Noise Source Evaluation of Misalignment and

UNIVERSITY OF CINCINNATI

Noise Source Evaluation of Misalignment and Elastomeric Couplings using Nearfield Acoustic Holography

by Anton Aleksandr Filyayev

A thesis submitted in partial fulfillment for the degree of Master of Science in the Dept. of Mechanical and Materials Engineering

July 2018

Abstract This study concerns the effects of two different elastomeric (spider) coupling materials and their interaction with misalignment on the distribution and severity of noise sources in a custom-fabricated direct-drive dynamometer style rotating rig. The rig contained a motor, gearbox, alternator, electrical load, and mounting system. The test cases utilized buna-neoprene couplings and urethane couplings and a fixed amount of angular misalignment for each coupling material for a total of four cases. Using a 56-channel microphone array and the technique of patch Nearfield Acoustic Holography (NAH), the acoustic intensity field was decomposed using the measured pressure fields. The individual frequency-dependent noise sources of the rig were extensively analyzed in the form of colormap acoustic images and compared with a partial modal analysis test at 90 Hz, 670 Hz, 744 Hz, 1000 Hz, and 1282 Hz. It was found that the noise sources matched well with certain mode shapes of the rig and resulted in a few possible critical speeds. The third order was highly affected from adding the urethane coupling and induced misalignment, as well as being a critical speed. The addition of misalignment had a notable effect on amplifying individual noise sources with each respective coupling and occasionally adding additional sources. The effect of changing the spider coupling affected the position of many of the noise sources in the rig completely, resulting in a seemingly different system altogether. The input and output speeds of the rig were not very affected by the change in coupling material or misalignment.

Acknowledgements I’d like to thank all of the people that stuck with me and supported me in my journey to complete this thesis and my M.S. Degree. It was incredibly rewarding to learn and explore my potential as a member of UC-SDRL. Much of this work was possible because of Dr. Susan Declercq and her past research at SDRC in which I’m grateful to be able to continue. Her practical based publications have helped markedly in the world of experimental microphone array techniques. Her NAH software makes it possible for UC-SDRL to continue work in experimental NAH research and she has been a great help throughout the process, so thanks! I also want to extend my thanks to Dr. Dave Brown and Dr. Jay Kim for being on my committee. I appreciate Bruce Lachey and Chad Kallmeyer from The Modal Shop for letting me use their instrumentation over the last couple years. Thanks to all of my labmates who were extremely helpful over the last 2 years through all my hounding! A special thanks to Ron Hudepohl in the Rhodes machine shop, who was there from the very beginning, and was instrumental in helping me make my designs a reality. I’d also like to thank Jordan Graff at Victory Parkway who handled all of the odd welding needs; which I could not have done on my own. I was pleased to have worked for Dr. Allyn Phillips and Dr. Aimee Frame who gave me the chance to further develop my engineering skills, face my fears of public speaking, and give me the responsibility as a teaching assistant. This was one of the most rewarding and beneficial experiences of my college career! Finally, I want to extend my most sincere thanks to Dr. Randy Allemang who provided the funding for me, agreeing to be my thesis advisor, and to allow me to independently research a topic that was of

ii

iii interest to me. Working for him was truly a humbling and inspiring experience. To all others, thank you!!

Contents Abstract

i

Acknowledgements

ii

List of Figures

vi

List of Tables

vii

Abbreviations

viii

1 Introduction 1.1 Nearfield Acoustic Holography and Fault Diagnosis . . . . . . . . . . . . . 1.2 Motivation for Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 Scope and Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Background 2.1 Nearfield Acoustic Holography . . . . . . . . . . . . . 2.1.1 Theory . . . . . . . . . . . . . . . . . . . . . . 2.1.2 Source Detection using Acoustic Intensity . . . 2.1.3 Experimental Assumptions and Considerations 3 Experimental Setup and Test Methodology 3.1 Rotating Test Rig . . . . . . . . . . . . . . 3.1.1 Components . . . . . . . . . . . . . 3.1.2 Couplings and Mounting . . . . . . . 3.2 Microphone Array and Data Acquisition . . 3.2.1 Case 3 and 4 Induced Misalignment 3.3 NAH Post Processing . . . . . . . . . . . . 3.4 Test Rig Partial Modal Analysis . . . . . .

. . . . . . .

. . . . . . .

. . . . . . .

. . . . . . .

. . . . . . .

. . . . . . .

. . . .

. . . . . . .

. . . .

. . . . . . .

. . . .

. . . . . . .

. . . .

. . . . . . .

. . . .

. . . . . . .

. . . .

. . . . . . .

. . . .

. . . . . . .

. . . .

. . . . . . .

4 Results 4.1 NAH Results for Test Cases . . . . . . . . . . . . . . . . . . . . . . . 4.2 Test Rig Partial Modal Analysis . . . . . . . . . . . . . . . . . . . . 4.3 Discussion of Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.1 Effects of Misalignment Variable (Cases 1/3 & Cases 2/4) . . 4.3.2 Effects of Spider Coupling Variable (Cases 1/2 & Cases 3/4) 4.3.3 Comparison of NAH data to modal data and critical speeds . iv

. . . .

. . . . . . .

. . . . . .

1 2 3 4

. . . .

7 . 7 . 8 . 10 . 11

. . . . . . .

. . . . . . .

14 14 14 18 21 27 28 29

. . . . . .

31 32 36 38 39 40 41

. . . . . .

v

Contents

4.4

4.3.3.1 Third Order Misalignment Characteristic Discussion of Errors . . . . . . . . . . . . . . . . . . . . . 4.4.1 Measurement Challenges . . . . . . . . . . . . . . . 4.4.1.1 NAH Assumptions . . . . . . . . . . . . . 4.4.1.2 Test Procedure and Test Time . . . . . .

5 Conclusions and Future Work 5.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . 5.2 Recommendations for Future Work . . . . . . . . . . 5.2.1 Recommendations for Future NAH Analysis . 5.2.2 Recommendations for Test Rig Modifications

. . . .

. . . .

. . . .

. . . . .

. . . .

. . . . .

. . . .

. . . . .

. . . .

. . . . .

. . . .

. . . . .

. . . .

. . . . .

. . . .

. . . . .

. . . .

. . . . .

. . . .

. . . . .

43 45 47 48 49

. . . .

53 53 54 54 55

A MATLAB Code 57 A.1 NAH Data Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 A.2 Tachometer Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 B Additional Data 65 B.1 Additional NAH Images . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 C Instrumentation and Gearbox Schematic C.1 Array Microphone Datasheet . . . . . . . . . . . . . . . . . . . . . . . . . C.2 Reference Microphone Datasheet . . . . . . . . . . . . . . . . . . . . . . . C.3 Gearbox Schematic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

68 69 70 71

Bibliography

73

List of Figures 1.1 1.2

Angular misalignment and lack of collinearity . . . . . . . . . . . . . . . . Buna-Neoprene elastomeric spider coupling and jaw hubs . . . . . . . . .

2 5

3.1

Unloaded rotating test rig showing motor (right), gearbox (center), and alternator (left). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Alternator load circuit schematic. Note: Internal voltage regulator and inverter components are not diagrammed. . . . . . . . . . . . . . . . . . 3.3 Electrical load connections . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Isolation air mounts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5 Microphone array and rig . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6 Five stationary reference microphones and two tachometers . . . . . . . 3.7 Simplified NAH setup configuration . . . . . . . . . . . . . . . . . . . . 3.8 Gap distance for different coupling diameters . . . . . . . . . . . . . . . 3.9 Shimmed Misalignment for Cases 3 and 4 . . . . . . . . . . . . . . . . . 3.10 Impact test configuration for rotating rig . . . . . . . . . . . . . . . . . .

. . . . . . . . .

16 17 21 22 23 25 27 28 30

4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 4.10 4.11

. . . . . . . . . . .

32 33 34 35 36 37 37 38 42 44 49

Active intensity at 670 Hz, k = 0.40 . . . . . . . . . . . . . . . . . . . Active intensity at 744 Hz, k = 0.37 . . . . . . . . . . . . . . . . . . . Active intensity at 1000 Hz, k = 0.48 . . . . . . . . . . . . . . . . . . . Active intensity at 1282 Hz, k = 0.60 . . . . . . . . . . . . . . . . . . . Modal Vector Complexity Plots . . . . . . . . . . . . . . . . . . . . . . Weighted AutoMAC plot of modes, Pole Weight = 5 . . . . . . . . . . Modal component geometry . . . . . . . . . . . . . . . . . . . . . . . . Mode animations near NAH frequencies . . . . . . . . . . . . . . . . . Typical input tachometer data showing average RPM of 1787.7 RPM. Normal modes near third order . . . . . . . . . . . . . . . . . . . . . . Speaker source test to determine plate influence . . . . . . . . . . . . .

. . . . . . . . . . .

. 15

B.1 Active intensity at 818 Hz, k = 0.60 . . . . . . . . . . . . . . . . . . . . . 66 B.2 Active intensity at 1946 Hz, k = 0.60 . . . . . . . . . . . . . . . . . . . . . 67 C.1 Gearbox Schematic (pt. 1) . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 C.2 Gearbox Schematic (pt. 2) . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

vi

List of Tables 1.1

Test cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.1 3.2

Array measurement parameters . . . . . . . . . . . . . . . . . . . . . . . . 23 NAH test DSP parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

4.1 4.2 4.3

Critical speeds and NAH to modal analysis noise source comparison . . . 41 Third order reference autopower amplitude . . . . . . . . . . . . . . . . . 44 Climate conditions for NAH data . . . . . . . . . . . . . . . . . . . . . . 46

vii

5

Abbreviations NAH

Nearfield Acoustic Holography

FFT

Fast Fourier Transform

FRF

Frequency Response Function

RPM

Revolutions Per Minute

GF F

Autopower matrix of reference microphones

GXX

Autopower matrix of array microphones

GXF

Crosspower matrix between array microphones and reference microphones

c

Speed of sound (air); 344 m/s, 1129 ft/s

f

Frequency, Hz

W

Power, Watts

A

Current, Amperes

V

Voltage, Volts

λ

Wavelength

ω

Angular frequency, rad/s, ω = 2πf

F

Operation of Fast Fourier Transform

F−1

Operation of Inverse Fast Fourier Transform √ Complex number, j = −1

j ∆f

Frequency resolution

kn

Wavenumber in the nth direction, k = 2π/λ

p

Sound pressure, time domain

P

Sound pressure, frequency domain

Z

Measurement plane distance, also called measurement height

Fmax

Maximum frequency to be studied

Fmin

Maximum frequency to be studied

dx, dy

Array microphone spacing in x and y dimensions, respectively viii

Chapter 1

Introduction We depend on machines in a variety of industries to perform smoothly in their functions. When a machine has excessive noise or vibration, it could be the result of a fault within one of its components. This not only impacts occupational hearing safety, but can also cause excessive wear on components which leads to downtime and unnecessary cost in repair. Misalignment is one of the most common machinery faults and can be caused by many factors. Proper alignment must always be performed before a machine is put into service. Misalignment occurs when two shafts are not properly aligned in the same plane; in other words they are not colinear. This can lead to additional forces that will affect numerous components such as bearings, shafts, couplings, gears, and mounting systems. Bearing faults are commonly one of the largest indicators of misalignment in a system. Misalignment can appear in different forms such as angular and parallel misalignment which can be either vertical or horizontal and there is often a combination. An example is seen in Fig. 1.1 [1].

