Experimental and numerical investigation of the structure-borne noise transmitted from the gearbox to fuselage of a helicopter

R. Di Sante1, M. Vanali2, E. Manconi2, A. Perazzolo3 1University of Bologna, Department of Industrial Engineering –DIN

Via Fontanelle 40, 47121, Forlì, Italy

e-mail: raffaella.disante@unibo.it

2University of Parma, Department of Industrial Engineering

Via delle Scienze 181/A, 43124, Parma, Italy

3Leonardo Helicopter Division, Interior Acoustics – Aerodynamics

Via G. Agusta 520, 21017, Cascina Costa di Samarate, Italy

Abstract In order to predict the interior noise level of a helicopter using the Statistical Energy Analysis (SEA)

approach, the mechanical powers transmitted to the fuselage by the main gearbox are needed as external

inputs to the vibroacoustic model. In this work, the power values were estimated experimentally from the

mechanical mobility at the fuselage attachment points and in-flight acceleration measurements. The

experimentally-obtained dynamical powers were then applied to the SEA model at the connecting points

between the main gearbox to the fuselage, i.e. the antitorque plate and struts.

The good correlation of the SEA model with testing results in terms of sound pressure level in the cabin

proved that the numerical-experimental methodology is reliable and can therefore be used for current and

future design of Leonardo helicopters.

1 Introduction

In recent years, the expanding market of VIP helicopters has required increased on-board comfort and

therefore a significant improvement of the cabin interior acoustics. Consequently, an enhanced noise

simulation capability is currently needed in order to optimize the design, reduce the prototyping phase and

the number of test flights, and finally ensure that the desired target in noise reduction is achievable.

The most important source of vibration in a helicopter, and therefore of structure-borne noise, is that

generated by the main sustaining rotor rotating system. Moments and forces are transmitted through the

main gearbox via the fuselage attachments, resulting in vibration and noise in the cabin.

A well-suited method to predict the vibroacoustic behavior of such a complex mechanical system is the

Statistical Energy Analysis (SEA) [1, 2] which allows a quick response at the system level and at high

frequency, not possible using for example finite element and boundary element methods.

According to the type of excitation at the contact points, force sources or velocity sources can be considered

for predicting the power transmitted from the source to the receiver using SEA [3]. However, often there

are issues related to the location of the input forces or difficulty to place force transducers on the structure.

Also, in many practical situations direct measurement of the interface forces is difficult if not impossible,

as in the helicopter case. Thus, velocity sources must be used and the power transmitted must be evaluated

using the mechanical impedance matrices of the coupled structure.

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In order to estimate the mechanical power transmitted from the main gearbox (MGB) of the helicopter to

the fuselage and then to the cabin, the velocities and the mechanical mobility values at the attachment points

were used in this work. The velocities were obtained from the accelerations measured during flight, while

the mobility matrix was calculated from ground tests aimed at the estimation of the frequency response

functions (FRFs) of both the bare cabin and the complete helicopter. Firstly, the fuselage as a single

substructure was investigated and then the whole helicopter, in order to evaluate the variation in the

mechanical impedance due to the added mass and changed stiffness in the final configuration.

The experimentally-obtained mechanical powers were applied to the vibroacoustic SEA model at each

interface point coupling the main gearbox to the fuselage. Then other airborne sources were added to

complete the airborne and structure-borne noise paths for the prediction of the full cabin interior noise in

order to simulate the in-flight operating conditions.

The paper is organized as follows. The technique used to estimate the mechanical power as an input for the

SEA model is described in Section 2, while the experimental procedure adopted to obtain the mechanical

mobility values is presented in Section 3. The results, in terms of mechanical power obtained from the

experiments during flight and on ground, are reported in Section 4. An overall description of the SEA model

of the helicopter and the comparison between the predicted and measured sound pressure level (SPL) in the

cabin are both presented in Section 5. Concluding remarks are finally made in Section 6.

2 Time average energy flow - power transmitted from the source to the receiver

As stated in the introduction, the transmitted mechanical power needs to be estimated in order to be used as

an input to the SEA model. In this section the power transmitted is calculated using the impedance Z (or

apparent mass A) matrices and velocity (or acceleration) signals measured in flight at the connecting points

between the main gearbox and fuselage.

