Influence of Toothed Rail Parameters on Impact Vibration Meshing of Mountainous Self-Propelled Electric Monorail Transporter
Abstract
:1. Introduction
2. MRGTR Mechanism and Meshing Impact Vibration Analysis
2.1. MRGTR Mechanism Analysis
2.1.1. Displacement Model of MSEMT
2.1.2. The Meshing Angle β at Initial Position
2.1.3. Instantaneous Velocity Model of MSEMT
2.2. MRGTR Impact Vibration
2.2.1. Force Analysis of the Driving Mechanism
2.2.2. Dynamic Model of Meshing Impact Vibration of MSEMT
2.2.3. Numerical Validation
3. Materials and Methods
3.1. Test Material
3.2. Test Platform and Equipment
3.3. Experiment Design
3.4. Evaluation and Calculation Method
4. Results and Analysis
4.1. Processing and Analysis of Vibration Signal Results
4.2. Orthogonal Test Results and Analysis
5. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Parameter | Toothed Rail 1 | Toothed Rail 2 | Toothed Rail 3 | Toothed Rail 4 |
---|---|---|---|---|
Pressure Angle α (°) | 15 | 15 | 25 | 25 |
Pitch p (mm) | 30.9 | 31.99 | 30.9 | 34.09 |
Wheel-tooth ratio | 1 | cosα | 1 | cosα |
Height of tooth hf (mm) | 35.5 | 35.5 | 35.5 | 35.5 |
Parameter | Numerical |
---|---|
Empty mass of MSEMT M0 (kg) | 175 |
The rated speed of motor n (r/min) | 1500 |
Transmission ratio i | 17.143 |
Roller gear rotational speed nr (r/min) | 81.67~93.33 |
Given speed vd (m/min) | 25.65~29.32 |
Number of rollers z | 10 |
Radius of the central circle of roller R (mm) | 50 |
Radius of roller r (mm) | 7 |
Levels | Factor A | Factor B | Factor C |
---|---|---|---|
Pressure Angle α (°) | Wheel-Tooth Ratio | Load Mass M2 (kg) | |
1 | 15 | 1 | 0 |
2 | 25 | cosα | 176 |
Type | Load Mass (kg) | Peak Frequency (Hz) | Amplitude (m/s2) | Average Peak Frequency (Hz) | Average Amplitude (m/s2) | ||||
---|---|---|---|---|---|---|---|---|---|
Group 1 | Group 2 | Group 3 | Group 1 | Group 2 | Group 3 | ||||
Toothed rail 1 | 0 | 13.87 | 13.87 | 13.87 | 0.5321 | 0.6117 | 1.1530 | 13.87 | 0.7656 |
27.73 | 27.73 | 27.73 | 0.3490 | 0.3619 | 0.8353 | 27.73 | 0.5154 | ||
41.6 | 41.6 | 41.6 | 0.2264 | 0.2679 | 0.5619 | 41.6 | 0.3521 | ||
55.47 | 55.47 | 55.47 | 0.1258 | 0.1354 | 0.3972 | 55.47 | 0.2195 | ||
176 | 13.67 | 13.67 | 13.67 | 0.5974 | 0.6102 | 0.5691 | 13.67 | 0.5922 | |
27.34 | 27.34 | 27.34 | 0.3838 | 0.3684 | 0.3977 | 27.34 | 0.3833 | ||
41.02 | 41.02 | 41.02 | 0.2602 | 0.2355 | 0.2216 | 41.02 | 0.2391 | ||
54.69 | 54.69 | 54.69 | 0.1459 | 0.1459 | 0.1398 | 54.69 | 0.1439 | ||
68.36 | 68.36 | 68.36 | 0.1196 | 0.0966 | 0.1080 | 68.36 | 0.1081 | ||
Toothed rail 2 | 0 | 14.84 | 15.23 | 15.04 | 0.3093 | 0.3013 | 0.3325 | 15.04 | 0.3144 |
176 | 14.06 | 14.06 | 14.06 | 0.3641 | 0.3762 | 0.3594 | 14.06 | 0.3666 | |
Toothed rail 3 | 0 | 15.23 | 15.04 | 15.04 | 0.4167 | 0.9276 | 0.3825 | 15.10 | 0.5756 |
