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CHILDREN'S SCIENTIFIC LABORATORY
Fight against centrifugal force. Children's Science Lab
Directory / Children's Science Lab Let's talk about a physical phenomenon that gives all modellers and technicians a lot of trouble. His name is imbalance. We will also offer weapons that can be used to defeat him. Who is she disturbing? What is centrifugal force, even those who have not yet studied mechanics know. After all, everyone had to twirl a toy tied with a thread on their finger. The force with which the toy pulls you by the finger is centrifugal. More strictly speaking, centrifugal force is the force exerted on the axis of rotation by a rotating body. Such forces accompany any rotation. But who needed to fight them and why? First of all, this question can be answered by someone who himself washes clothes in a washing machine. Let's remember how the laundry is wrung out during machine washing. If the laundry inside the rotating drum - the centrifuge - is poorly packed, the machine begins to tremble and rumble as if it wants to turn into a small car. Who is pushing her from the inside? Of course, the centrifugal force acting from the linen that has strayed into a lump. We have to tame it - stop the machine and lay the laundry more evenly. The good thing is that the centrifuge does not rotate too fast: 300-500 rpm, so it can be stopped at the touch of a button. But in technology, we now and then encounter much higher rotation speeds and huge rotating masses. Then unbalanced centrifugal forces can cause serious harm. They cause vibration, increase friction and wear on bearings. As a result, the machine quickly fails. In some cases, centrifugal force may not allow the boulder to take the desired rotational speed at all. Let's conduct a small experiment: take a microelectric motor and attach its contacts to the battery poles. Listen for the subtle buzz of a spinning rotor: its angular velocity is about 70 rpm. Now let's try to equip the motor with a flywheel. To begin with, roughly, by hand, cut out the wheel from the eraser, mark its center with a pencil by eye and put it on the shaft with a little effort. Let's turn on the engine. Do you feel how it beat in your hand, how the sound has changed compared to before? It has become much lower, because the rotor speed has decreased by 5-10 times. This is due to the unbalanced centrifugal force created by the rubber flywheel. Now it is clear why fight with centrifugal forces. How to get rid of them - or rather, from their undesirable action? The balancing of centrifugal forces applied to a rotating body is called balancing in the technique. The simplest example of balancing is stacking laundry in the centrifuge of a washing machine. Chasing a spinning vector Unfortunately, in the vast majority of cases, balancing is much more complicated. The theory of rotor balancing was developed relatively recently - in 1935 - by the remarkable scientist, mechanic and shipbuilder A.N. Krylov. Let's get acquainted with the basics of this theory. Let a small body of mass m (material point) rotate in a circle, making n revolutions per minute. In mechanics, the speed of rotation is usually measured by the angle of rotation in one second; this quantity is called angular velocity and is denoted by the Greek letter ω (omega). In one minute - 60 s, in one revolution - 2Pi radians, therefore ω = 2Pi*n/60=0,1n. Denote by R the vector directed from the axis to the rotating body. Its length is equal to the radius of the circle of revolution, so R is called the radius vector (Fig. 1).
It turns out that the centrifugal force vector F is obtained by multiplying the radius vector by the body mass and by the square of the angular velocity: F=m*ω2*R (it is clear that the vectors F and R have the same direction). According to Newton's III law, the centripetal force applied to a rotating body and holding it on a circle has the same value, but the opposite direction. If the body cannot be represented as a material point (this is the majority of bodies), the centrifugal force is calculated in exactly the same way, but instead of R, r is taken - the radius vector of the body's center of mass (Fig. 1). The center of mass is the point at which the entire mass of the body is concentrated. For symmetrical bodies (for example, a cylinder or a ball), the center of mass coincides with the center of symmetry. However, it is impossible to make a perfectly symmetrical body, so the position of the center of mass is never exactly known. It is because of this that there is a need to balance rotating bodies. The product of two factors - the radius vector of the center of mass and the mass of the body - is commonly called the imbalance vector or simply imbalance: d=m*r. Unbalance is measured in kg*m. It vanishes only when the axis of rotation passes through the center of mass. When the body rotates, the imbalance vector rotates with it. so that its direction coincides with the centrifugal force. Let's go back to our experience with the flywheel and try to calculate the imbalance and centrifugal force. Let the flywheel mass m=30g, and the distance from the axis to the center of mass r=2 mm. The imbalance value in this case is 0,002*0,03=6*10-5 kg. It would seem very little. But suppose now that the rotor rotates at a speed of 4500 rpm (this is exactly the rotation speed of a conventional microelectric motor). Then ω\u450d XNUMX rad / s, and centrifugal force F \uXNUMXd d *ω2=12N. Such a load is prohibitively large for a micromotor: the friction force in the bearings will not allow the rotor to rotate at all. Even with such a small flywheel, if it is unbalanced, the micromotor will not be able to reach its nominal speed! What unbalance value is acceptable and what is not depends mainly on the design and speed of rotation of the rotor. A low-speed hydraulic turbine weighing tens of tons can have an imbalance of 10 kg * m without the slightest damage, but a gas turbine, for which 30 thousand rpm is not the limit, even 10-6kg * m - too much.
