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.

A Gear Load Distribution Model for a Planetary Gear Set With a Flexible Ring Gear Having External Splines

2019 ◽  
Vol 141 (5) ◽  
Author(s):  
Yong Hu ◽  
David Talbot ◽  
Ahmet Kahraman
Keyword(s):  
Load Distribution ◽  
Planetary Gear ◽  
System Level ◽  
Distribution Model ◽  
Ring Gear ◽  
Baseline Model ◽  
Gear Mesh ◽  
Load Distributions ◽  
Planetary Gear Sets ◽  
Flexible Ring

In order to accurately predict ring gear deformations and to investigate the effects of ring gear flexibility on quasi-static behaviors of planetary gear sets, a complete load distribution model of planetary gear sets having flexible ring gears will be formulated here based on the baseline model proposed by the same authors (Hu, Y., Talbot, D., and Kahraman, A., 2018, “A Load Distribution Model for Planetary Gear Sets,” ASME J. Mech. Des., 140(5), p. 053302). Direct comparisons to published experiments are provided to assess the accuracy of the proposed load distribution methodology. Example analyses with flexible ring gear rims are performed indicating that ring gear flexibility could influence gear mesh-level and planetary gear set system-level behaviors. Influence of spline supporting a ring gear is also investigated revealing that positions of planet branches with respect to external splines could influence ring deflections and resultant gear mesh load distributions.

A Load Distribution Model for Planetary Gear Sets

2018 ◽  
Vol 140 (5) ◽  
Author(s):  
Y. Hu ◽  
D. Talbot ◽  
A. Kahraman
Keyword(s):  
Load Distribution ◽  
Planetary Gear ◽  
System Level ◽  
Distribution Model ◽  
Gear Mesh ◽  
Position Errors ◽  
Unequally Spaced ◽  
Planetary Gear Sets ◽  
Mesh Phasing ◽  
Gear Meshes

A load distribution model of planetary gear sets presented is capable of simulating planetary gear sets having component- and system-level design variations such as component supporting conditions, different kinds of gear modifications and planetary gear sets with different numbers of equally or unequally spaced planets as well as different gear set kinematic configurations while considering gear mesh phasing. It also accounts for classes of planetary gear set manufacturing and assembly related errors associated with the carrier or gears, i.e., pinhole position errors, run-out errors, and tooth thickness errors. Example analyses are provided to indicate the need for a model of this type when studying load distribution of planetary gear sets due to unique loading of the gear meshes associated with planetary gear sets. Comparisons to measurements existing in the literature are provided.

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 Load Distribution Model for Planetary Gear Sets

2017 ◽  
Author(s):  
Yong Hu ◽  
David Talbot ◽  
Ahmet Kahraman
Keyword(s):  
Load Distribution ◽  
Planetary Gear ◽  
Distribution Model ◽  
Component Level ◽  
Gear Mesh ◽  
Position Errors ◽  
Unequally Spaced ◽  
Planetary Gear Sets ◽  
Mesh Phasing ◽  
Gear Meshes

Here, a load distribution model of planetary gear sets is presented capable of dealing with planetary gear sets with any component level and gear set level design variations such as component supporting conditions, different kinds of gear modifications and planetary gear sets with different numbers of equally or unequally spaced planets as well as different gear set kinematic configurations while considering gear mesh phasing. It also accounts for classes of planetary gear set manufacturing and assembly related errors associated with the carrier or gears, i.e. pinhole position errors, run-out errors and tooth thickness errors. Example analyses are provided to indicate the need for a model of this type when studying load distribution of planetary gear sets due to unique loading of the gear meshes associated with planetary gear sets. Comparisons to measurements existing in the literature are provided.

A theoretical study of the overall transmission error in planetary gear sets

2019 ◽  
Vol 233 (21-22) ◽  
pp. 7200-7211 ◽  
Author(s):  
Y Hu ◽  
L Ryali ◽  
D Talbot ◽  
A Kahraman
Keyword(s):  
Planetary Gear ◽  
Transmission Error ◽  
Diagnostic Value ◽  
Distribution Model ◽  
Gear Mesh ◽  
Manufacturing Errors ◽  
Time Histories ◽  
Gear Manufacturing ◽  
Planetary Gear Sets ◽  
Error Behavior

In this study, a theoretical investigation on the overall loaded motion transmission error of planetary gear sets is presented. Planetary gear set load distribution model is employed to predict the input-to-output transmission error of planetary gear sets having distinct planet phasing conditions, to establish nominal transmission error behavior. Impact of carrier manufacturing errors resulting in unequal planet-to-planet load sharing on the gear set transmission error is quantified. Gear manufacturing imperfections such as run-out errors at their relative angles are introduced to observe their signatures on the resultant transmission error. Simplified formulations are presented to combine individual gear mesh transmission error functions with required modifications in order to obtain the overall transmission error. The predicted transmission error time histories are examined in the frequency domain to explore their diagnostic value in determining what errors the gear set possesses.

