9. Measuring instruments and their characteristics In the scientific literature, technical measuring instruments are divided into three large groups. These are: measures, gauges and universal measuring instruments, which include measuring instruments, control and measuring instruments (CIP), and

16. Errors of measuring instruments Errors of measuring instruments are classified according to the following criteria: 1) according to the method of expression; 2) according to the nature of manifestation; 3) in relation to the conditions of use. According to the method of expression, there are absolute and relative

2 Classification of measurements Classification of measuring instruments can be carried out according to the following criteria.1. According to the characteristic of accuracy, measurements are divided into equal and unequal. Equal-precision measurements of a physical quantity are called a series of measurements of some

3. The main characteristics of measurements The following main characteristics of measurements are distinguished: 1) the method by which measurements are taken; 2) the principle of measurements; 3) the measurement error; 4) the accuracy of measurements; 5) the accuracy of measurements; 6) the reliability of measurements. The measurement method is

8. Measuring instruments and their characteristics In the scientific literature, technical measuring instruments are divided into three large groups. These are: measures, gauges and universal measuring instruments, which include measuring instruments, control and measuring instruments (CIP), and

13. Measurement error In the practice of using measurements, their accuracy becomes a very important indicator, which is the degree of closeness of the measurement results to some actual value, which is used for qualitative comparison

16. Errors of measuring instruments Errors of measuring instruments are classified according to the following criteria: 1) by the method of expression; 2) by the nature of manifestation; 3) in relation to the conditions of use. By the method of expression, absolute and relative errors are distinguished.

18. Choice of measuring instruments When choosing measuring instruments, first of all, the permissible error value for a given measurement, established in the relevant regulatory documents, should be taken into account. If the permissible error is not provided for in

21. Verification and calibration of measuring instruments

General Measurement Issues When Measurement Becomes a Problem First, when a new quantity is to be measured. There is a subtlety here - what does “new value” mean? Physicists and engineers believe that there is something that can be measured. To the extent that we

Processing of measurement results No data without processing and no processing without prior information. When we measure the mains voltage with a tester, we immediately draw our conclusion - “normal” or “low for this time of day” or “why so much, tester

Measurement- finding the value of a physical quantity empirically using special technical means.

From the term "Measurement" comes the term "measure". Other terms should not be used - “measure”, “measure”, “measure”, “measure”. They do not fit into the system of metrological terms.

To carry out the measurement, it is necessary to have: a physical quantity; measurement method; measuring instruments; operator; conditions required for measurement.

The purpose of measurement is to obtain the value of a physical quantity in the most convenient form for use.

What is meant by a physical quantity, the value of which is found empirically?

Physical quantity, as noted above, this is a characteristic of a physical object (physical system, phenomenon or process), which is qualitatively common for many physical objects, but quantitatively individual for each of them.

Individuality is understood in the sense that a property can be more or less for one object in a certain number of times than for another object. Density, melting point, refractive index of light, and many others can serve as examples of physical quantities.

A physical quantity is characterized by size, value, numerical value, true and real values.

The size of the physical quantity - quantitative certainty of a physical quantity inherent in a particular material object, system, phenomenon or process.

The value of the physical quantity - expression of the size of a physical quantity in the form of a certain number of units accepted for it.

Numerical value of a physical quantity- an abstract number included in the value of the quantity.

“Value” is a multi-species concept. But the term "quantity" often expresses the size of a particular physical quantity. It is wrong to say “speed value”, “voltage value”, since both speed and voltage are quantities.

There is a difference between size and value. The size of the value really exists. You can express the size of a quantity by any of the units of a given quantity using a numerical value. The numerical value changes depending on the selected units, while the physical size of the quantity remains unchanged.

Unit physical quantity- a physical quantity of a fixed size, which is conventionally assigned a numerical value equal to 1.

The physical quantity characterizes it true value, which ideally reflects in qualitative and quantitative terms the corresponding property of the object.

Valid called meaning physical quantity, found experimentally and so close to the true value that for this purpose can be used instead of it.

Kinds measurements. By method of obtaining the numerical value of the measured value, all measurements are divided into four main types: direct, indirect, cumulative and joint.

Direct called measurements in which the desired value of a physical quantity is obtained directly from experimental data (for example, measuring the mass on a balance, the length of a part with a micrometer).

Strictly speaking, measurement is always direct and is regarded as a comparison of a quantity with its unit. In this case, it is better to use the term "direct measurement method".

