Municipal educational institution

"Yagodninskaya secondary school"

Methodological development of laboratory work

Physics teacher:

Open lesson in 10th grade on the topic: laboratory work "Measuring the elastic modulus of rubber"

Lesson objectives: ensuring a more complete assimilation of the material, the formation of an understanding of scientific knowledge, the development of logical thinking, experimental skills, and research skills; skills in determining errors when measuring physical quantities, the ability to draw correct conclusions based on the results of work.

Equipment: installation for measuring Young's modulus of rubber, dynamometer, weights.

Lesson plan:

I. Org. moment.

II. Repetition of material knowledge of which is necessary to complete laboratory work.

III. Performing laboratory work.

1. The order of the work (as described in the textbook).
2. Determination of errors.
3. Carrying out the practical part and calculations.
4. Conclusion.

IV. Lesson summary.

V. Homework.

DURING THE CLASSES

Teacher: In the last lesson you learned about the deformations of bodies and their characteristics. Let's remember what deformation is?

Students: Deformation is a change in the shape and size of bodies under the influence of external forces.

Teacher: The bodies around us and we are subject to various deformations. What types of deformations do you know?

Student: Deformations: tension, compression, torsion, bending, shear, shear.

Teacher: What else?

Elastic and plastic deformations.

Teacher: Describe them.

Student: Elastic deformations disappear after the cessation of external forces, while plastic deformations remain.

Teacher: Name elastic materials.

Student: Steel, rubber, bones, tendons, the entire human body.

Teacher: Plastic.

Student: Lead, aluminum, wax, plasticine, putty, chewing gum.

Teacher: What happens in a deformed body?

Student: Elastic force and mechanical stress appear in a deformed body.

Teacher: What physical quantities can characterize deformations, for example, tensile deformation?

Student:

1. Absolute elongation

2. Mechanical stress?

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Teacher: What does it show?

Student: How many times is the absolute elongation less than the original length of the sample?

Teacher: What's happened E?

Student: E– coefficient of proportionality or modulus of elasticity of the substance (Young’s modulus).

Teacher: What do you know about Young's modulus?

Student: Young's modulus is the same for samples of any shape and size made from a given material.

Teacher: What characterizes Young's modulus?

Student: The elastic modulus characterizes the mechanical properties of the material and does not depend on the design of the parts made from it.

Teacher: What mechanical properties are inherent in substances?

Student: They can be brittle, plastic, elastic, durable.

Teacher: What characteristics of a substance must be taken into account when using it in practice?

Student: Young's modulus, mechanical stress and absolute elongation.

Teacher: What about when creating new substances?

Student: Young's modulus.

Teacher: Today you will do a lab to determine the Young's modulus of rubber. What is your goal?

Using rubber as an example, learn to determine the modulus of elasticity of any substance.

Knowing the elastic modulus of a substance, we can talk about its mechanical properties and practical applications. Rubber is widely used in various aspects of our lives. Where is rubber used?

Student: In everyday life: rubber boots, gloves, rugs, elastic bands, plugs, hoses, heating pads, etc.

Student: In medicine: tourniquets, elastic bandages, tubes, gloves, some parts of devices.

Student: In transport and industry: tires and wheel tires, gear belts, electrical tape, inflatable boats, ladders, O-rings and much more.

Student: In sports: balls, fins, wetsuits, expanders, etc.

Teacher: There is a lot that can be said about the use of rubber. In each specific case, rubber must have certain mechanical properties.

Let's move on to doing the work.

You have already noticed that each row received its own task. The first row works with an elastic band. The second row contains fragments of a hemostatic tourniquet. The third row is with fragments of the expander. Thus, the class is divided into three groups. All of you will determine the elastic modulus of rubber, but each group is invited to conduct their own small research.

1st group. Having determined the elastic modulus of rubber, you will receive results, after discussing which, draw a conclusion about the properties of the rubber used to make underwear elastic.

2nd group. Working with different fragments of the same hemostatic tourniquet and determining the elastic modulus, draw a conclusion about the dependence of Young’s modulus on the shape and size of the samples.

3rd group. Study the device of the expander. After completing laboratory work, compare the absolute elongation of one rubber string, several strings and the entire expander harness. Draw a conclusion from this and, perhaps, come up with some of your own proposals for the manufacture of expanders.

When measuring physical quantities, errors are inevitable.

What is error?

Student: Inaccuracy in the measurement of a physical quantity.

Teacher: What will guide you when measuring the error?

Student: Data from Table 1 p.205 of the textbook (the work is performed according to the description given in the textbook)

After completing the work, a representative of each group makes a report on its results.

Representative of the first group:

When performing laboratory work, we obtained the values ​​of the elastic modulus of the elastic band:

E1 = 2.24 105 Pa
E2 = 5 107 Pa
E3 = 7.5 105 Pa

The modulus of elasticity of a linen elastic band depends on the mechanical properties of the rubber and the threads braiding it, as well as on the method of weaving the threads.

