Planetary Transmission Research Articles

A novel method for ring-planet gear mesh force identification via SVD-based Kalman filter

Dynamic mesh forces are the primary vibration excitations of the planetary gear transmission systems. However, they are difficult to measure directly, and conventional indirect measurement methods are typically only applicable to specific planetary gear sets with special measuring equipment. This study proposes a more widely applicable method for identifying the mesh forces of ring-planet gear pairs by utilizing vibration signals. To this end, a ring gear dynamic model is established based on the elastic theory of the thick ring in the form of a space state system. The state vector of the model is constructed from parameters of ring gear vibration responses, while the input state vector is derived from parameters of dynamic mesh forces. A singular value decomposition (SVD)-based Kalman filter is employed to provide a stable solution for the estimation of state vector and input vector simultaneously. A mesh force indirect measurement method based on tooth fillet strain signals collected by strain gauges is adopted to evaluate the accuracy of identification results. Results of dynamic experiments conducted in a planetary gear set test rig demonstrate that compared with measured results, the proposed method can obtain acceptable estimated mesh forces of ring-planet gear pairs by using vibration signals.

Dynamic modeling and vibration analysis of an RV reducer with defective needle roller bearings

The rotate vector (RV) reducer's needle roller bearings (NRBs) are vulnerable to wear and flaws such as fatigue spalling of the raceway material. Studying the vibration mechanism and the excitation laws of NRB failures is essential to enhancing the RV reducer's performance and comprehending its operating state. This paper presents a dynamic model of the RV reducer based on the theory of contact multibody dynamics. It integrates internal and external raceway defects and takes into account the synchronous contact interaction between NRB groups and the crankshaft and cycloidal gears, as well as the time-varying mesh stiffness in the planetary gear transmission and cycloidal pin transmission. The study demonstrates that the rolling of bearings and the meshing of internal transmission components are the primary causes of vibration in a healthy RV reducer through experimental verification and dynamic simulation analysis of the system with and without NRB failures. Both the crankshaft rotation frequency and the cycloidal gear rotation frequency affect the vibration excitation source's characteristic frequency. The vibration amplitude of the RV reducer is influenced by bearing flaws on a periodic basis. The impact of internal raceway defects is greater than that of external raceway faults, resulting in a notable rise in vibration amplitude.

Analysis of vibration and load-sharing characteristics of two-stage planetary gear transmission system with cracks

To reveal the influence of cracks on the dynamic characteristics of a two-stage planetary gear transmission system (TSPGTS), a nonlinear dynamic model with 30-DOF in bending and torsion was constructed, taking into account parameters of different crack degrees (depth, angle, length), as well as factors such as error, time-varying meshing stiffness (TVMS), and damping. In the model, the TVMS model of components with cracks was established using the potential energy method. By incorporating the crack factor into the model, time domain, frequency domain, phase diagram, and Poincare diagram characterizing the dynamic load characteristics were obtained, as well as the curve of dynamic load-sharing characteristics changing with cracks. The influence of different crack degrees on the displacement vibration and dynamic load characteristics of the system was analyzed, and vibration testing experiments were conducted on the system with planetary gear cracks. The results indicate that when the gear contains cracks, it will lead to a decrease in the stiffness of the system, when cracks appear on the II-stage planetary gear, the system will experience impact components with intervals of the rotation period of the II-stage planetary gear, and obvious sidebands will appear near the meshing frequency doubling. These situations will become more pronounced as the degree of cracks intensifies. As the degree of cracks in the II-stage planetary gear increases, the dynamic load-sharing characteristics of the TSPGTS will first improve and then deteriorate, and as the degree of cracks increases, the external and internal dynamic load coefficients continue to increase. Through experiments, the influence of normal gears and cracked gears on system vibration changes was compared and analyzed, and the theoretical results were in good agreement with experimental results, verifying the correctness of the theoretical model. This provides a theoretical basis for fault diagnosis and reliability research of the system.

