Number Of Planet Gears Research Articles

Experimental evaluation of the mesh load factor (Kγ) of a 6MW wind turbine gearbox

The significant increase in rotor diameters seen in modern wind turbines has pushed gearbox manufacturers to introduce technological innovations to increase the torque density of current designs. Driven by the need to lower the cost of energy from wind and size limitations imposed by logistic constraints in onshore wind, a trend has emerged to increase the number of planetary stages and the number of planet gears per stage. One of the main challenges of next-generation gearbox designs is sharing the load evenly between a high number of planets. This paper presents an experimental evaluation of the mesh load factor of a modern 6MW wind turbine gearbox with five planets in the first planetary stage. Results from the traditional method, based on tooth root strain gauges, and from strain measurements in the outer surface of the ring gear are described and assessed. Both experimental approaches have yielded lower mesh load factor values than the default values required in the standard “Design requirements for wind turbine gearboxes” IEC 61400-4. Since the mesh load factor is used for gear rating and sizing, a lower value allows a more optimized gearbox design, which leads to a significant improvement in torque density and cost.

Perturbation analysis of the two-to-one internal resonance of planetary gear trains

In this study, the two-to-one internal resonance between the first two rotational modes of planetary gear trains (PGTs) is investigated. A purely rotational model is applied considering mesh stiffness variations, tooth separations, and tooth profile modifications (TPMs). Semi-analytical solutions for the internal resonance case are obtained using the method of multiple scales (MMS). The solution equations indicate that the mesh stiffness variations and tooth separations are the main factors causing internal resonance. A validation of the MMS was performed by numerical integration (NI). The results from an example analysis indicate that there exists an internal resonance phenomenon in the case of ωN+2 ≈ ω2, where ω2 and ωN+2 are the natural frequencies associated with the rotational modes, and N is the number of planet gears. Internal resonance in PGTs causes chaos, and part of the energy is transmitted from the ring gear to the sun gear through shocks. Proper TPMs that eliminate the tooth separations could suppress the internal resonance. The internal resonance, in turn, affects the optimal areas of the TPM magnitudes.

An improved phenomenological model of vibrations for planetary gearboxes

Interpreting and understanding vibration characteristics are the cornerstone for health condition monitoring schemes of a planetary gearbox. Phenomenological modeling provides a concise and efficient mathematical description of sensor-related vibration measurements, thus allowing prior guidance for spectrum analysis to be relied on. In this paper, some overlooked problems during the modeling process in previous researches are pointed out and analyzed. Some discoveries are consequently obtained: First, the asymmetry of spectrum structure should be attributed to the magnitude randomness of gear meshing vibration rather than different phase angles of multiple-planet gears; Second, the basic frequency component to constitute a model, namely a product of the rotational frequency of a planet carrier and the number of planet gears, is far from sufficient to describe the actual vibrations; Finally, improper function the phases of multiple-planet gears will lose some sidebands that should have been. For these reasons, we map the phase variation of multiple-planet gears into the time-varying propagating distance, therefore, solving the neutralization phenomena of the frequency components. With consideration of the attenuation effect and random gear meshing magnitudes, an improved model is proposed to provide a more reasonable representation of the vibration behaviors, both for the dominant frequency components and structure. Simulation and experimental studies both demonstrate the higher fidelity and descriptive capability than the traditional models.

Experimental Study on the Carrier Pinhole Position Error Affecting Dynamic Load Sharing of Planetary Gearboxes

In gearbox design, small size, light weight, and long service life are important factors that must be considered. The planetary gear train structure has been widely used to realize these characteristics. In this study, the effects of increasing the torque on and changing the rotation direction of a planetary gearbox on the dynamic load sharing among the planet gears were analyzed experimentally using a planet carrier manufactured at an industrial site. When the number of planet gears was even, one pair of planet gears exhibited higher load sharing than the other two pairs among the three pairs of planet gears, where the two gears in each pair faced each other directly, regardless of the rotation direction of the gearbox. In addition, increasing the torque of the planetary gearbox improved the mesh load factor. The mesh load factor varied significantly as to the rotation direction changed, due to the phase change of the carrier pinhole position error.

유성기어박스의 캐리어 핀홀 위치 오차의 위상에 따른 유성기어의 하중 분할 연구

The planetary geartrain can be reduced in size and weight, and has excellent durability since the input torque is divided by the number of planet gears when the power is transmitted. In order to improve its durability, the load sharing among planet gears must be even. However, of the various manufacturing errors possible, the carrier pinhole position error has the greatest influence on load sharing. This study compared and analyzed the load sharing and the gear safety of planetary gears, according to the phase of the carrier pinhole position error. We confirmed that load sharing among the planet gears varied, depending on the phase of the carrier pinhole position error. The mesh load factor is inversely related to the gear safety factor for bending and contact, and affects the durability of the planetary geartrain. Also, in the design of the planetary geartrain, the load sharing among planet gears is directly affected by the carrier pinhole position error and its phase. Therefore, the geometric tolerance must be managed efficiently, which needs to be reflected in the production drawings.

