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Helicopter interior noise reduction using compounded periodic struts
Accepted Manuscript Helicopter interior noise reduction using compounded periodic struts Yang Lu, Fengjiao Wang, Xunjun Ma
PII:
S0022-460X(18)30468-1
DOI:
10.1016/j.jsv.2018.07.024
Reference:
YJSVI 14266
To appear in:
Journal of Sound and Vibration
Received Date: 31 October 2017 Revised Date:
5 June 2018
Accepted Date: 12 July 2018
Please cite this article as: Y. Lu, F. Wang, X. Ma, Helicopter interior noise reduction using compounded periodic struts, Journal of Sound and Vibration (2018), doi: 10.1016/j.jsv.2018.07.024. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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Helicopter interior noise reduction using compounded periodic struts
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Fengjiao Wang, Yang Lu, and Xunjun Ma National Key Laboratory of Rotorcraft Aeromechanics, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, China
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This paper characterizes the performance of a novel compounded gearbox periodic strut
controlling the noise in helicopter cabin through modeling, simulation and experimental research. The strut exhibits low transmissibility in the specified frequency ranges, called “stop bands”.
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Based on a certain helicopter model, a dynamic acoustic-structure coupling system is firstly built by using the finite element method and the transfer matrix method. Subsequently, according to the gear mesh vibration transmission path, vibration and noise reduction characteristics analysis are conducted respectively. Comparing with the plain strut, attenuations of both vibration and noise in excess of 60dB are obtained in simulations. On a specially designed helicopter platform,
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experimental research is carried out simultaneously in two aspects of fuselage vibration and cabin noise. The effectiveness of the novel strut used for helicopter cabin broadband noise reduction is demonstrated by the coincidence of the simulation and experimentation results, where attenuations
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of measured fuselage vibration and cabin noise exceed the level of 40dB and 30dB respectively in
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the frequency range from 300 to 2000 Hz.
I.
Introduction
The vibration of mid- and high-frequency harmonic generated by gear meshing in the main gearbox is one of the dominant sources of helicopter cabin noise [1-3]. The typical frequency range locates between 500 Hz and 2000 Hz which influences human’s subjective reaction greatly [1]. The vibration can be carried by the support struts between the main gearbox and the fuselage, and radiate structure-borne noise into the cabin [4-5]. Thus, the cabin noise can be controlled by suppressing the vibration transferred to the fuselage. Currently, two main methods are used to address this problem.
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One method is to actively isolate the gear mesh vibration using actuators installed on the supported struts or nearby the mounting points of the struts as secondary forces [3, 6-10]. The feasibility and effectiveness have been demonstrated within multiple flight tests. Eurocopter Deutschland and the EADS Corporate Research Center, which
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introduced smart struts to control the structure-borne sound transmitted, are the typical representatives of research departments [7, 8]. The smart strut consists of piezoelectric actuators that are directly bonded to the BK117 support struts and provides good effectiveness at controlling the noise of multiple gear mesh frequencies in a flight test. In addition, the Sikorsky Aircraft Corporation and the Boeing Company respectively utilized different point force
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actuators mounted near the support struts [3, 9]. The active noise control (ANC) systems use cabin noise as feedback and produce a high capability to reduce the primary gear mesh tone over a wide range of steady and transient flight
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conditions.
Comprehensive experiments and analysis have shown that active methods can manage multiple gear mesh frequency components effectively. However, the ability of broadband noise reduction is very limited. In addition, several inherent problems are presented, such as actuator/sensor location optimization, stability of active control algorithms, and high cost [11, 12].
An alternative is to embed periodic structures into the transmission path, which have unique dynamic
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characteristics of restricting wave propagation within specific frequency bands. With proper design, the periodic structure can realize broadband vibration attenuation from the gearbox to the fuselage. A typical application is illustrated in Figure 1 [2]. As shown in the figure, the metal/rubber periodic structures are embedded into the
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supporting struts as an isolator.
Fig. 1 Metal/rubber periodic structure in the strut. According to the concept, a considerable number of studies have been performed by Pennsylvania State University and University of Maryland. In Pennsylvania State University, Szefi et al. designed an axial layered isolator for helicopter gearbox as shown in figure 1 [13-16]. Following from that, Autran et al. developed a layered
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isolator with alternating materials of steel and rubber in radial direction, which can be installed around the bearings of the gearbox input shaft to isolate the gear mesh vibration [17]. In the University of Maryland, Richards and Pines designed a periodic shaft with geometrical discontinuity to reduce the gear mesh vibration from being transmitted
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along the shaft [18]. Subsequently, in 2003, Asiri et al. firstly proposed the concept of gearbox periodic strut, which can be designed with differing material properties as well as geometrical variations [19]. A simple test platform supported by four periodic struts was employed to verify the feasibility of this concept. The experimental results showed that reductions of measured acceleration reached 28dB in the frequency range of 600 to 2000 Hz.
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Considering the complexity of the helicopter gearbox, both the radial periodic isolator installed outside the bearings [17] and the periodic gear shaft [18] mentioned above have some limitations in size, weight and vibration
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control effect [20]. Szefi’s layered isolators [13] and Asiri’s periodic struts [19] can be designed to meet these requirements, especially to present good abilities to control the mid- and high-frequency vibration. However, as the main connection structure between the main gearbox and the fuselage, they cannot work normally under realistic pull-pull alternating loading generated by rotor. To solve this problem, a kind of series/parallel compounded gearbox periodic strut for helicopter cabin noise reduction was proposed by the authors [21]. The broadband vibration attenuation characteristics have been preliminarily verified through modeling and simulation analysis.
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In order to further study the performance of the compounded periodic strut used for helicopter cabin noise reduction, this paper carries out relevant researches in three parts: theoretical modeling, simulation analysis and experimental verification.
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A new dynamic model of the vibro-acoustic coupling system is firstly constructed based on an existing helicopter model in authors’ group which consists of the supporting struts, the gearbox, the fuselage and the cabin
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cavity. According to this dynamic model, the importance of the struts in the transmission path of the gear meshing vibration can be observed easily. On this basis, simulation research of the coupling system is presented. As a contrast, the same research simultaneously proceeds when the gearbox is supported by compounded periodic struts and plain struts respectively. So that the control effect of the new struts on the aspects of vibration and noise can be predicted. Further, the experimental rig consists of the basic helicopter structure, as well as the power and the gearbox system, it is established to generate complex vibro-acoustic environment similar to a real helicopter. A series of experiments are carried out from two desired perspectives of fuselage vibration and cabin noise. The
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experimental data is manipulated to assess the feasibility and effectiveness of the novel periodic strut used for helicopter cabin broadband noise reduction.
Dynamics Modeling of Coupled Acoustic-Structure System
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II. A. Overview
First of all, a brief introduce of the novel type strut is given here. The schematic drawing is illustrated in figure 2. As shown in the figure, the strut can be divided into three parts: joints, a cylindrical shell, and a compounded
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periodic structure that is embedded in the cylindrical shell. The compounded periodic structure is mainly composed of two types of cells, called a-cells and b-cells, with series-parallel connections along the z-axis. In order to enable
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the elastic material maintaining at the state of compression under both tensile and compressive loading conditions, the components inside the compounded periodic structure are subjected to axial precompression. For a helicopter, the gear meshing noise transmission path through the support struts to the cabin is a typical acoustic-structure coupling process. Here both structure vibration and acoustic behavior are involved. Also the role of the strut in the system should be observed conveniently. Considering these reasons, the methods of finite element
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and transfer matrix are used to model. With the principle of simple to complex, three models have been constructed in this section, one for the compounded periodic strut, another for the gearbox system, and a third for the whole coupling system. The analytical models have been kept as simple as possible to try and achieve some insight into the
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vibration and noise transmission characteristics of the system assembled with the novel struts.
B. Dynamics of the Element
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Based on the finite element method, the fuselage, gearbox and struts in the helicopter model can be divided into elements with finite numbers. The dynamical equation of motion for an element can be described as follow:
&& + Ceu& + Ke u = F Me u
(1)
where Me , Ce and K e are the mass, damping and stiffness matrices of an element, respectively. In addition, u is the displacement vector of nodes, F is the load vector. Subscript e defines the element. For a sinusoidal excitation at a frequency ω , equation (1) can be rearranged as
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(2)
F = Kd u where the dynamic stiffness matrix can be given as
K d = − M eω 2 + C eω i + K e
&& = 0 M e p && p + Ce p p& + K e p p + M ec u
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The motion equation of acoustic fluid in the cabin cavity can be obtained as follow:
(3)
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where M e p , Ce p and K e p are the mass, damping and stiffness matrices of a fluid element, respectively. In addition,
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M ec is the coupled mass matrix, p is the pressure vector of nodes. Superscript p defines the fluid element.
