Fault Detection of Planetary Gears Based on Signal Space Constellations

A new method to process the vibration signal acquired by an accelerometer placed in a planetary gearbox housing is proposed, which is useful to detect potential faults. The method is based on the phenomenological model and consists of the projection of the healthy vibration signals onto an orthonormal basis. Low pass components representation and Gram–Schmidt’s method are conveniently used to obtain such a basis. Thus, the measured signals can be represented by a set of scalars that provide information on the gear state. If these scalars are within a predefined range, then the gear can be diagnosed as correct; in the opposite case, it will require further evaluation. The method is validated using measured vibration signals obtained from a laboratory test bench.

ПІДБІР КІЛЬКОСТІ ЗУБЦІВ ПЛАНЕТАРНИХ МЕХАНІЗМІВ СХЕМ AA, II, AI, IA, І ЗА ДОПОМОГОЮ ПРОГРАМНОГО ЗАБЕЗПЕЧЕННЯ

Most of the methods for selecting the numbers of teeth of planetary mechanisms are based on general equations that take into account three main conditions for their existence: 1) ensuring a given gear ratio, 2) the condition of alignment, 3) the condition of assembly. The rest of the conditions are not included in the system of equations to be solved and are checked additionally. However, this approach has a number of disadvantages associated with the discreteness of the general equations depending on several parameters. Therefore, a method is proposed for selecting the number of teeth using equations obtained only when taking into account two mandatory conditions for the existence of planetary mechanisms: 1) ensuring a given gear ratio, 2) the condition of alignment. Equations for fitting by this method are presented. The remaining conditions for the existence of planetary gears are checked separately and as a result, unsuitable solutions are excluded. This approach ensures the selection of all existing solutions in a given range of teeth numbers with a relatively small number of iterations, but it is rational only when used on a computer. In this regard, the corresponding software has been written - the Planmex.exe program. A description of this program is given, which allows you to select the number of teeth of the wheels of the proposed schemes of planetary gears with a whole and fractional gear ratio, different modules of wheels on a double satellite, a different number of satellites in a given range of numbers of teeth, depending on the selected driving link. Three variants of optimization of the obtained results of selection of the number of teeth are proposed: 1) minimum mass, 2) maximum speed, 3) maximum efficiency. Coefficients are introduced to compare the results within each optimization option and equations are proposed to determine them. An example of the selection of the number of teeth for different modules of gears on a double satellite of the planetary mechanism of the AI scheme by the proposed method using the Planmex.exe program is given. The optimization of the obtained results is made according to three criteria, taking into account the region of existence of the given scheme.

An Analysis of the Gear Meshing Characteristics of the Main Planetary Gear Trains of Helicopters Undergoing Shafting Position Changes

The complex three-shaft three-reducer structural designs of helicopter transmission systems are prone to changes in the relative positions of shafting under the conditions of main rotor and tail rotor loads. These changes will affect the transmission characteristics of the entire transmission system. In this study, the planetary gear trains of helicopters were examined. Due to the fact that these structures are considered to be the most representative structures of the main reducers of helicopters, they were selected as the study objects for the purpose of examining the meshing characteristics of planetary gear trains when the relative positions of the shafting changed due to the position changes of the main rotor shafts under variable load conditions. It was found that by embedding the comprehensive time-varying meshing stiffness values of the main rotor shafts at different positions, a dynamic model of the relative position changes of the planetary gear trains could be established. Then, combined with the multibody dynamics software, the meshing characteristics of the sun gears, and the planetary gears, the planetary gears and the inner ring gears were simulated and analyzed under different inclinations and offsets of the shafting. The results obtained in this study revealed the following: (1) the average meshing force of the gears increased with the increases in the angle inclinations, and the meshing force between the sun gears and the planetary gears increased faster than the meshing force between the planetary gears and the inner ring gears. It was observed that during the changes in the shafting tilt positions, obvious side frequency signals had appeared around the peak of the meshing frequency in the spectrum. Then, with the continuous increases in the tilt position, the peak was gradually submerged; (2) the average meshing force of the gears increased with the increases in the offset, and the increasing trend of the meshing force between the sun gears and the planetary gears was similar to that observed between the planetary gears and the inner ring gears. It was found that when the shafting offset position changed, there were obvious first and second frequency doubling in the spectrum; (3) the mass center orbit radii of the sun gears increased with the increases in the shafting position changes, and the changes in the angular tilt position were found to have greater influencing effects on the mass center orbit radii of the sun gears than the changes in the offset positions. This study’s research findings will provide a theoretical basis for future operational status monitoring of the main transmission systems of helicopters and are of major significance for improvements in the operational stability of helicopter transmission systems, which will potentially ensure safe and efficient operations.

Electrified Powertrain with Multiple Planetary Gears and Corresponding Energy Management Strategy

Modern hybrid electric vehicles (HEVs) like the fourth generation of Toyota Prius incorporate multiple planetary gears (PG) to interconnect various power components. Previous studies reported that increasing the number of planetary gears from one to two reduces energy consumption. However, these studies did not compare one PG and two PGs topologies at their optimal operation. Moreover, the size of the powertrain components are not the same and hence the source of reduction in energy consumption is not clear. This paper investigates the effect of the number of planetary gears on energy consumption under optimal operation of the powertrain components. The powertrains with one and two PGs are considered and an optimal simultaneous torque distribution and mode selection strategy is proposed. The proposed energy management strategy (EMS) optimally distributes torque demands amongst the power components whilst also controlling clutches (i.e., mode selection). Results show that increasing from one to two PGs reduces energy consumption by 4%.

GEOMETRIC SYNTHESIS OF INVOLUTE PLANETARY GEARS WITH CONNECTED GEAR WHEELS OF TYPE 2K-H

Based on the basic law of flat interlocking, the paper considers a possibility of increasing the gear ratio of low module involute cylindrical planetary gears by using asymmetric tooth profile for the purposes of measuring devices. An example of the synthesis of such reduction gearing by optimal choice of asymmetry between the profiles and Possibility of generation III is presented. Also presented is a planar matching of the unconditional existence areas in the field of independent coefficients of instrument displacement by the straight optimization method and pre-set qualitative indicators of the gearing.

Analysis of flow regimes and associated sources of dissipation in splash lubricated planetary gear sets

Planetary gears are used in several applications given that they provide high reduction ratio in a compact size. Two kind of lubrication are used in this applications: injection or splash lubrication. In case of splash lubrication, the authors already highlighted the importance of the centrifugal effects leading to the formation of an oil ring inside the reducer, therefore giving a method to compute churning power losses. In this paper, another flow regime is underlined when centrifugal forces are not sufficient to turn the oil sump into a ring. In addition to this observation, an in-depth analysis is given regarding the dependence of the churning power losses with operating conditions and oil characteristics.