Indirect measurements - determination of the desired value of a physical quantity based on the results of direct measurements of other physical quantities functionally related to the sought value.

Indirect measurements are carried out when:

* the value of the measured quantity is easier to find by indirect measurements than by direct measurements;

* there are no direct measurements of one or another quantity;

* Indirect measurements give less error than direct measurements.

Indirect measurements equation: y \u003d f (x (, x 2, ... x p), where y is the desired value, which is a function of the arguments x, x 2, ..., x p obtained by direct measurements.

An example of indirect measurements is the determination of the hardness (HB) of metals by pressing a steel ball of a certain diameter (D) with a certain load (P) and obtaining a certain indentation depth (h): HB = P / (tcD h).

Aggregate are called simultaneous measurements of several quantities of the same name, in which the values ​​of the desired quantities are found by solving a system of equations obtained by direct measurements.

For example, measurements in which the masses of individual weights of a set are 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 - these are simultaneous measurements of two or more dissimilar quantities to find a functional relationship between them. For example, determining the dependence of body length on temperature, boiling and melting points on pressure, etc.

Measurements can be classified:

a) according to the accuracy characteristic - equivalent(a series of measurements of any quantity, made by measuring instruments of the same accuracy and under the same conditions) and unequal(a series of measurements of a quantity made by several
measuring instruments with different accuracy and (or) under several different conditions);

b) by the number of measurements in a series of measurements - single and many multiples;

c) in relation to the change in the measured value - static(measurement of a physical quantity that has not changed in time, for example, measuring the length of a part at normal temperature, or measuring the size of a piece of land) and dynamic(measurement of a physical quantity that varies in size, for example,
measurement of alternating voltage of electric current, measurement
distance to ground level from a descending aircraft);

d) according to the expression of the measurement result - absolute(measurement based on direct measurements of quantities and (or) the use of values ​​of physical constants, for example, the measurement of force F is based on the measurement of the basic quantity of mass m and the use of a physical constant - the acceleration of gravity g) and relative(measurement of the ratio of a quantity to the quantity of the same name, which acts as a unit).

It is possible to measure the composition or property of substances or to measure a physical quantity using one or another measurement method.

Method of measurement- this is a method or a set of methods for comparing the measured composition or property of a substance or a measured physical quantity with a known composition or property of a substance or with a unit of physical quantity in accordance with the realized measurement principle.

Measuring principle is the phenomenon or effect underlying the measurements.

Let's consider some principles which are the basis of measurements.

If you heat the junctions of two electrodes made of various materials, then an EMF occurs. This phenomenon is the basis for temperature measurement with high accuracy (thermocouples).

When electrical conductors and semiconductors are heated, their resistance changes. This phenomenon makes it possible to obtain high accuracy of temperature measurement, especially with the use of platinum. The use of semiconductors makes it possible to measure small temperature ranges and the temperature of bodies with very small volumes.

When stretching or compressing some materials, their electrical resistance changes, which is the basis for measuring small deformations of bodies, as well as high and ultrahigh pressures. At the boundary of a metal and a semiconductor, when illuminated, an EMF occurs, the so-called photoelectric effect. Photocells are based on the use of the photoelectric effect, which are used in many measuring instruments.

The brightness of the glow of the body depends on the temperature, which, in turn, depends on the strength of the current glowing the body. The non-contact method of temperature measurement (optical pyrometer) is based on this phenomenon.

Lecture plan:

1 Classification of measurements

2 Physical quantities. Classification of physical quantities

3 Basic measurement equation. Measuring transformation

4 Postulates of the theory of measurements

5 Testing and control, measurement limits

Classification of measuring instruments can be carried out according to the following criteria.

1. According to the accuracy characteristic measurements are divided into equal and unequal.

Equivalent measurements a physical quantity is a series of measurements of a certain quantity made using measuring instruments (SI) with the same accuracy, under identical initial conditions.

Unequal measurements physical quantity on the a series of measurements of a certain quantity is called, made using measuring instruments with different accuracy, and (or) in different initial conditions.

2. By number of measurements measurements are divided into single and multiple.

Single measurement is a measurement of one quantity, made once. Single measurements in practice have a large error, in this regard, it is recommended to perform measurements of this type at least three times to reduce the error, and take their arithmetic mean as a result.

Multiple measurements is a measurement of one or more quantities performed four or more times. A multiple measurement is a series of single measurements. The minimum number of measurements for which a measurement can be considered multiple is four. The result of multiple measurements is the arithmetic mean of the results of all measurements taken. With repeated measurements, the error is reduced.

