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Figure 3-10.—Right-hand rule for determining direction of precession.
This three-finger rule is useful for analyzing any gyroscope motion problem because if the directions of any
two of the three vectors are known, the direction of the third vector can be found and the motion around this
vector may be determined.
Q-9. What type of force acts ONLY through the center of gravity of a gyro, and does NOT cause precession?
Q-10. The amount of precession that results from a given force is determined by what quantity?
Q-11. What factor determines the direction a gyro will precess in response to a particular force?
Q-12. When using the tight-hand rule to determine precession, which finger indicates the direction of the applied force?
DEGREES OF FREEDOM
A gyro can have different degrees of freedom, depending on the number of gimbals in which it is supported and
the way the gimbals are arranged. Do not confuse the term "degrees of freedom" with an angular value such as
degrees of a circle. The term, as it applies to gyros, is an indication of the number of axes about which the
rotor is free to precess.
A gyro mounted in two gimbals has two degrees of freedom. When two gimbals are used, the gyro is said to be UNIVERSALLY MOUNTED. This arrangement provides two axes about which the gyro can precess. These two axes and the spin axis intersect at the center of gravity of the entire system (excluding the support). Because of this arrangement, the force of gravity does not exert a torque to cause precession. The rotor, inner gimbal, and outer gimbal are balanced about the three principal axes.
TWO DEGREES-OF-FREEDOM GYROS
The two-degrees-of-freedom (free) gyros can be divided into two groups. In the first group, the gyro's spin axis is perpendicular to the surface of the Earth. Thus the gyro's rotor will spin in a horizontal
plane. These gyros are used to establish vertical and horizontal planes to be used where stabilized reference planes are needed.
In the second group, the gyro's spin axis is either parallel to the surface of the Earth or at some angle other than perpendicular. The spin axis of the gyro in the gyrocompass, for example, is maintained in a plane parallel to the surface of the Earth It is aligned in a plane of the north-south meridian. Once set, it will continue to point north as long as no disturbing force causes it to precess out of the plane of the meridian.
Effect of Rotation of the Earth
As you have learned, a free gyro maintains its spin axis fixed in space, and not fixed relative to the Earth's surface. To understand this, imagine yourself in a space ship somewhere out in space and looking at the South Pole of the Earth. You see a sphere rotating clockwise, with the South Pole in the center. Maneuver your ship until it is on a direct line with the South Pole and then cut in the automatic controls to keep it in this position. You will now see the Earth make a complete rotation every 24 hours.
You could keep track of that rotation by driving a big post into the Equator as shown in view A of figure 3-11. If this post were upright at 1200, the Earth's rotation would carry it around so it would be pointing to your right at 1800. Likewise, the Earth's rotation would carry the post around so that at 2400 it would be upside down. Then, at 0600 the next day, the post would be pointing to your left. Finally, at 1200 the next day the post would be back in its original position, having been carried, with the Earth, through its complete rotation. Notice that the post has many positions as you observe it—because it is attached to the Earth's surface and does not have rigidity in space.
Figure 3-11A.—Fixed direction in space. Post on the equator viewed from space.
If you put a gyroscope in place of the stake, you will see a different action. Imagine a gyroscope mounted at
the Equator with its spin axis aligned with the E/W axis of the Earth. The gyro is spinning and has rigidity in
space. Now look at view B. At 1200 the spinning axis is horizontal with respect to the Earth's surface. At 1800
the spinning axis is vertical with respect to the Earth's surface; but the gyro is still spinning in the same
plane as before, and the black end is pointing away from the Earth's surface. At 2400, the spinning axis is again
horizontal. At 0600 the spinning axis is again vertical, and the black end points toward the Earth. Finally, at
1200 the next day, the gyro is in the same position as when it started. The plane of spin of the gyro wheel did
not change direction in space while the gyro rotated with the
Earth. This is because the gyro is rigid in space.
Figure 3-11B.—Fixed direction in space. Gyro on equator viewed from space.
