Statistical and dynamic balancing of critical parts. Balancing rotating parts. Static balancing devices

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

At high rotational 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 balancing methods: static and dynamic. In 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 displaced, or increasing the mass on the diametrically opposite side. In this method, the part is in a static state and if it is balanced (balanced), the part will remain in any position in which it rotates relative to the axis of rotation A diagram of balancing parts of different lengths (A, A1) is shown in Fig. 130.

Rice. 130. Diagram of balancing parts of different lengths: 1 - unbalanced mass; 2 - balanced mass

Static equilibration 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 counterbalanced part can roll.

The knives are verified with a level in two mutually perpendicular directions. For balancing massive parts (pump pulleys), roller or disc stands are used, which have ball bearings or rollers instead of knives.

Static balancing is performed as follows. The counterbalanced part is installed on the stand, and its balance is determined by turning it at a certain angle. When unbalanced, the heavy part of the part returns downward, and when it is balanced, it remains in the position to 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 weakened during drilling, then in this case, a balancing mass (weight) in the form of separate plates is installed on the diametrically opposite guard with the help of screws.

For a disc-shaped part having a small length compared to its diameter, the static balancing method will be sufficient, since the unbalanced and balanced masses are located on the transverse axis of the part or close to it. 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 having a relatively long length (V-belt transmission pulleys), one method of static balancing will not be enough, since the unbalanced and balanced mass 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 the pair of forces can only be eliminated 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.

Control questions to chapter X

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

2. What types are bolts classified into?

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

4. What are the washers for?

5. What methods of locking threaded connections are used?

6. What type of wrenches are used?

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

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

9. What kind of spline profiles are used?

10. What methods are used for press connections?

11. What couplings are there?

12. How are the shafts connected with tire-pneumatic couplings aligned?

13. What are the elements of the cardan transmission?

14. What gear drives are there?

15. What methods are used to check the clearances of the gearing?

16. What are the components of the roller drive chain?

17. What are plain bearing shells used for?

18. What are the designs of rolling bearings?

19. What methods are used to press-fit bearings?

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 THE ROOM CONSTRUCTION

One of the reasons for the reduction in the resource of the engine 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 with. This is increased wear of parts, and extremely uncomfortable operation of the engine, and worse dynamics, and increased fuel consumption, etc., and so on. All these passions have already 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 can be, and then consider how to deal with it.

To begin with, let's decide why introduce the concept of imbalance at all, because the cause of vibrations is the inertial forces that arise during rotation and uneven translational movement of parts. Perhaps it is 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 is pressing, how many kilos falls on which support ... But the fact is that the magnitude of the inertial force depends on the rotational speed, more precisely on the square of the frequency or acceleration during translational motion, and this, in contrast to the mass and radius of rotation, the quantities are variable. 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 inertial force is:

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

Not higher mathematics, of course, but I don’t want to recount it 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 the units of measurement, since in the vastness of the world network, and in print, in numerous articles devoted to balancing, there is so much more ... Here are grams divided by centimeters, and the definition of imbalance in grams (not grams and whatever you want, then think), and analogies with the units of torque (it seems like - kg m, but here g mm ..., but the physical meaning is completely different ...). In general, we will be careful!

So, the first kind of imbalance- static or, they say, static imbalance. Such an imbalance will occur if any weight 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 imbalance is characteristic of disc-shaped rotors2, flywheels, for example, or grinding wheels. This imbalance can be eliminated using special devices - knives or prisms. The heavy side3 will rotate the rotor due to gravity. Noticing this place, it is possible to install such a load by simple selection to the opposite side, which will bring the system to equilibrium. However, this process is quite lengthy and painstaking, therefore, it is still better to eliminate static imbalance on balancing machines - and faster and more accurately, but more on that below.

The second type of imbalance- instant. This imbalance can be caused by sticking a pair of identical weights to 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 a certain angle. What is so remarkable about this type of imbalance? Indeed, at first glance, in "nature" it can only be found by a "lucky" accident ... The insidiousness of such imbalance lies in the fact that it manifests itself only when the shaft rotates. Place the rotor with the momentary imbalance on the knives, and it will be completely at rest, no matter how many times it is shifted. However, as soon as you spin it, a strong vibration will immediately appear. It is possible to eliminate such an imbalance only on a balancing machine.

