The Concept of Gyroscope - Essay Example

INSTRUMENTATION SYSTEM By: Course: Tutor: University: Date: TABLE OF CONTENTS PG No. SECTION A: THE ANALYSIS OF THE CALIBRATION RESULTS……………………..3 TABLE 1: A Converted Table i.e. From Psi Into Pascal The Si Unit Of Pressure………………………………………………………………………………….3 TABLE 2: Shows The Output And The Si Units……………………………………4 TABLE 3: The Accuracy Of Percentage Error Of The Full-Scale Deflection………5 GRAPH 1: A graph of SI units against the Loading Output in psi units……………7 GRAPH 2: A graph of SI Units against the Unloading Output Pressure…………….7 SECTION B: INVESTIGATION REPORT…………………………………………………8 Introduction……………………………………………………………………………8 Components of Gyroscope……………………………………………………………9 Working of Gyroscope………………………………………………………………10 a. How MEMS gyroscope sense angular velocity………12 b. The principle of gyro sensor…………………………14 Application of Gyroscope……………………………………………………………16 Conclusion…………………………………………………………………………….18 References………………………………………………………………………………19 SECTION A: THE ANALYSIS OF THE CALIBRATION RESULTS Section A: The Analysis of the Calibration Results LOADING UNLOADING Applied Pressure SI Units indicated Pressure SI Units Applied Pressure SI Units Indicated Pressure SI Units 0 psi 0 pa 5 psi 34473.78645 Pa 0 psi 0 pa 7 psi 48263.30102999999508 Pa 10 psi 68947.5729 Pa 15 psi 103421.35935 Pa 10 psi 68947.5729 Pa 17.5 psi 120658.2525749999913 Pa 20 psi 137895.1458 Pa 26 psi 179263.68954 Pa 20 psi 137895.1458 Pa 28.5 psi 196500.582765 Pa 30 psi 206842.7187 Pa 34 psi 234421.7478599999740 Pa 30 psi 206842.7187 Pa 37 psi 255106.0197299999709 Pa 40 psi 275790.2916 Pa 45 psi 310264.0780499999528 Pa 40 psi 275790.2916 Pa 48 psi 330948.3499199999496 P 50 psi 344737.8644999999669 Pa 55 psi 379211.65095 Pa 50 psi 344737.8644999999669 Pa 58 psi 399895.92282 Pa 60 psi 413685.4374 Pa 65 psi 448159.2238499999512 Pa 60 psi 413685.4374 Pa 67 psi 461948.7384299999685 Pa 70 psi 482633.0102999999654 Pa 74 psi 510212.0394599999418 Pa 70 psi 482633.0102999999654 Pa 75.5 psi 520554.1753949999693 Pa 80 psi 551580.5832 Pa 86 psi 592949.12694 Pa 80 psi 551580.5832 Pa 87 psi 599843.88423 Pa 90 psi 620528.156099999906 Pa 95 psi 655001.942549999920 Pa 90 psi 620528.156099999906 Pa 96 psi 661896.699839999899 Pa 100 psi 689475.728999999934 Pa 105 psi 723949.51545 Pa 100 psi 689475.728999999934 Pa 105 psi 723949.51545 Pa Table 1: A converted table i.e. from psi into Pascal the SI Unit of Pressure The above table shows the values of the converted measure of the pound per square inch to the standard international units (SI Units) of pressure which is Pascal. For every one psi unit, there is 6894.75729 Pascal. Therefore, we can say that, 1 psi = 6894.75729 Pascal. From this background, we have been able to convert the rest of the result into the standard units of pressure. LOADING OUTPUT SI UNITS UNLOADING OUTPUT SI UNITS 5 psi 34,473.78645 Pa 7 48263.30102999999508 pa 5 psi 34,473.78645 pa 7.5 51710.679675 Pa 6 psi 41,368.5437 pa 8.5 58605.4369649999935 Pa 4 psi 27579.02916 pa 7 48263.30102999999508 pa 5 psi 34,473.78645 Pa 8 55158.05832 Pa 5 psi 34,473.78645 Pa 8 55158.05832 Pa 5 psi 34,473.78645 Pa 7 48263.30102999999508 pa 4 psi 27579.02916 pa 5.5 37921.165095 Pa 6 psi 41,368.5437 pa 7 48263.30102999999508 pa 5 psi 34,473.78645 Pa 6 41368.54373999999370 Pa 5 psi 34,473.78645 Pa 5 34,473.78645 Pa Table 2: Shows the output and the SI Units To get the output data of the experiment, the difference of the applied pressure and the indicated pressure is determined. Therefore, the applied pressure is deducted from the indicated pressure and their difference is the one that is termed to be the output pressure. For instance, from the first row of table 1, the applied pressure is 0 psi while the indicated pressure is 5 psi. The output pressure in this case is 5 psi – 0 psi = 5 psi. The same procedure is done to the proceeding values in both loading and unloading column to get the corresponding pressure output. Loading output Unloading output Error Percentage error (%) 5 psi 7 2 5 5 psi 7.5 2.5 5.2 6 psi 8.5 2.5 5.2 4 psi 7 3 5.9 5 psi 8 3 5.9 5 psi 8 3 5.9 5 psi 7 2 5 4 psi 5.5 1.5 4.8 6 psi 7 1 3 5 psi 6 1 3 5 psi 5 0 0.6 Total Loading output Total unloading output Total error Total Percentage error 55 76.5 21.5 49.5 Table 3: The accuracy of percentage error of the Full-scale deflection David, (2013) suggest that in case you want to determine the accuracy of a given experiment, the percent error is the best tool to evaluate the precision of the procedure. In calculating the percentage error, these are the steps followed. 1. Subtract the value of the output pressure of the loading output pressure from that of the unloading pressure output. The difference might bring a negative sign but ignore it and assume it is positive. The value gotten is the error. 