Multiaxial Fatigue Analysis of Connecting Bolt at High-Speed Train Axle Box under Structural Subharmonic Resonance
<p>Structure of the axle box of high-speed train.</p> "> Figure 2
<p>Vibration test bench.</p> "> Figure 3
<p>Vertical vibration characteristics of the front cover in bench test. (<b>a</b>) Time-domain signal of acceleration; (<b>b</b>) time-frequency analysis result; (<b>c</b>) jump phenomenon in acceleration process (amplification of the signal in box 1 of <a href="#sensors-23-07962-f003" class="html-fig">Figure 3</a>a); (<b>d</b>) jump phenomenon in deceleration process (amplification of the signal in box 2 of <a href="#sensors-23-07962-f003" class="html-fig">Figure 3</a>a).</p> "> Figure 4
<p>Spectral analysis results of vertical vibration signals of the front cover. Excitation frequency of 20th-order polygonization was (<b>a</b>) 550 Hz under wheel radial deviation of 0.075 mm; (<b>b</b>) 280 Hz under wheel radial deviation of 0.1 mm.</p> "> Figure 5
<p>Frequency response curve of linear and nonlinear system.</p> "> Figure 6
<p>Frequency-response curve of the governing Equation (5).</p> "> Figure 7
<p>Vertical acceleration signals of the front cover. (<b>a</b>) Test signal; (<b>b</b>) the optimal number of mode decomposition.</p> "> Figure 8
<p>VMD results of the test signal.</p> "> Figure 9
<p>Comparison of the experimental and numerical signal.</p> "> Figure 10
<p>HHT of (<b>a</b>) test signal and (<b>b</b>) numerical signal.</p> "> Figure 11
<p>Effect of multiple parameters on vertical resonance of the front cover. (<b>a</b>) Effect of excitation amplitude and linear damping; (<b>b</b>) effect of nonlinear terms.</p> "> Figure 12
<p>Axial stress measuring bolt.</p> "> Figure 13
<p>Multiaxial acceleration excitations in time domain and frequency domain. (<b>a</b>) Longitudinal excitation; (<b>b</b>) lateral excitation; (<b>c</b>) vertical excitation.</p> "> Figure 14
<p>Time history of the bolt axial stress.</p> "> Figure 15
<p>OMA results of the bolted front cover. (<b>a</b>) The analytical model composed of the acceleration measuring points; (<b>b</b>) the first-order mode.</p> "> Figure 16
<p>(<b>a</b>) FE model of the front cover; (<b>b</b>) stress distribution of the preloaded bolt.</p> "> Figure 17
<p>Modal analysis results of the front cover and bolts. (<b>a</b>) the first-order mode; (<b>b</b>) the second-order mode.</p> "> Figure 18
<p>(<b>a</b>–<b>c</b>) represent vertical acceleration FRFs of the front cover under the excitation of longitudinal load, lateral load, and vertical load, respectively; (<b>d</b>–<b>f</b>) represent axial stress FRFs at bolt shank under the excitation of longitudinal load, lateral load, and vertical load, respectively.</p> "> Figure 19
<p>Comparison between the experimental and numerical results. (<b>a</b>,<b>b</b>) are time domain signals of the front cover and bolt, respectively; (<b>c</b>,<b>d</b>) are frequency domain signals of the front cover and bolt, respectively.</p> "> Figure 20
<p>(<b>a</b>–<b>c</b>) represent transverse stress FRFs at thread root under the excitation of longitudinal load, lateral load, and vertical load, respectively; (<b>d</b>–<b>f</b>) represent axial stress FRFs at thread root under the excitation of longitudinal load, lateral load, and vertical load, respectively.</p> "> Figure 21
<p><b>Dynamic stress simulation results and local amplification.</b> (<b>a</b>) transverse dynamic stress and (<b>b</b>) axial dynamic stress at thread root.</p> "> Figure 22
<p>Rain-flow count results for (<b>a</b>) transverse stress time history and (<b>b</b>) axial stress time history of node 233773.</p> "> Figure 23
<p>Transverse stress at the thread root and local amplification when there was no wheel polygonization.</p> ">
Abstract
:1. Introduction
1.1. Literature Survey
1.2. Research Background and Method
2. Assessment for Effectiveness of Common Prevention Method
2.1. Dynamic Characteristics of the Bolted Front Cover under Condition of Wheel Polygonization
2.1.1. Subharmonic Resonance
2.1.2. Superharmonic Resonance
2.1.3. Jump Phenomenon
2.2. Nonlinear Modeling of the Bolted Front Cover
2.3. Effect of Multiple Parameters on Structural Subharmonic Resonance
2.3.1. Parameter Setting
2.3.2. Comparison between the Test Signal and Numerical Signal
2.3.3. Qualitative Analysis for Effect of Multiple Parameters
2.3.4. Evaluation of the Common Prevention Methods
3. Feasibility Analysis for the Stress Simulation Method
3.1. Theoretical Background of the Stress Simulation Method
3.2. Acquisition of Vibration Signals
3.2.1. Fabrication and Calibration of Axial Load Measuring Bolt
3.2.2. Measurement of Multiaxial Excitations and Bolt Axial Load Variation
3.2.3. Modal Test of the Front Cover
3.3. Finite Element Analysis
3.3.1. Finite Element Modeling
3.3.2. Modal Analysis
3.3.3. FRF Calculation
3.4. Acceleration and Stress Simulation of the Bolted Front Cover
4. Analysis of Multiaxial Fatigue Behavior of Connecting Bolt
4.1. Calculation of Dynamic Stress at Bolt Thread
4.2. Analysis of Bolt Fatigue Strength
4.2.1. Criteria of Stresses Combination and Fatigue Life Calculation
4.2.2. Fatigue Life Prediction of Bolt
5. Method for Improving Fatigue Life of Connecting Bolt
6. Conclusions
- The SODF nonlinear modeling method is reasonable for the bolted front cover. The common prevention methods for bolt failure were theoretically proved ineffective under structural subharmonic resonance of order 1/2.
