TM1004 Gyroscope. User Guide. TecQuipment Ltd 2013

Transcription

1 TM1004 Gyroscope User Guide TecQuipment Ltd 2013 Do not reproduce or transmit this document in any form or by any means, electronic or mechanical, including photocopy, recording or any information storage and retrieval system without the express permission of TecQuipment Limited. TecQuipment has taken care to make the contents of this manual accurate and up to date. However, if you find any errors, please let us know so we can rectify the problem. TecQuipment supply a Packing Contents List (PCL) with the equipment. Carefully check the contents of the package(s) against the list. If any items are missing or damaged, contact TecQuipment or the local agent. DB/0913

2 : User Guide TecQuipment Ltd

3 Contents Introduction Description The Base Unit and Gyroscope The Controls Versatile Data Acquisition System (VDAS) Technical Details Noise Levels Assembly and Installation Installation Connection to VDAS Electrical Connection Theory Notation Units Conversions Speed and Angular Velocity Gyroscopes Rotation, Precession and Couple Moment of Inertia (I) Gyroscopic Couple Directions of Forces and Couples Experiments Safe Use Directions Around the Gyroscope Experiment 1 - Gyroscopic Couple Direction Aims Procedure Results Analysis Experiment 2 - Magnitude of Gyroscopic Couple Aims Procedure 1 - Fixed Precession, Varied Rotor Velocity Procedure 2 - Fixed Rotor, Varied Precession Velocity Results Analysis TecQuipment Ltd User Guide

4 Typical Results Experiment 1 - Gyroscopic Couple Direction Experiment 2 - Magnitude of Gyroscopic Couple Procedure 1 - Fixed Precession, Varied Rotor Velocity Procedure 2 - Fixed Rotor, Varied Precession Velocity Maintenance, Spare Parts and Customer Care Maintenance General Electrical Spare Parts Customer Care

5 TM1004 Gyroscope User Guide Introduction Figure 1 Gyroscope (TM1004) This product works with VDAS Many machines use large rotating parts - particularly vehicles. These rotating parts can create a problem. When the machine or an external force tries to change the axis of the part; gyroscopic action creates unwanted reaction forces. For example, the wheels of road or track vehicles become gyroscopes as they rotate. When the vehicle changes direction, they create unwanted reaction forces that may destabilize the vehicle. In a conventional single propellor light aeroplane, the propellor becomes a gyroscope. When the pilot tries to change the flight direction, the gyroscope creates reaction forces that try to turn the aeroplane in unwanted directions. Sometimes these forces can be useful, for example, rotating bicycle and motorcycle wheels become gyroscopes, resisting axial movement. This helps keep the machine balanced and upright when moving in a straight line. Also, navigational equipment uses gyroscopic action in its instruments to measure changes in axis or to keep a piece of sensitive equipment balanced and upright. Even some boats and ships use them as stabilizers (anti-rolling gyroscopes). TecQuipment Ltd 1 User Guide

6 The unwanted gyroscopic reaction forces may add extra stress on other machine parts such as shaft bearings or supports. However, they may also help relieve stress, allowing manufacturers to make parts more economically. So, engineers need to know how to predict these gyroscopic reaction forces to use or allow for them in their designs. TecQuipment s Gyroscope (TM1004) uses motors and sensors to create controllable gyroscopic actions and measure the forces and velocities. It shows how to predict the directions and magnitudes of couples in a simple gyroscope. To automatically record your experiment results and save time, the apparatus works with TecQuipment s Versatile Data Acquisition System (VDAS ). VDAS is a registered trademark of TecQuipment Ltd. User Guide 2 TecQuipment Ltd

7 Description Flywheel Safety Dome Counterweights Figure 2 Gyroscope (TM1004) The Base Unit and Gyroscope The gyroscope is the middle part or rotor of an electric motor and a flywheel on a common shaft supported horizontally in a gimbal assembly. The gyroscope spins and rotates under a protective clear dome on the top of a solid base unit. The base unit contains electrical circuits, displays and velocity controls. It also contains a precession motor, mounted vertically, that turns a belt and pulley system (similar to a turntable) to rotate the gyroscope assembly around a vertical axis. A force sensor supports the gyroscope horizontally and can therefore measure the vertical force (reaction) on the gyroscope shaft at a known distance from the gimbal pivot (allowing calculation of the reaction moment - or couple ). Sensors detect the spin of the rotor and the precession. The sensors connect to the digital displays to the front of the base unit to display velocities, force, couple and moment. NOTE The display of force is for reference only, the polarity and magnitude of couple are the important values for you experiments. A clear safety dome covers the gyroscope so you can see it moving in safety. An interlock disconnects power to the motors when you open the dome. TecQuipment Ltd 3 User Guide