An Automated Design Search for Single and Double-Planet Planetary Gear Sets

2014 ◽  
Vol 136 (6) ◽  
Author(s):  
H. S. Kwon ◽  
A. Kahraman ◽  
H. K. Lee ◽  
H. S. Suh
Keyword(s):  
Performance Metrics ◽  
Gear Tooth ◽  
Planetary Gear ◽  
Automated Design ◽  
Geometric Design ◽  
System Level ◽  
Design Parameters ◽  
Tooth Contact Analysis ◽  
Gear Mesh ◽  
Planetary Gear Sets

Design of planetary gear sets is more involved than the design of their counter-shaft counterparts as it involves simultaneous design of a set of internal and external gear meshes while complying with a large number of systems and gear mesh related requirements for assembly, durability, noise, and efficiency. A manual iterative design process often results in suboptimal designs that fail to meet all these requirements simultaneously. In this paper, a methodology for an automated design search of single and double-planet planetary gear sets is proposed. With the input of a number of system-level constraints associated with the spacing and phasing of the planets, and acceptable ranges of basic geometric design parameters, this methodology defines a large design space in that a large number of geometric design concepts are identified and checked for any interferences. The external and internal meshes of these concepts are evaluated by using computationally efficient loaded gear tooth contact analysis model to predict their performance metrics such as transmission error amplitudes and contact and root stresses. They are then rank-ordered based on their performance metrics to identify balanced planetary gear set designs meeting all requirements equally well. At the end, results of an example design search were presented to demonstrate the effectiveness of the proposed methodology in defining a balanced solution that is acceptable in terms of all of its requirements.

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

2017 ◽  
Vol 139 (3) ◽  
Author(s):  
N. Leque ◽  
A. 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 (3D) 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 the three types of manufacturing errors, namely, constant errors such as carrier 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.

Experimental and Theoretical Investigation of Quasi-Static System Level Behavior of Planetary Gear Sets

2021 ◽  
Vol 143 (10) ◽  
Author(s):  
Lokaditya Ryali ◽  
Abhishek Verma ◽  
Isaac Hong ◽  
David Talbot ◽  
Farong Zhu
Keyword(s):  
Load Distribution ◽  
Planetary Gear ◽  
Load Sharing ◽  
Operating Conditions ◽  
Experimental Methodology ◽  
System Level ◽  
Distribution Model ◽  
Design Parameters ◽  
Static System ◽  
Planetary Gear Sets

Abstract This study presents a unique experimental methodology that synchronously measures various quasi-static responses of a simple four-planet planetary gear set, namely, planet load sharing, overall transmission error (OTE), and floating sun gear orbits. Strain gauges mounted directly on the planet pins were used to monitor the load shared among the planets, which is a crucial design criterion for durability and performance. High-precision optical encoders were used to measure the OTE of the gear set to explore its diagnostic value in identifying system errors. Radial motions of the floating sun gear, which are critical to the self-centering and load sharing behavior of the gear set, were monitored using magnetic proximity probes. The influence of various design parameters and operating conditions such as planet mesh phasing, carrier pin position errors, gear tooth modifications, and input torque on the system’s response will be investigated by performing an extensive set of experiments in a repeatable and accurate manner. Finally, these experimental results will be recreated theoretically using the static planetary load distribution model of Hu et al. (2018, “A Load Distribution Model for Planetary Gear Sets,” ASME J. Mech. Des., 140(5), p. 53302) to not only validate the model but also comprehend the measured behavior.

An Experimental Study on the Motion Transmission Error of Planetary Gear Sets

2015 ◽  
Author(s):  
B. Boguski ◽  
A. Kahraman
Keyword(s):  
Experimental Study ◽  
Power Flow ◽  
Critical Factor ◽  
Planetary Gear ◽  
Transmission Error ◽  
Ring Gear ◽  
Gear Mesh ◽  
Fixed Ring ◽  
Planetary Gear Sets ◽  
Planet Gear

An experimental study on the overall loaded motion transmission error of planetary gear sets is presented in this study. A test rig is designed and procured for the purpose of measuring the input-to-output transmission error of planetary gear sets within a range of input torque. The test matrix includes three distinct phasing conditions (in phase, sequentially phased and counter-phased) of a four-planet gear set as well as two planet tooth profile modifications. Two different power flow conditions with a fixed planet carrier and a fixed ring gear are considered. The transmission error results indicate that the phasing condition of the gear set is the most critical factor resulting in varying levels and numbers of modulation sidebands around the gear mesh orders. Planetary gear sets having in-phase planet meshes exhibit dominant gear mesh harmonic orders with little sideband activity, while sequentially-phased and counter-phased gear sets show an increase in planetary sideband orders associated with the sun, ring and planet gears. In addition, the power flow condition with fixed carrier is shown to have higher root-mean-square amplitudes of transmission error than configuration with a fixed ring gear.

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].

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