Liquids with a high coefficient of expansion. Thermal expansion coefficient

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The tensile strength of a liquid is not taken into account when solving practical problems. The temperature expansion of dropping liquids is characterized by thermal expansion coefficient β t, expressing the relative increase in the volume of liquid with an increase in temperature by 1 degree, i.e.:

Where W - initial volume of liquid; Δ W - change in this volume with an increase in temperature by an amount ΔT . The coefficient of thermal expansion of dropping liquids, as can be seen from Table. 5 is insignificant.

Table 5

Thermal expansion coefficient of water
Pressure Pa∙10 4	At temperature, °С

So, for water when the temperature changes from 10 to 20 ° C and at a pressure of 10 5 Pa β t=0.00015 1/deg. With significant temperature differences, the effect of temperature on the specific gravity in some cases has to be taken into account. The density and specific gravity of dropping liquids, as follows from the previous considerations, change little with changes in pressure and temperature. We can approximately assume that the density does not depend on pressure and is determined only by temperature. From expressions (9) and (1), one can find an approximate relationship for calculating the change in the density of dropping liquids with temperature:

The values ​​of the coefficient in (10) are found from tables within a given temperature range (see, for example, Table 5). The ability of liquids to change density (specific gravity) with temperature changes is widely used to create natural circulation in boilers, heating systems, to remove combustion products, etc. B table. 6 shows the density of water at different temperatures.

Table 6

Dependence of density ρ, kinematic ν and dynamic μ viscosity of water on temperature
Temperature, °С		ν∙10 4 , m 2 /s	μ∙10 3 , Pa∙s

In contrast to dropping liquids, gases are characterized by significant compressibility and high values ​​of the thermal expansion coefficient. The dependence of the density of gases on pressure and temperature is established by the equation of state. The simplest properties are possessed by a gas rarefied to such an extent that the interaction between its molecules can be ignored - the so-called perfect ( ideal) gas. For perfect gases, the Clapeyron equation is valid, which makes it possible to determine the density of a gas at known pressure and temperature:

(11)

Where R - absolute pressure; R - specific gas constant, different for different gases, but independent of temperature and pressure [for air R=287 J/(kg∙K)] ; T is the absolute temperature. The behavior of real gases under conditions far from liquefaction differs only slightly from the behavior of perfect gases, and for them one can use the equations of state of perfect gases in a wide range. In engineering calculations, the density of a gas usually results in normal physical conditions (t=0°; p=101 325 Pa) or to standard conditions (t=20° С; р= 101325 Pa). Air density at R=287 J/(kg∙K) under standard conditions according to formula (11) will be equal to ρ 0 =101325/287/(273+20)=1.2 kg/m 3 . The density of air under other conditions is determined by the formula:

(12)

On fig. 1 shows the graphs of the dependence of air density on temperature determined by this formula at different pressures.

Rice. 1 Dependence of air density on barometric pressure and temperature

For an isothermal process (T=const) from formula (12) we have:

(13)

(14)

Where k=s p /s ν is the adiabatic constant of the gas; c p is the heat capacity of the gas at constant pressure; with ν - the same, at a constant volume. The compressibility of gases depends on the nature of the state change process. For an isothermal process:

(15)

For an adiabatic process:

It follows from expression (15) that the isothermal compressibility for atmospheric air is ~9.8∙10 4 Pa ​​(about 1 atm), which is about 20 thousand times higher than the compressibility of water. Since the volume of a gas depends to a large extent on temperature and pressure, the conclusions obtained from the study of dropping liquids can be extended to gases only if, within the limits of the phenomenon under consideration, changes in pressure and temperature are insignificant. Significant pressure differences, which cause a significant change in the density of gases, can occur when they move at high speeds. The ratio between the velocity of the fluid and the speed of sound in it makes it possible to judge the need to take into account the compressibility in each specific case. In practice, the gas can be taken incompressible at speeds not exceeding 100 m/s. Viscosity of liquids. Viscosity is the property of liquids to resist shear. All real liquids have a certain viscosity, which manifests itself in the form of internal friction during the relative movement of adjacent fluid particles. Along with easily mobile liquids (for example, water, air), there are very viscous liquids, the shear resistance of which is very significant (glycerin, heavy oils, etc.). Thus, viscosity characterizes the degree of fluidity of a liquid or the mobility of its particles. Let the fluid flow along a flat wall in layers parallel to it (Fig. 2), as is observed in laminar motion. Due to the decelerating effect of the wall, the fluid layers will move at different velocities, the values ​​of which increase with distance from the wall.

Rice. 2 Velocity distribution for fluid flow along a solid wall

Consider two layers of fluid moving at a distance Δу from each other. Layer A moving at a speed u , a layer AT - with speed u + Δu . Due to the difference in velocities per unit time, the layer AT shifts relative to layer A by Δ u . Value Δ u is the absolute shift of layer A along layer B, and Δ u /Δ y is the velocity gradient (relative shift). The tangential stress that appears during this movement (friction force per unit area) will be denoted by . Then, similarly to the shear phenomenon in solids, we obtain the following relationship between stress and strain:

(17)

Or, if the layers are infinitely close to each other,

(18)

