The problem of choosing a system of units of physical quantities quite recently could not fully relate to our arbitrariness. From the point of view of materialistic philosophy, it was not easy for us to convince anyone that a large branch of the natural sciences, related to ensuring the unity of measurements, is based on the dependence of the main points on our consciousness. It is possible to discuss whether the system of units of physical units is well or poorly composed, but the fact that basically any system of quantities and units has an arbitrariness associated with human consciousness remains indisputable.
In this section, using various examples, we will consider the possibilities of constructing systems of units of physical quantities, so that in the future, when describing the SI system of units or any other systems, it would be possible to evaluate the positive and negative aspects of each of them.
First of all, let's start with definitions.
Units of physical quantities are divided into basic and derivative. Until 1995, there were still additional units - units of flat and solid angles, radians and steradians - but in order to simplify the system, these units were transferred to the category of dimensionless derived units.
Basic physical quantities are quantities chosen arbitrarily and independently of each other.
The basic units are chosen in such a way that, using a regular relationship between quantities, it would be possible to form units of other quantities. Accordingly, the quantities and units formed in this way are called derivatives.
The most important question in the construction of systems of units is how many basic units should there be, or, more precisely, what principles should be followed in constructing a particular system? Partially in the metrological literature one can find the statement that the main principle of the system should consist in the minimum number of basic units. In fact, this approach is incorrect, since following this principle, such a value and unit can be one. For example, almost any physical quantity can be expressed through energy, since in mechanics energy is equal to:
kinetic energy
(1.3)
where m is the mass, -o is the speed of the body;
potential energy
(1.4)
where m - mass, d - acceleration, H - height (length).
In electrical measurements, charge energy
(1.5)
where q is the charge, U is the potential difference.
In optics and quantum mechanics, the energy of a photon
where P is Planck's constant, v is the radiation frequency.
In thermal physics, the energy of the thermal motion of particles
(1.7)
where k is the Boltzmann constant, T is the temperature.
Using these laws and relying on the law of conservation of energy, you can determine any physical quantity, regardless of what phenomena it refers to - mechanical, electrical, optical or thermal.
In order to make what has been said more convincing, let us consider the basic mechanical units adopted in most systems - units of length, time and mass. These quantities are basic, that is, they are chosen arbitrarily and independently of each other. Consider now what is the degree of this independence and whether it is possible to reduce the number of arbitrarily chosen basic mechanical units.
Most of us are used to Newton's second law being written as
(1.8)
where F is the interaction force, m is the mass of the body, and is the acceleration of motion, and this expression is the definition of inertial mass. On the other hand, the gravitational mass, according to the law of universal gravitation, is determined from the relation
(1.9)
where r is the distance between the bodies and γ is the gravitational constant equal to
Considering, for example, uniform motion one body around another in a circle, when the force of inertia F i is equal to the force of gravity F g , and given that the mass m in both laws is the same value, we get:
(1.11)
(1.12)
where T is the circulation period, we get
(1.13)
This is an expression for Keppler's third law, which has long been known for the motion of celestial bodies, i.e. we got the relationship between time T, length r and mass m in the form
(1.14)
This means that it suffices to set the coefficient K equal to one, and the unit of mass will be determined in terms of length and time. The value of this coefficient
(1.15)
is a consequence only of the fact that we have arbitrarily chosen a unit of mass and, in order to bring the situation in line with physical laws, we must introduce an additional factor K in Keppler's law. side, i.e., it completely depends on our choice, determined by the convenience of the practical use of the system.
Naturally, having arbitrarily chosen any unit as the main one, we arbitrarily choose the size of this unit. In mechanical measurements, we have the ability to compare length, time and mass with any quantities of the same name chosen as initial ones. As metrology developed, the definitions of the size of the values of the basic units were repeatedly changed, however, this did not affect either the physical laws or the unity of measurements.
Let us show that the arbitrariness of the choice of the size of the unit takes place not only for the basic, arbitrarily chosen quantities, but also for the quantities of derivatives, i.e., associated with some basic physical law. As an example, let us return to the definitions of force through the inertial properties of bodies or through the gravitational properties. We assume that the main quantities are length, time and mass. Nothing prevents us from considering the coefficient of proportionality equal to unity in the law of universal gravitation, i.e., to assume that
(1.16)
Then in Newton's second law we will have to introduce a proportionality factor called the inertial constant, i.e.
(1.17)
The value of the inertial constant should be equal to
(1.18)
A similar picture can be traced by expressing and accepting a unit area. We are accustomed to the fact that the unit of area is the area of a square with a side unit of length - a square meter, a square centimeter, etc. However, no one forbids choosing the area of a circle with a diameter of 1 meter as a unit of area, i.e., consider What
In this case, the area of the square is
(1.20)
Such a unit of area, called the "round meter", is very convenient in measuring the areas of circles. It is obvious that a "round meter" will be 4/tg times less than a "square meter".
The next issue in the problem of choosing the units of the system is to determine the expediency of introducing new basic units when considering a new class of physical phenomena. Let's start with electromagnetic phenomena. It is well known that electrical phenomena are based on Coulomb's law, which relates mechanical quantities - the force of interaction and the distance between charges - with electrical quantity- charge:
(1.21)
In Coulomb's law, as in other laws where vector quantities are mentioned, we omit the unit vector for the sake of simplicity. In Coulomb's law, the coefficient of proportionality is equal to 1. If we take this as a basis, which is done in some systems of units, then the electrical basic unit is not needed, since the unit of current strength can be obtained from the ratio
(1.22)
where q is the charge defined by Coulomb's law; t - time. All other units of electrical quantities are determined from the laws of electrostatics and electrodynamics. Nevertheless, in most systems of units, including the SI system, electrical phenomena arbitrarily introduce their own electrical basic unit. In the SI system, this is Ampere. By choosing Ampere arbitrarily, the charge will be expressed from the ratio as
(1.23)
As a result, the situation discussed above was repeated, when the same physical quantity is determined twice. Once through the mechanical quantities - formula (1.21). Another time through the Ampere formula (1.23). Such ambiguity forces us to introduce an additional coefficient into Coulomb's law, called the "vacuum permittivity". Coulomb's law takes the form:
(1.24)
Questions are often asked about the physical meaning of the vacuum dielectric constant when they want to find out the degree of understanding of the essence of Coulomb's law. From a metrological point of view, everything is simple and clear: introducing arbitrarily the basic unit of electricity - the ampere - we must take measures to ensure that there is a correspondence between the mechanical units introduced earlier and their new possible expression using the ampere.
Exactly the same situation can be traced in temperature measurements with the introduction of an arbitrarily basic unit - Kelvin, as well as in optical measurements with the introduction of the candela.
Here, the situation with the choice of units of basic physical quantities and with the choice of their size is considered in detail in order to prove the essence of the main principle of constructing systems of units of physical units.
