Fundamentals of performance of technical systems of road transport. Basic concepts in the field of operability of technical systems

20.06.2020

Salon

Ministry of Education and Science of the Russian Federation

Saratov State Technical University

A.S. Denisov

Fundamentals of operability of technical systems

Textbook

Approved by the UMO of universities of the Russian Federation for education

in the field of transport vehicles

and transport and technological complexes

as a textbook for university students,

students in specialties

"Service of transport and technological

machinery and equipment (Automobile

transport)" and "Automobiles and automotive

economy” areas of training

"Operation of land transport

and transport equipment"

Saratov 2011

UDC 629.113.004.67

Reviewers:

Department "Reliability and repair of machines"

Saratov State Agrarian University

them. N.I. Vavilov

Doctor of Technical Sciences, Professor

B.P. Zagorodsky

Denisov A.S.

D 34 The basis of the performance of technical systems: Textbook / A.S. Denisov. - Saratov: Sarat. state tech. un-t, 2011. - 334 p.

ISBN 978-5-7433-2105-6

The textbook provides data on the content of various technical systems. The elements of the mechanics of destruction of machine parts are analyzed. The laws of wear, fatigue failure, corrosion, plastic deformation of parts during operation are substantiated. Methods for substantiating the standards for ensuring the operability of machines and adjusting them according to operating conditions are considered. Regularities of satisfaction of service needs are substantiated using the provisions of the queuing theory.

The textbook is intended for students of the specialties "Service of transport and technological machines and equipment (Motor transport)" and "Automobiles and automotive economy", and can also be used by employees of car service, car repair and motor transport enterprises.

UDC 629.113.004.67

ISBN 978-5-7433-2105-6 Technical University, 2011

Denisov Alexander Sergeevich - Doctor of Technical Sciences, Professor, Head of the Department "Automobiles and Automotive Industry" of the Saratov State Technical University.

In 2001 he received the academic title of professor, in 2004 he was elected an academician of the Academy of Transport of Russia.

Scientific activity of Denisov A.S. is devoted to the development of the theoretical foundations of the technical operation of vehicles, the substantiation of the system of patterns of changes in the technical condition and indicators of the efficiency of the use of vehicles during operation in various conditions. He developed new methods for diagnosing the technical condition of vehicle elements, monitoring and controlling their operating modes. Theoretical developments and experimental studies Denisova A.S. contributed to the foundation and approval of a new scientific direction in the science of machine reliability, which is now known as the “Theory of the formation of resource-saving maintenance and repair cycles of machines”.

Denisov A.S. has more than 400 publications, including: 16 monographs and manuals, 20 patents, 75 articles in central journals. Under his scientific guidance, 3 doctoral and 21 master's theses were prepared and successfully defended. At the Saratov State Technical University Denisov A.S. created a scientific school developing the theory of machine service, which is already well known in the country and abroad. Awarded with badges of honor "Honorary Worker of Transport of Russia", "Honorary Worker of Higher Professional Education of the Russian Federation".

INTRODUCTION

Technique (from the Greek word techne - art, skill) is a set of means of human activity created to carry out production processes and meet the non-productive needs of society. Technology includes the whole variety of created complexes and products, machines and mechanisms, industrial buildings and structures, instruments and assemblies, tools and communications, devices and devices.

The term "system" (from the Greek systema - a whole made up of parts) has a wide range of meanings. In science and technology, a system is a set of elements, concepts, norms with relationships and connections between them, forming a certain integrity. An element of a system is understood as a part of it, designed to perform certain functions and indivisible into parts at a given level of consideration.

This paper considers a part of technical systems - transport and technological machines. The main attention is paid to cars and technological auto service equipment. Over the entire service life, the costs of ensuring their performance are 5 to 8 times higher than the costs of manufacturing. The basis for reducing these costs are the patterns of changes in the technical condition of machines during operation. Up to 25% of failures of technical systems are caused by errors of maintenance personnel, and up to 90% of accidents in transport, in various power systems are the result of erroneous actions of people.

The actions of people, as a rule, are justified by the decisions they make, which are selected from several alternatives based on the information collected and analyzed. Information analysis is based on knowledge of the processes occurring when using technical systems. Therefore, when training specialists, it is necessary to study the patterns of changes in the technical condition of machines during operation and methods for ensuring their performance.

This work was prepared in accordance with the educational standard for the discipline "Fundamentals of the performance of technical systems" for the specialty 23100 - Service of transport and technological machines and equipment (road transport). It can also be used by students of the specialty "Automobiles and automotive economy" when studying the discipline "Technical operation of vehicles", specialty 311300 "Mechanization of agriculture" in the discipline "Technical operation of vehicles".

BASIC CONCEPTS IN THE FIELD OF PERFORMANCE OF TECHNICAL SYSTEMS

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MINISTRY OF EDUCATION AND SCIENCE OF THE RUSSIAN FEDERATION

FEDERAL STATE BUDGET EDUCATIONAL

INSTITUTION OF HIGHER EDUCATION

"SAMARA STATE TECHNICAL UNIVERSITY"

Faculty Correspondence

Department of Transport Processes and Technological Complexes

COURSE PROJECT

by academic discipline

"Fundamentals of the performance of technical systems"

Completed:

N.D. Tsygankov

Checked:

O.M. Batishcheva

Samara 2017

ABSTRACT

The explanatory note contains: 26 printed pages, 3 figures, 5 tables, 1 application and 7 references.

CAR, LADA GRANT 2190, REAR SUSPENSION, UNIT DESIGN ANALYSIS, STRUCTURING OF FACTORS INFLUENCING THE UNIT PERFORMANCE DECREASE, THE CONCEPT OF INPUT CONTROL, DETERMINATION OF SAMPLE PARAMETERS, DETERMINATION OF THE PERCENTAGE OF DEFECTIVE IN PART AI.

The purpose of this work is to study the factors influencing the decrease in the performance of technical systems, as well as to gain knowledge about the quantitative assessment of marriage based on the results of input control.

Works on the study of theoretical material, as well as work with real details and samples of the systems under study, have been completed. Based on the results of the input control, a number of tasks were performed: the distribution law, the percentage of rejects and the volume of the sample set of products were determined to ensure the specified control accuracy.

INTRODUCTION

1. ANALYSIS OF FACTORS INFLUENCING THE DECREASE IN THE PERFORMANCE OF TECHNICAL SYSTEMS

1.1 Rear suspension design

1.2 Factor structuring

1.3 Analysis of factors affecting the rear suspension of the Lada Grant 2190

1.4 Analysis of the influence of processes on the change in the state of the elements of the rear suspension of the Lada Grants

RESULTS OF INPUT CONTROL

2.1 The concept of input control, basic formulas

2.2 Check for gross error

2.3 Determining the number of intervals by splitting the control setpoints

2.4 Building a histogram

2.5 Determination of the percentage of defects in the lot

CONCLUSION

LIST OF USED SOURCES

INTRODUCTION

In order to effectively manage the processes of changing the technical condition of machines and justify measures aimed at reducing the intensity of wear of machine parts, it is necessary to determine the type of surface wear in each specific case. To do this, it is necessary to set the following characteristics: type of relative displacement of surfaces (friction contact scheme); the nature of the intermediate medium (type of lubricant or working fluid); main wear mechanism.

According to the type of intermediate medium, wear is distinguished during friction without lubricant, during friction with a lubricant, during friction with an abrasive material. Depending on the properties of the materials of parts, lubricant or abrasive material, as well as on their quantitative ratio in interfaces, various types of surface destruction occur during operation.

In real conditions of operation of machine interfaces, several types of wear are observed simultaneously. However, as a rule, it is possible to establish the leading type of wear, which limits the durability of parts, and to separate it from the other, accompanying types of surface destruction, which insignificantly affect the performance of the interface. The mechanism of the main type of wear is determined by studying worn surfaces. Observing the nature of the manifestation of wear of friction surfaces (presence of scratches, cracks, traces of chipping, destruction of the oxide film) and knowing the properties of the materials of parts and lubricant, as well as data on the presence and nature of the abrasive, wear intensity and the mode of operation of the interface, it is possible to fully substantiate the conclusion on the type of interface wear and develop measures to improve the durability of the machine.

1. ANALYSIS OF FACTORS INFLUENCING THE REDUCTION OF WORKABOUTCAPACITY OF TECHNICAL SYSTEMS

1.1 Rear suspension design

The suspension provides an elastic connection between the body and the wheels, softening shocks and shocks when the car moves over uneven roads. Thanks to its presence, the durability of the car increases, and the driver and passengers feel comfortable. The suspension has a positive effect on the stability and controllability of the car, its smoothness. On a Lada Granta car, the rear suspension repeats the design of previous generations of LADA cars - the VAZ-2108 family, the VAZ-2110 family, Kalina and Priora. The rear suspension of the car is semi-independent, made on an elastic beam with trailing arms, coil springs and double-acting telescopic shock absorbers. The rear suspension beam consists of two trailing arms connected by a U-shaped cross member. Such a section provides the connector (crossbar) with greater bending rigidity and less torsional rigidity. The connector allows the levers to move relative to each other within a small range. The levers are made of a tube of variable cross-section, which gives them the necessary rigidity. Brackets are welded to the rear end of each lever for attaching a shock absorber, a rear brake shield and a wheel hub axle. At the front, the beam levers are bolted to the removable brackets of the body side members. The mobility of the levers is provided by rubber-metal hinges (silent blocks) pressed into the front ends of the levers. The lower eye of the shock absorber is attached to the beam arm bracket. The shock absorber is attached to the body by a rod with a nut. The elasticity of the upper and lower connections of the shock absorber is provided by the pillows of the rod and the rubber-metal bushing pressed into the eye. The shock absorber rod is covered with a corrugated casing that protects it from dirt and moisture. In the event of suspension breakdowns, the shock absorber stroke is limited by a compression stroke buffer made of elastic plastic. The suspension spring, with its lower coil, rests on the support cup (stamped steel plate welded to the shock absorber body), and with its upper coil rests against the body through a rubber gasket. The axle of the rear wheel hub is mounted on the flange of the beam lever (it is fastened with four bolts). The hub with a double-row roller bearing pressed into it is held on the axle by a special nut. The nut has an annular collar, which securely locks the nut by jamming it into the axis groove. The hub bearing is of a closed type and does not require adjustment and lubrication during vehicle operation. Rear suspension springs are divided into two classes: A - more rigid, B - less rigid. Class A springs are marked with brown paint, class B - blue. Springs of the same class must be installed on the right and left sides of the vehicle. Springs of the same class are installed in the front and rear suspension. In exceptional cases, it is allowed to install class B springs in the rear suspension if class A springs are installed in the front suspension. The installation of class A springs on the rear suspension is not allowed if class B springs are installed in the front suspension.

Fig. 1 Rear suspension Lada Grant 2190

1.2 Factor structuring

During the operation of the car, as a result of the impact on it of a number of factors (impact of loads, vibrations, moisture, air flows, abrasive particles when dust and dirt get on the car, temperature effects, etc.), an irreversible deterioration of its technical condition occurs due to wear and damage to its parts, as well as a change in a number of their properties (elasticity, plasticity, etc.).

The change in the technical condition of the car is due to the operation of its components and mechanisms, the influence of external conditions and storage of the car, as well as random factors. Random factors include hidden defects in car parts, structural overload, etc.

The main permanent causes of changes in the technical condition of the vehicle during its operation were wear, plastic deformation, fatigue failure, corrosion, as well as physical and chemical changes in the material of parts (aging).

Wear is the process of destruction and separation of material from the surfaces of parts and (or) the accumulation of residual deformations during their friction, which manifests itself in a gradual change in the size and (or) shape of the interacting parts.

Wear is the result of the wear process of parts, which is expressed in a change in their size, shape, volume and mass.

Distinguish between dry and liquid friction. With dry friction, the rubbing surfaces of parts interact directly with each other (for example, the friction of brake pads on brake drums or discs, or the friction of a clutch disc on a flywheel). This type of friction is accompanied by increased wear of the rubbing surfaces of parts. With liquid (or hydrodynamic) friction between the rubbing surfaces of the parts, an oil layer is created that exceeds the microroughness of their surfaces and does not allow their direct contact (for example, crankshaft bearings during steady state operation), which dramatically reduces wear on parts. In practice, during the operation of most automobile mechanisms, the above main types of friction constantly alternate and pass into each other, forming intermediate types.

The main types of wear are abrasive, oxidative, fatigue, erosive, as well as wear by seizing, fretting and fretting corrosion.

Abrasive wear is a consequence of the cutting or scratching effect of solid abrasive particles (dust, sand) trapped between the rubbing surfaces of mating parts. Getting between the rubbing parts of open friction units (for example, between brake pads and discs or drums, between leaf springs, etc.), hard abrasive particles sharply increase their wear. In closed mechanisms (for example, in the crank mechanism of the engine), this type of friction manifests itself to a much lesser extent and is the result of abrasive particles getting into the lubricants and the accumulation of wear products in them (for example, when the oil filter and oil in the engine are not replaced in time, when untimely replacement of damaged protective covers and grease in swivel joints, etc.).

Oxidative wear occurs as a result of exposure to the rubbing surfaces of mating parts of an aggressive environment, under the influence of which fragile oxide films are formed on them, which are removed during friction, and the exposed surfaces are oxidized again. This type of wear is observed on the parts of the cylinder-piston group of the engine, parts of the hydraulic brake and clutch cylinders.

Fatigue wear consists in the fact that the hard surface layer of the material of the part becomes brittle as a result of friction and cyclic loads and collapses (crumbles), exposing the less hard and worn layer underlying it. This type of wear occurs on the raceways of rolling bearing rings, gear teeth and gear wheels.

Erosion wear occurs as a result of exposure of the surfaces of parts to liquid and (or) gas flows moving at high speed, with abrasive particles contained in them, as well as electrical discharges. Depending on the nature of the erosion process and the predominant effect on the details of certain particles (gas, liquid, abrasive), gas, cavitation, abrasive and electrical erosion are distinguished.

Gas erosion consists in the destruction of the material of a part under the action of mechanical and thermal effects of gas molecules. Gas erosion is observed on valves, piston rings and the mirror of the engine cylinders, as well as on parts of the exhaust system.

Cavitation erosion of parts occurs when the continuity of the liquid flow is violated, when air bubbles are formed, which, bursting near the surface of the part, lead to numerous hydraulic shocks of the liquid against the metal surface and its destruction. Engine parts that come into contact with the coolant are susceptible to such damage: the internal cavities of the cylinder block cooling jacket, the outer surfaces of the cylinder liners, and the cooling system pipes.

