The development of modern society differs from the ancient one in that people have invented and learned to use all kinds of machines. Now, even in the most distant villages and the most backward tribes, they are enjoying the fruits of technological progress. Our whole life is accompanied by the use of technology.

In the process of development of society, as production and transport mechanized, and the complexity of structures increased, the need arose not only unconsciously, but also scientifically to approach the production and operation of machines.

From the middle of the XIX century in the universities of the West, and a little later at St. Petersburg University, an independent course "Machine Parts" was introduced into teaching. Today, without this course, the training of a mechanical engineer of any specialty is unthinkable.

The training process for engineers around the world has a single structure:

1. In the first courses, fundamental sciences are introduced, which provide knowledge about the general laws and principles of our world: physics, chemistry, mathematics, computer science, theoretical mechanics, philosophy, political science, psychology, economics, history, etc.
2. Then they begin to study applied sciences, which explain the operation of the fundamental laws of nature in private spheres of life. For example, technical thermodynamics, strength theory, materials science, strength of materials, computer technology, etc.
3. Starting from the 3rd year, students begin to study general technical sciences, such as "Machine parts", "Basics of standardization", "Materials processing technology", etc.
4. At the end, special disciplines are introduced, when the qualifications of an engineer in the relevant specialty are determined.

The academic discipline "Machine parts" aims at studying the structures of parts and mechanisms of devices and installations by students; physical principles of operation of devices, physical installations and technological equipment used in the nuclear industry; design methods and calculations, as well as methods of design documentation. In order to be ready to comprehend this discipline, it is necessary to possess the basic knowledge that is taught in the courses "Physics of Strength and Strength of Materials", "Fundamentals of Materials Science", "Engineering Graphics", "Computer Science and Information Technology".

The subject "Machine parts" is compulsory and basic for courses where it is supposed to conduct a course project and diploma design.

Machine parts as a scientific discipline considers the following main functional groups.

1. Body parts, bearing mechanisms and other units of machines: plates supporting machines, consisting of separate units; stands supporting the main units of machines; frames of transport machines; rotary machine casings (turbines, pumps, electric motors); cylinders and cylinder blocks; gearboxes, gearboxes; tables, skids, supports, consoles, brackets, etc.
2. Transmissions are mechanisms that transfer mechanical energy over a distance, as a rule, with the transformation of speeds and moments, sometimes with the transformation of the types and laws of motion. Transmissions of rotary motion, in turn, are divided according to the principle of operation into gearing transmissions that work without slipping - gear drives, worm drives and chain drives, and friction drives - belt drives and friction drives with rigid links. By the presence of an intermediate flexible link, which provides the possibility of significant distances between the shafts, there are transmissions with a flexible connection (belt and chain) and transmissions by direct contact (gear, worm, friction, etc.). According to the mutual arrangement of the shafts - gears with parallel axes of the shafts (cylindrical gear, chain, belt), with intersecting axes (bevel gear), with crossing axes (worm, hypoid). According to the main kinematic characteristic - the gear ratio - there are gears with a constant gear ratio (reducing, boosting) and with a variable gear ratio - stepped (gearboxes) and continuously variable (variators). Gears that convert rotary motion into continuous translational or vice versa are divided into gears: screw - nut (sliding and rolling), rack - rack gear, rack - worm, long half-nut - worm.
3. Shafts and axles are used to support rotating machine parts. There are gear shafts, bearing parts of gears - gear wheels, pulleys, sprockets, and main and special shafts, carrying, in addition to gear parts, working bodies of engines or machine tools. Axles, rotating and stationary, are widely used in transport vehicles to support, for example, non-driving wheels. Rotating shafts or axes rest on bearings, and translationally moving parts (tables, calipers, etc.) move along guides. Rolling bearings are most often used in machines; they are manufactured in a wide range of outer diameters from one millimeter to several meters and weighing from fractions of a gram to several tons.
4. Couplings are used to connect the shafts. This function can be combined with fabrication and assembly error compensation, dynamic mitigation, control, etc.
5. Elastic elements are designed for vibration isolation and shock energy damping, for performing engine functions (for example, clock springs), for creating gaps and tension in mechanisms. A distinction is made between coil springs, coil springs, leaf springs, rubber elastic elements, etc.
6. Fittings are a separate functional group. Distinguish between: one-piece connections, which do not allow the separation without destruction of parts, connecting elements or connecting layer - welded, brazed, riveted, glue, rolled; detachable connections, allowing separation and carried out by the mutual direction of parts and friction forces or only by mutual direction. According to the shape of the connecting surfaces, joints are distinguished along planes and along surfaces of revolution - cylindrical or conical (shaft-hub). Welded joints are widely used in mechanical engineering. Of the detachable connections, the most widespread are threaded connections made with screws, bolts, studs, nuts.

So, "Machine parts" is a course in which they study the basics of designing machines and mechanisms.

What are the stages in the development of the design of a device, device, installation?

First, a design specification is set, which is the initial document for the development of a device, device or installation, which indicates:

a) the purpose and scope of the product; b) operating conditions; c) technical requirements; d) development stages; e) type of production and more.

The terms of reference may have an attachment containing drawings, sketches, diagrams and other necessary documents.

The technical requirements include: a) designation indicators that determine the intended use and application of the device (measurement range, efforts, power, pressure, sensitivity, etc.; b) the composition of the device and design requirements (dimensions, weight, use of modules, etc.) ; c) requirements for protective equipment (against ionizing radiation, high temperatures, electromagnetic fields, moisture, aggressive environment, etc.), interchangeability and reliability, manufacturability and metrological support; d) aesthetic and ergonomic requirements; e) additional requirements.

The design normative base includes: a) a unified system of design documentation; b) a unified system of technological documentation c) State standard of the Russian Federation on the system of development and launching of products for production of SRPP - GOST R 15.000 - 94, GOST R 15.011 - 96. SRPP

Basic concepts and course definitions

We will define the basic concepts at the very beginning of work to systematize the educational material and to avoid ambiguous interpretation.

Let's arrange concepts according to the degree of complexity.

In the standard GOST 15467-79 PRODUCTS - the result of activities or processes. Products may include services, equipment, recyclable materials, software, or a combination of these.

According to GOST 15895-77, PRODUCTis a unit of industrial production. PRODUCT - any item or set of production items manufactured by an enterprise. A product is understood as any product manufactured according to design documentation. The types of products are parts, kits, units, mechanisms, aggregates, machines and complexes. Products, subject to availability orthe absence of components in them are divided: 1) into unspecified (details) - having no component parts; 2) on the specified(assembly units, complexes, kits) - consisting of two andmore component parts. The components of the machine are: a part,assembly unit (unit), complex and kit.

MACHINE PARTS - a scientific discipline dealing with the study, design and calculation of machine parts and general-purpose units. Mechanisms and machines are made up of parts. Bolts, shafts, gears, bearings, couplings found in almost all machines are called general-purpose assemblies and parts.

DETAIL – (frenchdetail - a piece) - a product made of a material homogeneous in name and brand without the use of assembly operations (GOST 2.101-68). For example, a roller made of one piece of metal; cast body; bimetallic plate, etc. Parts can be simple (nut, key, etc.) or complex (crankshaft, gear housing, machine bed, etc.).

Among the wide variety of parts and units of machines, there are those that are used in almost all machines (bolts, shafts, couplings, mechanical transmissions, etc.). These parts (nodes) are called general purpose parts and study in the course "Machine parts". All other parts (pistons, turbine blades, propellers, etc.) belong to parts for special purposes and are studied in special courses. Details general purposeused in mechanical engineering in very large quantities. Therefore, any improvement in the methods of calculation and design of these parts, which makes it possible to reduce material costs, reduce the cost of production, increase durability, brings great economic effect.

ASSEMBLY UNIT - a product, the components of which are to be connected at the manufacturing plant by means of assembly operations (screwing, joining, soldering, crimping, etc.), (GOST 2.101-68).

KNOT - a complete assembly unit consisting of general functional parts and performing a specific function in products of one purpose only in conjunction with other component parts of the product (couplings, rolling bearings, etc.). Complex nodes can include several simple nodes (subnodes); for example, a gearbox includes bearings, shafts with gears mounted on them, and the like.

SET (repair kit) is a set of individual parts used to perform operations such as assembly, drilling, milling, or for repairing certain machine components. For example, a set of attachment or socket wrenches, screwdrivers, drills, cutters or a repair kit for a carburetor, fuel pump, and so on.

MECHANISM- a system of movably connected parts designed to transform the movement of one or several bodies into expedient movements of other bodies (for example, a crank mechanism, mechanical transmissions, etc.).

According to their functional purpose, machine mechanisms are usually divided into the following types:

Transmission mechanisms;

Executive mechanisms;

Management, control and regulation mechanisms;

Feeding, transportation and sorting mechanisms.

LINK - a group of parts that forms a mechanical system of bodies moving or stationary relative to each other.

A link taken for a fixed link is called resistant.

Input link is called the link to which the movement is imparted, which is converted by the mechanism into the movements of other links.

The weekend link is called a link making a movement, for which the mechanism is intended.

Between the input and output links can be located intermediate links.

In each pair of jointly working links in the direction of the power flow are distinguished leading and slave links.

In modern mechanical engineering, mechanisms are widely used, which include elastic (springs, membranes, etc.) and flexible (belts, chains, ropes, etc.) links.

Kinematic pair call the connection of two touching links, allowing their relative movement. Surfaces, lines, points of a link along which it can come into contact with another link, forming a kinematic pair, are called elements of a kinematic pair. Functionally, kinematic pairs can be rotational, progressive, screw etc.

A connected system of links forming kinematic pairs with each other is called kinematic chain . Thus, every mechanism is based on a kinematic chain.

APPARATUS – (lat.apparatus - part) a device, a technical device, a device, usually some autonomous-functional part of a more complex system.

UNIT – (lat.aggrego - attach) a unified functional unit with full interchangeability.

DRIVE UNIT - a device through which the movement of the working bodies of machines is carried out. In TMM, an adequate term is used - a machine unit.

CAR– (greek "m ahina" - huge, formidable) a system of parts that makes a mechanical movement to convert energy, materials or information in order to facilitate labor. The machine is characterized by the presence of a power source and requires the presence of an operator for its control. The astute German economist K. Marx noticed that every machine consists of a motor, transmission and executive mechanisms. The category "machine" in everyday life is often used as the term "technique".

TECHNICS - these are man-made material means,used by him to expand his functionalityin various fields of activity in order to satisfy material and spiritual needs.

By the nature of the work process, all the variety of machines can besplit into classes: energy, technological, transport and informational.

ENERGY MACHINES are devices designed for energy conversion of any kind (electrical, steam, thermaletc.) into mechanical. These include electrical machines(electric motors), electromagnetic current converters, steam machines, internal combustion engines, turbines, etc. To varietypower machines include CONVERTER MACHINES , serving to convert mechanical energy into energy of any kind. These include generators, compressors, hydraulicspersonal pumps, etc.