Value µ , similar to the shear coefficient in solids and characterizing the resistance of a liquid to shear, is called dynamic or absolute viscosity. The existence of relation (18) is first indicated by Newton, and therefore it is called Newton's law of friction. In the international system of units, dynamic viscosity is expressed in H s / m 2 or Pa s. In the technical system of units, dynamic viscosity has the dimension kgf∙s∙m -2 . In the CGS system, a poise (P) is taken as a unit of dynamic viscosity in memory of the French doctor Poiseuille, who studied the laws of blood movement in the vessels of the human body, equal to 1 g∙cm -1 ∙s -1; 1 Pa s \u003d 0.102 kgf s / m 2 \u003d 10 P. The viscosity of liquids is highly dependent on temperature; in this case, the viscosity of dropping liquids decreases with increasing temperature, and the viscosity of gases increases. This is explained by the fact that the nature of the viscosity of dropping liquids and gases is different. In gases, the average speed (intensity) of the thermal motion of molecules increases with increasing temperature, therefore, the viscosity increases. In dropping liquids, molecules cannot move, as in a gas, in all directions, they can only oscillate around their average position. With an increase in temperature, the average velocities of the vibrational movements of molecules increase, due to which the bonds holding them are more easily overcome, and the liquid acquires greater mobility (its viscosity decreases). So, for pure fresh water, the dependence of dynamic viscosity on temperature is determined by the Poiseuille formula:

(19)

Where µ - absolute (dynamic) viscosity of the liquid in P; t - temperature in ° C. With an increase in temperature from 0 to 100 ° C, the viscosity of water decreases by almost 7 times (see Table 6). At a temperature of 20°C, the dynamic viscosity of water is 0.001 Pa∙s=0.01 P. Water belongs to the least viscous liquids. Only a few of the practically used liquids (eg ether and alcohol) have a somewhat lower viscosity than water. Liquid carbon dioxide has the lowest viscosity (50 times less than the viscosity of water). All liquid oils have a much higher viscosity than water (castor oil at 20°C has a viscosity 1000 times greater than water at the same temperature). B table. 1.7 shows the viscosity values ​​​​of some liquids.

Table 7

Kinematic and dynamic viscosity of dropping liquids (at t=20° C)
Liquid		ν∙10 4 , m 2 /s
Fresh water
Glycerin Anhydrous
Kerosene (at 15°C)
Gasoline (at 15°C)
Castor oil
Mineral oil
Oil at 15°C
Anhydrous ethyl alcohol

To determine the value of the dynamic viscosity of air in the MKGSS system, the Millikan formula is used:

What gives at t \u003d 15 ° С \u003d 1.82 ∙ 10 -6 kgf s / m 2 (~ 1.82 ∙ 10 -5 Pa s). The dynamic viscosity of other gases is about the same order of magnitude. Along with the concept of absolute or dynamic viscosity, the concept of kinematic viscosity; which is the ratio of the absolute viscosity to the density of the liquid:

(21)

This viscosity is called kinematic, since there are no units of force in its dimension. In fact, by substituting the dimension µ and ρ , we get [ v]=[L 2 /T]. In the international system of units, kinematic viscosity is measured in m 2 / s; the unit for measuring kinematic viscosity in the CGS system is stokes (in honor of the English physicist Stokes): 1 St = 1 cm 2 / s = 10 -4 m 2 / s. The hundredth part of Stokes is called centistokes (cSt): 1 m 2 / s \u003d 1 ∙ 10 4 St \u003d 1 ∙ 10 6 cCt. In table. Figure 7 shows the numerical values ​​of the kinematic viscosity of dropping liquids; 3 - dependence of the kinematic viscosity of water and industrial oil on temperature. For preliminary calculations, the value of the kinematic viscosity of water v can be taken equal to 0.01 cm 2 / s = 1.10 -6 m 2 / s, which corresponds to a temperature of 20 ° C.

Rice. 3 Dependence of the kinematic viscosity of water and oil on temperature

The kinematic viscosity of dropping liquids at pressures encountered in most cases in practice (up to 200 atm) depends very little on pressure, and this change is neglected in conventional hydraulic calculations. The kinematic viscosity of gases depends on both temperature and pressure, increasing with increasing temperature and decreasing with increasing pressure (Table 8). Kinematic viscosity of air for normal conditions (temperature 20 ° C, pressure ~ 1at) v= µ/ ρ \u003d 1.57 ∙ 10 -5 m 2 / s, i.e. about 15 times more than for water at the same temperature. This is explained by the fact that the denominator of the expression for the kinematic viscosity (21) includes the density, which is much less for gases than for dropping liquids. To calculate the kinematic viscosity of air at different temperatures and pressures, you can use the graph (Fig. 4).

Table 1.8

Values ​​of kinematic ν and specific gas constant K for some gases
	ν∙10 4 , m 2 /s at temperature in °C				R, J/(kg∙K)
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15.07.2012
Physical properties of hydraulic oils and their effect on performance

1. Viscosity, viscosity-temperature characteristics
Viscosity is the most important criterion for evaluating the carrying capacity of a hydraulic oil. Viscosity is differentiated by dynamic and kinematic indicators.
Industrial lubricating oils and hydraulic oils are classified according to ISO viscosity grades based on their kinematic viscosity, which in turn is described as the ratio of dynamic viscosity to density. The reference temperature is 40 °C. The official unit of measurement ( St) for kinematic viscosity is m 2 /s, and in the oil refining industry, the unit for kinematic viscosity is cSt(centistokes) or mm 2 /s. Viscosity classification ISO, DIN 51519 for liquid industrial lubricants describes 18 grades (classes) of viscosity from 2 to 1500 mm 2 / s at a temperature of 40 ° C. Each grade is determined by the average viscosity at 40 ° C and with a tolerance of ± 10% from this value. Viscosity-temperature dependence is of great importance for hydraulic oils. Viscosity increases sharply with decreasing temperature and decreases with increasing temperature. In practical terms, the threshold viscosity of the fluid (permissible start-up viscosity, approx. 800-2000 mm 2 /s) is necessary for use in various types of pumps. The minimum allowable viscosity at high temperatures is determined by the onset of the boundary friction phase. The minimum viscosity should not be lower than 7-10 mm 2 /s in order to avoid unacceptable wear of pumps and motors. The curves on the viscosity-temperature graphs describe the dependence of the viscosity of hydraulic fluids on temperature. In line conditions V-T- the curves are hyperbolic. By mathematical transformation, these V - T- curves can be represented as straight lines. These lines allow accurate determination of viscosity over a wide temperature range. Viscosity index (VI) is a criterion V - T- dependencies, and V-T- curve - gradient on the chart. The higher the VI of the hydraulic fluid, the smaller the change in viscosity with temperature, i.e., the more V - T- curve. Hydraulic oils based on mineral oils usually have a natural IV of 95-100. Synthetic hydraulic oils based on esters have a limiting VI of 140-180, and polyglycols have a natural IV of 180-200 (Fig. 1)

