Dynamic modeling method for bolt boundary cone-column combined shell under non-uniform temperature field

Abstract

The invention relates to the technical field of dynamics, and discloses a dynamic modeling method for a bolt boundary cone-column combined shell under a non-uniform temperature field, and the method comprises the steps: integrating the temperature dependence of material performance and a thermally induced stress field, developing a nonlinear bolt connection interface model, and considering the dynamic evolution characteristic of a friction coefficient along with the temperature. Accurate characterization of structural dynamic behaviors in a non-uniform thermal environment is realized, a non-uniform temperature field is efficiently reproduced based on a built-in heat source experimental platform, the reliability of a model is verified by combining modal and response tests, and the influence of thermally induced material degradation and an interface stick-slip mechanism on structural rigidity and damping is disclosed. The accuracy of vibration characteristic prediction in a high-temperature environment is improved, algorithm type refined matching is carried out based on the combination information of the static and dynamic waveforms of the track in combination with the artificial intelligence bionic algorithm and the standard waveform information stored by big data, the combination data of the static and dynamic waveform parameters of the track is constructed, and reliable support is provided for algorithm matching.

Description

Technical Field

[0001] The invention relates to the field of dynamics technology, in particular to a dynamics modeling method for a bolt-boundary cone-cylinder composite shell under a non-uniform temperature field. Background Art

[0002] Bolted flange connections are widely used in aerospace, machinery manufacturing, construction, and other fields due to their advantages such as disassembly, easy assembly, and high load-bearing capacity. However, due to the complex and nonlinear mechanical properties of bolted flange connections, their dynamic behavior is difficult to accurately predict using simplified theoretical analysis methods.

[0003] However, existing technologies have several problems: 1. Idealized boundary conditions; 2. Inadequate thermal field characterization; and 3. Lack of a thermal-mechanical coupling mechanism. Therefore, the present invention provides a method for dynamic modeling of bolted-boundary conical-cylinder composite shells under non-uniform temperature fields. These limitations make it difficult to accurately predict the dynamic response of bolted conical-cylinder composite shells under non-uniform temperature fields, hindering the reliability design and vibration control of high-temperature aerospace equipment. There is an urgent need to establish a comprehensive dynamic model that integrates bidirectional temperature gradients, material thermal degradation characteristics, and the nonlinear behavior of bolt interfaces to provide theoretical support for structural safety in extreme thermal environments. Summary of the Invention

[0004] (1) Technical problems solved

[0005] In view of the shortcomings of the existing technology, the present invention provides a dynamic modeling method for a bolt-boundary cone-cylinder composite shell under a non-uniform temperature field, which solves the problems raised in the above background technology.

[0006] (2) Technical solution

[0007] To achieve the above objectives, the present invention provides the following technical solutions: a method for dynamic modeling of a bolted boundary cone-cylinder composite shell under a non-uniform temperature field, comprising the following steps:

[0008] S1. Construct a cone-cylinder composite shell structure model, define the geometric parameters of the cone and cylinder segments and the bolt connection distribution, and establish global and local coordinate systems to represent the displacement field;

[0009] S2. Establish a bidirectional non-uniform temperature field model based on the steady-state heat conduction equation to quantify the axial and radial temperature gradients and the thickness-direction thermal stress distribution;

[0010] S3. Define a temperature-dependent material parameter degradation model and characterize the nonlinear changes of Young's modulus, Poisson's ratio, density and thermal expansion coefficient with temperature through polynomial functions;

[0011] S4. Construct a nonlinear mechanical model of the bolt connection interface, combining the temperature-dependent friction coefficient with the amplitude-dependent equivalent stiffness-damping model to characterize the stick-slip contact characteristics;

[0012] S5. Derive the thermal-mechanical coupling energy equation, integrate the thermal stress effect and geometric nonlinear deformation, and form the dynamic control equation;

[0013] S6. Experimental Verification: Build an experimental platform with a built-in heater to monitor the temperature gradient distribution in real time. Use the hammering method to obtain the frequency response curve from room temperature to high temperature. Inversely identify the bolt connection stiffness parameters. Compare the resonant frequency deviation between the theoretical model and the experimental results, and verify that the error is less than 2.8%;

[0014] S7. Iteratively solve the nonlinear vibration response, dynamically switch the contact state according to the displacement amplitude of the bolt point, update the equivalent stiffness and damping, and obtain the time domain vibration characteristics through numerical integration.