1

2

Introduction

Figure 1.1: Angular misalignment and lack of collinearity

1.1

Nearfield Acoustic Holography and Fault Diagnosis Nearfield Acoustic Holography (NAH) is an acoustic measurement technique

first proposed by Williams and Maynard [26], which involves measuring a system by using a microphone array in the nearfield and imaging its resulting acoustic field. NAH is commonly used to obtain information about sound sources within a given area, which are then visualized in the form of a 2-dimensional or 3-dimensional acoustic field depicting the sound source information and propagation of these sources within the test aperture. NAH offers an advantage of improved source resolution compared to other acoustic holography methods and far-field techniques like beamforming. The sound field is very sensitive to localized fault excitations and thus can be a good tool for fault diagnosis [19]. What is advantageous about using an NAHbased approach is that it analyzes information about the actual spatial distribution and patterns of the incoherent sources distributed in the structure. NAH has previously been used in a variety of fault diagnosis applications. In [20][15][16], gearbox tooth faults including pitting and broken gear teeth were analyzed with NAH and automated using feature extraction algorithms with robust accuracy.

Introduction

3

Lu et al. and Coutable et al. successfully examined bearing faults using in [19][5]. A custom-test rig was built in this study. Driveshaft bending modes were successfully imaged using NAH and correlated with accelerometer FRF data in [4]. Benko et al. used general acoustic source analysis using microphones to examine vacuum cleaner faults including bearing faults [2].

1.2

Motivation for Thesis Traditionally misalignment is detected using vibration analysis. Since sensors

must be placed as close to the source as possible, this may not be possible for some machines. When two couplings are misaligned, it can be difficult to obtain an accurate vibration reading from the rotating components themselves since sensor mounting is limited to the housing and thus could give misleading data. Lower rotational speeds might induce only weak vibrations in bearings. Higher speeds can induce more housing vibration due to the flow of a fan impeller [2]. The motivation for this thesis offers a different approach for the detection of misalignment. Although there is abundant research with NAH being used for detection of other machinery faults, there is very little work done in cases of misalignment. By using acoustic imaging, the frequency dependent sources can be analyzed spatially, especially when these sources occur directly at the couplings or other rotating components where sensor placement is not possible. Analysis of the distribution of sources and severity can offer meaningful information of the condition of a machine if sources have increased in acoustic intensity or have appeared in other places in the machine. It is hypothesized that as misalignment is prevalent in a system, it will cause a forcing function at the coupling and appear as a source at certain frequencies at this

Introduction

4

point. This could in turn cause additional noise sources in bearings or mountings, since bearings are usually the most common failures in misalignment. This approach takes advantage of NAH’s high source detection capabilities because it is able to identify multiple close sources that other acoustic imaging methods might not able to at further distances. One other expected result is high amplitude in the first three orders of RPM, which is generally a classic indicator of misalignment [9]. The eventual motivation for this study was to use the data in a feature extraction and pattern recognition scheme using acoustic intensity images to automate the misalignment detection process. This will be further discussed in Section 5.2.1.

1.3

Scope and Outline This study will compare the effects of elastomeric coupling material and angular

misalignment on the distribution and severity of noise sources involved in single-speed rotating machinery. Elastomeric couplings, also known as flexible couplings, are inserts used to connect two other shaft couplings. The subtype of elastomeric coupling explored in this thesis is a spider coupling used to connect two half jaw, or LoveJoy couplings, shown in Fig. 1.2. These couplings are what transmit the torque between the coupling hubs. The elastic material in the spider will wear out before the actual coupling does; an advantage over rigid couplings. Spider couplings also allow for a small amount of misalignment and have vibration damping properties depending on the material used.

5

Introduction

Figure 1.2: Buna-Neoprene elastomeric spider coupling and jaw hubs

The two coupling materials explored are Buna-Neoprene (Buna-N), which has a rubbery feel, and a urethane material, which is more rigid. Normally, the need for a more rigid spider coupling arises when there are torque losses from a driving shaft and they need to be minimized [18]. Since torque losses were already minimal in the study, the damping properties are the primary focus of the study. The four cases studied are summarized in Table 1.1. Cases 1 and 2 explore the Buna-N couplings and urethane couplings, respectively. Cases 3 and 4 use same two couplings on the input and output shafts, but with an added amount of downward angular misalignment. Only a small amount of misalignment is induced across the cases because a more rigid spider increases installation difficulty. Table 1.1: Test cases

Case Number Case 1 Case 2 Case 3 Case 4

Coupling Type Buna-N Urethane Buna-N Urethane

Condition Normal Alignment Normal Alignment Misaligned Misaligned

Background

6

Since a test article was not available, a generous portion of time was spent on the design and fabrication of a new rotating rig built for this study and will be discussed in Chapter 3. The acoustic intensity field of the rig was decomposed for each of the four cases for a single operating speed. The noise sources were then compared and contrasted between the different cases. The cases were also compared to a partial modal analysis test done to examine any resonances of the rig near dominant NAH frequencies. Chapter 4 will present these results and the subsequent analysis, followed by pertinent conclusions in Chapter 5. First, however, it is essential to understand the process and theory of NAH, and thus the next chapter will focus on the background needed to understand the technique.

Chapter 2

Background

2.1

Nearfield Acoustic Holography NAH forms one branch of the many types of acoustic holography, which are part

of a larger subset of acoustic array imaging techniques. NAH also allows for different boundary conditions such as free-field, reflecting ground plane, infinite duct, and more. Different types of microphone array geometries can be utilized in NAH such as cylindrical and spherical arrays, but the following theory is based on planar NAH (PNAH), which uses a simpler 2-D microphone array and is less computationally intensive. It should also be noted that the following theory is FFT based NAH. Other sophisticated NAH methods which use more robust algorithms currently exist, but they will not be discussed in this thesis.

7

8

Background

2.1.1

Theory

The linear homogeneous wave equation is shown in Eq. 2.1.

∇2 p −

1 ∂2p =0 c2 ∂t2

(2.1)

In PNAH, a 2-dimensional microphone array is used to measure the 2-D pressure field of a structure which becomes an assumed solution of Eq. 2.1. Using a 2-D FFT, the measured pressure is transformed to the wavenumber space and produces the angular spectrum, which becomes a function of array distance (Z) and wavenumber components in the x and y directions, kx , and ky respectively (Eqs. 2.2-2.3).

∇2 P + k 2 P = 0

(2.2)

Given a known pressure zh , the pressure on any given plane z can be shown as

P (kx , ky , z) = P (kx , ky , zh )ejkz (z−zh )

(2.3)

The pressure z = zh is effectively the measurement plane, and the source plane of the system is z = zs . When z < zh the pressure is to be backpropagated to the source plane and the problem is deemed an inverse problem. Applying the inverse FFT, we have: −1 p(x, y, zs ) = F−1 x Fy [Fx Fy [p(x, y, zh )G(kx , ky , zs − zh )]

where G ≡

kz jkz (z−zh ) , ρck e

the velocity propagator term.

(2.4)

9

Background

When the angular spectrum is convolved with the inverse of the velocity propagation term, the 2-D or 3-D pressure field can be defined at the source surface and then can be used to predict how the pressure field will propagate [25][7]. Now that the backpropagated acoustic pressure field is found, the complex acoustic intensity field can be derived. Sound intensity is a vector quantity, so first the velocity field must be found. The velocity vector field at the distance z is given by Eq. 2.5 [25]:

→

v=

1 → ∇p jωp

(2.5)

In discrete form for each direction, the velocity can be expressed by:

vx =

1 −1 F [kx F [p(x, y, zh )]G(m, n)] ρf

vy =

1 −1 F [ky F [p(x, y, zh )]G(m, n)] ρf

vz =

1 −1 F [kz F [p(x, y, zh )]G(m, n)] ρf

Where G(m, n) = ejωkz (z−zh ) and kz =

p

(2.6)

kx + ky

The total complex acoustic intensity, defined as the rate of energy flow of sound through a given area (W/m2 ) [23] is then given by Eq. 2.7 [11]:

→ → I c= I

→

→

+j J

→

Where I is the active intensity and J is the reactive intensity.

(2.7)

10

Background For any generic pressure field, Eq. 2.7 can be re-written as:

1 → I (x, y, z) = p(x, y, z) v (x, y, z) 2

→

(2.8)

The active intensity is the real part of the sound intensity, while the reactive portion is the imaginary part. The active intensity is what propagates into the farfield and contributes to the overall radiated sound power. The reactive portion is described as the sound intensity that does not radiate into the farfield and is less useful for describing the sound power and source localization. Since only the active intensity is the part that propagates into the farfield, the total sound power is given by Eq. 2.9.

Π(ω) =

2.1.2

Z

∞ −∞

Z

∞

Re[Iz (x, y, z)]dxdy

(2.9)

−∞

Source Detection using Acoustic Intensity

Since NAH-based methods have the advantage of finding the complex-valued intensity field of the structure, this is particularly useful for source detection and dynamic characterization. Historically, sound intensity measurements have been very expensive and time consuming because an intensity probe would be scanned for each discrete area. Dumbacher et al shows that NAH intensity measurements are comparable to those of an intensity probe [3]. Since the active intensity is directly related to the sound power, the acoustic intensity map shows the individual contribution of sources and gives a better indication of sources than the sound pressure map. Because the intensity is a vector and the

Background

11

pressure is a scalar, the intensity will provide an indication of direction of energy flow as well and can be measured in any sound field [23].

2.1.3

Experimental Assumptions and Considerations

As the NAH name suggests, the measurements are made in the nearfield, which impose several important practical assumptions required for the reconstruction to be accurate. The maximum source resolution is limited by a half wavelength because planar waves require at least one node point to resolve the wave [7]. The nearfield of an acoustic field contains evanescent waves. These contain valuable information about the incoherent, or out-of-phase, sound sources in the structure and allow for sub-wavelength resolution. The evanescent waves can, however, pose a problem when the pressure values are backpropagated to the source plane. Higher order terms can be amplified by the inversion process, so a low pass filter (commonly referred to as a wavenumber or k-filter) is applied to the acoustic maps [12]. The filter cutoff values range from 0 to 1 signifying the percentage of evanescent waves that are present in the reconstruction. For example, using a cutoff of 0.40 signifies 40% of the evanescent waves are present. Too low of a cutoff value limits source resolution. Higher values use more nearfield information which will increase the source resolution, but will introduce artifacts into the maps if it is set too high. This is because it will recognize random error as sources. Generally, the higher the reconstruction frequency, the higher the wavenumber filter could be used without significantly introducing artifacts. The proper cutoff is greatly aided by user experience.