The viscosity index can also be improved with additives (polymeric additives that must be shear resistant) called VI improvers or viscosity additives. High VI hydraulic oils provide easy starting, reduce performance loss at low ambient temperatures, and improve sealing and wear protection at high operating temperatures. High index oils increase system efficiency and extend the life of wear parts and components (the higher the viscosity at operating temperatures, the better the volume ratio).

2. Pressure dependence of viscosity
The bearing capacity of the lubricating film is determined by the pressure dependence of the viscosity of the lubricant. The dynamic viscosity of liquid media increases with increasing pressure. The following is a method for controlling dynamic viscosity versus pressure at constant temperature.
The dependence of viscosity on pressure, namely the increase in viscosity with increasing pressure, has a positive effect on the specific load (for example, on bearings), because the viscosity of the lubricating film increases under the action of a high partial pressure from 0 to 2000 atm. Viscosity HFC liquid increases twice, mineral oil - 30 times, in HFD liquids - 60 times. This explains the relatively short service life of roller bearings if they are lubricated using ( HFA, HFC) water-based lubricating oils. On fig. 2 and 3 show viscosity versus pressure for various hydraulic fluids.

Viscosity-temperature characteristics can also be described by an exponential expression:

η = η ο · e α P ,

Where η ο is the dynamic viscosity at atmospheric pressure, α is the coefficient of the "viscosity-pressure" dependence, R-pressure. For HFCα \u003d 3.5 10 -4 atm -1;
for HFDα \u003d 2.2 10 -3 atm -1; for HLPα \u003d 1.7 10 -3 atm -1

3. Density
Losses of hydraulic fluids in piping and in the elements of the hydraulic system are directly proportional to the density of the fluid. For example, pressure loss is directly proportional to density:

Δ P= (ρ/2) ξ with 2 ,

Where ρ is the density of the liquid, ξ, is the drag coefficient, with is the fluid flow rate, and Δ P- loss of pressure.
Density ρ is the mass per unit volume of a liquid.

ρ = m/V(kg / m 3).

The density of a hydraulic fluid is measured at a temperature of 15 °C. It depends on temperature and pressure, since the volume of a liquid increases with increasing temperature. Thus, the change in the volume of the liquid as a result of heating occurs according to the equation

Δ V=Vβ temp Δ T,

What leads to a change in density:

Δρ = ρ β rate Δ T.

In hydrostatic conditions at temperatures from -5 to +150 °C, it is sufficient to apply a linear formula to the above equation. Thermal expansion coefficient βtemp can be applied to all types of hydraulic fluids.

Since the coefficient of thermal expansion of mineral oils is approximately 7 x 10 -4 K -1, the volume of the hydraulic fluid increases by 0.7% if its temperature rises by 10 °C. On fig. 5 shows the dependence of the volume of hydraulic fluids on temperature.

The density-pressure relationship of hydraulic fluids should also be included in the hydrostatic evaluation, as the compressibility of fluids negatively affects their dynamic performance. The dependence of density on pressure can simply be read from the corresponding curves (Fig. 6).

4. Compressibility
The compressibility of hydraulic fluids based on mineral oils depends on temperature and pressure. At pressures up to 400 atm and temperatures up to 70 °C, which are the limit for industrial systems, the compressibility is revalent to the system. The hydraulic fluids used in most hydraulic systems can be considered incompressible. However, at pressures from 1000 to 10,000 atm, changes in the compressibility of the medium can be observed. The compressibility is expressed by the coefficient β or modulus M(Fig. 7, M = To).

M\u003d 1 / β atm \u003d 1 / β 10 5 N m 2 \u003d 1 / β 10 5 Pa.

Volume change can be determined using the equation

Δ V=V · β( P max- R beginning)

Where Δ V— volume change; R max is the maximum pressure; R initial - initial pressure.

5. Solubility of gases, cavitation
Air and other gases can dissolve in liquids. The liquid can absorb the gas until it is saturated. This should not adversely affect the characteristics of the fluid. The solubility of a gas in a liquid depends on the underlying component of the gas type, pressure and temperature. At pressures up to ≈300 atm. the solubility of a gas is proportional to pressure and follows Henry's law.