TRANSPORTING MACHINES - convert engine energy intoenergy of movement of masses (products, products). To transportingmachines include conveyors, elevators, bucket elevators, cranesand lifts.

INFORMATION (COMPUTING) MACHINES - intended forreceiving and transforming information.

TECHNOLOGICAL MACHINES - designed to transform the processingthe object (product) being washed, consisting in changing its size, forms, properties or states.

Technological machines consist of an energy machine (engine), transmission and executive mechanisms. The most importantin the car is ACTUATING MECHANISM , defining technological possibilities, degree of versatility and namecars. Those parts of the machine that come in contact withproduct and affect it, are called WORKING BODY MACHINE .

In the field of machine design(mechanical engineering) category widely used TECHNICAL SYSTEM , underwhich is understood as artificially created objects intendedto meet a specific need that is inherentthe ability to perform at least one function, multi-element, hierarchy of structure, multiplicity of connections between elements,multiple changes and variety of consumer qualities. TOtechnical systems include individual machines, devices, devicesry, structures, hand tools, their elements in the form of nodes, blocks,units and other assembly units, as well as complex complexes of mutualrelated machines, apparatus, structures, etc.

DRIVE UNIT- a device that sets a machine or mechanism in motion.

The drive consists of:

Energy source;

Transmission mechanism;

Control equipment.

MACHINE UNIT called a technical system consisting of one or more machines connected in series or in parallel and designed to perform any required functions. Typically, a machine unit includes: an engine, a transmission mechanism and a working or power machine. Currently, the composition of the machine unit often includes control and manageror a cybernetic machine. The transmission mechanism in the machine unit is necessary to match the mechanical characteristics of the engine with the mechanical characteristics of the working or power machine. Depending on the operating conditions of the machine unit, the control mode can be carried out manually or automatically.

COMPLEX Is also an assembly unit of separate interconnected machines, automatic machines and robots, controlled from a single center for performing technological operations in a certain sequence.For example, RTK - robotic systems, automatic lines without human participation when performing technological operations; production lines where people are involved in some operations, for example, when removing feathers of birds.

MACHINE – (greek " and utomotos"- self-propelled) a machine working according to a given program without an operator.

ROBOT – (czech . robot - worker) a machine that has a control system that allows it to independently make executive decisions in a given range.

Requirements for technical objects

When developing a technical object, it is necessary to take into account the requirements that the designed object must satisfy.

In 1950, the German engineer F. Kesselring made an attempt to collect all the requirements that designers set themselves in order to decompose the design process, i.e. dividing a complex task into a number of simpler ones, turning design into a process of consistently meeting one requirement after another - like a school task in several actions.

F. Kesselring's list included more than 700 requirements. This was not an exhaustive list; more than 2500 requirements are known today.

Kesselring was unable to solve the problem, since many requirements contradict each other. For example, the requirement to increase the level of automation of a technical object contradicts the requirement of comprehensive simplification of the design, etc.

Thus, in each case, the designer must decide which requirement should be satisfied and which should be neglected.

Nevertheless, the existence of the list of requirements and its replenishment is extremely useful, since it forces you to pay attention to those aspects of the object that sometimes seem trivial, but in fact are missed.

Below are some examples of requirements:

Subordinate design to the task of increasing the economic effect, determined primarily by the useful return of the machine, its durability and the cost of operating costs for the entire period of use of the machine;

To maximize the useful return by increasing the productivity of the machine and the volume of operations performed by it;

To achieve every possible reduction in the cost of operating machines by reducing energy consumption, maintenance and repair costs;

Increase the degree of automation of machines in order to increase productivity, improve product quality and reduce labor costs;

Increase the durability of machines;

To ensure a long moral service life by putting high initial parameters into the machines and providing for reserves for the development and improvement of machines;

To lay the prerequisites for intensifying their use in machines by increasing their versatility and reliability;

Provide for the possibility of creating derivative machines with the maximum use of the structural elements of the base machine;

Strive to reduce the number of standard sizes of machines;

Strive to eliminate major repairs through the availability of replaceable parts;

Consistently adhere to the principle of aggregation;

Eliminate the need to select and fit parts during assembly, ensuring their interchangeability;

Exclude operations of reconciliation, adjustment of parts and assemblies in place; provide in the structure, fixing elements that ensure the correct installation of parts and assemblies during assembly;

Provide you with the strength of parts by giving them rational forms, using materials of increased strength, introducing hardening treatment;

Introduce elastic elements that soften load fluctuations into machines, units and mechanisms operating under cyclic and dynamic loads;

Make cars easy to maintain, eliminate the need for periodic adjustments, etc.;

To prevent the possibility of overvoltage of the machine, for which to introduce automatic regulators, safety and limit devices, excluding the possibility of operating the machine in dangerous modes;

Eliminate the possibility of improper assembly of parts and assemblies that require precise mutual coordination by introducing a lock;

Replace periodic lubrication with continuous automatic;

Avoid open mechanisms and gears;

Provide reliable insurance for threaded connections against self-turning;

Prevent corrosion of parts;

Strive for the minimum weight of machines and minimum metal consumption.

This point is worth dwelling on. A number of facts indicate that in terms of the metal consumption of the structure we are still far behind in a number of branches of mechanical engineering from the developed capitalist countries.

So, the material consumption of the EO-6121 excavator is 9 tons higher than the Poklein excavator (FRG), the KB-405-2 tower crane is 26 tons heavier than the analogue manufactured by the Reiner company (Germany), the metal consumption of the T-130M tractor is higher than the American analog D-7R by 730 kg. Kamaz has 877 kg of its own weight per 1 ton of carrying capacity, and Magirus (Germany) has 557 kg / 1 ton.

For the transportation of its own weight surplus "Kamaz" overruns 3 t / year for 1 vehicle.

Simplify the design of machines in every possible way;

Replace, where possible, rectilinear reciprocating mechanisms with rotary mechanisms;

Provide maximum manufacturability of parts and assemblies;

Reduce the amount of machining, providing for the production of blanks with a shape approaching the final shape of the product;

Carry out the maximum unification of elements in the use of normalized parts;

Save expensive and scarce materials;

To give the car a simple and smooth outer shape that makes it easier to keep the car tidy;

Comply with the requirements of technical aesthetics;

Make accessible and easy to inspect units that need periodic inspection;

Ensure the safe operation of the unit;

Continuously improve the design of machines in serial production;

When designing new structures, check all the elements of the novelty of experiments;

To make wider use of experimentally executed structures, the experience of related, and, if necessary, distant engineering industries.

A reasonable combination of requirements is achieved by design optimization. In some cases, optimization problems can be solved quite simply. In other cases, the solution of such problems has to be dealt with by entire institutions.

The stated requirements are not isolated, random recommendations that are in no way related to each other. They are a reflection of the impact of modern scientific and technological revolution on technology. In the work "Scientific and technological revolution and the advantages of socialism", [Thought, 1975] it is noted: "Generalization of the trend in the development of technology and scientific developments makes it possible to note the following features of the working machines being created:

A. In the field of using the forces of nature - the increasing use of physical, chemical, biological processes, the transition to complex technology, new types of motion of matter, high and low potentials (pressures, temperatures, etc.).

B. In the field of structural and organizational-technical forms - increasing the unit capacity, integrating processes in one organ, increasing the strength of connections, ensuring the dynamism of structures, the widespread use of artificial materials, the integration of machines into ever larger systems-lines, sections, units, complexes. The development of dynamism is achieved by increasing standardization, unification, universalization, blockiness and aggregation... This dynamism reflects the diversity of technology functions. The progress of standardization, aggregation characterizes the unity of technology on a natural science basis.

C. In the field of the principles of influence on the subject of labor - the maximum possible, direct use of the forces of nature, the tendency to change the fundamental foundations of the processed substances and the receipt of the final product.

Mechanisms and their classification

The mechanisms used in modern machines and systems are very diverse and are classified according to many characteristics.

1. By field of application and functional purpose:

Aircraft mechanisms;

Machine tools;

Mechanisms of forging machines and presses;

Internal combustion engine mechanisms;

Industrial robot mechanisms (manipulators);

Compressor mechanisms;

Pump mechanisms, etc.

2. By the type of transfer function to mechanisms:

With constant transfer function;

With variable transfer function:

With unregulated (sinus, tangent);

With adjustable:

With step regulation (gearboxes);

Infinitely variable (variators).

3. By the type of motion transformation:

Rotational to rotational (gearboxes, multipliers, couplings)

Rotational to translational;

Translational to rotational;

Translational to translational.

4. By the movement and location of links in space:

Spatial;

Flat;

Spherical.

5. By the changeability of the structure of the mechanism into mechanisms:

With an immutable structure;

With a variable structure.

6. According to the number of movements of the mechanism:

With one mobility W= 1;

With multiple mobility W> 1:

Summing (integral);

Separating (differential).

7. By the type of kinematic pairs (KP):

With lower KPs (all KPs of the mechanism are lower);

With higher CP (at least one CP is higher);

Articulated (all gearboxes are rotational - hinges).

8. By the method of transmission and transformation of the flow of energy:

Friction (clutch);

Gearing;

Wave (creating wave deformation);

Pulse.

9. By form, design and movement of links:

Lever;

Serrated;

Cam;

Frictional;

Screw;

Worm gear;

Planetary;

Manipulators;

Flexible link mechanisms.

In addition, there are a large number of different composite or combined mechanisms, which are various combinations of mechanisms of the types listed above.

However, for a fundamental understanding of the functioning of machines, the basic classification feature is structure of mechanisms - the totality and relationships of the elements included in the system.

Studying flat lever mechanisms with lower kinematic pairs, professor of St. Petersburg University L.V. Assur discovered in 1914 that any most complex mechanism actually consists not just of individual links, but of the simplest structural groups formed by links and kinematic pairs - small open kinematic chains. He proposed an original structural classification, in which all mechanisms consist of primary mechanisms and structural groups (groups of zero mobility or "Assur groups").

In 1937, the Soviet academician I.I. Artobolevsky improved and supplemented this classification, extending it up to spatial mechanisms with translational kinematic pairs.

The essence of structural classification is to use the concept of a structural group, of which all mechanisms are composed.

The importance of transmission mechanisms in mechanical engineering

Main functions transmission mechanisms are:

Transfer and transformation of motion;

Change and regulation of speed;

Distribution of power flows between different executive bodies of this machine;

Start, stop and reverse motion.

These functions must perform flawlessly with the specified degree of accuracy and performance over a specified period of time. At the same time, the mechanism must have minimum overall dimensions, be economical and safe in operation. In a number of cases, other requirements may be imposed on transmission mechanisms: reliable operation in a polluted or aggressive environment, at high or very low temperatures, etc. Meeting all these requirements is a difficult task and requires the designer to be able to navigate well in the variety of modern mechanisms, knowledge of modern structural materials, the latest methods of calculating machine parts and elements, acquaintance with the influence of the manufacturing technology of parts on their durability, efficiency, etc.