Background

12

The acoustic images are reconstructed individually at each frequency line, since sound sources are highly dependent on their frequency content. For example, a motor operating at 6,000 RPM will exhibit a strong harmonic and resulting source information at 100 Hz because of its rotational speed, but might not show any useful source information at 243 Hz if there is nothing of relevance in the system at this frequency. Though it is possible to also construct a map based on frequency bands such as octave bands or third-octave bands, the resulting images will not be as useful because the resulting source information will be smeared across many frequencies. Because of the use of the FFT in transforming to the wavenumber domain, the same signal processing criteria are made such as Shannon’s Sampling Theorem and the Rayleigh Criterion. The FFT also assumes linearity within the structure, thus PNAH would not be suitable for nonlinear systems. Spatial leakage can also occur when pressure is not zero at the edges of the array. For this reason, it is suggested that the total array size must be 1.5-2 times larger in both x and y directions to allow for the pressure to fully decay [7]. A spatial window can also be applied if this is not possible. The microphone spacing must be less than or equal to half the wavelength of the highest frequency to ensure that all sources are successfully imaged. If the system is steady-state, the data can be taken in sets with smaller subarrays and stationary reference microphones at each of the suspected sources used to phase-lock the array. Transient data requires the full scan to be taken at once and does not require reference microphones [7] [12]. The frequency resolution of NAH is related to the dimensions of the array, the microphone spacing, and the measurement distance, Z. The relationship between Fmax and the microphone spacing is given by Eqs. 2.10- 2.11 [7].

13

Experimental Setup and Test Methodology

λ 2

(2.10)

c λ = max(dx, dy) 2

(2.11)

max(dx, dy) ≤

Fmax ≥

c Fmax

=

Ensuring that the array is within the proper nearfield distance, Z, from the source plane allows for this Fmax relation to be true. The nearfield distance Z is:

Z≤λ

(2.12)

min(dx, dy) ≤ Z ≤ 2max(dx, dy)

(2.13)

Finally, the low frequency limit is determined by the overall dimensions of the array and requires at least one full wavelength for each dimension to be resolved, given by:

Fmin =

c max(Lx , Ly )

(2.14)

Where Lx , Ly = total length of array, effectively number of microphones times microphone spacing.

Chapter 3

Experimental Setup and Test Methodology The following chapter is a detailed outline of the design of the experimental test rig, microphone array, and data acquisition system. The test methodology and NAH post-processing are also discussed. The rig was entirely self-fabricated at the UC Rhodes Hall machine shop, with some work being performed at the UC Victory Parkway machine shop.

3.1 3.1.1

Rotating Test Rig Components

The full experimental rig consists of a 200 lb mounting plate, a 3-phase AC induction motor, gearbox, alternator, and a power inverter with a set of incandescent light bulbs wired in parallel. Strut channel and various angle brackets were used to mount the

14


15

components to the base plate. The rig is essentially a limited speed dynamometer which allows a variable electromechanical load to be placed onto the system. The unloaded test rig can be seen in Fig. 3.1.

Figure 3.1: Unloaded rotating test rig showing motor (right), gearbox (center), and alternator (left).

The motor is a 3 Horsepower 3-phase Dayton Electric motor that runs at an a nominal operating speed of 1790 RPM (rated 1745 RPM), but ultimately fluctuated between 1786 RPM and 1790 RPM. The gearbox is a FlowFit brand hydraulic power take off (PTO) gearbox that is designed to connect a tractor PTO shaft to a pump. The transmission ratio is 1:1.5; thus it is a speed increasing gearbox in which the output shaft rotates nominally at 2685 RPM. The schematic is seen in Appendix C.3. There are several reasons why this particular gearbox was chosen for the design. The maximum output speed for these gearboxes are rated at 3000 RPM. Because there was no way to control the speed of motor this was the only transmission ratio that would allow the output speed to stay under this limit. Its simplicity of two spur gears and minimal components are cost effective and simple enough for the scope of this


16

research. Finally, since an alternator was chosen as a means to provide a load for the system, a speed increasing gearbox was important. Alternator output current is generally proportional to its shaft speed, and requires at least 2000 RPM to generate any current [8]. The alternator is a 12V, 30A Motorola tractor alternator. The alternator requires several electrical connections to apply an electrical load. The schematic diagram is seen in Fig 3.2. In order to generate any current through rotation of the shaft, a small input current must be applied through the field coil. A 12V battery was connected in series with a momentary switch, a small light bulb, and finally the field coil.

Figure 3.2: Alternator load circuit schematic. Note: Internal voltage regulator and inverter components are not diagrammed.

The momentary switch was only turned on briefly to provide the initial current into the field coil. The bulb serves as a diagnostic tool to indicate there is unregulated current flowing to the alternator stator [8], which should only be briefly connected because the battery is not rechargeable. This process is akin to turning on the ignition switch of a car. The voltage regulator mounted on the alternator serves to regulate the constant DC output voltage produced through the positive post. The regulator output terminal was connected to the positive output post of the alternator which produces a constant


17

14.4V, regardless of the shaft speed. An 1100W inverter was wired to the positive post which receives the constant 14.4V DC and converts it to 110V AC. The negative battery and inverter terminals were connected to ground, which was used as the alternator bracket and test plate. A set of parallel light sockets were plugged into the inverter to allow for a constant and predictable load to be put onto the system. Since an incandescent lightbulb was used, it acts as a resistive load. The full system load can be seen in Fig. 3.3.

Figure 3.3: Electrical load connections

To keep efficiency high in the motor, it was desired for the final load be 50-75% of its maximum load [21], which was about 2237 W. At about 50%, 1100 W would require a considerable amount of DC current to be able to operate, which would have required an additional bank of batteries wired in parallel to supply additional amp-hours


18

to run the test. This is because even at a full current draw of 30 A, this would only sustain 430 W, which might burn out the alternator at the current operating speed. A deep cycle battery could be used to supply additional current, though this would have been expensive for the power requirements needed to safely discharge one. The final load was a single 200 W light bulb, which drew about 220 W, or 10% of the maximum motor output. This was found to be sufficient enough because the alternator was operating at half its current capacity and resulted in a noticeable change in the sound of the rig. Any more current expected would have required a faster shaft speed or else risk burning out the alternator. With this load, the system was found to be at a sufficiently steady-state.

3.1.2

Couplings and Mounting

The shafts were all direct-driven and connected using half-jaw LoveJoy couplings which included a spider coupling. This system was chosen over a belt and pulley system because slippage could have interfered with the operating speed, which would have caused non steady-state conditions. A direct-drive system also allowed for the components to be in line, which simplified assembly geometry and allowed an even and symmetric measurement plane to be studied from either side without possible sources from an off axis plane. Because there were limited options for a gearbox that would satisfy the adequate requirements detailed above, there were several accommodations that needed to be made to fit this particular gearbox as well. First, the input shaft was a standard 1 3⁄8” splined shaft, but there was no option of a low-cost suitable adapter that would connect it to a


19

standard keyway for a LoveJoy coupling. Instead, a female 1 3⁄8” coupling was welded onto a LoveJoy coupling with the required approximate outer diameter. Since the material was sintered steel, which is made from granulated steel particles, it required special low hydrogen stick electrodes to weld. While this solution was not ideal, it was necessary to continue with the assembly and could be improved in the future. The output shaft of the gearbox also required special fabrication because of the output spline pattern in the gearbox. A splined shaft was sent from the manufacturer because it was nonstandard in the U.S. and would have been very costly to machine. The splined shaft was welded onto a 1” keyed shaft in order to accommodate a LoveJoy coupling. Since the two shafts were a few millimeters off in diameter, a 5⁄16” center hole was tapped into each rod using a precision lathe and a setscrew installed prior to welding. This helped reduce misalignment of the two rods. The mounting structure was based off of Unistrut channel because it allowed for a low-cost mounting system without having to purchase dual-plane alignment bases for the motor and alternator. The Unistrut contains case-hardened channel nuts which form very tight connections when locked into place, but can allow for movement along the channel and re-alignment when the components are loosened. Each component has a main lengthwise strut channel. The gearbox brackets are mounted to this directly because it is the stationary component in the system. The motor and alternator were mounted onto two width-wise pieces of strut channel which means they could be aligned in two planes for each shaft. The main strut bolts were all 1⁄2” bolts tightened to 80 lb-ft and sealed with liquid threadlocker to avoid loosening from the base plate during testing.


20

It is worth noting that the test plate lies on three legs, rather than four. This is because stability will be increased with three points of contact. Four would require exceptionally even legs, or else wobbling may occur. This was also the reason the more massive driving components were placed on the size with two legs so as to reduce possibility of excitation of a torsional mode by evenly distributing the mass. The final process was alignment of the rig. Since a precision alignment system was not available, the shafts were aligned as best as possible using a straight edge and a set of custom shims. The alternator and the motor were both carefully shimmed with the gearbox and aligned horizontally to ensure the couplings fit evenly and smoothly. Several iterations were performed. Checking for soft foot is another stage of the misalignment process, which is when any of the corners do not sit evenly on the base, similar to a wobbly stool. A dial gauge is set near a bolt and its value is measured as that bolt is loosened. If the value is higher than 0.02” inch, shims are added to level the base. Soft foot was checked on each connection bolt as well by checking each foot at a time. The bolts were always locked in a cross-torquing method to further ensure even placement. The entire rig was hoisted onto three air isolation mounts, which ensured the rig did not transfer any vibration to the floor and microphone array. The mounts also helped to reduce rigid body modes. These air mounts can be seen in Fig. 3.4.


21

Figure 3.4: Isolation air mounts

3.2

Microphone Array and Data Acquisition The datasets were all measured in a fully anechoic chamber to allow for free-field

boundary conditions using X-Modal. X-Modal is a MATLAB-based software developed and maintained by UC-SDRL for the acquisition and analysis of structural dynamic data. All microphones were calibrated with a speakerphone using X-Modal’s calibration option. The speakerphone used a 114 dB-SPL pressure wave at 259 Hz to measure the sensitivity in mV/Pa. The microphone array, seen in Fig. 3.5, was made up of a four equally sized 1⁄2” rods that contained 14 microphones at a spacing of 3” in each dimension; effectively a 4x14 subarray, or 56 output channels. Each row of microphones were made up of 47” steel rods epoxied to a set of PVC couplings and thumbscrews to lock the rods in place onto a set of stands. The stands were epoxied to concrete patio blocks to help stabilize the microphone array so as to help the array from tipping over at any point. The stands


22

were set onto foam pads to further isolate the array from any noise paths through the floor gratings. Foam pads were also added to the corners of the plate to damp noise paths through the array cables.

Figure 3.5: Microphone array and rig

Five stationary reference microphones were set up to phase-lock the array with the suspected sources. The microphone positions can be seen in Fig. 3.6. Throughout all four cases, care was taken to leave these microphones in the same positions to further reduce any variability between cases. The references were set as the inputs of the system.

