Home

DESIGN AND IMPLEMENTATION OF A VIBRATION ANALYSIS TOOL

Contents

1. 13 2 5 Frequency response of Butterworth filters of varying order 15 2 6 Poles of a 4th order Butterworth filter 16 2 7 DFT example with an integer frequency value 19 2 8 DFT example with a non integer frequency value 19 29 EFT example s xtd out uoto Kd I ed ob pa Se Read oh de Ahh s 23 2 10 Filtered vs Unfiltered Orbit Example 25 2 11 Filtered Orbits and their FFTs 06 ia amp ete ee ope Bee ates amp 26 2 12 Waveforms generated by a vibrating machine in the X Y and Z axes 27 2 13 Waveforms generated by a vibrating machine with noise 28 2 14 Ellipse example showing major and minor axes 30 2 15 Examples of orbital trajectories with various eccentricities 30 3 1 Portable machinery vibration analyser and data logger 32 3 2 Data Acquisition Hardware Prototype 0 33 3 3 Best fit line for x axis measurements under 2 5 g mode 37 4 1 A waterfall process with feedback ooa a a loin 40 xi xii LIST OF FIGURES 5 1 Data Flow in the System 4 uud erga ra Soe ane ee uM 53 5 2 The model view controller architecture 54 5 3 Alternate model view controller architecture 55 5 4 Depiction of the main system loops les 56 5 5 Module interaction diagram 2 uot Se Pee Bote S 60 6 1 An illustration of the circular queue data structure 8
2. 4 The application shall perform an FFT on the data in order to determine the fundamental frequency 5 The application shall perform an ellipse fitting on the data in order to determine the phase and eccentricity of the machine s elliptical motion 6 The application shall perform a calculation to determine the machine s RPM 7 The application shall perform a calculation to determine the strokes in all three axes as well as the main stroke 8 The application shall perform a calculation to determine the g force in all three axes as well as the main g force 44 4 Requirements Specification 4 2 4 Logging Requirements The following are requirements describing how the data is logged on the machine and how it is thereafter read The logging involves storing the raw data as well as logging the acquisition information such as the customer the machine number etc 1 The application shall log the calibrated unfiltered data into a file 2 The application shall allow the user to determine when the logging should start and when it should end 3 The application shall create a separate file each of the used sensor locations for logging its data 4 The application shall log information related to the acquisition into a separate file This information is to include at least the following Customer machine model date and number of bearings on the machine 5 The application shall log information related to the s
3. 64 6 Software Implementation e Understandability The developed software is easy to understand primarily due to its modularity In addition the code is well documented and commented to allow for developers to continue working on it in the future 6 3 Software Libraries Used The following is a list of the main software libraries used as part of the developed application A brief description accompanies each library e Threading This module provides a high level threading interface providing accessibility to threads and their methods It is used in both the Reader module and the Device Discovery helper module e PyBluez This module creates python wrappers around system Bluetooth re sources to allow for easy and quick creation of Bluetooth applications It works on GNU Linux and Windows XP Microsoft and Widcomm Bluetooth stacks It is used in both the Reader module and the Device Discovery helper module e PySerial This module encapsulates the access for the serial port It is used by the Reader module in the case of the software being run on Mac OS since PyBluez is not available there e NumPy This is the fundamental package needed for scientific computing with Python It contains a powerful N dimensional array object basic linear algebra functions and basic Fourier Transforms It is used in the Sensor Manager module the Viewer module the Filter module the FFT module the Ellipse Fitter module and the Report
4. This parameter is measured in seconds think of it as 5 seconds back in time for example and can be changed as in Figure A 11 BOX History Length Enter the period of time to plot back in history in seconds Cane OD Figure A 11 Update history setting FFT Size This parameter defines the size of data to perform the FFT compu tation on The larger the size the more accurate the results are but the more expensive the computation becomes This parameter has to be a power or two and is therefore chosen from a list of predefined values as in Figure A 12 Acceptance Levels The acceptance levels correspond to the accepted deviations in the tuning report These values are stored in a file and can be edited using this command A window as in Figure A 13 will appear and once all the values have been entered the Save button should be pressed If the user would like to go back to the original values prior to saving the Reset button can be used The Exit button will exit without saving Bearings This command will allow you to add new bearing diameters along with their basic loads into a file where all the bearings are stored This in formation is later used in the tuning report generation When selecting this option a window as in Figure A 14 will appear You can add a new bearing by entering its diameter in millimetres in the Bearing Diameter box and its basic dynamic load in kilo Newton in th
5. between the XY XZ and YZ planes The application shall allow the user to choose whether the enlarged orbit shall display filtered or unfiltered data The application shall allow for adjusting the centre frequency used for the filter The application shall allow the user to choose the unit used to display the stroke mm or inches The application shall allow the user to view generated reports directly from within the application 4 2 7 Reporting Requirements The application must allow for the generation of three types of reports as required by the client The following is a description of these reports 4 Requirements Specification 47 Single Point Report Such a report is generated for each of the mounted sensors providing in depth analysis on each of the individual measuring points An FFT plot a waveform plot and an orbit plot with both filtered and unfiltered data is generated along with a summary of the numerical values for that specific location Orbit Summary Report This report must contain orbit plots of all the mounted sensors as well as their numerical values The orbits shall appear in their filtered state allowing the user to determine whether or not the machine is performing normally The machine s behaviour is deemed normal if the orbits have the same size the left side of the machine mirrors the right side and the overall acceleration levels are within their expected range Tuning R
6. e Sensor Mounting When mounting a sensor on the vibrating screen the orientation should be in a such a way that the x axis of the sensor is aligned with the screen s inclination and the positive side of the x axis points toward the screen s feed end If a magnet is used to mount the sensor then the magnet should sit tight on the surface of the machine e Sensor Locations The predefined locations that the sensors are mounted to on the vibrating screen and named as follows e LFB RFB Left Right Feed end bracket e LDB RDB Left Right Discharge end bracket e LSF RSF Left Right Sidearm Feed end e LSD RSD Left Right Sidearm Discharge end On the two bearing screen machines the positions are marked as in Figure 2 2 whereas on the four bearing screen machines the positions are marked as in Figure 2 3 10 2 Vibration Analysis Flow of Material Figure 2 2 Measurement points on a two bearing horizontal screen Flowof Material Figure 2 3 Measurement points on a four bearing inclined screen 2 Vibration Analysis 11 2 3 Filtering 2 3 1 Overview Raw vibration signals coming directly from the acquiring sensor always contain com ponents which are contamination noise and frequently some actual components which may partially obscure other components that are the important part of the measurements taken 1 This makes filtering the most common signal conditioning operation in s
7. if you would like to connect to the available sensor units and acquire data A 2 File Simulation Mode Upon choosing File Simulation the main file simulation window will appear as in Figure A 3 Next you can open files by accessing the File menu and selecting either Open Directory or Open Old File The Open Directory option will allow you to choose a directory containing one or more files corresponding to one or more sensors 99 100 A User Manual Please select your language Figure A 1 Language Selection Menu A User Manual 101 Please select a mode Data Acquisition File Simulation Figure A 2 Mode Selection Menu A User Manual Apes 005 00S L NUS Uew oeg 2H besa xew 144 sepu uuu PONENS f sanne WN 340S ZH upimpueg enuey O DLE Ut A 8 eomog basy ued 2H fouenbe anued 901 2290 ASSAZO DEDO pPa ayynO x sazO aszO PUBS X AQ pares o Buuew4 uonewevO 1001 uL sisfjeuyIB N V 2 A L UOHEJQIA Figure A 3 Main view of File Simulation Mode 102 A User Manual 103 used to acquire data during that acquisition These folders are named with the date and time the data was acquired On the other hand the Open Old File option should be used when you would like to playback a file that was acquired using the old system Note that in
8. 1 1 Thesis Motivation va re AAA 1 1 2 Thesis Objective la hea a hee e SAS S ox 3 1 3 Thesis Contributions o ooa a a 3 LA Thesis ONCE WS ess dey ede ds NI Bi A A MS 4 2 Vibration Analysis 5 A II eR A ee ta laon 2 2 Terminology and Units mox eee aN RR 4 2 3 A e a a oer bo ear icut Ye Der Oe auo 11 A O Overview Do mda o A BG anode SR sten Te e rice 11 2 3 2 The Butterworth Bandpass Filter 14 2 4 Fundamental Frequency Estimation 17 2 5 G Force RPM and Stroke Calculations 20 2I A A d t rp Qe te IR HIE th Bs BE A Rr Tg 20 2 5 2 RPM oe Rus tx ree ERR IR ae Se ed PTA Lhe EIS DAT TE 21 2D USIFDEG Goeth i kou ou E Sce CAE d Les t S fee n etta i died tg 21 2 6 Frequency Analysis s cd sS LAN Eee eeq te 21 2 6 1 Fast Fourier Transform coe y oz RR 22 vi CONTENTS 2 0 2 Fast Wavelet Transform 4 ap Se ai eA A 23 Bot WOR DIE Analysis aa a da 24 2 8 Waveform Analysis A en erc n SE eS d 26 29 Elipse ities 3 8 2 x ueque oe eee eee a See SIDER SSS 28 2 9 1 Ellipse Fitting Method 2e Praderas de 29 292 Phase DE Goo 3 8 sn e II a a ere d a a 29 29 9 ECCeNntricity us do Bu e Old ee OR ee Sb e E d S 29 3 Data Acquisition 31 Dol ENE A dow th oe de dr MG A wie 6 em O18 ee a ee Se dt 31 3 2 Hardware Overview 4 2 zoom Shag omo E ew ee E 32 BO A ote PLE OE BR Hah qe Sel Shed Re ee 33 dul Accelerometer thos o gt id Oh oa eem ente ok Eee 34 3 5 Blu tooth De
9. DiscoveryThread This class is implemented as a thread and is responsible for discovering the available bluetooth devices within range It returns only those ones whose names start with SparkFun BT representing the bluetooth devices in each of the data acquisition units 6 4 12 Unpacker This module is a helper module for the Reader and is implemented in C as its methods are called frequently Its responsibility is in unpacking the data read from the handlers bluetooth or file according to a predefined format they are expected to be in and based on the sensor s orientation i e whether the sensor is mounted to the top or the side of the machine If the sensor is mounted to the top simply the y and z values read from the sensor are swaped This module s methods are Method get_values for file simulation This method is responsible for unpacking data read from a file handler e Inputs The handler s raw data array its length the orientation of the sensor associated with that hander the handler s x y and z arrays and a pointer to a num_values integer that represents the number of values that were unpacked 84 6 Software Implementation e Description Unpacks the raw data based on the given format Note that file simulation uses calibrated float values so the format is Byte Byte float float float Byte Also note that the file handler will put data in this format in order to make the unpack operation similar to t
10. The Reader module is responsible for reading data from the handlers A handler can be either a file in the File Simulation mode or a serial connection in the Data Acquisition mode The left part of Figure 5 4 illustrates the main loop of the reader module As soon as the acquisition or simulation is started on the event run the reader module starts reading data from the handlers and putting it in queues one for each handler for the sensor managers see Section 5 3 2 to pull data from later The Reader module stops reading on the stop event 56 5 Software Design Reader Run Read data from handler sensor or file and put in queue Numerical Values Display Waveform plots Update FFT plots Stop i T O O Figure 5 4 Depiction of the main system loops 5 Software Design 57 5 3 2 Sensor Manager For each handler object created a Sensor Manager module exists The Sensor Man ager represents the view in the MVC architecture described in Section 5 1 Its main responsibilities are in reading data from the queues calibrating the data if being read directly from the sensor communicating with the Filter module in order to filter the raw data communicating with the FFT module in order to perform an FFT computation on the raw data and storing both filtered and unfiltered data for the View module to access Figure 5 4 displays in the middle the main loop of the Sensor Manage
11. The ellipse s phase angle is the angle between the x axis and the major axis of the ellipse Therefore An ellipse with its major axis lying on the x axis has an angle equal to 0 Knowing the length of the semimajor and semiminor axes a b respectively and the distance between the foci 2c please refer to Figure 2 14 the phase angle 9 also referred to as the angle of rotation can be computed as follows 1 c a 6 cott 50 2 18 2 9 3 Eccentricity The eccentricity e of an ellipse is a measure of the shape of the ellipse Mathemati cally the eccentricity is the ratio of the distance between the centre of the ellipse and one of the foci c to the length of the ellipse s semimajor axis a or E 6 6 2 19 30 2 Vibration Analysis sixp ouha major axis Figure 2 14 Ellipse example showing major and minor axes When e 0 the resulting shape is a circle since the foci are at the centre so c 0 and when 1 the shape becomes a parabola Therefore for an ellipse the eccentricity value is expected to be 0 lt e lt 1 Please refer to Figure 2 15 e 1 e 2 e 0 5 Figure 2 15 Examples of orbital trajectories with various eccentricities Chapter 3 Data Acquisition The first step in vibration data analysis is acquiring the data This chapter details the hardware used in performing this task The software running on the chip was developed as part of a different thesis work and
12. This noise can be caused by the machine itself e g a 2 Vibration Analysis 23 0 5 100 15 200 250 300 350 40 450 500 0 50 100 15 200 250 300 350 40 450 500 Figure 2 9 FFT plots for the X Y and Z axes of a vibrating machine damaged component or from the surrounding environment This example demon strates the power of the FFT algorithm in such an application in that it provides information that is very helpful in troubleshooting the rotating device Since its development the FFT algorithm has introduced many new ideas in vibration analysis One important aspect the FFT algorithm has introduced is the ability to diagnose vibration problems Once FFT spectrums have been produced for various situations where a problem has occurred e g by a physical fault in the machine future spectrums can be compared against them aiding in the diagnosis of the problem 2 6 2 Fast Wavelet Transform Wavelet Transforms are a powerful extension of the Fourier Transform 1 Just like the FFT is a fast numerical computation of the Fourier Transforms there ex ists a similar method for the Wavelet Transforms the FWT Fast Wavelet Trans 24 2 Vibration Analysis form The Wavelet Transform provides capabilites of isolating signal discontinuities with high resolution and detailed frequency analysis over long time windows yielding wavelets useful fo
13. options panel to the right of Part C Part D is a smaller representation of the orbit for a specific sensor assigned to a specific location Part E is the values panel where the acceleration stroke RPM phase and eccentricity values are displayed It is important to understand that the values read from the sensors are accel erations in the X Y and Z directions These values include three different types of data 2 Vibration Analysis 7 Left Sidearm Feed Left Sidearm Discharge Left Discharge Bracket mening lect 9 Filtered 2 56 Unfiltered 3 3G 6 76 106 Centre Freq Source 2 Defined by FFT Defined Manual Stroke Unit 9 Millimeters CO Inches Figure 2 1 Part of the interface of the developed Vibration Analysis Tool 8 2 Vibration Analysis 1 Wanted data representing the normal motion of the machine that it was de signed for 2 Unwanted data representing the abnormal motion of the machine produced from a mechanical problem 3 Noise coming from other sources such as the sensor units or the surrounding environment Based on the discussion above the vibration analysis tool will have to process the data in such a way that the wanted data is kept the unwanted data is reduced and the noise is completely eliminated This chapter first introduces some terminology commonly used in the field of vibration analysis and then discusses a few methods that are used in this thesis wor
14. the phase angle and the x y and z g forces The orbit summary report allows for comparing the orbits visually as well as by the parameters provided in the tables 122 C Reports Date Wed 16 07 08 Customer test3 Machine No Bearings 2 Serial No Start Time 15h15m15s End Time 15h18m02s mana 45 4 5 6 1 Z 0 4 Figure C 2 Example of an orbit summary report Discharge LSF RSF i Feed TYCAN Vibration Analysis Vibration Analysis Tool mana 45 OX 4 LY s m Zz 04 4 5 6 1 4 5 4 1 0 4 mana 45 4 5 6 1 Z 0 4 C Reports 123 C 3 Tuning Report Figure C 3 is an example of a tuning report for a 2 bearing screen The report includes the following information 1 A table of deviations The values appear in red if they exceed the acceptance levels shown in the Deviation Acceptance Levels table which can be adjusted by the user through the Settings menu in the application 2 A table summarizing the g forces and stroke values 3 A table displaying the RPM measured the inclination entered by the user the motor sheave entered by the user the number of shafts entered by the user the drive inclination entered by the user and the calculated recommended machine acceleration 4 A table displaying the bearing diameter the friction compensation t
15. 100 if unknown Main Bearing Diameter mm Number of Shafts 2 per Exciter Drive Inclination DEG Friction Compensation Total Pull per Machine Ibs in or 0 if unknown Max Machine Pull Ibs in or 0 if unknown Feed End to Discharge End Distance in Feed End to Weight Distance in Resulting Vibrating Weight Recommended Machine Acceleration g Feed End to Centre Gravity Distance in Additional Weight Required Ibs New Stroke in New Pull Ibs in New Pull with body balancing Ibs in New RPM New Motor Sheave OD in or if Motor Sheave OD unknown Figure A 15 Tuning Report Menu 00 A User Manual 115 Additionally the user can perform the following 1 Restart the data acquisition by using the Restart Data Acquisition button which will take the user back to the acquisition information gathering window and will rediscover the available bluetooth devices 2 Go back to the main menu by using the Back to Main Menu button which will take the user back to the language selection menu 3 Exit the application using the Exit button Appendix B Internationalization B 1 Editing the translation files The following are the steps for editing the translation files 1 Download and install a program called Poedit which will make the task of applying the translation very easy It is cross platform and can be download it at http www poedit net download php 2
