Statistical and dynamic balancing of critical parts. Balancing rotating parts. Devices for static balancing

The unbalance of rotating parts (pulleys of pumps and transmission units, tire-pneumatic couplings, gear wheels) is obtained when their mass is shifted in one direction, as a result of which the center of gravity is shifted relative to the axis of rotation, as well as when the axis of rotation is shifted relative to the center of gravity. The mass of the part is shifted due to the inhomogeneity of the material, inaccuracies in machining and as a result of one-sided wear during operation. The axis of rotation relative to the center of gravity is shifted due to distortions during assembly or manufacturing inaccuracies.

At high rotation speeds of unbalanced parts, unbalanced centrifugal forces arise, leading to vibration of the part and the unit as a whole and its premature wear. Therefore, rotating parts must be carefully balanced.

There are two ways of balancing: static and dynamic. With static "balancing, the part is balanced relative to the axis of rotation by reducing its mass on the side where the center of gravity is shifted, or by increasing the mass on the diametrically opposite side. With this method, the part is in a static state and if it is balanced (balancing), the part will remain in any position in which it rotates relative to the axis of rotation.The scheme for balancing parts of different lengths (A, A 1) is shown in Fig. 130.

Rice. 130. Balancing scheme for parts of different lengths: 1 - unbalanced mass; 2 - balanced mass

Static balancing is carried out on horizontal prisms, rollers or rollers. The simplest device for static balancing is parallel stands, which are two guides in the form of knives fixed on the bases, along which the part to be balanced can roll.

Knives are aligned with a level in two mutually perpendicular directions. To balance massive parts (pulley pulleys), roller or disk stands are used, which have ball bearings or rollers instead of knives.

Static balancing is performed as follows. The part to be balanced is installed on the stand and its balance is determined by turning through a certain angle. When unbalanced, the heavy part of the part returns down, and when balanced, it remains in the position in which it turns. The unbalanced mass of the part is removed by drilling along the mark on both sides of it. If the design of the part weakens during drilling, then in this case, a balancing mass (load) in the form of separate plates is installed on the diametrically opposite guard using screws.

For a disk-shaped part having a short length compared to its diameter, the static balancing method will be sufficient, since the unbalanced and balanced masses are on or close to the transverse axis of the part. In this case, when the part rotates, the centrifugal forces of the masses will be in the same or close planes and will not have an additional effect on the shaft and bearings.

For a cylindrical part with a relatively large length (V-belt transmission pulleys), one method of static balancing will not be enough, since the unbalanced and balanced masses during balancing can be removed from the transverse axis of the part by a distance a. When the part rotates, the centrifugal forces of these masses, "located in different planes, create a pair of forces that will rotate the part about the axis of rotation and create additional loads on the shaft and bearings. In this case, the effect of a pair of forces can be eliminated only by dynamic balancing, in which the position and the value of the balancing mass is determined in the dynamic state of the part - during its rotation.

The process of dynamic balancing is carried out on special machines or directly in machines and mechanisms on their own bearings using special devices: vibrometers, vibroscopes.

test questions to chapter X

1. What types of plumbing work are performed during the construction of drilling rigs?

2. What types of bolts are divided into?

3. In what cases are bolts, studs, screws used?

4. What are washers for?

5. What methods of locking threaded connections are used?

6. What kind of wrenches are used?

7. What keys are used for stressed and non-stressed connections?

8. What is the advantage of spline connections over keyed ones?

9. What spline profiles are used?

10. How are press connections made?

11. What are the union connections?

12. How are shafts connected by tire-pneumatic couplings centered?

13. What elements does the driveline consist of?

14. What are the gears?

15. What are the ways to check the gaps of the gears?

16. What elements does the drive roller chain consist of?

17. What are plain bearing shells used for?

18. What are the designs of rolling bearings?

19. How are bearings pressed in?

20. How is the clearance in thrust and tapered bearings adjusted?

21. What is the balancing of rotating parts?

22. How and when is static and dynamic balancing performed?

ORGANIZATION OF PRODUCTION AND LABOR, ECONOMY AND PLANNING OF DRILL RIG CONSTRUCTION

One of the reasons for reducing the engine's service life is vibrations resulting from the imbalance of its rotating parts, namely the crankshaft, flywheel, clutch basket, etc. It's no secret what these vibrations threaten. This includes increased wear of parts, and extremely uncomfortable operation of the motor, and worse dynamics, and increased fuel consumption, and so on and so forth. All these passions have been discussed more than once both in print and on the Internet - we will not repeat ourselves. Let's talk better about balancing equipment, but first, let's briefly analyze what this imbalance is, and what types it is, and then we'll look at how to deal with it.

To begin with, let's decide why to introduce the concept of imbalance at all, because the cause of vibrations is the inertia forces that arise during rotation and uneven translational movement of parts. It might be better to operate with the magnitudes of these forces? I translated them into kilograms “for clarity” and it seems to be clear where, what and with what effort presses, how many kilos fall on which support ... But the point is that the magnitude of the inertia force depends on the rotational speed, more precisely, on the square of the frequency or acceleration in translational motion, and this, in contrast to the mass and radius of rotation, are variables. Thus, it is simply inconvenient to use the force of inertia when balancing, you will have to recalculate these same kilograms each time depending on the square of the frequency. Judge for yourself, for rotational motion the inertia force is:

m- unbalanced mass;
r is the radius of its rotation;
w is the angular velocity of rotation in rad/s;
n- rotational speed in rpm.

