1
Czech Technical University in Prague
Faculty of Electrical Engineering
Department of Measurement
Bachelor's Thesis
System for vibration testing
Michal Stach
Supervisor: Ing. Martin ’ipo²
Study Programme: Electrical Engineering and Information Technology
Branch of Study: Cybernetics and Measurement
27. 5. 2011
CZECH TECHNICAL UNIVERSITY IN PRAGUE
FA
Faculty of Electrical Engineering
Department of Measurement
Academic year 2010-2011
BACHELOR’S THESIS STATEMENT
Student:
Michal Stach
Major:
Cybernetics and Measurement
Title in Czech:
PracovištČ pro testování vlivu vibrací
Title in English:
System for vibration testing
Instructions for thesis elaboration:
Design and implement system for vibration testing. System will consist of vibration table and graphical
user interface, which will control the vibration table through GPIB or measuring card. The environment
will provide generating vibrations based on real data from the airplane. Graphical user interface
implemented in CVI/Labwindows will be able to calibrate vibration table according to parameters of
measured sensor. Verify the interface by using the inclinometer EZ-Tilt-2000-008. Interface will allow
to set manufacturer-defined parameters and to save measured data into a file. Measure influence of
vibrations to the inclinometer. Using device with the Motorola processor, create a conversion module
of the data from the inclinometer (RS232) to CANaerospace format.
References:
[1] Hlaváþ, V., Sedláþek, M.: Zpracování signálĤ a obrazĤ 1. vyd. Praha, ýVUT, 2000
[2] Stock Flight Systems, CANAerospace [online], 2010, [cit. 2010-11-24], dostupný z www:
http://www.stockflightsystems.com/index.php?option=com_content&task=view&id=13&Itemi
d=53.
[3] Dokumentace k prostĜedí LabWindows CVI.
Supervisor:
Ing. Martin Šipoš
Date of statement:
October 20th, 2010
1
Valid until :
rd
February 3 , 2012
L.S.
Prof. Ing. Pavel Ripka, CSc.
Head of the department
Doc. Ing. Boris Šimák, CSc.
Dean of the faculty
th
In Prague, October 20 , 2010
_______________________________
1
Statement validity is limited to three following semesters.
Aknowledgements
To be honest with, this thesis gave me a lot of experiences and there are many important
people to give thanks to. Firstly, I would like to give many thanks to my family, without
their support I would not be where I am. Special thanks goes to my Taiwanese friends
Sophie Fang and Annie Hsin-Yun Chang for supporting me as well. Also, this way I want
to highlight help of my roommates Martin Frodl and Pavel Otta in sharing the experiences
from their theses. Many thanks goes to Ing. Jan Rohá£, Ph.D. for giving me directions
about this project and last but not least I would like to express my thanks to the leader of
my bachelor's thesis Ing. Martin ’ipo².
Abstract
This thesis aims to create the independent system for testing the vibration inuence to
various types of sensors. Project will include three applications, each one controlling dierent part of the system. User will be able to load and simulate vibrations from real aircraft,
check the accuracy of articial vibrations and save them into the le. Tested inclinometer will have its own application, giving the possibility to change one's parameters or for
example getting the angular data. Inclinometer will be able to work in CANAerospace communication networks thanks to the third program for converting the data from inclinometer
to CANAerospace.
Abstrakt
Cílem této práce je vytvo°it zcela nezávislý systém pro testování vlivu vibrací pro r·zné
typy senzor·. Projekt se bude skládat ze t°í aplikací, kaºdá komunikující s jinou £ástí
systému. Uºivatel bude moci nahrát a odsimulovat data z reálného letadla, porovnat a
ov¥°it tato data s um¥le vygenerovanými vibracemi a nam¥°ená data uloºit do souboru.
Testovaná elektronický inklinometr bude mít sv·j vlastní program, nabízející moºnost zm¥nit
parametry nebo nap°íklad vy£ítat úhlové hodnoty. Elektronický inklinometr bude schopen
komunikovat s CANAerospace sít¥mi díky t°etímu programu, který bude provád¥t konverzi
dat z inklinometru do formátu CANAerospace.
iii
Contents
List of Figures
vi
List of Tables
viii
List of Acronyms
ix
List of DVD Contents
x
1 Introduction
1
2 Theory
2
2.1
2.2
2.3
The DFT and the FFT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
CANAerospace Standard . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
IVI and VISA Libraries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3 Sensor and Measuring System Instruments
3.1
3.2
3.3
Inclinometer . . . . . . . . . . . . . . .
Universal Communication Board . . . .
System for Vibration Testing . . . . . .
3.3.1 Arbitrary Waveform Generator
3.3.2 Data Acquisition System . . . .
3.3.3 Crossbow Accelerometer . . . .
3.3.4 Power Amplier . . . . . . . . .
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4 Sensor and Measuring System Software Development
4.1
4.2
4.3
User Interface for the Inclinometer . . . .
4.1.1 Port Settings Tab . . . . . . . . . .
4.1.2 Measure Tab . . . . . . . . . . . .
4.1.3 Calibration and Tilt Settings Tab .
User Interface for Vibration Testing . . . .
4.2.1 CSV File Reader and FFT Analysis
4.2.2 Calibration Procedure . . . . . . .
4.2.3 Arbitrary Waveform Generator . .
4.2.4 Agilent U2531 Data Acquisition . .
CAN Programming . . . . . . . . . . . . .
5 Measurements
5.1
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Data structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
iv
2
3
4
6
6
8
9
9
10
10
11
12
12
12
13
15
17
19
20
22
24
25
27
28
CONTENTS
5.2 Input Data Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3 Inuence of Vibrations to the Inclinometer . . . . . . . . . . . . . . . . . . .
5.4 Mass Inuence to Generated Vibrations . . . . . . . . . . . . . . . . . . . . .
v
29
30
32
6 Conclusion
33
Bibliography
34
A
38
B
40
C
46
List of Figures
2.1
2.2
CANAerospace frame description . . . . . . . . . . . . . . . . . . . . . . . .
VISA standard hierarchy . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
Measuring system ow chart . . . . . . . . . . . .
One axis tilt sensor . . . . . . . . . . . . . . . . .
EZ-TILT-2000-008 inclinometer . . . . . . . . . .
Universal Communication Board . . . . . . . . . .
System for vibration testing . . . . . . . . . . . .
Agilent 33220A, the arbitrary waveform generator
Agilent U2531A data acquisition system . . . . .
Crossbow CXL02LF3 accelerometer . . . . . . . .
The YAMAHA P7000S power amplier . . . . . .
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6
7
7
8
9
9
10
10
11
4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8
4.9
4.10
4.11
4.12
4.13
4.14
4.15
4.16
4.17
4.18
4.19
4.20
4.21
Connecting the inclinometer through the RS232 . . . . . . . . . . . . . . . .
