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

2007 ◽  
Author(s):  
Avinash Singh ◽  
Ahmet Kahraman ◽  
Haris Ligata
Keyword(s):  
System Analysis ◽  
Gear Tooth ◽  
Planetary Gear ◽  
Load Sharing ◽  
Companion Paper ◽  
System Level ◽  
Outer Diameter ◽  
Ring Gear ◽  
Analysis Model ◽  
Position Errors

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 is 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 pin hole position errors on the 3, 4, 5, and 6 planet test gear sets. These predictions also agree well with the planet load sharing experiments presented in a companion paper [20].

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

2008 ◽  
Vol 130 (7) ◽  
Author(s):  
Avinash Singh ◽  
Ahmet Kahraman ◽  
Haris Ligata
Keyword(s):  
System Analysis ◽  
Gear Tooth ◽  
Planetary Gear ◽  
Load Sharing ◽  
Companion Paper ◽  
System Level ◽  
Outer Diameter ◽  
Ring Gear ◽  
Analysis Model ◽  
Position Errors

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 multibody 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.

scholarly journals Analytical study of floating effects on load sharing characteristics of planetary gearbox for off-road vehicle

2020 ◽  
Vol 12 (7) ◽  
pp. 168781402094046
Author(s):  
Woo-Jin Chung ◽  
Joo-Seon Oh ◽  
Hyun-Woo Han ◽  
Ji-Tae Kim ◽  
Young-Jun Park
Keyword(s):  
Safety Factor ◽  
Planetary Gear ◽  
Load Sharing ◽  
Position Error ◽  
System Level ◽  
Load Factor ◽  
Road Vehicle ◽  
Design Modification ◽  
Planetary Gearbox ◽  
Position Errors

Uneven load sharing of a planetary gear set is the main cause of preventing the miniaturization and weight reduction of a planetary gearbox. Non-torque loads and carrier pinhole position errors are the main factors that worsen the load-sharing characteristics. However, their effects are seldom analyzed at a system level especially for an off-road vehicle. To make up this gap, some simulation models are proposed to investigate the effects of floating members on the load-sharing characteristics and the strength of a planetary gear set with non-torque load and carrier pinhole position error. When the error is not considered, the mesh load factor converges to unity irrespective of the type and number of floating members and the safety factors for pitting and bending are increased slightly. When the carrier pinhole position error is considered, the mesh load factor dramatically worsens. Although it is improved using the floating members, it does not converge to unity. However, the bending safety factor of the planet gear with the error is increased by 26%. This indicates that the design modification for the original planetary gearbox is needed to satisfy the safety factor requirement, but the problem is solved using only floating members.

Influence of Gear Rim Deflections on Planetary Gear Set Behavior

2009 ◽  
Author(s):  
H. Ligata ◽  
A. Kahraman ◽  
A. Singh
Keyword(s):  
Deformable Body ◽  
Planetary Gear ◽  
Load Sharing ◽  
Ring Gear ◽  
Hoop Strain ◽  
Position Errors ◽  
Study Results ◽  
Planetary Gear Sets ◽  
Support Conditions ◽  
Major Factors

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.

A Load Distribution Model for Double-Planet Planetary Gear Sets

2019 ◽  
Author(s):  
Yong Hu ◽  
David Talbot ◽  
Ahmet Kahraman
Keyword(s):  
Load Distribution ◽  
Gear Tooth ◽  
Planetary Gear ◽  
System Level ◽  
Distribution Model ◽  
Ring Gear ◽  
Gear Mesh ◽  
Manufacturing Errors ◽  
Planetary Gear Sets ◽  
Bearing Stiffness

Abstract In this paper, a load distribution model for a double-planet planetary gear set is developed by modifying an existing single-planet planetary gear set model [1] to account for an additional planet to planet gear mesh and their impact on phasing relationship among different sun-planet, planet-planet and planet-ring gear meshes. Similar to the single-planet planetary gear set model, the double-planet planetary gear set model accounts for effects of various component and system level variations such as supporting conditions, gear tooth modifications, manufacturing errors and kinematic configurations. The double-planet planetary gear load distribution model is derived for both rigid and flexible ring gear rim, while only parametric studies for a rigid ring gear rim is presented in this paper to demonstrate load distribution characteristics of double-planet planetary gear sets with different planet bearing stiffness and combination of various types of manufacturing errors, including pin hole position error and runout errors.

