The measurement of physical quantities consists of comparing a quantity with a homogeneous quantity taken as a unit. In metrology, the term “measurement” is used, which means finding the value of a physical quantity experimentally using special technical means.

Measurements performed using special technical means are called instrumental. The simplest example of such measurements is determining the size of a part using a ruler with divisions, that is, comparing the size of the part with the unit of length stored by the ruler.

A derivative of the term "measurement" is the term "to measure", widely used in practice. There are terms “measure”, “measure”, “measure”, but their use in metrology is unacceptable.

To streamline measurement activities, measurements are classified according to the following criteria:

General methods of obtaining results - direct, indirect, compatible, cumulative;

Number of measurements in a series – single and multiple;

Metrological purposes – technical, metrological;

Characteristics of accuracy - equal and unequal;

Relation to changes in the measured value – statistical and dynamic;

Expression of measurement results – absolute and relative;

Direct measurements are measurements in which the desired value of a quantity is found directly from experimental data (measurements of mass on scales, temperature of thermometers, length using linear measures). In direct measurements, the object of study is brought into interaction with measuring instruments and, according to the readings of the latter, the value of the measured quantity is measured. Sometimes the instrument readings are multiplied by a coefficient, appropriate corrections are introduced, etc. These measurements can be written in the form of an equation: X = C X P,

where X is the value of the measured quantity in units accepted for it;

C – the price of a scale division or a single reading of a digital reading device in units of the measured value;

Х П – counting according to the indicator device in scale divisions.

Indirect measurements are measurements in which the desired value is found on the basis of a known relationship between this value and values ​​obtained by direct measurements (determining the density of a homogeneous body by its mass and geometric dimensions, the electrical resistivity of a conductor by its resistance, length and cross-sectional area). In general, this dependence can be represented as a function X = (X1,X2,....,Xn), in which the value of the arguments X1, X2, ....,Xn is found as a result of direct, and sometimes indirect, joint or cumulative measurements .

For example, the density of a homogeneous solid body ρ is found as the ratio of mass m to its volume V, and the mass and volume of the body are measured directly: ρ=m/V.

To increase the accuracy of measurements of density ρ, measurements of mass m and volume V are carried out repeatedly. In this case, the body density

ρ = m/V, m is the result of measuring body mass, m = 1/n Σ m i;

V=ΣVi/n - the result of measuring the volume of the body Π.

Cumulative measurements - measurements of several homogeneous quantities, in which the desired value of the quantities is found by solving a system of equations obtained by direct measurements of various combinations of these quantities (measurements in which the mass of individual weights of a set is found from the known mass of one of them and from the results of direct comparisons of the masses of various combinations of weights ).

Joint measurements are simultaneous measurements of two or more opposite quantities to find the relationship between them (simultaneous measurements of the increment in the length of a sample depending on changes in its temperature and determination of the linear expansion coefficient).

Joint and cumulative measurements are very close in their methods of finding the desired values ​​of the measured quantities. The difference is that with cumulative measurements, several quantities of the same name are simultaneously measured, and with joint measurements, they measure different quantities. The values ​​of the measured quantities x1, ..., xn are determined on the basis of cumulative equations;

F1 (X1, ..., Xm, X11, ... , X1n);

F2 (X1, ..., Xm, X21, ... , X1n);

Fn (X1, ..., Xm, Xk1, ... , Xkn),

where X11, X21, ……………..Xk n are quantities measured by direct methods.

Joint measurements are based on well-known equations that reflect the connections existing in nature between the properties of objects, i.e. between quantities.

Absolute measurements are measurements based on direct measurements of one or more basic quantities and the use of physical constants.

Relative measurements - obtaining the ratio of a quantity to a quantity of the same name, which plays the role of a unit, or a change in a quantity in relation to a quantity of the same name, taken as the initial one.

Single measurements - a measurement performed once (measurement of a specific time using a clock).

Multiple measurements are measurements of the same physical quantity, the result of which is obtained from several successive measurements. Typically, multiple measurements are those that are made more than three times.

Technical measurements - measurements performed using working measuring instruments for the purpose of monitoring and managing scientific experiments, monitoring product parameters, etc. (measurement of air pressure in a car chamber).

Metrological measurements are measurements using standards and reference measuring instruments for the purpose of innovating units of physical quantities or transferring their sizes to working measuring instruments.

Equal-precision measurements are a series of measurements of any quantity made by measuring instruments of equal accuracy under the same conditions.

Non-equivalent measurements are a series of measurements of any quantity, performed with different accuracy with measuring instruments and under different conditions.

Static measurements are measurements of a physical quantity that, in accordance with a specific measurement task, is accepted as unchanged throughout the measurement time (measuring the size of a part at normal temperature).

Dynamic measurements are measurements of a physical quantity whose size changes over time (measuring the distance to ground level from a descending aircraft).

Measuring instruments

Measuring instruments are technical means used in measurements and having standardized metrological properties. The correct determination of the value of the measured quantity in the process of its measurement depends on the measuring instruments. Measuring instruments include: measures: measuring instruments, measuring installations, measuring systems.

A measure is a measuring instrument designed to reproduce a physical quantity of a given size (a weight is a measure of mass, a generator is a measure of the frequency of electrical oscillations). Measures, in turn, are divided into single-valued and multi-valued.

An unambiguous measure that reproduces a physical quantity of one size (plane-parallel gauge block, normal element, constant capacitance capacitor),

a multi-valued measure that reproduces a number of physical quantities of the same name of various sizes (ruler: in millimeter divisions, variable capacitor).

A set of measures is a specially selected set of measures used not only individually, but also in various combinations for the purpose of reproducing a number of quantities of the same name of various sizes (a set of weights, a set of plane-parallel gauge blocks).

A measuring device is a measuring instrument designed to generate a signal of measuring information in a form accessible to direct perception by an observer. The measurement results are produced by the reading devices of the instruments, which can be scale, digital and recording.

Scale reading devices consist of a scale, which is a set of marks and numbers depicting a series of sequential values ​​of the measured quantity, and a pointer (arrow, electron beam, etc.) associated with the moving system of the device.

Scale marks with numerical values ​​represented are called numeric scale marks. The main characteristics of the scale are the length of the scale division, expressed by the distance between the axes of two adjacent scale lines, and the value of the scale division, representing the value of the measured quantity, causing the pointer to move one division.

It is also customary to distinguish the following concepts: measurement range and reading range.

The measurement range is part of the reading range for which the limits of permissible errors of measuring instruments are normalized. The smallest and largest values ​​of the measurement range are called the lower and upper limits of measurements, respectively.

The value of a quantity, determined by the reading device of a measuring instrument and expressed in the accepted units of this quantity, is called the reading of the measuring instrument.

The measured value is determined either by multiplying the number of scale divisions by the value of the scale division or by multiplying the numerical value read on the scale by the scale constant.

Currently, either mechanical or light-based digital reading devices are widely used.

Recording and reading devices consist of a writing or printing mechanism and a tape. The simplest writing device is a pen filled with ink, recording the measurement result on a paper tape. In more complex devices, the measurement result can be recorded by a light or electron beam, the movement of which depends on the values ​​of the measured quantities.

The Federal Law “On Ensuring the Uniformity of Measurements” dated April 27, 1993 regulates relations related to ensuring the uniformity of measurements in the Russian Federation in accordance with the Constitution of the Russian Federation.

The main articles of the Law establish:

• basic concepts used in the Law;
• organizational structure of state management ensuring the uniformity of measurements;
• regulatory documents to ensure the uniformity of measurements;
• units of quantities and state standards of units of quantities;
• measurement tools and techniques.

The law defines the State Metrological Service and other services to ensure the uniformity of measurements, metrological services of state government bodies and legal entities, as well as the types and scope of distribution of state metrological control and supervision.

Separate articles of the Law contain provisions for calibration and certification of measuring instruments and establish types of liability for violation of the Law.

The emergence of market relations left its mark on the article of the Law, which defines the basis for the activities of metrological services of government bodies and legal entities. Issues related to the activities of structural units of metrological services at enterprises are stimulated by purely economic methods.

In those areas that are not controlled by government agencies, it is created Russian calibration system, also aimed at ensuring uniformity of measurements. The State Standard of the Russian Federation has appointed the Department of Technical Policy in the Field of Metrology as the central body of the Russian calibration system.

The regulation on licensing metrological activities is aimed at protecting the rights of consumers and covers areas subject to state metrological control and supervision. The right to issue a license is granted exclusively to the bodies of the State Metrological Service.

The law creates conditions for interaction with international and national measurement systems of foreign countries. This is primarily necessary for mutual recognition of test, calibration and certification results, as well as for the use of global experience and trends in modern metrology.