Not higher mathematics, of course, but I don’t want to recalculate once again. That is why the concept of imbalance was introduced, as the product of an unbalanced mass by the distance to it from the axis of rotation:

D– imbalance in g mm;
m- unbalanced mass in grams;
r is the distance from the axis of rotation to this mass in mm.

This value is measured in units of mass multiplied by a unit of length, namely in g mm (often in g cm). I specifically focus on units of measurement, because in the vastness of the global network, and in print, in numerous articles devoted to balancing, you won’t find anything ... There are grams divided by centimeters, and the definition of imbalance in grams (not multiplied by anything, just grams and whatever you want, then think), and analogies with units of measurement of torque (it seems like - kg m, and here g mm ... but the physical meaning is completely different ...). In general, we will be careful!

So, the first type of imbalance- static or, they say, static imbalance. Such an imbalance will occur if a load is placed on the shaft exactly opposite its center of mass, and this will be equivalent to a parallel displacement of the main central axis of inertia 1 relative to the axis of rotation of the shaft. It is easy to guess that such an imbalance is characteristic of disc-shaped rotors2, flywheels, for example, or grinding wheels. You can eliminate this imbalance on special devices - knives or prisms. The heavy side3 will turn the rotor under the force of gravity. Having noticed this place, it is possible to install such a load by simple selection on the opposite side, which will bring the system to equilibrium. However, this process is quite lengthy and painstaking, so it is still better to eliminate static imbalance on balancing machines - both faster and more accurately, but more on that below.

The second type of imbalance- momentary. Such an imbalance can be caused by sticking a pair of identical weights on the edges of the rotor at an angle of 180 ° to each other. Thus, although the center of mass will remain on the axis of rotation, the main central axis of inertia will deviate by some angle. What is remarkable about this type of imbalance? After all, at first glance, in "nature" it can only be found by a "happy" accident ... The insidiousness of such an imbalance lies in the fact that it manifests itself only when the shaft rotates. Put a rotor with a torque imbalance on the knives and it will be completely at rest, no matter how many times it is shifted. However, it is worth unwinding it, so the strongest vibration will immediately appear. To eliminate such an imbalance is possible only on a balancing machine.

And finally most general case- dynamic imbalance. Such an imbalance is characterized by a shift of the main central axis of inertia both in angle and in place relative to the axis of rotation of the rotor. That is, the center of mass is shifted relative to the axis of rotation of the shaft, and with it the main central axis of inertia. At the same time, it also deviates by a certain angle so that it does not cross the axis of rotation4. It is this type of imbalance that occurs most often, and it is precisely this type of imbalance that is so habitually eliminated in tire shops when changing rubber. But if we all go to tire fitting in spring and autumn, then why do we ignore engine parts?

A simple question: after grinding the crankshaft to the repair size, or, even worse, after straightening it, can you be sure that the main central axis of inertia exactly coincides with the geometric axis of rotation of the crankshaft? And the second time to disassemble and assemble the motor, do you have time and desire?

So, in what to balance shafts, flywheels and so on. needed, no doubt. The next question is how to balance?

As already mentioned, in static balancing, you can get by with prism knives if you have enough time, patience, and the tolerance margins for residual unbalance are large. If you appreciate work time, care about the reputation of your company, or just worry about the resource of your motor parts, then the only balancing option is a specialized machine.

And there is such a machine - a machine for dynamic balancing of the Liberator model manufactured by Hines (USA), please love and favor!

This pre-resonance machine is designed to determine and eliminate the imbalance of crankshafts, flywheels, clutch baskets and so on.

The entire imbalance elimination process can be roughly divided into three parts: preparing the machine for operation, measuring the imbalance, and eliminating the imbalance.

At the first stage, it is necessary to install the shaft on the fixed supports of the machine, attach a sensor to the end of the shaft that will monitor the position and speed of the shaft, put on a drive belt, with which the shaft will unwind during the balancing process and enter the shaft dimensions, position coordinates and radii into the computer correction surfaces, select unbalance measurement units, etc. By the way, the next time, again, you won’t have to enter all this, since it is possible to save all the entered data in the computer’s memory, exactly as it is possible to erase, change, overwrite, or change them at any time without saving. In short, since the machine computer operates under operating system Windows XP, then all the tricks of working with it will be quite familiar to the average user. However, for a mechanic inexperienced in computer matters, it will not be too difficult to master several on-screen menus of the balancing program, especially since the program itself is very clear and intuitive.

The unbalance measurement process itself takes place without the participation of the operator. He just needs to press the desired button and wait until the shaft starts to rotate, and then he stops. After that, everything necessary to eliminate the imbalance will be displayed on the screen, namely: the magnitude and angles of the imbalances for both correction planes, as well as the depth and number of drillings that need to be done to eliminate this imbalance. The hole depths are derived, of course, based on the previously entered drill diameter and shaft material. By the way, these data are displayed for two correction planes if dynamic balancing was selected. With static balancing, of course, everything will be displayed the same, only for one plane.

