gyroscope
- 1. jahangirabad institute of technology
- 3. jahangirabad institute oftechnology 3 What is a gyroscope? Device used to measure or maintain orientation Works on the principals of angular momentum Initial axis of rotation is conserved Consists of a spinning mass on an axel
- 4. How Gyroscopes Work Mechanical Gyroscope Spinning mass mounted on gimbals Free-output vs. Fixed-output Sensors on axis to detect rotation Procession Electronic Gyroscope Coriolis vibratory gyroscope Proof mass fed oscillating current to induce vibrations Vibrating mass tends to oscillate in initial plane of reference When rotated, oscillations in orthogonal plane detected by circuitry jahangirabad institute oftechnology 4
- 5. Common Uses Gyrocompass Used by ships to find true north Seeks minimum potential energy Stability Assistance Hubble Space Telescope Bicycles Inertial Guidance System Guided Missiles Measure angular velocity in inertial reference frame Detect changes to orientation Combined with accelerometer for 6 axis sensor jahangirabad institute oftechnology 5
- 6. Angular Momentum What is the time derivative of the angular momentum about the pivot point for the gyroscope? jahangirabad institute oftechnology 6
- 7. Gyroscopic couples Consider a disc spinning with an angular velocity ω rad/s about the axis of spin OX, in anticlockwise direction when seen from the front, as shown in Fig. Since the plane in which the disc is rotating is parallel to the plane YOZ, therefore it is called plane of spinning. jahangirabad institute oftechnology 7
- 8. Gyroscopic stabilization Effect of the Gyroscopic Couple on an Aero plane jahangirabad institute oftechnology 8
- 10. Terms Used in a Naval Ship The top and front views of a naval ship are shown in Fig. The fore end of the ship is called bow and the rear end is known as stern or aft. The left hand and right hand sides of the ship, when viewed from the stern are called port and star-board respectively. We shall now discuss the effect of gyroscopic couple on the naval ship in the following three cases: 1. Steering, 2. Pitching, and 3. Rolling. jahangirabad institute oftechnology 10
- 12. Effect of Gyroscopic Couple on a Naval Ship during Steering jahangirabad institute oftechnology 12 Fig - Naval ship taking a left turn.
- 13. The effect of this reactive gyroscopic couple is to raise the bow and lower the stern. 1. The effect of this reactive gyroscopic couple is to raise the bow and lower the stern. 2. When the rotor rates in the anticlockwise direction, when viewed from the stern and the ship is steering to the left, then the effect of reactive gyroscopic couple will be to lower the bow and raise the stern. 3. When the ship is steering to the right under similar conditions as discussed in note 2 above, then the effect of reactive gyroscopic couple will be to raise the bow and lower the stern. jahangirabad institute oftechnology 13
- 14. Effect of gyroscopic couple on a naval ship during pitching Pitching is the movement of a complete ship up and down in a vertical plane about transverse axis, as shown in Fig jahangirabad institute oftechnology 14 Fig- Effect of gyroscopic couple on a naval ship during pitching.
- 15. Stability of a four wheel drive moving in a curved path Consider the four wheels A, B, C and D of an automobile locomotive taking a sturn towards left as shown in Fig. The wheels A and C are inner wheels, whereas B and D are outer wheels. The centre of gravity (C.G.) of the vehicle lies vertically above Let m = Mass of the vehicle in kg, W = Weight of the vehicle in Newton = m.g, rW = Radius of the wheels in meters, R = Radius of curvature in metres the road surface. jahangirabad institute oftechnology 15
- 16. Continue… h = Distance of centre of gravity, vertically above the road surface in metres, x = Width of track in metres, IW = Mass moment of inertia of one of the wheels in kg-m2, ωW = Angular velocity of the wheels or velocity of spin in rad/s, IE = Mass moment of inertia of the rotating parts of the engine in kg-m2, ωE = Angular velocity of the rotating parts of the engine in rad/s, G = Gear ratio = ωE /ωW, v = Linear velocity of the vehicle in m/s = ωW.rW jahangirabad institute oftechnology 16
- 17. Effect of the gyroscopic couple on 4wheel drive We know that velocity of precession, ωP = v/R ∴ Gyroscopic couple due to 4 wheels, CW = 4 IW.ωW.ωP and gyroscopic couple due to the rotating parts of the engine, CE = IE.ωE.ωP = IE.G.ωW.ωP ∴ Net gyroscopic couple, C = CW ± CE = 4 IW.ωW.ωP ± IE.G.ωW.ωP = ωW.ωP (4 IW ± G.IE) The positive sign is used when the wheels and rotating parts of the engine rotate in the same direction. If the rotating parts of the engine revolves in opposite direction, then negative sign is used. jahangirabad institute oftechnology 17
- 18. Vibration Vibration: When elastic bodies such as a spring, a beam and a shaft are displaced from the equilibrium position by the application of external forces, and then released, the execute a vibratory motion. jahangirabad institute oftechnology 18
- 19. Types of vibratory motion 1. Free or natural vibrations. When no external force acts on the body, after giving it an initial displacement, then the body is said to be under free or natural vibrations. The frequency of the free vibrations is called free or natural frequency. 2. Forced vibrations. When the body vibrates under the influence of external force, then the body is said to be under forced vibrations. 3. Damped vibrations. When there is a reduction in amplitude over every cycle of vibration, the motion is said to be damped vibration. jahangirabad institute oftechnology 19
- 20. Types of free vibrations 1. Longitudinal vibrations, 2. Transverse vibrations, and 3. Torsional vibrations. jahangirabad institute oftechnology 20
- 21. Free vibration When a system is initially disturbed by a displacement, velocity or acceleration, the system begins to vibrate with a constant amplitude and frequency depend on its stiffness and mass. This frequency is called as natural frequency, and the form of the vibration is called as mode shapes jahangirabad institute oftechnology 21
- 22. jahangirabad institute oftechnology 22 Single degree free and damped vibration. Single degree free and damped vibration. If the coordinates x and y are used to describe the motion, it must be recognized that these coordinates are not independent.
- 23. Two degree of freedom freedom system Some examples of two degree of freedom systems are shown in the figure. The first figure shows a two mass – two spring system that is described by two linear coordinates x1 and x2. The second figure denotes a two rotor system whose motion can be specified in terms of θ1 and θ2. The motion of the system in the third figure can be described completely either by X and θ or by x, y and X. jahangirabad institute oftechnology 23
- 24. Whirling of shaft In actual practice, a rotating shaft carries different mountings and accessories in the form of gears, pulleys, etc. When the gears or pulleys are put on the shaft, the centre of gravity of the pulley or gear does not coincide with the centre line of the bearings or with the axis of the shaft, when the shaft is stationary. jahangirabad institute oftechnology 24
- 25. jahangirabad institute oftechnology 25 Critical speed. The speed at which the shaft runs so that the additional deflection of the shaft from the axis of rotation becomes infinite, is known as critical or whirling speed. Fig- Critical or whirling speed of a shaft.