Deals with issues of theory and practice of ensuring the uniformity of measurements metrology. Metrology is the science of measurements, methods and means of ensuring their unity and ways of achieving the required accuracy.

Metrology is of great importance for the progress of natural and technical sciences, since increasing the accuracy of measurements is one of the means of improving the ways of human knowledge of nature, discoveries and practical application of precise knowledge.

To ensure scientific and technological progress, metrology must be ahead of other areas of science and technology in its development, because for each of them, accurate measurements are one of the main ways to improve them.

The main objectives of metrology are:

• establishment of units of physical quantities, state standards and standard measuring instruments;
• development of theory, methods and means of measurement and control; ensuring uniformity of measurements;
• development of methods for assessing errors, the state of measuring and control equipment;
• development of methods for transferring unit sizes from standards or reference measuring instruments to working measuring instruments.

By measuring is a set of operations for the use of a technical means that stores a unit of physical quantity, ensuring the determination of the relationship of the measured quantity with its unit (comparison) and obtaining the value of this quantity. Measurements must be made in generally accepted units.

Metrological support(MO) - establishment and application of scientific and organizational foundations, technical means, rules and regulations necessary to achieve the unity and required accuracy of measurements.

The list of main tasks of metrological support in technology includes:

• identifying ways to most effectively use scientific and technical achievements in the field of metrology;
• standardization of basic rules, regulations, requirements and norms of metrological support;
• harmonization of instruments and measurement methods, carrying out joint measurements using domestic and foreign equipment (intercalibration);
• determining a rational nomenclature of measured parameters, establishing optimal standards of measurement accuracy, the procedure for selecting and assigning measuring instruments;
• organizing and conducting metrological examination at the stages of development, production and testing of products;
• development and application of advanced measurement methods, techniques and measuring instruments;
• automation of collection, storage and processing of measurement information;
• implementation of departmental control over the condition and use of standard, working and non-standardized measuring instruments at industry enterprises;
• carrying out mandatory state or departmental verification of measuring instruments and their repair;
• ensuring constant readiness for measurements;
• development of the industry's metrological service, etc.

Physical quantity - one of the properties of a physical object (physical system, phenomenon or process), common in qualitative terms for many physical objects, but quantitatively individual for each of them.

The unit of measurement must be established for each of the physical quantities, and it must be taken into account that many physical quantities are interconnected by certain dependencies. Therefore, only part of the physical quantities and their units can be determined independently of others. Such quantities are called main ones. Derivative physical quantity - a physical quantity included in a system of physical quantities and determined through the basic physical quantities of this system.

A set of physical quantities formed in accordance with accepted principles, when some quantities are taken as independent, and others are determined as functions of independent quantities, is called system of units of physical quantities. The unit of a basic physical quantity is basic unit systems. International System of Units (SI system; SI - from French. Systeme International - The International System of Units was adopted by the XI General Conference on Weights and Measures in 1960.

The SI system is based on seven basic and two additional physical units. Basic units: meter, kilogram, second, ampere, kelvin, mole and candela (Table 1.1).

Meter - the length of the path traveled by light in a vacuum in a time interval of 1/299,792,458 seconds.

Kilogram - a unit of mass defined as the mass of the international prototype kilogram, which is a cylinder made of an alloy of platinum and iridium.

Second is equal to 9,192,631,770 periods of radiation corresponding to the energy transition between two levels of the hyperfine structure of the ground state of the cesium-133 atom.

Ampere - the force of an unchanging current, which, passing through two parallel straight conductors of infinite length and negligibly small circular cross-sectional area, located at a distance of 1 m from each other in a vacuum, would cause an interaction force equal to 2 10“ 7 N (newton) on each section of the conductor 1 m long.

Table 1.1. International System of Units

Magnitude
Name	Dimension	Name	Designation
			international
Basic units
		kilogram
Electric current strength
Temperature
Quantity substances
The power of light
Additional units
Flat angle
Solid angle		steradian

Kelvin - a unit of thermodynamic temperature equal to 1/273.16 of the thermodynamic temperature of the triple point of water, i.e., the temperature at which the three phases of water - vapor, liquid and solid - are in dynamic equilibrium.

Mole - an amount of substance containing the same number of structural elements as is contained in a 0.012 kg sample of carbon-12.

Candela - the luminous intensity in a given direction of a source emitting monochromatic radiation with a frequency of 540 10 12 Hz, whose radiative energy in this direction is "/ 683 W/sr (sr - steradian).

Additional SI units are intended and used to form units of angular velocity and angular acceleration. Additional physical quantities of the SI system include plane and solid angles.

Radian (rad) - the angle between two radii of a circle whose arc length is equal to that radius. In practical cases, the following units of measurement of angular quantities are often used:

degree - 1° = 2l/360 rad = 0.017453 rad;

minute - 1" = 1°/60 = 2.9088 10 4 rad;

second - 1" = Г/60 = 1°/3600 = 4.8481 10“ 6 rad;

radian - 1 rad = 57°17"45" = 57.2961° = (3.4378 10 3)" = (2.0627 10 5)".

Steradian (avg) - a solid angle with its vertex at the center of the sphere, cutting out on its surface an area equal to the area of ​​a square with a side equal to the radius of the sphere.

Derived units of the SI system are formed from basic and supplementary units. Derived units can be coherent or incoherent. Coherent called a derived unit of quantity related to other units of the system by an equation in which the numerical factor is one (for example, speed And uniform linear motion is related to the path length / and time t ratio and =//G). Other derived units - incoherent. In table 1.2 shows the main derived units.

The dimension of a physical quantity is one of its most important characteristics, which can be defined as a literal expression reflecting the relationship of a given quantity with quantities accepted as basic in the system of quantities under consideration. In table 1.2 for quantities the following dimensions are accepted: for length - L, mass - M, time - T, electric current - I. Dimensions are written in capital letters and printed in roman font.

Among the widely used off-system units, we note the kilowatt-hour, ampere-hour, degree Celsius, etc.

Abbreviations for units, both international and Russian, named after great scientists, are written in capital letters; for example ampere - A; om - Om; volt - V; farad - F. For comparison: meter - m, second - s, kilogram - kg.

The use of whole units is not always convenient, since the resulting measurements result in too large or small values. Therefore, the SI system establishes decimal multiples and submultiples, which are formed using multipliers. Decimal factors correspond to prefixes

Table 1.2. Derived SI units

Magnitude
Name	Dimension	Name	Designation
			international
Energy, work, amount of heat
Strength, weight
Power, energy flow
Amount of electricity
Electrical voltage, electromotive force (EMF), potential
Electrical capacity	b- 2 M >T 4 1 2
Electrical resistance	b 2 MT- 3 1-2
Electrical conductivity	b- 2 m-1T 3 1 2
Magnetic induction
Magnetic flux	C 2 MT- 2 1-1
Inductance, mutual inductance	b 2 MT- 2 1-2

(Table 1.3), which are written together with the name of the main or derived unit, for example: kilometer (km), millivolt (mV), megahertz (MHz), nanosecond (ns).

If a physical unit is an integer number of times larger than the system unit, it is called multiple of one for example kilohertz (10 3 Hz). submultiple unit physical quantity - a unit that is smaller than the system one by an integer number of times, for example, microhenry (KG 6 Hn).

A measure of physical quantity or simply measure is a measuring instrument intended for reproducing and (or) storing a physical quantity of one or more specified sizes, the values ​​of which are expressed in established

Table 1.3. Factors and prefixes to form SI decimal multiples and submultiples

Factor	Console	Prefix designation
		international

units and are known with the required accuracy. The following types of measures are distinguished:

• unambiguous measure - a measure that reproduces a physical quantity of one size (for example, a 1 kg weight);
• multivalued measure - a measure that reproduces a physical quantity of different sizes (for example, a line measure of length);
• set of measures - a set of measures of the same physical quantity, but of different sizes, intended for use in practice, both individually and in various combinations (for example, a set of gauge blocks);
• shop measures - a set of measures structurally combined into a single device, which contains devices for connecting them in various combinations (for example, a store of electrical resistances).

Electrical measuring instruments are electrical measuring instruments designed to generate information about the values ​​of the measured quantity in a form accessible to direct perception by an observer, for example, ammeter, voltmeter, wattmeter, phase meter.

Measuring transducers are called electrical measuring instruments designed to generate measurement information in a form convenient for transmission, further transformation, processing or storage, but not amenable to direct perception by the observer. Measuring transducers can be divided into two types:

• converters of electrical quantities into electrical ones, for example shunts, voltage dividers or amplifiers, transformers;
• converters of non-electrical quantities into electrical ones, for example thermoelectric thermometers, thermistors, strain gauges, inductive and capacitive converters.

