Method for calculating flow-induced stress and fatigue life of corrugated pipe

Abstract

The invention discloses a method for calculating flow-induced stress and fatigue life of a corrugated pipe, which comprises the following steps of: on the basis of structural parameters and medium parameters of the corrugated pipe, sequentially resolving to obtain modal frequencies of all orders, modal excitation flow velocities of all orders, radial acoustic modal frequencies of a first order and flow velocities of media of the corrugated pipe; further, the excitation mode is determined, and the excitation flow velocity of the excitation mode is determined; on the basis, calculating to obtain the stress of the corrugated pipe; further, according to an acoustic resonance result, certain uncertainty is considered, and the stress, obtained through calculation, of the corrugated pipe is corrected; and finally, according to the corrected stress of the corrugated pipe, calculating to obtain the fatigue damage of the corrugated pipe in each excitation mode. According to the method, the excitation mode can be judged according to the structural size and the medium parameters of the corrugated pipe, and then the flow-induced stress is estimated, so that the generated fatigue damage of the corrugated pipe is evaluated, and the problems of vibration, fatigue and the like caused by fluid scouring cannot be considered in the prior art are solved.

Description

Technical Field

[0001] The invention belongs to the technical field of bellows testing, and in particular relates to a method for calculating flow-induced stress and fatigue life of a bellows. Background Art

[0002] Bellows are generally used as compensation components in the booster delivery system of launch vehicles. When the medium flows inside the bellows, pressure pulsation may occur. When the frequency of the pressure pulsation is coupled with the structural frequency of the bellows, the bellows may resonate, generate flow-induced stress, and cause fatigue failure. How to evaluate the flow-induced stress and fatigue life of the bellows under medium flow is the key to solving the problem of flow-induced vibration fatigue caused by the bellows' resistance to medium erosion.

[0003] At present, the commonly used bellows fatigue damage assessment method is as follows: calculate the stress distribution of the bellows under a given boundary displacement through finite element software, determine whether the stress meets the requirements through the SN curve, and calculate the damage of each working condition and the total damage through the stress and cycle number of four working conditions. The selection and matching of the bellows are carried out in the early design and development stage of the bellows of the engine exhaust system. This solution can only realize the fatigue damage calculation under static cycles, and does not take into account the vibration fatigue of the bellows under medium scouring. Summary of the invention

[0004] The technology of the present invention solves the problem: overcomes the shortcomings of the prior art and provides a method for calculating the flow-induced stress and fatigue life of a bellows. The exciting mode can be determined according to the structural dimensions and medium parameters of the bellows, and then the flow-induced stress can be estimated, thereby evaluating the fatigue damage of the bellows, solving the problems of vibration and fatigue caused by fluid scouring that cannot be considered in the prior art.

[0005] In order to solve the above technical problems, the present invention discloses a method for calculating flow-induced stress and fatigue life of a bellows, comprising:

[0006] Step 1, according to the inner diameter, wave height, number of layers, single layer wall thickness and wave pitch of the bellows, calculate the modal frequencies of each order of the bellows; wherein the modal frequencies of each order include: axial modal frequencies of each order and local bending modal frequencies;

[0007] Step 2, according to the modal frequencies of the bellows calculated in step 1, combined with the Stuhal number and the wave distance, calculate the excitation flow velocities of the bellows of various modes;

[0008] Step 3, calculating the flow rate of the medium according to the density and mass flow rate of the medium inside the bellows and the inner diameter cross-sectional area of ​​the bellows;

[0009] Step 4, calculating the first-order radial acoustic mode frequency of the bellows according to the inner diameter, wave height, average fillet radius and sound velocity of the medium of the bellows;

[0010] Step 5, comparing the flow velocity of the medium calculated in step 3 with the excitation flow velocity of each order mode of the bellows calculated in step 2; if the flow velocity of the medium reaches or exceeds the excitation flow velocity of a certain order mode of the bellows, it is determined that the certain order mode is excited, and combined with step 1, the frequency of the excited mode is obtained;