One of the objectives of the course "Machine parts" is to teach methods of designing general-purpose transmission mechanisms.

Most modern machines and devices are created according to the engine - transmission - working body (actuator) scheme. The need to introduce a transmission as an intermediate link between the engine and the working bodies of the machine is associated with the solution of a number of problems.

For example, in cars and other transport vehicles, it is required to change the speed and direction of movement, and on inclines and when starting off, it is necessary to increase the torque on the driving wheels several times. The car engine itself cannot fulfill these requirements, since it operates stably only in a narrow range of changes in the magnitude of the torque and angular velocity. If this range is exceeded, the engine stops. Like a car engine, many other motors are poorly regulated, including most electric ones.

In some cases, regulation of the engine is possible, but it is impractical for economic reasons, since outside the nominal operating mode, the efficiency of the engines is significantly reduced.

The mass and cost of an engine with the same power decrease with an increase in the angular velocity of its shaft. The use of such motors with a gear reducing the angular velocity instead of motors with a low angular velocity without a gear is more economically feasible.

In connection with the widespread use of complex mechanization and automation of production, the importance of gears in machines increases even more. The branching of energy flows and the simultaneous transmission of motion with different parameters to several executive bodies from one source - the engine is required. All this makes transmissions one of the essential elements of most modern machines and installations.

Classification of machine parts

There is no absolute, complete and complete classification of all existing machine parts; their designs are diverse and, moreover, new ones are constantly being developed.

Depending on the complexity of manufacturing, parts are divided into simpleand complex... Simple parts for their manufacture require a small number of already known and well-mastered technological operations and are manufactured in mass production on automatic machines (for example, fasteners - bolts, screws, nuts, washers, cotter pins; gear wheels of small sizes, etc.) ... Complex parts most often have a rather complex configuration, and in their manufacture rather complex technological operations are used and a significant amount of manual labor is used, for which robots are increasingly used in recent years (for example, in the assembly and welding of car bodies).

According to their functional purpose, units and parts are divided into typical groups according to the nature of their use.

- TRANSFERS designed for the transmission and transformation of motion, energy in machines. They are divided into gearing transmissions, transmitting energy through the mutual engagement of teeth (gear, worm and chain), and friction transmissions, transmitting energy through frictional forces caused by the initial tension of the belt (belt drives) or pressing one roller against another (frictional transmissions).

- SHAFTS and AXES. The shafts are used to transmit torque along their axis and to support rotating gear parts (gear wheels, sprocket pulleys) mounted on the shafts. The axles serve to support rotating parts without transmitting useful torques.

- SUPPORTSare used to install shafts and axles.

- BEARINGS. Designed to secure shafts and axles in space. Shafts and axes are left with only one degree of freedom - rotation around their own axis. Bearings are divided into two groups depending on the type of friction in them: a) rolling; b) sliding.

- COUPLINGSare designed to transfer torque from one shaft to another. Couplings are permanent, which do not allow the shafts to be disengaged during machine operation, and clutch, which allow the shafts to be engaged and disengaged.

- CONNECTING PARTS (CONNECTIONS) connect the parts together.

They are of two types:

a) detachable - they can be disassembled without destruction. These include threaded, pin, keyed, slotted, terminal;

b) one-piece - the separation of parts is impossible without their destruction or is associated with the danger of damage. These include welding, gluing, riveting, press connections.

- ELASTIC ELEMENTS. They are used: a) to protect against vibration and shock; b) to perform useful work for a long time by preliminary accumulation or accumulation of energy (springs in a clock); in) to create an interference fit, reverse motion in cam and other mechanisms, etc.

- INERTIAL PARTS AND ELEMENTSare designed to prevent or weaken vibrations (in linear or rotational movements) due to the accumulation and subsequent return of kinetic energy (flywheels, counterweights, pendulums, women, shabots).

- PROTECTIVE PARTS AND SEALS are designed to protect the internal cavities of units and assemblies from the action of adverse environmental factors and from the leakage of lubricants from these cavities (pleviki, oil seals, covers, shirts, etc.).

- HOUSING PARTS are intended for placement and fixation of moving parts of the mechanism, for their protection from adverse environmental factors, as well as for fastening mechanisms as part of machines and assemblies. Often, in addition, body parts are used to store an operational stock of lubricants.

- CONTROL AND CONTROL PARTS AND UNITS are designed to influence units and mechanisms in order to change their operating mode or maintain it at an optimal level (rods, levers, cables, etc.).

- SPECIFIC PARTS. These include devices for contamination protection, lubrication, etc.

The scope of the training course does not allow you to study all varieties of machine parts and all the nuances of design. However, knowledge of at least typical parts and general principles of machine design gives the engineer a solid foundation and a powerful tool for performing design work of almost any complexity.

In the following chapters, we will consider techniques for calculating and designing typical machine parts.

Basic principles and stages of development and design of machines

The process of developing machines has a complex, branched, ambiguous structure and is usually called a broad term. design - creation of a prototype of an object, representing in general terms its main parameters.

Design (according to GOST 22487-77) - the process of compiling a description necessary to create a still non-existent object (an algorithm for its functioning or a process algorithm), by transforming the primary description, optimizing the given characteristics of the object (or its functioning algorithm), eliminating the incorrectness of the primary description and sequential presentation (if necessary) descriptions in different languages. In the conditions of an educational institution (in comparison with the conditionsenterprises), these design stages are somewhat simplified.

Project (from lat. projectus - thrown forward) - a set of documents and descriptions in different languages \u200b\u200b(graphical - drawings, diagrams, diagrams and graphs; mathematical - formulas and calculations; engineering terms and concepts - description texts, explanatory notes), necessary to create any structure or product ...

Engineering design - a process in which scientific and technical information is used to create a new system, device or machine that brings a certain benefit to society.

Design methods:

Direct analytical synthesis methods (developed for a number of simple standard mechanisms);

Heuristic design methods - solving design problems at the level of inventions (for example, an algorithm for solving inventive problems);

Synthesis by methods of analysis - enumeration of possible solutions according to a certain strategy (for example, using a random number generator - the Monte Carlo method) with a comparative analysis on a set of qualitative and operational indicators (optimization methods are often used - minimization of the objective function formulated by the developer that determines the set of qualitative product characteristics);

Computer-aided design systems or CAD - a computer software environment simulates the design object and determines its quality indicators, after a decision is made - the designer chooses the parameters of the object, the system automatically issues design documentation;

Other design methods.

The main stages of the design process.

1. Awareness of the social need for a product being developed.

2. Terms of reference for design (primary description).

3. Analysis of existing technical solutions.

4. Development of a functional diagram.

5. Development of a structural diagram.

6. Metric synthesis of the mechanism (synthesis of the kinematic scheme).

7. Static force calculation.

8. Draft project.

9. Kinetostatic power calculation.

10. Force calculation taking into account friction.

11. Calculation and design of parts and kinematic pairs (strength calculations, balancing, balancing, vibration protection).

Here it is advisable to do the following:

Clarify the service purpose of the assembly unit,

Disassemble the kinematic diagram of the assembly (mechanism), i.e. highlightcomponents of the links of the kinematic chain, specify the followerenergy transfer from the initial link along the kinematic chain tothe final link, select the fixed link (body, rack, etc.), relative to which all other links move, specifythe connection between the links, that is, the type of kinematic pairs, to establish themastic functions of the fixed link and all moving links,

Start designing a site from the most critical linkdetermine its type, highlight its constituent elements, by calculation or constructively determine the main dimensions of the kinematic elementspairs and link elements,

Consecutively design all the links of the knot, performing the prora the processing of their elements,

Sketch the fixed link of a detail,

Clarify the division of each link into parts,

Divide every detail into its constituent elements,

Set the service function (s) and the purpose of eachelement and its relationship with other elements,

Select mating, adjacent and free surfaceseach element of the part,

Establish the final shape of each surface and its pololiving,

Finalize the image of every detail on the imagethe assembly unit.

12. Technical design.

13. Detailed design (development of working drawings of parts, manufacturing and assembly technologies).

14. Manufacturing of prototypes.

15. Tests of prototypes.

16. Technological preparation of serial production.

17. Serial production of the product.

Depending on the needs of the national economy, products are produced in different quantities. The production of products is conventionally divided into single, small batch, medium batch and massive production.

Under single means the manufacture of a product according to the prepared NTD, in a single copy and is not repeated in the future.

The design of machines is carried out in several stages, established by GOST 2.103-68. For singleproduction is:

1. Development of a technical proposal in accordance with GOST 2.118-73.

2. Development of a draft design in accordance with GOST 2.119-73.

3. Development of a technical project in accordance with GOST 2.120-73.

4. Development of documentation for the manufacture of the product.

5. Correction of documentation based on the results of manufacturing and testing of the product.

Design stages at serialproduction is the same, but only the adjustment of the documentation has to be repeated several times: first for a prototype, then for a pilot batch, then according to the results of manufacturing and testing of the first industrial batch.

In any case, starting each stage of design, as well as any work in general, it is necessary to clearly identify three positions:

Initial data - any objects and information related to the case ("what do we have?").

goal - expected results, values, documents, objects ("what do we want to get?").

Means to an end - design techniques, calculation formulas, tools, sources of energy and information, design skills, experience ("what and how to do?").

The activity of a designer-designer becomes meaningful only if there is a customer - a person or organization that needs a product and finances the development.

Theoretically, the customer should draw up and issue to the developer the Terms of Reference - a document in which all the technical, operational and economic parameters of the future product are correctly and clearly indicated. But, fortunately, this does not happen, since the customer is absorbed in his departmental tasks, and, most importantly, does not have sufficient design skills. Thus, the engineer does not remain without work.

The work begins with the fact that the customer and the contractor jointly compose (and sign) Technical task. At the same time, the contractor should receive as much information as possible about the needs, wishes, technical and financial capabilities of the customer, the obligatory, preferred and desirable properties of the future product, the features of its operation, repair conditions, and the possible sales market.

A careful analysis of this information will allow the designer to correctly build the logical chain "Task - Objective - Means" and to carry out the project as efficiently as possible.

Technical task - a list of requirements, conditions, goals, tasks set by the customer in writing, documented and issued to the contractor for design and research work. Such a task usually precedes the development of construction, design projects and is designed to orient the designer to create a project that meets the wishes of the customer and corresponds to the conditions of use, application of the project being developed, as well as resource constraints.

Development of Technical Proposal begins with studying the Terms of Reference. The purpose, the principle of the device and the methods of connecting the main assembly units and parts are clarified. All this is accompanied by the analysis of scientific and technical information about similar structures. Kinematic calculations, design calculations for strength, stiffness, wear resistance and performance criteria are performed. All standard products are preselected from the catalogs - bearings, couplings, etc. The first sketches are being made, which are gradually refined. It is necessary to strive for maximum compactness of arrangement and convenience of assembly and disassembly of parts.