Conclusion: underwear elastic is very widely used in underwear, children's clothing, sportswear and outerwear. Therefore, for its production, various types of rubber, threads and various methods of weaving are used.

Representative of the second group:

Our results:

E1 = 7.5 106 Pa
E1 = 7.5 106 Pa
E1 = 7.5 106 Pa

Young's modulus is the same for all bodies of any shape and size made from a given material

Representative of the third group:

Our results:

E1 = 7.9 107 Pa
E2 = 7.53 107 Pa
E3 = 7.81 107 Pa

To make expanders, you can use different types of rubber. The expander harness is assembled from individual strings. We've looked into this. The more strings, the larger the cross-sectional area of ​​the bundle, the lower its absolute elongation. Knowing the dependence of the properties of the tourniquet on its size and material, it is possible to make expanders for various physical education groups.

Lesson summary.

Teacher: To create and use various materials, you need to know their mechanical properties. The mechanical properties of a material are characterized by its elastic modulus. Today you have practically defined it for rubber and drawn your conclusions. What are they?

Student: I learned to determine the elastic modulus of a substance, evaluate errors in my work, made scientific assumptions about the mechanical properties of materials (in particular, rubber) and the practical application of this knowledge.

Students hand in control sheets.

For home: repeat § 20-22.

In the cereal industry, non-metallic materials (rubber, abrasive, etc.) are widely used for the manufacture of working parts of hulling and grinding machines.

Rubber. Rubber differs from other technical materials in a unique set of properties, the most important of which is high elasticity. This property inherent in rubber, the main component of rubber, makes it an indispensable structural material in modern technology.

Unlike metals, plastics, abrasives, wood, leather and other materials, rubber is capable of very large (20..30 times more than steel), almost completely reversible deformations under the influence of relatively small loads.

The elastic properties of rubber are maintained over a wide range of temperatures and deformation frequencies, and deformation is established in relatively short periods of time.

The elastic modulus of rubber at room temperature is in the range of (10... 100) 105 Pa (the elastic modulus of steel is 2000000 10 5 Pa).

An important feature of rubber is also the relaxation nature of deformation (a decrease in stress over time to an equilibrium value). Rubber lends itself well to mechanical cutting and grinds well.

The elasticity, strength and other properties of rubber depend on temperature. The elastic modulus and shear modulus of most types of rubber remain approximately constant when the temperature rises to 150 C; with a further increase in temperature, they decrease and the rubber softens. At approximately 230°C, rubber (almost all types) becomes sticky, and at 240°C it completely loses its elastic properties.

Rubber is distinguished by extremely low volumetric compressibility and a high Poisson's ratio of 0.4...0.5 (for steel 0.25). The exceptional ability for highly elastic deformation and high fatigue strength of certain types of rubber are combined with a number of other valuable technical properties: significant wear resistance, high coefficient of friction (from 0.5 and above), tensile and impact strength, good resistance to cuts and their growth, gas , air and water resistance, petrol and oil resistance, low density (from 0.95 to 1.6), high chemical resistance, dielectric properties, etc. Thanks to the unique set of technical properties, rubber has become one of the most important structural materials for various types of transport, agriculture, mechanical engineering, as well as for the production of sanitary and hygiene products, consumer goods.

The efficient operation of machinery and equipment in many industries largely depends on the durability and reliability of rubber products.

Rubber hardness. Rubber hardness refers to its ability to resist being pressed into it by an indenter (a steel needle with a blunt end or a steel ball). Knowing the hardness of rubber is necessary for a comparative assessment of the hardness of rubber parts. Of great practical importance is the fact that the hardness of rubber can be used to approximately determine many of its other properties, in particular the elastic modulus of rubber.

The most common method is to determine the hardness of rubber with a hardness tester: TIR-1 according to GOST 263 - 75. The deviation of the hardness value from its average value is usually no more than ±4% for soft rubber, and ±15% for the hardest grades.

The measurement of rubber hardness occurs in the region of its elastic deformations, as a result of which the hardness of rubber is a characteristic of its elastic, not plastic properties. This makes the hardness of rubber different from the hardness of metals, which is characterized by plastic deformations. Therefore, the hardness value of a rubber can be used to determine its elastic properties, such as elastic modulus or shear modulus.

In technical specifications, the modulus of elasticity and shear are usually not indicated, but the hardness of the rubber is almost always given. Therefore, knowledge of the dependence of moduli on hardness is very important, especially for preliminary calculations of the elasticity characteristics of rubber products.

It should also be taken into account that rubber hardness can be measured on almost any rubber product, but special samples are needed to determine the elasticity and shear moduli.

Numerous studies have established that the elastic modulus E and the shear modulus G are related to each other by the ratio E = 3 G and almost do not depend on the brand or composition of rubber, in particular on the type of rubber on the basis of which the rubber is made, but depend only on the hardness of the rubber. For rubber of different compositions of equal hardness, the elastic moduli and shear moduli differ by no more than 10%.

