fortfarande¨arietttidigtstadium.Syftetmeddettaexamensarbetevarattutv¨arderaolika Sammanfattning

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Evaluation of methods for fault detection of planetary gears for nutrunners

JON BOMAN

GUSTAV STORCK

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Evaluation of methods for

fault detection of planetary gears for nutrunners

Jon Boman Gustav Storck

Master of Science Thesis MMK 2014:48 MDA 487

KTH Industrial Engineering and Management

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Examensarbete MMK2014:48 MDA 478 Utv¨ardering av metoder f¨or feldetektering av

planetv¨axlar f¨or mutterdragare Jon Boman

Gustav Storck

Godk¨ant Examinator Handledare

2014-06-19 Lei Feng Bj¨orn M¨oller

Uppdragsgivare Kontaktperson

Atlas Copco

Industrial Technique AB

Per Forsberg .

Sammanfattning

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Atlas Copco utför accelererade livslängdsprov p˚a sina planetväxlar för mutterdragare genom att köra dem med konstant hastighet och konstant moment tills de havererar. Företaget önskade ett sätt att under drift detektera tidiga fel i växeln för att kunna avbryta testerna medan skadorna fortfarande är i ett tidigt stadium. Syftet med detta examensarbete var att utvärdera olika metoder för feldetektering av planetväxlar.

En bakgrundsstudie utfördes för att finna tidigare forskning inom omr˚adet. Sen utfördes tester i en testrigg där Normalised Summation of Difference Spectrum (NSDS) och Filtered Root Mean Square (FRMS), beräknade fr˚an den uppmätta transversal- och torsionsvibrationen, användes som indikatorer för växelns hälsotillst˚and.

Resultaten fr˚an testerna antydde att NSDS och FRMS förm˚aga att indikera tidiga fel i växeln var bristfälliga. Dock s˚a kunde liknande mönster i torsionsvibrationen observeras för de växlar

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Master of Science Thesis MMK2014:48 MDA 478 Evaluation of methods for fault detection of planetary

gears for nutrunners Jon Boman Gustav Storck

Approved Examiner Supervisor

2014-06-19 Lei Feng Bj¨orn M¨oller

Commissioner Contact person

Atlas Copco

Industrial Technique AB

Per Forsberg .

Abstract

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Atlas Copco performs accelerated life testing on their planetary gears for nutrunners by running them at constant speed and torque until they fail. The company desired a way to detect initial gear faults during operation in order to stop the tests while the damages were still in an early stage. The purpose of this thesis was to investigate different methods for planetary gear fault detection.

An initial background study was performed to investigate previous research within the field.

Then tests were performed in a test rig where the Normalised Summation of Difference Spectrum (NSDS) and Filtered Root Mean Square (FRMS), calculated from the measured transversal and

torsional vibration, were used as indicators of the gears health state.

The results from the tests indicated that the NSDS and FRMS were deficient as indicators of initial gear faults. However, similar behaviour in the torsional vibration could be observed for

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Preface

After five tough years of studying at KTH this master’s thesis was the final obstacle to overcome, la grande finale, before we could officially call ourselves fully fledged engineers. Since you are reading this report, we apparently made it.

We would like to thank all of you that we have come in contact with during our time at Atlas Copco, especially Per Forsberg and Johan Hedek¨all who have been our eminent supervisors. You have been encouraging and helpful throughout the whole process which we are eternally grateful for.

We also want to thank our supervisor at KTH, Bj¨orn M¨oller, who has given us valuable feedback and guided us in our work.

Finally we would like to thank Anton Lagerholm and Staffan Molinder who did their master’s thesis simultaneously at Atlas Copco. All conversations about existential questions during our shared lunch breaks have helped to keep our spirits high in times of darkness.

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List of Figures

1.1 Example of nutrunner. . . 1

2.1 Planetary gear with names of components and direction of rotation when annular gear is fixed. . . 3

2.2 Examples of different gear failure modes. . . 5

2.3 More examples of different gear failure modes. . . 6

2.4 Example of how synchronous averaging increases the signal-to-noise ratio. . . 8

2.5 Example of an amplitude modulated signal. . . 9

2.6 Example of a frequency modulated signal. . . 9

3.1 Example of how the propagation difference for the vibration varies over time causing an AM-effect on the signal perceived by the transducer. . . 12

4.1 The planetary gear used for testing. . . 16

4.2 The rig used for testing. . . 17

4.3 Drawing of gear mounted in holder. . . 18

4.4 DEWE-43 USB DAQ used for collecting data. . . 18

5.1 Flowchart of the data processing. . . 23

6.1 Frequency spectrum of the signal from torque sensor connected to gear 1. Nor- malised by the 2nd stage carrier frequency. The red/dotted lines indicate the locations of identified sidebands. . . 28

6.2 Frequency spectrum of signal from accelerometer mounted directly on the annulus of gear 1. Normalised by the 2nd stage carrier frequency. The blue/dotted lines indicate the locations of identified sidebands. . . 29

6.3 Investigation of NSDS health parameter from the original test plan. . . 30

6.4 Investigation of FRMS health parameter from original test plan. . . 31

6.5 2nd stage sun gear worn down in test 8. . . 32

6.6 NSDS health parameter from the revised test plan. . . 33

6.7 FRMS health parameter from the revised test plan. . . 34 6.8 How the sideband fm− 2 × 3f^s−c= 22.5 Hz changes over time in the different tests. 35

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List of Tables

3.1 Vibration spectrum sidebands for different fault modes. . . 12

4.1 Number of gear teeth for the gear used. . . 15

5.1 Selected fault modes for testing. . . 21

5.2 Contents in dataset exported from Dewesoft X. . . 22

5.3 Reset revolutions for planetary gear. . . 24

5.4 Frequencies in Hz filtered in FRMS. . . 25

6.1 Gear frequencies in Hz. Normalised by the 2nd stage carrier frequency. . . 27

6.2 Failure modes in tests 7-11, determined by visual inspection of the gears. . . 32

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Chapter 1

Introduction

Atlas Copco is a Swedish-based industrial group operating within four different business areas:

compressor technique, mining and rock excavation technique, industrial technique and construction technique. This master’s thesis has been carried out at the division Atlas Copco Industrial Technique AB in Stockholm which provides tools for customers in the automotive and aerospace industries, industrial manufacturing and maintenance, and in vehicle service. Their pneumatic and electric industrial tools and assembly systems assist customers in achieving fastening within narrow tolerances, minimising errors and interruptions in production.