Port settings tab . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Measure tab . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Asynchronous timer scheduling . . . . . . . . . . . . . . . . . . . . . . . . .
Reading pitch and roll . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Dierence between reference data and non-calibrated output . . . . . . . . .
Dierence between reference data and calibrated output . . . . . . . . . . . .
Calibration tab . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Read and write window . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Read/write function represented by a ow chart . . . . . . . . . . . . . . . .
Main window of user interface for vibration testing . . . . . . . . . . . . . .
CSV le read and further processing . . . . . . . . . . . . . . . . . . . . . .
Automatic calibration window . . . . . . . . . . . . . . . . . . . . . . . . . .
Calibration example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Procedure of calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Initiating Agilent 33220A with a logical name . . . . . . . . . . . . . . . . .
Main window to control Agilent 33220A and error message of output current
Generating arbitrary waveform by Agilent 33220A . . . . . . . . . . . . . . .
Main window of User Interface for Vibration Testing . . . . . . . . . . . . .
Describing the DAQ communication . . . . . . . . . . . . . . . . . . . . . . .
CAN communication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
13
13
14
14
15
16
17
17
18
18
19
20
21
21
22
23
23
24
25
25
26
5.1
5.2
5.3
System for vibration testing . . . . . . . . . . . . . . . . . . . . . . . . . . .
Source data of revolutions for Matlab preprocessing . . . . . . . . . . . . . .
Source data of acceleration for Matlab preprocessing . . . . . . . . . . . . .
27
28
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vi
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3
5
LIST OF FIGURES
5.4
5.5
5.6
5.7
5.8
vii
Source le vib1-real.csv for AWG . . . . . . . . . . . . . . . .
Response to vib1-real.csv considering vibration table tilt 0 deg
Vibration table's positioning during the measurements . . . .
Vibration table 45 deg positioning . . . . . . . . . . . . . . . .
Selected resonance curves of vibration table . . . . . . . . . .
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30
30
31
31
32
A.1 Source le vib2-real.csv for AWG . . . . . . . . . . . . . . . . . . . . . . . .
A.2 Source le vib3-real.csv for AWG . . . . . . . . . . . . . . . . . . . . . . . .
A.3 Source le vib4-real.csv for AWG . . . . . . . . . . . . . . . . . . . . . . . .
38
38
39
B.1 Response
B.2 Response
B.3 Response
B.4 Response
B.5 Response
B.6 Response
B.7 Response
B.8 Response
B.9 Response
B.10 Response
B.11 Response
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40
40
41
41
42
42
43
43
44
44
45
C.1 New system for vibration testing . . . . . . . . . . . . . . . . . . . . . . . .
C.2 Old system for vibration testing . . . . . . . . . . . . . . . . . . . . . . . . .
46
47
to
to
to
to
to
to
to
to
to
to
to
vib1-real.csv
vib1-real.csv
vib2-real.csv
vib2-real.csv
vib2-real.csv
vib3-real.csv
vib3-real.csv
vib3-real.csv
vib4-real.csv
vib4-real.csv
vib4-real.csv
considering
considering
considering
considering
considering
considering
considering
considering
considering
considering
considering
vibration
vibration
vibration
vibration
vibration
vibration
vibration
vibration
vibration
vibration
vibration
table
table
table
table
table
table
table
table
table
table
table
tilt
tilt
tilt
tilt
tilt
tilt
tilt
tilt
tilt
tilt
tilt
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45 deg
90 deg
0 deg .
45 deg
90 deg
0 deg .
45 deg
90 deg
0 deg .
45 deg
90 deg
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List of Tables
2.1
Mandatory commands of SCPI
. . . . . . . . . . . . . . . . . . . . . . . . .
5
3.1
3.2
Specications of EZ-TILT-2000-008 inclinometer . . . . . . . . . . . . . . . .
Specications of Crossbow CXL02LF3 accelerometer . . . . . . . . . . . . .
8
11
5.1
5.2
Source les for AWG . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Maximum peak-to-peak angles caused by generated vibrations . . . . . . . .
29
32
viii
List of Acronyms
API
ASCII
AWG
CAN
DAQ
DFT
ENU
FFT
GPIB
IVI
LED
NOD
PWM
RoTiP
SCPI
SPI
UCB
USB
VISA
VXI
Application Programming Interface
American Standard Code for Information Interchange
Arbitrary Waveform Generator
Controller Area Network
Data Acquisition
Discrete Fourier Transform
East North Up
Fast Fourier Transform
General Purpose Interface Bus
Interchangeable Virtual Instruments
Light Emitting Diode
Normal Operation Data
Pulse Width Modulation
Rotational-Tilt Platform
Standard Commands for Programmable Instruments
Serial Peripheral Interface
Universal Communication Board
Universal Serial Bus
Virtual Instrument Software Architecture
VMEbus Extensions for Instrumentation
ix
List of DVD Contents
•
Bachelor's Thesis in PDF format
•
Source codes of applications
•
Datasheets
•
Software drivers
•
Measured and processed data
•
Photos of System for vibration testing
x
Chapter 1
Introduction
Vibrations form an indivisible part of aerospace engineering and its inuence to a measuring system, such as electrolytic inclinometer, is a fact that has to be considered. Purpose
of this thesis is to give a user the idea about inuence of vibrations by much more convenient way with a reasonable accuracy. In other words, user is not required to have the actual
airplane, however can still get complex behaviour of a measuring system in the laboratory
by both much more cheaper and comfortable way. This is why the system for vibration
inuence testing is so important.
Project consists of three independent programs, allowing user to control separate parts
of the system individually. That way it is possible to set up the system for generating
vibrations as desired and then process the data acquired from measured system. The whole
system includes a communication device supporting the CANAerospace standard, so the
inclinometer included in the system is possible to use in any aerospace system.
This thesis gives a basic knowledge of theory used for developing the system in the
beginning, as well as shows hardware parameters of included instruments. Furthermore the
software and programming methods are broken down and in the last chapters, the measured
data and results are shown.
1
Chapter 2
Theory
2.1 The DFT and the FFT
A method of computing Discrete Fourier Transform (DFT) by Cooley and Tukey suddenly
became widely known and caused progress in many elds. The Fast Fourier Transform (FFT)
eciently computes the DFT.
State that the DFT of a complex input vector of length N is X = (X (0) . . . , X (N − 1),
then X gives another vector of length N given by the formula
(k) =
X
N
−1
X (j) WNjk
(2.1)
j=0
where WN = e . The DFT is an invertible transform with inverse given by
2πj
N
N −1
1 X (k)j WN−jk .
X (j) =
N k=0
(2.2)
If proceeding Equations 2.1 and 2.2 directly, the DFT would require N 2 operations,
however the FFT uses for computing N log N operations instead [1].