Electroerosive wear is manifested in the erosion wear of the surfaces of parts as a result of the action of discharges during the passage of electronic current, for example, between the electrodes of spark plugs or breaker contacts.

Abrasive erosion occurs when the surfaces of parts are mechanically affected by abrasive particles contained in liquid flows (hydroabrasive erosion) and (or) gas (gaseous erosion), and is most typical for external car body parts (wheel arches, bottom, etc.). Jamming wear occurs as a result of seizing, deep pulling out of the material of the parts and transferring it from one surface to another, which leads to the appearance of scuffs on the working surfaces of the parts, to their jamming and destruction. Such wear occurs when local contacts occur between rubbing surfaces, on which, due to excessive loads and speed, as well as lack of lubrication, the oil film breaks, strong heating and “welding” of metal particles occur. A typical example is jamming of the crankshaft and rotation of the liners in case of malfunction of the engine lubrication system. Fretting wear is the mechanical wear of parts in contact with small oscillatory movements. If at the same time, under the influence of an aggressive environment, oxidative processes occur on the surfaces of mating parts, then wear occurs during fretting corrosion. Such wear can occur, for example, at the points of contact between the crankshaft journals and their beds in the cylinder block and bearing caps.

Plastic deformations and destruction of car parts are associated with the achievement or excess of the yield or strength limits, respectively, for ductile (steel) or brittle (cast iron) materials of parts. These damages are usually the result of a violation of the rules of operation of the car (overloading, mismanagement, as well as a traffic accident). Sometimes plastic deformations of parts are preceded by their wear, which leads to a change in geometric dimensions and a decrease in the safety margin of the part.

Fatigue failure of parts occurs under cyclic loads that exceed the endurance limit of the metal of the part. In this case, gradual formation and growth of fatigue cracks occur, leading to the destruction of the part at a certain number of load cycles. Such damage occurs, for example, at springs and axle shafts during long-term operation of the vehicle in extreme conditions (long-term overloads, low or high temperatures).

Corrosion occurs on the surfaces of parts as a result of chemical or electrochemical interaction of the material of the part with an aggressive environment, leading to oxidation (rusting) of the metal and, as a result, to a decrease in strength and deterioration in the appearance of parts. Salts used on the roads in winter, as well as exhaust gases, have the strongest corrosive effect on car parts. The retention of moisture on metal surfaces strongly contributes to corrosion, which is especially characteristic of hidden cavities and niches.

Aging is a change in the physical and chemical properties of materials of parts and operating materials during operation and during storage of a car or its parts under the influence of the external environment (heating or cooling, humidity, solar radiation). So, as a result of aging, rubber products lose their elasticity and crack, fuels, oils and operating fluids experience oxidative processes that change their chemical composition and lead to a deterioration in their performance properties.

The change in the technical condition of the car is significantly influenced by the operating conditions: road conditions (technical category of the road, type and quality of the road surface, slopes, uphill slopes, curvature radii of the road), traffic conditions (heavy city traffic, traffic on country roads), climatic conditions ( ambient temperature, humidity, wind loads, solar radiation), seasonal conditions (dust in summer, dirt and moisture in autumn and spring), aggressiveness of the environment (sea air, salt on the road in winter, which increase corrosion), as well as transport conditions ( vehicle loading).

The main measures that reduce the rate of wear of parts during vehicle operation are: timely control and replacement of protective covers, as well as replacement or cleaning of filters (air, oil, fuel) that prevent abrasive particles from entering the rubbing surfaces of parts; timely and high-quality performance of fastening, adjusting (adjustment of valves and engine chain tension, wheel alignment angles, wheel bearings, etc.) and lubrication (replacement and topping up of oil in the engine, gearbox, rear axle, replacement and addition of oil to the hubs wheels, etc.) works; timely restoration of the protective coating of the bottom of the body, as well as the installation of fender liner protecting the wheel arches.

To reduce corrosion of car parts and, first of all, the body, it is necessary to maintain their cleanliness, timely care for the paintwork and its restoration, and perform anti-corrosion treatment of body cavities and other parts subject to corrosion.

Serviceable is the condition of the car, in which it meets all the requirements of regulatory and technical documentation. If the car does not meet at least one requirement of the regulatory and technical documentation, then it is considered faulty.

A working state is such a state of the car, in which it meets only those requirements that characterize its ability to perform the specified (transport) functions, i.e., the car is operable if it can carry passengers and goods without a threat to traffic safety. A serviceable vehicle may be faulty, for example, have low oil pressure in the engine lubrication system, deteriorated appearance, etc. If the vehicle does not meet at least one of the requirements characterizing its ability to perform transport work, it is considered inoperable.

The transition of the car to a faulty, but operable state is called damage (violation of the serviceable state), and to an inoperable state is called a failure (violation of the operable state). operability wear deformation part

The limiting state of a car is a state in which its further use for its intended purpose is unacceptable, economically inexpedient, or restoring its serviceability or performance is impossible or impractical. Thus, the car goes into the limit state when unrecoverable violations of safety requirements appear, the costs of its operation unacceptably increase, or an unrecoverable output of technical characteristics beyond acceptable limits occurs, as well as an unacceptable decrease in operating efficiency.

The adaptability of the car to withstand the processes that occur as a result of the above harmful environmental influences when the car performs its functions, as well as its fitness to restore its original properties, is determined and quantified using indicators of its reliability.

Reliability is the property of an object, including a car or its component parts, to maintain in time within the established limits the value of all parameters characterizing the ability to perform the required functions in given modes and conditions of use, maintenance, repairs, storage and transportation. Reliability as a property characterizes and allows quantifying, firstly, the current technical condition of the vehicle and its components, and secondly, how quickly their technical condition changes when operating under certain operating conditions.

Reliability is a complex property of a car and its components and includes the properties of reliability, durability, maintainability and storability.

1.3 Analysis of factors affecting the rear suspension of the Lada Grant 2190

Consider the factors that affect the decrease in the performance of the car.

Malfunctions and breakdowns can be with any car, especially with regard to the suspension. This is due to the fact that the suspension tolerates constant vibration during movement, softens shocks, and takes the entire weight of the car, including passengers and luggage, on itself. Based on this, the Grant in the liftback body is more prone to breakage than the sedan, since the liftback body has a larger luggage compartment, designed for more weight. The first problem most often encountered is the presence of knocking or extraneous noise. In this case, it is necessary to check the shock absorbers, as they need to be replaced in a timely manner, and can often fail. Also, the cause may be not fully tightened shock absorber mounting bolts. Also, with a strong impact, not only the bushings, but also the racks themselves can be damaged. Then the repair will be more serious and expensive. The last reason for suspension knocking may be a broken spring. (Fig. 2) In addition to knocking, you need to check the suspension mechanism for drips. If such traces are found, then this can only indicate one thing - a malfunction of the shock absorbers. If all the liquid flows out and the shock absorber dries, then when it hits the hole, the suspension will offer poor resistance, and the vibration from the impact will be very strong. The solution to this problem is quite simple - replace the worn element. The last malfunction that occurs on the Grant is when braking or accelerating, the car leads to the side. This indicates that on this side, one or two shock absorbers are worn out and sag a little more than the rest. Because of this, the body is overweight.

1.4 Analysis of the influence of processes on the change in the state of the elements of the rear suspension of the Lada Grants

To prevent accidents on the road, it is necessary to timely diagnose the car in general and critical components in particular. The best and qualified place to find a faulty rear suspension is a car service. You can also assess the technical condition of the suspension yourself while the car is moving. When driving at low speed on uneven roads, the suspension should work without knocks, squeaks and other extraneous sounds. After driving over an obstacle, the vehicle must not sway.

Checking the suspension is best combined with checking the condition of the tires and wheel bearings. One-sided wear of the tire tread indicates deformation of the rear suspension beam.

In this section, the influencing factors on the decrease in vehicle performance were considered and analyzed. The influence of factors leads to the loss of performance of the unit and the vehicle as a whole, so it is necessary to take preventive measures to reduce the factors. After all, abrasive wear is a consequence of the cutting or scratching effect of solid abrasive particles (dust, sand) trapped between the rubbing surfaces of mating parts. Getting between the rubbing parts of open friction units, hard abrasive particles sharply increase their wear.

Also, to prevent damage and increase the life of the rear suspension, you should strictly follow the rules for operating the car, avoiding its operation in extreme conditions and with overloads, this will extend the life of critical parts.

2. QUANTITATIVE ASSESSMENT OF MARRIAGE IN THE LOTS OF RERESULTS OF INPUT CONTROL

2.1 The concept of input control, basic formulas

Quality control refers to the verification of the conformity of the quantitative or qualitative characteristics of a product or process, on which product quality depends, to established technical requirements.

Product quality control is an integral part of the production process and is aimed at checking the reliability in the process of its manufacture, consumption or operation.

The essence of product quality control at the enterprise is to obtain information about the state of the object and compare the results obtained with the established requirements recorded in the drawings, standards, supply contracts, technical specifications.

Control involves checking products at the very beginning of the production process and during the period of operational maintenance, ensuring, in case of deviation from the regulated quality requirements, the adoption of corrective measures aimed at the production of products of good quality, proper maintenance during operation and full satisfaction of customer requirements.

Incoming product quality control should be understood as quality control of products intended for use in the manufacture, repair or operation of products.

The main tasks of input control can be:

Obtaining with high reliability an assessment of the quality of products presented for control;

Ensuring the unambiguity of mutual recognition of the results of product quality assessment carried out according to the same methods and according to the same control plans;

Establishing the compliance of product quality with established requirements in order to timely submit claims to suppliers, as well as for operational work with suppliers to ensure the required level of product quality;

Prevention of launching into production or repair of products that do not meet the established requirements, as well as authorization protocols in accordance with GOST 2.124.

Quality control is one of the main functions in the quality management process. This is also the most voluminous function in terms of applied methods, which is the subject of a large number of works in various fields of knowledge. The value of control lies in the fact that it allows you to detect errors in time, so that you can quickly correct them with minimal losses.

Incoming product quality control refers to the control of products received by the consumer and intended for use in the manufacture, repair or operation of products.

Its main goal is to exclude defects and conformity of products to the established values.

When conducting input control, plans and procedures for conducting statistical acceptance control of product quality on an alternative basis are used.

The methods and means used in the input control are selected taking into account the requirements for the accuracy of measuring the quality indicators of the controlled products. The departments of material and technical supply, external cooperation, together with the department of technical control, technical and legal services, form the requirements for the quality and range of products supplied under contracts with supplier enterprises.

For any randomly selected product, it is impossible to determine in advance whether it will be reliable. Of the two engines of the same brand, failures may soon occur in one, and the second will be serviceable for a long time.

In this part of the course project, we will determine the quantitative assessment of marriage in the batch based on the results of the input control using a spreadsheet Microsoft Excel. A table is given with the values of time to first failure due to the release of Lada Grant 2190 (Table 1), this table will be the initial data for calculating the percentage of rejects and the volume of the sample number of products.

Table 2 Time to first failure

2.2 Gross error check

Gross error (miss) - this is the error of the result of a single measurement included in a series of measurements, which for given conditions differs sharply from the rest of the results of this series. The source of gross errors can be abrupt changes in measurement conditions and errors made by the researcher. These include a breakdown of the instrument or a shock, incorrect reading on the scale of the measuring instrument, incorrect recording of the observation result, chaotic changes in the parameters of the voltage supplying the measuring instrument, etc. Misses are immediately visible among the results obtained, because. they are very different from other values. The presence of a miss can greatly distort the result of the experiment. But the thoughtless rejection of measurements that are sharply different from other results can also lead to a significant distortion of the measurement characteristics. Therefore, the initial processing of experimental data recommends that any set of measurements be checked for the presence of gross misses using the "three sigma" statistical test.

The "three sigma" criterion is applied to the results of measurements distributed according to the normal law. This criterion is reliable for the number of measurements n>20…50. The arithmetic mean and standard deviation are calculated without taking into account extreme (suspicious) values. In this case, a gross error (miss) is the result if the difference exceeds 3y.

The minimum and maximum values of the sample are checked for gross error.

In this case, all measurement results should be discarded, the deviations of which from the arithmetic mean exceed 3 , and the judgment about the variance of the general population is made on the basis of the remaining measurement results.

Method 3 showed that the minimum and maximum value of the initial data is not a gross error.

2.3 Determining the number of intervals by splitting a taskncontrol values

It is essential for constructing a histogram to choose the optimal partition, since as the intervals increase, the detail of the distribution density estimate decreases, and as the interval decreases, the accuracy of its value decreases. To select the optimal number of intervals n Sturges' rule is often applied.

The Sturges rule is an empirical rule for determining the optimal number of intervals into which the observed range of variation of a random variable is divided when constructing a histogram of its distribution density. Named after the American statistician Herbert Sturges.

The resulting value is rounded up to the nearest integer (Table 3).

Breaking into intervals is done in the following way:

The lower limit (n.g.) is defined as:

Table 3 Spacing table



Average value min
Average value max
For MAX FOR MIN
Dispersion

FOR For MIN
Dispersion

Gross error 3? (min)
Gross error 3? (max)
Number of intervals
Interval length

The upper limit (b.g.) is defined as:

The subsequent lower bound will be equal to the upper previous interval.

The interval number, the values of the upper and lower limits are indicated in Table 4.

Table 4 Boundary definition table

Interval number

2.4 Building a histogram

To construct a histogram, it is necessary to calculate the average value of the intervals and their average probability. The average value of the interval is calculated as:

The values of the average values of the interval and probability are presented in Table 5. The histogram is shown in Figure 3.

Table 5 Table of means and probabilities

Interval midpoint	The number of input control results that fall within these boundaries	Probability

Fig.3 Histogram

2.5 Determination of the percentage of defects in the lot

A defect is each individual non-compliance of a product with the established requirements, and a product that has at least one defect is called defective ( marriage, defective products). Defect-free products are considered good.

The presence of a defect means that the actual value of the parameter (for example, L e) does not correspond to the specified normalized value of the parameter. Therefore, the condition of no marriage is determined by the following inequality:

d min? L d? d max ,

Where d min, d max -- the smallest and largest maximum permissible values of the parameter, setting its tolerance.
The list, type and maximum permissible values of the parameters characterizing defects are determined by the product quality indicators and the data given in the regulatory and technical documentation of the enterprise for manufactured products.

Distinguish fixable manufacturing defect And final manufacturing defect. Correctable products include products that are technically possible and economically feasible to correct in the conditions of the manufacturing enterprise; to the final - products with defects, the elimination of which is technically impossible or economically unprofitable. Such products are subject to disposal as production waste, or are sold by the manufacturer at a price significantly lower than the same product without defects ( discounted goods).

