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Copyright of Journal of Ordnance Equipment Engineering is the property of Chongqing University of Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Lubrication Engineering (0254-0150) is the property of Editorial Office of LUBRICATION ENGINEERING and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Focusing on center distance adjustment, fatigue life balance, undercutting avoidance, wear improvement and load carrying capacity enhancement industrial applications, profile-shifted design is widely used in the planetary gear transmission system. However, there is little research on the influence of profile shift on the dynamic characteristics of planetary gears. A nonlinear planetary gears dynamic model of coupled translational–torsional is established, which considers the time-vary meshing stiffness (TVMS), backlash, friction and gyroscopic effect. Innovatively, using tooth contact analysis (TCA) to solve the meshing points of the profile-shifted planetary gears for calculating TVMS. The dynamic characteristics of profile-shifted planetary gears with friction are analyzed. The result can show that the motion state of planetary gears at high speed is more sensitive to profile shift compared with low speed, the impact caused by the reverse friction can reduce when meshing node is located in the double-tooth meshing area, the service life of the bearing can improve even if the lubrication conditions become worse when appropriate profile shift coefficient is selected. These results provide a reference for the dynamic performance improvement of the profile-shifted planetary gears. [ABSTRACT FROM AUTHOR]

Within planetary gear transmissions (PGTs), mode shapes and eigenfrequencies hold a crucial significance in operational reliability and efficacy. Mode shapes explain the unique motion patterns inherent in PGT systems. Conversely, eigenfrequencies describe the inherent frequencies at which PGT systems undergo vibration or oscillation upon exposure to external forces or disruptions. This research paper presents a comprehensive investigation into the dynamic behavior of a three-stage PGT utilized in medium and heavy trucks. This study introduces the Rayleigh energy method to assess system dynamics, revealing a bounded Rayleigh quotient related to the highest related eigenvalue. Then, this study delves into eigenfrequencies and the mode shape behavior of the adopted PGT model. The eigenfrequencies are identified as encompassing diverse vibrational modes of central components and planet gears. Moreover, a multi-scale analysis of the adopted PGT model is presented by deriving matrices for mass, bearing stiffness, and mesh stiffness. Comparisons with the Rayleigh energy method demonstrate the new approach's efficiency, exhibiting a low margin of error in the determination of eigenfrequencies. This investigation also highlights the alignment of identified mode shapes with the established literature, detailing the multi-scale approach's minor deviation in mode shape determination compared to the Rayleigh energy method. [ABSTRACT FROM AUTHOR]

Within planetary gear transmissions (PGTs), mode shapes and eigenfrequencies hold a crucial significance in operational reliability and efficacy. Mode shapes explain the unique motion patterns inherent in PGT systems. Conversely, eigenfrequencies describe the inherent frequencies at which PGT systems undergo vibration or oscillation upon exposure to external forces or disruptions. This research paper presents a comprehensive investigation into the dynamic behavior of a three-stage PGT utilized in medium and heavy trucks. This study introduces the Rayleigh energy method to assess system dynamics, revealing a bounded Rayleigh quotient related to the highest related eigenvalue. Then, this study delves into eigenfrequencies and the mode shape behavior of the adopted PGT model. The eigenfrequencies are identified as encompassing diverse vibrational modes of central components and planet gears. Moreover, a multi-scale analysis of the adopted PGT model is presented by deriving matrices for mass, bearing stiffness, and mesh stiffness. Comparisons with the Rayleigh energy method demonstrate the new approach’s efficiency, exhibiting a low margin of error in the determination of eigenfrequencies. This investigation also highlights the alignment of identified mode shapes with the established literature, detailing the multi-scale approach’s minor deviation in mode shape determination compared to the Rayleigh energy method.