Look at figure 2. Here is a wheel of radius R with an imbalance d. Let's say that we can place additional corrective weights on the wheel rim, for example, stick plasticine balls. Then it is very easy to compensate for the imbalance: it is enough to place a piece of plasticine of mass mk=d/R at point A. In fact, now the wheel imbalance will be equal to zero: d=d+RA*d/R=dd. Note that the radius R can be chosen by anyone, but the mass of the corrective weight will also change. And vice versa, if the mass m'k>=d/R, then the additional load must be placed at a distance d/m'k from the center. Take a closer look at the wheels of cars. On the rims of some of them you will see small oval weights. By now you should understand their purpose. More often, however, corrective masses are not added, but removed. After all, adding a load of mass mk to a point with radius vector RA is equivalent to the removal of a load of the same mass at a diametrically opposite point (-RA) (Fig. 2). In technology, this is often done: at the desired point, a shallow hole is drilled that does not violate the strength of the part to be balanced, thereby removing the required mass. Such holes can often be seen on the flywheels and rotors of electric motors. Balancing machine on your desk It is not only in machine-building plants and in car repair shops that balancing of various rotating parts is necessary. Every young technician or modeler may well face such a task in his work. Many models have a flywheel. This is a very useful detail: the flywheel is able to smooth out the uneven operation of the engine. An unbalanced flywheel, on the other hand, will cause a lot of vibration and prevent the engine from gaining momentum. All the advantages of the flywheel can be used only by carefully balancing it. A simple machine that we bring to your attention will help you with this. It is a flat spring fixed at one end, on which a micromotor with a balanced flywheel is mounted (Fig. 3). As a spring, you can take the contact plate from the old relay. A long and light splinter or a straw with a pointed end should be attached to its end. Turn on the motor: a vibration will immediately begin, the magnitude of which will be reported by the swing of the straw tip. To measure it, place a transparent ruler with a millimeter scale near the tip. As the engine spins up, this range will either increase or decrease again. It is possible that at maximum speed the tip will be almost motionless. Not, of course, because the centrifugal force has disappeared: it's just that the sensitivity of the spring to high-frequency vibration is relatively small. For this reason, the largest swing of the tip oscillations is measured "on the freewheel" - during the braking of the engine after the power is turned off. The length of the straw, the thickness of the spring and the location of the engine on it must be selected so that the span is as large as possible, thereby increasing the sensitivity of your device. So, the magnitude of the imbalance is measured by the swing of the tip of the straw. Of course, we do not know how much unbalance exactly corresponds to, say, a span of 7 mm (our device does not have a graduated scale), but we can say with confidence that the larger the span, the greater the unbalance. Now you need to stock up on plasticine and start balancing. However, first we outline a plan to "chase" the imbalance vector. Let's represent it as a sum of projections onto two perpendicular axes: d=dx+dy (Fig. 3).
These axes (OX and OY) should be drawn on the flywheel completely arbitrarily before balancing. We will compensate for the imbalance components in turn: first dx, then dy. By placing a corrective weight at any point A on the OX axis, we do not change the component dy - after all, OA is perpendicular to the OS; only d will changex. Moving a piece of plasticine along the OX axis, find its position at which the swing of the tip (and with it the imbalance) is the smallest. If this point is close to the flywheel rim, take a larger piece; if close to the center - smaller. Just keep in mind that you need to move the plasticine weight without removing the flywheel from the axle. In general, if after the start of balancing you for some reason change the position of the flywheel on the axle, you will have to start balancing again. Having achieved the minimum swing of the straw, take another piece of plasticine and repeat the same procedure, only now with the y axis (the first weight, of course, must remain in its place). Thus, without changing the imbalance component dx, reduce as much as possible the component dy. Since the total imbalance d=(dx2+dy2)0.5, as a result, it can be completely eliminated. In fact, however, neitherx, nor dy are not compensated with absolute accuracy, so the complete disappearance of vibration cannot be expected. To minimize it, the correction of the imbalance components is carried out several times in a row. In addition, the measurement itself can be made in a different way: first determine the direction of the imbalance, and then compensate for it. Author: M.Markish
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