Research on Curvature Interference Characteristics of Conical Surface Enveloping Cylindrical Worm–Face Worm Gear Drive
Abstract
:1. Introduction
2. Cutting Engagement of Worm
2.1. Generating Surface Equation of Grinding Wheel
2.2. Equation of Worm Tooth Surface
2.3. Function of Curvature Interference Limit Line
3. Curvature Interference Limit Function of Meshing
4. Curvature Interference Characteristic Analysis Based on PINN Technology
5. Numerical Examples
5.1. Numerical Results of Curvature Interference Limit Lines
5.2. Influence of Design Parameters on Curvature Limit Lines
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Nomenclature (Unit) | Symbols/Formulas | Results |
---|---|---|
Center distance (mm) | 100 | |
Transmission ratio | 55 | |
Number of worm threads | 1 | |
Number of worm gear teeth | 55 | |
Radius of worm pitch circle (mm) | 20 | |
Modulus (mm) | 4 | |
Spiral parameters of worm (mm) | 2 | |
Worm axial mounting distance (mm) | 60 | |
Worm’s actual face width (mm) | 73 | |
Radius of worm addendum circle (mm) | 34 | |
Radius of worm dedendum circle (mm) | 26 | |
Tooth width of face worm gear (mm) | kg | 0.5 |
Nomenclature (Unit) | Symbols/Formulas | Results |
---|---|---|
Radius of grinding wheel (o) | 150 | |
Half taper angle of grinding wheel for i-flank (o) | 65 | |
Tilt angle of grinding wheel for i-flank (o) | 5 | |
Half taper angle of grinding wheel for e-flank (o) | 60 | |
Tilt angle of grinding wheel for e-flank (o) | 5 | |
Operating center distance (mm) | , | 165.57 |
Curvature Interference Limit Line ① | ||||||
Key Point | P1 | P2 | P3 | P4 | P5 | |
/o | Values | 178.89 | 179.20 | 179.49 | 179.79 | 180.08 |
Error, PINN | −4.18 × 10−13 | −1.47 × 10−12 | 9.34 × 10−14 | 3.91 × 10−13 | 3.67 × 10−13 | |
Error, Fsolve | −5.53 × 10−12 | −2.70 × 10−11 | 8.17 × 10−14 | −1.07 × 10−13 | 1.39 × 10−13 | |
u/mm | 171.15 | 165.40 | 159.84 | 154.37 | 148.95 | |
/o | 1733.3 | 1841.4 | 1949.6 | 2056.9 | 2162.9 | |
/o | 1579.4 | 1681.8 | 1786.2 | 1890.9 | 1994.9 | |
xR1/mm | −76.58 | −77.42 | −78.36 | −79.32 | −80.26 | |
yR1/mm | 11.42 | 16.29 | 21.06 | 25.79 | 30.49 | |
xR2/mm | 10.91 | 15.61 | 20.31 | 25.01 | 29.71 | |
yR2/mm | 105.28 | 106.37 | 107.12 | 107.66 | 108.07 | |
Curvature Interference Limit Line ② | ||||||
Key Point | P1 | P2 | P3 | P4 | P5 | |
/o | Values | 177.52 | 177.27 | 177.02 | 176.78 | 176.53 |
Error, PINN | 3.32 × 10−13 | −2.37 × 10−15 | −1.79 × 10−14 | 1.48 × 10−11 | 9.46 × 10−13 | |
Error, Fsolve | −2.09 × 10−10 | −1.82 × 10−12 | −2.74 × 10−10 | −4.75 × 10−10 | 2.13 × 10−13 | |
u/mm | 171.15 | 198.19 | 203.29 | 208.45 | 213.65 | |
/o | 1733.3 | 2291.4 | 2190.3 | 2088.0 | 1986.2 | |
/o | 1579.4 | 2196.4 | 2091.5 | 1987.8 | 1886.0 | |
xR1/mm | −76.58 | −109.89 | −108.98 | −108.06 | −107.18 | |
yR1/mm | 11.42 | 13.19 | 17.54 | 21.98 | 26.49 | |
xR2/mm | 10.91 | 10.91 | 15.61 | 20.31 | 25.01 | |
yR2/mm | 105.28 | 108.24 | 108.71 | 109.02 | 109.23 |
Curvature Interference Limit Line ① | ||||||
