1. Brief Introduction to Planetary Gear Transmission

2. Material Selection for Planetary Gear Transmission

• Common Materials for Sun and Planet Gears: 20CrMnTi, 20CrMo, 20CrMnMo, etc. Japanese enterprises mainly use SCM420 (equivalent to 20CrMo), while German and Italian enterprises prefer 20CrMnMo and 18CrNiMo7-6.
• Common Materials for Gear Rings: 42CrMo, 20CrMo.

3. Heat Treatment of Gears

• Sun Gear and Planet Gear: Typically undergo carburizing and quenching or carbonitriding. The surface hardness reaches 58-62 HRC, and the core hardness is 30-45 HRC. This results in a contact fatigue limit (σHlimC) of 1500 MPa and a bending fatigue limit (σFlimC) of 500 MPa.
• Internal Gear Ring: Usually adopts nitriding. The surface hardness is 550-700 HV, with a contact fatigue limit (σHlimC) of 750 MPa and a bending fatigue limit (σFlimC) of 310 MPa.

4. Key Fatigue Limits and Influencing Factors

4.1 Bending Fatigue Limit (σFlim)

• Material and Heat Treatment: Material composition, mechanical properties, and heat treatment processes (such as carburizing, nitriding) directly affect σFlim. For example, the effective hardened layer depth of carburized gears should be ≥ 0.15 mm, and that of nitrided gears should be 0.4-0.6 mm.
• Structural Parameters: Tooth root fillet radius, surface roughness (Ra ≤ 1.6 μm), and tooth width influence stress distribution and fatigue performance.
• Load and Working Conditions: For gears with bidirectional bending, σFlim should be multiplied by 0.7; for symmetric bidirectional bending (such as planet gears), it is also multiplied by 0.7. High-speed gears require consideration of lubrication methods (grease lubrication, splash lubrication, or forced lubrication).

4.2 Contact Fatigue Limit (σHlim)

• Basic Measurement Method: Determined through standard tests (such as rolling contact tests) under 10⁷ cycles. For example, the typical value of carburized and quenched steel is 1300-1500 MPa.
• Key Correction Factors:
  • Lubrication conditions: Derating is required when the oil film thickness is insufficient.
  • Surface hardness gradient: The hardened layer depth should be ≥ 0.2 times the module.
  • Roughness correction factor ZL: Take 1.0 when Ra ≤ 0.4 μm.
  • Safety factor SH: Usually ≥ 1.0.
• Test Standard Parameters (refer to GB/T 14229): Standard spur gear parameters (module 3-5 mm, surface roughness Rz = 3 μm, linear speed 10 m/s); lubricant viscosity 100 mm²/s (ZL = 1).
• Typical Failure Mode: Pitting fatigue spalling (pockmarked damage).

5. Contact Fatigue Strength Check

• ZE: Elastic coefficient, related to material Poisson's ratio and elastic modulus.
• Ft: Tangential load.
• b: Tooth width.
• d1: Pitch circle diameter of the pinion.
• u: Gear ratio.
• KA, KV, KHβ, KHα: Load coefficients (application factor, dynamic load factor, tooth trace load distribution factor, tooth load distribution factor).

6. Bending Fatigue Strength Check

6.1 Evaluation Standards

• Method A: Any suitable method (finite element method, integral method, conformal mapping method) or actual measurement (such as photoelastic detection, strain measurement) can be used, but it requires significant workload and is only for special occasions.
• Method B: The maximum tensile stress at the tooth root of the loaded side tooth profile is taken as the nominal bending stress, which is corrected by corresponding coefficients as the calculated tooth root stress. This method assumes that the maximum tooth root bending stress occurs at the outermost point of single-tooth meshing of the gear pair.

6.2 Calculation of Tooth Root Bending Stress

7. Summary