By the time of detection, a manufacturing defect of a product can be internal(identified at the production stage or in the factory warehouse) and external(detected by the buyer or other person using this product, a defective product).

During operation, the parameters characterizing the system performance change from the initial (nominal) y n to the limit y n. If the parameter value is greater than or equal to y, then the product is considered defective.

The limiting value of the parameter for nodes that ensure road safety is taken at a probability value of b = 15%, and for all other units and nodes at b = 5%.

The rear suspension is responsible for road safety, so the probability b = 15%.

At b = 15%, the limit value is 16.5431, all products with a measured parameter equal to or higher than this value will be considered faulty

Thus, in the second section of the course project, the limit value of the controlled parameter was determined based on the error of the first kind.

CONCLUSION

In the first section of the course project, the influencing factors on the decrease in the performance of the car were considered and analyzed. Factors that directly affect the selected node - the ball joint were also considered. The influence of factors leads to the loss of performance of the unit and the vehicle as a whole, so it is necessary to take preventive measures to reduce the factors. After all, abrasive wear is a consequence of the cutting or scratching effect of solid abrasive particles (dust, sand) trapped between the rubbing surfaces of mating parts. Getting between the rubbing parts of open friction units, hard abrasive particles sharply increase their wear.

In the second section of the course project, the limit value of the controlled parameter was determined based on the error of the first kind.

LIST OF USED SOURCES

1. A collection of technological instructions for the maintenance and repair of the car Lada Grant JSC "Avtovaz", 2011, Tolyatti

2. Avdeev M.V. etc. Technology of repair of machines and equipment. - M.: Agropromizdat, 2007.

3. Borts A.D., Zakin Ya.Kh., Ivanov Yu.V. Diagnostics of the technical condition of the car. M.: Transport, 2008. 159 p.

4. Gribkov V.M., Karpekin P.A. Handbook of equipment for TO and TR vehicles. M.: Rosselkhozizdat, 2008. 223 p.

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"COURSE OF LECTURES ON THE DISCIPLINE "FUNDAMENTALS OF THE OPERATING CAPABILITY OF TECHNICAL SYSTEMS" 1. Basic provisions and dependencies of reliability General dependencies..."

COURSE OF LECTURES ON THE DISCIPLINE

"FUNDAMENTALS OF THE PERFORMANCE OF TECHNICAL

1. Basic provisions and dependencies of reliability

General dependencies

Significant dispersion of the main reliability parameters predetermines

the need to consider it in a probabilistic aspect.

As was shown above with the example of distribution characteristics,

Reliability parameters are used in the statistical interpretation for state estimation and in the probabilistic interpretation for prediction. The former are expressed in discrete numbers, they are called estimates in the theory of probability and the mathematical theory of reliability. With a sufficiently large number of tests, they are taken as true reliability characteristics.

Consider the tests or operation of a significant number N of elements carried out to assess the reliability during time t (or operating time in other units). Let by the end of the test or service life there will be Np operable (non-failed) elements and n failed ones.

Then the relative number of failures Q(t) = n / N.

If the test is carried out as a sample, then Q(t) can be considered as a statistical estimate of the probability of failure or, if N is large enough, as the probability of failure.

In the future, in cases where it is necessary to emphasize the difference between the probability estimate and the true probability value, the estimate will be additionally equipped with an asterisk, in particular Q*(t) The probability of failure-free operation is estimated by the relative number of operable elements P(t) = Np/N = 1 n/N) Since uptime and failure are mutually opposite events, the sum of their probabilities is equal to 1:

P(t)) + Q(t) = 1.

The same follows from the above dependencies.

At t=0 n = 0, Q(t)=0 and Р(t)=1.

For t= n=N, Q(t)=1 and P(t)= 0.

The time distribution of failures is characterized by the distribution density function f(t) of time to failure. In the () () statistical interpretation of f(t), in the probabilistic interpretation. Here = n and Q are the increment in the number of failed objects and, accordingly, the probability of failures over time t.

The probabilities of failures and trouble-free operation in the density function f(t) are expressed by the dependencies Q(t) = (); at t = Q(t) = () = 1 P(t) = 1 – Q(t) = 1 - () = 0 () Failure rate o in (t) in contrast to the distribution density ratio

– – –

Let us consider the reliability of the simplest design model of a system of series-connected elements (Fig. 1.2), which is the most typical for mechanical engineering, in which the failure of each element causes the failure of the system, and the failures of the elements are assumed to be independent.

P1(t) P2(t) P3(t)

– – –

Р (t) = e(1 t1 + 2 t2) This dependence follows from the probability multiplication theorem.

To determine the failure rate based on experiments, the average time to failure is estimated mt = where N is the total number of observations. Then = 1/.

Then, taking the logarithm of the expression for the probability of failure-free operation: lgР(t) =

T lg e \u003d - 0.343 t, we conclude that the tangent of the angle of the straight line drawn through the experimental points is tg \u003d 0.343, whence \u003d 2.3tg With this method, there is no need to complete the testing of all samples.

For the system Рst (t) = e it. If 1 \u003d 2 \u003d ... \u003d n, then Рst (t) \u003d enit. Thus, the probability of failure-free operation of a system consisting of elements with the probability of failure-free operation according to the exponential law also obeys the exponential law, and the failure rates of individual elements are added. Using the exponential distribution law, it is easy to determine the average number of products i that will fail by a given point in time, and the average number of products Np that will remain operational. At t0.1n Nt; Np N(1 - t).

– – –

The distribution density curve is sharper and higher, the smaller S. It starts from t = - and extends to t = + ;

– – –

Operations with a normal distribution are simpler than with others, so they are often replaced by other distributions. For small coefficients of variation S/m t, the normal distribution replaces well the binomial, Poisson, and lognormal distributions.

The mathematical expectation and variance of the composition are, respectively, m u = m x + m y + m z ; S2u = S2x + S2y + S2z where t x, t y, m z - mathematical expectations of random variables;

1.5104 4104 Solution. Find the quantile up = = - 2.5; according to the table, we determine that P (t) = 0.9938.

The distribution is characterized by the following function of the probability of failure-free operation (Fig. 1.8) Р(t) = 0

– – –

Combined action of sudden and gradual failures The probability of failure-free operation of the product for a period t, if before that it worked for time T, according to the probability multiplication theorem is P(t) = Pv(t)Pn(t), where Pv(t)=et and Pn (t)=Pn(T+t)/Pn(T) - probabilities of absence of sudden and, accordingly, gradual failures.

– – –

2. Reliability of systems General information The reliability of most products in technology has to be determined when considering them as systems. Complex systems are divided into subsystems.

From the standpoint of reliability, systems can be sequential, parallel and combined.

The most obvious example of sequential systems is automatic machine lines without backup circuits and drives. They take the name literally. However, the concept of "sequential system" in reliability problems is wider than usual. These systems include all systems in which the failure of an element leads to the failure of the system. For example, a mechanical transmission bearing system is considered to be in series, although the bearings of each shaft operate in parallel.

Examples of parallel systems are power systems of electrical machines operating on a common grid, multi-engine aircraft, ships with two machines, and redundant systems.

Examples of combined systems are partially redundant systems.

Many systems consist of elements, the failures of each of which can be considered as independent. Such consideration is widely used for operational failures and sometimes, as a first approximation, for parametric failures.

Systems may include elements whose parameters change determines the failure of the system as a whole or even affects the performance of other elements. This group includes the majority of systems when they are accurately considered in terms of parametric failures. For example, the failure of precision metal-cutting machines according to the parametric criterion - loss of accuracy - is determined by the cumulative change in the accuracy of individual elements: spindle assembly, guides, etc.

In a system with parallel connection of elements, it is of interest to know the probability of failure-free operation of the entire system, i.e. of all its elements (or subsystems), a system without one, without two, etc. elements within the limits of the system's operability, even with greatly reduced performance.

For example, a four-engine aircraft may continue to fly after two engines fail.

The operability of a system of identical elements is determined using the binomial distribution.

The binomial m is considered, where the exponent m is equal to the total number of elements operating in parallel; P (t) and Q (t) - the probability of failure-free operation and, accordingly, the failure of each of the elements.

We write down the results of the decomposition of binomials with exponents of 2, 3 and 4, respectively, for systems with two, three and four elements operating in parallel:

(P + Q)2 = P2 -\- 2PQ + Q2 = 1;

(P + Q)2 = P3 + 3P2Q + 3PQ2 + Q3 = 1;

(P + Q)4 = P4 + 4P3Q + 6P2Q2 + 4PQ3 + Q4 = 1.

In them, the first terms express the probability of failure-free operation of all elements, the second - the probability of failure of one element and the failure-free operation of the rest, the first two terms - the probability of failure of no more than one element (no failure or failure of one element), etc. The last term expresses the probability of failure all elements.

Convenient formulas for technical calculations of parallel redundant systems are given below.

The reliability of a system of series-connected elements obeying the Weibull distribution Р1(t)= and P2(t) = also obeys the Weibull distribution Р(t) = 0, where the parameters m and t are quite complex functions of the arguments m1, m2, t01 and t02 .

Using the method of statistical modeling (Monte Carlo) on a computer, graphs for practical calculations were built. The graphs make it possible to determine the average resource (until the first failure) of a two-element system as a fraction of the average resource of an element of greater durability and the coefficient of variation for the system depending on the ratio of average resources and coefficients of variation of the elements.

For a system of three or more elements, you can use the graphs sequentially, and it is convenient to use them for elements in ascending order of their average resource.

It turned out that with the usual values of the coefficients of variation of the resource elements = 0.2 ... 0.8, there is no need to take into account those elements whose average resource is five times or more higher than the average resource of the least durable element. It also turned out that in multi-element systems, even if the average resources of the elements are close to each other, there is no need to take into account all the elements. In particular, with coefficients of variation of the resource of elements of 0.4, no more than five elements can be taken into account.

These provisions are largely extended to systems subject to other close distributions.

Reliability of a sequential system with a normal load distribution over the systems If the load dispersion over the systems is negligible, and the bearing capacities of the elements are independent of each other, then the failures of the elements are statistically independent and therefore the probability Р(RF0) of the failure-free operation of the sequential system with the carrying capacity R under the load F0 is equal to the product of the probabilities of failure-free operation of the elements:

P(RF0)= (Rj F0)=, (2.1) where Р(Rj F0) is the probability of non-failure operation of the j-th element under load F0; n is the number of elements in the system; FRj(F0) - distribution function of the bearing capacity of the j-th element with the value of the random variable Rj equal to F0.

In most cases, the load has a significant dissipation in systems, for example, universal machines (machine tools, cars, etc.) can be operated in different conditions. When the load is dissipated across systems, the assessment of the probability of failure-free operation of the system Р(R F) in the general case should be found using the total probability formula, dividing the range of load dispersion into intervals F, finding for each load interval the product of the probability of failure-free operation Р(Rj Fi) for the j-th element at a fixed load on the probability of this load f(Fi)F, and then, summing these products over all intervals, Р(R F) = f (Fi)Fn P(Rj Fi) or, proceeding to integration, Р(R F) = () , (2.2) where f(F) - load distribution density; FRj(F) - distribution function of the bearing capacity of the j-th element with the value of the bearing capacity Rj = F.

Calculations according to formula (2.2) are generally laborious, since they involve numerical integration, and therefore, for large n, they are only possible on a computer.

In order not to calculate P(R F) using formula (2.2), in practice, the probability of failure-free operation of systems P(R Fmax) is often estimated at the maximum possible load Fmax. Take, in particular, Fmax=mF (l + 3F), where mF is the expectation of the load and F is its coefficient of variation. This value Fmax corresponds to the largest value of a normally distributed random variable F over an interval equal to six standard deviations of the load. This method of assessing reliability significantly underestimates the calculated indicator of system reliability.

Below we propose a fairly accurate method for a simplified assessment of the reliability of a sequential system for the case of normal load distribution across systems. The idea of the method is to approximate the law of distribution of the bearing capacity of the system by a normal distribution so that the normal law is close to the true one in the range of reduced values of the bearing capacity of the system, since it is these values that determine the value of the system reliability index.

Comparative calculations on a computer according to formula (2.2) (exact solution) and the proposed simplified method, given below, showed that its accuracy is sufficient for engineering calculations of the reliability of systems in which the coefficient of variation of the bearing capacity does not exceed 0.1 ... 0.15 , and the number of system elements does not exceed 10...15.

The method itself is as follows:

1. Set by two values FA and FB of fixed loads. According to formula (3.1), the probabilities of failure-free operation of the system under these loads are calculated. The loads are selected so that when assessing the reliability of the system, the probability of failure-free operation of the system is within P(RFA)=0.45...0.60 and P(RFA) = 0.95...0.99, i.e. . would cover the interval of interest.

Approximate load values can be taken close to the values FA(1+F)mF, FB(1+ F)mF,

2. According to the table. 1.1 find the quantiles of the normal distribution upA and upB corresponding to the found probabilities.

3. The law of distribution of the bearing capacity of the system is approximated by a normal distribution with the parameters of the mathematical expectation mR and the coefficient of variation R. Let SR be the standard deviation of the approximating distribution. Then mR - FA + upASR = 0 and mR - FB + upBSR = 0.

From the above expressions, we obtain expressions for mR and R = SR/mR:

R = ; (2.4)

4. The probability of failure-free operation of the system Р (R F) for the case of normal distribution of the load F over systems with the parameters of the mathematical expectation m F and the coefficient of variation R is found in the usual way by the quantile of the normal distribution up. The quantile ip is calculated using a formula that reflects the fact that the difference between two normally distributed random variables (the bearing capacity of the system and the load) is normally distributed with a mathematical expectation equal to the difference between their mathematical expectations and a root mean square equal to the root of the sum of the squares of their standard deviations:

up = ()2 + where n=m R /m F - conditional margin of safety for the average values of the bearing capacity and load.

Let's use the above method with examples.

Example 1. It is required to estimate the probability of failure-free operation of a single-stage gearbox, if the following is known.

The conditional safety margins for the average values of the bearing capacity and load are: gear 1 =1.5; input shaft bearings 2 = 3 = 1.4; output shaft bearings 4 = 5 = 1.6, output and input shafts 6 = 7 = 2.0. This corresponds to the mathematical expectations of the bearing capacity of the elements 1 = 1.5; 2 3 \u003d 1.4; 4 \u003d 5 \u003d 1.6;

6=7=2. Often in gearboxes n 6 and n7 and, accordingly, mR6 and mR7 are much larger. It is specified that the bearing capacities of the transmission, bearings and shafts are normally distributed with the same coefficients of variation 1 = 2 = ...= 7 = 0.1, and the load on the gearboxes is also distributed normally with a coefficient of variation = 0.1.