ДОСЛІДЖЕННЯ ПЕРЕДАТНИХ ВІДНОШЕНЬ ПЛАНЕТАРНИХ ПЕРЕДАЧ ПІДЙОМНО-ТРАНСПОРТНИХ МАШИН

Lifting and transporting machines (PTM) are one of the important equipment for the mechanization of work in various spheres of the national economy. In addition to the multi-rescue system, the cargo lifting mechanism also includes a winch. Winches with one drum, which have standard parameters - traction force from 3.2 to 125 KN at rope speed from 0.5 to 0.1 m/s, are most often used in PTM. Such winches include a two-stage gear reducer that connects the electric motor with the drum. Such a winch drive scheme is quite large and has considerable weight. One of the areas that will help reduce these indicators is the use of planetary gearboxes. They allow the use of winches in which the electric motor and gearbox are coaxial, and the planetary gearbox itself can be mounted in the drum. Such a drive scheme of the load lifting mechanism allows to reduce the dimensions and weight of the winch. The paper considers the calculation and compares the transmission ratios of planetary gears, which are used and can be used in lifting and transporting machines to reduce the dimensions and weight of cargo lifting mechanisms. Schemes of simple and closed planetary gears, as well as a scheme with three central gears, are given. The scheme of the planetary transmission with free gear wheels is considered. The presence of internal gears and several satellites makes planetary gears compact and light in weight. AII transmission with two internal gears and a free carrier allows to obtain significant transmission ratios with a small number of gears. Schemes of planetary gears with free gears allow you to change the angular speed of the output shaft.

Automatic configuration analysis method of planetary gear automatic transmission

Planetary gear trains (PGT) with the aim of achieving multiple speed ratios are widely used in automatic transmission (AT). A fast configuration analysis method is of significance for improving the efficiency of AT design, and it is essential to study the automatic configuration analysis method for AT. For this purpose, the AT configuration is represented by a matrix model, which includes the structural matrix of PGT and shifting elements (SEs) matrix. Based on the proposed matrix representation, the speed relation and torque relation matrices of AT are automatically derived to analyze the kinematics and dynamics. Five performance indexes of AT configuration, specifically transmission ratio, rotation speed of components, torque transmitted by SEs, power flow, and transmission efficiency, are automatically calculated through the analysis result. The entire analysis process can be completed in 1 s on the computer. The proposed matrix model offers a unified representation for the configuration of AT derived from different synthesis algorithms. It facilitates rapid automated configuration analysis and performance evaluation, thereby positively influencing the design of automatic transmissions. Furthermore, the matrix model can be applied to the configuration synthesis of AT.

Design, Simulation and Multi-Objective Optimization of a Micro-Scale Gearbox for a Novel Rotary Peristaltic Pump.

Peristaltic pumps are widely used in biomedical applications to ensure the safe flow of sterile or medical fluids. They are commonly employed for drug injections, IV fluids, and blood separation (apheresis). These pumps operate through a progressive contraction or expansion along a flexible tube, enabling fluid flow. They are also utilized in industrial applications for sanitary fluid transport, corrosive fluid handling, and novel pharmacological delivery systems. This research provides valuable insights into the selection and optimal design of the powertrain stages for peristaltic pumps implemented in drug delivery systems. The focus of this paper lies in the simulation and optimization of the performance of a power transmission gearbox by examining the energy consumption, sound levels, reliability, and volume as output metrics. The components of the powertrain consist of a helical gear pair for the first stage, a bevel gear pair for the second one, and finally a planetary transmission. Through extensive simulations, the model exhibits promising results, achieving an efficiency of up to 90%. Furthermore, alternative configurations were investigated to optimize the overall performance of the powertrain. This process has been simulated by employing the KISSsoft/KISSsys software package. The findings of this investigation contribute to advancements in the field of biomedical engineering and hold significant potential for improving the efficiency, reliability, and performance of drug delivery mechanisms.

PROCESSING OF VIBRO - ACOUSTIC SIGNALS OF PRECESSIONAL PLANETARY TRANSMISSIONS

The operation of working machines is accompanied by the constant occurrence of vibrations and shocks, generated by various constructive, kinematic and dynamic factors. The study of the vibro-acoustic aspect of mechanical transmissions and, in particular, of precessional planetary ones is a primary concern for engineers in the field of machine building technologies. The paper presents the research of precessional planetary transmissions under the vibro-acoustic aspect in the anechoic chamber, which is a room, insulated with sound-absorbing material against external noises and isolated anti-vibration. To process the vibro-acoustic signals received as a result of the measurements, the Fourier harmonic series will be applied, a mathematical function that can be used to find the basic frequencies that make up a wave. The final result is the detection of vibration and noise generating sources, the decoding of signals by means of Fourier series and the advancement of constructive-technological solutions to minimize the vibro-acoustic level.