16. 5 Acquisition Information Gathering Menu 106 A User Manual Vibration Analysis Tool Available Devices Location Top or Side Piceviysranrunsrcoves CO GS DEE O CS Figure A 6 Device Selection Menu A User Manual 107 Upon pressing the Done button the main view of the data acquisition mode will appear with the selected sensors appearing on the right as in Figure A 7 Upon pressing the Connect button the system will connect to the chosen bluetooth devices and will obtain the battery and temperature readings from each device Moreover the g value chosen in the options panel will be sent to each of the devices so data can be acquired within that g range Next you can press the Run button to start reading the data from the sensors As soon as the system has stabilized the Start Recording button will be enabled Press it to start recording the data into files and press the Stop Recording button to end the recording Pressing the Stop button will stop reading the data from the sensors and will update the battery and temperature values A 4 Settings The following settings are available under the Settings menu in both modes 1 Centre Frequency Tolerance This is the tolerance on the centre frequency mea sured in Hz used to determine whether or not the bandpass filter used should be updated and new coefficients for it should be computed Figure A 8 displays how this tole
17. a C value The conversion steps are as follows 1 Computing the A D convertor s conversion factor which is given by conversion 3 3 x 1000 256 mv bit since it is an 8 bit A D conversion and the input source is 3 3 V 2 Computing the bit value of the offset the sensor reads 424 mV at 0 Cel sius This is given by offset 424 conversion 3 Computing the bit value of the slope this comes from the temperature sensor s datasheet This is given by slope 6 25 conversion 4 The final temperature value is value offset slope where value is the second byte read back from the socket 6 Software Implementation 69 e getCalibratiobParameters This method should read the sensor s calibration parameters based on the given g value from the PIC attached to the sensor The values are currently hardcoded and have been computed manually as described in 3 6 In the future these values should come from the acquisition unit and should be computed for each unit using a test rig for different g values and different temperature ranges e setGValue sets the g value on the sensor to the requested g value by sending followed by a byte representing the g value according to the following mapping 2 5 0xa8 3 3 0xa9 6 7 0xaa 10 0xab where the value on the left is the g value and the value on the right is its byte representation on the sensor Finally it reads back the echoed byte Class ReaderThread This c
18. in connecting with the sensors reading the acquired values performing signal conditioning on the data plotting the required graphs logging the data and generating reports In addition to reading from the sensors it allows for the playback of the data that has been perviously logged into files The tool is to have two different interfaces with the same functionality to run on two devices with different display areas The first is a PDA which has a small display area and the other is a PC with a larger display area Therefore in terms of the interface two designs have to be made The requirements document is an essential document acting as a contract between the developer and the client Figure 4 1 is an illustration of the Waterfall Model used frequently in software engineering The design and implementation of the Vibration Analysis Tool produced as part of this thesis work is based on this model As can be 39 40 4 Requirements Specification seen the requirements stage is a critical stage in the life cycle of the software and is referred to throughout all its successive stages in order to verify the satisfaction of the requirements This chapter discusses the application requirements Figure 4 1 A waterfall process with feedback 4 1 1 User Classes and Characteristics Various users will have access to the developed Vibration Analysis Tool These users differ based on their frequency of use of the tool the subset of fu
19. lost with one of the sensors the software will notify the user and normally keep on running with the other sensors without causing a crash to occur In general the implementation was conducted in such a way that guarantees robustness Try Except state ments were used only when needed and when used exceptions were explicitly defined Moreover in the model view controller architecture used when the model the Sensor Manager module is changing parts of the view the Viewer module events are used in order to guarantee that they occur correctly Fi nally when using threads it was kept in mind not to have any shared state between the threads and that data structures used with threads are accessed in a safe manner This is the case of the Circular Queue module which will be explained in the following section e Reusability One of the main goals of object oriented programming is to achieve reusability Since the developed software was implemented in python object oriented programming was used and reusability was ensured through the creation of classes that can be used in both the PDA and the PC applications A great amount of code was reused between the two applications allowing for easy maintenance without having to change the code twice The only module that is not completely common between the two applications is the Viewer module and even here inheritance was used in order to keep as many things as possible common and therefore reusable
20. representing a sine and a cosine wave The magnitude of the DFT results is directly proportional to N and the DFT s frequency resolution is f N Note that as N increases the DFT resolution becomes smaller but the DFT evaluation becomes more expensive Figure 2 7 which is taken from 9 is an example of a DFT of a signal whose frequency is an integer value equal to 3Hz The fundamental frequency that is being detected in the case of rotating machin ery is the frequency with the highest magnitude component in X m However due to what is referred to as the DFT leakage problem this is not the most accurate value The DFT leakage problem arises when the input signal s frequency is not exactly at a DFT bin centre This causes this frequency to leak into all of the other DFT output bins see Figure 2 8 which is taken from 9 One solution to this problem is by performing a parabolic interpolation around the frequency with the highest magnitude The following outlines the procedure for doing this 1 The DFT is computed on the N samples 2 The frequency with the highest magnitude in the DFT is determined Let this frequency be the th sample 3 A parabolic interpolation on three points i 1 2 i 1 is performed to obtain an equation of a parabola y x ax bx c The fundamental frequency has 2 Vibration Analysis 19 Input frequency 3 0 cycles m 4 analysis frequency 35 DFT output magnitude i i H i i
21. sight positioning of connected devices 2 This is fairly important in such an application since often times the vibrating machines are at locations that are hard to come close to or are blocked by some objects depending on the site they are located at Finally Bluetooth technology is much cheaper compared to other wireless technologies where the cost of Bluetooth chips is under 3 USD 2 The Bluetooth device that was utilized as part of the hardware component in this thesis work is the Bluetooth WRL 08461 One feature of this device is that its Bluetooth stack is completely encapsulated The end user just sees serial characters being transmitted back and forth Pressing the A character from a terminal program on the computer will cause an A to be pushed out the TX pin of the Bluetooth module 13 Also this device operates on a low power or 3 3V which is important especially since some of the machines will be monitored over a long period of time Finally these devices have been pre programmed with a unique MAC address and unit name of SparkFun BT allowing for easy detection of the devices by the computer used for acquisition as well as a UART interface of adjustable to a baud rate of 115 200 bps meeting the data sampling requirement on the system 3 6 Calibration Data received from the sensor unit is scaled to the range of values available on the A D convertor The A D convertor used has a 12 bit range meaning values are in
22. start The setup process involves the following 1 Reading the CONNECT message 20 bytes 2 Sending r and reading back 10 bytes 3 Sending ATMF r and reading back 6 bytes character then waits for the stop e stop data stops reading by sending the message to be sent back to ensure that the reading has stopped The stop message consists of 4 FF bytes in a row 68 6 Software Implementation e stop_reader stops the communication by closing the socket e getBatteryLevel The battery level is read by sending lt to the socket The value read is then converted so that it appears as a percentage value The minimum battery level allowed equivalent to a 0 is when the power drops by 2V from the maximum which is 6V Therefore the conversion is done as follows 1 Computing the A D convertor s conversion factor which is given by conversion 3 3 x 1000 256 mv bit since it is an 8 bit A D conversion and the input source is 3 3 V 2 Computing the bit value of the offset 2V allowed for the voltage to drop by This is given by offset 2 0 conversion 3 The bit value of the maximum voltage is 256 12 bit A D convertor Therefore the final battery percentage is 100 x value offset 256 where value is the second byte read back from the socket e getTemperature The temperature is read by sending to the socket The value read is then converted so that it appears as
23. stroke as follows Mai Main stroke nU ME 6 14 1000 2 RPM 60 e Outputs Strokes for x y z axes and main stroke 6 Software Implementation 81 6 4 9 Ellipse Fitter Uses numpy Note The implementation of the ellipse fitting method is based on the Matlab ellipse fitting module Additionally at least five points are required to perform the ellipse fitting on the more points passed to the function the better fitted will the ellipse be Method getEllipseParameters e Inputs Lists of filtered data in the x and y axis which determine the machine s main movement e Description Performs the following 1 Finds the estimate of the conic equation representing the ellipse which is given by ax bry cy dz ey f 0 6 15 2 Using the given points solves the equation using the linear least squares method The stsq function provided by numpy linalg is used here 3 Extracts the parameters a b c d e from the conic equation 4 Checks that the conic equation represents an ellipse This is done by checking if a x c gt 0 5 Calculates the ellipse s major and minor axes lengths This is done as follows F 14 4 d 4 a e 4x c 6 16 a Ffa 6 17 b F c 6 18 major_axis 2 x max a b 6 19 minor_axis 2 x min a b 6 20 82 6 Software Implementation 6 Computes the ellipse s foci as follows foci y major_axis 2 0 2 minor axis 2 0 2 6 21
24. the ap plication Chapter 2 Vibration Analysis 2 1 Overview Vibration is the most regularly measured condition parameter in modern rotating machinery and is nowadays continuously monitored in numerous important appli cations 1 Such applications appear in various energy and process industries such as petrochemical refining power generation and numerous others 14 Vibration monitoring or analysis was first used in the mid 1950s 1 when vibration sensors were first developed At that time the main use of vibration monitoring was in providing warnings when a machine was producing excessively high frequency vibra tions that could potentially damage its parts Numerous experimental results have been reported showing that high frequency vibrations are associated with bearing deterioration 8 This application of vibration monitoring is refered to as preventive maintenance Nowadays vibration monitoring is being used more extensively Predictive main tenance which is an extension of the traditional preventive maintenance is one of the most common applications One version of predictive maintenance is where the machine is provided specific maintenance actions based upon its monitored condi tion instead of a fixed time maintenance cycle 1 The motivation behind predictive maintenance is in reducing maintenance costs This cost reduction is mainly done 6 2 Vibration Analysis by making large reductions in the amount of m
25. the frequencies e A method for scaling the data on the y axis of the FFT plots This data represents the gains Note that all gains plotted are a ratio of that gain to the maximum gain meaning that the maximum gain appears as 1 on the y axis 6 4 14 Circular Queue This is a helper module for the SensorManager module providing it with a data structure to store m unfiltered and filtered data where m is the size of the queue The main feature of this data structure is that it will always return the most recent n data where n is the requested data size Since data is appended as soon as it is read then data is being put in the queue as a rate of 1000 samples sec Data is then pulled out of the queue when the viewer is ready to view it In order to ensure that all the data stored is viewed data should be pulled at a faster rate than that it is being put in Figure 6 1 illustrates how the queue works The Circular Queue module is implemented in C to improve performance and consists of the following class Class CircularQueue This class represents the circular queue data structure described above Upon its creation it is passed a size parameter defining the maximum data size it can hold at once It internally keeps track of a start and end pointer to indicate the oldest and the newest data Its methods are e append This method received 3 data points x y and z and append them as a tuple at the end of the queue incrementing
26. the range of 0 2 or equivalently 0 4096 However data processed by the vibration analysis tool needs to be within the range of the selected g force It is therefore important to calibrate each of the sensor units in order to obtain calibration parameters that are thereafter used to perform a scaling on the raw values so that they appear within the selected g range The following describes the method that the calibration is done through 36 3 Data Acquisition 1 Three measurements at predefined g values first need to be taken for each of the three axes The simplest measurements that can be acquired are at 1g Og and 1g To ensure the most accurate measurements possible the sensor unit must be sitting on a surface completely level It is important to note that by merely placing the device on the surface one cannot guarantee that is it not experiencing a slight g force in the x and y directions This is due to the way the device is packaged or any kinds of shifts from within its structure One manual method to perform measurements that will return a reliable and accurate result is by rotating the device from 1g to 1g for each of the three axes 15 The maximum value recorded during this rotation will correspond to a 1g force and the minimum value will correspond to a 1g force Afterwards assuming that the sensitivity is symmetric from zero to positive and from zero to negative the sensitivity of the device can be calculated
27. time as opposed to the Finite Impulse Response filters whose impulse response is on a fixed duration 2 Vibration Analysis 15 Frequency response o Qo Magnitude o o 0 o 0 2 0 4 0 6 0 8 1 GT Figure 2 5 Frequency response of Butterworth filters of varying order let A be the permitted magnitude deviation within the passband and A be the minimum attenuation relative to the passband peak response in the stopband Both A and A are measured in dB Then the minimum Butterworth filter order to meet those specifications is given by 2 1 log 104 19 1 104 10 1 12 log ws wy Second the centre frequency of the filter is to be determined Section 2 4 explains N 2 1 exactly how this is done Once the order N and centre frequency we of the Butterworth bandpass filter are determined the filter can be designed The general magnitude squared frequency response for a transfer function with finite poles and all zeros at infinity is given as follows K2 a au w The coefficients K a are to be determined 2 2 can be expressed as follows K 1 x N ao Y po Pkw Hjw 2 2 2 3 H jw 16 2 Vibration Analysis where Bk a ao Performing long division and expansion as described in Chap ter 3 of 3 the following equation is derived K 1 Hjwl x 2 4 pu Xa ae 2 4 Finally letting K a 9 be unity and By be 1 w2F the Butterworth response
28. to the calling function In addition to creat ing the packet and in order to simulate the receiving from a bluetooth socket a sleep is added every file_sleep_frequency times for the length of file_sleep_time This will make it look closer to a sensor read where data is not always available to be read 6 Software Implementation 67 Class FileHandler This class is used when wanting to simulate running data from a predetermined file It is a handler whose socket is of type FileSimulation described above Class SerialSimulation Similar to the FileSimulation class this class allows for the creation of a simulated socket object that can be used by the serial bluetooth handler It inherits from the Serial class provided by the serial library and is used when acquiring data on the Mac OS since the bluetooth library is not available for it Therefore its send method simply calls the serial write method and its recv method simply calls the serial read method with the required characters passed Class SerialBluetoothHandler This class is similar to BluetoothHandler described below except that its socket is of type SerialSumulaion rather than BluetoothSocket Class BluetoothHandler This class is used when acquiring data from the bluetooth its socket is of type Blue toothSocket The following are the most important methods of this class e setupBlueTooth sets up the bluetooth connection so that the data reading can
29. 1QT from Freescale Semiconductor It is a low cost accelerometer that features signal conditioning a 1 pole low pass filter temperature compensation and g Select which allows for the selection among four sensitivities 2 5g 3 3g 6 7g and 10g 4 Addi tionally this sensor operates at a low power of 3 3V and can obtain measurements in three different axes This sensor also features a Sleep Mode making it ideal for handheld battery operated devices like those used for the data acquisition When the Sleep Mode is active the device outputs are turned off providing a significant re duction in the operating current Finally the sensor can operate under temperatures ranging between 40 and 105 degrees Celsius making it ideal for use in cold climates as well as hot ones 3 5 Bluetooth Device Bluetooth is a wireless technology that allows for the transferring of data between devices Two main devices are involved the Bluetooth device that sends the data and the device that receives the data Compared to other wireless communication technologies such as Wi Fi IEEE 802 11 the Bluetooth technology was found to work best for the data acquisition part of the Vibration Analysis Tool for many 3 Data Acquisition 35 reasons First it can operate over a distance of 10 meters or 100 meters depending on the class of Bluetooth devices used Secondly it is able to penetrate solid objects and it is omni directional and does not require line of