[0015] Preferably, the geometric parameters of the cone segment in step S1 satisfy:

[0016] Minimum radius R o =0.4226R, length Thickness h = 0.01R;

[0017] Cylindrical segment length L y =R, bolt connection points are evenly distributed along the circumference N s =16, preload force F p =12N\cdotpm;

[0018] Among them, R o is the minimum radius of the cone segment, R is the reference radius, L o is the length of the cone section, α is the semi-cone angle of the cone, h is the shell thickness, N s is the number of bolt connection points, F p is the bolt preload.

[0019] Preferably, the temperature gradient distribution in step S2 is determined by eight temperature measurement points:

[0020] The axial gradient measurement points P1-P3 are arranged at the top, connection and bottom of the outer surface, and P4-P6 correspond to the same positions on the inner surface;

[0021] Radial gradient measurement points P7-P8 are arranged at 90° intervals in the middle of the cone section, and the temperature sampling frequency is greater than 1Hz.

[0022] Based on the steady-state heat conduction equation, the temperature gradient distribution along the axial and radial directions is determined, and a linear temperature change function in the thickness direction of the shell is established.

[0023]

[0024] Where λ represents the axial dimensionless coordinate, ΔT is the temperature difference between the inner and outer surfaces, T is the temperature field function, and z T is the thickness direction coordinate, T1(λ) is the inner surface temperature, and h is the shell thickness.

[0025] Preferably, Young's modulus E, Poisson's ratio ν, density ρ and thermal expansion coefficient α T Expressed as a cubic polynomial function of temperature T

[0026] P=P0(P -1 T -1 +1+P1T+P2T 2 +P3T 3 )

[0027] Where P is the temperature-related material parameter, P0, P -1 , P1, P2, P3 are the material temperature correlation coefficients, which are the inherent property parameters of the constituent materials, and T represents the Kelvin temperature;

[0028] The temperature function coefficient of the material parameter in step S3 is:

[0029] E's P0=201.04GPa, P1=3.079×10 -4 ,P2=-6.534×10 -7 ;

[0030] νP0=0.3262,P1=-2.002×10 -4 ,P2=3.797×10 -7 ;

[0031] α T P0 = 12.33 × 10 -6 / ℃,P1=8.086×10 -4 .

[0032] Preferably, the nonlinear contact force model in step S4 is specifically:

[0033] When the displacement amplitude of the bolt connection point γ<γc, the viscous state model is adopted

[0034] f w =K bw (w s -w so )+f w0

[0035] When γ≥γc, the slip state model is adopted

[0036] f w =±μ(T)F p

[0037] Where the critical displacement γc =

[0038]

[0039] Equivalent stiffness

[0040]

[0041] Equivalent damping

[0042]

[0043] Where γ is the displacement amplitude of the bolt connection point, γc is the critical displacement amplitude, and f w is the contact force at the bolt connection point, K bw is the initial stiffness of the bolt connection, w s is the current displacement of the bolt connection point, w so is the initial displacement of the bolt connection point, f w0 is the initial contact force, μ(T) is the temperature-related friction coefficient, F p is the preload force, K eq is the equivalent stiffness, C eq is the equivalent damping, ω is the vibration angular frequency, This is the angle variable that appears in the formula. Its specific meaning needs to be determined based on the model.

[0044] Preferably, the calculation of the thermal stress term in step S5 includes:

[0045] Axial thermal stress

[0046]

[0047] Circumferential thermal stress

[0048]

[0049] Bending thermal stress

[0050]

[0051] Among them, N x τ,T is the resultant axial thermal stress, is the resultant circumferential thermal stress, M x τ,T is the resultant moment of axial bending thermal stress, Q 11 ,Q 12 ,Q 22 is the elastic stiffness coefficient of the material, α T is the thermal expansion coefficient, ΔT is the temperature difference in the thickness direction, z τ is the thickness direction coordinate.