Technical proposal (P) - a set of design documents that must contain technical and feasibility studies for the feasibility of developing product documentation based on an analysis of the customer's technical specifications and various options for possible product solutions, a comparative assessment of solutions taking into account the design and operational features of the developed and existing products and patent research.

On the stage Draft Design refined and verification calculations of parts, product drawings in main projections are carried out, the design of parts is worked out in order to maximize their manufacturability, mating of parts is selected, the possibility of assembly-disassembly and adjustment of units is being worked out, a lubrication and sealing system is selected. The draft design must be reviewed and approved, after which it becomes the basis for the Technical Design. If necessary, product models are made and tested.

Draft project (E) - a set of design documents, which should contain fundamental design solutions that give a general idea of \u200b\u200bthe device and the principle of operation of the product, as well as data that determine the purpose, main parameters and overall dimensions of the product being developed. The draft design after agreement and approval in the prescribed manner serves as the basis for the development of a technical design or working design documentation.

Technical project must necessarily contain a general drawing, a statement of technical design and an explanatory note. A general drawing in accordance with GOST 2.119-73 should provide information about the design, the interaction of the main parts, the operational and technical characteristics and the principles of the product. The Statement of the Technical Design and the Explanatory Note, like all text documents, must contain comprehensive information on the design, manufacture, operation and repair of the product. They are drawn up in strict accordance with the rules and regulations of the ESKD (GOST 2.104-68; 2.105-79; 2.106-68). The technical project, after agreement and approval in the prescribed manner, serves as the basis for the development of working design documentation.

Thus, the project takes on its final form - drawings and an explanatory note with calculations, called working documentation,designed so that they can be used to manufacture a product and control their production and operation.

Detailed design (I) - development of design documentation for a prototype, manufacturing, testing, adjustment based on test results. The final development and approval of drawings of parts and assemblies and other normative and technical documentation for the manufacture and assembly of products for testing.

Manufacturing, testing, fine-tuning and development of a prototype. Development of a prototype device.

Basic concepts are also required here.

Design documents include graphic and text documents that, individually or in combination, determine the composition and structure of a product and contain the necessary data for its development or manufacture, acceptance, operation and repair.

Design documents are divided into:

Originals - documents executed on any material and intended for the execution of originals on them.

Originals - documents executed with genuine established signatures and executed on any material that allows multiple reproduction of copies from them. It is allowed to use the original as the original.

Duplicates - copies of the originals, ensuring the identity of the reproduction of the original, made on any material that allows making copies from them.

Copies- documents executed in a way that ensures their identity with the original.

Technical task - a document drawn up jointly by the customer and the developer, containing a general idea of \u200b\u200bthe purpose, technical characteristics and fundamental structure of the future product.

Technical Proposal - additional or clarified requirements for the product, which could not be specified in the terms of reference (GOST 2.118-73).

Creation - a specific material or spiritual activity that generates something new or a new combination of the known.

Invention - a new solution to a technical problem that has a positive effect.

Sketching - the process of creating a sketch (from French. exquisse – from reflections), a preliminary drawing or sketch that captures the idea and contains the main outlines of the object being created.

Layout - the location of the main parts, assembly units, assemblies, and modules of the future object.

Payment - numerical determination of efforts, stresses and deformations in details, establishing the conditions for their normal operation; performed as needed at each design stage.

Drawing - an accurate graphic representation of an object, containing complete information about its shape, dimensions and basic technical conditions of manufacture.

Assembly drawing - a document containing an image of an assembly unit and other data necessary for its assembly (manufacturing) and control. Assembly drawings also include drawings, according to which hydraulic installation and pneumatic installation are performed.

General view drawing - a document that defines the design of the product, the interaction of its constituent parts and explains the principle of operation of the product.

Theoretical drawing - a document defining the geometric shape (contours) of the product and the coordinates of the location of the component parts.

Outline drawing - a document containing an outline (simplified) image of a product with overall, mounting and connecting dimensions.

Wiring drawing - a document containing the data required for the electrical installation of the product.

Installation drawing - a document containing an outline (simplified) image of the product, as well as the data necessary for its installation (mounting) at the site of use. Installation drawings also include drawings of foundations specially designed for the installation of the product.

Packing drawing - a document containing the data required for packaging the product.

Scheme - a document on which the component parts of the product and the connections between them are shown in the form of conventional images and symbols.

Explanatory note - a text document (GOST 2.102-68) containing a description of the device and the principle of operation of the product, as well as technical characteristics, economic justification, calculations, instructions for preparing the product for operation.

Specification - a textual tabular document defining the composition of an assembly unit, complex or kit (GOST 2.102-68).

Specification Sheet - a document containing a list of all specifications of the component parts of the product with an indication of their quantity and availability.

List of reference documents - a document containing a list of documents that are referenced in the design documents of the product.

List of purchased products - a document containing a list of purchased products used in the product being developed.

i style \u003d "mso-bidi-font-style: normal"\u003e Approval list for purchased products - a document containing a list of purchased products permitted for use in accordance with GOST 2.124-85.

List of original holders - a document containing a list of enterprises (organizations) that store the originals of documents developed and (or) used for this product.

Technical proposal sheet - a document containing a list of documents included in the technical proposal.

Schematic design sheet - a document containing a list of documents included in the draft design

Technical project sheet - a document containing a list of documents included in the technical design.

Technical condition - a document containing requirements (a set of all indicators, norms, rules and regulations) for the product, its manufacture, control, acceptance and delivery, which are inappropriate to indicate in other design documents.

Test program and methodology - a document containing technical data to be verified during product testing, as well as the procedure and methods for their control.

Table - a document containing, depending on its purpose, the corresponding data, summarized in a table.

Payment - a document containing calculations of parameters and quantities, for example, calculation of dimensional chains, strength calculation, etc.

Repair documents - documents containing data for carrying out repair work at specialized enterprises.

Instructions - a document containing instructions and rules used in the manufacture of the product (assembly, adjustment, control, acceptance, etc.).

Operational document - a design document that, individually or in combination with other documents, defines the rules for the operation of the product and reflects information that certifies the values \u200b\u200bof the main parameters and characteristics (properties) of the product guaranteed by the manufacturer, guarantees and information on its operation during the specified service life.

Operational documents of products are intended for operation and familiarization with their design, study of operating rules (intended use, maintenance, routine repair, storage and transportation), reflection of information confirming the values \u200b\u200bof the main parameters and characteristics of the product guaranteed by the manufacturer, guarantees and information on its operation for the entire period, as well as information on its disposal.

Preliminary design - the first stage of design (GOST 2.119-73), when fundamental design and circuit solutions are established that give general ideas about the device and operation of the product.

A draft design is usually developed in several versions withdetailed computational analysis, as a result of which a variant is selected for further development.

At this design stage, a kinematic calculation is performed.drive, calculation of gears with sketched layouttheir details, reflecting the fundamental design solutions andgiving a general idea of \u200b\u200bthe device and principle of operationof the designed product. It follows from the above that the calculations are necessarydimo perform with simultaneous drawing of the product design,since many dimensions are required for the calculation (distances betweenshaft supports, places of application of loads, etc.), can only be obtainedfrom the drawing. At the same time, the step-by-step drawing of the structure in the calculation process is a check of this calculation. Wrongthe result of the calculation is manifested in violation of proportionality part design when performing a sketched product layout.

First design calculations at the stage of draft designperform, as a rule, simplified and approximate. Graduatedcalculation is a check for a given (already planned)product design.

Many dimensions of the elements of the part during the design are not calculatedmelt, but accept in accordance with the experience of designing similarstructures generalized in standards and normative referencedocuments, textbooks, reference books, etc.

The draft design, after approval, serves as the basis for developmenttechnical design or working design documentation.

Technical project - the final design stage (GOST 2.120-73), when the final technical solutions are identified that give a complete picture of the product.

The technical design after approval serves as the basis fordevelopment of working documentation.

Development of working documentation - final stage of the projecttirovanie necessary for the manufacture of all unnormalizedparts, as well as for registration of an application for the purchase of standardproducts.

In an educational institution, the scope of work at this stage of design is usually established by the decision of the department and is indicated in the technicalcom task. When designing a drive, working documentation is usuallyincludes a drawing of its general view or outline drawing, assembly gearbox drawing, working drawings of the main parts (shaft, wheel,sprockets or pulleys, etc.)

Any machine, mechanism or device consists of separate parts that are combined into assembly units.

A part is called a part of a machine, the manufacture of which does not require assembly operations. In terms of their geometric shape, the parts can be simple (nuts, keys, etc.) or complex (body parts, machine beds, etc.).

An assembly unit (node) is a product, the components of which are to be connected together by screwing, welding, riveting, gluing, etc. The parts that make up individual assembly units are connected to each other movably or motionlessly.

Of the wide variety of parts used in machines for various purposes, one can single out those that are found in almost all machines. These parts (bolts, shafts, gear parts, etc.) are called general parts and are the subject of the Machine Parts course.

Other parts that are specific to a particular type of machine (pistons, turbine blades, propellers, etc.) are called special parts and are studied in the corresponding special disciplines.

The Machine Parts course sets out the general requirements for the design of machine parts. These requirements must be taken into account three design and manufacture of different machines.

The perfection of the design of machine parts is assessed by their performance and efficiency. Performance combines requirements such as strength, stiffness, wear resistance and heat resistance. Efficiency is determined by the cost of the machine or its individual parts and operating costs. Therefore, the main requirements that ensure economic efficiency are the minimum weight, simplicity of design, high manufacturability, use of non-scarce materials, high mechanical efficiency and compliance with standards.

In addition, the course "Machine Parts" provides recommendations on the choice of materials for the manufacture of machine parts. The choice of materials depends on the purpose of the machine, the purpose of the parts, the methods of their manufacture and a number of other factors. The correct choice of material greatly affects the quality of the part and the machine as a whole.

Connections of parts in machines are divided into two main groups - movable and fixed. Movable joints are used to provide relative rotational, translational or complex movement of parts. Fixed joints are designed for rigid fastening of parts to each other or for installing machines on bases and foundations. Fixed connections can be detachable and one-piece.

Detachable connections (bolted, keyed, toothed, etc.) allow multiple assembly and disassembly without destroying the connecting parts.

One-piece joints (riveted, welded, glued, etc.) can only be disassembled by destroying the connecting elements - rivets, weld, etc.

Consider detachable connections.

For mechanical and engineering specialties

Made up

ph.D., Assoc. Eremeev V.K.