Due to the symmetrical flank configuration, herringbone gears have no resulting axial forces and a smaller tooth width than helical gears. Because of existing manufacturing limitations, currently only double helical gears with wide center space or assembled herringbone gears are applied. In the present work, a novel machining method for herringbone gears by power skiving is presented. For this purpose, tool and technology are designed using a mathematical process model and tested subsequently. It is shown that the process can produce the required geometry with significant improvements on productivity and accuracy. Additionally, the unused center area can be eliminated. [ABSTRACT FROM AUTHOR]

Monitoring transmission systems is a huge scientific focus to prevent any anomaly and malfunctioning damaging the system. Several methods were used to investigate the gears behaviour and mainly its state. And until the last century, vibrations signals were the most performing technique in this field. However, nowadays, other alternatives are considered more accurate and accessible such as controlling the motor current signals to study the behaviour of the mechanical system. Within this context, this paper aims to study the electromechanical interaction between a double stage of planetary gearboxes driven by an asynchronous machine. The model used is based on a Park transformation for modelling the asynchronous machine and a torsional model to describe the dynamic behaviour of the double-stage planetary gearbox. Through this approach, the numerical simulations illustrate the impact of the tooth gear defect on the signature of the motor current. The results obtained from the simulations will be presented in the time domain and the frequency domain using the fast Fourier transform and the Hanning window to highlight the mechanical frequencies in the phase current spectrum. This work will be distinguished by validating the numerical results using experimental measurements, which will be displayed in order to justify the sensitivity of the model developed.

Wear debris generated in a pitting process of planetary gearboxes carries valuable information about health status. However, RGB images of online wear debris are often affected by image blur caused by Gaussian noise, high-frequency noise, and other random noises besides Gaussian noise, including bubbles in lubricating oil, dark oil caused by contamination, and the temperature rise of electronic components. To address these issues, in this work, an image denoising model WVBOD was proposed based on the fusion of wavelet, variational mode decomposition and non-local mean filtering, which makes full use of the advantages of above three denoising methods, removes the noise in the image and preserves the details of the image information. Comparing the peak signal-to-noise ratio and structural similarity of the denoised image using different models, the WVBOD objectively acquired better denoising result than other advanced denoising methods. In addition, the previous online wear debris features mainly focus on using changes in particle concentration to reveal the deterioration of the wear state. Based on the fact that the quantity of large wear debris increases with the evolution of gear pitting, a novel wear index $Z(i)$ , representing the size gradient of large wear debris and sensitive to an increase in large wear debris, is proposed for the denoising image. Then early fault warning can be realized for the planetary gearbox. Finally, it is verified by the size and quantity features extracted by using offline oil analysis techniques.

Planetary gear trains (PGTs) are widely used in many industrial applications from wind turbines to automobile transmissions due to their high power-to-weight ratio. Since PGT can be subjected to faults and prone to failure over time, a non-intrusive method of monitoring the condition of PGT is required. Vibration-based machine learning algorithms are mostly used in fault diagnosis and classification in PGT, but due to the epicyclic motion of gears, vibration signals from one gear can get neutralized or amplified by signals from another gear. In addition, identification of smaller cracks in the sun gear can be challenging when using vibration-based fault diagnosis alone due to cancelation effects from the planet pinions. In this paper, epicyclic drivetrain of a Chevy Volt hybrid car is considered to study two scenarios: (1) detecting microcracks (0.02 mm) and (2) identifying faults in sun gear while its signal is affected by cracks at the planetary gears. Four different cases: a healthy PGT, PGT with a sun crack, PGT with a planet crack, and a PGT with a sun and a planet crack, were considered and simulated using the MSC ADAMS software. The joint forces at the exterior ring gear were extracted, and a Blackman function was applied to conversion to frequency-domain values. Each of the frequency-domain amplitude values was converted to pixel values in a grayscale image, and the generated images were fed into a convolutional neural network (CNN) to train, validate, and test the datasets. The results indicated that the proposed grayscale 2D CNN algorithm has an accuracy of 92% for the test set. [ABSTRACT FROM AUTHOR]