[0052] Preferably, the experimental verification in step S6 specifically includes:

[0053] Equipped with 4 symmetrically distributed quartz heating tubes, heating power 2.5kW, heating rate 3℃ / s;

[0054] The frequency response curve at the η = 0.25 position was collected using a Polytec laser vibrometer with a bandwidth of 750 Hz.

[0055] The first four modal frequencies are identified by frequency domain decomposition method, and the deviation from the theoretical value is controlled within ±3%.

[0056] Preferably, the iterative solution in step S7 includes:

[0057] Initialize all bolt points to a viscous state and calculate the initial response γ0; S82, detect the displacement amplitude γ of each point i ,γ i >γ c It is marked as slip state, where γ i is the displacement amplitude of the i-th bolt connection point, γ c is the critical displacement amplitude;

[0058] Update the K of the sliding point eq and C eq , maintain the sticking point stiffness K b w=2×10 8 N / m, where K b w is the bolt connection stiffness in the viscous state;

[0059] The updated dynamic equations are solved using the variable step-size Runge-Kutta method until the response error between adjacent iterations is less than 1%.

[0060] Preferably, the method further includes a heat source configuration optimization method:

[0061] Automatically adjust the number of quartz tubes N according to the target temperature gradient t ,satisfy The cooling system is started at this time, and the axial temperature difference ΔT is maintained by the PID controller x ≤50℃ / m, radial temperature difference ΔT r ≤30℃, where T1, T2, T4 and T5 are the temperatures of the measuring points.

[0062] Preferably, a nonlinear vibration analysis model is established:

[0063] Constructing an amplitude-frequency response surface function

[0064]

[0065] The damping ratio ζ n(T) = ζ0[1+0.015(T-300)], frequency temperature coefficient ω n (T) = ω n0 [1-β(T-300)],β=2.3×10 -4 / ℃;

[0066] A(ω,T) is the vibration amplitude at angular frequency ω and temperature T, n is the modal order, a n is the amplitude coefficient of the nth-order mode, ω n (T) is the natural angular frequency of the nth mode at temperature T, ζ n (T) is the damping ratio of the nth mode at temperature T, ζ0 is the damping ratio at the reference temperature, ω n0 is the natural angular frequency at the reference temperature, and β is the frequency temperature coefficient.

[0067] (3) Beneficial effects

[0068] Compared with the prior art, the present invention provides a dynamic modeling method for bolted boundary cone-cylinder composite shells under non-uniform temperature fields, which has the following beneficial effects:

[0069] 1. Establish a bidirectional temperature gradient theoretical model

[0070] By integrating the temperature dependence of material properties and thermally induced stress fields, and developing a nonlinear bolt connection interface model, the dynamic evolution of the friction coefficient with temperature is taken into account to accurately characterize the structural dynamic behavior in a non-uniform thermal environment. Based on the built-in heat source experimental platform, the non-uniform temperature field is efficiently reproduced. The reliability of the model is verified by combining modal and response tests, revealing the influence of thermally induced material degradation and interface stick-slip mechanisms on structural stiffness and damping, and improving the accuracy of vibration characteristic prediction in high-temperature environments.

[0071] 2. Realize intelligent screening of track mileage calibration algorithms

[0072] By combining the track geometry static and dynamic waveform combination information with artificial intelligence bionic algorithms and standard waveform information stored in big data, we can perform fine matching of algorithm types, build track geometry static and dynamic waveform parameter combination data, provide reliable support for algorithm matching, and dynamically search for the optimal calibration algorithm type with the Osprey optimization algorithm to improve the accuracy and adaptability of track geometry dynamic waveform mileage calibration.

