Planetary Gear Train Research Articles

Dynamic analysis of two-stage steering reducer for electric vehicle based on ROMAX

Abstract. With the rapid development of electric vehicles in the modern market, the efficiency and performance requirements of electric vehicle transmission systems are getting higher and higher. As an important part of the electric vehicle reducer, the steering reducer can make full use of the advantages of the two-stage deceleration transmission, achieve more efficient power transmission, and improve the acceleration performance and driving performance of electric vehicles. This paper aims to design a two-stage steering reducer for an electric vehicle, which adopts planetary gear transmission type. Firstly, the working principle of the electric vehicle steering reducer is analyzed, and the overall design scheme of the reducer is drawn up. Secondly, the transmission system parameters of the reducer are designed and calculated, including transmission ratio distribution, tooth number ratio calculation, etc. Secondly, the transmission structure of the reducer is designed, including input shaft, output shaft, first planetary gear train, second planetary gear train, reducer shell, bearing, etc., and the reducer model is drawn by three-dimensional software Solidworks. Finally, the strength and deformation check analysis of the two-stage reducer is carried out by using the finite element software ROMAX to evaluate the performance of the designed reducer under this working condition. The full text design has a certain reference, and can be applied to other electric vehicle reducer design to provide theoretical guidance.

Power Losses of Oil-Bath-Lubricated Ball Bearings—A Focus on Churning Losses

This study investigates the power losses of rolling element bearings (REBs) lubricated using an oil bath. Experimental tests conducted on two different deep-groove ball bearings (DGBBs) provide valuable insights into the behaviour of DGBBs under different oil levels, generating essential data for developing accurate models of power losses. Observations of the oil bath dynamics reveal the formation of an oil ring at high oil levels, as observed for planetary gear trains, leading to modifications in the oil flow behaviour. The experiments demonstrate that oil bath lubrication generates power losses comparable to injection lubrication when the oil level is low. However, as the oil level increases, so do the power losses due to increased drag within the bearing. This study presents a comprehensive model for calculating drag losses. The proposed drag power loss model accounts for variations in oil level and significantly improves loss predictions. A comparison of existing models with the experimental results shows good agreement for both bearings, demonstrating the effectiveness of the developed model in accounting for oil bath height in loss calculations.

A study on load sharing characteristics of the planetary gear train system with cracked gears

Load sharing characteristic is very important for the reliability of the planetary gear train. Cracked gears can make the load sharing performance become worse. Nevertheless, previous studies have not paid enough attention to the influence of cracked gears on the load sharing behavior, when compared with the impact of multiple factors under healthy condition. An 18 degrees of freedom dynamic model for the spur planetary gear train is established based on the centralized parameters theory in this paper. The influences of cracked gears on the load sharing behavior are investigated, which include the cracked sun gear, the planet gear containing cracked side meshing with the sun gear, the planet gear having cracked side meshing with the ring gear and the cracked ring gear. Additionally, the sensitivity analysis of the external and internal load sharing behavior to different cracked components is conducted. The results indicate that the load distribution becomes more uneven with the propagation of crack in the sun gear and ring gear, while the change regulation is different for each cracked planet gear. Moreover, the load sharing characteristic of the external meshing is more sensitive to the cracked sun gear and the planet gear 1, which has the crack side meshing with the ring gear. While the load sharing characteristic of the internal meshing is more sensitive to the cracked ring gear and the planet gear 3, which owns the crack side meshing with the ring gear than others. The output of this paper will be useful for the crack fault diagnose and fault source identification of the planetary gear train system.

Investigation of contact ratio and dynamic characteristics of non-circular planetary gear train in hydraulic motor

As a basic component of the non-circular gear hydraulic motor (NGHM), the non-circular planetary gear train (NPGT) offers a number of advantages, including low velocity, high output torque and compact design. Two different types of NPGT pitch curves have been designed using the 4-6 type of NGHM as an example. Aiming at two kinds of pitch curves, the contact ratio solution methods for the planetary gear meshing respectively with the sun gear and the inner gear ring are proposed. A comparative analysis of an integrated pitch curve design and a segmented pitch curve design is conducted to evaluate the effects of varying addendum coefficient (AC) and tool tooth profile angle (TTPA) on the contact ratio. Furthermore, the influence of load, velocity, and contact ratio on the dynamic characteristics (DC) of the NPGT with a segmented pitch curve is investigated through dynamic simulation. The results show that AC and TTPA significantly affect the contact ratio, with an increase in contact ratio observed as TTPA decreases and AC increases. Additionally, the load has a notable impact on the dynamic meshing force and its fluctuation. A higher contact ratio is associated with greater transmission stability in the gear train. This study provides a theoretical foundation for the design and optimization of NGHMs, and expands the potential application of contact ratio effects on NPGTs in this field.

