Gyroscopic effect on rotor
- 1. Presented by: RONAK D. SONI Assistant Professor CHAPTER 1: GYROSCOPE GYROSCOPIC EFFECT ON ROTOR
- 2. 2By: Ronak Soni (RDS) Gyroscopic effect on Rotor
- 3. 3 Consider a disc fixed rigidly to a rotating shaft such that the polar axis of the disc makes an angle with the shaft axis, as shown in Figure. By: Ronak Soni (RDS) Gyroscopic effect on Rotor
- 4. 4 Let the shaft rotates with an angular velocity ω rad/s in the clockwise direction when viewed from the front. A little consideration will show that the disc will also rotate about OX with the same angular velocity ω rad/s. Let OP be the polar axis and OD the diametral axis of the disc. Angular velocity of the disc about the polar axis OP or the angular velocity of spin = ωcosθ ... (Component of in the direction of OP) Since the shaft rotates, therefore the point P will move in a plane perpendicular to the plane of paper. In other words, precession is produced about OD. Angular velocity of the disc about the diametral axis OD or the angular velocity of precession = ωsinθ By: Ronak Soni (RDS) Gyroscopic effect on Rotor
- 5. If IP is the mass moment of inertia of the disc about the polar axis OP, then gyroscopic couple acting on the disc, CP = IP. ωcosθ.ωsinθ = ½×IP.ω2sin2θ; (∵ 2 sinθ cosθ=sinθ2) The effect of this gyroscopic couple is to turn the disc in the anticlockwise when viewed from the top, about an axis through O in the plane of paper. Now consider the movement of point D about the polar axis OP. In this case, OD is axis of spin and OP is the axis of precession. Angular velocity of disc about OD or angular velocity of spin, = ωsinθ and angular velocity of D about OP or angular velocity of precession = ωcosθ 5By: Ronak Soni (RDS) Gyroscopic effect on Rotor
- 6. 6 If ID is the mass moment of inertia of the disc about the diametral axis OD, then gyroscopic couple acting on the disc, CD = ID. ωcosθ.ωsinθ = ½×ID.ω2sin2θ The effect of this couple will be opposite to that of CP. Resultant gyroscopic couple acting on the disc, C = CP – CD =1/2×ω2sin2θ (IP – ID) This resultant gyroscopic couple will act in the anticlockwise direction as seen from the top. In other words, the shaft tends to turn in the plane of paper in anticlockwise direction as seen from the top, as a result the horizontal force is exerted on the shaft bearings. By: Ronak Soni (RDS) Gyroscopic effect on Rotor
- 7. 7By: Ronak Soni (RDS) Gyroscopic effect on Rotor
- 8. ANY QUERY PLEASE? 8By: Ronak Soni (RDS) Gyroscopic effect on Rotor