23


Figure 3.6: Five stationary reference microphones and two tachometers

Using Eqs. 2.11-2.14, the array paramaters for NAH were found and are listed in Table 3.1. Table 3.1: Array measurement parameters

Parameter Reference mics Scans Full array size Total array mics dx, dy Fmax Z distance Fmin (x) Fmin (y)

Value 5 3 10x14 140 3 in. 2258 Hz 3-3.25 in. 322.6 Hz 451.6 Hz

56 microphones were chosen to keep the maximum channels under 64, because additional channels were required for reference microphones. Additionally, two channels were connected to infrared tachometers to monitor the input and output speeds for each case. Data was acquired through X-Modal using a VXI frontend system. All sensors besides the tachometers required IEPE signal conditioning. The first 32 channels utilized


24

PCB rack mount signal conditioning, while the latter 32 channels utilized breakout boxes that contained IEPE. The rack mount signal conditioning was used because of limited availability of IEPE breakout boxes. Three scans of the array were taken for each data set. However, due to the rig geometry, three full scans of the subarray were not able to be taken. The components lie along the center of the plate, and thus the array was not able to extend lower than the plate. To circumvent this problem, one scan was taken with only two rows of microphones, followed by two scans that used all four rows. This meant the full array size was effectively 10x14. This was done in order to keep the measurement plane in the nearfield of the system. Length measurements were taken in between scans with a ruler to ensure equal microphone spacing and to help move the microphones into an equal measurement plane. This served to reduce microphone positioning errors. The Z distance was 3” from the nearest surface, which was the motor. This distance varied by 1⁄4” between the motor side and the alternator bracket because the the motor surface extended out further than the alternator bracket. This was to ensure the array was parallel to the driving shaft instead of the outer components since the coupling sources were of highest interest. If the array was kept parallel to the plate surface, it would actually increase this discrepancy. This could be a result of minor errors in the fabrication process A 3” distance was chosen so as to also keep the array in the nearfield of the driving shafts since the main coupling was 6” from the array; the maximum distance for 2258 Hz. A simplified geometry of the scan configuration is shown in Fig. 3.7 which shows the way the scans are taken. The full 10x14 subarray, microphone spacing, and Z distances can be accurately visualized in this figure.


25

Figure 3.7: Simplified NAH setup configuration

An infrared thermometer was used during data acquisition to monitor alternator and gearbox temperature. This served two important purposes. First and foremost, it was important to stay under the maximum temperature rating of the microphones (See Appendix B) which could have damaged the microphones or thrown them out of calibration. Second, uneven operating temperature conditions could have influenced the steady-state conditions of the system. It was desired to minimize error as much as possible, so each scan had a relative range of temperatures for both the alternator and gearbox before data was acquired

26


since these were the elements that heated up the fastest. For each scan, the alternator temperature varied from around 116◦ F-140◦ F (±5◦ ). The gearbox temperature varied from 97◦ F to 103◦ F(±3◦ ). If the temperature exceeded this, the system was shut off and allowed to cool to the lower bound before continuing to test. The motor heat was not of concern since it was well ventilated. The DSP parameters are listed in Table 3.2. For each scan, the data saved were the autopower spectra (GF F and GXX ), crosspower spectrum (GXF ), FRF, coherence, and 60 seconds of time data. FRF and coherence were not used in the NAH analysis, but were saved anyways in case the quality of data was required to be verified. The Table 3.2: NAH test DSP parameters

Parameter Fmax ∆f T Window Function Number of Averages

Value 2000 Hz 2 Hz 0.5 sec Kaiser Bessel (β = 5) 70

autopower spectra matrices are shown in Eq. 3.1 and Eq. 3.2 and the crosspower spectrum matrix is shown in Eq. 3.3.


27

GF F (f ) = GF (f )G∗F (f )

(3.1)

GXX (f ) = GX (f )G∗X (f )

(3.2)

GXF (f ) = GX (f )G∗F (f )

(3.3)

Where: GF = FFT spectrum of the reference microphones GX = FFT spectrum of the array microphones G∗ = complex conjugate spectrum.

3.2.1

Case 3 and 4 Induced Misalignment

Angular misalignment is measured in coupling gap distance, that is the amount of air gap difference per coupling diameter. This is because larger coupling diameters result in larger gap distances, seen in Fig. 3.8 [22]. The addition of these shims amounted to a gap distance of 0.015” (or 15 thou) per coupling diameter. For the diameter of the couplings used, the angular misalignment tolerance would be 0.00105” (or 1.05 thou).

Figure 3.8: Gap distance for different coupling diameters


28

In Cases 1 and 2, the rig was run with the Buna-N and urethane couplings respectively. In Cases 3 and 4, misalignment was induced and tests were repeated for each coupling type. 0.039” (39 thou) of combined shims were added to the back feet of the motor to induce downward angular misalignment, seen in Fig. 3.9.

Figure 3.9: Shimmed Misalignment for Cases 3 and 4

After the shims were added, the bolts were first re-tightened in the same crosstorquing procedure as before. Only then was the half jaw coupling put into place and setscrews locked. Even this small amount of misalignment proved difficult to join the couplings, especially the Case 4 urethane coupling.

3.3

NAH Post Processing The full data scans were imported into MATLAB which extracted the individual

data components. The NAH software used was originally written by Dr. Susan Declercq in an older version of MATLAB, which required modifications to be able to run in a


29

recent version. The data required for the NAH processing were the autopower spectra of each of the reference microphonesand for each of the array microphones, and the crosspowers between each array microphone and each reference microphone. In order to process steady-state data, the NAH software required equal sized subarray data scans. Since one data scan was not the same size as the two others, the data were further processed to combine them into one large data set that included all of the scans. The mean of all of the scanned reference microphone autopowers was the GF F matrix used when importing data into the NAH program. Positive and negative standard deviation from the mean were analyzed through MATLAB to perform all autopower analysis instead of using the NAH program to do this. This helped determine which frequencies were steady-state within 2 dB [7].

3.4

Test Rig Partial Modal Analysis Finally, the rig underwent a partial modal analysis test to analyze the dominant

modes of the rig in the frequency range of the NAH tests. This was used to determine possible critical speeds of the system. The test was a multiple reference roving hammer impact test in which eleven accelerometers were mounted about the structure; nine on the rig and two on the plate. Thirty-four locations were impacted, mostly in the Y (vertical) dimension. The input and output locations were chosen similar to where many of the acoustic sources were found. In addition, several points along the test plate were impacted to help determine whether it could be having an effect on the test components during operation. The experimental DOF’s chosen were used to help correlate the validity of the NAH spatial source data. The important modal parameters to be extracted were simply

30

Results

the modal frequencies and mode shape data. A complete modal analysis was thus not required and so only a limited number of sensors and impact locations were used. The modal parameter estimation was performed with several algorithms, but Rational Fraction Polynomial-Z (RFP-Z) and Polyreference Frequency Domain-Z (PFDZ) proved to be most useful since the structure was heavily damped. The configuration of the modal analysis test can be seen in Fig. 3.10. The green/blue dots indicate impact locations.

Figure 3.10: Impact test configuration for rotating rig

Chapter 4

Results This chapter will be used to present the acoustic source plane images and modal test results in sections 4.1 and 4.2. The results will be analyzed in the following fashion: • Comparison of cases when misalignment is added (Section 4.3.1) • Comparison of cases when spider coupling material is modified (Section 4.3.2) • Comparison of NAH data to modal data and critical speeds (Section 4.3.3) • Discussion of errors and measurement challenges (Section 4.4)

Because of the large amount of data acquired, only five frequencies will be analyzed in this section for the sake of brevity. Four of these frequencies are visualized using NAH, while one more is later described in Section 4.3.3.1 using the autopower amplitude and modal analysis. Additional sets of NAH images at two more frequencies can be found in Appendix B.1. The relative scales for each frequency are shown to relate the actual acoustic intensities of each case along the same amplitude scale, based on the maximum intensity for that respective frequency. The actual NAH images are along their own scales so as to show the pattern of source distribution more clearly, and this is the focus of the discussion. A reminder of each test case description can be found in Table 1.1. 31

32

Results

4.1

NAH Results for Test Cases

(a) Case 1

(b) Case 2

(c) Case 3

(d) Case 4

Figure 4.1: Active intensity at 670 Hz, k = 0.40

Fig. 4.1 shows the active intensity at 670 Hz with the relative scale to the right. This frequency shows similar source patterns throughout all the cases, especially near the lower left gearbox bearing. A second source is observed near the motor feet. Cases 1-3 all see an increase in the motor base acoustic intensity distribution. Cases 1 and 3 show a more consistent pattern since the sources aren’t fully separated and mostly increase in intensity. Case 3 shows more intensity throughout the gear pear and output coupling as well. Case 4 shows most of the energy concentrated at the lower left gearbox bearing, with some aberrations near the top and base of the motor.

33

Results

(a) Case 1

(b) Case 2

(c) Case 3

(d) Case 4


Fig. 4.2 shows the active intensity at 744 Hz and relative scale on the right. Similar source patterns occur mostly across the same coupling types. Cases 1 and 3 show two clearly separated sources. As misalignment was introduced, most of the energy was concentrated in the output coupling instead of in the lower left part of the gearbox. The source at the motor shaft grew in intensity with misalignment added. There is even a slight third source near the back of the motor that increases as well. Cases 2 and 4 show mostly concentrated sources in the lower left gearbox bearing, but also growing in intensity as misalignment is introduced. Case 4 shows a slightly different source pattern near the gearbox base compared to the other three intensities.

34

Results

(a) Case 1

(b) Case 2

(c) Case 3

(d) Case 4


Next, the active intensity of 1000 Hz is visualized in Fig. 4.3 with the relative scale on the right. The primary source pattern is seen across the main input shaft and a smaller source from the plate on the motor side. These patterns are consistent in all cases with source maxima appearing at different areas in the shaft as the cases progress. Case 1 and 3 show a very similar pattern, while Cases 2 and 4 show an increase in the intensity at the motor shaft and a new source appearing at the gearbox shaft. The plate source has reduced as well. This frequency was a slightly wider peak in the autopower spectrum.

35

Results

(a) Case 1

(b) Case 2

(c) Case 3

(d) Case 4


The last NAH frequency to be discussed is 1282 Hz, which is seen in Fig. 4.4 with the relative scale to the right. Case 3 shows increased intensity at the gearbox and mounting plate compared to Case 1, with additional distributed sources at the input coupling and motor appearing as well. Cases 2 and 4 show similar data, yet the sources are harder to identify. Case 2 shows sources at the plate, with increased intensity in case 4 throughout. Error sources appear in the upper left corner in both images, as well as another error source in the lower left corner in Case 4.

36

Results

4.2

Test Rig Partial Modal Analysis As stated previously, the modes identified from the modal analysis test were

derived mostly with RFP-Z. Several iterations of this procedure were attempted using PFD-Z as well. Because of the quality of the data at certain nodes, some data was forced to be sieved in order to fit the normal modes. The full FRF matrix was of the dimensions 11x34 (No x Ni ), which indicate 11 fixed response DOFs with 34 roving impact locations. The modal vector complexity plot of all of the modes derived is seen in Fig. 4.5, which shows the imaginary vs. real plot of the poles estimated from the modal parameter estimation. Most of the mean phase collinearity (MPC) of the modes are generally higher than 70%, and many of the phase angles are near 90 degrees.