In 1965 Cooley and Tukey shown [2] that if N in 2.1 is a product, considering for example
N = ab, one can express the series as an a-point series of b-point subseries. This fact reduces
the number of multiplications and additions for complex data from N 2 to N (a + b). It is
clear this may be repeated for more factors of N and that if N is a power of two, an algorithm
taking N log2 N operations is obtained.
2
2.2. CANAEROSPACE STANDARD
3
2.2 CANAerospace Standard
CANAerospace is a very lightweight protocol and data format which was designed for the
highly reliable communication of systems based on microcomputers in airborne applications
via Controller Area Network (CAN). The main aim of CANAerospace is to satisfy requirements like ecient data ow monitoring and easy time-frame synchronization with redundant
systems. Important is that the denition is widely opened allowing user to implement variety
of user-dened messages.
The CANAerospace data format denition species 5 basic message types, which are
used for dierent network services. Each message type has an associated CAN-ID range
dening the message priority. The identier assignment within the specied ranges are up
to user. However, a proposal for an identier list addressing commonly used data objects
and devices in aerospace applications has been made. For data representation, the most
commonly used basic data types are dened as well. All CAN messages consist of 4 header
bytes for identication and between 1 and 4 data bytes for the actual data.
The general message format uses a header consisting of a 4 byte message for node identication, data type, message code and service code (for Normal Operation Data (NOD), the
service code eld is user-dened). This allows identication of each message by any receiving
unit without the need for additional information. Every message type uses the same layout
for the CAN data bytes 0-3, while the number and the data type used for CAN data bytes
4-7 is user-dened, which is shown in Figure 2.1.
Figure 2.1: CANAerospace frame description [3]
Some system architectures employ backup units which become active if the main unit
fails. The Node-ID allows to immediately identify this situation and react accordingly.
CANAerospace supports multiple data types for every message. Backup units or units from
dierent vendors may use dierent data types while performing identical functions. Specifying the data type with each message allows automatic system conguration, even during
runtime. For Normal Operation Data, this byte should continously reect the status of the
CHAPTER 2. THEORY
4
data (or the transmitting unit) to support data integrity monitoring within receiving units.
With this information, the validity of data is known at any given time. Message numbering
allows to detect if messages are missing and if the transmitting unit is operating properly
and can be used to compare the "age" of messages from redundant sources as well.
To support the interface denition, the most commonly used data for aerospace application has been assigned xed identiers. For this purpose, the available identiers for normal
operation data have been grouped for the various aircraft systems, thereby reserving the
identier range 200-1499. The identiers from 1500-1799 are unassigned and may be used
for other aerospace specic data at the user's discretion [3].
2.3 IVI and VISA Libraries
By the example, the VXIplug&play drivers do not provide a common programming interface. Without consistency across instruments manufactured by dierent vendors, many
programmers still had to spend a lot of time learning each instruments driver individually.
To carry VXIplug&play drivers a step further, in 1998 a group of end users, instrument vendors, software vendors, system suppliers, and system integrators joined together to
form a consortium called the Interchangeable Virtual Instruments (IVI) Foundation. Even
though they were competitors, all of them agreed on the need to promote specications for
programming test instruments that provide better performance, reduce the cost of program
development and maintenance, and simplify interchangeability [4].
Virtual Instrument Software Architecture (VISA) is a standard I/O language for instrumentation programming and by itself does not provide any instrumentation programming
capability. VISA however is a high-level API that calls into lower level drivers, capable of
controlling VMEbus Extensions for Instrumentation (VXI), General Purpose Interface Bus
(GPIB), or Serial instruments as shown in Figure 2.2 and makes the appropriate driver calls
depending on the type of instrument being used.
One of VISA's advantages is using many of the same operations to communicate with
instruments regardless of the interface type. For example, the VISA command to write an
ASCII string to a message-based instrument is the same whether the instrument is Serial,
GPIB, or VXI. Thus, VISA provides interface independence. This can make it easy to switch
interfaces and also gives users who must program instruments for dierent interfaces a single
language they can learn [5].
Besides VISA commands, the Standard Commands for Programmable Instruments (SCPI)
can be distinguished. These are the commands independable to hardware either as to com-
2.3. IVI AND VISA LIBRARIES
5
Figure 2.2: VISA standard hierarchy
munication protocol. SCPI denes a mandatory commands 2.1, which can be used in every
single message-based instrument connected to a computer [6].
Command Explanation
*CLS
*ESE
*ESE?
*ESR
*IDN?
*OPC
*OPC?
*RST
*SRE
*SRE?
*STB?
*TST?
*WAI
Clear Status Command
Standard Event Status Enable Command
Standard Event Status Enable Query
Standard Event Status Register Query
Identication Query
Operation Complete Command
Operation Complete Query
Reset Command
Service Request Enable Command
Service Request Enable Query
Read Status Byte Query
Self-Test Query
Wait-to-Continue Command
Table 2.1: Mandatory commands of SCPI [6]
Chapter 3
Sensor and Measuring System
Instruments
One of the main requests to the measuring system was to be easily controllable. Because
of that, appropriate hardware topology and software had to be selected. PC represents
a central point of the system and is responsible for both acquisition and processing the
data, software solution will be described later. Computer controls the System for Vibration
Testing (SVT) that has the measured system attached. Measured System (MS) is capable of
communicating through RS232 port or CAN interface. In the Figure 3.1, the empty arrow
represents devices are linked mechanically, otherwise they are connected electrically.
Figure 3.1: Measuring system ow chart
3.1 Inclinometer
Inclinometers, as well known as electrolytic tilt systems, are capable of producing very
accurate pitch and roll measurements in dierent kinds of applications. Operating range of
tilt is mostly from ±10 deg to ±75 deg depending on height of electrolytic tilt sensor.
6
CHAPTER 3. SENSOR AND MEASURING SYSTEM INSTRUMENTS
8
Communication with a computer is established by RS232 port and power supply range is
6-12 V. Parameters of standard EZ-TILT-2000-008 are shown in Table 3.1, however for this
thesis, other kind of tilt sensor with 50 % higher viscosity was used and that way inclinometer
has longer response so one is more resistant to vibrations.
Specication
Data
Description/units
range
power supply
resolution
response time
sensing element
-15 to +15
6 to 12
12
40 ms
dual axis DX-008
arcdeg after calibration
Vdc
bit
10 % - 90 % output
construction
shatter proof
hi-temperature advanced polymer
temperature
-40 to +60
degC
RS232
300-38 kb/s, 8, N, 1
any standard COM port
included
Table 3.1: Specications of EZ-TILT-2000-008 inclinometer [8]
3.2 Universal Communication Board
The Universal Communication Board (UCB) (Figure 3.4) allows connection of sensors
with SPI, CAN, USB, and RS232 interfaces [10]. That way board has the USB, CAN, SPI
and RS232 connectors.