1.1 Background and problem definition

Atlas Copco is continuously improving the planetary gear design for their electric nutrunners, see Figure 1.1, in order to increase life-span and power handling while maintaining a light and compact unit that can fit inside a hand-held tool. As in all product development processes, performance tests are essential, Atlas Copco performs unit tests on their planetary gears in a lab environment by applying a constant torque and running the gears at constant speed until they fail completely. This approach accelerates the testing making it less time-consuming compared to testing the gear in an actual tool, which would require millions of joint tightenings. However, after the initial fault occurs, the gear deteriorates and may cause damage to additional components.

Consequently making it difficult to identify the initial cause of failure and draw conclusions of what the needed design improvements are.

Figure 1.1: Example of nutrunner.

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Chapter 1 - Introduction

To improve the test process a method is desired that can detect when the first fault occurs and automatically abort the test, providing an opportunity for the development engineer to examine the gear before failing completely. Based on the problem presented, the aim of the master’s thesis is to develop this method. In order to succeed with the adopted challenge, the following research question requires to be explored:

Is it possible and which methods are suitable for early stage fault detection in Atlas Copco’s planetary gears for nutrunners.

The following factors are to be considered when comparing and evaluating the different methods performance:

• What is the size of detectable damages.

• Which fault modes are detectable.

• Possibility to identify the nature of the damage (e.g. pitting, tooth crack etc.).

• Repeatability.

• How do external factors affect the method (e.g. sensor placement, gear drive load etc.).

The ability to determine the gears health condition is also a function that may be integrated in future versions of electric nutrunners. The opportunity of detecting damages before complete failure would bring value to Atlas Copco’s customers since it would increase the possibility of performing predictive maintenance, reducing the risk of unforeseen stops in the production due to tools failing.

1.2 Delimitations

The focus for this master’s thesis is to evaluate methods aimed to be used in a lab environment.

When choosing amongst different methods, the ones believed to generate the best results in a lab environment are to be investigated before the ones that have potential of being integrated in future versions of Atlas Copco’s tools.

There exists several different models of planetary gears for different tools and applications, but for this evaluation testing will be performed on one single model selected by Atlas Copco.

1.3 Report structure

This thesis report starts with Chapter 2 explaining a few concepts and theories that are fundamental for the research conducted. It is followed by Chapter 3 which is a summary of previous research, relevant for this thesis, within the same and adjacent fields. Then Chapter 4 presents the test set-up with the planetary gear examined, the test rig and measurement equipment. This is followed by Chapter 5 which describes the method and approach used for testing. The test results are presented in Chapter 6 and are analysed in Chapter 7 where the authors thoughts on future improvements also are discussed. The thesis report ends with Chapter 8 containing conclusions drawn from the research conducted.

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Chapter 2

Frame of reference

This chapter can be seen as a guide to matters that are discussed in the report but may be unfamiliar to the reader. It will present what a planetary gear is and what frequencies are associated with it, and some common fault modes. Some signal analysis methods will also be presented.

2.1 Fundamentals of planetary gears

The design of planetary gears (alt. epicyclic gears) provides advantages such as large gear ratio, high load-bearing capacity and high efficiency in a smaller and lighter format compared to ordinary fixed shaft gears according to Jelaska [1].

Planetary gears consist of a central gear with external teething, or sun gear, placed coaxially with a larger gear with internal teething, or annular gear, and a planet carrier which supports one or more planet gears. The illustration in Figure 2.1 shows an overview of the gear configuration and how members move relative to each other when the annular gear is fixed. Depending on which member is held fixed the planetary gear has different properties, but as the fixed annular gear configuration is the one used in the actual tool, that will be the one treated in this report.

sun annulus

planet carrier

(a) Gear scheme.

annulus

planet carrier

sun

fs fc

fp−c

(b) Overview

Figure 2.1: Planetary gear with names of components and direction of rotation when annular gear is fixed.

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Chapter 2 - Frame of reference

2.2 Periodicities in planetary gears

There are a lot of periodic behaviour in planetary gears, where several can be identified by vibration measurements. Some are best described by their individual frequencies, while the number of revolutions is more interesting for others.

2.2.1 Frequencies in planetary gears

The frequency spectrum for a planetary gear is more complex than for a fixed shaft gear. The reason is that the design of the planetary gear leads to more gear pairs meshing, as there are a number of planet gears and they all mesh with both the sun gear and the annular gear simultaneously.

The fundamental frequencies in this section are given by Collacott [2]. They are calculated from the number of teeth on the sun ts, planet tp and annular gear ta. The sun gear rotational frequency fsin Hz relative to the fixed annulus is

fs= Ns

60, (2.1)

where Ns is the suns rotational speed in revolutions per minute. The carrier frequency fc is fc= ts

ts+ ta

fs. (2.2)

These frequencies can be seen as absolute since they are relative to a fixed system, the annular gear. For some gear members it may be more interesting to calculate their frequencies relative to other non-stationary members. The planets frequency relative to the carrier fp−cis

fp−c= tsta

tp(ts+ ta)fs= ta

tp

fc (2.3)

and the sun frequency relative the carrier fs−cis f_s−c= ta

ts+ ta

fs=ta

ts

fc. (2.4)

The mesh frequency for a planetary gear with fixed annular gear is given by fm= tsta

ts+ ta

fs (2.5)

and combining Equation (2.5) with (2.2) yields

fm= tafc. (2.6)

If a gear member has a local fault on a single tooth it will excite a certain frequency depending upon if it is the sun, planet or annular gear. These characteristic frequencies are often called overrun or high spot frequencies. They are based on the carrier frequency and the number of planet gears, as it determines how often the damaged tooth is in mesh with a planet gear. The overrun frequencies of the sun, planet, and annular gears respectively are given by

f_s^∗= nta

tsfc (2.7)

f_p^∗= 2ta

tp

fc (2.8)

f_a^∗= nfc, (2.9)

where n is the number of planet gears. There is a factor 2 in Equation (2.8) since the planets mesh both with the sun and annulus in one complete revolution.

