Analysis Of Planetary Gear Trains Research Articles

Graphical method for the analysis of planetary gear trains

The main purpose of this paper is to propose a new graphical method for a planetary gear train (PGT) analysis. This is a fully graphical method that determines the rotational speeds of all transmission components, as well as the torque, power flow, power losses, and efficiency of any PGT. With this method, a sketcher workbench available in any modern computer-aided design (CAD) system can be used. This provides an interactive way to work. Both the construction of the geometric model and the interpretation of the results are intuitive, which facilitates error identification. Observing the impact of the selected input data or model parameters on the model behavior is extremely easy and can even be animated. It is believed that the presented method can streamline the PGT design process.

Comparison Of Tests For Isomorphism In Planetary Gear Trains

There are plenty of ways available for synthesis and analysis of Planetary Gear Trains (PGTs) of one DOF. However, every method has its own shortcomings. In this paper a comparison is made between Characteristic polynomial, Eigenvalues and Eigenvectors, Hamming Number Method and Modified Path Matrix (MPM) method. There are many methods available to test isomorphism in PGTs, out of which these four methods wasanalyzed in this paper. For a given PGT with a number of links and a single Degree of Freedom (DOF), adjacency matrix is enough to find out the Eigenvalues and Eigenvectors. Isomorphism of PGT is determined using the Eigenvalues. If Eigenvalues are similar then the PGTs are isomorphic. Similarly, if the characteristic polynomials of two PGTs are samethen it represents the isomorphic PGTs. Characteristic polynomials are determined from the Adjacency matrix. Hamming method also uses adjacency matrix to generate Hamming matrix. Hamming strings are developed from Hamming Matrix. Uniform hamming strings of two PGTsindicates isomorphism in PGTs. Along with isomorphism, Symmetry also known from the Hamming method. Modified path matrix method uses a connectivity matrix to generate MPM. If train values of two PGTs are same then they will be isomorphic otherwise non isomorphic. As per literature as the number of links increases the results may not be accurate with Characteristic coefficients and Eigenvalues methods, though all these methods are used to detect isomorphism among a group of PGTs. Whereas with the Hamming number approach, one can detect isomorphism, symmetry and number of possible level combinations of an PGT with a single hamming matrix.

The homotopy analysis for the nonlinear dynamics of planetary gear trains

In this paper, the nonlinear oscillation of planetary gear trains is investigated by the homotopy analysis method. The nonlinearity of planetary gear trains due to the periodically time-varying mesh stiffness and contact loss are included. In contrast to the perturbation analysis, the homotopy analysis method is independent of the contact loss ratio, and then can be applied to both small and large contact loss ratios. In this article, firstly the closed-form approximations for the primary resonance, sub-harmonic resonance, and super-harmonic resonance are obtained by homotopy analysis method. The accuracy of homotopy analysis method solutions is evaluated by numerical integration simulations. Results indicate that with relatively large contact loss ratios, the amplitude–frequency curves obtained by homotopy analysis method agree better with the results obtained by numerical integration than those obtained by the method of multiple scales. This study lays a higher accurate foundation for more complex nonlinear dynamic analysis of planetary gear trains.

Dynamic Analysis of Planetary Gear Train Based on ADAMS

Automatic pin machine is a kind of typical equipment widely used in mechanical and electronic industry, which is mainly used for automatic assembly of pinhole parts. In order to improve the efficiency and stability of the transmission system, the dynamic performance of planetary gears is studied. This paper uses UG to establish the dynamic model of planetary gears. Dynamic simulation and its motion law are obtained using Adams. The contact force between the planet gear and the center gear fluctuates around 5000N, and increases with the load. The results show that Adams can provide an effective prediction of the dynamic characteristics of planetary gear trains, and have a certain reference value for future structural improvements.

Kinematic Analysis of Planetary Gear Trains Based on Topology

Planetary gear trains (PGTs) are used in automatic transmission to achieve any desired speed ratios. At present, the study on the relationship between speed ratio and topology is not significant. Therefore, this paper focuses on studying the speed ratio based on topology. For this purpose, the graph theory is used to represent PGTs, and a concept of the speed topological graph is introduced. Based on the proposed graph representation, the relationship between the speed ratio and topology is studied. Three types of topological graphs are analyzed, which includes path, tree, and unicyclic graph, and necessary results are presented. The results reveal the relationship between speed ratio and topology, which helps in understanding the PGTs further. The result can help engineers to arrange the clutches and brakes to achieve desired speed ratio during the conceptual design phase, which can greatly improve the design efficiency of PGTs. The presented kinematics analysis method can be extended to analyze multi-input and multi-output planetary transmission.

