Planetary Gear Train Dynamics

1994 ◽  
Vol 116 (3) ◽  
pp. 713-720 ◽  
Author(s):  
A. Kahraman
Keyword(s):  
Dynamic Behavior ◽  
Linear Time ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Planetary Gear ◽  
Gear Train ◽  
Planetary Gear Train ◽  
Gear Teeth ◽  
Linear Time Invariant ◽  
Mesh Phasing

A model to simulate the dynamic behavior of a single-stage planetary gear train with helical gears is developed. The three-dimensional dynamic model includes all six rigid body motions of the gears and the carrier. The generic nature of the formulation allows the analysis of a planetary gear set with any number of planets. Planets can be arbitrarily spaced (equally or unequally) around the sun gear. The model is also capable of handling different planet meshing conditions which are functions of number of gear teeth and planet positions. The linear time-invariant equations of motion are solved to obtain the natural modes and the forced vibration response due to static transmission errors. The proposed model is employed to describe the effects of the planet mesh phasing conditions on the dynamic behavior of a four-planet system.

Study on the Nonlinear Dynamics of a Single-Stage Gear Vibro-Impact System

2014 ◽  
Vol 697 ◽  
pp. 161-167 ◽  
Author(s):  
Ruo Yu Sheng ◽  
Yong Wang ◽  
Li Na Zhang
Keyword(s):  
Dynamic Model ◽  
Periodic Motion ◽  
Linear Time ◽  
Gear Tooth ◽  
Equations Of Motion ◽  
Simulation Method ◽  
Spur Gear ◽  
Single Stage ◽  
Gear Train ◽  
Linear Time Invariant

A vibro-impact dynamic model of a typical single-stage spur gear train has been proposed in this study. The lumped parameter dynamic model includes the constant meshing stiffnesses, the linear time-invariant viscous damping values and the gear clearance (backlash) non-linearity allowing teeth separations. With taking account of the effect on impact of gear tooth when meshing, the dynamic equations of motion are solved for the steady period response by use of analytical method under given periodic motion conditions. The feasibility of the given periodic motion conditions is demonstrated by comparing the analytical results with that of numeric simulation method. A Poincaré map of the system is established. The stability and bifurcation of the system are studied using analytical methods. Finally, the theoretical analyses are verified using numerical simulation.

scholarly journals Impacts of Backlash on Nonlinear Dynamic Characteristic of Encased Differential Planetary Gear Train

2019 ◽  
Vol 2019 ◽  
pp. 1-15 ◽  
Author(s):  
Zengbao Zhu ◽  
Longchao Cheng ◽  
Rui Xu ◽  
Rupeng Zhu
Keyword(s):  
Dynamic Equation ◽  
Nonlinear Dynamic ◽  
Planetary Gear ◽  
Gear Train ◽  
Planetary Gear Train ◽  
Gear Teeth ◽  
Nonlinear Dynamic Equation ◽  
Motion State ◽  
Nonlinear Dynamic Characteristic ◽  
The Impact

A multifreedom tensional nonlinear dynamic equation of encased differential planetary gear train with multibacklash and time-varying mesh stiffness was developed in the present research. The nonlinear dynamic response was obtained by solving the formulated nonlinear dynamic equation, and the impacts of backlash on dynamic characteristics of the gear train were then analyzed by combining time process diagram, phase diagram, and Poincaré section. The results revealed that bilateral shock in meshing teeth was caused due to smaller backlash, thus causing dramatic changes in meshing force; hence, the gears were found to be in a chaotic state. Further, during stable motion state, no contact between intermeshing teeth with bigger backlash was noticed; thus, they were in a stable quasiperiodic motion state in the absence of teeth exciting force. Therefore, in order to avoid a bilateral shock in gears as well as to maintain gear teeth lubrication, a slightly bigger backlash is required. The backlash change in any transmission stage caused significant impacts on gear force and the motion state of its own stage; however, the impact on gear force of another stage was quite small, whereas the impact on the motion state of another stage was quite large.

scholarly journals Effect of Tooth Profile Modification on Dynamic Tooth Load of Planetary Gear Train