Now it remains only to drill the proposed holes without removing the shaft from the supports. For this, a drilling machine is located behind, which can move on an air cushion along the entire bed. The depth of drilling, depending on the configuration, can be controlled either by a digital indicator of spindle movement, or by a graphic display displayed on a computer monitor. The same machine can be used when drilling or milling, for example, connecting rods for weight distribution. To do this, simply turn the caliper 180° so that it is above the special table. This table can be moved in two directions (the table is supplied as an accessory).

It only remains to add here that when calculating the drilling depth, the computer takes into account even the sharpening cone of the drill.

After the unbalance is eliminated, the measurements must be repeated again to make sure that the residual unbalance is within the allowable values.

By the way, about the residual imbalance or, as they sometimes say, the tolerance for balancing. Almost every motor manufacturer must give residual unbalance values in their parts repair instructions. However, if this data could not be found, then you can use general recommendations. Both the domestic GOST and the global ISO standard offer, in general, the same thing.

First you need to decide which class your rotor belongs to, and then use the table below to find out the balancing accuracy class for it. Suppose we are balancing the crankshaft. It follows from the table that "the crankshaft assembly of an engine with six or more cylinders with special requirements" has an accuracy class 5 according to GOST 22061-76. Let's assume that our shaft has very special requirements - let's complicate the task and assign it to the fourth accuracy class.

Further, assuming the maximum rotational speed of our shaft equal to 6000 rpm, we determine from the graph that the value of est. (specific imbalance) is within the boundaries between two straight lines that define the tolerance field for the fourth class, and is from 4 to 10 microns.

Now according to the formula:

D st.additional– allowable residual imbalance;
e Art.- tabular value of the specific imbalance;
m rotor is the mass of the rotor;

trying not to get confused in units of measurement and assuming the mass of the shaft is 10 kg, we get that the permissible residual imbalance of our crankshaft should not exceed 40 - 100 g mm. But this applies to the entire shaft, and the machine shows us an imbalance in two planes. This means that on each support, provided that the center of mass of the shaft is exactly in the middle between the corrective planes, the permissible residual imbalance on each support should not exceed 20 - 50 g mm.

Just for comparison: the permissible imbalance of the crankshaft of the D-240/243/245 engine with a shaft weight of 38 kg, according to the manufacturer's requirements, should not exceed 30 g cm. Remember, I paid attention to the units of measurement? This imbalance is indicated in g cm, which means it is equal to 300 g mm, which is several times greater than that calculated by us. However, nothing surprising - the shaft is heavier than what we took for an example, and it rotates at a lower frequency ... Calculate in reverse side and you will see that the balancing accuracy class is the same as in our example.

It should also be noted here that strictly speaking, the allowable imbalance is calculated by the formula:

D st.t.- the value of the main vector of technological imbalances of the product resulting from the assembly of the rotor, due to the installation of parts (pulleys, half-couplings, bearings, fans, etc.), which have their own imbalances, due to deviations in the shape and location of surfaces and seats, radial clearances, etc.;
D st.e.- the value of the main vector of operational imbalances of the product arising from uneven wear, relaxation, burning out, cavitation of rotor parts, etc. for a given technical resource or before a repair involving balancing.

It sounds scary, but as practice has shown in most cases, if you choose the value of the specific unbalance at the lower limit of the accuracy class (in this case, the specific unbalance is 2.5 times less than the specific unbalance defined for the upper limit of the class), then the main vector of the allowable imbalance can be calculated by the formula given above, according to which we actually considered. Thus, in our example, it is still better to take the allowable residual imbalance equal to 20 g mm for each correction plane.

Moreover, the proposed machine, unlike the ancient domestic analog machines, miraculously preserved after the well-known sad events in our country, will easily provide such accuracy.

Okay, but what about the flywheel and clutch basket? Usually, after the crankshaft has been balanced, a flywheel is attached to it, the machine is put into static balancing mode and only the flywheel is unbalanced, considering the crankshaft to be perfectly balanced. There is one big plus in this method: if the flywheel and clutch basket are not disconnected from the shaft after balancing and these parts are never changed, then the unit balanced in this way will have less unbalance than if each part was balanced separately. If you still want to balance the flywheel separately from the shaft, then for this, the machine is equipped with special, almost perfectly balanced, shafts for balancing flywheels.

Both methods, of course, have their pros and cons. In the first case, when replacing any of the parts previously involved in the balancing assembly, an imbalance will inevitably appear. But on the other hand, if you balance all the parts separately, then the tolerance for the residual imbalance of each part will have to be seriously tightened, which will lead to a lot of time spent on balancing.

Despite the fact that all the operations described above for measuring and eliminating imbalances on this machine are implemented very conveniently, they save a lot of time, insure against possible errors associated with the notorious "human factor" and so on, in fairness it should be noted that at the very least, but many other machines will be able to do the same. Moreover, the considered example did not represent anything particularly complicated.