Figure 4.5: Modal Vector Complexity Plots

Fig. 4.6 shows the pole-weighted modal assurance criterion (MAC) plot of all of the modes found. Because there are several high values in the off diagonals, there is indication that many of these modes are not fully observable and additional sensors

37

Results

would be needed to fully analyze the mode shapes. This makes sense since many of the nodes focused on the Y dimension.

Figure 4.6: Weighted AutoMAC plot of modes, Pole Weight = 5

Figure 4.7: Modal component geometry

The geometry and components of the modal test are seen in Fig. 4.7. Three of the NAH frequencies analyzed are at or near one of the natural frequencies of the test rig, which are 745 Hz, 1001 Hz, and 1293 Hz. These three mode shapes are shown in Fig. 4.8. All three modes show fairly high MPC coefficients of 73.2% to 90% and near 90◦ phase shifts from Fig. 4.5. The 745 Hz mode exclusively shows the nodes near on the input coupling affected. This could indicate a torsion mode since two dimensions

38

Results

are affected. The mode seems strongly coupled with the 1020 Hz mode because of the high MAC value shared. The 1001 Hz mode is shown to be mostly linearly independent in the MAC plot, and appears to be dominantly a torsion mode of the test plate, while also affecting the motor base, gearbox and alternator brackets, and gearbox. Lastly, the 1293 Hz mode is showing a mode of the motor base and alternator bracket.

(a) 745 Hz mode

(b) 1001 Hz mode

(c) 1293 Hz mode Figure 4.8: Mode animations near NAH frequencies

4.3

Discussion of Results The NAH frequencies chosen for analysis were based on several criteria. The au-

topower spectrum of the reference microphones were analyzed for each case to determine

39

Results

notable frequencies. These frequencies were analyzed for noise sources and stationarity and a sufficient wavenumber filter value was chosen. The frequencies that were found to be the least error prone and steady-state across all the data cases were chosen to be discussed. Certain bearing harmonic frequencies were also analyzed, but no significant correlation was found. Frequencies that were near rig modes were also prioritized so that these data could be compared more easily. Although maximum active intensity and sound power values were yielded for each of the acoustic images, they too are not fully representative of the actual 3dimensional intensity radiation and realistic sound power. The planar array is only able to measure the component of intensity normal to the rig surface and thus the intensity measured is only the amount of sound radiating through the array surface. In the relative amplitude scales, this can help explain why the cases with the most sources do not necessarily equate to the highest active intensity, such as at 744 Hz. Though it would be ideal to perform a quantitative analysis on the acoustic images, it would be difficult without some sort of color histogram or other statistical image analysis tools. Color histograms give merely the distribution of colors in an image, but are inaccurate when attempting to quantify spatial distribution of colors. Thus, a qualitative comparison will be used to compare the NAH frequencies.

4.3.1

Effects of Misalignment Variable (Cases 1/3 & Cases 2/4)

When the spider coupling is kept constant and the amount of misalignment is varied, the noise sources generally grew in intensity and had very noticeable effects. When comparing the Buna-N coupling in Cases 1 and 3, this can be seen at most of the frequencies described. In Figs. 4.1a and 4.1c at 670 Hz, the main source pattern at the

40

Results

gearbox grew in intensity with maxima occurring near the output coupling as well. The source at the motor feet also grew in intensity for this frequency. Since this is where the misalignment was induced, there could be reaction forces appearing here caused from the forces created at the coupling. Figs. 4.2a and 4.2c at 744 Hz also show an increase in intensity from Case 1 to case 3 at the motor shaft. At 1000 Hz, the difference is more clear between Case 2 and 4 where the sources along the shaft grew in intensity. Figs. 4.4a and 4.4c show increased intensity at the gearbox and mounting plate, but also additional distributed sources at the input coupling and motor. Spatially, the misaligned cases caused many more sources to appear when compared to their respective baseline cases. Cases 2 and 4 with the urethane coupling show some consistency as well with sources generally becoming more intense as misalignment is introduced, but are more error prone. Figs. 4.2b and 4.2d at 744 Hz show only a single source at the lower left gearbox bearing. The misaligned Case 4 shows much more acoustic intensity spread around the full gearbox.

4.3.2

Effects of Spider Coupling Variable (Cases 1/2 & Cases 3/4)

Comparing the cases between the two different spider couplings yielded subtle results. At some frequencies, a dominant noise source was observed, and changed slightly between the two cases. The NAH images at 670 Hz and 1000 Hz are good examples of this, where the system only slightly changed. At 670 Hz in particular, Cases 1 and 2 (Figs. 4.1a and 4.1c) match closer than Cases 3 and 4 (Figs. 4.1b and 4.1d). This could be due to invariability in Case 4 or simply more affected by the fact that Case 4 was also misaligned.

41

Results

1000 Hz showed a more predictable pattern, especially when comparing Cases 3 and 4 (Figs. 4.3c and 4.3d) which showed an increase in source strength as the rigid urethane coupling was introduced. The difference between Cases 1 and 2 (Figs. 4.3a and 4.3b) showed that the rigid urethane coupling reduced source strength overall, mostly in the gearbox shaft. The main source still remained in the motor shaft, albeit less intense. At other frequencies such as 744 Hz and 1282 Hz, it seemed as if two different systems were observed because the noise sources occurred at completely different places. These frequencies showed more consistency when the misalignment was varied, rather than the spider coupling. This suggests that the rigidity of the spider coupling played a large role in changing the system at these frequencies.

4.3.3

Comparison of NAH data to modal data and critical speeds

With any rotating system, critical speeds can play a significant role in amplifying certain modes of a vibration through rotation of a main shaft. Three of the NAH frequencies discussed are at or near a mode of vibration of the rig. The critical speeds and cases where there is agreement of sources is summarized in Table 4.1. The check marks indicate cases where there was good agreement between the NAH and modal data. The actual order multiple values are listed for completeness; no analysis of components at these orders was performed. Table 4.1: Critical speeds and NAH to modal analysis noise source comparison

Modal Freq. 745 Hz 1001 Hz 1282 Hz

NAH Freq. 744 Hz 1000 Hz 1293 Hz

Order 25X 33.55X 43X

Case 1

Case 2

Case 3

Case 4

42

Results

With regard to the tachometer data, the average speed was found to vary only within 1 RPM for all cases, indicating that neither the couplings or the misalignment had a major effect on speed. Critical speeds were all calculated with an average RPM of 1788 RPM after the tachometer data were processed and spline fitted. The output speed was also not affected, showing an average of 2648 RPM, which confirms the gearbox transmission ratio to 1.48 (nominal 1.5) A typical processed input tach response is seen in Fig. 4.9, which shows the changing speed of the motor.

Figure 4.9: Typical input tachometer data showing average RPM of 1787.7 RPM.

By comparing the mode shapes to the NAH images, it is expected to see some agreement of the noise sources with components that are seen in the modal analysis. At 744 Hz, Figs. 4.2 and 4.8a show agreement in noise sources at the motor shaft for the Buna-N coupling (cases 1 and 3) directly where this mode lies. Next, it can be seen from Figs. 4.3 and 4.8b which show that 1000 Hz is a major modal frequency of the entire system that is a plate torsion and rig mode. Since the brackets, motor base, and gearbox are affected by the mode, this could influence reaction forces that allow the energy to be redistributed back into the driving shaft

43

Results

during operation. There is more mass on the motor side, and could be allowing for the plate noise source seen in all four NAH cases. The heavier mass on this side could be inducing reaction forces specifically at the motor shaft, which is manifested as a noise source in several of the NAH cases. Finally, the 1293 Hz mode is closely related to the NAH frequency studied at 1282 Hz, seen in Figs. 4.4 and 4.8c. This mode is shown to correlate more with the urethane coupling cases (Cases 2 and 4), showing sources near the motor base. Since the NAH data does not show as much agreement with the modal data across all of the cases, it is possible there is not much energy at the NAH frequency to excite the mode.

4.3.3.1

Third Order Misalignment Characteristic

One other major point to discuss is another frequency that was found to be greatly affected in the analysis, and this is 90 Hz. Due to the lower frequency limits of NAH, it is difficult to reconstruct the acoustic image at this frequency without a larger microphone array. Nevertheless, this frequency is important because it happens to be the third order multiple of the rotating input shaft (89.4 Hz). As previously mentioned, high amplitude responses in the first, second, /or third order are common in misaligned systems. Because the reference microphones were kept in exactly the same positions throughout all the cases, the reference autopowers can be easily compared. Each value is averaged from all three scans taken. Table 4.2 shows the highest mean∗ reference ∗

”Highest mean” refers to the reference microphone with the greatest mean amplitude at this frequency. Since each reference microphone autopower was averaged from three scans, each one is itself a mean amplitude, but the mean values will differ depending on the amount of sound pressure near the individual microphones.

44

Results

autopower for each case at the third order. As misalignment was introduced, the autopower amplitude increased, with the highest occurring in Case 4. The third order for Case 1 fell into the 88 Hz bin, whereas all others fell into the 90 Hz bin. Table 4.2: Third order reference autopower amplitude


Frequency Bin 88 Hz 90 Hz 90 Hz 90 Hz

Autopower Amplitude 71.09 dB 71.18 dB 79.34 dB 90.46 dB

Because this is a common order affected by misalignment, this result was expected when misalignment was introduced. What was harder to predict was the effect of each individual spider, with only the urethane coupling affecting the order when misalignment was present in Case 4. This value was 14% higher than Case 3 and 27% higher than the first two cases. Another major component of this order analysis involves two normal modes near this frequency, one at 86.20 Hz, and another at 91.55 Hz. The 91.55 Hz mode in particular was one of the easiest resonant frequencies to obtain stable consistency diagrams compared to most of the others. These modes are visualized in Fig. 4.10.

(a) 86.2 Hz Mode

(b) 91.55 Hz Mode

Figure 4.10: Normal modes near third order

45

Results

In Fig. 4.10a it can be seen that 86.2 Hz is likely a torsion mode affecting the plate. There is also motion in the shaft in the Z dimension indicating that this could be a lateral bending mode or torsion mode. At 91.55 Hz, the greatest amount of motion occurs as a bending mode of the shaft and the motor, as seen in 4.10b. Because these components are primarily responsible for driving the rig, it would seem that the misalignment could be exciting this mode. There are two possible explanations for what could be causing the increase in amplitude between Cases 3 and 4 in Table 4.2. First, it would make sense that a more rigid urethane spider would increase the overall noise level since this would contain less damping than the Buna-N spider, thus allowing the mode to excite more freely when the shaft is spinning. Second, because there are several locations around the rig where there is higher amplitude in the mode, higher rigidity between the two half jaw couplings could allow for more vibration to be transferred in the mode to other locations throughout the rig. An increase in acoustic pressure at 90 Hz is generally caused by structure borne noise paths. Because of the proximity of these resonant frequencies near this autopower data and because they are exciting major torque transmission components, they are likely critical speeds of the system.

