48660 Dynamics and Control Project 2 – Modelling of a 2 DOF System (Part 1), Vibration Analysis (Part 2) and Experimental Verification (Part 3) The Shake Table rig (Figure 1) was designed to model the behaviour of a building during an earthquake scenario. The rigs have been developed as two-storey structures that emulate vibrations in a single direction with 2 degrees of freedom. The rigs were designed to help students to break down and understand the complex dynamics of such a system. Students will model the 2 DOF system (using the simplified diagram in Figure 2), perform a vibration analysis and verify the results experimentally both in MATLAB and using the remote lab rigs. You are required to read the document “Shake_Table_User_Guide_V2-1.pdf” for detailed information about the shake table rigs. Variance data on each of the rigs can be found in “Shake_Table_Variance_Data_2014-08-20.pdf”. Students are required to produce a report detailing the three parts to the project, along with an insightful discussion and reflection relating to the tasks completed. Figure 1- 2 Degrees of Freedom Shake TablePart 1: Modelling of a 2DOF System 1. Draw the free body diagrams for the two masses in the system based on the simplified diagram in Figure 2. 2. Derive the differential equations of motion for the system. The displacements 𝐱(𝐩 of 𝐱 and 𝐲(𝐩 of 𝐲 are measured from the rest positions of the masses. Figure 2 shows a shear building with base motion. This building is modelled as a 2 DOF dynamic system where: 𝐱 = 𝐲 = 𝐠= 1.178 𝐵 𝐱 = 𝐲 = 𝐠= 370.374 𝑄𝐍 𝐱 = 𝐲 = 𝐠= 0.05 𝐮 𝑄𝐍 𝐨𝐩 = 𝐰 sin(𝐵) Where 𝐠and 𝐠are the total values of stiffness and damping for each of the levels of the structure. Figure 2 - A 2 Degree of Freedom Vibration SystemPart 2: Vibration Analysis 1. By assuming undamped free vibration, calculate the natural frequencies of the system: 𝐱 and 𝐲. 2. Calculate the normal modes of vibration corresponding to 𝐱 and 𝐲, and draw their modal shapes: 𝐠⃑(1) = {𝐠𝐱 2 ( (1 1) )} 𝐠⃑(2) = {𝐠𝐱 2 ( (2 2) )} 3. Obtain the transfer functions for each of the masses, based on the differential equations of motion from Part 1 (Damped, Forced Vibration): 𝐱(𝐩 𝐨𝐩 𝐲(𝐩 𝐨𝐩 4. Using MATLAB/Simulink, analyse the responses 𝐱(𝐩 and 𝐲(𝐩 due to the following inputs: Unit step base movement: 𝐨𝐩 = 1 Harmonic motion of the base: 𝐨𝐩 = 0.7 sin(𝐱𝐩 Harmonic motion of the base: 𝐨𝐩 = 0.7 sin(𝐲𝐩Part 3: Experimental Verification Record and plot the actual responses (i.e. produce two graphs) from the UTS remote vibration (Shaker Table) laboratory by setting the frequencies of the base movement to 𝐠1 = 𝐱 2𝐍 and 𝐲 = 𝐲 2𝐍 . Students should set the total system damping (% on the remote lab interface, given 𝐱 = 𝐲 = 0.05 𝐮 𝑄𝐩 using the information below. Note: The relationship between the damping interface control value (%) and damping coefficient (𝐮 𝑄𝐩 is shown in Figure 3 and is given by the following equation: 𝐠= 1.669𝐲 Figure 3 - Force/Velocity Coefficient (N.s/m) vs. Interface Control Value (%)Discussion and Reflection Provide an insightful, clear, relevant but brief discussion and reflection on the tasks performed in this report. Draw some conclusions about why modelling such a system might be useful in real life engineering practice. Also discuss how the simulated results compare with the real life experimental (shaker table) results. Additional Notes • Students must include units for all quantities measured or derived. • Students should consult the marking guide provided on UTSOnline. • The main body of the reports must be limited to 8 pages or less (i.e. not including title page, table of contents etc.). • Scanned hand written reports are acceptable, so long as they are neat and easily readable. Any hand written work should be written on blank, unruled paper and scanned in only. Digital photographs of hand written work will attract deductions for the report presentation. Graphs and figures should be made using software and annotated appropriately (with legends, titles, captions, axis labels). • Submission is via UTS Online under the Assignments tab; follow the instructions provided. SHAKE TABLE RIG LABORATORY USER GUIDE VERSION 2.1 Partnered with… University of Technology, Sydney © 2014Shake Table Rig Laboratory User Guide Version 2.1 University of Technology, Sydney © 2014 Page 1 Table of Contents 1 Introduction................................................................................................................................................. 2 1.1 Remote Laboratories ..........................................................................................................................2 1.2 Shake Table - The Rig Apparatus .......................................................................................................3 1.2.1 The Base........................................................................................................................................ 3 1.2.2 Displacement Sensors................................................................................................................... 