Two mechanisms of vinification rubbing stiffness. Opіr kochennyu and promyslovі wheels. Orientation value of the coefficient of weight loss for different pairs of nodding
Let the wrapper on the body, which is rotting on the support, blow: P - external force, which helps to bring the body into the camp of stiffness, or lifts the stiffness and directs the support, N - force that presses and Rp - the force of the reaction of the support.
Yakscho vector sum Since all forces reach zero, then all the symmetry of the body collapses evenly and straight, or becomes overwhelmed with unruliness. Vector Ft=-P signifies strength by rubbing stiffness, which resists the rush. Tse means that the force that presses on is equal to the vertical warehouse reaction of the support, and the external force is equal to the horizontal warehouse reaction of the support.
Ft R = Nf
Zvіdsi force rubbing stiffness is more:
Pokhodzhennya rubbing stiffness can be visually revealed like this. If cool or the cylinder rolls on the surface of another body, the trochs are pressed into the surface of that body, and the trochs themselves are squeezed. In such a rank, the body, what to roll, the whole hour nibi roam on the weight. At the same time, it is necessary to wind up the occupants of the same surface in the distance, and the forces of the bond, which develop between these surfaces, cross over. Offended by the appearances, they call out the forces of rubbing stiffness. The harder the surface, the less pressing and the less rubbing of the stiffness.
Designation:
ft- rubbing force
f- Coefficient of stubbing, what can be the difference of time (m) μ , which is unfathomable)
R- body radius
N- Pressing force
P- Zovnіshnya force, as if trying to bring the body to the camp of stiffness, or to lift the stiffness and direct the support;
Rp- Support reaction.
Tertyam kochennya is called rukh ruhu, in some cases, the sharpness of dotik bodies at the points of dotik is the same for the meanings and directly.
As if two dotikh tіl vіdbuvaєtsya with one-hour stubble and forging, then in the same vein rubbing stiffness from licking .
Look at the stiffness without forging the cylinder with a vaga G that radius r along the horizontal reference plane (Div. Fig. 1). Inheritance of diї forces G there will be deformation of the cylinder and the bearing surface in the area of the dot. How strong is P not dіє, then strength G bude vrіvnovazhuvatsya reaction R the bearing surface and the cylinder are rebuffed at a quiet (reaction R be vertical). Yakshcho to the cylinder to report a small force R , then wine, like before, we will be calm. When you see it, you reapplied the vise to the supporting surface and that's the same reaction. R pass through deaku point BUT i through a dot Pro (Sgіdno theorem about the equality of three non-parallel forces).
For some critical power R the cylinder will soon collapse and will evenly move along the supporting plane, and the point BUT borrow from your extreme right camp. It can be seen that rubbing the head can calmly change from zero to some maximum value, and the maximum will be at the moment the cob collapses.
Significantly k maximum leverage G shodo points BUT . Todi at the time of equal displacement of the cylinder (Tobto jealous):
ΣM BUT = 0 or - Pr + Gh = 0 ,
why the shoulder of strength R due to the insignificance of the deformation of tіl vvvazhemo equal to the radius of the cylinder r (strength R - Horizontal). From the rest of the evenness, the strength is significant, which is necessary for the equal shaking of the cylinder:
Р = kg/r
The maximum value of the shoulder k is called the coefficient of stiffness; Vіn maє razmіrnіst dovzhini i vyyavlyaєєtsya in centimeters and millimeters.
From the taken formula it can be seen that the scissilla, the necessary relocation of the cylindrical roller, is directly proportional to the vase G i back proportional to radius r kovzanka. Why does it stand out, what is a kovzanka, what has a larger diameter, it is easier to migrate.
The coefficient of rubbish is marked by the last path, and its value of different minds is brought to the bottom. Below is the orientation value of the coefficient of the rubbish k for flat ironing (cm):
Soft steel on soft steel .............................0.005
Hardened steel on hardened steel ............... 0.001
Chavun by chavun ............................................... .0.005
Wood steel .............................................0.03...0.04
Wood on wood ................................... 0.05 ... 0.08
Gum tire along the highway ............................... 0.24
Coefficient of rubbish is not enough to lie in the dryness of the body.
In a number of fluctuations in the case of warping, the active reactive forces that blow on a forging can be visualized in a different way (Div. malyunok 2a, b).
Let's rehearse the reaction R supporting surfaces in warehouses N і F tr then:
R=N+F tr ,
de F tr - Power rubbing stiffness; N – reaction is normal up to the undeformed support surface.