Meshing characteristics and dynamic characteristics of planetary transmission system with new tooth-type flexible ring gear

As one of the important components of the planetary transmission system, dynamic meshing characteristics of ring gear directly affect the performance of planetary transmission system load sharing and dynamic load factor. With the help of the flexibility of ring gear, the planetary gear system with flexible ring gear (FRG) can compensate for the uneven transmission torque of each branch caused by the machining error and installation error and improve the system's load sharing and dynamic load performance. An L-shaped FRG was developed in Italy to improve the traditional ring gear and was used in the latest AW101 helicopter with good feedback. By increasing the ring flexibility, the load distribution between planetary gears is more uniform, and the load-sharing performance of the system is significantly improved. Tooth wear and fracture caused by uneven load distribution can be improved. However, the structure has problems such as unbalanced loading, strength weakening, and stress concentration. In this article, the FRG's meshing and structural characteristics are analyzed in detail by constructing the parametric finite element model. Differences, advantages, and disadvantages of FRG and traditional ring gear are compared. A new type of tooth-type FRG is proposed. It has excellent structural flexibility meshing characteristics of tooth surface and avoids generating stress concentration. It improves the planetary gear train's load-sharing performance and overcomes tooth surface unbalanced loading and large amplitude fluctuation of loaded transmission errors.

Influence of ring gear flexibility on the fatigue reliability of planetary gear systems in heavy helicopters

Flexibility of ring gear rims significantly affects the mechanical properties of planetary transmissions at both levels of gear tooth meshing and system power sharing, and is one of the important design factors determining the service reliability of large aviation planetary systems. Therefore, to analyze the mechanism by which the flexibility of ring gear rims affects the fatigue reliability of planetary systems, in the framework of the stress-strength interference theory, a reliability assessment model for the planetary system is constructed based on a calculation logic extension for the full probability formula. Starting from balancing evaluation accuracy and evaluation cost, a hybrid finite element method and a gear tooth lifetime transformation test are employed to provide load and strength input variables for the reliability model respectively. Finally, a mapping relationship from ring gear rim flexibility to planetary system fatigue reliability is established. For the specific design scheme of planetary systems, a lower limit of the ring gear rim thickness can be determined according to the requirements of reliability indexes, so that the balance between reliability and lightweight can be achieved to some extent.

Tooth Profile Construction and Experimental Verification of Non-Circular Gear Based on Double Arc Active Design

The double arc pitch curve is a novel way for creating a non-circular gear tooth profile. Aiming at the problems of the rounding of non-integer teeth and the nonlinear equation system in the construction of double circular arc tooth profile, an active design method based on planetary gear transmission kinematics and gear-meshing theory is proposed. By studying the double arc pitch curve of the three engagement positions, combined with the uniform theory of the relative curvature of surfaces, the distribution characteristics of the solution of the nonlinear equation system are analyzed in depth, leading to the optimal solution of the characteristic parameter values of the pitch curve. Combined with UG modeling and ADAMS motion simulation, the gear engagement force and the angular velocity of the planetary gear around the center are compared and analyzed in the case of integer tooth ratio and non-integer tooth profile. The results show that the engagement force of the gear pair constructed by integer teeth is reduced by about 17%. The optimal combination of the numbers of teeth is determined by orthogonal experiments, on which trial production and hydraulic load tests are based. The results reveal that the torque of the product at a rated speed is about 2.6% higher than that of foreign prototypes, which verifies the effectiveness of the design method proposed in this paper.

Dynamic modeling and analysis of high-speed flexible planetary gear transmission systems

Modern planetary gear transmissions are often made with flexible components and operated at high or varying speed. Despite advances in understanding their dynamic performance, they remain vulnerable to problems leading—in some cases—to subsequent system failure. In this study, using angular and translational displacements as generalized coordinates, we establish lumped-parameter dynamic sub-models of the sun and planet gears that accurately consider gear-tooth dynamic behavior; we also develop reduced-order finite-element sub-models that fully consider the flexibility of the housing and carrier. Investigating the coupling between these sub-models in depth enables us to construct a complete hybrid dynamic model that can be used for coupling-dynamics analysis of flexible planetary gears under high- and variable-speed conditions. The accuracy of our planetary-gear-dynamics model is verified by comparing simulation data in the time and frequency domains to the results of experiments conducted on a planetary gear transmission system test bench specially built for this purpose. Finally, the dynamic characteristics of high-speed flexible planetary gears are studied at low speed, high speed, and high acceleration.