8 Fixed counterweights balance the gyroscope assembly in the gimbal assembly, to allow for the slightly off-centre construction. CAUTION TecQuipment set the counterweights accurately to balance the gyroscope assembly. Do not adjust the counterweights or the gyroscope assembly. WARNING Users do not need to open the dome during the experiments. Only open the dome for stationary demonstrations (with no rotations) or unpacking and maintenance. Never try to bypass the safety interlock. The Controls The base unit has three controls, two control the velocities of the rotor and the precession, both in a clockwise direction and an anticlockwise direction. The lights next to the controls indicate the direction. The third control is a tare button that allows you to zero the reading from the force sensor before each experiment. The velocity controls have three options: Normal turning clockwise and anticlockwise to change the velocity with a fine adjustment. Pressing in while turning clockwise and anticlockwise to change the velocity with a coarse adjustment. Pressing in for longer than three seconds to reset the velocity to zero. NOTE The velocity resets to zero when you switch off the power or lift the safety dome. The velocities will take a few seconds to reach zero when you press the buttons - they ramp down. The motor controls use pulse width modulation (PWM) to control motor speed. This varies the electrical supply ( on time) pulse to the motor, but at a fixed frequency. Short pulses give lower motor speed and longer pulses give higher motor speed. The PWM frequency is within normal hearing range, so the operator may hear the motors buzzing when they turn. This is normal. For added safety, each motor has an overheat protection thermostat. This prevents each motor overheating in the unlikely event of a mechanical restriction (something preventing the motor from turning). The thermostat disconnects power to the motor until it returns to a safe temperature. User Guide 4 TecQuipment Ltd

9 Versatile Data Acquisition System (VDAS) Figure 3 The VDAS Hardware and Software TecQuipment s VDAS is an optional extra for the Gyroscope apparatus. It is a two-part product (Hardware and Software) that will: automatically log data from your experiments automatically calculate data for you save you time reduce errors create charts and tables of your data export your data for processing in other software NOTE You will need a suitable computer (not supplied) to use TecQuipment s VDAS. TecQuipment Ltd 5 User Guide

10 User Guide 6 TecQuipment Ltd

11 Technical Details Part Operating Environment Dimensions and Weight Electrical Supply External Connections Fuse Details Indoor (laboratory) Altitude up to 2000 m Temperature range 5 C to 40 C Maximum relative humidity 80% for temperatures up to 31 C, decreasing linearly to 50% relative humidity at 40 C Overvoltage category 2 (as specified in EN ). Pollution degree 2 (as specified in EN ). 600 mm wide x 600 mm front to back x 370 mm high and 17 kg 90 VAC to 250 VAC 50 Hz to 60 Hz 0.3 A Type RJ45 sockets for VDAS Extra Low Voltage <25 VDC 20 mm 6.3 A Type F Nominal Maximum Precession Velocity 300 rev.min -1 Nominal Maximum Rotor Velocity 2500 rev.min -1 Nominal Moment of inertia of rotor (combined flywheel and motor rotor) Torque Arm Length I = kg.m 2 L T = 90 mm Noise Levels In normal use, the gyroscope emits sound levels lower than 70 db(a). TecQuipment Ltd 7 User Guide