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KTH Royal Institute of Technology - 2014

2.2.2 Resets of planetary gears

In order to achieve distributed wear on all teeth, planetary gears are preferably designed so that a tooth on one gear member will mesh with all teeth on the mating part before meshing with the same tooth again. In this report, the period for the gear pair to return to the initial state (i.e. same two teeth in mesh) will be denoted as a ”reset”. The reset is calculated for both sun and planet gears for each stage and is given in revolutions of the carrier relative to the gear of interest. According to Samuel et al. [3] the reset can be calculated by

Reset = LCM (tg, ta) ta

, (2.10)

where LCM refers to the least common multiple, ta is the number of teeth on the annular gear and tg is the number of teeth on the gear of interest, i.e. the sun or planet gear. The LCM of all individual resets yields the reset of the entire gear in revolutions of the planet carrier.

2.3 Planetary gear failure modes

The following section is a summary of commonly occurring gear failures described in Reference [4] and [5].

2.3.1 Pitting

Pitting is caused by cyclically varying contact stress in the tooth flank in the presence of a lubricant. Surface and subsurface fatigue cracks causes small pieces of material detaching, leaving cavities in the tooth’s contact surface, see Figure 2.2a and 2.2b. As this process is repeated, more and more pits appear and eventually the tooth surface may be severely damaged.

(a) Pitting on sun. (b) Pitting and spalling on sun.

Figure 2.2: Examples of different gear failure modes.

2.3.2 Scuffing

Scuffing can occur at high temperatures and high loads when the lubricant film breaks between the tooth flanks in mesh, which may lead to local micro-welding causing bays and fissures in the direction of sliding. Scuffing may also lead to severe flank damage, increase of operating

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temperature, dynamic forces, vibrations, noise and loss of power. Compared to pitting and tooth breakage which often occur after millions of load cycles, scuffing can appear after a short-term overload. However, if only light scuffing has occurred and the temporary overload is reduced, the flanks can smoothen themselves again when running under normal conditions for a period of time.

2.3.3 Deformation

Plastic deformation occurs when stresses in the gear exceed the yield strength in the material, causing a deformation that remains after the applied load is removed, see Figure 2.3a. This may result in deformed teeth and displacement of material due to the sliding/rolling action of gears operating under high loads and friction.

2.3.4 Cracks

Cracks in gears can occur due to multiple causes, fatigue cracks are caused by alternating or cyclic normal stress in the tooth when meshing. The initial crack is often very small and grows under operation until the tooth fractures.

2.3.5 Lubrication failure

During long-time operation the gears lubricant can be used up, escape through seals or loose its lubricating properties. This may cause an increase in friction and temperature, bearing failure and a decrease of the gears efficiency, see Figure 2.3b.

(a) Teeth deformation on planet. (b) Bearing failure has caused temperature increase on planet gear shaft.

Figure 2.3: More examples of different gear failure modes.

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2.4 Signal analysis

Signal analysis is a vital part of understanding measured signals and there are a few fundamental tools that have been utilized in this thesis project. They are the Fourier Transform, Root Mean Square (RMS) and Synchronous averaging and will be described shortly in the following sections.

2.4.1 Fourier Transform

The following section is based on Bod´en et al. [6] and Wallin et al. [7]. The measured vibration from most systems are a combination of several vibrations with varying period length. Identifying individual frequency components in the sampled signal can be difficult in the time domain.

However, in the frequency domain all periodic contributions can be observed as peaks in the frequency spectrum. Converting a continuous signal x (t) from the time domain to the frequency domain is done by using the Fourier Transform

X (ω) = Z ∞

−∞

x (t) e^−iωtdt, (2.11)

where ω is the frequency of interest. However, a sampled signal is by default a discrete signal, and the Fourier Transform needs to be adapted. The result is the Discrete Fourier Transform, defined as

X (k) = 1 N

N−1

X

n=0

x (n) e⁻^i2πnk^N , (2.12)

where x (n) is the nth sample of the continuous signal x (t) and k is the index of the frequency of interest. The Discrete Fourier Transform is a computationally heavy algorithm, where N² operations is required for a signal of length N . By taking advantage of the symmetric properties of the trigonometric functions involved, computation time can be saved. The algorithm using this property is called Fast Fourier Transform (FFT) and reduces the number of calculations required to N log₂(N ), if N is a power of 2. In practice it is difficult to collect an exact power of 2 sample points, this can be solved by appending zeros or resampling the signal to the appropriate length.

2.4.2 Root Mean Square

There are several ways to extract valuable information from signals. With a sinusoidal signal it may be interesting to look at its amplitude, since it gives the maximum value of the signal. If the signal is more complicated, and especially if it is a sampled signal with much noise, the amplitude will not give much information about the signal, simply because the signal does not have the same peak value over time. To smooth noisy data a mean value can be calculated, however in the case of signals with sinusoidal behaviour the mean will only be the offset from zero, which is in most cases not interesting. But if each value is squared before the mean is calculated and the square root is calculated of the mean, the result will be the Root Mean Square (RMS). For a discrete signal it is given by

RMS = v u u t1

N

X

n=1

[x (n)]², (2.13)

and is a measure of the power content.

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2.4.3 Synchronous averaging

Sampled signals are always riddled with noise. A technique called Synchronous averaging can be very effective in reducing the noise in vibration signals from rotating machinery. It is applied in the time-domain and takes advantage of the periodic nature of such machinery where mechanical signals repeat cyclically every rotational cycle.

Synchronous averaging is performed by dividing the complete signal into subsets corresponding to one rotational cycle with the same number of equidistant sample-points. To compensate for varying rotational speeds of the machine, causing the number of samples per rotational cycle to differ, a measurement system that records the angular position can be used. Then the signal can be resampled by interpolation ensuring that the vibration is sampled at the same position in every rotational cycle.