For harmonic excitation, the time average power is given as the sum of the power input at each point

(1)

Where and , are the velocity and acceleration responses

respectively, at the N driving points. Complex quantities are considered and denotes Hermitian transpose.

The formulation of the time average power in equation (1) is exact for periodic signals or, in case of non-

periodic signals, if the sampling time tends to infinite. In a real situation, for example when the signals are

sampled experimentally, the expected value of the time average power can be practically computed by: i)

taking a long enough measurement interval; ii) dividing this interval in a series of N sub-intervals; iii)

computing the active power for each sub-interval; iv) averaging the results. The average power then

becomes:

(2)

Given that the operational acceleration or velocities can be often measured experimentally, the most difficult

task for the vibroacoustic prediction of complex structures is the overall Z and A matrix estimation. This

will be discussed in the next section.

1 2[ , , ... , ]T

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Na a aa

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*1 1Re Im

2 2P

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* *

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Re Im1 1

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N Ni i i i i i

i i

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Z v v A a a

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3 Mechanical impedances evaluation

In common practice, mechanical impedances are evaluated on ground by means of impact testing and FRF

evaluation techniques [4]. The typical test condition deal with the bare cabin since this is the easiest

configuration to be checked, being fully accessible. In this paper, both the bare cabin and the ready-to-fly

layout (with the MGB mounted on top and fully accessorized), have been tested in order to highlight possible

differences in terms of mechanical impedance values.

The mechanical impedance was evaluated at all the connecting points between the main gearbox (vibration

source) and the cabin (vibration receiver). The test points are shown in Figure 1. The accelerance matrices

were measured via impact testing. All data were sampled at 6400 Hz and their coherence was checked for

all impact/response functions.

Figure 1: Measurement points on the bare cabin

The bare cabin was tested both in suspended (free-free) and supported conditions, while the complete

machine only in supported conditions.

It was found out that there are no significant differences between the results for the supported and suspended

bare cabin. As an example, Figure 2 shows the direct FRF magnitude measured in the Z direction at point 3

for the suspended (red line) and supported (blue line) conditions.

Figure 2: Direct FRF, Point 3 direction Z, Supported Vs Suspended bare cabin

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Relevant discrepancies were instead found between the FRFs of the bare cabin vs the fully equipped cabin

(with the MGB and all equipment). As an example, Figure 3 shows the direct FRF magnitude measured in

the Z direction at point 3 for the bare cabin (red line) and fully equipped cabin (blue line) conditions.

Figure 3: Direct FRF, Point 3 direction Z, Bare Vs Fully Equipped cabin

Instead of using such an experimental procedure, another approach might consists in numerically coupling

the impedances of the source (MGB) and the receiver (cabin). This has been investigated in [5-7]. However,

it was demonstrated that this procedure can lead to inaccurate results mainly due to the difficulties in

measuring rotational degrees of freedom responses.

4 Power estimation results

The power was calculated using equation (2), where the full impedance matrix is estimated experimentally

on ground, while the accelerations are measured in flight. The measurement locations are the same as those

depicted in Figure 1. In the case of flight testing, attention was focused on the cruise condition, being this

the longest experienced by passengers during a typical flight.

In Figure 4 the 3rd octave band acceleration spectrum is shown for all measured channels.

Figure 4: 3rd octave band in flight acceleration RMS values

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As it can be seen, three main band are highlighted. The lowest frequency one, being around 30 Hz, is not

interesting in terms of structural-borne sound (i.e., if A-weighted). The mechanical transmitted power was

estimated via the same measured accelerations. Both the impedances estimated for the empty and fully

equipped cabin were used.

Results are given in Figure 5 in terms of the total power transmitted to the cabin at the connecting points.

Figure 5: Transmitted power in narrow frequency band

Figure 5 shows that the main power contributions are in the band highlighted in Figure 4. Using the fully-

equipped cabin impedance leads to a more reliable transmitted power estimation, since it can also be noticed

that in these bands the power is mainly flowing to the cabin, as expected. The total transmitted power for

the fully-equipped cabin is then computed in 3rd octave band. The results obtained in this case are shown in

Figure 6.