- The results of bolt stress measurement show that the dynamic behaviors of bolt under a nonlinear vibration state should be assessed due to the increasing of bolt stress.
- Although the vibration amplitude of the front cover in the direction of the bolt axis was small, the axial resonance stress at the bolt thread’s root could not be neglected due to the first-order bending modes of bolts.
- Feasibility of the linear stress simulation method was proved in terms of the transverse stiffness and axial stiffness of the bolted joint. It indicated that the method was accurate enough to simulate the subharmonic resonance stress of bolts even if the nonlinearity of the bolted joint was ignored.
- Resonance stresses at the root of the first engaged bolt thread were much larger than the resonance stress at the bolt shank, and the axial resonance stress was more predominant at the bolt thread than the transverse resonance stress.
- Since the multiaxial stresses were caused by the homologous excitations, the octahedral shear stress criterion was suitable for equivalent stress calculation. The fatigue life of the bolt was about 26.8 h, which means that the connecting bolts were prone to multiaxial fatigue failure when the front cover was in subharmonic resonance of order 1/2 for a long time.
- The fatigue life of the bolts is greatly improved when the front cover is not in subharmonic resonance. Consequently, the probability of fatigue failure of bolts could be reduced effectively by shortening the reprofiling interval to reduce the wear of the polygon.
Author Contributions
Funding
Institutional Review Board Statement
Data Availability Statement
Conflicts of Interest
Nomenclature
EMA | Experimental modal analysis | the imaginary part of H(Ω) | |
EMD | empirical mode decomposition | HHT | Hilbert-Huang transform |
f(n) | the discrete acceleration excitation signal | IMF | intrinsic mode functions |
F(Ω) | FFT result of f(n) | ke | number of external loadings |
the real part of F(Ω) | MAPE | mean absolute percentage error | |
the imaginary part of F(Ω) | N | length of f(n) | |
FE | finite element | OMA | operational modal analysis |
FEA | finite element analysis | SDOF | single degree of freedom |
FEM | finite element method | STFT | short-time Fourier transform |
FRF | frequency response function | S-N | stress-number of cycles |
FFT | fast Fourier transform | VMD | variational mode decomposition |
H(Ω) | the acceleration-stress FRF | frequency domain signal of simulation stress | |
the real part of H(Ω) | time domain signal of simulation stress |
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Curve Number | Linear Damping Coefficient μ | Excitation Amplitude k (g) | Nonlinear Coefficients | Initial Condition x0 | ||
---|---|---|---|---|---|---|
α2 | α3 | α4 | ||||
O | 4.3 | 20 | −4.6 | 5 | 3 | (0.03 0.1) |
μ | 3.5 | 20 | −4.6 | 5 | 3 | (0.03 0.1) |
k | 4.3 | 12 | −4.6 | 5 | 3 | (0.03 0.1) |
α2 | 4.3 | 20 | −7 | 5 | 3 | (0.03 0.1) |
α3 | 4.3 | 20 | −4.6 | 8 | 3 | (0.03 0.1) |
α4 | 4.3 | 20 | −4.6 | 5 | 4.4 | (0.03 0.1) |
x0 | 2 | 20 | −4.6 | 5 | 3 | (0 0) |
Mode | 1 | 2 | 3 | 4 |
---|---|---|---|---|
Frequency (Hz) | 274.52 | 276.51 | 394.80 | 614.65 |
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Feng, Y.; Li, F.; Shu, K.; Dai, H. Multiaxial Fatigue Analysis of Connecting Bolt at High-Speed Train Axle Box under Structural Subharmonic Resonance. Sensors 2023, 23, 7962. https://doi.org/10.3390/s23187962
Feng Y, Li F, Shu K, Dai H. Multiaxial Fatigue Analysis of Connecting Bolt at High-Speed Train Axle Box under Structural Subharmonic Resonance. Sensors. 2023; 23(18):7962. https://doi.org/10.3390/s23187962
Chicago/Turabian StyleFeng, Yaqin, Fansong Li, Kang Shu, and Huanyun Dai. 2023. "Multiaxial Fatigue Analysis of Connecting Bolt at High-Speed Train Axle Box under Structural Subharmonic Resonance" Sensors 23, no. 18: 7962. https://doi.org/10.3390/s23187962
APA StyleFeng, Y., Li, F., Shu, K., & Dai, H. (2023). Multiaxial Fatigue Analysis of Connecting Bolt at High-Speed Train Axle Box under Structural Subharmonic Resonance. Sensors, 23(18), 7962. https://doi.org/10.3390/s23187962