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Fig. 2 Schematic illustration of a compounded periodic strut for a gearbox.
C. Dynamics of the Compounded Periodic Strut The compounded periodic strut can be regarded as a series-parallel complicated structure consisting of multiple elements. Based on the dynamics of the element, we can deduce the dynamics of the entire periodic strut as follow. If m elements are connected in parallel, the dynamic stiffness matrix K p can be calculated directly with the following summation operation:
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(4)
m
Kp = ∑ Kd j j=1
where j defines the number of element, and j = 1, 2,3L .
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However, if m elements are connected in series, the dynamic stiffness matrix of every element K d j should be firstly expanded to the matrix as follows:
exp and
K d j → K d j m× m
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where m × m is the dimension of the entire series structure.
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So that the dynamic stiffness matrix K s of m elements in series can be obtained by the following relation:
m
(5)
Ks = ∑ K d j j=1
Based on equation (4) and equation (5), the dynamical equation of the entire compounded periodic strut can be derived as follows:
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with
KUI K II K LI
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FU KUU F = K I IU FL K LU
KUL uU K IL uI K LL uL
(6)
FU = F1 , FL = Fn ; uU = u1 , uL = un
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FI = [ F2
F3 L Fn−1 ]T , uI = [ u2
u3 L un−1 ]T
where subscripts U , I and L define the upper, interface and lower sides of the strut, respectively. U and L are used here to replace the 1st and nth nodes, with n denoting the number of nodes. If there is no load on the interface sides of the strut, i.e., FI = 0 . Then
uI = [− K II −1 K IU As a result, the dimension of the strut can be reduced to
u − K II −1 K IL ] U uL
(7)
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I uU u = − K −1 K IU I II 0 uL
u − K II K IL U uL I 0
−1
(8)
−1 FU KUU − KUI K II K IU = F −1 L K LU − K LI K II K IU
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Substituting equation (8) into equation (6), the dynamics equation of the entire periodic strut gives
KUL − KUI K II −1 K IL uU K LL − K LI K II −1 K IL uL
D. Dynamics of the Gearbox System
(9)
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Figure 3 shows the schematic drawing of a simplified gearbox system with three focused compounded periodic struts, which are numbered 1#, 2# and 3#. The struts are used to connect the gearbox to the fuselage through the
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installation angle α and the mounting points M1, M2 and M3.
O
F0
Gearbox
3#
2#
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1#
•
M1 •
α
M3
Z
•
M2
Y
X
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Fig. 3 Schematic illustration of a simplified gearbox system.
Considering the weight and the connection stiffness of the fuselage, the boundary conditions at the mounting
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points can be seemed as fixed constraints. It can be expressed as
uL = 0
(10)
−1 FU KUU − KUI K II K IU uU F = −1 L K LU − K LI K II K IU
(11)
Then equation (9) can be reduced to
Therefore, the transfer relation of two ends of the periodic strut can be derived as
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(
FL = K L:U − K LI K II −1 K IU
)( K
UU
− KUI K II −1 K IU
)
−1
FU
(12)
According to this equation, we can obtain both the transfer functions of the strut in x, y and z direction. It should
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be noted here that only the axial (z direction) transmission of the strut is considered, because the contribution of the lateral (x and y directions) motion and rotation motion are much lower than that of the axial direction over the frequency range concerned in this paper [1]. The axial transfer function of the strut is defined as Tz .
Similarly, we can obtain the vibration transfer function from the gear mesh point to the ith periodic strut, which
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is defined as Tgi including both of the three translation directions. The subscript g represents the gearbox and
i = 1, 2,3 which respresents the location of the strut.
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Under the excitation of the gear meshing force F0 , the force applying along the axis of the strut can be described as:
Fax = AcoeTg F0
with
Fax3 ] , Tg = Tg1 Tg 2 Tg 3 T
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Fax = [ Fax1
T
− cos 30o cos α sin 30o cos α sin α 0 sin α = − cos α cos 30o cos α sin 30o cos α sin α
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Acoe
Fax 2
(13)
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According to equation (12), the reaction force at the mounting point Mi can be obtained as
Fre = Tz Fax
(14)
Hence, if there is a force F0 generated by the gear meshing, the force will be transmitted through the main gearbox and the support strut, thereby reaching the mounting points with force Fre , and inducing fuselage vibration.
E. Dynamics of the Coupled Acoustic-Structure System Based on the dynamic models of the periodic strut and the gearbox system, the sound pressure of a field point in the cabin can be determined through summing all the pressure generated by every excitation point. Namely
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P = TPTz AcoeTg F0
(15)
with
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TP = [TP1 TP2 TP3 ] where TPi is the noise transfer function from the periodic strut mounting point Mi to any field point.
According to the same method presented above, when the gearbox is supported by the plain struts, the sound
P% = T%PT%z AcoeT%g F0
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pressure of a field point in the cabin at the same excitation conditions can be obtained as follows:
(16)
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where T%g , T%z and T%P define the vibration transfer function from the gear mesh point to the plain strut, the transfer function of the plain strut and the noise transfer function from the mounting point to any field point in the cabin, respectively.
Equation (15) and equation (16) clearly show that the vibration transmission characteristics of the gearbox supporting struts have a significant influence on the cabin noise.
A. Overview
Simulation Study of the helicopter model
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III.
Following dynamics modeling of the whole system in section 2, simulation research was conducted to predict the
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control effect of the new periodic strut on the gear meshing cabin noise. Both the structural and acoustic characteristics analysis were studied. To evaluate the advantages of the new periodic struts, the same research was
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carried out with plain struts (i.e., thin-wall cylinder steel struts) .
B. Model Parameters 1. Helicopter Model
According to the shape of an actual helicopter and the layout of the gearbox, a helicopter model was developed to simulate the complex vibro-acoustic environment generated by the main gearbox. A three-dimensional diagram showing how model fuselage and gearbox system are configured is shown in Figure 4a. The fuselage is 2065 mm long, 580 mm wide and 564 mm high. The gearbox, which is 30 kilograms weight with two pairs of gears inside, is
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supported by three supporting struts. The outer diameter, inner diameter and length of the plain strut are 30 mm, 24
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mm and 220 mm, respectively.
Fig. 4 Three-dimensional diagrams of the helicopter model and the compounded periodic strut.
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2. Compounded Periodic Strut
As shown in figure 4b, a sample of the compounded periodic strut was designed to replace the plain strut as the
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supporting structure of the gearbox according to the design process and the parameter analysis results in [21]. Material parameters and main geometric dimensions are shown in table 1 and table 2.The periodical number of series is 2, and the total rubber compression deformation is 5 mm. With these design parameters, the strut can meet the working requirements of the helicopter model as follows: 1)
Vibration attenuation requirements: the stop band ranges from 300 to 2000 Hz. The targeted tones of gear
2)
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mesh occur at 360 Hz and 900 Hz.
Stiffness requirements: the axial and lateral stiffness of the strut is designed to ensure the proper alignment of the engine-transmission shafts and drive shaft.
3)
Strength requirements: the stress under realistic loading conditions is less than the material allowable stress,
Space requirements: the total length is less than 240 mm, and the diameter is less than 130 mm.
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4)
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and the compressive deformation of the rubber is less than the maximum permissible deformation.
Material
Nitrile rubber 45# steel
Table 1 Material characteristics
Elastic modulus (GPa) 0.005 210
Density (kg/m3)
Poisson’ s ratio
Loss factor
1000 7860
0.49 0.3
0.3 \
Allowable stress (MPa) 3 355
Table 2 Main geometric dimensions Structure
Material
Upper cylinder
Rubber Metal
Length (mm) 30 22
External Diameter(mm) 70 70
Inner Diameter(mm) 35 35
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Lower cylinder
Rubber Metal
30 22
70 70
/ /
3. Field Points in Cabin
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The field points were also chosen specially inside the cabin to study the acoustic characteristics. According to the measurement standard of the cabin noise in an actual helicopter, the points should be located in the nominal ears of all the pilots and several representative passengers [22]. Figure 5 presents the chosen four field points which represent the nominal ears location of main pilot, co-pilot, and two passengers, respectively. The coordinate
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locations are shown in Table 3.