Multimode hybrid powertrains have captured the attention of automotive OEMs for their flexible nature and ability to provide better and optimized efficiency levels. However, the presence of multiple actuators, with different efficiency and dynamic characteristics, increases the problem complexity for minimizing the overall power losses in each powertrain operating condition. The paper aims at providing a methodology to select the powertrain mode and set the reference torques and angular speeds for each actuator, based on the power-weighted efficiency concept. The power-weighted efficiency is formulated to normalize the efficiency contribution from each power source and to include the inertial properties of the powertrain components as well as the vehicle motion resistance forces. The approach, valid for a wide category of multimode powertrain architectures, is then applied to the specific case of a two-mode hybrid system where the engagement of one of the two clutches enables an Input Split or Compound Split operative mode. The simulation results obtained with the procedure prove to be promising in avoiding excessive accelerations, drift of powertrain components, and in managing the power flow for uphill and downhill vehicle conditions. [ABSTRACT FROM AUTHOR]

A method is proposed for determining the radius of curvature of transition curves in satellite-teeth profiles of planetary gears with internal engagement. The teeth are cut by a tool with a modified initial contour and are characterized by high flexural strength. The radii of curvature of tooth profiles cut by a standard tool and nonstandard (gear-shaping and rack) tools are compared. [ABSTRACT FROM AUTHOR]

Multimode hybrid powertrains have captured the attention of automotive OEMs for their flexible nature and ability to provide better and optimized efficiency levels. However, the presence of multiple actuators, with different efficiency and dynamic characteristics, increases the problem complexity for minimizing the overall power losses in each powertrain operating condition. The paper aims at providing a methodology to select the powertrain mode and set the reference torques and angular speeds for each actuator, based on the power-weighted efficiency concept. The power-weighted efficiency is formulated to normalize the efficiency contribution from each power source and to include the inertial properties of the powertrain components as well as the vehicle motion resistance forces. The approach, valid for a wide category of multimode powertrain architectures, is then applied to the specific case of a two-mode hybrid system where the engagement of one of the two clutches enables an Input Split or Compound Split operative mode. The simulation results obtained with the procedure prove to be promising in avoiding excessive accelerations, drift of powertrain components, and in managing the power flow for uphill and downhill vehicle conditions.

The article uses LabView to develop a fault diagnosis system for wind power planetary transmissions. First, use LabView software to create a signal acquisition system. Then, the built wind turbine planetary transmission experiment platform was combined with the NI9171 data acquisition card and the upper computer. The hysteresis brake was used in the laboratory to simulate the external wind environment, and the planetary gear transmission planetary gear crack fault diagnosis and testing experiments were performed. The frequency domain signal is obtained from the initial time domain signal obtained by the experiment through the EMD and envelope demodulation method. The frequency of the corresponding planetary gear crack in the frequency domain signal is compared with the theoretical calculation of the planetary gear crack failure frequency. The results show that the frequency of the corresponding planetary gear cracks in the frequency domain spectra obtained by the experiment is basically consistent with the theoretical calculation of the frequency of cracks in planetary gears. The fault diagnosis system developed by LabView is reliable. The experiment provides a theoretical basis for fault diagnosis, optimisation design, and life prediction of wind turbine planetary transmissions.

• A deformable transfer path premised model presents the vibration signal of planetary gears. • A numerical method presents to quantify signal respecting frequency and amplitude features. • The approaches are practical tools to predict spectral features of planetary gears with defects. • The validity of the methodology is verified by simulation and experimental signals. Planetary gear drives pose complex vibration signals due to that the excitations of the signal are the space-time varying meshing forces and the transfer paths for the excitations are time-varying systems. It brings about difficulties in machine diagnostics field to model, to predict, and to interpret the spectrum mechanism of the signal. This paper suggests a space-time model for this time-varying problem. Premised on deformable-body transfer path, the model formulates the response signal in frequency-domain as an integral transform of the excitations, where the transform kernel is formulated by the product of the Fourier kernel and the Frequency Response Function of the transfer path. A corresponding numerical method is also proposed for the numerical computation of the signal. Comparing with the existing model and method premised on rigid body transfer path, the proposed approach presents higher accuracy on signal prediction and spectral feature interpretation with respect to the frequency, amplitude and modal information. [ABSTRACT FROM AUTHOR]

