RU2570222C2 - Method of mechanical operability estimation of loaded and reinforced products - Google Patents

Abstract

FIELD: testing equipment.

SUBSTANCE: invention relates to studies, when operability of the reinforced and loaded products is estimated during designing, and during operation. Essence of the invention: fields of failure-free operation probability are plotted as per product volume according to strength and rigidity (ultimate strain) criteria considering operation time and temperature dependence.

EFFECT: increased degree of estimation of products mechanical operability.

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Description

The invention relates to the field of research, during which the performance of reinforced and exposed to load products is evaluated during their design, as well as during operation.

Known are the traditional methods in the engineering practice and the course “Resistance of Materials” for determining mechanical working capacity under conditions of strength and stiffness [1, 2].

Strength conditions:

σ _max ≤ [σ],

τ _max ≤ [τ],

where σ _max , τ _max - the current maximum normal and shear stresses;

[σ], [τ] - allowable normal and shear stresses.

Hardness conditions:

Δl≤ [Δl],

Δφ≤ [Δφ],

where Δl, Δφ - current maximum elongation, twist angle;

[Δl], [Δφ] - allowable elongation, twist angle.

Based on the results of calculating the effective stresses, diagrams are constructed — graphs of changes in stresses and strains along the length or section of the product. The current maximum stresses and elongations (twist angles) are determined from the diagrams. The diagrams clearly show the changes in stresses and elongations (twist angles) and their maximum values are determined.

A known method for assessing mechanical performance by fields of stress and strain (the closest analogue [2]). This method is based on a comparison of the current maximum stresses and strains in the product with the permissible values of stresses and strains.

The disadvantages of this performance assessment is that the magnitude of the permissible stresses is arbitrary and is assigned based on the experience of operating parts of machines for various purposes. Permissible stresses are not a normative characteristic of the material of the part. In addition, the estimate is deterministic and does not take into account the spread of maximum and ultimate stresses.

The proposed method solves the problem of assessing the mechanical performance of products by constructing the probability fields of failure-free operation (FBG) based on a statistical array of experimental data and a well-known approach to assessing the strength reliability [3-5].

Evaluation of the strength reliability of the product lies in the fact that the product or its element has a certain strength, exceeding which there is a loss of its performance - destruction. On the one hand, the factors determining the strength of the elements of the product are random variables, and therefore, the strength will be a random variable. On the other hand, the stress arising in the element of the product depends on many variables (elastic, deformation, dilatometric characteristics, etc.) with variability or dissipation. The reasons for scattering are differences in the structure of the material of the sample, the degree of its defectiveness, the difference in size, the accuracy of determination of the measured characteristics, the stability of the test conditions, etc. This leads to the fact that the stresses in the element also become random variables. The normal distribution of random variables is applied in those cases when they depend on a large number of independent influences.

Consider the definition of the probability of failure-free operation with a normal distribution of limiting and equivalent voltages. Normal distribution is the most commonly used statistical model.

Thus, to assess reliability by the criterion of strength, it is necessary to determine the probability that the strength of the product or its element is greater than the calculated stress [3-5].

и средним квадратическим отклонением S_σэкв, а также предела текучести ƒ_σ(σ_пр) со средним значением

и средним квадратическим отклонением S_σпр.In FIG. Figure 1 shows the overlap of the distribution of equivalent stresses at a hazardous point of the product ƒ _σ (σ _equiv ) with an average

and the standard deviation S _σekv and yield strength ƒ _{σ (σ pr)} with the mean value

and standard deviation S _σpr .

Denote the new random variable

y = σ _pr -σ _equiv,

then the probability of uptime R (t) can be represented as

R (t) = P (y> 0).

