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.

Mechanical Efficiency Analysis of a 16-Speed Bicycle Transmission Hub

2013 ◽  
Vol 284-287 ◽  
pp. 810-814 ◽  
Author(s):  
Yi Chang Wu ◽  
Pei Wun Ren
Keyword(s):  
Analytical Method ◽  
Power Flow ◽  
Planetary Gear ◽  
Mechanical Efficiency ◽  
Angular Speed ◽  
Efficiency Analysis ◽  
Gear Train ◽  
Flow Diagram ◽  
Gear Mesh ◽  
Analysis Process

This paper proposes an analytical method to evaluate the mechanical efficiency of the bicycle transmission hub. A 16-speed transmission hub, which consists of two transmission units and one differential unit, is presented first. By applying the concept of fundamental circuits, a step by step analysis process is then described to numerically calculate the angular speed, ideal torque and power flow, and actual torque and power flow by considering the gear-mesh loss of each link of the planetary gear train. Based on the power flow diagram, the mechanical efficiency at each speed of the transmission hub can be estimated.

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.

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.

Dynamics of the Gear Train Set in Wind Turbine

2011 ◽  
Vol 697-698 ◽  
pp. 701-705
Author(s):  
D.D. Ji ◽  
Y.M. Song ◽  
J. Zhang
Keyword(s):  
Wind Turbine ◽  
Dynamic Model ◽  
Harmonic Balance Method ◽  
Planetary Gear ◽  
Gear Train ◽  
Dynamic Responses ◽  
Multi Stage ◽  
Lumped Parameter ◽  
Cartesian Coordinate ◽  
The Impact

A lumped-parameter dynamic model for gear train set in wind turbine is proposed to investigate the dynamics of the speed-increasing gear box. The proposed model is developed in a universal Cartesian coordinate, which includes transversal and torsional deflections of each component, time-varying mesh stiffness, gear profile errors and external excitations. By solving the dynamic model, a modal analysis is performed. The results indicate that the modal properties of the multi-stage gear train in wind turbine are similar to those of a single-stage planetary gear set. A harmonic balance method (HBM) is used to obtain the dynamic responses of the gearing system. The responses give insight into the impact of excitations on the vibrations.

Signal Flow Graphs for Spatial Gear Trains

1994 ◽  
Vol 116 (1) ◽  
pp. 326-331 ◽  
Author(s):  
R. Ma ◽  
K. C. Gupta
Keyword(s):  
Operations Research ◽  
Equations Of Motion ◽  
Planetary Gear ◽  
Gear Train ◽  
Signal Flow ◽  
Signal Flow Graphs ◽  
Planetary Gear Trains ◽  
Gear Trains ◽  
System Variables ◽  
Flow Graphs

Signal flow graphs (SFG) have been applied in many areas such as circuit analysis, controls, mechanical vibrations, statistics, and operations research. They have also been applied to the analysis of planetary gear trains which are planar, i.e., where all of the gear axes are parallel. In this paper, signal flow graphs are applied to spatial planetary gear trains. Some additional terminology and rules which are needed for this important application are developed in this paper and illustrated by examples. The significance of applying SFG to a gear system is that the graph describes the interrelationship among the system variables by linking causes and effects, offers the information about the topology of system connection, and the kinematic equations of motion can be written easily by inspection. In this way, it helps use to visualize and understand spatial gear train systems better.

EMBODIMENT DESIGN OF NOVEL 5-SPEED REAR DRIVE HUBS FOR BICYCLES

2015 ◽  
Vol 39 (3) ◽  
pp. 431-441 ◽  
Author(s):  
Yi-Chang Wu ◽  
Tze-Cheng Wu
Keyword(s):  
Power Flow ◽  
Degrees Of Freedom ◽  
Planetary Gear ◽  
Gear Train ◽  
Main Body ◽  
Direct Drive ◽  
Drive Gear ◽  
Planetary Gear Train ◽  
Embodiment Design ◽  
The Relationship

This paper presents embodiment design of 5-speed rear drive hubs for bicycles. A 7-link, 2-degrees of freedom (DOF) compound planetary gear train as the main body of a rear drive hub is introduced. The relationship between the number of coaxial links of a planetary gear train and the number of gear stages that a drive hub can provide with is discussed. By means of kinematic analysis, four speed ratios of the planetary gear train are derived, which represents four forward gears of the rear drive hub. By adding a direct-drive gear, five forward gears can be provided and two feasible clutching sequence tables are synthesized. Manual translational-type gear-shifting mechanisms are further designed to incorporate with the planetary gear train for appropriately controlling the gear stage. The power-flow path at each gear stage is checked to verify the feasibility of the proposed design. Finally, two novel 5-speed bicycle rear drive hubs are presented.