By taking the average value of the matching sample points across all subsets, the signal-to-noise ratio is increased since non-periodic components (i.e. noise) are suppressed and the periodic signal will be enhanced. An example of the methods effectiveness can be seen in Figure 2.4.

0 2 4 6 8 10

−1 0 1

Time [s]

Amplitude

(a) One period of a sine signal with random noise.

0 2 4 6 8 10

−1 0 1

Time [s]

(b) Synchronous average over 20 subsets.

Figure 2.4: Example of how synchronous averaging increases the signal-to-noise ratio.

2.4.4 Signal modulation

Consider a sine signal

y (t) = A sin (ω0t) (2.14)

with amplitude A and angular frequency ω0. A modulation is when the amplitude or frequency of the signal is modified by another periodic signal with an angular frequency ω1that is less than the carrier frequency ω0, according to Roder [8]. If the signal amplitude is subject to the periodic variation

Aam(t) = A (1 + k sin (ω1t)) , (2.15) where k determines the amplitude of the modulation, the signal is Amplitude Modulated (AM), yielding

yam(t) = Aam(t) sin (ω0t). (2.16) As seen in Figure 2.5a the amplitude of the original signal in the time domain has a sinusoidal wave form. In the frequency domain this can be seen as a pair of sidebands around the carrier frequency, see Figure 2.5b.

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0 0.2 0.4 0.6 0.8 1

−2 0 2

Time [s]

Amplitude

Modulated signal, 40 Hz Modulation signal, 5 Hz

(a) Time domain.

35 40 45

0 0.5 1

Frequency [Hz]

Amplitude

Modulated spectrum Carrier frequency

5 Hz

(b) Frequency domain.

Figure 2.5: Example of an amplitude modulated signal.

In the other case where the carrier frequency varies periodically ωf m(t) = ω0

t + k

ω1sin (ω1t)

(2.17)

the signal is Frequency Modulated (FM), yielding

yf m(t) = A sin (ωf m(t)). (2.18)

In time domain the carrier signal will be compressed and expanded by the modulation, see Figure 2.6a. In the frequency domain an infinite number of sidebands will appear, see Figure 2.6b.

0 0.2 0.4 0.6 0.8 1

−2 0 2

Time [s]

Amplitude

Modulated signal Modulation signal

(a) Time domain.

35 40 45

0 0.5 1

Frequency [Hz]

Amplitude

Modulated spectrum Carrier frequency

(b) Frequency domain.

Figure 2.6: Example of a frequency modulated signal.

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Chapter 3

Literature review

Machine monitoring is an art which has been practised for a long time, just by listening to the machine a skilled operator can estimate its condition. By experience he or she recognises the sound character of a healthy machine, and can therefore detect when the sound character changes due to wear or failure of different components. In order to prevent machine breakdowns in the industry, with high costs as a consequence, a lot of effort has been put into developing methods for automated machine monitoring. The ability to estimate the current state of health of machines enables the possibility to perform predictive maintenance which often is more cost-efficient than repairing at breakdowns, according to Bod´en [6]

Health monitoring and fault detection of gears specifically has been extensively researched over several decades since they are an essential component in many machines, therefore vast amounts of literature can be found on the topic. In a review on the research available specifically on planetary gear monitoring, Lei et al. [9] conclude that the majority of earlier work focused on fixed shaft gear drives which are less complex compared to planetary gears. However, they made the observation that the amount of publications on specifically planetary gears had increased rapidly in recent years. Especially in the aeronautical industry, several attempts have been made to develop Health and Usage Monitoring or Prognostic and Health Management systems for use in helicopter transmissions, where drive train failure is one of the most common cause of accidents, according to Samuel and Pines [10].

The gears in Atlas Copco’s tools are considerably smaller in size compared to helicopter transmissions, which is a factor that limits the methods available since there is no space to mount sensors on individual components inside the gear drive.

The background study conducted for this thesis project has focused on the planetary gears complex spectral structure and how it changes over time with wear and damages. Understanding this has been vital in order to know what to search for when analysing and post processing measurement data.

3.1 Vibration monitoring

All machines with moving components generate vibrations with varying frequencies that are transferred throughout the system. Every machine element has a characteristic vibration signature and the art of machine vibration monitoring is to understand how wear and damages to the different components affects the vibration signal picked up by the transducer.

3.1.1 Transversal vibration

In fixed shaft gears, the mesh frequency is commonly one of the dominant frequency components in the vibration signal due to the cyclically varying contact force between the teeth pair in mesh. For planetary gears however, observations has shown that when measuring the transversal

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Chapter 3 - Literature review

vibrations with a transducer mounted on the annular gear, it is the modulation sidebands to the meshing frequency that are dominant. While the meshing frequency in some cases can be completely suppressed. According to McFadden and Smith [11] this phenomenon is due to the planets moving in relation to the annular gear causing the mesh location to vary over time. The vibration generated from the meshing of the sun and planet pair will propagate to the transducer via the sun, bearings and annulus. The vibration generated from the meshing of the planet and annulus is transmitted directly through the annulus. As the carrier rotates, the distance from meshing location to the transducer will vary, as seen in Figure 3.1. Assuming that the annular gear flexes, the varying transmission distance causes a modulation effect on the vibration perceived by the transducer. This is because the vibration contribution from one individual planet is greatest when it is passing the transducer and least when it is farthest away.

Accelerometer

Mesh freq.

Sidebands

Time domain Frequency domain f t

Figure 3.1: Example of how the propagation difference for the vibration varies over time causing an AM-effect on the signal perceived by the transducer.

