Page 175 - The Tribology Handbook

Gears B3

GEAR PERFORMANCE

A number of methods of estimating the expected performance of gears have been published as Standards. These use a large
number of facrors to allow for operational and geometric effects, and for new designs leave a lot to the designers’ judgement,
for the matching of the design to suit a particular application. They are, however, more readily applicable to the
development of existing designs.

Early methods
Lewis Formula .- Dates back to 1890s and is used to calculate the shear strength of the gear tooth and relate it to the yield
strength of the material.
Buckinghain Stress Formula - Dates back to mid 1920s and compares the dynamic load with the beam strength of the gear
tooth. and a limit load for wear.

British Standard 436 Part 3 1986

Provides methods for determining the actual and permissible contact stresses and bending stresses in a pair of involute spur
or helical gears.
Factors covered in this stan’dard include:
Tangential Force The nominal force for contact and bending stress.
Zone factor Accounts for the influence of tooth flank curvature at the pitch point on Hertzian stress.

Contact ratio factor: Accounts for the load sharing influence of the transverse contact ratio and the overlap
ratio on the specific loading.

Elasticity factor: Takes into account the influence of the modulus of elasticity of the material and Poisson’s
ratio on the Hertzian stress.
Basic endurance limit: The basic endurance limit for contact takes into account the surface hardness.

Material quality: This covers the quality of the material used.

Lubricant influence, The lubricant viscosity, surface roughness and pitch line speed affect the lubricant film
roughness and speed factor: thickness which affects the Hertzian stresses.
Work hardening factor: Accounts for the increase of surface durability due to meshing.

Size factor: Covers the possible influences of size on the material quality and its response to
manufacturing processes.

Life factor: Accounts for the increase in permissible stress when the number of stress cycles is less
than the endurance life.
Application factor: This allows for load fluctuations from the mean load or loads in the load histogram
caused by sources external to the gearing.

Dynamic factor: Allows for load fluctuations arising from contact conditions at the gear mesh.

Load distribution: Accounts for the increase in local load due to mal-distribution of load across the face of
the gear caused by deflections, alignment tolerances and helix modifications.
Minimum demanded and The minimum demanded safety factor is agreed between the supplier and the purchaser.
actual safety factor: The actual safety factor is calculated.

Geometry factors: Allow for the influence of the tooth form, the effect of the fillet and the helix angle on the
nominal bending stress for application of load at the highest point of single pair tooth
contact.

Sensitivity factor: Allows for the sensitivity of the gear material to the presence of notches, ie: the root fillet.
Surface condition factor: Accounts for the reduction ofendurance limit due to flaws in the material and the surface
roughness of the tooth root fillets.

B3.5