V G= V Fα V P/P o ,

Where VG is the volume of dissolved gas; V F is the volume of liquid, R o - atmospheric pressure, P— liquid pressure; α V is the Bunsen distribution coefficient (1.013 mbar, 20 °C).
The Bunsen coefficient is highly dependent on the base fluid and indicates how much (%) the gas is dissolved in a unit volume of liquid under normal conditions. Dissolved gas can be released from the hydraulic fluid at low static pressure (high flow rate and high shear stress) until a new saturation point is reached. The rate at which the gas leaves the liquid usually exceeds the rate at which the gas is absorbed into the liquid. Gas escaping from a liquid in the form of bubbles changes the compressibility of the liquid in a manner similar to air bubbles. Even at low pressures, a small amount of air can drastically reduce the incompressibility of a fluid. In mobile systems with high liquid circulation rates, the content of undissolved air can reach values ​​up to 5%. This undissolved air has a very negative effect on the performance, load-bearing capacity and dynamics of the system (see section 6 - deaeration and section 7 - foaming). Since the compressibility of fluids in systems is usually very fast, air bubbles can suddenly reach high temperatures (adiabatic compression). In extreme cases, the flash point of the liquid can be reached and microdiesel effects can occur.
Gas bubbles can also explode in pumps as a result of compression, which can cause damage due to erosion (sometimes called cavitation or pseudo-cavitation). The situation can be exacerbated if vapor bubbles form in the liquid. Thus, cavitation occurs when the pressure falls below the solubility of a gas or below the saturation vapor pressure of a liquid.
Cavitation mainly occurs in open systems with a constant volume, that is, the danger of this phenomenon is relevant for inlet and outlet circuits and pumps. It can be caused by too low absolute pressure due to flow velocity losses in narrow cross-sections, filters, manifolds and dampers, due to excessive inlet head or pressure losses due to excessive fluid viscosity. Cavitation can lead to pump erosion, reduced efficiency, pressure peaks and excessive noise.
This phenomenon can adversely affect the stability of throttling regulators and cause foaming in containers if the liquid-water mixture is returned to the container at atmospheric pressure.

6. Deaeration
When hydraulic fluids are returned back to the reservoirs, the fluid flow is capable of entraining air with it. This can occur due to leaks in the piping at constriction and partial vacuum. Turbulence in a tank or localized cavitation indicates the formation of air bubbles in the liquid.
The air trapped in this way must escape to the surface of the liquid, otherwise, if it enters the pump, it may cause damage to other components of the system. The rate at which air bubbles rise to the surface depends on the diameter of the bubbles, the viscosity of the fluid, and the density and quality of the base oil. The higher the quality and purity of the base oil, the faster the deaeration occurs. Low viscosity oils generally deaerate faster than high viscosity base oils. This is related to the rate at which the bubbles rise.

C = (ρ FL -ρ L )Χ/η,

Where ρ FL is the density of the liquid; p L— air density; η is dynamic viscosity; X is a constant depending on the density and viscosity of the liquid.
Systems must be designed in such a way that no air enters the liquid, and if it does, entrained air bubbles can easily escape. The critical areas are the tanks, which must be fitted with baffles and baffles, and the configuration of the piping and circuits. Additives cannot positively influence the air release properties of hydraulic fluids. Surfactants (particularly silicone-based anti-foam additives) and contaminants (eg greases and corrosion inhibitors) adversely affect the air release characteristics of hydraulic oils. Mineral oils generally have better air release properties than fire resistant fluids. Air release properties HPLD hydraulic fluid can be comparable to the properties of hydraulic fluids HLP.
The test for determining the air release properties is described in the standard DIN 51 381. This method consists in forcing air into the oil. The deaeration number is the time it takes for air (minus 0.2%) to leave a liquid at 50°C under given conditions.
The proportion of dispersed air is determined by measuring the density of the oil-air mixture.

7. Foaming
Surface foaming occurs when the deaeration rate is higher than the rate at which air bubbles burst on the surface of the liquid, i.e. when there are more bubbles formed than collapsed. In the worst case, this foam can be squeezed out of the tank through the holes or carried into the pump. Silicone-based or silicone-free anti-foam additives can accelerate the breakdown of bubbles by reducing the surface tension of the foam. They also negatively affect the air release properties of the fluid, which can cause compressibility problems and cavitation. Therefore, antifoam additives are used in very low concentrations (≈ 0.001%). Defoamer concentrations can progressively decrease as a result of aging and deposition on metal surfaces, and foaming problems often occur with older fluids that have already worked. Subsequent addition of an antifoam agent should only be done after consultation with the hydraulic fluid manufacturer.
The volume of foam formed on the surface of the liquid is measured over time (immediately, after 10 minutes) and at different temperatures (25 and 95 °C). Surfactants, detergents or dispersants, contaminants in the form of grease, corrosion inhibitors, cleaning agents, coolants, oxidation by-products, etc. can adversely affect the effectiveness of antifoam additives.

8. Demulsification
Demulsibility is the ability of a hydraulic fluid to repel infiltrated water. Water can enter the hydraulic fluid as a result of heat exchanger leakage, condensation in reservoirs due to significant changes in oil levels, poor filtration, water contamination due to seal failures, and extreme environmental conditions. Water in hydraulic fluid can cause corrosion, cavitation in pumps, increased friction and wear, and accelerated degradation of elastomers and plastics. Free water should be removed as quickly as possible from the hydraulic fluid containers via the drain cocks. Contamination with water-soluble coolants, especially on machine tools, can cause sticky residues to form after the water has evaporated. This can cause problems in pumps, valves and cylinders. The hydraulic fluid must quickly and completely repel water that has penetrated into it. Demulsification is determined by DIN 51 599, but this method is not applicable to hydraulic fluids containing detergent-dispersant ( DD) additives. Demulsification is the time it takes for oil and water mixtures to separate. The demulsification parameters are:
. viscosity up to 95 mm 2 /s at 40 °C; test temperature 54 °C;
. viscosity > 95 mm 2 /s; temperature 82 °C.
In hydraulic oils containing DD additives, water, liquid and solid contaminants are kept in suspension. They can be removed with appropriate filter systems without using the hydraulic function of the machine, eliminating the negative effect on the hydraulic fluid. So DD hydraulic fluids are often used in hydrostatic machine tools and mobile hydraulic systems.
For machines with high circulation rates, requiring constant availability and permanently exposed to the risk of water and other contaminants, the use of hydraulic fluids is a primary area. Hydraulic fluids with demulsifying properties are recommended for use in steelmaking and rolling shops, where large volumes of water are present and low circulation ratios allow separation of emulsions in the tank. Demulsibility properties in a modified form are used to determine the compatibility of equipment with hydraulic oils. The aging of the hydraulic fluid negatively affects the de-emulsifying properties.