And if you have to balance the shaft, say, from the V8? The task is also, in general, not the most difficult, but still it is not to balance the four in-line. After all, you can’t just put such a shaft on the machine, you need to hang special balancing weights on the connecting rod journals. And their mass depends, firstly, on the mass of the piston group, that is, the mass of parts moving exclusively progressively, and secondly, on the weight distribution of the connecting rods, then there is on what mass of the connecting rod relates to rotating parts, and what to progressively moving parts, and finally, thirdly, from the mass of parts only rotating. You can, of course, consistently weigh all the details, write down the data on a piece of paper, calculate the difference between the masses, then mix up which entry refers to which piston or connecting rod, and do all this several more times.

And you can use the automated weighing system "Compu-Match" offered as an option. The essence of the system is simple: electronic scales are connected to the machine's computer, and when parts are sequentially weighed, the data table is filled in automatically (by the way, it can also be printed out). It also automatically finds the lightest part in the group, such as the lightest piston, and automatically determines for each part the mass that needs to be removed to equalize the weights. No confusion will arise with the determination of the mass of the upper and lower heads of the connecting rods (by the way, everything necessary for weight distribution is supplied with the scales). The computer directs the actions of the operator, who simply needs to carefully follow the instructions step by step. After that, the computer will calculate the mass of balancing weights based on the mass of a particular piston and the weight distribution of the connecting rods. It remains only to add that when calculating the masses of these goods, even the mass engine oil, which will be in the shaft lines during engine operation. By the way, different sets of weights can be ordered separately. The loads, of course, are type-setting, that is, washers of different masses are hung on the stud and fixed with nuts.

And a few more words about weighing the piston and the weight distribution of the connecting rods. At the very beginning of this article, we noticed that “one of the causes of engine vibrations is the imbalance of its rotating parts ...”, “one of ...”, but far from the only one! Of course, we will not be able to “overcome” many of them. For example, uneven torque. But something can still be done. Let's take a conventional inline four-cylinder engine as an example. From the course of internal combustion engine dynamics, everyone knows that the first-order inertia forces of such a motor are completely balanced. Amazing! But in the calculations it is assumed that the masses of all parts in the cylinders are exactly the same and the connecting rods are weighted perfectly. But in fact, during the cap. repair, does anyone weigh pistons, rings, fingers, align the masses of the lower and upper heads of the connecting rods? Hardly…

Of course, the difference in the masses of the parts is unlikely to cause large vibrations, but if it is possible to get at least a little closer to the design scheme, why not do it? Especially if it's that simple...

As an option, you can order a set of accessories and equipment for balancing cardan shafts ... But wait, that's a completely different story ...

* The axis OX is called the main central axis of inertia of the body if it passes through the center of mass of the body and the centrifugal moments of inertia J xy and J xz are simultaneously equal to zero. Unclear? There is really nothing complicated here. Simply put, the main central axis of inertia is that axis around which the entire mass of the body is distributed evenly. What does evenly mean? This means that if you mentally select some mass of the shaft and multiply it by the distance to the axis of rotation, then exactly opposite there will be, perhaps, another mass at a different distance, but having exactly the same product, that is, the mass we selected will be balanced.

Well, what is the center of mass, I think it's clear and so.

** Rotors in balancing are called everything that rotates, regardless of shape and size.

*** The heavy side or heavy point of the rotor is usually called the place where the unbalanced mass is located.

**** If the main central axis of inertia nevertheless crosses the axis of rotation of the rotor, then such unbalance is called quasi-static. It makes no sense to consider it in the context of the article.

***** Among other classifications of balancing machines, there is a division into pre-resonant and over-resonant ones. That is, the frequencies at which the shaft is balanced can be either below the resonant frequency or above the resonant frequency of the rotor. Vibrations that occur during the rotation of an unbalanced part have one interesting feature: Vibration amplitude increases very slowly as speed increases. And only near the resonant frequency of the rotor is a sharp increase observed (which, in fact, is dangerous resonance). At frequencies above the resonant one, the amplitude decreases again and practically does not change over a very wide range. Therefore, for example, on pre-resonance machines, it makes little sense to try to increase the shaft speed during balancing, since the oscillation amplitude recorded by the sensors will increase extremely slightly, despite the increase in centrifugal force that generates vibration.

****** Some machines have oscillating feet.

******* The correction surface is the place on the shaft where holes are supposed to be drilled to eliminate the imbalance.

******** Please note that the specific unbalance is in microns. This is not a mistake, here we are talking about specific imbalance, that is, related to a unit of mass. In addition, the index "st." indicates that this is a static imbalance, and it can be indicated in units of length, as the distance by which the main central axis of inertia of the shaft is displaced relative to its axis of rotation, see the definition of static imbalance above.

Wheel balancing is necessary so that during the movement of the car, the driver does not experience discomfort from such a phenomenon as wheel beating. This happens when there is an imbalance relative to the axis or plane of rotation.

Why do you need wheel balancing?

In the process of manufacturing discs, tubes and tires, it is impossible to make a perfectly balanced product. The main part of the imbalance is brought by the tire. Because it is farthest from the center of rotation. Hence the need for balancing. After all, improper wheel balancing not only makes driving uncomfortable, it also contributes to the rapid wear of suspension elements. First of all, the wheel bearing suffers, which will certainly have to be changed if you drove on unbalanced wheels.

Agree, it is much cheaper to do balancing than to change worn parts and tires. Until now, there are people who balance only the front wheels. Allegedly, only the leaders need this, and there is no need to spend extra money on balancing the rear ones. This is a delusion, and such savings will only kill the elements of the rear suspension.

