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.

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.

Time Varying Meshing Stiffness of Cracked Sun and Ring Gears of Planetary Gear Train

2015 ◽  
Vol 772 ◽  
pp. 164-168
Author(s):  
Arif Abdullah Muhammad ◽  
Guang Lei Liu
Keyword(s):  
Gear Tooth ◽  
Planetary Gear ◽  
Mesh Point ◽  
Gear Train ◽  
Time Varying ◽  
Planetary Gear Train ◽  
Meshing Stiffness ◽  
Face Width ◽  
The Face ◽  
Applied Forces

The time varying meshing stiffness of normal and cracked spur gears of planetary gear train is studied by applying the unit normal forces at mesh point on the face width along the line of action of the single gear tooth in FE based software Ansys Workbench 14.5. The tooth deflections due to the applied forces at one mesh point are noted and a deflection matrix is established which is solved using Matlab to get net deflection and finally the meshing stiffness of gear tooth at particular mesh point. The process is repeated for other mesh points of gear tooth by rotating it to get meshing stiffness for whole gear tooth.

scholarly journals Work of the planetary gear trains as differentials and their capabilities

2019 ◽  
Vol 287 ◽  
pp. 04001
Author(s):  
Kiril Arnaudov ◽  
Stefan Petrov ◽  
Emiliyan Hristov
Keyword(s):  
Degrees Of Freedom ◽  
Planetary Gear ◽  
Gear Ratio ◽  
Gear Train ◽  
Motor Drive ◽  
Planetary Gear Train ◽  
Maximum Security ◽  
Single Carrier ◽  
Planetary Gear Trains ◽  
Gear Trains

Planetary gear trains can work differently, namely, with F=1 degree of freedom, i.e. as reducers or multipliers, and also with F=2 degrees of freedom, i.e. as differentials. Moreover, with a two-motor drive they work as a summation planetary gear train and with a one-motor drive, they work as a division planetary gear train. The most popular application of planetary gear trains is as a differential which is bevel and is produced globally in millions of pieces. Some of the cylindrical planetary gear trains can also be used as differentials. Although less often, they are used in heavy wheeled and chain vehicles such as trailer trucks, tractors and tanks. They are also very suitable for lifting machines with a two-motor drive which provides maximum security for the most responsible cranes, such as the metallurgical ones. Initially the paper presents some simple, i.e. single-carrier cylindrical planetary gear trains, both with external and internal meshing, driven by 2 motors. Their kinematic capabilities and velocity, respectively, are considered to realize the necessary gear ratio. Finally, the case of a compound two-carrier planetary gear train is considered, which is composed of 2 simple planetary gear trains. This shows that not only the simple planetary gear trains, i.e. the single-carrier ones, can work as differentials.

scholarly journals Global Analysis of a Planetary Gear Train

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Tongjie Li ◽  
Rupeng Zhu
Keyword(s):  
Periodic Orbits ◽  
Shooting Method ◽  
Global Analysis ◽  
Planetary Gear ◽  
Mapping Method ◽  
Gear Train ◽  
Planetary Gear Train ◽  
Long Term Stability ◽  
Meshing Stiffness ◽  
Study Results

By using the Poincaré-like cell-to-cell mapping method and shooting method, the global characteristics of a planetary gear train are studied based on the torsional vibration model with errors of transmission, time-varying meshing stiffness, and multiple gear backlashes. The study results reveal that the planetary with a certain set of parameters has four coexisting periodic orbits, which are P-1, P-2, P-4, and P-8, respectively. P-1 and P-2 motions are not of long-term stability, P-8 motion is of local stability, and P-4 motion is of global stability. Shooting method does not have the capacity of searching coexisting periodic orbits in a global scope, and it is easy to omit some periodic orbits which are far away from the main gropes of periodic orbits.