9. Pour point
The pour point is the lowest temperature at which a liquid is still fluid. A sample of the liquid is systematically cooled and tested for fluidity with a decrease in temperature for every 3 °C. Parameters such as pour point and limiting viscosity determine the lowest temperature at which normal use of the oil is possible.

10. Copper corrosion (copper plate test)
Copper and copper-containing materials are often used in hydraulic systems. Materials such as brass, cast bronze or sintered bronze are found in bearings, guides or controls, sliders, hydraulic pumps and motors. Copper pipes are used in cooling systems. Copper corrosion can lead to failure of the entire hydraulic system, so a copper plate corrosion test is performed to obtain information on the corrosiveness of base fluids and additives to materials containing copper. The method for testing the corrosiveness of mineral-based hydraulic fluids, i.e., biodegradable fluids, against non-ferrous metals is known as the Linde method (selective test method for testing biodegradable oils for corrosiveness against copper alloys) ( SAE Technical Bulletin 981 516 April 1998), also known as VDMA 24570 (VDMA 24570 - Rapidly Biodegradable Hydraulic Fluids - Action on Non-Ferrous Alloys 03-1999 in German).
According to the standard DIN 51 759, corrosion on a copper plate can be expressed in the form of discoloration or flaking. The grinding copper plate is immersed in the liquid to be tested for a specified time at a specified temperature. Hydraulic and lubricating oils are usually tested at 100 °C. The degree of corrosion is evaluated in points:
1 - slight color change;
2 - moderate discoloration;
3 - strong color change;
4 - corrosion (darkening).

11. Water content (Karl Fischer method)
If water enters the hydraulic system partially finely dispersed to the extent that it penetrates into the oil phase, then, depending on the density of the hydraulic fluid, water may also be released from the oil phase. This possibility must be taken into account when taking samples to determine the water content.
Determining the water content in mg/kg (mass) according to the Karl Fischer method is associated with the introduction of the Karl Fischer solution in direct or indirect titration.

12. Resistance to aging (Baader method)
This is an attempt to replicate the study of the effects of air, temperature and oxygen on hydraulic fluids in the laboratory. An attempt has been made to artificially accelerate the aging of hydraulic oils by raising the temperature above practical application levels as well as oxygen levels in the presence of metal catalysts. The increase in viscosity and the increase in acid number (free acid) are recorded and evaluated. The results of laboratory tests are translated into practical conditions. The Baader method is a practical way to test hydraulic and lubricating oils for aging.
For a predetermined period of time, the samples are subjected to aging at a predetermined temperature and pressure of a stream of air while periodically immersing a copper coil in oil, acting as an oxidation accelerator. In accordance with DIN 51 554-3 C, CL and CLP liquids and HL, HLP, NM hydraulic oils are tested for oxidation stability at a temperature of 95 °C. The saponification number is expressed in mg KOH/g.

13. Resistance to aging (method TOST)
The oxidation stability of steam turbine oils and hydraulic oils containing additives is determined in accordance with DIN 51 587 Method TOST has been used for many years to test turbine oils and hydraulic fluids based on mineral oils. Modified (without water) dry TOST the method is used to determine the oxidation resistance of hydraulic oils based on esters.
The aging of lubricating oils is characterized by an increase in acid number when the oil is exposed to oxygen, water, steel and copper for a maximum of 1000 hours at 95°C (neutralization curve with aging). The maximum allowable increase in acid number is 2 mg KOH / g after 1000 hours.

14. Acid number (neutralization number)
The acid number of hydraulic oil increases as a result of aging, overheating or oxidation. The resulting aging products can act aggressively on the pumps and bearings of the hydraulic system. Therefore, the acid number is an important criterion for assessing the condition of a hydraulic fluid.
The acid number indicates the amount of acidic or alkaline substances in the lubricating oil. Acids in mineral oils can attack hydraulic system materials of construction. A high acid content is undesirable, as it is possible as a result of oxidation.

15. Protective anti-oxidation properties in relation to steel / ferrous metals
The antioxidant properties of turbine and hydraulic oils containing additives in relation to steel / ferrous metals are determined in accordance with the standard DIN 51 585.
Hydraulic fluids often contain dispersed, dissolved or free water, so the hydraulic fluid must provide corrosion protection to all wetted assemblies under all operating conditions, including water contamination. This test method determines the performance of anti-corrosion additives under a number of different operating conditions.
The oil to be tested is mixed with distilled water (method A) or artificial sea water (method B), stirring continuously (for 24 h at 60 °C) with a steel rod immersed in the mixture. After the steel rod is examined for corrosion. The results make it possible to evaluate the anti-corrosion protective properties of the oil in relation to steel components in contact with water or water vapor:
corrosion degree 0 means no corrosion,
grade 1 - slight corrosion;
degree 2 - moderate corrosion;
degree 3 - severe corrosion.