30. 6 A 1 Language Selection Menu pee eee 100 A 2 Mode Selection Menu e La dc 14 A es le RORUb E VI Rep d ed 101 A 3 Main view of File Simulation Mode 0 102 A 4 Main view of File Simulation Mode while running 104 A 5 Acquisition Information Gathering Menu 105 A 6 Device Selection Menu oe apa a a da 106 A 7 Main view of Data Acquisition Mode 108 A 8 Centre frequency tolerance setting 109 AS RPM tolerance setting vo a A RO a 109 A 10 Update frequency setting e 109 A 11 Update history setting dera qr go al a 110 A I2 RE Se settings id Ea ere e e Dp On js a BE A 111 A 13 Acceptance levels setting 111 A 14 Bearings settings ooo a o Re Rp Gee V ep dU E EA 112 A 15 Tuning Report Menu s cu a ala BCA pur Rad dut tn 114 C 1 Example of a single point report zu a a 120 C 2 Example of an orbit summary report ooo eR R0 122 C 3 Example of a tuning report ie Face oe a 124 Chapter 1 Introduction 1 1 Thesis Motivation The field of modern vibration analysis also referred to as condition monitoring for rotating machinery is now over 40 years into its development and thus is a matured technical subject However it continues to evolve and advance in response to new re quirements to further reduce machinery downtime and drastically reduce maintenance costs 1 Thi
31. 7 Computes the ellipse s eccentricity as follows eccentricity 2 x foci major axis 6 22 8 Computes the ellipse s phase angle as follows 1 foci major axis 2 0 minor axis 6 23 phase angle 0 5 x arctan e Outputs Eccentricity Phase angle 6 4 10 Report Generator Uses pylab reportlab numpy Class SinglePointReport The methods of this class are responsible for creating a PDF report for a single monitored location on the machine using the data passed to an object of this type open its creation Please refer to Appendix C for an illustration of the resulting single point report Class OrbitReport The methods of this class are responsible for creating a PDF report acting as a summary of the orbits produced by all the monitored locations The report is created using the data passed to an object of this type open its creation Please refer to Appendix C for an illustration of the resulting orbit summary report 6 Software Implementation 83 Class TuningReport The methods of this class are responsible for creating a PDF report providing recom mendations for adjusting the machine The report is created using the data passed to an object of this type open its creation The calculations performed here are all based on the old reports produced by the company Please refer to Appendix C for an illustration of the resulting tuning report 6 4 11 Device Discovery Uses threading Class
32. A RN 58 TIG Riter s LADERA A di A ts Ads 58 foe FET Computer s uu dad ds Re AA m eas d 58 5 3 8 Numerical Values Computer 59 9 3 9 Ellipse Fitter aene la doen pho dhe gk aos 59 5 3 10 Report Generator 2 2 04 s TREE AUREAS 59 5 4 Main Module Interaction 24x ace Ae a oe dar pur uer Pat ene o 59 6 Software Implementation 61 DT o SS Cet dese Mese cuidar Ace ae detur de UR EE ES 61 6 2 Implementation Considerations llle 61 6 3 Software Libraries Used o deut dT ete QURE dec te e Ded 64 6 4 Mod les A Gee Sg eS OR EORR D ERE ODE ea O 65 Ol Reader E fete ee ita A Ro deti pA d iA 65 6 4 2 Sensor Manager 6 Sut Kobe eu bea ER PUR Lala 70 Qd Ee Viewer NA IA A tic d LM aU 72 pd TGC He lu xg Eyed eA Ke vue aea TA oe A 76 viii CONTENTS Dub Calbrator tutto et wie SEP A a ne xe A 76 GAO Tier dad BO NUN eM SR IE EE Wed ms 77 OAT JER Computer ES ale oe late bulo lage e 78 6 4 8 Numerical Values Computer 80 O10 Ellips Fitter seis dass ote oe nee ew ates Tag een ge ek dee 81 6 4 10 Report Generator Led Be Sa ee Se 82 6 4 11 Device Discovery ira oars aha ee a DR SS 83 64 12 Dnpackee so e Bak OA 83 6 4 13 Screen Scaling 5626 71a Zn v TR A AA Se 84 OE Circ lar Queue 3 23 pru soie Peete ee Peet A uS 85 Software Testing 87 AR au xc MTM 87 ff Meek TA Leste ts oe Ee dd ts acht a 87 ToO System Testing s ee doi dm es a Si eS edi ue e 88 Error Analysis 91 BU UOVOPVIS
33. DESIGN AND IMPLEMENTATION OF A VIBRATION ANALYSIS TOOL DESIGN AND IMPLEMENTATION OF A VIBRATION ANALYSIS TOOL By SAHAR ABUGHANNAM B ENG A Thesis Submitted to the School of Graduate Studies in partial fulfilment of the requirements for the degree of M A Sc Department of Computing and Software McMaster University Copyright by Sahar Abughannam September 2008 ii MASTER OF APPLIED SCIENCE 2003 McMaster University Hamilton Ontario TITLE Design and Implementation of a Vibration Analysis Tool AUTHOR Sahar Abughannam B Eng McMaster University SUPERVISOR Dr Martin von Mohrenschildt NUMBER OF PAGES xii 123 Abstract This thesis work presents the software development stages for a vibration analysis tool developed for a company that produces mining machinery and is interested in monitoring their machines behaviour The developed application contributes directly to the field of vibration analysis which is widely applied in many areas nowadays Such areas include in addition to the mining industry the automotive industry and other industries producing rotating machinery The application developed interfaces with a device designed to acquire vibration data through a three axis acceleration sensor The device then sends the data wire lessly via Bluetooth technology to a computer on which the application is running The application then processes the data by applying signal conditioning functions on it These functions i
34. FFT plots Class WaveformPanel A panel the encapsulated the waveform plots 6 Software Implementation 75 Class LargeOrbitPanel A panel that encapsulated the large orbit plot Class SmallOrbitPlotsPanel A panel that encapsulated the small orbit plots Class ValuesPanel A panel displaying the numerical values associated with each of the active sensors Class OptionsPanel A panel encapsulating all the options available to the user 1 Setting on the g value 2 Choosing the orientation to plot the orbit plot in 3 Choosing the source of the centre frequency manual or from the FFT 4 Choosing the unit to display the stroke in mm or inches 5 A slider for setting the centre frequency The maximum allowed frequency is 100 this is caused by a 6000 RPM machine 6 A slider for setting the bandwidth used for the filter The maximum allowed bandwidth is 20 Hz 7 A slider for setting the maximum frequency to be displayed on the x axis of the FFT plots The maximum value is half the sampling frequency which is 500Hz 76 6 Software Implementation Class ReportingPanel This class exists only for the PC application It allows for a window to show up when the user chooses to generate a tuning report This window contains various parameters that the user is allowed to enter or adjust The user can preview the values generated based on these parameters before the PDF report is actually generated Wh
35. Generator module e gettext This module provides internationalization I18N and localization L10N services for the python application It is used in the Viewer module only for translation purposes of the labels and other controls with text 6 Software Implementation 65 e wxPython This module is a blending of the wxWidgets C class library with the Python programming language It provides GUI abilities and is therefore used in the Viewer module only e The Python Imaging Library PIL This library adds image processing capa bilities to the Python interpreter This library supports many file formats and provides powerful image processing and graphics capabilities It is used in the Viewer module only to generate the plot backgrounds and allow for updating them directly when the g range that is used and the maximum frequency to be shown on the FFT plot change e pylab Also called matplotlib is a python 2D plotting library which produces publication quality figures in a variety of hardcopy formats and interactive en vironments across platforms It is used in the Report Generator module only to generate the plots used in the reports e reportlab This library is open source and is one of the most full featured li braries for PDF creation available It is used in the Report Generator module for generating reports in PDF format 6 4 Modules The python code implementing the application is divided into python modules p
36. The folder locale contains subfolders for each one of the used languages de German en English this does not require translation and should be left untouched fr French pt Portuguese sp Spanish 3 Inside each one of the language folders there is a subfolder LC MESSAGES which contains two files gui xx mo and gui_xx po where xx stands for the language abbreviations given above Open the po file using Poedit 4 Once the po file is opened a list of the original strings in English used through out the program is displayed Upon clicking on a string two boxes at the bot 116 B Internationalization 117 tom will show up The top one contains the string in its original form and the bottom one where appropriate translation should be entered The translation should then show in the column entitled Translation beside the original string that was selected 5 Once all the translations are applied click Save This will overwrite the gui_xx mo file with the new translations B 2 Adding a language To add a new language perform the following steps 1 Add the language to the drop down list in the language selection frame 2 Add the following line at the top of the appropriate viewer module language gettext translation gui_xx locale languages xx Where language is the language name and zx is the language abbreviation 3 In the locale folder create a folder and name i
37. WO uox g a ee al ert cas as redet as os oce aoe ee eM ER RE a 91 5 2 Dypescol BIFODS Ltd Oo Rain PE Ral ok bE o a 91 Conclusion 94 9p DISCUSSION se a a A ts ORC UK Se ns ded 94 9 2 A ah le ho cay Been te ram ie dna a Se dost adh end ce did 95 User Manual 99 Al Cota Upset os OE Ge ere pide Gide We ae ee 99 A 2 File Simulation Mode qu ue de UC ans un ee Bene ewe een de 99 A 3 Data Acquisition Mode ool 103 ASA SELINE SE venera a dd citar aidez casa EO eque ye pr ee Sonera 107 A 5 Generating Reports qoe a bk SD IE Ro Sox RON A 112 AD 1 Other Commands 4 d n AN EA 113 CONTENTS ix B Internationalization 116 Bir Editing the translation files 220a xe ke RR ERR ox 116 B 2 Adding a language a 403 9o do adela e ar e gran d 117 B 3 Adding new strings to the source code 117 C Reports 119 Oak Sinele Poimt Report aea a ae Wg ee a E e dcr 119 C 2 Orbit Summary Report cse aee RON Ter ru e Bs 121 Coa ming Report axo uos x SLE aru a E haere poi ge 123 List of Tables 3 1 Calibration measurements using gravity 8 1 G ranges and their resolutions List of Figures 1 1 Types of machines produced and their motions 2 2 1 Part of the interface of the developed Vibration Analysis Tool 7 2 2 Measurement points on a two bearing horizontal screen 10 2 3 Measurement points on a four bearing inclined screen 10 2 4 Representation of a bandpass filter
38. aintenance required in addition to reducing technical support personnel Many methods are used in performing vibration analysis As discussed in 1 such methods include but are not limited to the following e Signal Conditioning This includes filtering discussed in Section 2 3 integra tion to calculate the velocity and displacement from the acceleration discussed in Section 2 5 and signal amplitude conversion which is part of the Fourier analysis discussed in Section 2 6 e FFT Spectrum This is discussed in Section 2 6 e Rotor Orbit Trajectories This is discussed in Section 2 7 e Bode Polar and Spectrum Cascade Plots Not a part of this thesis work e Wavelet Analysis Tools This is partially discussed in Section 2 8 e Chaos Analysis Tools This is not a part of this thesis work In addition to the above this thesis work involves not only visual orbit analysis but a mathematical analysis including the fitting of the orbit trajectory into an ellipse and the calculation of the ellipse s phase and eccentricity Figure 2 1 provides a layout of a section of the Vibration Analysis Tool developed as part of this thesis work Part A displays the Fast Fourier Transforms for the three axes Part B displays the waveforms for the three axes Part C is a depiction of the orbit in the Y vs X orientation The orbit in this figure is based on the filtered data however there is an option to view the orbit based on the unfiltered data in the
39. ally the addition of internationalization allows for the selection among various languages as requested by the company in order to make the software usable in different countries Maintainability Studies have shown that the majority of time spent on main tenance is spent on enhancing the product with features that were not in the original specifications Therefore the software was developed in order to allow for easy maintenance This was done primarily in the use of modularization in the design phase splitting the software responsibilities among various modules each with its own responsibility Moreover the use of the information hiding principle allowed for changes to be done on modules without affecting the rest 6 Software Implementation 63 e Correctness Reliability and Robustness These qualities are linked to gether and are very important in guaranteeing accurate results Joined together they characterize a software quality that implies that the application performs its functions as expected The software developed is correct in that adheres to its specifications implementing all its functions as specified in the requirements phase It is reliable in that its results are correct and that it behaves as expected over a long interval of time Finally the software is robust in that it behaves reasonably even in circumstances that were not anticipated in the requirements specification For example in the case that the connection is
40. ator module exists only in the data acquisition mode where data is read directly from the sensor This module has been kept separate in order to allow for easy change in the calibration method without affecting other modules One such module exists for each sensor handler based on that sensor s calibration parameters and the g range being used for aquisition Each Calibration module interfaces with the Sensor Manager module by receiving non calibrated data from from it and sending back calibrated data 5 3 6 Filter The Filter module contains sub modules each representing a different filter type It interfaces with the Sensor Manager modules by receiving unfiltered data and sending back filtered data This separation of concerns between the modules allows for changes in the way the filters are implemented without affecting the Sensor Manager modules 5 3 7 FFT Computer The FFT Computer module is responsible for applying an FFT computation on the unfiltered data that is received from the Sensor Manager modules It is also responsible for computing the fundamental frequency based on the data set it receives as well as the RPM which is based on the centre frequency and sending back these two values along with a list of frequencies and their absolute values for the Viewer module to access later for generating the FFT plots 5 Software Design 59 5 3 8 Numerical Values Computer This module is responsible for computing the g forces a
41. by dividing by 2 Now that the sensitivity is known the Og offset value can be calculated by adding the sensitivity to the minimum value or subtracting it from the maximum value This value should be very close to the Og offset value obtained by placing the device level The following table shows the measurements as read from one of the sensor units for each of the available g ranges in the 3 different orientations Orientation 2 5g 33g 6 7g 10 0g X 1g 1503 1635 1835 1903 X 0g 2114 2090 2063 2055 X lg 2606 2533 2284 2203 Y 1g 1414 1569 1802 1877 Y 0g 2028 2033 2034 2033 Y lg 2632 2483 2258 2183 Z 1g 1290 1473 1757 1850 Z 0g 1970 1978 2008 2018 Z 1g 2665 2506 2272 2195 Table 3 1 Calibration measurements using gravity 3 Data Acquisition 37 2 After the calibration data has been acquired the next step is to create the scaling functions The goal here is to compute linear functions for each of the three axes measured for each one of the g ranges This is performed by applying a linear least squares fitting method on the three points measured above to obtain the best fit line s equation which is then used as the scaling function For instance if this to be done for the x axis under 2 5 g mode then given the three points 1503 1 2114 0 2696 1 from above the goal is to obtain the best fit line represented by f x ax b Performing a linear least square calculation leads to the best fit line rep
42. cted bluetooth devices that are related to the vibration analysis tool You will then need to assign each device a location from the list as well as a top side orientation based on where it is attached on the machine You can uncheck the box beside each device if you do not want to connect to it This is shown in Figure A 6 A User Manual E E gt 80 so zo oo A L_ pe Fi rel 005 00S L I 0 00 ZH bala xew ldd a n eb UlOJaAEA Z m E go m 90 t mo I ti 1 19 EE IP AEVUM Ir L A O ES SV V eounog bai ue 2H Kouenbe anueg NE az L ve 501 ay e 296 ASAZO ee UWLUOJBARM A DEDO Pwapun X s zO N NR I v9 omn po go poe Z 2s zO pemyd X AQ i acu peajes 9 Buya UOneueUO of AA A A A A ita sa s EN i dois 00 1 RR sisAieuyIM NVOIA L uogesqIy 104 Figure A 4 Main view of File Simulation Mode while running A User Manual 105 HAVER amp BOECKER TYCAN THE SCREENING GROUP Please provide the following information while discovering available devices Customer Machine Model Number of Bearings Serial Number Date Figure A
43. e Basic Dynamic Load box Press the Add button to add the requested bearing information If a bearing with A User Manual 111 Choose the size of data used to perform the FFT Canes OD VA Figure A 12 FFT size setting Figure A 13 Acceptance levels setting 112 A User Manual the inputted diameter already exists a message will appear explaining that If the input was accepted the bearing will be added to the Available Bear ing Diameters and their Basicloads list Once you are done press the Exit button Bearing Diameter mm Basic Dynamic Load kN Figure A 14 Bearings settings A 5 Generating Reports In order to generate reports in Data Acquisition mode a recording of data must have taken place On the other hand in File Simulation mode reports can be generated right away after connecting to the files Single point reports can be generated by clicking on the Report button beside each appropriate device on the right side of the application An orbit summary report can be generated by clicking on the Generate Orbit Summary button and a tuning A User Manual 113 report can be generated by clicking on the Generating Tuning Report button The latter will lead to a window as displayed in Figure A 15 Here the user can insert the parameters that are to be used for generating the tuning report The user can press the Preview Res
44. e and phase angle are accommodated in the balancing procedures 1 In general synchronous band pass filtering increases the accuracy of rotor balancing which is an important procedure in the field of rotating machinery Figure 2 4 is an amplitude vs frequency representation of a bandpass filter The frequencies f and f are the cut off frequencies of the filter and fo is the centre frequency The cutoff frequencies are those at which the output signal power falls to half of its level at fo The difference between f and fa is referred to as the bandwidth of the filter Finally the range of frequencies between f and fa is referred to as the filter passband Notch filters operate in a such a way opposite to band pass filters Instead of passing the signal content within a specified range the content outside that range is passed and that within it is removed One interesting application 2 Vibration Analysis 13 Output signal power fa 100 50 L Passband Frequency Figure 2 4 Representation of a bandpass filter of notch filters in rotating machinery is with magnetic bearings Since the operation of magnetic bearings is based on displacement feedback control a notch filter us used to filter out the bearing force components occurring once per revolution so that they are not transmitted to the non rotating structure of the machine while the bearings continue to prov
