Measurements of physical quantities and their classification. Measurement of physical quantities Measurement of physical quantities measurement procedures
Physical venlens. Physical units
The wide development and dissemination of methods and means of metrology led to the creation of whole systems of measurement units of state and international organizations. At the present moment of general globalization, the role of metrology and the complexity of tasks is significantly increasing. Each qualitative feature of a physical object is called a physical quantity (length, mass, speed). A physical quantity has a certain size, which is expressed through a unit of measurement. Among physical quantities, basic and converted from basic are distinguished. Both of these physical quantities form a system of units. At different times, there were different systems of units of measurement. ISS system - meter, kilogram, second. The SGS system included centimeter, gram, second, etc. On the basis of them, the International System of Units (SI) was built, which was adopted at the XI International Conference on Weights and Measures in 1960 to introduce uniformity in units of measurement throughout the world.
The SI has seven basic units, using which it is possible to measure all mechanical, electrical, magnetic, acoustic, light and chemical parameters, as well as the characteristics of ionizing radiation. The main SI units are:
meter (m) - for measuring length;
kilogram (kg) - to measure mass;
second (s) - to measure time;
ampere (A) - to measure the strength of the electric current;
kelvin (K) - for measuring thermodynamic temperature;
mol (mol) - to measure the amount of a substance;
candela (cd) - to measure luminous intensity.
The SI adopted a new definition of the unit of length - the meter. Before the introduction of the SI, line measures made of a platinum-iridium alloy and having an X-shape in cross section were used as international and national standards of the meter. The meter was determined at a temperature of 20 ° C between the axes of the two middle lines of the measure with an accuracy of ± 0.1 µm.
In the new system of units, 1 m is expressed in the wavelengths of light waves of the krypton atom, that is, it is associated with a natural quantity. Now a meter is a length equal to 1,650,763.73 wavelengths in a vacuum of radiation corresponding to the orange line of the spectrum of krypton-86. With the new standard, the length of 1 m is now reproduced with an error of 0.002 microns, which is 50 times less than the error of the old artificial standard of the meter.
Measurement method- reception or a set of methods for comparing the measured physical quantity and its unit in accordance with the implemented measurement principle.
The measurement method is usually determined by the design of the measuring instrument. There are several basic measurement methods: direct assessment, comparison with a measure, differential, or difference, zero, contact and non-contact.
The measuring tool and the techniques for its use together form a measurement method. According to the method of obtaining the values of the measured quantities, two main methods of measurement are distinguished: the method of direct assessment and the method of comparison with a measure.
Direct assessment method- a measurement method in which the value of a quantity is determined directly from the reading device of a direct-acting measuring device.
For example, by measuring the length with a ruler, the dimensions of the parts with a micrometer, a caliper, the size value was obtained
Figure 7.1- Measurement scheme by the method of comparison with the measure
Comparison method with measure- measurement method in which the measured quantity is compared with the quantity reproduced by the standard. For example, to measure the height L details 1 (fig. 7.1) minimeter 2 fixed in the rack. The minimeter arrow is set to zero according to some sample (a set of gauge measures 3), having a height N, equal to the nominal height L the part to be measured. Then they start measuring batches of parts. About dimensional accuracy L judged by the deviation ± ∆ of the minimeter arrow relative to the zero position.
Depending on the relationship between the readings of the device and the measured physical quantity, measurements are divided into direct and indirect, absolute and relative.
At direct In measurements, the desired value of the quantity is found directly in the process of measurements, for example, measuring the angle with a goniometer, diameter - with a caliper, mass - on a dial balance.
At indirectly measurement, the value of the quantity is determined on the basis of the relationship between this quantity and the quantities subjected to direct measurements, for example, determining the average thread diameter using three wires on a vertical length gauge, the angle using a sine ruler, etc.
When measuring linear quantities, regardless of the methods considered, contact and non-contact measurement methods are distinguished.
Contact method is carried out by contact between the measuring surfaces of the tool or device and the part to be checked. Its disadvantage is the need for a certain effort when measuring, which causes additional errors (for example, measurements with a caliper, micrometer, lever-mechanical devices).
Non-contact method is devoid of the lack of contact, since during the measurement process there is no contact between the control tool and the product. This is a check on projectors, microscopes, using pneumatic devices.
The measurement of the surfaces of parts with a complex geometric shape (threads, spline joints) can be made either by element-by-element or by an integrated method.
By element-by-element method, for example, the thread of the average diameter is checked by the three-wire method, the outer diameter by a micrometer, and the profile angle by a universal microscope.
Complex method They are used when checking the thread with the help of screw plugs and rings for make-up, at the same time they check the pitch, profile angle and average thread diameter.
Measuring means (devices) are classified according to their purpose, structural and functional characteristics and technological features of manufacture. At the factories, specialized workshops and sections manufacture the following groups of measuring instruments.
1. Optical devices:
a) devices for measuring lengths and angles - long meters, profilometers, spherometers, instrumental and universal measuring microscopes, linear measuring instruments, machines, optical dividing heads, goniometers,
refractometers, autocollimation tubes, cathetometers, etc .;
b) microscopes (binocular, interference, biological, etc.);
c) observation devices - Galilean and prism binoculars, stereoscopes, periscopes;
d) geodetic instruments - levels, theodolites, optical range finders;
e) prismatic and diffraction spectral devices - microphotometers, interferometers, spectroprojectors.
2. Lever-optical devices: optimometers, ultra-meters, etc.
3. Lever-mechanical devices:
a) actually lever (minimeters, etc.);
b) gear (dial indicators, etc.);
c) lever-toothed (micrometers, etc.);
d) lever-screw (indicator-micrometer);
e) with a spring transmission (microcators, etc.).
4. Pneumatic instruments with manometer and rotameter.
5. Mechanical devices:
a) dashed lines, equipped with vernier (vernier tools and universal goniometers);
b) micrometric, based on the use of a screw transmission (micrometers, micrometer bore gauges, depth gauges, etc.).
6. Electrified devices (inductive, capacitive, photovoltaic, etc.).
7. Automatic devices: control and sorting machines, active control devices, etc.
Type of measuring instruments Is a set of measuring instruments intended for measurements of a given type of physical quantity.
The type of measuring instruments can include several types. For example, ammeters and voltmeters (in general) are types of measuring instruments, respectively, of electric current and voltage.