[0073] 3. Integrated thermal-mechanical coupling model and experimental verification platform

[0074] By constructing a complete framework for predicting the nonlinear vibration of bolted joint structures under non-uniform temperature fields, quantifying the interface friction dissipation and stiffness attenuation effects based on equivalent stiffness and equivalent damping, and combining the collaborative analysis of thermal load and excitation amplitude, effective control and optimization of vibration response can be achieved, significantly improving the structural reliability and vibration reduction design effectiveness in aerospace high-temperature applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0075] Figure 1 It is a schematic diagram of the overall system architecture of the present invention. DETAILED DESCRIPTION

[0076] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0077] See also Figure 1 The method for dynamic modeling of a bolted boundary cone-cylinder composite shell under a non-uniform temperature field includes the following steps:

[0078] S1. Construct a cone-cylinder composite shell structure model, define the geometric parameters of the cone and cylinder segments and the bolt connection distribution, and establish global and local coordinate systems to represent the displacement field;

[0079] S2. Establish a bidirectional non-uniform temperature field model based on the steady-state heat conduction equation to quantify the axial and radial temperature gradients and the thickness-direction thermal stress distribution;

[0080] S3. Define a temperature-dependent material parameter degradation model and characterize the nonlinear changes of Young's modulus, Poisson's ratio, density and thermal expansion coefficient with temperature through polynomial functions;

[0081] S4. Construct a nonlinear mechanical model of the bolt connection interface, combining the temperature-dependent friction coefficient with the amplitude-dependent equivalent stiffness-damping model to characterize the stick-slip contact characteristics;

[0082] S5. Derive the thermal-mechanical coupling energy equation, integrate the thermal stress effect and geometric nonlinear deformation, and form the dynamic control equation;

[0083] S6. Experimental Verification: Build an experimental platform with a built-in heater to monitor the temperature gradient distribution in real time. Use the hammering method to obtain the frequency response curve from room temperature to high temperature. Inversely identify the bolt connection stiffness parameters. Compare the resonant frequency deviation between the theoretical model and the experimental results, and verify that the error is less than 2.8%;

[0084] S7, iteratively solve the nonlinear vibration response, dynamically switch the contact state according to the displacement amplitude of the bolt point, update the equivalent stiffness and damping, and obtain the time domain vibration characteristics through numerical integration;

[0085] The geometric parameters of the cone segment described in step S1 are satisfied;

[0086] Minimum radius R o =0.4226R, length Thickness h = 0.01R;

[0087] Cylindrical segment length L y =R, bolt connection points are evenly distributed along the circumference N s =16, preload force F p =12N\cdotpm;

[0088] Among them, R o is the minimum radius of the cone segment, R is the reference radius, L o is the length of the cone section, α is the semi-cone angle of the cone, h is the shell thickness, N s is the number of bolt connection points, F p is the bolt preload;

[0089] The temperature gradient distribution in step S2 is determined by eight temperature measurement points:

[0090] The axial gradient measurement points P1-P3 are arranged at the top, connection and bottom of the outer surface, and P4-P6 correspond to the same positions on the inner surface;

[0091] Radial gradient measurement points P7-P8 are arranged at 90° intervals in the middle of the cone section, and the temperature sampling frequency is greater than 1Hz.

[0092] Based on the steady-state heat conduction equation, the temperature gradient distribution along the axial and radial directions is determined, and a linear temperature change function in the thickness direction of the shell is established.

[0093]

[0094] Where λ represents the axial dimensionless coordinate, ΔT is the temperature difference between the inner and outer surfaces, T is the temperature field function, and z T is the thickness direction coordinate, T1(λ) is the inner surface temperature, and h is the shell thickness;

[0095] Young's modulus E, Poisson's ratio ν, density ρ and thermal expansion coefficient α T Expressed as a cubic polynomial function of temperature T

[0096] P=P0(P -1 T -1 +1+P1T+P2T 2 +P3T 3 )

[0097] Where P is the temperature-related material parameter, P0, P -1 , P1, P2, P3 are the material temperature correlation coefficients, which are the inherent property parameters of the constituent materials, and T represents the Kelvin temperature;

[0098] The temperature function coefficient of the material parameter in step S3 is:

[0099] E's P0=201.04GPa, P1=3.079×10 -4 ,P2=-6.534×10 -7 ;

[0100] νP0=0.3262,P1=-2.002×10 -4 ,P2=3.797×10 -7 ;

[0101] α T P0 = 12.33 × 10 -6 / ℃,P1=8.086×10 -4 ;

[0102] The nonlinear contact force model in step S4 is specifically:

[0103] When the displacement amplitude of the bolt connection point γ<γc, the viscous state model is adopted