Irkutsk 2008

INTRODUCTION

The present lecture notes for the course "Machine parts" should be considered as a summary of the programmatic issues of the course, facilitating the assimilation of educational material and preparation for exams. The abstract is presented on the basis of the main textbooks of D.N. Reshetov,

M.I. Ivanova, P.G. Guzenkov "Machine parts" and the methodological manual of V.K. Eremeeva and Yu.N. Gornova “Machine parts. Course design ". The use of a synopsis in no way excludes training from textbooks, but only highlights the main provisions corresponding to the course "Machine parts" in engineering and mechanical specialties. In a number of places in the synopsis, instructions are given to those questions that need to be prepared only from textbooks, since, due to the brevity of the presentation, they were not included in the synopsis. This mainly concerns the descriptive side of the course and the design features of individual units and machine parts.

The abstract is designed for an abbreviated program - 70 lecture hours, so it did not include such sections of the course as: riveted joints, wedge joints and special types of gears. It is assumed that students can familiarize themselves with these questions on their own. The presentation of the educational material in the synopsis corresponds to the program of the course "Machine parts" and the content of examination tickets. The order of presentation of individual sections has been slightly changed in comparison with the main textbooks on the experience of teaching the subject by the author of this synopsis and with the aim of the possibility of early preparation of students in practical classes for the beginning of course design.

"Machine parts" is the first of the calculation and design courses, in which they studydesign basics machines and mechanismsmov.

Any machine (mechanism) consists of parts.

Detail - a part of the machine that is manufactured without assembly operations. Parts can be simple (nut, key, etc.), or complex (crankshaft, gear housing, machine bed, etc.). Parts (partially or completely) are combined into nodes.

Node- is a complete assembly unit consisting of a number of parts that have a common functional purpose (rolling bearing, coupling, gearbox, etc.). Complex nodes can include several simple nodes (subnodes); for example, a gearbox includes bearings, shafts with gear wheels mounted on them, etc.

Among the wide variety of parts and components of machines, there are those that are used in almost all machines (bolts, shafts, couplings, mechanical transmissions, etc.). These parts (nodes) are called detailgeneral purpose andstudy in the course "Machine parts". All other parts used only in one or several types of machines (pistons, turbine blades, propellers, etc.) are classified as special-purpose parts and are studied in special courses.

General-purpose parts are used in mechanical engineering in very large quantities (for example, in the USSR, until 1992, about a billion gear wheels were produced annually). Therefore, any improvement in the methods of calculation and design of these parts, which makes it possible to reduce material costs, lower production costs, and increase durability, brings a great economic effect.

Basic requirements for the design of machine parts.

The design perfection of the part is judged by herreliability and efficiency . Reliability is understood as property of a product to keep in timetheir efficiency.Efficiency is determined by the cost of the material, the cost of production and operation.

The main criteria for the performance and calculation of machine parts: strength, rigidity, wear resistance, heat resistance, vibrationstability.The value of this or that criterion for a given part depends on its functional purpose and working conditions. For example, for fastening screws, the main criterion is strength, and for lead screws, wear resistance. When designing parts, their performance is mainly ensured by the choice of an appropriate material, a rational design form and the calculation of dimensions according to one or more criteria.

Strength pain is the main criterion for performanceof details.Fragile parts cannot work. It should be remembered that damage to machine parts not only leads to downtime, but also to accidents.

Distinguish between the destruction of parts due to loss staticstrength or fatigue resistance.Loss of static strength occurs when the value of the working stresses exceeds the static strength of the material (for example, σ in ). This is usually associated with random overloads that were not taken into account in the calculations, or with hidden defects in parts (shells, cracks, etc.). Loss of fatigue resistance occurs as a result of prolonged exposure to alternating stresses that exceed the material's fatigue limit (for example, σ -1 ). Fatigue resistance is significantly reduced in the presence of stress concentrators associated with the structural shape of the part (fillets, grooves, etc.) or with manufacturing defects (scratches, cracks, etc.).

The basics of strength calculations are taught in the course on resistance of materials. In the machine parts course, general strength calculation methods are considered in application to specific parts and shaped. engineering calculations.

Rigidity characterized by a change in the size and shape of the part under load.

The stiffness analysis provides for limiting the elastic displacements of parts within the limits permissible for specific operating conditions. Such conditions can be: operating conditions of mating parts (for example, the quality of gearing of gear wheels and operating conditions of bearings deteriorate with large deflections of the shafts); technological conditions (for example, the accuracy and productivity of machining on metal-cutting machines are largely determined by the rigidity of the machine and the workpiece).

Rigidity standards for parts are established based on operating practice and calculations. The value of stiffness calculations is increasing due to the widespread introduction of high-strength steels, in which the strength characteristics (σ in and σ -1) increase, and the elastic modulus

E (stiffness characteristic) remains almost unchanged. In this case, cases are more common when the dimensions obtained from the calculation of strength are insufficient in rigidity.

Wear - the process of gradual resizing of parts as a result of friction. At the same time, the clearances in the bearings, in the guides, in the gearing, in the cylinders of piston machines, etc. increase. An increase in the clearances reduces the quality characteristics of mechanisms: power, efficiency, reliability, accuracy, etc. Parts worn out more than normal , rejected and replaced during repair. Untimely repairs lead to a breakdown of the machine, and in some cases to an accident.

Wear rate and part life depend on pressure, sliding speed, coefficient of friction and wear resistance of the material. To reduce wear, lubrication of rubbing surfaces and protection from contamination are widely used, antifriction materials, special types of chemical-thermal surface treatment, etc. are used.

It should be noted that wear and tear destroys a large number of machine parts. It significantly increases the cost of operation, necessitating periodic repairs. The high cost of repairs is due to the significant costs of manual, highly skilled labor, which is difficult to mechanize and automate. For many types of machines, over the entire period of their operation, the costs of repair and maintenance due to wear are several times higher than the cost of a new machine. The wear resistance of machine parts is significantly reduced in the presence of corrosion. Corrosion is the cause of premature failure of many machines. Due to corrosion, up to 10% of the smelted metal is lost annually. To protect against corrosion, anti-corrosion coatings are used or parts are made of special corrosion-resistant materials. At the same time, special attention is paid to parts operating in the presence of water, steam, acids, alkalis and other aggressive media.

Heat resistance ... Heating of machine parts can cause the following harmful consequences: lowering the strength of the material and the appearance of creep; a decrease in the protective ability of oil films and, consequently, an increase in the wear of parts; change in clearances in mating parts, which can lead to seizure or jamming; Decrease in the accuracy of the machine (for example, precision machines).

In order to prevent the harmful effects of overheating on the operation of the machine, thermal calculations are performed and, if necessary, appropriate design changes are made (for example, artificial cooling).

Vibration resistance . Vibrations cause additional alternating stresses and, as a rule, lead to fatigue failure of parts. In some cases, vibrations reduce the quality of the machines. For example, vibrations in machine tools reduce machining accuracy and degrade the surface quality of the workpiece. Resonant vibrations are especially dangerous. The harmful effect of vibrations is also manifested due to an increase in the noise characteristics of mechanisms.In connection with an increase in the speed of movement of machines, the danger of vibrations increases, therefore, calculations for vibrations are becoming increasingly important.

Features of the calculation of machine parts. In order to compose a mathematical description of the object of calculation and, if possible, simply solve the problem, in engineering calculations, real structures are replaced by idealized models or calculation schemes. For example, in strength calculations, a substantially discontinuous and inhomogeneous material of parts is considered to be continuous and homogeneous, and supports, loads and the shape of parts are idealized. Wherein the calculation becomes approximate,In approximate calculations, the correct choice of the design scheme, the ability to assess the main and discard secondary factors, is of great importance.

The errors of approximate calculations are significantly reduced when using the experience of designing and operating similar structures. As a result of the generalization of previous experience, norms and recommendations are developed, for example, the norms of permissible stresses or safety factors, recommendations for the choice of materials, design load, etc. These norms and recommendations are attached to the calculation of specific details in the relevant sections of this lecture notes. Here we note that inaccuracies in calculationsstrength is compensated mainly by safety margins.Wherein the choice of safety factors becomes veryresponsible stage of the calculation.An underestimated value of the safety factor leads to the destruction of the part, and an overestimated value leads to an unjustified increase in the mass of the product and an overuse of material. In conditions of a large volume of production of general-purpose parts, the overrun of material becomes very significant.

The factors affecting the safety margin are numerous and varied: the degree of responsibility of the part, the homogeneity of the material and the reliability of its tests, the accuracy of the calculation formulas and determination of the design loads, the influence of the quality of technology, operating conditions, etc. Taking into account all the variety of operating conditions of modern machines and parts, as well as the methods of their production, then great difficulties in separate quantitative assessment of the influence of the listed factors on the value of safety margins will become obvious. Therefore, in each branch of mechanical engineering, based on their experience, they develop their own safety standards for specific parts. Safety margins are not stable. They are periodically adjusted as experience is gained and the level of technology increases.

In engineering practice, there are two types of calculation - design and verification.

Design calculation - preliminary, simplified calculation performed in the process of developing the design of a part (machine) in order to determine its dimensions and material.

Verification payment - an updated calculation of a known structure, carried out in order to check its strength or determine the load norms.

In design calculations, the number of unknowns usually exceeds the number of design equations. Therefore, some unknown parameters are set, taking into account experience and recommendations, and some secondary parameters are simply not taken into account. Such a simplified calculation is necessary to determine those dimensions, without which the first drafting study of the structure is impossible. In the design process, the calculation and drawing design of the structure is performed in parallel. In this case, a number of dimensions required for the calculation are determined by the designer according to the sketch drawing, and the design calculation takes the form of a check for the intended structure. In search of the best design option, you often have to perform several design options. In difficult cases, search calculations are conveniently performed on a computer. The fact that the designer himself chooses the design schemes, safety margins and unnecessary unknown parameters, leads to ambiguity of engineering calculations, andhence, the operability of structures.Each design reflects the designer's creativity, knowledge and experience. The most advanced solutions are being implemented.

Calculated loads. When calculating machine parts, the design and nominal load are distinguished. Design load such as torque T,defined as the product of the rated torque T n on the dynamic load factor K * T \u003d T n *TO.

The nominal torque corresponds to the nameplate (design) power of the machine. Coefficient TOtakes into account additional dynamic loads associated mainly with uneven movement, starting and braking. The value of this factor depends on the type of motor, drive and driven machine. If the operating mode of the machine, its elastic characteristics and mass are known, then the value TOcan be determined by calculation. In other cases, the value TOchoose based on recommendations. Such recommendations are made on the basis of experimental research and operating experience of various machines.

When calculating some mechanisms, additional load factors are introduced, taking into account the specific features of these mechanisms, see, for example, gear drives, Ch. 4.

The choice of materials for machine parts is a critical design stage. Correctly selected material largely determines the quality of the part and the machine as a whole. In presenting this issue, it is assumed that the students know basic information about the properties of machine-building materials and methods of their production from courses in materials science, materials technology, and strength of materials.

