Gear Transmission: Design, Verification And Application

Publish Time: 2025-12-02 Origin: Site

Gears are core components in mechanical transmission systems, and their load-carrying capacity directly determines the reliability and service life of the entire transmission system. The load-carrying capacity of gears mainly involves two critical aspects: tooth surface contact fatigue strength and tooth root bending fatigue strength.

Common Gear Failure Modes

Gears may experience various failure forms under service conditions:

Tooth Surface Pitting: Metal spalling on the surface caused by cyclic contact stress.
Tooth Surface Scuffing: Adhesion of metal surfaces due to high-speed and heavy-load operations.
Tooth Surface Wear: Material loss on the tooth surface resulting from friction.
Tooth Breakage: Caused by bending fatigue or overload.
Plastic Deformation: Material flow on the tooth surface under heavy loads.

Core Design and Calculation of Load-Carrying Capacity

The basic design process involves determining transmission parameters (power, rotational speed, transmission ratio, etc.), selecting gear materials and heat treatment processes, initially defining gear parameters (module, number of teeth, tooth width, etc.), conducting load-carrying capacity calculations, optimizing design parameters, and completing detailed design.

1. Tooth Surface Contact Fatigue Strength Calculation

Based on the ISO 6336 standard, the fundamental formula is:σH = ZH × ZE × Zε × Zβ × √[(Ft/(b·d1))·(u+1)/u] ≤ σHPWhere:

σH = Calculated contact stress (MPa)
ZH = Node zone factor, ZE = Material elastic coefficient, Zε = Contact ratio factor, Zβ = Helix angle factor
Ft = Tangential force on the reference circle of the end face (N)
b = Tooth width (mm), d1 = Reference circle diameter of the pinion (mm), u = Gear ratio (u=z2/z1)
σHP = Allowable contact stress (MPa), calculated as σHP = σHlim·ZN·ZL·Zv·ZR·ZW·ZX/SHmin (σHlim = Contact fatigue limit of test gears; ZN = Life factor; ZL = Lubricant factor; Zv = Speed factor; ZR = Surface roughness factor; ZW = Work hardening factor; ZX = Size factor; SHmin = Minimum safety factor)

2. Tooth Root Bending Fatigue Strength Calculation

The basic formula is:σF = (Ft/(b·mn))·YF·YS·Yβ·YB ≤ σFPWhere:

σF = Calculated bending stress (MPa)
mn = Normal module (mm)
YF = Tooth profile factor, YS = Stress correction factor, Yβ = Helix angle factor, YB = Tooth width factor
σFP = Allowable bending stress (MPa), calculated as σFP = σFlim·YN·YδrelT·YRrelT·YX/SFmin (σFlim = Bending fatigue limit of test gears; YN = Life factor; YδrelT = Relative tooth root fillet sensitivity factor; YRrelT = Relative surface condition factor; YX = Size factor; SFmin = Minimum safety factor)

Load-Carrying Capacity Verification

Contact Fatigue Strength Verification: Verify that σH ≤ σHP by calculating ZH, determining ZE, computing Zε, considering Zβ, calculating Ft, confirming correction factors, and comparing σH with σHP.
Bending Fatigue Strength Verification: Ensure σF ≤ σFP through defining YF, calculating YS, accounting for Yβ, computing YB, identifying correction factors, and comparing σF with σFP.
Special Working Condition Verification: Include short-term overload verification (considering maximum instantaneous load), impact load verification (introducing dynamic load factor), high-temperature condition verification (accounting for material performance changes), and low-speed heavy-load verification (focusing on plastic deformation).