12 User Guide 8 TecQuipment Ltd

13 Assembly and Installation The terms left, right, front and rear of the apparatus refer to the operators position, facing the unit. NOTE A wax coating may have been applied to parts of this apparatus to prevent corrosion during transport. Remove the wax coating by using paraffin or white spirit, applied with either a soft brush or a cloth. Follow any regulations that affect the installation, operation and maintenance of this apparatus in the country where it is to be used. Installation 1. Use the Gyroscope in a clean laboratory or classroom type area. 2. Put the Gyroscope on a solid, level table or workbench. NOTE If your support table is not solid or level, it will affect your experiments and your results will be wrong. WARNING Use assistance to move the apparatus, the handles are far apart and it is fairly heavy (see Technical Details). 3. Make sure the clear dome fits correctly. 4. Connect the equipment to the optional VDAS if needed. 5. Connect the equipment to the electrical supply as shown in Electrical Connection. Connection to VDAS Use the cables supplied with VDAS to connect the two sockets marked VDAS on the TM1004 to any of the six Digital Input sockets on the VDAS Interface. Electrical Connection Use the cable supplied with the equipment to connect it to an electrical supply. WARNING The mains supply connector at the back of the base unit is its mains disconnect device. Make sure it is always easily accessible. Connect the apparatus to the supply through a plug and socket. The apparatus must be connected to earth. TecQuipment Ltd 9 User Guide

14 These are the colours of each individual conductor: GREEN AND YELLOW: EARTH E OR BROWN: LIVE or L1 or Hot 1 BLUE: NEUTRAL User Guide 10 TecQuipment Ltd

15 Theory Notation Symbol Details Units I Moment of Inertia kg.m 2 ω ω r ω p Angular velocity Angular velocity of the rotor (spin) Angular velocity of the precession radians per second rad.s -1 m Mass kg F Force N θ Angle Radians L Length m D Diameter m r Radius m t Time Seconds T Torque Nm Units Conversions Speed and Angular Velocity The displays show the rotational velocities (speeds) of the gyroscope in revolutions per minute (rev.min -1 ) and radians per second (rad.s -1 ). 2π (6.28) radians = 360 degrees = one revolution. One radian = degrees. 1 rev.min -1 = 1/60 rev.s -1 ( rev.s -1 ) = 2π/60 rad.s -1 ( rad.s -1 ) TecQuipment Ltd 11 User Guide

16 Gyroscopes Scientists and engineers did not fully understand the importance and usefulness of gyroscopes until the 19th century, when the first practical use was by a French physicist - Leon Foucault who used one to simulate the movement of the planet Earth. Later in that century, engineers used electric motors to keep the gyroscopes spinning - creating gyrocompasses for use in navigational equipment. A traditional gyroscope (see Figure 4) has a spinning central core or disc (the rotor) mounted on a shaft. The gyroscope sits in a gimbal frame that allows it to spin and move in different planes. Rotor Gimbal frame Figure 4 A Traditional Gyroscope User Guide 12 TecQuipment Ltd

17 Rotation, Precession and Couple Rotation or Spin Precession Couple Couple Figure 5 Rotation, Precession and Couple Rotation or Spin of a gyroscope is the angular movement of the rotor around its central axis. Precession is the (usually) slow movement of the axis of a spinning body around another axis. In a gyroscope it is the slow movement of the rotor spin axis around the gyroscope support axis. A couple is a turning or angular force, similar to a moment or torque, caused by two opposing forces. TecQuipment Ltd 13 User Guide

18 Moment of Inertia (I) Sometimes called rotational inertia or mass moment of inertia, this is the inertia of the rotor and flywheel combined. The simple mathematical method of finding this is to think of the rotor and flywheel as one solid cylinder and find I x (in the direction of the centreline) from its mass and radius, as in Figure 6, where: r m x I x = 0.5 mr 2 Figure 6 Simple Method of Finding Moment of Inertia However, the simple method assumes a uniform solid cylinder. Although the flywheel is a uniform cylinder, the rotor is not, so you cannot accurately determine its moment of inertia using this method. Refer to the Technical Details on page 7 for the nominal value. User Guide 14 TecQuipment Ltd

19 Gyroscopic Couple Take a non-spinning flywheel on a shaft, supported, but free to rotate about an axis. Any couple applied to the system causes the shaft to move in the plane of application of the couple (see Figure 7). Horizontal Axis ( X) Vertical Axis ( Y) Horizontal Axis ( Z) Non-spinning Flywheel Movement Couple Movement Figure 7 Non-spinning Flywheel Y Z B A O r X p Figure 8 Principle of Gyroscopic Action Now consider the case in Figure 8. The flywheel disc spins with angular velocity (ω r ) around axis X. The axis of spin (along the shaft) also rotates in the horizontal plane ZOX with angular velocity (ω p ) (precession). Vector OA represents the angular momentum of the disc at one instant. Vector OB represents the angular momentum after a short interval of time δt. The momentum vector lies along the axis of rotation, in a direction such that the rotation is clockwise when viewed in the direction of the vector, or anticlockwise when viewed directly at the vector (right-hand screw rule). TecQuipment Ltd 15 User Guide