45. e procedure for doing this is by 1 Finding the minimum Min and maximum Maz acceleration values for each set of readings 2 Computing the average g for that axis which is equal to Max Min 2 The Main g force is computed as well giving the machine s main acceleration based on the two axis determining its main motion For example if the main motion is determined by the X and Y axis then the Main g Force is computed as follows Main g Force max y 1 y vx X y Y 2 12 2 Vibration Analysis 21 2 5 2 RPM The machine s RPM can be calculated from the FFT results As described in section 2 4 performing an interpolation on the FFT is done to determine the fundamen tal frequency of the machine The RPM is then calculated from the fundamental frequency fo as follows RPM revolutions minute fo revolutions sec x 60 sec minute 2 13 2 5 3 Stroke The stroke is the displacement of the machine Since the machine can move in three axes the stroke can be computed for each of these axis as follows X Y Z Average G Force x 1000 2 x RPM 60 X Y Z Stroke mm l 2 14 Similarly the machine s main stroke can be computed from the Main g Force see section 2 5 1 as follows Main G Force x 1000 2 x RPM 60 Main Stroke mm 2 15 2 6 Frequency Analysis Frequency analysis is done through two methods FFT Fast Fourier Transform and FWT Fast Wavelet Transform which are b
46. en they are satisfied with the results after tuning the parameters as required they can choose to generate the report 6 4 4 Logger Class Logger An object of type Logger is responsible for logging the data it receives Such an object is instantiated for each location being monitored i e for each sensor manager Each object has its own log and stop_logging methods The log method can be modified in order to allow for a different logging scheme 6 4 5 Calibrator Class Calibration This class is part of the scaling package and is implemented in C to increase perfor mance Upon creating an object of this type it should be passed the slopes and the offsets used to create the lines that are used to calibrate the data in all three axes When its scale method is called with the x y and z values that are to be scaled the calibrated data is computed as follows for each axes x x_slope x x z of f set 6 1 Finally the calibrated x y and z values are returned 6 Software Implementation 77 6 4 6 Filter The Filter module is implemented as a python package which includes sub modules each representing a filter type Filters created in the future should be added to this package Each filter should be implemented as a class with a method named calc performing the filter s calculation The calc method accepts a list of samples as an input and returns a list of those sample but filtered Other methods providing services to t
47. ensor units used This information should include at least the following for each used sensor Sensor ID location on machine orientation on the top or on the side of the machine battery level and temperature level 6 The application shall log the start and end times of the acquisition 7 The application shall log the g force level used throughout the acquisition 4 2 5 Display Requirements The following requirements apply to how the data is displayed on the screen The display of data can be in two forms graphical and numerical 1 The application shall display plots of the machine s motion in the XY XZ and YZ planes 4 Requirements Specification 45 10 11 The application shall allow for displaying the orbits based on both the filtered and unfiltered data The application shall display small views of the orbits of all the locations used to perform the acquisition at the same time The application shall display values related to all the locations used to perform the acquisition at the same time The application shall display plots representing the FFTs in all three axes for each of the sensors The frequencies displayed shall be of a minimum of 10Hz and a maximum of the Nyquist frequency given by half the sampling rate The application shall display plots of the signals waveforms in all three axes for each of the sensors The application shall display the machine s RPM computed fr
48. epartment at the U S Department of Labor has issued a new act stating the following The MINER Act requires that mine operators adopt wireless communications and elec tronic tracking systems by June 2009 http www msha gov This is an indicator of the advancement level of the developed tool 9 2 Future Work The following is a list of future work that can be based on the developed vibration analysis tool or added as an extension to improve its performance 1 As presented briefly in Section 2 6 2 Fast Wavelet Transform Analysis can be applied in addition to the Fourier Analysis in order to better analyse the acquired data and detect unwanted noise 2 As mentioned in Section 3 6 a more accurate method for calibrating the sensors can be employed One such method would involve a test rig with a predefined set of g ranges that it can operate on onto which the sensors can be attached in order to acquire data for calibration in all three axes Additionally the effect of 96 9 Conclusion temperature on the readings should be taken into consideration and calibration should be performed on various temperature ranges utilizing the temperature sensors that are a part of each acquisition device Researches interested in performing diagnostics on the acquired data are able to base their work on the developed tool Diagnostics are then performed by creating a set of predefined mechanical problems that can occur on the
49. eport This report summarizes the vertical and the horizontal strokes and g forces for the entire set of sensors mounted to the machine It is mainly used to determine any deviations between the measured data and the expected machine behaviour The results of the deviations are used to provide tuning recommendations to the client based on physical principles that apply to any vibrating machine The following are requirements that relate to the reporting part of the application 1 The application shall allow for the creation and storage of a single point report for each sensor location 2 The application shall allow for the creation and storage of an orbit summary report summarizing the behaviour that all of the mounted sensor units acquired 3 The application shall allow for the creation and storage of a tuning report detailing the machine s behaviour and providing recommendations for adjusting 48 4 Requirements Specification the machine The application shall allow for the adjustment of the values used to generate the turning report before the report is actually generated Such values include the bearing diameter the friction compensation the inclination angle and other important parameters In the tuning report the application shall allow the user to manually enter values for missing sensors based on their location and the readings from the other sensors The application shall allow for the viewi
50. erformance A software s performance is linked to its usability and reliability The better the software performs the more usable and reliable it is In terms of vibration analysis performance is a major software quality that needs to be considered The values are acquired at a rate of 1000 Hz and are to be processed by the vibration analysis tool at a rate that will guarantee all the data being processed Therefore the software was implemented in such a way that will allow for that Most importantly was the use of pyrex in order to convert some parts of the program into a C implementation The parts that are converted are those that are called most often and involve the data processing unpacking the data coming from the sensors storing the data in a circular queue applying filters on the data etc Usability A software is considered usable if its users find it easy to use After discussing user interface aspects with the personnel who would be using the tool most often at the company an interface for the software was designed The interface was implemented in such a way that allows for easy access to various commands Moreover it provides a clear view of the plots that display different forms of the acquired data The reports are also generated in a format approved by the company and in the case of the Tuning Report the user is allowed to enter all the parameters required and preview the results before actually generating the report Fin
51. f a system is its design Software design is a fundamental step in the software development process as it acts as a bridge between the requirements and the implementation of the system The main goal of software design is to decompose the system into parts assign responsibilities to each part and ensure that the parts fit together to achieve the global goals of the system 7 This chapter discusses the software design of the vibration analysis tool It starts by explaining the method used for structuring the design and thereafter discusses the main system modules and how they interact 5 2 Design Method The first step that was taken in order to design the system was to determine the system tasks A flowchart was used in order to illustrate the flow of tasks in the system and is depicted in Figure 5 1 The next step was to divide the system into modules or components keeping in mind the software design principle of information hiding where each module hides internally information that can be kept secret from all the other modules This 52 53 5 Software Design 1ejndujo senjeA EOLSLUNN SY ui Xoq e SE uMous JOU SI 9J0j8J8u pue sajnpoui Jaylo Duisn eua saqyiqisuodsa s ajnpow saGeuey Josuas au ajnpow J M JA au JO Wed S xoq panop e ui peurejuoo jou Buiuue 3 81oN LU LU uonoajas voyoajas aenfue7 e Figure 5 1 Data flow in the system 54 5 Software Design technique ensures that t
52. filtered and unfiltered data orbits plotted on top of each other to allow for analysing the data better 2 Waveform plots for the x y and z axes 3 FFT plots for the x y and z axes 4 A table summarizing the acceleration stroke RPM and phase angle as acquired from that location on the machine 5 A table summarizing the accelerations and strokes for each of the x y and z axes 119 120 C Reports Date Wed 16 07 08 Customer test3 Machine No Bearings 2 Serial No Start Time 15h15m15s TYCAN ibration Analysis Tool End Time 15h18m02s LDB Side Accel Stroke RPM Phase al Aet A E ee ee ee ee ee 2 0 Ei all bl b bib daga ab c o BM MISSA ic A d i o z s a55 edo soo T50 x o 00 do abu soo Time Frea Hz z eer 10 A en T eL Bun I 3 N ll 2 oo A AA AA EEE A AA A 0 1 HF i E nn 3i m Ies D a i P E SL Deb Heme RERO enn bie 0 45 200 400 600 300 100 30 Time Frea Hz TYCAN Vibration Analysis Figure C 1 Example of a single point report C Reports 121 C 2 Orbit Summary Report Figure C 2 is an example of an orbit summary report The report includes the fol lowing 1 For each of the monitored locations an orbit plot representing the filtered data coming from the sensor on that location 2 For each of the monitored locations a table summarizing the main g force
53. g systems so that multiple decoy signals could not be dis tinguished from authentic reflections 1 Since then the FFT algorithm has gained huge interest in the signal analysis field in general and in vibration signal analysis in particular The importance of the FFT algorithm lies in providing a way to transform time varying signals from the time domain into the frequency domain on the spot This provides a very useful method for analyzing the signal since when plotted the signal s frequency components are displayed Prior to the development of the FFT algorithm the primary method for displaying the vibrating signals was in the time domain using an oscilloscope Other methods proved to be impractical especially since they required experience in tuning and adjusting the bandwidth filters in order to operate successfully Figure 2 9 depicts an example of an FFT spectrum of a rotating machine s vibra tion signal The frequencies appear on the x axis and their amplitudes on the y axis It is worth noting that the plots have been scaled so that all the y values are ratios of the maximum y value In the example depicted by Figure 2 9 the frequency component with the highest amplitude in the X and Y directions is approximately 15Hz This normally would be the machine s running frequency Other high frequency low amplitude components appear as a sign of noise particularly on the Z axis which is perpendicular to the machine s main movement
54. gh endurance Additionally for power sensitive applications such as the data acquisition application the PIC devices work best since they require low power to operate The exact PIC used as part of this thesis work is the PIC18F2423 which features a 12 bit Analog to Digital convertor which allows for the coversion of data with low error please see Chapter 8 for an in depth error analysis Moreover it features a serial communication capability which allows for using it with a Bluetooth device Finally it has a small size which helps in decreasing the total size of the acquiring device 34 3 Data Acquisition 3 4 Accelerometer An accelerometer or an acceleration sensor is a sensor used for measuring the acceleration of the object it is attached to Accelerometers come in a variety of types mostly differing by the number of axes they can obtain measurements in and by the range of g values that they can pick up An accelerometer is composed of an internal mass compressed in contact with a relatively stiff force measuring load cell this is usually a piezoelectric crystal by a relatively soft preload spring In response to dynamic loading those piezoelectric load cells produce a self generated electrical output at a very high impedance which gets converted internally through electronics to a low impedance output suitable for data acquisition systems 1 The particular accelerometer used as part of this thesis work is the MMA726
55. gles and the eccentricities of the orbits formed by the vibration of the rotating especially since the orbits are expected to be elliptical When more than one sensor is used to acquire data on different locations on the machine it is very helpful to know the phase angles and the eccentricities of the ellipses created by each sensor s readings It might be hard to distinguish visually between the various ellipses when plotting the orbits so those two numerical values help in analysing the machine s vibration This section will explain the method used to perform ellipse fitting and how the phase angle and eccentricity quantities are determined 2 Vibration Analysis 29 2 9 1 Ellipse Fitting Method Ellipse fitting on the acquired data is conducted by using the classical linear least squares method An ellipse can be described by the conic equation az bry cy dr ey f 20 2 17 Then as explained in 5 the constants a b c d e and f are solved for using the least squares method on the given points The minimum number of points required to fit an ellipse is five points 11 however in order to get a more accurate result more points are used in the Vibration Analysis Tool produced Finally the ellipse parameters major and minor axes as well as distance between the ellipse s foci are computed using the determined constants and are thereafter used in computing the phase angle and the eccentricity 2 9 2 Phase Angle
56. gnal content below the cutoff frequency is attenuated and that above the cut off frequency is passed As mentioned above since routine rotating machinery vibration 12 2 Vibration Analysis analysis is usually not concerned with frequency components above 10 times the spin speed high pass filters are not a common tool in rotating machinery signal conditioning Band pass filters operate based on a range of frequencies called the frequency band of the filter A band pass filter s operation is similar to applying a low pass filter and a high pass filter in series with the condition that the low pass filter s cut off frequency is higher than the high pass filter s cut off frequency The frequency band of the band pass filter is centred at a point called the centre frequency of the filter This frequency is determined first and then a range is defined around it allowing signal content within that range to be passed and that outside it to be removed The standard method of determining the centre frequency of the band pass filter in rotating machinery applications is by using the machine s speed also referred to as its RPM For purposes of rotor balancing only the synchronous vibration components are used 1 The reason for this is that the application of balancing is based on the assumption that the vibrating system overall is linear This means that only the forcing frequency which occurs once per revolution vibration amplitud
57. hat of the bluetooth allowing for the reuse of code e Outputs Returns a pointer to the last point unpacked in the raw data array for the next time this function is called Method get_values This method is responsible for unpacking data read from the bluetooth handler It shares the same interface as the get_values_for_file_simulation but calls the my_unpack method to perform the unpacking on the values Method my_unpack This method unpacks data based on the 9 byte packet format used for the bluetooth handlers The format is as follows Byte FF Byte FF Short 2 Bytes x value Short 2 Bytes y value Short 2 Bytes Z value Byte F0 6 4 13 Screen Scaling This class is part of the scaling package and is implemented in C to increase per formance Its methods deal with scaling the data so that it appears correctly on the plots displayed on the screen It is therefore dependant on the display size It contains the following methods e 4 methods for scaling the data on the orbit plot Each one is related to a different g range and based on the g value passed to orbit_scale the appropriate method is used e 4 methods for scaling the data on the waveform plots Each one is related to a different g range and based on the g value passed to waveform_scale the 6 Software Implementation 85 appropriate method is used e A method for scaling the data on the x axis of the FFT plots This data represents
58. he calc method can be implemented as part of each filter class Class AllPass The Allpass filter is applied to the z axis values perpendicular to the machine s main movement only These values do not represent the machine s main movement and are therefore not that important to filter This class s calc method simply returns the values passed to the filter untouched Class Butterworth The Butterworth filter is the bandpass filter used to produce the filtered data used throughout the application This module is implemented in C in order to improve performance as the filtering occurs on every data sample read from the sensror Its calc method implements an IIR filter used to filter a list of samples the IIR filter computation is implemented in such a way that allows for an increase in performance namely by eliminating the need to re compute values through the reuse of data For this reason the filter is to be applied on arrays of samples whose length is a multiple of four The following equations explain how this is done on every 4 samples example based on a 2nd order filter result y n aix n aaxz n 1 byy n 1 bay n 2 6 2 result y n 1 aya n 1 asx n byresult bay n 1 6 3 results y n 2 ayx n 2 asx n 1 bjresulta baresult 6 4 78 6 Software Implementation result y n 3 aya n 3 azx n 2 byresulta baresult 6 5 Once the filter is c