[0011] Step 6, comparing the frequency of the excited mode obtained in step 5 with the first-order radial acoustic mode frequency of the bellows calculated in step 4 to obtain an acoustic resonance result; wherein, if the frequency of the excited mode reaches or exceeds the first-order radial acoustic mode frequency of the bellows, the acoustic resonance result is: there is an acoustic resonance; otherwise, the acoustic resonance result is: there is no acoustic resonance;

[0012] Step 7, according to the frequency of the excited mode obtained in step 5, combined with step 2, the excited flow velocity of the excited mode is obtained; according to the obtained excited flow velocity of the excited mode, combined with the density of the medium, the pulsating pressure is calculated;

[0013] Step 8, calculating the cross-sectional area of ​​the bellows according to the outer diameter and inner diameter of the bellows;

[0014] Step 9, calculating the force of the medium on the bellows according to the pulsating pressure calculated in step 7 and the cross-sectional area of ​​the bellows calculated in step 8;

[0015] Step 10, calculating the single-wave displacement of the bellows according to the force of the medium on the bellows calculated in step 9 and the single-wave stiffness of the bellows;

[0016] Step 11, calculating the stress of the bellows according to the single wave displacement of the bellows calculated in step 10;

[0017] Step 12, according to the acoustic resonance result obtained in step 6, taking into account a certain uncertainty, correcting the stress of the bellows calculated in step 11 to obtain a corrected bellows stress;

[0018] Step 13, based on the corrected bellows stress calculated in step 12 and the SN curve of the bellows material, the fatigue damage of the bellows under each excitation mode is calculated according to the fixed frequency vibration.

[0019] In the above-mentioned method for calculating the flow-induced stress and fatigue life of the bellows, in step 2, the calculation formula for the excitation flow velocity of each order mode of the bellows is as follows:

[0020] The excitation flow velocity of each mode of the bellows = each mode frequency of the bellows × wave pitch / Stuhal number.

[0021] In the above bellows flow-induced stress and fatigue life calculation method, in step 3, the flow rate of the medium is calculated as follows:

[0022] The flow rate of the medium = the mass flow rate of the medium / the density of the medium / the inner diameter cross-sectional area of ​​the bellows.

[0023] In the above bellows flow-induced stress and fatigue life calculation method, in step 7, the calculation formula of the pulsating pressure is as follows:

[0024] Pulsating pressure = 0.5 × medium density × excitation flow rate of the excitation mode 2 .

[0025] In the above-mentioned method for calculating the flow-induced stress and fatigue life of the bellows, in step 8, the calculation formula for the cross-sectional area of ​​the bellows is as follows:

[0026] The cross-sectional area of ​​the bellows = π × (outer diameter of the bellows 2 -Inner diameter of the bellows 2 ) / 4.

[0027] In the above bellows flow-induced stress and fatigue life calculation method, in step 9, the calculation formula of the force exerted by the medium on the bellows is as follows:

[0028] The force exerted by the medium on the bellows = pulsating pressure × cross-sectional area of ​​the bellows.

[0029] In the above-mentioned method for calculating the flow-induced stress and fatigue life of the bellows, in step 10, the calculation formula for the single wave displacement of the bellows is as follows:

[0030] The single wave displacement of the bellows = the force exerted by the medium on the bellows / the single wave stiffness of the bellows.

[0031] In the above-mentioned method for calculating the flow-induced stress and fatigue life of the bellows, in step 12, the stress of the bellows calculated in step 11 is corrected by the following formula:

[0032] Corrected bellows stress = bellows stress × amplification factor × uncertainty.

[0033] In the above-mentioned method for calculating flow-induced stress and fatigue life of a bellows, in step 12, if the existence of acoustic resonance is determined according to the acoustic resonance result obtained in step 6, then the amplification factor is not equal to 1.

[0034] In the above-mentioned method for calculating flow-induced stress and fatigue life of a bellows, in step 12, if it is determined that there is no acoustic resonance according to the acoustic resonance result obtained in step 6, then the amplification factor is equal to 1.