2. Find a quotient of the error with the output loading pressure. 3. Multiply the result with 100 to convert it into percentage. The value realized is the percentage error. The formula for the percentage error is as follows; Percentage = Loading Output – Unloading Output X 100 Full Scale Deflection (FSD) Graph 1: A graph of SI units against the Loading Output in psi units. Graph 2: A graph of SI units against Unloading Output in psi units. SECTION B: INVESTIGATION REPORT Introduction The term gyroscope refers to a spinning helm in which the rotational axis of is liberated to presuppose any compass reading by itself (Andrew, 2009). This device uses the gravity force of the Earth to determine the orientation. The gyroscope structure comprises of a loosely rotating disk known as the rotor, which is built on a spiraling axis at the central of a larger and stabilized wheel. As the axis rotates, the rotor maintains it stationary position indicating the central gravitational force (Ash et. al., 2010).  Range, et. al., (2015) has suggested that gyroscope as an immovable gyratory object which is regular on the subject of one axis. In most cases, the gyroscope is used specifically for raw-boned movement of a body. When revolving, the compass reading of such axis is not interfered with by the slanting or rotation of the escalating, following the change of the pointed impetus (Andrew, 2009). As a result of this, gyroscopes are important for determining and upholding orientation. Gyroscopes operating principles are applicable in various faculties. Some of these areas of application include; internal navigation systems, for instance, situations in which the magnetic compasses fail to work as found in Hubble telescope (Ash et. al., 2010). Also, the principle of the gyroscope can be used for stabilizing a flying vehicle such as radio-piloted helicopters and unmanned in-flight vehicles. The gyroscope is characterized by their exactitude, a feature that makes them fundamental in gyro theodolites for maintaining the direction, especially in the tunnel mining (Tong, 2011). In general, the gyroscope is used to establish gyrocompasses which are the foil for to magnetic compasses. It is usually employed in ships, spacecraft, aircraft; generally, in vehicles. The gyrocompass that is created by gyroscope helps in maintain stability in Hubble Space Telescope, motorcycles, ships, and bicycles. I also used as a common and integral component of an inertial guidance system (Range, et. al., 2015). Components of Gyroscope In every mechanical operational system or device, a conventional gyroscope is involved and of much importance (Tong, 2011). Therefore, this gyroscope is known to be a mechanism that is composed of a rotor journeyed to revolve around a single axis, the journals of the rotor mounting in an interior ring also known as gimbals; these inner gimbals are journaled for vacillation in an exterior ring for an entirety of double gimbals (David, 2013). Figure 1: Shows a gyro wheel. Reaction arrows about the output axis (blue) correspond to forces applied about the input axis (green) and vice versa. The external or the exterior gimbal/ring is the frame of the gyroscope. This part is mounted and inclined at an angle to pivot an axis in its plane. The position of the axis is determined by the pivotal support offered by the outer ring of the gyroscope. The outer ring acquires a single degree of gyratory freedom while its axis acquires none (Range, et. al., 2015). The adjacent interior ring is built up in the gyroscope structure that is the outer gimbal. The reason behind this is to provide the essential support for an alignment in its level surface that is usually vertical to the crucial alliance with the gyroscope structure; the outer gimbal/ring. Unlike the outer gimbals, the inner gimbals possess two degrees of the gyratory freedom (David, 2013). Figure 2: Shows a gyroscope The other crucial part of the gyroscope is the axle of the rotary wheel. It is from this section that the spinning axis is known and defined. The rotor is built in that it spins about an axis, and usually, this spinning is vertical to the axis of the interior ring (Peter & Hughes, 2014). Therefore, the rotor in this axis acquires three degrees of rotational freedom while its axis gains two degrees. The wheel reacts back to the force posed in the effort axis by a rejoinder force on the amount produced axis. Working of the Gyroscope The following is an account of working physics that explain the manner in which gyroscope operates. According to David, (2013), as an alternative of a full rim, the