This principle is the convenience of practical use. Only these considerations determine the number of basic units, the choice of their size, and all additional, secondary principles are repelled from this as from the main one. Such, for example, is the well-known principle, which says that as the main quantity one must choose one whose unit can be reproduced with the highest possible accuracy. However, this is desirable, but in some cases it is impractical. In particular, in mechanical measurements, the unit of frequency - hertz - is reproduced with the highest accuracy, however, the frequency did not fall into the category of basic units.
In electrical measurements, Ampere can be more precisely reproduced Volt - a unit of potential difference. In optics, the utmost accuracy has been achieved in energy measurements by counting quanta. For these reasons, the generally accepted expression of quantities and units becomes predominant over the desire to choose the one that is most accurately reproduced as the basic unit.
The final confirmation of the choice of a system of units based on the principle of usability is two points.
The first is the presence in the international SI system of two basic units of the amount of a substance - the kilogram and the mole. Nothing but the convenience of use in chemical processes, the introduction of another basic unit - the mole - this fact can not be explained.
The second is the fact that, in a number of cases, systems of units other than the SI system are used. For many years and decades, metrologists have been trying to leave one single system of units. Nevertheless, in calculations of atomic and molecular structures, the SI system is inconvenient, and people continue to use the atomic system of units, in which the main quantities are determined by the size of the atom and the processes occurring in the atom. When considering various systems of units, we will dwell in detail on the construction of this system. Similarly, the SI system turns out to be inconvenient when measuring distances to space objects. This area has developed its own specific system of units and quantities.
Summarizing, the choice in metrology of a system of units of physical quantities is mainly related to the convenience of their use and to a large extent relies on traditions in solving the problem of ensuring the uniformity of measurements.
Lecture 1
Introductory lesson. Subject "Metrology", tasks, principles, objects and means of metrology, standardization and certification. Law of the Russian Federation "On ensuring the uniformity of measurements". International Organizations for Metrology.
Word metrology formed from two Greek words metronome(measure) and logos(teaching, skill) and means - the doctrine of measures. Metrology in the modern sense is the science of measurements, methods and means of ensuring their unity and ways to achieve the required accuracy.
unity of measurements the state of measurements is called, in which their results are expressed in legal units and the errors are known with a given probability.
For a long time, metrology was basically a descriptive science of various measures and the relationships between them. But in the process of development of society, the role of measurements increased, and since the end of the last century, thanks to the progress of physics, metrology has risen to a qualitatively new level.
Today, metrology is not only the science of measurements, but also an activity that involves the study of physical quantities, their reproduction and transmission, the use of standards, the basic principles and methods for creating measuring instruments, the assessment of their error, as well as metrological control and supervision.
The purpose of metrology is to ensure the uniformity of measurements, i.e. comparability and consistency of their results, regardless of where, when and by whom these results were obtained.
Since responsible decisions are made based on the results of measurements, the appropriate accuracy, reliability and timeliness of measurements must be ensured.
Three can be distinguished main functions measurements in the national economy:
1) product accounting National economy, calculated by mass, length, volume, consumption, power, energy;
2) measurements carried out to control and regulate technological processes and to ensure the normal functioning of transport and communications;
3) measurements of physical quantities, technical parameters, composition and properties of substances, carried out at scientific research, testing and control of products in various sectors of the national economy.
The significance of measurements is especially important in the transition to market relations associated with competition between manufacturers and, accordingly, with increased requirements for quality and technical parameters of products. Improving the quality of measurements and the introduction of new measurement methods depend on the level of development of metrology.
The main tasks of metrology are;
Provision of research, production and operation of technical devices;
condition monitoring environment;
Provision of institutions of organizations with appropriate measuring instruments.
Metrology is divided into
general - theoretical and experimental;
applied (practical);
Legislative.
Theoretical metrology deals with issues of fundamental research, the creation of a system of units of measurement, physical constants, the development of new measurement methods.
Experimental metrology- issues of creating standards, samples of measures, development of new measuring instruments, devices and information systems.
Applied (practical) metrology deals with issues practical application in various fields of activity the results of theoretical research within the framework of metrology.
legal metrology includes a set of interrelated and interdependent general rules, as well as other issues, the regulation and control of which are necessary on the part of the state and to ensure the uniformity of measurements and the uniformity of the measurement system.
Metrological Service- a set of subjects of activity and types of work aimed at ensuring the uniformity of measurements.
The law specifies that State metrological service is under the jurisdiction of the State Standard of Russia and includes: state scientific metrological centers; bodies of the State Metrological Service on the territory of the republics within the Russian Federation, the autonomous region, autonomous districts, territories, regions, cities of Moscow and St. Petersburg.
Gosstandart of Russia manages the State Service for Time and Frequency and Determination of the Parameters of the Earth’s Rotation (GSVCH), the State Service for Reference Materials of the Composition and Properties of Substances and Materials (GSSO) and the State Service for Standard Reference Data on Physical Constants and Properties of Substances and Materials (GSSSD) and coordinates their activities.
The objects of state supervision are:
1. normative documents on standardization and technical documentation;
2. products, processes and services;
3. other objects in accordance with the current legislation on state supervision.
In 1993, the "Law of the Russian Federation on Ensuring the Uniformity of Measurements" was adopted, which establishes the legal basis for ensuring the uniformity of measurements in the Russian Federation. The law regulates the relations of state authorities of the Russian Federation with legal entities and individuals on the manufacture, production, operation, repair, sale and import of measuring instruments and is aimed at protecting the rights and legitimate interests of citizens, the established legal order and the economy of the Russian Federation from the negative consequences of unreliable measurement results .
The law "On Ensuring the Uniformity of Measurements" consists of seven sections: general provisions; units of quantities, means and methods for performing measurements; metrological services; state metrological control and supervision; calibration and certification of measuring instruments; liability for violation of the law and financing of work to ensure the uniformity of measurements.
In the first section, the Law "On Ensuring the Uniformity of Measurements" establishes and legislates the basic concepts adopted for the purposes of the Law: the uniformity of measurements, the measuring instrument, the state standard of the unit of quantity, regulatory documents for ensuring the uniformity of measurements, the metrological service, metrological control and supervision, verification and calibration of measuring instruments, certificate of approval of the type of measuring instruments, accreditation for the right to verify measuring instruments and calibration certificate. The first article of the law provides the following definition of the concept of "uniformity of measurements".
unity of measurements- the state of measurements, in which their results are expressed in legal units of quantities and measurement errors do not go beyond established boundaries with a given probability.
The concept of "uniformity of measurements" covers the most important tasks of metrology: the unification of units, the development of systems for reproducing units and transferring their sizes to working measuring instruments With the established accuracy, carrying out measurements with an error not exceeding the established limits, etc. The unity of measurements must be maintained with any measurement accuracy required by the industry.
Ensuring the uniformity of measurements is task of metrological services.
A set of regulatory, regulatory, technical and methodological documents of the intersectoral level that establishes rules, norms, requirements aimed at achieving and maintaining the uniformity of measurements in the country with the required accuracy, is state system for ensuring the uniformity of measurements(GSI).
The CSI identifies basic standards that establish general requirements, rules and regulations, as well as standards covering a specific area or type of measurement.