[0104] f w =K bw (w s -w so )+f w0

[0105] When γ≥γc, the slip state model is adopted

[0106] f w =±μ(T)F p

[0107] Where the critical displacement γc =

[0108]

[0109] Equivalent stiffness

[0110]

[0111] Equivalent damping

[0112]

[0113] Where γ is the displacement amplitude of the bolt connection point, γc is the critical displacement amplitude, and f w is the contact force at the bolt connection point, K bwis the initial stiffness of the bolt connection, w s is the current displacement of the bolt connection point, w so is the initial displacement of the bolt connection point, f w0 is the initial contact force, μ(T) is the temperature-related friction coefficient, F p is the preload force, K eq is the equivalent stiffness, C eq is the equivalent damping, ω is the vibration angular frequency, It is the angle variable that appears in the formula, and its specific meaning needs to be determined according to the model;

[0114] The thermal stress calculation in step S5 includes:

[0115] Axial thermal stress

[0116]

[0117] Circumferential thermal stress

[0118]

[0119] Bending thermal stress

[0120]

[0121] Among them, N x τ,T is the resultant axial thermal stress, is the resultant circumferential thermal stress, M x τ,T is the resultant moment of axial bending thermal stress, Q 11 ,Q 12 ,Q 22 is the elastic stiffness coefficient of the material, α T is the thermal expansion coefficient, ΔT is the temperature difference in the thickness direction, z τ is the thickness direction coordinate;

[0122] Step S6 experimental verification specifically includes:

[0123] Equipped with 4 symmetrically distributed quartz heating tubes, heating power 2.5kW, heating rate 3℃ / s;

[0124] The frequency response curve at the η = 0.25 position was collected using a Polytec laser vibrometer with a bandwidth of 750 Hz.

[0125] The first four modal frequencies were identified by frequency domain decomposition method, and the deviation from the theoretical value was controlled within ±3%;

[0126] The iterative solution in step S7 includes:

[0127] Initialize all bolt points to a viscous state and calculate the initial response γ0; S82, detect the displacement amplitude γ of each point i ,γ i >γ c It is marked as slip state, where γ i is the displacement amplitude of the i-th bolt connection point, γ c is the critical displacement amplitude;

[0128] Update the K of the sliding point eq and C eq , maintain the sticking point stiffness K b w=2×10 8 N / m, where K b w is the bolt connection stiffness in the viscous state;

[0129] The updated dynamic equations are solved using the variable step-size Runge-Kutta method until the error between adjacent iteration responses is less than 1%.

[0130] Also includes heat source configuration optimization methods:

[0131] Automatically adjust the number of quartz tubes N according to the target temperature gradient t ,satisfy The cooling system is started at this time, and the axial temperature difference ΔT is maintained by the PID controller x ≤50℃ / m, radial temperature difference ΔT r ≤30℃, where T1, T2, T4, and T5 are the temperatures at the measuring points;

[0132] Establish a nonlinear vibration analysis model:

[0133] Constructing an amplitude-frequency response surface function

[0134]

[0135] The damping ratio ζ n (T) = ζ0[1+0.015(T-300)], frequency temperature coefficient ω n (T) = ω n0 [1-β(T-300)],β=2.3×10 -4 / ℃;

[0136] A(ω,T) is the vibration amplitude at angular frequency ω and temperature T, n is the modal order, a n is the amplitude coefficient of the nth-order mode, ω n (T) is the natural angular frequency of the nth mode at temperature T, ζ n (T) is the damping ratio of the nth mode at temperature T, ζ0 is the damping ratio at the reference temperature, ω n0 is the natural angular frequency at the reference temperature, and β is the frequency temperature coefficient.

[0137] Example 1: Experiment on the influence of bolt preload on high temperature vibration characteristics

[0138] 1. Variable parameter experimental design:

[0139] Set three groups of bolt preload conditions:

[0140] Working condition A: standard preload force 12N·m;

[0141] Working condition B: under preload 8N·m;

[0142] Working condition C: over preload 16N·m;

[0143] Constant thermal environment: built-in 4 1500W heating tubes, maintaining the connection temperature at 300℃;

[0144] Excitation settings: sweep frequency 300 Hz, acceleration amplitude step change.

