Surface stresses

Surface Stresses

Surface StressesMating gear have a combination of rolling and sliding at their interface. The stresses at tooth surface are dynamic Hertzian contact stresses in combined rolling and sliding. The surface stresses in the gear teeth were investigated by Buckingham who recognized that two cylinders having the same radius of curvature as the gear teeth at the pitch point and radially loaded in rolling contact.

Surface Stresses

Where Wt is tangential load or force.D is the pitch diameter of the two gears in mesh. F is the face width. I is the dimensionless surface geometry factor for pitting resistance.Cp is an elastic coefficient that accounts for differences in the gear and pinion material constants.

Surface StressesThe factors Ca , Cm , Cv and Cs are equal respectively to Ka, Km, Kv and Ks.Surface geometry factor I: This factor takes into account the radii of curvature of the gear teeth and pressure angle. p and g are radii of curvature of the pinion and gear . The radii of the curvature of the teeth are calculated from the mesh geometry.

Surface StressesElastic Coefficient Cp: The elastic coefficient accounts for differences in tooth materials.

Ep and Eg are moduli of elasticity for pinion and gear.p and g are the Poissons ratios.

Surface StressesSurface Finish Factor Cf: It is used to account for unusually rough surface finishes on gear teeth. For the conventional methods of gear Cf be set to 1.

Surface Stresses analysis of spur gear trainEXAMPLE: Determine the surface stresses in the gear teeth of the 3-gear train containing a pinion, an idler and gear. The transmitted load on the gear teeth is 432 lb. The pinion has 14 teeth , a 25 pressure angle , and pd = 6.The idler has 17 teeth and gear has 49 teeth. Pinion speed is 2500 rpm. Face width is 2 inches.Assumptions: The teeth are standard AGMA full depth profiles. The load and source are both uniform in nature. A quality index of 6 will be used. All gears are made of steel with = 0.28.

Surface Stresses analysis of spur gear train





Material strengthsSince both of the gear failure modes involve fatigue loading, material fatigue strength data are needed, both for bending stresses and for surface contact stresses. Test data for fatigue strengths of most gear materials have been compiled by AGMA.AGMA BENDING FATIGUE STRENGTHS FOR GAER MATERIALS: The published AGMA data for both bending and surface- strengths are in effect, partially corrected fatigue strengths, since they are generated appropriately sized parts having the same geometry, surface finish etc.

LIFE FACTOR KL: Since the test data are for a life of 1E7 cycles. A shorter or longer cycle life will require modification of the bending fatigue strength based on the S N relationship for the material. The number of load cycles in this case is defined as the number of mesh contacts.Figure shows the S N curves for the bending fatigue strength of steels having several different tensile strengths as defined by their Brinell hardness numbers. Curve fitted equations are also shown in the figure for each S N line. These equations can be used to compute the appropriate KL factor for a required number of load cycles N.

The upper portion of the shaded zone can be used for commercial applications. The lower portion of the shaded zone is typically used for critical service applications where little pitting and tooth wear is permissible and where smooth ness of operation and low vibration levels are required.TEMPERATUE FACTOR KT: The lubricant temperature is reasonable measure of gear temperature. For steel materials in oil temperatures up to about 250F, KT can be set to 1. For higher temperature KT can be estimated from

SURFACE LIFE FACTOR CL : Since the test data are for a life of 1E7 cycles. A shorter or longer cycle life will require modification of the bending fatigue strength based on the S N relationship for the material. The number of load cycles in this case is defined as the number of mesh contacts. Figure shows the S N curves for the surface fatigue strength of steels having several different tensile strengths as defined by their Brinell hardness numbers. Curve fitted equations are also shown in the figure for each S N lines. These equations can be used to compute the appropriate CL factor for a required number of load cycles N.

The upper portion of the shaded zone can be used for commercial applications. The lower portion of the shaded zone is typically used for critical service applications where little pitting and tooth wear is permissible and where smooth ness of operation and low vibration levels are required.HARDNESS RATIO FACTOR CH: This factor is a function of the gear ratio and relative hardness of pinion and gear, CH is always 1.0. CH is only applied to the gear- tooth strength. Two formulas for its calculation are suggested in the standard.

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Surface stresses