VIBRATION ANALYSIS AND NOISE REDUCTION OF DUCTED FANS
B. Magyar
Student, Department of Applied Mechanics, Budapest University of Technology and Economics, H-1111. Budapest, Muegyetem rkp. 5. Tel: (1) 463 1369, e-mail: balint.b.magyar@gmail.com
G. Stépán
Professor of Mechanics, Head of Department, Member of the Hungarian Academy of Sciences,Department of Applied Mechanics, Budapest University of Technology and Economics
H-1521. Budapest, Tel: (1) 463 3470, e-mail: stepan@mm.bme.hu
Abstract: A robot is under development to be used in a home and/or in a workplace environment for manipulating small objects autonomously or in close cooperation with humans. The position control of the robot’s swinging unit is aided by two parallel axial flow ducted fan in the lab prototype. The construction appeared to be much louder than would be acceptable for a household device. The aims of this research are identifying noise components of the ducted fans, and based on these results, making suggestions for the redesigned construction.
Keywords: Ducted fan, Noise reduction, Finite element frequency analysis
1. ACOUSTIC PRESSURE LEVEL ESTIMATION [1]
We can make a crude estimation on the intensity of the emitted noise of an average axial flow ducted fan. The empirical formula in [1] gives usLW
[
dBW]
, the acoustical capacity level, according to the flow rate qv ⎥⎦
⎢ ⎤
⎣
⎡ s m3
, and the total pressure change ∆pö
[ ]
Pa . The value of q1 and ∆p1 are ⎥⎦
⎢ ⎤
⎣
⎡ s m3
1 and 1
[ ]
Pa in this empirical formula:⎟⎟⎠
⎜⎜ ⎞
⎝
⎛
∆ + ∆
⎟⎟⎠
⎜⎜ ⎞
⎝ + ⎛
=
1 1
lg 20 lg
10
40 p
p q
LW qv ö (1)
After algebraic transformations, and introducing Pe
[ ]
W , the effective power is:⎟⎟⎠
⎜⎜ ⎞
⎝
⎛
∆
⋅∆ +
=
⎟⎟
⎟⎟
⎟⎟
⎠
⎞
⎜⎜
⎜⎜
⎜⎜
⎝
⎛
∆
⋅∆
∆
⋅∆ +
=
1 1 1
1 1
lg 10 40 lg
10 40
1
p p P P p
p p p q
L q ö e ö
P P
ö W v
e
43 42 1
(2)
Assuming that the ventilators produce small dynamic pressure change, we can therefore estimate thrust force with the product of the total pressure change and the cross section area.
Introducing the thrust force F[N] and the cross section area A[m2], we have
⎟⎟⎠
⎜⎜ ⎞
⎝
⎛
⋅ ⋅ + ⋅
⎟⎟=
⎠
⎜⎜ ⎞
⎝
⎛ ⋅
∆
⋅∆ +
⎟⎟=
⎠
⎜⎜ ⎞
⎝
⎛
∆
⋅∆ +
=
1 1
1 1
1 1
1
lg 10 40 lg
10 40 lg
10
40 P F
A A
F P A
A p p P P p
p P
LW Pe ö e ö e . (3)
All quantities with subscript 1 have unit values. Applying far field approximation on the monopole source [2], we obtain
11 lg 10 lg
10 2+ −
−
=L r D
L W (4)
where r [m] is the distance from the source, L[dB] is the acoustic pressure level, and D=1, because the source is radiating to the whole space. If we substitute Pe =100
[ ]
W , F =5[N] and r=1 [m], the result will be the acoustic pressure level depending on the diameter of the ducted fan.30 40 50 60 70 80
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
D [m]
L [dB]
Figure 1. Empirical curve, estimate of acoustic pressure level vs.
ducted fan cross section diameter
The estimation on the A-weighted acoustic pressure level of the lab prototype with diameter ]
[ 245 ,
0 m
D= , effective power Pe =100
[ ]
W , thrust force F =5[N] and distance r=1 [m]for the two fans and by adding a source means an additional6[dBA] is:
] [ 75 ] [ 6 ] [
69dBA dBA dBA
LA = + = .