Feng and Zuo [12] also points to the fact that the time-varying nature of the sun-planet and planet-annular meshing results in amplitude modulation effects. In their publication they present vibration signal models for fault diagnosis of planetary gears where they consider the AM and FM effects due to damaged gears and vibration transmission paths. Considering several different fault modes, signal models were derived and validated through experimental and industrial test data. Suppose that a gear tooth develops a local fault, such as a pit or root crack, that causes a change in the flank working surface or the meshing stiffness compared to other teeth. When the damaged tooth engages with the mating gear tooth, the local fault will cause an impulse in the vibration signal with a meshing characteristic different from the undamaged teeth. Assuming that the gears rotational speed is constant, this impulse will repeat periodically with a frequency corresponding to the rotating frequency of the damaged gear and appear as a sideband to the mesh frequency in the vibration spectrum, see Table 3.1. Even a healthy gear may generate these sidebands due to imperfections from the manufacturing process, but Feng and Zuo show that amplitude changes for the sidebands indicates damages to the corresponding gear.

Table 3.1: Vibration spectrum sidebands for different fault modes.

Damaged gear Sideband location

Annulus kfm± nfa^∗

Planet kfm± nfp^∗ and kfm± f^c± nfp^∗

Sun kfm± nfs^∗and kfm± f^s± nfs^∗

k, n = 1, 2, 3, . . .

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3.1.2 Torsional vibration

As explained in the previous section, the transversal vibrations of planetary gears have a complex spectral structure due to the AM and FM nature. In this section, an alternative approach proposed by Feng and Zuo [13] is described where the torsional vibration is used as an alternative to the transversal vibration. They comment in their article that when conducting their background study, they had no success in finding earlier publications attempting to use the torsional vibration for the purpose of planetary gear fault diagnosis. In the writing of this thesis, two years after Feng and Zuo’s article was published, their work was still the only one found on the topic.

The fundamental idea to observing the torsional vibration for planetary gear fault detection is the same as for observing the transversal vibration. Gear faults will change the meshing stiffness causing an impulse also in the torque perceived by the transducer, and by detecting these impulses one can identify gear faults.

As mentioned earlier the planets orbits around the sun gear, causing the planet-sun and planet-annular meshing locations to change over time. In contrast to the transversal vibration, this will not cause an AM effect on the torsional vibration since the propagation distance from the meshing location to the torque transducer, connected to either the input or output shaft, is constant over time. However, compared to fixed shaft gears where only the meshing gear pair affect the modulation of the torsional vibration; planetary gears have multiple gear pairs that affect the torsional vibration perceived by the torque transducer. Suppose one of the planets is damaged, in that case the torsional vibration is affected by the meshing of both the planet-sun and planet-annular gear pair. If instead the sun or annular gear is damaged, only the meshing of planet-sun or planet-annular gear pair affects the torsional vibration. But there are still multiple gear pairs modulating the signal since the sun and annular gear is engaged with all planets.

By deriving a model for the torsional vibration Feng and Zuo show that the AM and FM parts of the torsional vibration signal contains information of the faulty gear. They show that distributed gear faults can be diagnosed by monitoring the change in the mesh frequency’s sidebands associated with the faulty gears frequency relative to the planet carrier, i.e. fs−c, fp−c

and fr−c. Local gear faults can also be diagnosed in the same manner, but the local fault also causes sidebands associated with the faulty gears overrun frequencies f_s^∗, f_p^∗ and f_a^∗.

3.2 Diagnostic parameters

One major challenge identified when performing the literature review was that most of the methods developed, specifically for planetary gears, rely on visual inspection of collected data. The consequence is that the methods performance largely depend on the expertise of the investigator to spot features indicating gear damage, thus making it complicated to develop automated algorithms with adequate performance.

For fixed shaft gears there has been several diagnostic parameters designed for the purpose to aid in gear health monitoring. Two examples are the FM0 and FM4 presented by Stewart [14] in the late 1970s. Where FM0 indicates distributed gear faults by detecting major changes in the mesh pattern and FM4 indicates the occurrence of local faults on a limited number of teeth by detecting higher-order sidebands appearing in the vibration signal. These parameters have also been tested on planetary gears by Lei et al. [15] but were not considered very effective.

The following section will present two diagnostic parameters specially designed for planetary gears.

3.2.1 FRMS and NSDS

Lei et al. [15] published an article where they introduce two diagnostic parameters for planetary gears. First the Filtered Root Mean Square (FRMS) which is as the name suggests the RMS of a

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Chapter 3 - Literature review

vibration signal after applying a filter cancelling certain frequencies. It is calculated by

FRMS = v u u t1

N

X

n=1

[y (n)]², (3.1)

where y (n) is the nth data point of the filtered signal with length N samples. The process of implementing FRMS is as follows:

1. Calculate the Fourier transform of the sampled vibration signal.

2. Apply a filter in the frequency domain that removes the shaft frequency and its five-order harmonics, the gear meshing frequency and its three-order harmonics, and the modulation sidebands and its harmonics.

3. Calculate the inverse Fourier transform of the filtered signal, yielding the filtered signal y (n).

4. Calculate the RMS of y (n).

The authors reasoning is that the vibration spectrum for a planetary gearbox has rich modulation sidebands in addition to the shaft frequency and mesh frequency with their respective harmonics.

They mean that the vibration signal from both healthy and damaged gears have these modulation sidebands and are therefore not indicators of faults. The second parameter they introduce is the Normalised Summation of Difference Spectrum (NSDS). It is calculated by normalising the sum of positive amplitudes of the difference vibration spectrum between the healthy and faulty gear, mathematically expressed as

NSDS =

I

P

i=1

Xd(i)

I

P

i=1

Xg(i)

(3.2)

Xd(i) =

Xg(i)− X^h(i) if Xg(i) > Xh(i) 0 if Xg(i) 6 Xh(i)

where Xh(i) and Xg(i) are the frequency spectra of the vibration signal from a healthy and unknown gear, respectively. Since they believed that the vibration signal and the corresponding frequency spectrum would change when damages to the gear occur, the idea was that the NSDS would detect these changes.

Lei et al. evaluated the parameters performance by testing them on a healthy gear, a gear with pitted sun gear and a gear with cracked sun gear. The vibration data was collected from a test rig running at three different speeds, with and without applying load. Their observation was that the parameters could clearly distinguish the different health conditions, although the FRMS was sensitive to the gear speed and the normalisation factor in the NSDS was not perfect. They comment that the performance of the proposed parameters might be reduced if the applied load varies largely since the gears vibration characteristics would probably change.