4 1.2.3 Linear Variable Differential Transformer (LVDT)............................................................................ 4 1.2.4 Eddy Current Coil Damping ........................................................................................................... 4 1.2.5 Data Acquisition and Feedback ..................................................................................................... 4 2 Rig Session ................................................................................................................................................ 5 2.1 Selecting a Rig....................................................................................................................................5 2.2 Queuing for a Rig................................................................................................................................5 2.3 Controlling a Rig .................................................................................................................................6 3 Rig Control Software .................................................................................................................................. 6 3.1 Layout .................................................................................................................................................6 3.2 Motor Control ......................................................................................................................................8 3.3 Eddy Current Damping Control...........................................................................................................8 3.4 Coupling Motor & Damping Control....................................................................................................9 3.5 Displacement Measurement...............................................................................................................9 3.6 Fast Fourier Transform (FFT) Graph ................................................................................................10 3.7 Lissajous Graph................................................................................................................................11 4 Rig Data Acquisition ................................................................................................................................. 12 4.1 Logging Displacement & Coil Damping Data ...................................................................................12 4.2 Exporting Fast Fourier Transform (FFT) Data ..................................................................................14 5 FAQ & Troubleshooting ............................................................................................................................ 15 5.1 Contacting Support ...........................................................................................................................15 5.2 Providing Feedback ..........................................................................................................................15 Revision History 0.1 22/09/2009 First draft LY 0.2 21/06/2010 Revision LY 1.0 14/09/2010 Internal Release EB 1.1 12/11/2010 Revision and general formatting EB 1.2 02/05/2011 Screenshot update EB 1.3 01/07/2011 Labshare logo update EB 2.0 12/08/2011 Updated for Shake Table v1.10 LJC 2.1 25/03/2014 Updated for new web interface. MDShake Table Rig Laboratory User Guide Version 2.1 University of Technology, Sydney © 2014 Page 2 1 Introduction 1.1 Remote Laboratories Remote laboratories enable students to access physical laboratory apparatus through the internet, providing a supplement to their studies and existing hands-on experience. Students carry out experiments using real equipment, but with much greater flexibility since access can occur from anywhere and at any time. Their interaction with the remote equipment is assisted by the use of data acquisition instrumentation and cameras, providing direct feedback to students for better engagement. Traditional engineering laboratories require students to be physically present in order to work with equipment, which may limit student flexibility. Conversely, remote laboratories let students work in their own time and even repeat experiments for better learning outcomes. Of course students cannot actually touch and feel the equipment in a remote laboratory, but they can still perform most other tasks relevant to their learning. Sometimes, separation from potentially hazardous equipment is preferable from a safety point of view. Due to the increased use of remote operation in industry, where machinery and entire plants are often controlled from a distant location, students may directly benefit from learning how to remotely control equipment. Furthermore, remote laboratories provide the opportunity to access a wider range of experiments as costly or highly specialised equipment may not be locally available. This presents the opportunity to share laboratory facilities between institutions. Significant research and pilot studies have been undertaken in Australia and by several groups around the world