Note for Dynamics of Machinery - DM By JNTU Heroes

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SYLLABUS UNIT – I PRECESSION : Gyroscopes, effect of precession motion on the stability of moving vehicles such as motor car, motor cycle, aero planes and ships. Static and dynamic force analysis of planar mechanisms. UNIT – II FRICTION : Inclined plane, friction of screw and nuts, pivot and collar, uniform smartworlD.asia pressure, uniform wear, friction circle and friction axis : lubricated surfaces, boundary friction, film lubrication. UNIT –III Clutches: Friction clutches- Single Disc or plate clutch, Multiple Disc Clutch, Cone Clutch, Centrifugal Clutch. BRAKES AND DYNAMOMETERS : Simple block brakes, internal expanding brake, band brake ofvehicle. Dynamometers – absorption and transmission types. General description and methods of operations. UNIT – IV TURNING MOMENT DIAGRAM AND FLY WHEELS : Turning moment – Inertia Torque connecting rod angular velocity and acceleration, crank effort and torque diagrams – Fluctuation of energy – Fly wheels and their design. 1

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UNIT-V GOVERNERS : Watt, Porter and Proell governors. Spring loaded governors – Hartnell and hartung with auxiliary springs. Sensitiveness, isochronism and hunting. UNIT – VI BALANCING : Balancing of rotating masses Single and multiple – single and different planes. UNIT –VII Balancing of Reciprocating Masses: Primary, Secondary, and higher balancing of reciprocating masses. Analytical and graphical methods. Unbalanced forces and couples – examination of “V” multi cylinder in line and radial engines for primary and secondary balancing, locomotive balancing – Hammer blow, Swaying couple, variation of tractive efforts. UNIT – VIII smartworlD.asia VIBRATION : Free Vibration of mass attached to vertical spring – oscillation of pendulums, centers of oscillation and suspension. Transverse loads, vibrations of beams with concentrated and distributed loads. Dunkerly’s methods, Raleigh’s method. Whirling of shafts, critical speeds, torsional vibrations, two and three rotor systems. Simple problems on forced damped vibration Vibration Isolation & Transmissibility TEXT BOOKS : 1. Theory of Machines / S.S Ratan/ Mc. Graw Hill Publ. 2. Theory of Machines / Jagadish Lal & J.M.Shah / Metropolitan. REFERENCES: 1. Mechanism and Machine Theory / JS Rao and RV Dukkipati / New Age 2. Theory of Machines / Shiegly / MGH 3. Theory of Machines / Thomas Bevan / CBS Publishers 4. Theory of machines / Khurmi/S.Chand. 2

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UNIT – I PRECESSION Introduction ‘Gyre’ is a Greek word, meaning ‘circular motion’ and Gyration means the whirling motion. A gyroscope is a spatial mechanism which is generally employed for the study of precessional motion of a rotary body. Gyroscope finds applications in gyrocompass, used in aircraft, naval ship, control system of missiles and space shuttle. The gyroscopic effect is also felt on the automotive vehicles while negotiating a turn. A gyroscope consists of a rotor mounted in the inner gimbal. The inner gimbal is mounted in the outer gimbal which itself is mounted on a fixed frame as shown in Fig.. When the rotor spins about X-axis with angular velocity ω rad/s and the inner gimbal precesses (rotates) about Y-axis, the spatial mechanism is forced to turn about Z-axis other than its own axis of rotation, and the gyroscopic effect is thus setup. The resistance to this motion is called smartworlD.asia gyroscopic effect. ANGULAR MOTION A rigid body, (Fig.) spinning at a constant angular velocity ω rad/s about a spin axis through the mass centre. The angular momentum ‘H’ of the spinning body is represented by a vector whose magnitude is ‘Iω’. I represents the mass amount of inertia of the rotor about the axis of spin. 3

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The direction of the angular momentum can be found from the right hand screw rule or the right hand thumb rule. Accordingly, if the fingers of the right hand are bent in the direction of rotation of rotor, then the thumb indicates the direction of momentum. GYROSCOPIC COUPLE smartworlD.asia Consider a rotary body of mass m having radius of gyration k mounted on the shaft supported at two bearings. Let the rotor spins (rotates) about X-axis with constant angular velocity ω rad/s. The X-axis is, therefore, called spin axis, Y-axis, precession axis and Z-axis, the couple or torque axis (Fig.). The angular momentum of the rotating mass is given by, 4