CN118133557A - Equivalent residual stress characterization modeling method based on equal moment - Google Patents

Abstract

The invention discloses an equivalent residual stress characterization modeling method based on equal moment, which comprises the following steps: s1, setting that the moment of the actual residual stress and the moment of the equivalent residual stress relative to the middle surface of the thin-wall part are equal to each other for the thin-wall part, and calculating to obtain the equivalent residual stress through an equivalent residual stress characterization modeling method; s2, representing the characteristics of a residual stress influence layer facing deformation analysis through the equivalent residual stress obtained through S1 calculation; and S3, verifying a residual stress characteristic parameter characterization model of the titanium alloy shot peening strengthening processing. The invention provides an equivalent residual stress characterization modeling method based on equal moment, which can calculate equivalent residual stress used for characterizing a residual stress influence layer under different parameters of different processes according to the equivalent residual stress characterization modeling method based on the equal moment of a thin-wall part, and can be used for quantitative analysis in processing residual stress induced deformation research.

Description

Equivalent residual stress characterization modeling method based on equal moment

Technical Field

The invention relates to the field of mechanical manufacturing of thin-wall parts. More particularly, the invention relates to an equivalent residual stress characterization modeling method based on equal moment.

Background

Residual stress is the stress that exists to maintain the internal equilibrium of an object when no external force is applied. When the external environment does not transmit stress to the interior of the object through the surface of the object, a stress system for maintaining balance in the interior of the object is called internal stress or inherent stress or initial stress. Residual stress is one of the internal stresses. The material may cause uneven plastic deformation due to processing, i.e., the plastic deformation amounts of different portions of the material are different, which necessarily causes relative compression or tension deformation between the different portions, thereby generating residual stress. The processing techniques such as rolling, drawing, extrusion, cutting, shot blasting and the like all cause uneven plastic deformation, and further cause macroscopic deformation of the part.

Objective drawbacks of the prior art: the processing residual stress has an important influence on deformation, and the quantitative analysis of the residual stress influence layer is needed when the processing residual stress deformation is analyzed. The residual stress influence layer is a field variable distributed in three dimensions, and can only test the average value of the surface or the surface layer under a certain depth in a certain range during testing, even if the surface or the surface layer is fitted according to the depth distribution by a mathematical function, only a depth distribution curve can be obtained, and the relation of the residual stress on deformation cannot be quantitatively studied.

Disclosure of Invention

It is an object of the present invention to address at least the above problems and/or disadvantages and to provide at least the advantages described below.

To achieve these objects and other advantages and in accordance with the purpose of the invention, as embodied and broadly described herein, there is provided an equivalent residual stress characterization modeling method based on equal moment, comprising:

S1, setting that the moment of the actual residual stress and the moment of the equivalent residual stress relative to the middle surface of the thin-wall part are equal to each other for the thin-wall part, and calculating to obtain the equivalent residual stress through an equivalent residual stress characterization modeling method;

s2, representing the characteristics of a residual stress influence layer facing deformation analysis through the equivalent residual stress obtained through S1 calculation;

And S3, verifying a residual stress characteristic parameter characterization model of the titanium alloy shot peening strengthening processing.

Preferably, in S1, the equivalent residual stress characterization modeling method includes:

S11, carrying out interpolation processing on the measured depth direction residual stress data and fitting to obtain a corresponding residual stress depth distribution curve sigma (h _r);

S12, assuming that the blade width of the test piece is l due to the stress σ being the force per unit area, it is known that based on σ (h _r):

F＝σ_r(h_r)×l×Δh_r

In the above formula, F represents force, Δh _r represents unit depth per unit area, σ _r represents residual stress, and h _r represents depth under the blade surface;

S13, the thickness of the test piece is 2H _d, the distance from the surface to the middle surface is H _d, the distance from the residual stress influencing layer to the middle surface is H _rd, and the moment of the residual stress influencing layer relative to the middle surface can be expressed as:

In the above formula, M represents moment, H represents residual stress depth value, and d is the subscript of H _d;

Let the equivalent substituted residual stress be a constant value σ _E and the depth be H _E, then:

in the above formula, M _E represents an equivalent moment;

from the principle of equal moment, m=m _E, then:

and because l is a constant, then:

The calculation formula for obtaining the equivalent residual stress is as follows:

preferably, in S3, the verification method includes:

S31, processing the test piece by adopting two groups of parameter shot blasting, and measuring the residual stress of the processed surface and surface layer;

S32, processing the depth of the residual stress influence layer and the residual stress value by adopting a normalization method of the following formula;

x_nor＝(x_at-x_min)/(x_max-x_min)

In the above formula, x _nor is a normalized value, x _at is an actual measured value, x _max is a maximum value of actual data, and x _min is a minimum value of actual data;

And S33, solving the normalized data in the S32 by adopting a calculation formula of equivalent residual stress to obtain corresponding equivalent residual stress, and setting the depth of an equivalent residual stress influence layer to be consistent with the depth of an actual residual stress influence layer so as to judge whether the accuracy of the characterization model meets the requirement or not based on the difference between the actual value and the calculated value.