Key Point | P1 | P2 | P3 | P4 | P5 | |
/o | Values | 269.08 | 269.33 | 269.59 | 269.85 | 270.12 |
Error, PINN | −1.84 × 10−11 | −8.73 × 10−11 | 6.46 × 10−14 | 2.06 × 10−12 | −6.71 × 10−14 | |
Error, Fsolve | −1.42 × 10−13 | −1.84 × 10−11 | −4.97 × 10−14 | 2.45 × 10−13 | 4.98 × 10−10 | |
u/mm | 171.15 | 177.36 | 171.87 | 166.34 | 160.77 | |
/o | 1733.3 | 3619.5 | 3510.0 | 3396.8 | 3282.4 | |
/o | 1579.4 | 3825.4 | 3712.7 | 3597.0 | 3480.8 | |
xR1/mm | −76.58 | −110.74 | −110.12 | −109.38 | −108.62 | |
yR1/mm | 11.42 | 12.82 | 17.26 | 21.78 | 26.33 | |
xR2/mm | 10.91 | 10.91 | 15.61 | 20.31 | 25.01 | |
yR2/mm | 105.28 | 107.67 | 108.23 | 108.61 | 108.89 | |
Curvature Interference Limit Line ② | ||||||
Key Point | P1 | P2 | P3 | P4 | P5 | |
/o | Values | 267.81 | 267.56 | 267.31 | 267.06 | 266.82 |
Error, PINN | 1.68 × 10−12 | −4.08 × 10−13 | −4.91 × 10−14 | 1.82 × 10−14 | −6.14 × 10−13 | |
Error, Fsolve | 2.56 × 10−13 | −2.27 × 10−13 | 2.63 × 10−13 | −2.34 × 10−13 | 2.81 × 10−13 | |
u/mm | 171.15 | 205.87 | 211.87 | 217.72 | 223.51 | |
/o | 1733.3 | 3137.6 | 3249.2 | 3364.8 | 3481.9 | |
/o | 1579.4 | 3176.1 | 3282.9 | 3395.3 | 3510.1 | |
xR1/mm | −76.58 | −77.29 | −77.68 | −78.30 | −79.00 | |
yR1/mm | 11.42 | 11.35 | 16.19 | 20.96 | 25.69 | |
xR2/mm | 10.91 | 10.91 | 15.61 | 20.31 | 25.01 | |
yR2/mm | 105.28 | 104.89 | 105.96 | 106.72 | 107.29 |
Nomenclature (Unit) | Symbols/Formulas | Results |
---|---|---|
Radius of grinding wheel (o) | 150 | |
Half taper angle of grinding wheel for i-flank (o) | 65 | |
Tilt angle of grinding wheel for i-flank (o) | 5 | |
Half taper angle of grinding wheel for e-flank (o) | 60 | |
Tilt angle of grinding wheel for e-flank (o) | −5 | |
Operating centre distance (mm) | , | 165.57 |
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Mu, S.; Sun, X.; Dong, Z.; Yang, H.; Liu, Y.; Zhang, W.; Qu, S.; Zhao, H.; Zhao, Y. Research on Curvature Interference Characteristics of Conical Surface Enveloping Cylindrical Worm–Face Worm Gear Drive. Appl. Sci. 2025, 15, 6298. https://doi.org/10.3390/app15116298
Mu S, Sun X, Dong Z, Yang H, Liu Y, Zhang W, Qu S, Zhao H, Zhao Y. Research on Curvature Interference Characteristics of Conical Surface Enveloping Cylindrical Worm–Face Worm Gear Drive. Applied Sciences. 2025; 15(11):6298. https://doi.org/10.3390/app15116298
Chicago/Turabian StyleMu, Shibo, Xingwei Sun, Zhixu Dong, Heran Yang, Yin Liu, Weifeng Zhang, Sheng Qu, Hongxun Zhao, and Yaping Zhao. 2025. "Research on Curvature Interference Characteristics of Conical Surface Enveloping Cylindrical Worm–Face Worm Gear Drive" Applied Sciences 15, no. 11: 6298. https://doi.org/10.3390/app15116298
APA StyleMu, S., Sun, X., Dong, Z., Yang, H., Liu, Y., Zhang, W., Qu, S., Zhao, H., & Zhao, Y. (2025). Research on Curvature Interference Characteristics of Conical Surface Enveloping Cylindrical Worm–Face Worm Gear Drive. Applied Sciences, 15(11), 6298. https://doi.org/10.3390/app15116298