Solution. We set the loads FA and FB. We accept FA = 1.3, FB = 1.1mF, assuming that these values will give close to the required values of the probabilities of non-failure operation of systems at fixed loads P(R FA) and P(R FB).

We calculate the quantiles of the normal distribution of all elements corresponding to their probabilities of failure-free operation under loads FA and FB:

1 1,3 1,5 1 = = = - 1,34;

– – –

According to the table, we find the required probability corresponding to the obtained quantile: (F) = 0.965.

Example 2. For the conditions of the example considered above, let's find the probability of no-failure operation of the gearbox under the maximum load in accordance with the methodology used earlier for practical calculations.

We accept the maximum load Fmax \u003d tp (1 + 3F) \u003d mF (1 + 3 * 0.1) \u003d 1.3mF.

Solution. Under this load, we calculate the quantiles of the normal distribution of the probabilities of failure-free operation of elements 1 = - 1.333; 2=3=-0.714;

4 = 5 = - 1,875; 8 = 7 = - 3,5.

According to the table, we find the probabilities corresponding to the quantiles Р1 (R Fmax) = 0.9087;

P2(R Fmax) = P3(R Fmax) = 0.7624; P4(R Fmax) = P5(R Fmax) = 0.9695;

P6(RFmax)=P7(R Fmax)=0.9998.

The probability of failure-free operation of the gearbox under load Pmax is calculated by formula (2.1). We get P (P ^ Pmax) = 0.496.

Comparing the results of solving two examples, we see that the first solution gives a reliability estimate that is much closer to the real one and higher than in the second example. The actual value of the probability, calculated on a computer according to the formula (2.2), is 0.9774.

Reliability assessment of a chain type system The bearing capacity of the system. Often sequential systems consist of the same elements (load or drive chain, gear wheel, in which the elements are links, teeth, etc.). If the load is scattered across systems, then an approximate estimate of the reliability of the system can be obtained by the general method described in the previous paragraphs. Below we propose a more accurate and simpler method for assessing reliability for a particular case of sequential systems - chain-type systems with a normal distribution of the bearing capacity of elements and load across systems.

The law of distribution of the bearing capacity of a chain consisting of identical elements corresponds to the distribution of the minimum member of the sample, i.e., a series of n numbers taken randomly from the normal distribution of the bearing capacity of the elements.

This law differs from the normal one (Fig. 2.1) and the more significant the larger n. The mathematical expectation and standard deviation decrease with increasing n. As n increases, it approaches the double exponential. This limit distribution law of the bearing capacity R of the circuit P (R F 0), where F0 is the current load value, has the form P (R F0) R/ =ee. Here and (0) are the distribution parameters. For real (small and medium) values of n, the double exponential distribution is unsuitable for use in engineering practice due to significant calculation errors.

The idea of the proposed method is to approximate the law of distribution of the bearing capacity of the system by a normal law.

The approximating and real distributions should be close both in the middle part and in the region of low probabilities (the left “tail” of the distribution density of the system’s carrying capacity), since it is this distribution region that determines the probability of the system’s failure-free operation. Therefore, when determining the parameters of the approximating distribution, the equalities of the functions of the approximating and real distributions are put forward at the median value of the system's bearing capacity corresponding to the probability of the system's failure-free operation.

After approximation, the probability of failure-free operation of the system, as usual, is found by the quantile of the normal distribution, which is the difference between two normally distributed random variables - the bearing capacity of the system and the load on it.

Let the laws of distribution of the bearing capacity of the elements Rk and the load on the system F be described by normal distributions with mathematical expectations, respectively, m Rk and m p and standard deviations S Rk and S F.

– – –

Considering that and depend on up, calculations by formulas (2.8) and (2.11) are carried out by the method of successive approximations. As a first approximation for determining and take up = - 1.281 (corresponding to P = 0.900).

Reliability of systems with redundancy To achieve high reliability in mechanical engineering, design, technological and operational measures may not be sufficient, and then redundancy must be used. This is especially true for complex systems for which it is not possible to achieve the required high reliability of the system by increasing the reliability of the elements.

Here, structural redundancy is considered, which is carried out by introducing into the system redundant components in relation to the minimum required structure of the object and performing the same functions as the main ones.

Redundancy reduces the probability of failures by several orders of magnitude.

Apply: 1) permanent redundancy with a loaded or hot reserve; 2) redundancy by replacement with an unloaded or cold standby; 3) redundancy with a backup operating in light mode.

Redundancy is most widely used in electronic equipment, in which the redundant elements are small and easily switched.

Features of redundancy in mechanical engineering: in a number of systems, standby units are used as working units during peak hours; in a number of systems, redundancy ensures the preservation of operability, but with a decrease in performance.

Redundancy in its pure form in mechanical engineering is mainly used in case of danger of accidents.

In transport vehicles, in particular in automobiles, a double or triple brake system is used; in trucks - double tires on the rear wheels.

In passenger aircraft, 3 ... 4 engines and several electric machines are used. The failure of one or even several machines, except for the last one, does not lead to an aircraft accident. In sea vessels - two cars.

The number of escalators, steam boilers is chosen taking into account the possibility of failure and the need for repair. At the same time, all escalators can work during peak hours. In general engineering, critical units use a double lubrication system, double and triple seals. The machines use spare sets of special tools. At factories, unique machines of the main production are trying to have two or more copies. In automatic production, accumulators, backup machines and even duplicate sections of automatic lines are used.

The use of spare parts in warehouses, spare wheels on vehicles can also be considered as a type of reservation. Reservation (general) should also include the design of a fleet of machines (for example, cars, tractors, machine tools), taking into account their downtime for repairs.

With constant redundancy, reserve elements or circuits are connected in parallel with the main ones (Fig. 2.3). The probability of failure of all elements (main and reserve) according to the probability multiplication theorem Qst(t) = Q1(t) * Q2(t) *… Qn(t)= (), where Qi(t) is the probability of element i failure.

Probability of failure-free operation Pst(t) = 1 – Qst(t) If the elements are the same, then Qst(t) = 1 (t) and Рst(t) = 1 (t).

For example, if Q1 = 0.01 and n = 3 (double redundant), then Pst = 0.999999.

Thus, in systems with series-connected elements, the probability of failure-free operation is determined by multiplying the probabilities of failure-free operation of elements, and in a system with parallel connection, the probability of failure is determined by multiplying the probabilities of element failure.

If in the system (Fig. 2.5, a, b) a elements are not duplicated, and b elements are duplicated, then the reliability of the system is Pst (t) = Pa (t) Pb (t); Pa(t) = (); Pb(t) = 1 2 ()].

If there are n main and m reserve identical elements in the system, and all elements are constantly on, operate in parallel and the probability of their failure-free operation P obeys an exponential law, then the probability of the system’s failure-free operation can be determined from the table:

n+m n 2P – P2 1 P - - P2 - 2P3 6P2 – 8P3 + 3P4 10P – 20P3 + 15P4 P2 2 - 4P3 – 3P4 10P3 – 15P4 + 6P5 3 - - P3 5P4 – 4P5 P4 4 - - - from the corresponding sums of terms of the expansion of the binomial (P + Q) m + n after substituting Q=1 - P and transformations.

In the case of redundancy and replacement, reserve elements are switched on only if the main ones fail. This activation can be done automatically or manually. Redundancy can include the use of backup units and tool blocks installed instead of failed ones, and these elements are then considered as part of the system.

For the main case of an exponential distribution of failures for small values of t, i.e., with a sufficiently high reliability of the elements, the probability of system failure (Fig. 2.4) is equal to () Qst (t).

If the elements are the same, then () () Qst(t).

The formulas are valid provided that the switching is absolutely reliable. In this case, the probability of failure in n! times less than with permanent reservation.

The lower chance of failure is understandable as fewer elements are under load. If the switching is not reliable enough, then the gain can be easily lost.

To maintain the high reliability of redundant systems, failed elements must be repaired or replaced.

Redundant systems are used in which failures (within the number of redundant elements) are established during periodic checks, and systems in which failures are recorded when they occur.

In the first case, the system can start working with failed elements.

Then the calculation for reliability is carried out for the period from the last check. If immediate failure detection is envisaged and the system continues to operate during the replacement of elements or restoration of their operability, then failures are dangerous until the end of the repair, and during this time the reliability is assessed.

In systems with redundant substitution, the connection of redundant machines or units is made by a person, an electromechanical system, or even purely mechanically. In the latter case, it is convenient to use overrunning clutches.

It is possible to install the main and standby engines with overrunning clutches on the same axle with automatic activation of the standby engine upon a signal from the centrifugal clutch.

If idle operation of the reserve engine (unloaded reserve) is permissible, then the centrifugal clutch is not installed. In this case, the main and standby engines are also connected to the working body through overrunning clutches, and the gear ratio from the standby engine to the working body is made somewhat smaller than from the main engine.

Let us consider the reliability of duplicated elements during the periods of restoration of the failed element of the pair.

If we designate the failure rate of the main element, p of the reserve and

The average repair time, then the probability of failure-free operation Р(t) = 0

– – –

To calculate such complex systems, Bayes' total probability theorem is used, which, when applied to reliability, is formulated as follows.

The probability of system failure Q st \u003d Q st (X is operable) Px + Qst (X is inoperative) Q x, where P x and Q x are the probability of operability and, accordingly, the inoperability of element X. The structure of the formula is clear, since P x and Q x can be represented as a fraction of time with an operable and, accordingly, inoperable element X.

The probability of failure of the system with the operability of element X is determined as the product of the probability of failures of both elements, i.e.

Q st (X is operational) \u003d Q A "Q B" \u003d (1 - P A ") (1 - P B") The probability of system failure when the element X is inoperable Qst (X is inoperative) \u003d Q AA "Q BB" \u003d (1 - P AA")(1 - P BB") Probability of system failure in the general case Qst = (1 - P A")(1- P B")P X + (1 - P AA")(1 - P BB")Q x .

In complex systems, you have to apply the Bayes formula several times.

3. Reliability testing Specifics of machine reliability assessment based on test results Calculation methods for reliability assessment have not yet been developed for all criteria and not for all machine parts. Therefore, the reliability of machines as a whole is currently assessed by the results of tests, which are called determinative. Definitive testing tends to bring it closer to the product development stage. In addition to the identification tests, control tests for reliability are also carried out in the serial production of products. They are designed to control the compliance of serial products with the reliability requirements given in the technical specifications and taking into account the results of the identification tests.

Experimental methods for assessing reliability require testing a significant number of samples, a long time and costs. This does not allow for proper reliability testing of machines produced in small series, and for machines produced in large series, it delays the receipt of reliable information on reliability until the stage when the tooling is already made and it is very expensive to make changes. Therefore, when evaluating and monitoring the reliability of machines, it is important to use possible methods to reduce the amount of testing.

The scope of tests required to confirm the given reliability indicators is reduced by: 1) forcing modes; 2) reliability assessments for a small number or absence of failures; 3) reducing the number of samples by increasing the duration of the tests; 4) the use of versatile information about the reliability of parts and components of the machine.

In addition, the scope of testing can be reduced by scientific design of the experiment (see below), as well as by improving the accuracy of measurements.

According to the test results for non-repairable products, as a rule, the probability of failure-free operation is estimated and controlled, and for recoverable products - the mean time between failures and the mean recovery time of a working state.

Definitive tests In many cases, reliability tests must be carried out before failure. Therefore, not all products (the general population) are tested, but a small part of them, called a sample. In this case, the probability of non-failure operation (reliability) of the product, the mean time between failures and the mean recovery time may differ from the corresponding statistical estimates due to the limited and random composition of the sample. To take into account this possible difference, the concept of confidence probability is introduced.

Confidence probability (reliability) is the probability that the true value of the estimated parameter or numerical characteristic lies in a given interval, called the confidence interval.

The confidence interval for the probability Р is limited by the lower Рн and upper РВ confidence limits:

Ver(Рн Р Рв) =, (3.1) the probability of falling into an interval bounded on both sides. Similarly, the confidence interval for the mean time between failures is limited by T H and T B, and for the average recovery time by the boundaries of T BH, T BB.

In practice, the main interest is the one-sided probability that the numerical characteristic is not less than the lower or not higher than the upper bound.

The first condition, in particular, refers to the probability of failure-free operation and mean time between failures, the second - to the mean recovery time.

For example, for the probability of failure-free operation, the condition has the form Ver (Рн Р) =. (3.2) Here - one-sided confidence probability of finding the considered numerical characteristic in the interval limited on one side. The probability at the stage of testing samples experiments is usually taken equal to 0.7 ... 0.8, at the stage of transferring development to mass production 0.9 ... 0.95. The lower values are typical for the case of small-scale production and high cost of testing.

Below are formulas for estimates based on the results of tests of the lower and upper confidence limits of the considered numerical characteristics with a given confidence probability. If it is necessary to introduce bilateral confidence limits, then the above formulas are also suitable for such a case.

In this case, the probabilities of reaching the upper and lower boundaries are assumed to be the same and are expressed through a given value.

Since (1 +) + (1 -) = (1 -), then = (1+) / 2 Non-recoverable products. The most common case is when the sample size is less than a tenth of the general population. In this case, the binomial distribution is used to estimate the lower Р n and the upper Р within the limits of the probability of failure-free operation. When testing n products, the confidence probability 1- of reaching each of the boundaries is taken equal to the probability of occurrence in one case no more than m failures, in the other case no less than m failures!

(1 n) n1 = 1 – ; (3.3) =0 !()!

(1 c) n = 1 – ; (3.4) !()!

– – –

Forcing the test mode.

Reducing the scope of tests by forcing the mode. Typically, the life of the machine depends on the voltage level, temperature and other factors.

If the nature of this dependence is studied, then the duration of the tests can be reduced from time t to time tf by forcing the test mode tf = t/Ky, where Ku = acceleration coefficient, a, f - mean time to failure in normal and forced modes.

In practice, the duration of the tests is reduced by forcing the mode up to 10 times. The disadvantage of the method is the reduced accuracy due to the need to use deterministic dependences of the limiting parameter on the operating time for conversion to real operating modes and due to the danger of switching to other failure criteria.

The ky values are calculated from the dependency that links the resource to the forcing factors. In particular, with fatigue in the zone of the inclined branch of the Wöhler curve or with mechanical wear, the relationship between the resource and stresses in the part has the form mt = const, where m is on average: in bending for improved and normalized steels - 6, for hardened - 9 .. 12, under contact loading with an initial touch along the line - about 6, during wear under conditions of poor lubrication - from 1 to 2, with periodic or constant lubrication, but imperfect friction - about 3. In these cases, Ku \u003d (f /) t , where and f are voltages in nominal and boosting modes.