Electrical measuring installation consists of a number of measuring instruments (measures, measuring instruments, measuring transducers) and auxiliary devices located in one place. Using such installations, in some cases it is possible to make more complex and more accurate measurements than using individual measuring instruments. Electrical measuring installations are widely used, for example, for checking and calibrating electrical measuring instruments and testing various materials used in electrical structures.

Measurement information systems They are a set of measuring instruments and auxiliary devices interconnected by communication channels. They are designed to automatically receive, transmit and process measurement information from many sources.

Depending on the method of obtaining the result, measurements are divided into direct and indirect.

Direct are measurements whose results are obtained directly from experimental data. Examples of direct measurements: measuring current with an ammeter, length of a part with a micrometer, weight on a scale.

Indirect are measurements in which the desired quantity is not directly measured, but its value is found based on the results of direct measurements of other physical quantities that are functionally related to the desired quantity. For example, power R in DC circuits is calculated using the formula R = W, voltage And in this case, it is measured with a voltmeter, and the current / is measured with an ammeter.

Depending on the set of measurement techniques, all methods are divided into direct assessment methods and comparison methods.

Under direct assessment method understand the method by which the measured quantity is determined directly from the reading device of a direct-acting measuring device, i.e., a device that converts the measuring signal in one direction (without using feedback), for example, measuring current with an ammeter. The direct assessment method is simple, but has relatively low accuracy.

Comparison method called a method by which the measured value is compared with the value reproduced by the measure. A distinctive feature of the comparison method is the direct participation of the measure in the measurement process, for example, measuring resistance by comparing it with a measure of resistance - a standard resistance coil, measuring mass on a lever scale with balancing with weights. Comparison methods provide greater measurement accuracy than direct assessment methods, but this comes at the cost of complicating the measurement process.

Chapter 1. MEASUREMENT OF PHYSICAL QUANTITIES

The wide variety of phenomena encountered in practical activities determines a wide range of quantities to be measured. The main object of study in metrology is the measurement of physical quantities. In all cases of measurements, regardless of the value, method and measuring instrument, there is a common thing that forms the basis of measurements - this is a comparison of the size of a given quantity with the unit stored by the measuring instrument. With any measurement, we use experiment to determine quantitatively a physical quantity in the form of a certain number of units accepted for it, i.e. we find the value of the size of a physical quantity. The measurement is carried out using a scale - a pre-compiled, ordered set of sequences of physical quantities, accepted by agreement.

The choice of units for measuring quantities is of great importance for comparing results obtained using different methods, means and under different measurement conditions. Therefore, it is customary to establish their sizes by law. The International System of Units, approved by the XI General Conference on Weights and Measures, created real prospects for the complete unification of units of measurement in all countries of the world community.

Measurement objects

Measurement scales

Measurement scale serves as the initial basis for measuring this quantity. It represents an ordered collection of quantity values.

Practical activity has led to the formation of various types of measurement scales for physical quantities, the main ones of which are four, discussed below.

1. Scale of order (ranks) represents a ranked series – a sequence of quantities, ordered in ascending or descending order, characterizing the property being studied. It allows you to establish an order relationship based on increasing or decreasing quantities, but there is no way to judge how many times (or how much) one quantity is larger or smaller compared to another. In order scales, in some cases there may be a zero (zero mark); the fundamental thing for them is the absence of a unit of measurement, because its size cannot be determined; mathematical operations (multiplication, summation) cannot be performed on quantities in these scales.

An example of an order scale is the Mohs scale for determining the hardness of bodies. This is a scale with reference points, which contains 10 reference (reference) minerals with different hardness numbers. Examples of such scales are also the Beaufort scale for measuring wind force (speed) and the Richter earthquake scale (seismic scale).

2. Interval (difference) scale differs from the order scale in that for measured quantities, not only order relations are introduced, but also summations of intervals (differences) between various quantitative manifestations of properties. Difference scales may have conventional reference zeros and measurement units established by agreement. Using an interval scale, you can determine how much one value is greater or less than another, but you cannot tell by how many times. Interval scales measure time, distance (if the beginning of the journey is not known), temperature in Celsius, etc.

Interval scales are more advanced than order scales. In these scales, additive mathematical operations (addition and subtraction) can be performed on quantities, but multiplicative ones (multiplication and division) cannot be performed.

3.Relationship scale describes the properties of quantities for which the relations of order, summation of intervals and proportionality are applicable. In these scales there is a natural zero and the unit of measurement is established by agreement. The ratio scale serves to present measurement results obtained in accordance with the basic measurement equation (1.1) by experimentally comparing the unknown quantity Q with its unit [Q]. Examples of ratio scales are scales of mass, length, speed, and thermodynamic temperature.

The ratio scale is the most advanced and most common of all measurement scales. This is the only scale on which you can set the value of the measured size. Any mathematical operations are defined on the ratio scale, which allows you to make multiplicative and additive corrections to the readings on the scale.

4. Absolute scale has all the features of a ratio scale, but in addition there is a natural, unambiguous definition of the unit of measurement. Such scales are used to measure relative quantities (gain, attenuation, efficiency, reflection, absorption, amplitude modulation, etc.). A number of such scales have boundaries between zero and one.

Interval and ratio scales are combined under the term “metric scales.” The order scale is classified as a conditional scale, i.e. to scales in which the unit of measurement is not defined and is sometimes called non-metric. Absolute and metric scales are classified as linear. The practical implementation of measurement scales is carried out by standardizing both the scales and measurement units themselves, and, if necessary, the methods and conditions for their unambiguous reproduction.

Basic SI units

Basic unit quantity is called the unit of the basic physical quantity, i.e. a quantity that is conventionally accepted as independent of other quantities of the system. When choosing the basic SI units, we proceeded from the following: 1) to cover all areas of science and technology with the system; 2) create a basis for the formation of derivative units for various physical quantities; 3) adopt practical dimensions of basic units that have already become widespread; 4) select units of such quantities that can be reproduced with the help of standards with the greatest accuracy.

The main SI units with abbreviations in Russian and Latin letters are given in Table. 1.1.

Table 1.1.

Basic SI units

The definitions of basic units according to the decisions of the General Conference on Weights and Measures are as follows.

Meter equal to the length of the path traveled by light in a vacuum in 1/299,792,458 of a second.

Kilogram equal to the mass of the international prototype kilogram.

Second equal to 9,192,631,770 periods of radiation corresponding to the transition between two hyperfine levels of the ground state of the cesium-133 atom.

Ampere is equal to the strength of a constant current, which, when passing through two parallel straight conductors of infinite length and a negligibly small circular cross-sectional area, located at a distance of 1 m from each other in a vacuum, causes an interaction force equal to 2 × 10 –7 on each section of the conductor 1 m long N.

Kelvin equal to 1/273.16 of the thermodynamic temperature of the triple point of water.

Mole equal to the amount of substance in a system containing the same number of structural elements as there are atoms in carbon-12 weighing 0.012 kg.

Candela equal to the luminous intensity in a given direction of a source emitting monochromatic radiation with a frequency of 540×10 12 Hz, the luminous energy intensity of which in this direction is 1/683 W/sr.

The first three SI units (meter, kilogram and second) allow the formation of derived units for measuring mechanical and acoustic quantities. By adding the unit of temperature (kelvin), it is possible to form derived units for measuring thermal quantities.

The meter, kilogram, second and ampere serve as the basis for the formation of derived units in the field of electrical, magnetic and ionizing radiation measurements, and the mole is used to form units in the field of physicochemical measurements.

Derived SI units

Derived units of the International System of Units are formed from the basic ones using equations for the relationship between quantities in which the numerical coefficients are equal to one. For example, to establish the unit of linear velocity v, one should use the equation of uniform linear motion

where l is the length of the path traveled (in meters); t - time (in seconds).

Therefore, the SI unit of speed - meter per second - is the speed of a rectilinearly and uniformly moving point at which it moves a distance of 1 m in 1 s.

Derived units may be named after famous scientists. Thus, the unit of pressure 1 N/m2 was given a special name - pascal (Pa) named after the French mathematician and physicist Blaise Pascal. Derived units with special names are given in table. 1.2.

Table 1.2.