Figure 3.4: Universal Communication Board [10]
To control the whole UCB, the MC9S12XDT512 Freescale microcontroller was used. This
microcontroller is 16-bit and is a part of MC9S12 microprocessor family [11]. Circuit board
3.3. SYSTEM FOR VIBRATION TESTING
9
schematic, except the microcontroller introduced in schematics is MC9S12DT256MFU, can
be found at [12] - [15] as well as the source les, necessary libraries and a template project.
3.3 System for Vibration Testing
System for vibration testing is a sophisticated system, used for simulating the real vibrations. Consisting of 5 individual parts, is described by Figure 3.5. Signal from Arbitrary
Waveform Generator (AWG) is in order to get a better sensitivity split in Voltage Divider
(VD) and sent to the Power Amplier (PA). Power amplier supplies the Vibration Table
(VT) that has the Crossbow Accelerometer (CA) mechanically attached. Output of the system are the data sent by the Data Acquqisition Device (DAQ), ready for further processing.
Figure 3.5: System for vibration testing
3.3.1 Arbitrary Waveform Generator
Arbitrary waveform generator (3.6) is one of the most critical devices of the whole project,
because it is technically responsible for generated vibrations. For this thesis, Agilent 33220A
has been selected. One can generate arbitrary signal and can load to volatile memory a
waveform consisting of up to 65536 samples.
Figure 3.6: Agilent 33220A, the arbitrary waveform generator [16]
±
3.3. SYSTEM FOR VIBRATION TESTING
11
Specication
Data
Description/units
Transverse Sensitivity (%FS)
Non-Linearity (%FS)
Alignment Error (deg)
Bandwidth (Hz)
Temperature Range (degC)
Shock (g)
Supply Voltage (V)
Zero g Output (V)
Supply Current (mA)
±5
±2
±2
DC-50
-40 to +85
2000
±5 ±0.25
±2.5 ±0.15
2/axis
Max
Typical
Typical
Typical
@ +25 degC
Typical
Table 3.2: Specications of Crossbow CXL02LF3 accelerometer [18]
3.3.4 Power Amplier
Signal from the arbitrary waveform generator has to be amplied, because the output
current the vibration device has to be supplied with on low frequencies can go all the way to
2 Amps. This would cause inaccuracy or after reaching current limit of Agilent 33220A, the
output would have been disabled. For this reason, the system was equipped with YAMAHA
P7000S (3.9) 2x950 W power amplier. As shown before, requirements for output current
are not very high, however this amplier has very low noise and allows the system more
portability thanks to its weight.
Figure 3.9: The YAMAHA P7000S power amplier [19]
Chapter 4
Sensor and Measuring System Software
Development
Programs for communicating with the inclinometer through RS232 and to control system for vibration testing were developped in CVI/LabWindows environment. Advantage
of this programming language by National Instruments (NI) is that it has source codes for
graphic features already included, that way the programmer can focus on what is the most
important - the main source code and the logics behind the program.
4.1 User Interface for the Inclinometer
Main purpose of this application is to gather both tilt data (pitch and roll angles) and
to give user the choice to save them into the .CSV le for further proccessing for instance
in Matlab environment. Additionally, it is possible to read/write all the important settings,
such as baud rate, averaging, sampling frequency etc.
4.1.1 Port Settings Tab
Maintenance of this program had to be simple, so the tab layout was selected. The rst
tab establishes connection through RS232 port.
Figure 4.1 describes proccess of initiating the connection with the inclinometer. Firstly,
the conguration parameters such as COM port, baud rate, parity, data bits and stop bits
need to be dened. If the inclinometer is connected to the right port, program goes on,
otherwise function is terminated. The inclinometer has to be able to measure immediately,
thus default calibration data are loaded and the handshake support is turned o. Hereafter,
the thread for recognizing inclinometer's response is scheduled.
12
4.1. USER INTERFACE FOR THE INCLINOMETER
13
Figure 4.1: Connecting the inclinometer through the RS232
If the inclinometer is already plugged in to the power supply, program immerdiately
responds and appropriate message emmerges (Figure 4.2). If the inclinometer is connected
to the power supply later on, program holds until a header is retained and then lets user know
the connection was successful. Finally, measure tab and tab for tilt settings and calibration
are enabled.
Figure 4.2: Port settings tab
4.1.2 Measure Tab
This subsection delivers measured data and shows them in the plot (4.3). User can simply
change delay among scans and save the data into a le. Also if the range of inclinometer is
exceeded, program automatically displays "Out of the range" message.
Pressing the measure button calls the function expressed by Figure 4.4. Very rst pressing the button creates the asynchronous timer, where afterwards the delay between scans
14CHAPTER
4. SENSOR AND MEASURING SYSTEM SOFTWARE DEVELOPMENT
Figure 4.3: Measure tab
schedules frequency of timer's cycles. Variable carrying the information about the timer is
reset to 0, which means in the next loop, the timer is just resumed.
For precise timing, the asynchronous timer have been implemented into the soure code.
This kind of timer runs in a separate thread, so it does not aect uency of the program.
Figure 4.4: Asynchronous timer scheduling
The asynchronous timer periodically schedules thread function (4.5) for reading and
writing the data from and into the inclinometer. In the rst loop, default settings, such as
clearing the graph or disabling the variable for the rst measure, are loaded and then the
rst command is written. To get informations about inclinometer's tilt, the s?\r command is
4.1. USER INTERFACE FOR THE INCLINOMETER
15
sent. This command requests informations about both axes. In the next loop the requested
data are obtained. Inclinometer's answer is represented by the following format:
s?\r\rR
x.xxx
P
x.xxx
\r #LF>
where x.xxx is either positive or negative value of pitch or roll. This procedure follows until
the measure button is turned o.
Figure 4.5: Reading pitch and roll
4.1.3 Calibration and Tilt Settings Tab
For the calibration, polynomial of up to the fth order has been selected (Equations 4.1
and 4.2), considering the polynomial's order can be reduced by setting appropriate coecients to zero. User has a free choice of selecting default calibration data or can put in desired
coecients of the polynomial and optionally save them into the le (4.8). Calibration and
its results are shown in Figures 4.6 and 4.7.
Initially, the highest angle dierence (before calibration) was for pitch 0.669 deg and for
roll 0.353 deg. The highest announced dierence between the angles of sensor of reference and
inclinometer's calibrated angles for pitch was 0.025 deg and for roll 0.035 deg (4.7). That way,
main inaccuracy had been eliminated, however output can be still inuenced by hysteresis,
temperature, null repeatability and stability of initial null angle. The calibration itself was
measured by Rotational-Tilt Platform (RoTiP) platform in range of (-8 up to +8) deg, the
16CHAPTER
4. SENSOR AND MEASURING SYSTEM SOFTWARE DEVELOPMENT
angular resolution for pitch was 3.3 ×10−4 deg and for roll 6.5×10−4 deg [9].