For electrical insulation, the “rule of 10 degrees” is approximately fair: with a temperature increase of 10 °, the insulation resource is halved. The resource of oils and greases in bearings decreases by half with increasing temperature: by 9...10° for organic oils and 12...20° for inorganic oils and greases. For insulation and lubricants, Ky = (f/)m can be taken, where and F

Temperature in nominal and boost modes, °С; m is for insulation and organic oils and greases - about 7, for inorganic oils and greases - 4 ... 6.

If the mode of operation of the product is variable, then the acceleration of tests can be achieved by excluding from the spectrum of loads that do not cause a damaging effect.

Reducing the number of samples by assessing the reliability of the absence or a small number of failures. From the analysis of the graphs, it follows that in order to confirm the same lower limit Рn of the probability of failure-free operation with a confidence probability, it is required to test the fewer products, the higher the value of the particular operability preservation P* = l - m/n. The frequency P*, in turn, grows with a decrease in the number of failures m. This implies the conclusion that by obtaining an estimate by a small number or absence of failures, it is possible to somewhat reduce the number of products required to confirm the given value of Рн.

It should be noted that in this case, the risk of not confirming the setpoint Рн, the so-called manufacturer's risk, naturally increases. For example, at = 0.9 to confirm Pn = 0.8, if 10 is tested; 20; 50 products, then the frequency should not be less than 1.0, respectively; 0.95; 0.88. (The case P* = 1.0 corresponds to the failure-free operation of all products in the sample.) Let the probability of failure-free operation P of the tested product be 0.95. Then, in the first case, the risk of the manufacturer is large, since on average, for each sample of 10 products there will be half a defective product and therefore the probability of obtaining a sample without defective products is very small, in the second - the risk is close to 50%, in the third - the smallest.

Despite the high risk of rejecting their products, product manufacturers often plan tests with a zero failure rate, reducing the risk by introducing the necessary reserves into the design and the associated increase in product reliability. it is necessary to test lg(1) n= (3.15) on the product, provided that there are no failures during testing.

Example. Determine the number n of products required for testing at m = 0, if Pn = 0.9 is specified; 0.95; 0.99 s = 0.9.

Solution. Having done the calculations according to the formula (3.15), respectively, we have n = 22; 45; 229.

Similar conclusions follow from the analysis of formula (3.11) and the values of Table. 3.1;

to confirm the same lower limit Tn of the mean time between failures, it is required to have the shorter the total test duration t, the smaller the allowable failures. The smallest t is obtained at m=0 n 1;2, t = (3.16) while the risk of not confirming Tn is the greatest.

Example. Determine t at Tn = 200, = 0.8, t = 0.

Solution. From Table. 3.10.2;2 = 3.22. Hence t \u003d 200 * 3.22 / 2 \u003d 322 hours.

Reducing the number of samples by increasing the duration of the test. In such tests of products subject to sudden failures, in particular electronic equipment, as well as recoverable products, the results are in most cases recalculated for a given time, assuming the fairness of the exponential distribution of failures over time. In this case, the volume of tests nt remains practically constant, and the number of test specimens becomes inversely proportional to the test time.

The failure of most machines is caused by various aging processes. Therefore, the exponential law for describing the resource distribution of their nodes is not applicable, but the normal, logarithmically normal laws or the Weibull law are valid. With such laws, by increasing the duration of the tests, it is possible to reduce the amount of tests. Therefore, if the probability of failure-free operation is considered as a reliability indicator, which is typical for non-repairable products, then with an increase in the duration of tests, the number of tested samples decreases more sharply than in the first case.

In these cases, the assigned resource t and the distribution parameters of the time to failure are related by the expression:

under normal law

– – –

Bearings, worm gears Pinching, Heat resistance of thrust transmission To recalculate reliability estimates from a longer time to a shorter time, you can use the distribution laws and the parameters of these laws that characterize the dissipation of the resource. For bending fatigue of metals, creep of materials, aging of grease impregnated in plain bearings, aging of grease in rolling bearings, and erosion of contacts, the logarithmically normal law is recommended. The corresponding standard deviations of the logarithm of the resource Slgf, substituted into formula (3.18), should be respectively taken as 0.3; 0.3; 0.4; 0.33; 0.4. For rubber fatigue, wear of machine parts, wear of electric machine brushes, the normal law is recommended. The corresponding coefficients of variations vt, substituted into formula (3.17), are 0.4; 0.3; 0.4. For rolling bearing fatigue, the Weibull law (3.19) is valid with a form factor of 1.1 for ball bearings and 1.5 for roller bearings.

Data on distribution laws and their parameters were obtained by summarizing the results of tests of machine parts published in the literature and the results obtained with the participation of the authors. These data make it possible to estimate the lower bounds on the probability of the absence of certain types of failures based on the test results during the time t and t. When calculating estimates, formulas (3.3), (3.5), (3.6), (3.17)...(3.19) should be used.

To reduce the duration of the tests, they can be forced with the acceleration coefficient Ku, found according to the recommendations given above.

The values K y, tf where tf is the time of testing samples in the forced mode, are substituted instead of t in formulas (3.17) ... (3.19). In the case of using formulas (3.17), (6.18) for recalculation, with a difference in the characteristics of the dissipation of the resource in the operational vt Slgt and forced tf, Slgtf modes, the second terms in the formulas are multiplied by the ratios, respectively, tf /t or Slgtf / Slgt According to performance criteria, such as static strength, heat resistance, etc., the number of test samples, as shown below, can be reduced by tightening the test mode for the parameter that determines performance compared to the nominal value of this parameter. In this case, it is sufficient to have the results of short-term tests. The ratio between the limiting Xpr and the effective X$ values of the parameter, assuming their normal distribution laws, can be represented as

– – –

where ip, uri - quantiles of the normal distribution, corresponding to the probability of no failure in the nominal and toughened modes; Khd, Khdf - nominal and tightened value of the parameter that determines the performance.

The Sx value is calculated by considering the health parameter as a function of random arguments (see example below).

Combining probabilistic estimates into a machine reliability estimate. For some of the criteria, the probability of the absence of failures is found by calculation, and for the rest - experimentally. Tests are usually carried out at loads that are the same for all machines. Therefore, it is natural to obtain calculated reliability estimates for individual criteria also at a fixed load. Then the dependence between failures for the obtained reliability estimates for individual criteria can be considered largely eliminated.

If by all criteria it was possible to calculate accurately enough the values of the probability of the absence of failures, then the probability of failure-free operation of the machine as a whole during the assigned resource would be estimated by the formula P = =1. However, as noted, a number of probabilistic estimates cannot be obtained without testing. In this case, instead of estimating Р, the lower bound of the probability of non-failure operation of the machine Рн with a given confidence probability =Ver(РнР1) is found.

Let the probabilities of absence of failures be found according to h criteria by calculation, and according to the rest l = - h experimentally, and tests during the assigned resource for each of the criteria are assumed to be failure-free. In this case, the lower limit of the probability of failure-free operation of the machine, considered as a sequential system, can be calculated by the formula Р = Рн; (3.23) =1 where Pнj is the smallest of the lower bounds Рнi...* Pнj,..., Рнi of the probability of absence of failures according to l criteria found with a confidence probability a; Pt is the estimated probability of the absence of failure according to the i-th criterion.

The physical meaning of formula (3.22) can be explained as follows.

Let n consecutive systems be tested and no failures during the test.

Then, according to (3.5), the lower bound on the probability of failure-free operation of each system will be Рп=У1-а. The test results can also be interpreted as fail-safe tests of the first, second, etc. elements separately, tested on n pieces in the sample. In this case, according to (3.5), the lower limit Рн = 1 is confirmed for each of them. It follows from a comparison of the results that, with the same number of tested elements of each type, Рп = Рнj. If the number of tested elements of each type were different, then Pn would be determined by the value of Pnj obtained for the element with the minimum number of tested specimens, i.e. P = Pn.

At the beginning of the stage of experimental testing of the design, there are frequent cases of machine failures due to the fact that it has not yet been sufficiently finished. In order to monitor the effectiveness of the reliability measures carried out during the design development process, it is desirable to estimate, at least roughly, the value of the lower bound on the probability of failure-free operation of the machine from the results of tests in the presence of failures. To do this, you can use the formula n \u003d (Pn / P)

– – –

P is the largest of the point estimates 1 *… *; mj is the number of failures of tested products. The rest of the notation is the same as in formula (3.22).

Example. It is required to estimate c = 0.7 Рn of the machine. The car is intended for work in the range of ambient temperatures from + 20 ° to - 40 °C within the appointed resource t = 200 h. 2 samples were tested for t = 600 h at normal temperature and 2 samples for a short time at -50 °C. There were no responses. The machine differs from the prototypes, which have proven themselves to be trouble-free, by the type of lubrication of the bearing assembly and the use of aluminum for the manufacture of the bearing shield. The standard deviation of the gap-interference between the contact parts of the bearing assembly, found as the root of the sum of the squares of the standard deviations: the initial clearance of the bearing, the effective gaps-interferences in the bearing-shaft interface and the bearing with the end shield, is S = 0.0042 mm. The outer diameter of the bearing D = 62mm.

Solution. We accept that the possible types of machine failures are bearing failure due to aging of the lubricant and bearing pinching at low temperatures. Failure-free testing of two products is given by formula (3.5) at = 0.7 Рнj = 0.55 in the test mode.

The distribution of lubricant aging failures is assumed to be logarithmically normal with the parameter Slgt = 0.3. Therefore, we use formula (3.18) for recalculations.

Substituting into it t = 200 h, ti = 600 h, S lgt = 0.3 and the quantile corresponding to the probability of 0.55, we obtain the quantile, and on it the lower limit of the probability of no failures due to aging of the lubricant, equal to 0.957.

Pinching of the bearing is possible due to the difference in the coefficients of linear expansion of steel st and aluminum al. As the temperature drops, the risk of pinching increases. Therefore, we consider the temperature as a parameter that determines the performance.

In this case, the bearing preload depends linearly on temperature with a proportionality factor equal to (al - st) D. Therefore, the standard deviation of the temperature Sx, causing the gap to be sampled, is also linearly related to the standard deviation of the gap - interference Sx=S/(al-st)D. Substituting in the formula (3.21) Хд = -40°С; HDF = -50°С; Sx = 6° and quantile u and the corresponding probability of 0.55 and finding the probability from the obtained value of the quantile, we obtain the lower bound on the probability of the absence of pinching 0.963.

After substituting the obtained values of the estimates into formula (3.22), we obtain the lower bound on the probability of failure-free operation of the machine as a whole, equal to 0.957.

In aviation, the following method of ensuring reliability has long been used:

the aircraft is put into serial production if the bench tests of the units in the limiting modes of operation establish their practical reliability and, in addition, if the leader aircraft (usually 2 or 3 copies) flew without failure for a triple resource. The above probabilistic assessment, in our opinion, provides additional justification for assigning the required scope of design tests according to various performance criteria.

Verification tests Verification of the compliance of the actual level of reliability with the specified requirements for non-repairable products can be checked most simply by a single-stage control method. This method is also convenient for controlling the average recovery time of remanufactured products. To control the mean time between failures of remanufactured products, the most effective method is the sequential control method. In single-stage tests, the reliability conclusion is made after the appointed test time and according to the total test result. With the sequential method, verification of the compliance of the reliability indicator with the specified requirements is done after each successive failure and at the same time points it is found out whether the tests can be stopped or they should be continued.

When planning, the number of tested samples n, the testing time of each of them t and the permissible number of failures t are assigned. The initial data for assigning these parameters are: the risk of the supplier (manufacturer) *, the risk of the consumer *, the acceptance and rejection value of the controlled indicator.

Supplier risk is the probability that a good lot, whose products have a reliability level equal to or better than a specified one, is rejected by the test results of a sample.

The customer risk is the probability that a bad batch, whose products have a reliability level worse than the specified one, is accepted according to the test results.

The values * and * are assigned from a series of numbers 0.05; 0.1; 0.2. In particular, it is legitimate to designate * = * Non-repairable items. The rejection level of the probability of failure-free operation P(t), as a rule, is taken equal to the value Pn(t) specified in the technical specifications. The acceptance value of the probability of failure-free operation Pa(t) is taken as large P(t). If the test time and operating mode are taken equal to the specified ones, then the number of tested samples n and the permissible number of failures t with a single-stage control method are calculated by the formulas!

(1 ()) () = 1 – * ;

– – –

For a particular case, graphs of successive reliability tests are shown in Fig. 3.1. If after the next failure we get on the graph in the area below the compliance line, then the test results are considered positive, if in the area above the non-compliance line - negative, if between the compliance and non-compliance lines, then the tests continue.

– – –

9. Predict the number of failures of the tested specimens. It is believed that the node has failed or will fail during operation during the time T / n, if: a) by calculation or testing for failures of types 1, 2 of Table. 3.3 it is established that the resource is less than Tn or operability is not ensured; b) calculation or testing for failure type 3 of Table. 3.3 the mean time between failures is obtained, less Tn; c) there was a failure during the tests; d) by predicting the resource, it is established that for any failure of the types 4 ... 10 tab. 3.3 tiT/n.

10. Divide the primary failures that occurred during testing and predicted by calculation into two groups: 1) determining the frequency of maintenance and repairs, i.e. those that can be prevented by carrying out regulated work is possible and expedient; 2) determining the mean time between failures, i.e. those, the prevention of which by carrying out such work is either impossible or inappropriate.

For each type of failure of the first group, activities for routine maintenance are developed, which are included in the technical documentation.

The number of failures of the second type is summed up and, according to the total number, taking into account the provisions of clause 2, the results of the tests are summed up.

Average recovery time control. The rejection level of the average recovery time Тв is taken equal to the value Твв specified in the technical specifications. The acceptance value of the recovery time T is taken as less Tv. In a particular case, you can take T \u003d 0.5 * TV.

Control is conveniently carried out by a single-stage method.

According to the formula TV 1 ;2 =, (3.25) TV;2

– – –

This ratio is one of the basic equations of the reliability theory.

Among the most important general dependences of reliability are the dependences of the reliability of systems on the reliability of elements.

Let us consider the reliability of the simplest design model of a system of series-connected elements (Fig. 3.2), which is the most typical for mechanical engineering, in which the failure of each element causes the failure of the system, and the failures of the elements are assumed to be independent.

