Influence of Carrier and Gear Manufacturing Errors on the Static Load Sharing Behavior of 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.

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

Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science ◽

10.1177/0954406219830436 ◽

2019 ◽

Vol 233 (21-22) ◽

pp. 7200-7211 ◽

Cited By ~ 5

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.

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Quasi-Static Load Sharing Characteristics of a Planetary Gear Set with Planet Journal Bearings

Applied Sciences ◽

10.3390/app10031113 ◽

2020 ◽

Vol 10 (3) ◽

pp. 1113

Author(s):

Zhiqiang Guo ◽

Shenlong Li ◽

Wei Wu ◽

Liuyang Zhang

Keyword(s):

Static Load ◽

Dynamic Performance ◽

Planetary Gear ◽

Load Sharing ◽

Journal Bearings ◽

Operating Conditions ◽

Computation Method ◽

Analysis Method ◽

Planetary Gear Sets ◽

Bearing Stiffness

The quasi-static load sharing characteristics of a planetary gear set with planet journal bearings are numerically investigated. The application of journal bearings instead of rolling bearings in planetary gear sets is an alternative to increase the rotation speed. Therefore, an effective analysis method is needed to estimate the dynamic performance of a planetary gear set with planet journal bearings. Here, an available load sharing factor computation method is developed considering the effect of the variable journal bearing stiffness. Results of an experiment are used to validate the effectiveness of the computation method. Furthermore, the load sharing characteristics of a planetary gear set with planet journal bearings are influenced by bearing parameters and operating conditions significantly due to the changing bearing stiffness of journal bearings. The effects on the load sharing factor and the bearing stiffness are studied in detail simultaneously based on the proposed analysis method. The load sharing factor of a planetary gear set with planet journal bearings has a similar variation with the bearing support stiffness under the same load. These researches provide a theoretical basis for the application of journal bearings in planetary gear sets.

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Investigation of Dynamic Load Sharing Behavior for Herringbone Planetary Gears considering Multicoupling Manufacturing Errors

Shock and Vibration ◽

10.1155/2021/5511817 ◽

2021 ◽

Vol 2021 ◽

pp. 1-15

Author(s):

Fei Ren ◽

Jinchen Ji ◽

Guofu Luo ◽

Shaofu Zhao ◽

Liya Zhao ◽

...

Keyword(s):

Planetary Gear ◽

Load Sharing ◽

Gear Train ◽

Actual Structure ◽

Lumped Parameter ◽

Manufacturing Errors ◽

Main Components ◽

Gyroscopic Effects ◽

Profile Errors ◽

Sharing Behavior

In this study, based on the lumped-parameter theory and the Lagrange approach, a novel and generalized bending-torsional-axial coupled dynamic model for analyzing the load sharing behavior in the herringbone planetary gear train (HPGT) is presented by taking into account the actual structure of herringbone gears, manufacturing errors, time-dependent meshing stiffness, bearing deflections, and gyroscopic effects. The model can be applied to the analysis of the vibration of the HPGT with any number of planets and different types of manufacturing errors in different floating forms. The HPGT equivalent meshing error is analyzed and derived for the tooth profile errors and manufacturing eccentric errors of all components in the HPGT system. By employing the variable-step Runge–Kutta approach to calculate the system dynamic response, in conjunction with the presented calculation approach of the HPGT load sharing coefficient, the relationships among manufacturing errors, component floating, and load sharing are numerically obtained. The effects of the combined errors and single error on the load sharing are, respectively, discussed. Meanwhile, the effects of the support stiffness of the main components in the HPGT system on load sharing behavior are analyzed. The results indicate that manufacturing errors, floating components, and system support stiffness largely influence the load sharing behavior of the HPGT system. The research has a vital guiding significance for the design of the HPGT system.

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Load-sharing analysis of two-stage three-branch star gearing based on deformation compatibility

Advances in Mechanical Engineering ◽

10.1177/1687814018819542 ◽

2018 ◽

Vol 10 (12) ◽

pp. 168781401881954 ◽

Cited By ~ 2

Author(s):

Jinfu Du ◽

Jin Mao ◽

Kai Liu ◽

Yahui Cui ◽

Guorui Zhao

Keyword(s):

Planetary Gear ◽

Load Sharing ◽

Gear Transmission ◽

Analysis Model ◽

Two Stage ◽

Manufacturing Errors ◽

Gear Manufacturing ◽

Central Gear ◽

Deformation Compatibility ◽

Branch Star

A load-sharing analysis methodology was proposed for the multiple-branch star gear transmission which is composed of a number of closed-loop power flows. The moment equilibrium and deformation compatibility equations for the two-stage star gearing were derived, which are clearly different from that used in planetary gear transmission. Then the load-sharing analysis model was established and employed to systematically study the load-sharing behavior of the two-stage three-branch star gearing, some untouched aspects were investigated. Results show that the most sensitive directions of the central and star gear assembly errors on load-sharing are along the meshing line. The effects of the size and direction of the central gear–manufacturing errors on load sharing are the same for each branch, the initial directions of the central or a certain star gear–manufacturing errors will have no effect on the load-sharing coefficient of the system, but the initial directions of the assembly errors will. The conditions in which the load distribution curves repeat the first track were also obtained. Finally, a numerical example of a three-branch star gear aviation reducer was adopted to verify the feasibility of this proposed method, and the calculation results show good agreement with a previously published and validated model.

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

Journal of Mechanical Design ◽

10.1115/1.4035554 ◽

2017 ◽

Vol 139 (3) ◽

Cited By ~ 12

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.

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Static Load Sharing Characteristics of Transmission Planetary Gear Sets: Model and Experiment

10.4271/1999-01-1050 ◽

1999 ◽

Cited By ~ 27

Author(s):

Ahmet Kahraman

Keyword(s):

Static Load ◽

Planetary Gear ◽

Load Sharing ◽

Planetary Gear Sets

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Pinion Assembly Strategies for Planetary Gear Sets

Journal of Mechanical Design ◽

10.1115/1.4023965 ◽

2013 ◽

Vol 135 (5) ◽

Cited By ~ 1

Author(s):

Pei-en Feng ◽

Yuxuan Qi ◽

Qingying Qiu

Keyword(s):

Mathematical Model ◽

Planetary Gear ◽

Load Sharing ◽

Assembly Sequence ◽

Statistical Calculation ◽

Phase Rule ◽

Position Errors ◽

Planetary Gear Sets ◽

Sharing Behavior ◽

Sequence Rules

Previous works illustrate that the orientation of pinion run-out errors has strong effect on the load sharing behavior of floating planetary gear sets. To minimize the inequality of load sharing, an in-phase rule for assembling pinions is recommended by other researchers, while a theoretical proof is still lacking. In this paper, not only the orientation but also the assembly sequence of the pinions is under scrutiny. A generalized mathematical model is developed in order to study the best load sharing conditions and floating gear sets with 4-6 pinions are specially treated. Through statistical calculation, several pinion sequence rules and orientation rules are extracted. By numerical simulation, four different pinion assembly strategies, which originate from the combinations of the existing rules and methods, are compared with each other. The most effective assembly strategies for systems with 4-6 pinions are proposed. The statistical analysis indicates that the proposed strategies significantly improve the load sharing behavior if only pinion run-out errors are considered and retain their effectiveness when pinhole position errors and tooth thickness errors are introduced as interference factors.

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