Reading device the indicating device may have a scale and a pointer. Pointer performed in the form of an arrow, a light beam, etc. Currently, readout devices with digital indication are widely used. Scale is a set of marks and affixed to some of them with reference numbers or other symbols corresponding to a series of successive values of the quantity. The interval between two adjacent scale marks is called dividing the scale.
Scale division interval- the distance between two adjacent scale marks. Most measuring instruments have a scale interval of 1 to 2.5 mm.
Figure 7.2- Scale ranges
Scale division- the difference in the values of the quantities corresponding to two adjacent scale marks. For example (see Fig.), The indicator has a graduation of 0.002 mm.
Initial and final scale value (measurement limit)- respectively, the smallest and largest values of the measured value indicated on the scale, characterizing the capabilities of the scale of the measuring instrument and determining the range of indications.
1.5 Measurement uncertainty and its sources
When analyzing a measurement, the true values of physical quantities are compared with the measurement results. Deviation ∆ of the measurement result X from the true value Q the measured quantity is called measurement error:
∆ = X-Q.
Measurement errors are usually classified by reason of their occurrence and by the type of error. Depending on the causes of the occurrence, the following measurement errors are distinguished.
Method error- This is a component of the measurement error, which is a consequence of the imperfection of the measurement method. The total error of the measurement method is determined by the totality of errors of its individual components (instrument readings, gauge blocks, temperature changes, etc.).
Readout error- the component of the measurement error, which is a consequence of the insufficiently accurate reading of the readings of the measuring instrument and depends on the individual abilities of the observer.
Instrumental error- the component of the measurement error, depending on the errors of the used measuring instruments. Distinguish between basic and additional errors of measuring instruments. Per basic error accept the error of the measuring instrument used in normal conditions. Additional error is the sum of additional errors of the measuring transducer and the measure caused by the deviation from normal conditions.
If the temperature of the item under test differs from the temperature at which the control is carried out, it will cause errors resulting from thermal expansion. To avoid their appearance, all measurements should be carried out at normal temperature (+ 20 ° C).
Inaccurate installation of the part under control and device installation errors also affect the measurement accuracy. For example, a vernier caliper should be installed perpendicular to the surface to be measured when measuring. However, there may be distortions during the measurement process, which leads to measurement errors.
To the listed errors, you can add errors that arise when the performer is reading the size due to his subjective data, errors from the non-density of contact between the measuring surfaces and the product.
All measurement errors are subdivided by type into systematic, random and gross.
Under systematic understand errors that are constant or regularly varying with repeated measurements of the same quantity. Random errors - the components of the measurement error that change randomly when repeated measurements of the same quantity. TO rude refers to random errors that are much larger than those expected under the given measurement conditions (eg, wrong readings, jolts and impacts of the instrument).
Calibration is the establishment of metrological characteristics of measuring instruments, which are not covered by state metrological supervision; calibration is performed by calibration laboratories.
The threshold of sensitivity (response) is the smallest increase in the input quantity, which causes a noticeable change in the output quantity.
An elementary error is a component of an error that, in a given analysis, does not need to be further divided into components. There are no universal methods for detecting systematic errors. Therefore, different methods are used to reduce or eliminate them. Gross errors in the measurement results are excluded using the criterion of abnormal results for which I take the interval relative to the distribution center in fractions of the standard deviation. Usually, if the measurement value is more than 3 σ, then such a deviation is referred to as abnormal.
To ensure the metrological uniformity of measurements, metrological certification of measuring instruments is carried out in measuring laboratories.
Verification- establishing the suitability of a measuring instrument for use on the basis of the compliance of the experimentally determined metrological characteristics and control with the established requirements.
The main metrological characteristic of a measuring instrument, determined during verification, is its error. As a rule, it is found on the basis of a comparison of the calibrated measuring instrument with an exemplary measuring instrument or standard, i.e., with a more accurate means intended for verification.
Distinguish between checks: state and departmental, periodic and independent, extraordinary and inspection, complex, element-by-element, etc. Verification is carried out by metrological services, which are given the right to do so in the prescribed manner. The verification is carried out by specially trained specialists who have a certificate for the right to carry it out.
The results of verification of measuring instruments recognized as suitable for use are formalized by issuing verification certificates, applying a verification mark, etc. All measuring instruments used in the national economy are subject to verification.
In enterprises, the main means of preserving measures of length are end measures. All workshop measuring instruments are subject to verification in control and measuring laboratories with exemplary measuring instruments.
Physical quantities. Units of quantities
Physical quantity is a property that is qualitatively common for many physical objects, but quantitatively individual for each of them.
Physical quantity value is a quantitative estimate of the size of a physical quantity, presented in the form of a certain number of units adopted for it (for example, the value of the resistance of a conductor is 5 ohms).
Distinguish true the value of a physical quantity that ideally reflects the property of the object, and valid found experimentally close enough to the true value to be used instead, and measured the value measured by the reading device of the measuring instrument.
The totality of quantities, interconnected by dependencies, form a system of physical quantities, in which there are basic and derived quantities.
The main physical quantity is a quantity included in the system and conventionally accepted as independent of other quantities of this system.
Derivative a physical quantity is a quantity included in the system and determined through the basic quantities of this system.
An important characteristic of a physical quantity is its dimension (dim). Dimension- this is an expression in the form of a power monomial, composed of the products of symbols of basic physical quantities and reflecting the relationship of a given physical quantity with physical quantities taken in this system of quantities as basic ones with a proportionality coefficient equal to one.
Physical unit - it is a specific physical quantity, defined and accepted by convention, with which other quantities of the same kind are compared.
In accordance with the established procedure, the units of quantities of the International System of Units (SI), adopted by the General Conference on Weights and Measures, recommended by the International Organization of Legal Metrology, are allowed to be used.
Distinguish between basic, derivatives, multiples, fractional, coherent, systemic and non-systemic units.
Basic unit of the system of units- the unit of the basic physical quantity chosen when constructing the system of units.
Meter is the length of the path traversed by light in a vacuum for a time interval of 1/299792458 fractions of a second.
Kilogram- unit of mass equal to the mass of the international prototype of the kilogram.
Second- time equal to 9192631770 periods of radiation, corresponding to the transition between two hyperfine levels of the ground state of the atom of Cesium-133.
Ampere- the force of a constant current, which, when passing through two parallel rectilinear conductors of infinite length and negligible circular cross-sectional area, located in a vacuum at a distance of 1 m from one another, would cause an interaction force equal to 2 ∙ 10 in each section of a conductor 1 m long -7 N.
Kelvin- a unit of thermodynamic temperature, equal to 1 / 273.16 of the thermodynamic temperature of the triple point of water.
