Planet Modes Research Articles

Natural Frequencies and Vibrating Modes for a Magnetic Planetary Gear Drive

In this paper, a dynamic model for a magnetic planetary gear drive is proposed. Based on the model, the dynamic equations for the magnetic planetary gear drive are given. From the magnetic meshing forces and torques between the elements for the drive system, the tangent and radial magnetic meshing stiffness is obtained. Using these equations, the natural frequencies and the modes of the magnetic planetary gear drive are investigated. The sensitivity of the natural frequencies to the system parameters is discussed. Results show that the pole pair number and the air gap have obvious effects on the natural frequencies. For the planetary gear number larger than two, the vibrations of the drive system include the torsion mode of the center elements, the translation mode of the center elements, and the planet modes. For the planetary gear number equal to two, the planet mode does not occur, the crown mode and the sun gear mode occur.

Natural frequencies and vibrating modes for a magnetic planetary gear drive

In this paper, a dynamic model for a magnetic planetary gear drive is proposed. Based on the model, the dynamic equations for the magnetic planetary gear drive are given. From the magnetic meshing forces and torques between the elements for the drive system, the tangent and radial magnetic meshing stiffness is obtained. Using these equations, the natural frequencies and the modes of the magnetic planetary gear drive are investigated. The sensitivity of the natural frequencies to the system parameters is discussed. Results show that the pole pair number and the air gap have obvious effects on the natural frequencies. For the planetary gear number larger than two, the vibrations of the drive system include the torsion mode of the center elements, the translation mode of the center elements, and the planet modes. For the planetary gear number equal to two, the planet mode does not occur, the crown mode and the sun gear mode occur.

Two output ways for electromechanical integrated toroidal drive

The electromechanical integrated toroidal drive has two kinds of output ways: rotor output and stator output. The differences between them in operating behavior have not been known yet. Here, using electromagnetic and mechanic theories, the equations of speed ratio of the drive system for two output ways are deduced. The generalized dynamic equations of the drive system for two output ways are presented. The differences in kinetics and dynamics of the drive system for different output ways are analyzed. Results show that the output ways of the drive system influence its vibrating modes. Changes of the natural frequencies along with output ways depend on the mass of the elements, the lead angles of the worm and stator, the supporting and meshing stiffness for coupled modes. For planet modes, the mass of the elements does not influence the natural frequencies of the drive system. The results are useful for prediction of the operating behaviors of the drive system for two output ways.

Effect of mesh phase on wave vibration of spur planetary ring gear

Abstract The distinctive wave vibration of a ring gear affected by mesh effect is investigated based on the inherent symmetry of spur planetary gears. Compared to prior analysis, this work mainly examines the forced flexural and extensional vibrations. The superposition principle and the Fourier series are introduced to jointly deal with the wave vibrations. The dynamics of the ring gear shows that the effect of the mesh phase on the wave vibration is mainly embodied by the specific relationships between the tooth number, the planet number, the largest common factor of them, the planets’ circumferential position, and the excited wave numbers in the typical rotational, translational and planet modes. For the equal systems, the three modes can be possibly excited depending on the specific mesh phase. And the dominant vibration orders of them are 0, 1 and 2, respectively. The non-zero lowest order is equal to the largest common factor of the two numbers. But for the diametrical ones, only the first two modes can be excited, and the dominant orders of them are 0 and 1, respectively. And the lowest non-zero wave number is 2 for even tooth number and 1 for odd tooth number. As a typical application, these relationships can be used to predict and suppress some potential wave resonances of the ring gear by optimizing the ring-planet mesh phase. The main results are demonstrated with finite element examples and comparisons with the existing literature.

Dynamic Characteristics of Planetary Gearbox of Shield Tunnelling Machine

Shield tunneling machine(STM) is a safety and high-efficiency excavator in the subway tunnel project, but the dynamics of whose multi-stage planetary gearbox is still a critical issue. In this paper, the torsional dynamic model for three-stage planetary gears train(PGT) is developed by lumped parameter method. According to the configuration and design parameters of the planetary gearbox, the natural frequencies are calculated, and the vibration modes are also analyzed. The natural modes can be classified into one of the three categories: rigid-body mode, distinct modes and planet modes. By using finite element(FE) method, the vibration characteristics of gearbox housing are also computed and analyzed for lucubrating vibration transfer and coupling between planetary gears train and housing, which is the important foundation for dynamic optimization of planetary gearbox.

Purely rotational model and vibration modes of compound planetary gears

This study develops a rotational degree of freedom model of general compound planetary gears . The model clarifies the conflicting gear mesh deflection expressions in prior research. For systems with identical, equally spaced planet trains in each stage, all vibration modes are classified into one of two types: overall modes and planet modes. In overall modes, all planet trains in the same planet set move identically. In planet modes, only one planet set has motion, and the motion of each planet train in this planet set is a scalar multiple of that of the arbitrarily chosen first planet train in this set. These structured vibration properties are analytically proven in this study.