The value of permissible compressive and shear stresses for rubber products. The permissible compressive stresses are several times higher than the permissible tensile stresses, which is explained by the sensitivity of stretched rubber to local defects and surface damage.

The permissible stresses in parallel shear and torsion are lower than the permissible tensile stresses, especially under long-term dynamic loading. The possibility of a short-term impact load in most cases does not lead to a reduction in permissible stresses if the rubber operates at normal temperatures. With long-term dynamic loads, the permissible stresses are significantly reduced.

In the domestic literature, for rubber parts, the permissible compressive stress is recommended to be 11 10 5 Pa. It belongs to general purpose rubber of medium hardness. However, in many cases, rubber products work well for a long time at significantly higher stresses. This indicates that for some brands of rubber the permissible stress values ​​are underestimated.

When assessing the strength of rubber-metal products, the permissible stresses must be selected taking into account not only the tensile strength of the rubber, but also the strength of the fastening of the rubber to the metal.

The tear strength of attaching rubber to metal using an ebonite layer is usually determined by the strength of the rubber and is in the range (40...60) * 10 3 N/m.

Heat resistance of rubber. This indicator characterizes the performance of rubber at elevated temperatures. Heat resistance is determined by the change with temperature of those indicators of material properties that are most important for the specific conditions of use of the tested rubber. Heat resistance is characterized by a heat resistance coefficient, which is the ratio of rubber property indicators selected as a comparison criterion at elevated and room (23 ± 2 C) temperatures. Typical property indicators used to evaluate the heat resistance of rubber often use the results of measurements of tensile strength, elongation at break, or any other characteristics that are important for the specific conditions of use of the material.

Wear resistance of rubber. Rubbers and products made from them are often used in conditions of prolonged friction that occurs under significant loads.

Therefore, it is important to know how a product wears out due to friction. Since it is difficult to reproduce all possible friction conditions, the assessment of rubber wear resistance is based on determining its behavior under two extreme conditions - friction on a smooth surface or friction on a very rough surface, for which abrasive paper is used.

When testing rubber samples for abrasion under rolling conditions with slipping, the operation of various products, but primarily tires, is simulated. Therefore, this test method is used to evaluate the properties of rubber used for the manufacture of wheel treads.

A quantitative characteristic of abrasion is the ratio of the loss of material due to its intense abrasion to the work of friction forces expended in this case. Abrasion is expressed in m3/MJ. Sometimes the inverse value is also measured - abrasion resistance. It represents the amount of work of friction forces that must be done in order for a sample to be abraded in a volume of 1 cm 3; abrasion resistance is expressed in MJ/m 3.

Fatigue endurance of rubber. Under operating conditions, rubber products very often experience repeated periodic loads. In this case, the destruction of the sample (product) does not occur immediately, but after a certain, sometimes very large number of loading cycles. This is due to the gradual accumulation of microscopic damage in the sample, which ultimately, adding to each other, leads to a catastrophic phenomenon - destruction. An indicator of fatigue endurance is the number of cycles of repetitive loading that a rubber sample can withstand before failure. The fatigue endurance test of rubber is carried out under strictly fixed conditions with repeated stretching of the samples, carried out at a frequency of 250 or 500 cycles per minute with relatively small deformations.

Frost resistance of rubber. This indicator characterizes the ability of the material to work at low temperatures. As the temperature decreases, any rubber gradually “hardens”, becomes stiffer and loses its main quality used for making products from it - easy deformability under relatively small loads and the ability to undergo large reversible deformations.

The behavior of rubber at low temperatures is characterized by the frost resistance coefficient and the brittleness temperature.

The tensile frost resistance coefficient is understood as the ratio of elongation at a certain low temperature to elongation at room temperature under the same load, and the load is selected in such a way that the relative elongation of the sample at room temperature is 100%. Rubber is considered frost-resistant at the selected test temperature if the frost resistance coefficient does not decrease below 0.1, i.e. the rubber can still stretch by 10% without breaking.

The brittleness temperature is determined as follows. The sample is fixed in a cantilever and a load is sharply (impacted) applied. The brittleness temperature is understood as the maximum temperature (up to 0°C) at which a sample is destroyed under the influence of an impact or a crack appears in it.

Rubberized rollers. Rubber-coated rollers used in A1-ZRD type machines are the main working parts. A rubberized roller consists of metal reinforcement and a rubber coating, which are connected to each other with glue during the vulcanization process. The roll reinforcement is a steel pipe (sleeve) 400 mm long with an outer diameter of 159 mm and an inner diameter of 150 mm.

At the ends of the reinforcement, grooves measuring 12 x 12 mm are milled, which are used for installing a rubber roller on the axle shafts of the device for fastening the rolls.

A layer of rubber coating 20 mm thick is applied to the surface of the reinforcement using injection molding followed by vulcanization. The rubber mixture intended for the manufacture of rolls is made according to recipe No. 2-605.