P1(t) P2(t) P3(t) 3.2. Sequential system Let us use the well-known probability multiplication theorem, according to which the probability of a product, i.e., the joint manifestation of independent events, is equal to the product of the probabilities of these events. Therefore, the probability of failure-free operation of the system is equal to the product of the probabilities of failure-free operation of individual elements, i.e. Р st (t) = Р1 (t) Р2 (t) ... Рn (t).

If Р1(t) = Р2(t) = … = Рn(t), then Рst(t) = Рn1(t). Therefore, the reliability of complex systems is low. For example, if the system consists of 10 elements with a probability of failure-free operation of 0.9 (as in rolling bearings), then the total probability is 0.910 0.35 Usually, the probability of failure-free operation of the elements is quite high, therefore, by expressing P1(t), P 2 (t ), … Р n (t) through the probabilities of rollbacks and using the theory of approximate calculations, we obtain Рst(t) = … 1 – , since the products of two small quantities can be neglected.

For Q 1 (t) = Q 2 (t) =...= Qn(t) we get Рst = 1-nQ1(t). Let in a system of six identical consecutive elements P1(t) = 0.99. Then Q1(t)=0.01 and Рst(t)=0.94.

The probability of failure-free operation must be able to determine for any period of time. By the probability multiplication theorem (+) P(T + l) = P(T) P(t) or P(t) =, () where P (T) and P (T + t) are the probabilities of no-failure operation during the time T and T + t, respectively; P (t) is the conditional probability of failure-free operation for time t (the term "conditional" is introduced here, since the probability is determined on the assumption that the products did not have a failure before the start of the time interval or operating time).

Reliability during normal operation During this period, gradual failures do not yet appear and reliability is characterized by sudden failures.

These failures are caused by an unfavorable combination of many circumstances and therefore have a constant intensity, which does not depend on the age of the product:

(t) = = const, where = 1 / m t ; m t - mean time to failure (usually in hours). Then it is expressed as the number of failures per hour and, as a rule, is a small fraction.

Probability of no-failure operation P(t) = 0 = e - t It obeys the exponential law of distribution of the time of no-failure operation and is the same for any identical period of time during the period of normal operation.

The exponential distribution law can approximate the uptime of a wide range of objects (products): especially critical machines operated in the period after the end of running-in and before a significant manifestation of gradual failures; elements of radio electronic equipment; machines with successive replacement of failed parts; machines together with electrical and hydraulic equipment and control systems, etc.; complex objects consisting of many elements (at the same time, the uptime of each may not be distributed according to an exponential law; it is only necessary that the failures of one element that does not obey this law do not dominate the others).

Let us give examples of an unfavorable combination of operating conditions for machine parts that cause their sudden failure (breakdown). For a gear train, this can be the action of the maximum peak load on the weakest tooth when it engages at the apex and interacts with the tooth of the mating wheel, in which pitch errors minimize or exclude the participation of the second pair of teeth. Such a case may occur only after many years of operation or not at all.

An example of an unfavorable combination of conditions that causes a shaft breakage can be the action of the maximum peak load at the position of the most weakened ultimate fibers of the shaft in the load plane.

An essential advantage of the exponential distribution is its simplicity: it has only one parameter.

If, as usual, t 0.1, then the formula for the probability of failure-free operation is simplified as a result of expanding into a series and discarding small terms:

– – –

where N is the total number of observations. Then = 1/.

You can also use the graphical method (Fig. 1.4): put the experimental points in the coordinates t and - lg P (t).

The minus sign is chosen because P(t)L and, therefore, lg P(t) is a negative value.

Then, taking the logarithm of the expression for the probability of failure-free operation: lgР(t) = - t lg e = - 0.343 t, we conclude that the tangent of the angle of the straight line drawn through the experimental points is equal to tg = 0.343, whence = 2.3tg complete the testing of all specimens.

A probability paper (a paper with a scale in which the curved distribution function is shown as a straight line) should have a semi-logarithmic scale for the exponential distribution.

For the system Рst (t) =. If 1 \u003d 2 \u003d ... \u003d n, then Рst (t) \u003d. Thus, the probability of failure-free operation of a system consisting of elements with the probability of failure-free operation according to the exponential law also obeys the exponential law, and the failure rates of individual elements are added. Using the exponential distribution law, it is easy to determine the average number of products i that will fail by a given point in time, and the average number of products Np that will remain operational. At t0.1n Nt; Np N(1 - t).

Example. Estimate the probability P(t) of the absence of sudden failures of the mechanism during t = 10000 h if the failure rate is = 1/mt = 10 – 8 1/h 10-4 0.1, then we use the approximate dependence P (t) = 1- t = 1 - 10- 4 = 0.9999 Calculation according to the exact dependence P (t) = e - t within four decimal places gives an exact match .

Reliability in the period of gradual failures Gradual failures 1 require laws of distribution of uptime, which give at first a low distribution density, then a maximum, and then a drop associated with a decrease in the number of operable elements.

Due to the variety of causes and conditions for the occurrence of failures during this period, several distribution laws are used to describe reliability, which are established by approximating the results of tests or observations in operation.

– – –

where t and s are estimates of the mathematical expectation and standard deviation.

The convergence of parameters and their estimates increases with the number of trials.

Sometimes it is more convenient to operate with the dispersion D = S 2.

The mathematical expectation determines on the graph (see Fig. 1.5) the position of the loop, and the standard deviation determines the width of the loop.

The distribution density curve is sharper and higher, the smaller S.

It starts from t = - and extends to t = + ;

This is not a significant disadvantage, especially if mt 3S, since the area outlined by the branches of the density curve going to infinity, expressing the corresponding failure probability, is very small. Thus, the probability of failure for the period of time before mt - 3S is only 0.135% and is usually not taken into account in the calculations. The probability of failure to mt - 2S is 2.175%. The largest ordinate of the distribution density curve is 0.399/S

– – –

Operations with a normal distribution are simpler than with others, so they are often replaced by other distributions. For small coefficients of variation S/mt, the normal distribution replaces well the binomial, Poisson, and lognormal distributions.

Distribution of the sum of independent random variables U = X + Y + Z, called the composition of distributions, with a normal distribution of terms is also a normal distribution.

The mathematical expectation and variance of the composition are, respectively, m u = m x + m y + mz ; S2u = S2x + S2y + S2z where mx, my, mz are the mathematical expectations of random variables;

X, Y, Z, S2x, S2y, S2z - dispersion of the same values.

Example. Estimate the probability P(t) of non-failure operation during t = 1.5 * 104 hours of the wearable movable interface, if the wear resource obeys a normal distribution with parameters mt = 4 * 104 hours, S = 104 hours.

1.5104 4104 Solution. Find the quantile up = = - 2.5; according to Table 1.1, we determine that P(t) = 0.9938.

Example. Estimate the 80% resource t0.8 of the tractor caterpillar, if it is known that the caterpillar durability is limited by wear, the resource obeys a normal distribution with parameters mt = 104 h; S = 6*103 h.

Solution. At Р(t) = 0.8; up = - 0.84:

T0.8 \u003d mt + upS \u003d 104 - 0.84 * 6 * 103 5 * 103 h.

The Weibull distribution is quite universal, covering a wide range of cases of changing probabilities by varying the parameters.

Along with the logarithmically normal distribution, it satisfactorily describes the fatigue life of parts, the life to failure of bearings, electronic tubes. It is used to assess the reliability of parts and components of machines, in particular, cars, hoisting and transport and other machines.

It is also used to assess the reliability of running-in failures.

The distribution is characterized by the following function of the probability of failure-free operation (Fig. 1.8) Р(t) = 0 Failure rate (t) =

– – –

we introduce the notation y \u003d - lgР (t) and take the logarithm:

log = mlg t – A, where A = logt0 + 0.362.

Plotting the test results on the graph in the coordinates lg t - lg y (Fig.

1.9) and drawing a straight line through the obtained points, we get m=tg ; lg t0 = A where is the angle of inclination of the straight line to the x-axis; A - a segment cut off by a straight line on the y-axis.

The reliability of a system of identical elements connected in series, obeying the Weibull distribution, also obeys the Weibull distribution.

Example. Estimate the probability of failure-free operation P(t) of roller bearings for t=10 h if the bearing life is described by the Weibull distribution with parameters t0 = 104

– – –

where the signs and П mean the sum and the product.

For new products T=0 and Pni(T)=1.

On fig. 1.10 shows the probability curves for the absence of sudden failures, gradual failures and the probability curve for no-failure operation under the combined action of sudden and gradual failures. Initially, when the gradual failure rate is low, the curve follows the PB(t) curve and then drops off sharply.

During the period of gradual failures, their intensity, as a rule, is many times higher than that of sudden failures.

Peculiarities of Reliability of Remanufactured Products Primary failures are considered for non-repairable products, primary and repeated failures for recoverable products. All reasoning and terms for non-repairable products apply to primary failures of remanufactured products.

For refurbished products, the operation graphs of Fig. 1 are indicative.

1.11.a and work fig. 1.11. b remanufactured products. The first show periods of work, repair and prevention (inspections), the second - periods of work. Over time, the periods of work between repairs become shorter, and the periods of repair and maintenance increase.

For restored products, the failure-free properties are characterized by the value (t) - the average number of failures over time t (t) =

– – –

As is known. In case of sudden product failures, the law of distribution of time to failure is exponential with intensity. If the product is replaced with a new one upon failure (restorable product), then a flow of failures is formed, the parameter of which (t) does not depend on t, i.e. (t) = const and is equal to the intensity. The flow of sudden failures is assumed to be stationary, i.e., the average number failures per unit of time are constant, ordinary, in which no more than one failure occurs simultaneously, and without aftereffect, which means the mutual independence of the occurrence of failures in different (non-overlapping) time intervals.

For a stationary, ordinary flow of failures (t)= =1/T, where T is the mean time between failures.

Independent consideration of gradual failures of recoverable products is of interest, because the recovery time after gradual failures is usually significantly longer than after sudden failures.

With the combined action of sudden and gradual failures, the parameters of the failure flows are added.

The flow of gradual (wear and tear) failures becomes stationary when the operating time t is much greater than the average value. So, with a normal distribution of time to failure, the failure rate increases monotonously (see Fig. 1.6. c), and the failure rate parameter (t) first increases, then oscillations begin, which decay at the level 1 / (Fig. 1.12). The observed maxima (t) correspond to the mean time to failure of the first, second, third, etc. generations.

In complex products (systems), the failure flow parameter is considered as the sum of the failure flow parameters. Component flows can be considered by nodes or by types of devices, for example, mechanical, hydraulic, electrical, electronic and others (t) = 1(t) + 1(t) + …. Accordingly, the mean time between failures of the product (during normal operation)

– – –

where Tr Tp Trem - the average value of operating time, downtime, repair.

4. PERFORMANCE OF MAIN ELEMENTS

TECHNICAL SYSTEMS

4.1 Operability of the power plant Durability - one of the most important properties of the reliability of machines - is determined by the technical level of products, the adopted system of maintenance and repairs, operating conditions and operating modes.

Tightening the operating mode for one of the parameters (load, speed or time) leads to an increase in the wear rate of individual elements and a reduction in the service life of the machine. In this regard, the rationale for the rational mode of operation of the machine is essential to ensure durability.

The operating conditions of power plants of machines are characterized by variable load and speed modes of operation, high dust content and large fluctuations in ambient temperature, as well as vibration during operation.

These conditions determine the durability of engines.

The temperature regime of the power plant depends on the ambient temperature. The design of the engine must ensure normal operation at ambient temperature C.

The intensity of vibration during the operation of machines is estimated by the frequency and amplitude of oscillations. This phenomenon causes an increase in wear of parts, loosening of fasteners, leakage of fuels and lubricants, etc.

The main quantitative indicator of the durability of the power plant is its resource, which depends on the operating conditions.

It should be noted that engine failure is the most common cause of machine failures. At the same time, most of the failures are due to operational reasons: a sharp excess of the permissible load limits, the use of contaminated oils and fuels, etc. The engine operation mode is characterized by developed power, crankshaft speed, operating temperatures of oil and coolant. For each engine design, there are optimal values of these indicators, at which the efficiency of use and durability of the engines will be maximum.

The values of indicators deviate sharply when starting, warming up and stopping the engine, therefore, in order to ensure durability, it is necessary to justify the methods of using engines at these stages.

The start of the engine is due to the heating of the air in the cylinders at the end of the compression stroke to a temperature tc, which reaches the self-ignition temperature of the fuel tt. Usually it is considered that tc tT +1000 С. It is known that tт = 250...300 °С. Then the condition for starting the engine is tc 350 ... 400 °С.

The air temperature tc, °C, at the end of the compression stroke depends on the pressure p and the ambient temperature and the degree of wear of the cylinder-piston group:

– – –

where n1 is the exponent of the compression polytrope;

pc is the air pressure at the end of the compression stroke.

With severe wear of the cylinder-piston group during compression, part of the air from the cylinder passes through the gaps into the crankcase. As a result, the values of pc and, consequently, tc also decrease.

The rate of rotation of the crankshaft significantly affects the wear rate of the cylinder-piston group. It must be high enough.

Otherwise, a significant part of the heat released during air compression is transferred through the walls of the coolant cylinders; in this case, the values of n1 and tc decrease. So, with a decrease in the crankshaft speed from 150 to 50 rpm, the value of n1 decreases from 1.32 to 1.28 (Fig. 4.1, a).

The technical condition of the engine is important in ensuring a reliable start. With an increase in wear and clearance in the cylinder-piston group, the pressure pc decreases and the starting speed of the engine shaft increases, i.e. minimum crankshaft speed, nmin, at which a reliable start is possible. This dependence is shown in fig. 4.1, b.

– – –

As can be seen, at pc = 2 MPa, n = 170 rpm, which is the limit for serviceable starting facilities. With a further increase in wear of parts, starting the engine is impossible.

The possibility of starting is significantly affected by the presence of oil on the walls of the cylinders. Oil contributes to the sealing of the cylinder and significantly reduces the wear of its walls. In the case of forced oil supply before start-up, the wear of cylinders during start-up decreases by 7 times, pistons - by 2 times, piston rings - by 1.8 times.

The dependence of the wear rate Vn of engine elements on the operating time t is shown in fig. 4.3.

Within 1 ... 2 minutes after start-up, wear is many times higher than the steady-state value in operating conditions. This is due to the poor conditions for lubricating surfaces during the initial period of engine operation.