Moth- the amount of matter in a system containing as many structural elements as there are atoms in carbon-12 weighing 0.012 kg.
Candela- luminous intensity in a given direction of a source emitting monochromatic radiation with a frequency of 540 ∙ 10 12 Hz, the luminous intensity of which in this direction is 1/683 W / sr.
There are also two additional units provided.
Radian- the angle between two radii of a circle, the length of the arc between which is equal to the radius.
Steradian- a solid angle with a vertex in the center of the sphere, cutting out on the surface of the sphere an area equal to the area of a square with a side equal to the radius of the sphere.
Derived unit of system of units- a unit of the derived physical quantity of the system of units, formed in accordance with the equation connecting it with the basic units or with the basic and already defined derivatives. For example, a unit of power, expressed in SI units, 1W = m 2 ∙ kg ∙ s -3.
Along with SI units, the Law "On Ensuring the Uniformity of Measurements" allows the use of off-system units, i.e. units not included in any of the existing systems. It is customary to distinguish several types non-systemic units:
Units allowed along with SI units (minute, hour, day, liter, etc.);
Units used in special fields of science and technology
(light year, parsec, diopter, electron volt, etc.);
Obsolete units (millimeter of mercury,
horse power, etc.)
Multiple and sub-multiple units of measurement, which sometimes have their own names, for example, the unit of mass is a ton (t), are also included in the number of non-systemic ones. In general, decimal, multiples and sub-multiples are formed using multipliers and prefixes.
Measuring instruments
Under measuring instrument(SI) means a device intended for measurements and having standardized metrological characteristics.
According to their functional purpose, measuring instruments are subdivided into: measures, measuring instruments, measuring transducers, measuring installations, measuring systems.
Measure- a measuring instrument designed to reproduce and store a physical quantity of one or more dimensions with the required accuracy. A measure can be represented as a body or a device.
Measuring device(IP) - a measuring instrument designed to extract measurement information and transform
it into a form accessible for direct perception by the operator. Measuring instruments, as a rule, include
measure. According to the principle of operation, IPs are distinguished between analog and digital. According to the method of presenting the measuring information, the measuring devices are either indicating or registering.
Depending on the method of converting the signal of measuring information, direct conversion devices (direct action) and equilibration conversion (comparison) devices are distinguished. In direct conversion devices, the measurement information signal is converted the required number of times in one direction without the use of feedback. In equilibrium conversion devices, along with a direct conversion circuit, there is an inverse conversion circuit and the measured value is compared with a known value, which is homogeneous with the measured value.
Depending on the degree of averaging of the measured value, devices are distinguished that give readings of instantaneous values of the measured value, and integrating devices, the readings of which are determined by the integral over time of the measured value.
Measuring transducer- a measuring instrument designed to convert a measured value into another value or a measuring signal convenient for processing, storage, further transformations, indication or transmission.
Depending on the place in the measuring circuit, primary and intermediate converters are distinguished. Primary transducers are those to which the measured value is fed. If the primary converters are placed directly at the research object, remote from the processing site, then they are sometimes called sensors.
Depending on the type of input signal, converters are divided into analog, analog-to-digital and digital-to-analog. Large-scale measuring transducers are widely used, designed to change the size of a quantity by a given number of times.
Measuring setup is a set of functionally combined measuring instruments (measures, measuring instruments, measuring transducers) and auxiliary devices (interface, power supply, etc.) intended for one or more physical quantities and located in one place.
Measuring system- a set of functionally combined measures, measuring transducers, computers and other technical means located at different points of the controlled object, in order to measure one or more physical quantities.
Types and methods of measurements
In metrology, measurement is defined as a set of operations performed with the help of a technical + - means storing a unit of a physical quantity, allowing one to compare the measured quantity with its unit and obtain the value of this quantity.
The classification of types of measurements according to the main classification features is presented in Table 2.1.
Table 2.1 - Types of measurements
Direct measurement- measurement, in which the initial value of the quantity is found directly from the experimental data as a result of the measurement. For example, measuring the current strength with an ammeter.
Indirect measurement - a measurement in which the desired value of a quantity is found on the basis of a known relationship between this quantity and quantities that are directly measured. For example, measuring the resistance of a resistor with an ammeter and voltmeter using a relationship that relates resistance to voltage and current.
Joint measurements are measurements of two or more non-identical quantities to find the relationship between them. A classic example of joint measurements is finding the dependence of the resistance of a resistor on temperature;
Aggregate measurements are measurements of several quantities of the same name, in which the sought-for values of quantities are found by solving a system of equations obtained from direct measurements and various combinations of these quantities.
For example, finding the resistances of two resistors by measuring the resistances of the series and parallel connections of these resistors.
Absolute measurements - measurements based on direct measurements of one or more quantities and the use of values of physical constants, for example, measurement of current in amperes.
Relative measurements - measurements of the ratio of the value of a physical quantity to the quantity of the same name or changes in the value of the quantity in relation to the quantity of the same name, taken as the initial one.
TO static measurements include a measurement in which the SI operates in a static mode, i.e. when its output signal (for example, pointer deflection) remains unchanged during the measurement time.
TO dynamic measurements include measurements made by the SI in a dynamic mode, i.e. when its readings depend on dynamic properties. The dynamic properties of the SI are manifested in the fact that the level of variable impact on it at any moment in time determines the output signal of the SI at the next moment in time.
Measurements with the highest possible accuracy achieved at the current level of development of science and technology. Such measurements are carried out when creating standards and measuring physical constants. Estimation of errors and analysis of the sources of their occurrence are characteristic of such measurements.
Technical measurements are measurements carried out under specified conditions according to a specific methodology and carried out in all sectors of the national economy, with the exception of scientific research.
The set of techniques for using the principle and measuring instruments is called measuring method(Figure 2.1).
Without exception, all measurement methods are based on comparing the measured value with the value reproduced by the measure (single-valued or multi-valued).
The method of direct assessment is characterized by the fact that the values of the measured quantity are read directly from the reading device of the direct-acting measuring device. The scale of the device is pre-calibrated using a multivalued measure in the units of the measured value.
Comparison methods with a measure involve comparing a measurable quantity and a quantity reproduced by a measure. The following comparison methods are most common: differential, null, substitution, coincidence.
Figure 2.1 - Classification of measurement methods
With the zero measurement method, the difference between the measured value and the known value is reduced to zero during the measurement, which is fixed by a highly sensitive zero indicator.