2019 ◽  
Vol 2019 ◽  
pp. 1-20
Author(s):  
Jiaming Zhou ◽  
Fengyan Yi ◽  
Xiangyang Xu ◽  
Junbin Lai ◽  
Yanfang Liu ◽  
...  
Keyword(s):  
Dynamic Response ◽  
Linear Time ◽  
Planetary Gear ◽  
Tooth Profile ◽  
Gear Train ◽  
Time Varying ◽  
Planetary Gear Train ◽  
Profile Modification ◽  
Tooth Profile Modification ◽  
Deviation Factor

This paper aims at investigating the effects of tooth profile modification (TPM) on the dynamic response of planetary gear train (PGT). A numerical model is carried out to calculate two major excitation sources of PGT, time-varying mesh stiffness (TVMS), and transmission errors (TEs). On this basis, a linear time-varying dynamic model of a PGT considering TVMS, TEs, and TPM is developed. Dynamic deviation factor is further introduced to describe the dynamic response of the PGT. In this paper, TPM is only applied to the external meshes firstly. Effects of TPM parameters, such as amount of TPM, normalized modification angle, and modification curve, on the excitation sources and dynamic response of the PGT are discussed in detail. Subsequently, investigation on the effects of TPM only applied to internal meshes is conducted. Finally, with the aim to obtain the optimal TPM for the minimization of dynamic load of PGT in both external and internal gear meshes, the genetic algorithm (GA) is employed. This research may shed light upon design optimization of PGT with respect to improvement of vibration performance by means of optimized TPM.

Non-linear dynamic behaviour of compound planetary gear trains: Model formulation and semi-analytical solution

2009 ◽  
Vol 223 (3) ◽  
pp. 199-210 ◽  
Author(s):  
A Al-Shyyab ◽  
K Alwidyan ◽  
A Jawarneh ◽  
H Tlilan
Keyword(s):  
Power Flow ◽  
Linear Time ◽  
Equations Of Motion ◽  
Harmonic Balance Method ◽  
Planetary Gear ◽  
Periodic Variation ◽  
Gear Train ◽  
Gear Mesh ◽  
Non Linear ◽  
Direct Numerical Integration

A discrete, non-linear, time-varying, torsional dynamic model of a multi-stage planetary train that is formed by any number of simple planetary stages is proposed in this study. Each planetary stage has a distinct fundamental mesh frequency and any number of planets spaced in any angular positions. The model allows the analysis of the gear train in all possible power flow configurations suitable for various gear drive ratios. It includes periodic variation of gear mesh stiffnesses as well as clearance (backlash) non-linearities that allow tooth separations. Equations of motion for the general case are formulated and solved semi-analytically using a hybrid harmonic balance method (HBM) in conjugate with inverse Fourier transform. Relative mesh displacements along lines of action of individual gear pairs were used as the continuation parameters to pass singular points and ill-conditioned equations in their proximity. At the end, a case study of a two-stage planetary train is used to demonstrate the effectiveness of the model and solution methods. The HBM solutions are compared to those obtained by a direct numerical integration method to assess their accuracy.

Dynamic Characteristics of Double Helical Planetary Gear Train With Tooth Friction

2015 ◽  
Author(s):  
Fengxia Lu ◽  
Rupeng Zhu ◽  
Haofei Wang ◽  
Heyun Bao ◽  
Miaomiao Li
Keyword(s):  
Degrees Of Freedom ◽  
Sliding Friction ◽  
Planetary Gear ◽  
Gear Train ◽  
Variable Step Size ◽  
Step Size ◽  
Planetary Gear Train ◽  
Gear Mesh ◽  
Meshing Stiffness ◽  
Nonlinear Dynamics Model

A new nonlinear dynamics model of the double helical planetary gear train with 44 degrees of freedom is developed, and the coupling effects of the sliding friction, time-varying meshing stiffness, gear backlashes, axial stagger as well as gear mesh errors, are taken into consideration. The solution of the differential governing equation of motion is solved by variable step-size Runge-Kutta numerical integration method. The influence of tooth friction on the periodic vibration and nonlinear vibration are investigated. The results show that tooth friction makes the system motion become stable by the effects of the periodic attractor under the specific meshing frequency and leads to the frequency delay for the bifurcation behavior and jump phenomenon in the system.

Specific Conditions of A I ¯ -Planetary Gear Train

2019 ◽  
pp. 27-30
Author(s):  
Kiril Arnaudov ◽  
Dimitar Petkov Karaivanov
Keyword(s):  
Planetary Gear ◽  
Gear Train ◽  
Planetary Gear Train
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