ϕrollnew = − 1.343 × 10−5 ϕ5rollinit − 1.002 × 10−5 ϕ4rollinit + 5.83 × 10−4 ϕ3rollinit +
+ 1.169 × 10−3 ϕ2rollinit + 1.016 × ϕrollinit − 0.2606 × ϕrollinit
ϕpitchnew = − 1.052 × 10−5 ϕ5pitchinit − 3.397 × 10−5 ϕ4pitchinit + 2.26 × 10−4 ϕ3pitchinit −
− 4.335 × 10−5 ϕ2pitchinit + 1.019 × ϕpitchinit + 0.6045 × ϕpitchinit
(4.1)
(4.2)
Angle difference between reference and output data for non−calibrated output
Roll difference
Pitch difference
Angular difference (deg)
0.4
0.2
0
−0.2
−0.4
−0.6
−8
−6
−4
−2
0
Input angle (deg)
2
4
6
8
Figure 4.6: Dierence between reference data and non-calibrated output
EZ-TILT-2000-008 inclinometer oers various read/write commands (4.9) for changing its
internal parameters or inuencing one's output. It is possible to change baud rate, thermal
coecients, decimal resolution or measure the temperature of the environment etc.
Small issue of the CVI environment is it does not support passing the names of objects
as string variables into the functions. Solution is a reverse algorithm, using CVI panel
attributes as ATTR_PANEL_FIRST_CTRL and ATTR_CONSTANT_NAME, seeking
for the proper ID names. Giving the example by the read function (4.10), integer references
(basicly handles) of objects with a names of CHECK and SETTING are saved into the 2D
array for further processing. If the checkbox matching to its SETTING object is checked,
appropriate command is sent through RS232, then inclinometer's response is processed and
the value of the parameter is set.
4.2. USER INTERFACE FOR VIBRATION TESTING
17
Angle difference between reference and output data for calibrated output
0.04
Angular difference (deg)
0.03
0.02
0.01
0
−0.01
−0.02
Roll difference
Pitch difference
−0.03
−8
−6
−4
−2
0
Input angle (deg)
2
4
6
8
Figure 4.7: Dierence between reference data and calibrated output
Figure 4.8: Calibration tab
4.2 User Interface for Vibration Testing
Requirements for the capabilities of this software were quite complex. Main request was it
to be one program, able to process data acquired from real aircraft pre-formatted in Matlab
environment.
The fact that the tilt of vibration table and generally various conditions can change
needed to be considered and because of that, the software for sure had to have a calibra-
18CHAPTER
4. SENSOR AND MEASURING SYSTEM SOFTWARE DEVELOPMENT
Figure 4.9: Read window (on the left side)/Write window (on the right side)
Figure 4.10: Read/write function represented by a ow chart
tion procedure. Environment also includes the data acquisition system, which is used in
calibration as well as for viewing generated vibrations.
4.2. USER INTERFACE FOR VIBRATION TESTING
19
4.2.1 CSV File Reader and FFT Analysis
User can select desired data from .CSV le and based on FFT result, one can dene
output voltage of the Agilent arbitrary generator. Input FFT algorithm considers the sensor
for acquiring the real data can get the data with various sampling frequency, which gives the
application more of interchangeability (Figure 4.11).
Figure 4.11: Main window of user interface for vibration testing
Reading and processing data from .CSV le is desribed by the Figure 4.12. Event enabled
by clicking the "Import CSV le!" calls the
FileSelect
function giving a user the opportunity
to select preformatted le. Afterwards, the le length is retained and the time axis loaded.
At this point, the minimum length of data as the input for the FFT function, was selected
to 512 datapoints. The reason is not to lose the resolution of frequence spectrum in case of
processing the data acquired from the sensor with high sampling rate. Thus, if the le has
a lack of data, the rest of time behaviour is lled in with zeros. That way, the resolution
keeps still with reasonable accuracy. Algorithm is equipped with FFTEx function, able to
determine both real and imaginary part of the FFT spectrum. Final value is calculated as
the absolute value of real and imaginary parts and plotted in the graph.
In fact before this procedure, it is necessary to calibrate whole system, due to the conditions described before. User has a free choice of selecting default calibration le, but to be
20CHAPTER
4. SENSOR AND MEASURING SYSTEM SOFTWARE DEVELOPMENT
Figure 4.12: CSV le read and further processing
more accurate, it is recommended to calibrate the device after every change of the device's
position, environment or switching to any other measured system.
4.2.2 Calibration Procedure
To be a convenient application, the calibration procedure is fully automatic, measured
data are plotted online and saved into the table and after about 5 minutes, when calibration
is done, the resonance curve is plotted as well (4.13). Data from the table, which contain
informations about measured frequency and acceleration in (g) can be saved into the .CSV
le. This feature is useful for example when the device is not moved and just the measured
sensor is mounted again. Generally, the .CSV was selected, because one is easily importable
into the Matlab software.
The calibration itself works on partly linear approximation principle and is dependable
on the range of generated vibrations, which is technically based on the input sampling
frequency. By the example, the sampling frequency of the real measured data is let's say
43 Hz. Considering an aliasing, it would be possible to generate 21.5 Hz in maximum.
Lowest possible frequency to generate is due to limits of the device set up to 3 Hz and
according to maximum of 21.5 Hz the calibration would gather frequencies from 3 to 22 Hz
with increment of 1 Hz as it was selected for measuring the data in this thesis. If user
is to set a nonintegral frequency, algorithm nds two closest integral frequencies and by
linear approximation evaluates desired acceleration. Example of calibration is shown in the
Figure 4.14.
Calibration procedure is broken down into few steps (4.15). In the beginning, the frequency range has to be determined and Agilent instruments are initiated. Hereafter, the
4.2. USER INTERFACE FOR VIBRATION TESTING
21
Figure 4.13: Automatic calibration window
Resonance curve of vibration table
0.5
0.45
0.4
acceleration (g)
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
3
5
7
9
11
13
frequency (Hz)
15
17
19
21
Figure 4.14: Calibration example
program works in a for loop, where initially sets the rst sinewave with the lowest frequency,
process the arbitrary waveform and send one into AWG. Afterwards, the measurement is
requested (by default the DAQ device measures 5000 datapoints by 1 kHz sampling fre-
22CHAPTER
4. SENSOR AND MEASURING SYSTEM SOFTWARE DEVELOPMENT
quency, means 5s of measuring) and output data from DAQ system are processed by the
FFT algorithm. Calibration procedure then nds a maximum of FFT spectrum and writes
it along with the measured frequency into the table. At the end of the loop, the resonance
curve is plotted and all the calibration data are saved into the calibration vector.