In the differential method, on the scale of the measuring device, the difference between the measured value and the value reproduced by the measure is counted. The unknown value is determined from the known value and the measured difference.
The substitution method provides for alternately connecting the measured and known values to the indicator input, i.e. measurements are carried out in two steps. The smallest measurement error is obtained when, as a result of the selection of a known value, the indicator gives the same reading as with an unknown value.
The coincidence method is based on measuring the difference between the measured value and the value reproduced by the measure. When measuring, use the coincidence of the marks of the scales or periodic signals. The method is used, for example, when measuring frequency and time from reference signals.
Measurements are performed with single or multiple observations. Observation is understood here as an experimental operation performed in the process of measurement, as a result of which one value of a quantity is obtained, which is always random in nature. In measurements with multiple observations, statistical processing of the observation results is required to obtain the measurement result.
Measurement methods are determined by the type of measured values, their dimensions, the required accuracy of the result, the required speed of the measurement process and other data.
There are many measurement methods, and with the development of science and technology, the 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.
Straight measurements are called in which the desired value of the quantity is found directly from experimental data (for example, the measurement of mass on a dial or equal-arm balance, temperature - with a thermometer, length - using linear measures).
Indirect measurements are called in which the desired value of the quantity is found on the basis of the known relationship between this quantity and the quantities subjected to direct measurements (for example, the density of a homogeneous body by its mass and geometric dimensions; determination of electrical resistance by the results of measuring the voltage drop and current strength).
Aggregate measurements 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 by direct measurements of various combinations of these quantities (for example, measurements in which the masses of individual weights of a set are set according to the known mass of one of them and according to the results of straight lines comparisons of masses of different combinations of weights).
Earlier it was said 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 by the following methods:
1) Direct assessment method - the value of the quantity is determined directly by the reading device of the measuring device (pressure measurement - 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 (mass measurement with a beam balance with weights balancing).
3) Differential method - the method of comparison with a measure, in which the difference between the measured value and the known value reproduced by the measure acts on the measuring device (measurements performed when checking the measures of length by comparison with a reference measure on a comparator).
4) Zero method - the method of comparison with a measure, when the resulting effect of the influence of the quantities on the comparator is brought to zero (measurement of the electrical resistance by the bridge with its complete equilibration).
5) Coincidence method - a method of comparison with a measure, in which the difference between the measured value and the value reproduced by the measure is measured using the coincidence of the marks of the scales or periodic signals (measuring the length using a vernier caliper, when the coincidence of marks on the scales of the caliper and the vernier 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 alternate placing of the measured mass and weights on the same pan).
End of work -
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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 to achieve the required accuracy. In practical life, a person is
The concept of measuring instruments
A measuring instrument (SI) is a technical means (or a set of technical means) intended for measurement, having a normalized metrological character
Metrological characteristics of measuring instruments
Metrological characteristics of measuring instruments are characteristics of properties that affect the results and measurement errors. Appointment information meter
Factors Affecting Measurement Results
In metrological practice, when carrying out measurements, it is necessary to take into account a number of factors that affect the measurement results. It is an object and subject of measurement, a method of measurement, cf.
Formation of the measurement result. Measurement errors
The measurement procedure consists of the following main stages: 1) adoption of the object measurement model; 2) the choice of the measurement method; 3) selection of measuring instruments;
Presentation of measurement results
There is a rule: the measurement results are rounded to the nearest "error". In practical metrology, rules have been developed for rounding results and measurement errors. Wasps
Reasons for measurement errors
There are a number of error terms that dominate the total measurement error. These include: 1) Measurement-dependent errors. But
Multiple measurement processing
We assume that the measurements are equally accurate, i.e. are performed by one experimenter, under the same conditions, with one device. The technique boils down to the following: n observations are carried out (one
Student's distribution (t-test)
n / α 0.40 0.25 0.10 0.05 0.025 0.01 0.005 0.0005
Measurement Techniques
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The concept of metrological support
Metrological support (MO) is understood as the establishment and application of scientific and organizational foundations, technical means, rules and norms, necessary
A systematic approach to the development of metrological support
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Basics of metrological support
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RF legislation on ensuring the uniformity of measurements
The regulatory framework for ensuring the uniformity of measurements is shown in Figure 2.
National system for ensuring the uniformity of measurements
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The main types of metrological activities to ensure the uniformity of measurements
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Conformity assessment of measuring instruments
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Type approval of measuring instruments
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Certification of measurement procedures
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Verification and calibration of measuring instruments
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The structure and functions of the metrological service of an enterprise, organization, institutions that are legal entities
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Interchangeability concept
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Qualities, main deviations, plantings
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Designation of fields of tolerances, maximum deviations and landings in the drawings
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Unspecified limit deviations of dimensions
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Recommendations for the use of clearance landings
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Recommendations for the use of transitional landings
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Recommendations for the use of interference fits
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The concept of surface roughness
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Roughness parameters
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General terms and definitions
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Deviations and tolerances of the form
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Deviations and tolerances of location
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Total deviations and tolerances of the shape and location of surfaces
The total deviation of the shape and location is called the deviation, which is the result of the joint manifestation of the deviation of the shape and the deviation of the location of the element in question (turn
Dependent and independent tolerance of shape and location
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Numerical values of the tolerances of the shape and location of surfaces
According to GOST 24643 - 81, 16 degrees of accuracy are established for each type of tolerance of the shape and location of surfaces. The numerical values of the tolerances from one degree to another change
Designation in the drawings of the tolerances of the shape and location
The type of tolerance of the form and location according to GOST 2.308 - 79 should be indicated on the drawing by the signs (graphic symbols) given in Table 4. I enter the sign and the numerical value of the tolerance
Unspecified form and position tolerances
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Base definition rules
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Rules for determining the defining size tolerance
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Surface waviness
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Rolling bearing tolerances
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 rolling bearing landings
The fit of the 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 conventions