[0035] The present invention has the following advantages:

[0036] (1) The present invention discloses a method for calculating the flow-induced stress and fatigue life of a bellows. Based on the flow-induced vibration phenomenon and mechanism of the bellows, a theoretical calculation method for the flow-induced stress and fatigue life is established.

[0037] (2) The present invention discloses a method for calculating the flow-induced stress and fatigue life of a bellows, taking into account various axial modes and local bending modes of the bellows, and comprehensively analyzing possible excitation modes.

[0038] (3) The present invention discloses a method for calculating the flow-induced stress and fatigue life of a bellows, and proposes a method for calculating the excitation flow velocity of each mode of the bellows, as well as an excitation determination method.

[0039] (4) The present invention discloses a method for calculating the flow-induced stress and fatigue life of a bellows, and proposes a method for calculating the single-wave resultant force of the fluid on the bellows by using the dynamic pressure of the bellows medium as the pulsating pressure and the structural dimensions of the bellows.

[0040] (5) The present invention discloses a method for calculating the flow-induced stress and fatigue life of a bellows, which adopts a method for calculating the single-wave displacement and structural stress of the bellows through the single-wave force on the bellows, and obtains the structural stress of the bellows under flow-induced vibration.

[0041] (6) The present invention discloses a method for calculating the flow-induced stress and fatigue life of a bellows. The method takes into account the amplification effect of the acoustic resonance of the bellows on the mechanical vibration through the first-order radial acoustic mode of the bellows.

[0042] (7) The present invention discloses a method for calculating the flow-induced stress and fatigue life of a bellows. By using the material SN curve and the method of equating the flow-induced vibration to single-frequency vibration, the flow-induced vibration fatigue life can be evaluated. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 It is a flow chart of a method for calculating flow-induced stress and fatigue life of a bellows in an embodiment of the present invention. DETAILED DESCRIPTION

[0044] In order to make the objectives, technical solutions and advantages of the present invention more clear, the embodiments disclosed in the present invention will be further described in detail below with reference to the accompanying drawings.

[0045] Reference Figure 1 In this embodiment, the bellows flow-induced stress and fatigue life calculation method includes:

[0046] Step 1: Calculate the modal frequencies of the bellows according to the inner diameter, wave height, number of layers, single-layer wall thickness and wave pitch of the bellows.

[0047] In this embodiment, each order of modal frequency includes: each order of axial modal frequency and local bending modal frequency.

[0048] Step 2: Calculate the excitation flow velocity of each mode of the bellows according to the modal frequencies of each order of the bellows calculated in step 1 in combination with the Stuhal number and the wave distance.

[0049] In this embodiment, the calculation formulas for the excitation flow velocities of each order of the bellows are as follows:

[0050] The excitation velocity of each mode of the bellows = each mode frequency of the bellows × wave distance / Stuchal number

[0051] Step 3, calculating the flow rate of the medium according to the density and mass flow rate of the medium inside the bellows and the inner diameter cross-sectional area of ​​the bellows.

[0052] In this embodiment, the calculation formula of the flow rate of the medium is as follows:

[0053] Flow rate of medium = mass flow rate of medium / density of medium / inner diameter cross-sectional area of ​​bellows

[0054] Step 4: Calculate the first-order radial acoustic modal frequency of the bellows according to the inner diameter, wave height, average fillet radius and sound velocity of the medium of the bellows.

[0055] Step 5, compare the flow velocity of the medium calculated in step 3 with the excitation flow velocity of each order mode of the bellows calculated in step 2; if the flow velocity of the medium reaches or exceeds the excitation flow velocity of a certain order mode of the bellows, it is determined that the certain order mode is excited, and combined with step 1, the frequency of the excited mode is obtained.

[0056] Step 6, comparing the frequency of the excited mode obtained in step 5 with the first-order radial acoustic mode frequency of the bellows calculated in step 4 to obtain an acoustic resonance result.

[0057] In this embodiment, if the frequency of the excited mode reaches or exceeds the first-order radial acoustic mode frequency of the bellows, the acoustic resonance result is: there is an acoustic resonance; otherwise, the acoustic resonance result is: there is no acoustic resonance.