Thus, in order to ensure a reliable start at positive temperatures, minimal wear of engine elements and the greatest durability, it is necessary to observe the following rules during operation:

Before starting, ensure the supply of oil to the friction surfaces, for which it is necessary to pump oil, crank the crankshaft with a starter or manually without fuel supply;

During engine start, ensure maximum fuel supply and its immediate reduction after start-up until idling;

At temperatures below 5 °С, the engine must be preheated without load with a gradual increase in temperature to operating values (80...90 °С).

Wear is also affected by the amount of oil entering the contact surfaces. This quantity is determined by the supply of the engine oil pump (Fig. 4.3). The graph shows that for trouble-free operation of the engine, the oil temperature must be at least 0 ° C at a crankshaft speed of n900 rpm. At negative temperatures, the amount of oil will be insufficient, as a result of which damage to the friction surfaces (melting of bearings, scuffing of cylinders) is not ruled out.

– – –

According to the graph, it can also be established that at an oil temperature of 1 tm \u003d 10 ° C, the engine shaft speed should not exceed 1200 rpm, and at tu \u003d 20 ° C - 1,550 rpm. At any speed and load conditions, the engine in question can work without increased wear at a temperature of tM=50 °C. Thus, the engine must be warmed up by gradually increasing the shaft speed as the oil temperature rises.

The wear resistance of engine elements in the load mode is estimated by the wear rate of the main parts at a constant speed and variable fuel supply or variable throttle opening.

With increasing loads, the absolute value of the wear rate of the most critical parts that determine the engine life increases (Fig. 4.4). At the same time, the utilization efficiency of the machine is increased.

Therefore, to determine the optimal load mode of the engine, it is necessary to consider not absolute, but specific values of indicators Vi, MG/h. 4.4. Dependence of wear rate and piston rings on diesel power N: 1-3 - numbers of rings

– – –

Thus, to determine the rational mode of operation of the engine, it is necessary to draw a tangent to the curve tg/p = (p) from the origin.

The vertical passing through the point of contact determines the rational load mode at a given engine crankshaft speed.

The tangent to the graph tg = (p) determines the mode that provides the minimum wear rate; at the same time, wear indicators corresponding to the rational mode of operation of the engine in terms of durability and efficiency of use are taken as 100%.

It should be noted that the nature of the change in hourly fuel consumption is similar to the dependence tg \u003d 1 (pe) (see Fig. 4.5), and the specific fuel consumption is similar to the dependence tg / р \u003d 2 (р). As a result, the operation of the engine, both in terms of wear indicators and in terms of fuel efficiency in low load modes, is economically unprofitable. At the same time, with an overestimated fuel supply (increased p value), a sharp increase in wear indicators and a reduction in engine life (by 25...

30% with an increase in p by 10%).

Similar dependences are valid for engines of various designs, which indicates a general pattern and the expediency of using engines at load conditions close to maximum.

At various speeds, the wear resistance of engine elements is evaluated by changing the crankshaft speed with a constant supply of fuel by a high-pressure pump (for diesel engines) or at a constant throttle position (for carburetor engines).

Changing the speed regime affects the processes of mixture formation and combustion, as well as mechanical and thermal loads on engine parts. With an increase in the crankshaft speed, the values of tg and tg/N increase. This is caused by an increase in the temperature of the mating parts of the cylinder-piston group, as well as an increase in dynamic loads and friction forces.

When the crankshaft speed drops below the specified limit, the wear rate may increase due to the deterioration of the hydrodynamic lubrication regime (Fig. 4.6).

The nature of the change in the specific wear of the crankshaft bearings, depending on the frequency of its rotation, is the same as that of the parts of the cylinder-piston group.

The minimum wear is observed at n = 1400...1700 rpm and is 70...80% of wear at the maximum speed. Increased wear at a high speed is due to an increase in pressure on the supports and an increase in the temperature of the working surfaces and lubricant, at a low speed - the deterioration of the operating conditions of the oil wedge in the support.

Thus, for each engine design, there is an optimal speed mode, in which the specific wear of the main elements will be minimal, and the engine durability will be maximum.

The temperature regime of the engine during operation is usually estimated by the temperature of the coolant or oil.

– – –

800 1200 1600 2000 rpm Fig. 4.6. Dependences of the concentration of iron (CFe) and chromium (CCg) in oil on the crankshaft speed n Total engine wear depends on the temperature of the coolant. There is an optimal temperature regime (70 ... 90 ° C), at which engine wear is minimal. Overheating of the engine causes a decrease in oil viscosity, deformation of parts, breakdown of the oil film, which leads to increased wear of parts.

Corrosion processes have a great influence on the wear rate of cylinder liners. At low engine temperatures (70 °C), individual areas of the sleeve surface are moistened with water condensate containing combustion products of sulfur compounds and other corrosive gases. There is a process of electrochemical corrosion with the formation of oxides. This contributes to intensive corrosion-mechanical wear of the cylinders. The effect of low temperatures on engine wear can be represented as follows. If we take wear at an oil and water temperature of 75 "C as a unit, then at t \u003d 50 ° C, wear will be 1.6 times more, and at t \u003d - 25 ° C - 5 times more.

This implies one of the conditions for ensuring the durability of engines - operation at the optimum temperature regime (70 ... 90 ° C).

As shown by the results of a study of the nature of changes in engine wear under unsteady operating conditions, the wear of such parts as cylinder liners, pistons and rings, main and connecting rod bearing shells increases by 1.2 - 1.8 times.

The main reasons causing an increase in the intensity of wear of parts in unsteady modes in comparison with steady ones are an increase in inertial loads, deterioration in the operating conditions of the lubricant and its purification, and disruption of normal fuel combustion. The transition from liquid friction to boundary friction with rupture of the oil film, as well as an increase in corrosive wear, is not excluded.

Durability is significantly affected by the intensity of changes in carburetor engines. So, at p = 0.56 MPa and n = 0.0102 MPa/s, the wear intensity of the upper compression rings is 1.7 times, and that of the connecting rod bearings, 1.3 times greater than under steady-state conditions (n = 0). With an increase in n to 0.158 MPa/s at the same load, the connecting rod bearing wears out 2.1 times more than with n = 0.

Thus, during the operation of machines, it is necessary to ensure the constancy of the engine operation mode. If this is not possible, then transitions from one mode to another should be carried out smoothly. This increases the life of the engine and transmission elements.

The main influence on the performance of the engine immediately after it is stopped and during the subsequent start-up is exerted by the temperature of parts, oil and coolant. At high temperatures, after the engine is stopped, the lubricant flows from the cylinder walls, which causes increased wear of parts when the engine is started. After the circulation of the coolant stops, vapor locks form in the high-temperature zone, which leads to deformation of the elements of the cylinder block due to uneven cooling of the walls and causes cracks. Silencing an overheated engine also leads to a violation of the tightness of the cylinder head due to the unequal coefficient of linear expansion of the materials of the block and power pins.

In order to avoid these malfunctions, it is recommended to stop the engine at a water temperature not higher than 70 °C.

The temperature of the coolant affects the specific fuel consumption.

At the same time, the optimal mode in terms of efficiency approximately coincides with the mode of minimum wear.

The increase in fuel consumption at low temperatures is mainly due to its incomplete combustion and an increase in the friction torque due to the high viscosity of the oil. Increased heating of the engine is accompanied by thermal deformations of parts and disruption of combustion processes, which also leads to increased fuel consumption. The durability and reliability of the power plant are due to strict observance of the rules of running-in and rational modes of running-in of engine parts during commissioning.

Serial engines in the initial period of operation must undergo preliminary running-in for up to 60 hours at the modes established by the manufacturer. Engines are run-in directly at manufacturing plants and repair plants for 2...3 hours. During this period, the process of forming the surface layer of parts is not completed, therefore, in the initial period of operation of the machine, it is necessary to continue running-in the engine. For example, the run-in without load of a new or overhauled DZ-4 bulldozer engine is 3 hours, then the machine is run in transport mode without load for 5.5 hours. At the last stage of running-in, the bulldozer is gradually loaded while operating in various gears for 54 hours. The duration and efficiency of running-in depend on the loading conditions and the lubricants used.

It is advisable to start the operation of the engine under load with a power of N \u003d 11 ... 14.5 kW at a shaft speed of rotation n \u003d 800 rpm and, gradually increasing, to bring the power to 40 kW at a nominal value of n.

The most effective lubricant used in the process of running in diesel engines is currently DP-8 oil with an additive of 1 vol. % dibenzyl disulfide or dibenzylhexasulfide and a viscosity of 6...8 mm2/s at a temperature of 100°C.

It is possible to significantly accelerate the running-in of diesel parts during factory running-in by adding ALP-2 additive to the fuel. It has been established that by intensifying the wear of the parts of the cylinder-piston group due to the abrasive action of the additive, it is possible to achieve complete running-in of their surfaces and stabilize the oil consumption for waste. Factory run-in of a short duration (75...100 min) with the use of ALP-2 additive provides almost the same quality of parts running-in as a long-term run-in for 52 hours on standard fuel without additive. At the same time, wear of parts and oil consumption for waste are almost the same.

Additive ALP-2 is an organometallic aluminum compound dissolved in diesel oil DS-11 in a ratio of 1:3. The additive is easily soluble in diesel fuel and has high anti-corrosion properties. The action of this additive is based on the formation of finely dispersed solid abrasive particles (aluminum oxide or chromium oxide) during the combustion process, which, getting into the friction zone, create favorable conditions for running-in the surfaces of parts. The ALP-2 additive most significantly affects the running-in of the upper chrome-plated piston ring, the ends of the first piston groove and the upper part of the cylinder liner.

Taking into account the high wear rate of the parts of the cylinder-piston group during the running-in of engines with this additive, it is necessary to automate the fuel supply when organizing tests. This will allow strictly regulating the supply of fuel with an additive and thereby eliminating the possibility of catastrophic wear.

4.2. Performance of transmission elements Transmission elements operate under conditions of high shock and vibration loads in a wide temperature range with high humidity and a significant content of abrasive particles in the environment. Depending on the design of the transmission, its influence on the reliability of the machine varies widely. In the best case, the proportion of transmission element failures is about 30% of the total number of machine failures. In order of increasing reliability, the main elements of the transmission of machines can be distributed as follows: clutch - 43%, gearbox - 35%, driveline - 16%, rear axle gearbox - 6% of the total number of transmission failures.

The transmission of the machine includes the following main elements:

friction clutches, gear reducers, brake devices and control drives. Therefore, it is convenient to consider the operating modes and durability of the transmission in relation to each of the listed elements.

Friction clutches. The main working elements of clutches are friction discs (side clutches of bulldozers, clutches of machine transmissions). High disc friction coefficients (= 0.18 ... 0.20) determine a significant slipping work. In this regard, mechanical energy is converted into thermal energy and intensive wear of the disks occurs. The temperature of parts often reaches 120 ... 150 ° C, and the surfaces of friction discs - 350 ... 400 ° C. As a result, friction clutches are often the least reliable power transmission element.

The durability of friction discs is largely determined by the actions of the operator and depends on the quality of adjustment work, the technical condition of the mechanism, operating modes, etc.

The wear rate of machine elements is significantly affected by the temperature of the friction surfaces.

The process of heat generation during friction of the clutch discs can be approximately described by the following expression:

Q=M*(d - t)/2E

where Q is the amount of heat released during slipping; M is the moment transmitted by the clutch; - slipping time; E - mechanical equivalent of heat; d, t - angular velocity, respectively, of the leading and driven parts.

As follows from the above expression, the amount of heat and the degree of heating of the surfaces of the disks depend on the duration of slipping and the angular velocities of the driving and driven parts of the clutches, which, in turn, are determined by the actions of the operator.

The most difficult for the disks are the operating conditions at m = 0. For the coupling of the engine with the transmission, this corresponds to the moment of starting off.

The operating conditions of friction discs are characterized by two periods. First, when the clutch is engaged, the friction discs approach each other (section 0-1). The angular velocity d of the leading parts is constant, and that of the driven parts t is zero. After the discs touch (point a), the car moves off. The angular velocity of the driving parts decreases, and the driven parts increase. There is a slipping of the disks and a gradual alignment of the values of q and m (point c).

The area of the triangle abc depends on the angular velocities d, t and the time interval 2 - 1 i.e. on the parameters that determine the amount of heat released during slipping. The smaller the difference 2 - 1 and q - m, the lower the temperature of the disk surfaces and the less their wear.

The nature of the influence of the clutch engagement duration on the load of the transmission units. With a sharp release of the clutch pedal (minimum duty cycle), the torque on the driven shaft of the clutch can significantly exceed the theoretical value of the engine torque due to the kinetic energy of the rotating masses. The possibility of transferring such a moment is explained by an increase in the coefficient of adhesion as a result of the summation of the elastic forces of the pressure plate springs and the inertia force of the progressively moving mass of the pressure plate. The dynamic loads that occur in this case often lead to the destruction of the working surfaces of the friction discs, which negatively affects the durability of the clutch.

Gear reducers. The operating conditions of machine gearboxes are characterized by high loads and a wide range of changes in load and speed modes. The wear rate of gear teeth varies over a wide range.

On the shafts of gearboxes, the places of the movable connection of the shafts with the plain bearings (necks), as well as the splined sections of the shafts, wear out most intensively. The wear rate of rolling and plain bearings is 0.015...0.02 and 0.09...0.12 µm/h, respectively. Splined sections of gearbox shafts wear out at a rate of 0.08 ... 0.15 mm per 1,000 hours.

Here are the main reasons for the increased wear of gearbox parts: for gear teeth and plain bearings - the presence of abrasive and fatigue chipping (pitting); for shaft necks and sealing devices - the presence of an abrasive; for splined sections of shafts - plastic deformation.

The average service life of gears is 4000...6000 hours.

The wear rate of gearboxes depends on the following operational factors: speed, load, temperature modes of operation; lubricant quality; the presence of abrasive particles in the environment. So, with an increase in frequency, the resource of the gearbox and the main gearbox of the asphalt distributor of rotation of the engine shaft decreases.

With an increase in the load, the resource of the gearbox gear decreases as the contact stresses in the engagement increase. One of the main factors determining contact stresses is the assembly quality of the mechanism.

An indirect characteristic of these stresses can be the dimensions of the tooth contact patch.

The quality and condition of lubricants have a great influence on the durability of gears. During the operation of gearboxes, the quality of lubricants deteriorates due to their oxidation and contamination with wear products and abrasive particles entering the crankcase from the environment.

The antiwear properties of oils deteriorate as they are used. Thus, the wear of gears with an increase in the time interval between transmission oil changes increases in a linear relationship.