[0145] 2. Preload-temperature coupling effect test:

[0146] Natural frequency attenuation characteristics:

[0147]

[0148] Where Δf is the natural frequency attenuation percentage, f 25℃ is the natural frequency at room temperature, f 300℃ is the natural frequency at high temperature;

[0149] Condition A: attenuation 3.6%;

[0150] Condition B: attenuation 6.1%;

[0151] Condition C: attenuation 2.3%;

[0152] Critical slip displacement change:

[0153]

[0154] Among them, γ crit is the critical slip displacement, μ(T) is the temperature-related friction coefficient, F p is the bolt preload, K bw is the radial stiffness of the bolt connection;

[0155] At 300℃, μ(300)=0.22,γ crit It dropped from 12.7μm in working condition A to 8.5μm in working condition B.

[0156] 3. Nonlinear response analysis

[0157] Resonance amplitude comparison:

[0158]

[0159] Dynamic softening phenomenon:

[0160] Under 5g excitation, the resonance peak of working condition B shifts to the left by 18Hz;

[0161] Working condition C maintains linear characteristics, and the resonance frequency shift is <2Hz;

[0162] 4. Characterization of energy dissipation mechanism

[0163] Equivalent damping ratio change:

[0164] Calculation result C eq =1.7×10 5 N·s / m, improved compared with working condition A;

[0165] Friction power consumption ratio:

[0166]

[0167] Among them, η diss is the percentage of friction energy consumed in the total vibration energy, f w is the radial constraint force of the bolt, ω is the excitation angular frequency, m is the equivalent mass, and γ is the displacement amplitude;

[0168] Working condition B reached 52.3%.

[0169] 5. Engineering optimization verification

[0170] Application in the conical column connection section of a certain type of rocket fuel delivery pipe:

[0171] Original design: preload force 10N·m, amplitude 0.38mm at 300℃;

[0172] Optimization solution: increased to 14N·m, amplitude reduced to 0.21mm;

[0173] Fatigue life: increased from 1.2×106 times to 2.5×106 times.

[0174] Example 2: Experiment on the influence of heat source intensity on vibration characteristics

[0175] 1. Variable parameter test design

[0176] Set three groups of heat source configurations: N t =4, N t =2, N t =1

[0177] Control variables: Bolt preload 12 N·m, excitation amplitude 1 g

[0178] 2. Thermal-vibration coupling response results

[0179] Temperature evolution: N t = 4 hours 400 seconds to 200℃; N t =1 hour 1200 seconds only reaches 102.9℃

[0180] Frequency attenuation rate:

[0181]

[0182] N t =4: First-order frequency attenuation 3.6%

[0183] N t =1: first-order frequency attenuation 1.4%

[0184] Resonance amplitude amplification effect: N at 200℃ t =4 groups with amplitude N t = 2.3 times of 1 group

[0185] 3. Characterization of nonlinear behavior

[0186] Typical soft spring characteristics appear at high excitation amplitudes

[0187] The resonance peak at 300Hz is shifted 12Hz to the left

[0188] Thermal environment expands the nonlinear range to ±25Hz

[0189] Energy dissipation at the bolt interface:

[0190] At 300℃, friction power consumption accounts for 35.7% of kinetic energy

[0191] Slip phase angle lag 52°

[0192] Example 3: Engineering application verification

[0193] This model was implemented in the cone-column connection section of a certain type of aircraft engine nacelle:

[0194] 1. Calculate thermal stress distribution based on measured temperature field

[0195] 2. Dynamic identification of bolt equivalent stiffness K eq , optimize the preload to 20N-m

[0196] 3. Result: Reduced vibration amplitude under high temperature conditions, and fatigue life increased to 2.8 times the original design

[0197] It should be noted that, in this document, relational terms such as first and second, etc., are used only to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply the existence of any such actual relationship or order between these entities or operations. Moreover, the terms "comprises," "comprising," or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article, or device comprising a series of elements includes not only those elements, but also other elements not explicitly listed, or elements inherent to such process, method, article, or device. In the absence of further limitations, an element defined by the phrase "comprising a ..." does not exclude the presence of other identical elements in the process, method, article, or device comprising the element.