The designation system for ball and roller bearings is established by GOST 3189 - 89. Bearing designation gives a complete picture of its overall dimensions, design, manufacturing accuracy
Angular tolerances
Tolerances of angular dimensions are assigned in accordance with GOST 8908 - 81. Angle tolerances AT (from the English Angle tolerance) should be assigned depending on the nominal length L1 of the shorter side
System of tolerances and fits for tapered connections
The conical connection has advantages in comparison with the cylindrical one: it is possible to adjust the size of the gap or tightness by the relative displacement of the parts along the axis; with a fixed connection
Basic Parameters of Metric Fastening Threads
Cylindrical thread parameters (Figure 36, a): average d2 (D2); outer d (D) and inner d1 (D1) diameters on
General principles of the interchangeability of cylindrical threads
The systems of tolerances and fits, ensuring 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 a gap
Tolerances of metric threads with coarse and small pitches for diameters 1 - 600 mm are regulated by GOST 16093 - 81. This standard sets the maximum deviations for thread diameters in
Interference and transitional thread tolerances
The fits under consideration are mainly used to connect studs with body parts, if screw or bolt-nut connections cannot be used. These landings are used in fasteners
Standard threads for general and special purpose
Table 9 shows the names of standard general-purpose threads, the most widespread in mechanical engineering and instrument making, and examples of their designation in the drawings are given. 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
Smoothness of transmission
This transmission characteristic is determined by the parameters, the errors of which are repeatedly (cyclically) manifested per revolution of the gear wheel and also constitute part of the kinematic linear
Contact of teeth in gear
To increase the wear resistance and durability of gears, it is necessary that the completeness of contact of the mating flank surfaces of the teeth of the wheels is greatest. With incomplete and ineffective
Side clearance
To eliminate possible jamming when the gear is heated, to ensure the conditions for the flow of lubricant and to limit the backlash when reversing the counting and dividing real gears
Accuracy designation of wheels and gears
The manufacturing accuracy of gear wheels and gears is set by the degree of accuracy, and the requirements for the lateral clearance - by the type of mating according to the lateral clearance norms. Examples of designation symbols:
Selection of the degree of accuracy and controllable parameters of gears
The degree of accuracy of wheels and gears is set 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 system of tolerances for gear bevel (GOST 1758 - 81) and hypoid gears (GOST 9368 - 81) are similar to the principles of constructing a system for cylindrical gears
Tolerances of helical worm gears
For cylindrical worm gears, GOST 3675 - 81 establishes 12 degrees of accuracy: 1, 2,. ... ., 12 (in decreasing order of precision). For worms, worm wheels and worm gears each
Tolerances and fits of straight flank connections
According to GOST 1139 - 80, tolerances are established for joints centered on the inner d and outer D diameters, as well as on 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 joints with an involute profile (Figure 58), the nominal dimensions of the rollers (Figure 59) and the length of the common normal for individual measurements of the spline shafts and bushings must
Accuracy control of spline connections
Splined joints are controlled with complex bore gauges (Figure 61) and element-by-element non-bore gauges.
Dimensional chain design method for complete interchangeability
To ensure complete interchangeability, dimensional chains are calculated by the maximum-minimum method, in which the tolerance of the closing size is determined by the arithmetic addition of the tolerances.
Probabilistic-theoretical 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 sizes is possible.
Selective assembly group interchangeability method
The essence of the method of group interchangeability is the manufacture of parts with relatively wide technologically feasible tolerances, selected from the relevant standards, grade
Adjustment and fit method
Regulation method. The control method is understood as the calculation of dimensional chains, in which the required accuracy of the initial (closing) link is achieved by deliberate changes
Calculation of planar and spatial dimensional chains
Plane and spatial dimensional chains are calculated using the same methods as linear ones. It is only necessary to bring them to the form of linear dimensional chains. This is achieved by designing
Historical foundations of the development of standardization
Man has been standardizing since ancient times. For example, writing is at least 6 thousand years old and arose according to the latest finds in Sumer or Egypt.
Legal framework for standardization
The legal basis for standardization in the Russian Federation is established by the Federal Law "On Technical Regulation" dated December 27, 2002. It is mandatory for all government agencies.
Principles of technical regulation
Currently, the following principles have been established: 1) the application of uniform rules for establishing requirements for products or for related design processes (including research), production
Objectives of technical regulations
The Law on Technical Regulation establishes a new document - technical regulation. Technical regulations - a document adopted by an international treaty of Russia
Types of technical regulations
In the Russian Federation, two types of technical regulations are applied: - general technical regulations; - special technical regulations. General technical regulations of the ra
Standardization concept
The content of the terms of standardization has come a long evolutionary path. The refinement of this term took place in parallel with the development of standardization itself and reflected the achieved level of its development on the p
Objectives of standardization
Standardization is carried out in order to: 1) Increase the level of safety: - 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 similar 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: 1) voluntary application of documents in the field of standardization
International standardization
International Standardization (IS) is an activity involving two or more sovereign states. MS plays a prominent role in deepening world economic cooperation, in m
Complex 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 effect, which replaced the "State Standardization System" complex. it
Structure of standardization bodies and services
The national standardization body is the Federal Agency for Technical Regulation and Metrology (Rostekhregulirovanie), which replaced Gosstandat. It obeys directly
Normative documents on standardization
Normative 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. Standards notation
The categories of standardization are distinguished by the level at which standards are adopted and approved. Four categories are established: 1) international; 2) intergo
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 exercised 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. State control bodies of the region
Organization Standards (STO)
The organization and procedure for the development of the STO is contained in GOST R 1.4 - 2004. Organization - a group of workers and the necessary funds with the distribution of responsibility, powers and relations
Preferred Numbers Required (IF)
The introduction of the inverter is caused by the following considerations. The use of a frequency converter allows the best possible coordination of the parameters and dimensions of a single product with all associated
Series based on arithmetic progression
Most often, the series of IF 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 "gold &
Series based on geometric progression
Long-term practice of standardization has shown that the most convenient are the series built on the basis of a geometric progression, since in this case the same relative difference between
Preferred Number Series Properties
The series of the inverter have the properties of a geometric progression. The series of IF 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.
Constrained, sampled, compound and approximate series
Limited ranks. If necessary, limiting the main and additional series in their designations indicate the limiting terms, which are always included in the limited series. Example. R10 (
Concept and types of unification
During unification, the minimum permissible, 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 unified constituent elements; details, modules, nodes. The main quantitative indicators of the level of product unification
Determination of the indicator of the level of unification
The assessment of the level of unification is based on the correction of the following formula:
History of certification development
"Certificate" translated from Latin means "done right." Although the term "certification" has become familiar in everyday life and commercial practice
Terms and definitions in the field of attestation of conformity
Conformity assessment is a direct or indirect determination of compliance with the requirements for an object. A typical example of an assessment activity is
Objectives, principles and objects of conformity confirmation
Confirmation of conformity is carried out in order to: - certify 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 a combination of the same
Product certification schemes for compliance with the requirements of technical regulations
A certification scheme is a defined set of actions, officially accepted as proof of product compliance with specified requirements.