16. Anti-wear properties (four-ball machine Shell; VKA, DIN 51350)
Four-ball apparatus of the company Shell is used to measure the anti-wear and extreme pressure properties of hydraulic fluids. The bearing capacity of hydraulic fluids is tested under boundary friction conditions. The method is used to determine the values ​​for lubricating oils with additives that withstand high pressure under conditions of boundary friction between sliding surfaces. Lubricating oil is tested in a four-ball apparatus, which consists of one (central) rotating ball and three fixed balls arranged in a ring. Under constant test conditions and for a specified duration, the diameter of the contact patch on the three stationary balls or the load on the rotating ball, which can increase before welding with the remaining three balls, is measured.

17. Shear stability of lubricating oils containing polymers
To improve the viscosity-temperature characteristics, polymers are introduced into lubricating oils, which are used as additives that improve the viscosity index. As the molecular weight increases, these substances become more and more sensitive to mechanical loads, such as those that exist between a piston and its cylinder. To evaluate the shear stability of oils under various conditions, there are several test methods:
DIN 5350-6, four ball method, DIN 5354-3,FZG method and DIN 51 382, ​​diesel fuel injection method.
Relative viscosity reduction due to shear after 20 hour test DIN 5350-6 (determination of shear stability of lubricating oils containing polymers used for tapered roller bearings) is applied in accordance with DIN 51 524-3 (2006); less than 15% shear viscosity reduction is recommended.

18. Mechanical testing of hydraulic fluids in rotary vane pumps ( DIN 51 389-2)
Testing on Vickers pumps and pumps from other manufacturers allows for a realistic assessment of the performance of hydraulic fluids. However, alternative test methods are currently under development (in particular, the project DGMK 514 - mechanical tests of hydraulic fluids).
The Vickers method is used to determine the anti-wear properties of hydraulic fluids in a rotary vane pump at given temperatures and pressures (140 atm, 250 h operating fluid viscosity of 13 mm 2 /s at varying temperatures). At the end of the test, the rings and wings are examined for wear ( vickers V-104With 10 or vickers V-105With ten). Maximum allowable wear values:< 120 мг для кольца и < 30 мг для крыльев.

19. Anti-wear properties (test on gear FZG stand; DIN 534-1and-2)
Hydraulic fluids, especially high viscosity grades, are used as hydraulic and lubricating oils in combined systems. Dynamic viscosity is the main factor in anti-wear performance in hydrodynamic lubrication. At low sliding speeds or high pressures under boundary friction conditions, the antiwear properties of the fluid depend on the additives used (formation of a reactive layer). These boundary conditions are reproduced when tested for FZG stand.
This method is mainly used to determine the boundary properties of lubricants. Certain gears rotating at a certain speed are lubricated by splashing or spraying oil, the initial temperature of which is recorded. The load on the roots of the teeth is increased stepwise and the characteristics of the appearance of the roots of the teeth are recorded. This procedure is repeated until the final 12th load stage: Hertzian pressure at the 10th load stage in the engagement band is 1539 N/mm2; at stage 11 - 1,691 N / mm 2; at the 12th stage - 1,841 N / mm 2. The initial temperature at stage 4 is 90 °C, the peripheral velocity is 8.3 m/s, the temperature limit is not determined; gear geometry is used.
The load stage of failure is determined by DIN 51 524-2. For a positive result, it must be a step of at least 10th. Hydraulic fluids that meet the requirements ISO VG 46, which do not contain anti-wear additives, usually reach load stage 6 (≈ 929 N/mm 2). Hydraulic fluids containing zinc usually reach at least the 10-11th load stage before failure. Zinc-free so-called ZAF hydraulic fluids can withstand load stage 12 or higher.

Roman Maslov.
Based on materials from foreign publications.

When the temperature changes, a change in the size of a solid occurs, which is called thermal expansion. There are linear and volumetric thermal expansion. These processes are characterized by coefficients of thermal (thermal) expansion: - average coefficient of linear thermal expansion, average coefficient of volumetric thermal expansion.

DEFINITION

Thermal expansion coefficient called a physical quantity characterizing the change in the linear dimensions of a solid body with a change in its temperature.

Apply, usually the average coefficient of linear expansion. This is a characteristic of the thermal expansion of a material.

If the initial length of the body is , - its elongation with an increase in body temperature by , then it is determined by the formula:

The coefficient of linear elongation is a characteristic of relative elongation (), which occurs with an increase in body temperature by 1K.

As the temperature increases, the volume of the solid increases. As a first approximation, we can assume that:

where is the initial volume of the body, is the change in body temperature. Then the coefficient of volumetric expansion of the body is a physical quantity that characterizes the relative change in the volume of the body (), which occurs when the body is heated by 1 K and the pressure remains unchanged. The mathematical definition of the coefficient of volumetric expansion is the formula:

The thermal expansion of a solid body is associated with the anharmonicity of the thermal vibrations of the particles that make up the crystal lattice of the body. As a result of these oscillations, with an increase in body temperature, the equilibrium distance between neighboring particles of this body increases.

When the volume of a body changes, its density changes:

where is the initial density and is the density of the substance at the new temperature. Since the value then expression (4) is sometimes written as:

Thermal expansion coefficients depend on the substance. In general, they will depend on temperature. Thermal expansion coefficients are considered independent of temperature in a small temperature range.

There are a number of substances that have a negative coefficient of thermal expansion. Thus, as the temperature rises, such materials shrink. This usually occurs within a narrow temperature range. There are substances in which the coefficient of thermal expansion is almost equal to zero around a certain temperature range.

Expression (3) is used not only for solids, but also for liquids. At the same time, it is considered that the coefficient of thermal expansion for dropping liquids does not change significantly with temperature. However, when calculating heating systems, it is taken into account.