New Graph Representation for Planetary Gear Trains

Planetary gear trains (PGTs) are widely used in machinery to transmit angular velocity ratios or torque ratios. The graph theory has been proved to be an effective tool to synthesize and analyze PGTs. This paper aims to propose a new graph model, which has some merits relative to the existing ones, to represent the structure of PGTs. First, the rotation graph and canonical rotation graph of PGTs are defined. Then, by considering the edge levels in the rotation graph, the displacement graph and canonical displacement graph are defined. Each displacement graph corresponds to a PGT having the specified functional characteristics. The synthesis of five-link one degree-of-freedom (1DOF) PGTs is used as an example to interpret and demonstrate the applicability of the present graph representation in the synthesis process. The present graph representation can completely avoid the generation of pseudo-isomorphic graphs and can be used in the computer-aided synthesis and analysis of PGTs.

Detection of Degenerate Structure in Single Degree-of-Freedom Planetary Gear Trains

Graph theory is a powerful tool in structural synthesis and analysis of planetary gear trains (PGTs). In this paper, a new algorithm has been developed for detecting degenerate structure in planetary gear trains. The proposed algorithm is based on the concept of fundamental circuits' rotation graphs. Detection of degeneracy is entirely based on finding one key element. The key element or link that makes planetary gear train into two groups is found in this work. The main advantage of the proposed method lies in the drastic reduction in the required combinatorial analysis compared to other methods available.

Damage Analysis of Planetary Gear Train in Wind Turbine Gearbox

Wind turbine industry is meaningful for the energy safety, but there are still some bottlenecks with the development of the wind turbine technology. How to improve the fatigue life and reliability of wind turbines has become a major problem. In this paper, the 1.5MW wind turbine gearbox was used as an example to study the damage mechanism of the planetary gear train. First, the chemical compositions, tensile properties, Rockwell hardness, impact energy and carburized depth of the gear and bearing material were measured, and the result shows that all the above-mentioned parameters can meet the design requirements, which means they are not the reasons causing the damage of the gear. Second, based on the actual patterns of the damaged components, the main source of damage is deduced to be the inner-hole surface of the planet gear. Further, the curves of the maximum sliding distance with respect to load under different fit tolerances (P6 & R6) were compared. As a result, P6 is found not a rational fit tolerance for the planetary gear train, and it is the main reason causing the damage of the gearbox. Therefore, fit tolerance R6 should be chosen for the design.

A universal kinematic analysis of geared mechanisms

A methodology for the kinematic analysis of planetary gear trains is presented. First, a definition for the gear train entity (GTE) is introduced, using the planet gears as the dividing element. Second, it is shown that the speed ratio of a GTE can simply be expressed symbolically in terms of its planet gear ratios. Then, for any planetary configuration, however complex, a single governing kinematic equation is developed, which then is manipulated to determine all possible overall speed ratios. Algebraic expressions for the speed ratios, of any GTE and/or planetary gear mechanism, can be obtained in terms of the teeth numbers, easily. Finally, three examples are presented; one includes a complicated fifteen-link PGT, to illustrate the simplicity of the method, the other compares the results of a bevel gear train with those of previous study.

M-DOF dynamic model for load sharing behavior analysis of PGT

A Multi-degree-of-freedom (M-DOF) nonlinear dynamic model for n-pinion Planetary gear train (PGT) is presented in this paper to investigate load sharing behavior of planet gears. In this dynamic model, manufacturing and assembly errors, elastic deformation and time-varying mesh stiffness are considered. Two sets of elastic compatibility equations are proposed to describe compatibility relationship between displacements, errors and elastic deformations. By means of Ishikawa formula, time-varying mesh stiffness of the gear pair is determined. The dynamic motion equations are solved with Runge-Kutta numerical integral method, which yields the displacements and deformations of each component. With the model, dynamic load sharing behavior of planet gears is evaluated. An example of 3-pinion PGT dynamic modeling is included, for which the influence of floating sun gear and adding flexible planet pin on the load sharing characteristics is analyzed.

Generalized kinematic analysis of planetary gear trains

This paper presents a generalised approach for the kinematic analysis of all types or planetary gear trains. The concept of generalized fundamental circuit equation is introduced to relate angular displacements and velocities for members of each fundamental circuit. According to fundamental circuits, generalised fundamental circuit equations and compatibility equations, are derived and solved systematically. Several examples, including planetary bevel–gear trains, worn–gear differentials and Bendix wrists, are illustrated in detail.

Vibration Analysis of Planetary Gear Trains Based on a Discrete-continuum Dynamic Model

A discrete-continuum dynamic model for spur planetary gear trains(SPGTs) is developed by using the sub-structure synthesis method. By combining the equation of motion of an elastic continuum ring subjected to internal and external constraints with lumped parameter equations of motion of rigid bodies, the system governing equations are obtained. A modal analysis is conducted to reveal the modal properties of spur planetary gear trains. The free vibration characteristics of the system are classified into four distinct modes: rotational, translational, planet and ring. For each vibration mode, the properties and reduced-order formulae are derived. The effect of ring elasticity on system natural characteristics is then discussed. The simulation results show that the elastic ring gear decreases the lower order natural frequencies and introduces a new vibration mode i.e. the ring mode. And the natural frequencies of the ring mode locate at the middle and low region of the overall system frequencies. The simulation indicates that the elasticity of ring gear must be considered during the dynamic design of planetary gear trains. A back-to-back test rig is constructed and some vibration tests are conducted. The experimental results agreed well with the theoretical and numerical analysis.