20 Momentum vector Momentum vector Rotation Figure 9 Right Hand Rule The vector AB shows that the angular momentum changes. This change in momentum must be produced by the action of a couple in the disc. The applied couple is equal to the rate of change of angular momentum, so the couple (torque) is given by: T = δ( Iω r ) δt The vector AB represents the change of angular momentum, so we can write δ( Iω r ) = AB = OA δθ where δθ is the angle through which the axis of spin rotates in time δt. T OA δθ δθ = = Iω δt r δt In the limit when δt O, δθ Torque (or Gyroscopic Couple) T = Iω r = Iω (1) δt r ω p From Figure 8, the vector AB lies in the XOZ plane and in the limit when δθ is very small, its direction is perpendicular to OA, that is to say, perpendicular to the XOY plane. The direction of the vector lies along the axis about which the couple acts, so the applied couple must therefore act in the XOY plane. To conform to the right-hand screw rule, its sense must be clockwise when viewed in the direction ABN, that is when viewed in the direction OZ. The applied couple represents the couple required to keep the axis of the disc rotating in the XOZ plane. By rotating the axis of the disc, the disc produces a couple, which acts in the opposite direction to the applied couple, that is to say, anti-clockwise about the OZ axis. This is the gyroscopic couple. If this couple is not resisted, any attempt to rotate the axis of the disc in the XOZ plane would result in the axis tipping in the anti-clockwise direction about the OZ axis. User Guide 16 TecQuipment Ltd

21 In the TecQuipment Gyroscope, the rotor motor forms a torque arm between the pivot and the connection to the force sensor. Multiplying the torque arm length by the force measured at the force sensor gives a turning moment (or torque) equal to the gyroscopic couple. Flywheel Torque Arm Length = L T Couple = Fx L T Rotor Motor Force Sensor Force = F Positive = Down = Clockwise Couple Negative = Up = Anticlockwise Couple Figure 10 Torque Arm Therefore, the gyroscopic couple: T = F L T (2) NOTE A positive force gives a positive and therefore clockwise couple (when viewed as in Figure 10). The display of force is for reference only, the polarity and magnitude of couple are the important values for your experiments. TecQuipment Ltd 17 User Guide

22 Directions of Forces and Couples p Rotor Flywheel r a Couple b c d Figure 11 Directions of Forces and Couples The gyroscopic couple caused by precessing the gyroscope always acts about an axis perpendicular to both the gyroscope rotor and precession axes. The precession direction and rotor rotation direction determine the couple direction.the couple will try to tip the gyroscope in the same direction as the leading edge of the rotor or flywheel (the leading edge faces the direction of travel). For example: In diagram (a) the flywheel spins clockwise and the precession is anticlockwise, so the leading edge of the flywheel moves downwards. The gyroscopic couple tries to tip the rotor downwards. In diagram (b) both the flywheel and precession turn anticlockwise, so the leading edge of the flywheel moves upwards. The gyroscopic couple tries to tip the rotor upwards. User Guide 18 TecQuipment Ltd

23 Experiments Safe Use Wait for the gyroscope to stop before you remove the safety dome. WARNING Fit the safety dome securely before using the gyroscope. If you do not use the equipment as described in these instructions, its protective parts may not work correctly. Directions Around the Gyroscope Precession = Anticlockwise Precession = Clockwise Force Direction = Up = Anticlockwise Force Direction = Down = Clockwise Couple = Clockwise Rotor = Clockwise Rotor = Anticlockwise Couple = Anticlockwise Figure 12 Directions TecQuipment Ltd 19 User Guide