59. he orbit based on unfiltered data whereas part b displays the orbit based on the filtered data after passing through a 4th order Butterworth bandpass filter In addition to visually analysing the utilized filter s performance orbit analysis can help in diagnosing mechanical problems in the machine Figure 2 11 illustrates an example of a rotating machine where a progressively worsening influence on the 2 Vibration Analysis 25 Figure 2 10 Filtered and unfiltered orbits of a rotating machine machine causes a progressively increasing static radial force on the rotor and therefore on the bearings Part a is the case where there is a normal radial load the machine s main frequency is at N and its motion is synchronous and linear between the various parts of the machine Part b is the same as part a but with a moderate increase in the radial load Part c shows the case where there is a substantial radial load the motion becomes nonlinear and a frequency component appears at 2N Finally part d is where there is a very high radial load the machine s motion is nonlinear and there is a high frequency component at 2N It is worth mentioning here that these orbits represent what are referred to as Lissajous plots Lissajous plots are generated when graphing a system of parametric equations which is exactly what is being done here Each of the axis generates its own signal which is sinusoidal please see sec
60. he system is structured in such a way that allows for future changes and therefore makes it more maintainable and easy to extend If a change is to occur in the method that data is logged for example only the logger module refer to Section 5 3 4 would have to change its log function Additionally since the software to be developed has a significant amount of user interaction one well known software architecture to be used in this case is the model view controller MVC architecture MVC is composed of three components the model which models an object in the real world the view which displays the model to the user and the controller which communicates with the user and controls the other two components 7 This type of architecture is beneficial in that it makes multiple views possible for the same model and changes can be made to the view without affecting the model and vice versa Figure 5 2 depicts the MVC architecture Controller View interacts with the user displays model to the user Model stores data related to an object Figure 5 2 The model view controller architecture In the vibration analysis tool designed here the model represents a location being monitored on the vibrating machine This model stores any information relevant to that location such as its g forces in all three axes the strokes calculated from the g forces the resulting ellipse phase its filtered and unfiltered data and so on The view
61. he total pull per machine and the maximum machine pull which are all entered by the user Additionally the resulting vibrating weight is calculated and displayed 5 A Recommendations table providing recommendations to change the stroke by changing the pull to a calculated value with a body balance of a calculated value or to change the speed to a calculated recommended RPM by changing the motor sheave OD to a calculated value 6 A table providing estimations on the expected lifetime of the machine 124 C Reports Date Wed 16 07 08 Customer test3 Machine No Bearings 2 Serial No Start Time 15h15m15s End Time 15h18m02s Eee Vibration Analysis Tool Deviation Acceptance Levels L R 8 F D 1696 Twist 596 gForce 12096 Deviations Left Right Feed Discharge RPM measured Inclination Motor Sheave OD in No Shafts 2 per Exciter Drive Inclination 30 0 DEG Recommended Machine Acceleration H 4 10 V 4 50 LDB Material Flow Legend meme 0 Dichare tra_ ves I Fee TeiPulperMaenne bsun 909 Max macine Pui tosin 09 Recommendations Estimations Existing New New Stroke L10 Setup Stroke Speed Body Balance Body Balancing Change Stroke to Or Change 0 5 in Speed To FB to DB 200m Py Changing Pull to 1095 7 RPM FB to Weight 144 2 lbs in By Changing Motor Weight 294 8 216 3 lbs in 126 6
62. hed via a wire to the vibrat ing screen Secondly acquiring data from different points on the vibrating screen at different times did not prove to be useful The purpose of vibration monitoring is to gain as much information about the screen at once and that was not the case Other reasons existed for the company s desire to replace their current solution one of which is in the method of computing the centre frequency used in the bandpass filter that was utilized in filtering the acquired data The current method was based on finding the maxima points on a signal and calculating the period of time between them The period was then inverted to calculate the frequency of the signal which was used as the centre frequency of the bandpass filter This method did not give reliable results for noisy signals and a better method was required Additionally the current hard ware was very expensive to produce and they wished to replace it with a hardware that is as efficient yet with a less expensive price Finally the company was open to 1 Introduction 3 any new ideas that could be added to the current vibration analysis tool which could improve its efficiency and possibly allow for additional features This thesis work is mainly a development of a vibration analysis tool that fits this company s needs 1 2 Thesis Objective The goal of this thesis work is the development of a complete vibration analysis application that performs at lea
63. hod described here adds is in the use of Bluetooth as the communication method rather than a wired serial connection This increases the safety of the users by eliminating the wires attaching the analyser which the user holds to the vibrating machine Download of coliected 7s vibration data to PC P Hand Held Vibration Analyzer Data Logger axial vibration readings are collect Figure 3 1 Portable machinery vibration analyser and data logger This chapter discusses the hardware used for the data acquisition as well as describe the method used to calibrate the sensor readings 3 2 Hardware Overview A prototype of the hardware used as part of this thesis work is displayed in Figure 3 2 The three main parts of the hardware are the PIC micro controller shown in Part A the Bluetooth device shown in Part B and the accelerometer shown in Part C The following three sections will detail each of these three units 3 Data Acquisition 33 Figure 3 2 Data Acquisition Hardware Prototype 3 3 PIC The PIC micro controller acts as a micro computer on the acquisition device receiving data from the sensor passing it through an A D convertor and finally sending it off to the Bluetooth device Other vital operations occur on the PIC but are not discussed as part of this thesis work The main advantages of the PIC devices are in that they offer high computational performance at an economical price as well as hi
64. i i i i 30 25 20 15 10 5 b O 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 M Freq Figure 2 7 DFT on 64 samples a the input signal with frequency equal to 3H z b DFT output magnitude Input frequency 3 4 cycles m 4 analysis frequency A 30 DFT output magnitude b 0246 8 10 12 14 16 18 20 22 24 26 28 30 req Figure 2 8 DFT on 64 samples a the input signal with frequency equal to 3 4H z b DFT output magnitude 20 2 Vibration Analysis the highest magnitude meaning it appears at the peak of the parabola where the slope is zero Therefore a better estimation of the fundamental frequency is computed by solving for the point where 2ax b 0 where a and b are defined in the parabola s equation 4 The result obtained from step 3 is multipled by the DFT frequency resolution to obtain the final estimate of the fundamental frequency 2 5 G Force RPM and Stroke Calculations Other than filtering signal conditioning approaches include integration to calculate the velocity and displacement from the measured acceleration The following sub sections will explain how each of the g force acceleration RPM velocity and the stroke displacement are calculated Please refer to Section 2 2 for the definition of each of these quantities 2 5 1 G Force The goal here is to calculate the average acceleration for each axis based on a number of sensor readings for that axis Th
65. ide static load support capacity and damping 1 e Tracking filters are any of the above filters with the added feature that the cutoff frequency or frequencies in the case of the band pass and notch filters is made to track a specified signal component In rotor vibration analysis the main application of tracking filters is when using a band pass filter and tracking its centre frequency As the machine is slowly brought up to its operating speed or brought down to shutoff its RPM is changing and is therefore tracked and used as the filter s centre frequency Based on the previous discussion it is clear that the most effective filter in terms of rotating machinery signal processing is the band pass filter The next section 14 2 Vibration Analysis discusses a specific type of band pass filter namely the Butterworth filter which is used as part of this thesis work 2 3 2 The Butterworth Bandpass Filter The most commonly used method for the design of IIR digital filters is the bilinear transformation of the classical analog filters 10 such as Chebyshev Type I and Type II the Bessel filter and the Butterworth filter This section will discuss the design of a digital IIR Butterworth filter Introduced by Butterworth 1930 the Butterworth filter is one of the earliest systematic analog filter design methods It is also one of the most widely used due to its maximally flat property The main feature of the Butterworth f
66. ilter is that its frequency response is maximally flat in the passband and rolls off towards zero in the stopband This allows frequencies to be passed without distortion or causes them to be removed completely Figure 2 5 taken from 12 displays the frequency response of a number of Butterworth filters with orders from 0 to 10 It can be seen that as the order N increases the filter approaches an ideal low pass filter When designing a Butterworth bandpass filter two quantities have to be deter mined First the filter s order and second its cutoff frequencies based on its centre frequency and bandwidth First since the current vibration analysis tool that this thesis work is an extension for uses a 4th order Butterworth filter it was decided to use the same order Higher order filters would provide a cleaner filtering however they require additional computations in order to calculate their coefficients Since such an application is performed real time and speed is a major factor there is a tradeoff when selecting the order of the filter However there exists a mathematical method for determining the minimum required order Let the filter s passband be between w frequencies greater than this are passed and w frequencies less than this are stopped Also LA filter with the property of Infinite Impulse Response This means that the filter has an impulse response function which is non zero over an infinite length of
67. is defined as follows 1 Hjw 2 5 Hju CUR 2 5 From 2 5 the Laplace Transform can be calculated as follows 1 Pc dece D 2 6 Next the poles of 2 6 are found by setting s jw 1 and solving for the values of s For a 4th order Butterworth filter normalized for w 1 the 4 poles of H s are e amp 57 8 9377 5 Figure 2 6 shows a plot of the poles of H s H s Note that the poles are equally spaced on the unit circle and those corresponding to H s appear on the left half of the s plane Figure 2 6 Poles of a 4th order Butterworth filter Finally the transfer function H s can be written as 1 H s 2 7 i s 0 7653669s 1 s 1 847759s 1 2r 2 Vibration Analysis 17 Or equivalently 1 H s 2 8 5 2796131068 4 34142135 4 26131265 1 2 8 The denominator of 2 8 is the fourth order Butterworth polynomial Comparing it to H s Y us the a coefficients of the denominator can be determined The numerator coefficients are all zeros except for by 1 Using the and b coefficients determined above a recursive IIR filter can be implemented as follows y n y x n m b m y y n m a m 2 9 L 1 M 1 m 0 m 1 Finally the Butterworth filter is updated whenever the centre frequency or band width change Every time such an update is requested the coefficients of the filter are recalculated 2 4 Fundamental Fre
68. is basically the main frame of the application which acts as a listener for the model and updates its components the waveform plots the orbit plots the FFT plots and the numerical values display based on the model As for the controller often times in such user interactive applications it ends up being the same component as the view 5 Software Design 55 Please refer to Figure 5 3 This is the case in the vibration analysis tool developed where the main frame of the application contains an options component which allows the user to adjust specific settings such as those related to the filter its bandwidth and centre frequency or select whether filtered or unfiltered data is to be displayed Other options include the selection of the g range the orientation Y vs X Y vs Z X vs Z to be displayed on the orbit plots the maximum frequency to be displayed on the FFT plots and the unit used to display the stroke values in View Controller displays model to the user Model stores data related to an object interacts with the user Figure 5 3 Alternate model view controller architecture The following section lists the main system modules and their responsibilities 5 3 Main Modules The following are the main system modules Each of these modules encapsulates some of the tasks shown in Figure 5 1 In the implementation phase each of these modules contains sub modules represented as classes 5 3 1 Reader
69. is therefore not discussed here 3 1 Overview There is a considerable variety of methods used to acquire and log vibrations The methods and corresponding products available to accomplish data acquisition tasks constitute an ever changing field that parallels the rapid advancements in PCs and workstations 1 This chapter provides a description of one such method used specif ically for the vibration analysis tool developed as part of this thesis work The most common monitored vibration signals are sound displacement velocity and acceleration The vibration signals monitored as part of the developed Vibration Analysis Tool are accelerations in the X Y and Z axes The acquisition of these signals is done through a sensor called an accelerometer and from its name measures the change in acceleration The signals are then passed through an Analog to Digital A D converter located on a PIC micro controller and finally the digitized data is transferred through a Bluetooth device to the computer on which the Vibration Analysis Tool is running 31 32 3 Data Acquisition Figure 3 1 displays the sequence of electronics that the data travels through It gets acquired by the sensors mounted on the vibrating machine then transferred to the portable vibration analyser which in our case is a PDA and finally downloaded to a PC where in depth analysis can be performed and data can be stored permanently One major feature that the acquisition met
70. k to perform the analysis 2 2 Terminology and Units The following terms are frequently used in the field of vibration analysis and are worth defining here e RPM The number of revolutions the machine performs in a minute This is equivalent to 60 x fo where fo is the fundamental frequency of the machine e Stroke The radius of the circle that the machine s main movement creates This quantity is measured in mm or inches e g Force The acceleration of the machine in a certain direction This quantity is measured in g which is equivalent to 9 8m s e Numerical Values The g force RPM stroke phase and eccentricity refer to Section 2 9 values based on the data coming from a sensor mounted to a specific location Vibration Analysis 9 e Running Frequency The main frequency of the machine also referred to as the Fundamental Frequency fo which represents the main movement that the machine was designed to have This quantity is measured in Hz e Bandwidth The range of frequencies in the bandpass filter where all the frequencies in this range are passed through the filter and frequencies outside this range are removed This quantity is measured in Hz e Sampling Rate The rate at which the data read by the sensor is sampled The sampling rate is measured in Hz e Material Flow This is the direction that the material moves It starts from the feed end of the machine and ends at the discharge end
71. lass represents a thread that is spawned when the user presses the Run button The thread is killed when the user presses the Stop button Upon its creation it is passed the handler objects whose sockets it will be reading data from and it creates a dictionary SocketsDict mapping the socket ID s to the handlers While the thread is alive it performs the following 1 Opens a connection with each one of the sockets by sending the character and read the byte echoed back to make sure it is this indicates a successful connection 2 Calls the appropriate read method fileRead blueToothRead or serialBlue toothRead according to the handler type Each one of these methods will keep calling in a while loop the method socketRead explained below with the appro priate parameters The while loop terminates when the thread is requested to be aborted via its abort method 70 6 Software Implementation Method socketRead e Inputs The socket ID a boolean value indicating whether it is a file or a bluetooth socket and the number of bytes to read from the socket e Description Reads the required number of data bytes from the socket calls the appropriate function to unpack the data see the Unpacker module sends the data to the Sensor Manager through its processData method only in multiples of four packets the bandpass filter requires that Method safeRead This method takes a socket and a number of b
72. lication shall read data coming from each of the sensor units 5 The application shall send the selected g value back to the sensor unit 6 The application shall read the battery level coming from the sensor unit 7 The application shall read the temperature level from coming from the sensor unit 4 2 2 Mode Requirements The following are requirements related to the two modes that the application can be in 1 The application shall allow the user to choose between two different modes File Simulation and Data Acquisition 4 Requirements Specification 43 2 In the File Simulation mode the application shall allow the user to a list of files to play back data from 3 In the Data Acquisition mode the application shall allow the user to choose which devices to connect to from the available bluetooth devices 4 2 3 Signal Processing Requirements The following are requirements that deal with the signal processing part of the ap plication They describe the type of calculations that need to be performed on the acquired data before it is displayed 1 The application shall perform use the sensors calibration information to cali brate the data so that it appears within the selected g range 2 The application shall pass the raw data through a DC filter prior to plotting it in order to eliminate the effect of gravity on the sensor unit 3 The application shall apply a filter on the raw data in order to eliminate noise
