gyroscope

jahangirabad institute of technology

Dynamics Of Machine

NME:603

Presented byMD GULFARAZ ALAMAssistant professorJETGI Barabanki

jahangirabad institute oftechnology 2

UNIT 2Gyroscope


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


How Gyroscopes WorkMechanical 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


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


Angular MomentumWhat is the time derivative of the angular

momentum about the pivot point for the gyroscope?


Gyroscopic couplesConsider 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.


Gyroscopic stabilizationEffect of the Gyroscopic Couple on an Aero plane


Continue…


Terms Used in a Naval ShipThe 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 theeffect of gyroscopic couple on the naval ship in the

following three cases:1. Steering, 2. Pitching, and 3. Rolling.


Continue…


Effect of Gyroscopic Couple on a Naval Ship during Steering

Fig - Naval ship taking a left turn.


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.


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

Fig- Effect of gyroscopic couple on a naval ship during pitching.


Stability of a four wheel drive moving in a curved pathConsider 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

aboveLet 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.


Continue…h = Distance of centre of gravity, verticallyabove the road surface in metres,x = Width of track in metres,IW = Mass moment of inertia of one of thewheels in kg-m2,ωW = Angular velocity of the wheels or velocityof spin in rad/s,IE = Mass moment of inertia of the rotatingparts of the engine in kg-m2,ωE = Angular velocity of the rotating parts ofthe engine in rad/s,G = Gear ratio = ωE /ωW,

v = Linear velocity of the vehicle in m/s = ωW.rW


Effect of the gyroscopic couple on 4wheel driveWe 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 samedirection. If the rotating parts of the engine revolves in opposite

direction, then negative sign is used.


VibrationVibration: 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.


Types of vibratory motion1. 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.


Types of free vibrations1. Longitudinal vibrations, 2. Transverse vibrations,

and 3. Torsional vibrations.


Free vibrationWhen 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


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.


Two degree of freedom freedom systemSome 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.


Whirling of shaftIn 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.


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.


Thank you

Engineering

gyroscope