The fundamental basic standards include, for example, GOST 8.417 “GSI. Units of physical quantities”, GOST 16363 “Metrology. Terms and definitions”. Basic standards can be divided into groups depending on the object of standardization:
standards of units of physical quantities;
transfer of information about the size of a unit from standards to measuring instruments;
· the order of standardization of metrological characteristics of measuring instruments;
rules for the implementation and presentation of measurement results;
Uniformity of measuring instruments;
metrological supervision of the development, condition and use of measuring instruments;
· public service of standard reference data.
Currently, the regulatory framework of the GS I includes more than 2,600 documents, including 388 GOSTs, about 2,000 guidelines of metrological institutes, 77 guidance documents and 87 instructions.
The network of organizations that are responsible for the metrological support of measurements constitutes the metrological service. There are two levels of the metrological service - the state metrological service and the metrological services of legal entities (enterprises and associations).
The civil service includes territorial bodies and state scientific metrological centers (NII Gosstandart of Russia). The structure of the state metrological service also includes specialized services: the state service of time and frequency - GSVCH, the state service of reference samples - GSSO, the state service of standard reference data - GSSSD.
The main types of metrological activities include metrological support of production preparation, state testing of measuring instruments, verification of measuring instruments.
Metrological support of production preparation- this is a set of organizational and technical measures aimed at determining with the required accuracy the parameters of products (products, assemblies, materials) and raw materials, technological processes and equipment and allowing to achieve High Quality products, as well as reducing unproductive costs for its release.
Works on metrological support of production preparation are carried out by metrological, design, technological services of enterprises from the moment of receipt of the initial documents for the product being mastered.
Tests of measuring instruments are carried out by state scientific centers of the State Standard of Russia.
The committee consists of representatives of:
· the state center of testing of measuring instruments;
the customer of measuring instruments;
departmental metrological service;
development organization;
the manufacturer of measuring instruments.
In case of successful testing of the measuring instrument, as a result of which all parameters and characteristics of the measuring instruments are confirmed, the documentation is submitted to the State Standard of Russia and a decision is made to approve the type of the measuring instrument. This decision is certified by a type approval certificate for measuring instruments. The approved type is entered in the state register of measuring instruments.
State metrological control and supervision is a technical and legal activity carried out by the bodies of the state metrological service in order to verify compliance with the rules of legal metrology - the Law of the Russian Federation "On ensuring the uniformity of measurements", regulations on metrology.
The objects of state metrological control and supervision include:
measuring instruments;
standards used for verification of measuring instruments;
methods of performing measurements;
the number of packaged goods in packages of any kind during their sale and packaging.
State metrological control (GMK) is distributed:
1. for health, veterinary, environmental protection, safety;
2. trading operations and mutual settlements between the buyer and the seller;
3. state accounting operations;
4. ensuring defense;
5. geodetic and hydrometeorological works;
6. banking, tax, customs and postal operations;
7. products supplied under government contracts;
8. testing and quality control of products for compliance with the mandatory requirements of standards and with mandatory certification of products;
9. measurements carried out on behalf of the court, prosecutor's office, arbitration, other government bodies;
10. registration of national and international sports records.
Characteristic types of public metrological control and supervision.State metrological control and supervision includes:
1. state metrological supervision of the quantity of goods alienated in the course of trading operations; for the quantity of packaged goods in packages of any kind during their packaging and sale;
2. verification of measuring instruments, including standards;
3. approval of the type of measuring instruments;
licensing of the activities of legal entities and individuals in the manufacture, repair, sale, rental of measuring instruments. Trade operations are subject to state metrological control, in the course of which the mass, volume, consumption and other quantities characterizing the quantity of goods alienated are determined.
State metrological supervision in the field of banking operations is subject to measuring instruments for the identification of securities and currencies (for example, currency detectors, banknote counters), electronic signatures, collateral values. When accepting for deposit storage such valuables as, for example, precious metals, precious stones, banks must ensure that their quantity and composition are measured with the required accuracy.
State metrological supervision is subject to packaged goods in packages of any kind during their sale or packaging, in cases where the contents of the package cannot be changed without opening or deforming it, and the amount of the content is indicated by the mass value printed on the package. When carrying out supervision, they check the correspondence of the actual value of the mass, volume and other quantities to the quantity of the goods actually contained in the package and the value printed on the package.
Measuring instruments used in the specified areas of state metrological control and supervision are subject to verification by the bodies of the state metrological service during production and after repair, during operation and sale, and import. Verification of measuring instruments is carried out by persons certified as verification officers in the bodies of the state metrological service. Positive results of verification of measuring instruments are certified with a verification mark or a verification certificate. The sign of the verification mark is applied to the measuring instruments and to the operational documentation, and in the case of issuing a verification certificate, to the certificate. If the sign of the verification mark is damaged, and also if the certificate is lost, the measuring instrument is recognized as unsuitable for use.
Measuring instruments intended for release or import by import are subject to mandatory tests followed by type approval. The decision to approve the type of measuring instrument is taken by the State Standard of Russia and certified by a certificate. The approved type is entered into the State Register of Measuring Instruments. In necessary cases, the type of measuring instrument is also subject to mandatory certification for safety of use in accordance with the legislation on protecting the health, life and property of citizens, labor protection and the environment.
Organization of state metrological control and supervision. Control and supervision are carried out by state inspectors of the bodies of the state metrological service. State inspectors freely visit facilities where measuring instruments are used in order to verify them, select samples of goods for control during their sale and packaging, and other types of control. If a violation is detected, the state inspector has the right to prohibit the use of measuring instruments of unapproved, as well as unverified types; extinguish marks or cancel the verification certificate in cases where the measuring instrument gives incorrect readings or the calibration interval is overdue; give mandatory instructions and set deadlines for eliminating violations of metrological rules; draw up protocols on the administrative responsibility of violators of metrological rules for making decisions on the application of sanctions.
Legal entities and individuals are obliged to assist the inspector in the performance of the duties assigned to him. Persons who impede the implementation of state metrological control and supervision are liable in accordance with applicable law.
In accordance with the current legislation, violation of the rules of legal metrology provides for administrative and criminal liability, economic sanctions.
Administrative responsibility for violation of the rules is borne by the heads and officials of legal entities, as well as individuals through whose fault the violations were committed. Administrative penalties are imposed in the form of a fine. The basis for the penalty is non-compliance with the rules of metrology in the sale and packaging of goods in packages, non-compliance with the rules for verifying measuring instruments, obstruction of the exercise of metrological control and supervision by authorized bodies.