points A, B, C, and D represents the four main masses of the area of the rim. These masses are imperative in envisaging the workability of the gyroscope. The base axis is made of immobile, however, can pivot in every direction. When a slanting energy is applied to the apex axis, the point A moves up while C moves down (the Fig. 1 above). Given that the gyroscope rotates in a clockwise route, point A will assume the position of point B after the gyroscope makes a 90-degree turn. The occurrence is similar to both point C and D. Point A still moves upward when it has made 90 degrees turn (figure 2 above), similarly, point C will be moving downwards. The motion combination of both point A and C makes the axis swivel in “precession plane” towards right direction (figure 2 above). A gyroscope axis moves at an angle of 90 degrees to a swiveling movement towards the right direction. In case the gyroscope was rotating counterclockwise, its axis would travel in the precession plane but to towards the left direction. However, if the motion of gyro was clockwise and the tilting energy was a pull as a substitute of push, the precession turns to the left direction also. After the gyroscope has turned another 90 degrees (figure 3), point C assumes the position of point A during the first application of the tilting force (Foucault, 2012). The downward movement of point C is counteracted by the slanting energy, therefore; the axis doesn’t turn around in the tilting force plane. When the tilting force pushes the axis intensively, the rim pushes the axis back, especially when the rim has made a 180 degrees turn. In such cases, the axis moves in the tilting force’s direction (Peter & Hughes, 2014). a. How MEMS gyroscope sense angular velocity Sternberg & Schwalm (2012) suggests that the gyroscope sensor contained by the Micro-electro Mechanical Systems (MEMS) is minutiae. They are 1 to 100 micrometer which is equivalent to human hair. When the gyroscope is swiveled, a small reverberating mass is changed while the angular velocity shifts. Figure 3: Internal operational view of a MEMS gyro sensor MEMS gyroscopes are of different types. Each type comprises of some forms of vacillating elements from where the velocity and direction shift is sensed (Sternberg & Schwalm 2012). This is possible because, according to the law of motion conversion, a vibrating item will continue to vibrate in the parallel plane and any pulsation change is used to obtain a deviation in the direction (Peter & Hughes, 2014). The deviation is as the result of Coriolis force, usually orthogonal to the pulsating object. For instance, Tuning Fork Gyroscope is built with a pair of lots mainly motivated to oscillate with equivalent amplitude, however, operate in opposite directions (Peter & Hughes, 2014). When it has rotated, the Coriolis force establishes an orthogonal pulsation that is detected by different mechanisms (Provatidis, 2012). The diagram below applies the comb-type framework to direct the regulation fork into reverberation. Figure 4: The rotary impacts the verification masses to pulsate out of the level surface whereby such movement is detected capacitive with a convention CMOS ASIC b. The principle of gyro sensor The gyroscope instrument works under the principle underlying in the operation of the gyro sensor (Walter, 2012).  Gyro sensors are also known as angular rate sensors/angular velocity sensors. As the name goes, this device is used to sense the angular velocity of the gyroscope. Angular velocity Figure 5: The angular velocity The literature of Provatidis, (2012) gives the definition of the angular velocity is as the change in rotary angle in every unit of time. Therefore, angular velocity is given in degrees/seconds (deg/s) Especially vibration gyro sensors, the working mannerism, are quite precise and simple. The vibration gyro sensor detects angular velocity mainly from the Coriolis power useful to a vibrating item (Walter, 2012).  To explain how the angular velocity sensor operates, the framework and the theoretical work of Epson’s Double-T-structure crystal element. 1. Usually, a drive arm pulsates in a definite direction. 2. Direction of rotation 3. When the gyro is rotated, the Coriolis force acts on the drive arms, producing vertical vibration. 