You have just imagined observing the gyro from space. Now, let's come back to Earth and stand right next to the gyro. Look at the gyro in view C. From your viewpoint on Earth, the spinning axis appears to make one complete rotation in one day. As you know, the gyro is rigid, and both you and the Earth are rotating. The effect of the Earth's rotation on a gyro is sometimes called APPARENT DRIFT, APPARENT PRECESSION, or APPARENT ROTATION.
Figure 3-11C.—Fixed direction in space. Gyro on equator viewed from earth.
Effect of Mechanical Drift
A directional error in a gyro is produced by random inaccuracies caused by mechanical drift and the effect of the Earth's rotation (apparent drift).
We shall see later how it is corrected for in the equipment. First, let's consider the causes of mechanical drift.
There are three general sources of mechanical drift:
1. Unbalance. A gyro often becomes dynamically unbalanced when operated at a speed or temperature other than that for which it was designed. The static balance of the gyro is upset when its center of gravity is not at the intersection of the three major axes. Some unbalance of both types will exist in any gyro since manufacturing processes cannot produce a perfectly balanced gyro.
2. Bearing friction. Friction in the gimbal bearings results in loss of energy and incorrect gimbal positions. Friction in the rotor bearings causes mechanical drift only if the friction is not symmetrical. An even amount of friction all around in a rotor bearing results only in a change of the speed of rotation.
3. Inertia of gimbals. Energy is lost whenever a gimbal rotates because of the inertia of the gimbal.
The greater the mass of the gimbal, the greater the drift from this source.
The complete elimination of mechanical drift in gyros appears to be an impossibility. However, by proper design it has been kept to a minimum. Any error that still exists can be corrected for.
Q-13. A universally mounted gyro has how many degrees of freedom?
Q-14. If a free gyro is placed at the equator at 1200 in a vertical position; in what position should it be at 1800?
Q-15. What are the three causes of mechanical drift in a gyro?
Establishing and Maintaining a Fixed Position
You now know that a free gyro maintains a fixed position in space. Because of this property, a free gyro can be used to establish a stable, unchanging reference, in any plane (horizontal, vertical, or any specific position in between). The gyro-erecting system has the function of positioning the gyro to the desired position and helping to keep it there.
Any gyro-erecting system must meet the following requirements:
1. The system must provide torques (forces) of sufficient magnitude and direction to precess the gyro so that its spin axis is brought to the desired position after the rotor is spinning at its operating speed.
2. The system must provide torques to precess the gyro back to the required position at the proper rate and direction to cancel the effects of apparent and mechanical drift.
Erection may be done mechanically or electrically, depending on the type of power available. Specific erection systems are many and varied. We will briefly discuss only two of them.
Mercury Erecting System
One of the common erection systems used for vertical gyros uses mercury as the element for sensing gyro position with respect to vertical. Mercury also provides the force to precess the gyro toward vertical when the gyro drifts.
This system consists of two tanks of mercury fastened to opposite sides of the gyro case and connected by a small mercury tube as shown in figure 3-12. A small air tube is also connected between the tanks to prevent a vacuum from forming. If the spin axis tilts away from the vertical, as shown, the mercury will flow from one tank to the other. The added weight in the left tank provides a torque which causes the gyro to precess. At this point, if you were to apply the rule for precession, you would see that the precession would be 90º away from the desired direction.
Figure 3-12.—Mercury erecting system.
To overcome this difficulty, the point where the torque is applied must be moved. The torque point is moved by
causing the gimbal assembly to slowly and continuously rotate in the proper direction. This is done in the
following manner. With a small mercury tube, the mercury will take nearly a second to find its level. At the same
time the mercury is flowing, a small motor is rotating the gimbal supporting the gyro about 18 times a minute.
Therefore, during the time that it takes the mercury to flow into the low tank, the entire gimbal assembly has
rotated 90º. The torque will now be applied at a point which causes the gyro to precess in the proper direction to
maintain the gyro spin axis in a vertical position.