Figure 4.15: Procedure of calibration
4.2.3 Arbitrary Waveform Generator
When the FFT analysis of given vibration data was performed, the maximum amount of
4 sinewaves was found out. Main purpose of the arbitrary waveform generator used in this
thesis is to generate arbitrary signal and according to FFT results, the output signal will
be consisting of up to 4 sinewaves of both dierent frequency and voltage. In this case two
solutions might be acceptable. The rst one would be a subsystem built from 4 sinewave
generators and an additive element. This solution however, is too complicated to control
and synchronize. Idea of using just one programmable generator is more complex due to the
driver compatibility, however much more convenient for a user as well as cheaper and nally,
more accurate. Agilent 33220A with its IVI drivers provides a suitable solution.
Both default calibration le and actual calibration leads to enable the Agilent generator.
First, it is necessary to initiate one through IVI drivers. To communicate with such an
instrument using NI software, the Logical name has to be set up. If the Logical name is
correct (Figure 4.16) and connection is successful, the main window of generator is enabled
(Figure 4.17). As mentioned in 3.3.1 it is possible to set up desired output of Agilent 33220A
consisting of up to 4 sinewaves.
Due to the output limit of actual amplier, the safety lock of arbitrary waveform was set
up to maximum of 2.5 V. This prevents of both misstyping the (g) value and not knowing
W V F RM [dn] =
4
i=1
AiCORR sin
2πfi dn
Fs
24CHAPTER
4. SENSOR AND MEASURING SYSTEM SOFTWARE DEVELOPMENT
where dn is datapoint number, W V F RM [dn] is output value of waveform for concrete
datapoint, AiCORR is corrected voltage value, Fs is a sampling frequency and fi is one of the
desired frequencies to generate.
Allowed frequency resolution for all the input frequencies is 0.1 Hz and considering
5000 S/s, with length of generating 10 s, 50000 datapoints need to be calculated for the
output waveform. Waveform data are checked by a current protection mentioned above,
plotted in the graph and sent to the AWG.
Figure 4.18: Generating arbitrary waveform by Agilent 33220A
4.2.4 Agilent U2531 Data Acquisition
The third subsection of user interface, the data acquisition system, was also developped
to be ecient. The purpose of one is to gather dened amount of information about acceleration, convert data formats and plot the time behaviour and the FFT of the signal with
possibility to save the data into .CSV le. Due to the positioning of the Crossbow sensor,
dierent mean values of acceleration data can be obtained. Program can supress this kind
of oset by setting the value of "Oset [V ]" numeric. For example the accelerometer tilt
to 45 deg is equals to 1.809 V with the Crossbow accelerometer. To reduce the oset, the
numeric is set to the same value (4.19).
Algorithm for reading the generated vibrations (4.20) works the way, the Agilent U2531A
is intiated rst, then the thread for reading/writing is scheduled. In this thread, the data are
requested by the WAV:STAT?\n command and afterwards the DAQ system response has to
be determined. If ones response is FRAG, then the data have been still acquiring, otherwise
the DATA string is obtained and algorithm can follow further instructions, such as reading
concrete acceleration data, processing the FFT and plotting nal datapoints into the graph.
\
Chapter 5
Measurements
Figure 5.1: System for vibration testing
As a functional demonstration of the system for vibration inuence testing, couple measurements were accomplished (Figure 5.1). All the input data (sources for vibrations) were
preprocessed in Matlab Environment based on constant revolution sections (Figure 5.2)
from the vibration data acquired from the real airplane (Table 5.1). Figure 5.3 introduces
matching acceleration data from z-axis from 3-axis accelerometer, the frame-of-reference was
East-North-Up (ENU). According to the system, these data were also used in CVI program
27
CHAPTER 5. MEASUREMENTS
28
mentioned in Section 4.2.1, where appropriate frequencies and acceleration amplitudes were
dened and sent to AWG. As the output of the system, Crossbow accelerometer acquired
data from the articial vibrations and the algorithm shown in Section 4.2.4 evaluated the
spectrum of generated vibrations and saved them into .CSV le. Selected data format is
easily importable to Matlab software, where all the plots were done.
5.1 Data structures
Revolutions of real airplane
5500
5000
revolutions (rpm)
4500
4000
3500
3000
2500
2000
1500
0
0.5
1
1.5
2
2.5
datapoints (−)
3
3.5
4
4
x 10
Figure 5.2: Source data of revolutions for Matlab preprocessing
Acceleration data
1
0.8
acceleration (g)
0.6
0.4
0.2
0
−0.2
−0.4
−0.6
−0.8
−1
0
500
1000
1500
2000
2500
3000
datapoints (−)
3500
4000
4500
5000
Figure 5.3: Source data of acceleration for Matlab preprocessing
5.2. INPUT DATA COMPARISON
29
From the real data, 4 reasonable structures were separated. The aim of analyzing initial
structure was to get acceleration data according to as constant sequence of revolutions as
possible. These 4 structures were saved into .CSV le by following names introduced in
Table 5.1.
le name
vib1-real.csv
vib2-real.csv
vib3-real.csv
vib4-real.csv
datapoint
range
domain frequencies matching amplitudes
(Hz)
(g)
21350-21930
6.5
11.9
5
10.5
3
8
12.7
5
20.1
26070-26800
15210-16730
3043-4893
0.027
0.05
0.05
0.02
0.022
0.015
0.04
0.012
0.04
Table 5.1: Source les for AWG
Selected parameters such as domain frequencies and its amplitudes do not clearly match
to the FFT data of real vibrations due to limits of current vibration table. Firstly, lowest
possible frequency was locked to 3 Hz to supress current overload of the output and hereafter
amplitudes especially on lower frequencies were lowered because of mechanical limits of the
vibration table.
5.2 Input Data Comparison
The rst le (Figure 5.4) captures vibrations during high revolutions with mean value of
approximately 4900 rpm. One contains lowest amount of datapoints, however in time values
lasts for about 13.5 s (580 datapoints by sampling frequency 43 Hz). Parameters captured
from the Figure 5.4 and all the other input le gures can be found in the Table 5.1.
File vib2_real.csv (Attachment A.1) contains acceleration data where average level of
revolutions is 2150 rpm. Data length is 730 datapoints which corresponds to about 17 s.
Informations about high revolutions are also included in the third le (Attachment A.2),
with average of 4980 rpm. Gathered time behaviour contains over 35 s of data. Last le (Attachment A.3) has the length of 1850 datapoints and the engine of the airplane ran with a
frequency of 49 Hz (2940 rpm).