We store three equal equal rinks:
∑X = 0; P - F tr = 0; ΣY = 0; N - G = 0;
ΣM A = 0; - Pr+Gk=0.
Z tsikh rivnyan maєmo:
P=F tr ;N=G ;Pr = Gk .
Introduced value Pr=M , Gk = M tr , de M - the moment of rubbing stiffness, M tr - Lost a moment.
It is possible to have such a name for the head of a cylindri- cal cat:
M ≥ M tr , ale R< F tr - May the place be less than stiffness;
M< М tr , ale Р > F tr - there is less space for forging;
M > M tr , ale Р > F tr - stiffness with licking;
M< М tr , ale R< F tr - the kovzanka is resting at the station of calm.
When rubbing the stiffness in more vipadkіv less rubbing the forging, then the deputy of the bearings of the forging widely zastosovuyut sacks, rollers or other bearings of the stiffness, yakі, regardless of the higher varіst, give a significant gain in saving energy through the change.
Mastilny materials
Mastilnye materials are classified, nasampered, behind the physical camp.
Іsnuyut:
consistent
solid oiling materials
gas-like
Mastilnye materiali are designated for reduction of wear and tear.
Zalezhno vіd navantazhennya stench vykonuyut so zavdannya:
introduction of heat
zahist on top
passing the struma
Vikonuyuchi tsі zavdannya, raznі mastilnі materiali behave unequally.
Rare oiling materials
introduction of heat
zahist on top
passing the struma
the introduction of particles that call for wear
Rare oily materials can be seen:
fat olives
mineral oils
synthetic oils
Fat olives are not suitable for oiling. If you want stench and may have a strong protective effect, stench is not resistant to low temperatures and sensitive to oxidizing. In technical areas, the leaders are mineral oils.
At our hour, synthetic oils are gaining more and more importance
Їх advantages:
increased stability to oxidation
resistance to low and high temperatures
dovgotrivale mastilo, mastilo for the whole term of the service to the virob
Anti-corrosion materials and distribution agents are special products, one of the factories of which is oil.
Consistent oiling materials
Qi materials vykonuyut so zavdannya:
zahist on top
passing the struma
embarrassment from the hit of third-party speeches
To consistent oily materials can be seen:
plastic oil
oil paste
waxing waxes
Maschuvalnі waxes mayut vysokomolecular vuglevodnevy basis. The most important areas of їх zastosuvannya є borderline and partial butter at low dryness. Plastic oils are prepared on the basis of oils and wash the consistent structure of the zavdyak to the gusher. You can zastosovuvat yak with elastic hydrodynamic oil, so with boundary oil and partial oil of details. Mastilni pasti v_znyayutsya high in the mist of solid oils. The stench zastosovyatsya at the boundary and partial color of parts for loose, transitional or press fit. Consistent oiling materials can be fixed only if, through an insufficiently narrowed gap, the oil is not guilty of wicking and/or if the oil can be stable to the point. In our days, materials can be of great importance, so for their minimum staining, the maximum term of service of parts is ensured.
Hard oil materials
Qi materials can be used as follows:
zahist on top
materials for tribosystems
varnishes for smearing
Krіm tsgogo, before them are powdered polymers or metal materials, as well as minerals, for example, polytetrafluoroethylene, copper, graphite or molybdenum disulfide. For zastosuvannya like stink powders fit badly. To that they vikoristovuyut like additives, yakі zabezpechuyut zakhist like rubbing, so і іd wear. Hard oil materials are used, as a rule, for dry oil. As a result, marginal oil comes out, as when rare or consistent oils are included in the material for tribosystems, it can be victorious for partial oil. Solid oily materials are more important in quiet situations, if through functional features or sparse or thick oily oils are not an ideal solution to the problem, but for it the power of solid oily materials is enough to overcome them.
Forces of rubbing are blamed for non-intermediate contact on top of two solid bodies. Razrіznyayut forces rubbing - calm, forging that stiffness. If the body does not forge on top of another body, but rolls, then the strength of rubbing the stiffness is given to the opir. Rubbing stiffness ten times less than rubbing forging. Let's figure it out by the mechanism of vindication of strength.