[0058] Step 7, according to the frequency of the excited mode obtained in step 5, combined with step 2, the excited flow velocity of the excited mode is obtained; according to the obtained excited flow velocity of the excited mode, combined with the density of the medium, the pulsating pressure is calculated.

[0059] In this embodiment, the calculation formula of the pulsating pressure is as follows:

[0060] Pulsating pressure = 0.5 × medium density × excitation flow rate of the excitation mode 2

[0061] Step 8, calculate the cross-sectional area of ​​the bellows according to the outer diameter and inner diameter of the bellows.

[0062] In this embodiment, the calculation formula of the cross-sectional area of ​​the bellows is as follows:

[0063] The cross-sectional area of ​​the bellows = π × (outer diameter of the bellows 2 -Inner diameter of the bellows 2 ) / 4

[0064] Step 9, according to the pulsating pressure calculated in step 7 and the cross-sectional area of ​​the bellows calculated in step 8, calculate the force exerted by the medium on the bellows.

[0065] In this embodiment, the calculation formula of the force exerted by the medium on the bellows is as follows:

[0066] The force of the medium on the bellows = pulsating pressure × cross-sectional area of ​​the bellows

[0067] Step 10, based on the force of the medium on the bellows calculated in step 9 and the single-wave stiffness of the bellows, the single-wave displacement of the bellows is calculated.

[0068] In this embodiment, the calculation formula of the single wave displacement of the bellows is as follows:

[0069] Single wave displacement of bellows = force exerted by medium on bellows / single wave stiffness of bellows

[0070] Step 11, according to the single wave displacement of the bellows calculated in step 10, calculate the stress of the bellows.

[0071] Step 12, based on the acoustic resonance result obtained in step 6 and taking into account a certain uncertainty, the stress of the bellows calculated in step 11 is corrected to obtain a corrected bellows stress.

[0072] In this embodiment, the stress of the bellows calculated in step 11 is corrected by the following formula:

[0073] Corrected bellows stress = bellows stress × amplification factor × uncertainty

[0074] If the acoustic resonance result obtained in step 6 determines that there is an acoustic resonance, the amplification factor is not equal to 1; if the acoustic resonance result obtained in step 6 determines that there is no acoustic resonance, the amplification factor is equal to 1.

[0075] Step 13, based on the corrected bellows stress calculated in step 12 and the SN curve of the bellows material, the fatigue damage of the bellows under each excitation mode is calculated according to the fixed frequency vibration.

[0076] Although the present invention has been disclosed as above in the form of a preferred embodiment, it is not intended to limit the present invention. Any person skilled in the art may make possible changes and modifications to the technical solution of the present invention by using the methods and technical contents disclosed above without departing from the spirit and scope of the present invention. Therefore, any simple modifications, equivalent changes and modifications made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solution of the present invention shall fall within the protection scope of the technical solution of the present invention.

[0077] The contents not described in detail in the specification of the present invention belong to the common knowledge of the professionals in this field.