Criminal liability arises in the case of the use of unverified or other unsuitable measuring instruments in the retail trade network or in the field of public catering, healthcare, environmental protection, and security. Depending on the degree of violation of the metrological rules, a large fine, correctional labor, deprivation of the right to hold positions related to measurement, and imprisonment are provided. Economic sanctions are usually applied to legal entities. The amount of sanctions is determined by the current legislation.
| Composition of the State Metrological Service of the Russian Federation (GMS). | |||
| Name of institution | Functions of the institution | ||
| Federal Agency for Technical Regulation and Metrology - headed by the State Migration Service | Development, discussion, approval and accounting of technical regulations, national standards, all-Russian classifiers, cataloging systems, etc. Leadership_coordination of activities of the GMS. Holding competitions for awards of the Government of the Russian Federation. | ||
| State scientific metrological centers (GNMC) -7VNII | Storage of state standards, research; development of high-precision measurement methods and regulatory documents | ||
| Regional Centers for Standardization, Metrology and Certification (CSM and C) - more | State control and supervision of ensuring the uniformity of measurements in the region, metrological support of enterprises, verification and calibration of measuring instruments, accreditation of measuring laboratories, training and certification of verification officers, development of new measuring instruments, maintenance and repair. | ||
| public service Time, Frequency and Earth Rotation Parameters (GRSH) | Inter-regional and inter-branch coordination of work in this area, storage and transmission of the unit of time and frequency, coordinates of the earth's poles. Measurement information is used by navigation and control services for ships, aircraft and satellites, etc. | ||
| State Service for Reference Materials of Composition and Properties of Materials (GSSO) | They provide the development of means for comparing standard samples with the characteristics of substances and materials that are produced by industrial and agricultural enterprises, for their identification and control. | ||
| State Service for Standard Reference Data on Physical Constants and Properties of Substances and Materials (GSSSD) | They ensure the development of reliable data on physical constants, properties of substances, oil, gas, etc. The information is used by organizations that create new technology. | ||
| International metrology organizations | ||
| Name of company | Goals, objectives and activities of the organization | |
| 1. International Organization of Legal Metrology (OIML) | Created in 1955. It unites more than 80 states. Objectives: development of general issues of legal metrology, incl. establishment of MI accuracy classes, ensuring uniformity in the definition of types and samples of MI systems, recommendations for testing and training. supreme body international Conference legal metrology. It is convened once every 4 years. Decisions are advisory in nature. Russia is represented in the OIML by the Federal Agency for Technical Regulation and Metrology, as well as 12 ministries and departments. The participation of Russia makes it possible to influence the content of the adopted recommendations, achieving their compliance with Russian standards, and makes it possible to improve metrological work. | |
| 2. International Organization of Weights and Measures (IOMB) | It was created in 1875 - the Metrological Convention was signed. Goals: unification of national units of measurement and establishment of common actual standards of length and mass. BIPM is a research laboratory that stores and maintains international standards. ITS main task is the comparison of national standards with international ones, the improvement of measurement systems. The supreme body of the MOMB is the General Conference of Weights and Measures. (1 time in 4 years). The work of the IPM between conferences is managed by the International Committee of Weights and Measures, which includes the largest physicists and metrologists of the world, incl. Russian representatives. There are 18 members in total. The most important result of the activity is the transition of countries to common units and standards. | |
| 3. International Organization for Standardization (ISO) | Created in 1946. ISO members are national organizations for standardization of the countries of the world. 135 countries are represented. The scope of ISO covers all areas except electrical and electronic engineering. Main tasks: development of standardization, metrology and certification in order to ensure the exchange of goods and services, development of cooperation in the scientific, technical and economic fields. ISO standards are the most widely used in the world, their total number exceeds 12,000. About 1,000 standards are adopted and revised annually. They are not binding on ISO member countries. Everything depends on the degree of participation of the country in the international division of labor and the state of its foreign trade. In Russia, there is an active process of introducing ISO standards and the national standardization system. | |
| 4. International Electrotechnical Commission (IEC) | Established in 1906. Autonomous organization within the ISO. The main goal is defined by the Charter - to promote international cooperation in standardization in the field of electrical and radio engineering through the development of standards. Countries are represented in the IEC by their national authority | |
| standardization (RF - Federal Agency for Technical Regulation and Metrology). The supreme governing body of the IEC is the Council of National Committees of all countries. IEC has adopted more than 2000 standards. They are more specific than ISO standards and therefore more suitable for use in IEC member countries. More than half of the standards adopted by the IEC have been implemented in Russia. | ||
| European Organization for Metrology (EUROMET) | Regional international organization. Works in the field of research and development of national standards, promotes the development of verification services, develops methods of the highest accuracy. | |
International Organization of Weights and Measures(IOM) ensures the storage and maintenance of international standards of various units and the comparison of state standards with them and consists of the General Conference of Weights and Measures, the International Committee on Weights and Measures, the International Bureau of Weights and Measures (BIPM).
In most countries of the world, measures to ensure the uniformity of measurements are established by law. Therefore, one of the sections of metrology is called legal metrology and includes a set of general rules, requirements and norms aimed at ensuring the uniformity of measurements and the uniformity of measuring instruments. For uniformity in units of measurement, in 1978 the International Standard "Units of Physical Quantities" (SI) was approved, which was introduced on January 1, 1979 as mandatory in all areas of the national economy, science, technology and teaching.
Basic concepts and definitions accepted in metrology. Physical quantities. Scale types. Concepts about the system of physical quantities.
The main terms and definitions are formulated in a number of normative and technical documents.
Physical quantity- a property of a physical object, phenomenon or process, which is qualitatively common for many physical objects, but in quantitative terms is individual for each of them, for example, length, mass, electrical resistance.
Measurement- a set of operations for the application technical means, which stores a unit of a physical quantity, consisting in comparing the measured quantity with a unit.
Measuring range- the range of values within which the permissible error limits are normalized. Quantity values that limit the measurement range from below or above (left or right) are called the lower limit or upper limit of measurements.
Sensitivity threshold- the smallest value of the measured value, which causes a noticeable change in the output signal. For example, if the sensitivity threshold of the balance is $Q mi" to, this means that a noticeable movement of the balance needle is achieved with such a small change in mass as 10 mg.
MEASUREMENT SCALE
Measurement scale- this is an ordered set of values of a physical quantity that serves as the basis for measuring this quantity. The ordering of the values of a physical quantity can be achieved in different ways.
Name scale is characterized only by the equivalence relation of various qualitative manifestations of the property. These scales do not have a zero mark, units of measurement, they do not have comparison relationships such as more, less, better, worse, etc. For example, in the color scale, the measurement process is achieved by determining the equivalence of the test sample with one of the standards included in the color atlas during visual observation.
The simplest way obtaining information that allows you to get some idea of the size of the measured value, is to compare it with another according to the principle “what is more (less)?”, Or “what is better (worse)?”.
In this case, the number of sizes compared with each other can be quite large. Arranged in ascending or descending order, the dimensions of the measured quantities form order scales.
The operation of arranging dimensions in ascending or descending order in order to obtain measurement information on an order scale is called ranking . To facilitate measurements on the order scale, some points on it can be fixed as reference (reference). Scale points can be assigned numbers, often referred to as points. For example, knowledge is assessed on a four-point reference scale, which looks like this: unsatisfactory, satisfactory, good, excellent. The reference scales measure the hardness of minerals, the sensitivity of films and other quantities (the intensity of earthquakes is measured on a 12-point scale, called the international seismic scale).