4.4

Discussion of Errors There are several variables which could have influenced the data that were not

easy to control in the tests. First, since the rig was built with a special welded output shaft and welded coupling, there was an excessive amount of runout in each of these components. Runout is defined as two components which rotate slightly out of a true center axis or if they are out of round.

46

Results

In the case of the welded output splined shaft, the center tapped setscrew did help align the two shafts before welding, yet still had a measured runout of 0.017”. The input coupling which connects the gearbox to the motor shaft yielded a runout value of 0.035”. The acceptable tolerance for runout is 0.002”. Since these two components were unchanged throughout, this yielded systematic error throughout all of the cases. Since the anechoic chamber was not climate controlled, variability in the temperature and humidity could have induced error. Though the NAH software accounts for temperature (ref. to 20°C), the humidity is not taken into account. Table 4.3 lists the humidity and temperature for the four cases. Table 4.3: Climate conditions for NAH data


Temperature 24°C 24°C 26°C 25°C

Relative Humidity 20% 27% 37% 41%

Humidity usually plays a larger role in the absorption of sound above 2000 Hz [13]. However, it is unknown if this range is acceptable for this type of study in anechoic conditions. The temperature variation will undoubtedly affect the speed of sound, yet as previously explained this is accounted for in the NAH software. Calibration error in the array microphones could have also influenced the acoustic intensity images. Though most of the array microphones were within the accepted 25% of the nominal value, some of the array microphones were up to 45% out of this range. These microphones were put at the outer edges of the array to help minimize as much calibration error near the positions of the sources as possible. The Z distance being 0.25” off between the edges of the array could have also added error. Generally, it is advised that the measurement plane be perfectly parallel

47

Results

to the projection plane. Because of the geometry of the rig, adding 0.25” on one side seemed to allow for the array to be more parallel with the driving shaft, which was where many sources were of interest. With regard to the vibration data, a force and exponential window pair was chosen for windowing of the data. The exponential window added artificial damping which to the time domain block of the FFT so that the system transient decayed completely. This was not a good decision in hindsight, however, because since the structure was already heavily damped the response already decayed to zero in the time block. This would have definitely influenced the modal damping and made it more difficult to correctly estimate the modes. Certain impact nodes such as near the welds were subject to repeatably poor data and common high frequency overloads. Different amplitudes and ranges were attempted, but still resulted in relatively poor data, especially at higher frequencies. Ultimately some of these points were not used in the modal parameter estimation because of the poor data.

4.4.1

Measurement Challenges

Several measurement challenges affected the data acquisition process. Because of the limited scope of the thesis and the undertaking of designing and building a low cost rig, the conditions were not ideal for the highest quality of data. The largest challenge was that the speed of the motor was not constant; it fluctuated between 1786 RPM and 1790 for the cases. Because of the high channel count, many cables had to be neatly organized at all times or else tight creases or bends in the cables would cause channel

48

Results

errors. Apart from this, certain difficulties and limitations of assumptions presumably caused many of the errors seen in the data.

4.4.1.1

NAH Assumptions

Because the array could not capture the plate while maintaining nearfield distance, these data might not have fully conformed to the free-field boundary conditions. Though there was some distance from the sides and top of the array sufficient for the pressure to decay to near zero levels, the bottom of the array was not. The 2-D window ensured that the NAH processing worked, but it likely did affect amplitude values, depending on where the sources were. Certain frequencies were ineligible to study because the sources simply could not be reconstructed into anything meaningful or contained great amounts of error. This could be from fan noise causing false sources, non-linearities, non-planar source plane, or non-steady state conditions at these frequencies. Much of the difficulty was due to the changing speed of the motor because all of the frequencies of interest were at harmonics of rotating components. This affected whether the system was steady state or not. The speed change could have especially caused non-linearities in some of these components such as the gearbox because the gear-mesh process often contains nonlinear dynamic stiffness characteristics. A speaker test was performed to test the possible interaction of the plate on source reconstruction. The speaker was placed near the coupling, which was the main source of interest and played random white noise from a signal generator at 85 dB. Due to the geometry of the rig and speaker, the speaker had to be placed 9” from the array,

49

Results

which caused the Fmax for the test to be around 1505 Hz. Spatial aliasing affected the data beyond this frequency. Fig. 4.11 shows the results of this test which include the setup in Fig. 4.11a and the active intensity field summed from 650 Hz to 1450 Hz in 4.11b. This shows that overall in this frequency range, the plate might have had a slight effect of a false source near the alternator bracket, but overall provides good source resolution from where the speaker was without much error.

(a) Speaker test setup

(b) Intensity from 650 Hz to 1450 Hz

Figure 4.11: Speaker source test to determine plate influence

4.4.1.2

Test Procedure and Test Time

The effect of changing speed was apparent in the test process as well. Based on tachometer readings, this was only about 4 RPM, but it was enough to induce smearing of the frequency domain data. When data was initially acquired, the ∆f value was set to be 0.5 Hz in order to maintain good harmonic resolution in case half order harmonics were present and to help minimize leakage. As data was averaged, the energy fell into different spectral lines, causing wider peaks and lower effective amplitude. Another way to think about this is that each averaged time block contained more time where the

50

Results

speed varied. Because of this, the NAH reconstruction proved cumbersome and did not yield conclusive results. When the tests were originally performed, too many reference microphones were selected; a total of seven used. It was hypothesized that as cases of misalignment and rigid couplings occurred, more sources in the test aperture would appear. Since data storage was not a problem, the goal was to have redundant distribution of references in case more incoherent sources would appear. However, this substantially increased test time since larger auto and crosspower matrices needed to be gathered for each average. This meant that fewer averages could be taken due to the machine heating up in the appropriate test window. A singular value decomposition (SVD) of the reference autopowers of each of the data cases was performed in order to help determine the maximum number of microphones needed. A spectral decomposition was performed on the individual singular values to reduce the dimensionality [17]. The maximum number of microphones needed to satisfy Eq. 4.2 was chosen as the optimum number, plus one for noise [7]. Eq. 4.2 describes the ratio of singular values in the numerator compared to the total amount of singular values needed to describe 95% of the relevant data. The optimal amount was found to be five microphones maximum for the Case 4, and as little as three microphones for Case 1.

51

Results UDVH = M Pk 2 i=1 σi P ≥ 0.95 σ2

(4.1)

(4.2)

Where: U = Matrix of left singular vectors, D = Matrix of singular values, VH = Hermitian matrix of right singular values, M = Data matrix of reference microphone autopower data, σi = Individual singular values of D For the results shown in Section 4.1, using fewer reference microphones and a wider ∆f value significantly improved the test time and allowed for more averages. 60 seconds of time capture data were also taken for each scan as well. The last point to add was certain array microphones were commonly affected in the data acquisition process. During data acquisition, in monitoring output multiple coherence, overloads caused certain array channels to stop working mid-scan, even when overloads were supposedly rejected by X-Modal Typically, the multiple coherence would be acceptable until a certain average where in one or more channels it suddenly drops because of an overload. The channels with overloads showed high broadband response in the FRF which dominated all other channels. This would translate to noise or false sources in the acoustic NAH reconstruction since the overloaded channels sometimes had the highest responses. One solution was adding extra overhead range to these channels that overloaded, but the problem nevertheless persisted. The motor cooling fan could have been the result of some of these overloads as it blew directly into several array mics consistently and

Conclusions

52

was largely unpredictable. If these errors occurred, it greatly added to test time since the rig would need to cool down to the appropriate test temperature for a restart of the scan. In some cases, it was completely unavoidable despite many retries. The fans could not be bypassed because this could cause overheating of the motor.

Chapter 5

Conclusions and Future Work

5.1

Conclusions A test rig was successfully designed and built to study misalignment and the

effects of two different elastomeric spider couplings with different amounts of damping. Although this work was by no means exhaustive, it served as a proof of concept of the acoustical imaging of local faults within an industrial-grade machine using the active nearfield intensity. A partial modal analysis was performed to extract the modal frequencies and mode shapes in the frequency range of interest and correlated well with the noise sources found using NAH. By utilizing four test cases, it was shown that the the addition of misalignment with each respective coupling increased the severity of the noise sources and added additional sources at certain frequencies when compared to the cases without misalignment. Changing the spider coupling had less repeatable results and may have resulted in a different system altogether.

53

Conclusions

54

The third order of the input shaft was exacerbated by both misalignment and rigidity of the spider coupling, which may have allowed the excitation of nearby rig modes. The urethane coupling had more of an effect in the misaligned system compared to the normal system with the urethane coupling, adding roughly 10 dB to the autopower spectrum at the third order. Lastly, neither the change in elastomeric spider coupling material nor added misalignment influenced the input or output speed to a high degree.

5.2 5.2.1

Recommendations for Future Work Recommendations for Future NAH Analysis

Because of the compromises that had to be made to analyze the rig in this study, there are several recommendations that could be used to improve the acoustic imaging of this system. First, testing the rig on a reflecting ground plane boundary condition has been recommended by the committee. Second, the changing speed can make it difficult to study through steady-state NAH. 3-D enclosed arrays be could be made for each of the components (motor, gearbox, and alternator) and then studied in a single-scan transient fashion to study the noise sources of the components separately. This study was originally meant to develop a supervised machine learning (ML) scheme for the automation of fault detection. Support vector machine (SVM) was the intended pattern recognition algorithm to be used since SVM has provided robust accuracy for fault detection in previous work. As such, the acoustic images used in this study would be the starting point for such an endeavor. The images will need to be used as training data for the classification of misalignment. Then, additional misalignment datasets would need to be used upon these training sets in order to test the robustness

Conclusions

55

of the ML algorithm. More information about this type of research can be found in sources [16][19][20].

5.2.2

Recommendations for Test Rig Modifications

The test rig designed and built reflects the first iteration in its conception. Though it was adequate for the scope of the study, there are several modifications made that could be recommended to improve the rig for use in acoustic imaging, fault detection, and other rotating system measurements. It would be strongly advised to run the motor at 50-70% of its rated load to increase efficiency. There are two ways this solution could be approached. The easiest would be to change out the motor for one of less horsepower. Since the gearbox is not being used for its intended purpose of driving a pump, less input torque could potentially be used. This would also allow for less of a load to be applied to the system. If the motor is changed, it must not be larger than the motor brackets would allow. Custom vertical spacers will probably need to be fabricated so that the shafts will be at a level position. Additionally, it cannot operate above 2000 RPM since the gearbox output shaft is rated for 3,000 RPM max. If the motor is not changed out, then an additional current bank such as a deep cycle battery wired in parallel will need to be added since the alternator cannot supply enough current to run such a high load. This would be the more expensive option as a proper deep cycle battery would need to be selected for safe discharge in the test window. Installing a Variable Frequency Drive (VFD) or some other speed controlling device would be recommended so that better order analysis and tracking methods could

Appendix

56

be performed. Lastly, re-fabricating or buying another specialized coupling could help eliminate or reduce the amount of runout in the input shaft. Currently, this adds variability to the results. However, it would not be recommended to use a fully rigid coupling to connect the gearbox to the motor unless a precision alignment system is used.