Derived SI units with special names

Magnitude	Unit
Name	Dimension	Name	Designation	Expression in SI units
Frequency	T -1	hertz	Hz	s -1
Strength, weight	LMT-2	newton	N	m kg s -2
Pressure, mechanical stress	L -1 MT -2	pascal	Pa	m -1 kg s -2
Energy, work, amount of heat	L 2 MT -2	joule	J	m 2 kg s -2
Power	L 2 MT -3	watt	W	m 2 kg s -3
Amount of electricity	T.I.	pendant	Cl	s A
Electrical voltage, potential	L 2 MT -3 I -1	volt	IN	m 2 kg s -3 A -1
Electrical capacity	L -2 M -1 T 4 I 2	farad	F	m -2 kg -1 s 4 A 2
Electrical resistance	L 2 MT -3 I -2	ohm	Ohm	m 2 kg s -3 A -2
Electrical conductivity	L -2 M -1 T 3 I 2	Siemens	Cm	m -2 kg -1 s 3 A 2
Magnetic flux	L 2 MT -2 I -1	weber	Wb	m 2 kg s -2 A -1
Magnetic induction	MT -2 I -1	tesla	Tl	kg s -2 A -1
Inductance	L 2 MT -2 I -2	Henry	Gn	m 2 kg s -2 A -2
Radionuclide activity	T -1	becquerel	Bk	s -1
Absorbed radiation dose	L 2 T -2	gray	Gr	m 2 s -2
Equivalent radiation dose	L 2 T -2	sievert	Sv	m 2 s -2

The radian and steradian are used to measure plane and solid angles in SI, respectively.

Radian(rad) - a unit of plane angle is the angle between two radii of a circle, the arc between which is equal in length to the radius. In degrees, a radian is equal to 57°17"48".

Steradian(cf) - a unit of solid angle is a solid angle whose vertex is located at the center of the sphere and which cuts out on the surface of the sphere an area equal to the area of ​​a square with a side length equal to the radius of the sphere.

The radian and steradian themselves are used mainly for theoretical calculations; in practice, angle measurements are made in angular degrees (minutes, seconds). It is in these units that most goniometric measuring instruments are calibrated.

Multiples and submultiples

There are multiple and submultiple units of quantities. Multiple unit is a unit of physical quantity that is an integer number of times greater than a systemic or non-systemic unit. For example, the unit of length kilometer is equal to 10 3 m, i.e. is a multiple of a meter. submultiple unit– a unit of physical quantity, the value of which is an integer number of times less than a systemic or non-systemic unit. For example, the unit of length millimeter is equal to 10 -3 m, i.e. is subordinate.

For the convenience of using SI units of physical quantities, prefixes have been adopted to form the names of decimal multiples and submultiples, Table. 1.3.

Table 1.3.

Factors and prefixes for the formation of decimal multiples and submultiples and their names

Factor	Console	Prefix designation
Russian	international
10 24	iotta	Y	AND
10 21	zetta	Z	Z
10 18	exa	E	E
10 15	peta	P	R
10 12	tera	T	T
10 9	giga	G	G
10 6	mega	M	M
10 3	kilo	To	k
10 2	hecto	G	h
10 1	soundboard	Yes	da
10 -1	deci	d	d
10 -2	centi	With	c
10 -3	Milli	m	m
10 -6	micro	mk	m
10 -9	nano	n	n
10 -12	pico	P	p
10 -15	femto	f	f
10 -18	atto	A	a
10 -21	zepto	z	h
10 -24	iocto	y	And

In accordance with international rules, multiple and submultiple units of area and volume should be formed by adding prefixes to the original units. Thus, degrees refer to those units that are obtained as a result of attaching prefixes. For example, 1 km 2 = 1 (km) 2 = (10 3 m) 2 = 10 6 m 2.

Types and methods of measurements

Measurement concept

Measurement is the most important concept in metrology. As mentioned above, it is the process of finding the value of a physical quantity using special technical means (measuring instruments). When measuring, carry out observations behind the measurement object in order to make a timely and correct reading. The object of measurement can be a technical device (for example, a chamber furnace), technological processes, the environment, consumption of substances and materials, human vital signs, etc. The physical quantity that is selected for measurements is called measurable quantity.

In addition to the measured quantity, the measurement object and, accordingly, the measurement result are influenced by other physical quantities that are not measured by a given measuring instrument. They are called influencing physical quantities. The influencing quantities are divided into the following groups:

climatic (ambient temperature, air humidity, atmospheric pressure);

electrical and magnetic (electric current fluctuations, voltage in an electrical circuit, alternating current frequency, magnetic field);

external loads (vibrations, shock loads, ionizing radiation).

The effect of these quantities on the measurement result, as well as imperfect manufacturing of the measuring instrument, subjective errors of the human operator and a number of other factors are the reasons causing the inevitable occurrence of measurement error.

The process of solving any measurement problem usually includes three stages:

1) preparation for measurements (selection of methods and measuring instruments, provision of measurement conditions, etc.);

2) carrying out measurements (measuring experiment);

3) processing of measurement results.

During the measurement experiment presented in Fig. 1.2, the object of measurement and the measuring instrument are brought into interaction. In this case, the measured quantity, acting on the measuring instrument, is converted into a signal that is perceived by a person or various technical devices - consumers of measuring information.

Rice. 1.2. Diagram of the measurement acquisition process

This signal is functionally related to the measured physical quantity, therefore it called the measuring signal information. The most commonly used signals are:

constant level signals (constant electric current and voltage, compressed air pressure, luminous flux);

sinusoidal signals (alternating electric current and voltage);

sequence of rectangular pulses (electrical, light).

The received measurement information signals can then be processed in order to present the measurement result in the most convenient way. Such processing may include statistical processing (for multiple measurements of a value), additional calculations (for indirect measurements), rounding, etc. Issues related to processing measurement results are discussed below (section 2.4).

Classification of measurements

The measurements are very diverse, and they can be classified according to various criteria, the most important of which are shown in Fig. 1.3.

Rice. 1.3. Classification of measurements

Firstly, measurements are determined by the physical nature of phenomena (processes), according to which certain sets of physical quantities have developed that are related in nature or application in certain fields of science and technology - mechanical, thermal, physicochemical and other measurements.

Secondly, measurements, depending on the method of obtaining measurement results, are divided into direct and indirect. Direct– these are measurements in which the desired value of a physical quantity is found directly from experimental data. In this case, the measurement object is brought into interaction with the measuring instrument and, based on its readings, the value of the measured quantity is determined. Examples of direct measurements: measuring length with a ruler, time with a watch, mass with a scale, temperature with a thermometer, current with an ammeter, etc. Direct measurements include measurements of the vast majority of parameters of technological processes.

Indirect– these are measurements in which the desired quantity is determined based on the results of direct measurements that are functionally related to it. The value of Q is found by calculating using the formula

Q = f (X 1 , X 2 ,…X m), (1.5)

where X 1, X 2,…X m are quantities whose size is determined from direct measurements

Examples of indirect measurements: determining the density of a homogeneous body by its mass and volume, the electrical resistance of a conductor by voltage drop and current, power by current and voltage.

Indirect measurements are widely used in cases where the desired quantity is impossible or too difficult to measure directly, or when direct measurement gives a less accurate result. Their role is especially great when measuring quantities that are inaccessible to direct experimental comparison, for example, dimensions of the astronomical or subatomic order.

According to metrological purposes, measurements are divided into technical and metrological. Technical measurements are carried out using working measuring instruments in order to determine the value of the measured quantity, as well as during its control. These measurements are the most common and are performed in all branches of industry and science. Metrological measurements are performed using standards in order to reproduce units of physical quantities and to transfer their size to working measuring instruments (during verification and calibration work carried out by metrological services).

Based on the number of measurements performed to obtain the result, a distinction is made between single and multiple measurements. One-time called a measurement performed once. For example, measuring time using a clock. If greater confidence in the result obtained is required, then multiple measurements of the same quantity, the result of which is usually taken to be the arithmetic mean of individual measurements. Typically, for multiple measurements, the number of measurements is n ³3.

Based on the dependence of the measured value on time, measurements are divided into static and dynamic. At static In measurements, a physical quantity is taken as constant throughout the measurement time (for example, measuring the length of a part at normal temperature). If the size of a physical quantity changes over time, then such measurements are called dynamic(for example, measuring the distance to the surface of the earth from a descending aircraft).

Depending on the accuracy of the measuring instruments used and the measurement conditions, they are divided into equal and unequal precision. Equally accurate are measurements of a quantity carried out with measuring instruments of equal accuracy under the same conditions and with the same care. If measurements were made with measuring instruments that differ in accuracy and (or) under different conditions, then they are called unequal.

In addition to those shown in Fig. 1.3. Other characteristics of measurement classification for specific cases can be used if necessary. For example, measurements can be divided depending on the place of execution into laboratory and industrial; depending on the form of presentation of results - absolute and relative.

The above measurements can be carried out using various methods, i.e. ways to solve the measurement problem.