4. The stationary part bends due to vertical drive arm vibration, producing a sensing motion in the sensing arms. 4. The movement of a pair of detecting arms generates a potential difference under which angular velocity is detected (Provatidis, 2012). The angular velocity is transmitted to, and output as, an electrical signal. Application of Gyros According to E.S. Snell (2010), the precession property of gyroscope is useful in keeping the monorail trains upright when negotiating a corner. The hydraulic cylinder pulls and pushes, as required by a single alliance of a heavy gyroscope. When items turn around an axis, they possess angular velocity. In the figure below, the z-axis aligns with the axis of the rotary on the helm (Foucault, 2012). Figure 6: A triple axis MEMS gyro If a sensor is attached to the wheel as it is above, an angular velocity of z-axis can be measured, unlike other axes which will not give a measurement of any rotary (E.S. Snell, 2010). A triple axis MEMS gyro shown above is used to measure the rotary revolving within the three axes; x, y and z. Gyroscopes are usually applicable to the objects that are spinning slowly (Provatidis, 2012). Like aircraft where the gyroscope is applicable does not spin, however, they revolve for a few degrees of every alignment (Foucault, 2012). By sensing these minutiae changes, gyroscopes assist the air travel of the aircraft. Conclusion According to Andrew Gray (2009), gyroscope is applied in almost every rotary performance. In mechanics and engineering faculties, gyroscope is very essential since it’s the focal point as well as a pivotal to many of the developments. Demonstration gyroscopes are mainly available in mostly in the learning environments especially in schools such as colleges to educate about physics of gyroscopes. The traditional gyroscopes are gimbaled to give room for the users to comprehend how the gyroscope can persistently point in a focused direction. A gimbaled gyroscope permits the user to position powers to single axis to observe the manner in which gyroscope will respond (Tong, 2011). There are a number of computer pointing devices (in effect a mouse) on the market that have gyroscopes inside them allowing you to control the mouse cursor while the device is in the air!  They are also wireless so are perfect for presentations when the speaker is moving around the room Andrew Gray (2009). The gyroscope inside tracks the movements of your hand and translates them to cursor movements. The concept of gyroscope cannot be avoided at any point in the history of the humanity. We should embrace the concept and value it much. For instance, Tuning Fork Gyroscope is built with a pair of lots mainly motivated to oscillate with equivalent amplitude, however, operate in opposite directions (Peter & Hughes, 2014). When it has rotated, the Coriolis force establishes an orthogonal pulsation that is detected by different mechanisms (Provatidis, 2012). References Andrew Gray (2009). A Treatise on Gyrostatics and Rotational Motion: Theory and Applications (Dover, New York) Ash, M E; Trainor, C V; Elliott, R D; Borenstein, J T; Kourepenis, A S; Ward, P A; Weinberg, M S (14–15 September 2010). "Micromechanical inertial sensor development at Draper Laboratory with recent test results". Symposium Gyro Technology Proceedings. C. Tong (2011). American Journal of Physics vol. 77, pages 526–537 David May (2013). "Modeling the dynamically tuned gyroscope in support of high-bandwidth capture loop design". Proc. SPIE 3692: 101–111.Doi: 10.1117/12.352852 E.S. Snell (2010) Drawings of Walter R. Johnson's gyroscope (“rotascope”) was used to illustrate phenomena in the following lecture: disturbances, “Board of Regents, Tenth Annual Report of the Board of Regents of the Smithsonian Institution.... (Washington, D.C.: Cornelius Wendell, 2008), pages 175–190. Einstein.stanford.edu. "The GP-B instrument is designed to measure changes in gyroscope spin axis orientation to better than 0.5 milliarcseconds (1.4x10-7 degrees) over a one-year period" H. Sternberg; C. Schwalm (2012). "Qualification Process for MEMS Gyroscopes for the Use in Navigation Systems" (PDF). International Society for Photogrammetric and Remote Sensing Proceedings. Archived from the original (PDF) on 2 October 2011.  Foucault (2012) On the phenomena of the orientation of rotating bodies carried along by an axis fixed to the surface of the earth — New perceptible signs of the daily movement. Académie des Sciences (Paris), vol. 35, pages 424–427. Available on-line Peter C. Hughes (2014). Spacecraft Attitude Dynamics I Provatidis, C. G. (2012). Revisiting the Spinning Top, International Journal of Materials and Mechanical Engineering, Vol. 1, No. 4, pp. 71–88, open access at Ijm-me.org Range, Shannon K'doah; Mullins, Jennifer. (2015) "Brief History of Gyroscopes". Archived from the original on 2015-07-10 Walter R. Johnson (January 2012). "Description of an apparatus called the rotascope for exhibiting several phenomena and illustrating certain laws of rotary motion", The American Journal of Science and Art, 1st series, vol. 21, no. 2, pages 265–280. Read More