Schemes for declaring conformity for compliance with the requirements of technical regulations
Table 17 - Schemes for declaring conformity for compliance with the requirements of technical regulations
Service certification schemes
Table 18 - Schemes for certification of services Scheme No.
Conformity assessment 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 adopted. First of all, this form of confirmation of conformity d
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 a contract
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 goes through the following main stages: 1) Submission of an application for certification; 2) Consideration and decision making on the application; 3) Selection, id
Certification bodies
Certification body - a legal entity or individual entrepreneur accredited in accordance with the established procedure to carry out certification work.
Testing laboratories
Testing laboratory - 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 the accreditation body of the competence of physical
Service certification
Certification is carried out by accredited service certification bodies within their scope of accreditation. The certification checks the characteristics of the services and uses
Quality systems certification
In recent years, the number of companies in the world that have certified their quality systems in accordance with ISO 9000 series standards has been rapidly growing. Currently, these standards are applied
Chapter 1. MEASUREMENT OF PHYSICAL QUANTITIES
A wide variety of phenomena that one has to encounter in practice 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 carrying out measurements, regardless of the size, 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, with the help of an experiment, we determine quantitatively a physical quantity in the form of a certain number of units adopted for it, i.e. we find the value of the size of the physical quantity. The measurement is carried out using a scale - a predetermined ordered set of a sequence of physical quantities, adopted by agreement.
The choice of units of measurement of quantities is of great importance for the comparison of results obtained using different methods, means and under different conditions of measurement. Therefore, it is customary to establish their size by legislative means. The International System of Units, approved by the XI General Conference on Weights and Measures, has 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 is an ordered collection of quantity values.
Practical activity has led to the formation of various types of scales for measuring physical quantities, the main of which are four, discussed below.
1. Order scale (ranks) is a ranked series – an ascending or descending sequence of values that characterize the property under study. It allows you to establish the ratio of the order in ascending or decreasing quantities, but there is no way to judge how many times (or how much) more or less one quantity compared to another. In order scales, in a number of cases, there may be zero (zero mark); its size cannot be established; in these scales, mathematical operations (multiplication, summation) cannot be performed on values.
An example of a scale of order 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 conditional hardness numbers. Examples of such scales are also the Beaufort scale for measuring the strength (speed) of the wind and the Richter earthquake scale (seismic scale).
2. Scale of intervals (differences) differs from the scale of order in that not only order relations are introduced for the measured quantities, but also the summation of intervals (differences) between various quantitative manifestations of properties. Difference scales can have conventional zero-reference points and units of measurement established by agreement. On the scale of intervals, you can determine how much one value is greater or less than another, but you cannot say how many times. The interval scales measure time, distance (if the beginning of the path is not known), temperature in Celsius, etc.
Interval scales are more perfect than order scales. In these scales, additive mathematical operations (addition and subtraction) can be performed on quantities, but multiplicative operations (multiplication and division) are not allowed.
3.Relationship scale describes the properties of quantities for which the ordering, summation of intervals and proportionality relations are applicable. In these scales, there is a natural zero and, by agreement, the unit of measurement is established. The scale of ratios serves to represent the results of measurements 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, velocity, thermodynamic temperature.
The ratio scale is the most perfect and most common of all measurement scales. This is the only scale by 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 plotted on the scale.
4. Absolute scale possesses all the signs of the scale of relations, but in addition there is a natural unambiguous definition of the unit of measurement in it. Such scales are used to measure relative values (gain, attenuation, efficiency, reflection, absorption, amplitude modulation, etc.). A number of such scales have boundaries between zero and one.
Scales of intervals and ratios are united by the term "metric scales". The order scale is referred to as conditional scales, 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 units of measurement themselves, and, if necessary, the methods and conditions for their unambiguous reproduction.
SI base units
Basic unit quantity is called the unit of the basic physical quantity, i.e. value, which is conventionally accepted as independent of other values of the system. When choosing the basic SI units, we proceeded from the fact that: 1) the system should cover all areas of science and technology; 2) create a basis for the formation of derived units for various physical quantities; 3) to accept the sizes of the basic units, which are already widespread, which are convenient for practice; 4) choose units of such quantities, the reproduction of which with the help of standards is possible with the greatest accuracy.
The basic SI units with the indication of abbreviated designations in Russian and Latin letters are given in table. 1.1.
Table 1.1.
SI base units
The definitions of the base units, consistent with the decisions of the General Conference on Weights and Measures, are as follows.
Meter is equal to the length of the path traveled by light in a vacuum in 1/299 792 458 fractions of a second.
Kilogram is equal to the mass of the international prototype kilogram.
Second is 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 rectilinear conductors of infinite length and negligible circular cross-sectional area located at a distance of 1 m from one another in vacuum, causes an interaction force equal to 2 × 10 -7 in each section of a conductor 1 m long N.
Kelvin is equal to 1 / 273.16 of the thermodynamic temperature of the triple point of water.
Moth is equal to the amount of matter in a system containing as many structural elements as there are atoms in carbon-12 weighing 0.012 kg.
Candela is 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 intensity of which in this direction is 1/683 W / sr.
The first three SI units (meter, kilogram and second) make it possible to form derived units for measuring mechanical and acoustic quantities. When adding a unit of temperature (kelvin) to them, you can 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 measurements and measurements of ionizing radiation, and the mole is used to form units in the field of physicochemical measurements.
SI derived units
Derived units of the International System of Units are formed from the basic ones using the relationship equations between quantities, in which the numerical coefficients are equal to one. For example, to establish a unit of linear velocity v, one should use the equation of uniform rectilinear motion
where l is the length of the covered path (in meters); t - time (in seconds).
Consequently, the SI unit of speed - a meter per second - is the speed of a straight and uniformly moving point, at which it moves a distance of 1 m in a time of 1 s.
Derived units may be named after famous scientists. Thus, the unit of pressure 1 N / m 2 was given a special name - pascal (Pa) after the French mathematician and physicist Blaise Pascal. Derived units with special names are given in table. 1.2.
Table 1.2.