Modeling and Bifurcation Characteristics of Double Stage Planetary Gear Train With Multiple Clearances

2015 ◽  
Author(s):  
Rupeng Zhu ◽  
Dongping Sheng ◽  
Fengxia Lu ◽  
Miaomiao Li ◽  
Heyun Bao
Keyword(s):  
Strong Coupling ◽  
Chaotic Motion ◽  
Damping Ratio ◽  
Period Doubling ◽  
Planetary Gear ◽  
Gear Train ◽  
Variable Step Size ◽  
Bifurcation Parameter ◽  
Planetary Gear Train ◽  
Motion State

This paper proposes a new non-linear transverse-torsional coupled model for double stage planetary gear train, and gear’s geometric eccentricity error, synthetical transmission error, time-varying meshing stiffness, sun-planet and planet-ring gear pair’s backlashes and sun gear’s bearing clearance are taken into account. The differential governing equations of motion are derived and solved by applying variable step-size Runge-Kutta numerical integration method. The system motion state is investigated systematically and qualitatively, and exhibits diverse bifurcation and chaos characteristics under different bifurcation parameters including meshing frequency, sun-planet backlash and planet-ring backlash. Analysis results showed that the increasing damping could suppress the region of chaotic motion and improve the system’s stability significantly; the route of period-doubling to chaotic motion was observed for both first and second stage’s motion state under the bifurcation parameter of meshing frequency; The routes of period doubling and crisis to chaos were identified under the bifurcation parameter of sun-planet backlash; Besides, the increasing damping ratio could split the bifurcation diagram window into different sections and strong coupling effects are generated to second stage’s motion. Several different types of routes to chaos were observed under the bifurcation parameter of planet-ring backlash including period doubling and 3T-periodic channel; Besides, it concluded that planet-ring backlash could generate a strong coupling effect to both stage’s nonlinear behavior.

Capturing Assembly Constraints of Experimental Setups in a Virtual Laboratory Environment

2012 ◽  
Author(s):  
El-Sayed Aziz ◽  
Yizhe Chang ◽  
Sven K. Esche ◽  
Constantin Chassapis
Keyword(s):  
Degrees Of Freedom ◽  
Planetary Gear ◽  
Gear Train ◽  
Virtual Laboratory ◽  
Assembly Process ◽  
Laboratory Equipment ◽  
Planetary Gear Train ◽  
Laboratory Environment ◽  
Assembly Constraints ◽  
Train System

Recently, multi-player game engines have been explored regarding their potential for implementing virtual laboratory environments for engineering and science education. In these developments, the virtual assembly process of the laboratory equipment is a critical step, and a detailed formalized description of how different components of the experimental equipment are to be joined in the assembly process is necessary. This description includes the joint types (lower and upper kinematic pairs) and the associated degrees of freedom, the resulting mobility of the assembly as well as the joint fit requirements. In this paper, a formalized representation of the assembly process that captures the information on the joint kinematics and the components’ degrees of freedom generated when assembling laboratory equipment in a virtual laboratory environment will be discussed. A planetary gear train system will be used as an example to illustrate the proposed method. In particular, the structure of the assembly of a planetary gear train system involves assembly constraints between a group of components (sun, planet and ring gears, shafts, planet carrier assembly, etc.) that generate the desired relationship between the input and output motions. This paper will identify important requirements for modeling different configurations of planetary gear train assemblies within a game-based virtual laboratory environment. These requirements include the positioning and the orienting of the components, the verification of the kinematic joints, the propagation of the mating constraints and the capturing of the joint attributes.

The principles of selecting floating members of 2K-H planetary gears for load balancing design

2015 ◽  
Vol 231 (9) ◽  
pp. 1589-1598
Author(s):  
Tang Jinyuan ◽  
Liu Yang ◽  
Cai Weixing
Keyword(s):  
Load Balancing ◽  
Mechanical Model ◽  
Load Transfer ◽  
Planetary Gear ◽  
Gear Train ◽  
Planetary Gear Train ◽  
Vector Method ◽  
Planetary Gears ◽  
Meshing Stiffness ◽  
Manufacturing Errors

This paper studies the load balancing problems caused by manufacturing and assembly errors of 2K-H planetary gear train. Based on the geometric equivalent relationship and spring mechanical model of load transfer, the relations between the load balancing of planetary gears and the mesh clearance and meshing stiffness are derived. Besides, the vector method is also derived to calculate the meshing clearance which is a result of the deviation of the component center caused by manufacturing errors and assembly errors. On the basis of the meshing clearance calculation formulas, the balanced load structure based on floating members is analyzed, and the results show: 1) when the number of planet gears is [Formula: see text], the floating of the basic members can compensate for the errors of the planet wheels; 2) when the number of planet gears is [Formula: see text], the errors of the planet wheels cannot be compensated by floating the basic components, and the compensation can only be made through the floating of the planetary gear. In addition, a number of recommendations are proposed to improve the performance of the planetary gear train set.

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