When choosing a material, the following factors are mainly taken into account: compliance of material properties with the main criterion of performance (strength, wear resistance, etc.); requirements for the mass and dimensions of the part and the machine as a whole; other requirements related to the purpose of the part and the conditions of its operation (anti-corrosion resistance, frictional properties, electrical insulating properties, etc.); conformity of the technological properties of the material to the structural form and the intended method of processing the part (stamping, weldability, casting properties, machinability, etc.); cost and scarcity of material.

Black metals , subdivided into cast irons and steels are the most widespread. This is primarily due to their high strength and rigidity, as well as their relatively low cost. The main disadvantages of ferrous metals are their high density and poor corrosion resistance.

Non-ferrous metals - copper, zinc, lead, tin, aluminum and some others - are mainly used as components of alloys (bronzes, brasses, babbits, duralumin, etc.). These metals are much more expensive than ferrous ones and are used to fulfill special requirements: lightness, antifriction, anti-corrosion, etc.

Non-metallic materials - wood, rubber, leather, asbestos, cermets and plastics are also widely used.

Plastics and Composites - relatively new, but already well mastered by production, the use of which in mechanical engineering is increasingly expanding. The modern development of the chemistry of high-molecular compounds makes it possible to obtain materials that have valuable properties: lightness, strength, heat and electrical insulation, resistance against the action of aggressive media, frictional or antifrictional properties, etc.

Plastics are technologically advanced. They have good casting properties and are easily processed by plastic deformation at relatively low temperatures and pressures. This makes it possible to obtain articles of almost any complex shape from plastics using high-performance methods: injection molding, stamping, drawing or blowing. Another advantage of plastics and composites is the combination of lightness and high strength. According to this indicator, some of their types can compete with the best grades of steel and duralumin. The high specific strength allows the use of these materials in structures, the weight reduction of which is of particular importance.

The main consumers of plastics are currently the electrical, radio and chemical industries. Here, housings, panels, pads, insulators, tanks, pipes and other parts that are exposed to acids, alkalis, etc. are made from plastics. pads, bushings, handwheels, handles ...

The technical and economic efficiency of the use of plastics and composite materials in mechanical engineering is determined mainly by a significant reduction in the mass of machines and an increase in their performance, as well as the economy of non-ferrous metals and steels. Replacing metal with plastics significantly reduces the labor intensity and cost of engineering products. When replacing ferrous metals with plastics, the labor intensity of manufacturing parts decreases by an average of 5. .6 times, and the cost price - 2.. .6 times. When plastics replace non-ferrous metals, the cost is reduced by 4.. .10 times.

Powder materials obtained by method powder metallurgy,the essence of which consists in the manufacture of parts from metal powders by pressing and subsequent sintering in molds. Powders are used that are homogeneous or from a mixture of various metals, as well as from a mixture of metals with non-metallic materials, such as graphite. This produces materials with different mechanical and physical properties (for example, high-strength, wear-resistant, antifriction, etc.).

In mechanical engineering, the most widespread are parts based on iron powder. Powder metallurgy parts do not require post-cutting, which is very effective in mass production. In the conditions of modern mass production, the development of powder metallurgy is greatly influenced.

Using probabilistic calculation methods.

The foundations of probability theory are studied in special sections of mathematics. In the course of machine parts, probabilistic calculations are used in two forms: they take tabular values \u200b\u200bof physical quantities calculated with a given probability (such quantities include, for example, the mechanical characteristics of materials σ in, σ_ 1, hardness Hand others, the service life of rolling bearings, etc.); take into account the given probability of deviation of linear dimensions when determining the calculated values \u200b\u200bof clearances and tightness, for example, in the calculation of joints with an interference fit and clearances in plain bearings in the regime of fluid friction.

It was found that deviations of hole diameters D and shafts d obey the normal distribution law (Gauss's law). In this case, to determine the probability gaps S p and tightness N p dependencies obtained:

Sp min - max \u003d,
,

where the upper and lower signs refer to the minimum and maximum clearance or interference, S \u003d 0.5 (S min + S max), N \u003d 0.5 (Nmin + N max), respectively; tolerances T D = ES- EJ and T d \u003d es-ei ; ES, es-upper, a EJ, ei-lower limit deviations of dimensions.

Coefficient C depends on the accepted probability Rensuring that the actual value of the gap or interference is within the range S P min ... S P max or N P min ... N P max:

P ……… .. 0.99 0.99 0.98 0.97 0.95 0.99

C ……… 0.5 0.39 0.34 0.31 0.27 0.21

In fig. presents a graphical representation of the parameters of the formula for an interference fit. Here f(D) and f(d) density
probability distributions of random variables D and d. Shaded sections of curves that are not taken into account as unlikely in calculations with the accepted probability R.

The use of probabilistic calculations can significantly increase the permissible loads with a low probability of failure. In conditions of mass production, this gives a great economic effect.

Machine reliability.

The following reliability indicators are adopted:

Reliability indicators

Probability of uptime - the probability that, within a given operating time, a failure will not occur.

Mean time to failure Is the mathematical expectation of the operating time to failure of a non-recoverable product.

Mean time between failures - the ratio of the operating time of the restored object to the mathematical expectation of the number of its failures during this operating time.

Failure rate - an indicator of the reliability of non-recoverable products, equal to the ratio of the average number of failed objects per unit time to the number of objects that remained operational.

Failure flow parameter - an indicator of the reliability of recoverable products, equal to the ratio of the average number of failures of the recoverable object for its arbitrary small operating time to the value of this operating time (corresponds to the failure rate for non-repairable products, but includes repeated failures).

Durability indicators

Technical resource (resource) - the operating time of the object from the beginning of its operation or resumption of operation after repair to the limiting state of operability. The resource is expressed in units of operating time (usually in hours), or travel distance (in kilometers), or in the number of units of production.

Life time - calendar operating time to the limit state of operability (in years).

Indicators of maintainability and preservation

Average recovery time to operational state.

The likelihood of recovery to an operational state at a given time.

Shelf life: average andγ - percentage.

Complex indicators (for complex machines and production lines.)

There are three periods on which reliability depends: design, production, operation.

When designing the foundations of reliability are laid.Poorly thought out, unfinished designs are never reliable. The designer must reflect in the calculations, drawings, specifications and other technical documentation all factors that ensure reliability.

In production all means of exceeding reliability are providedness laid down by the designer.Deviations from design documentation compromise reliability. In order to eliminate the influence of manufacturing defects, all products must be carefully controlled.

During operation product reliability is realized.Reliability concepts such as reliability and durability,appear only during the operation of the machine and depend on the methods and conditions of its operation, the adopted repair system, maintenance methods, operating modes, etc.

The underlying reasons for reliability contain elements of chance. There are random deviations from the nominal values \u200b\u200bof material strength characteristics, nominal dimensions of parts and other indicators that depend on the quality of production; random deviations from the design modes of operation, etc. Therefore, to describe reliability, the theory of probability is used.

Reliability is assessed by the probability of maintaining for a given service life . Loss of performance is called rejection . If, for example, the probability of failure-free operation of a product for 1000 hours is 0.99, this means that out of a large number of such products, for example, out of 100, one percent or one product will lose its performance before 1000 hours . The probability of no-failure (or reliability factor) for our example is equal to the ratio of the number of reliable products to the number of products under observation:

P (t) \u003d 99/100 \u003d 0.99.

The value of the reliability factor depends on the observation period t, which is included in the designation of the coefficient. Have a worn out car R(t) less than that of a new one (except for the running-in period, which is considered separately).

The reliability factor of a complex product is expressed by the product of the reliability factors of the constituent elements:

P(t)= P 1 (t) P 2 (t)... P n (t).

Analyzing this formula, the following can be noted;

- the reliability of a complex system is always less than the reliability of theunreliable element, therefore it is importantdo not allow anyweak element.

- the more elements a system has, the less its reliability.If, for example, the system includes 100 elements with the same reliability R p (t) \u003d 0.99, then reliability P (t) \u003d 0.99 100 0.37. Such a system, of course, cannot be recognized as workable, since it is idle more than it works. This makes it possible to understand why the problem of reliability has become especially relevant in the modern period of development of technology along the way of creating complex automatic systems. It is known that many such systems (automatic lines, rockets, airplanes, mathematical machines, etc.) include tens and hundreds of thousands of elements. If these systems do not provide sufficient reliability for each element, then they become unusable or ineffective.

Reliability is studied by an independent branch of science and technology.

The following are the main ways to improve reliability at the design stage, which are of general importance for the study of this course.

1. From the previous it is clear that a reasonable approach to obtaining high reliability consists of in designing as simple as possibleproducts with fewer parts.Each part must be provided with a sufficiently high reliability equal to or close to the reliability of the other parts.

2. One of the simplest and most effective measures to improve reliability is to reduce the stress of parts (increase safety margins). However, this requirement of reliability is in conflict with the requirements for reducing the size, weight and cost of products. To reconcile these conflicting claims rational use of high-strength materials and reinforcingtechnology:alloyed steels, thermal and chemical-thermal treatment, surfacing of hard and antifriction alloys on the surface of parts, surface hardening by shot blasting or rolling with rollers and

etc. So, for example, by means of heat treatment it is possible to increase the load capacity of gears by 2 - 4 times. Chrome plating of the crankshaft journals of automobile engines increases the wear life by 3 - 5 and more times. Shot-peening hardening of gears, springs, springs, etc. increases the fatigue life of the material by 2-3 times.

An effective measure to improve reliability is goodlubrication system:the correct choice of oil grade, a rational system for supplying lubricant to the rubbing surfaces, protection of the rubbing surfaces from abrasive particles (dust and dirt) by placing products in closed cases, installing effective seals, etc.

Statically defined systems are more reliable.These systems are less likely to have the detrimental effect of manufacturing defects on load distribution.

If the operating conditions are such that accidental overloads are possible, then the design should include protecttel devices(safety clutches or overcurrent relays).

Extensive use of standard assemblies and parts,as well as standard structural elements (threads, fillets, etc.) increases reliability. This is due to the fact that standards are developed on the basis of extensive experience, and standard units and parts are manufactured in specialized factories with automated production. This improves the quality and uniformity of the products.

7. In some products, mainly in electronic equipment, to improve reliability, not sequential, but parallel connection of elements and the so-called redundancy.When the elements are connected in parallel, the reliability of the system is significantly increased, since the function of the failed element is assumed by the parallel or backup element. In mechanical engineering, parallel connection of elements and redundancy are rarely used, since in most cases they lead to a significant increase in the mass, dimensions and cost of products.A justified use of a parallel connection can be aircraft with two and four engines. An aircraft with four engines does not tolerate accidents when one or even two engines fail.

8. For many machines, maintainability.The ratio of repair downtime to working time is one of the indicators of reliability. The design should provide easy accessibility to components and parts for inspection or replacement. Replacement parts must be interchangeable withspare parts.In the design, it is desirable to highlight the so-called repair units. Replacing a damaged unit with a prepared one significantly reduces the repair downtime of the machine.