Random Vibration Analysis of Planetary Gear Trains

This article investigates the vibration response of a planetary gear train under excitations of both deterministic and random loads. A lumped parameter model has been used in this investigation and the random excitations are represented by white noise. One version of the stochastic Newmark algorithms is employed to solve for both sample path response and the statistics of the response. The mean and the variance for all state variables are obtained through the same algorithm. The effects of three different levels of noise on the statistics are compared against each other.

Vibrational Analysis of Planetary Gear Trains by Finite Element Method

Planetary gear trains produce several advantages, including high speed reduction, compactness, greater load sharing and higher torque to weight ratio, which are used widely in wind turbine, automobiles, robot and other applications. In some important transmission applications, the noise and vibration are key concerns in design. In this paper, a 3D dynamic contact and impact analysis model of planetary gear trains has been proposed. Tooth surface friction, backlash, tolerance of peg hole, and time-varying stiffness were considered in this dynamic model. The ANSYS / LS-DYNA were utilized to analyze the dynamic responses of gear transmission of the planetary gears. The vibration behavior of an actual gear set under dynamic loading was simulated in the dynamic model. The stiffness and elastic deformation of gear teeth are calculated using the finite element method with actual geometry and positions of the gears. The time-varying position of the carrier defined as the vibration and noise source. After impact analysis, the numerical results of vibration of carrier involved with the transient and steady states. Through the Fast Fourier Transform (FFT) methods, frequency spectrums of the transient and steady states of the calculated vibration of planet carrier are obtained for the gearbox designer to avoid the resonance zone.

A Simplified Approach Based Phase Angle for Tooth Contact Analysis of Planetary Gear Trains

Planetary gear trains have many advantages in applications. In these advantages, quiet noise and slight vibration may be contribute to low Transmission Error (TE), which can be calculated by Tooth Contact Analysis (TCA). However, to obtain numerical solution of the meshing equations based on TCA for planetary gear trains is very difficult because of a large number of nonlinear equations and unknowns. A simplified method utilizing planet phase angle is investigated and the numerical solution of planetary gear trains TE by TCA can be realized in this paper.

Tooth Contact Analysis of Planetary Gear Trains with Equally Spaced Planets

Based on Tooth Contact Analysis (TCA), a feasible approach for Transmission Error (TE) of planetary gear train is proposed in this paper. With a view to getting the total TE curve of the planetary gear train, a specific analysis of the TE from the planetary gear train with only one planet should be proceed firstly, the second step is to calculate each phase difference of planets in the gear train. The applicable conditions for the simplified calculation are spur gear or involute gear pairs in the gear train. Due to equal space between them, planets have the same phase angle.

The Analysis of Planetary Gear Trains

The generalized lever is a new tool in gear train representation. It extends the traditional concept of a lever representation of a planetary gear set to 1 that includes negative lever ratios. This allows an exhaustive permutation of the nodes of a lever, thereby leading to all possible topological arrangements of a planetary gear train. Consequently, we achieve a compact representation of large families of planetary gear trains, which would otherwise have to be dealt with on a case-by-case basis.

Survey of dynamics of planetary gear trains

Planetary gear trains (PGT) have been widely used in many industries due to their unique advantages over parallel shaft gear trains. With increased demand for high speed and low vibration and low noise machinery, dynamic analysis of PGT has gained importance. In this paper, the progress in dynamics of PGT made in the past two decades is reviewed. Discussion of the mathematical models used in dynamic investigation is presented first, followed by the solution methods. The discussion is organised into several distinct subtitles, including dynamic model, free vibration, forced vibration, load sharing, mesh phasing, and parametric stability, which covers the main aspects of PGT dynamics.

グラフ理論を用いた遊星歯車機構の運動解析

This paper facilitates the conception of signal flow graph theory, which makes it possible to determine, the angular velocity of the planetary gear trains. In design of the planetary gear train, the determination of the angular velocity of these is one of the important subjects. In almost the method used for kinematics analysis of planetary gear train are inherent for gearing itself and are tedius. In order to make these analysis of the planetary gear train understandable, the article proposes the representation by algebraic vector equation and graph theory for these problems. Moreover, the article presents examples of the application of this method for the complex type, 2K-H type and 3K type paradox gear trains.

Signal Flow Graphs for Spatial Gear Trains

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.