The invention at least comprises the following beneficial effects: according to the equivalent residual stress characterization modeling method of the thin-wall part based on the equal moment, the equivalent residual stress used for representing the residual stress influence layer under different parameters of different processes can be calculated, and the calculation method can be used for quantitative analysis in the research of the influence of the processing parameters on the residual stress and the processing residual stress induced deformation.

Additional advantages, objects, and features of the invention will be set forth in part in the description which follows and in part will become apparent to those having ordinary skill in the art upon examination of the following or may be learned from practice of the invention.

Drawings

FIG. 1 is a schematic view of the residual stress depth profile of the present invention;

FIG. 2 is a schematic diagram showing the comparison of actual values and calculated values when the characterization model is verified by using the 1 st set of parameters;

FIG. 3 is a schematic diagram showing the comparison of actual values and calculated values when the characterization model is verified by using the 2 nd set of parameters;

FIG. 4 is a graph showing the comparison of equivalent residual stress and the effect layer depth under different shot blasting parameters.

Detailed Description

The present invention is described in further detail below with reference to the drawings to enable those skilled in the art to practice the invention by referring to the description.

In order to be able to carry out transverse comparison of the residual stresses under different processing parameters, and to quantitatively analyze the influence of the processing parameters on the residual stress influencing layer and the influence relationship of the residual stress influencing layer on deformation. The invention provides an equivalent residual stress characterization modeling method based on equal moment for deformation analysis by combining a residual stress depth distribution cosine function model, and provides technical support for processing residual stress deformation research.

1. Equivalent residual stress characterization modeling method for thin-wall part based on equal moment

Fitting the processing residual stress depth distribution data by a cosine function formula (1).

Wherein: σ _r represents the residual stress; h _r denotes the subsurface depth; a represents the amplitude of the underdamped oscillation; λ represents a damping coefficient; ω represents the frequency of damping; θ represents a phase angle; d represents an offset parameter.

In general, the invention combines the residual stress depth value H and the residual stress depth distribution cosine function formula (1), and describes the characteristics of a residual stress field facing deformation analysis by calculating and processing equivalent residual stress.

Specifically, the equivalent residual stress refers to a assumed constant residual stress value having an equivalent effect on the test piece as the actual residual stress. The equivalent residual stress of the invention is used to describe the residual stress field for deformation analysis, so that the calculation is based on the principle of 'equal moment'. For the thin-wall part, the moment of the actual residual stress and the moment of the equivalent residual stress relative to the middle surface of the thin-wall part are set to be equal, and then the equivalent residual stress can be obtained through integral calculation. The specific method comprises the following steps:

① The measured residual stress data in the depth direction is subjected to interpolation processing and fitting, and a residual stress depth distribution curve sigma (h _r) shown in fig. 1 is obtained.

② Due to the stress sigma being a force per unit area

③ With reference to FIG. 1, assuming a blade width of l, it can be seen that

F＝σ_r(h_r)×l×Δh_r (4)

F represents force, Δh _r represents unit depth per unit area, σ _r represents residual stress, and h _r represents depth below the blade surface;

④ As shown in FIG. 1, assuming that the test piece has a thickness of 2H _d, a distance from the point A of the surface to the point B of the middle plane is H _d, and a distance from the residual stress-affecting layer to the middle plane is H _rd, the moment of the residual stress-affecting layer with respect to the middle plane can be expressed as

In the above formula, M represents moment, H represents residual stress depth value, d is the subscript of H _d, and is used for distinguishing from H;

⑤ Let the equivalent residual stress be a constant value sigma _E and the depth be H _E, then

M _E represents the moment of equivalent residual compressive stress relative to the mid-plane, namely equivalent moment;

⑥ By the principle of equal moment, m=m _E, then

⑦ And l is a constant

⑧ So the equivalent residual stress is

Substituting the functions of H _d,H,H_E and sigma _r(h_r) into the formula (9) to obtain the equivalent residual stress value sigma _E. The residual stress influencing layer may be commonly characterized by an Equivalent Residual Stress (ERS) σ _E and its influencing depth H _E.

2. Titanium alloy shot peening strengthening processing residual stress characterization model verification

In order to verify an equivalent residual stress characterization modeling method of a thin-wall part based on equal moment, residual stress data of titanium alloy shot peening strengthening processing is selected for analysis and comparison. And selecting two groups of basic shot blasting tests, and verifying a characterization model based on the characteristic parameters according to the measured residual stress. The method comprises the steps of firstly testing the residual stress of the surface and the surface layer of a test piece after shot blasting processing by adopting two groups of parameters, then processing the test piece by a normalization method, and describing the test piece in a cosine function mode.