There are several types of balancing:

on the machine, with the removal of the wheel;
finishing, produced directly on the car;
automatic (powder, bead).

There is also a division into dynamic and static.

How is balancing done

static

In the case when the wheel has a static imbalance, its weight along the axis of rotation is uneven, it has a heavy place. This place will hit the road with more force, and the greater the speed of its rotation, the stronger the static imbalance will be.

To avoid this phenomenon, static balancing is done. This service in our country is provided by all tire shops. The wheel is placed on a special machine, in the process of rotation, the automation determines the degree of imbalance, and indicates where it is necessary to install an additional load.

Loads are of two types:

with a bracket, mounted on the edge of the disk and are used, as a rule, on stamped disks;
adhesive-based, convenient for balancing cast, forged wheels.

Dynamic

It should be noted right away that not every tire fitting station can offer this service. Since the equipment used in most cases is old, we can say trophy.

So what is dynamic balancing for? The wider the profile of the wheel, the more likely it is to get a dynamic imbalance during movement, relative to the plane of its rotation.

Finishing

This type of balancing is performed after the main static, and if possible dynamic. Special equipment, a balancing stand, is installed under a suspended car, the wheel spins up to a speed of 90 km / h, and the automation takes measurements and indicates in what place and what load should be installed. For this balancing, equipment is needed, which is often available only professional centers tire fitting.

Automatic

Automatic only applies to trucks and buses. This happens as follows - special balancing granules, small beads, less often sand are poured into the wheel, because the latter has a high abrasive effect. During driving, under the influence of centrifugal force, the balancing material is attracted to the inner surface of the tire, which leads to self-balancing.

On passenger transport this species balancing is not used due to the fact that there is no way to determine exactly how much material needs to be poured into each wheel. Additionally, its weight also increases.

Proper wheel balancing

There are a number of rules, the implementation of which guarantees the highest quality balancing.

the disc must be cleaned of dirt. After all, it is often quite a lot both on the outside and on the inside. Automation calculates how many grams of cargo to hang on one or another part of the wheel. Having balanced a dirty wheel, you run the risk of losing balance on the very first bump, when a large piece of dirt falls off the disk and all the work goes down the drain;
be sure to remove all old balancing weights;
still quite often there is a situation when the tire simply did not fully fit into place. It is not always possible to notice this from the outside, but it can affect the balancing quite strongly;
various plastic caps, which are put on immediately after leaving the tire shop, are also capable of introducing an imbalance into a newly balanced wheel.

How often should you do wheel balancing?

Recommended frequency varies. Someone says that it is necessary every 10 thousand kilometers, someone insists on 20 thousand. If you feel that the steering wheel beats while driving, there is excessive vibration of the body, do not be too lazy to visit a tire shop. By doing so, you may save on more expensive repairs.
We hope that after reading this article, you will no longer have questions about why wheel balancing is needed, and whether it should be done.

A repaired unit is considered balanced if, during its operation, the resultant of all forces acting on the unit's supports remains constant in magnitude and direction.

Dynamic loads on the supports of the operating unit are due to the forces of inertia of parts that move translationally or rotate. The unit will be balanced if it is assembled from parts of the same name, moving forward, the same mass and rotating parts that have been balanced.

Moving parts change their mass or become unbalanced during operation as a result of the accumulation of contaminants on their surfaces, uneven wear and deformation. This leads to additional loads in the kinematic pairs and the accumulation of fatigue damage in the shaft journals, which in turn reduces the durability of the units.

Parts are balanced during their restoration (crankshafts, flywheels, etc.), and assembly units (clutches, crankshafts assembled with flywheels and clutches, etc.) after the assembly.

Balancing- this is balancing the forces of inertia of parts of a rotating product by combining its center of mass, axes of inertia and rotation by removing excess metal or installing counterweights.

When balancing rotating products, they ensure that the loads on their supports from inertia forces are equal to zero. The rotating product is fully balanced under the conditions

where M- weight of the product, g; rs- distance from the center of mass of the product to its axis of rotation, cm; J(- centrifugal moment of inertia of the product, g-cm 2 ; m jy g - And lj- mass (g) of the element of the product, distance (cm) from the center of its mass to the axis of rotation of the product and shoulder (cm) of the element's inertia force relative to the axis passing through the center of mass of the product, respectively; i == 1... to - the number of elements of the product.

The product is considered to be statically balanced if the first condition is met, and dynamically balanced if the second condition is met. In real conditions, there are static, dynamic and mixed unbalance of rotating parts or assembly units.

static imbalance (Fig. 2.57, but) observed in parts such as discs with a small length (flywheels, pressure and driven clutch discs, cast iron pulleys, etc.), in which an unbalanced inertia force is possible. The measure of static imbalance is the unbalance, the direction of which coincides with the unbalanced force of inertia, and the value is equal to the product Mrs(g-cm). Static balancing methods consist in combining the center of mass of the part with its axis of rotation by removing excess metal or installing a counterweight. In this case, the direction of the imbalance is determined, then in this direction to

Rice. 2.57.but - static; b - dynamic; in - mixed

product surfaces remove excess metal on one side with an unbalanced mass from the axis of rotation or add metal if the unbalanced mass is located on the other side of the axis of rotation of the part. mass T(d) removed (added) metal is determined by the formula

where R- distance from the axis of rotation to the center of mass of the removed (added) metal, see Fig.