Roll easier, lower pull
At everyday life we are koristuєmosya with the words of the stiffness of the practical day:
- Heavy, oversized objects can be easily moved by pushing round rollers under them or blowing them. For example, to cover with asphalt a 1-tonne chavun blank, it is necessary to apply a force of 200 kgf - on such a building only strongmen can do it. And it is possible to wind a child on a piglet, even for which a force of no more than 10 kgf is required;
- Usі transport zasobi, scho move on the surface of the earth, spinning wheels;
- For ease of lifting important objects to a height, a block is installed to make the shape of the wheel;
- Roller and sump bearings are fixed at all outbuildings, if it is necessary to obtain a minimum amount of rub in the details that are wrapped.
Obviously, wine wheels are one of the most important achievements of human civilization.
Rice. 1. Apply strength when rubbing the stiffness.
Ozhe, the power of rubbing the stiffness is the same strength that is due to the roaming of the body on the surface without licking. At this very moment, those who have been appointed to forge vinyatok, to that, when forged, they grow dozens of times!
Why blame the force rubbing stiffness
A round object (disk, sack, cylinder) is slightly pressed into the surface when it is stiff, making a “hole and a hump”. To go out like this, body, to roll, with a fluffy vag you make yourself a jump (hump), and do yoga like bi roaming all the time uphill. At the same time, the body is also deformed.
Another reason is the strength of adhesion (adhesion), which is due to the surfaces at the time of contact. Adhesion due to intermolecular interaction.
Rice. 2. Viniknennya force rubbing stiffness.
The harder the surface, which the body rolls, the less will be the “fossa” (pressure) and, therefore, the less force is rubbing the stiffness. Opir less stiffness, lower rubbing forging, to that the area of contact sounds even smaller, and to that the force is normal, which presses the body to the surface, it is also small and insufficient, so as to save the body's movement.
For transshipment transport, the wheels and rails are steel, the wear time is much less, lower for vintage car tires. If the surface of the boules were absolutely hard, then the force of the rub would be zero.
Vіd what to lay and why dovnyuє force rubbing kochennya
Like a round body, for example, a wheel with a radius R to roll on the surface, then for the formula of force rubbing stiffness F t rightly such a viraz:
$ F_t = N * (μ \over R) $ (1),
N- Pressing force, N;
μ - Coefficient of weight loss, m/N.
3 formulas are obvious, scho F t grows with the increase in the weight of the body and changes with the increase in the radius of the wheel R. Tse th understood: chim bigger wheel it is less important for the new unevenness of the surface (humps), but it looks like it will.
Coefficient of rubbish μ $[m/N]$ rozmіrnіst vіdmіnu kofіtsієnta tertya forging k, What a bezromirny.
Rice. 3. Formula for strength rubbing stiffness.
Bearings
To reduce the rubbing of the forge, the bulo was found to be oiled, as it was allowed to achieve a change by rubbing 8-10 times. The first time, like the nineteenth century, the idea of replacing the forged rubble with the rubble was brought to the bearing. Qiu replace spools and roller bearings. When wrapping the wheel or the motor shaft, the bags (or rollers) are rolled along the bushings (clip for the bags), and the shaft or the entire wheel - along the bags. In such a way, it was possible to reduce the cost of dozens of times.
What did we recognize?
Otzhe, we recognized that it is the power of rubbing stiffness. We looked at two main mechanisms that invoke this force. According to formula (1), the wear force increases due to the increase in body shaft and changes with an increase in the radius of the wheel. Roller and ball bearings know their position in most outbuildings, what details are wrapped.
Topic quiz
Assessment of additional
Average rating: 4.2. Usy otrimano ratings: 285.
Trennia goydannya- Opir Ruhu, which blames for the hour of the migration of a friend one by one. opir kochennyu of one body (skating rink) on top of another. The reason for the rubbing of stiffness is the deformation of the cat and the supporting surface, as well as the forces of adhesion. The contact stress in the plasma leads to spring and / or plastic deformation of the body, which causes micro-slipping of the surface, plastic flow in the plasma contact and viscous hysteresis. As adhesive interactions, these processes are thermodynamically irrevocable and lead to energy consumption, tobto. call out opir kochennyu. When it sounds, it sounds like it’s dead, it’s rolling (the wheel) doesn’t affect the traction or galvanic function (for example, the wheel of a locomotive, which opens up the warehouse or the car wheel is galvanized), so if you blame the additives, spend on not rubbing in the flames of contact, for reasons normal contact voltage, dragging and dotichnym, tobto. under the rubble of frostbite to understand cleanly rubbing stiffness.