Figure 6: Total Transmitted power in 3rd octave band

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This data values are then feed into the SEA model described in the next section.

5 SEA Model and in flight measurements

The experimental activities allowed the determination of the accelerance matrix during ground testing and

estimation of the in-flight vibration levels. In the case of flight testing, attention was focused on the cruise

phase, being this the longest flight condition experienced by passengers during a typical flight.

As explained in section 4, these two sets of values were subsequently combined in order to obtain the

mechanical powers transmitted by the MGB into the fuselage via the attachment points, i.e. the anti-torque

plate and the four struts ends.

Figure 7: Longitudinal section of the SEA helicopter model

These datasets together with the airborne noise sources (upper deck cavity noise and aerodynamic excitation

due to the turbulent boundary layer on the fuselage skin) were applied as loads to the vibroacoustic SEA

model shown in Figure 7. In Figure 8 a detail of the upper deck area is shown, where the red arrows indicate

the connecting points of the anti-torque plate and the orange ones the locations of the four struts. These are

the same points in which impedance and acceleration measurements have been taken (see Figure 1).

Figure 8: Upper deck (roof) area with indicated anti-torque plate and struts attachment points

In the model, the properties of the soundproofing materials (damping, blanket and barriers), the lining’s

upholstery and the seats are included in order to reproduce the fully trimmed VIP layout accurately. In

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particular, the initial soundproofing package was defined based on the experience gained from previous

projects, and the available maximum weight allowed for the trim package.

Results obtained from the simulation were finally compared with the targeted noise values ensuring the best-

in-class product from an acoustical point of view. This aspect is very important since the VIP marketing is

highly competitive and today’s customers demand increased acoustic and vibration comfort on board.

After preliminary evaluations, the vibroacoustic SEA model was extensively used in order to optimize the

material allocation and save as much soundproofing weight as possible without affecting the acoustic

performance. The most satisfying soundproofing material layout was then identified and implemented in

the prototype of the first VIP-configured aircraft. The latter was used for in-flight interior noise

measurements with the aim to check final performance and validate the mathematical model.

Figure 9: HEAD/Squadriga 2 digital recorder

During flight the noise level was measured by a state-of-the-art digital recorder, shown in Figure 9,

connected to ICP microphones distributed inside the cabin to capture the noise radiation and perform the

test according to the SAE-ARP 1964 standard. The signal traces were then processed by the HEAD/Artemis

acoustic software in order the extract the overall noise level and the 1/3-octave spectrum.

Finally, the measured noise level was compared with the simulated one obtaining a good agreement as

shown in Figure 4 for two locations (rearward cabin on the left and forward cabin on the right) inside the

passenger compartment.

Figure 10: Comparison between SPL of simulation and of testing in two locations - the green and blue

curves relate to the simulation and the red and magenta relate to testing

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Not only the experimental trend but also the two peak levels in the noise spectra are well reproduced by the

simulation. The first peak at 800 Hz is generated by a mix of sources (i.e. hydraulic, mechanic components)

while the second peak at 2.5 kHz is mainly related to the transmission gear.

The obtained results are consistent with the targeted noise levels. In addition, the successful comparison

between simulation and testing confirmed the reliability of the mechanical loads obtained from the newly

proposed methodology. Consequently, the latter is considered validated and applicable for future design.

6 Conclusions

In this paper, a numerical-experimental methodology was developed to predict the noise inside a helicopter,

based on the SEA technique.

The methodology requires the use of the velocity (or accelerations) data at the connecting points between

the main gearbox and fuselage under operating conditions, together with the mechanical mobility estimated

on ground at the same locations.

The mechanical mobility values are measured on ground via impact testing on the complete helicopter, since

measurements on the bare cabin only, which might simplify the execution of the experiments, has

demonstrated to give misleading results.

Numerical results, in terms of the sound pressure level estimated in different locations inside the cabin, were

in good agreement with the experimental ones, obtained during flight. This methodology may therefore be

successfully used to predict the noise level for current and future helicopter designs.

References

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