The objective of this work was to design and build a fully mechanical knee orthosis. A knee orthosis should both allow control of the angle of flexion of the knee during the stance phase of the gait cycle and leave the joint free during the swing phase. Knee orthoses are normally used to assist the walking of people suffering from muscle weaknesses or gait pathologies in order to avoid excessive knee flexion during the stance phase. The design of the orthosis proposed in the present work is characterized by allowing the knee to be locked at any angle of flexion during the stance phase, and because the orthosis can be unlocked to allow the joint to be released in the swing phase without the action of any external agent, i.e., without requiring external electrical or electronic systems for the control and performance of the orthosis. These characteristics mean that the design can be adapted to the gait of any user. The proposed design consists of a set of three rods, one attached to the user's thigh, another to the calf, and the other to the foot, connected to each other by a self-locking planetary gear train (PGT). [ABSTRACT FROM AUTHOR]

In order to accurately predict ring gear deformations and to investigate the effects of ring gear flexibility on quasi-static behaviors of planetary gear sets, a complete load distribution model of planetary gear sets having flexible ring gears will be formulated here based on the baseline model proposed by the same authors (Hu, Y., Talbot, D., and Kahraman, A., 2018, "A Load Distribution Model for Planetary Gear Sets," ASME J. Mech. Des., 140(5), p. 053302). Direct comparisons to published experiments are provided to assess the accuracy of the proposed load distribution methodology. Example analyses with flexible ring gear rims are performed indicating that ring gear flexibility could influence gear mesh-level and planetary gear set system-level behaviors. Influence of spline supporting a ring gear is also investigated revealing that positions of planet branches with respect to external splines could influence ring deflections and resultant gear mesh load distributions. [ABSTRACT FROM AUTHOR]

Abstract In this paper, a two-stage planetary gear (TSPG) system with sliding friction and elastic continuum ring gear is presented to investigate the modal properties and avoid resonance through employing the lumped parameter method. For this purpose, this study addresses a new elastic-discrete model of the planetary gear, in which the sliding friction and elastic continuum ring gear are considered simultaneously. Compared with the present literature, the majority of previous works modeled ring gear as a rigid body and completely ignored the sliding friction. Additionally, the previous studies published are mainly about single-stage planetary gear. In this study, the translational-torsional motion equations of the new elastic-discrete model with sliding friction are derived theoretically. Afterwards, the effect of sliding friction on the time varying mesh stiffness is carried out. In order to clearly show the effect of the elasticity of ring gear, the modal properties for the TSPG system with different planet number, ring bending stiffness and sliding friction coefficient are investigated. The natural frequencies calculated by the elastic-discrete model are compared with the results obtained by lumped parameter model. Finally, the effect of sliding friction coefficient on the natural frequency is also analyzed. [ABSTRACT FROM AUTHOR]

The structural synthesis of planetary gear trains (PGTs) is helpful for innovating transmission systems in machinery. A great deal of research has been devoted to the synthesis of one-degree-of-freedom (1-DOF) PGTs over the past half century. However, most synthesis methods are limited to PGTs with no more than eight links. Moreover, the synthesis results are not consistent with each other. Until now, the inconsistency of synthesis results is still unresolved and exact synthesis results remain elusive. This paper presents a systematic and fully automatic method based on parent graphs to synthesize 1-DOF PGTs. The complete database of rotation graphs (r-graphs) and displacement graphs (d-graphs) of 1-DOF PGTs with up to nine links is established for the first time. All possible reasons for the contradictory synthesis results in the literature are analyzed and the controversy in the existing synthesis results which has lasted for nearly half a century is completely resolved. The exact results of the 6-, 7-, and 8-link r-graphs are confirmed to be 27, 152, and 1070, respectively. The exact results of the 6-, 7-, and 8-link d-graphs are confirmed to be 81, 647, and 6360, respectively. Additionally, the new results of 8654 r-graphs and 71,837 d-graphs of 9-link PGTs are provided for the first time. [ABSTRACT FROM AUTHOR]

