Kinematics Modeling and Analysis of Mid-Low Speed Maglev Vehicle with Screw and Product of Exponential Theory
Abstract
:1. Introduction
2. Forward Kinematics Modeling for a Mid-Low Speed Maglev Train
- (1)
- There is a rotational degree of freedom along the z-direction between base 0 and anti-roll beam 1, whose twist coordinate is . This degree of freedom can decouple the motion of the left and right modules of the suspension frame in the running direction.
- (2)
- The ball joint between the anti-roll beam 1 and the hanger rod 2, respectively, includes three rotational degrees of freedom along x, y, and z. Considering the constraint relationship between the two anti-roll beams, the rotational degree of freedom in the z-direction can be ignored. Thus, the rotational degrees of freedom in the x- and y-directions are just considered, and the twists of rotation are and , respectively.
- (3)
- The hanger rod 2 has a telescopic translational freedom, and its twist is .
- (4)
- The ball joint between the anti-roll beam 1 and the hanger 2 respectively includes three rotational degrees of freedom. The degree of freedom in the z-direction is ignored, and the rotational freedom in the x-direction is retained and the twist is .
- (5)
- There is a rotational degree of freedom in the z-direction between the anti-roll beam 3 and the right module 4, whose twist coordinates are .
3. Solution of Reverse Motion of a Mid-Low Speed Maglev Train
4. The Relationship of the Vehicle/Track Position–Posture on the Transition Curve Track
4.1. Parametric Description of the Transition Curve
4.2. The Track Coordinate System on the Transition Curve
4.3. The Posture Matrix of Train Reference System Relative to Track Reference System
5. The Motion Analysis of the Maglev Train
6. Conclusions
Author Contributions
Funding
Conflicts of Interest
Appendix A
Appendix A.1. Each Element in Equation (4)
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Parameters | Value | Parameters | Value |
---|---|---|---|
Minimum Curve Radius | 1000 m | m | |
Maximum transverse slope angle | m | ||
Gauge D | 2 m | m | |
The length of electromagnet l | m | m | |
The distance between adjacent magnets | m | m | |
The distance of the air spring on the same module | m | m | |
The distance of adjacent air springs | m | The length of transition curve | 36 m |
Number | (degree) | (degree) | (degree) | (mm) | (degree) | (degree) |
---|---|---|---|---|---|---|
1 | 0.42 | −0.33 | −0.00 | −5.58 | 0.01 | −0.42 |
2 | −0.29 | −0.33 | 0.00 | 5.59 | −0.00 | 0.29 |
3 | 0.46 | −0.33 | −0.00 | −5.58 | 0.01 | −0.46 |
4 | −0.33 | −0.33 | −0.00 | 5.59 | −0.00 | 0.33 |
5 | 0.50 | −0.33 | −0.00 | −5.58 | 0.01 | −0.50 |
6 | −0.37 | −0.33 | −0.00 | 5.59 | −0.00 | 0.37 |
7 | 0.54 | −0.33 | −0.00 | −5.57 | 0.01 | −0.54 |
8 | −0.41 | −0.33 | −0.00 | 5.59 | −0.00 | 0.41 |
9 | 0.58 | −0.33 | −0.01 | −5.57 | 0.01 | −0.58 |
10 | −0.44 | −0.33 | −0.00 | 5.59 | −0.00 | 0.44 |
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Leng, P.; Li, J.; Jin, Y. Kinematics Modeling and Analysis of Mid-Low Speed Maglev Vehicle with Screw and Product of Exponential Theory. Symmetry 2019, 11, 1201. https://doi.org/10.3390/sym11101201
Leng P, Li J, Jin Y. Kinematics Modeling and Analysis of Mid-Low Speed Maglev Vehicle with Screw and Product of Exponential Theory. Symmetry. 2019; 11(10):1201. https://doi.org/10.3390/sym11101201
Chicago/Turabian StyleLeng, Peng, Jie Li, and Yuxin Jin. 2019. "Kinematics Modeling and Analysis of Mid-Low Speed Maglev Vehicle with Screw and Product of Exponential Theory" Symmetry 11, no. 10: 1201. https://doi.org/10.3390/sym11101201
APA StyleLeng, P., Li, J., & Jin, Y. (2019). Kinematics Modeling and Analysis of Mid-Low Speed Maglev Vehicle with Screw and Product of Exponential Theory. Symmetry, 11(10), 1201. https://doi.org/10.3390/sym11101201