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Chapter 4

Experimental set-up

The experimental set-up will be presented in this chapter. Descriptions of the specific planetary gear as well as descriptions of the test rig and which sensors and data acquisition units used are provided.

4.1 The planetary gear

The gear provided by Atlas Copco was a two stage planetary gear with fixed annulus and a rated torque of 36 Nm. A photograph and drawing of the gear can be seen in Figure 4.1. When mounted in the tool the input shaft is the 1st stage sun gear and the output shaft is the 2nd stage planet carrier. However, in the test rig the planetary gear was fitted in the reverse direction so the input shaft was the 2nd stage planet carrier and output the 1st stage sun gear, thus requiring lower maximum speed from the rig drive motor.

In Table 4.1 the number of teeth for each gear member is presented. With this configuration the gear ratio for the 1st stage is

i1= 1 +ta1

ts1 ≈ 7.43 (4.1)

and the 2nd stage gear ratio is

i2= 1 +ta2

ts2

= 4.75 (4.2)

which gives a total gear ratio of

itot= i1× i²≈ 35.29. (4.3)

Table 4.1: Number of gear teeth for the gear used.

Gear stage Sun Planet Annular No. of planets

1st 7 18 45 3

2nd 12 16 45 3

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Chapter 4 - Experimental set-up

Sun, 1st stage Annulus 1st stage 2nd stage

(a) Photograph of the gear.

Sun, 1st stage

Carrier, 1st stage/

Sun, 2nd stage

Carrier, 2nd stage Planet, 2nd stage

Annulus

Planet, 1st stage Planet bearing

(b) Drawing of the gear.

Figure 4.1: The planetary gear used for testing.

4.2 The test rig

A power recirculating or back-to-back test rig was used to perform the tests. The advantage with this type of rig is that the only input power needed from the drive motor is to cover the power losses in the system, as the gear torque is not generated by applying a braking torque but is generated from torsional shafts.

The rig consisted of two straight parallel axes that were connected by sprockets and toothed belts, see Figure 4.2. The bottom axis consisted of the two torsion shafts which were used to set the torque applied to the gears. While one of the shafts was held fixed, torque was manually applied to the other with a lever generating torsion in the shafts. When the desired gear torque was set, the two shafts were interlocked rotationally by tightening a friction coupling. The planetary gears were connected to the upper shaft, placed in holders fixating the annular gear as seen in Figure 4.3. Due to the back-to-back design, two planetary gears with the same ratio were required in order to match the rotational speeds. The torque in each gear was measured with

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two in-line transducers connected to the 2nd stage carrier on each gear, which also measured the angular position of the carriers. To compensate for axial misalignment bellows couplings were connected on either side of the transducers. To measure transversal vibrations an accelerometer was mounted with an adhesive directly on the annular gear of gear 1. The temperatures of the gears were measured on the annulus by two IR-thermometers. The rig was monitored by an Agilent DAQ configured to turn off the rig if either the measured torque or temperature deviated from a predefined range.

(a) Photograph of the rig.

Drive motor

Gear 1

Bellows coupling

Friction coupling

Nc2 Ns1 Nc2

Toothed belt drive

Gear 2

Torsion shaft

Nc2 Nc2

Accelerometer

Torque transd. 1 Torque transd. 2

(b) Illustration of the rig.

Figure 4.2: The rig used for testing.

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Chapter 4 - Experimental set-up

Gear holder

Bellows coupling connector

Ball bearing Spacer

Guide

Shaft to mating gear

Gear Annular gear rotational fixation

Figure 4.3: Drawing of gear mounted in holder.

4.3 Sensors and data acquisition

Choosing the equipment to collect data was an important part of the test set up, that includes deciding what was to be measured, how to measure it and the resolution of the measurements. In this case the focus was on transversal and torsional vibrations and therefore accelerometers and torque transducers connected to a data acquisition system was used.

4.3.1 Data acquisition system

The data acquisition hardware used during tests was a DEWE-43 [16] with 8 analogue and 8 digital counter channels which can be seen in Figure 4.4. 24-bit sigma-delta analog-digital converters converted the analogue signals at a maximum rate of 200 000 samples per second. All sensors except the thermometers were connected and sampled by the DEWE-43. Because of the low rotational speed of the test rig, the frequencies within the planetary gears were relatively low with the main frequencies of interest ranging from 5 to 250 Hz. The sampling rate was therefore set to 4 kHz. The DEWE-43 was connected to a computer via USB and the data was stored by using the software Dewesoft X [17].

Figure 4.4: DEWE-43 USB DAQ used for collecting data.

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4.3.2 Torque transducer

The torque transducer used was a Magtrol TM-312 [18] which was an in-line torque transducer with a rated maximum torque of±200 Nm, with an analogue output signal of ±10 VDC. It had a built-in 2nd order Butterworth low-pass filter with 12 predefined cut-off frequencies ranging from 1 to 5000 Hz. During the tests it was set to 1000 Hz. The transducer also included a incremental rotary encoder that outputted a digital signal with a resolution of 60 pulses/rev.

4.3.3 Charge accelerometer

Due to the small size of the planetary gears tested, the choice of accelerometers was limited. The accelerometer of choice was a Br¨uel & Kjær Type 4374 [19] with a base diameter of 5 mm, height of 6.7 mm and a frequency range spanning from 1 to 26000 Hz. This was a charge accelerometer and an amplifier was needed to convert the vibration signal to an analogue voltage signal required by the DEWE-43. This was done by a Br¨uel & Kjær Type 2635 [19]. The amplifiers low-pass filter was set to 1000 Hz.

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Chapter 5

Method

In this chapter the original and revised test plan are described. The following sections are devoted to the data collection procedure, the implementation of the synchronous average and the calculation of the health parameters.

