Related Resources: calculators

AGMA Gear Tooth Bending Stress Formula and Calculator

Gear Engineering and Design

AGMA Gear Tooth Bending Stress Formula and Calculator

Per standard ANSI/AGMA D04 Fundamental Rating Factors and Calculation Methods for Involute Spur and Helical Gear Teeth:

Preview: AGMA Gear Tooth Bending Stress Calculator

The fundamental formula for bending stress number in a gear tooth is:

Eq. 1
s_t = W_t · K_o · K_v · K_s · P_d / F · K_m · K_B / J

Eq. 2
P_d = π / ( p _x · tan ψ_s ) = P_nd · cos ψ_s for helical gears

where
P_nd = normal diametral pitch, in^-1;
p_x = axial pitch, in;
ψ_s = helix angle at standard pitch diameter.

Eq. 3
ψ_s = arcsin [ π / ( p_x / ( p_x · P_nd ) ]

Transmitted tangential load, W_t
Eq. 4
W_t = 33,000 P / v_t = 2 T / d = 396,000 P / ( π n_p d )

where:

P = transmitted power, hp;
T = transmitted pinion torque, lb in;
v_t = pitch line velocity at operating pitch diameter, ft/min.

where;

Eq. 5
v_t = π n_p d / 12

d = operating pitch diameter of pinion, in.
for external gears
Eq. 6
d = 2C / ( m_G + 1 )

Notes:

Rim thickness factor, K_B - Where the rim thickness is not sufficient to provide full support for the tooth root, the location of bending fatigue failure may be through the gear rim, rather than at the root fillet. Published data suggest the use of a stress modifying factor, KB, in this case. The rim thickness factor, K_B, is not sufficiently conservative for components with hoop stresses, notches or keyways. This data is based on external gears with smooth bores and no notches or keyways.

The rim thickness factor, K_B, adjusts the calculated bending stress number for thin rimmed gears. It is a function of the backup ratio, m_B,

Eq. 2
m_B = t_R · h_t

where
t_R = gear rim thickness below the tooth root, in;
h_t = gear tooth whole depth, in.

The effects of webs and stiffeners can be an improvement

The effect of tapered rims has not been investigated. When previous experience or detailed analysis justifies, lower values of K_B may be used.

K_B is applied in addition to the 0.70 reverse loading factor where it is applicable

The geometry factor, I, evaluates the radii of curvature of the contacting tooth profiles based on tooth geometry. These radii are used to evaluate the Hertzian contact stress in the tooth flank. Effects of modified tooth proportions and load sharing are considered.

The geometry factor, J, evaluates the shape of the tooth, the position at which the most damaging load is applied, and the sharing of the load between oblique lines of contact in helical gears. Both the tangential (bending) and radial (compressive) components of the tooth load are included.

Related:

• Gear Tooth Contact Stress Number Equation and Calculator
• AGMA Allowable Contact Stress for Steel Gears Table
• AGMA Major Metallurgical Factors
• Spur Gear Generator with Download Spur Gear Generator is unitless: you may choose inches, cm or millimeters when importing your DXF file as you will have the same value for D/P as it is set above or as imported (SI or imperial units).
• Spur Gear and Assembly Builder Spur Gear and Assembly Builder calculates and models individual Spur Gears and Gear assembly. File down loads available with Premium Account.
• Gear Design Handbook Premium Membership Required
• AGMA Spur Gear Profile Calculator Spread Sheet - Three excel calculation sheets that include the following input data/variables, calculated data and chart graphics.
• AGMA Worm and Spur Gear Design Equations and Calculators Worm gear sets are generally rated by their capacity to handle a particular level of input power, output power, or allowable torque at a particular speed for the input or output shaft.
• AGMA Worm gear Equations For Rating Factors Values for the ratio correction factor, the velocity factor, and materials factors can be found from tables provided in the ANSI/AGMA 6034-B92 standard.
• Practical Gear Design and Manufacture Handbook 872 pages, Premium account required, Gears are produced in enormous amounts - billions of gears are produced by industries every year. While the automotive industry ranks as the primary consumer of gears, numerous other industries also require huge amounts of gears: aerospace (helicopter transmission, etc. ), construction machinery, and agricultural machinery, to name a few.
• AGMA Fine Pitch Tolerances for Gears Gear tolerance chart below, lists the more common tolerance or quality specifications assigned for Spur, Helical and Herringbone type gears. Source:

ANSI/AGMA American Nation Standards Institutue . American Gear Manufacturers Association