In our earlier posts, we discussed about the free gyro, Gyroscope conversion, damped oscillation and its settling period. In this post, we will discuss about undamped oscillation of Gyro.
The free gyro does not contain any instrument which may be called a compass. The direction of the spin axis relative to the earth’s’ surface continually changes unless directed towards one of the celestial poles. Even then unwanted frictional forces in the bearings would cause the axis to wander. In order to make the spin axis of a gyro point in any constant direction with respect to the earth’s surface, the present drifting and tilting action caused by the rotation of the the Earth must be compensated by equal and opposite motions. To produce a Gyroscope, we have to make it seek and settle in the meridian, and it should automatically return to meridian, if disturbed.
The first step in converting a free gyro compass is to ‘control’ the gyro or make it north seeking. In general, this is done by creating torque about the horizontal east west axis, which is effective when the gyro tilts out of the horizontal. This torque will produce a precession in azimuth which causes the spin axis to seek the meridian.
For this we take a Gyro rotor contained within a rotor case. The rotor is supported through the spin axis bearings. A Control weight is attached to the top of the rotor case such that when the spin axis is horizontal the vertical through the center of gravity of the weight passes through the center of the rotor. In this condition, the weight will produce no torque on the rotor and is completely ineffective.
The spin axis of the rotor, if initially horizontal, will not remain so. The rotation of the earth will cause the spin axis to develop a tilt. If the spin axis is directed to the east of the meridian, that end will tilt upwards. The weight now causes a torque about the horizontal axis which tends to topple the gyro even further out of the horizontal. If this point is imagined to be carried 90° around in the direction of spin, which is anticlockwise as viewed from the south, it will be evident that the spin axis will precess in azimuth such that the north end moves to the west, that is towards the meridian. This precession is called the control precession.
The direction of spin of the rotor must be in such a direction as to produce a westerly precession of the north end of the spin axis when that end is tilted upwards, and an easterly precession of that end when it is tilted downwards. It must be understood that the control precession will not always be directed towards the meridian. As long as the north end of the spin axis is tilted upwards the precession will carry that end towards the west. The precession will continue even after the axis has passed to the west of the meridian, and will then be carrying the north end away from the meridian.
Similarly when the north end is tilted downwards and directed to the east of the meridian there will be an easterly precession taking that end away from the meridian. The result of the torque about the horizontal axis is to produce a precession about the vertical axis and that is a precession in azimuth. Thus, the north end of the spin axis precess to the west when that end is tilted upwards, and to the east when it is tilted downwards. When the rotor is rotating, the gyro compass is kept at any intermediate latitude, both the force will effect to poles of gyro compass, the resultant of both will trace a elliptical path.
When the gyro compass comes towards meridian it has got maximum tilt and when it goes away from meridian its tilt is decreasing and so the torque is also decreasing. The torque is directly proportional to tilt angle which try to bring the gyro poles towards the meridian.