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Design of Spur GearsMTE 427 MACHINE DESIGN

14 Sep, 2008

Lewis Bending Equation

Lewis Bending Equation: Dynamic Effect

Dynamic Factor

As a general rule, spur gears should have a face width F from 3 to 5 times the circular pitch p.

Lewis Bending Equation: Dynamic Effect

Do Ex 14-2 as Homework according the changes.

In these equations l and t are from the layout in Fig. 14–1, is the pressure angle, isthe fillet radius, b is the dedendum, and d is the pitch diameter.

Stress Concentration Factor

Surface Compressive Stress

AGMA Stress Equation

Two fundamental stress equations are used in the AGMA methodology, one for bending stress and another for pitting resistance (contact stress).


AGMA Stress Equation: Bending Stress


AGMA Stress Equation: Pitting Resistance

Two fundamental strength equations are used in the AGMA methodology, one for bending stress and another for pitting resistance (contact stress).

AGMA Strength Equation: Bending Stress

AGMA Strength Equation: Pitting Resistance

Two fundamental strength equations are used in the AGMA methodology, one for bending stress and another for pitting resistance (contact stress).

AGMA Strength Equation: Allowable Bending Strength

AGMA Strength Equation: Allowable Contact Strength

AGMA Factors

• Geometry Factor• Elastic Coefficient• Dynamic Factor• Overload Factor• Surface Condition Factor• Size Factor• Load-distribution Factor• Hardness-ration Factor• Stress Cycle Factors• Reliability Factor• Temperature Factor• Rim-thickness Factor• Safety Factors

Important factors of AGMA used for gear analysis are as following,

AGMA Factors: Geometry Factors

Bending-strength Geometry Factor, J (YJ)

AGMA Factors: Geometry Factors

Bending-strength Geometry Factor, I (ZI)

AGMA Factors: Elastic Coefficient

Elastic coefficient CP (ZE)

AGMA Factors: Dynamic Factor

Dynamic factor, KV

AGMA Factors: Overload Factor

Overload factor, KO

AGMA Factors: Surface Condition Factor

Surface condition factor, Cf (ZR)

The surface condition factor Cf (ZR) is used only in the pitting resistance equation. It depends on

• Surface finish as affected by, but not limited to, cutting, shaving, lapping, grinding, shot peening• Residual stress• Plastic effects (work hardening) Standard surface conditions for gear teeth have not yet been established.

When a detrimental surface finish effect is known to exist, AGMA specifies a value of Cf (ZR) greater than unity.

AGMA Factors: Size Factor

Size factor, KS

If KS is less than 1, use KS = 1.

AGMA Factors: Load-distribution Factor

Load-distribution factor, Km

AGMA Factors: Hardness-ratio Factor

Hardness-ratio factor, CH

The hardness-ratio factor CH is used only for the gear. Its purpose is to adjust the surface strengths for this effect.

AGMA Factors: Hardness-ratio Factor

Hardness-ratio factor, CH

When surface-hardened pinions with hardnesses of 48 Rockwell C scale (Rockwell C48) or harder are run with through-hardened gears (180–400 Brinell), a work hardening occurs. The CH factor is a function of pinion surface finish fP and the mating gear hardness.

AGMA Factors: Stress Cycle Factors

Stress Cycle Factor, YN and ZN

AGMA Factors: Reliability Factor

Reliability Factor, KR (YZ)

The reliability factor accounts for the effect of the statistical distributions of material fatigue failures.

AGMA Factors: Temperature Factor

Temperature Factor, KT (Y)

For oil or gear-blank temperatures up to 250°F (120°C), use

KT = Y = 1.0. For higher temperatures, the factor should be

greater than unity. Heat exchangers may be used toensure that operating temperatures are considerably below this value, as is desirable for the lubricant.

AGMA Factors: Rim-thickness Factor

Temperature Factor, KB

When 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 tooth fillet. In such cases, the use of a stress-modifying factor KB or (tR) is recommended. This factor, the rim-thickness factor KB, adjusts the estimated bending stress for the thin-rimmed gear.

AGMA Factors: Safety Factor

Safety Factor, SF and SH

To render SH linear with the transmitted load, it could have been defined as

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