Measurement methods

Method of measurement is a technique or set of techniques for comparing a measured quantity with its unit in accordance with the implemented measurement principle. Under measurement principle understand the physical effects (phenomena) underlying measurements. For example, measuring temperature using the thermoelectric effect. The measurement method is usually determined by the design of the measuring instruments.

There are many measurement methods, and as science and technology advance, their number increases. Each physical quantity can be measured, as a rule, by several methods. To systematize them, it is necessary to identify common characteristic features. One of these signs is the presence or absence of a measure when measuring. Depending on this, two measurement methods are distinguished: the method of direct assessment and the method of comparison with a measure (Fig. 1.4). Measure is a measuring instrument designed to reproduce and (or) store a physical quantity of one or more specified dimensions, the values ​​of which are expressed in established units and are known with the required accuracy. For more information about the types of measures, see paragraph 3.1.

Rice. 1.4. Classification of measurement methods

Most common direct assessment method. Its essence lies in the fact that the value of the measured quantity is determined directly from the reading device of the measuring device, for example, measuring voltage with a voltmeter, weighing a load on a spring scale (Fig. 1.5). In this case, the mass of the load X is determined on the basis of a measurement transformation based on the deformation value d of the spring.

Rice. 1.5. Direct assessment measurement scheme

Measurements using the direct assessment method are usually simple and do not require highly skilled operators, since there is no need to create special measuring installations or perform any complex calculations. However, the measurement accuracy most often turns out to be low due to the influence of influencing quantities and the need to calibrate instrument scales.

The most numerous group of instruments used for measurement using the direct assessment method are indicating instruments (including pointer instruments). These include pressure gauges, dynamometers, barometers, ammeters, voltmeters, wattmeters, flow meters, liquid thermometers and many others. Measurements using an integrating counter or recording device are also classified as direct assessment methods.

When carrying out more accurate measurements, preference is given to method of comparison with measure, in which the measured value is found by comparison with the value reproduced by the measure. A distinctive feature of this method is the direct participation of the measure in the measurement process.

Comparison methods, depending on the presence or absence when comparing the difference between the measured value and the value reproduced by the measure, are divided into zero and differential. In both of these methods, a distinction is made between methods of opposition, substitution and coincidence.

Zero measurement method – this is a comparison method with a measure , in which the resulting effect of the influence of the measured quantity and measure on the comparison device is brought to zero. In this case, the value of the measured quantity is taken equal to the value of the measure. The coincidence of the values ​​of the measured quantity and the measure is noted using a zero pointer (null indicator). Examples of the zero measurement method: weighing on equal-arm scales; measurement of resistance, inductance and capacitance using a balanced bridge; temperature measurement in an optical pyrometer using a standard incandescent lamp (respectively, a balance, a galvanometer and the human eye are zero pointers).

Differential measurement method(also called difference) is a method of comparison with a measure in which the measured quantity is compared with the measure, and the difference between these two quantities is measured. The measure must have a value that is slightly different from the value of the measured quantity. An example of a differential method: measuring the length of a part by the difference between the measured length and the gauge length (in the field of linear and angular measurements, this method is called relative); measuring resistance, inductance and capacitance using an unbalanced bridge; weighing on unequal scales. The use of a null pointer is not required in this method.

Method of opposition lies in the fact that the measured quantity and the quantity reproduced by the measure simultaneously influence the comparison device, with the help of which the relationship between these quantities is established. An example of the zero opposition method is weighing a load X on an equal-arm scale (Fig. 1.6, a), when the measured mass of the load X is equal to the mass of the weights balancing it. The state of equilibrium is determined by the position of the zero indicator pointer (it must be at the zero mark). When weighing a load in the case of a differential opposition method, the mass of the load X is balanced by the mass of the weight and the force of elastic deformation of the spring (Fig. 1.6, b), the value of which is measured on the scale of the device. The mass of the load is determined as the sum of the mass of the weight and the readings measured on the scale.

A)

b)

Rice. 1.6. Scheme of measurement by comparison with a measure: a – zero, b – differential

The contrast method is widely used to measure various physical quantities. As a rule, it provides greater measurement accuracy than the direct estimation method by reducing the impact of instrument errors and influencing quantities on the measurement result.

Varieties of the method of comparison with a measure include substitution method, widely used in the practice of precision metrological research. The essence of the method is that the measured quantity is replaced by a measure with a known value of the quantity, i.e. The measured quantity and the measure sequentially influence the measuring device. In the zero method, the measured value is completely replaced by a measure, and the measurement result is taken equal to the value of the measure. In the differential method, it is not possible to carry out a complete substitution, and to obtain the value of the measured quantity, the value by which the instrument reading has changed must be added to the value of the measure.

Due to the fact that the measured quantity and the measure are included one after another in the same part of the measuring circuit of the device, the accuracy of measurements is significantly increased compared to measurements carried out using other types of comparison method, where the asymmetry of the circuits in which the compared quantities are included leads to to the occurrence of systematic errors. The substitution method is often used in electrical measurements using AC bridges.

Match method is a type of comparison method with a measure in which the difference between the measured quantity and the value reproduced by the measure is measured using the coincidence of scale marks or periodic signals. Based on the principle of the coincidence method, a vernier is built, which is part of a number of measuring instruments (for example, calipers).

In addition to the considered measurement methods, a distinction is also made between contact and non-contact, depending on the presence (or absence) of direct contact between the sensitive element of the measuring instrument and the measurement object. Examples of the contact method are measuring the diameter of a shaft with a caliper, measuring body temperature with a thermometer. Examples of a non-contact method are measuring the temperature in a blast furnace with a pyrometer, measuring the distance to an object with a radar.

Measurement errors

The result of measuring a quantity depends on many factors: the choice of method and measuring instrument, the conditions for its implementation (for example, temperature, pressure, ambient humidity), the method of processing measurement results, the qualifications of the operator performing the measurements, etc. These factors lead to differences in the value the result of measuring a quantity and its true value, i.e. to error. One of the main tasks of metrology is the development of methods for determining measurement errors.

Depending on the degree of approximation to the objectively existing value of a quantity, one should distinguish between the true value of the quantity and the result of its measurement, as well as its actual value.

True meaning X and quantities refer to a value that ideally characterizes the corresponding physical quantity in qualitative and quantitative terms. It can only be obtained as a result of an endless process of measurements with endless improvement of methods and measuring instruments.

Measurement result X is the value obtained when measuring it using specific methods and measuring instruments.

Measurement result error(or measurement error) D is the deviation of the measurement result from the true value of the measured value, i.e.

D = X measurement – ​​X i.

But since the true value of the measured quantity is unknown, the measurement errors are also unknown; therefore, in practice, to determine the error, the so-called real value of the quantity is used, which replaces the true value.

Real value X d values – this value is obtained experimentally and is so close to the true value that it can be used instead in the given measurement task. The actual value is found using more accurate methods and measuring instruments. The higher the accuracy of the means and method of measurement with which X d is determined, the more confidently it is considered as close to the true. Therefore, in practice, the measurement error D (here we mean the absolute error) is found using the formula

D = X measured – X d (1.6)

It is impossible to completely eliminate errors, but they can be reduced using the methods discussed below.

Accuracy of measurement result– this is one of the most important characteristics (indicators) of measurement quality, reflecting the proximity to zero error of the measurement result. In addition, indicators of the quality of measurements are convergence, reproducibility, correctness and reliability of measurement results, which will be discussed below.

Three sigma rule

A characteristic property of the normal distribution is that about 68% of all its measurement results are in the ± 1s interval. In the range ± 2s] - 95%. In the range ± 3s] - 99.73% (Fig. 1.12). Consequently, almost all measurement results lie in the 6s interval (three s in each direction from M[X]). Outside this interval, 0.27% of the total data may be located (approximately three out of a thousand measurement results).

Rice. 1.12. Illustration of the three sigma rule

It follows that if any value of a quantity goes beyond ±3s, then with a high probability it can be considered erroneous.

Based on this, it was formulated three sigma rule: if, during repeated measurements (n > 25...30) of the same constant size value, the dubious result X doubt of an individual measurement (maximum or minimum) differs from the average value by more than 3s, then with a probability of 99.7% it is erroneous, i.e. .e.

if > 3s, (1.12)

then X doubt is a miss; it is discarded and not taken into account in further processing of measurement results.

The law of normal distribution works when the number of measurement results is n = ¥. In reality, a finite number of measurements are obtained, which obey the Student distribution law. When n>25, the Student distribution tends to normal.