Relationship of coefficients of thermal expansion

Units

The basic unit of measurement for thermal expansion coefficients in the SI system is:

Examples of problem solving

EXAMPLE 1

Exercise

In order to determine the coefficient of volumetric expansion of liquids, devices called pycnometers are used. These are glass flasks with a narrow neck (Fig. 1). On the neck put marks on the capacity of the vessel (usually in ml). How are pycnometers used?

Decision

The volume expansion coefficient is measured as follows. The pycnometer is filled with the investigated liquid, up to the chosen mark. The flask is heated, noting the change in the level of the substance. With such known values ​​as: the initial volume of the pycnometer, the cross-sectional area of ​​the channel of the neck of the flask, the temperature change determines the proportion of the initial volume of liquid that entered the neck of the pycnometer when heated by 1 K. It should be taken into account that the expansion coefficient of the liquid is greater than the obtained value, as there was heating and expansion and flasks. Therefore, to calculate the coefficient of expansion of the liquid, the coefficient of expansion of the substance of the flask (usually glass) is added. It must be said that, since the coefficient of volumetric expansion of glass is significantly less than that of liquids, in approximate calculations, the expansion coefficient of glass can be neglected.

EXAMPLE 2

Exercise

What are the characteristics of water expansion? What is the significance of this phenomenon?

Decision

Water, unlike most other liquid substances, expands when heated only if the temperature is above 4 o C. In the temperature range, the volume of water decreases with increasing temperature. Fresh water at has a maximum density. For sea water, the maximum density is reached at. An increase in pressure lowers the temperature of the maximum density of water. Since almost 80% of the surface of our planet is covered with water, the features of its expansion play a significant role in creating the climate on Earth. The rays of the sun, falling on the water surface, heat it. If the temperature is below 1-2 o C, then the heated layers of water have a higher density than the cold ones and sink down. At the same time, their place is occupied by colder layers, which in turn heat up. So there is a constant change of layers of water and this leads to heating of the water column, until the maximum density is reached. A further increase in temperature leads to the fact that the upper layers of water reduce their density and remain at the top. So, it turns out that a large layer of water warms up to the temperature of maximum density quite quickly, and a further increase in temperature is slow. As a result, deep water bodies of the Earth from a certain depth have a temperature of about 2-3 o C. At the same time, the temperature of the upper layers of water in the seas of warm countries can have a temperature of about 30 o C and higher.

The bonds between liquid particles, as we know, are weaker than between molecules in a solid. Therefore, it should be expected that liquids expand to a greater extent than solids under the same heating. This is indeed confirmed by experience.

Fill a flask with a narrow and long neck with a tinted liquid (water or better kerosene) to half the neck and mark the liquid level with a rubber ring. After that, lower the flask into a vessel with hot water. First, a decrease in the liquid level in the neck of the flask will be seen, and then the level will begin to rise and rise significantly above the initial one. This is due to the fact that at first the vessel is heated and its volume increases. This causes the liquid level to drop. Then the liquid is heated. Expanding, it not only fills the increased volume of the vessel, but also significantly exceeds this volume. Therefore, liquids expand to a greater extent than solids.

The temperature coefficients of volumetric expansion of liquids are much greater than the coefficients of volumetric expansion of solids; they can reach a value of 10 -3 K -1 .

The liquid cannot be heated without heating the vessel in which it is located. Therefore, we cannot observe the true expansion of the liquid in the vessel, since the expansion of the vessel underestimates the apparent increase in the volume of the liquid. However, the coefficient of volumetric expansion of glass and other solids is usually much less than the coefficient of volumetric expansion of a liquid, and if measurements are not very accurate, the increase in the volume of the vessel can be neglected.

Water expansion features

The most common liquid on Earth - water - has special properties that distinguish it from other liquids. In water, when heated from 0 to 4 ° C, the volume does not increase, but decreases. Only from 4 °C does the volume of water begin to increase when heated. At 4°C, therefore, the volume of water is minimal and the density is maximum*. Figure 9.4 shows an approximate relationship between water density and temperature.

* These data refer to fresh (chemically pure) water. Sea water has its highest density at about 3°C.

The noted special property of water has a great influence on the nature of heat transfer in water bodies. When water is cooled, the density of the upper layers first increases, and they sink down. But after the air reaches a temperature of 4 ° C, further cooling already reduces the density, and cold layers of water remain on the surface. As a result, in deep reservoirs, even at very low air temperatures, the water has a temperature of about 4 °C.

The volume of liquid and solid bodies increases in direct proportion to the increase in temperature. An anomaly is found near water: its density is maximum at 4 °C.

§ 9.4. Accounting and use of thermal expansion of bodies in engineering

Although the linear dimensions and volumes of bodies change little with temperature changes, nevertheless, this change often has to be taken into account in practice; at the same time, this phenomenon is widely used in everyday life and technology.

Accounting for thermal expansion of bodies

The change in the size of solids due to thermal expansion leads to the appearance of huge elastic forces if other bodies prevent this change in size. For example, a steel bridge beam with a cross section of 100 cm 2, when heated from -40 ° C in winter to +40 ° C in summer, if the supports prevent its elongation, creates pressure on the supports (stress) up to 1.6 10 8 Pa, i.e., it acts on supports with a force of 1.6 10 6 N.

The given values ​​can be obtained from Hooke's law and formula (9.2.1) for the thermal expansion of bodies.

According to Hooke's law, mechanical stress
,where
- elongation,a E- Young's modulus. According to (9.2.1)
. Substituting this value of relative elongation into the formula of Hooke's law, we obtain

(9.4.1)

Steel has Young's modulus E= 2.1 10 11 Pa, temperature coefficient of linear expansion α 1 \u003d 9 10 -6 K -1. Substituting these data into expression (9.4.1), we obtain that for Δ t = 80 °С mechanical stress σ = 1.6 10 8 Pa.

