A method for constructing an ultrasonic stress theoretical model

Abstract

The present invention discloses a method for constructing a theoretical model of ultrasonic stress, which comprises the following steps: obtaining the relationship between the elastic modulus E and temperature T of a material through experiments; obtaining the relationship between the sound velocity C and temperature T of the material through experiments; establishing a theoretical model of ultrasonic stress Δσ. The present invention proposes a method for determining the stress caused by the transmission of ultrasonic waves in a medium (also known as ultrasonic stress) by combining experimental data of partial parameters with the theory of ultrasonic vibration stress. This patent provides a method for systematically establishing ultrasonic stress under different working conditions, significantly reducing the experimental cost and number of times, and providing a method for calculating the acoustic characteristic parameters of subsequent aviation parts.

Description

Technical Field

[0001] The present invention relates to the field of machining, and particularly to a method for constructing a theoretical model of ultrasonic stress. Background Art

[0002] Ultrasonic stress is an important characteristic parameter of aviation components in sonic motion. Based on the author's research, existing theoretical models of ultrasonic stress usually establish models based on acoustic theory. In these experiments, there is a lack of ultrasonic stress experimental data considering the influence of temperature on elastic modulus and sound velocity. Summary of the Invention

[0003] The present invention aims to solve at least one of the technical problems existing in the prior art. For this purpose, the present invention provides a method for constructing a theoretical model of ultrasonic stress, which provides a method for establishing ultrasonic stress under different working conditions for the system.

[0004] A method for constructing a theoretical model of ultrasonic stress according to an embodiment of the first aspect of the present invention includes the following steps: obtaining the relationship between the elastic modulus E of a material and the temperature T through experiments; obtaining the relationship between the sound velocity C of the material and the temperature T through experiments; establishing a theoretical model of ultrasonic stress Δσ.

[0005] A method for constructing a theoretical model of ultrasonic stress according to an embodiment of the present invention has at least the following technical effects: providing a method for determining the stress caused by the transmission of ultrasonic waves in a medium (also known as ultrasonic stress) by combining experimental data of partial parameters with the ultrasonic vibration stress theory. The present invention provides a method for establishing ultrasonic stress under different working conditions for the system, significantly reducing the experimental cost and number of times, and providing a method for calculating the acoustic characteristic parameters of subsequent aviation parts.

[0006] In some embodiments of the present invention, multiple groups of temperature T i and E i are linearly fitted to obtain the relationship with temperature as the independent variable and elastic modulus as the dependent variable:

[0007] E = ξT + ψ

[0008] where E is the elastic modulus, T is the temperature, and ξ and ψ are the coefficients obtained by fitting; T i is the experimental temperature, and E i is the elastic modulus corresponding to temperature T i .

[0009] In some embodiments of the present invention, the process of obtaining multiple groups of temperature T i and E i is as follows: taking n measurement points within the temperature range T q ~T m , and the n measurement points are T1, T2,..., T i, …, T n , where T1 = T q , T m = T n , and the temperature difference between adjacent measurement points is ΔT Take 5 groups of samples and conduct 5 groups of tests to obtain the stress σ i of each group of materials at temperature T i,j and the stress σ i,j corresponding strain γ i,j , j = 1, …, 5; σ i,j is the stress corresponding to T i in the j-th group of tests. Then, take the average of multiple stresses and strains at the same temperature, and we get σ i represents the average stress at temperature T i ; γ i represents the average strain at temperature T i ; The equivalent elastic modulus at temperature T i

[0010] In some embodiments of the present invention, the relationship between the sound velocity C and the temperature T is obtained through the following steps:

[0011] Measure the transmission velocity C of sound waves in the medium under different temperature T i conditions; i ;

[0012] Perform linear fitting on multiple groups of T i and C i to obtain a relationship with temperature as the independent variable and sound velocity as the dependent variable

[0013] Linear fitting to obtain a functional relationship with temperature as the independent variable and elastic modulus as the dependent variable: C = αT + β

[0014] where C is the sound velocity, T is the temperature, and α, β are the coefficients obtained by fitting.