[0198] While embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions, and variations may be made to these embodiments without departing from the principles and spirit of the invention, and that the scope of the invention is defined by the appended claims and their equivalents.

Claims

1. A dynamic modeling method for bolted boundary cone-cylinder composite shell under non-uniform temperature field, characterized by: The following steps are involved: S1. Construct a cone-cylinder composite shell structure model, define the geometric parameters of the cone and cylinder segments and the bolt connection distribution, and establish global and local coordinate systems to represent the displacement field; S2. Establish a bidirectional non-uniform temperature field model based on the steady-state heat conduction equation to quantify the axial and radial temperature gradients and the thickness-direction thermal stress distribution; S3. Define a temperature-dependent material parameter degradation model and characterize the nonlinear changes of Young's modulus, Poisson's ratio, density and thermal expansion coefficient with temperature through polynomial functions; S4. Construct a nonlinear mechanical model of the bolt connection interface, combining the temperature-dependent friction coefficient with the amplitude-dependent equivalent stiffness-damping model to characterize the stick-slip contact characteristics; S5. Derive the thermal-mechanical coupling energy equation, integrate the thermal stress effect and geometric nonlinear deformation, and form the dynamic control equation; S6. Experimental Verification: Build an experimental platform with a built-in heater to monitor the temperature gradient distribution in real time. Use the hammering method to obtain the frequency response curve from room temperature to high temperature. Inversely identify the bolt connection stiffness parameters. Compare the resonant frequency deviation between the theoretical model and the experimental results, and verify that the error is less than 2.8%; S7. Iteratively solve the nonlinear vibration response, dynamically switch the contact state according to the displacement amplitude of the bolt point, update the equivalent stiffness and damping, and obtain the time domain vibration characteristics through numerical integration.

2. The method for dynamic modeling of a bolted-boundary cone-cylinder composite shell under a non-uniform temperature field according to claim 1, characterized in that: The geometric parameters of the cone segment described in step S1 are satisfied; Minimum radius R o =0.4226R, length Thickness h = 0.01R; Cylindrical segment length L y =R, bolt connection points are evenly distributed along the circumference N s =16, preload force F p =12N\cdotpm; Among them, R o is the minimum radius of the cone segment, R is the reference radius, L o is the length of the cone section, α is the semi-cone angle of the cone, h is the shell thickness, N s is the number of bolt connection points, F p is the bolt preload, and cdotpm represents the substance concentration per unit area.

3. The method for dynamic modeling of a bolted-boundary cone-cylinder composite shell under a non-uniform temperature field according to claim 1, characterized in that: The temperature gradient distribution in step S2 is determined by eight temperature measurement points: The axial gradient measurement points P1-P3 are arranged at the top, connection and bottom of the outer surface, and P4-P6 correspond to the same positions on the inner surface; Radial gradient measurement points P7-P8 are arranged at 90° intervals in the middle of the cone section, and the temperature sampling frequency is greater than 1Hz. Based on the steady-state heat conduction equation, the temperature gradient distribution along the axial and radial directions is determined, and a linear temperature change function in the thickness direction of the shell is established. Where λ represents the axial dimensionless coordinate, ΔT is the temperature difference between the inner and outer surfaces, T is the temperature field function, and z T is the thickness direction coordinate, T1(λ) is the inner surface temperature, and h is the shell thickness.

4. The method for dynamic modeling of a bolted-boundary cone-cylinder composite shell under a non-uniform temperature field according to claim 1, characterized in that: Young's modulus E, Poisson's ratio ν, density ρ and thermal expansion coefficient α T Expressed as a cubic polynomial function of temperature T P=P0(P -1 T -1 +1+P1T+P2T 2 +P3T 3 ) Where P is the temperature-related material parameter, P0, P -1 , P1, P2, P3 are the material temperature correlation coefficients, which are the inherent property parameters of the constituent materials, and T represents the Kelvin temperature; The temperature function coefficient of the material parameter in step S3 is: E's P0=201.04GPa, P1=3.079×10 -4 ,P2=-6.534×10 -7 ; νP0=0.3262,P1=-2.002×10 -4 ,P2=3.797×10 -7 ; α T P0 = 12.33 × 10 -6 / ℃,P1=8.086×10 -4 .