Chapter 2. MEASURING INSTRUMENTS

One of the most important elements of the measurement process, which allows you to directly obtain measurement information, is the measuring instrument. Every day a huge number of measurements are carried out using a whole “army” of various measuring instruments. There are many of them, they can be easy to use, such as a ruler, or they can be very complex devices that require highly qualified maintenance, such as a radio navigation system. Regardless of the complexity, purpose and principle of operation, they all perform the same function - they compare the unknown size of a physical quantity with its unit. At the same time, it is important that the measuring instrument “skillfully” stores (and reproduces) a unit of physical quantity in such a way that the requirement of invariance of the size of the stored unit over time is met. It is this “skillful storage” that distinguishes measuring instruments from other technical means. Thus, measuring instrument is a technical device (or a complex thereof) intended for measurements, having standardized metrological characteristics, reproducing and (or) storing a unit of physical quantity, the size of which is assumed unchanged (within limits)

Measurement of a physical quantity- a set of operations for the use of a technical means that stores a unit of physical quantity, ensuring that the relationship (explicitly or implicitly) of the measured quantity with its unit is found and the value of this quantity is obtained.

In the simplest case, applying a ruler with divisions to any part, essentially compare its size with the unit stored by the ruler, and, having made a reading, obtain the value of the value (length, height, thickness and other parameters of the part). Using a measuring device, the size of the quantity converted into the movement of the pointer is compared with the unit stored by the scale of this device, and a count is made.

The definition of the concept of “measurement” satisfies the general measurement equation, which is of significant importance in streamlining the system of concepts in metrology. It takes into account the technical side (set of operations), reveals the metrological essence of measurements (comparison with a unit) and shows the epistemological aspect (obtaining the value of a quantity).

Types of measurements

Measurement area- a set of measurements of physical quantities characteristic of any field of science or technology and distinguished by its specificity. Note - There are a number of measurement areas: mechanical, magnetic, acoustic, measurements of ionizing radiation, etc.

Type of measurements- part of the measurement area, which has its own characteristics and is characterized by the homogeneity of the measured values. Example - In the field of electrical and magnetic measurements, the following types of measurements can be distinguished: measurements of electrical resistance, electromotive force, electrical voltage, magnetic induction, etc.

There are several types of measurements.

According to the nature of the dependence of the measured value on time, measurements are divided into:

static measurements;

dynamic measurements.

According to the method of obtaining measurement results, they are divided into:

indirect;

cumulative;

joint.

According to the conditions that determine the accuracy of the result, measurements are divided into:

metrological measurements;

control and verification measurements;

technical measurements.

According to the method of expressing the results, they are distinguished:

absolute measurements;

relative measurements.

According to the characteristics of the measuring instrument, they are distinguished:

equal-precision measurements;

unequal measurements.

By the number of measurements in a series of measurements:

single measurements;

multiple measurements.

Measurements are distinguished by the method of obtaining information, by the nature of changes in the measured value during the measurement process, by the amount of measurement information in relation to the basic units.

Based on the method of obtaining information, measurements are divided into direct, indirect, cumulative and joint.

Direct measurements are a direct comparison of a physical quantity with its measure. For example, when determining the length of an object with a ruler, the desired value (the quantitative expression of the length value) is compared with the measure, i.e., the ruler.

Indirect measurements differ from direct ones in that the desired value of a quantity is established based on the results of direct measurements of such quantities that are associated with the desired specific relationship. So, if you measure the current with an ammeter and the voltage with a voltmeter, then from the known functional relationship of all three quantities you can calculate the power of the electrical circuit.

Cumulative measurements involve solving a system of equations compiled from the results of simultaneous measurements of several homogeneous quantities. Solving the system of equations makes it possible to calculate the desired value.

Joint measurements are measurements of two or more inhomogeneous physical quantities to determine the relationship between them.

Cumulative and joint measurements are often used to measure various parameters and characteristics in the field of electrical engineering.

According to the nature of the change in the measured value during the measurement process, there are statistical, dynamic and static measurements.

Statistical measurements are associated with determining the characteristics of random processes, sound signals, noise levels, etc. Static measurements take place when the measured value is practically constant.

Dynamic measurements are associated with quantities that undergo certain changes during the measurement process. Static and dynamic measurements in an ideal form are rare in practice.

Based on the amount of measurement information, a distinction is made between single and multiple measurements.

Single measurements are one measurement of one quantity, i.e. the number of measurements is equal to the number of measured quantities. The practical application of this type of measurement is always associated with large errors, so at least three single measurements should be carried out and the final result should be found as the arithmetic mean value.

Multiple measurements are characterized by an excess of the number of measurements in the number of measured quantities. The advantage of multiple measurements is a significant reduction in the influence of random factors on the measurement error. measurement metrological scale

Measurement methods are determined by the type of measured quantities, their sizes, the required accuracy of the result, the required speed of the measurement process and other data.

There are many measurement methods, and as science and technology develop, their number is increasing.

According to the method of obtaining the numerical value of the measured value, all measurements are divided into three main types: direct, indirect and cumulative.

Direct are called measurements in which the desired value of a quantity is found directly from experimental data (for example, measuring mass on a dial or equal-arm scale, temperature with a thermometer, length with linear measures).

Indirect are called measurements in which the desired value of a quantity is found on the basis of a known relationship between this quantity and quantities subjected to direct measurements (for example, the density of a homogeneous body based on its mass and geometric dimensions; determination of electrical resistance from the results of measuring voltage drop and current).

Cumulative are called measurements in which several quantities of the same name are simultaneously measured, and the desired value of the quantities is found by solving a system of equations obtained from direct measurements of various combinations of these quantities (for example, measurements in which the masses of individual weights of a set are determined from the known mass of one of them and from the results of direct comparisons of masses of different combinations of weights).

It was said earlier that in practice direct measurements are most widespread due to their simplicity and speed of execution. Let us give a brief description of direct measurements.

Direct measurements of quantities can be made using the following methods:

1) Direct assessment method – the value of the quantity is determined directly from the reading device of the measuring device (measurement of pressure - with a spring pressure gauge, mass - with dial scales, electric current - with an ammeter).

2) Comparison method with measure – the measured value is compared with the value reproduced by the measure (measuring mass with lever scales balanced with weights).

3) Differential method – a method of comparison with a measure, in which the measuring device is affected by the difference between the measured value and the known value reproduced by the measure (measurements performed when checking length standards by comparison with a standard measure on a comparator).

4) Null method – a method of comparison with a measure, when the resulting effect of the influence of quantities on a comparison device is brought to zero (measurement of electrical resistance with a bridge with its complete balancing).

5) Match method – a method of comparison with a measure, in which the difference between the measured quantity and the value reproduced by the measure is measured using the coincidence of scale marks or periodic signals (length measurement using a vernier caliper, when the coincidence of marks on the caliper and vernier scales is observed).

6) Substitution method – method of comparison with a measure, when the measured value is replaced by a known value, reproducible by the measure (weighing with alternately placing the measured mass and weights on the same pan of scales).

End of work -

This topic belongs to the section:

Metrology

The concept of metrology as a science metrology is the science of measurement methods and.. basic concepts associated with objects of measurement..

If you need additional material on this topic, or you did not find what you were looking for, we recommend using the search in our database of works:

What will we do with the received material:

If this material was useful to you, you can save it to your page on social networks:

Tweet

All topics in this section:

The concept of metrology as a science
Metrology is the science of measurements, methods and means of ensuring their unity and ways of achieving the required accuracy. In practical life, a person is entirely

Concept of measuring instruments
A measuring instrument (MI) is a technical means (or a set of technical means) intended for measurement, having a standardized metrological character

Metrological characteristics of measuring instruments
Metrological characteristics of measuring instruments are characteristics of properties that influence the results and errors of measurements. Information about the purpose of the meter

Factors influencing measurement results
In metrological practice, when carrying out measurements, it is necessary to take into account a number of factors that influence the measurement results. This is the object and subject of measurement, measurement method, cf.

Formation of measurement results. Measurement errors
The measurement procedure consists of the following main stages: 1) adoption of the object measurement model; 2) choice of measurement method; 3) choice of measuring instruments;

Presentation of measurement results
There is a rule: measurement results are rounded to the nearest “error”. In practical metrology, rules have been developed for rounding results and measurement errors. OS

Causes of measurement errors
There are a number of error terms that are dominant in the overall measurement error. These include: 1) Errors depending on the measuring instruments. But

Handling multiple measurements
We assume that the measurements are equally accurate, i.e. performed by one experimenter, under the same conditions, with one device. The technique boils down to the following: n observations are made (one

Student distribution (t-test)
n/α 0.40 0.25 0.10 0.05 0.025 0.01 0.005 0.0005

Measurement techniques
The main loss of accuracy during measurements occurs not due to a possible metrological malfunction of the measuring instruments used, but primarily due to the imperfection of the method

The concept of metrological support
Metrological support (MS) refers to the establishment and application of scientific and organizational foundations, technical means, rules and regulations, necessary

Systematic approach to the development of metrological support
When developing MO, it is necessary to use a systematic approach, the essence of which is to consider MO as a set of interrelated processes united by one goal - achieved

Fundamentals of metrological support
Metrological support has four bases: scientific, organizational, regulatory and technical. Their content is shown in Figure 1. Certain aspects of MO are discussed in the recommendation

Legislation of the Russian Federation on ensuring the uniformity of measurements
The regulatory framework for ensuring the uniformity of measurements is presented in Figure 2.