Modal properties of three-dimensional helical planetary gears

The structured modal properties of single-stage helical planetary gears with equally spaced planets are categorized and mathematically proved. Compared to prior two-dimensional analyses of spur gears, this study examines the three-dimensional motion of the helical gears and shafts. A lumped-parameter model is formulated to obtain the equations of motion. The gear-shaft bodies are modeled as rigid bodies with compliant bearings at arbitrary axial locations on the shafts. A translational and a tilting stiffness account for the force and moment transmission at the gear mesh interface. The derived modal properties generalize those of two-dimensional spur planetary gears; there are twice as many degrees of freedom and natural frequencies due to the added tilting and axial motion. All vibration modes are categorized as rotational–axial, translational–tilting, and planet modes. The modal properties are shown to hold even for configurations that are not symmetric about the gear plane, due to, for example, shaft bearings not being equidistant from the gear plane.

Free Vibration for Toroidal Drive

In this paper, a multi-freedom dynamic model of the toroidal drive is presented. Using the model, the natural frequencies and vibration modes of the drive system are investigated. For identical, equally spaced planets, the resulting cyclic symmetry gives well-defined structure to the natural frequencies and vibration modes. The vibration modes are classified into rotational modes, planet modes, and single planet modes. The vibration and frequency characteristics of different modes are obtained. The relation between modes and half cone angle of the planet tooth is discussed. When the half angle equals zero, the single planet modes occur and numbers of the rotational modes and planet modes are reduced.

Structured Vibration Modes of General Compound Planetary Gear Systems

This paper extends previous analytical models of simple, single-stage planetary gears to compound, multi-stage planetary gears. This model is then used to investigate the structured vibration mode and natural frequency properties of compound planetary gears of general description, including those with equally spaced planets and diametrically opposed planet pairs. The well-defined cyclic structure of simple, single-stage planetary gears is shown to be preserved in compound, multi-stage planetary gears. The vibration modes are classified into rotational, translational, and planet modes and the unique properties of each type are examined and proved for general compound planetary gears. All vibration modes fall into one of these three categories. For most cases, both the properties of the modes and the modes themselves are shown to be insensitive to relative planet positions between stages of a multi-stage system.

Suppression of Planet Mode Response in Planetary Gear Dynamics Through Mesh Phasing

Abstract This work analytically derives design rules to suppress certain harmonics of planet mode response in planetary gear dynamics through mesh phasing. Planet modes are one of three categories of planetary gear vibration modes. In these modes, only the plantes deflect while the carrier, ring, and sun gears have no motion (Lin, J., and Parker, R. G., 1999, ASME J. Vib. Acoust., 121, pp. 316–321;J. Sound Vib, 233(5), pp. 921–928). The dynamic mesh forces are not explicitly modeled for this study; instead, the symmetry of planetary gear systems and gear tooth mesh periodicity are sufficient to establish rules to suppress planet modes. Thus, the conclusions are independent of the mesh modeling details. Planetary gear systems with equally spaced planets and with diametrically opposed planet pairs are examined. Suppression of degenerate mode response in purely rotational degree-of-freedom models achieved in the limit of infinite bearing stiffness is also investigated. The mesh phasing conclusions are verified by dynamic simulations of various planetary gears using a lumped-parameter analytical model and by comparisons to others’ research.

Free torsional vibration characteristics of compound planetary gear sets

A family of torsional dynamic models of compound gear sets is developed to predict the free vibration characteristics under different kinematic configurations resulting in different speed ratios. The compound gear sets considered consist of two planes of single- or double-planet gear sets connected by a straight long planet. All of the planets are mounted on a single carrier. The system matrices are derived for each power flow configuration separately and natural frequencies and the mode shapes are solved using the corresponding eigenvalue problem. Based on the predictions, the natural modes are classified into three groups: a rigid body mode, asymmetric planet modes and axi-symmetric overall modes. Smaller sub-system models are also proposed to predict each group of modes separately.

Analytical Characterization of the Unique Properties of Planetary Gear Free Vibration

This work develops an analytical model of planetary gears and uses it to investigate their natural frequencies and vibration modes. The model admits three planar degrees of freedom for each of the sun, ring, carrier and planets. It includes key factors affecting planetary gear vibration such as gyroscopic effects and time-varying stiffness. For the linear, time-invariant case, examination of the associated eigenvalue problem reveals the well-defined structure of the vibration modes, where the special structure results from the cyclic symmetry of planetary gears. Vibration modes are classified into rotational, translational and planet modes. The unique characteristics of each type of mode are analytically investigated in detail. For each class of mode, reduced-order eigenvalue problems are derived.