Claims

1. A method for calculating flow-induced stress and fatigue life of a bellows, characterized in that: include: Step 1, according to the inner diameter, wave height, number of layers, single layer wall thickness and wave pitch of the bellows, calculate the modal frequencies of each order of the bellows; wherein the modal frequencies of each order include: axial modal frequencies of each order and local bending modal frequencies; Step 2, according to the modal frequencies of the bellows calculated in step 1, combined with the Stuhal number and the wave distance, calculate the excitation flow velocities of the bellows of various modes; Step 3, calculating the flow rate of the medium according to the density and mass flow rate of the medium inside the bellows and the inner diameter cross-sectional area of ​​the bellows; Step 4, calculating the first-order radial acoustic mode frequency of the bellows according to the inner diameter, wave height, average fillet radius and sound velocity of the medium of the bellows; Step 5, comparing the flow velocity of the medium calculated in step 3 with the excitation flow velocity of each order mode of the bellows calculated in step 2; if the flow velocity of the medium reaches or exceeds the excitation flow velocity of a certain order mode of the bellows, it is determined that the certain order mode is excited, and combined with step 1, the frequency of the excited mode is obtained; Step 6, comparing the frequency of the excited mode obtained in step 5 with the first-order radial acoustic mode frequency of the bellows calculated in step 4 to obtain an acoustic resonance result; wherein, if the frequency of the excited mode reaches or exceeds the first-order radial acoustic mode frequency of the bellows, the acoustic resonance result is: there is an acoustic resonance; otherwise, the acoustic resonance result is: there is no acoustic resonance; Step 7, according to the frequency of the excited mode obtained in step 5, combined with step 2, the excited flow velocity of the excited mode is obtained; according to the obtained excited flow velocity of the excited mode, combined with the density of the medium, the pulsating pressure is calculated; Step 8, calculating the cross-sectional area of ​​the bellows according to the outer diameter and inner diameter of the bellows; Step 9, calculating the force of the medium on the bellows according to the pulsating pressure calculated in step 7 and the cross-sectional area of ​​the bellows calculated in step 8; Step 10, calculating the single-wave displacement of the bellows according to the force of the medium on the bellows calculated in step 9 and the single-wave stiffness of the bellows; Step 11, calculating the stress of the bellows according to the single wave displacement of the bellows calculated in step 10; Step 12, according to the acoustic resonance result obtained in step 6, taking into account a certain uncertainty, correcting the stress of the bellows calculated in step 11 to obtain a corrected bellows stress; Step 13, based on the corrected bellows stress calculated in step 12 and the SN curve of the bellows material, the fatigue damage of the bellows under each excitation mode is calculated according to the fixed frequency vibration.

2. The method for calculating flow-induced stress and fatigue life of a bellows according to claim 1, characterized in that: In step 2, the calculation formula for the excitation flow velocity of each order mode of the bellows is as follows: The excitation flow velocity of each mode of the bellows = each mode frequency of the bellows × wave pitch / Stuhal number.

3. The method for calculating flow-induced stress and fatigue life of a bellows according to claim 1, characterized in that: In step 3, the flow rate of the medium is calculated as follows: The flow rate of the medium = the mass flow rate of the medium / the density of the medium / the inner diameter cross-sectional area of ​​the bellows.

4. The method for calculating flow-induced stress and fatigue life of a bellows according to claim 1, characterized in that: In step 7, the pulsating pressure is calculated as follows: Pulsating pressure = 0.5 × medium density × excitation flow rate of the excitation mode 2 .

5. The method for calculating flow-induced stress and fatigue life of a bellows according to claim 1, characterized in that: In step 8, the cross-sectional area of ​​the bellows is calculated as follows: The cross-sectional area of ​​the bellows = π × (outer diameter of the bellows 2 -Inner diameter of the bellows 2 ) / 4.

6. The method for calculating flow-induced stress and fatigue life of a bellows according to claim 1, characterized in that: In step 9, the formula for calculating the force exerted by the medium on the bellows is as follows: The force exerted by the medium on the bellows = pulsating pressure × cross-sectional area of ​​the bellows.

7. The method for calculating flow-induced stress and fatigue life of a bellows according to claim 1, characterized in that: In step 10, the calculation formula of the single wave displacement of the bellows is as follows: The single wave displacement of the bellows = the force exerted by the medium on the bellows / the single wave stiffness of the bellows.

8. The method for calculating flow-induced stress and fatigue life of a bellows according to claim 1, characterized in that: In step 12, the stress of the bellows calculated in step 11 is corrected by the following formula: Corrected bellows stress = bellows stress × amplification factor × uncertainty.

9. The method for calculating flow-induced stress and fatigue life of a bellows according to claim 8, characterized in that: In step 12, if the acoustic resonance is determined to exist according to the acoustic resonance result obtained in step 6, the amplification factor is not equal to 1.

10. The method for calculating flow-induced stress and fatigue life of a bellows according to claim 8, characterized in that: In step 12, if it is determined that there is no acoustic resonance according to the acoustic resonance result obtained in step 6, the amplification factor is equal to 1.

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