New automatic sketching method for planetary gear train

New automatic sketching method for planetary gear train

Dynamic Forces and Vibrations of the Planetary Gear-Set Radial Bearings with the Roller Dimension Deviation

Double planetary gear trains (DPGTs) have high loading capacity and transmission, making them indispensable in various heavy rotating machinery applications. However, the presence of planetary gear-set radial bearing roller dimension deviation (PBRDD) from real-world manufacturing discrepancies poses a significant challenge to the dynamics of the DPGTs. Previous dynamic models often overlooked the internal excitations of the planetary gear-set radial bearing, focusing only on the single planetary gear train dynamics, rendering them inadequate for studying the impact of the PBRDD on DPGTs. Therefore, this paper proposes a coupling method integrating the PBRDD model with the DPGT dynamic model, taking into consideration the planetary gear-set radial bearing’s internal excitations, to reveal the impact of PBRDD on DPGTs’ dynamics. Specifically, the changes in roller–ring contact force and roller–cage collision force induced by PBRDD are considered. Through comprehensive simulation and experimental analyses, the accuracy of the dynamic model is assessed and its efficacy in capturing the effects of PBRDD on DPGTs’ dynamics is validated. The results show that the DPGTs’ dynamics increment with the increment of PBRDD.

Design of a 2R Open-Chain Plug Seedling-Picking Mechanism and Control System Constrained by a Differential Non-Circular Planetary Gear Train

With a focus on the problems of complex structure and accumulated lateral clearance in the single degree of freedom non-circular wheel system seedling-picking mechanism, which leads to poor motion accuracy, trajectory, and attitude, this study developed a 2R open-chain chili plug seedling-picking mechanism (SPM) constrained by a differential non-circular wheel system. The picking arm was driven by a single-stage non-uniform speed transmission mechanism to reproduce the seedling-picking trajectory and attitude. A protruding seedling-picking device, SPM control system, and test bench were designed. A kinematic model of a differential non-circular gear system was established, and an optimization design software for the SPM was developed based on kinematic analysis. The kinematic characteristics of the SPM were analyzed under optimal parameters. This study completed the seedling-picking performance test of the SPM on the control panel. The test showed that the designed chili SPM can sequentially complete the processes of seedling picking, conveying, retracting, pushing, and returning under the automatic control of the test bench without damaging the main root. The lateral root damage rate was 15.7%, effectively ensuring the integrity of the seedling bowl substrate.

Artificial immune systems (GA-AIS) enabled power loss mitigation in distributed generation: X3PAIS optimization approaches

The distribution network is a crucial component of the power system, with industrialization driving increased energy demand. Traditional power-generating techniques, such as thermal and hydroelectric are not enough to meet this demand, leading to the development of Distributed Generation (DG). DG requires an extensive re-evaluation of the current power system, as it modifies energy losses and line flows. Inadequate integration of DG can cause power outages, disruption of protection coordination, and lead to islanding. AI can help overcome this issue by determining the best system architecture. Researchers have been interested in the Artificial Immune System (AIS) algorithm, which has room for development and lacks a fixed template. In order to improve AIS, X3PAIS, a hybridization strategy that combines clonal selection with a three-parent crossover has been developed within the scope of the study. X3PAIS was pre-tested using applications in a planetary gear train, a wastewater treatment facility, and mathematical calculations, showcasing its robustness and versatility. In the context of power distribution, X3PAIS is used in the multiple DG architecture of the power distribution system, reducing power losses by placing DG units in the best locations and sizing them to match load profiles. The four DGs' experiment results show that X3PAIS can minimize power losses by more than 89 %. To optimize power losses in the power distribution system, X3PAIS may be improved with a three-parent multiple-point crossover operation.

Extended crack propagation in nitrided and carburised steels subject to rolling contact fatigue

To predict the Rolling Contact Fatigue life of components such as rolling element bearings, it is important to understand the failure mechanisms. A rather unusual failure was observed on integrated races into a planetary gear train. The failure of the planet of this gearbox was attributed to the very long propagation, at an unusual depth, of a crack, which probably started at the surface. The present preliminary study aims to gain a better understanding of the factors that can lead to this type of failure. Firstly, a twin-disc machine is used to reproduce the contact conditions identified in the application. A second set of more severe conditions is also tested. A comparison is made between a carburised steel (16NiCrMo13) and a nitrided one (32CrMoV13). Two distinct crack patterns and spalling characteristics between the two materials are observed. Some unusual crack characteristics are observed in the carburised sample for a specific set of contact conditions.