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Fig. 5 Schematic illustration of the field points location. Table 3 Field points location
U/ mm
V/ mm
W/ mm
Location
U/ mm
V/ mm
W/ mm
Point S1 Point S2
85 -85
210 210
200 200
Point S3 Point S4
75 -75
80 80
200 200
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Location
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Based on these parameters, simulation study of the helicopter model can be further carried out.
C. Simulation Results and Analysis 1. Modal Analysis
This section gives the modal analysis of the helicopter model in the frequency range of interest. The model fuselage was clamped supported constraint at the bottom. In this case the modal number of the helicopter model increases from 751 to 856 when the plain supporting struts are replaced by the compounded periodic struts. Four modal results in the vicinity of 360 Hz and 900 Hz (i.e., base frequencies of gear mesh) are illustrated in figure 6. It
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can be seen from the figure that the fuselage modes have changed a lot, including both natural frequencies and
b) Compounded periodic struts 358.9 Hz
c) Plain struts 899.9 Hz
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a) Plain struts 357.7Hz
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modal shapes.
d) Compounded periodic struts 898.5 Hz
Fig. 6 Modal results of the helicopter model. 2. Transfer Functions
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The transfer functions from the fuselage to the cabin field points, as well as that from the gear mesh location to the struts were calculated to comprehend the influence of the replacement of the struts. For example, the magnitude curves of the transfer function from M1 to S1are shown in Figure 7. Here, the connection point M1 is assumed to be
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excited by an acceleration source which is in the axial direction of the strut 1#, thereby causing sound response at S1. The figure shows that the noise transfer function with newly designed periodic struts has no significant change
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compared with plain struts. So, it can be written as T%P1 ≈ TP1 . Meanwhile, comparison of other sets of data indicates that T%Pi ≈ TPi and T%gi ≈ Tgi . So, for the vibro-acoustic transmission characteristics from the fuselage to the cabin, as well as the vibration transmission performance of the gearbox, the changes caused by the replacement of the compounded periodic struts can be ignored.
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100
60
40
20 0
500
1000 Frequency/Hz
1500
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80
2000
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Transmissibility/dB
Periodic Strut Plain Strut
3. Simulation Results of Vibration Response
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Fig. 7 Magnitude of noise transfer functions from M1 to S1.
Based on the fuselage modal results, vibration responses of the helicopter model were obtained to predict the control effect on the fuselage vibration. As shown in Figure 3, the excitation is located in the projection point of the struts’ focal point O on the top of the gearbox; meanwhile, the test points of the vibration response are located in the gearbox mounting points (M1 –M3) at the bottom of the struts. The excitation was 1N sinusoidal load with scan
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frequency between 0 – 2000 Hz and scan step size of 10 Hz. In simulation, there are no machining and installation errors between three struts, so transmission characteristics of them are identical. Figure 8 shows the mean acceleration response magnitude at the mounting points. Comparison
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with the plain strut suggests that the new periodic strut has obvious broadband vibration attenuation performance in the frequency range of 300 - 2000Hz, and the maximum acceleration attenuation exceeds 60dB.
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This is because the transmissibility of the periodic strut among the stop band frequency range is much smaller than that of the plain strut. Namely
Ti
T%i
(17)
Combining equation (17) with equation (14), it can be concluded that the newly developed strut can effectively isolate the gearbox vibrations from transferring to the fuselage.
20 periodic strut plain strut
0 300Hz
-40 -60 -80 -100 0
500
1000 Frequency/Hz
1500
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-20
2000
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Average over 3accelerometers/dB
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4. Simulation Results of Acoustic Response
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Fig. 8 Mean acceleration response at the gearbox mounting points.
The cabin is full of air and it was divided by number of fluid elements. When the gearbox vibration transmitted to the bulkhead, the acoustic-structure coupling occurred. In order to evaluate the performance of the compounded periodic strut as means for attenuating the cabin noise, vibro-acoustic response case in the cabin were further
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simulated using the mode superposition method. The sound signal is expressed into sound pressure level (SPL) by
SPL = 20 log(
Pe ) dB P0
(10)
where pe is the measured sound pressure; P0 = 2 ×10−5 Pa is the reference sound pressure.
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1) Cabin SPL distribution results
Figure 9 displays the SPL color map in the cabin at two basic frequencies of the gearbox. As can be seen in the
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figure, the SPL distribution characteristic with the compounded periodic strut is much similar to that of the plain strut. For example, at 360Hz, both Figure 9a and Figure 9b indicate that the SPL increases gradually from the middle of the cabin to the two edges. However, the SPL value is much more different. With the plain struts in Figure 9a, the minimum and maximum of the SPL are 36.2dB and 72.6dB respectively. When the struts are changed to the new struts, as shown in Figure 9b, the minimum SPL in the middle of the cabin reduces to 11.9dB and the maximum SPL at edges just is 60.7dB. Therefore, it is not difficult to find that the compounded periodic struts cause the overall attenuation of the SPL in the cabin.
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b) Compounded periodic struts 360Hz
c) Plain struts 900Hz
d) Compounded periodic struts 900Hz
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a) Plain struts 360Hz
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Fig. 9 SPL cloud charts in the cabin.
2) SPL frequency response in the field points
To observe the control effect over the whole concerned frequency range, frequency response analysis was carried out. Figure 10 gives the mean SPL frequency response curves of four filed points (S1 – S4). As can be seen in the figure, when the gearbox is supported by the new periodic struts, the SPL begins to attenuate at around 300 Hz,
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which is the beginning frequency of the new strut. Besides, the maximum SPL attenuation exceeds 60dB in the
100
300Hz
periodic strut plain strut
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SPL,Average over 4mics/dB
designed stop band of the new periodic strut.
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50
0
500 Fig. 10
1000 Frequency/Hz
1500
2000
Mean SPL frequency response curves of the cabin filed points.
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From the above simulations, great noise reduction performance of the compounded periodic strut has been shown in the frequency range of the gear mesh vibration. The effectiveness of the new strut has been demonstrated preliminarily.
Experimental Study of the Helicopter Model
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IV. A. Overview
A series of experiments were carried out to study the performance of the new periodic strut in more realistic conditions. The experimental rig was designed to simulate the basic helicopter structure together with the power and
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the gearbox system. The test system can generate complex vibro-acoustic environment similar to a real helicopter. Like the simulation studies, the experimental investigations were conducted from two perspectives as well,
B. Experimental Program and Facilities
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including fuselage vibration attenuation and cabin noise reduction.
Figure 11 shows the scheme of the test system which is composed of the structure of the helicopter model and hardware for measuring target vibration and noise. As shown in the figure, the compounded periodic struts are
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installed on the support points of the gearbox to replace the original plain struts. To compare the performance, the
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fuselage vibration and the cabin noise should be tested and analyzed before and after replacement.
Fig. 11
Vibration and noise test scheme with the new periodic strut.
The actual test system is depicted in figure 12, and the dimensions of the helicopter model are presented in section 3. As shown in the figure, the gearbox gears are driven by the electric motor, thereby generate gear mesh harmonic vibrations which are transmitted into the fuselage through the support struts. This process can be used to
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simulate the transmission path of the real helicopter gearbox vibration. The gearbox is supported respectively by the
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plain struts and the compounded periodic struts as shown in the photographs in Figure 12a and Figure 12b.
Fig. 12
Test system of the helicopter model.
Besides, six accelerometers and four microphones were employed in this study. As shown in Figure 13, three three-axis accelerometers (model: LC0111, sensitivity: 500 mV/g, from Lance Ltd.) were installed at the bottom of
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the struts (M1 –M3) to measure the fuselage vibration signals. Meanwhile, three other accelerometers at the top of the struts were used to monitor the vibration coming from the gearbox. The four microphones (model: 378B11, sensitivity: 50mv/Pa, from PCB Piezotronics Inc.) were mounted at the four chosen filed points (S1 –S4) to obtain
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the cabin noise signals.
a) Accelerometers Fig. 13 C. Experimental Results and Analysis 1. Spectrum of Gearbox Vibration
b) Microphones
Installation Positions of the test sensors.