2. NOISE COMPONENTS OF DUCTED FANS
We can separate two major groups of the noise components according to the method of the phonation: flow source noises, and mechanical source noises [1].
2.1. Flow source noises
Basically we have three major types of flow source noises:
• Trace noise
• Noise of the turbulent boundary layer
• Noise of the separated flow region 2.1.1. Trace noise
As a consequence of Γ≠0, meaning the circulation around the airfoil is not zero, the velocity of the flow reaching the edge from the low pressure region differs from the velocity of the flow from the high pressure region, and this causes shear flow illustrated in Figure 2.
Figure 2. Flow filed behind an airfoil, CFD simulation, website of the University of Erlangen
Trace noise is not a significant component, and it originates from normal working conditions.
2.1.2. Noise of the turbulent boundary layer
In the turbulent boundary layer there is a low pressure region that causes drag force, which is the component of the reaction force parallel to the flow direction. In this region, the pressure is fluctuating, creating a dipole noise source.
Figure 3. Illustration of the boundary layer and reaction force components Hand drawing, University of Sheffield
In order to minimize the noise of the turbulent boundary layer, we have to choose an airfoil which has been optimized to the lift drag coefficient defined as
drag lifting
F
S = F (5)
2.1.3. Noise of the separated boundary layer
The separation of the boundary layer occurs only under abnormal circumstances; in case of boundary layer separation the emitted noise increase can be up to 10 – 15 [dB]. The separation is caused by improper direction of the velocity on the entrance edge. If the ventilator blade is working in a turbulent region, where the directions of the velocities are fluctuating, boundary layer separation on the airfoil will possibly occur.
Figure 4. The separation of the boundary layer, CFD simulation University of Erlangen
We can prevent the separation by designing a proper entrance region for the ducted fan.
We should consider two principals: the entrance edge of the ducted fan should have a filleted inner corner, and the fan should be close to the intake trunking.
Figure 5. Improper construction, (1): separated flow
Figure 6. Improper construction, (1): laminar boundary layer (2): turbulent boundary layer
Figure 7: Proper construction for intake trunking
2.2. Mechanical source noises
In our case, two major types of mechanical source noises occur:
• Noise of the drive train
• Noise of the excited cover 2.2.1. Noise of the drive train
Trivially, this component is the noise of the motor and drive train; if we buy complete drive trains, this issue deserves no further discussion.
2.2.2. Noise of the excited cover
Rotating parts always have eccentricity, and the periodically fluctuating reaction force acted on the shaft excites the ducted fans cover [3]. For the examination of this excitation process, it is necessary to carry out the modal analysis of the structure. Since the complexity of the structure does not allow us to use analytical solutions, finite element analysis is chosen as a good alternative.
Figure 8. Photo of the swinging unit Figure 9. Solid Edge model
Figure 10. Finite element model, COSMOS/M
The finite element model contains shell, beam and concentrated mass elements. The model has 26824 elements and 162168 DOF. COSMOS/M finite element solver has been used.
2.2.2.1. Results
Since the aim is the identification of the natural frequencies, the model has no structural constrains on nodal displacements. Therefore the first six natural frequencies are zero, related to translational and rotational mode shapes. The available version of COSMOS/M could only calculate the first 200 natural frequencies, shown in figure 11. The first six zero-frequencies have been removed from this graph.
Figure 11. Natural frequencies, calculated by COSMOS/M
The natural frequencies are relatively close to each other; for further examination it appeared to be useful to introduce frequency density, defined as the number of natural frequencies in the particular 20 [Hz] wide range.