As S \u003d 10 -2 m 2, then the force F = σS = 1.6 10 6 N.

To demonstrate the forces that appear when a metal rod is cooled, the following experiment can be done. We heat an iron rod with a hole at the end into which a cast-iron rod is inserted (Fig. 9.5). Then we insert this rod into a massive metal stand with grooves. When the rod is cooled, it contracts, and such large elastic forces arise in it that the cast-iron rod breaks.

The thermal expansion of bodies must be taken into account when designing many structures. Measures must be taken to ensure that bodies are free to expand or contract as the temperature changes.

It is impossible, for example, to tightly pull telegraph wires, as well as wires of power lines (power lines) between supports. In summer, the sagging of wires is noticeably greater than in winter.

Metal steam pipelines, as well as water heating pipes, have to be provided with bends (compensators) in the form of loops (Fig. 9.6).

Internal stresses can arise during uneven heating of a homogeneous body. For example, a glass bottle or glass made of thick glass may burst if hot water is poured into them. First of all, the internal parts of the vessel in contact with hot water are heated. They expand and put a lot of pressure on the outer cold parts. Therefore, the destruction of the vessel may occur. A thin glass does not burst when hot water is poured into it, since its inner and outer parts warm up equally quickly.

Quartz glass has a very low temperature coefficient of linear expansion. Such glass withstands, without cracking, uneven heating or cooling. For example, cold water can be poured into a red-hot quartz glass flask, while an ordinary glass flask bursts during such an experiment.

Dissimilar materials subjected to periodic heating and cooling should be joined together only when their dimensions change in the same way with temperature changes. This is especially important for large product sizes. So, for example, iron and concrete expand in the same way when heated. That is why reinforced concrete has become widespread - a hardened concrete solution poured into a steel lattice - reinforcement (Fig. 9.7). If iron and concrete expanded differently, then as a result of daily and annual temperature fluctuations, the reinforced concrete structure would soon collapse.

A few more examples. Metal conductors soldered into glass bulbs of electric lamps and radio lamps are made of an alloy (iron and nickel) that has the same expansion coefficient as glass, otherwise the glass would crack when the metal was heated. The enamel with which the dishes are coated, and the metal from which these dishes are made, must have the same coefficient of linear expansion. Otherwise, the enamel will burst when the dishes covered with it are heated and cooled.

Significant forces can also be developed by a liquid if it is heated in a closed vessel that does not allow the liquid to expand. These forces can lead to the destruction of vessels that contain liquid. Therefore, this property of the liquid also has to be considered. For example, water heating pipe systems are always provided with an expansion tank attached to the top of the system and vented to the atmosphere. When water is heated in the pipe system, a small part of the water passes into the expansion tank, and this eliminates the stressed state of water and pipes. For the same reason, an oil-cooled power transformer has an oil expansion tank on top. When the temperature rises, the oil level in the tank rises, when the oil cools, it decreases.

The thermal expansion of a liquid is that it can change its volume with a change in temperature. This property is characterized by temperature coefficient of volumetric expansion , representing the relative change in the volume of liquid with a change in temperature per unit (by 1 o C) and at constant pressure:

By analogy with the compressibility property of a liquid, we can write

or through density

The change in volume with a change in temperature occurs due to a change in density.

For most liquids, the coefficient  t decreases with increasing pressure. Coefficient  t with a decrease in the density of oil products from 920 before 700 kg/m 3 increases from 0,0006 before 0,0008 ; for hydraulic fluids  t usually taken independent of temperature. For these liquids, an increase in pressure from atmospheric to 60 MPa leads to growth  t for about 10 – 20 % . At the same time, the higher the temperature of the working fluid, the greater the increase  t . For water with increasing pressure at temperatures up to 50 about C  t grows, and at temperatures above 50 about C decreases.

Dissolution of gases

Dissolution of gases - the ability of a liquid to absorb (dissolve) gases in contact with it. All liquids absorb and dissolve gases to some extent. This property is characterized solubility coefficient k R .

E If a liquid in a closed vessel is in contact with a gas at pressure P 1 , then the gas will begin to dissolve in the liquid. After a while

the liquid will be saturated with gas and the pressure in the vessel will change. The solubility coefficient relates the change in pressure in the vessel with the volume of dissolved gas and the volume of liquid by the following relationship

where V G is the volume of dissolved gas under normal conditions,

V well is the volume of the liquid,

P 1 and P 2 are the initial and final gas pressures.

The solubility factor depends on the type of liquid, gas and temperature.

At a temperature 20 ºС and atmospheric pressure, water contains about 1,6% dissolved air by volume ( k p = 0,016 ). With increasing temperature from 0 before 30 ºС the coefficient of solubility of air in water decreases. Solubility coefficient of air in oils at temperature 20 ºС is about 0,08 – 0,1 . Oxygen has a higher solubility than air, so the oxygen content of air dissolved in a liquid is approximately 50% higher than atmospheric. When the pressure decreases, gas is released from the liquid. The process of gas evolution proceeds more intensively than dissolution.

Boiling

Boiling is the ability of a liquid to change into a gaseous state. Otherwise, this property of liquids is called evaporation .

A liquid can be brought to a boil by raising the temperature to values ​​greater than the boiling point at a given pressure, or by lowering the pressure to values ​​less than the saturation vapor pressure. p np liquids at a given temperature. The formation of bubbles when the pressure is reduced to saturated vapor pressure is called cold boiling.

A liquid from which the gas dissolved in it has been removed is called degassed. In such a liquid, boiling does not occur even at a temperature higher than the boiling point at a given pressure.