Nonlinear dynamic characteristics analysis method of planetary gear train torsional vibration considering meshing oil film force

Planetary gear train is an important part of automatic transmission. The oil film between teeth is one of the key factors affecting the torsional vibration of planetary gear train. Selecting the appropriate oil film stiffness is of great significance for analyzing the nonlinear dynamic characteristics of planetary gear train. A method for analyzing the nonlinear dynamic characteristics of planetary gear system torsional vibration considering the oil film force between teeth is proposed in this paper. A 3-DOF torsional vibration model of planetary gear train considering oil film is established. In this model, the oil film between teeth is equivalent to a time-varying nonlinear spring-damper element, and nonlinear factors such as backlash and meshing error are also considered. The effects of meshing oil film thickness on oil film stiffness and damping are analyzed, and the torsional vibration characteristics of planetary gear train under different meshing stiffness, meshing damping ratio, and rotational speed are analyzed based on bifurcation diagrams. The results show that in one meshing cycle, the meshing oil film thickness first becomes larger and then becomes smaller. When the meshing oil film thickness increases, the meshing oil film stiffness and the equivalent meshing oil film damping become smaller. The torsional vibration of planetary gear train can be effectively reduced by increasing meshing stiffness, damping ratio, rotational speed within a certain range. This method provides technical support for reducing torsional vibration of planetary gear train and realizing stable transmission of planetary gear train.

Fault Diagnosis of Planetary Gear Train Crack Based on DC-DRSN

To solve the problem that the existing planetary gear train fault diagnosis methods have, namely their low diagnostic accuracy under low signal-to-noise ratio (SNR), a fault diagnosis method based on a double channel-deep residual shrinkage network (DC-DRSN) is proposed. The short-time Fourier transform (STFT) is used to convert the original vibration signal into a two-dimensional time-frequency graph, which effectively enhances the ability to express information. A DC-DRSN model is constructed, and the optimal number of residual shrinkage modules is determined by combining the diagnostic characteristics with different noises, which effectively improves the accuracy and anti-noise ability of fault diagnosis. The results of bearing and planetary gear train crack fault diagnosis show that the diagnosis method based on DC-DRSN has higher diagnostic accuracy while realizing fault diagnosis, which is better than other deep learning diagnosis methods. At the same time, the method can adapt to fault diagnosis in different noise environments, and has good expression ability and generalization ability.

Research on the micro-vibration mechanism of the planetary gear train based on fractal theory

Research on the micro-vibration mechanism of the planetary gear train based on fractal theory

Fault modulation mechanism and kinematic modeling of planetary gear with local fault

A planetary gear train involves multiple components and has more complex kinematic relationships than a parallel gear train. Consequently, the fault characteristics extraction is more complicated. To ensure safe operation, it is necessary to properly understand the fault behavior of the planetary gear train. In the previous kinematic modeling, the relationship between the faulty tooth meshing location and the fault impact response phase is not fully considered. However, the fault impact response phase variation plays an important role in accurately characterizing the fault characteristics in the planetary gear train. To solve this problem, we analyze the relationship between the faulty tooth location variation and the fault impact response phase variation and then a novel fault response model is established. Based on this model, a revised planetary damage detection scheme is formulated. Through the simulated data analysis, it is revealed that the faulty tooth location variation not only affects the fault impact response phase, but also reallocates the sideband distributions in the response spectrum. Finally, using a laboratory planetary gear set, it is validated that the proposed model is able to reflect the real damage response better. Therefore, using the proposed model, more accurate damage features are able to be extracted from the measured vibration responses.

Analysis of the Dynamic Characteristics of Coaxial Counter-Rotating Planetary Transmission System

This paper presents a coaxial counter-rotating planetary transmission system. The transmission system under study is a two-stage planetary gear train (PGT) comprising a fixed-axes PGT and a differential PGT. A dynamic model of the transmission system is established, considering both the excitations caused by the time-varying mesh stiffness (TMS) and the transmission errors, respectively. The Runge–Kutta algorithm is used to calculate and analyze the dynamic characteristics of the system. This includes studying dynamic meshing forces, planet gear displacements, and load-sharing coefficients (LSCs) under both internal and external excitations, as well as different input torques. The results indicate that when considering external excitations, the variations in the meshing force curves become more pronounced. The radial displacements of the planet gears in the differential PGT are greater than that in the fixed-axes PGT. With increasing input torque, the average displacements of the planet gears in all directions tend to increase. The differential PGT, transmitting a higher power, demonstrates a better load-sharing performance compared to the fixed-axes PGT.