A large number of machineries, such as long-wall shearer and tunnel boring machine, contain the multi-stage gear transmission system with planetary gears driven by electric motor, whose electromechanical characteristics have significant effect on the performance of machineries. Therefore, a test rig of this kind of transmission system is established, and the electromechanical dynamic model is also constructed for it, including the electric motor and the gear transmission. Moreover, to obtain more accurate simulation results, a method is proposed to estimate the equivalent damping value of the gear transmission system in the aspect of energy based on the testing data. Next, the electromechanical dynamic characteristics, including the motor current and the internal load of the gear transmission, are investigated by experiment and simulation under shock and step load to provide some guidance for improvingthe dynamic performance and monitoring the working state. The electromechanical dynamic modeling method is also well validated by the comparison between the simulating and test results. [ABSTRACT FROM AUTHOR]

Planetary gear trains (PGTs) are widely used in transmission systems. The structural synthesis of PGTs is an effective way to create novel and excellent transmissions. In the structural synthesis of PGTs, the isomorphism detection (ID) is an essential and especially important process. The ID aims to avoid duplication and guarantee the uniqueness of each PGT. The reliability of the ID method directly determines the accuracy of the synthesis result. Unfortunately, when the existing ID methods are used to synthesize PGTs, the synthesis results are not consistent with each other. A very important reason is that the ID methods fail to work in some cases. This fact gives rise to the need of an extremely reliable ID method, which may resolve the contradiction in the existing synthesis results in the future. In this paper, our previous perimeter loop-based ID method, which is applicable for linkage kinematic chains and has been proved to be reliable and efficient, is improved to detect isomorphic PGTs. The improvements relative to our previous method are discussed in detail. The present method is fully automated with the aid of a computer program, and verified by the atlas of PGTs with up to six links, as well as some PGTs with seven, eight, and ten links. [ABSTRACT FROM AUTHOR]

• Contributions of position errors on time-varying mesh phasing are investigated. • Frequency modulation mechanism of planetary gear vibrations is clarified. • Experimental method for measuring the meshing phase is proposed. This paper studies the changes in behavior, in terms of mesh phasing modulation, of planetary gear transmissions (PGTs) due to various gear pinhole position errors. An advanced model of the spur PGT is established to explore the effects of the position errors on mesh phasing relations and an analytical determination of the relative mesh phasing variation is derived. Furthermore, the vibration performance of planetary gears is investigated by developing a novel dynamic model and components of the vibration signals are clarified using the proposed model. Additionally, we further perform several experiments to measure the mesh phasing variations using strain gauges and collect the gear vibration signals using accelerometers. Finally, simulation and experimental results are compared to verify the proposed models, and the results indicate that the presented models provide the opportunity for the researchers to quantify the mesh phasing relations relative to the gear position errors as well as clarify the frequency modulation mechanism of gear vibrations in PGTs. [ABSTRACT FROM AUTHOR]

The tooth contact stiffness is very often included in dynamic mathematical models of gear drives. It is an important value for calculation of torsion eigenfrequencies as well as the dynamic properties of the whole transmission systems. Planetary gear drives have several advantages over simple parallel axis gears, especially due to theirs compact design and great torque-to-weight ratio caused by multiple parallel paths. However, the dimensional or mounting errors can cause that some planets have the tendency to take more load than the others. One of the ways how to improve load sharing is the application of flexible planetary pins or by using a free central wheel. However in such cases, the wheels motion is defined in one rotation coordinate and two translation coordinates — tangential and radial. The reaction force at radial change of axis distance is usually neglected. The focus of this contribution is to derive the stiffness of this radial connection and to analyse the influence of radial stiffness on planetary gear dynamics.

