Printed with permission of the copyright holder, the American Gear Manufacturers Association, 1001 N. Fairfax Street, Fifth Floor, Alexandria, VA 22314-1587. Statements presented in this paper are those of the author(s) and may not represent the position or opinion of the American Gear Manufacturers Association. Introduction Inspection of the cutting blades is an important step in the bevel gear manufacture. The proper blade geometry ensures that the desired gear tooth form can be achieved. The accuracy of the process can be compromised when the blade profile consists of several small sections such as protuberance, main profile, top relief and edge radius. Another common obstacle — are outliers which can be caused by dust particles, surface roughness and also floor vibrations during the data acquisition. This paper proposes the methods to improve the robustness of the inspection process in such cases. The authors propose a procedure for using larger (combined) portions of the blades to evaluate the properties of the small features. This method was inspired by the standard AGMA/ANSI ISO 13281-B14 for the evaluation of tooth profiles on cylindrical gears. An example of the application could be the assessment of the pressure angle and blade distance in case when the blades have large toprem and flankrem sections (short cutting/ clearance edge portion). In cases where the measured data contains outliers, the filtering is proposed using the random sample consensus (RANSAC) procedure. The authors show the effectiveness of the procedure using the actual measurement data. Finally, the proposed methods were Figure 1 Face cutter head (Face Milling) with stick blades (Ref. 2).

A practical application of the spherical involute surface to the forged straight bevel gears is provided and demonstrated in this work. Conjugate (pure involute) theoretical surfaces are developed from the input design parameters. The surfaces are modified to suit the actual application (automotive differential). The unloaded (or low load) tooth contact analysis of modified surfaces is performed to obtain the prediction of the contact pattern. In order to verify the procedure and predictions, actual straight bevel gears are forged by using provided surfaces, and their contact pattern is compared to the predictions. Influence of the misalignments on the gear performance is investigated in order to provide more robust design.

In this study, results of an experimental and theoretical study on the influence of rim thickness of the ring gear on rim deflections and stresses and planet load sharing of a planetary gear set are presented. The experimental study consists of measurement of ring gear deflections and strains for gear sets having various numbers of planets, different ring gear rim thicknesses, as well as various carrier pinhole position errors. Root and hoop strain gauges and displacement probes are placed at various locations so that the variations due to external splines of the stationary ring gear can also be quantified. A family of quasistatic deformable-body models of the test planetary gear sets is developed to simulate the experiments. The predictions and measurements are compared with the assessment of the accuracy of the models within wide ranges of parameters. The influence of rim thickness on ring gear stresses and deflections and planet load sharing are quantified together with the interactions between the rim flexibility and the spline conditions. The results from this study confirm that the ring gear deflections and the ring gear support conditions must be included in the design process as one of the major factors.

A simplified discrete model to predict load sharing among the planets of a planetary gear set having carrier planet position errors is presented in this study. The model proposes a translational representation of the torsional system and includes any number of planets positioned at any spacing configuration. The discrete model predictions are validated by comparing them to (i) the predictions of a deformable-body planetary gear set model and (ii) planet load sharing measurements from planetary gear sets having three to six planets. A set of closed-form planet load sharing formulas are derived from the discrete model for gear sets having equally-spaced planets for conditions when all of the planets are loaded. These formulas allow, in an accurate and direct way, calculation of planet loads as a function of position errors associated with each planet.