When determining the frequency of oil change in gearboxes, it is necessary to take into account the unit costs for lubrication and repair work Court, rub./h:

Jd=C1/td+ C2/t3+ C3/to where C1 C2, C3 are the costs of adding oil, replacing it and eliminating failures (malfunctions), respectively, rub.; t3, td, tо the frequency of adding oil, replacing it and failures, respectively, h.

The optimal oil change interval corresponds to the minimum unit reduced costs (topt). Operating conditions affect the oil change interval. Oil quality also affects gear wear.

The choice of lubricant for gears depends mainly on the circumferential speed of the gears, the specific loads and the material of the teeth. At high speeds, less viscous oils are used in order to reduce the power consumption for mixing the oil in the crankcase.

Brake devices. The operation of brake mechanisms is accompanied by intensive wear of friction elements (average wear rate is 25...125 µm/h). As a result, the resource of such parts as brake pads and bands is 1,000...2,000 hours.

The frequency and duration of the brakes affect the temperature of the friction surfaces of the friction elements. With frequent and prolonged braking, intensive heating of the friction linings occurs (up to 300 ...

400 °C), as a result of which the coefficient of friction decreases and the wear rate of the elements increases.

The wear process of asbestos-bakelite friction pads and rolled brake bands, as a rule, is described by a linear relationship.

Control drives. The operating conditions of control drives are characterized by high static and dynamic loads, vibration and the presence of abrasive on friction surfaces.

In the design of machines, mechanical, hydraulic, and also combined control systems are used.

The mechanical drive is a swivel with rods or other actuators (gear racks, etc.). The resource of such mechanisms is determined mainly by the wear resistance of hinged joints. The durability of hinged joints depends on the hardness of abrasive particles and their number, as well as on the values and nature of dynamic loads.

The wear intensity of the hinges depends on the hardness of the abrasive particles. An effective method of increasing the durability of mechanical drives during operation is to prevent abrasive particles from entering the hinges (sealing the interfaces).

The main cause of hydraulic system failures is the wear of parts.

The wear rate of hydraulic drive parts and their durability depend on operational factors: fluid temperature, the degree and nature of its contamination, the condition of filtering devices, etc.

With an increase in the temperature of the liquid, the process of hydrocarbon oxidation and the formation of resinous substances also accelerates. These oxidation products, settling on the walls, pollute the hydraulic system, clog the filter channels, which leads to machine failure.

A large number of hydraulic system failures are caused by contamination of the working fluid with wear products and abrasive particles, which cause increased wear and, in some cases, jamming of parts.

The maximum particle size contained in the liquid is determined by the fineness of the filtration.

In the hydraulic system, the filtration fineness is about 10 microns. The presence of larger particles in the hydraulic system is due to the penetration of dust through the seals (for example, in a hydraulic cylinder), as well as the heterogeneity of the pores of the filter element. The wear rate of the hydraulic drive elements depends on the size of the contaminants.

A significant amount of contaminants are introduced into the hydraulic system with topped-up oil. The average operating flow rate of the working fluid in the hydraulic systems of machines is 0.025...0.05 kg/h. At the same time, 0.01 ... 0.12% of contaminants are introduced into the hydraulic system with the added oil, which is 30 g per 25 liters, depending on the filling conditions. Operating instructions recommend flushing the hydraulic system before changing the working fluid.

The hydraulic system is flushed with kerosene or diesel fuel in special installations.

Thus, in order to increase the durability of the elements of the hydraulic drive of machines, it is necessary to carry out a set of measures aimed at ensuring the purity of the working fluid and the recommended thermal regime of the hydraulic system, namely:

strict observance of the requirements of the operating instructions for the hydraulic system;

oil filtration before filling the hydraulic system;

Installation of filters with a fineness of filtration up to 15...20 microns;

Prevention of liquid overheating during machine operation.

4.3. Efficiency of elements of the undercarriage According to the design of the undercarriage, caterpillar and wheeled vehicles are distinguished.

The main cause of caterpillar undercarriage failures is abrasive wear of tracks and track pins, drive wheels, axles and roller bushings. The wear rate of undercarriage parts is affected by the pretensioning of the track. With a strong tension, the wear intensity increases due to an increase in the friction force. With a weak tension, a strong beating of the tracks occurs. Track chain wear is highly dependent on the operating conditions of the machine. The increased wear of the chassis parts is explained by the presence of water with abrasive in the friction zone and corrosion of the surfaces of the parts. The technical condition of the tracks is evaluated by the wear of the tracks and pins. For example, for excavators, the wear of the track eye in diameter by 2.5 mm and wear of the pins by 2.2 mm serve as signs of the limit state of the caterpillar track. The extreme wear of parts leads to an elongation of the caterpillar track by 5 ... 6%.

The main factors that determine the operational properties of the wheel mover are the air pressure in the tires, toe-in and camber.

Tire pressure affects the durability of the machine. Reducing the resource at reduced pressure is caused by large deformations of the tire, its overheating and delamination of the tread. Excessive tire pressure also leads to a reduction in the resource, since this causes large loads on the carcass, especially at the time of overcoming an obstacle.

Tire wear is also affected by wheel alignment and camber angle. Deviation of the toe angle from the norm leads to slipping of the tread elements and its increased wear. An increase in the toe angle leads to more intensive wear of the outer edge of the tread, and a decrease in the inner edge. When the camber angle deviates from the norm, pressures are redistributed in the plane of contact of the tire with the ground and one-sided tread wear occurs.

4.4. Efficiency of electrical equipment of machines Electrical equipment accounts for approximately 10 ... 20% of all machine failures. The least reliable elements of electrical equipment are batteries, a generator and a relay-regulator. Battery life depends on operational factors such as electrolyte temperature and discharge current. The technical condition of the batteries is evaluated by their actual capacity. The decrease in battery capacity (relative to the nominal value) with decreasing temperature is explained by an increase in the density of the electrolyte and a deterioration in its circulation in the pores of the active mass of the plates. In this regard, at low ambient temperatures, the batteries must be thermally insulated.

The performance of batteries depends on the strength of the discharge current Ip. The higher the discharge current, the greater the amount of electrolyte must enter the plates per unit time. At high values of Ip, the depth of electrolyte penetration into the plates decreases and the capacity of the batteries decreases. For example, at Ip = 360 A, a layer of active mass about 0.1 mm thick undergoes chemical transformations, and the battery capacity is only 26.8% of the nominal value.

The greatest load on the battery is observed during the operation of the starter, when the discharge current reaches 300 ... 600 A. In this regard, it is advisable to limit the time of continuous operation of the starter to 5 s.

The frequency of their inclusions significantly affects the performance of batteries at low temperatures (Fig. 4.20). The fewer breaks in work, the faster the batteries are completely discharged, so it is advisable to turn on the starter again no sooner than after 30 seconds.

During the life of the batteries, the capacity of the batteries changes. In the initial period, the capacity increases somewhat due to the development of the active mass of the plates, and then remains constant for a long period of operation. As a result of the wear of the plates, the capacity of the battery decreases, and it fails. The wear of the plates consists in corrosion and deformation of the gratings, sulfation of the plates, precipitation of the active mass from the gratings and its accumulation at the bottom of the battery case. The performance of rechargeable batteries also deteriorates due to their self-discharge and a decrease in the electrolyte level. Self-discharge can be caused by many factors that contribute to the formation of galvanic microelements on positively and negatively charged plates. As a result, the battery voltage drops. The value of self-discharge is affected by the oxidation of cathode lead under the action of air oxygen dissolved in the upper electrolyte layers, the heterogeneity of the grating material and the active mass of the plates, the uneven density of the electrolyte in different sections of the battery, the initial density and temperature of the electrolyte, as well as contamination of the outer surfaces of the batteries. At temperatures below -5 oC, there is practically no self-discharge of the batteries.

With an increase in temperature to 5 ° C, self-discharge appears up to 0.2 ... 0.3% of the capacity per day, and at temperatures of 30 ° C and above - up to 1% of the battery capacity.

The electrolyte level decreases at high temperatures due to water evaporation.

Thus, in order to increase the durability of batteries during their operation, the following rules should be observed:

insulate batteries when used in cold weather;

Reduce to a minimum the duration of the starter switching on with intervals between switching on of at least 30 s;

store batteries at a temperature of about 0o C;

Strictly observe the nominal density of the electrolyte;

Avoid contamination of external surfaces of batteries;

when the electrolyte level drops, add distilled water.

One of the main reasons for the failure of the generator is the increase in its temperature during operation. The heating of the generator depends on the design and technical condition of the electrical equipment elements.

4.5. Methodology for determining the optimal durability of machines Under the optimal durability of machines, they mean the economically justified period of their use before overhaul or decommissioning.

Machines are limited for any of the following reasons:

the impossibility of further operation of the machine due to its 1) technical condition;

2) inexpediency of further operation of the machine from an economic point of view;

3) the inadmissibility of using the machine from the point of view of safety.

When determining the optimal resource of machines before overhaul or decommissioning, technical and economic methods are widely used, which are based on the criterion of economic efficiency of using machines in operation.

Let us consider the sequence of estimating the optimal durability of machines using the techno-economic method. The optimal resource of the machine in this case is determined by the minimum of the unit reduced costs for its acquisition and operation.

The total specific reduced costs Sud (in rubles per unit of operating time) include Spr - specific reduced costs for the purchase of a machine; Cp is the average unit cost of maintaining the machine's performance during operation; C - unit costs for storing the machine, maintenance, refueling it with fuels and lubricants, etc.

– – –

An analysis of the expression shows that with an increase in the operating time T, the value of Cp decreases, the value of Cp (T) increases, and the costs C remain constant.

In this regard, it is obvious that the curve describing the change in the total specific reduced costs must have an inflection at a certain point corresponding to the minimum value of Cmin.

Thus, the optimal resource of the machine before overhaul or decommissioning is determined according to the objective function

– – –

3 +1 = 2 + 2 0 + 3 0 + + 0 2 3 4 + 1 4 The last equation makes it possible to determine T0 by iteration.

Due to the fact that the determination of the optimal resource requires a large amount of calculations, it is necessary to use a computer.

The described method can also be used in determining the optimal durability of overhauled machines.

In this case, in the objective function (5), instead of the cost of purchasing a machine Ср, the specific reduced costs for the overhaul of this machine Ср are taken into account:

L kr \u003d P where S is the cost of overhaul, rub.; E - coefficient of efficiency of capital investments; K - specific investment, rub.; SK - liquidation value, rub.; Fri - technical productivity of the machine, units / h; T - overhaul life, h.

The objective function in determining the optimal resource of overhauled machines has the form Cud(T)= min [Ccr(T)+Cr(T)+C], 0TTn where Tn is the optimal value of the resource of a machine that has not undergone any major repairs.

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The main processes that cause a decrease in the efficiency of machines are considered: friction, wear, plastic deformation, fatigue and corrosion failure of machine parts. The main directions and methods of ensuring the operability of machines are given. Methods for assessing the performance of elements and technical systems as a whole are described. For university students. It can be useful for specialists in the service and technical operation of cars, tractors, construction, road and municipal vehicles.

Technical progress and reliability of machines.
With the development of scientific and technological progress, more and more complex problems arise, the solution of which requires the development of new theories and research methods. In particular, in mechanical engineering, due to the complexity of the design of machines, their technical operation, as well as technological processes, generalization and a more qualified, rigorous engineering approach are required to solve the problems of ensuring the durability of equipment.

Technological progress is associated with the creation of complex modern machines, instruments and working equipment, with a constant increase in quality requirements, as well as with a tightening of operating modes (increase in speeds, operating temperatures, loads). All this was the basis for the development of such scientific disciplines as reliability theory, tribotechnics, technical diagnostics.

CONTENT
Foreword
Chapter 1. The problem of ensuring the operability of technical systems
1.1. Technological progress and machine reliability
1.2. The history of the formation and development of tribotechnics
1.3. The role of tribotechnics in the system of ensuring the operability of machines
1.4. Triboanalysis of technical systems
1.5. Reasons for the decline in the performance of machines in operation
Chapter 2. Properties of working surfaces of machine parts
2.1. Detail profile parameters
2.2. Probabilistic characteristics of profile parameters
2.3. Contact of working surfaces of mating parts
2.4. Structure and physical and mechanical properties of the material of the surface layer of the part
Chapter 3
3.1. Concepts and definitions
3.2. Interaction of working surfaces of parts
3.3. Thermal processes accompanying friction
3.4. The influence of the lubricant on the friction process
3.5. Factors that determine the nature of friction
Chapter 4
4.1. General wear pattern
4.2. Types of wear
4.3. abrasive wear
4.4. fatigue wear
4.5. Seizure wear
4.6. Corrosion-mechanical wear
4.7. Factors affecting the nature and intensity of wear of machine elements
Chapter 5
5.1. Purpose and classification of lubricants
5.2. Lubrication types
5.3. The mechanism of the lubricating action of oils
5.4. Properties of liquid and grease lubricants
5.5. Additives
5.6. Requirements for oils and greases
5.7. Changing the properties of liquid and grease lubricants during operation
5.8. Formation of a complex criterion for assessing the state of machine elements
5.9. Restoring the performance properties of oils
5.10. Restoring the performance of machines with oils
Chapter 6
6.1. Conditions for the development of fatigue processes
6.2. Mechanism of material fatigue failure
6.3. Mathematical description of the process of fatigue failure of a material
6.4. Calculation of fatigue parameters
6.5. Evaluation of fatigue parameters of the material of a part by accelerated testing methods
Chapter 7
7.1. Classification of corrosion processes
7.2. Mechanism of corrosion destruction of materials
7.3. Influence of the corrosive environment on the nature of the destruction of parts
7.4. Conditions for the occurrence of corrosion processes
7.5. Types of corrosion damage of parts
7.6. Factors affecting the development of corrosion processes
7.7. Methods for protecting machine elements from corrosion
Chapter 8
8.1. General concepts of machine performance
8.2. Machine Reliability Planning
8.3. Machine Reliability Program
8.4. Life cycle of machines
Chapter 9
9.1. Presentation of the results of triboanalysis of machine elements
9.2. Determination of performance indicators of machine elements
9.3. Machine Life Optimization Models
Chapter 10
10.1. The performance of the power plant
10.2. The performance of transmission elements
10.3. The performance of the undercarriage elements
10.4. Operability of electrical equipment of machines
10.5. Methodology for determining the optimal durability of machines
Conclusion
Bibliography.

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Course of materials science in questions and answers, Bogodukhov S.I., Grebenyuk V.F., Sinyukhin A.V., 2005
Reliability and diagnostics of automatic control systems, Beloglazov I.N., Krivtsov A.N., Kutsenko B.N., Suslova O.V., Shirgladze A.G., 2008