73. liptical plot is produced describing the machine s main movement Therefore comparing the X and the Y 2 Vibration Analysis 27 X Waveform 10 0 Y Waveform 02 0 5 08 1 0 Z Waveform 02 05 08 10 02 0 5 0 8 1 0 Figure 2 12 Waveforms generated by a vibrating machine in the X Y and Z axes waveforms allows for a method of detecting problems in the machine Waveforms can help detect faults in the rotating machine Although the wave forms will still appear to be sinusoidal even with noise faults can be detected when seeing non smooth peaks in the sinusoid After discussing such situations with ex perienced engineers in the vibration analysis filed it was determined that such ir regularities appear usually as an M or a W shape at the peaks indicating an additional frequency caused by noise This noise will usually appear as a sign of a mechanical failure such as a loose bolt Figure 2 13 which is produced from the same rotating machine that the FFTs in Figure 2 9 and the orbits in Figure 2 10 are based on depicts such a situation 28 2 Vibration Analysis X Waveform Figure 2 13 Waveforms generated by a vibrating machine with noise 2 9 Ellipse Fitting The motivation for performing ellipse fitting in our Vibration Analysis Tool is in providing a method to calculate the phase an
74. m the transmitter on the acquisition device increases 3 Testing how well the system performs at the minimum and maximum temperatures the sensor can operate at This test was not conducted but is recommended for the future 4 Testing how well the system performs at the point where the battery level approaches zero e Robustness In order to test for robustness the system was tested under unex pected conditions such as 1 Erroneous user commands This could happen when setting values through the settings menu or when assigning sensors to locations on the machine The viewer module is responsible for checking the data entered and noti fying the user of any errors 2 Erroneous data coming from the sensor units The reader module is re sponsible for checking this by parsing the data and making sure it complies with the packet structure it should be in 3 Loss of connection with the sensor units due to a bluetooth error or discon nection The system is responsible for detecting this and notifying the user while allowing the rest of the system to continue running uninterrupted 90 7 Software Testing e Portability This was tested by running the system on the platforms stated in the requirements document and ensuring it operates as expected The platforms that the system was tested on are Mac OS Windows XP and the version of Linux running on the PDA e Usability This was tested by having regular users of the
75. machines and comparing acquired data against them This will prove to be very beneficial for the company in that it will help detect problems at an early stage which will help decrease machine down time and maintenance costs Researches interested in performing feedback control on the machines can base their work on the developed vibration analysis tool A method of sending signals based on the acquired data back to the machine s motors would have to be developed and would ultimately allow for the control of the machine s behaviour Bibliography 1 9 M L Adams Rotating Machinery Vibration From Analysis to Troubleshooting CRC Press 2001 Bluetooth http www bluetooth com last visited June 7 2008 L D Paarmann Design and Analysis of Analog Filters A Signal Processing Perspective Springer 2001 Freescale Semiconductor 2 5g 10g Three Axis Low g Micromachined Accelerom eter 2007 MMA7261QT W Gander G H Golub and R Strebel Least square fitting of circles and ellipses BIT vol 43 pp 558 578 1994 D Gerhard Pitch extraction and fundamental frequency History and current techniques Tech Rep TR CS 2003 06 Department of Computer Science Uni versity of Regina 2003 C Ghezzi M Jazayeri and D Mandrioli Fundamentals of Software Engineering Prentice Hall 2002 L Kim A Review of Rolling Element Bearing Health Monitoring Engine Labo ratory Division of Mecha
76. manufacturer of the vibrating screen TYCAN Vibration Analysis Figure C 3 Example of a tuning report
77. n the stub or they can be read from a file or asked to be inputted by the user Drivers on the other hand simulate the use of the module being tested The driver sets the values of the data as it would be set in the real application by the missing modules In general unit testing allows for verifying the correctness of the system s func tions In order to verify the system s software qualities system testing is performed 7 3 System Testing System testing involves testing the system as a whole and is often referred to as Testing in the large When performing system testing the method of separation of concerns should be employed in order to design test cases that will test various aspects of the system reflecting the system s requirements document It is important to verify 7 Software Testing 89 all the software qualities meaning that not only should testing address compliance with the functional requirements but also with non functional requirements such as performance robustness and usability The following is a discussion of some software qualities and how they were tested e Performance In order to test for performance the system was tested under peak conditions The most important tests here are 1 Testing the system when communicating with eight sensors at once which is the maximum number of sensors the system can communicate with 2 Testing how well the bluetooth receiver performs as its distance fro
78. nclude filtering Fast and Fourier Transforms Plots are then generated in order to monitor the machine s behaviour Additionally the unfiltered data is logged into a file which allows for playing it back for a more in depth analysis in the future The application also provides a reporting system that generates reports providing a summary of the machine s behaviour and recommendations for adjusting the machine in order to obtain a better performance This application provides the company with a reliable and practical way of mon itoring their machines and acts as a solid base for future research that could involve diagnostics and control ill Acknowledgements I would like to thank my supervisor Dr von Mohrenschildt for his guidance and support over my graduate studies period Also the co operation of the engineers at the company the software was developed for as well as the company s financial support as part of an Industrial NSERC scholarship is greatly appreciated Jay Parlar who is a fellow graduate student working on a Ph D thesis related to this work provided a large amount of suggestions and support throughout the implementation phase of the project and I would like to acknowledge him for that Finally I would like to gratefully thank my husband Majd for his love and tremendous support as well as my family members for their continuous encouragement iv Contents Abstract ili Acknowledgements iv 1 Introduction 1
79. nctions they access and their technical expertise Mainly the users will either be technicians acquiring data on site or expert engineers who would like to look at the acquired data more in depth and produce the reports containing recommendations to the client Based on that the tool will have to be designed in such a way that allows the technicians to acquire data easily at the same time allowing expert engineers to access more detailed functions Such detailed functions include adjusting the filter parameters changing the predefined acceptance levels used in the reports adding additional bearings with new diameters and producing the final reports after making certain expert decisions 4 Requirements Specification 41 4 1 2 User Documentation In addition to the Vibration Analysis Tool software user documentation is provided This documentation is in the form of a user manual detailing the various functions in the tool and how they are used In addition the user manual explains how the various plots are to be read and how the reports are to be generated and interpreted 4 1 3 Assumptions The following is a list of assumptions that the design of the Vibration Analysis Tool is based on 1 The tool shall only connect to at most eight sensor units at a time 2 The sensor units must operate normally at any temperature between 40 and 50 degrees Celsius 3 The sensor units must operate normally under the circumstances expec
80. nd the strokes based on the filtered data it receives from the Viewer module The computed values are then sent back to the Viewer module so that they can be stored in the Sensor Manager modules and displayed on the numerical values display 5 3 9 Ellipse Fitter The Ellipse Fitter module is responsible for performing an ellipse fitting on the filtered data it receives from the Viewer module Additionally it is responsible for computing the phase and eccentricity of the ellipse and sending these two parameters back to the Viewer in order to display them on the numerical values display and store the phase parameter in the Sensor Manager modules for the report generation 5 3 10 Report Generator The Report Generator module contains three sub modules each responsible for gen erating a different type of report The Single Point Report module which generates a report for each monitored location on the machine the Orbit Summary Report which generates a summary report for all the monitored locations and the Tuning Report which based on certain parameters entered by the user generates a report containing recommendations for tuning the machine in order to achieve better performance 5 4 Main Module Interaction Figure 5 5 illustrates how the main modules discussed above interact It is worth mentioning here that the Viewer module which is basically the user interface also receives events from the user such as initiating or stopping the acq
81. ng of the reports if they have already been created and the creation of reports otherwise The application shall generate reports in the formats predetermined by the client The application shall include a header section on each of the reports with the customer machine date and time information as well as the company logo 4 3 Nonfunctional Requirements An application s non functional requirements are those not related directly to its be haviour but are more concerned with its properties or characteristics The following are the non functional requirements that have been found to be related to the Vibra tion Analysis Tool 4 3 1 Performance Requirements Performance requirements are most important in hard real time systems where failing to meet a time requirement causes the entire system to fail This is not exactly the case in vibration analysis since not meeting a deadline will not cause a system failure 4 Requirements Specification 49 however it may cause unreliable data For this reason the following requirements are necessary 1 The application shall generate plots and display data read from the sensor at a frequency defined by the user and not exceeding 1000Hz 2 The application shall log all data read from all sensors 4 3 2 Platform Requirements The following are requirements related to the operating system and devices that the application will run on 1 The application shall
82. ng to the data acquisition Class DeviceDiscovery Panel Provides a panel that displays the discovered bluetooth devices allowing the user to select the ones they would like to connect to and assign them locations and orientations Class MainFrame Two kinds of main frames exist a Main File Frame created in File Simulation mode which allows for the opening of files and a Main Sensor Frame created in Data Acquisition mode which allows the connection to sensors and the recording of data 74 6 Software Implementation Class AcceptanceLevelsPanel A panel that allows for the setting of the acceptance levels used in the tuning report generation Class BearingsPanel A panel that allows for adding new bearings and their diameters which are then used in the tuning report generation Class InfoPanel A panel that is part of the main frame and consists on a common info panel and a sensors info panel as described below Class CommonInfoPanel A panel that provides the acquisition information customer data etc as well as buttons for connection starting stopping starting recording and stopping recording Class SensorsInfoPanel A panel that provides information about the sensors their locations battery and tem perature readings as well as buttons for generating the reports in data acquisition mode and exiting and restarting the application Class FFTPanel A panel that encapsulates the
83. nical Engineering National Research Council Canada 1982 R G Lyons Understanding Digital Signal Processing Prentice Hall 2004 97 98 BIBLIOGRAPHY 10 T W Parks and C S Burrus Digital Filter Design New York Wiley 1987 11 P L Rosin Further five point fit ellipse fitting in British Machine Vision Conference 1999 12 I W Selesnick and C S Burrus Generalized digital butterworth filter design IEEE Transactions on Signal Processing Vol 46 No 6 June 1998 13 SparkFun http www sparkfun com last visited June 7 2008 14 G Thomas M Simpson R D Winton and S D Robinson System analysis of rotors supporting structures and their foundations tech rep Structural Dynamics Research Corporation 1982 15 K Tuck Implementing auto zero calibration technique for accelerometers Tech Rep AN3447 Freescale Semiconductor 2007 Appendix A User Manual This appendix serves as a guide for the user on how to use the vibration analysis tool A 1 Start Up Upon starting the application you will be asked select their language of preference as in Figure A 1 Once the you have selected your language from the drop down list press the Done button Next you are asked to select the mode you would like to start the application in as in Figure A 2 Choose File Simulation if you would like to play back previ ously acquired files or choose Data Acquisition
84. om each of the sensors The application shall display the stroke in all three axes for each of the sensors as well as the average stroke The application shall display the g force in all three axes for each of the sensors as well as the avergae g force The application shall display the phase and eccentricity after performing the ellipse fitting on each of the sensor locations The application shall display the information related to the acquisition This includes the customer the machine model the date the start and end times and the number of bearings 4 2 6 Graphical User Interface Requirements The following are requirements pertaining to the Graphical User Interface and de scribe the types of menus controls and messages that are to be used 46 4 Requirements Specification 10 11 The application shall allow the user to choose the g force the machine is oper ating on The application shall allow the user to pick a sensor to display its enlarged orbit plot FFT plots and waveform plots The application shall allow for the pausing and resuming of the data display The application shall allow for initiating and stopping the recording of the data The application shall allow for the adjusting of the filter bandwidth The application shall allow for the adjusting of the FFT frequency range The application shall allow the user to change the orientation of the orbit plots
85. operate on Linux for the PDA application and Windows for the PC application 2 The application shall run on both a PDA device selected by the client as well as a PC laptop or desktop with no less than a 12 display 4 3 3 Safety Requirements Since the vibration analysis tool is not a safety critical application not many require ments exist in terms of safety The following is a requirement on the connection with the sensor units 1 The application shall connect to the sensor units via bluetooth This will allow for a wireless connection that increases the safety of the person acquiring the data since they will no longer be holding a device that is connected by a wire to the vibrating machine 4 3 4 Maintainability Requirements The maintainability requirements focus on both the maintenance of the application as well as the ability of adding features later on 50 4 Requirements Specification 1 The application shall be designed in a manner allowing for easy maintenance as well as in an easy way to add features in the future 4 3 5 Reliability Requirements Informally a software is reliable if the user can depend on it 7 The reliability in the vibration analysis tool comes from the reliability of the data being read The following are requirements concerning the reliability of the application 1 The application shall read the data coming from the sensor in a reliable manner meaning that data shall n
86. ot be dropped or misread 2 The application shall produce reliable plots as determined by the engineers at the company 3 The application s signal processing calculations shall deliver reliable results as determined by the engineers at the company 4 The reports produced by the application shall contain reliable results as deter mined by the engineers at the company 4 3 6 Usability Requirements A software system is usuable if its human users find it easy to use 7 As discussed earlier more than one type of users may be using the application and therefore the application should be usable for every type The following are requirements on the usability of the application 1 The application shall have a Graphical User Interface GUI and shall use con trols that allow the user to access its various functions 2 The application s interface shall be easy to use as determined by its various types of users 4 Requirements Specification 51 3 The application shall allow for the display of text on labels button etc in any of the predefined languages 4 The application shall use fonts that are legible to an average user 5 The application shall use colours that convey meanings to the user while main taining the look of the application 6 The application shall use consistent colours fonts and designs Chapter 5 Software Design 5 1 Overview The step after the requirements specification o
87. oth discussed in this section Founded by the mathematician Joseph Fourier in the early 1800s the Fourier Transform s idea is that a function e g a time domain based signal in the case of vibration analy sis can be constructed from a summation of sinusoidal functions with a continuous distribution of frequencies from zero to a suitable cutoff frequency Based on that transforming a signal into the frequency domain will identify all the components that contribute in creating that signal This in turn helps identify sources of noise and or frequencies that are caused by any damage in the vibrating object In additon to the Fourier transform there is a simple but more restrictive version called the Fourier 22 2 Vibration Analysis series The Fourier series method is mostly used for periodic repeating signals and works by summing sinusiodal componvbents only at a discrete set of frequencies which are integer multiples of a specified base frequency 27 t where t is the du ration of the signal s period The problem with the Fourier series in the case of machinery vibration is that the frequencies are often not all integer multiples of a single frequency this is why the Fourier transform proves to be more effective 2 6 1 Fast Fourier Transform The FFT algorithm was developed in the mid 1960s as an effective means for quickly mimicking the frequently changed radar signal spectrum of enemy ground based an tiaircraft missile targetin
88. quency Estimation Fundamental Frequency estimation is a popular topic in many fields of research The need for detecting the fundamental frequency in vibration signal monitoring is in the calculation of the rotating machine s RPM as well as in determining the centre frequency for the utilized bandpass filter Many techniques exist for estimating the fundamental frequency of a signal but not all perform well when there exists noise in the signal In 6 various methods are suggested for pitch detection which is the same as fundamental frequency detection both in the Time Domain and the Frequency Domain Since in this thesis work the FFT is calculated in order to perform the FFT analysis as described in 2 6 in the interest of speed the calculated FFT can be used to estimate the fundamental frequency The FFT is an implementation of the DFT Discrete Fourier Transform which is one of the two most common and powerful procedures encountered in the field of digital signal processing Digital filtering is the other 9 Let f be the sampling 18 2 Vibration Analysis frequency that the data is sampled at and N be the number of samples that go through the DFT Then the DFT equation is given by N 1 X m S DR pee 2 10 n 0 Or in rectangular form N 1 X m y x n cos 2rnm N jsin 21nm N 2 11 n 0 This shows that each DFT output term is the sum of the term by term products of an input time domain sequence with sequences
