Residual Stress Distribution Design for Gear Surfaces Based on Genetic Algorithm Optimization
Abstract
:1. Introduction
2. Residual Stress Distribution
- (1)
- σsurface—the RS at the surface;
- (2)
- σmax—the peak RS;
- (3)
- ymax—the depth of σmax;
- (4)
- ycore—the depth where RS vanishes.
3. Gear Contact Model
4. Fatemi–Socie Multiaxial Fatigue Criterion
5. Optimization Scheme
- (1)
- The generation number reaches the prescribed upper limit Gmax;
- (2)
- The relative change in the highest fitness over Gs generations is less than the function tolerance value e.
6. Results and Discussion
6.1. Mechanism for RS to Increase (Nf)min
6.2. Increase in (Nf)min Induced by the Optimum RS Distribution
6.3. Effect on (Nf)min When the RS Distribution Deviates from the Optimum
7. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Nomenclature
critical plane | The plane that has the maximum shear strain range over a loading cycle |
FSDP | Fatemi–Socie damage parameter |
RS | Residual stress |
DFS | The maximum FSDP on all the critical planes of a material point |
(DFS)max | The maximum DFS of all material points |
Nf | Fatigue initiation life of a material point |
(Nf)min | Minimum fatigue initiation life of all material points or fatigue initiation life of the gear surface |
α | Plane orientation |
αc | The orientation of the critical plane corresponding to DFS |
Δγ | The maximum shear strain range on a plane over a loading cycle |
σn,max | Maximum normal stress on a plane over a cycle |
σsurface | RS at the surface |
σmax | Peak RS |
ymax | Depth of σmax |
ycore | Depth where RS vanishes |
σmax,t | The transition value for σmax |
Subscripts | |
opt | Values associated with the optimum RS distribution |
1, 2, 3, … | Values associated with plane 1, 2, 3, … |
Appendix A
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Parameter | Pinion | Gear |
---|---|---|
Normal module mn/mm | 5.645 | |
Pressure angle α/◦ | 15 | |
Helix angle β/◦ | 22.3 | |
Contact ratio εα | 1.746 | |
Face width L/mm | 54 | |
Tooth number | z1 = 37 | z2 = 48 |
Radius at the pitch point/mm | R1 = 27.029 | R2 = 35.065 |
Rated output torque Trated/(N·m) | 3000 | |
Rotating speed n/(r/min) | 500 | |
Material | AISI 8620RH | |
Young’s modulus/GPa | E1 = E2 = 210 | |
Poisson’s ratio ν | ν1 = ν2 = 0.3 | |
Yield strength Y/MPa | 1300 |
Population size, N | 200 |
Maximum generation number, Gmax | 500 |
Maximum stall generation number, Gs | 20 |
Function tolerance, e | 10−6 |
Crossover fraction, Pc | 0.8 |
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Chen, Z.; Jiang, Y.; Tong, Z.; Tong, S. Residual Stress Distribution Design for Gear Surfaces Based on Genetic Algorithm Optimization. Materials 2021, 14, 366. https://doi.org/10.3390/ma14020366
Chen Z, Jiang Y, Tong Z, Tong S. Residual Stress Distribution Design for Gear Surfaces Based on Genetic Algorithm Optimization. Materials. 2021; 14(2):366. https://doi.org/10.3390/ma14020366
Chicago/Turabian StyleChen, Zhou, Yibo Jiang, Zheming Tong, and Shuiguang Tong. 2021. "Residual Stress Distribution Design for Gear Surfaces Based on Genetic Algorithm Optimization" Materials 14, no. 2: 366. https://doi.org/10.3390/ma14020366