These factors allow us to conclude that the reliabilityis one of the main indicators of product quality. On hopethe quality of the product can be judged by the quality of the designwork, production and operation.

Introduction

Goals and objectives of the course "Machine parts", its relationship with other subjects

0.1. The course "Machine parts" is the final section of the discipline "Technical Mechanics", studied in secondary specialized educational institutions. The Machine Parts course is the link between general technical and special disciplines. Within the limits stipulated by the curriculum and program, this course studies the basics of calculating the strength and stiffness of general-purpose machine parts, the choice of materials, the design of parts, taking into account the manufacturing technology and operation of machines. Theoretical knowledge is reinforced by a course project.

What subjects is the Machine Parts course based on?

0.2. The proposed tutorial examines the theoretical foundations of the calculation and design of parts and assembly units (assemblies) of general purpose. The studied parts and general-purpose units are divided into three main groups:

Details of connections (bolts, studs, screws, etc.);

Mechanical transmissions (gear, worm, screw-nuts, chain, belt, friction, etc.);

Parts and gear units (shafts, bearings, couplings, etc.).

Parts and assemblies that are found only in special types of machines are called special-purpose parts and assemblies (valves, pistons, connecting rods, machine tool spindles, etc.); they are studied in special courses (Internal Combustion Engines, Metal-Cutting Machines, etc.).

Taking into account the previously studied general technical disciplines, give a definition of what a detail is.

0.3. A machine is a mechanical device designed to perform the required useful work associated with the production or transportation process, or with the process of converting energy or information.

The machine is assembled from mechanisms, parts and assemblies. From the answer to the question posed in step 0.2 (see page 17), you know what is called a part.

Mechanismis called a system of movably connected bodies, designed to transform the motion of one or more bodies into expedient movements of other bodies (for example, a crank-slider mechanism, mechanical transmissions, etc.).

A node is an assembly unit that can be assembled separately from the product as a whole,performing a specific function in products of the same purpose only in conjunction with other component parts of the product (couplings, rolling bearings, etc.).

By the nature of the work process and the purpose of the machine, it can be divided into three classes:

I class - engine machines,converting one or another type of energy into mechanical work (internal combustion engines, turbines, etc.);

Class II - converting machines(generators), converting mechanical energy (received from a machine-engine) into another type of energy (for example, electric machines - current generators);

III class - machine-tools(working machines) that use mechanical energy received from a machine-engine to perform a technological process associated with changing the properties, state and shape of the object being processed (metalworking machines, agricultural machines, etc.), as well as machines designed to perform transport operations (conveyors, cranes, pumps, etc.). This class also includes machines that partially replace human intellectual activity (for example, computers).

By the nature of the work process and purpose, to what class can such machines as a compressor, an electric motor, a press belong?

The main directions in the development of mechanical engineering. Requirements for the designed machines, units and parts

When designing new and modernizing old machines, assemblies and parts, it is necessary to take into account the latest achievements in the field of science and technology.

0.4 . Requirements for the designed machines:

Increase in power with the same overall dimensions;

Increased speed and performance;

Increasing the efficiency (efficiency);

Automation of machine operation;

Use of standard parts and typical assemblies;

Minimum weight and low manufacturing cost. Examples of implementing the requirements of step 0.4 in mechanical engineering.

1. The capacity of one electric generator of the Volkhovskaya power plant, built in 1927, is 8000 kW, the Krasnoyarsk (1967) - 508,000 kW, ie, an increase of 63 times.

2. Compare the speed of aircraft of the forties with the speed of a modern supersonic airliner.

3. In railway transport, steam locomotives, which had a low efficiency, were replaced by diesel and electric locomotives, the efficiency of which is many times higher.

4. Comprehensive automation becomes the basis for the organization of all sectors of the national economy. Automatic factories for the production of rolling bearings have been created; control of technological processes and production management are mechanized and automated.

5. Any machine (mechanism) consists of standard parts and assemblies (bolts, screws, couplings, etc.), which simplifies and reduces the cost of manufacturing.

0.5. The main requirementswhich parts and assemblies of machines must satisfy are:

Strength (see step 0.6 for details);

Wear resistance (see step 0.8);

Hardness (see step 0.7);

Heat resistance (see step 0.9);

Vibration resistance (see step 0.10).

Additional requirements:

Corrosion resistance. To protect against corrosion, parts are made of corrosion-resistant steel, non-ferrous metals and alloys based on them, bimetals - metallic materials consisting of two layers (for example, steel and non-ferrous metal), and various coatings are used (anodizing, nickel plating, chrome plating , tinning, enameling and coating with paints);

Reduced weight of parts. In aircraft construction and some other industries, the fulfillment of this requirement is one of the main computational and design tasks;

Use of non-scarce and cheap materials. This condition should be the subject of special attention in all cases when designing machine parts. It is necessary to save non-ferrous metals and alloys based on them;

Ease of manufacture and manufacturability of parts and assemblies should be the subject of every possible attention;

Ease of use. When designing, it is necessary to strive so that individual nodes and parts can be removed or replaced without disrupting the connection of adjacent nodes. All lubrication devices must operate flawlessly and seals must be oil-tight. Moving parts that are not enclosed in the machine body must have guards for the safety of the operating personnel;

Transportability of machines, assemblies and parts, i.e. the possibility and convenience, their transportation and transportation. For example, electric motors and gearboxes must have an eyebolt on the housing, by which they are lifted when moving. Large parts, hydraulic turbine housings, stators of large electric current generators are made from separate parts at the manufacturing site, and assembled into one whole at the installation site;

Standardization is of great economic importance, as it provides high quality products, interchangeability of parts and allows assembly under conditions of mass production;

The beauty of forms. The design of units and parts that define the external outlines of the machine must be beautiful and meet the requirements of artistic construction (design). Forms of external parts are developed with the participation of designers to create an attractive appearance. Colors for painting are specially selected;

The economy of the design is determined by the wide use of standard and unified parts and assemblies, a thoughtful choice of materials, and the design of parts taking into account the technological capabilities of the enterprise that manufactures them.

List the requirements for the design of parts and assemblies of machines (write in the summary).

Specify the sequence of the verification calculation.

Check card 0.1

Question	Answer	The code
Specify general machine parts	Rotor Piston Lathe Chuck Valve General purpose parts not listed
From the listed parts, name the parts that belong to the part-connection group	Couplings Keys Rivets Bearings Shafts
List the main criteria for the performance of general-purpose parts	Strength Rigidity Durability Heat resistance Vibration resistance
What is the name of the calculation that determines the actual characteristics (parameters) of the part	Design Calculation Check Calculation
Determine in a tabular way the permissible safety factor (part material - high-strength steel)	1,5-2,2 2,0-3,5 1,5-1,7

Answers on questions

0.1. The course "Machine parts" is based on the subjects: mathematics, physics, chemistry, technology of structural metals, theoretical mechanics, resistance of materials, interchangeability, standardization and technical measurements, drawing.

0.2. A part is a product made of a homogeneous material, made without the use of assembly operations (sometimes a part is called a separate, non-disassembled elementary part of a machine, made of several elements connected by welding, riveting, etc.).

0.3. By the nature of the working process and purpose, the compressor can be classified as class II, the electric motor in class I, and the press in class III.

0.5 ... Strength of parts, rigidity, durability, heat resistance, vibration resistance, corrosion resistance, weight reduction of parts, use of non-scarce materials, ease of manufacture and manufacturability of design, ease of use, transportability of parts, aesthetics and cost-effectiveness.

0.6. Strength is understood as the ability of the material of a part in certain conditions and limits, without collapsing, to perceive certain influences (to resist destruction or the occurrence of plastic deformations under the action of loads applied to it).

0.7. The stiffness condition of the part: the arising (working) elastic displacements (deflections, angles of rotation of cross-sections, etc.) in the parts under the action of working loads must be less than or equal to the permissible ones.

0.8. Wear is a change in the size, shape, mass or condition of the surface of parts due to the destruction (wear) of the surface layer during friction. Good lubrication, increased hardness, coatings, correct selection of mate pair materials and other measures will reduce wear.

0.9. The bearing capacity of the part will decrease, the appearance of permanent deformations, etc., is possible; the liquid lubrication regime will be disrupted and the wear of parts will increase; the gaps in the mating rubbing parts will decrease, and therefore parts may jam, and, consequently, their failure, a decrease in accuracy.

0.10. In metal-cutting machines, vibrations reduce machining accuracy and degrade the surface quality of the workpiece.

0.12. According to the formula (0.4), the working tensile stress arising in the round bar is determined, and comparing it with the permissible stress. for a given material, make a conclusion about the strength. For known dimensions of the part (according to the calculated page), select the material from the table. Formula (0.4) - for checking calculation.

0.13. Ultimate stress (endurance limit) depends on the material of the part, the type of stress state and the nature of the stress change over time. The endurance limit also depends on the structural form of the part, its size, the aggressiveness of the environment, etc. (the state of the surface, hardening processing).

When stresses occur in the part that are variable over time.

0.14. For steel castings (second case of loading): [s] \u003d 1.7 ÷ 2.2 (see Table 0.1).

0.15. When choosing a material for a designed part, they usually proceed from the following basic requirements:

Operational - the material must meet the working conditions of the part;

Technological - the material must satisfy the possibility of manufacturing a part for the selected technological process;

Economic - the material should be beneficial in terms of the cost of the part.