Rubber-fabric plates. Rubber-fabric plates RTD-2 are used for the manufacture of decks of rolling deck machines 2DSHS-ZA. Decks are made directly at the millet mill by assembling and fastening rubber-fabric plates in a deck holder. The plates are made by vulcanization from a rubber mixture of type 4E-1014-1 and rubberized fabric. The plate contains eight layers of rubber and seven layers of rubberized fabric.

Rubber-fabric plates RTD-2 are produced according to TU 38 of the Ukrainian SSR 20574-76.

For the manufacture of brake strips in RC-125 grinding units, rubber plates are used that are approved for contact with food products (GOST 17133 - 83). Plates are produced of low (M), medium (C) and high (P) hardness with a thickness from 1 to 25 mm and square side dimensions from 250 to 750 mm.

According to physical and mechanical indicators, this rubber is characterized by the following data: conditional tensile strength from 3.9 to 8.8 MPa (based on natural rubbers); relative elongation after rupture from 200 to 350%; hardness according to TIR 35...55; 50...70 and 65...90 arb. units (three ranges).

Abrasive materials. Any mineral of natural or artificial origin, the grains of which have sufficient hardness and cutting (scratching) ability, is called an abrasive material.

Abrasive materials used for the manufacture of abrasive wheels are divided into natural and artificial.

Natural abrasive materials of industrial importance are minerals: diamond, corundum, emery, garnet, flint, quartz, etc. The most common are diamond, corundum and emery.

Corundum is a mineral consisting of aluminum oxide (70...95%) and impurities of iron oxide, mica, quartz, etc. Depending on the content of impurities, corundum has different properties and color.

Emery is a fine-grained rock consisting mainly of corundum, magnetite, hematite, quartz, gypsum and other minerals (corundum content reaches 30%). Compared to ordinary corundum, emery is more fragile and has less hardness. The color of emery is black, reddish-black, gray-black.

Artificial abrasive materials include diamond, CBN, Slavutich, boron carbide, silicon carbide, electrocorundum, etc.

Artificial abrasive materials have limited the use of natural ones, and in some cases have replaced the latter.

Silicon carbide is an abrasive material, which is a chemical compound of silicon and carbon, produced in electric furnaces at a temperature of 2100...2200 °C from quartz sand and coke.

For abrasive processing, the industry produces two types of silicon carbide: green and black. They differ slightly in chemical composition and physical properties, but green silicon carbide contains fewer impurities, has slightly increased fragility and greater abrasive ability.

Electrocorundum is an abrasive material produced by electrical surfacing of materials rich in aluminum oxide (for example, bauxite and alumina).

The grain size (grain size of abrasive materials) is determined by the size of the sides of the cells of two sieves through which the selected abrasive grains are sifted. The grain size is taken to be the nominal size of the side of the cell in the light of the mesh, on which: the grain is retained. The grain size of abrasive materials is designated by numbers.

The bond serves to bind individual abrasive grains into one body. The type of bond of an abrasive tool significantly affects its strength and operating modes.

Ligaments are divided into two groups: inorganic and organic.

Inorganic binders include ceramic, magnesia and silicate.

The ceramic bond is a glassy or porcelain-like mass, the constituent parts of which are refractory clay, feldspar, quartz and other materials. A mixture of binder and abrasive grain is pressed into a mold or cast. Cast wheels are more fragile and porous than pressed ones. The ceramic bond is the most common, since its use in abrasive tools is rational for the greatest number of operations.

The magnesium binder is a mixture of caustic magnesite and a solution of magnesium chloride. The process of making a tool using Loy bond is the simplest - making a mixture of emery and magnesium bond in a given ratio, compacting the mass in a mold and drying.

The silicate binder consists of liquid glass mixed with zinc oxide, chalk and other fillers. It does not provide strong fixation of the grains in the wheel, since liquid glass weakly adheres to the abrasive grains.

Organic binders include bakelite, glyphthalic and vulcanite.

Bakelite bond is bakelite resin in the form of powder or bakelite varnish. This is the most common of the organic ligaments.

Glyphthalic binder is obtained by the interaction of glycerin and phthalic anhydride. An instrument made with a glypthal bond is approximately the same as with a bakelite bond.

Vulcanite bond is based on synthetic rubber. To make wheels, abrasive material is mixed with rubber, as well as sulfur and other components in small quantities.

The following conventions are used for ligaments: ceramic - K, magnesia - M, silicate - C, bakelite - B, glyphthalic - GF, vulcanite - V.

The hardness of an abrasive wheel refers to the resistance of the bond to the tearing of grinding grains from the surface of the wheel under the influence of external forces. It is practically independent of the hardness of the abrasive grain. The harder the wheel, the more force must be applied to tear the grain out of the bunch. An indicator of the hardness of an abrasive tool is the depth of the hole on the surface of the circle (when using the sandblasting method for measuring hardness) or the reading of the Rockwell instrument scale (when using the ball indentation method). Abrasive wheels are made in a variety of shapes and sizes.