into the educational effectiveness of using remote laboratories. These studies have consistently shown that, if used appropriately in a way that is cognizant of the intended educational outcomes of the laboratory experience, remote laboratories can provide significant benefits. Indeed, multiple research studies have demonstrated that whilst there are some learning outcomes that are achieved more effectively through hands-on experimentation (e.g. identification of assumptions, specific haptic skills), there are other learning outcomes that are achieved more effectively through remotely accessed laboratories (e.g. processing of data, understanding of concepts). Engineering students are able to access the Shake Table rigs to help them develop and verify their mathematical models of the complex system dynamics. The Shake Table allows students to:  Characterise the behaviour of a 2 degree of freedom system.  Acquire experimental data to assist in developing a simplified model of the system.  Analyse the system response across a range of frequencies by measuring displacement, performing a Fast Fourier Transform (FFT) on the data in real-time or generating Lissajous curves for each level in real-time.Shake Table Rig Laboratory User Guide Version 2.1 University of Technology, Sydney © 2014 Page 3 1.2 Shake Table - The Rig Apparatus The Shake Table Laboratory was designed to model the behaviour of a building during an earthquake scenario. It is hosted by UTS remotelabs and helps students break down and understand the complex dynamics of such a system. Four rigs were developed as two-storey structures that emulate vibrations in a single direction with 2 degrees of freedom. One extra rig was also developed with three-stories to model movement with 3 degrees of freedom. Each Shake Table rig consists of the following main components:  A building model;  Where each level has a known mass.  Connected by a material with a known stiffness coefficient.  Displacement sensors for each level of the building.  The base plus a motor to provide appropriate excitation.  Damping coils with a known damping coefficient.  Data acquisition and control hardware.  A web camera for visual feedback.  A control interface written using web technologies. Figure 1: 2 Degrees of Freedom Shake Table with base displacement measurement (LVDT). 1.2.1 The Base The model itself sits on the Shake Table platform where the base level (i.e. level 0) glides along a low-friction guide rail. Rotational motion from an electric motor is converted into linear motion via a ‘scotch yoke’ mechanism, providing base excitation at a user-specified frequency. Changing this frequency allows the user to model different earthquake vibration conditions. The base amplitude of displacement during an earthquake is modelled by setting the stroke on the motor, which can be adjusted manually. Level 0 Level 2 Electric Level 1 Motor Eddy Current Coil Dampers LVDT Displacement Sensors Guide Rail Scotch Yoke MechanismShake Table Rig Laboratory User Guide Version 2.1 University of Technology, Sydney © 2014 Page 4 1.2.2 Displacement Sensors The displacement of each level is measured by a contactless MTS C-series Magnetostrictive Linear-Position Sensor. Button magnets are fixed at the back of each level, which travel up and down the waveguide sensing element during vibration. The effect of the external magnetic field causes the ferromagnetic material of the waveguide to change its shape at that particular point on the sensor. To read the magnets’ position, an “interrogation current pulse” is sent along the waveguide from the base of the sensor, which generates a radial magnetic field as it travels. When it reaches the point at which the button magnet is placed, the two magnetic files interact with one another. Then a mechanical strain pulse is emitted back towards the base of the sensor (in the form of an “impact soundwave”) which is detected and converted into a voltage signal by the sensor electronics. The button magnets are attached to the center of each level, with the rest position of the building structure roughly between 70-75 mm, in absolute displacement. 1.2.3 Linear Variable Differential Transformer (LVDT) The displacement of the base (level 0) is measured by a Solartron Metrology DG Series Linear Variable Differential Transformer (LVDT). The LVDT has three solenoid coils placed within a tube. A ferromagnetic core is attached to the object requiring position measurement and this moves along the axis of the tube. An alternating current is driven through the primary (centre) solenoid coil, which mutually induces a voltage in the secondary coils. As the ferromagnetic core moves, the induced voltages change and the position can be measured by measuring the difference between (i.e. the differential) the two secondary coil voltages. 