SI derived units with special names
| The quantity | Unit | |||
| Name | Dimension | Name | Designation | Expression in SI units |
| Frequency | T -1 | hertz | Hz | s -1 |
| Strength, weight | LMT -2 | newton | H | 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 |
| Electricity quantity | TI | pendant | CL | s A |
| Electric voltage, potential | L 2 MT -3 I -1 | volt | V | m 2 kg s -3 A -1 |
| Electric 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 |
| Flux of magnetic induction | L 2 MT -2 I -1 | weber | Wb | m 2 kg s -2 A -1 |
| Magnetic induction | MT -2 I -1 | tesla | T | kg s -2 A -1 |
| Inductance | L 2 MT -2 I -2 | Henry | Mr. | m 2 kg s -2 A -2 |
| Radionuclide activity | T -1 | becquerel | Bq | s -1 |
| Absorbed radiation dose | L 2 T -2 | gray | Gr | m 2 s -2 |
| Equivalent dose of radiation | L 2 T -2 | sievert | Sv | m 2 s -2 |
To measure plane and solid angles in SI, radians and steradians are intended, respectively.
Radian(rad) - the unit of a plane angle is the angle between two radii of a circle, the arc between which is equal in length to the radius. In degree terms, a radian is 57 ° 17 "48".
Steradian(cf) - the unit of the solid angle is the solid angle, the vertex of which is located in 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.
By themselves, the radian and steradian are used mainly for theoretical calculations; in practice, angles are measured in angular degrees (minutes, seconds). It is in these units that most goniometric measuring instruments are calibrated.
Multiples and submultiples
Distinguish between multiples and submultiple units. Multiple unit Is a unit of physical quantity that is an integer number of times greater than a system or non-system unit. For example, the unit of length, kilometer, is equal to 10 3 m, i.e. multiple of a meter. Fractional unit- a unit of physical quantity, the value of which is an integer number of times less than a system or non-system unit. For example, the unit of length, millimeter, is equal to 10 -3 m, i.e. is fractional.
For the convenience of using SI units of physical quantities, prefixes are adopted for the formation of names of decimal multiples of units and fractional units, table. 1.3.
Table 1.3.
Multipliers and prefixes for the formation of decimal multiples and sub-multiples and their names
| Factor | Prefix | Prefix designation | |
| russian | international | ||
| 10 24 | iotta | Y | AND |
| 10 21 | zetta | Z | Z |
| 10 18 | exa | NS | E |
| 10 15 | peta | NS | 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 | santi | with | c |
| 10 -3 | Milli | m | m |
| 10 -6 | micro | mk | m |
| 10 -9 | nano | n | n |
| 10 -12 | picot | NS | p |
| 10 -15 | femto | f | f |
| 10 -18 | atto | a | a |
| 10 -21 | zepto | z | s |
| 10 -24 | iokto | y | and |
In accordance with international rules, multiples and sub-multiples of area and volume units should be formed by attaching 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 observation behind the measurement object in order to timely and correctly count. The object of measurement can be a technical device (for example, a chamber furnace), technological processes, the environment, the consumption of substances and materials, indicators of human vital activity, etc. The physical quantity that is selected for measurements is called measured value.
In addition to the measured value, the object of measurement and, accordingly, the measurement result, is influenced by other physical quantities that are not measured by this measuring instrument. They are called influencing physical quantities... Influence quantities are subdivided into the following groups:
climatic (ambient temperature, air humidity, atmospheric pressure);
electric and magnetic (fluctuations in electric current, voltage in an electric circuit, frequency of alternating current, magnetic field);
external loads (vibrations, shock loads, ionizing radiation).
The effect of these quantities on the measurement result, as well as the imperfection of the manufacturing of the measuring instrument, subjective errors of the human operator and a number of other factors are the reasons for the inevitable appearance of the measurement error.
The process of solving any measuring problem, as a rule, 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 shown in Fig. 1.2, the measuring object and the measuring instrument are brought into interaction. In this case, the measured value, 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 its called the signal of the measuring 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 signals of the measurement information can be further processed in order to present the measurement result in the most convenient way. Such processing may include statistical processing (with multiple measurements of a quantity), additional calculations (with indirect measurements), rounding, etc. The issues related to the processing of measurement results are considered below (clause 2.4).
Measurement classification
The measurements are very diverse, and they can be classified according to various criteria, the most important of which are reflected in Fig. 1.3.
Rice. 1.3. Measurement classification
First, measurements are determined by the physical nature of phenomena (processes), in accordance with which certain sets of physical quantities, related in nature or application in certain fields of science and technology, have developed - 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 the physical quantity is found directly from the experimental data. In this case, the measurement object is brought into interaction with the measuring instrument and, according to its indications, the value of the measured quantity is determined. Examples of direct measurements: measurement of length with a ruler, time with a clock, mass with a balance, 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 value is determined on the basis of the results of direct measurements, functionally related to it. The value of Q is found by calculating by the formula
Q = f (X 1, X 2, ... X m), (1.5)
where X 1, X 2, ... X m - quantities, the size of which is determined from direct measurements
Examples of indirect measurements: determination of the density of a homogeneous body by its mass and volume, electrical resistance of a conductor by voltage drop and current strength, power by current strength and voltage.
Indirect measurements are widespread in cases where the desired value is impossible or too difficult to measure directly, or when a direct measurement gives a less accurate result. Their role is especially great when measuring quantities that are inaccessible to direct experimental comparison, for example, the dimensions of the astronomical or intra-atomic order.
For metrological purposes, measurements are subdivided into technical and metrological ones. Technical measurements are carried out by 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).
According to the number of measurements performed to obtain a result, one can distinguish between single and multiple measurements. One-time refers to a measurement taken once. For example, measuring time by hours. If you need more confidence in the result obtained, then carry out multiple measurements of the same quantity, the result of which is usually taken as the arithmetic mean of individual measurements. Usually, for multiple measurements, the number of measurements is n ³3.
According to the dependence of the measured value on time, measurements are subdivided into static and dynamic. At static In measurements, a physical quantity is taken to be unchanged over 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 ground from a descending aircraft).
Depending on the accuracy of the measuring instruments used and the measurement conditions, they are divided into equal and unequal. Equal refers to measurements of a quantity made with the same precision measuring instruments under the same conditions with the same thoroughness. If the measurements were performed with measuring instruments differing in accuracy and (or) in different conditions, then they are called unequal.
In addition to those shown in Fig. 1.3. For specific cases, there are others that can be used if necessary for classification of measurements. For example, measurements can be subdivided depending on the place of implementation into laboratory and industrial; depending on the form of presentation of the results - in absolute and relative.
The above measurements can be performed using various methods, i.e. ways of solving the measuring problem.