Interval scale (differences) describes the properties of a quantity not only with the help of equivalence relations, but also with the help of summation and proportionality of the intervals between the quantitative manifestations of the property. An example is the time scale, which is divided into large intervals - years, into smaller ones - days, etc.
On the scale of intervals, one can judge not only that one size is larger than another, but also how much larger. However, on the scale of intervals, it is impossible to estimate how many times one size is larger than the other. This is due to the fact that only the scale is known on the interval scale, and the origin can be chosen arbitrarily.
The most perfect is relationship scale. An example of it is the Kelvin temperature scale, the Celsius scale, mass scales, etc.
On the ratio scale, you can determine not only how much one size is larger than the other, but also how many times larger or smaller.
PHYSICAL QUANTITIES
main object measurements in metrology are physical quantities. The physical quantity is used to describe material systems, objects, phenomena, processes studied in any sciences. There are basic and derived quantities. The values that characterize the fundamental properties of the material world are chosen as the main ones. GOST 8. 417 establishes seven basic physical quantities: length, mass, time, thermodynamic temperature, amount of substance, light intensity, current intensity. Measured quantities have quantitative and qualitative characteristics.
A formalized reflection of the qualitative difference between the measured quantities is their dimension. In accordance with ISO documents, dimension is denoted by the symbol dim (from Latin dimension - measurement).
The dimension of the basic physical quantities - length, mass, time - is indicated by the corresponding capital letters:
dim t= T.
The dimension of a physical quantity is written as a product of the symbols of the corresponding basic physical quantities raised to a certain degree - the dimension indicator:
Where L, M, T- dimensions of basic physical quantities;
Dimension indicators (exponents of the degree to which the dimensions of the basic physical quantities are raised).
For example: the dimension of acceleration is m/s 2
Each measure can be positive or negative, integer or fractional, zero. If all dimensions are equal to zero, then the value is called dimensionless.
The quantitative characteristic of the measured quantity is its size. Obtaining information about the size of a physical quantity is the content of any measurement.
Measured value- an estimate of the size of a physical quantity in the form of a certain number of units accepted for it.
For example: L= 1 m = 100 cm = 1000 mm.
The abstract number included in it is called numerical value. In the given example it is 1, 100, 1000.
The value of a physical quantity is obtained as a result of its measurement or calculation in accordance with the basic measurement equation:
where Q is the value of a physical quantity;
X- numerical value of the measured quantity in the accepted unit; [Q] - selected unit for measurement.
Suppose the length of a straight line segment of 10 cm is measured using a ruler with divisions in centimeters and millimeters. For this case:
At the same time, the use of different units (1 cm and 1 mm) led to a change in the numerical value of the measurement result.
Principles of construction of the International system of units. Benefits of SI.
Unit of physical quantity is a physical quantity that is assigned a numerical value by definition, equal to one(1 m, 1 lb, 1 cm). System of units of physical quantities- a set of basic and derived units related to a certain system of quantities and formed in accordance with accepted principles.
In Russia, as in almost all countries of the world, the International System of Units operates, the main physical quantities of which are the meter, kilogram, second, ampere, candela, kelvin, mole. The international system was approved in 1960 at the XI Conference of Weights and Measures.
Units of physical quantities of the international system of physical quantities are formed on the basis of laws establishing a relationship between physical quantities, or on the basis of physical quantities accepted in certain research institutes.
For uniformity in units of measurement, in 1978 the International Standard "Units of Physical Quantities" (SI) was approved, which was introduced on January 1, 1979 as mandatory in all areas of the national economy, science, technology and teaching.
SI contains seven basic units that affect the measurement of various parameters: mechanical, thermal, electrical, magnetic, light, acoustic and ionizing radiation and in the field of chemistry. The main units are set: meter (m) - for measuring length; kilogram (kg) - for measuring mass; second (s) - for measuring time; ampere (A) - for measuring the strength of an electric current; Kelvin (K) - for measuring temperature; candela (candle) cd - to measure the intensity of light, mole - to measure the amount of a substance.
Until 1960, the distance between the midpoints of two strokes on an X-shaped bar made of an alloy of platinum and iridium was taken as an international standard and a national standard of length 1 m. With this standard, the distance between the midpoints of the strokes could not be measured more accurately than ±0.1 µm, which did not meet the requirements of the current state of science and technology. The disadvantage of the standard was also the fact that it was a metal bar, which during a natural disaster (for example, an earthquake or flood) could disappear or lose the exact value of the meter over time.
Principles of construction of the International System of Units
The first system of units of physical quantities, although it was not yet a system of units in the modern sense, was adopted by the National Assembly of France in 1791. It included units of length, area, volume, capacity and mass, the main of which were two units: meter and kilogram.
The system of units as a set of basic and derived units was first proposed in 1832 by the German scientist K. Gauss. He built a system of units, where he took the units of length (millimeter), mass (milligram) and time (second) as the basis, and called it the absolute system
Unit of length(meter) is the length of the path traveled by light in vacuum in 1/299,792,458 of a second.
Mass unit(kilogram)- mass equal to the mass of the international prototype of the kilogram.
Even in ancient times, the advantages of using systems of interrelated measures and units in comparison with separate, disparate measures and units of measurement were recognized.
The first systems that could reasonably be called systems of units were Gaussian (milligram, millimeter, second) and a number of CGS systems (centimeter, gram, second). Further development of such systems led to the development and adoption in 1960 by the XI General Conference on Weights and Measures of the International System of Units (Le Systeme international d'unites - abbreviated - SI).
The starting point for SI is, of course, metric system, proposed in 1791. The next stage is the signing of the diplomatic document of the metric conference of 1875 by the seventeen leading industrial powers of the world.
In 1881, the CGS system appeared (development of the Gaussian system) and later, due to the need to use it to measure not only mechanical, but also electromagnetic quantities, its varieties (the most famous are CGSE and CGSM). The next important stage was the adoption in 1950 of the MKSA system - the Georgi system, in which the fourth basic unit appeared - the ampere. MKSA entered the SI as its component used for electrical and magnetic quantities. The need to include thermal and light quantities in the system led to the inclusion of two more basic units in the SI - kelvin and candela. In 1971, the mole was included in the basic units. Before proceeding to a detailed consideration of SI, it is necessary to dwell on general principles building systems of units of measurement.
Principles for constructing systems of units of measurement
The method of constructing systems of units, in its original form, was developed by F. Gauss. According to this method, the construction of systems of units of measurement begins with the choice of the minimum number of basic units through which all practically used units of measurement are expressed - called derivatives. It is interesting to note that there are no theoretically substantiated algorithms that make it possible to unambiguously determine the set (set) of the basic units necessary to build a system. The only criterion in choosing the basic units can only be the effectiveness and expediency of using this system. Different systems are based on different numbers of base units. As already mentioned, the metric system of 1791 was based on one basic unit - the meter, then on two - the meter and the kilogram. The Gaussian system and the CGS system - on three. GHS options - GHSέ0; CGSµ0; SGSF; SGSB - on four. The ISS system is again on three, its variants are MKSK, MKSA, MKSµ0; MKSKD and MKSLM - on four. SI includes 7 basic units. This is the maximum number for all known systems of units.