5.1 Original test plan

In order to evaluate the methods presented the following test plan was constructed:

1. Run-in the gear.

2. Take reference measurements of the healthy gear at different speeds and loads.

3. Disassemble the gear and exchange one gear member with one that has a known fault.

4. Take measurements of the damaged gear.

5. Reassemble the gear with its original parts.

6. Take additional measurements to detect changes from the ones taken in step 2.

This process was to be repeated on several gears for the different fault modes selected, with the purpose to determine the methods performance considering the factors mentioned in the introduction. To further investigate the possibility to find faults at different speeds and loads, the speed was to be changed in three steps; 30, 60 and 90 rpm while the load was set to the rated torque, 36 Nm, and approximately half the rated torque, 15 Nm.

Given the limited time frame dedicated for testing only a few faults modes were selected. The fault modes chosen can be seen in Table 5.1 and were chosen based on experience from earlier tests done at Atlas Copco. Focus was set on the gear’s 2nd stage where the meshing forces are larger than in the 1st stage, thus more prone to fail according to Per Forsberg at Atlas Copco.

Table 5.1: Selected fault modes for testing.

Test Fault mode

1 Distributed wear, 2nd stage sun gear 2 Distributed wear, 2nd stage planet gear 3 Pitting, 2nd stage sun gear

4 Pitting, 2nd stage planet gear 5 Planet bearing running dry

6 Bearing wear, 2nd stage planet gear

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Chapter 5 - Method

Due to the gear members small size it was considered hard to introduce faults manually, instead already faulty parts from earlier tests were planned to be used. By doing this the damage was considered to be realistic and reproducible as the same part could be used for several different gears.

5.2 Revised test plan

After starting out performing tests according to the original test plan presented in the previous section, results showed that uncertainties were introduced in the disassembly and reassembly of the gear causing incoherent results. Since the time dedicated for testing was running out, another approach had to be chosen in order to generate results reliable enough to draw conclusions from.

Instead of disassembling gears and exchanging healthy gear members for damaged ones, new gears were run continuously until they failed by natural wear. Measurements were taken periodically throughout the whole test. This eliminated the uncertainties introduced by the reassembly of the gears, but also made it impossible to control the fault leading to a breakdown.

The tests were run with the rated torque 36 Nm at 60 rpm which was the highest speed possible without overheating the gear.

5.3 Data collection and processing

The following section refers to the steps 1 to 5 in Figure 5.1 and describes how the data collection and post-processing were performed.

1. Since every test ran for approximately 48 hours, sampling continuously was not considered necessary or practical due to the great amount of data that would have been stored.

Therefore, the system was set up so that the data acquisition software, Dewesoft X, ran continuously monitoring the number of revolutions completed but only saved data for a period of 5 gear resets every 35th reset. By using this approach, the total amount of data was reduced and made it possible to continuously export the datasets, see Table 5.2, to MAT-files [20] as the test was running.

2-3. The MAT-files were individually loaded in Matlab where the torque and accelerometer data was divided into five smaller subsets where every subset corresponded to one reset-period.

4. Using the position data (No. of revolutions completed, Table 5.2) every subset was resampled using linear interpolation yielding five signals with the same number of uniformly distributed sample points. The synchronous average was then calculated by using all the subsets. By subtracting the signals mean value, the DC-gain was removed.

5. The synchronous averaged signal was used to calculate the health parameters presented in Section 3.2. The steps 2 to 5 was repeated for each dataset collected during the test. The health parameter calculated was plotted to visualise the change during the gears life-span.

Table 5.2: Contents in dataset exported from Dewesoft X.

Signal Unit

Torque 1 Nm

Torque 2 Nm

Acceleration m/s²

No. of revolutions completed rev

Speed rpm

Sample point time stamp s

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2 4 6 8 10 12 14 16

25 30 35 40

Timedomainsignal

2 4 6 8 10 12 14 16

0 0.2 0.4 0.6 0.8 1

T im e [s]

Period

2.1.

4.3.

5.

3)

4)

5) Torque

Acceleration

2)

1)

0 2 4 6 8 10 12

x 10⁴ 0

0.05 0.1 0.15 0.2 0.25 0.3 0.35

Nr of revolutions completed [rev]

Healthparameter

10 20 30 40 50 60 70 80

25 30 35 40

Timedomainsignal

10 20 30 40 50 60 70 80

0 0.2 0.4 0.6 0.8 1

T i m e [ s]

Period 1. 2. 3. 4. 5.

0 2 4 6 8 10 12 14 16

−6

−4

−2 0 2 4 6

Po sitio n [rev]

Synchronisedaverage

...

test10_001.mat test10_002.mat

Figure 5.1: Flowchart of the data processing.

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Chapter 5 - Method

5.4 Synchronous average in practice

When performing the synchronous average two parameters needed to be determined, namely the period length of each subset and the number of subsets to average over. The latter was decided by calculating the synchronous average by averaging over 10, 7, 5, and 3 subsets and comparing the results. Visual inspection showed that there was no significant difference when averaging over 10 subsets compared to only 5. Therefore 5 subsets were used throughout all tests.

The period length selected corresponded to 16 complete revolutions of the 2nd stage carrier.

It should be noted that 16 revolutions of the carrier do not correspond to a reset of the entire planetary gear. The resets for the annular-sun and annular-planet for both stages calculated by Equation (2.10) can be found in Table 5.3. Calculating the LCM of these resets yields the total reset for the entire planetary gear,

Reset = LCM(7, 2, 4, 16) = 112. (5.1)

Running the rig at 60 rpm, it would have taken 5× 112 s = 560 s to collect one dataset. To decrease the amount of data another approach was tested where the reset of the 1st stage annular-sun was neglected. The idea was that the meshing of this gear pair had minimal effect on the torque and acceleration signal seen by the transducers, since the 1st stage meshing forces are smaller than those for the 2nd stage. Another factor is that the vibrations from the 1st stage have to travel through the 2nd stage gears before reaching the torque transducer. The longer propagation distance may dampen these vibrations. Neglecting the reset of the 1st stage annular-sun yielded a period length of

Reset = LCM(2, 4, 16) = 16 (5.2)

revolutions of the 2nd stage carrier, corresponding to 5× 16 s = 80 s at 60 rpm.