The surface from which the metal is removed or the counterweight is fixed should be of the largest radius, since in this case the mass of the removed (added) material is minimal.

Balancing is carried out on rollers, horizontal prisms, oscillating disks and on machines.

Devices for static balancing of parts on rollers and horizontal prisms are shown in fig. 2.58 a, b. Detail 1 mounted without a gap on the mandrel 2, which in turn is mounted on rollers or prisms. An unbalanced part under the action of gravity will turn around its axis, while its "heavy" part will be at the bottom. Balancing on prisms gives more accurate results, however, in this case, their working surfaces are required to be horizontal. These devices show only the directions of the imbalance, determining its value is difficult and requires practical skill.

Rice. 2.58.but- on rollerskates: 1 - detail; 2 - mandrel; 3 - videos; b- on prisms: 1 - detail; 2 - mandrel; 3 - prisms; in- on a swinging disk: 1 - arrow; 2 - detail; 3 - point; 4 - support

A device for static balancing of parts on an oscillating disk (Fig. 2.58, in) devoid of the above disadvantage. Its statically balanced disk has supports (cylindrical surface and plane) for the part to be balanced. The tip is installed coaxially with the cylindrical surface 3, which is in contact with the mating conical recess of the support 4. two arrows 1 disks are located in mutually perpendicular directions. The part is mounted on a disk and oriented with a centering belt. If the disk with the part is tilted under the action of gravity, then they are brought to a horizontal position by moving a compensating weight along the surface of the part. The location of the load and its mass show the direction and magnitude of the imbalance.

Static balancing of products (flywheels, pressure and driven clutch disks, clutch assemblies, etc.) in dynamic mode (with their forced rotation) is performed on a model 9765 machine. This type of balancing is more accurate than previously considered.

Dynamic b) for a statically balanced product (the center of mass is on the axis of rotation) occurs if there are two unbalanced masses T, which are located on opposite sides of the axis of rotation at a distance G. During the rotation of the product, a moment arises S from two equal forces of inertia R on the shoulder /. Moment S causes variables in the direction of the load on the support of the product during its rotation. Dynamic imbalance is eliminated by removing or adding two equal masses in the plane of action of the moment S, so that a new moment appears, balancing the initial one. This type of imbalance is detected when the product is forced to rotate. Dynamic imbalance is measured in newton square meter (Nm2).

mixed imbalance (see Fig. 2.57, in) most often occurs in real conditions, when there is an unbalanced inertia force and a moment from two equal inertia forces. This type of imbalance is typical for long parts or assembly units such as shafts (N m).

The system of any number of unbalanced inertial forces is reduced to two forces, which are located in two arbitrarily chosen planes perpendicular to the axis of the part, convenient for balancing. Such planes are called correction planes. For example, at the crankshaft, these planes pass through the extreme counterweights.

Let there be a number of forces, including R 1 And R 2 from unbalanced masses and t 2 - Let's replace centrifugal forces R x And R 2 their constituents R And R" And R "2 And R 2 in correction planes located at a distance / from each other. We add these components in each plane according to the parallelogram rule and obtain the resultant and T 2 . At the point of application of force T ( apply two equal but oppositely directed forces T 2 . The result is two unbalanced forces T 2 And Q in the planes of correction. Strength Q is the vector sum of forces T ( And T 2 . Moment T 2 1 determines the dynamic imbalance, and the force Q- static. Full balancing of the product is achieved by installing counterweights t b And t 4 in the planes of correction on the lines of action of forces T 2 And That

The direction (angle) and the value of the imbalance in each shaft correction plane is determined on balancing machines of models, for example, BM-4U, KI-4274, MS-9716 or Schenk (Germany). On machines, assembly units (crankshafts with flywheels, cardan shafts, etc.) are balanced, rotating during the operation of the unit in two or more supports.

The principle of operation of the balancing machine (Fig. 2.59) is as follows. The product is installed on elastic supports (cradles) 1 and set in rotation with a frequency of 720 ... 1100 min -1 from the electric motor 6. Under the action of centrifugal forces of inertia, the support with the product will oscillate along the horizontal axis. With the moving supports, the windings of the displacement sensors 2, which are located

Rice. 2.59.

1 - supports (cradles); 2 - displacement sensor; 3 - amplification block; 4 - milliammeter; 5 - strobe lamp; 6 - electric motor; 7 - strobe limb; 8 - flywheel

in the magnetic field of permanent magnets. In each winding, an EMF is induced, the value of which is proportional to the amplitude of the oscillations. The signal from the sensor enters the amplification unit 3 and in a modified form is fixed by a milliammeter 4, the scale of which is compiled in unbalance units (g cm). The signal about the angle of rotation of the spindle, at which the support has moved to the maximum distance, is fed to a low-inertia lamp 5 stroboscope, the flash of which illuminates a small section of the rim of the rotating limb 7 with angular divisions from 0 to 360 °. The worker perceives the limb as stopped with fixed numbers. The value and direction of the unbalance of the product are alternately determined on each of the two supports of the machine.