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This section gives the spectrum analysis result of the gearbox vibration to determine whether the frequency distribution meets the requirement of the experimental conditions in the range between 0 and 2000 Hz. In the experiments, the motor speed is 900r/min. The corresponding harmonic frequencies of gear mesh are 360
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Hz, 720 Hz, 900 Hz, 1080 Hz, 1440 Hz, and 1800 Hz, where 360 Hz and 900 Hz are two basic gear tooth passage frequencies. Figure 14 shows the frequency responses on the attachment points nearby the gearbox in the range between 0 and 2000 Hz. The figure shows that the gearbox generates obvious gear mesh harmonic tones, along with some other frequency components of 540 Hz and 1350 Hz, etc., which are caused by the wear of gears, etc. In
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conclusion, the vibration spectrum of the experimental gearbox can be used to simulate the helicopter gearbox excitation conditions.
540Hz
0.5
900Hz
1080Hz
0.4
720Hz
0.3 0.2 0.1 0 0
1350Hz
360Hz
500
1000 Frequency/Hz
1500
2000
Frequency spectrum on the attachment points nearby the gearbox.
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Fig. 14
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0.6
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Average over 3accelerometers/g
0.7
2. Vibration Test Results and Analysis
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.Figure 15 shows the magnitude of experimental acceleration frequency response based on the test results at the three mounting points M1 – M3.Three measurement directions are all considered in this research. As shown in Figure 15a, when the gearbox is supported by the plain struts, the curve of acceleration frequency response has several resonant peaks at the gear mesh harmonic tones where the maximum occurs at 900 Hz. This result is similar to the gearbox excitation frequency distribution. Comparing with the plain strut, the frequency response curve with the compounded periodic struts is obviously steeper. It indicates that the new periodic strut exhibits broadband vibration attenuation characteristics in the
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frequency range of 300 – 2000 Hz, which is coincident with simulation. Maximum acceleration reduction is over 40dB. To clearly observe the performance of the compounded periodic strut at the gear mesh harmonic tones, Figure
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15b illustrates the acceleration magnitudes of these frequencies. By comparison with the plain strut, it can be seen
40 20
900Hz
360Hz
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0
Periodic Strut Plain Strut
-20 -40 -60 -80 0
500
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Average over 3accelerometers/dB
clearly that the new strut has excellent vibration attenuation characteristics in all gear meshing harmonic frequencies.
1000 Frequency/Hz
1500
2000
10 0 -10
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20
Plain Strut Periodic Strut
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Average over 3accelerometers/dB
a) Broadband
-20
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-30 -40 -50
Fig. 15
360
540
720 900 1080 1350 Frequency/Hz
b) Harmonic tones
Mean frequency spectrum at the mounting points M1 – M3.
3. Noise Test Results and Analysis
The cabin noise results were tested simultaneously with the vibration response. Figure 16 shows the cabin SPL frequency spectrum, which is the mean value of the SPL at the four typical locations S1 – S4. Figure 16a indicates
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that the cabin SPL spectrum with the plain strut has two obvious resonant peaks at the two basic frequencies of the gearbox. When the struts are replaced by the compounded periodic struts, however, the spectrum changes a lot as follows: 1) The two basic frequency resonant peaks disappear. 2) Obvious SPL attenuation happens over the
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frequency range 300 -2000 Hz. 3) Maximum noise attenuation is more than 30dB. These conclusions indicate that the compounded strut can efficiently reduce the cabin noise at the gear mesh harmonic tones and also has good broadband performance for the cabin noise attenuation.
900Hz 360Hz
80 60 40 20 0
500
1000 Frequency/Hz
80
2000
Plain Strut Periodic Strut
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SPL,Average over 4mics/dB
100
1500
Broadband
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a)
120
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100
Periodic Strut Plain Strut
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SPL,Average over 4mics/dB
120
60
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40 20
0
360
540 b)
Fig. 16
720 900 1080 1350 Frequency/Hz Harmonic tones
Mean frequency spectrum at the field points S1 – S4.
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V.
Conclusion
In order to research the performance of the novel compounded gearbox periodic strut to control the noise in helicopter cabin, based on a certain helicopter model, this paper carried out the relevant studies through modeling,
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simulation and experimental researches. The main conclusions are summarized as below: 1) Based on the dynamics model of the helicopter model, the simulation was carried out. The simulation results indicate the installation of the compounded periodic strut has little influence on the vibro-acoustic transmission characteristics from the fuselage to the cabin, as well as the transmission performance of the
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gearbox itself. However, it can cause the obvious broadband fuselage vibration and cabin noise attenuation in the range of 300 - 2000Hz, and maximum acceleration attenuation exceed 60dB. Therefore, the newly
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developed strut can effectively isolate the gearbox vibrations from transferring to the fuselage, and then achieve the cabin noise reduction in the designed stop band.
2) The broadband vibration attenuation performance of the compounded periodic strut in its designed stop band has been verified through experimental studies. The experiments were performed on the helicopter model with a special designed gearbox, which can generate gear mesh vibration/noise similar to a real helicopter.
exceeds 40dB.
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Results from experimental studies are much similar to the simulations. While, the maximum attenuation
3) Experimental studies also demonstrate the effectiveness of the compounded periodic strut for attenuating the cabin noise caused by the gearbox. Test results show obvious broadband cabin SPL attenuation over the
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frequency range 300 - 2000Hz, with attenuation of more than 30dB at the gear mesh harmonic tones.
Acknowledgments
The author(s) would like to thank the National Key Laboratory Foundation (No.61422200402162220003) and
National Natural Science Foundation of China (No.51375229).
References
[1] Brennan, M. J., Pinnington, R. J., and Elliott, S. J., “Mechanisms of Noise Transmission through Helicopter Gearbox Support Struts,” Journal of Vibration and Acoustics, Vol. 116, No. 4, 1994, pp. 548-554.
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[2] Szefi, J. T., “Helicopter gearbox isolation using periodically layered fluidic isolators,” Ph.D. Dissertation, Mechanical and Nuclear Engineering Dept., Pennsylvania State Univ., University Park, PA, 2003. [3] Millott, T. A., Welsh, W. A., Yoerkie, C. A., Macmartin, D. G., and Davis, M. W., “Flight test of active gear-mesh noise
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control on the S-76 aircraft,” Proceedings of the 1998 54th Annual Forum. Part 2, Vol. 1, Washington, DC, 1998, pp. 241-
[4] Pollard, J. S., "Helicopter gear noise and its transmission to the cabin," 3rd European Rotorcraft and Powered Lift Aircraft Forum, Aix-en-Provence, Sep. 1977, pp. 52.1-52.10.
[5] Yoerkie, C. A., Moore, J. A., and Manning, J. E., "Development of rotorcraft interior. Noise control concepts. Phase 1:
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Definition study," NASA CR-166101, 1983.
[6] Sutton, T. J., Elliot, S. J., Brennan, M. J., Heron, K. H., and Jessop, D. A. C., “Active Isolation of Multiple Structural Waves
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on a Helicopter Gearbox Support Strut,” Journal of Sound and Vibration, Vol. 205, No. 1, 1997, pp. 81-101. [7] Maier, R., Hoffmann, F., Tewes, S., and Bebesel M., “Active vibration isolation system for helicopter interior noise reduction,” 8th AIAA/CEAS Aeroacoustics Conference and Exhibit, AIAA Paper 2002-2495, June 2002. [8] Hoffmann, F., Maier, R., Janker, P., Hermle, F., and Berthe, A., “Helicopter interior noise reduction by using active gearbox struts,” 12th AIAA/CEAS Aeroacoustics Conference, AIAA Paper 2006-2604, May 2006. [9] Mathur, G. P., O’Connell, J., Janakiram, R., and Fuller, C. R., “Analytical and experimental evaluation of active structural
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acoustic control (ASAC) of helicopter cabin noise,” 40th AIAA Aerospace Sciences Meeting and Exhibit, AIAA Paper 20021035, Jan. 2002.
[10] Lu, Y., Ma, X. J., “Active control of multifrequency helicopter vibrations using discrete model predictive sliding mode control,” Proc IMechE Part G: J Aerospace Engineering, Vol. 230, No. 4, 2016, pp. 668-680.
