Avinash Singh

An Experimental Study of the Influence of Manufacturing Errors on the Planetary Gear Stresses and Planet Load Sharing

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.

Application of a System Level Model to Study the Planetary Load Sharing Behavior

In planetary transmissions, the input torque is split between a number of parallel sun-pinion-ring gear paths. Under ideal conditions, each parallel path carries the same amount of torque. However, manufacturing errors in the pinion pin-hole location cause unequal load sharing between the parallel paths. The nature of this load sharing behavior depends upon the number of pinions in the planetary system. This load sharing behavior is studied for 4, 5, and 6-pinion variants of a planetary transmission. Critical manufacturing tolerances are identified and loss function curves are generated. The effects of sun gear support stiffness and pinion needle bearing stiffness on the load sharing results are also studied. It is shown that as the number of pinions in a planetary transmission increases, the pin-hole position error tolerance has to be tightened in order to reap the full benefits of load sharing between the pinions. Gear system analysis modules (GSAM) is an analytical tool that can model entire gear systems and will be used in this paper to quantify the load sharing between pinions. The numerical techniques implemented in GSAM will be briefly reviewed.

Internal Gear Strains and Load Sharing in Planetary Transmissions: Model and Experiments

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.

A Closed-Form Planet Load Sharing Formulation for Planetary Gear Sets Using a Translational Analogy

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.

Influence of Ring Gear Rim Thickness on Planetary Gear Set Behavior

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.

Influence of Planetary Needle Bearings on the Performance of Single and Double Pinion Planetary Systems

Planetary gears are widely used in automotive and aerospace applications. Due to demands for greater power density, these gearsets often operate at extremely high stress levels. This has caused system level influences once considered secondary to become critical to the success of planetary gears. One such system level effect that has been largely overlooked is the influence of support structures like planetary needle bearings. There are interactions between the gear distributed loads and the resulting bearing loads and deflections that have implications for both gear and bearing designs. Also, double pinion planetary arrangements are increasingly becoming common. There are still greater interactions between the gear and bearing components in double pinion planetary arrangements. In this paper, we will examine the influence of the bearing deflections (tilt) on the gear load distribution and contact pattern. We will also show the influence of distributed gear loads on the bearing loads (moments) and deflections (tilts). Both, single and double pinion planetary arrangements will be considered. It will be shown that the tilting stiffnesses of the needle bearings have a major influence on gear contact pattern and consequently on contact and bending stresses. It will also be shown that the double pinion planetary arrangement is more likely to result in off-centered loading. Parametric studies will be performed to show the influence of a few design parameters. Theoretical derivations will be validated by numerical simulations. A system level gear analysis model will be used to illustrate the issues involved and quantify the results.

An Experimental Investigation of Bending Fatigue Initiation and Propagation Lives

It has long been recognized that the fatigue life of a component can be divided into a crack initiation phase and a crack propagation phase, but researchers have typically ignored one phase or the other in their analytical models. Even in the stress-life method of life prediction, which implicitly includes both phases, no distinction is made between the initiation and propagation phases. In this paper a methodology for generating initiation and propagation S-N curves will be outlined. It will be shown that fbr components like gears, both phases represent significant portions of total life. It will also be shown that gear bending fatigue lives for variable amplitude load tests are better predicted by a two-stage linear damage theory compared to the commonly used Miners total life linear damage theory.

Development and Validation of an S-N Based Two Phase Bending Fatigue Life Prediction Model

The stress-life (S-N) method along with the Palmgren-Miner cumulative damage theory is the simplest and the most commonly used fatigue life prediction technique. Its main advantage is that the material properties needed are easy to collect and life calculation is simple. However under many variable amplitude loading conditions, life predictions have been found to be unreliable. Various modifications have been proposed to the Palmgren-Miner theory, but they have not lead to more reliable life predictions. In this paper, a two-stage cumulative damage model will be developed and validated. This model divides fatigue life into two phases-a crack initiation phase and a crack propagation phase. It will be shown that the proposed method results in greatly improved life prediction capabilities. Also, the proposed method retains the simplicity of the S-N based approach in that the material data is still relatively simple to generate and the calculations are straightforward.

Development and Validation of an Automotive Axle Power Loss Model

ABSTRACT This study proposes a methodology to predict power losses of automotive axle units, including both load-dependent (mechanical) and load-independent (spin) loss components. This methodology combines a mechanical hypoid gear mesh power loss model, a new tapered roller bearing mechanical power loss model, a gear drag loss model, and empirical viscous bearing power loss formulae to determine the total power loss of an axle unit. The proposed methodology captures the effects of operating conditions (speed and torque and oil temperature and level), contact surface roughness amplitudes, as well as bearing preload on power loss. The model is employed to simulate published axle efficiency experiments. Direct comparisons between measured and predicted power losses are presented to demonstrate the accuracy of the proposed modeling methodology.

An Experimental Investigation of Churning Power Losses of a Gearbox

.............................................................................................................................. ii Acknowledgements ............................................................................................................ iv Vita .......................................................................................................................................v List of Tables ................................................................................................................... viii List of Figures .................................................................................................................... ix Nomenclature ................................................................................................................... xiii