Finally, most general case- dynamic imbalance. Such an imbalance is characterized by a displacement 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 displaced relative to the axis of rotation of the shaft, and with it the main central axis of inertia. Moreover, it also deviates by a certain angle so that it does not intersect the axis of rotation4. It is this type of imbalance that occurs most often, and it is it that is so habitually eliminated by us in tire shops when changing tires. But if we all go to tire fitting as one in the spring and autumn, then why do we ignore the engine parts?

A simple question: after grinding the crankshaft to a 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 is the time and desire?

So, balancing shafts, flywheels and so on. need, no doubt about it. The next question is how to balance?

As already mentioned, with static balancing, prism knives can be dispensed with if there is enough time, patience, and the tolerance ranges for residual imbalance are large. If you appreciate work time, you 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 detect and eliminate imbalances in crankshafts, flywheels, clutch baskets, etc.

The whole process of eliminating the imbalance 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, which will track the position and frequency of rotation of the shaft, put on a drive belt with which the shaft will untwist during the balancing process and enter the shaft dimensions, position coordinates and radii into the computer correction surfaces, select unbalance units, etc. By the way, next time, you won't have to re-enter all this, since it is possible to save all the entered data in the computer's memory, just as there is an opportunity to erase, change, overwrite, or change them for a while without saving them at any time. In short, since the machine computer operates under operating system Windows XP, then all the methods of working with it will be quite familiar to the average user. However, even for a mechanic inexperienced in computer matters, it will not be very difficult to master several on-screen menus of the balancing program, especially since the program itself is very clear and intuitive.

The very process of measuring the imbalance occurs without the participation of the operator. He just has to press the right button and wait for the shaft to rotate, and then he will stop. After that, the screen will display everything necessary to eliminate the imbalance, namely: the values and angles of the imbalances for both correction planes, as well as the depth and number of drills that need to be done to eliminate this imbalance. The hole depths are, of course, derived from the previously entered drill diameter and shaft material. By the way, this data is output for two correction planes if dynamic balancing has been selected. With static balancing, of course, everything will be displayed the same, only for one plane.

Now all that remains is 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 the spindle movement, or by a graphical 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, you just need to 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).

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

After removing the imbalance, you need to repeat the measurements again to make sure that the residual imbalance is within the permissible values.

By the way, about the residual imbalance or, as they sometimes say, the balancing tolerance. Almost every motor manufacturer in the instructions for the repair of parts should give the value of the residual unbalance. 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 what class your rotor belongs to, and then, using the table below, find out the balance 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 a 5th accuracy class in accordance with GOST 22061-76. Suppose that our shaft has very special requirements - let's complicate the task and class it as the fourth accuracy class.

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

Now according to the formula:

D art. Add.- permissible residual imbalance;
e Art.- tabular value of specific imbalance;
m rotor- rotor mass;

trying not to get confused in the units of measurement and taking the shaft mass equal to 10 kg, we get that the permissible residual unbalance of our crankshaft should not exceed 40 - 100 g mm. But this applies to the entire shaft, and the machine shows us the unbalance 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 correction planes, the permissible residual unbalance on each support should not exceed 20-50 g mm.

Just for comparison: the permissible unbalance of the crankshaft of the D-240/243/245 engine with a shaft mass 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 more than the one calculated by us. However, there is nothing surprising - the shaft is heavier than what we took as an example, and it rotates at a lower frequency ... reverse side and you will see that the balancing accuracy class is the same as in our example.

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

D art.- 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, coupling halves, bearings, fans, etc.) that have their own imbalances due to deviations in the shape and location of surfaces and seats, radial clearances, etc .;
D art.- 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 repairs involving balancing.

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

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

Well, okay, 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 imbalance is eliminated, considering the crankshaft to be perfectly balanced. There is one big plus in this method: if the flywheel and clutch basket after balancing are not disconnected from the shaft and these parts are never replaced, then a unit balanced in this way will have less imbalance than if each part were balanced separately. If you still want to balance the flywheel separately from the shaft, then for this in the machine configuration there are special, almost perfectly balanced, shafts for balancing the 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 unbalance on this machine are very convenient, they save a lot of time, insure against possible mistakes connected with the notorious "human factor" and so on. In fairness it should be noted that at the very least, many other machines will be able to do the same. Moreover, the example considered was not particularly complicated.

And if you have to balance the shaft, say, from a V8? The task is also, in general, not the most difficult, but still it is not a four-in-line to balance. You can't just put such a shaft on the machine, you need to hang special balancing weights on the connecting rod journals. there is from what mass of the connecting rod belongs to rotating parts, and what to translationally moving, and finally, thirdly, from the mass of only rotating parts. 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 confuse which record refers to which piston or connecting rod, and do all this several more times.