Appendix A

MATLAB Code A.1

NAH Data Processing

1 2 3

clear all close all ;

4 5 6 7 8 9

fLines fMax = df =2; Nout = Nref =

= 1001; 2000; 56; 5;

10 11

f = linspace (0 , fMax , fLines ) ;

12 13 14 15

scan01 = load ( ’ d a t a s e t 3 C a s e 2 _ s c a n 0 1 . mat ’) ; scan02 = load ( ’ d a t a s e t 3 C a s e 2 _ s c a n 0 2 . mat ’) ; scan03 = load ( ’ d a t a s e t 3 C a s e 2 _ s c a n 0 3 . mat ’) ;

16 17

% EXTRACT ALL DATA

18 19 20 21 22 23

% -------------------------------------------------------------------------% SCAN03 % -------------------------------------------------------------------------c = 0; dof = Nout * Nref ; % Array Mics * Reference Mics

24 25 26 27

% EXTRACT FRF AND XPOWER H_03 = zeros ( Nref , Nout , fLines ) ; Gxf_03 = zeros ( Nref , Nout , fLines ) ;

28 29 30 31

index = dof + Nout + Nref ^2; for jj = 1: Nref for ii = 3: Nout +2;

32 33 34

H_03 ( jj , ii -2 ,:) = scan03 . UFCELLS { ii + c * Nout ,1}. DataValues ; Gxf_03 ( jj , ii -2 ,:) = scan03 . UFCELLS { ii + index + c * Nout ,1}. DataValues ;

35 36 37 38 39 40 41

ii + c * Nout ; end c = c +1; end H_03 = permute ( H_03 ,[2 1 3]) ; Gxf_03 = permute ( Gxf_03 ,[2 1 3]) ;

42 43 44

% COHERENCE AND GXX GxxIndex = index + dof ;

45 46 47

Gxx_03 = zeros ( Nout , fLines ) ; COH_03 = zeros ( Nout , fLines ) ;

57

Appendix 48 49 50 51 52

for ii = 3: Nout +2; COH_03 ( ii -2 ,:) = scan03 . UFCELLS { ii + dof ,1}. DataValues ; Gxx_03 ( ii -2 ,:) = scan03 . UFCELLS { GxxIndex + ii ,1}. DataValues ; end

53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69

% GFF in = 338; for q = 1: Nref for p = 1: Nref in + p ; Gff_03 (p ,q ,:) = scan03 . UFCELLS { p + in ,1}. DataValues ; end in = in + Nref ; end % Gff_03 = conj ( Gff_03 ) ; % AUTOPOWER GFF in = 339; add = Nref +1; for ii = 0: Nref -1 GffReal_03 ( ii +1 ,:) = scan03 . UFCELLS { in + ii * add ,1}. DataValues ; end

70 71 72 73 74 75 76

% This clunky format is simply to separate all Gff ’ s because NAH software % was having trouble loading it properly . Gff21_03 = squeeze ( Gff_03 (2 ,1 ,:) ) . ’; Gff31_03 = squeeze ( Gff_03 (3 ,1 ,:) ) . ’; Gff41_03 = squeeze ( Gff_03 (4 ,1 ,:) ) . ’; Gff51_03 = squeeze ( Gff_03 (5 ,1 ,:) ) . ’;

77 78 79 80

Gff32_03 = squeeze ( Gff_03 (3 ,2 ,:) ) . ’; Gff42_03 = squeeze ( Gff_03 (4 ,2 ,:) ) . ’; Gff52_03 = squeeze ( Gff_03 (5 ,2 ,:) ) . ’;

81 82 83

Gff43_03 = squeeze ( Gff_03 (4 ,3 ,:) ) . ’; Gff53_03 = squeeze ( Gff_03 (5 ,3 ,:) ) . ’;

84 85

Gff54_03 = squeeze ( Gff_03 (5 ,4 ,:) ) . ’;

86 87 88

apwr = [ GffReal_03 (1 ,:) ; GffReal_03 (2 ,:) ; GffReal_03 (3 ,:) ; GffReal_03 (4 ,:) ;... GffReal_03 (5 ,:) ; Gxx_03 ];

89 90 91

xpwr = [ squeeze ( Gxf_03 (: ,1 ,:) ) ; squeeze ( Gxf_03 (: ,2 ,:) ) ; squeeze ( Gxf_03 (: ,3 ,:) ) squeeze ( Gxf_03 (: ,4 ,:) ) ; squeeze ( Gxf_03 (: ,5 ,:) ) ];

92 93 94 95 96

xpwr2 = vertcat ( Gff21_03 , Gff31_03 , Gff41_03 , Gff51_03 ,... Gff32_03 , Gff42_03 , Gff52_03 ,... Gff43_03 , Gff53_03 ,... Gff54_03 ) ;

97 98

xpwr2_03 = conj ( xpwr2 ) ;

99 100

xpwr = vertcat ( xpwr2_03 , xpwr ) ;

101 102

% save ( ’ dataset3Case4IG03 ’ , ’ apwr ’ , ’ xpwr ’)

103 104 105 106 107 108 109 110

%% % -------------------------------------------------------------------------% SCAN02 % -------------------------------------------------------------------------c = 0; dof = Nout * Nref ; % Array Mics * Reference Mics

111 112 113 114


115 116 117 118

index = dof + Nout + Nref ^2; for jj = 1: Nref for ii = 3: Nout +2;

58

Appendix 119 120 121

H_02 ( jj , ii -2 ,:) = scan02 . UFCELLS { ii + c * Nout ,1}. DataValues ; Gxf_02 ( jj , ii -2 ,:) = scan02 . UFCELLS { ii + index + c * Nout ,1}. DataValues ;

122 123 124 125 126 127 128 129 130

ii + c * Nout ; end c = c +1; end H_02 = permute ( H_02 ,[2 1 3]) ; Gxf_02 = permute ( Gxf_02 ,[2 1 3]) ; % COHERENCE AND GXX GxxIndex = index + dof ;

131 132 133


134 135 136 137 138 139 140 141 142

for ii = 3: Nout +2; COH_02 ( ii -2 ,:) = scan02 . UFCELLS { ii + dof ,1}. DataValues ; Gxx_02 ( ii -2 ,:) = scan02 . UFCELLS { GxxIndex + ii ,1}. DataValues ; end % Test plots of coherence %{ figure for ii = 1: Nout

143 144 145 146

subplot (2 ,1 ,1) plot (f , COH_02 ( ii ,:) ) ; hold on xlim ([10 2250])

147 148 149 150

subplot (2 ,1 ,2) semilogy (f , squeeze ( abs ( H_02 ( ii ,2 ,:) ) ) ) ; hold on xlim ([10 2250])

151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169

end %} % GFF in = 338; for q = 1: Nref for p = 1: Nref in + p ; Gff_02 (p ,q ,:) = scan02 . UFCELLS { p + in ,1}. DataValues ; end in = in + Nref ; end % Gff_02 = conj ( Gff_02 ) ; % AUTOPOWER GFF in = 339; add = Nref +1; for ii = 0: Nref -1 GffReal_02 ( ii +1 ,:) = scan02 . UFCELLS { in + ii * add ,1}. DataValues ; end

170 171 172 173 174 175 176


177 178 179 180


181 182 183


184 185

Gff54_02 = squeeze ( Gff_02 (5 ,4 ,:) ) . ’;

186 187 188 189


59

Appendix 190 191


192 193 194 195 196


197 198


199 200


201 202


203 204 205 206 207 208 209 210

%% % -------------------------------------------------------------------------% SCAN01 % -------------------------------------------------------------------------c = 0; Nout = 28; dof = Nout * Nref ; % Array Mics * Reference Mics

211 212 213 214


215 216 217 218 219 220 221 222 223 224 225 226 227 228

index = dof + Nout + Nref ^2; for jj = 1: Nref for ii = 3: Nout +2; H_01 ( jj , ii -2 ,:) = scan01 . UFCELLS { ii + c * Nout ,1}. DataValues ; Gxf_01 ( jj , ii -2 ,:) = scan01 . UFCELLS { ii + index + c * Nout ,1}. DataValues ; ii + c * Nout ; end c = c +1; end H_01 = permute ( H_01 ,[2 1 3]) ; Gxf_01 = permute ( Gxf_01 ,[2 1 3]) ; % COHERENCE AND GXX GxxIndex = index + dof ;

229 230 231


232 233 234 235 236

for ii = 3: Nout +2; COH_01 ( ii -2 ,:) = scan01 . UFCELLS { ii + dof ,1}. DataValues ; Gxx_01 ( ii -2 ,:) = scan01 . UFCELLS { GxxIndex + ii ,1}. DataValues ; end

237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253

% GFF in = 170; for q = 1: Nref for p = 1: Nref in + p ; Gff_01 (p ,q ,:) = scan01 . UFCELLS { p + in ,1}. DataValues ; end in = in + Nref ; end % Gff_01 = conj ( Gff_01 ) ; % AUTOPOWER GFF in = 171; add = Nref +1; for ii = 0: Nref -1 GffReal_01 ( ii +1 ,:) = scan01 . UFCELLS { in + ii * add ,1}. DataValues ; end

254 255 256 257 258 259 260


60

Appendix 261 262 263 264


265 266 267


268 269

Gff54_01 = squeeze ( Gff_01 (5 ,4 ,:) ) . ’;

270 271 272


273 274 275


276 277 278 279 280


281 282


283 284


285 286


287 288 289 290 291

% Array node file Nrows = 8; Nmics = 14; % Number of Mics in each row Narray = Nmics * Nrows ;

292 293 294 295 296 297 298 299

NNUM = []; for ii = 1: Nrows for jj = 1: Nmics num = ( Nmics ) *( Nrows - ii ) + jj ; NNUM = vertcat ( NNUM , num ) ; end end

300 301

save ( ’ r ig2scans _node ’ , ’ NNUM ’)

302 303 304 305 306 307 308 309 310

% Check how many reference mics required [U ,S , V ]= svd ( GffReal_01 , ’ econ ’) ; % Start with 1 singular value in sum1 , then add singular values to sum1 % until sum3 95% value achieved , then add 1 mic for noise . sum1 = S (1 ,1) ^2 + S (2 ,2) ^2; % + S (3 ,3) ^2 %+ S (4 ,4) ^2; %+ S (5 ,5) ^2; sum2 = S (1 ,1) ^2 + S (2 ,2) ^2 + S (3 ,3) ^2 + S (4 ,4) ^2 + S (5 ,5) ^2; sum3 = sum1 / sum2 ;

311 312 313 314 315 316 317 318 319 320 321

% -------------------------------------------------------------------------% Compute mean and std deviation of reference autopowers % -------------------------------------------------------------------------for ii = 1: Nref GffC1 ( ii ,:) = Gff_01 ( ii , ii ,:) ; GffC2 ( ii ,:) = Gff_02 ( ii , ii ,:) ; GffC3 ( ii ,:) = Gff_03 ( ii , ii ,:) ; end GffCombo = cat (3 , GffC1 , GffC2 , GffC3 ) ; GffCombo = permute ( GffCombo , [3 1 2]) ;