Static imbalance of the abrasive wheel. In accordance with GOST 3060 - 75, static imbalance of the grinding wheel characterizes the imbalance of the grinding wheel caused by the mismatch of its center of gravity with the axis of rotation.

The measure of static imbalance is the mass of the load, which, being concentrated at a point on the periphery of the circle, opposite to its center of gravity, moves the latter to the axis of rotation of the circle,

Depending on the number of imbalance units and the height of the circle, four imbalance classes are established. As the imbalance class increases, a larger amount of unbalanced mass is allowed.

Abrasive wheels are the main working parts of a number of machines used for grinding grain during the production of cereals. Such machines include A1-ZShN-Z, A1-BShM-2.5, ZShN, RC-125, etc.

The abrasive wheels used in the A1-ZShN-Z and ZShN machines are prefabricated structures consisting of a grinding wheel mounted in two steel bushings. The bushings act as hubs through which the abrasive wheels are attached to the machine shaft. On the lower bushing there are 12 holes symmetrically located for installing a balancing weight and three spacer rods, ensuring the placement of circles on the shaft at intervals.

In this case, two types of PVD grinding wheels are used: flat with a double-sided groove and the same wheels with an external conical profile.

The A1-ZSHN-Z machine set includes five flat PVD circles with a double-sided groove and one flat circle with a double-sided groove and an external conical profile. The ZShN machine set includes one wheel with an external conical profile and six wheels with a straight profile. The A1-BShM-2.5 grinding machine uses eight abrasive wheels with a straight PP profile. Before installation in the machine, the circles are mounted on wooden bushings, the outer diameter of which is equal to the internal diameter of the hole of the circles. In this form, the circles are installed and secured on the shaft, forming a solid cylinder. Summary data of the abrasive wheels used in the A1-ZShN-Z, ZShN and A1-BShM-2.5 grinding machines are given in Table 1.

The main working part of the RC-125 grinding machine is a truncated conical drum, the side surface of which is covered with an artificial abrasive mass consisting of a mixture of emery, caustic magnesite and a solution of magnesium chloride. The grain size of the emery is selected taking into account the requirements for ensuring effective grinding of grain.

The worn-out rotor surface is usually restored in a cereal factory using the above technology for magnesium bonded abrasive products.

Sieve cylinders. In grinding machines, perforated cylinders of various designs are installed around abrasive wheels with a certain gap. Since the grain is processed between rotating abrasive wheels and a stationary perforated cylinder under the influence of friction forces, the cylinders are subject to intense wear.

The sieve cylinder of the A1-ZSHN-Z machine is made of perforated steel sheet with a thickness of 0.8... 1.0 mm with oblong holes measuring 1.2 x 20 mm. The cylinder is equipped with upper and lower rings. Two stops are attached to the upper ring to prevent circular movement of the cylinder while the machine is operating.

The design of the sieve cylinder for ZShN type machines is similar to that described above. Its internal diameter is 270 mm.

The sieve cylinder in the A1-BSHM-2.5 frame-type machine consists of two half-cylinders. The semi-cylinders are connected to each other at the top with bolts, and at the bottom with special clamps (hinged bolts). To make one half-cylinder, a sieve with oblong holes measuring 1.2 x 20 mm and a sheet thickness of 1 mm is used. Sheet dimensions 870 x 460 mm. The sieve is attached to the frame with easily removable races. This design of the sieve cylinder ensures a uniform working gap between it and the abrasive wheels, low labor intensity when replacing worn sieves and races, as well as installing cylinders in the machine. The service life of sieves with a thickness of 1 mm is about 200 hours.

Compressed air. The quantities characterizing air in a given state are called state parameters. Most often, the state of air is determined by the following parameters: specific volume, pressure and temperature. Using compressed air as a working agent for grain peeling, aerodynamic dependencies are used that explain and reveal the phenomena that occur when a high-speed air flow flows around a solid body (grain). When an air flow flows over its surface, tangential frictional forces or viscous forces arise, creating tangential stresses.

A characteristic feature of air is elasticity and compressibility. A measure of the elasticity of air is the pressure that limits its expansion. Compressibility is the property of air to change its volume and density with changes in pressure and temperature.

The thermal equation of state of an ideal gas is widely used in the study of thermodynamic processes and in thermotechnical calculations.

In most problems considered in aerodynamics, the relative speed of gas movement is high, and the heat capacity and temperature gradients are small, so heat exchange between individual streams of moving gas is practically impossible. This allows us to accept the dependence of density on pressure in the form of an adiabatic law.

A characteristic of the energy state of a gas is the speed of sound in it. The speed of sound in gas dynamics is understood as the speed of propagation of weak disturbances in a gas.

The most important gas-dynamic parameter is the Mach number M = c/a - the ratio of the gas velocity c to the local speed of sound a in it.

Outflow of gases through nozzles. In practical tasks, various types of nozzles (nozzles) are used to accelerate air flow.