89. r feature detection signal noise removal and data compression 1 Currently marketed machinery monitoring systems do not typically utilize wavelet transforms but it is believed that the capabilities of next generation machinery mon itoring systems will be considerably advanced by their use once wavelets and their advantages mainly in vibration based trouble shooting are familiar to machinery vibration engineers 1 Therefore wavelet transforms are not a part of this thesis work but are left as suggested future work 2 7 Orbit Analysis An Orbit is the two dimensional depiction of the machine s movement Orbits are in fact projectiosn of the phase plots on to the XY XZ and YZ planes Hence a machine with three degrees of freedom in the X Y and Z directions will produce three different orbits Once the data is acquired two types of analysis related to the orbits can be performed First by plotting the data visual analysis can be performed on the machine s movement When using a filter as described in Section 5 of this chapter plotting the orbits of the filtered data as well as the orbits of the unfiltered data helps analyse the filter s performance which in turn aids in adjusting the filter s parameters e g it s bandwidth and centre frequency in order to reach a point where it is performing as required Figure 2 10 displays an orbit produced by the same rotating machine producing the FFTs in Figure 2 9 Part a displays t
90. r in the computations performed in the vibration analysis application 8 2 Types of Errors Since the units that are used for data acquisition are composed of more than one type of electronic device and each device has its own resolution the constructed acquisition device will have a margin of error on the values sent from it through bluetooth The following is a list of sources of error caused by the different electronic parts used in the acquisition device 1 Error on the source voltage caused by the change in temperature The source voltage changes by 50 x 107 Volts for every degree Celsius change in the tem perature 91 92 8 Error Analysis The 12 bit A D convertor has its own resolution given by A D luti Source Voltage 3 3W 3 3 1000 mV resolution A D range oe 4096 0 8057 mv bit 8 1 This value is fixed for a fixed source voltage of 3 3V Electric error causing around 3 bits of inaccuracy on the A D convertor read ings This is noticed when monitoring a stable readings and noticing that its values fluctuate around the reading within a 3 bit range The sensor has a different resolution range for each one of the g levels that it can operate on Table 4 displays the 4 ranges and their corresponding resolutions G Range Resolution 25g 480 36 mV g 3 9 8 360 27 mV g 6 7 8 180 13 mV g 100g 1204 9 mV g Table 8 1 G ranges and their resolutions Tempera
91. r module Its run and stop events are synchronized with those of the Reader and Viewer modules 5 3 3 Viewer The Viewer module acts as both the view and the controller in the MVC architecture As the view and based on a timer that issues events it updates the waveform orbit and FFT plots as well as the numerical values display and the options panel e g the maximum value allowed for the bandwidth setting with the most recent data stored in the Sensor Manager modules As the controller it receives information from the user when changing settings in the options panel and updates the Sensor Manager modules accordingly Such information includes the bandwidth and the centre frequency used for the filter Figure 5 4 illustrates on the right the main loop of the Viewer module which is synchronized with the Reader and Sensor Manager modules on the run and stop events It is also worth noting that this is the only module that contains GUI related functionality which is abstracted away from all other modules 5 3 4 Logger As its name implies the Logger module s responsibility is in logging the data This module has been kept separate in order to facilitate for changes in the future which might include changes in the method data is logged The Logger module exists only 58 5 Software Design for data that is being read directly from the sensors One Logger module exists for each sensor handler object 5 3 5 Calibrator The Calibr
92. rance can be changed 2 RPM Tolerance This is the tolerance on the RPM measured in RPM used to determine whether or not the system has reached a stable point and recording of the data can be allowed Figure A 9 displays how this tolerance can be changed 3 Update Frequency This parameter defines how frequently the plots are updated with the data It is measured in seconds As its value increases the plots are updated slower This parameter can be changed as in Figure A 10 4 Update History This parameter defines the size of data the be plotted on every update As this size increases more data is being plotted in the past A User Manual Apes 005 00S L JU DP EVA EE CH acea nue ule 0 xoeg 2H besa xew 144 sepu i PONENS f sa e WN 340S ZH upimpueg renen O ct A 8 anog bay ueg ZH Acuanbasy anueo 50r 9 22 90 A SAZO EO Pvalun x s zO os 70 PaA X AQ pales 9 METE uoneiueuo jeuuo 1001 sisfjeuyIB N V 2 A L UOHEJQIA Figure A 7 Main view of Data Acquisition Mode 108 A User Manual Enter frequency tolerance in Hz A Figure A 8 Centre frequency tolerance setting Enter RPM tolerance in RPM A C Cancel GOK Figure A 9 RPM tolerance setting Enter the time used to update the plots in seconds C Figure A 10 Update frequency setting 110 A User Manual 5
93. reated and every time its bandwidth or centre frequency change when its update method is called the filter coefficients need to be computed Other helper methods exist as part of this class and are mostly based on the butterworth filter code provided by http www exstrom com journal sigproc index html Class DC This class is implemented in C to increase performance Its calc method applies a de filter to the incoming sample z as follows y n a n x n 1 4 R y n 1 6 6 where R is a constant value between 0 9 and 1 and depends on the sampling rate and the low frequency point 6 4 7 FFT Computer Uses numpy Method getFFT e Inputs Sequence of data to perform FFT on sampling rate e Description Peforms the following 1 Applies an FFT computation on the given data to obtain the frequencies and their absolute values 2 Calls polynomialInterpolation on the three values representing the abso lute values of the frequenxy with the highest absolute value and the two frequencies surrounding it 6 Software Implementation 79 3 Computes the fundamental frequency as follows fund freq max index 2 interpolant correction 6 7 where max index is the index of the frequency with the maximum absolute value interpolant is the result of polynomialInterpolation correction samplerate data length 4 Computes the RPM as follows rpm fund freq 60 e Outputs RPM frequencie
94. resented by f x 0 001676z 3 53 with a standard deviation of 0 0198 as displayed in Figure 3 3 0 5 zl 1400 1600 1800 2000 2200 2400 26002800 Figure 3 3 Best fit line for x axis measurements under 2 5 g mode Finally it is important to note that the suggested method for calibration does contain errors that will be discussed in Chapter 8 A more precise measurement approach can be employed such as building a testing rig that can operate on the 4 predefined g sensitivities The sensors can then be calibrated on the testing rig in order to obtain the readings required for all three axes One more point that should 38 3 Data Acquisition be noted is the effect of the temperature on the readings Chapter 8 will explain that more but it is important that the sensors be calibrated at various temperature ranges The temperature ranges can be defined by experiment and the temperature sensor built into each unit can be used to obtain the surrounding temperature during the calibration Chapter 4 Requirements Specification This chapter explains the requirements on the vibration analysis tool that is designed and implemented as part of this thesis work The requirements represent a contract between the developer and the client and are used throughout the software life cycle 4 1 Overview The vibration analysis tool that is designed and implemented as part of this thesis work has many functions Its main functions are
95. rs reflecting when appropriate the software design life cycle Chapter 2 introduces the field of vibration analysis and discusses the various methods that are practised when applying it Chapter 3 discusses the hardware used for acquiring data prior to performing the analysis on it as well as an explanation of the method used for calibrating the sensors used for the acquisition Chapter 4 acts as a requirements document for the developed vibration analysis system discussing both the functional and the non functional requirements of the system Chapter 5 serves as a software design document explaining the design decisions made as well as the design architecture used It also lists the software modules that the application consists of along with a description of how they interact Chapter 6 describes the implementation of the vibration analysis tool including the classes constructed in the implementation phase and how each one of these classes is implemented Chapter 7 discusses the testing stage of the developed tool Chapter 8 is a discussion of errors that affect the data and their tolerances Chapter 9 is a summary of the thesis work along with some suggested future work Appendix A is a user manual explaining how to use the application Appendix B explains the method of internationalization and the steps that need to be taken in order to apply it on a new language Appendix C contains the three different types of reports generated by
96. s ing it the current centre frequency for the appropriate axis as well as the current bandwidth value which is set by the user Method timeoutError This method is responsible for notifying the viewer that the bluetooth handler associated with this sensorManager object has timed out causing it to display an error message to the user Other methods exist representing setters and getters for the module s attributes 6 4 3 Viewer Since two applications have been developed to run on a PDA and on a PC and in order to make the code as reusable as possible all of the modules except for 6 Software Implementation 73 the Viewer module have been kept common between the two applications The Viewer module contains implementation related to the graphical user interface which is the only aspect that differs between the two applications Therefore two modules named PC_viewer and PDA_viewer have been implemented both inheriting from a module named base_viewer which includes the classes and methods that are common between the two applications The following are the classes that each viewer module is composed of Class LanguageSelectionPanel Provides a panel for selecting the language that is to be used Class ModeSelectionPanel Provides a panel for selecting the mode to start the application with File Simulation or Data Acquisition Class InfoGatheringPanel Provides a panel for the user to enter information pertaini
97. s frequency gains fundamental frequency Method polynomialinterpolation e Inputs 3 points to perform interpolation on e Description Peforms the following 6 8 1 Given the three points performs a polynomial interpolation on the poly nomial given by az br c 0 6 9 by solving for the point where the slope is zero this will give the frequency with the highest absolute value 2ar b 0 or equivalently x b 2a 6 10 6 11 The point x then is the point at the peak of the polynomial curve where the slope is zero e Outputs interpolant 80 6 Software Implementation 6 4 8 Numerical Values Computer Method getGForces e Inputs three lists of data x f y f and z f representing the filtered values in the x y and z axes e Description Computes the g forces as follows 1 Finds the minimum value for each axis 2 Finds the maximum value for each axis 3 Averages the minimum and maximum values for each axis 4 Computes the main g force as follows Main g force maxz 4 x y for x z f andy y f 6 12 e Outputs Average g forces for x y z axes and main g force Method getStrokes e Inputs RPM Average g forces for x y and z axes and main g force e Description Computes the strokes as follows 1 For each axis the stroke in mm is calculated as follows axis g force Stroke 6 13 OSE 1000 2 x RPM 60 HS 2 Computes the main
98. s is dependant on the fft_size parameter which can be set through the settings menu FFT size then the performFFT method is called frequency Check This method is responsible for checking when the centre frequency used for the band pass filter changes requiring the filter to be updated in order to obtain new coefficients The check relies on a frequency tolerance value which can be set in the settings menu using the Frequency Tolerance command Method applyFilters This method is responsible for applying the filters on the raw data producing the filtered data which is then stored in a circularqueue data structure named fil tered_storage 72 6 Software Implementation Method performFFT This method is responsible for requesting FFT computations on raw data in order to obtain the and store the following 1 The RPM values for all three axes 2 The frequencies and their absolute values which are later used by the Viewer module for plotting the FFT plots 3 The fundamental frequency for each axis used as the centre frequency for the bandpass filters This method also checks whether the system has stabilized or not allowing the user to start recording the data The condition for stability is dependant on an RPM toler ance value which can be set in the settings menu using the RPM tolerance command Method updateFilter This method is responsible for requesting an update on the bandpass filter by pas
99. s of testing schemes are conducted White box testing and Black box testing White box testing also referred to as structural testing uses the internal structure 87 88 7 Software Testing of the program to derive test data It tests what each module is actually doing For example white box tests may include testing loops to make sure they are finite testing if statements to make sure that all possible conditions are covered testing try except statements to make sure that appropriate exceptions are caught and so on Black box testing also referred to as functional testing does not deal with the internal structure of the module It tests what the module is supposed to do meaning it is based on the program s specification rather than its structure A method of applying black box testing is by categorizing input data that is then passed to the module and comparing the observed results against the expected ones As in many of the vibration analysis tool modules modules sometimes use other modules and therefore testing them requires information from the modules they use For example if a module uses an operation that is part of another module this operation needs to be simulated in order to test the original module In cases like this stubs and drivers are used Stubs are used to simulate a procedure with the same inputs and outputs as the missing procedure but with a simplified behaviour For example values can be hard coded i
100. s thesis work is part of this advancement We were approached by a company that produces vibrating screen machinery which is used mainly in the field of mining Figure 1 1 illustrates a portion of the types of machines produced along with their resulting motions Two main motions are produced circular and horiztonal based on the application the machine is used in As the cut size of the vibrating screen increases its amplitude increases as well Low cut size low amplitude machines are typically used for dry screening of fine materials such as lime chemicals fertilizers sand and have very high frequencies Whereas high cut size high amplitude machines are used for course materials such as coal and phosphate rock and can rotate at speeds as high as 1050 RPM The company had an existing vibration analysis tool which they wished to im prove The existing setup was such that only one part of the vibrating machine could be monitored at once The three axis accelerometer which would acquire the vibra 2 1 Introduction Oke Motion E w gt Cut Size Figure 1 1 Types of machines produced and their motions tion data from one point on the vibrating screen was connected through a wired serial connection to a laptop which had the vibration analysis tool on it The company s desire to replace this setup was for two reasons First and foremost for the safety of its technicians who would have to carry a laptop attac
101. software use the sys tem and obtain feedback from them regarding the usability of the system Both engineers and technicians who would be using the software regularly were in terviewed and their input on the usability of the developed software application was taken into consideration Finally both in lab and on the field tests were conducted in order to test the software system as a whole In the lab a calibration unit vibrating at a known frequency was utilized in order to test the system on a small scale This unit helped in verifying that each of the sensor units was working properly On the field multiple sensors were attached to different types of machines that the company produces and data was acquired After that reports were generated and their results were compared to results produced using the company s current solution This is also referred to as Parallel Testing Additionally we were provided with a large amount of data files containing vibration data that the company had acquired with their previous system These files were played back using the File Simulation mode in our tool and their numerical results such as resulting RPM stokes g values etc were compared to the results generated by our tool which helped increase our confidence level in it Chapter 8 Error Analysis 8 1 Overview This chapter discusses the various sources that can cause an error in the readings obtained by the data acquisition devices o
102. st the following e Obtain readings from the acquisition device introduced in Chapter 3 e Perform signal conditioning on the obtained readings This includes but is not limited to applying filters on the data performing calculations to obtain numerical values such as RPM stroke and acceleration and running an FFT Fast Fourier Transform on the data e Produce plots for each of the monitored locations representing the 2 dimensional motion acquired from a specific location the waveforms representing the signals coming from each of the individual axes and the frequency spectrum produced from applying an FFT on the data e Log the data and allow for playing it back in the future e Generate three types of reports Single point for each of the locations moni tored Orbit report a summary of all monitored locations and Tuning report providing recommendations to tune and adjust the machine 1 3 Thesis Contributions The main contribution of this thesis work is in developing a vibration analysis tool that can be used in wirelessly monitoring multiple locations on a vibrating machine at once and producing reports that provide recommendations for adjusting the machine The 4 1 Introduction developed tool allows researchers and engineers to conduct work in order to diagnose certain machine faults and to ultimately control the machine s behaviour 1 4 Thesis Overview This thesis is divided into the following chapte