322 323 324 325 326 327 328

for jj = 1: Nref for ii = 1: fLines GffMean ( jj , ii ) = mean ( GffCombo (: , jj , ii ) ,1) ; GffStd ( jj , ii ) = std ( GffCombo (: , jj , ii ) ,1) ; end end

329 330 331

GffStdP = GffMean + GffStd ; GffStdN = GffMean - GffStd ;

61

62

Appendix 332 333 334 335

GffMean =10* log10 ( GffMean /((20 e -6) ^2) ) ; GffStdP =10* log10 ( GffStdP /((20 e -6) ^2) ) ; GffStdN =10* log10 ( GffStdN /((20 e -6) ^2) ) ; k = 0;

% Converting to dB

336 337 338 339 340 341 342 343 344 345 346 347 348 349

% Plot Ref Autopowers for All References for ii = 1: Nref figure hold on plot (f , GffStdN ( ii ,:) , ’. - r ’) plot (f , GffStdP ( ii ,:) , ’. - b ’) plot (f , GffMean ( ii ,:) , ’g ’) ; title ( sprintf ( ’ Autopower for Reference Mic % d ’ , ii ) ) ylim ([40 95]) xlim ([10 2000]) ylabel ( ’ dB Magnitude ’) xlabel ( ’ Frequency ( Hz ) ’) end

350 351 352 353 354 355 356 357 358 359

figure for ii = 1: Nref plot (f , GffMean ( ii ,:) , ’ -- ’) ; hold on title ( ’ CASE 2 d3 : All Reference Autopowers Superimposed ’) ylim ([50 90]) xlim ([10 2000]) ylabel ( ’ Magnitude ( dB ) ’) xlabel ( ’ Frequency ( Hz ) ’) end

360 361 362 363 364 365 366 367 368 369

% Since Reference 7 was added as channel 1 , all references after 1 have to % be shifted up . 1 st autopower is now Motor rear . legend ( ’ Motor Front (1) ’ , ’ GB lower (2) ’ , ’ GB Upper (3) ’ , ’ Alt / Coupling 2 (4) ’ , ’ Coupling 1 (5) ’) %} % -------------------------------------------------------------------------% Combine All Data into One " Scan " % -------------------------------------------------------------------------apwr = [ GffMean (1 ,:) ; GffMean (2 ,:) ; GffMean (3 ,:) ; GffMean (4 ,:) ; GffMean (5 ,:) ;... Gxx_01 ; Gxx_02 ; Gxx_03 ];

370 371 372 373 374 375 376 377

% The way this is set up is to have full array to ref 1 , full array to ref % 2 , etc . xpwr = [ squeeze ( Gxf_01 (: ,1 ,:) ) ; squeeze ( Gxf_02 (: ,1 ,:) ) ; squeeze ( Gxf_03 (: ,1 ,:) ) ; squeeze ( Gxf_01 (: ,2 ,:) ) ; squeeze ( Gxf_02 (: ,2 ,:) ) ; squeeze ( Gxf_03 (: ,2 ,:) ) ; squeeze ( Gxf_01 (: ,3 ,:) ) ; squeeze ( Gxf_02 (: ,3 ,:) ) ; squeeze ( Gxf_03 (: ,3 ,:) ) ; squeeze ( Gxf_01 (: ,4 ,:) ) ; squeeze ( Gxf_02 (: ,4 ,:) ) ; squeeze ( Gxf_03 (: ,4 ,:) ) ; squeeze ( Gxf_01 (: ,5 ,:) ) ; squeeze ( Gxf_02 (: ,5 ,:) ) ; squeeze ( Gxf_03 (: ,5 ,:) ) ];

378

% Take average of xpwrs between ref microphones from all 3 scans xpwrR = ( real ( xpwr2_01 ) + real ( xpwr2_02 ) + real ( xpwr2_03 ) ) ./3; xpwrI = ( imag ( xpwr2_01 ) + imag ( xpwr2_02 ) + imag ( xpwr2_03 ) ) ./3; xpwrAvg = complex ( xpwrR , xpwrI ) ;

379 380 381 382 383 384

xpwr = vertcat ( xpwrAvg , xpwr ) ;

385 386

save ( ’ c a s e 1 D a t a s e t 4 C o m b i n e d R I G 0 1 ’ , ’ apwr ’ , ’ xpwr ’)

387 388 389 390 391 392

% Check References for Steady State via standard dev . for jj = 1: Nref for ii = 1: fLines if GffMean ( jj , ii ) >=55 % Set dB threshold ssMatrix ( jj , ii ) = GffStdP ( jj , ii ) - GffStdN ( jj , ii ) ;

393

else

394

ssMatrix ( jj , ii ) = 0;

395

end

396 397 398 399

end end

400 401

% Add Frequencies to sieve through and find out if they are SS

63

Appendix 402 403 404 405

analyzeFreqs = [88 120 132 176 210 240 388 418 626 670 714 730 744 760 804 818 834 854 ... 870 906 928 998 1002 1032 1194 1222 1252 1282 1326 1430 1446 1490 ... 1504 1548 1608 1652 1668 1680 1698 1710 1726 1850 1946];

406 407 408 409 410 411 412

output = zeros ( Nref +1 , length ( analyzeFreqs ) ) ; % freqCounter = 1; % ; freqCounter = freqCounter / df ; for jj = 1: Nref for f = 1: length ( analyzeFreqs ) for freqCounter = 1: fMax

413

if ( freqCounter / df ) +1/ df == analyzeFreqs (: , f ) / df

414 415

output ( jj , f ) = ssMatrix ( jj ,( freqCounter / df ) +1/ df ) ;

416 417

end

418

end

419

end

420 421

end

422 423

sieve dSSMatr ix = cat (1 , analyzeFreqs , output ) ;

A.2 1

Tachometer Processing

% Tach Script

2 3 4

clc clearvars

5 6 7

tachs = load ( ’ case4tachs . mat ’) ; % Load the data tach1 = tachs . UFCELLS {3 ,1}. DataValues ;

8 9 10 11 12

dt = 0 . 0 0 0 1 2 2 0 7 0 3 1 2 5 0 0 0 0 0 ; fNyq = 1/(2* dt ) ; fs = 1/ dt ;

13 14

t = linspace (0 , length ( tach1 ) * dt , length ( tach1 ) ) ; % Time data blocks

15 16 17

figure plot (t , tach1 )

18 19 20 21 22

% Center tach signals tach1 = tach1 - rms ( tach1 ) ; negOrPosTach1 = sign ( tach1 ) ;

23 24 25 26 27

k = 1; m = 1; % Use interpolation formula to find zero crossing for ii =1: length ( negOrPosTach1 ) -1

28 29 30 31 32 33

if negOrPosTach1 ( ii ) =0 xCrossing1 ( k ) =((0 - tach1 ( ii ) ) *( t ( ii +1) -t ( ii ) ) /( tach1 ( ii +1) - tach1 ( ii ) ) ) + t ( ii ) ; k = k +1; end end

34 35 36 37 38 39

% RPM estimate for ii = 1: length ( xCrossing1 ) -1 rpm1 ( ii ) = 60/( xCrossing1 ( ii +1) - xCrossing1 ( ii ) ) ; rpmTime1 ( ii ) = ( xCrossing1 ( ii +1) + xCrossing1 ( ii ) ) /2; end

40 41

% Spline Fit

Appendix 42 43 44 45 46 47 48 49 50 51 52 53

64

% Set Spline Lengths , going from begining of time to end of time , divided in % an N number of splines . xq = linspace ( rpmTime1 (1) , rpmTime1 ( length ( rpmTime1 ) ) ,36) ; tach1Spline = interp1 ( rpmTime1 , rpm1 , xq , ’ spline ’) ; m = round ( mean ( rpm1 ) ,5) ; % Plot Smoothed Tach Signals figure plot ( rpmTime1 , rpm1 ) hold on ; plot ( xq , tach1Spline , ’ LineWidth ’ ,1) xlabel ( ’ Time ( s ) ’) ; ylabel ( ’ RPM ’) ; title ( sprintf ( ’ Case 3: Smoothed Tach Overlay , Mean = % d RPM ’ ,m ) ) ; axis tight ; legend ( ’ Zero - Crossing ’ , ’ Spline Fit ’) ;

Appendix B

Additional Data B.1

Additional NAH Images

65

66

Appendix

(a) Case 1

(b) Case 2

(c) Case 3

(d) Case 4

Figure B.1: Active intensity at 818 Hz, k = 0.60

67

Appendix

(a) Case 1

(b) Case 2

(c) Case 3

(d) Case 4

Figure B.2: Active intensity at 1946 Hz, k = 0.60

Appendix C

Instrumentation and Gearbox Schematic

68

Appendix

C.1

Array Microphone Datasheet

69

Reference Microphone Datasheet C.2

70 Appendix

378B02

Model Number

Performance Nominal Microphone Diameter Frequency Response Characteristic(at 0° incidence) Sensitivity Sensitivity(± 1.5 dB) Frequency Range(± 2 dB) Frequency Range(± 1 dB) Lower Limiting Frequency(-3 dB) Inherent Noise Dynamic Range(3% Distortion Limit) TEDS Compliant

Environmental Temperature Range(Operating) Temperature Coefficient of Sensitivity(+14 to +158°F (-10 to +70°C)) Static Pressure Coefficient Humidity Coefficient of Sensitivity(0 to 100%, non-condensing) Influence of Axial Vibration(0.1g (1 m/s²))

Electrical

SI

[2] [2] [4]

[1]

[5]

[2]

OPTIONAL VERSIONS

Prepolarized Typical. re 250 Hz TEDS Capable Digital Communication, compliant with IEEE 1451.4 Venting through Preamp. See PCB Declaration of Conformance PS064 for details.

Revision: F

ECN #: 47338

Entered: LK

Engineer: MT

Date: 10/17/2017

Sales: MV

Date: 10/17/2017

Approved: MT

Spec Number:

57824

Phone: 716-684-0001 Fax: 716-684-0987 E-Mail: [email protected]

Date: 10/17/2017

3425 Walden Avenue, Depew, NY 14043

Date: 10/17/2017

Model ACS-63 Calibration (with TEDS) of Precision Condenser Microphones and Preamplifiers together (mated pair). (1)

SUPPLIED ACCESSORIES:

[1] [2] [3] [4] [5] [6]

NOTES:

Optional versions have identical specifications and accessories as listed for the standard model except where noted below. More than one option may be used.

ICP MICROPHONE SYSTEM ENGLISH 1/2" Free-Field 50 mV/Pa -26 dB re 1 V/Pa 3.75 to 20,000 Hz 7 to 10,000 Hz 1.0 to 3.0 Hz 15.5 dB(A) re 20 µPa 137 dB re 20 µPa Yes [3] [3]

1/2" Free-Field 50 mV/Pa -26 dB re 1 V/Pa 3.75 to 20,000 Hz 7 to 10,000 Hz 1.0 to 3.0 Hz 15.5 dB(A) re 20 µPa 137 dB re 20 µPa Yes

0V 20 to 30 VDC 2 to 20 mA 10 to 14 VDC ± 7 Vpk