PART I

MECHANICAL GEARS

Chapter 1

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2.3. {!LANG-e684dd01af62f362f866bf460e13403e!} {!LANG-842282d0c2e41a252c202e036538059e!}{!LANG-76a4de8c10d049db1d5fe559dad1d324!}

2.5. {!LANG-1538bb34daaac1934a93610566515f68!}

2.7. {!LANG-2e7ab0de43e9e0ad615159f1b197fc8a!} {!LANG-a8fdf4aee4f35c9fb69c210500291365!}{!LANG-146978f098a18bae1c238df28b227b77!} {!LANG-152b61337f9d459683f4c4519b55ecbd!}{!LANG-996b6927370955a5cf8ae0156822f79c!}

2.8 {!LANG-df001770f043b207f0a05448c312e02c!}

2.9. {!LANG-ea9dacea4dc8c4b920a5d5ecc6da1e52!} 2, {!LANG-131331db3326f9f261138aed854d6bc9!}

{!LANG-8a93e8250871a79a62bf775e611114f8!} 3 {!LANG-24ee9bfb590a4c640862fff902d79e4d!} 2 {!LANG-d1697d5905bd9722438d697db00ab72d!}

2.11 {!LANG-4d862f9d9d62f19caf71f8302118344b!} {!LANG-d7e7758fe461000ea141fc68c8075bc5!}{!LANG-cfa7a9383da32dc0119db0c0f78e4621!}

2.14. {!LANG-8cca4218c3f0e8d5dc750b261777f4f5!} {!LANG-5cd9906cf164c53fe758955cd42d5fd0!}{!LANG-ad0f278bbfb36a2de9040ced1bcdd131!} {!LANG-5e48fa6cc2ae4f953008939e1b38274b!}{!LANG-8bc17abff0364b8e2102186b3e4f70e0!} {!LANG-a8fdf4aee4f35c9fb69c210500291365!}{!LANG-75f5f2290c557d025c7824c1b1876794!} {!LANG-6325b04aa4fa8057506ddfee7df94363!}

2.15. {!LANG-4ed4f3a0e384cc3920e4ab95786b6ab8!} {!LANG-173ec2b4464549b118eaaf3debeb70f6!}{!LANG-aaf420f20328d6de98ac4bc4314f4532!} {!LANG-d6eb8a82dc93fce82deee66683d61ce3!}{!LANG-57e5327664660289ad297ad5b91e977d!} {!LANG-2083544da8e7d556654af3eac18440b5!}

2.16. {!LANG-c4b58b6c90205aabdb527a7fb3d3cffd!}

2.18. {!LANG-a25485a16013b57c58dd5a104da9f314!} {!LANG-acc99e98f76c1997a8ad7eb19e1db4d2!}

2.19. {!LANG-5761a274431c451bbea13d87a81a724e!}

2.22. {!LANG-36091bb7ce7fa10eb09fcc2254a90762!} 2 {!LANG-b25c715b19fff13ffcf5c2d52091e381!} {!LANG-a8fdf4aee4f35c9fb69c210500291365!}{!LANG-de501e95a686e8d56900727ada0dd5af!} {!LANG-498e10c1f4c5c9c4ed40d9bec410d416!}{!LANG-698a2ad6684d32c0f630833bcda41293!}

2.24. {!LANG-89fd0b316cb77e8973cf4cfc467094ec!} {!LANG-498e10c1f4c5c9c4ed40d9bec410d416!}{!LANG-882df3f980612588ceb0cf419168ffc9!}

2.25. {!LANG-089a2c0f7d8e20daaab05e1111ca1059!} .

2.26. {!LANG-cbd745fabbb147a95448387791080c18!}

{!LANG-900d71a124b310d382837ab75e05d921!}

2.27. {!LANG-f18cbd188ef8bce916155499ecad840b!} 4 {!LANG-1ee8c80357647b5ba75fcb202b4150b7!} 3, {!LANG-48d79807ce26dfe7f1b7923e9d79645c!} and{!LANG-3ee998e7c301d2805bc764c4ff0be883!}

2.28. {!LANG-b36dbc7dc692098576831ed6afa83ac9!} 3 {!LANG-7889c3425b05180ef10afa2ce881096c!} {!LANG-597822466cda1c6d4f67c339fd4aa6ca!}{!LANG-34cc4087e06c2851fe7440eccb7595c7!} {!LANG-de87bae2a4109541a7e42a3ee247ecf5!}{!LANG-659f62ce1ebb9861e0631a3e01bbc743!} .

{!LANG-e5b8843f768f099f49aa421856a52acb!} {!LANG-4bfb6432d7bb214319efc6d48e31988d!}< {!LANG-16e7a6e18aedb09c408034880f15742d!}

{!LANG-22e7021150c01dd7f388cd2b5fcdef6d!}

{!LANG-61f695e98e08612d38db1f1c3ec9b8a9!}

{!LANG-eb5c5cb080be49b726e22eae719e2a97!}

Question	{!LANG-b4bf50479836a26fb4006b5d89c42f89!}	The code
{!LANG-e375c1c61876a9441b633a7117b77ece!}	{!LANG-eb29566ced8e9fd85f4128b0e9613a76!}
{!LANG-60185de9af03031252c5a1e081f5a205!}	{!LANG-e113665cc1c61c8a34f365e123b5b4a3!}
{!LANG-5f9af5bdb402643a3556082a7b0a5acb!}	{!LANG-024a4a59c9654072239ce80a62e3778d!}
{!LANG-e4910817e816830d676b461247efca6f!}	{!LANG-008b1094aab43dc62d3e734388d71a40!}
{!LANG-41c1ff97786d1fb2da0a55974ba412c3!}	{!LANG-a1754f78c68e0c6125cd1a60c1d81375!}

{!LANG-fb33c2ce137b4b2604a6717838b662e5!}

3.12. {!LANG-4d3725b9fc58b0748aa51eb67904275a!} {!LANG-431e44acf4d3468f4feba73f51f09dec!}{!LANG-5f382eed8f16fce662ad0e979dd11dc2!} {!LANG-3abe7366ee33f8d303ad96d2cddccdc9!}{!LANG-4554849a574a3a9560afdc01042d866a!}

{!LANG-1563a9ec66e3142ca6945be5aa713f3e!}

{!LANG-8c30dd1fbd252f28bf477af242d5cb99!}{!LANG-c7ac4acd8192cb7b122c2d5b983f98a9!}

{!LANG-770d4ce9053bfb8909c341aa512dfc33!}{!LANG-02e1d2a741f9dccd11dbf56b4c71a010!}

{!LANG-69944ba89b059df73e0d4f3760ec18fc!}{!LANG-d0c0c217327bb3c2df441ee61c39f7e8!}

d{!LANG-6af2e486fb052bcc13fdef5f2cfa80c9!}

{!LANG-cf9a2cec0f661ae70b64ef89b5f4c61d!}{!LANG-496f91833bee45db0a8471329fb845eb!}

{!LANG-01fbdc44ef819db6273bc30965a23814!}{!LANG-0be2145669516ae4814a97fb591bcac6!}

{!LANG-6494a79a10630bc3d659f48b2c05bc09!}{!LANG-70515af676eb52b03b4230e5163063fb!}

{!LANG-3c02438beb1e30ea50235cf6d2f903d8!}

{!LANG-3b5d5c3712955042212316173ccf37be!}{!LANG-2e301ea32b967ba4b715dfe18a03b857!}

{!LANG-bf717517d011d76e4cb521af3a29df98!}{!LANG-f2b53a937089b92b4483b39f6029b09d!}

{!LANG-3aa03fafdd27e9ee8d280c7dcd8f36cc!}{!LANG-19251b8f055be3b19197c9fb29a2fa99!}

{!LANG-5fd959ada1ea922584f7f8339d01d86c!}{!LANG-af116f006e27709980d1bcc49989fa96!}

{!LANG-4d6e8fbe640c83e860a1b550ae3f64e0!}{!LANG-63f3012eba04b0bf754c7933eb4e038e!}

{!LANG-41ff0912a07fdc52799ff27b38e7f140!}{!LANG-a2e772c3e45bb6f7b8f40a8f838a0654!}

{!LANG-d0315507352ffcd16c5352dde8ba8c2b!}

{!LANG-16d2e45f182b1654ce3b04503d1cacaa!}

{!LANG-0a42a1bb1c3affbd5d1ea14a9f357568!}{!LANG-2f15f0578db4ade19edaa9f32c1917cc!}

{!LANG-25c579d73745962bb2059e8a13ac4583!}

{!LANG-cf93beab4a3620ac972d75a9f110a9ad!}

{!LANG-e38b8f5bb418d33de794ea0aa5d7cd07!}

{!LANG-957a7441176af1baf96ac3de4ebe2692!} {!LANG-0f43cf58fe9397c72d8a0af071c28e34!}{!LANG-e2fffd22ab1e93212745f16d09adf777!}

{!LANG-6e37a9df0b7ba39864ca59c11304f39e!} 1. {!LANG-810abfa7bac691b422d5dde661e25af9!}

{!LANG-d076ca4830c756e65420e5dffaababcd!}	{!LANG-a68db4d386d8cf3e766e1c7457edd210!}	{!LANG-d076ca4830c756e65420e5dffaababcd!}	{!LANG-a68db4d386d8cf3e766e1c7457edd210!}	{!LANG-d076ca4830c756e65420e5dffaababcd!}	{!LANG-a68db4d386d8cf3e766e1c7457edd210!}	{!LANG-d076ca4830c756e65420e5dffaababcd!}	{!LANG-a68db4d386d8cf3e766e1c7457edd210!}
	1,125		3,5
1,25	1,375		4,5
1,5	1,75		5,5
	2,25
2,5	2,75	8.

{!LANG-fef671c5608ca196f3d7186cc0b30d75!}{!LANG-5e61071c589755b2d6feeddf07c0ee29!}

{!LANG-e78127b86b5109cf9356de55ad684080!}

Question	{!LANG-b4bf50479836a26fb4006b5d89c42f89!}	The code
{!LANG-1e95ce58e33fb9246076d3b6fe9bb1c0!}	{!LANG-58d8c469515633fb167e539947d61980!}
{!LANG-e055c6d416d53df271ecb7fc1b577b35!}	{!LANG-bbeedb6b6e856ddb45fe2edc4d1ca23a!}
{!LANG-f7f82f73b9da546121f6b11fc9c0d817!}	{!LANG-4a5c5026c0faa2dac84803e287e258e9!}
{!LANG-7dd450fe72df44b9ffaf88be4d189a5a!}	{!LANG-fc5f82128ef79b2621c113059f8a7a52!}
{!LANG-79b6953a8fd4ab072e072c1cb8221cbb!}	{!LANG-eccb70955b98b5f931b2ba844ab879ec!}

{!LANG-15d536c7e6f6f8ad16e2deb0e1761cf8!}

{!LANG-32ba2f96028df4ce5d0816b83648f78e!}

Question	{!LANG-2b6a2f2d7c54b6dbd162af7592fd5d06!}	{!LANG-21cd96a9bfd173db6d7fdf204a54a9cf!}
{!LANG-9b2aaf012d5ce151c6d34504777309cc!}	{!LANG-c38f73e6a0d2394d8e5f5aa1bb3bc62b!} {!LANG-5cf6b7a26bd75c492acdd292b74bade1!}{!LANG-7b3e00dec9fba83830da874aef598c92!}
{!LANG-e3c4d1695c46c7f26537e4913afa3af4!}	{!LANG-735e4c740b941317d2d71d60ffceecc1!} {!LANG-b238bc9f5c020a4dd3e507639a60b72a!}{!LANG-8da566b72a590e49cd1248aa728ef56a!} {!LANG-8844c201a79992c37c3ec73fa3d736d0!}{!LANG-7f58966fb816fbabbdb300b082cfca7e!}
{!LANG-8be7ae050406b943f27b37e751422187!}	{!LANG-bb8bbbe90cc6aa4039c4d9f08b516d6f!}
{!LANG-cf79b20eff4de4cc0c07510433119c47!}	{!LANG-8c31810b5ce213be82bd7e2294349a3b!}
{!LANG-37f704506c13ba90de9a1a850efe3ca3!}	{!LANG-3382764791ac11345c6637a2484e35b1!}

{!LANG-37f9106bbda73fd336e370f3ae038a16!}