The random variable y has a normal distribution with a mathematical expectation

and standard deviation

The uptime probability expressed in terms of y can be written

Expressing the probability of uptime R (t) through the normalized normal distribution function, we have

- математическое ожидание предельных напряжений (предела текучести, максимальной прочности при растяжении);

- математическое ожидание эквивалентного напряжения;

- среднее квадратическое отклонение предельных напряжений;

- среднее квадратическое отклонение эквивалентного напряжения.Where

- mathematical expectation of ultimate stresses (yield strength, maximum tensile strength);

- mathematical expectation of equivalent voltage;

- root mean square deviation of ultimate stresses;

- the standard deviation of the equivalent voltage.

, а

.The average value of a random variable is an estimate of the mathematical expectation, i.e.

, but

.

In the case when the limiting and equivalent stresses have different distribution laws, models have been developed to determine the probability of failure-free operation [4].

If the limiting and equivalent voltages are distributed exponentially, the probability of failure-free operation is determined

- среднее значение предельного напряжения;Where

- the average value of the limiting voltage;

σ _equiv - the average value of the equivalent voltage.

In the case when the limiting and equivalent voltages have a gamma distribution with parameters m, λ and n, μ, respectively, the probability of failure-free operation is determined

where r = µ / λ.

If the limit voltage and equivalent have Weibull distribution with parameters _σpr β, θ _σpr, σ and β _{pr0 σekv,} θ _σekv, σ _ekv0, the state probability is determined

Where

σ _CR0 , σ _EQ0 are the minimum values of ultimate and equivalent stresses.

The condition of operability by the criterion of strength, taking into account the operating time and temperature dependence, ultimate and calculated stresses with a deterministic approach, you can write:

σ _equiv (t, T °) <σ _ol (t, T °),

where σ _equiv (t, T °) are the equivalent stresses at the dangerous point of the product,

σ _ol (t, T °) - ultimate stresses (tensile strength, yield strength, endurance, etc.).

This condition of working capacity can be considered separately for aging the material at the same temperature and taking into account the temperature dependence of the limiting and calculated stresses of the starting material, and for taking these factors into account simultaneously [6].

больше, чем расчетные напряжения в тот же момент времени или при той же температуре. Примем в качестве предельных напряжений для материала изделия предел текучести как наиболее часто используемую характеристику в прочностных расчетах.An assessment of the reliability of products according to the strength criterion taking into account the aging of the material, as well as the temperature dependence of the limiting and calculated stresses, is the probability that the limiting stresses of the material of the product or its element at time t _i or at temperature

more than the calculated stresses at the same time or at the same temperature. We take as the ultimate stresses for the product material the yield strength as the most commonly used characteristic in strength calculations.

и средним квадратическим отклонением, S_om(t,T°).In FIG. Figure 2 shows the temperature dependences and the overlap of the equivalent stress distributions at the product hazard point ƒ _σ (σ _equiv ) with the average value of σ _equiv (t, T °) and the standard deviation S _σeq (t, T °), as well as the yield strength ƒ _σ ( σ _m ) with an average value

and standard deviation, S _om (t, T °).

Denote the new random variable y _i = σ _mi (t, T °) -σ _equiv (t, T °).

можно представить в видеThis random variable must be positive, i.e. the yield strength of the polymer material must be higher than the calculated equivalent stresses. Then the probability of failure of the element at time t _i at temperature

can be represented as

R (t) _i = P (y _i > 0) = σ _mi (t, T °) -σ _equiv (t, T °)

The random variable y _i has a normal distribution with a mathematical expectation

and standard deviation

The uptime probability expressed in terms of y _i can be written

Expressing the probability of uptime R (t) through the normalized normal distribution function, we have

- среднее значение максимальной прочности при растяжении;Where

- the average value of the maximum tensile strength;

σ _equiv - the average value of the equivalent voltage;

S _σeqi is the mean square deviation of the equivalent voltage;

S _omi is the standard deviation of the tensile strength.

The calculations of the probability of failure-free operation on the example of a pipe loaded with internal pressure.

In the probabilistic-statistical approach, control parameters (strength, elastic, dimensional) are set in accordance with the law of their distribution. Then, as a result of the calculation, a variant of the stress-strain state (VAT) is obtained, and a series of similar calculations — numerical experiments — provides a set of data on the VAT parameters that can be statistically analyzed.