24 User Guide 20 TecQuipment Ltd

25 Experiment 1 - Gyroscopic Couple Direction Aims To prove that there is no couple unless the gyroscope has both precession and rotation. To find the direction of gyroscopic couple in relation to the direction of gyroscope spin and precession. Procedure 1. Create a blank results table, similar to Table 1. Rotor Direction Velocity = 250 (rad.s -1 ) Precession Direction Velocity = 30 (rad.s -1 ) Predicted Couple Direction (clockwise or anticlockwise) Measured Couple Direction (clockwise or anticlockwise) Clockwise No Velocity No Velocity Clockwise Clockwise Clockwise Anticlockwise Anticlockwise Clockwise Anticlockwise Anticlockwise Clockwise Table 1 Blank Results Table 2. Using Figure 11 in the theory and Figure 12, try to predict the couple direction for each of the rotor and precession directions shown in Table Switch on the gyroscope. 4. Press the button to zero the force reading. 5. Remove the safety dome. Carefully and gently push down on the moment arm and note the sign of the couple reading (positive or negative force). Release the arm and then carefully and gently pull up, again noting the sign. 6. Refit the safety dome. 7. Now run the rotor and precession at the velocities and directions indicated in Table Note the couple direction for each line of your results. Results Analysis Compare your measured results with the predictions. Do they compare correctly? TecQuipment Ltd 21 User Guide

26 User Guide 22 TecQuipment Ltd

27 Experiment 2 - Magnitude of Gyroscopic Couple Aims To compare theoretical and actual values of gyroscopic couples. NOTE You could do the tests with clockwise or anticlockwise direction of precession and rotor (or a combination of the two). The results should be the same, but your chart axis would be different. Procedure 1 - Fixed Precession, Varied Rotor Velocity 1. Create a blank results table, similar to Table 2. Moment of Inertia of gyroscope I: Precession Direction and Velocity ω p : Clockwise 30 rad.s -1 Rotor Velocity ω r (rad.s -1 ) Predicted Couple magnitude T (Nm) Measured Couple magnitude T (Nm) Table 2 Blank Results Table 2. Use the given values of inertia and velocity with Equation 1 to predict the couple magnitude for each of the rotor velocities. 3. Switch on the gyroscope. 4. Press the button to zero the force reading. 5. Set the precession velocity to the fixed direction and value as shown. 6. Now adjust the rotor velocity from 250 rad.s -1 clockwise down to 50 rad.s -1 in steps of 50 rad.s -1. At each step, readjust the precession velocity if necessary, allow the velocities to stabilize and record the couple. 7. At each step, before you note the couple reading, tap the side of the unit to help remove any stiction in the force sensor. TecQuipment Ltd 23 User Guide

28 Procedure 2 - Fixed Rotor, Varied Precession Velocity 1. Create a blank results table, similar to Table 3. Moment of Inertia of gyroscope I: Rotor Direction and Velocity ω r : Clockwise (250 rad.s -1 ) Precession Velocity ω p (rad.s -1 ) Predicted Couple magnitude T (Nm) Measured Couple magnitude T (Nm) Table 3 Blank Results Table 2. Use the given values of inertia and velocity with Equation 1 to predict the couple magnitude for each of the precession velocities. 3. Switch on the gyroscope and adjust the controls if necessary to make sure that neither the rotor or precession motors are spinning. 4. Press the button to zero the force reading. 5. Set the rotor velocity to the fixed direction and value as shown. 6. Now adjust the precession velocity from 30 rad.s -1 clockwise down to 5 rad.s -1 in steps of 5 rad.s -1. At each step, readjust the rotor velocity if necessary, allow the velocities to stabilize and record the couple. 7. At each step, before you note the couple reading, tap the side of the unit to help remove any stiction in the force sensor. Results Analysis Create two charts (one for each table of results) of Couple Magnitude (vertical axis) against Velocity. Add your measured and predicted couple magnitudes to the charts to compare the accuracy of the predictions with actual results. What are the possible causes of error? Note the linearity of your results. Why is linearity useful? User Guide 24 TecQuipment Ltd

