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Load Distribution Factors - Analytical Methods for Cylindrical Gears

## AGMA 927-A01

SCOPE
This information sheet covers a method for the evaluation of load distribution across the teeth of parallel axis gears. A general discussion of the design and manufacturing factors which influence load distribution is included.

The load distribution factors for use in AGMA parallel axis gear rating standards are defined, to improve communication between users of those standards.

Historically, analytical methods for evaluating load distribution in both AGMA and ISO standards have been limited by the assumption that load is linearly distributed across the face width of the meshing gear set. The result of this assumption is often overly conservative (high) values of load distribution factors. The method given here is considered more correct.

Method
A simplified iterative method for calculation of the face load distribution factor based on combined twisting and bending displacements of a mating gear and pinion, is presented. The transverse load distribution (in the plane of rotation) is not evaluated in this information sheet. This method assumes that the mesh stiffness is a constant through the entire contact roll and across the face. General guidance for design modifications to improve load distribution is also included.

Limitations of Method
This method is intended to be used for general gear design and rating purposes. It is intended to provide a value of load distribution factor and a means by which different gear designs can be analytically compared. It is not intended for rigorous detailed analysis to calculate the actual distribution of load across the face width of gear sets.

The knowledge and judgment required to evaluate the results of this method come from experience in designing, manufacturing and operating gear units. This method is intended for use by the experienced gear designer, capable of understanding its limitations and purposes. It is not intended for use by the engineering public at large.

FOREWORD
[The foreword, footnotes and annexes, if any, in this document are provided for informational purposes only and are not to be construed as a part of AGMA Information Sheet, 927-A01, Load Distribution Factors – Analytical Methods for Cylindrical Gears.]

This information sheet provides an analytical method to calculate a numeric value for the face load distribution factor for cylindrical gearing.

This is a new document, which provides a description of the analytical procedures that are used in several software programs that have been developed by various gear manufacturing companies. The method provides a significant improvement from the procedures used to define numeric values of face load distribution factor in current AGMA standards. Current AGMA standards utilize either an empirical procedure or a simplified closed form analytical calculation. The empirical procedure which is used in ANSI/AGMA 2101-C95 only allows for a nominal assessment of the influence of many parameters which affect the numeric value of the face load distribution factor. The closed form analytic formulations which have been found in AGMA standards suffer from the limitation that the shape of the load distribution across the face width is limited to a linear form.

The limitations of the previous AGMA procedures are overcome by the method defined in this information sheet. This method allows for including a sufficiently accurate representation of many of the parameters that influence the distribution of load along the face width of cylindrical gears. These parameters include the elastic effects due to deformations under load, and the inelastic effects of geometric errors as well as the tooth modifications which are typically utilized to offset the deleterious effects of the deformations and errors.

The analytical method described in this information sheet is based on a ”thin slice” model of a gear mesh. This model treats the distribution of load across the face width of the gear mesh as being independent of the any transverse effects. The method also represents all of the elastic effects of a set of meshing teeth (tooth bending, tooth shear, tooth rotation, Hertzian deflections, etc.) by one constant, i.e., mesh stiffness (Cγm). Despite these simplifying assumptions, this method provides numeric values of the face load distribution factor that are sufficiently accurate for industrial applications of gearing which fall within the limitations specified.

The first draft of this information sheet was made in February, 1996. This version was approved by the AGMA membership on October 22, 2000.

Special mention must be made of the devotion of Louis Lloyd of Lufkin for his untiring efforts from the submittal of the original software code through the prodding for progress during the long process of writing this information sheet. Without his foresight and contributions this information sheet may not have been possible.

Reaffirmed January 2018

Pages: 38

ISBN: 1-55589-779-7

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