3. By type of value change measurements are divided into static and dynamic.

Static measurements are measurements of a constant, unchanging physical quantity. An example of such a time-constant physical quantity is the length of a land plot.

Dynamic measurements are measurements of a changing, non-constant physical quantity.

4. By destination measurements are divided into technical and metrological.

Technical measurements- these are measurements performed by technical measuring instruments.

Metrological measurements are measurements performed using standards.

5. By way of presentation measurement results are divided into absolute and relative.

Absolute measurements are measurements that are performed by means of a direct, direct measurement of a fundamental quantity and/or the application of a physical constant.

relative measurements are measurements in which the ratio of homogeneous quantities is calculated, and the numerator is the compared value, and the denominator is the comparison base (unit). The result of the measurement will depend on what value is taken as the basis of comparison.

6. By methods receiving measurement results are divided into direct, indirect, cumulative and joint.

Direct measurements are measurements performed using measures, i.e. the measured value is compared directly with its measure. An example of direct measurements is the measurement of the angle (measure - protractor).

Indirect measurements are measurements in which the value of the measurand is calculated using the values ​​obtained by direct measurements and some known relationship between these values ​​AND the measurand.

Cumulative measurements are measurements, the result of which is the solution of some system of equations, which with left from the equations obtained as a result of the measurement of possible combinations of measured quantities.

Joint measurements- These are measurements during which at least two inhomogeneous physical quantities are measured with in order to establish the relationship between them.

All objects of the surrounding world are characterized by their properties. A property is a philosophical category that expresses such a side of an object (phenomenon, process) that determines its difference or commonality with other objects (phenomena, processes) and is found in its relationship to them. Property is a quality category. For a quantitative description of various properties of processes and physical bodies, the concept of quantity is introduced. A value is a property of something that can be distinguished from other properties and evaluated in one way or another, including quantitatively. The value does not exist by itself, it exists only insofar as there is an object with properties expressed by this value. Ideal quantities are mainly related to mathematics, and are a generalization (model) of specific real concepts. They are calculated one way or another.

Many properties, in addition to the equivalence relation, also manifest themselves in relation to the presence of a quantitative ordinate of the property - intensity. When dismembering an object, such properties usually do not change and are called intensive quantities. By comparing the intensive quantities, one can determine their ratio, order according to the intensity of a given property. When comparing intensive quantities, the order relation (greater than, less than or equal to) is revealed, i.e. the ratio between the quantities is determined. Examples of intensive quantities are material hardness, smell, etc. Intensive quantities can be detected, classified by intensity, subjected to control, quantified by monotonically increasing or decreasing numbers. Based on the concept of "intensive quantity", the concepts of a physical quantity and its size are introduced. The size of a physical quantity is the quantitative content in a given object of a property corresponding to the concept of a physical quantity.

Intensive values ​​are displayed by quantitative, mainly expert, evaluation, in which properties with a large size are displayed in a larger number than properties with a smaller size. Intensive quantities are evaluated using the scales of order and intervals discussed below.

Objects characterized by intense values ​​can be subjected to control. Control is a procedure for establishing a correspondence between the state of an object and the norm. To implement the procedure of the simplest one-parameter control of the property X, exemplary objects are required that characterize the parameters equal to the lower X n and upper X, respectively, within the limits of the norm, and a comparison device. The control result Q is determined by the following equation: below the norm (X<Х н); норма (X>X n and X<Х в); выше нормы (X>X c).

If a physical quantity manifests itself in the relations of equivalence, order and additivity, then it can be: detected, classified, controlled and measured. These quantities, called extensive ones, usually characterize the physical material or energy properties of an object, for example, the mass of a body, the electrical resistance of a conductor, etc. When measuring an extensive quantity, an uncountable set of its sizes is mapped onto a countable subset in the form of a set of numbers Q, which must also satisfy the equivalence relations, order and additivity. Q numbers are measurement results and can be used for any mathematical operation. The set of such numbers Q must have the following properties:

For manifestation in relation to equivalence, the set of numbers Q, representing homogeneous quantities of different sizes, must be a set of identically named numbers. This name is a unit of a physical quantity or its fraction. The unit of a physical quantity [Q] is a physical quantity of a fixed size, which is conditionally assigned a numerical value equal to one. It is used to quantify homogeneous physical quantities.