Or you can use the Compu-Match automated weighing system offered as an option. The essence of the system is simple: electronic scales are connected to the machine's computer, and when the 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, for example, the lightest piston, and automatically determines the mass for each part that needs to be removed to equalize the weights. There will be no confusion with the determination of the mass of the upper and lower connecting rod heads (by the way, everything you need for weight distribution is supplied with the scales). The computer directs the actions of the operator, who just needs to carefully follow the instructions step by step. After that, the computer will calculate the mass of the balancing weights based on the mass of the specific piston and the weight of the connecting rods. It only remains to add that when calculating the masses of these loads, even the mass is taken into account engine oil, which will be in the shaft lines during engine operation. By the way, different sets of weights can be ordered separately. The weights, of course, are type-setting, that is, washers of different weights are hung on the hairpin and fixed with nuts.

And a few more words about weighing piston and 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, torque unevenness. But some things can still be done. Take a conventional in-line four-cylinder engine as an example. From the course of internal combustion engine dynamics, everyone knows that the forces of inertia of the first order of such a motor are completely balanced. Wonderful! But in the calculations it is assumed that the masses of all parts in the cylinders are absolutely the same and the connecting rods are weighed impeccably. But in fact, during the cap. repair, does anyone weigh the pistons, rings, pins, equalize the masses of the lower and upper connecting rod heads? Hardly…

Of course, the difference in the masses of the parts is unlikely to cause large vibrations, but if there is a possibility, even 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 driveshafts ... But wait, this is a completely different story ...

* The OX axis 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 the axis around which the entire mass of the body is evenly distributed. What does even 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 on the contrary there will be, maybe, another mass at a different distance, but having exactly the same product, that is, the mass selected by us will be balanced.

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

** Rotors in balancing refers to everything that rotates, regardless of shape and size.

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

**** If the main central axis of inertia nevertheless intersects the axis of rotation of the rotor, then such an imbalance is called quasi-static. There is no point in considering it in the context of an article.

***** Among other classifications of balancing machines, there is a division into pre-resonant and over-resonant. 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. The vibrations that occur during the rotation of an unbalanced part have one interesting feature: The vibration amplitude increases very slowly as the rotational speed increases. And only near the resonant frequency of the rotor, its sharp increase is observed (which, in fact, is dangerous for resonance). At frequencies above the resonant frequency, the amplitude decreases again and practically does not change over a very wide range. Therefore, for example, on pre-resonance machines, there is little sense in trying to increase the shaft rotation frequency during balancing, since the vibration amplitude recorded by the sensors will increase extremely insignificantly, despite the increase in the centrifugal force that generates vibration.

****** Some machines are equipped with oscillating feet.

******* Correction surface is the place of the shaft where holes are supposed to be drilled to eliminate unbalance.

******** Please note that the specific imbalance is indicated in microns. This is not a mistake, here we are talking about the specific imbalance, that is, referred to the unit of mass. In addition, the index "st." indicates that this is a static unbalance, 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 above the definition of static unbalance.

Wheel balancing is necessary so that while the car is moving, the driver does not experience discomfort from such a phenomenon as wheel beating. This happens when there is an imbalance about 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 tire introduces most of the imbalance. Since it is farthest from the center of rotation. Hence the need for balancing. After all, improper wheel balancing not only makes driving a car 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 have ridden on unbalanced wheels.

Agree, it's 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 leading ones need this, and there is no need to spend additional money on balancing the rear ones. This is a misconception, and such savings will only kill the rear suspension elements.

There are several types of balancing:

on the machine, with the removal of the wheel;
finishing, made directly by car;
automatic (powder, beaded).

There is also a division into dynamic and static.

How is balancing done

Static

In the case when the wheel has a static unbalance, 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 higher 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 the additional weight needs to be installed.

There are two types of cargo:

with a bracket, mounted on the edge of the disc and used, as a rule, on stamped discs;
on an adhesive basis, 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, it can be said that it was a trophy.

So what is dynamic balancing for? The wider the profile of the wheel, the more likely it is to get dynamic unbalance 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 the suspended vehicle, the wheel spins up to a speed of 90 km / h, and the automation takes measurements, and indicates in what place and what kind of load must be installed. This balancing requires equipment, which is often only available. professional centers tire fitting.

Automatic

Automatic applies only to trucks and buses. It happens as follows - special balancing granules, small beads, less often sand are poured into the wheel, because the latter has a high abrasive effect. While driving, centrifugal force causes the balancing material to be attracted to the inner surface of the tire, resulting in self-balancing.