1.2.4 Eddy Current Coil Damping A copper plate is fixed to each level of the building model, extending between a pair of coils which when turned on, generate a magnetic field that permeates through the copper. Motion in each storey of the model causes the copper to move at a given velocity relative to the coils, which generate eddy currents within the copper itself. These eddy currents in turn create a magnetic field of their own, resulting in a damping force that opposes the motion of the copper, hence suppressing vibration for that level. Note that the current in each coil is supplied by an amplifier and the temperature of each coil measured using a temperature diode. If the temperature rises above 85ºC, the system automatically turns off the coils to prevent damage to the equipment. The rig will not be operable until the temperature falls below this threshold. 1.2.5 Data Acquisition and Feedback Data acquisition and control is implemented using a LabJack UE9 device and National Instruments cRIO. These are linked to the rig server PC via an Ethernet connection. Software written using LabVIEW, Java, HTML, Javascript and CSS, allows users to gather the data and operate a single Shake Table Rig. An Apple iSight webcam gives the user visual feedback of the Shake Table in action, in real-time, accessible via the Internet from the Remote Labs web page. Remote data acquisition and feedback control on a fast moving, dynamic system is a challenge over the Internet. For a good control system to work, both the acquisition and feedback should be done within a very small timeframe to achieve a good response. In order to achieve this, data is constantly being streamed from the LabJack and cRIO using a fast, hardware timed acquisition rate.Shake Table Rig Laboratory User Guide Version 2.1 University of Technology, Sydney © 2014 Page 5 2 Rig Session The following section outlines the procedure for utilising the Shake Table Rig Laboratory, which is similar to other Remote Laboratory Rig types already in use. The software that runs the Remote Laboratories and provides access to the rigs through a web browser is called Sahara Labs. For the purpose of using the rig, it is assumed that users have access to a workstation that meets the system requirements. Users should refer to Labshare’s Generic Rig Access Guide for this information. 2.1 Selecting a Rig Once you have logged in, you will be directed to the Rig Selection page. On this page, click the “Shake Table” tab if it is not already selected. Now you can either select a specific rig to control or select from any of the available rigs. It is suggested to select from any of the available rigs. Click the “Shake Table” icon to make this selection. 2.2 Queuing for a Rig Once you’ve made your selection, you need to queue for the rig. After this step, when the rig is available, you will enter a session, whereby you are able to control the rig. Click the “queue” button or alternatively click “reserve”, if you wish to schedule a session for future use (see Labshare’s Generic Rig Access Guide for more information on reserving a rig). Figure 2 Choosing a rig type or specific rig Figure 3 Choosing to queue of reserve the selectionShake Table Rig Laboratory User Guide Version 2.1 University of Technology, Sydney © 2014 Page 6 2.3 Controlling a Rig If a rig is free, you will be redirected to the rig page, where you can access the Shake Table interface, otherwise you will be directed to the queue page and a rig will be provided as soon as one becomes available. 3 Rig Control Software 3.1 Layout The Shake Table interface contains all the controls needed to configure the rig actuators, view sensor outputs graphically and enable and retrieve logged data. The layout of the rig page is broken up into windows that contain an interface element for a specific purpose. The list of these windows is shown in the screenshot below (which is the default layout). Figure 4 Shake Table interface windows Logging Session Timer Video Display Graphical Representation Motor and Damping Coil Controls Graphs Session Controls Display ListShake Table Rig Laboratory User Guide Version 2.1 University of Technology, Sydney © 2014 Page 7 These windows are:  Session Timer – shows the amount of time you have remaining before the system will determine whether to extend your session or free the rig for another user.  Video Display – a live video stream of the rig you are controlling.  Graphical Representation – a model whose behaviour mimics movement reconstructed from displacement sensor readings.  Motor and Damping Controls – controls to enable and disable the motor and damping coil circuits, set the motor frequency, and dampening power.  Graphs – shows sensor readings in graphical forms. The graphs provide a time series of the displacement of each level, Lissajous graphs showing the phase relationship between levels and FFT graphs showing amplitude of levels against frequency.  Logging – controls to enable and disable logging and a list of files that can be selected to be downloaded.  Display List – a toggle list to selectively show or hide windows allowing user customisation of the interface.  