CHAPTER 5. MEASUREMENTS
30
Real vibrations − file: vib1−real.csv
Time behaviour of vibrations
acceleration (g)
1
0.5
0
−0.5
0
2
4
6
8
time (s)
Spectrum of vibrations
10
12
acceleration (g)
0.1
0.05
0
0
2
4
6
8
10
12
frequency (Hz)
14
16
18
20
Figure 5.4: Source le vib1-real.csv for AWG
5.3 Inuence of Vibrations to the Inclinometer
Angles from the inclinometer in each step were gathered for approximately 20 s, which
gives enough of accuracy. Data were measured mainly for low accelerations, where the highest
amplitudes were about 50 mg (Table 5.1) and the highest dierences of inclinometer's tilt
caused by vibrations are shown in Table 5.2. Example of FFT spectrum and time behaviour
of inclinometer's angles is shown in the Figure 5.5, for further informations refer to the
attachments.
acceleration (g)
Vibrations and tilt angles for 0 deg and input file vib1−real.csv
Vibrations spectrum
0.06
0.04
0.02
0
0
5
10
15
frequency (Hz)
Pitch and roll angles
20
25
angles (deg)
0.2
roll
pitch
0.1
0
−0.1
−0.2
0
2
4
6
8
10
time (s)
12
14
16
18
20
Figure 5.5: Response to vib1-real.csv considering vibration table tilt 0 deg
Vibration table has a manual positioning, whereas for the measurements, table was tilt
5.3. INFLUENCE OF VIBRATIONS TO THE INCLINOMETER
31
to 0 deg, 45 deg, and 90 deg, which is introduced in the Figure 5.6. Positioning of vibration
table to 45 deg is captured by Figure 5.7.
Figure 5.6: Vibration table's positioning during the measurements a) 0 deg from horizontal
plane, b) 45 deg from horizontal plane, c) 90 deg from horizontal plane
Figure 5.7: Vibration table 45 deg positioning
CHAPTER 5. MEASUREMENTS
32
lename
vib1
vib2
vib3
vib4
ϕ (deg)
0
45
90
0
45
90
0
45
90
0
45
90
Δϕrollmax (deg)
0.129
0.097
0.064
0.161
0.160
0.064
0.161
0.129
0.097
0.098
0.097
0.064
Δϕpitchmax (deg)
0.323
0.290
0.162
0.646
0.550
0.064
0.743
0.484
0.130
0.226
0.227
0.097
Table 5.2: Maximum peak-to-peak angles caused by generated vibrations
5.4 Mass Inuence to Generated Vibrations
This measurement should prove the fact the mass of measured sensor compared to mass
of vibration table does not aect the actual measurement, meanings the system for vibration
inuence testing does not have to be recalibrated. Figure 5.8 shows attaching lightweight
device such as inclinometer does not aect accuracy, where curves for situation with and
without the inclinometer dier at maximum by 0.025 g at 20 Hz. To put measured resonance
curves into the contrast, there was the resonance curve for tilt of vibration table at 45 deg
added, showing the dierence can be up to 0.1 g.
Resonance curves of vibration table with various conditions
0.5
0.45
0.4
acceleration (g)
0.35
0.3
0.25
0.2
0.15
0.1
angle 0 deg no device
angle 0 deg with inclinometer
angle 45 deg with inclinometer
0.05
0
3
5
7
9
11
13
frequency (Hz)
15
17
19
21
Figure 5.8: Selected resonance curves of vibration table
Chapter 6
Conclusion
The aim of this thesis was to establish ecient system for vibration inuence testing and
perform basic measurements to simulate and state for what kinds of data is the inclinometer
likely to use. Firstly, all the requirements for the system were accomplished, plus couple
additional features giving the applications more convenience were implemented.
Old system for vibration testing (C.2) worked as a feedback system and could generate
vibrations represented by only one sinewave. Hereafter, one used old power amplier that
was susceptible to generate vibrations with distinctive noise frequency at 50 Hz. Biggest
disadvantage of old system was it did not support generating data from real airplane, which
was accomplished by new system for vibration testing (C.1).
Now, user is able to select the data, analyze them fast, without dependance to any other
software environments. Hereafter, to be always as accurate as possible, application has convenient way to calibrate the whole system, thus calibration is fully automatic. If a very fast
measuring has to be done, previously acquired calibration data can be loaded. Furthermore,
the output of arbitrary waveform generator can be initiated, where arbitrary waveform can
be compounded of up to 4 sinewawes. Since the program is multi-threading application, user
can immediately perform measuring of articial vibrations and can immediately compare results of FFT analysis of the output and input. Accuracy of measurement can be inuenced
by both sampling frequency and acquired datapoints.
After dening desired vibrations, measuring system such as inclinometer can be measured. User interface for the inclinometer rstly establishes connection, loads default calibration data and then gives several possibilities. To customize most common inclinometer's
parameters, read/write windows were attached. If a user has new calibration data, these
can be loaded and give a future measurement more accuracy. Actual measuring reads both
angles, with frequency of reading at maximally 10 Hz. Program for data conversion from
33
CHAPTER 6. CONCLUSION
34
RS232 to CANAerospace gives the EZ-TILT-2000-008 more interchangeability and possibility to cooperate in CANAerospace systems.
In terms of measuring, lots of informations were gathered. Firstly, most of the inaccuracies were produced by the vibration table and its limits. According to input le resources,
the most accurate measuring was the one with the le vib4-real.csv. The reason is that its
domain frequency is high enough not to be inuenced by reaching the vibration table's limits.
Other 3 kinds of measurements (other 3 source les) were inuenced by this factor, which
caused vibrating not just on domain frequencies, but also on multiples of these frequencies.
Focus should be put on what was the main reason of the measuring. According to
the Table 5.2, the highest peak-to-peak dierence of output pitch angle (measurement was
performed in direction of pitch angle) was 0.743 deg with the le vib3-real.csv. The highest
dierence was announced, where the domain frequency were 3 Hz, 8 Hz and 12.7 Hz, with
amplitudes up to 40 mg. The highest angle dierence was captured in all the cases where
tilt of vibration table was 0 deg which is logical and matches to the theory. Generating
of vibrations within the 45 deg tilt caused in average supress of the inclinometer's angle
dierence in 15 %. Pitch and roll captured during generating vibrations, where the tilt of
vibration table was 90 deg, conrmed no such inuence to inclinometer's angle. Generally,
data from the roll axis can be moreless considered as the noise of the sensor, so the roll axis
is not inuenced by the vibrations.
Mass of inclinometer plus the stand device from the wood do not aect behaviour of
system for vibration inuence testing at all, because ones are too light to be considered.
On the other hand, as mentioned before, generating vibrations within any other angle than
0 deg can cause much higher inaccuracy than mass of the attached sensor, which is captured
by Figure 5.8, because of reaching the vibration table's constraints. For this concrete case, the
inaccuracy could be even about 40 %, so in these cases the calibration is highly recommended
to be performed.