Novel Configurations for Hybrid Transmissions Using a Simple Planetary Gear Train

2015 ◽  
Author(s):  
Huu-Tich Ngo ◽  
Hong-Sen Yan
Keyword(s):  
Hybrid Systems ◽  
Power Flow ◽  
Planetary Gear ◽  
Gear Train ◽  
Design Approach ◽  
Synthesis Process ◽  
Design Constraints ◽  
Planetary Gear Train ◽  
Operation Modes ◽  
Parallel Hybrid

This paper presents a design approach to systematically synthesize feasible configurations for series-parallel and parallel hybrid transmissions subject to design constraints and required operation modes using a simple planetary gear train (PGT). The configuration synthesis process includes two main steps: 1) assign inputs and output powers to the PGT subject to power constraints by the power arrangement process; and 2) assign clutches and brakes to the obtained systems subject to desired operation modes by the clutch arrangement process. By applying the proposed design approach, nine clutchless and 31 clutched configurations for series-parallel and parallel hybrid systems are synthesized, respectively. For each type of the hybrid systems, we analyzed kinematic and power flow of a new configuration to demonstrate the feasibility of the synthesized systems. The design approach can be used to systematically synthesize future hybrid transmissions with different mechanisms, design constraints, and desired operation modes.

Analysis of power flow in a counter-rotating epicyclic gearing for electrical propulsion system

2011 ◽  
Vol 225 (12) ◽  
pp. 2973-2980
Author(s):  
W K Shi ◽  
L J Li ◽  
D T Qin ◽  
T C Lim
Keyword(s):  
Power Distribution ◽  
Power Flow ◽  
Planetary Gear ◽  
Unmanned Vehicles ◽  
Propulsion System ◽  
Gear Train ◽  
Planetary Gear Train ◽  
Differential Gear ◽  
Electrical Propulsion ◽  
Single Input

A novel compound epicyclic gearing that combines a planetary gear train with a differential gear train is designed for an electrical propulsion system of underwater unmanned vehicles. This epicyclic gearing can transform a single input into two counter-rotating outputs with equal torque amplitudes and speeds. Based on the analysis method of power flow in the differential gear train, the character of the power flow of the compound epicyclic gearing was determined. After comparing with the power distribution of input flow, the condition of this mechanism without power recirculation was investigated. Because the reactive torque of the motor stator is balanced by the torque on ring gear of planetary gear train, no net torque acts on the vessel being propelled.

Analysis of the Non-Linear Dynamic Responses of an Elastic Rotor With a Slant Crack

2012 ◽  
Author(s):  
Xiangmin Zhang ◽  
Changping Chen ◽  
Liming Dai
Keyword(s):  
Equations Of Motion ◽  
Harmonic Balance Method ◽  
Rotor System ◽  
Dynamic Responses ◽  
Cracked Rotor ◽  
Lagrange Equations ◽  
Linear Dynamic ◽  
Slant Crack ◽  
Non Linear ◽  
Line Spring Model

Considering a rotor system with a slant crack, and using an equivalent line-spring model to simulate the slant crack of the rotor, the flexibility model of the slant-cracked rotor is derived. Then considered the geometric non-linearity and based on the Lagrange equations, the non-linear dimensionless differential equations of motion for the slant-cracked rotor are obtained. Further the non-linear dynamic responses of the single rotor system with a slant crack are discussed by the Galerkin method and the harmonic balance method. It’s detailedly studied that the angle, the depth and the position of the slant crack on the rotor all affect on the non-linear dynamic responses of the rotor system, and the conclusion is very significant to the design of the rotor system in the practical reference aspect.

scholarly journals Stress Assessment of Gear Teeth in Epicyclic Gear Train for Radial Sedimentation Tank

2020 ◽  
Vol 14 (3) ◽  
pp. 121-127
Author(s):  
Grzegorz Budzik ◽  
Tadeusz Markowski ◽  
Michał Batsch ◽  
Jadwiga Pisula ◽  
Jacek Pacana ◽  
...  
Keyword(s):  
Planetary Gear ◽  
Gear Train ◽  
Load Factor ◽  
The Finite Element Method ◽  
Gear Teeth ◽  
Gear Mesh ◽  
Sedimentation Tank ◽  
Epicyclic Gear ◽  
Comparison Of The Results ◽  
Root Stress

Abstract The paper presents the strength evaluation of planetary gear teeth designed for a radial sedimentation tank drive. A novel type of gear drive, composed of a closed epicyclic gear train and an open gear train with internal cycloidal gear mesh is proposed. Contact stress and root stress in the planetary gear train were determined by the finite element method and according to ISO 6336. The influence of the mesh load factor at planet gears on stress values was also established. A comparison of the results followed. It was observed that the mesh load factor on satellites depends mainly on the way the satellites and central wheels are mounted, the positioning accuracy in the carrier and the accuracy of teeth. Subsequently, a material was selected for the particular design of planetary gear and the assumed load. The analysis of the obtained results allowed assuming that in case of gears in class 7 and the rigid mounting of satellites and central wheels, gears should be made of steel for carburizing and hardening. In case of flexible satellites or flexible couplings in the central wheels and gears in class 4, gears can be made of nitriding steel.

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