Influence of Ring Gear Rim Thickness on Planetary Gear Set Behavior

2010 ◽  
Vol 132 (2) ◽  
Author(s):  
A. Kahraman ◽  
H. Ligata ◽  
A. Singh
Keyword(s):  
Deformable Body ◽  
Planetary Gear ◽  
Load Sharing ◽  
Ring Gear ◽  
Hoop Strain ◽  
Position Errors ◽  
Study Results ◽  
Planetary Gear Sets ◽  
Support Conditions ◽  
Major Factors

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 Three-Dimensional Load Sharing Model of Planetary Gear Sets Having Manufacturing Errors

2015 ◽  
Author(s):  
Nicholas D. Leque ◽  
Ahmet Kahraman
Keyword(s):  
Three Dimensional ◽  
Planetary Gear ◽  
Load Sharing ◽  
Distribution Model ◽  
Gear Mesh ◽  
Position Errors ◽  
Proposed Model ◽  
Manufacturing Errors ◽  
Manufacturing Tolerancing ◽  
Planetary Gear Sets

Planet-to-planet load sharing is a major design and manufacturing tolerancing issue in planetary gear sets. Planetary gear sets are advantageous over their countershaft alternatives in many aspects, provided that each planet branch carries a reasonable, preferably equal, share of the torque transmitted. In practice, the load shared among the planets is typically not equal due to the presence of various manufacturing errors. This study aims at enhancing the models for planet load sharing through a three-dimensional formulation of N-planet helical planetary gear sets. Apart from previous models, the proposed model employs a gear mesh load distribution model to capture load and time dependency of the gear meshes iteratively. It includes all three types of manufacturing errors, namely constant errors such as planet pinhole position errors and pinhole diameter errors, constant but assembly dependent errors such as nominal planet tooth thickness errors, planet bore diameter errors, and rotation and assembly dependent errors such as gear eccentricities and run-outs. At the end, the model is used to show combined influence of these errors on planet load sharing to aid designers on how to account for manufacturing tolerances in the design of the gears of a planetary gear set.

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

2009 ◽  
Vol 131 (2) ◽  
Author(s):  
H. Ligata ◽  
A. Kahraman ◽  
A. Singh
Keyword(s):  
Closed Form ◽  
Discrete Model ◽  
Deformable Body ◽  
Planetary Gear ◽  
Load Sharing ◽  
Position Errors ◽  
Model Predictions ◽  
Planetary Gear Sets ◽  
Torsional System

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.

Load Sharing in a Planetary Gear Stage in the Presence of Gear Errors and Misalignment

1985 ◽  
Vol 107 (1) ◽  
pp. 4-10 ◽  
Author(s):  
P. Ma ◽  
M. Botman
Keyword(s):  
Dynamic Analysis ◽  
Planetary Gear ◽  
Load Sharing ◽  
Dynamic Loads ◽  
Ring Gear

A method of analysis is described of dynamic loads occurring in the planetary gear stages of the gearboxes of PT6 turboprop engines. The dynamic loads are important for the design of lightweight and durable components. A rigorous dynamic analysis, which includes the effects of nonlinear tooth stiffnesses, ring gear flexibility, gear errors and misalignments, is necessary to determine dynamic tooth loads and the load sharing among the planets. Results are presented of sample calculations for a typical gear stage.

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

2004 ◽  
Vol 127 (3) ◽  
pp. 469-476 ◽  
Author(s):  
Avinash Singh
Keyword(s):  
System Analysis ◽  
Load Sharing ◽  
System Level ◽  
Bearing Stiffness ◽  
Level Model ◽  
System Level Model ◽  
Manufacturing Tolerances ◽  
Planetary Transmission ◽  
Sharing Behavior ◽  
Input Torque

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.

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

2003 ◽  
Author(s):  
Avinash Singh
Keyword(s):  
System Analysis ◽  
Load Sharing ◽  
System Level ◽  
Bearing Stiffness ◽  
Level Model ◽  
System Level Model ◽  
Manufacturing Tolerances ◽  
Planetary Transmission ◽  
Sharing Behavior ◽  
Input Torque

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, pinion needle bearing stiffness, and input torque 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.

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