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[11] Zhao, G., Alujevic, N., Depraetere, B., Pinte, G., Swevers, J., and Sas, P., "Active structural acoustic control of rotating machinery using piezo-based rotating inertial actuators." 26th International Conference on Noise and Vibration Engineering,
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ISMA, Leuven, Belgium, 2014, pp. 225-239. [12] Gulyas, K., Pinte, G., Augusztinovicz, F., Desmet, W., and Sas, P., “Active noise control in agricultural machines,” Proceedings of the 2002 International Conference on Noise and Vibration Engineering, ISMA, Leuven, Belgium, 2002, pp.11-21.
[13] Szefi, J. T., Smith, E. C., and Lesieutre, G. A., “Analysis and design of high frequency periodically layered isolators in compression,” 41st AIAA/ASME/AHS/ASC Structures, Structural Dynamics, and Materials Conference and Exhibit, AIAA Paper 2000-1373, April 2000.
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[14] Szefi, J. T., Smith, E. C., and Lesieutre, G. A., “Formulation and validation of a Ritz-based analytical model for design of periodically-layered isolators in compression,” 42nd AIAA/ASME/AHS/ASC Structures, Structural Dynamics, and Materials Conference and Exhibit, AIAA Paper 2001-1684, April 2001. [15] Szefi, J. T., Smith, E. C., and Lesieutre, G. A., “Design and Analysis of High-Frequency Periodically Layered Isolators for
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Helicopter Gearbox Isolation,” 44th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, AIAA Paper 2003-1784, April 2003.
[16] Szefi, J. T., Smith, E. C., and Lesieutre, G. A., “Design and Testing of a Compact Layered Isolator for Highfrequency Helicopter Gearbox Isolation,” 45th AIAA/ASME/ ASCE/AHS/ASC Structures, Structural Dynamics, and Materials
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Conference, AIAA Paper 2004-1947, April 2004.
[17] Autran, P., Materkowski, D. J., and Lesieutre, G. A., “Multilayered Radial Isolator for Helicopter Interior Noise Reduction,”
April 2013.
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54th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, AIAA Paper 2013-1831,
[18] Richards, D., Pines, D. J., “Passive reduction of gear mesh vibration using a periodic drive shaft,” Journal of Sound and Vibration, Vol. 264, No. 2, 2003, pp. 317-342.
[19] Asiri, S., Baz, A., and Pines, D., “Periodic struts for gearbox support system,” Journal of Vibration and Control, Vol. 11, No. 6, 2005, pp. 709-721.
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[20] Autran, P., “Radial multi-layered isolator for helicopter interior noise reduction,” Master Dissertation, Aerospace Engineering Dept., Pennsylvania State Univ., University Park, PA, 2012. [21] Wang, F. J., Lu, Y., “Research on a gearbox periodic strut for helicopter cabin noise reduction,” Acta Aeronautica et Astronautica Sinica, Vol. 37, No. 11, 2016, pp. 3370-3384.
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[22] Jiang, X. T., “Aircraft design manual: helicopter design,” Vol. 19, Aviation Industry Press, Beijing, 2005, p.418.
PII:
S0022-460X(18)30468-1
DOI:
10.1016/j.jsv.2018.07.024
Reference:
YJSVI 14266
To appear in:
Journal of Sound and Vibration
Received Date: 31 October 2017 Revised Date:
5 June 2018
Accepted Date: 12 July 2018
Please cite this article as: Y. Lu, F. Wang, X. Ma, Helicopter interior noise reduction using compounded periodic struts, Journal of Sound and Vibration (2018), doi: 10.1016/j.jsv.2018.07.024. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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Helicopter interior noise reduction using compounded periodic struts
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Fengjiao Wang, Yang Lu, and Xunjun Ma National Key Laboratory of Rotorcraft Aeromechanics, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, China
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This paper characterizes the performance of a novel compounded gearbox periodic strut
controlling the noise in helicopter cabin through modeling, simulation and experimental research. The strut exhibits low transmissibility in the specified frequency ranges, called “stop bands”.
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Based on a certain helicopter model, a dynamic acoustic-structure coupling system is firstly built by using the finite element method and the transfer matrix method. Subsequently, according to the gear mesh vibration transmission path, vibration and noise reduction characteristics analysis are conducted respectively. Comparing with the plain strut, attenuations of both vibration and noise in excess of 60dB are obtained in simulations. On a specially designed helicopter platform,
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experimental research is carried out simultaneously in two aspects of fuselage vibration and cabin noise. The effectiveness of the novel strut used for helicopter cabin broadband noise reduction is demonstrated by the coincidence of the simulation and experimentation results, where attenuations
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of measured fuselage vibration and cabin noise exceed the level of 40dB and 30dB respectively in
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the frequency range from 300 to 2000 Hz.
I.
Introduction
The vibration of mid- and high-frequency harmonic generated by gear meshing in the main gearbox is one of the dominant sources of helicopter cabin noise [1-3]. The typical frequency range locates between 500 Hz and 2000 Hz which influences human’s subjective reaction greatly [1]. The vibration can be carried by the support struts between the main gearbox and the fuselage, and radiate structure-borne noise into the cabin [4-5]. Thus, the cabin noise can be controlled by suppressing the vibration transferred to the fuselage. Currently, two main methods are used to address this problem.
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One method is to actively isolate the gear mesh vibration using actuators installed on the supported struts or nearby the mounting points of the struts as secondary forces [3, 6-10]. The feasibility and effectiveness have been demonstrated within multiple flight tests. Eurocopter Deutschland and the EADS Corporate Research Center, which
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introduced smart struts to control the structure-borne sound transmitted, are the typical representatives of research departments [7, 8]. The smart strut consists of piezoelectric actuators that are directly bonded to the BK117 support struts and provides good effectiveness at controlling the noise of multiple gear mesh frequencies in a flight test. In addition, the Sikorsky Aircraft Corporation and the Boeing Company respectively utilized different point force
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actuators mounted near the support struts [3, 9]. The active noise control (ANC) systems use cabin noise as feedback and produce a high capability to reduce the primary gear mesh tone over a wide range of steady and transient flight
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conditions.
Comprehensive experiments and analysis have shown that active methods can manage multiple gear mesh frequency components effectively. However, the ability of broadband noise reduction is very limited. In addition, several inherent problems are presented, such as actuator/sensor location optimization, stability of active control algorithms, and high cost [11, 12].
An alternative is to embed periodic structures into the transmission path, which have unique dynamic
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characteristics of restricting wave propagation within specific frequency bands. With proper design, the periodic structure can realize broadband vibration attenuation from the gearbox to the fuselage. A typical application is illustrated in Figure 1 [2]. As shown in the figure, the metal/rubber periodic structures are embedded into the
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supporting struts as an isolator.
Fig. 1 Metal/rubber periodic structure in the strut. According to the concept, a considerable number of studies have been performed by Pennsylvania State University and University of Maryland. In Pennsylvania State University, Szefi et al. designed an axial layered isolator for helicopter gearbox as shown in figure 1 [13-16]. Following from that, Autran et al. developed a layered
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isolator with alternating materials of steel and rubber in radial direction, which can be installed around the bearings of the gearbox input shaft to isolate the gear mesh vibration [17]. In the University of Maryland, Richards and Pines designed a periodic shaft with geometrical discontinuity to reduce the gear mesh vibration from being transmitted
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along the shaft [18]. Subsequently, in 2003, Asiri et al. firstly proposed the concept of gearbox periodic strut, which can be designed with differing material properties as well as geometrical variations [19]. A simple test platform supported by four periodic struts was employed to verify the feasibility of this concept. The experimental results showed that reductions of measured acceleration reached 28dB in the frequency range of 600 to 2000 Hz.
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Considering the complexity of the helicopter gearbox, both the radial periodic isolator installed outside the bearings [17] and the periodic gear shaft [18] mentioned above have some limitations in size, weight and vibration
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control effect [20]. Szefi’s layered isolators [13] and Asiri’s periodic struts [19] can be designed to meet these requirements, especially to present good abilities to control the mid- and high-frequency vibration. However, as the main connection structure between the main gearbox and the fuselage, they cannot work normally under realistic pull-pull alternating loading generated by rotor. To solve this problem, a kind of series/parallel compounded gearbox periodic strut for helicopter cabin noise reduction was proposed by the authors [21]. The broadband vibration attenuation characteristics have been preliminarily verified through modeling and simulation analysis.