The exhaust velocity and air flow rate, i.e., the amount of air flowing out per unit time, are determined using dependencies known in aerodynamics. In these cases, first of all, the ratio P 2 /P 1 is found, where P 2 is the pressure of the medium at the outlet of the nozzle; P 1 - medium pressure at the nozzle inlet.

To obtain exhaust velocities above critical (supersonic speeds), an expanding nozzle or a Laval nozzle is used.

Energy indicators of compressed air. The process of grain peeling using a jet of air flow moving at critical and supercritical speeds is based on the basic laws of high-speed aerodynamics. It should be noted that the use of a high-speed air jet for peeling is an energy-intensive operation, since significant energy costs are required to produce compressed air.

So, for example, for two-stage compressors with a final pressure of 8-105 Pa, the specific power consumption (in kW min/m3) depending on the capacity (m 3 /min) is characterized by the following data:

The use of compressed air for peeling is effective in cases where the cost of the processed raw materials is several times higher than the cost of energy or when it is impossible to achieve the required processing of the product by other means.

LABORATORY WORK No. 8

Subject:« Determination of the elastic modulus of a material (Young's modulus)"

Target: determine the modulus of elasticity of the rubber cord and evaluate the results of the experiment by comparing it with the table value.

Equipment: a tripod with a coupling and a foot, a rubber cord (with a cross-section in the shape of a circle), a cup for weights, a set of weights (weights), a measuring ruler with a millimeter scale.

Theoretical part

Young's modulus ( E) characterizes the elastic properties of any solid material. This value depends only on the substance itself and its physical state. Since Young's modulus is included in Hooke's law, which is valid only for elastic deformations, then Young's modulus characterizes the properties of a substance only under elastic deformations.

Young's modulus can be determined from Hooke's law: (1)

because and then , Then . (2)

Since quite large forces are required to deform rods made of rigid materials, in this laboratory work it is recommended to use materials with a low elastic modulus, such as rubber.

Work order:

Calculate the cross-sectional area of ​​the rubber cord using the formula:

(measure the diameter of the cord using a micrometer or ask your teacher).

Initial sample length

Absolute elongation of the sample

S – cross-sectional area of ​​the cord

F – elastic force , arising in a stretched cord and equal to the weight of the weights on the cup (P)

Carry out measurements and calculations three times under different loads, enter the results in the table.

1. Calculate the average value of the elastic modulus of the rubber cord.

Assess the accuracy of the measurements and calculations carried out by calculating the relative error, comparing the average result with the tabulated value of Young's modulus for rubber: E tab. = 1∙10 6 Pa.

Based on the results of the work draw a conclusion.

WORK REPORT

Control questions:

What deformations did you study in this work? Give a characteristic (definition) of this type of deformation.

Draw a stress-strain diagram of a solid. What relationship can be traced from this diagram?

ANSWERS TO TEST QUESTIONS:

Rubbers are network polymers with flexible molecular chains.

Rubber- a product of special processing (vulcanization) of the mixture rubber and sulfur with various additives. Rubber has high elastic properties. Has relative elongation d= 1000% over a wide temperature range. Longitudinal modulus of elasticity E= 1-200 MPa. The volumetric compressibility is low, and the volumetric modulus of elasticity is close to that of mineral oil. æ » 10 3 - 2.5 * 10 3 MPa or water and depends on pressure (for example, nairite at density r= = 1.32 g/cm 3 has a bulk modulus of elasticity æ= 2.27*10 3 MPa ) . Poisson's ratio m= 0.4-0.5 (for metals m= 0.25-0.30). Relaxation time for rubber t r= 10 -4 s and above.

Rubber is characterized by hysteretic power losses, leading to heating in the event of repeated harmonic influences. This reduces her performance. Rubbers are also characterized by high abrasion resistance, water resistance, relative gas impermeability, chemical resistance, in special cases, electrical insulating properties, low density r= 0.91-1.9 g/cm3.

Rubber deformation is a complex process. It is divided into 3 components: a) elastic deformation, similar to the deformation of solids and associated with changes in interatomic and intermolecular distances; b) highly elastic deformation associated with the movement of molecular links without relative movement of the molecules as a whole (in this case, molecular coils unwind, etc.); V) plastic deformation, associated with the relative movement of molecules as a whole.

High elasticity is characteristic only of rubbers and some polymers.

The essential features of high elasticity can be determined by uniform, shear-free deformation. With such a deformation, a cube with a side l o turns into a parallelepiped with sides l 1, l 2, l 3. Select the following variables l i, called multiplicities of stretching, in which the change in shape is separated from the change in volume l i = l i V -1/ 3. Here i= 1,2,3 and V= l 1 l 2 l 3- volume of the deformed sample. The stretching ratios satisfy the condition l 1 l 2 l 3= 1. Therefore, only two of them are independent, for example l 3 = 1/(l 1 l 2). If there is only a change in volume without a change in shape, when all the edges change proportionally, l i= 1.

Under uniaxial tension, the cube turns into a parallelepiped with a length l and square section: l 1 = l= lV -1/3 ; l 3 = l 2 = l -1/2.

