Variable-Coefficient Dynamic Modeling Method for a Ball Screw Feed System in the No-Extra-Load Running State
Abstract
:1. Introduction
2. Materials and Methods
2.1. Equivalent Dynamic Model
2.2. Variable-Coefficient Dynamic Equation
2.3. Determination of the Variable-Coefficient of the Dynamic Equation
2.3.1. Stiffness and Mass Matrices of the Equivalent Beam Element
2.3.2. Equivalent Axial Stiffness of the Screw Nut Joints
2.3.3. Equivalent Axial Stiffness of the Bearing Joints
2.3.4. Total Stiffness and Mass Matrices of the System Based on Changes in the No-Extra-Load Running State
3. Dynamic Measurement of a Ball Screw Feed System in Different Running States
4. Results and Discussion
4.1. Comparison of the Theoretical and Experimental Results Based on the Worktable Position
4.2. Comparison of the Theoretical and Experimental Results Based on the Feed Speed of the Worktable
4.3. Comparison of the Theoretical and Experimental Results Based on the Feed Acceleration of the Worktable
5. Conclusions
6. Future Directions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Parameter | Value | Parameter | Value | Parameter | Value |
---|---|---|---|---|---|
Fas−b/kN | 1.70 | Pd/kN | 163.4 | Aess/m2 | 4.8 × 10−3 |
αcb/° | 60 | Cp | 0.10 | Ass/m2 | 4.2 × 10−3 |
ib/nb | 2/29 | αcon/° | 60 | Ess/(N/m2) | 2.1 × 1011 |
cwb/cwn | 0.8 | φp/° | 3.643 | Gss/(N/m2) | 0.8 × 1011 |
mt/kg | 7400 | isn | 2.5 | ρss/(kg/m3) | 7.85 × 103 |
d0/mm | 80 | dsb/mm | 9.525 | Iρss/m4 | 3.6 × 10−6 |
pss/mm | 16 | Lfix/m | 5.3 |
Type | Number | Sensitivity (mV/g) | ||
---|---|---|---|---|
X | Y | Z | ||
356A66 | SN 190783 | 9.99 | 9.85 | 10.33 |
SN 190788 | 9.96 | 10.08 | 10.11 | |
SN 190789 | 9.95 | 9.78 | 9.82 | |
SN 190791 | 9.76 | 10.01 | 10.08 |
fthe (Hz) | fexp1 (Hz) | Error (%) | |
---|---|---|---|
fthe0 | 35.9 | 32.0 | 12.19 |
fthe1 | 33.7 | 32.0 | 5.31 |
fthe (Hz) | fexp2 (Hz) | Error (%) | |
---|---|---|---|
fthe1 | 33.7 | 35.2 | 4.26 |
fthe2 | 34.1 | 35.2 | 3.13 |
fthe (Hz) | fexp3 (Hz) | Error (%) | |
---|---|---|---|
fthe1 | 33.7 | 36.1 | 6.57 |
fthe3 | 34.7 | 36.1 | 3.88 |
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Zhang, H.; Zha, J.; Du, C.; Liu, H.; Li, Y.; Lv, D. Variable-Coefficient Dynamic Modeling Method for a Ball Screw Feed System in the No-Extra-Load Running State. Processes 2023, 11, 793. https://doi.org/10.3390/pr11030793
Zhang H, Zha J, Du C, Liu H, Li Y, Lv D. Variable-Coefficient Dynamic Modeling Method for a Ball Screw Feed System in the No-Extra-Load Running State. Processes. 2023; 11(3):793. https://doi.org/10.3390/pr11030793
Chicago/Turabian StyleZhang, Huijie, Jun Zha, Chao Du, Hui Liu, Yang Li, and Dun Lv. 2023. "Variable-Coefficient Dynamic Modeling Method for a Ball Screw Feed System in the No-Extra-Load Running State" Processes 11, no. 3: 793. https://doi.org/10.3390/pr11030793