27.54 | 30.27 | 30.27 | 0.2227 | 0.4285 | 0.1517 | 29.36 | 0.2676 | ||
176 | 14.84 | 15.04 | 15.04 | 0.3438 | 0.2682 | 0.1348 | 14.65 | 0.2489 | |
29.78 | 25.78 | 28.91 | 0.1597 | 0.1652 | 0.0626 | 28.16 | 0.1291 | ||
Toothed rail 4 | 0 | 14.84 | 15.04 | 15.04 | 0.1911 | 0.3277 | 0.2997 | 14.97 | 0.2728 |
25.59 | 28.52 | 32.03 | 0.2288 | 0.2224 | 0.1430 | 28.71 | 0.1981 | ||
176 | 14.65 | 14.65 | 14.84 | 0.3534 | 0.6664 | 0.533 | 14.71 | 0.5176 |
No. | Factors | |||||||
A Pressure angle | B Wheel-tooth ratio | A×B Interaction of pressure angle and wheel-tooth ratio | C Load mass | A×C Interaction of pressure angle and load mass | B×C Interaction of wheel-tooth ratio and load mass | A×B×C Interaction of pressure angle, wheel-tooth ratio and load mass | ||
1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | |
2 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | |
3 | 1 | 2 | 2 | 1 | 1 | 2 | 2 | |
4 | 1 | 2 | 2 | 2 | 2 | 1 | 1 | |
5 | 2 | 1 | 2 | 1 | 2 | 1 | 2 | |
6 | 2 | 1 | 2 | 2 | 1 | 2 | 1 | |
7 | 2 | 2 | 1 | 1 | 2 | 2 | 1 | |
8 | 2 | 2 | 1 | 2 | 1 | 1 | 2 | |
No. | Indicators | |||||||
Average maximum acceleration amplitude (m/s2) | Average attenuation time of the vibration (ms) | |||||||
1 | 5.9701 | 16.4678 | ||||||
2 | 4.6906 | 16.8427 | ||||||
3 | 3.7128 | 15.5683 | ||||||
4 | 3.2553 | 17.3349 | ||||||
5 | 7.1488 | 13.9068 | ||||||
6 | 4.9058 | 13.4467 | ||||||
7 | 4.4201 | 17.9550 | ||||||
8 | 5.8806 | 17.0068 |
Analysis | Average Maximum Acceleration Amplitude (m/s2) | Average Attenuation Time of the Vibration (ms) | ||||||
---|---|---|---|---|---|---|---|---|
B | A | B×C | A×B×C | A×B | B | A | A×C | |
SS | 3.708 | 2.792 | 2.560 | 1.038 | 8.031 | 6.482 | 1.900 | 1.575 |
df | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
MS | 3.708 | 2.792 | 2.560 | 1.038 | 8.031 | 6.482 | 1.900 | 1.575 |
F | 8.077 | 6.083 | 5.577 | 2.261 | 39.435 | 31.827 | 9.328 | 7.734 |
Sig. | 0.066 | 0.090 | 0.099 | 0.230 | 0.008 | 0.011 | 0.055 | 0.069 |
significance | * | * | * | ** | ** | * | * |
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Liu, Y.; Hong, T.; Li, Z. Influence of Toothed Rail Parameters on Impact Vibration Meshing of Mountainous Self-Propelled Electric Monorail Transporter. Sensors 2020, 20, 5880. https://doi.org/10.3390/s20205880
Liu Y, Hong T, Li Z. Influence of Toothed Rail Parameters on Impact Vibration Meshing of Mountainous Self-Propelled Electric Monorail Transporter. Sensors. 2020; 20(20):5880. https://doi.org/10.3390/s20205880
Chicago/Turabian StyleLiu, Yue, Tiansheng Hong, and Zhen Li. 2020. "Influence of Toothed Rail Parameters on Impact Vibration Meshing of Mountainous Self-Propelled Electric Monorail Transporter" Sensors 20, no. 20: 5880. https://doi.org/10.3390/s20205880