Initially, it was assumed that the basic units should be reproduced completely independently of each other. As will be shown below, in fact, significant deviations from this principle appeared in the systems of units.
The next stage in the development of the system is the assignment of letter symbols to the basic units of their dimensions. This is followed by the stage of including in the system a certain set of derived units, expressed in terms of the main ones and the dimensions assigned to them by substituting the symbols of the main units into the physical equations that define these units through the main ones.
Dimensionality of the measured quantities and units of measurements
Dimension is an expression in the form of a power monomial, composed of the products of symbols of basic units in various degrees and reflecting the connection of this derived unit with the main ones.
There are two interpretations of the concept of "dimension". One by one - the dimensions are assigned to the values, by the other - to the units. Obviously, units, being particular realizations of quantities, have the same dimensions with them, therefore there is no fundamental contradiction between these points of view. In all physical, metrological literature and in this book, dimension is understood, first of all, only a generalized expression of the dependence of a unit of a given quantity on basic units.
Thus, the dimensions assigned to the basic and derived units are at the same time the dimensions of the corresponding quantities. It is necessary to warn against the thoughtless, automatic, use of the terms "basic and derived quantities". All quantities denote existing properties, among which there are neither basic nor derivative ones. All quantities are equal in this sense. Another thing is the units within the framework of the system that unites them. Forming a system of units, we have the right to subdivide them into basic and derivative.
It follows from the theory of measurement scales that only units of metric scales of differences and ratios have dimensions. Units of absolute scales are dimensionless in principle, even when included in any system of units. Name and order scales do not have units of measurement, therefore, the concept of “dimension” is not applicable to numbers, points and other signs characterizing these scales.
Recall that most of the classics of physics and metrology believed and still believe that "the dimension of a quantity is not a property associated with its essence, but is a kind of convention associated with the choice of a system of units" (M. Planck, P. Bridgman and others .). This opinion is confirmed by the dependence of the dimension of units on the chosen system, the coincidence of the dimensions of quantities that have a different physical nature, the dimensions of a number of quantities that are difficult to physically interpret (for example, electric capacitance), and the fact that quantities that are dimensional in one system may be dimensionless in another.
Here is what G. Hartley wrote about this in his monograph “Analysis of dimensions”: “There is no such thing as the absolute dimension of a physical quantity ... Dimensions ... are relative by definition. The formula for the dimension of a physical quantity is based on the definition of this quantity using the basic units of measurement, the choice of which (within certain limits) is arbitrary. It can be seen from the foregoing that the dimension symbols are specific logical operators, functionally defined only within the framework of the corresponding systems of units. Dimension symbols are not ordinary quantities, and the abstract algebra of operations with them differs from ordinary algebra. The use of these operators outside of systems of units is meaningless.
In practice, we are not interested in dimensions, as such, but in expressions that relate units of measurement to the basic units of the system and to each other. In structure, they are similar, but not identical: dimension symbols are abstracted from the specific dimensions of units of measurement. It is no coincidence that in the tables of the international document "Le Systeme international d´unites" there is no column "dimension", but only expressions of the relationship between different units of measurement are given.
The dimension of a quantity is simultaneously the dimension of its unit. Example: the dimension of the area (values) is L², the dimension of the area unit is m², and also - L². The dimension of the basic unit of the system coincides with its symbol to a degree equal to 1. The degrees of symbols of the basic units included in the monomial can be integer, fractional, positive, negative, they are called indicators of the dimension of derived units. The set of dimensions of the basic and derived units of this system forms a dimensional system. Its base is the dimensions of the basic units. Over the dimensions, you can perform the formal operations of multiplication, division, exponentiation, root extraction. Adding and subtracting dimensions does not make sense. The dimension of units (values) depends on the accepted system of units. A unit in the dimension of which at least one of the basic units is raised to a non-zero power is called dimensional, otherwise it is called dimensionless. Recall that a unit of a particular quantity, which is dimensionless in one system, can be dimensional in another, and vice versa.
International system of units - SI
SI is a corent system built according to the decimal principle: multiples and submultiples are formed by multiplying the original units by factors equal to ten to a positive or negative integer degree, and in equations linking the units of the system, the numerical coefficients are equal to one.
The adoption of SI made it possible to unify the units of measurement - for each quantity one and only one unit was adopted. SI covers most areas of the natural sciences and engineering. Its units, as a rule, have dimensions that are convenient for practical use. The units of mass and force (weight) are clearly delineated. For all types of energy, one unit is set - the joule (thus, there is no need for various conversion factors). The writing of equations and formulas in various fields of science and technology has been simplified. But SI cannot be considered all-encompassing. It applies only to metric scales of scalar quantities. It must also be realized that, in fact, in the SI, dimensionless and counting units of absolute scales are used to form many derived units. Let us especially note the usual and unnoticed conventionality of the extension of SI to vector quantities, such as speed, acceleration, angular velocity of rotation, force, moment of force, electric and magnetic field etc. In fact, the corresponding units of measurement (m/s, m/s², rad/s, N, Nm, V/m, A/m) can only correspond to the modules of these vectors – scalar quantities. For full description vectors, including their direction, it is mandatory to use a coordinate system - three-dimensional combined scales. Although specifications for non-metric scales are generally based on SI units, these scales cannot in principle be covered by the SI.
In the standard GOST 8.417 - 2002 "GSI. Units of quantities" there is an indication that this standard does not establish units of quantities evaluated on conditional scales, units of the quantity of products (for example, units of the International Sugar Scale, hardness scales, scales of photosensitivity of photographic materials, etc., as well as counting units). In terms of the theory of measurement scales, this indication is inaccurate, the units of any scales, except for absolute ones, are conditional, i.e. accepted by agreement. Therefore, it is more correct to write that SI and the above standards do not apply to quantities and properties described by non-metric scales. Also, outside the SI, there are many widely used counting units, such as "pair", "bag", "package", etc.
Approved
Editorial and Publishing Council of the Voronezh
State Technical University as
textbook for students of engineering
specialties
Voronezh 2006
Metrology, standardization, certification: practical work. allowance / I.A. Frolov, V.A. Nilov, V.A. Muravyov, O.K. Bityutsky. Voronezh: GOU VPO "Voronezh State Technical University", 2006. 114 p.
The main issues included in the discipline "Metrology, standardization, certification" and forming the basis of practical classes are considered.
For each topic of the practical lesson, the manual provides the necessary theoretical materials, options for tasks, examples of their solutions and design in accordance with the requirements of the course of the discipline, as well as questions for testing knowledge.
The workshop is intended for conducting classes with students of specialties 150201 "Machines and technology of metal forming" and 150202 "Equipment and technology of welding production", 151001 "Technology of mechanical engineering", 151002 "Metalworking machines and complexes", 220402 "Robots and robotic systems", 200503 "Standardization and certification" of all forms of education.
Il. 26 Tab. 25 Bibliography: 10 titles.