29 Typical Results Note: These results are typical only. Actual results may differ slightly. Experiment 1 - Gyroscopic Couple Direction Rotor Direction Velocity = 2500 rev.min -1 Precession Direction Velocity = 300 rev.min -1 Predicted Couple Direction (clockwise or anticlockwise) Measured Couple Direction (clockwise or anticlockwise) Clockwise No Velocity 0 0 No Velocity Clockwise 0 0 Clockwise Clockwise Clockwise Clockwise Anticlockwise Anticlockwise Clockwise Clockwise Clockwise Anticlockwise Anticlockwise Anticlockwise Anticlockwise Clockwise Anticlockwise Anticlockwise Table 4 Typical Results Your results should show that the couple is zero* unless the gyroscope has both precession and rotation. NOTE *You may notice a very small couple (maximum 0.1 Nm), determined by how well you zeroed the force reading. Your results with both precession and rotation should be the same as indicated in Figure 11, showing that theory can accurately predict the directions of rotational movement and couples. TecQuipment Ltd 25 User Guide

30 Experiment 2 - Magnitude of Gyroscopic Couple Procedure 1 - Fixed Precession, Varied Rotor Velocity 1.4 Fixed Precession 30 rad.s -1 Both Clockwise 1.2 Couple (Nm) Measured couple Theory couple Rotor (rad.s -1 ) Figure 13 Typical Results for Procedure 1 - Fixed Precession, Varied Rotor Velocity User Guide 26 TecQuipment Ltd

31 Procedure 2 - Fixed Rotor, Varied Precession Velocity 1.4 Fixed Rotor 250 rad.s -1 Both Clockwise 1.2 Couple (Nm) Measured couple Theory couple Precession (rad.s -1 ) Figure 14 Typical Results for Procedure 2 - Fixed Rotor, Varied Precession Velocity Your actual and predicted results should compare well, showing that the theory can predict the magnitude of forces and couples around the gyroscope. You should also note that the results are linear, allowing you to extrapolate or extend them to predict forces in smaller or larger gyroscopes or at higher velocities. Slight differences in the moment of inertia value will affect the results, causing an error that increases with velocity. No two gyroscopes will have identical inertia values, due to the slight differences in the electric motor (which forms part of the gyroscope). The range of values should be within 5% of the nominal value, and can therefore cause an overall error of similar magnitude. Mechanical friction in the gimbal mechanism and the link to the load cell will affect results by a small amount and will also vary between units. It will also change slightly through use. TecQuipment Ltd 27 User Guide

32 User Guide 28 TecQuipment Ltd

33 Maintenance, Spare Parts and Customer Care Maintenance General Regularly check all parts of the equipment for damage, renew if necessary. When not in use, store the equipment in a dry dust-free area, preferably covered with a plastic sheet. If the equipment becomes dirty, wipe the surfaces with a damp, clean cloth. Do not use abrasive cleaners. Regularly check all fixings and fastenings for tightness; adjust where necessary. NOTE Renew or replace faulty or damaged parts or detachable cables with an equivalent item of the same type or rating. Electrical WARNING Only a qualified person may carry out electrical maintenance. Obey these procedures: Assume the apparatus is energised until it is known to be isolated from the electrical supply. Use insulated tools where there are possible electrical hazards. Confirm that the apparatus earth circuit is complete. Identify the cause of a blown fuse before renewing. To renew a broken fuse Isolate the apparatus from the electrical supply. Renew the fuse. Reconnect the apparatus to the electrical supply and switch on. If the apparatus fails again, contact TecQuipment Ltd or your agent for advice. Fuse Location The main fuse is on the back of the base unit at the IEC inlet. Use a flat-blade screwdriver to remove the fuseholder(s). TecQuipment Ltd 29 User Guide

34 Spare Parts Check the Packing Contents List to see what spare parts we send with the apparatus. If you need technical help or spares, please contact your local TecQuipment Agent, or contact TecQuipment direct. When you ask for spares, please tell us: Your Name The full name and address of your college, company or institution Your address The TecQuipment product name and product reference The TecQuipment part number (if you know it) The serial number The year it was bought (if you know it) Please give us as much detail as possible about the parts you need and check the details carefully before you contact us. If the product is out of warranty, TecQuipment will let you know the price of the spare parts. Customer Care We hope you like our products and manuals. If you have any questions, please contact our Customer Care department: Telephone: Fax: For information about all TecQuipment Products and Services, visit: User Guide 30 TecQuipment Ltd