Figure 12. Frequency density, calculated by COSMOS/M
3. MEASUREMENT
The measurement setup consisted of four channels: two accelerometer signals, a microphone signal, and a pulse counter. During each measurement step, the spectrum of each channel was recorded. The PWM controller reduced the rpm of the ducted fans step by step.
In the following chapter, the results of three runs will be introduced. The parameters of the three runs are summarized in Table 1.
Table 1. Measurement parameters
The change of RPM was not linear in time according to the data from the pulse counter.
Figure 13 represents the RPM graphs.
Figure 13. RPM vs. time according to the pulse counter
Figure 14. Photo of the measurement set
In Figure 14, yellow circles show the position of the accelerometers. These devices have magnetic bases, and were attached to heads of the screws.
A-weighted acoustic pressure levels were calculated form the microphone signal, instead of time; RPM is on the vertical axis in Figure 15, based on RPM vs. time data.
Figure 15. A-weighted acoustic pressure level, measured on the microphone
3.1. Waterfall diagrams
Figure 16 represents the waterfall diagram of the microphone signal, the color is proportional with the logarithm of the acoustic pressure amplitude. On the left side, blue lines show the values of natural frequencies calculated by COSMOS/M, the length of the lines are proportional with the frequency density, meaning the number of natural frequencies in each 20 [Hz] wide range.
Figure 16. Waterfall diagram of the microphone signal, 1st measurement
In the waterfall diagram of Figure 16, there are two different types of amplitude peaks:
there are time (RPM) independent peaks forming vertical lines, and time depending peaks. In the frequency region with the highest natural frequency density, noise has a relatively strong component, which is the RPM-independent noise of the excited cover.
In order to examine the characteristics of RPM-dependent noise amplitude peaks, we have to rescale the vertical axes as in Figure 17 using RPM instead of time, according to the data from the pulse counter.
Figure 17. Waterfall diagram of the microphone signal, 1st measurement, scaled to RPM
Figure 18. Waterfall diagram of the 2nd accelerometer signal, 3rd measurement
After rescaling, the characteristics of RPM-dependent noise amplitude peaks seem to be linear in Figure 17. It is fairly unusual that there are noise amplitude peak lines, with frequencies one hundred times the RPM. This should be an issue of further examination.
During the third measurement, we increased the cutting frequency for the FFT to 12 [kHz], in order to see the effect of the 8 [kHz] PWM control. Figure 18 represents the waterfall diagram of the second accelerometer. We can see the definite but thin vertical line at 8 [kHz]. This whistling noise is quite unpleasant, and though eliminating this noise component will not significantly decrease the A-weighted acoustic pressure level, the characteristic of the sound of the ducted fan will be definitely more acceptable.
4. CONCLUSIONS
4.1 Reduction or elimination of noise components:
• Flow source components
Trace noise - Not significant
Noise of the turbulent boundary layer - By choosing better airfoil
Noise of the separated flow region - Proper contstruction of the intake trunking
• Mechanical source components
Noise of the excited cover - By increasing stiffness, rarefying natural frequencies
Noise of the PWM control - By raising controller frequency above human hearing threshold
4.2. Estimated total possible noise reduction
Considering the suggestions above the estimated acoustic pressure decrease is about:
[
dBA]
LA =6~8
∆
Acknowledgement. This research was supported by the ACROBOTER Specific Targeted Research Project co-funded by the European Commission within the 6th Framework Programme.
REFERENCES
[1] Koscsó, Gábor, Zajvédelem, Budapest University of Technology and Economics, lecture notes, Budapest, 2006
[2] Koscsó, Gábor, Műszaki akusztika, Budapest University of Technology and Economics, lecture notes, Budapest, 2006
[3] Stépán, Gábor, Gépek dinamikája, Budapest University of Technology and Economics, lecture notes, Budapest, 2006
[4] Stoyan Gisbert: Numerikus módszerek, ELTE, Budapest, 1997
[5] Ewins, D. J., Modal testing: Theory and Practice, Wiley, New York, 1989