For manifestation in relations of equivalence and order, the number q 1 representing the larger value Q 1 >Q 2 is chosen to be greater than the number q 2 representing the smaller value Q 2 . In both cases, one unit of physical quantity is used. To fulfill this condition, an ordered set of real numbers with a natural order relation is chosen as the desired set q 1 ,…, q n.

For manifestation in relations of equivalence, order and additivity, an abstract number equal to the estimate of the total measured value Q, resulting from the addition of components of homogeneous quantities Q i , must be equal to the sum of numerical estimates qi of these components. The sum of the named numbers Q i , reflecting the components, must be equal to the named number Q, reflecting the total value:

If the condition [Q] = is implemented, i.e., there is an equality in the sizes of units for all named numbers that reflect the total value Q and its components Q i , then in this case the following concepts are introduced:

The value of the physical quantity Q is an estimate of its size in the form of a certain number of units accepted for it;

The numerical value of a physical quantity, q is an abstract number expressing the ratio of the value of the quantity to the corresponding unit of the given physical quantity.

The equation Q = q[Q] is called the basic measurement equation. The essence of the simplest measurement is to compare the size of the physical quantity Q with the size of the output quantity of the adjustable multi-valued measure q[Q]. As a result of the comparison, it is established that q[Q]

The condition for the implementation of the elementary direct measurement procedure is the following operations:

Reproduction of a physical quantity of a given size q[Q];

Comparison of the measured physical quantity Q with the reproducible measure q[Q].

Thus, based on the use of the general postulates of equivalence, order and additivity, the concept of direct measurement was obtained, which can be formulated as follows: measurement is a cognitive process that consists in comparing a given physical quantity by means of a physical experiment with a known physical quantity taken as a unit of measurement.

Like any other science, measurement theory is built on the basis of a number of fundamental postulates that describe its initial axioms. A large number of scientific studies have been devoted to the construction and study of these axioms-postulates.

It should be noted that any attempt to formulate the initial provisions (postulates) of the measurement theory encounters fundamental difficulties. This is due to the fact that, on the one hand, postulates should be objective statements, and on the other hand, measurements are the subject of metrology, i.e. the type of activity people undertake to achieve subjective goals. Therefore, it is necessary to formulate objective statements that would serve as the foundation of a scientific discipline that has an essential subjective element. The first postulate of metrology is postulate a: within the framework of the accepted model of the object of study, there is a certain measurable physical quantity and its true value. If, for example, we assume that the part is a cylinder (the model is a cylinder), then it has a diameter that can be measured. If the part cannot be considered cylindrical, for example, its cross section is an ellipse, then it is pointless to measure its diameter, since the measured value does not carry useful information about the part. And, therefore, within the framework of the new model, the diameter does not exist. The measured value exists only within the accepted model, i.e. makes sense only as long as the model is recognized as adequate to the object. Since different models can be compared to a given object for different purposes of research, the consequence a 1 follows from the postulate a: for a given physical quantity of the measurement object, there are many measured quantities and, accordingly, their true values.

So, from the first postulate of metrology it follows that the measured property of the measurement object must correspond to some parameter of its model. This model, during the time required for the measurement, should allow this parameter to be considered unchanged. Otherwise, measurements cannot be taken. This fact is described by the postulate b: the true value of the measured quantity is constant.

Having singled out the constant parameter of the model, we can proceed to the measurement of the corresponding value. For a variable physical quantity, it is necessary to select or select some constant parameter and measure it. In the general case, such a constant parameter is introduced using some functional. An example of such constant parameters of time-varying signals introduced by means of functionals are rectified mean or root-mean-square values. This aspect is reflected in corollary b1: to measure a variable physical quantity, it is necessary to determine its constant parameter - the measured quantity.

Measurements based on the use of the human senses (touch, smell, sight, hearing and taste) are called organoleptic. Measurement of time, for example, or gravity (by astronauts) are based on sensations. Even less perfect measurements on the scale of order are based on impressions.

Measurements based on intuition are called heuristic.

Measurements performed with the help of special technical means are called instrumental. Among them can be automated and automatic. With automated measurements, the role of a person is not completely excluded (to carry out the removal of data from the reporting device of a measuring device or a digital display). Automatic measurements are performed without human intervention. Their result is presented in the form of a document and is completely objective.

Indicators are technical devices designed to detect physical properties.

Measuring instruments are called all technical means used in measurements and having normalized metrological characteristics.

Real measures are designed to reproduce the physical quantity of a given size, which is characterized by the so-called nominal size.

Measuring transducers are measuring instruments that generate measurement information signals in a form convenient for further conversion, transmission, storage, processing, but, as a rule, inaccessible to direct perception by the observer.