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In order to further study the performance of the compounded periodic strut used for helicopter cabin noise reduction, this paper carries out relevant researches in three parts: theoretical modeling, simulation analysis and experimental verification.
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A new dynamic model of the vibro-acoustic coupling system is firstly constructed based on an existing helicopter model in authors’ group which consists of the supporting struts, the gearbox, the fuselage and the cabin
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cavity. According to this dynamic model, the importance of the struts in the transmission path of the gear meshing vibration can be observed easily. On this basis, simulation research of the coupling system is presented. As a contrast, the same research simultaneously proceeds when the gearbox is supported by compounded periodic struts and plain struts respectively. So that the control effect of the new struts on the aspects of vibration and noise can be predicted. Further, the experimental rig consists of the basic helicopter structure, as well as the power and the gearbox system, it is established to generate complex vibro-acoustic environment similar to a real helicopter. A series of experiments are carried out from two desired perspectives of fuselage vibration and cabin noise. The
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experimental data is manipulated to assess the feasibility and effectiveness of the novel periodic strut used for helicopter cabin broadband noise reduction.
Dynamics Modeling of Coupled Acoustic-Structure System
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II. A. Overview
First of all, a brief introduce of the novel type strut is given here. The schematic drawing is illustrated in figure 2. As shown in the figure, the strut can be divided into three parts: joints, a cylindrical shell, and a compounded
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periodic structure that is embedded in the cylindrical shell. The compounded periodic structure is mainly composed of two types of cells, called a-cells and b-cells, with series-parallel connections along the z-axis. In order to enable
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the elastic material maintaining at the state of compression under both tensile and compressive loading conditions, the components inside the compounded periodic structure are subjected to axial precompression. For a helicopter, the gear meshing noise transmission path through the support struts to the cabin is a typical acoustic-structure coupling process. Here both structure vibration and acoustic behavior are involved. Also the role of the strut in the system should be observed conveniently. Considering these reasons, the methods of finite element
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and transfer matrix are used to model. With the principle of simple to complex, three models have been constructed in this section, one for the compounded periodic strut, another for the gearbox system, and a third for the whole coupling system. The analytical models have been kept as simple as possible to try and achieve some insight into the
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vibration and noise transmission characteristics of the system assembled with the novel struts.
B. Dynamics of the Element
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Based on the finite element method, the fuselage, gearbox and struts in the helicopter model can be divided into elements with finite numbers. The dynamical equation of motion for an element can be described as follow:
&& + Ceu& + Ke u = F Me u
(1)
where Me , Ce and K e are the mass, damping and stiffness matrices of an element, respectively. In addition, u is the displacement vector of nodes, F is the load vector. Subscript e defines the element. For a sinusoidal excitation at a frequency ω , equation (1) can be rearranged as
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(2)
F = Kd u where the dynamic stiffness matrix can be given as
K d = − M eω 2 + C eω i + K e
&& = 0 M e p && p + Ce p p& + K e p p + M ec u
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The motion equation of acoustic fluid in the cabin cavity can be obtained as follow:
(3)
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where M e p , Ce p and K e p are the mass, damping and stiffness matrices of a fluid element, respectively. In addition,
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M ec is the coupled mass matrix, p is the pressure vector of nodes. Superscript p defines the fluid element.
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Fig. 2 Schematic illustration of a compounded periodic strut for a gearbox.
C. Dynamics of the Compounded Periodic Strut The compounded periodic strut can be regarded as a series-parallel complicated structure consisting of multiple elements. Based on the dynamics of the element, we can deduce the dynamics of the entire periodic strut as follow. If m elements are connected in parallel, the dynamic stiffness matrix K p can be calculated directly with the following summation operation:
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(4)
m
Kp = ∑ Kd j j=1
where j defines the number of element, and j = 1, 2,3L .
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However, if m elements are connected in series, the dynamic stiffness matrix of every element K d j should be firstly expanded to the matrix as follows:
exp and
K d j → K d j m× m
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where m × m is the dimension of the entire series structure.
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So that the dynamic stiffness matrix K s of m elements in series can be obtained by the following relation:
m
(5)
Ks = ∑ K d j j=1
Based on equation (4) and equation (5), the dynamical equation of the entire compounded periodic strut can be derived as follows:
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with
KUI K II K LI
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FU KUU F = K I IU FL K LU
KUL uU K IL uI K LL uL
(6)
FU = F1 , FL = Fn ; uU = u1 , uL = un
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FI = [ F2
F3 L Fn−1 ]T , uI = [ u2
u3 L un−1 ]T
where subscripts U , I and L define the upper, interface and lower sides of the strut, respectively. U and L are used here to replace the 1st and nth nodes, with n denoting the number of nodes. If there is no load on the interface sides of the strut, i.e., FI = 0 . Then
uI = [− K II −1 K IU As a result, the dimension of the strut can be reduced to
u − K II −1 K IL ] U uL
(7)
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I uU u = − K −1 K IU I II 0 uL
u − K II K IL U uL I 0
−1
(8)
−1 FU KUU − KUI K II K IU = F −1 L K LU − K LI K II K IU
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Substituting equation (8) into equation (6), the dynamics equation of the entire periodic strut gives
KUL − KUI K II −1 K IL uU K LL − K LI K II −1 K IL uL
D. Dynamics of the Gearbox System
(9)
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Figure 3 shows the schematic drawing of a simplified gearbox system with three focused compounded periodic struts, which are numbered 1#, 2# and 3#. The struts are used to connect the gearbox to the fuselage through the
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installation angle α and the mounting points M1, M2 and M3.
O
F0
Gearbox
3#
2#
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1#
•
M1 •
α
M3
Z
•
M2
Y
X
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Fig. 3 Schematic illustration of a simplified gearbox system.
Considering the weight and the connection stiffness of the fuselage, the boundary conditions at the mounting
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points can be seemed as fixed constraints. It can be expressed as
uL = 0
(10)
−1 FU KUU − KUI K II K IU uU F = −1 L K LU − K LI K II K IU
(11)
Then equation (9) can be reduced to
Therefore, the transfer relation of two ends of the periodic strut can be derived as
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(
FL = K L:U − K LI K II −1 K IU
)( K
UU
− KUI K II −1 K IU
)
−1
FU
(12)
According to this equation, we can obtain both the transfer functions of the strut in x, y and z direction. It should
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be noted here that only the axial (z direction) transmission of the strut is considered, because the contribution of the lateral (x and y directions) motion and rotation motion are much lower than that of the axial direction over the frequency range concerned in this paper [1]. The axial transfer function of the strut is defined as Tz .
Similarly, we can obtain the vibration transfer function from the gear mesh point to the ith periodic strut, which
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is defined as Tgi including both of the three translation directions. The subscript g represents the gearbox and
i = 1, 2,3 which respresents the location of the strut.
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Under the excitation of the gear meshing force F0 , the force applying along the axis of the strut can be described as:
Fax = AcoeTg F0
with
Fax3 ] , Tg = Tg1 Tg 2 Tg 3 T
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Fax = [ Fax1
T
− cos 30o cos α sin 30o cos α sin α 0 sin α = − cos α cos 30o cos α sin 30o cos α sin α
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Acoe
Fax 2
(13)
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According to equation (12), the reaction force at the mounting point Mi can be obtained as
Fre = Tz Fax
(14)
Hence, if there is a force F0 generated by the gear meshing, the force will be transmitted through the main gearbox and the support strut, thereby reaching the mounting points with force Fre , and inducing fuselage vibration.
E. Dynamics of the Coupled Acoustic-Structure System Based on the dynamic models of the periodic strut and the gearbox system, the sound pressure of a field point in the cabin can be determined through summing all the pressure generated by every excitation point. Namely
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P = TPTz AcoeTg F0
(15)
with
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TP = [TP1 TP2 TP3 ] where TPi is the noise transfer function from the periodic strut mounting point Mi to any field point.
According to the same method presented above, when the gearbox is supported by the plain struts, the sound
P% = T%PT%z AcoeT%g F0
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pressure of a field point in the cabin at the same excitation conditions can be obtained as follows:
(16)
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where T%g , T%z and T%P define the vibration transfer function from the gear mesh point to the plain strut, the transfer function of the plain strut and the noise transfer function from the mounting point to any field point in the cabin, respectively.
Equation (15) and equation (16) clearly show that the vibration transmission characteristics of the gearbox supporting struts have a significant influence on the cabin noise.