[0015] In some embodiments of the present invention, the theoretical model of ultrasonic stress is

[0016]

[0017] In some embodiments of the present invention, according to the relationship between the elastic modulus E, the sound velocity C, and the temperature T; the density of the medium inside the ultrasonic transmission can be obtained as:

[0018] Additional aspects and advantages of the present invention will be partially given in the following description, partially become apparent from the following description, or be understood through the practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS​

[0019] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0020] Figure 1 is the sound velocity of titanium alloys after age hardening treatment at different temperatures;

[0021] Figure 2 is the elastic modulus of titanium alloys after age hardening treatment at different temperatures;

[0022] Figure 3 is the sound velocity of titanium alloys after annealing hardening treatment at different temperatures;

[0023] Figure 4 is the elastic modulus of titanium alloys after annealing hardening treatment at different temperatures. Specific Embodiments

[0024] Embodiments of the present invention will be described in detail below. Examples of the embodiments are shown in the accompanying drawings, where the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described by referring to the accompanying drawings are exemplary and are only used to explain the present invention and should not be construed as a limitation of the present invention.

[0025] In the description of the present invention, it should be understood that the terms "center", "longitudinal", "transverse", "length", "width", "thickness", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", "axial", "radial", "circumferential", etc. indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and thus should not be construed as a limitation of the present invention. In addition, features defined as "first" and "second" may explicitly or implicitly include one or more of such features. In the description of the present invention, unless otherwise stated, the meaning of "a plurality" is two or more.

[0026] In the description of the present invention, it should be noted that unless otherwise clearly specified and defined, the terms "mounted", "connected", and "connected" should be understood in a broad sense. For example, it may be a fixed connection, a detachable connection, or an integral connection; it may be a mechanical connection or an electrical connection; it may be directly connected or indirectly connected through an intermediate medium, and it may be the communication inside two elements. For those of ordinary skill in the art, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0027] A method for constructing an ultrasonic stress theoretical model according to an embodiment of the present invention includes the following steps: obtaining the relationship between the elastic modulus E and the temperature T of the material through experiments; obtaining the relationship between the sound velocity C and the temperature T of the material through experiments; establishing a theoretical model of ultrasonic stress Δσ.

[0028] The specific steps for obtaining the relationship between the elastic modulus E and the temperature T are as follows:

[0029] Within the temperature range T q ~T m n measurement points are taken, where T q is the minimum value of the measurement temperature range, T m is the maximum value of the measurement temperature range, and the temperatures of the n measurement points are T1, T2,..., T i ,..., T n , where T1 = T q , T m = T n , and the temperature difference between adjacent measurement points is ΔT. n is the increment number. Generally, the more the number of times, the more accurate the data obtained by fitting according to the least squares method is in line with the actual situation. For example, if the increment number is set to 10 times and the target temperature range is 20 - 1020, the test temperatures are T1, T2,..., T9, T 10 , and the corresponding specific temperature values are 20, 120,..., 920, 1020.

[0030] Take 5 groups of samples and conduct 5 groups of tests to obtain the stress σ i of each group of materials at the temperature T i,j and the corresponding strain γ i,j corresponding to the stress σ i,j , j = 1,..., 5; σ i,j is the stress corresponding to T i in the j - th group of tests. Then, the average value of multiple stresses and strains at the same temperature is obtained, and

[0031] σ i represents the average stress at the temperature T i ;

[0032] γ i represents the average strain corresponding to σ i at the temperature T i ;

[0033] The equivalent elastic modulus at the temperature T i

[0034] Considering that even for the same material, due to differences in its internal structure and phase structure, its mechanical properties at different temperatures will also vary. Taking 5 groups of samples can reduce individual differences and improve accuracy. Of course, the number of experimental groups can be selected according to needs.

[0035] The steps to obtain the stress at the corresponding temperature are as follows: At this temperature, conduct experiments with ultrasonic amplitudes of w1, w2, and w3 and a frequency of 20000 Hz, obtain three stresses and average them to get the stress value at this temperature.

[0036] If the yield strength of the 5 types of samples at the same temperature exceeds 10%, then eliminate the two groups of test data with the largest difference, re-select 2 groups of materials for 2 groups of tests until the maximum difference among the 5 stress values at any temperature does not exceed 10%, and then calculate γ according to the above method. i and σ i .

[0037] Based on the relationship among stress σ, strain γ, and elastic modulus E:

[0038]

[0039] it can be obtained that E i is the elastic modulus corresponding to the temperature T i .

[0040] Perform linear fitting on multiple groups of temperature T i and E i to obtain the relationship with temperature as the independent variable and elastic modulus as the dependent variable:

[0041] E = ξT + ψ

[0042] where E is the elastic modulus, T is the temperature, and ξ, ψ are the coefficients obtained by fitting; T i is the experimental temperature, and E i is the elastic modulus corresponding to the temperature T i .