The unity of measurements is understood as such a state in which the results are expressed in legal units, and the accuracy of measurements is documented.

Metrological characteristics of measuring instruments are their technical characteristics that affect the results and accuracy of measurements.

The measurement scale of a quantitative property is a scale of a physical quantity. The scale of a physical quantity is an ordered sequence of values ​​of a physical quantity, adopted by agreement on the basis of the results of accurate measurements.

In accordance with the logical structure of the manifestation of properties, five main types of measurement scales are distinguished.

Name scale (classification scale). Such scales are used to classify empirical objects whose properties appear only in relation to equivalence. These properties cannot be considered physical quantities, therefore scales of this type are not scales of a physical quantity. This is the simplest type of scale, based on attributing numbers to the qualitative properties of objects, playing the role of names. An example of naming scales are widely used color atlases designed to identify colors.

Scale of order (scale of ranks). If a property of a given empirical object manifests itself in terms of equivalence and order in ascending or descending quantitative manifestation of the property, then an order scale can be constructed for it. It is monotonically increasing or decreasing and allows you to establish the ratio of more / less between the values ​​that characterize the specified property. In order scales, zero exists or does not exist, but in principle it is impossible to introduce units of measurement, since a proportionality relation has not been established for them and, accordingly, it is not possible to judge how many times more or less specific manifestations of a property are. Order scales with reference points marked on them are widely used. Such scales, for example, include the Mohs scale for determining the hardness of minerals, which contains 10 reference (reference) minerals with different conditional hardness numbers: talc - 1; gypsum - 2; calcium - 3; fluorite - 4; apatite - 5; orthoclase - 6; quartz - 7; topaz - 8; corundum - 9; diamond - 10. The assignment of a mineral to one or another gradation of hardness is carried out on the basis of an experiment, which consists in the fact that the test material is scratched by the reference. If, after scratching the tested mineral with quartz (7), a trace remains on it, and after orthoclase (6) it does not, then the hardness of the tested material is more than 6, but less than 7. The evaluation on order scales is ambiguous and very conditional, as evidenced by the considered example.

Interval scale (difference scale). These scales are a further development of scales of order and are used for objects whose properties satisfy the relations of equivalence, order, and additivity. The interval scale consists of identical intervals, has a unit of measurement and an arbitrarily chosen beginning - a zero point. Such scales include chronology according to various calendars, in which either the creation of the world, or the birth of Christ, etc. is taken as the starting point. The Celsius, Fahrenheit, and Réaumur temperature scales are also interval scales. There are practically two ways to set the scale. In the first of them, two values ​​Q 0 and Q 1 are selected, which are relatively simple to implement physically. These values ​​are called reference points, or basic benchmarks, and the interval is called the main interval (Q 1 -Q 0).

Relationship scale. These scales describe the properties of empirical objects that satisfy the relations of equivalence, order and additivity (scales of the second kind are additive), and in some cases proportionality (scales of the first kind are proportional). Their examples are the scale of mass (of the second kind), thermodynamic temperature (of the first kind). In relation scales, there is an unambiguous natural criterion for the zero quantitative manifestation of a property and a unit of measurement established by agreement. From a formal point of view, the scale of ratios is a scale of intervals with a natural reference point. All arithmetic operations are applicable to the values ​​obtained on this scale, which is important when measuring a physical quantity. Relationship scales are the most perfect.

Absolute scales. Some authors use the concept of absolute scales, which are understood as scales that have all the features of ratio scales, but additionally have a natural, unambiguous definition of the unit of measurement and do not depend on the accepted system of units of measurement. Such scales correspond to relative values: gain, attenuation, etc. For the formation of many derived units in the SI system, dimensionless and counting units of absolute scales are used.

Note that the scales of names and order are called non-metric (conceptual), and the scales of intervals and ratios are called metric (material). 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.

Test questions:

1 Define a physical quantity. Give examples of quantities belonging to different groups of physical processes.

2 What are extensive and intensive physical quantities? What are their similarities and differences? Give examples of physical quantities of each type.

3 What is the scale of a physical quantity? Give examples of different scales of physical quantities.

4 Name the main operations of the measurement procedure. Tell us how they are implemented when measuring the size of a part with a caliper.

5 Give examples of measuring transducers, multi-valued measures and comparison devices used in measuring instruments known to you.

6 What is a measuring instrument? Give examples of measuring instruments for various physical quantities.