Viyavlyaєєєєєєєєєєє, priklad, mizh elements podshipnikіv kochennya mizh car tire of the wheel of the car and the roadway. For more vipadkivs, the size of the shank is less than the size of the shank for other equal minds, and therefore the shank is a broader type of movement in technology. Rubbing the frostbite, weeping between two bodies, and to that it is classified as a good-looking rubbish.
Tertya kochennya plays the great role of modern technology. It is blamed when wrapping the number of other details that are wrapped, as it may be in all work stations and transport vehicles. The replacement of the forging of the wheel with a path of winemaking was the greatest success in the history of civilization.
Tertya is a physical phenomenon, with which a person struggles with the method of change in any wrapping and forged parts of mechanisms, without any, prote, impossibility of the same movement of these mechanisms. In the article, we can see from the look of physics what kind of force
How do you see the forces of losing ground in nature?
We look ahead of us, like a rubbish rubbish occupies the middle of the rubbish forces. Qi forces are blamed on the result of the contact of two different bodies. Tse can but the body is solid, rarely gas-like. For example, the watering of the air near the troposphere is accompanied by friction between the hull and molecules.
Looking at the hardness of the body, they see the forces rubbing calmness, forging that stiffness. Kozhen said from us: to destroy the boxes on the ground, it is necessary to apply force to the surface of the deak. The value of strength, as if I’ve seen the boxes, I’ll become calm, I’ll be more powerful in modulus, losing calm. The rest is between the bottom of the box and the surface of the underlays.
As soon as the box started its own ruh, it is necessary to report a permanent force in order to save this ruh equally. The reason for this fact is that between the contacts of the logs and the box for the rest of the day, the force of forging is lost. As a rule, there are dozens of dozens of hundred less won, less calm.
If you put round cylinders of hard material under the box, then moving it will become much easier. On the wrapper in the process of moving the cylinders under the box, Vaughn's force will sound richly less than the front two forces. For the very reason that the wheels of humanity were blamed for becoming a majestic streak at the beck of progress, even though people took away the ability to move more and more profits for the help of a small applied force.
Physical nature rubbing stiffness
What is the blame for the force rubbing stiffness? The food chain is unforgivable. For a look at the next step, look in detail at what is seen from the wheel and on the surface of the process of stiffening. In the first black, the stench is not ideally smooth - neither the surface of the wheel, nor the surface, which it looks like. Prote, tse is not the main reason for the appearance of rubbish. The main reason is the deformation of one chi both bodies.
Be it a body, from any solid material the stench did not add up, deformed. Chim more weight tіla, tim more than a vice to repair on the surface, which means that it deforms itself at the point of contact and deforms the surface. Tsya deformation in a number of folds of the flooring is small, so it does not outweigh the boundaries of springiness.
In the process of shaking the wheel, the deformation of the wheel after attaching to the contact with the surface restores the shape. Tim is not less, the deformations are cyclically repeated with a new turn of the wheel. Whether it is a cyclical deformation, it is possible to lie at the boundary of springiness, accompanied by hysteresis. In other words, on a microscopic level, the shape of the body is visible until after the deformation. The hysteresis of the cycles of deformation in the process of deforming the wheel is brought up to the "dispersion" of energy, which is manifested in practice when the force appears when deforming the deformity.
Ideal Body Swing
Under the ideal body to this particular type maєtsya on uvazі those that won't be deformed. In the case of an ideal wheel, the area of contact with the surface is equal to zero (there is a surface air line).
It is characterized by the forces that act on the wheel, which does not deform. First, there are two vertical forces: the weight of the body P and N. Offensive forces to pass through the center of the mass (all wheels), do not take part in the created moment that turns. For them, you can write:
In another way, there are two horizontal forces: the external force F, like the wheel is moving forward (it will pass through the center of the mass) and the force rubbing the stiffness f r . The rest is creating the moment to turn M. For them, you can write down the following equalities:
Here r is the radius of the wheel. Tsі vnostі vengeance for the important visnovok. If the force of rubbing f r will be infinitely small, all one will create a twisting moment, which will bring the wheels to ruin. Oskіlki zvn_shnya force F dovnіuє values \u200b\u200bf r, then whether it be infinitely small, the value of F will bring the wheel to a stiffness. Tse means that it’s a body of stiffness, ideal and not deformable in the process of collapse, then you can’t say anything about the power of losing stiffness.
The mustache of the body is real, so that you can see the deformation.