[0043] The relationship between the sound velocity C and the temperature T is obtained through the following steps:

[0044] Measure the transmission velocity C of sound waves in the medium under different temperature T i conditions; i ;

[0045] Perform linear fitting on multiple groups of T i and C i to obtain the relationship with temperature as the independent variable and sound velocity as the dependent variable: C = αT + β.

[0046] where C is the sound velocity, T is the temperature, and α, β are the coefficients obtained by fitting.

[0047] The theoretical model of ultrasonic stress is as follows:

[0048]

[0049] Where ω is the ultrasonic angular frequency and τ is the ultrasonic vibration amplitude.

[0050] The ultrasonic angular frequency is ω = 2πf v , f v is the excitation frequency of the ultrasonic horn.

[0051] According to the relationship between the elastic modulus E, the sound velocity C and the temperature T, the density of the medium in the ultrasonic wave transmission can be obtained as:

[0052] The ultrasonic stress models of two materials are constructed below by the above method.

[0053] When the temperature is within the range of 20 - 800, the material density is within the range of 4557 - 4355, and the fluctuation value is less than 5%. Its influence on the cutting process can be ignored. The velocities and elastic moduli at different temperatures are as Figures 1 to 4 shown. The straight dotted line in the figure is the fitted function relationship. Correspondingly, the linear fitting relationships of the sound velocity and elastic modulus of the age-hardened titanium alloy are

[0054] C1 = -0.8299T + 4906.1;

[0055] E1 = -0.0497T + 103.64.

[0056] The linear fitting relationships of the sound velocity and elastic modulus of the annealed-hardened titanium alloy are

[0057] C2 = -0.9605T + 4731;

[0058] E2 = -0.0414T + 100.29.

[0059] Where T is the temperature, and the ultrasonic principal stresses of the age-hardened titanium alloy and the annealed-hardened titanium alloy at different temperatures are

[0060]

[0061]

[0062] Based on the shear strain energy yield criterion, the corresponding ultrasonic shear stress value is

[0063]

[0064]

[0065] In the description of this specification, the descriptions with reference to the terms "one embodiment", "some embodiments", "illustrative embodiments", "examples", "specific examples", or "some examples", etc. mean that the specific features, structures, materials, or characteristics described in connection with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic descriptions of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials, or characteristics described can be combined in a suitable manner in any one or more embodiments or examples.

[0066] Although the embodiments of the present invention have been shown and described, those of ordinary skill in the art can understand that various changes, modifications, substitutions, and variations can be made to these embodiments without departing from the principles and spirit of the present invention, and the scope of the present invention is defined by the claims and their equivalents.

Claims

1. A method for constructing an ultrasonic stress theoretical model, characterized in that including the following steps: Obtain the relationship between the elastic modulus E of the material and the temperature T through experiments, including multiple sets of temperatures and Perform linear fitting to obtain the relationship with temperature as the independent variable and elastic modulus as the dependent variable: , where is the elastic modulus, is the temperature, , are the coefficients obtained by fitting; is the experimental temperature, is the temperature corresponding elastic modulus; The relationship between the sound velocity C of the material and the temperature T is obtained through experiments, including measuring the propagation velocity of sound waves in the medium under different temperature conditions , for multiple groups and perform linear fitting to obtain the relationship with temperature as the independent variable and sound velocity as the response variable: , , are the coefficients obtained by fitting; Establish the theoretical model of ultrasonic stress as follows: ， Among them, is the ultrasonic angular frequency, is the ultrasonic vibration amplitude, and the ultrasonic angular frequency is is the excitation frequency of the ultrasonic horn.

2. The method for constructing the ultrasonic stress theoretical model according to claim 1, wherein: Multiple groups of temperatures and are obtained as follows: Within the temperature range take n measurement points, and the n measurement points are respectively , , , , , , where , , and the temperature difference between adjacent measurement points is , , , , n; Take 5 groups of samples and conduct 5 groups of tests to obtain the stress of each group of materials at temperature and the stress corresponding strain , , , 5; is the stress corresponding to the temperature in the j-th group of tests. Then, take the average of multiple stresses and strains at the same temperature, and we get: , denotes the average stress at the temperature; , represents the average strain at a temperature; Equivalent elastic modulus at temperature .

3. The method for constructing the ultrasonic stress theoretical model according to claim 1, characterized in that According to the relationship between the elastic modulus E, the sound velocity C, and the temperature T, the density of the medium within the ultrasonic wave transmission can be obtained as follows: .

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