In FIG. Figure 3 shows the probability field of failure-free operation by volume of the pipe section according to the strength criterion from MPP 15-04 at a temperature of 60 ° C and a pressure of 1.7 MPa.

In FIG. Figure 4 shows the probability field of failure-free operation by volume of the pipe section according to the strength criterion from MPP 15-04 at a temperature of 20 ° C and a pressure of 4 MPa, performed in the ANSYS software package.

Assessment of the reliability of the structure with the approach under consideration is obtained in the form of the probability of failure-free operation of the material at all points of the product, which can be represented in the form of FBG distribution fields over the entire volume of the structure (Figs. 3 and 4). It can be seen that on the inner wall of the pipe the probability of failure-free operation is reduced.

The proposed approach is implemented in the form of constructing the probability field of failure-free operation [7] for the fan impeller, which is made of a polymer material. The fan wheel is mounted on the shaft of the AIR series electric motor. A two-way keyway is made on the impeller (Fig. 5). The stress state in the fan impeller arises due to the initial interference when landing on the shaft and during operation of the electric motor at negative temperatures.

Due to the presence of two mutually perpendicular axes of symmetry of the problem, the computational domain is considered, which is a quarter of the axial section of the fan sleeve, for which the plane problem of the theory of elasticity is solved (Fig. 6).

The problem is solved using the finite element method. The initial data for the calculation are the temperature dependences of the average value and the mean square deviation of the modulus of elasticity and tensile strength of the investigated materials and the design scheme of the product.

In FIG. Figure 7 illustrates the calculation results for the BSPE 22007-16 material at a temperature of -60 ° C, in the form of the probability field of failure-free operation over the cross section of the sleeve and the corresponding isolines. In the corner part of the groove, a decrease in the FBG values is observed, due to the stress concentration in this region.

The proposed method for constructing the probability fields of failure-free operation is effective in the selection of materials and structural solutions of products and structures, which will allow you to choose the best option.

Information sources

1. The calculation of the strength of machine parts: Reference / I.A. Birger, B.F. Shore, G.B. Iosilevich. - 3rd ed., Revised. and add. - M.: Mechanical Engineering, 1979. - 702 p.

2. Prigorovsky N.I. Methods and means of determining the fields of strains and stresses: Reference. - M.: Mechanical Engineering, 1983. - 248 p.: Ill.

3. Bolotin V.V. Methods of probability theory and reliability theory in the calculations of structures. - M.: Stroyizdat, 1982.- 351 p.

4. Rzhanitsin A.R. The theory of calculating building structures for reliability. - M.: Stroyizdat, 1978.- 239 p.

5. Kapoor K., Lumberson L. Reliability and system design. Per. from English / Ed. I.A. Ushakova. - M .: Mir, 1980 .-- 604 p.

6. Reutov A.I. Reliability forecasting of building products from polymeric materials: monograph / A.I. Reutov. - M .: LLC RIF "Building Materials", 2007. - 184 p.

7. Bochkareva S.A., Lukshin B.A., Reutov A.I., Dambaev Zh., V.A. Hoopoe, Kozlova L.A. Calculation of the probability of failure-free operation of the sealing element of the high-pressure emergency valve // "Problems of the Mechanics of Modern Machines", Materials of the V International Conference, June 25-30, 2012, Ulan-Ude, VSGUTU Publishing House, 2012, v. 2, p. 69-73.

8. Lyukshin B.A., Reutov A.I., Bochkareva S.A., Popovich SI. Assessment of the reliability of a structure based on the analysis of its stress-strain state // “Safety and survivability of technical systems”, Materials of the IV All-Russian Conference, October 9–13, 2012, Krasnoyarsk, VSGUTU publishing house, 2012, v. 2, p. 69-73.

Claims (1)

A method for assessing the mechanical performance of loaded and reinforced products, characterized in that the probability fields of failure-free operation are built according to the volume of the product according to the criteria of strength or stiffness (ultimate deformation), taking into account the operating time and temperature dependence.

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