When testing this alternative approach, no significant difference in the sampled signal was visually observed, neither in the time domain nor the frequency domain. Therefore, it was considered possible to select a period length of 16 carrier revolutions instead of 112, thus reducing the amount of data approximately with a factor of 7.

Table 5.3: Reset revolutions for planetary gear.

Gear stage Annular - Sun Annular - Planet

1st 7 2

2nd 4 16

5.5 FRMS and NSDS in practice

The FMRS was calculated according to Section 3.2. After the time signal was transformed into the frequency domain, the frequencies presented in Table 5.4 were filtered out using a 4th order Butterworth bandstop filter. These were the five first shaft frequency harmonics and the three first meshing frequency harmonics of the 1st and 2nd stage, calculated from the equations presented in Section 2.2.1, and will of course vary depending on the design of the planetary gear in question.

All other frequencies were left untouched and the signal was transferred back to the time domain.

The RMS was then calculated yielding the FRMS value.

The NSDS parameter was calculated using Equation (3.2). For the revised test plan, where the whole life-span of the planetary gear was measured, the healthy frequency spectrum Xh was chosen to be the third measurement. It was chosen since it was considered that the gear would be run-in by that point and therefore a good representative of the signal from a healthy gear. The interpolation performed in the synchronous averaging guaranteed that all subsets were of equal length, and the normalisation of the frequencies yields that the difference spectrum Xd could

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simply be calculated using element by element subtraction of the healthy frequency spectrum array and the unknown frequency spectrum array, as the peaks in the frequency spectra would correlate throughout all subsets. The sum of all frequency amplitudes in the difference spectrum Xd was then normalised by the sum of all frequency amplitudes in the unknown spectrum Xg

yielding the NSDS value.

Table 5.4: Frequencies in Hz filtered in FRMS.

Harmonic Shaft 1st stage mesh 2nd stage mesh

1 1 213.75 45

2 2 427.5 90

3 3 641.25 135

4 4 - -

5 5 - -

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Chapter 6

Results

6.1 Identification of fundamental frequencies

Since the test rig contains a large number of rotating components with greater inertia relative to the gear, one concern was that the frequencies not originating from the gear would dominate the torque and acceleration signals. Initial measurements were taken on a healthy gear in order to confirm that it was possible to obtain torque and acceleration signals where the frequencies of interest were able to be identified. The fundamental frequencies for the gear was calculated using the equations given in Section 2.2.1 and the numeric results can be seen in Table 6.1.

Table 6.1: Gear frequencies in Hz. Normalised by the 2nd stage carrier frequency.

Gear stage Mesh Abs. Rel. Char.

fm fc fs f_p−c f_s−c f_s^∗ f_p^∗ f_a^∗ 1st 213.8 4.8 35.3 11.9 30.5 91.6 23.8 14.3

2nd 45 1 4.8 2.8 3.8 11.3 5.6 3

In Figure 6.1 and 6.2 the spectrum for a torque and acceleration dataset is presented, respectively. The dataset was sampled on a healthy gear and synchronous averaging over five resets was performed on the time-domain signal before performing the Fourier Transform.

In Figure 6.1a and Figure 6.2a one can identify the 2nd stage mesh frequency (45 Hz) as a very dominant component, and several of the sidebands expected according to Section 3.1.2 can also be identified. That the 2nd stage mesh frequency is very significant may not be surprising since the torque sensor is connected directly to the 2nd stage planet carrier.

In Figure 6.1b and 6.2b the spectrum is zoomed in around the 1st stage mesh frequency (213.8 Hz). Here the mesh frequency is not dominant and only a few of the expected sidebands can be identified, even though the total number of sidebands is larger compared to the 2nd stage mesh frequency.

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Chapter 6 - Results

30 35 40 45 50 55 60

0 5· 10⁻² 0.1 0.15 0.2

fm fm+1fc fm+1fp−c fm+1fs fm+1fs−c fm−1fc

fm−1fp−c

fm−1fs fm−1fs−c fm+2fc fm+2fp−c fm+2fs

fm+2fs−c fm−2fc

fm−2fp−c

fm+3fs−c fm−3fc

fm−3fp−c

fm−3fs fm−3fs−c

Velocity normalised frequency [1/rev]

Amplitude

(a) 2nd stage mesh frequency with sidebands.

180 190 200 210 220 230 240 250

0 5· 10⁻² 0.1 0.15 0.2

fm fm+1fc fm+1fp−c fm+1fs fm+1fs−c fm−1fc

fm−1fp−c

fm+2fs−c fm−2fc

fm−2fp−c

fm+3fs−c fm−3fc

fm−3fp−c

fm−3fs fm−3fs−c

Amplitude

(b) 1st stage mesh frequency with sidebands.

Figure 6.1: Frequency spectrum of the signal from torque sensor connected to gear 1.

Normalised by the 2nd stage carrier frequency. The red/dotted lines indicate the locations of identified sidebands.

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25 30 35 40 45 50 55 60 65

0 5· 10⁻² 0.1 0.15 0.2

fm fm+1f^{∗ a}

fm−1f

∗ a

fm+2f

∗ a

fm−2f

∗ a

fm+3f

∗ a

fm−3f

∗ a

fm+4f

∗ a

fm−4f

∗ a

fm+5f

∗ a

fm−5f

∗ a

fm+6f

∗ a

fm−6f

∗ a

fm+1f

∗ s

fm−1f

∗ s

Amplitude

(a) 2nd stage mesh frequency.

190 200 210 220 230 240

0 0.2 0.4 0.6 0.8 1

fm fm+1f^{∗ a} fm−1f

∗ a

fm+1f

∗ p

fm−1f

∗ p

fm+fc−1f

∗ p

fm−fc+1f

∗ p

fm+1f

∗ s

fm+2f

∗ s

Amplitude

(b) 1st stage mesh frequency.

Figure 6.2: Frequency spectrum of signal from accelerometer mounted directly on the annulus of gear 1. Normalised by the 2nd stage carrier frequency. The blue/dotted lines indicate the locations of identified sidebands.