Scientific editor Ph.D. n., Assoc. B.B. Eskov
Reviewers: Department of Construction and Road Machinery VGASU (Head of the Department, Doctor of Engineering Sciences, Prof. P.I. Nikulin)
cand. tech. Sciences I.G. Radchenko
© Frolov I.A., Nilov V.A.,
Muravyov V.A., Bityutskikh O.K., 2006
© Registration of GOU VPO
"Voronezh State
Technical University", 2006
Introduction
Metrology- the science of measurements, methods and means of ensuring their unity and ways to achieve the required accuracy.
In metrology, the following main tasks are solved: development general theory measurements of units of physical quantities and their systems, development of methods and measuring instruments, methods for determining the accuracy of measurements, the basics for ensuring the unity and uniformity of measuring instruments, standards and samples of measuring instruments, methods for transferring unit sizes from standards and exemplary measuring instruments to working measuring instruments.
Elements of standardization appeared when there was no concept of this term yet. Examples are: construction in the III millennium BC. e. highest Egyptian pyramid Cheops from stones processed to strictly defined sizes; application of 410 × 200 × 130 bricks mm during the construction of the palaces of the pharaohs in Egypt, the method of proportional numbers in the creation of water wheels and catapults in Ancient Rome; the use by the Romans of pipes of certain diameters in the construction of urban water pipes; equipping the fleet in Venice in the ΧΙV-ΧV centuries. identical masts, sails, oars, rudders.
Examples of the use of standardization elements in past times can also be found in the history of the republics of the collapsed USSR. Architects of Armenia in the ΙΧ-Χ centuries. standard details were widely used in the construction of openwork vaults of the Mayr Tachara Cathedral, in the construction of four city gates and in laying water pipes; bricks of the same type were used at the same time in construction in Tajikistan.
Standardization was a radical means of improving machine production, designed to produce products in large quantities. significant event was the introduction in England in 1841 of the Unified screw thread system developed by John Whitworth.
In Russia, standardization was first applied in the middle of the ΧVΙ century. in the manufacture of shells for cannons. In the ΧVΙΙΙ c. (1706-1715) Peter I ordered the craftsmen in the manufacture of guns to follow the correct use of calibers, according to which the parts were made, and the uniformity of individual parts of the guns. In 1826, the principle of interchangeability in the production of weapons at the Tula Arms Plant was brilliantly demonstrated to foreign representatives. Thirty guns, taken from the warehouse without a choice, were disassembled and their parts were mixed. Then the guns were reassembled from the first parts that came in and operated flawlessly. At the beginning of the ΧΙΧ c. standardization received another impetus for development in connection with the beginning of railway construction. The track gauge, the color of the wagons, the height of the coupling devices, the diameters of the wheels and other elements were standardized.
In modern engineering, interchangeability is the main and necessary condition for mass and serial production. For example, with the mass production of standard fasteners (bolts, studs, screws, nuts, washers, etc.), bearings, gears, and a number of other parts and assemblies by specialized factories, the process of designing and manufacturing new machines is accelerated: the designer does not need to create on them drawings, and the plant - to spend time and money on their manufacture.
Measurements have great importance V modern society. They make it possible to ensure the interchangeability of components and parts, improve technology, labor safety and other types of human activity, product quality.
The range of quantities to be measured is determined by the variety of phenomena that a person has to face. If the Theory of Mechanisms and Machines, Machine Parts and Design Basics, Metal Technologies, etc. serve theoretical basis designing machines and mechanisms, this course "Metrology, standardization, certification" considers the issues of ensuring the accuracy of geometric parameters as a necessary condition for interchangeability and such important quality indicators as reliability and durability.
Purpose of the workshop– development of knowledge and practical skills for future engineers to use and comply with the requirements of GOST ( state standards), performing accurate calculations and metrological support in the manufacture, operation and repair of both road construction equipment and other machines. Objectives of the workshop: as a result of completing individual tasks in practical classes on the course "Metrology, standardization and certification", students should:
To study the basic concepts and terminology used in the course "Metrology, standardization and certification";
Learn to use standards in order to select the optimal tolerances in the design of machine parts;
Acquire skills in the calculation of dimensional chains when designing parts, assemblies or mechanisms;
Learn to distinguish landings in the "Holes" system from landings in the "Vala" system;
Acquire the skills of constructing tolerance fields for the dimensions of parts; landings with a gap, interference and transitional with justification of the conditions for their use.
The tutorial consists of eight sections:
1. Calculation (selection) of tolerances and fits of smooth cylindrical joints: a) with a gap; b) with an interference fit; c) transitional.
2. Determination of elements of connections subjected to selective assembly.
3. Calculation of dimensional chains: direct and inverse problems.
4. Calculation of the executive dimensions of calibers.
5. Calculation of landings of rolling bearings.
6. Calculation of tolerances and fits of threaded connections.
7. Calculation of tolerances and fits of keyed connections.
8. Calculation of tolerances and landings of straight-sided and involute splined tooth profiles.
The title of the section corresponds to the topic of the practical lesson.
Principles of building the International System
Units Basic concepts and definitions of tolerances
And landings
Given the need to cover the International System of Units (System International) in all areas of science and technology, seven units are chosen as the main ones.
In mechanics, these are units of length, mass and time; in electricity, a unit of electric current strength is added; in heat, a unit of thermodynamic temperature; in optics, a unit of light intensity; in molecular physics, thermodynamics and chemistry, a unit of the amount of matter. These seven units - meter, kilogram, second, ampere, kelvin, candela and mole - are chosen as the base units of the SI.
The unit of length (meter) is the length of the path traveled by light in vacuum in 1 / 299792458 fraction of a second.
The unit of mass (kilogram) is the mass equal to the mass of the international prototype of the kilogram.
The unit of time (second) is the duration of 9192631770 periods of radiation corresponding to the transition between two hyperfine levels of the ground state of the cesium-133 atom.
The unit of electric current strength (ampere) is the strength of an unchanging current, which, passing through two normal straight conductors of infinite length and negligible area of circular cross section, located at a distance of 1 m one from the other in a vacuum, causes an interaction force between the conductors equal to 2 × 10 -7 H for every meter of length.
Unit of thermodynamic temperature (Kelvin) - 1 / 273,16 thermodynamic temperature of the triple point of water. You can also use the Celsius scale.
The unit of luminous intensity (candela) is the luminous intensity in a given direction of a source emitting monochromatic radiation with a frequency of 540 × 10 12 Hz, the energy intensity of light of which in this direction is 1/683 W/sr.
Unit of amount of substance (mol) - the amount of substance of a system containing as many structural elements as there are atoms in carbon - 12 with a mass of 0.012 kg.
The international system of units also contains two additional units: for a flat angle - radian and for a solid angle - steradian.
Radian (glad) is a unit of a plane angle, equal to the angle between two radii of a circle, the length of the arc between which is equal to the radius. Degree 1 glad = 57 0 17"44,8"".
Steradian (Wed.) is a unit equal to the solid angle with the vertex at the center of the sphere, which cuts out on the surface of the sphere an area equal to the area of a square with a side equal to the radius of the sphere. Solid angle Ω measured indirectly - by measuring a flat angle α at the top of the cone, followed by calculation by the formula
Ω = 2π .