After each determination of the direction and unbalance value, the machine is stopped. When the electric motor is off, the cradles are locked with electromagnets. Then by rotating the product by hand on the flywheel 8 set it to the correct angle. With the help of a radial drilling machine or an electric drill, excess metal of the required mass is drilled out in the correction plane. The drilling length is proportional to the milliammeter readings.

After assembling a rotating assembly unit, which includes balanced parts (for example: shafts, shell gears, couplings, etc.) and other parts (keys, pins, locking screws, etc.), it becomes necessary to re-balance them, since the displacement of one of the parts, even within the clearances provided by the drawing, causes significant unbalance.

The discrepancy between the center of gravity of the part and the axis of rotation is commonly called static imbalance, and the inequality of zero centrifugal moments of inertia is called dynamic imbalance.

Static imbalance is easily detected when the part is mounted with support journals or on mandrels on horizontal parallels (knives, prisms, rollers) or rollers, and dynamic imbalance is detected only when the part is rotated. In this regard, balancing is static and dynamic.

Static balancing. There are several methods for performing static balancing. The most common in the machine tool industry are balancing on prisms and on disks. Knives, prisms and rollers must be hardened and ground and before balancing adjusted to the horizontal.

When balancing on horizontal parallels (Fig. 1), the allowable ovality and taper of the necks of the mandrel should not exceed 0.01-0.015 mm, and their diameters should be the same.

Rice. one. a - on horizontal parallels (1 - center of gravity of the part; 2 - corrective weight); b - on disks (1 - detail; 2 - corrective weight)

To reduce the coefficient of friction, the parallels and neck of the mandrel are recommended to be hardened and carefully ground. The working length of the parallels can be determined by the formula:

where d is the mandrel neck diameter.

The width of the working surface of the parallels (ribbons) is (cm):

where G is the force acting on the parallel, in kg; E is the modulus of elasticity of the material of the mandrel and parallels, in kg/cm2; σ is the allowable compressive stress at the points of contact between the neck and the parallel, in kg/cm 2 (for hardened surfaces σ=2 10 4 ÷ 3 10 4 kg/cm 2).

The value of d in cm is assigned from design considerations, taking into account the convenience of installing the part to be balanced on the mandrel.

The unbalance is determined by trial attachment of corrective weights on the surface of the part to be balanced. The imbalance is eliminated by removing an equivalent amount of material from the diametrically opposite side or by installing and securing appropriate counterweights (corrective weights).

Static balancing of a pulley can be done as follows. On the rim of the pulley, a line is first applied with chalk and rotation is imparted to it. The rotation of the pulley is repeated 3-4 times. If the chalk line stops at different positions, then this will indicate that the pulley is balanced correctly. If the chalk line stops in one position each time, then this means that the part of the pulley located below is heavier than the opposite one. To eliminate this, reduce the mass of the heavy part by drilling holes, or increase the mass of the opposite part of the pulley rim by drilling holes, and then fill them with lead.

Balancing sensitivity of parts weighing up to 10 tons on horizontal parallels (Fig. 1, a):

where F is the sensitivity of the method in G cm; f is the coefficient of rolling friction (f=0.001 ÷ 0.005 cm); G is the weight of the part or assembly unit in kg.

Sensitivity of balancing parts weighing up to 10 tons on disks (Fig. 1, b):

where F is the sensitivity of the method in G cm; f is the coefficient of rolling friction (f=0.001 ÷ 0.005 cm); G is the weight of the part or assembly unit in kg;  – coefficient of rolling friction in disc bearings; r is the radius of the trunnion of the discs, cm; d is the mandrel diameter in cm; D is the diameter of the disks in cm; α is the angle between the axis of the mandrel and the axes of the disks.

The balancing accuracy on discs is greater than on horizontal prisms. Static balancing is most often used for parts such as disks.

Balancing of parts and assembly units can be performed on balancing scales in the resonant mode of an oscillating system, which improves the balancing accuracy.

Balancing parts weighing up to 100 kg on a balancing scale is performed as follows (Fig. 2): the tested structure 1 is balanced by weights 3 and the rotating part 1 of the structure is accelerated to a rotational speed exceeding the oscillation frequency of the system. After acceleration, the electric motor is disconnected from the structure under test, the moving part of which continues to rotate freely, gradually reducing the speed. This eliminates the influence of disturbances from the drive motor on the oscillating system. The amplitude of the displacement of the reference point is measured by instrument 2 at the moment when the spindle speed coincides with the natural frequency of the oscillating system, i.e. at resonance, where the amplitude reaches its maximum value. The value of the residual imbalance at this method measurements should not exceed 1.5-2 G cm.

Rice. 2.

For a number of products, at present, on the basis of experience, the norms for the permissible displacement of the center of gravity of rotating parts have already been established (Table 1).

Table 1. Permissible amount of displacement of the center of gravity

Parts group	Name	Center Offset gravity, microns	Parts group	Name	Center Offset gravity, microns
BUT	Circles, rotors, shafts and pulleys of precise grinding machines	0,2-1,0	IN	Rigid small rotors electric motors, generators	2-10
B	high speed electric motors, grinding machine drives	0,5-2,5	G	Normal motors, fans, parts of machines and machine tools, high-speed drives, etc.	5-25

Sensitivity of balancing parts weighing up to 100 kg on balancing scales (Fig. 2): F=20 ÷ 30 G cm.