Session Controls – common controls to end the session, logout or request support from laboratory staff. The windows in the interface can be resized, repositioned and/or hidden allowing the user to create a customised interface relevant to their particular laboratory exercise. The screenshot below shows such a customised interface. Clicking the ‘Reset’ button in the Display List will return all windows to their default size and position. Figure 5 User customised interfaceShake Table Rig Laboratory User Guide Version 2.1 University of Technology, Sydney © 2014 Page 8 3.2 Motor Control Figure 6 Motor and Dampening Controls The motor frequency can be controlled by the slider in the middle of controls window. The frequency can be adjusted from 0 Hz (stopped, no rotation) to 8 Hz in intervals of 0.01 Hz. The motor has been calibrated for this frequency range. The frequency can be adjusted either by dragging the black slider marker left or right with your mouse cursor or by typing the desired frequency in the motor frequency input field. Be sure to press the ‘Enter’ key or remove focus from the text entry field so the value is sent to the server. The text field will validate the user specified value, ensuring a valid frequency between 0 Hz to 8 Hz has been entered. Be sure to click the “Motor” toggle button to put the motor in the enabled state (dark knob right) at the frequency you have set. The motor can be stopped by either toggling the button back to the disabled state (light knob left) or by adjusting the frequency to 0 Hz. 3.3 Eddy Current Damping Control In the same way that the motor frequency can be controlled, the eddy current dampers can be controlled, via the sliders for each level at the right of the controls window. The damping for each level can be adjusted from 0 to 100% in increments of 0.1%. This can be performed by either dragging the black slider marker up and down with your mouse cursor or by typing in the desired damping level in the damping level input field. Be sure to press the ‘Enter’ key or remove focus from the text entry field so the value is sent to the server. The text field will validate the user specified value, ensuring a valid percentage between 0% and 100% has been entered. Be sure to click the “Coils” toggle button to put the damper in the enabled state (dark knob right) at the damping level you have set. The damping can be removed by either toggling the button back to the disabled state (light knob left) or by adjusting the damping level to 0%.Shake Table Rig Laboratory User Guide Version 2.1 University of Technology, Sydney © 2014 Page 9 3.4 Coupling Motor & Damping Control In order to assist students with analysis of damping times – a ‘Couple’ button has been added to the controls. Figure 7 Couple Control This button exclusively couples the enable toggle buttons for the motor and damping control so either the motor or the coils are enabled, but not both or neither. The button works according to the following truth table: Couple Motor Enable Level 1 & Level 2 Damper Enable Disabled Independently-Toggled Independently-Toggled Enabled User-Enabled Auto-Disable Enabled User-Disabled Auto-Enabled e.g. If the Couple button is enabled and the user enables the motor, the damping will automatically be disabled. In enabling the ‘Couple’ button – the user can be sure that damping will consistently be applied (repeatable time-delay) when the motor is disabled. As a result, damping times can be compared and sources of error/variation removed from any damping-related experiments. 3.5 Displacement Measurement The displacement graph displays displacement sensor data for a 10 second interval from the “present time” (right hand side) to “present time - 10 seconds” (left hand side). Figure 8 Displacement graphShake Table Rig Laboratory User Guide Version 2.1 University of Technology, Sydney © 2014 Page 10 The vertical scale axis is used for displacement and measures from -60mm to +60mm. The base displacement, level 0, is indicated by the yellow line, level 1 is indicated by a red line and level 2 by a purple line. 3.6 Fast Fourier Transform (FFT) Graph A real-time Fast Fourier Transform (FFT) on 10 seconds of acquired displacement data is shown by the FFT graph. This can assist in finding the resonant modes or in performing various other frequency-based analysis techniques on the system. Be sure to click the ‘FFT’ tab to select the FFT graph to be shown. Figure 9 FFT Graph The FFT is a plot of the amplitude on the vertical scale axis against the frequency (Hz) along the horizontal axis. The figure above shows the FFT generated on the first few seconds of data at an excitation frequency of 1.75 Hz. The FFT performed on the base, level 0, data is indicated by the yellow line, level 1 by the red line and level 2 by the purple line. The ‘Export FFT’ button allows the generated FFT data to be downloaded by the user for offline analysis.Shake Table Rig Laboratory User Guide Version 2.1 University of Technology, Sydney © 2014 Page 11 3.7 Lissajous Graph A real-time Lissajous graph is provided plotting the relationship between displacement data of two levels. This allows you to determine the phase relationship of the various levels. Be sure to click the ‘Lissajous’ tab to select the Lissajous graph