The article uses LabView to develop a fault diagnosis system for wind power planetary transmissions. First, use LabView software to create a signal acquisition system. Then, the built wind turbine planetary transmission experiment platform was combined with the NI9171 data acquisition card and the upper computer. The hysteresis brake was used in the laboratory to simulate the external wind environment, and the planetary gear transmission planetary gear crack fault diagnosis and testing experiments were performed. The frequency domain signal is obtained from the initial time domain signal obtained by the experiment through the EMD and envelope demodulation method. The frequency of the corresponding planetary gear crack in the frequency domain signal is compared with the theoretical calculation of the planetary gear crack failure frequency. The results show that the frequency of the corresponding planetary gear cracks in the frequency domain spectra obtained by the experiment is basically consistent with the theoretical calculation of the frequency of cracks in planetary gears. The fault diagnosis system developed by LabView is reliable. The experiment provides a theoretical basis for fault diagnosis, optimisation design, and life prediction of wind turbine planetary transmissions. [ABSTRACT FROM AUTHOR]

This paper introduces a generic function for automated modeling and feedforward control of planetary gears (PGs). Given the information on configuration, namely, the internal connection relationship between each PG, location of external torques, location and locking state of each clutch, this function outputs a ready-to-use kinetic model. The derived model can then be converted into numeric form by substituting the symbols in the matrix with real values and used for simulation, analysis or controller design. Since the output of the function is in symbolic form, it provides the theoretically most accurate results. Furthermore, compared to other kinds of automated modeling techniques for PG, the proposed function is: (a) more "straightforward" in a sense that it relies solely on direct matrix formulation and no other methods such as system identification are needed and therefore can be implemented in a single environment such as matlab; (b) more "generic" since it is capable of deriving both full-degrees-of-freedom (DOF) and reduced-DOF models for virtually any configuration regardless of the number, connection, and location of input/output shafts or clutches. By exchanging certain variables in the list of unknowns and knowns, the function can also be used to facilitate the design of feedforward controllers. [ABSTRACT FROM AUTHOR]

This paper focuses on the modeling method and the gravity-induced dynamic response of a spur planetary gear system with journal bearings. The lumped-parameter model of a planetary gear system with journal bearings is established. Both contact on drive-side and back-side of the tooth are considered simultaneously. Linear and nonlinear bearing force models are introduced into the system model separately to take the planet bearing oil-film forces into account. A demonstration is given to show the adopted nonlinear oil-film force model is still valid for the lubrication of support for planet gears. Equilibrium positions of the planet gear are depicted under different input rotational speeds and input torques. Under gravity effect, system responses at different rotational speeds are calculated by employing Newmark integration; tooth wedging at ring-planet meshes is examined with different backlashes. The system responses are presented as vibration spectra, planet bearing forces, orbits of members, tooth forces, and the percentage of tooth wedging in one carrier cycle. The results show that the gravity effect dominates the response at low rotational speeds. The linear bearing force model is not valid in some cases. The fluctuation of the bearing force and the enlargement of the planet orbits are induced by gravity effect. Tooth wedging is the combined effect of gravity, centrifugal force, and planet bearing clearance. [ABSTRACT FROM AUTHOR]

In a planetary gear train (PGT), the power loss by tooth friction is a function of the potential power developed within the gear train elements rather than that being transmitted through it. In the present work, we focus on the operating conditions of two-degree-of-freedom (two-DOF) PGTs. Any operating condition induces its own internal power flow pattern; this implies that tooth friction loss depends on the mechanism of power loss developed in the gearing that differs from one case to another over the entire range of operating conditions. The approach adopted in this paper stems from a unification of the kinematics and tooth friction losses of PGTs and is based on potential powers and power ratios. The range of applicability of the power relations is investigated and clearly defined, and tooth friction loss formulas obtained by their use are tabulated. A short comparison with formulas currently available in the literature is also made. The simplicity of the proposed method for analyzing two-input or two-output planetary gear trains is helpful in the design, optimization, and control of hybrid transmissions. It assists particularly in choosing correctly the appropriate operating conditions to the involved application. [ABSTRACT FROM AUTHOR]