Effect of planet pin position errors on the fatigue reliability of large aviation planetary systems

doi:10.1007/s11465-024-0797-z

Front. Mech. Eng.

2024, Vol. 19

Issue (5) : 29 https://doi.org/10.1007/s11465-024-0797-z

Effect of planet pin position errors on the fatigue reliability of large aviation planetary systems

Ming LI¹(

), Zhixuan YANG¹, Liyang XIE²

¹. School of Mechatronics Engineering, Shenyang Aerospace University, Shenyang 110136, China
². Key Laboratory of Vibration and Control of Aero-Propulsion System (Ministry of Education), Northeastern University, Shenyang 110819, China

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Abstract

Planet pin position errors significantly affect the mechanical behavior of planetary transmissions at both the power-sharing level and the gear tooth meshing level, and its tolerance properties are one of the key design elements that determine the fatigue reliability of large aviation planetary systems. The dangerous stress response of planetary systems with error excitation is analyzed according to the hybrid finite element method, and the weakening mechanism of large-size carrier flexibility to this error excitation is also analyzed. In the simulation and analysis process, the Monte Carlo method was combined to take into account the randomness of planet pin position errors and the coupling mechanism among the error individuals, which provides effective load input information for the fatigue reliability evaluation model of planetary systems. In addition, a simulation test of gear teeth bending fatigue intensity was conducted using a power flow enclosed gear rotational tester, providing the corresponding intensity input information for the reliability model. Finally, under the framework of stress-intensity interference theory, the computational logic of total formula is extended to establish a fatigue reliability evaluation model of planetary systems that can simultaneously consider the failure correlation and load bearing time-sequence properties of potential failure units, and the mathematical mapping of planet pin positional tolerance to planetary systems fatigue reliability was developed based on this model. Accordingly, the upper limit of planet pin positional tolerance zone can be determined at the early design stage according to the specific reliability index requirements, thus maximizing the balance between reliability and economy.

Keywords planetary transmission manufacturing error system reliability tooth-root stress hybrid finite element gear test

Corresponding Author(s): Ming LI

Issue Date: 29 October 2024

Cite this article:

Ming LI,Zhixuan YANG,Liyang XIE. Effect of planet pin position errors on the fatigue reliability of large aviation planetary systems[J]. Front. Mech. Eng., 2024, 19(5): 29.

URL:

https://academic.hep.com.cn/fme/EN/10.1007/s11465-024-0797-z
https://academic.hep.com.cn/fme/EN/Y2024/V19/I5/29

Fig.1 Module division and implementation process.

Tab.1 Structural parameters of gears

Fig.2 Visualization model of planetary systems.

Fig.3 Meshing phases in planetary systems.

Fig.4 Geometric definition of planet pin position errors.

Fig.5 Carrier-pin and planet gear assembly. DoF: degree of freedom.

Fig.6 Solving the system control equations.

Tab.2 Support stiffness values used in the system model

Fig.7 Inter-planet power sharing and elastic deformation of planet carrier: (a1) balanced sharing; (b1) elastic deformation with no errors; (a2) unbalanced sharing; (b2) elastic deformation with errors. ND: node displacement.

Fig.8

e t 1

–

σ D

relationship plots: (a,e) ring gear teeth; (b,f) sun gear teeth; (c,g) planet gear teeth meshing with the ring gear; (d,h) planet gear teeth meshed with the sun gear.

Fig.9

e r 1

–

σ D

relationship plots: (a) ring gear teeth; (b) sun gear teeth; (c) planet gear teeth meshing with the ring gear; (d) planet gear teeth meshed with the sun gear.

Fig.10

e tr 1

–

σ D

relationship plots: (a) ring gear teeth; (b) sun gear teeth; (c) planet gear teeth meshing with the ring gear; (d) planet gear teeth meshed with the sun gear.

Fig.11

e t 12

–

σ D

relationship graph: (a) ring gear teeth; (b) sun gear teeth; (c) planet gear teeth meshing with the ring gear; (d) planet gear teeth meshed with the sun gear.

Fig.12 Planet pin position tolerance properties and errors point distribution.

Fig.13 Statistical flow chart of system load under different tolerance conditions.

Fig.14 Dangerous stress statistical results: (a) ring gear teeth; (b) sun gear teeth; (c) planet gear teeth meshing with the ring gear; (d) planet gear teeth meshed with the sun gear.

Fig.15 General layout of experimental equipment: (a) gear tester; (b) water tank; (c) vibration monitoring; (d) oil tank; (e) working principle schematic.

Fig.16 Test gearbox: (a) acceleration sensors; (b) gearbox interior structure.

Tab.3 Gear sample parameters

Fig.17 Gear sample: (a) sample appearance; (b) characteristics of broken tooth.

Fig.18 Schematic diagram of crack formation and extension.

Fig.19 Failure mechanism analysis and stress calculation: (a) tooth fracture; (b) stress calculation.

Fig.20 Statistical analysis of experimental data: (a) in the linear coordinate system; (b) in the single logarithmic coordinate system.

Component	Angular velocity	Relative angular velocity	Meshing times in time interval t
Sun	$ω S$	$p ? ω S / (1 + p)$	$n S (t) = p ? ω S ? t ? k P / (1 + p)$
Planet	$ω S / (1 − p)$	$2 p ? ω S / (1 − p 2)$	$n PS (t) = n PR (t) = 2 p ? ω S ? t / (p 2 − 1)$
Ring	0	$− ω S / (1 + p)$	$n R (t) = ω S ? t ? k P / (1 + p)$
Planet	$ω S / (1 + p)$	0	–

Tab.4 Kinematic parameters of planetary gear systems

Tab.5 Coefficient values and 95% confidence boundary

Fig.21 Running time (T)–fatigue reliability (R)–tolerance zone radius (r_IT) relationship curve.

Abbreviations
B	Planet bearing
C	Planet carrier
C+Pin	Carrier and planet pin assembly
P	Planet gear
Pin	Planet pin
R	Ring gear
RP	Ring-planet mesh
S	Sun gear
SR	Sun-ring mesh
SP	Sun-planet mesh
Variables
C	Gear tooth compliance matrix
D	Damping matrix
$e r j, e t j$	Radial and tangential position errors of planet pin
F	Gear mesh contact force vector
G	Geometric transformation matrix
I	Feature matrix
K_b	Support stiffness matrix
M	Mass matrix
n	Number of load cycles
q	Vector of unknown planet carrier modalities
RPi	Ring-planet mesh in the ith planet branch
SPi	Sun-planet mesh in the ith planet branch
T^ext	External load vector
T^fict	Fictitious load vector
T^grav	Gravitational load vector
$T ¯$	Net load vector
Y	Final separation vector
Z	Number of gear teeth
0	Nil matrix
σ	Stress level
ε	Initial separation vector
ε_er	Additional initial separation vector due to errors
Φ	Vibratory vector about the mean position
$Φ ˙$	Velocity vector
$Φ ¨$	Acceleration vector

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