103. sults produced by the vibration analysis application 3 Ellipse Fitting The accuracy of the phase angle and the eccentricity values generated based on fitting the data to an ellipse depends highly on the number of values the fitting is performed on As the size of the data used increases the more accurate the ellipse fitting result becomes but the more expensive the computation will be Chapter 9 Conclusion 9 1 Discussion The focus of this thesis work has been on the development of a vibration analysis tool that can be used specifically in the field of mining We believe that the developed tool has fulfilled its specified requirements Firstly it communicates wirelessly with data acquisition units which pick up data through acceleration sensors It can communicate with a maximum of eight units at once providing synchronous readings as opposed to most data acquisition methods which require acquiring data from one point of the machine at a time Secondly signal processing is applied on the acquired data The method for computing the centre frequency for the bandpass filters used to filter the noise from the signals is determined through a high precision method The method is based on performing an FFT computation on the data and thereafter performing an interpolation around the frequency with the highest amplitude bringing the result as close as possible to the actual fundamental frequency of the machine Of course the accuracy of
104. t with the language s abbreviation 4 Inside the new language folder create an LC_MESSAGES folder 5 Copy the messages pot file from the gui folder and paste it in the new LC_MESSAGES folder 6 Rename the file gui xx po where xx is the language abbreviation for the new language being added 7 Perform the steps required for editing the translation file as in Section B 1 B 3 Adding new strings to the source code If new translatable strings are added to the source code perform the following to translate them 118 B Internationalization Make sure they appear between _ For example This is a translatable string Open the app fil file under the gui folder and make sure that the python modules with the new translatable strings are added to the file On the command line go to the gui folder and run python mkil8n py p This will create a new messages pot file with the new string s added to it For each language open its po file using Poedit and then select Update from pot catalog and choose messages pot This will update the po file with the new strings Perform the steps required for editing the translation files as in Section B 1 to apply the translation to the added string s Appendix C Reports C 1 Single Point Report Figure C 1 is an example of a single point report The report includes the following 1 An orbit plot with the
105. ted at sites where the analysis is performed 4 The sensor units must detect g forces anywhere between 0 g and 10 g with a resolution of 0 01 g 5 The sensor units must have the capability to read the battery level on the unit and send it to the computer with the vibration analysis tool 6 The sensor units must have the capability to read the temperature level sur rounding the unit and send it to the computer with the vibration analysis tool 7 The sensor units must allow for the changing of the g select upon receiving a command from the computer with the vibration analysis tool 8 Data on the sensor unit is to be sampled at a rate of 1000Hz 9 The PDA interface is designed for a specific PDA 42 4 Requirements Specification 4 2 Functional Requirements An application s functional requirements are those describing its behaviour and are most likely implemented as functions in the implementation stage The following are the functional requirements related to the Vibration Analysis Tool The requirements and have been separated into sections based on the feature they deal with 4 2 1 Communication Requirements The following are requirements pertaining to the communication with the sensor units 1 The application shall discover all available sensor units within the range of the bluetooth device 2 The application shall connect to the selected devices 3 The application shall read each device s ID 4 The app
106. the start and the end pointers accordingly 86 6 Software Implementation Figure 6 1 An illustration of the circular queue data structure e get This method receives a length n of data points to send back It creates a getting pos pointer which will point to the last data point to read which is n points away from the end It sends back three separate lists of data for each one of the axes The data sent back is always the most recent n data points Chapter 7 Software Testing 7 1 Overview Software verification is the final step prior to the delivery of the software Verification of a software product involves all the activities that are undertaken to ascertain that the software meets its objectives 7 One such activity is testing Testing involves developing test cases or scenarios with specific inputs that the program is then run with in order to gain confidence about the quality of the software The approaches taken in order to test the vibration analysis tool developed here are discussed in the remainder of this chapter 7 2 Unit Testing Experimental data from industrial projects have shown that the cost of removing an error after the software has been developed completely is much higher than if errors are eliminated earlier 7 This is where unit testing proves to be very useful Unit testing often referred to as Testing in the small addresses the testing of individual modules When testing each module two type
107. this case the location battery and temperature values will not appear as they are not available in the old files and report generation is disabled Upon opening a file or a directory you will need to press the Connect button which will prepare to start simulating from the files Upon connection you will see File ready in the status bar press the Run button to start playing back the data as in Figure A 4 You can press the Stop button anytime to end the playback Additionally while the playback is stopped you can add additional directories to playback This is particularly useful if data had to be acquired on two separate acquisitions due to a lack of functional sensor units for example and the user would like to play back the data simultaneously since it was coming from the same machine This can be done by accessing the File menu and selecting the Add Directory option You will then need to press the Connect button again before running the simulation A 3 Data Acquisition Mode Upon choosing Data Acquisition you will be transferred to a window where you will enter information relating to that particular acquisition as in Figure A 5 While you are entering this information the available bluetooth devices will be detected Once the detection is complete the Done button will be enabled Once it is enabled press it to proceed to the next step The next window will display the dete
108. this method depends highly on the size of the data points passed to the FFT computation It is also worth mentioning here that the current version of the vibration analysis tool computes the fundamental frequencies based on the data acquired from all the used sensors This ensures that each location s data is being filtered with a bandpass filter centred at the fundamental frequency coming from 94 9 Conclusion 95 that location However if the performance of the tool becomes of importance and since an FFT computation along with the interpolation are expensive operations the performance can be boosted by obtaining a fundamental frequency estimation from one sensor only This estimation can be safely employed since the machine s fundamental frequency should be the same on all its parts If a significant noise occurs on one of the parts causing its fundamental frequency to change it will affect the remaining parts changing the overall fundamental frequency Lastly the vibration analysis tool developed provides reports that are used to tune and adjust the machines in order to increase their performance and lifetime We believe that this tool will prove to be very beneficial in the mining industry especially due to its wireless communication method which is a fairly new method in this field Soon all vibration analysis tools used in the mining field will need to allow for wireless communication The Mine Safety and Health Administration d
109. tion 2 8 Therefore what is being plotted are two functions versus each other where their values are in the form x Asin at y Bsin bt 2 16 The appearance of the curves is highly senstive to the ratio a b When a b the resulting plot is an ellipse which is the normal case in vibrating machinery As the 26 2 Vibration Analysis Frequency Frequency a b N X t 2N y ia es Frequency Frequency c d Figure 2 11 Filtered orbits and FFT for a rotating machine with increasing misalign ments 1 ratio increases curves as in Figure 2 11 are generated indicating mechanical faults in the machinery Second mathematical analysis is performed by calculating the phase angle of the orbit in rotating machines the orbits are usually elliptical as well as the eccentricity of the orbit Sections 8 and 9 in this chapter explain more on how this is done 2 8 Waveform Analysis Another useful tool in vibration analysis is plotting and visually analysing the wave forms A waveform is the signal produced by plotting the data in a certain axis against time In rotating machinery the waveforms in general appear to be sinusoidal Figure 2 12 depicts a waveform generated by a rotating machine It is clear from Figure 2 12 that the X and Y sinusoids are symmetric like a cosine and a sine wave in a sense that when plotting the Y values versus the X values producing the orbits from the previous section an el
110. ture noise on the sensor It is important to note that Table 4 repre sents the resolutions when the temperature is 25 C and the source voltage is 3 3V However any change in temperature will also add an error on the sensor readings and this is given by 0 03 C The temperature sensor itself has an accuracy range between 2 C and 43 C when the temperature is around 25 C Please refer to the temperature sensor datasheet that can be found at http cache national com ds L M L M60 pdf for more information RMS noise on the sensor Equivalent to an error of 4 7 mVrms Refer to the sensor data sheet Power Spectral Density RMS noise on the sensor Equivalent to an error of 350 ug v Hz Refer to the sensor data sheet 8 Error Analysis 93 The following are the sources of error that affect the results produced by the vibration analysis software sampling rate data length As the length of the data passed to the FFT function increases the resolution 1 FFT Resolution This is equivalent to decreases giving a more accurate fundamental frequency and therefore RPM result This resolution parameter is also refered to as the FFT bucket or bin size It is important to keep in mind that the data length should be a power of two in order to perform the FFT computation 2 Calibration As discussed in Section 3 6 the method used to calibrate the values read from the sensor units will highly affect the accuracy of the re
111. uch applications Prior to filtering the digital data once acquired and before passing it through the Analog to Digital AD convertor low pass analog filtering is inserted ahead of the AD converter to avoid aliasing Aliasing causes the reflection into the lower end of the spectrum of high frequency content that is above the sampling rate capability of the AD convertor 1 Therefore the low pass analog filter should have a cutoff frequency sufficiently below the Nyquist frequency which is I the sampling frequency The reason that the cutoff frequency of the analog filter has to be substantially below the Nyquist frequency is because no analog filter has a perfect frequency cutoff i e it has its rolloff above the cutoff frequency 1 On the digital side filters that are used commonly with vibration signals are low pass high pass band pass notch and tracking filters The following is a brief description of each of these types e Low pass filters are the most signal conditioning tool used in handling vibrat ing machinery signals 1 A low pass filter works by attenuating signal content above a specified frequency the cut off frequency and passing the signal con tent below it Since for routine rotating machinery vibration analysis frequency components above ten times the spin speed are usually not of interest 1 the low pass filter meets the requirement e High pass filters work in a way opposite of the low pass filters Si
112. uisition or sim ulation which correspondingly initiates or stops the Reader and Sensor Manager modules main loops Such events have not been included as part of the diagram and only the data transferred between the modules is shown 60 5 Software Design Module A uses services provided by Module B Figure 5 5 Module interaction diagram Chapter 6 Software Implementation 6 1 Overview This chapter discusses the implementation phase of the vibration analysis tool s Ilfe cycle It starts by a section discussing the considerations taken throughout the im plementation phase to ensure the development of a high quality software Then it lists the software libraries that were used as part of the implementation Afterwards the implementation of the main software modules discussed in Chapter 5 along with some helper modules is discussed 6 2 Implementation Considerations The following software qualities were considered throughout the implementation phase e Portability A software is considered portable if it can run on different envi ronments The software was developed using the Python programming language along with some libraries explained in Section 6 3 which are all guaranteed to run on both Windows and Linux platforms as requested by the company More over the software is portable in that it can run on different hardware as well on the PDA and on a PC 61 62 6 Software Implementation e P
113. ults button to preview the results that would show up in the report if they were to generate it This gives the experienced user the chance to adjust the parameters in order to come up with the best results Additionally the g values are displayed in this window as computed from the data and can be adjusted by the user For a 2 bearing screen 4 locations will appear and for a 4 bearing there will be 8 locations A 5 1 Other Commands The options panel includes the following controllers which the user can change anytime while the data is being processed e A radio box for selecting the orientation to be displayed on the large plot A radio box for selecting whether to display filtered or unfiltered data on the large plot A radio box for selecting the source of the centre frequency from the FFT computation or manually using the slider e A radio box for selecting the unit the stroke is to be displayed in mm or inches e A radio box for selecting the g value the sensors should operate at This is only enabled when the data reading is stopped and in data acquisition mode only e A slider for setting the centre frequency manually e A slider for setting the maximum frequency to be displayed on the x axis of the FFT plots This acts as zooming in on the x axis e A slider for setting the bandwidth for the bandpass filter 114 A User Manual ibration Analysis Tool Inclination DEG Motor Sheave OD in or
114. y files and python packages folders containing py files along with an __init__ py file The following is a description of each one of those modules or packages 6 4 1 Reader This module encapsulates classes representing three handler types as well as a thread which performs the reading and the sending of values to the sensor managers It is implemented in C to improve performance Uses Threading bluetooth serial 66 6 Software Implementation Class BaseHandler Represents a base class for the handlers to inherit from The inheritance is on at tributes only These attributes are e The x y and z arrays e The raw data array The socket object The g value associated with the sensor the handler represents The handler s sensor manager The length of the values unpacked Class FileSimulation An object of this class allows for the creation of a simulated socket that can be used by the file handler Upon its creation it is passed a file from which data is read and placed in three separate lists one for the x values one for the y values and one for the z values In order to give it the same interface as a bluetooth socket the following methods are implemented e fileno just returns the sensor number the file is associated with e send writes the character being sent to an input buffer e recv creates a packet in the format Byte FF Byte FF x value y value z value Byte FO which is sent back
115. yice amp s agoe ev e Uu bug ue ess 34 G0 o uz as efie ES A Vete ii o rk Rr SS eite 35 4 Requirements Specification 39 MERO a o A a a E a aa a e a e e 39 4 1 1 User Classes and Characteristics llle 40 4 1 2 User Documentation drug xe ep oaa A S 41 Z ASSIM aii 4 ari tte AS 41 4 2 Functional Requirements mo ie he i a Eds 42 4 21 Communication Requirements 42 4 2 2 Mode Requirements 4 ale 9 exu 9 ae o Se 42 4 2 3 Signal Processing Requirements len 43 4 2 4 Logging Requirements ec Sacr pat Reb E ue Rep Qa ed 44 42 5 Display Requirements 22h eo RR RE RR 44 4 2 6 Graphical User Interface Requirements 45 4 2 7 Reporting Requirements o 46 4 3 Nonfunctional Requirements ooa 48 4 3 1 Performance Requirements aooaa a 48 CONTENTS vii 4 3 2 Platform Requirements eee a ues AA 49 4 3 3 Safety Requirements be a a 49 4 3 4 Maintainability Requirements 49 4 3 5 Reliability Requirements ooa aa o 50 4 3 6 Usability Requirements 2 koa ee bee X GI E Ue 50 5 Software Design 52 Bub VEVI EW 24 AA SES hee A dou A Dd 52 5 2 Design Method 10 Laos o sued eec ee US 52 ds Main Modules ac irs os m do od MENSES dE NERVES 55 Dual Redes ns aep ts Seg a Biss Se AS A SIMA AAA 55 5 3 2 Sensor Manager e o coia ec ber ieu P qu qum qne Bich es 97 Ld VAIO WEE is a aa 57 odd A O ON 57 O
116. ytes n and reads from the socket exactly n bytes and finally returns the concatenation of those bytes 6 4 2 Sensor Manager Uses numpy Class SensorManager This module is implemented in C as it is responsible for cycling through the acquired data in order to apply filters on it log it perform FFT on it and store it in order for the viewer to access it Its methods are Method startUp This method is called until there is fft_size data this is determined by the settings menu FFT size option in order to perform an initial FFT on the data to obtain the centre frequencies for the bandpass filters Method processData e Inputs Three arrays of data x y and z values of the same length and their length 6 Software Implementation 71 e Description Performs the following Method Calls the startUp method until it is not required Calls the frequencyCheck method If it is a data acquisition handler is bluetooth calibrates and dc filters incoming data one axis at a time If it is a file simulation only dc filters the incoming data one axis at a time If it is a data acquisition logs the calibrated de filtered data one axis at a time Stores the data retrieved from the above steps in a circularqueue data structure named raw_storage Calls the applyFilters method to apply the required filters on the data Finally if enough data is received to apply the FFT computation thi

Download Pdf Manuals

Related Search

Related Contents

Admiral Craft HD-36 Owner's Manual  Page 1 6 7 Auto AGC control Auto control(set by user) Backlight  USER`S MANUAL - Wiredzone.com  安全上のご注意    intext:Bedienungsanleitung filetype:pdf  Notice d`instructions de la solution de contrôle BGStar  downloaden  Allied Telesis AT-x230-10GP  Ouvrir le mode d`emploi au format PDF  

Copyright © All rights reserved. Failed to retrieve file