National system for ensuring the uniformity of measurements
The National System for Ensuring the Uniformity of Measurements (NSOEI) is a set of rules for performing work to ensure the uniformity of measurements, its participants and rules

Main types of metrological activities to ensure the uniformity of measurements
The unity of measurements is understood as such a state of measurements in which their results are expressed in legal units of magnitude and error (indefinite

Conformity assessment of measuring instruments
When carrying out measurements related to the scope of state regulation to ensure the uniformity of measurements, measuring instruments must be used on the territory of Russia that meet the requirements

Type approval of measuring instruments
Type approval (except for SOSSVM) is carried out on the basis of positive test results. Approval of the SOSSVM type is carried out on the basis of positive results of the attestation

Certification of measurement techniques
A measurement technique is a set of operations and rules, the implementation of which ensures obtaining a measurement result with a specified error.

Verification and calibration of measuring instruments
Verification of measuring instruments is a set of operations performed to confirm the compliance of the actual values ​​of metrological characteristics

Structure and functions of the metrological service of an enterprise, organization, institution that is a legal entity
The metrological service of an enterprise, organization and institution enjoying the rights of a legal entity, regardless of the form of ownership (hereinafter referred to as the enterprise) includes a department (service)

The concept of interchangeability
Interchangeability is the property of the same parts, components or assemblies of machines, etc., which allows the installation of parts (assemblies, assemblies) during the assembly process or replacement

Qualifications, main deviations, landings
The accuracy of a part is determined by the dimensional accuracy, surface roughness, surface shape accuracy, positional accuracy, and surface waviness. To ensure

Designation of tolerance fields, maximum deviations and fits on drawings
Maximum deviations of linear dimensions are indicated in the drawings by conventional (letter) designations of tolerance fields or numerical values ​​of maximum deviations, as well as letter

Unspecified maximum dimensional deviations
Maximum deviations that are not indicated directly after the nominal dimensions, but specified by a general entry in the technical requirements of the drawing, are called unspecified maximum deviations.

Recommendations for the use of clearance fits
Fit H5/h4 (Smin= 0 and Smax = Td +Td) is prescribed for pairs with precise centering and direction, in which rotation and longitudinal movement are allowed

Recommendations for the use of transitional landings
Transitional fits Н/js, Н/k, Н/m, Н/n are used in fixed detachable connections for centering replaceable parts or parts that, if necessary, can move in the air

Recommendations for the use of interference fits
Landings N/r; Р/h – “light press” – characterized by a minimum guaranteed tension. Installed in the most precise grades (shafts 4 - 6, holes 5 - 7-

Concept of surface roughness
Surface roughness, according to GOST 25142 - 82, is a set of surface irregularities with relatively small steps, identified using the base length. Bazova

Roughness parameters
According to GOST 2789 - 73, the surface roughness of products, regardless of the material and manufacturing method, can be assessed by the following parameters (Figure 10):

General terms and definitions
Tolerances of the shape and location of the surfaces of machine parts and devices, terms, definitions related to the main types of deviations are standardized by GOST 24642 ​​- 81. The basis

Form deviations and tolerances
Shape deviations include deviations of straightness, flatness, roundness, longitudinal section profile and cylindricity. Deviations in the shape of flat surfaces

Deviations and location tolerances
The deviation of the location of a surface or profile is the deviation of the actual location of the surface (profile) from its nominal location. Quantitative deviations of location

Total deviations and tolerances of the shape and location of surfaces
The total deviation of shape and location is the deviation that is the result of the joint manifestation of the deviation of the form and the deviation of the location of the element in question (ver.

Dependent and independent tolerance of shape and location
Location or shape tolerances set for shafts or holes can be dependent or independent. Dependent is a tolerance of shape or location, the minimum value

Numerical values ​​of tolerances of shape and location of surfaces
According to GOST 24643 - 81, for each type of tolerance of the shape and location of surfaces, 16 degrees of accuracy are established. The numerical values ​​of tolerances change from one degree to another

Designation on drawings of tolerances of shape and location
The type of tolerance of shape and location in accordance with GOST 2.308 - 79 should be indicated on the drawing by the signs (graphic symbols) given in Table 4. I enter the sign and numerical value of the tolerance

Unspecified tolerances of shape and location
As a rule, the most critical tolerances for the shape and location of surfaces are indicated directly in the drawing. According to GOST 25069 - 81, all indicators of shape accuracy and location

Rules for defining bases
1) If a part has more than two elements for which the same unspecified location or runout tolerances are established, then these tolerances should be attributed to the same base;

Rules for determining the defining size tolerance
The defining tolerance of size is understood as: 1) When determining an unspecified tolerance of perpendicularity or axial runout - the tolerance of the size coordinating

Surface waviness
Surface undulation is understood as a set of periodically repeating irregularities in which the distances between adjacent hills or depressions exceed the base length l.

Tolerances of rolling bearings
The quality of bearings, other things being equal, is determined by: 1) the accuracy of the connecting dimensions and the width of the rings, and for roller angular contact bearings e

Selection of bearing fits
The fit of a rolling bearing on the shaft and in the housing is selected depending on the type and size of the bearing, its operating conditions, the value and nature of the loads acting on it and the type of loading of the rings

Solution
1) With a rotating shaft and a constant force Fr, the inner ring is loaded with circulation, and the outer ring with local loads. 2) Load intensity

Bearing symbols
The system of symbols for ball and roller bearings is established by GOST 3189 - 89. The symbol of a bearing gives a complete picture of its overall dimensions, design, manufacturing accuracy

Tolerances of angular dimensions
Tolerances of angular dimensions are assigned in accordance with GOST 8908 - 81. Angle tolerances AT (from English Angle tolerance) should be assigned depending on the nominal length L1 of the shorter side

Tolerance and fit system for conical connections
A conical connection has advantages over a cylindrical one: you can adjust the amount of clearance or tension by relative displacement of the parts along the axis; with stationary connection

Basic parameters of metric fastening threads
Parameters of cylindrical thread (Figure 36, a): average d2 (D2); outer d (D) and inner d1 (D1) diameters on

General principles of interchangeability of cylindrical threads
Systems of tolerances and fits that ensure the interchangeability of metric, trapezoidal, thrust, pipe and other cylindrical threads are built on a single principle: they take into account the presence of mutual

Tolerances and fits of threads with clearance
Tolerances of metric threads with large and small pitches for diameters 1 - 600 mm are regulated by GOST 16093 - 81. This standard sets the maximum deviations of thread diameters in

Tolerances of threads with interference fit and transition fits
The fits under consideration serve mainly for connecting studs to body parts if screw or bolt-nut connections cannot be used. These fits are used in fastening joints

Standard threads for general and special purposes
Table 9 shows the names of standard general-purpose threads, the most widely used in mechanical and instrument engineering, and gives examples of their designation in the drawings. To the most

Kinematic transmission accuracy
To ensure kinematic accuracy, standards are provided that limit the kinematic error of the transmission and the kinematic error of the wheel. Kinematic

Smooth transmission operation
This transmission characteristic is determined by parameters, the errors of which appear many times (cyclically) per revolution of the gear wheel and also form part of the kinematic linear

Tooth contact in gear
To increase the wear resistance and durability of gears, it is necessary that the completeness of contact of the mating lateral surfaces of the wheel teeth be as great as possible. With incomplete and unequal

Side clearance
To eliminate possible jamming when the gear is heated, to ensure conditions for the flow of lubricant and to limit the backlash when reversing the reading and dividing real gears

Designation of wheel and gear accuracy
The manufacturing accuracy of gears and gears is determined by the degree of accuracy, and the requirements for lateral clearance are determined by the type of mating according to lateral clearance standards. Examples of symbols:

Selecting the degree of accuracy and controlled parameters of gears
The degree of accuracy of wheels and gears is established depending on the requirements for kinematic accuracy, smoothness, transmitted power, as well as the peripheral speed of the wheels. When choosing the degree of accuracy

Tolerances of bevel and hypoid gears
The principles of constructing a tolerance system for bevel gears (GOST 1758 - 81) and hypoid gears (GOST 9368 - 81) are similar to the principles of constructing a system for cylindrical gears

Tolerances of worm gears
For worm cylindrical gears, GOST 3675 - 81 establishes 12 degrees of accuracy: 1, 2, . . ., 12 (in descending order of accuracy). For worms, worm wheels and worm gears each

Tolerances and fits of connections with straight-sided tooth profile
According to GOST 1139 - 80, tolerances are established for connections with centering along the internal d and external diameters D, as well as along the lateral sides of the teeth b. Since the view is centered

Tolerances and fits of spline joints with involute tooth profile
The nominal dimensions of spline connections with an involute profile (Figure 58), the nominal dimensions of the rollers (Figure 59) and the lengths of the common normal for individual measurements of spline shafts and bushings should

Monitoring the accuracy of spline connections
Spline connections are controlled with complex go-through gauges (Figure 61) and element-by-element non-go-through gauges.