Under the influence of applied force F even at constant pressures and temperatures, due to changes in internal energy, there is a slight increase in the volume of rubber, amounting to a fraction of a percent. The magnitude of highly elastic uniaxial deformation for l<2,5 can be determined using Bartenev's empirical formula

l= 1+ s/E, (3-1)

Where E- Young's modulus (elastic modulus), s- voltage.

Rubbers are widely used in the manufacture of automobile tires, flexible hoses, belts, conveyor belts, as a variety of sealing materials, etc.

In Fig. 3.2 shows some examples of the use of rubber products (RTI) in industry.

Fig.3.2. Using rubber matrix belts to transmit motion.

Rubber base is rubber, natural (NC) or synthetic (SC). Synthetic rubber was developed in the USSR by Academician S.V. Lebedev. in the 20s of the twentieth century.

To improve its properties, additives (ingredients) are added to it:

1. Sulfur, selenium or sulfur compounds for electrical rubber. When interacting with rubber, they form a polymer network.

2. Stabilizers (antioxidants, antioxidants) that slow down the aging process of rubber (paraffin, wax). External films can be applied for this purpose.

3. Softeners (plasticizers) - paraffin, petroleum jelly, bitumen...

4. Fillers, reinforcing and inert. They are introduced to increase strength, wear resistance, and reduce cost.

Reinforcing fillers are carbon black and white carbon, which increase mechanical properties. Inert - chalk, talc, barite. The latter are used to reduce the cost of rubber.

5. Dyes.

Vulcanization is called the process of chemical interaction between rubber and sulfur. As a result of vulcanization, rubber macromolecules have a sparsely networked structure. At the same time, the polymers that make up rubber are in a highly elastic state at operating temperatures.

At 1-5% S a sparse polymer network is formed. In this case, the rubber turns out to be highly elastic and soft. At 30% S A solid material is formed - ebonite. During vulcanization ( T= 160-200°C under pressure, T= 130-140°C by open method) the molecular structure of the polymer changes. A reaction of “cross-linking” rubber molecules with cross-links occurs. At this moment, a spatial grid is formed and strength increases to s vr= 35 MPa and wear resistance. Hardness also increases. It is usually assessed using the Shor method using the TShM-2 device. Here, a rubber ball is pressed into the sample and the hardness is assessed by the depth of its immersion under the influence of a given load. Typical Shore hardness values ​​are 30-90. At 30, the rubber is soft, and at 90, it is very hard. Rubber rings of this hardness seal connections with a pressure drop of up to 400 MPa.

Relationship between units of hardness and modulus of elasticity in compression.

The elastic characteristics of rubber are largely determined by its hardness. Table 3.2 shows the ratio of units of hardness and modulus of elasticity in compression.

Due to the fact that the elastic modulus of rubber is significantly, three orders of magnitude, lower than the elastic modulus of steel, this circumstance is used when introducing various shock-absorbing pads. Since it is the high compliance (elasticity) that causes a sharp decrease in the resonant frequency of the mechanical system and strong damping of vibrations.

The following rubbers are used in mechanical engineering:

1. Natural rubber (NK), which is a polymer of isoprene. At T³ 80-100°C it softens; at T = 200°C - decomposes. Amorphous. In case of long-term storage or stretching, crystallization may occur.

2. Synthetic butadiene rubber (SKB), obtained using the Lebedev method. May swell in solvents.

3. Synthetic styrene butadiene rubber (SKS)- The most common.

Some brands are SKS-10...SKS-50.

Rubbers SKS-10, SKD are classified as frost-resistant.

4. Synthetic isoprene rubber (SKI).

5. Domestic chloroprene rubber nairit. It has high elasticity, vibration resistance, oil and petrol resistance.

6. Synthetic nitrile butadiene rubber (SKN). Some brands are SKN-18, SKN-25, SKN-40. Foreign analogues - haikar, perbunal. They produce belts, sealing gaskets, and cuffs. Oil and petrol resistant.

7. Synthetic rubber is heat resistant (SKT). Operates at T= - 60...+250°C.

8. Light-resistant rubbers are made on the basis of fluorine-containing, ethylene-propylene rubbers and butyl rubbers. SKF-32, SKF-26, foreign analogues Kel-F, Viton.

9. Wear-resistant rubbers (SKU) have high strength and elasticity. They operate at T= -30...+130°C. Foreign analogues vulkolan, adiprene, jentan, urepan.

They manufacture tires, conveyor belts, pipe linings, etc. etc.

11. Electrical rubbers are made on the basis of non-polar rubbers NK, SKB, SKT and butyl rubber. Their electrical resistance can be r v= 10 11 - 10 15 Ohm/cm.

Electrically conductive rubbers used for shielded cables are made from NK, SKN, nairite, especially from polar SKN-26, by introducing carbon black and graphite into the composition. Electrical resistance is r v= 10 2 - 10 4 Ohm/cm.