5. The method for dynamic modeling of a bolted-boundary cone-cylinder composite shell under a non-uniform temperature field according to claim 1, characterized in that: The nonlinear contact force model in step S4 is specifically: When the displacement amplitude of the bolt connection point γ<γc, the viscous state model is adopted f w =K bw (w s -w so )+f w0 When γ≥γc, the slip state model is adopted f w =±μ(T)F p Where the critical displacement γc = Equivalent stiffness Equivalent damping Where γ is the displacement amplitude of the bolt connection point, γc is the critical displacement amplitude, and f w is the contact force at the bolt connection point, K bw is the initial stiffness of the bolt connection, w s is the current displacement of the bolt connection point, w so is the initial displacement of the bolt connection point, f w0 is the initial contact force, μ(T) is the temperature-related friction coefficient, F p is the preload force, K eq is the equivalent stiffness, C eq is the equivalent damping, ω is the vibration angular frequency, This is the angle variable that appears in the formula. Its specific meaning needs to be determined based on the model.

6. The method for dynamic modeling of a bolted-boundary cone-cylinder composite shell under a non-uniform temperature field according to claim 1, characterized in that: The thermal stress calculation in step S5 includes: Axial thermal stress Circumferential thermal stress Bending thermal stress in, is the resultant axial thermal stress, is the resultant circumferential thermal stress, is the resultant moment of axial bending thermal stress, Q 11 ,Q 12 ,Q 22 is the elastic stiffness coefficient of the material, α T is the thermal expansion coefficient, ΔT is the temperature difference in the thickness direction, z τ is the thickness direction coordinate.

7. The bolt boundary cone-column combination under non-uniform temperature field according to claim 1 Shell dynamics modeling method, characterized by: Step S6 experimental verification specifically includes: Equipped with 4 symmetrically distributed quartz heating tubes, heating power 2.5kW, heating rate 3℃ / s; The frequency response curve at the η = 0.25 position was collected using a Polytec laser vibrometer with a bandwidth of 750 Hz. The first four modal frequencies are identified by frequency domain decomposition method, and the deviation from the theoretical value is controlled within ±3%.

8. The method for dynamic modeling of a bolted-boundary cone-cylinder composite shell under a non-uniform temperature field according to claim 1, characterized in that: The iterative solution in step S7 includes: Initialize all bolt points to a viscous state and calculate the initial response γ0; S82, detect the displacement amplitude γ of each point i ,γ i >γ c It is marked as slip state, where γ i is the displacement amplitude of the i-th bolt connection point, γ c is the critical displacement amplitude; Update the K of the sliding point eq and C eq , maintain the sticking point stiffness K b w=2×10 8 N / m, where K b w is the bolt connection stiffness in the viscous state; The updated dynamic equations are solved using the variable step-size Runge-Kutta method until the response error between adjacent iterations is less than 1%.

9. The method for dynamic modeling of a bolted-boundary cone-cylinder composite shell under a non-uniform temperature field according to claim 1, characterized in that: Also includes heat source configuration optimization methods: Automatically adjust the number of quartz tubes N according to the target temperature gradient t ,satisfy The cooling system is started at this time, and the axial temperature difference ΔT is maintained by the PID controller x ≤50℃ / m, radial temperature difference ΔT r ≤30℃, where T1, T2, T4 and T5 are the temperatures of the measuring points.

10. The method for dynamic modeling of a bolted-boundary cone-cylinder composite shell under a non-uniform temperature field according to claim 1, characterized in that: Establish a nonlinear vibration analysis model: Constructing an amplitude-frequency response surface function The damping ratio ζ n (T) = ζ0[1+0.015(T-300)], frequency temperature coefficient ω n (T) = ω n0 [1-β(T-300)],β=2.3×10 -4 / ℃; A(ω,T) is the vibration amplitude at angular frequency ω and temperature T, n is the modal order, a n is the amplitude coefficient of the nth-order mode, ω n (T) is the natural angular frequency of the nth mode at temperature T, ζ n (T) is the damping ratio of the nth mode at temperature T, ζ0 is the damping ratio at the reference temperature, ω n0 is the natural angular frequency at the reference temperature, and β is the frequency temperature coefficient.

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