A method for calculating dimensional chains that ensures complete interchangeability
To ensure complete interchangeability, dimensional chains are calculated using the maximum-minimum method, in which the tolerance of the closing size is determined by the arithmetic addition of the composition tolerances

Theoretical-probability method for calculating dimensional chains
When calculating dimensional chains using the maximum-minimum method, it was assumed that during processing or assembly a simultaneous combination of the largest increasing and smallest decreasing dimensions is possible

Group interchangeability method for selective assembly
The essence of the group interchangeability method is to manufacture parts with relatively wide technologically feasible tolerances, selected from the relevant standards, grade

Adjustment and fitting method
Regulation method. The regulation method refers to the calculation of dimensional chains, in which the required accuracy of the initial (closing) link is achieved by deliberately changing

Calculation of plane and spatial dimensional chains
Planar and spatial dimensional chains are calculated using the same methods as linear ones. It is only necessary to reduce them to the form of linear dimensional chains. This is achieved by designing

Historical basis for the development of standardization
Man has been engaged in standardization since ancient times. For example, writing dates back at least 6 thousand years and arose according to recent discoveries in Sumer or Egypt.

Legal basis of standardization
The legal basis for standardization in the Russian Federation is established by the Federal Law “On Technical Regulation” of December 27, 2002. It is mandatory for all government

Principles of technical regulation
Currently, the following principles have been established: 1) application of uniform rules for establishing requirements for products or related design processes (including surveys), production

Objectives of technical regulations
The Law on Technical Regulation establishes a new document – ​​technical regulations. Technical regulations are a document adopted by the international treaty of Russia

Types of technical regulations
In the Russian Federation, two types of technical regulations are used: - general technical regulations; - special technical regulations. General technical regulations of the Republic of Armenia

Standardization concept
The content of standardization terms has gone through a long evolutionary path. The clarification of this term occurred in parallel with the development of standardization itself and reflected the achieved level of its development in the world.

Goals of standardization
Standardization is carried out in order to: 1) Increase the level of security: - life and health of citizens; - property of individuals and legal entities; - state

Object, aspect and scope of standardization. Levels of standardization
The object of standardization is a specific product, service, production process (work), or a group of homogeneous products, services, processes for which requirements are developed

Principles and functions of standardization
The basic principles of standardization in the Russian Federation, ensuring the achievement of the goals and objectives of its development, are as follows: 1) voluntary application of documents in the field of standardization

International standardization
International standardization (IS) is an activity in which two or more sovereign states participate. The IC plays a prominent role in deepening global economic cooperation, in

Set of standards of the national standardization system
To implement the Federal Law “On Technical Regulation”, since 2005, 9 national standards of the “Standardization of the Russian Federation” complex have been in force, which replaced the “State Standardization System” complex. This

Structure of standardization bodies and services
The national standardization body is the Federal Agency for Technical Regulation and Metrology (Rostekhregulirovanie), which replaced the State Standard. It reports directly

Regulatory documents on standardization
Regulatory documents on standardization (ND) - documents containing rules, general principles for the object of standardization and are available to a wide range of users. ND includes: 1)

Categories of standards. Standard designations
Categories of standardization are distinguished by the level at which standards are adopted and approved. Four categories have been established: 1) international; 2) between

Types of standards
Depending on the object and aspect of standardization, GOST R 1.0 establishes the following types of standards: 1) fundamental standards; 2) product standards;

State control over compliance with the requirements of technical regulations and standards
State control is carried out by officials of the state control body of the Russian Federation over compliance with the requirements of the TR concerning the stage of product circulation. Regional state control authorities

Organizational Standards (STO)
The organization and procedure for the development of STO is contained in GOST R 1.4 - 2004. An organization is a group of workers and the necessary funds with the distribution of responsibilities, powers and mutual

Necessity of Preferred Numbers (PN)
The introduction of IF was caused by the following considerations. The use of inverter allows the best coordination of the parameters and dimensions of a single product with all associated

Series based on arithmetic progression
Most often, IF series are built on the basis of a geometric progression, less often on the basis of an arithmetic progression. In addition, there are varieties of rows built on the basis of the "golden"

Series based on geometric progression
Long-term practice of standardization has shown that the most convenient are series constructed on the basis of a geometric progression, since this results in the same relative difference between

Properties of preferred number series
IF series have the properties of a geometric progression. The IF series are not limited in both directions, while numbers less than 1.0 and more than 10 are obtained by dividing or multiplying by 10, 100, etc.

Restricted, sample, composite and approximate series
Limited rows. If it is necessary to limit the main and additional series, their designations indicate limiting terms, which are always included in the limited series. Example. R10(

Concept and types of unification
When unifying, a minimum acceptable but sufficient number of types, types, standard sizes, products, assembly units and parts with high quality indicators is established

Indicators of the level of unification
The level of unification of products is understood as their saturation with standardized components; parts, modules, units. The main quantitative indicators of the level of product unification

Determination of the level of unification indicator
The assessment of the level of unification is based on the correction of the following formula:

History of certification development
"Certificate" in Latin means "done correctly." Although the term "certification" has become known in everyday life and commercial practice

Terms and definitions in the field of conformity assessment
Conformity assessment is a direct or indirect determination of compliance with the requirements for an object. A typical example of an assessment activity is

Goals, principles and objects of conformity assessment
Confirmation of conformity is carried out for the purposes of: - certifying the conformity of products, design processes (including surveys), production, construction, installation

The role of certification in improving product quality
A radical improvement in product quality in modern conditions is one of the key economic and political tasks. That is why the totality of the same is aimed at solving it

Product certification schemes for compliance with the requirements of technical regulations
A certification scheme is a certain set of actions officially accepted as evidence of product compliance with specified requirements.

Declaration of conformity schemes for compliance with the requirements of technical regulations
Table 17 - Schemes for declaring conformity for compliance with the requirements of technical regulations Designation of the scheme Contents of the scheme and its use

Service certification schemes
Table 18 - Service certification schemes Scheme No. Assessment of the quality of service provision Verification (testing) of service results

Compliance Schemes
Table 19 - Product certification schemes Scheme number Tests in accredited testing laboratories and other methods of proof

Mandatory confirmation of compliance
Mandatory confirmation of conformity can be carried out only in cases established by technical regulations and solely for compliance with their requirements. Wherein

Declaration of conformity
The Federal Law “On Technical Regulation” formulates the conditions under which a declaration of conformity can be accepted. First of all, this form of confirmation of conformity

Mandatory certification
Mandatory certification in accordance with the Federal Law “On Technical Regulation” is carried out by an accredited certification body on the basis of an agreement with the applicant.

Voluntary confirmation of compliance
Voluntary confirmation of conformity should be carried out only in the form of voluntary certification. Voluntary certification is carried out at the initiative of the applicant on the basis of agreement

Certification systems
A certification system is understood as a set of certification participants operating in a certain area according to the rules defined in the system. The concept of “certification system” in

Certification procedure
Product certification takes place in the following main stages: 1) Submitting an application for certification; 2) Consideration and decision-making on the application; 3) Selection, ID

Certification bodies
Certification body is a legal entity or individual entrepreneur accredited in the prescribed manner to carry out certification work.

Testing laboratories
Testing laboratory is a laboratory that conducts tests (certain types of tests) of certain products. When conducting ser

Accreditation of certification bodies and testing laboratories
According to the definition given in the Federal Law “On Technical Regulation”, accreditation is “the official recognition by an accreditation body of the competence of a physical

Service certification
Certification is carried out by accredited service certification bodies within their scope of accreditation. During certification, the characteristics of services are checked and methods are used.

Certification of quality systems
In recent years, the world has seen a rapid increase in the number of companies that have certified their quality systems to ISO 9000 series standards. Currently, these standards are used