Mercury Ballistic Erecting System
The erection system used in many horizontal gyros is very similar to the vertical gyro system just discussed. It is called the mercury ballistic erection system. The mercury ballistic system has the added feature of maintaining the spin axis not only in the horizontal plane, but also with the spin axis aligned North-South.
There are many different methods of causing free gyros to precess to either the vertical or the horizontal plane. All such systems use the forces of gravity to sense variation from the desired position: all systems also use the principles of precession to position the gyro property.
Q-16. What is the purpose of an erection system used with a gyro?
Q-17. What is the purpose of rotating the gimbal assembly in a gyro using a mercury erection system?
RATE GYROS are used in weapons control equipment, aircraft instrumentation, inertial navigation, and in many
other applications to detect and measure angular rates of change.
A rate gyro (sometimes called a rate-of-turn gyro) consists of a spinning rotor mounted in a single gimbal, as shown in figure 3-13. A gyro mounted in this manner has one degree of freedom; that is, it is free to tilt in only one direction. The rotor in a rate gyro is restrained from precessing by some means, usually a spring arrangement. This is done to limit precession and to return the rotor to a neutral position when there is no angular change taking place. Remember, the amount of precession of a gyro is proportional to the force that causes the precession.
Figure 3-13.—Rate gyro (single degree of freedom).
If you attempt to change the gyro's plane of rotor spin by rotating the case about the input axis, the gyro will precess as shown in figure 3-14. From what you learned earlier in this chapter, the gyro does not appear to be obeying the rules for precession. However, turning the gyro case has the same effect as applying a torque on the spin axis. This is illustrated by arrow F in figure 3-14. You can determine the direction of precession by using the right-hand rule we discussed earlier.
Figure 3-14.—Rate gyro precession.
The force applied at F will cause the gyro to precess at right angles to the force. Likewise, attempting to
turn the gyro case will cause the same result. The gyro will precess, as shown by the arrows, around the Y-Y axis
Since the rate of precession is proportional to the applied force, you can increase the precession by increasing the speed with which you are moving the gyro case. In other words, you have a rate gyro. The
faster you turn the case, the more the gyro will precess, since the amount of precession is proportional to the rate at which you are turning the gyro case.
This characteristic of a gyro, when properly used, fits the requirements needed to sense the rate of motion about any axis.
Figure 3-15 shows a method of restraining the precession of a gyro to permit the calculation of an angle. Springs have been attached to the crossarm of the output shaft. These springs restrain the free precession of the gyro. The gyro may use other types of restraint, but no matter what type of restraint is used, the gyro is harnessed to produce some useful work.
Figure 3-15.—Precession of a spring restrained rate gyro.
As the gyro precesses, it exerts a precessional force against the springs that is proportional to the momentum
of the spinning wheel and the applied force. For example, suppose you rotate the gyro case (fig. 3-15) at a speed
corresponding to a horizontal force of 2 pounds at F. Obviously, the gyro will precess; and as it does, it will
cause the crossarm to pull up on spring A with a certain force, say 1 pound. (This amount of force would vary with
the length of the crossarm.)
If you continue to turn the gyro case at this rate, the precession of the gyro will continually exert a pull on the spring. More precisely, the gyro will precess until the 1 pound pull of the crossarm is exactly counterbalanced by the tension of the spring; it will remain in a fixed position, as shown in figure 3-15. That is, it will remain in the precessed position as long as you continue to rotate the gyro case at the same, constant speed. A pointer attached to the output axis could be used with a calibrated scale to measure precise angular rates.
When you stop moving the case, you remove the force at F, and the gyro stops precessing. The spring is still exerting a pull, however, so it pulls the crossarm back to the neutral position and returns the pointer to "zero."
Suppose you now rotate the gyro case at a speed twice as fast as before, and in the same direction. This will be equal to a 4-pound force applied at F and a resulting 2-pound pull by the crossarm on spring
A. In this situation the gyro will precess twice as far before the tension on the restraining spring equals the pull on the crossarm. Precession increases when the rate of rotation increases, as shown in figure 3-16.
Figure 3-16.—Precession is proportional to the rate of rotation.