A. Overview
Simulation Study of the helicopter model
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III.
Following dynamics modeling of the whole system in section 2, simulation research was conducted to predict the
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control effect of the new periodic strut on the gear meshing cabin noise. Both the structural and acoustic characteristics analysis were studied. To evaluate the advantages of the new periodic struts, the same research was
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carried out with plain struts (i.e., thin-wall cylinder steel struts) .
B. Model Parameters 1. Helicopter Model
According to the shape of an actual helicopter and the layout of the gearbox, a helicopter model was developed to simulate the complex vibro-acoustic environment generated by the main gearbox. A three-dimensional diagram showing how model fuselage and gearbox system are configured is shown in Figure 4a. The fuselage is 2065 mm long, 580 mm wide and 564 mm high. The gearbox, which is 30 kilograms weight with two pairs of gears inside, is
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supported by three supporting struts. The outer diameter, inner diameter and length of the plain strut are 30 mm, 24
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mm and 220 mm, respectively.
Fig. 4 Three-dimensional diagrams of the helicopter model and the compounded periodic strut.
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2. Compounded Periodic Strut
As shown in figure 4b, a sample of the compounded periodic strut was designed to replace the plain strut as the
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supporting structure of the gearbox according to the design process and the parameter analysis results in [21]. Material parameters and main geometric dimensions are shown in table 1 and table 2.The periodical number of series is 2, and the total rubber compression deformation is 5 mm. With these design parameters, the strut can meet the working requirements of the helicopter model as follows: 1)
Vibration attenuation requirements: the stop band ranges from 300 to 2000 Hz. The targeted tones of gear
2)
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mesh occur at 360 Hz and 900 Hz.
Stiffness requirements: the axial and lateral stiffness of the strut is designed to ensure the proper alignment of the engine-transmission shafts and drive shaft.
3)
Strength requirements: the stress under realistic loading conditions is less than the material allowable stress,
Space requirements: the total length is less than 240 mm, and the diameter is less than 130 mm.
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4)
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and the compressive deformation of the rubber is less than the maximum permissible deformation.
Material
Nitrile rubber 45# steel
Table 1 Material characteristics
Elastic modulus (GPa) 0.005 210
Density (kg/m3)
Poisson’ s ratio
Loss factor
1000 7860
0.49 0.3
0.3 \
Allowable stress (MPa) 3 355
Table 2 Main geometric dimensions Structure
Material
Upper cylinder
Rubber Metal
Length (mm) 30 22
External Diameter(mm) 70 70
Inner Diameter(mm) 35 35
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Lower cylinder
Rubber Metal
30 22
70 70
/ /
3. Field Points in Cabin
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The field points were also chosen specially inside the cabin to study the acoustic characteristics. According to the measurement standard of the cabin noise in an actual helicopter, the points should be located in the nominal ears of all the pilots and several representative passengers [22]. Figure 5 presents the chosen four field points which represent the nominal ears location of main pilot, co-pilot, and two passengers, respectively. The coordinate
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locations are shown in Table 3.
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Fig. 5 Schematic illustration of the field points location. Table 3 Field points location
U/ mm
V/ mm
W/ mm
Location
U/ mm
V/ mm
W/ mm
Point S1 Point S2
85 -85
210 210
200 200
Point S3 Point S4
75 -75
80 80
200 200
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Location
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Based on these parameters, simulation study of the helicopter model can be further carried out.
C. Simulation Results and Analysis 1. Modal Analysis
This section gives the modal analysis of the helicopter model in the frequency range of interest. The model fuselage was clamped supported constraint at the bottom. In this case the modal number of the helicopter model increases from 751 to 856 when the plain supporting struts are replaced by the compounded periodic struts. Four modal results in the vicinity of 360 Hz and 900 Hz (i.e., base frequencies of gear mesh) are illustrated in figure 6. It
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can be seen from the figure that the fuselage modes have changed a lot, including both natural frequencies and
b) Compounded periodic struts 358.9 Hz
c) Plain struts 899.9 Hz
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a) Plain struts 357.7Hz
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modal shapes.
d) Compounded periodic struts 898.5 Hz
Fig. 6 Modal results of the helicopter model. 2. Transfer Functions
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The transfer functions from the fuselage to the cabin field points, as well as that from the gear mesh location to the struts were calculated to comprehend the influence of the replacement of the struts. For example, the magnitude curves of the transfer function from M1 to S1are shown in Figure 7. Here, the connection point M1 is assumed to be
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excited by an acceleration source which is in the axial direction of the strut 1#, thereby causing sound response at S1. The figure shows that the noise transfer function with newly designed periodic struts has no significant change
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compared with plain struts. So, it can be written as T%P1 ≈ TP1 . Meanwhile, comparison of other sets of data indicates that T%Pi ≈ TPi and T%gi ≈ Tgi . So, for the vibro-acoustic transmission characteristics from the fuselage to the cabin, as well as the vibration transmission performance of the gearbox, the changes caused by the replacement of the compounded periodic struts can be ignored.
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100
60
40
20 0
500
1000 Frequency/Hz
1500
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80
2000
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Transmissibility/dB
Periodic Strut Plain Strut
3. Simulation Results of Vibration Response
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Fig. 7 Magnitude of noise transfer functions from M1 to S1.
Based on the fuselage modal results, vibration responses of the helicopter model were obtained to predict the control effect on the fuselage vibration. As shown in Figure 3, the excitation is located in the projection point of the struts’ focal point O on the top of the gearbox; meanwhile, the test points of the vibration response are located in the gearbox mounting points (M1 –M3) at the bottom of the struts. The excitation was 1N sinusoidal load with scan
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frequency between 0 – 2000 Hz and scan step size of 10 Hz. In simulation, there are no machining and installation errors between three struts, so transmission characteristics of them are identical. Figure 8 shows the mean acceleration response magnitude at the mounting points. Comparison
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with the plain strut suggests that the new periodic strut has obvious broadband vibration attenuation performance in the frequency range of 300 - 2000Hz, and the maximum acceleration attenuation exceeds 60dB.
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This is because the transmissibility of the periodic strut among the stop band frequency range is much smaller than that of the plain strut. Namely
Ti
T%i
(17)
Combining equation (17) with equation (14), it can be concluded that the newly developed strut can effectively isolate the gearbox vibrations from transferring to the fuselage.
20 periodic strut plain strut
0 300Hz
-40 -60 -80 -100 0
500
1000 Frequency/Hz
1500
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-20
2000
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Average over 3accelerometers/dB
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4. Simulation Results of Acoustic Response
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Fig. 8 Mean acceleration response at the gearbox mounting points.
The cabin is full of air and it was divided by number of fluid elements. When the gearbox vibration transmitted to the bulkhead, the acoustic-structure coupling occurred. In order to evaluate the performance of the compounded periodic strut as means for attenuating the cabin noise, vibro-acoustic response case in the cabin were further
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simulated using the mode superposition method. The sound signal is expressed into sound pressure level (SPL) by
SPL = 20 log(
Pe ) dB P0
(10)
where pe is the measured sound pressure; P0 = 2 ×10−5 Pa is the reference sound pressure.
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1) Cabin SPL distribution results
Figure 9 displays the SPL color map in the cabin at two basic frequencies of the gearbox. As can be seen in the
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figure, the SPL distribution characteristic with the compounded periodic strut is much similar to that of the plain strut. For example, at 360Hz, both Figure 9a and Figure 9b indicate that the SPL increases gradually from the middle of the cabin to the two edges. However, the SPL value is much more different. With the plain struts in Figure 9a, the minimum and maximum of the SPL are 36.2dB and 72.6dB respectively. When the struts are changed to the new struts, as shown in Figure 9b, the minimum SPL in the middle of the cabin reduces to 11.9dB and the maximum SPL at edges just is 60.7dB. Therefore, it is not difficult to find that the compounded periodic struts cause the overall attenuation of the SPL in the cabin.
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b) Compounded periodic struts 360Hz
c) Plain struts 900Hz
d) Compounded periodic struts 900Hz
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a) Plain struts 360Hz
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Fig. 9 SPL cloud charts in the cabin.