The amount of imbalance:

where ω is the difference in instrument readings 2.

Dynamic balancing parts and assembly units is used to more accurately determine the imbalance that occurs during rotation under the action of centrifugal forces. To carry out dynamic balancing of parts and sets such as bodies of revolution, balancing machines are used.

Parts and sets such as couplings, gears, pulleys are balanced on mandrels. A mandrel with a part or an assembly unit for balancing is installed on a balancing machine and connected to the machine spindle.

The magnitude of the imbalance and its location are determined by the instruments installed on the machine. The imbalance is usually eliminated by drilling a hole in the part or by directing the metal on the side of the part opposite from the place of imbalance.

Required specifications balancing accuracy depends on the design and purpose of parts and assemblies, their rotation speed, permissible vibrations of the machine, and the required durability of supports.

Static balancing can balance a part relative to its axis of rotation, but cannot eliminate the action of forces that tend to rotate the part along its longitudinal axis.

Dynamic balancing eliminates both types of imbalance. High-speed parts with a significant ratio of length to diameter (rotors of turbines, generators, electric motors, fast-rotating spindles of machine tools, crankshafts of automobile and aircraft engines, etc.) are subjected to dynamic balancing.

Dynamic balancing is carried out on special machines by highly skilled workers. In dynamic balancing, the magnitude and position of the mass that must be applied to or removed from the part are determined so that the part is statically and dynamically balanced.

Centrifugal forces and moments of inertia caused by the rotation of an unbalanced part create oscillatory movements due to the elastic compliance of the supports. Moreover, their fluctuations are proportional to the magnitude of unbalanced centrifugal forces acting on the supports. Balancing of parts and assembly units of machines is based on this principle.

Dynamic balancing, performed on modern automated balancing machines, in the range of 1-2 minutes gives data: the depth and diameter of drilling, the mass of loads, the dimensions of the counterweights and the places where it is necessary to fix and remove the loads, as well as the amplitude of the oscillations of the supports.

Parts and assemblies with a length greater than the diameter (crankshafts, spindles, rotors of bladed machines, etc.) are subjected to dynamic balancing. The dynamic imbalance that occurs during the rotation of the part due to the formation of a pair of centrifugal forces P (Fig. 3, a) can be eliminated by applying a corrective moment from the forces P 1. The choice of correction planes is determined by the design of the part and the convenience of removing excess metal. The most common case of part unbalance encountered in practice is shown in Fig. 3b.

Rice. 3. Schematic diagram of dynamic balancing parts:a - dynamic unbalance of the part; P - centrifugal forces from unbalanced masses m, located on the arm r; Pt - centrifugal forces from corrective weights; b - static and dynamic unbalance of the part; P’ is the centrifugal force from the mass m’, decomposed into forces P and P”, causing static unbalance

Unbalance detection is carried out on balancing machines. In the conditions of individual production, dynamic balancing is performed using simple means, which include, for example, a device for installing supports of a balanced part on elastic beams or on elastic (rubber) linings.

The part is brought into rotation to a speed exceeding the conditions of resonance.

The drive is turned off (for example, by resetting the belt) and the amplitude of the maximum oscillations of one of the supports is measured. By attaching a test load to the part, the vibration of this support is stopped. A similar procedure is performed for the other support. Balancing ends when the oscillations of the supports stop.

with elastic supports, used for parts and assemblies weighing up to 100 tons (rotors of powerful turbines) - in fig. 4.

Rice. 4. 1 – balancing object; 2 - electromagnetic clutch; 3 - electric motor; 4 - bearings; 5 - supporting elastic racks (springs); 6 - stops, alternately locking the bearings; 7 - mechanical lever indicator for determining the plane of imbalance by marks 8 drawn by the tip of the indicator on the painted oscillating neck of the object; 9 - compensating test weights attached to the object

Balancing is carried out with alternately fixing the supports. The angular position of the imbalance is found using mechanical or electrical indicators. The amount of imbalance in the selected correction planes is determined by attaching test compensating weights. The sensitivity depends on the weight and dimensions of the object.

Balancing on frame type machines with adjustable imbalance compensators, it is mainly used for parts and assemblies of small and medium sizes weighing up to 100 kg.

Unbalance balancing is carried out manually and mechanically.

On fig. 5 shows a diagram of a balancing machine with manual movement of compensating weight 3 on the machine spindle.

Rice. five. 1 - frame; 2 - balanced part, assembly; 3 - imbalance compensator

The load 3 is moved in the radial and circumferential directions and its weight is adjusted manually. This determines the equivalent amount of material to remove from the part. The imbalance is determined only in the plane of correction 1–1. Therefore, to determine the imbalance of the part in another plane 2–2, it is necessary to reinstall it with a rotation of 180 ° to determine the size and location of the compensator in this plane. The machine requires pre-setting according to the reference part; frame oscillations around the horizontal axis are noted by a mechanical amplitude meter; the value of unbalanced moments in the selected correction planes is determined with an accuracy of 10 -15 G cm 2 .

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