For the vibratory apparatus to work
8 7954.7 7952.5 7954.1 7954.7 7952 correctly, it is necessary that the used ultrasonic
9 7957.1 7955.8 7956.5 7956.9 7956.7 horn to be dimensioned and calibrated at the
10 8580.5 8577.3 8577 8579 8577.4 limits of β0Ν±Ν0,5 kHz;
11 12530 12527 12527 12528 12529 - The simulation study comprised 20
12 12534 12531 12532 12534 12534 vibration modes regarding the ultrasonic horn
13 12795 12806 12805 12806 12808 with the total length of 154 mm, for 8 materials
14 13572 13571 13576 13573 13570 with different mechanic properties in the
15 14722 14722 14722 14722 14721 SolidWorks software, from which the
16 15323 15319 15318 15326 15319 simulation for the Titanium material continued
17 17489 17497 17497 17496 17499 up to the value of 20 kHz;
18 17526 17526 17531 17532 17535 - From the simulation results for the
19 19991 19998 19998 20003 20003 chosen materials, the searched for natural
20 21199 21195 21192 21198 21191 frequencies came close to the value of 20 kHz
only at the vibration mode number 19, where
the Titanium material registered the value of
20,041 kHz;
- Each time for the vibration mode number
19, the mass participation coefficient on the Y
direction has a greater value than the mass
participation coefficients on the X respectively

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