Optimization Design of Lubrication Performance of Planetary Gear Transmission

Due to the need to clarify the interaction between tooth surface lubrication characteristics and dynamic behavior, it is necessary to consider the influence of time-varying characteristics of lubrication contact on dynamic behavior and the effect of dynamic gear tooth force on lubrication characteristics, establish a friction dynamics coupling analysis model for spur gears, and achieve accurate prediction of dynamic response and lubrication characteristics. In this paper, the planetary gear transmission system model is built, the planetary gear transmission system model is solved, and the lubrication performance of planetary gear transmission is analyzed.

Similarity and vibration signal prediction of planetary gear transmission system based on hierarchy analysis

Large high-power gear transmission systems, especially complex gear systems, have problems such as high processing costs, long manufacturing cycles, and difficult testing, resulting in the inability to implement performance evaluation and structural optimization of gear systems. To solve this problem, the similarity and vibration signal prediction method of planetary gear transmission system (PGTS) is studied based on hierarchical analysis. The similarity relationship analysis is completed based on the similarity theory of complex systems. According to the hierarchical idea, the PGTS can be divided into subsystems at different levels from top to bottom, which can be divided into the component layer at least. The concepts of functional similarity and structural similarity are proposed, and the similarity conditions of each subsystem are formulated. Based on the equation analysis method, the dynamic similarity relationship of the PGTS is deduced. Furthermore, the parameter design and working condition design of the scale model is completed. The scale model can predict the time and frequency domain curves of each vibration signal of the prototype. Under different working conditions, the scale model can accurately predict the vibration signal and floating amount of the prototype. The similarity analysis method applicable to PGTSs has been verified.

The GAPS programme at TNG

Aims. We aim to extract the transmission spectrum of the HI Balmer lines of the ultra-hot Jupiter (UHJ) KELT-20b/MASCARA-2b from observations and to further compare the results with what was obtained through forward modelling, accounting for non-local thermodynamic equilibrium (NLTE) effects. Methods. We extracted the line profiles from six transits obtained with the HARPS-N high-resolution spectrograph attached to the Telescopio Nazionale Galileo telescope. We computed the temperature-pressure (TP) profile employing the HELIOS code in the lower atmosphere and the CLOUDY NLTE code in the middle and upper atmosphere. We further used CLOUDY to compute the theoretical planetary transmission spectrum in LTE and NLTE for comparison with observations. Results. We detected the Hα (0.79±0.03%; 1.25 Rp), Ηβ (0.52±0.03%; 1.17 Rp), and Ηγ (0.39±0.06%; 1.13 Rp) lines, and we detected the Ηδ line at almost 4σ (0.27±0.07%; 1.09 Rp). The models predict an isothermal temperature of ≈2200 K at pressures >10−2 bar and of ≈7700 K at pressures <10−8 bar, with a roughly linear temperature rise in between. In the middle and upper atmosphere, the NLTE TP profile is up to ~3000 K hotter than in LTE. The synthetic transmission spectrum derived from the NLTE TP profile is in good agreement with the observed HI Balmer line profiles, validating our obtained atmospheric structure. Instead, the synthetic transmission spectrum derived from the LTE TP profile leads to significantly weaker absorption compared to the observations. Conclusions. Metals appear to be the primary agents leading to the temperature inversion in UHJs, and the impact of NLTE effects on them increases the magnitude of the inversion. We find that the impact of NLTE effects on the TP profile of KELT-20b/MASCARA-2b is larger than for the hotter UHJ KELT-9b, and thus NLTE effects might also be relevant for planets cooler than KELT-20b/MASCARA-2b.