There are many brands of tires. For example: 15-RI-10 (based on NK), 3826 (based on SKN-26), V-14-1 (based on SKN), NO-68-1 (based on Nairit), IRP-1287 (based on SKF-26).

During operation and storage under the influence of external factors, rubber getting old with deterioration of properties:

1. Ozone and atmospheric conditions lead to cracking.

2. Light causes photo-oxidation of rubbers.

3. At elevated temperatures (>150°C), many rubbers lose strength after 1-10 hours of heating.

4. At low temperatures, rubber becomes glassy, ​​and its rigidity increases sharply.

5. Radiation leads to an increase in hardness and longitudinal modulus of elasticity, and a decrease in elasticity.

6. In a vacuum, some rubbers lose mass. Others SKI-3, SKD, SKF-4, SKT are stable in vacuum.

Typically, enterprises indicate a shelf life of 1 year for rubberized parts.

Our robot recognized:
Lab 2

Measuring the elastic modulus of rubber

Work couldn't be more fun: usually the first few minutes

Rubber claps all over the classroom and muffled noises. voices What are you doing! Now you will receive... and so on. To quickly finish with this necessary ritual and move on to what is in the textbook, let’s do a little mental exercise.

Let's mentally take the new steps! cord and mentally attach a hundred-gram weight to it. Let's mentally pull the cord by the weight and mentally unclench our fingers. Advice You can answer the following questions in writing: 1 What trajectory will the weight fly and what will happen at the end of the path

With its fragile hooks 2 like o green I nr south pa llr pear:

Used laboratory cabinet, glass and thermometers:

In the head of the person sitting in front, and will she be able to do anything mentally after that?

In short, we are in tenth grade, guys. We are beginning to wean ourselves from tomfoolery. To prevent the above-described accident from happening without malicious intent, remember: hang weights on the cord carefully, do not stretch the cord more than necessary; When going to Kamchatka for a ruler, make sure that the structure is not attached to the lizhak and is not being pulled after you by the cocked catapult. Those who are more cautious can come to class wearing a hockey helmet - this is not prohibited by the school curriculum.

It’s nice to use a ready-made formula, but it’s even nicer to know where this formula came from. We got it from Hooke's law. If you remember, this law is valid for severe deformations of the body. Another argument in favor of the fact that rubber cannot be stretched too much and looks like this:

H Young's modulus, from here it is equal

Mechanical stress is determined

In the following way:

The sign of the modulus in the formula for the angle of the body, and when compressing the body: since V of the modulus we use ordinary brackets

This is our working formula. The last obstacle you have to overcome is the definition of K I area of ​​hyperemia o a

Stump ish r.;: I .,-.:m secsile cr>. .those. ,. her.....ri-oo;. o.o.my gch.sh

Rubber-5 and multiply the width by the thickness. The cord is greyuln and generally has a shaped cross-section, you are unlikely to

Distance 1, m.07

Distance 1, m 0.088

Width shshr, 1 i, m 0.01

Cord thickness/, m 0.0005

Cross-sectional area K. m 50-

Elastic force U. N z

Calculated

Instrumental gkm rs.....chs1 ь tsigeiki. D,1, m 0.0001

Length reading error, D-.1, m 0.0005

Absolute error. A1. m 0.0006

Instrumental micrometer error. LL. m +0.000005

Thickness reading error. L.L m +0.000005

Absolute error Li m 0.00001

Them:...-.:; ;1Ш10С1к dynamometer, DR. H 0.005

Force reading error, L-, R. 11 0.05

Lbeo.ikch pan error LC. H 0.055

Young's modulus W. Pa 2.3x o

Relative error e, 14

Absolute error of LG. Pa.1.22x10

Cord cross-sectional area: 5 l b

5 0.01 m 0.0005 m 0.000005 m2 5x 10 mg.

Young's modulus: E,.,.

7 2.3x10 Pa.

From 5x106m20.088m-0.07m

E The calculation of the error in our example is complicated by the fact that, as you already understood, the cord has a rectangular cross-section: we measured it with a ruler, and we measured it with a micrometer, that is, with instruments of varying accuracy. However, with some care, it is not difficult to understand the subsequent calculation. Ichmerchnin error:

D1 - D1 + 4.1; D1 0.0001 m + 0.0005 m 0.0006 m; b DCL + AB; AB 0.000005 m - 0.000005 m - 0.00001 m: DG - D,G + DR; DR 0.005 N + 0.05 N 0.055 11. Relative error: DR D! D1 Dy. D1 E R +1+ a+ b +21-1
0.055 P 0.0006 m 0.0006 m 0.00001 m 0.0006 m

E ZN + 0.07 m + 0.01 m 0.0005 m 0.088 m - 0.07 m

0.018 + 0.008 + 0.06 + 0.02 + 0.033 - 0.14 14 Dosol Yu1 error: DE - Ee; DE 2.3x106 Pa 0.14 3.22x105. Answer: E 2.3x10 3.22x10 Pa.