Random Vibration Fatigue Analysis Using a Nonlinear Cumulative Damage Model
Abstract
:Featured Application
Abstract
1. Introduction
2. Theorical Background
2.1. Random Vibration
2.2. Nonlinear Fatigue Damage Accumulation
3. Modified Nonlinear Fatigue Damage Accumulation Model Considering the Vibration Load Effect
3.1. Calculating the Bending Stress
3.2. Vibration Cycle Counting
3.3. Total Cycle Determination
4. Fatigue Damage Accumulation Procedure
4.1. Study Case
4.2. Bending Stress
4.3. Vibration Cycles Counting
4.4. Total Cycles Determination
4.5. Fatigue Damage Accumulation
5. Conclusions
- (1)
- Since the inputs for the nonlinear model are the response acceleration’s values, and because, by using the dynamic factor , the vibration bending stresses’ values can be determined, then the proposed model can be applied in any mechanical component analysis submitted to random vibration forces where values are known.
- (2)
- Since the dynamic factor allows us to obtain stress units from acceleration units, then the vibration bending stress values can be used in the proposed model Equation (14) to calculate the fatigue damage accumulation induced by the random vibration.
- (3)
- The constant exponent parameter value of 0.4 in the Manson–Halford model has been replaced by a vibration bending stress relation that considers the effect sequence and interaction loads induced by the applied PSD.
- (4)
- As a result of the mechanical component case study, the model proposed to predict the fatigue damage accumulation shows good agreement with the reported experimental data. The model predicts 28 cycles of load to reach the failure (D = 1), and the experiment data collected from the vibration shaker showing, after 28 cycles of load, the deformation on the component’s material can be considered as a failure.
- (5)
- The efficiency of the model proposed offers the advantage that even though random vibration (PSD) provides a complex loading history, based on the corresponding PSD, it is possible to obtain the fatigue damage accumulation through general analysis.
- (6)
- Since the proposed method is based on the bending stress induced by random vibration PSD function and its response acceleration, then, knowing that the fatigue damage accumulation can also be analyzed from a strain and crack growth propagation point of view, it seems that the proposed model could also be used in those cases, but more research must be undertaken.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Rainflow Cycles | ||
---|---|---|
Path | Cycles | Stress Span |
A–B | 0.5 | 2 |
B–C | 0.5 | 3 |
C–D | 0.5 | 5 |
E–F | 1 | 2 |
Frequency (Hz) | Accel. (G) | Accel. (G2/Hz) |
---|---|---|
10 | 0.210 | 0.004 |
20 | 0.666 | 0.022 |
30 | 1.383 | 0.063 |
40 | 2.359 | 0.139 |
50 | 3.900 | 0.300 |
55 | 4.664 | 0.400 |
Frequency (Hz) | Accel. Base Input (G) | Accel. Response (G) |
---|---|---|
10 | 0.21 | 0.69 |
20 | 0.67 | 3.06 |
30 | 1.38 | 5.58 |
40 | 2.36 | 9.09 |
50 | 3.90 | 13.68 |
55 | 4.66 | 12.31 |
Frequency (Hz) | Accel. Response (G) | Dynamic Factor Equation (22) | Bending Stress Equation (24) |
---|---|---|---|
10 | 0.69 | 22.22 | 15.33 |
20 | 3.06 | 67.97 | |
30 | 5.58 | 123.95 | |
40 | 9.09 | 201.91 | |
50 | 13.68 | 303.87 | |
55 | 12.31 | 273.44 |
Frequency (Hz) | |
---|---|
10 | 70,292 |
20 | 140,210 |
30 | 92,650 |
40 | 10,869 |
50 | 3010 |
55 | 816 |
Frequency (Hz) | Bending Stress Equation (24) | Total Cycle Equation (29) |
---|---|---|
10 | 15.33 | 2.24 × 1020 |
20 | 67.97 | 5.60 × 1012 |
30 | 123.95 | 4.81 × 109 |
40 | 201.91 | 1.55 × 107 |
50 | 303.87 | 1.27 × 105 |
55 | 273.44 | 4.40 × 105 |
10 Hz | 20 Hz | 30 Hz | 40 Hz | 50 Hz | 55 Hz | |
---|---|---|---|---|---|---|