to be shown. Figure 10 Lissajous graph The graph of “Level X vs Level Y” can be selected by clicking the appropriate tab at the left of the graph. The phase relationship can be determined by the curve shape.Shake Table Rig Laboratory User Guide Version 2.1 University of Technology, Sydney © 2014 Page 12 4 Rig Data Acquisition Users are able to save sensor data for displacement, coil damping as well as export generated Fast Fourier Transform (FFT) data. 4.1 Logging Displacement & Coil Damping Data Figure 11 Log controls window Displacement data can be saved whilst your session is active by clicking the ‘Logging’ toggle button. Data will be recorded and saved to a file at 0.01 second intervals. The data is divided up into columns, with the column order being:  Time (s)  Level 0 Displacement (mm)  Level 1 Displacement (mm)  Level 2 Displacement (mm)  Level 1 Coil Output (%)  Level 2 Coil Output (%) The data will continue to be saved until the ‘Logging’ toggle button is disabled by clicking it or the session is finished by user request, session expiry or inactivity by closing the web page. Once a file is no longer being logged to and a short system processing lag has elapsed, a download link will be activated in Logging window file list. This is shown by black text and border around the file link. A user may chose the file to be generated as a plain text comma separated file (.csv), an Excel spread sheet (.xlsx) or a legacy Excel spread sheet (.xls). Irrespective of chosen format, the column positioning and data are equivalent. Logging Enable Format selection File list that is automatically populated as files are logged Logging is enabled Number of seconds the current file has been logged to. File currently being logged to. It cannot be downloaded. File ready to download.Shake Table Rig Laboratory User Guide Version 2.1 University of Technology, Sydney © 2014 Page 13 The log file is stored to the UTS remotelabs server so the user may at a later time retrieve the file. When outside a session, click the ‘Data Files’ heading on the UTS remotelabs website. A list of previously saved data files will appear, allowing the user to download and save the file to their computer, by clicking the text file title (e.g. 20110812_163753.txt). After clicking the text file title, a browser-specific download window will appear - be sure to click “Save File” or similar in this window to save the file in an appropriate location on your computer. Please note storage space is limited and a shared resource across all users so saved data files may be removed from the system after completion of semester.Shake Table Rig Laboratory User Guide Version 2.1 University of Technology, Sydney © 2014 Page 14 4.2 Exporting Fast Fourier Transform (FFT) Data Real-time Fast Fourier Transform (FFT) data can be exported when the FFT graph is being displayed, by clicking the ‘Export FFT’ button. Data will be recorded and saved to a tab-delimited text (.csv) file. The data is divided up into columns, with the column order being:  Frequency (Hz)  Level 0 Amplitude  Level 1 Amplitude  Level 2 Amplitude Since the FFT data is purely real-time acquisition (i.e. a snapshot of the last 10 seconds), there are no other buttons to press, consequently no need to stop saving the data. As the FFT is a snapshot, stored in a transient file that is not kept on the UTS remotelabs server, the user must download the file when the download prompt is presented by the web browser. If the user chooses not to download the FFT file, it will no longer be accessible. Figure 13 FFT export download prompt FFT graph selected File ready to download. Figure 12 FFT graph and export buttonShake Table Rig Laboratory User Guide Version 2.1 University of Technology, Sydney © 2014 Page 15 5 FAQ & Troubleshooting 5.1 Contacting Support Any questions regarding the nature of assessment tasks should initially be directed to the relevant academic. If the user encounters any difficulties during the course of using the rigs, the ‘Contact Support’ button should be used to request assistance and report an incident. The following popup will appear – please enter your name and a valid email address, followed by a category from the “Type” drop down list. You may then enter a brief statement regarding the nature of the request in the “Purpose” field. Before sending the support request, ensure the following questions have been answered in the ‘Feedback’ field: 1. What am I trying to access? 2. What subject am I enrolled in that utilises a rig? 3. What do you expect to occur? 4. What is actually occurring? 5. What, if any, troubleshooting steps have you taken? 6. How can your error be reproduced? Remember, the more detailed the descriptions you provide, the more speedily support staff can resolve your problem. 5.2 Providing Feedback Users are strongly encouraged to leave feedback and comments of their experience with the rigs to help improve the system, as well as any suggestions for additional features to be included in the future. For any enquires or assistance, contact the Labshare helpdesk at: [email protected]