Design and Analysis of a Novel Actuator with a Double-Roller Gear Drive

In recent years, with the development of robot transmission technology, the market demand for high-performance actuators, which can be applied to lower limb exoskeleton assist robots, is increasing. These robots help achieve human–robot interaction through rigid and flexible coupling, and they can ensure the flexibility of the elderly or patients in daily walking and rehabilitation training. A novel actuator with a double-roller gear drive structure is proposed with high bearing capability and high transmission efficiency due to multi-tooth rolling contact with small tooth difference such that friction is greatly reduced in the transmission process compared to what occurs in involute planetary transmission. The bearing capacity of the tooth surface was analyzed by using the loaded contact analysis method. Finally, a prototype was manufactured with the 3D printer, and the maximum output torque of the developed actuator was tested with an experimental setup. The results show that this novel actuator, with its double-roller gear drive, has huge potential for use in the hip joint of an exoskeleton robot.

A Study of a Domain-Adaptive LSTM-DNN-Based Method for Remaining Useful Life Prediction of Planetary Gearbox

Remaining Useful Life (RUL) prediction is an important component of failure prediction and health management (PHM). Current life prediction studies require large amounts of tagged training data assuming that the training data and the test data follow a similar distribution. However, the RUL-prediction data of the planetary gearbox, which works in different conditions, will lead to statistical differences in the data distribution. In addition, the RUL-prediction accuracy will be affected seriously. In this paper, a planetary transmission test system was built, and the domain adaptive model was used to Implement the transfer learning (TL) between the planetary transmission system in different working conditions. LSTM-DNN network was used in the data feature extraction and regression analysis. Finally, a domain-adaptive LSTM-DNN-based method for remaining useful life prediction of Planetary Transmission was proposed. The experimental results show that not only the impact of different operating conditions on statistical data was reduced effectively, but also the efficiency and accuracy of RUL prediction improved.

Equal Strength Optimal Design of Planetary Gear Transmission

In the design of planetary gear transmission, some gears are damaged during early use because of low strength, yet some are big structure sizes with high strength. In the paper, gears’ equal strength and minimum volume of the gearbox is regarded as optimization objective, and the exterior point penalty function method is used to solve them. Last, we obtain the design parameters under the condition of equal strength of the planetary transmission. Compared to the conventional design method, the weak strength of some gears is enhanced, the whole life is increased, and the overall volume is decreased. It shows we can get ideal results by equal strength optimization in the planetary transmission design.

Resampling Technique-Based Demodulation Analysis for Planet Bearing Cage Fault Diagnosis Under Nonstationary Conditions

Vibration signals of the planetary transmission system usually contain excitation responses from different structures. The fault characteristic of the planet bearing cage is weak, which is often overwhelmed by strong noise and other irrelevant vibration components. Therefore, fault feature extraction of the planet bearing cage is a challenging topic. In this paper, a novel fault feature extraction method is proposed to extract weak fault features of the planet bearing cage. The general parameterized time-frequency transform is employed to accurately extract instantaneous rotational speed information from the planet bearing vibration signal for resampling. It can obtain the accurate rotational speed result even though under power frequency interference conditions. The influence of the deterministic components excited by the gear can be reduced by using the spectral pre-whitening and the interference of noise and random impact can be reduced in the selection of the optimal resonance frequency band by using autogram analysis. The fault characteristic components of the planet bearing cage can be extracted from the square envelop spectrum. The neighborhood power density ratio index is further constructed to distinguish the health bearing state from the cage fault bearing state and evaluate the degree of faults. Experiments designed in a planetary transmission system test rig of an armored vehicle have verified the potential and effectiveness of the proposed fault feature extraction method in exhibiting planet bearing cage fault features.

Dynamic modeling and vibration analysis of planetary gear sets concerning mesh phasing modulation

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.

Load sharing performance analysis of planetary gear system considering the coupling effects of gear pair and journal bearing

In this paper, a load-sharing performance analysis method of the planetary gear system is proposed considering the coupling effects of double-helical gear and journal bearing. Firstly, the coupling effects between the meshing characteristics of the double-helical gear pair and the dynamic characteristics of journal bearing under the actual operation state are studied, the dynamic model of the double-helical gear planetary transmission system is established, and the load sharing coefficient before and after considering the coupling effects are calculated; secondly, the load sharing characteristic test rig of planetary transmission system is built, and the load sharing coefficient of gear system under the test condition is measured to verify the accuracy of the proposed method; finally, the effects of operating parameters and structural parameters on the load sharing characteristic of gear system are discussed.