As a result of the measuring, the EZ-TILT-2000-008 is likely to be used in such an
aircraft, with acceleration parameters specied in the data mentioned before. In these cases,
peak-to-peak dierence of the output of the inclinometer is not higher than 1 deg.
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Appendix A
Real vibrations − file: vib2−real.csv
Time behaviour of vibrations
acceleration (g)
1
0.5
0
−0.5
−1
0
2
4
6
8
10
time (s)
Spectrum of vibrations
12
14
16
acceleration (g)
0.2
0.15
0.1
0.05
0
0
2
4
6
8
10
12
frequency (Hz)
14
16
18
20
Figure A.1: Source le vib2-real.csv for AWG
Real vibrations − file: vib3−real.csv
Time behaviour of vibrations
acceleration (g)
1
0.5
0
−0.5
−1
0
5
10
15
20
time (s)
Spectrum of vibrations
25
30
35
acceleration (g)
0.2
0.15
0.1
0.05
0
0
2
4
6
8
10
12
frequency (Hz)
14
16
18
Figure A.2: Source le vib3-real.csv for AWG
38
20
39
Real vibrations − file: vib4−real.csv
Time behaviour of vibrations
acceleration (g)
1
0.5
0
−0.5
0
5
10
15
20
25
time (s)
Spectrum of vibrations
30
35
40
acceleration (g)
0.06
0.04
0.02
0
0
2
4
6
8
10
12
frequency (Hz)
14
16
18
Figure A.3: Source le vib4-real.csv for AWG
20
Appendix B
acceleration (g)
Vibrations and tilt angles for 45 deg and input file vib1−real.csv
Vibrations spectrum
0.06
0.04
0.02
0
0
5
10
15
frequency (Hz)
Pitch and roll angles
20
25
angles (deg)
0.2
roll
pitch
0.1
0
−0.1
−0.2
0
2
4
6
8
10
time (s)
12
14
16
18
20
Figure B.1: Response to vib1-real.csv considering vibration table tilt 45 deg
acceleration (g)
Vibrations and tilt angles for 90 deg and input file vib1−real.csv
Vibrations spectrum
0.03
0.02
0.01
0
0
5
10
15
frequency (Hz)
Pitch and roll angles
20
25
angles (deg)
0.3
roll
pitch
0.2
0.1
0
−0.1
0
2
4
6
8
10
time (s)
12
14
16
18
20
Figure B.2: Response to vib1-real.csv considering vibration table tilt 90 deg
40
41
acceleration (g)
Vibrations and tilt angles for 0 deg and input file vib2−real.csv
Vibrations spectrum
0.06
0.04
0.02
0
0
5
10
15
frequency (Hz)
Pitch and roll angles
20
25
angles (deg)
0.4
roll
pitch
0.2
0
−0.2
−0.4
0
2
4
6
8
10
time (s)
12
14
16
18
20
Figure B.3: Response to vib2-real.csv considering vibration table tilt 0 deg
acceleration (g)
Vibrations and tilt angles for 45 deg and input file vib2−real.csv
Vibrations spectrum
0.06
0.04
0.02
0
0
5
10
15
frequency (Hz)
Pitch and roll angles
20
25
angles (deg)
0.4
roll
pitch
0.2
0
−0.2
−0.4
0
2
4
6
8
10
time (s)
12
14
16
18
20
Figure B.4: Response to vib2-real.csv considering vibration table tilt 45 deg
APPENDIX B.
42
acceleration (g)
Vibrations and tilt angles for 90 deg and input file vib2−real.csv
Vibrations spectrum
0.06
0.04
0.02
0
0
5
10
15
frequency (Hz)
Pitch and roll angles
20
25
angles (deg)
0.04
roll
pitch
0.02
0
−0.02
−0.04
0
2
4
6
8
10
time (s)
12
14
16
18
20
Figure B.5: Response to vib2-real.csv considering vibration table tilt 90 deg
acceleration (g)
Vibrations and tilt angles for 0 deg and input file vib3−real.csv
Vibrations spectrum
0.06
0.04
0.02
0
0
5
10
15
frequency (Hz)
Pitch and roll angles
20
25
angles (deg)
0.4
roll
pitch
0.2
0
−0.2
−0.4
0
2
4
6
8
10
time (s)
12
14
16
18
20
Figure B.6: Response to vib3-real.csv considering vibration table tilt 0 deg
43
acceleration (g)
Vibrations and tilt angles for 45 deg and input file vib3−real.csv
Vibrations spectrum
0.04
0.03
0.02
0.01
0
0
5
10
15
frequency (Hz)
Pitch and roll angles
20
25
angles (deg)
0.4
roll
pitch
0.2
0
−0.2
−0.4
0
2
4
6
8
10
time (s)
12
14
16
18
20
Figure B.7: Response to vib3-real.csv considering vibration table tilt 45 deg
acceleration (g)
Vibrations and tilt angles for 90 deg and input file vib3−real.csv
Vibrations spectrum
0.03
0.02
0.01
0
0
5
10
15
frequency (Hz)
Pitch and roll angles
20
25
angles (deg)
0.1
roll
pitch
0.05
0
−0.05
−0.1
0
2
4
6
8
10
time (s)
12
14
16
18
20
Figure B.8: Response to vib3-real.csv considering vibration table tilt 90 deg
APPENDIX B.
44
acceleration (g)
Vibrations and tilt angles for 0 deg and input file vib4−real.csv
Vibrations spectrum
0.04
0.03
0.02
0.01
0
0
5
10
15
frequency (Hz)
Pitch and roll angles
20
25
angles (deg)
0.2
roll
pitch
0.1
0
−0.1
−0.2
0
2
4
6
8
10
time (s)
12
14
16
18
20
Figure B.9: Response to vib4-real.csv considering vibration table tilt 0 deg
acceleration (g)
Vibrations and tilt angles for 45 deg and input file vib4−real.csv
Vibrations spectrum
0.06
0.04
0.02
0
0
5
10
15
frequency (Hz)
Pitch and roll angles
20
25
angles (deg)
0.2
roll
pitch
0.1
0
−0.1
−0.2
0
2
4
6
8
10
time (s)
12
14
16
18
20
Figure B.10: Response to vib4-real.csv considering vibration table tilt 45 deg
45
acceleration (g)
Vibrations and tilt angles for 90 deg and input file vib4−real.csv
Vibrations spectrum
0.04
0.03
0.02
0.01
0
0
5
10
15
frequency (Hz)
Pitch and roll angles
20
25
angles (deg)
0.05
roll
pitch
0
−0.05
0
2
4
6
8
10
time (s)
12
14
16
18
20
Figure B.11: Response to vib4-real.csv considering vibration table tilt 90 deg
Appendix C
Figure C.1: New system for vibration testing
46
47
Figure C.2: Old system for vibration testing