By car given view balancing is not used due to the fact that it is not possible to determine exactly how much material needs to be poured into each wheel. Its weight also increases.

Correct 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, there is often quite a lot of it both on the outside and on the inside. Automation calculates how many grams of cargo you need to hang on this or that part of the wheel. By balancing a dirty wheel, you risk losing balance on the very first bump, when a large piece of dirt falls off the disc and all the work goes down the drain;
it is imperative to remove all old balancing weights;
still quite often there is a situation when the tire simply did not fully fit into its 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 in a newly balanced wheel.

How often should you balance the wheels

The recommended frequency is different. Someone says that it is needed 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 the tire service. Thus, you may save on more expensive repairs.
We hope that after reading this article, you will no longer have any questions about why you need wheel balancing, and whether you need to do it.

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

Dynamic loads on the supports of the operating unit are due to the inertial forces of parts that move translationally or rotate. The unit will be balanced if it is assembled from parts of the same name, moving translationally, of 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 dirt 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 assembly.

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

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

where M- product weight, g; r s- 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 г - and l j- mass (g) of a product element, distance (cm) from the center of mass to the axis of rotation of the product and the shoulder (cm) of the inertial force of the element relative to the axis passing through the center of mass of the product, respectively; i = = 1... To - the number of items in the item.

The article is considered to be statically balanced if the first condition is satisfied, and dynamically balanced if the second condition is satisfied. In real conditions, static, dynamic and mixed imbalance of rotating parts or assembly units are distinguished.

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

Rice. 2.57.a - static; b - dynamic; v - mixed

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

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

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 discs and on machine tools.

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

Rice. 2.58.a- on rollerskates: 1 - detail; 2 - mandrel; 3 - rollers; b- on prisms: 1 - detail; 2 - mandrel; 3 - prisms; v- on a swinging disk: 1 - arrow; 2 - detail; 3 - tip; 4 - support

Device for static balancing of parts on a swinging disc (Fig. 2.58, v) is devoid of the above disadvantage. Its statically balanced disc 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 discs are located in mutually perpendicular directions. The part is installed on the disk and oriented with a centering collar. If the disk with the part tilted under the action of gravity, then they are brought to a horizontal position by moving the compensating weight over the surface of the part. The location of the load and its mass indicate the direction and magnitude of the imbalance.

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

Dynamic b) for a statically balanced product (the center of mass is located 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 occurs S from two equal forces of inertia R on the shoulder /. Moment S causes variable 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 moment action 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 (Nm 2).

Mixed imbalance (see fig. 2.57, v) most often occurs in real conditions, when there are unbalanced inertial forces and a moment from two equal inertial 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 selected 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 - Replace centrifugal forces P x and R 2 their constituents R and R" and R "2 and R 2 in the correction planes located at a distance / from each other. We add these components in each plane according to the parallelogram rule and get the resultant and T 2. At the point of application of force T ( we apply two equal, but oppositely directed forces T 2. As a result, we get two unbalanced forces T 2 and Q in the planes of correction. Power Q is the vector sum of forces T ( and T 2. Moment T 2 1 defines dynamic imbalance, and strength Q- static. Complete equilibration 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 unbalance in each plane of the shaft correction are determined on balancing machines of models, for example, BM-4U, KI-4274, MS-9716 or Schenk (Germany). On the machines, assembly units (crankshafts with flywheels, cardan shafts, etc.) are balanced, rotating in two or more supports during operation of the unit.

The principle of operation of the balancing machine (Fig. 2.59) is as follows. The product is installed on elastic supports (cradles) 1 and put into 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 vibrate 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 unit; 4 - milliammeter; 5 - strobe lamp; 6 - electric motor; 7 - strobe limb; 8 - flywheel

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

After each determination of the direction and value of the unbalance, 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 desired angular position. With the help of a radial drilling machine or an electric drill, the excess metal of the required mass is drilled in the correction plane. The drilling length is proportional to the milliammeter reading.

After assembling a rotating assembly unit, which includes balanced parts (for example: shafts, shaft gears, couplings, etc.) and other parts (keys, pins, locking screws, etc.), it becomes necessary to rebalance them, since the displacement of one from parts, even within the gaps provided for in the drawing, causes significant imbalance.

The misalignment of the center of gravity of the part with the axis of rotation is usually 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 installed with support journals or on mandrels on horizontal parallels (knives, prisms, rollers) or rollers, while dynamic imbalance is detected only when the part rotates. In this regard, balancing is static and dynamic.