Measurement methods
Method of measurement is a technique or a set of techniques for comparing a measured value with its unit in accordance with the implemented measurement principle. Under measuring principle understand the physical effects (phenomena) underlying measurements. For example, temperature measurement using the thermoelectric effect. The measurement method is usually determined by the design of the measuring instrument.
There are many measurement methods, and with the development of science and technology, their number increases. Each physical quantity can be measured, as a rule, by several methods. For their systematization, it is necessary to highlight 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 refers to 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 details on the types of measures, see p. 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 by the reading device of the measuring device, for example, measuring voltage with a voltmeter, weighing a load on a spring balance (Fig. 1.5). In this case, the mass of the load X is determined on the basis of a measuring transformation according to the value of the deformation d of the spring.
Rice. 1.5. Direct measurement setup
Direct measurement measurements are generally straightforward and do not require high operator qualifications, since there is no need to create special measurement setups and 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 the instrument scales.
The most numerous group of instruments used to measure by the method of direct assessment are indicating instruments (including pointer instruments). These include pressure gauges, dynamometers, barometers, ammeters, voltmeters, wattmeters, flow meters, liquid thermometers and many others. Measurements with an integrating meter or recorder are also referred to as direct evaluation.
When making 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 the methods of opposition, substitution, and coincidence.
Zero measurement method - this is a comparison method with a measure , in which the resulting effect of the measured value 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 value and the measure is marked using a zero pointer (zero indicator). Examples of the zero measurement method: weighing on an equal-arm scale; measurement of resistance, inductance and capacitance using a balanced bridge; temperature measurement in an optical pyrometer using an exemplary incandescent lamp (respectively, the scales, galvanometer and human eye are zero pointers).
Differential measurement method(also called difference) is a measure-to-measure method in which a measurand is compared to a measure and the difference between the two is measured. The measure should have a value that slightly differs 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 gage block (in the field of linear and angular measurements, this method is called relative); measurement of resistance, inductance and capacitance using an unbalanced bridge; weighing on unequal scales. The use of a null pointer is not required in this method.
Contrast method consists in the fact that the measured value and the value reproduced by the measure simultaneously affect the comparison device, with the help of which the relationship between these values is established. An example of the zero method of opposition is weighing the load X on an equal-arm balance (Fig. 1.6, a), when the measured mass of the load X is equal to the mass of the weights that balance 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 the differential method of opposition, 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, counted on the scale.
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Rice. 1.6. Measurement scheme by the method of 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 assessment method, by reducing the impact on the measurement result of the error of the measuring instrument and the influencing quantities.
The varieties of the method of comparison with the measure include substitution method widely used in the practice of precise metrological research. The essence of the method is that the measured value is replaced by a measure with a known value of the quantity, i.e. the measured value and the measure sequentially act on the measuring device. In the zero method, a complete substitution of the measured value with a measure is carried out, 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 in order to obtain the value of the measured quantity, the value by which the reading of the instrument has changed must be added to the value of the measure.
Due to the fact that the measured value and the measure are included one after another in the same part of the measuring circuit of the device, the measurement accuracy is significantly increased in comparison with measurements carried out using other varieties of the comparison method, where the asymmetry of the circuits in which the compared values are included leads to the occurrence of systematic errors. The substitution method is often used in electrical measurements with AC bridges.
Coincidence method is a variation of the comparison method with a measure in which the difference between the measured value and the value reproduced by the measure is measured using the coincidence of scale marks or periodic signals. The vernier is built on the principle of the coincidence method, which is part of a number of measuring instruments (for example, a vernier caliper).
In addition to the considered measurement methods, contact and non-contact are also distinguished, 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 - measuring the shaft diameter with a caliper, measuring body temperature with a thermometer. Examples of the 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 measurement of a quantity depends on many factors: the choice of the method and measuring instrument, the conditions for its implementation (for example, temperature, pressure, ambient humidity), the method of processing the measurement results, the qualifications of the operator performing the measurements, etc. These factors lead to a difference in the value the result of measuring the quantity and its true value, i.e. to the 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 designate a value that ideally characterizes the corresponding physical quantity in qualitative and quantitative terms. It can be obtained only as a result of an endless measurement process with an endless improvement of methods and measuring instruments.
Measurement result X meas is called the value obtained when measuring it using specific methods and measuring instruments.
Measurement error(or measurement error) D is the deviation of the measurement result from the true value of the measured quantity, i.e.
D = X meas - X and.
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 is replaced by the true value.
Actual value X d values – it is a value obtained experimentally and is so close to the true value that it can be used instead of it in the given measurement problem. The actual value is found by more accurate methods and measuring instruments. The higher the accuracy of the instrument and method of measurement, with the help of which X d is determined, the more confidently it is considered as close to true. Therefore, in practice, the measurement error D (here we mean the absolute error) is found by the formula
D = X meas - X d (1.6)
It is impossible to completely eliminate errors, but you can reduce them using the methods discussed below.
Measurement accuracy- this is one of the most important characteristics (indicators) of the measurement quality, reflecting the proximity to zero of the measurement result error. In addition, the indicators of the quality of measurements are the repeatability, reproducibility, correctness and reliability of the measurement results, which will be discussed below.
The 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 of this interval, 0.27% of the data from their total number may be located (approximately three out of a thousand measurements).
Rice. 1.12. Three sigma rule illustration
It follows from this that if any value of the quantity goes beyond ± 3s, then with a high probability it can be considered erroneous.
Based on this, it was formulated the three sigma rule: if with multiple measurements (n> 25 ... 30) of the same constant size the dubious result X doubt of an individual measurement (maximum or minimum) differs from the mean value by more than 3s, then with a probability of 99.7% it is erroneous, i.e. .e.
if> 3s, (1.12)
then X is doubtful; it is discarded and not taken into account in further processing of the measurement results.
The normal distribution law works when the number of measurement results is n = ¥. In reality, a finite number of measurements are obtained, which obey the Student's distribution law. For n> 25, the Student's 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 measurement instrument. Every day, a huge number of measurements are carried out with the help of a whole "army" of various measuring instruments. There are many of them, they can be easy to use, such as a ruler, or represent the most complex devices that require highly qualified service, 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 a measuring instrument “skillfully” store (and reproduce) a unit of a physical quantity in such a way that the requirement for the size of the stored unit to remain unchanged over time is fulfilled. It is this "skillful storage" that distinguishes measuring instruments from other technical means. Thus, measuring instrument is a technical means (or their complex) intended for measurements, having normalized metrological characteristics, reproducing and (or) storing a unit of physical quantity, the size of which is assumed unchanged (within