2) SPL frequency response in the field points
To observe the control effect over the whole concerned frequency range, frequency response analysis was carried out. Figure 10 gives the mean SPL frequency response curves of four filed points (S1 – S4). As can be seen in the figure, when the gearbox is supported by the new periodic struts, the SPL begins to attenuate at around 300 Hz,
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which is the beginning frequency of the new strut. Besides, the maximum SPL attenuation exceeds 60dB in the
100
300Hz
periodic strut plain strut
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SPL,Average over 4mics/dB
designed stop band of the new periodic strut.
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50
0
500 Fig. 10
1000 Frequency/Hz
1500
2000
Mean SPL frequency response curves of the cabin filed points.
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From the above simulations, great noise reduction performance of the compounded periodic strut has been shown in the frequency range of the gear mesh vibration. The effectiveness of the new strut has been demonstrated preliminarily.
Experimental Study of the Helicopter Model
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IV. A. Overview
A series of experiments were carried out to study the performance of the new periodic strut in more realistic conditions. The experimental rig was designed to simulate the basic helicopter structure together with the power and
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the gearbox system. The test system can generate complex vibro-acoustic environment similar to a real helicopter. Like the simulation studies, the experimental investigations were conducted from two perspectives as well,
B. Experimental Program and Facilities
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including fuselage vibration attenuation and cabin noise reduction.
Figure 11 shows the scheme of the test system which is composed of the structure of the helicopter model and hardware for measuring target vibration and noise. As shown in the figure, the compounded periodic struts are
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installed on the support points of the gearbox to replace the original plain struts. To compare the performance, the
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fuselage vibration and the cabin noise should be tested and analyzed before and after replacement.
Fig. 11
Vibration and noise test scheme with the new periodic strut.
The actual test system is depicted in figure 12, and the dimensions of the helicopter model are presented in section 3. As shown in the figure, the gearbox gears are driven by the electric motor, thereby generate gear mesh harmonic vibrations which are transmitted into the fuselage through the support struts. This process can be used to
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simulate the transmission path of the real helicopter gearbox vibration. The gearbox is supported respectively by the
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plain struts and the compounded periodic struts as shown in the photographs in Figure 12a and Figure 12b.
Fig. 12
Test system of the helicopter model.
Besides, six accelerometers and four microphones were employed in this study. As shown in Figure 13, three three-axis accelerometers (model: LC0111, sensitivity: 500 mV/g, from Lance Ltd.) were installed at the bottom of
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the struts (M1 –M3) to measure the fuselage vibration signals. Meanwhile, three other accelerometers at the top of the struts were used to monitor the vibration coming from the gearbox. The four microphones (model: 378B11, sensitivity: 50mv/Pa, from PCB Piezotronics Inc.) were mounted at the four chosen filed points (S1 –S4) to obtain
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the cabin noise signals.
a) Accelerometers Fig. 13 C. Experimental Results and Analysis 1. Spectrum of Gearbox Vibration
b) Microphones
Installation Positions of the test sensors.
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This section gives the spectrum analysis result of the gearbox vibration to determine whether the frequency distribution meets the requirement of the experimental conditions in the range between 0 and 2000 Hz. In the experiments, the motor speed is 900r/min. The corresponding harmonic frequencies of gear mesh are 360
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Hz, 720 Hz, 900 Hz, 1080 Hz, 1440 Hz, and 1800 Hz, where 360 Hz and 900 Hz are two basic gear tooth passage frequencies. Figure 14 shows the frequency responses on the attachment points nearby the gearbox in the range between 0 and 2000 Hz. The figure shows that the gearbox generates obvious gear mesh harmonic tones, along with some other frequency components of 540 Hz and 1350 Hz, etc., which are caused by the wear of gears, etc. In
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conclusion, the vibration spectrum of the experimental gearbox can be used to simulate the helicopter gearbox excitation conditions.
540Hz
0.5
900Hz
1080Hz
0.4
720Hz
0.3 0.2 0.1 0 0
1350Hz
360Hz
500
1000 Frequency/Hz
1500
2000
Frequency spectrum on the attachment points nearby the gearbox.
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Fig. 14
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0.6
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Average over 3accelerometers/g
0.7
2. Vibration Test Results and Analysis
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.Figure 15 shows the magnitude of experimental acceleration frequency response based on the test results at the three mounting points M1 – M3.Three measurement directions are all considered in this research. As shown in Figure 15a, when the gearbox is supported by the plain struts, the curve of acceleration frequency response has several resonant peaks at the gear mesh harmonic tones where the maximum occurs at 900 Hz. This result is similar to the gearbox excitation frequency distribution. Comparing with the plain strut, the frequency response curve with the compounded periodic struts is obviously steeper. It indicates that the new periodic strut exhibits broadband vibration attenuation characteristics in the
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frequency range of 300 – 2000 Hz, which is coincident with simulation. Maximum acceleration reduction is over 40dB. To clearly observe the performance of the compounded periodic strut at the gear mesh harmonic tones, Figure
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15b illustrates the acceleration magnitudes of these frequencies. By comparison with the plain strut, it can be seen
40 20
900Hz
360Hz
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0
Periodic Strut Plain Strut
-20 -40 -60 -80 0
500
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Average over 3accelerometers/dB
clearly that the new strut has excellent vibration attenuation characteristics in all gear meshing harmonic frequencies.
1000 Frequency/Hz
1500
2000
10 0 -10
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20
Plain Strut Periodic Strut
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Average over 3accelerometers/dB
a) Broadband
-20
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-30 -40 -50
Fig. 15
360
540
720 900 1080 1350 Frequency/Hz
b) Harmonic tones
Mean frequency spectrum at the mounting points M1 – M3.
3. Noise Test Results and Analysis
The cabin noise results were tested simultaneously with the vibration response. Figure 16 shows the cabin SPL frequency spectrum, which is the mean value of the SPL at the four typical locations S1 – S4. Figure 16a indicates
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that the cabin SPL spectrum with the plain strut has two obvious resonant peaks at the two basic frequencies of the gearbox. When the struts are replaced by the compounded periodic struts, however, the spectrum changes a lot as follows: 1) The two basic frequency resonant peaks disappear. 2) Obvious SPL attenuation happens over the
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frequency range 300 -2000 Hz. 3) Maximum noise attenuation is more than 30dB. These conclusions indicate that the compounded strut can efficiently reduce the cabin noise at the gear mesh harmonic tones and also has good broadband performance for the cabin noise attenuation.
900Hz 360Hz
80 60 40 20 0
500
1000 Frequency/Hz
80
2000
Plain Strut Periodic Strut
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SPL,Average over 4mics/dB
100
1500
Broadband
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a)
120
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100
Periodic Strut Plain Strut
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SPL,Average over 4mics/dB
120
60
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40 20
0
360
540 b)
Fig. 16
720 900 1080 1350 Frequency/Hz Harmonic tones
Mean frequency spectrum at the field points S1 – S4.
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V.
Conclusion
In order to research the performance of the novel compounded gearbox periodic strut to control the noise in helicopter cabin, based on a certain helicopter model, this paper carried out the relevant studies through modeling,
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simulation and experimental researches. The main conclusions are summarized as below: 1) Based on the dynamics model of the helicopter model, the simulation was carried out. The simulation results indicate the installation of the compounded periodic strut has little influence on the vibro-acoustic transmission characteristics from the fuselage to the cabin, as well as the transmission performance of the
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gearbox itself. However, it can cause the obvious broadband fuselage vibration and cabin noise attenuation in the range of 300 - 2000Hz, and maximum acceleration attenuation exceed 60dB. Therefore, the newly
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developed strut can effectively isolate the gearbox vibrations from transferring to the fuselage, and then achieve the cabin noise reduction in the designed stop band.
2) The broadband vibration attenuation performance of the compounded periodic strut in its designed stop band has been verified through experimental studies. The experiments were performed on the helicopter model with a special designed gearbox, which can generate gear mesh vibration/noise similar to a real helicopter.
exceeds 40dB.
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Results from experimental studies are much similar to the simulations. While, the maximum attenuation
3) Experimental studies also demonstrate the effectiveness of the compounded periodic strut for attenuating the cabin noise caused by the gearbox. Test results show obvious broadband cabin SPL attenuation over the
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frequency range 300 - 2000Hz, with attenuation of more than 30dB at the gear mesh harmonic tones.
Acknowledgments
The author(s) would like to thank the National Key Laboratory Foundation (No.61422200402162220003) and
National Natural Science Foundation of China (No.51375229).
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