Another type of rate gyro (often used in inertial navigation equipment) is the floated gyro unit. This unit generally uses a restraint known as a torsion bar. The advantage of the torsion bar over the spring is that the torsion bar needs no lever arm to exert torque. The torsion bar is mounted along the output axis (fig. 3-17), and produces restraining torque in either direction by twisting instead of pulling. Also, there is no gimbal bearing friction to cause interference with gyro operation.
Figure 3-17.—Torsion bar-restrained floated rate gyro.
A fluid surrounds the gyro sphere and provides flotation. It also provides protection from shock, and damps the oscillations resulting from sudden changes in the angular rate input. In this gyro, the inner gimbal displacement must be measured with some type of electrical pickoff. As the gyro case is rotated about the input axis, clockwise or counterclockwise, a precession torque will be developed about the
output axis that will cause the inner gimbal to exert torque against the torsion bars. The torsion bars provide a restraining torque proportional to the amount of the inner gimbal's displacement. When the exerted gimbal torque is exactly opposed by the restraining torque provided by the torsion bars, the inner gimbal displacement will be proportional to the rate of rotation of the gyro case about the input axis. The pickoff measures this displacement and provides a signal whose amplitude and polarity (or phase) represent the direction and magnitude of the input angular velocity.
The important point to remember is that every "rate" gyro measures the RATE OF ROTATION ABOUT ITS INPUT AXIS.
Up to this point, we have illustrated only basic gyros. We used these basic, or simple, gyros to explain their principles of operation In actuality, the rate gyros used in typical modern day weapon systems are considerably more complex, and in some cases, very compact. Figure 3-18 shows a cutaway view of a rate gyro used in our Navy's missile systems and aircraft.
Figure 3-18.—Rate gyro, cutaway view.
Q-18. What are rate gyros primarily used for?
Q-19. How many degrees-of-freedom does a rate gyro usually have?
Q-20. What gyro characteristic provides the basis of the operation of a rate gyro?
An accelerometer is a device that gives an indication, usually in the form of a voltage, that is proportional to the acceleration to which it is subjected. The operation of an accelerometer is based on the property of INERTIA (Newton's First Law of Motion). A simple demonstration of inertia happens to us almost every day. You know that if your automobile is subjected to acceleration in a forward direction, you are forced back in the seat. If your auto comes to a sudden stop, you are drawn forward. When your
auto goes into a turn, you tend to be forced away from the direction of the turn-that is, if your auto turns left, you are forced to the right, and vice versa.
If we replace the human in an auto with a mass suspended in an elastic mounting system, as shown in figure 3-19, any acceleration of the auto will cause movement of the mass relative to the auto. The amount of displacement is proportional to the force causing the acceleration. The direction the mass moves is always opposite to the direction of the auto's acceleration.
Figure 3-19.—Auto with spring-suspended now.
The mass moves according to Newton's second Law of Motion which states: when a body is acted on by force, its
resulting acceleration is directly proportional to the force and inversely proportional to the mass of the body.
When no acceleration is present, the mass will be at rest. When acceleration is present, the mass will lag in proportion to the acceleration force. In other words, the car moves but the mass wants to remain at rest.
Accelerometers are used principally in inertial navigation systems. They are used in aircraft and missile navigation systems as well as aboard ship. Some common types of accelerometers are described briefly in the following paragraphs.
THE BASIC ACCELEROMETER
Figure 3-20 is a simplified drawing of a basic accelerometer. It consists of a mass that is free to slide along the sensitive axis within the case. The movement of the mass is limited by the springs. When the case is accelerated, the mass, because of its inertia, tends to remain stationary. This results in a relative movement of the mass with respect to the case. When the stretch of the springs overcomes the inertia of the mass, the springs cause the mass to stop moving with respect to the case. The displacement of the mass with respect to the case is directly proportional to the acceleration of the case. When the case stops accelerating, the springs return the mass to its zero position (the reference position). To keep the springs from causing the mass to overshoot and oscillate about the reference position, some form of damping is needed. This is usually provided by an oil-filled case with vanes for oil to bypass the mass.