In this study, results of an experimental and theoretical study on the influence of rim thickness of the ring gear on rim deflections and stresses, and planet load sharing of a planetary gear set are presented. Experimental study consists of measurement of ring gear deflections and strains for gear sets having various numbers of planets, different ring gear rim thicknesses as well as various carrier pin hole position errors. Root and hoop strain gauges and displacement probes are placed at various locations so that the variations due to external splines of the stationary ring gear can also be quantified. A family of quasi-static deformable-body models of the test gear planetary gear sets is developed to simulate the experiments. The predictions and the measurements are compared to assess the accuracy of the models within wide ranges of parameters. Influence of rim thickness on ring gear stresses and deflections and planet load sharing are quantified together with the interactions between the rim flexibility and the spline conditions. The results from this study confirm that the ring gear deflections and the ring gear support conditions must be included in the design process as one of the major factors.Copyright © 2009 by ASME and General Motors

This paper presents results of a comprehensive experimental and theoretical study to determine the influence of certain key factors in planetary transmissions on gear stresses and planetary load sharing. A series of tests are conducted on a family of planetary gear sets, and strains are recorded at various locations on the outer diameter and gear tooth fillet of the ring gear. Pinion position errors are introduced as a representative key manufacturing tolerance, and the resultant changes in the planetary behavior are observed. The experimental data are compared to the predictions of a state-of-the-art multi-body contact analysis model-Gear System Analysis Modules (GSAM). This model is capable of including the influences of a number of system-level variables and quantifying their impact on gear strains. The model predictions are shown to compare well with the measured strain at the ring gear outer diameter and tooth fillet. GSAM predictions of planet load sharing are then used to quantify the influence of tangential pinhole position errors on three-, four-, five-, and six-planet test gear sets. These predictions also agree well with the planet load sharing experiments presented in a companion paper.

In this paper, results of an experimental study are presented to describe the impact of certain types of manufacturing errors on gear stresses and the individual planet loads of an n-planet planetary gear set (n=3-6). The experimental setup includes a specialized test apparatus to operate a planetary gear set under typical speed and load conditions and gear sets having tightly controlled intentional manufacturing errors. The instrumentation system consists of multiple strain gauges mounted on the ring gear and a multichannel data collection and analysis system. A method for computing the planet load-sharing factors from root strain-time histories is proposed. Influence of carrier pinhole position errors on gear root stresses is quantified for various error and torque values applied to gear sets having three to six planets. The results clearly indicate that manufacturing errors influence gear stresses and planet load sharing significantly. Gear sets having larger number of planets are more sensitive to manufacturing errors in terms of planet load-sharing behavior.

In this paper, results of an experimental study are presented to describe the impact of certain types of manufacturing errors on gear stresses and the individual planet loads of an n-planet planetary gear set (n = 3 to 6). The experimental set-up includes a specialized test apparatus to operate a planetary gear set under typical speed and load conditions and gear sets having tightly controlled intentional manufacturing errors. The instrumentation system consists of multiple strain gauges mounted on the ring gear and a multi-channel data collection and analysis system. A method for computing the planet load sharing factors from root strain time histories is proposed. Influence of carrier pinhole position errors on gear root stresses are quantified for various error and torque values applied to gear sets having 3 to 6 planets. The results clearly indicate that manufacturing errors influence gear stresses and planet load sharing significantly. Gear sets having larger number of planets are more sensitive to manufacturing errors in terms of planet load sharing behavior.Copyright © 2007 by ASME and General Motors

A generalized formulation for analyzing speeds and forces of the gear components of planetary automatic transmissions is proposed. The formulation is capable of analyzing any typical one-degree-of-freedom automatic transmission gear train containing any number of simple, compound or complex-compound planetary gear sets. The formulation consists of three components: a kinematic analysis formulation to compute rotational speeds of gears and carriers, a gear ratio and kinematic configuration search algorithm, and a power flow analysis formulation. The kinematics component computes rotational speeds of gears and carriers. Given the type and number of planetary gear sets, the search algorithm determines all possible kinematic configurations and gear tooth count combinations that result in a required set of gear ratios while eliminating all kinematic redundancies and unfavorable clutching sequences. The third component, the power-flow analysis formulation, performs a complete static force (power-flow) analysis to determine all gear and bearing forces and moments, and clutch and connection torque values. A five-speed transmission example is considered to highlight the capabilities of the proposed formulation.