Block No. | D1 | D1+2 | D1+2+3 | D1+2+3+4 | D1+2+3+4+5 | D1+2+3+4+5+6 |
1 (2 h) | 3.14 × 10−16 | 3.14 × 10−16 | 3.16 × 10−16 | 3.44 × 10−16 | 2.36 × 10−2 | 2.41 × 10−2 |
2 (2 h) | 2.41 × 10−2 | 2.41 × 10−2 | 2.42 × 10−2 | 2.46 × 10−2 | 4.83 × 10−2 | 4.90 × 10−2 |
3 (2 h) | 4.90 × 10−2 | 4.90 × 10−2 | 4.93 × 10−2 | 5.01 × 10−2 | 7.37 × 10−2 | 7.48 × 10−2 |
4 (2 h) | 7.48 × 10−2 | 7.48 × 10−2 | 7.53 × 10−2 | 7.64 × 10−2 | 1.00 × 10−1 | 1.01 × 10−1 |
5 (2 h) | 1.01 × 10−1 | 1.01 × 10−1 | 1.02 × 10−1 | 1.04 × 10−1 | 1.27 × 10−1 | 1.29 × 10−1 |
6 (2 h) | 1.29 × 10−1 | 1.29 × 10−1 | 1.30 × 10−1 | 1.32 × 10−1 | 1.55 × 10−1 | 1.57 × 10−1 |
7 (2 h) | 1.57 × 10−1 | 1.57 × 10−1 | 1.58 × 10−1 | 1.60 × 10−1 | 1.84 × 10−1 | 1.86 × 10−1 |
8 (2 h) | 1.86 × 10−1 | 1.86 × 10−1 | 1.87 × 10−1 | 1.90 × 10−1 | 2.14 × 10−1 | 2.16 × 10−1 |
9 (2 h) | 2.16 × 10−1 | 2.16 × 10−1 | 2.17 × 10−1 | 2.20 × 10−1 | 2.44 × 10−1 | 2.47 × 10−1 |
10 (2 h) | 2.47 × 10−1 | 2.47 × 10−1 | 2.48 × 10−1 | 2.52 × 10−1 | 2.75 × 10−1 | 2.78 × 10−1 |
11 (2 h) | 2.78 × 10−1 | 2.78 × 10−1 | 2.80 × 10−1 | 2.84 × 10−1 | 3.08 × 10−1 | 3.11 × 10−1 |
12 (2 h) | 3.11 × 10−1 | 3.11 × 10−1 | 3.13 × 10−1 | 3.17 × 10−1 | 3.41 × 10−1 | 3.44 × 10−1 |
13 (2 h) | 3.44 × 10−1 | 3.44 × 10−1 | 3.46 × 10−1 | 3.51 × 10−1 | 3.75 × 10−1 | 3.78 × 10−1 |
14 (2 h) | 3.78 × 10−1 | 3.78 × 10−1 | 3.81 × 10−1 | 3.86 × 10−1 | 4.10 × 10−1 | 4.13 × 10−1 |
15 (2 h) | 4.13 × 10−1 | 4.13 × 10−1 | 4.16 × 10−1 | 4.22 × 10−1 | 4.45 × 10−1 | 4.49 × 10−1 |
16 (2 h) | 4.49 × 10−1 | 4.49 × 10−1 | 4.52 × 10−1 | 4.59 × 10−1 | 4.82 × 10−1 | 4.87 × 10−1 |
17 (2 h) | 4.87 × 10−1 | 4.87 × 10−1 | 4.90 × 10−1 | 4.96 × 10−1 | 5.20 × 10−1 | 5.25 × 10−1 |
18 (2 h) | 5.25 × 10−1 | 5.25 × 10−1 | 5.28 × 10−1 | 5.35 × 10−1 | 5.59 × 10−1 | 5.25 × 10−1 |
19 (2 h) | 5.25 × 10−1 | 5.25 × 10−1 | 5.67 × 10−1 | 5.75 × 10−1 | 5.99 × 10−1 | 6.04 × 10−1 |
20 (2 h) | 6.04 × 10−1 | 6.04 × 10−1 | 6.07 × 10−1 | 6.16 × 10−1 | 6.39 × 10−1 | 6.45 × 10−1 |
21 (2 h) | 6.45 × 10−1 | 6.45 × 10−1 | 6.49 × 10−1 | 6.58 × 10−1 | 6.81 × 10−1 | 6.87 × 10−1 |
22 (2 h) | 6.87 × 10−1 | 6.87 × 10−1 | 6.91 × 10−1 | 7.01 × 10−1 | 7.24 × 10−1 | 7.30 × 10−1 |
23 (2 h) | 7.30 × 10−1 | 7.30 × 10−1 | 7.35 × 10−1 | 7.45 × 10−1 | 7.68 × 10−1 | 7.74 × 10−1 |
24 (2 h) | 7.74 × 10−1 | 7.74 × 10−1 | 7.79 × 10−1 | 7.90 × 10−1 | 8.13 × 10−1 | 8.20 × 10−1 |
25 (2 h) | 8.20 × 10−1 | 8.20 × 10−1 | 8.25 × 10−1 | 8.36 × 10−1 | 8.60 × 10−1 | 8.66 × 10−1 |
26 (2 h) | 8.66 × 10−1 | 8.66 × 10−1 | 8.72 × 10−1 | 8.83 × 10−1 | 9.07 × 10−1 | 9.14 × 10−1 |
27 (2 h) | 9.14 × 10−1 | 9.14 × 10−1 | 9.20 × 10−1 | 9.32 × 10−1 | 9.56 × 10−1 | 9.63 × 10−1 |
28 (2 h) | 9.63 × 10−1 | 9.63 × 10−1 | 9.69 × 10−1 | 9.82 × 10−1 | 1.01 × 100 | 1.01 × 100 |
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Barraza-Contreras, J.M.; Piña-Monarrez, M.R.; Molina, A.; Torres-Villaseñor, R.C. Random Vibration Fatigue Analysis Using a Nonlinear Cumulative Damage Model. Appl. Sci. 2022, 12, 4310. https://doi.org/10.3390/app12094310
Barraza-Contreras JM, Piña-Monarrez MR, Molina A, Torres-Villaseñor RC. Random Vibration Fatigue Analysis Using a Nonlinear Cumulative Damage Model. Applied Sciences. 2022; 12(9):4310. https://doi.org/10.3390/app12094310
Chicago/Turabian StyleBarraza-Contreras, Jesús M., Manuel R. Piña-Monarrez, Alejandro Molina, and Roberto C. Torres-Villaseñor. 2022. "Random Vibration Fatigue Analysis Using a Nonlinear Cumulative Damage Model" Applied Sciences 12, no. 9: 4310. https://doi.org/10.3390/app12094310
APA StyleBarraza-Contreras, J. M., Piña-Monarrez, M. R., Molina, A., & Torres-Villaseñor, R. C. (2022). Random Vibration Fatigue Analysis Using a Nonlinear Cumulative Damage Model. Applied Sciences, 12(9), 4310. https://doi.org/10.3390/app12094310