Influence of the Number of Planet Gears on Planetary Meshing Noise

Influence of the Number of Planet Gears on Planetary Meshing Noise

Frequency response model and mechanism for wind turbine planetary gear train vibration analysis

Frequency components of complicated asymmetric modulation sidebands, existing in the vibration of the healthy planetary gear train, are prone to be erratically diagnosed as fault characteristics, which leads to difficulties in fault diagnosis of wind turbine planetary gearbox. The factors affecting the modulation sideband, i.e. the periodical time-varying transmission path and meshing force direction, are analysed. Considering both the meshing vibrations of the planet–ring and planet–sun gear pairs, a mathematical model was developed to analyse the planetary gear train's vibration response. Simulation and experiments were conducted, and the mechanism of vibration modulation sidebands was revealed. The modulation sideband is not caused by the meshing vibration itself, but by the testing method that sensors are fixed on the ring gear or gearbox casing. The frequency components and amplitudes of the sidebands are determined by the tooth number of the ring gear and sun gear, the number of planet gears and their initial assembling phases. The asymmetric modulation sideband is mainly caused by the phase difference of the initial planets' assembling phase.

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

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.

A novel order tracking method for wind turbine planetary gearbox vibration analysis based on discrete spectrum correction technique

Wind turbine gearboxes generally exhibit complex vibration characteristics due to wide variations in the operating conditions, and dynamics of the structure coupled with flexible supports. Conventional spectral analysis method may not provide reliable health monitoring and fault diagnosis of the gearbox. In this study, a novel order tracking method based on discrete spectrum correction technique is proposed to analyze wind turbine gearbox vibration for the purposes of health monitoring and fault diagnosis. The effectiveness and robustness of the proposed method are demonstrated through simulations and engineering tests. The results show that the shaft rotating speed could be accurately identified from the vibration signal together with amplitudes of significant gear meshing components. Modulation sidebands of both the planetary and fixed-shaft gears in a healthy wind turbine gearbox were further analyzed, which revealed inherent shaft misalignment in the fixed-shaft gear. Meshing frequency of the planetary gear was modulated by both the rotating frequencies of sun gear and planetary carrier, while fundamental modulation frequency of the planetary carrier was found to be related to rotating frequency of the carrier multiplied by the number of planet gears. The monitoring of such particular vibration features would be helpful in enhancing the operational performance of wind turbines through reliable health monitoring of gearboxes and reducing the misdiagnosis of faults.

Operation and Kinematic Analysis of a Cam-Based Infinitely Variable Transmission

In this paper, the operation and analysis of a novel, highly configurable, infinitely variable transmission of the ratcheting drive type is presented. This particular drive uses a cam and a number of cam followers rotatably mounted to a carrier plate to generate an oscillatory motion in an equal number of planet gears. A number of indexing clutches are then used to rectify this motion into a rotational output. A full description of the mechanism, including its components, operation, and kinematic equations, are presented. There are a number of inversions of this device, and their characteristics and limitations are discussed. In addition, a method is presented to select the most suitable inversion, gearing, and maximum follower velocity for a given set of requirements.

ＮｄＦｅＢ磁石を使用した磁気式遊星・差動歯車装置の試作研究

Magnetic gearing has many advantages. For example, it has noncontact meshing, is noiseless, oil-free and maintenance-free. We tried various types of magnetic gearing and investigated their performance characteristics. All magnetic gearing has some typical characteristics. A spur gear has internal and external meshing by changing the center distance of the gear. Recently, we tested the magnetic planetary gearing for use in wind power generators. This report describes performance characteristics, specifically, transmitted power efficiency and load-carrying capacity, of planetary gearing with full depth using the rare earth permanent magnet NdFeB. The main test parameters were the number of planet gears, input speed, and differential speed. Our results clarified the performance characteristics of magnetic planetary and differential gearing. The gear system was able to maintain a constant output speed for the sun gears by a differential operating outer ring gear despite a random input speed for the planetary gear. This system would be effective for wind power generators.

Effects of errors of elements on load distribution in planetary gears with various load equalizing mechanisms.

Equations of the equilibrium of statical forces acting on elements of planetary gear drive are deduced. Then using the equations, effects on the load equalizing mechanism, run-out and attachment errors of elements and the number of planet gears on load distribution rates of planet gears are obtained, with the following conclusions : In the case of three planet gears, one element among a sun gear, an internal gear and a planet carrier should be movable. Whereas in cases where the number of planet gears is more than four, the planet gears should be movable. Each direction of the run-out error of the planet gear at the initial state should be in the radial direction to the center of the planet carrier. The circumferential position of the planet gear shaft as well as radial one should be composed with special care.

薄肉内歯平歯車の作用線方向のたわみと剛性

A deflection of an internal gear with thin rim is composed of both the deflection of tooth and that of rim. Therefore an equation of deflection of a tooth of the internal gear is obtained by replacing the tooth by a cantilever composed of two trapezoid and an equation of deflection of a rim of the internal gear is obtained by replacing the internal gear by an equivalent ring. Then using the equations mentioned above and an equation of deflection of an external gear, which is widely used, the stiffness of a pair of teeth between the internal gear and a planet gear is illustrated against the number of teeth of the internal gear and that of the planet gear, and also the stiffness of the rim is illustrated against the number of planet gears, the number of teeth of the internal gear and the rim thickness. Further a load sharing rate of the internal gear with thin rim is discussed.