Real body rocking
Now, the situation is more clearly described, more than a drop of real (deformable) bodies. The area of wheel torsion and the surface is no longer equal to zero, it’s more than a lifetime value.
Let's analyze the forces. Let's have a look at the vertical forces that support the reaction. Stink, like before, equal one to one, tobto:
However, the force N now moves vertically uphill through the entire wheel, and the rest is shifted from it to the top d. If you show the area of \u200b\u200bthe circle of the wheel from the surface at the sight of the area of \u200b\u200bthe rectangle, then the back of the rectangle will be the width of the wheel, and the width will be more 2 * d.
Now let's move on to looking at horizontal forces. The external force F, like before, does not create a wrapping moment and more powerful force, losing f r beyond the absolute value, so:
The moment of forces, which leads to the wrapping, is created by losing f r that reaction of the support N. Moreover, these moments will be straightened out at the different sides. Vidpovidny viraz may look:
In a time of equal motion, the moment M is equal to zero, so we take:
The rest of the rewriting of other formulas can be rewritten like this:
In fact, we took away the head for the sake of understanding the strength, rubbing the stiffness of the formula. We then carried out a її analysis.
Coefficient of support for headstock
This coefficient was introduced earlier. Also, a geometric explanation was given. Find the value of d. Obviously, the greater the value, the greater the moment is created by the reaction force of the support, as if overcoming the rotation of the wheel.
The coefficient of support for stiffness d, on the basis of the coefficients, rubbing calmly and forging, is a dimensional value. Vіmiryuєtsya vіn odinіtsyah dozhini. In the tables, induce sound in millimeters. For example, for the wheels of the train, which are made of steel laths, d = 0.5 mm. The value of d is determined depending on the hardness of the two materials, on the wheel bearing, on the temperature of those other materials.
Coefficient of rubbish
It is not necessary to stray yoga with the forward coefficient d. The coefficient of the loss of stiffness is denoted by the symbol C r and calculated using the following formula:
Tsya equanimity means that the value of C r є is limitless. Itself won't be directed at a number of tables, to remove information about the analysis of the type of rubbish. This coefficient is handily victorious for practical rozrahunkiv, shards of wine convey knowledge of the radius of the wheel.
The value of C r in the most important fluctuations is less, lower coefficient of calmness. For example, for car tires, which are crumbling with asphalt, the value of C r is in the range of decile cox (0.01 - 0.06). However, there is a significant increase in Russia when the wheels are lowered on grass and sand (≈0.4).
Analysis of the original formula for the force fr
Let's write down once again the formula for strength when rubbing stiffness:
Z rіvnostі vyplivaє, scho chim greater diameter of the wheel, tim less force F next to report, schob started ruh. Now let's write qi equanimity through the coefficient C r maєmo:
As you can see, the force of rubbing is directly proportional to the vase of the body. In addition, with a significant increase in the value of P, the coefficient C r itself changes (wine increases through the increase in d). Most practical vipadkіv C r lie at the borders of a few hundred. At one's hand, the value of the coefficient of rubbish is to lie at the borders of ten. Oskіlki for forces rubbing stiffness and such forging formulas are the same, then stiffness appears to be a viable energy point of view (the force f r is less by an order of magnitude of forging strength in most practical situations).
Umov's stiffness
It’s rich that someone has told us about the problem of slipping when the car is moving for an hour on ice or in the woods. Why do you care? The key to the vitality of nutrition lies in the spіvvіdnoshennі absolute value of the forces of the numbness and peace. Once again, we write down the formula for stiffness:
If the force F will be greater or more durable, then the wheel will be more compact. However, as soon as the strength exceeds the magnitude of the loss of calmness, the sooner the wheels will lick, lower the stiffness.
In this way, the effect of slickness is attributed to the spivvіdnanceny koefіtsієntіv rubbing calm and rubbing stiffness.
Ways to prevent car wheel slippage
Rubbing the stiffness of a car wheel, which is on a slimy surface (for example, on ice), is characterized by a coefficient C r \u003d 0.01-0.06. The values of such an order are typical for the coefficient of calmness.
To hide the risk of forging the wheel, to beat the special "winter" gum, in the yak the metal spikes are screwed. Stop, vrіzayuchis at krizhan surface, zbіlshuyut koefіtsієnt terya calm.
The second way to improve the rub is to calmly lie in the modification of the surface, as if the wheel is collapsing. For example, for help, sip sip chi sill.
Enthusiasm...