The depth of the residual stress-influencing layer and the residual stress value are normalized by equation (10).

x_nor＝(x_at-x_min)/(x_max-x_min) (10)

Where x _nor is the normalized value, x _at is the actual measured value, x _max is the maximum value of the actual data, and x _min is the minimum value of the actual data. Wherein the numerical value is set as follows: σ _min＝0MPa,σ_max＝-1000MPa,h_min＝0mm,h_max =0.15 mm.

And (3) solving the equivalent residual stress according to a fitting formula (9), and setting the equivalent residual stress influence layer depth consistent with the actual residual stress influence layer depth. The results are shown in fig. 2-3, and the difference between the actual value and the calculated value is less than 10%, which indicates that the accuracy of the characterization model is high.

The characterization amount of the residual stress of 29 groups of different shot blasting parameters is calculated, the characterization amount of the residual stress under the condition of different shot blasting parameters is shown in table 1, and the comparison result of the characterization parameters of different groups is shown in fig. 4.

TABLE 1

The analysis of fig. 4 shows that the table residual stress influencing layer Depth (DRSA) and the Equivalent Residual Stress (ERS) for different sets of residual stresses differ by different parameters. Meanwhile, the equivalent residual stress of each group is found to be obviously different due to different parameters, and the purpose of representing the residual stress influence layer under the condition of different parameters is achieved.

According to the equivalent residual stress characterization modeling method of the thin-wall part based on the equal moment, the equivalent residual stress for characterizing the residual stress influence layer under different parameters of different processes can be calculated, and the calculation method can be used for quantitative analysis in the processing residual stress induced deformation research.

The above is merely illustrative of a preferred embodiment, but is not limited thereto. In practicing the present invention, appropriate substitutions and/or modifications may be made according to the needs of the user.

The number of equipment and the scale of processing described herein are intended to simplify the description of the present invention. Applications, modifications and variations of the present invention will be readily apparent to those skilled in the art.

Although embodiments of the invention have been disclosed above, they are not limited to the use listed in the specification and embodiments. It can be applied to various fields suitable for the present invention. Additional modifications will readily occur to those skilled in the art. Therefore, the invention is not to be limited to the specific details and illustrations shown and described herein, without departing from the general concepts defined in the claims and their equivalents.

Claims (3)

1. The equivalent residual stress characterization modeling method based on the equal moment is characterized by comprising the following steps of:

S1, setting that the moment of the actual residual stress and the moment of the equivalent residual stress relative to the middle surface of the thin-wall part are equal to each other for the thin-wall part, and calculating to obtain the equivalent residual stress through an equivalent residual stress characterization modeling method;

s2, representing the characteristics of a residual stress influence layer facing deformation analysis through the equivalent residual stress obtained through S1 calculation;

And S3, verifying a residual stress characteristic parameter characterization model of the titanium alloy shot peening strengthening processing.

2. The equivalent residual stress characterization modeling method based on equal torque according to claim 1, wherein in S1, the equivalent residual stress characterization modeling method includes:

S11, carrying out interpolation processing on the measured depth direction residual stress data and fitting to obtain a corresponding residual stress depth distribution curve sigma (h _r);

S12, assuming that the blade width of the test piece is l due to the stress σ being the force per unit area, it is known that based on σ (h _r):

F＝σ_r(h_r)×l×Δh_r

In the above formula, F represents force, Δh _r represents unit depth per unit area, σ _r represents residual stress, and h _r represents depth under the blade surface;

S13, the thickness of the test piece is 2H _d, the distance from the surface to the middle surface is H _d, the distance from the residual stress influencing layer to the middle surface is H _rd, and the moment of the residual stress influencing layer relative to the middle surface can be expressed as:

In the above formula, M represents moment, H represents residual stress depth value, and d is the subscript of H _d;

Let the equivalent substituted residual stress be a constant value σ _E and the depth be H _E, then:

in the above formula, M _E represents an equivalent moment;

from the principle of equal moment, m=m _E, then:

and because l is a constant, then:

The calculation formula for obtaining the equivalent residual stress is as follows:

3. the equivalent residual stress characterization modeling method based on equal torque according to claim 2, wherein in S3, the verification method includes:

S31, processing the test piece by adopting two groups of parameter shot blasting, and measuring the residual stress of the processed surface and surface layer;

S32, processing the depth of the residual stress influence layer and the residual stress value by adopting a normalization method of the following formula;

x_nor＝(x_at-x_min)/(x_max-x_min)

In the above formula, x _nor is a normalized value, x _at is an actual measured value, x _max is a maximum value of actual data, and x _min is a minimum value of actual data;

And S33, solving the normalized data in the S32 by adopting a calculation formula of equivalent residual stress to obtain corresponding equivalent residual stress, and setting the depth of an equivalent residual stress influence layer to be consistent with the depth of an actual residual stress influence layer so as to judge whether the accuracy of the characterization model meets the requirement or not based on the difference between the actual value and the calculated value.