Static balancing. There are several methods for performing static balancing. Most often found in machine tool balancing on prisms and discs. Knives, prisms and rollers must be hardened and ground and checked for horizontal alignment before balancing.

When balancing on horizontal parallels (Fig. 1), the permissible ovality and taper of the mandrel necks 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 friction coefficient of the parallel and the mandrel journal, it is recommended to harden and carefully grind. The working length of the parallels can be determined by the formula:

where d is the diameter of the mandrel neck.

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

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

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

The imbalance is determined by trial attachment of correction 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 preliminarily applied with chalk and rotation is given to it. The rotation of the pulley is repeated 3-4 times. If the chalk line stops at different positions, it will indicate that the pulley is properly balanced. If the chalk line stops in one position each time, 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 filling them with lead.

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

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

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

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

The balancing of parts weighing up to 100 kg on a balancing balance is performed as follows (Fig. 2): the tested structure 1 is balanced with weights 3 and the rotating part 1 of the structure is accelerated to a rotational speed that exceeds the system oscillation frequency. After acceleration, the electric motor is disconnected from the test structure, the movable part of which continues to rotate freely, gradually decreasing the speed. This eliminates the influence of disturbances from the drive motor on the oscillating system. The amplitude of the displacement of the control point is measured by the device 2 at the moment the spindle speed coincides with the natural frequency of the oscillating system, that is, 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 of permissible displacement of the center of gravity of rotating parts have already been established (Table 1).

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

Parts group	Name	Center offset gravity, microns	Parts group	Name	Center offset gravity, microns
A	Circles, rotors, shafts and pulleys of precise grinding machines	0,2-1,0	V	Rigid small rotors electric motors, generators	2-10
B	High-speed electric motors, grinding machine drives	0,5-2,5	G	Normal electric 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.

Unbalance value:

where ω is the difference between the readings of the device 2.

Dynamic balancing parts and assembly units are used to more accurately determine the imbalance that occurs during rotation under the action of centrifugal forces. Balancing machines are used to dynamically balance parts and sets of the type of bodies of revolution.

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

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

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

Static balancing can balance a part about its axis of rotation, but it cannot eliminate the effect of forces tending to rotate the part along its longitudinal axis.

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

Dynamic balancing is carried out on special machines by highly qualified workers. With dynamic balancing, the amount and position of the mass that must be applied to or subtracted from the part is 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 the unbalanced centrifugal forces acting on the supports. The balancing of parts and assembly units of machines is based on this principle.

Dynamic balancing, carried out on modern automated balancing machines, gives data in an interval of 1-2 minutes: drilling depth and diameter, weight of loads, sizes of counterweights and places where it is necessary to fix and remove weights, as well as the amplitude of oscillations of the supports.

Parts and assemblies with a length greater than the diameter (crankshafts, spindles, rotors of blades, etc.) are subjected to dynamic balancing. The dynamic imbalance arising 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 correcting 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 imbalance encountered in practice is shown in Fig. 3, b.

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

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

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

The drive is turned off (for example, by dropping the belt) and the amplitude of the maximum vibrations of one of the supports is measured. By attaching a test weight to the part, the oscillation of this support is stopped. A similar procedure is followed 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 - balanced object; 2 - electromagnetic clutch; 3 - electric motor; 4 - bearings; 5 - supporting elastic struts (springs); 6 - stops alternately locking the bearings; 7 - mechanical lever indicator for determining the plane of unbalance according to marks 8 drawn by the indicator tip on the painted oscillating neck of the object; 9 - compensating trial weights attached to the object

Balancing is carried out by alternately fixing the supports. The angular position of the unbalance is found using mechanical or electrical indicators. The amount of unbalance in the selected correction planes is determined by attaching trial compensating weights. Sensitivity depends on the weight and size of the object.

Balancing on frame machines with adjustable unbalance compensators is used mainly for small and medium-sized parts and assemblies weighing up to 100 kg.

Unbalance balancing is done manually and mechanically.

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

Rice. 5. 1 - frame; 2 - part to be balanced, assembly; 3 - unbalance compensator

The weight 3 is moved in the radial and circumferential directions and its weight is manually adjusted. This determines the equivalent amount of material to be removed from the part. The imbalance is determined only in the correction plane 1–1. Therefore, to determine the unbalance of a 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 preliminary adjustment for the reference part; frame vibrations around the horizontal axis are noted with 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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