Basic concepts and definitions of tolerances and landings
In the connection of two parts that are included one into the other, there are female and male connection surfaces. In cylindrical joints, the female surface is commonly referred to as "hole", and covered - "shaft". The terms “hole” and “shaft” are conventionally applicable to other female and male surfaces as well. Designate: D- nominal hole size, d- nominal shaft size. These dimensions are the same.
limiting two limit values \u200b\u200bof the size are called, between which the actual size must be. Most of them are called the largest size limit lesser - smallest size limit. They are designated for the hole Dmax And Dmin, and for the shaft - dmax And d min .
Upper limit deviation- algebraic difference between the largest limit size and nominal. Designate: ES- upper limit deviation of the hole, es- the upper limit deviation of the shaft.
ES = Dmax - D;
es = d max - d.
ES
Ecart– deviation;
Superieur- top.
Lower limit deviation- algebraic difference between the smallest size limit and the nominal one. Designate: EI- lower limit deviation of the hole, ei- the lower limit deviation of the shaft.
EI = D min - D;
ei = d min - d.
EI- initial letters French words;
Ecart– deviation;
Inferieur- lower;
ES- upper deviation of the hole;
EI- lower deviation of the hole;
es- the upper deviation of the shaft;
ei- the lower deviation of the shaft.
Size tolerance is the difference between the largest and smallest limits. Designate: TD- hole tolerance Td- shaft tolerance. Tolerance is always a positive number.
TD = Dmax - Dmin = ES - E;
Td = d max - d min = es - ei.
Rice. 1. Graphic representation of connection details:
a) a diagram of the details of the connection; b) the layout of the tolerance fields of the connection details
The line corresponding to the nominal size, from which dimensional deviations are plotted in the graphic representation of tolerances and fits, is called zero line. If the zero line is located horizontally, then positive deviations are plotted upwards from it, and negative deviations downwards.
Actual deviation- algebraic difference between actual and nominal sizes.
Tolerance field- the range of sizes, limited by the limiting sizes; it is determined by the tolerance value and its location relative to the nominal size.
In the diagram, the tolerance field is depicted as a zone between the lines corresponding to the upper and lower limit deviations. The upper limit of the tolerance field corresponds to the largest limit size, the lower one - to the smallest limit size.
Gap S- positive difference between the hole and shaft dimensions (the hole size is greater than the shaft size).
Preload N- positive difference between the dimensions of the shaft and the hole before the assembly of parts (the size of the shaft is larger than the size of the hole).
largest gap Smax is the positive difference between the largest hole size limit Dmax and the smallest limiting shaft size dmin.
Smax = Dmax - dmin = ES - ei.
Smallest clearance Smin- positive difference between the smallest hole size limit Dmin and the largest limiting shaft size dmax.
S min \u003d D min - d max \u003d EI - es.
The greatest tightness Nmax- positive difference between the largest shaft size limit dmax and the smallest limit hole size Dmin.
N max \u003d d max - D min \u003d es - EI.
Least preload Nmin- positive difference between the smallest shaft size limit dmin and the largest limit hole size Dmax.
N min \u003d d min - D max \u003d ei - ES.
Landing- this is the nature of the connection of parts, determined by the magnitude of the gaps or interferences resulting in it. Landing characterizes greater or lesser freedom of relative movement of the parts to be joined in the case of a gap or the degree of resistance to their mutual displacement (in the case of interference).
Similar information.
The numerical values of the measured values depend on the units of measurement used. Therefore, the role of the latter is very great. If we allow arbitrariness in the choice of units, then the measurement results will be incomparable among themselves, i.e., the unity of measurements. To prevent this from happening, units of measurement are established according to certain rules and fixed by law. The presence of legal metrology distinguishes this science from other natural sciences (mathematics, physics, chemistry, etc.) and is aimed at combating arbitrariness in the choice of such decisions that are not dictated by objective laws, but are made by agreement.
The set of units of measurement of basic and derived quantities is called unit system. Not in all areas of measurement, systems of units have finally formed and are fixed by the relevant legislative acts. The best situation in this regard is in the field of measurement of physical quantities.
Let there be n equations of connection between the numerical values of N physical quantities. Each equation has its own proportionality coefficient, which can be given any value and, in particular, equated to unity. Therefore, in the connection equations, the coefficients are known numbers, and the PV are unknown. Really always the number N of physical quantities more number n connection equations. If you choose your own independent units for N-n FV, then they become known numbers and n equations are solved with respect to the remaining n FV. Such a system is considered optimal from a theoretical point of view. These N-n PV are called, as you know, basic, and the rest n - derivatives.
In practice, it may be convenient to choose not N-n PVs as the main ones, but a larger number of them, equal to N-n + p. In this case, it is no longer possible to assign any numerical values to all the coefficients, since the p coefficients become as unknown as the remaining n-p derivatives of the PV in this case.
The number of basic units is closely related to the number of coefficients in expressions for physical laws and definitions. The coefficients of proportionality, depending on the choice of basic units and constitutive equations, are called fundamental, or world constants. In the SI system, these include the gravitational constant, Planck's constant, Boltzmann's constant, and luminous efficiency. They should be distinguished from the so-called specific constants, which characterize various properties of individual substances, for example, the mass of an electron, its charge, etc.
It should be remembered that fundamental constants are present in the expressions for all physical laws, but by the appropriate choice of units, a certain number of them is equated to some constant numbers, most often to one. Further, it will be shown that the more basic units are adopted when building a system, the more fundamental constants will be in the formulas. A reduction in the number of basic units is necessarily accompanied by a decrease in the number of fundamental constants.
In the limiting case, one can choose its own unit for each of the PVs. But then, instead of a system of units, a set of units will turn out, all n coefficients will become experimentally determined world constants, derivative quantities will disappear, and regular connections will turn out to be of little use for practice. Therefore, scientists strive to create a theoretically optimal system of units, or as close as possible to it.
The rules according to which one or another set of units is chosen as the main one cannot be substantiated theoretically. The only arguments in favor of the choice can only be the effectiveness and expediency of using this system. For practical measurement purposes, the base quantities and units should be those that can be reproduced with the greatest accuracy. The formation of a system of units is based on objective regular relationships between physical quantities and on the arbitrary, but reasonable will of people and their agreements, the final of which is adopted at the General Conference on Weights and Measures.
When constructing or introducing a new system of units, scientists are guided by only one single principle - practical expediency, i.e. ease of use of units in human activities. This principle is based on the following basic criteria:
Ease of formation of PV derivatives and their units, i.e. equating to unity the coefficients of proportionality in the equations of communication;
High accuracy of materialization of basic and derived units and transfer of their size to lower standards;
Indestructibility of standards of basic units, i.e. the possibility of their reconstruction in case of loss;
Continuity of units, preservation of their sizes and names with the introduction of a new system of units, which is associated with the exclusion of material and psychological costs;
The proximity of the sizes of basic and derived units to the sizes of PV, most often encountered in practice.
