Quick start#

Describe the cutting tool, the material, both gears and how the pair is driven, then ask for the pitting check. The pair below is the one used throughout this documentation: 22 and 40 teeth, module 2.5 mm, 34 mm face width, 40 kW at 1450 rpm.

from dataclasses import replace
from gearbox import Gear, Lubricant, Material, MaterialType, ShaftArrangement, Tool, Transmission
from gearbox.standards import iso6336

tool = Tool(addendum_coefficient=1.0, dedendum_coefficient=1.25, root_fillet_radius_coefficient=0.38)
steel = Material(
    material_type=MaterialType.NITROCARBURIZED_STEEL,
    contact_stress_limit=1500.0, bending_stress_limit=460.0, brinell_hardness=286.7,
)
pinion = Gear(
    tool=tool, material=steel, number_of_teeth=22, module=2.5, face_width=34.0,
    quality_grade=6, surface_roughness=3.67, shaft_diameter=35.0,
    shaft_arrangement=ShaftArrangement.BETWEEN_BEARINGS_TOWARDS_TORQUED_END,
    bearing_span=60.0, offset=15.0, favorable_contact=True,
)
wheel = replace(pinion, number_of_teeth=40, shaft_diameter=50.0, offset=35.0)
transmission = Transmission(
    pinion=pinion, wheel=wheel, lubricant=Lubricant(kinematic_viscosity_40c=160),
    pinion_speed_rpm=1450.0, power_kw=40.0, design_life_hours=10_000.0, application_factor=1.3,
)

pitting = iso6336.calculate_pitting(transmission)
bending = iso6336.calculate_bending(transmission)
print(f"flank: sigma_H = {pitting.contact_stress_pinion:.0f} MPa, S_H = {pitting.safety_factor_pinion:.2f}")
print(f"root:  sigma_F = {bending.tooth_root_stress_pinion:.0f} MPa, S_F = {bending.safety_factor_pinion:.2f}")

flank: sigma_H = 1492 MPa, S_H = 0.85
root:  sigma_F = 457 MPa, S_F = 1.76

The verdict: the root is comfortable (\(S_F = 1.76\)), but the flank is not safe (\(S_H = 0.85 < 1\)). This pair would pit before reaching ten thousand hours.

Reading the result#

pitting carries the contact stress of each gear, the stress it may take and the resulting safety factor, plus every factor of the standard under its full name: dynamic_factor (\(K_v\)), life_factor_pinion (\(Z_{NT}\)), zone_factor (\(Z_H\)) and so on. The symbol is in each field’s docstring (see PittingResult).

print(pitting.dynamic_factor, pitting.face_load_factor, pitting.transverse_load_factor)
# K_v = 1.028, K_Hbeta = 1.087, K_Halpha = 1.000

What if?#

Every model is immutable, so trying a variant is one replace away. A wider face width fixes the flank:

wider = replace(transmission,
    pinion=replace(pinion, face_width=50.0), wheel=replace(wheel, face_width=50.0))
print(iso6336.calculate_pitting(wider).safety_factor_pinion)    # 1.00

The same check with AGMA 2001-D04:

from gearbox.standards import agma2101
print(agma2101.calculate_pitting(transmission).contact_stress)

Choices that select a table#

Options that pick a table of the standard are named, not numbered: MaterialType, ShaftArrangement (ISO 6336-1 figure 13), LeadModification, FlankModification, Crowning, AssemblyCondition, GearingType. See gearbox.enums.

Special gears#

  • Helical gears: helix_angle=15.0 on both gears. Helical pairs assume unmodified flanks (FlankModification.NONE, the safe side) unless you say otherwise.

  • Double helical gears: double_helical=True on both gears; face_width is the width of one helix (ISO 6336 only).

  • Internal gears: internal=True on the wheel, a shaper cutter (Tool(cutter_type="shaper", cutter_teeth=…)) for the bending check, and Transmission(dynamic_factor_method="C").

Next steps#