FE-analytical slice model and verification test for load distribution analysis and optimization of planetary gear train in wind turbine

Load distribution behavior of planetary gear train (PGT) is crucial for the contact and bending fatigue failure of wind turbine transmission system. With the increasing power of wind turbines, the load and failure rate of wind turbine become larger, which leads to the demand of accurate and efficient modeling, analysis and optimization for load distribution of PGT. In this paper, a new efficient and accurate FE-analytical slice model for load distribution analysis and optimization of PGT in wind turbine is proposed, which is explicitly formulated by the geometry slice model of external/internal gear contact, original FE-analytical slice model for local contact deformation, and efficient finite element (FE) model for global structural deformation. In the FE-analytical slice model, geometry errors are effectively descripted by discretizing gears into a series of slices, while gear tooth contact elasticity and structural elasticity are addressed by the FE-analytical method accurately and efficiently. Upon the proposed model, the load distribution behaviors of PGT with coupling effects of elasticity and errors are revealed and optimized by tooth modification and in-phase eccentricity arrangement strategy. The load distribution tests of PGT in wind turbine are conducted, verifying the proposed FE-analytical slice model which is significant to improve the load-bearing capacity and avoid the fatigue failure of wind turbine transmission system.

Mechanical Design of Variable Stiffness Joint Based on Planetary Gear Train and Modular Elastic Element

Methods:: By referring and combining existing mechanical design ideas of some series configuration VSJs with good stiffness adjustment mechanism schemes, a novel series configuration VSJ based on an equivalent lever mechanism and relying on adjusting the position of the lever pivot to change joint stiffness has been implemented through CAD drawing, 3D printing, and assembly. Results:: Due to the wide movable range of the lever pivot, the designed VSJ has a wide adjustable range of stiffness. Moreover, assembly design and modular design have been achieved in terms of elastic output and power transmission, for easy installation and maintenance. The movability and stiffness adjustability of the designed VSJ were preliminarily verified through manual adjustment. Conclusion:: The assembly model of the VSJ demonstrates the feasibility of structural design. The stiffness adjustment experiment showed the variable stiffness ability of the designed VSJ.

Linear complementarity formulations for contact analysis and wear prediction in gears

This work presents linear complementarity based formulations for contact analysis and wear prediction in gear trains. Assuming steady motion of gears transmitting constant input torque without transmission errors, three sets of linear complementarity formulations are proposed, first for rigid gear teeth, second for gear teeth with skin compliance, and third for gear teeth with full compliance, the last two being new in linear complementarity literature. The developed formulations are used for contact analysis of two examples of gear trains, a pair of spur gears in mesh, and a planetary gear train. The accuracy of the method is tested by considering various time step sizes and stability of the formulations demonstrated for wide range of time steps. Contact forces between meshing teeth are calculated at a pre-defined set of points on the path of contact, and then wear is calculated on gear tooth flank using Archard’s wear equation. These wear calculations are compared with existing results in literature which demonstrate the applicability of the developed LC formulations. Future work is projected to include more state-of-art friction models and extension to 3D contact analysis in helical gear trains.

Assembly accuracy prediction method of planetary gear train considering bolt-bearing-shaft-gear coupling effects

Planetary gear train (PGT) is a complex transmission system composed of gears, shafts, bearings and bolted joints, of which the assembly accuracy affects the transmission accuracy and dynamic behavior. In this paper, a new assembly accuracy prediction method is proposed for PGT considering gear-shaft-bearing-bolt coupling effects. The new method is formulated by establishing three models for bolt assembly, shaft error motion and assembly accuracy (transmission error) of PGT. The model for bolt assembly is an original FE-analytical model to analyze the bolt assembly effect on elastic deformation of bearing cap, which is developed by finite element (FE) method and analytical method for addressing the elastic effect of bearing cap and elastic interaction between bolts. The models for shaft error motion and assembly accuracy are performed by the three-dimensional contact analysis with errors and preload of bearing cap based on analytical method and kinematic geometry relationship. Combining the three models, the assembly accuracy can be predicted by simulations. The simulations indicate that the proper bolt assembly parameters can alleviate the influence of manufacturing errors on assembly accuracy. The assembly accuracy tests of PGT are conducted. The results well agree with the simulations’, and the assembly accuracy is improved by the proper bolt assembly parameters.

The effect of floating spline parameter on the dynamic characteristic of encased differential planetary gear train

The load sharing performance of encased differential planetary system has a great impact on the operating performance and service life of the transmission system of the coaxial high speed helicopter. In order to improve the load-sharing performance of the gear pair, the influence of different floating spline structural parameters on the load sharing characteristics of the system was studied. Considering the manufacturing error, installation error, time varying meshing stiffness and other factors, the Lagrange equation is used to construct the dynamic model of encased differential planetary gear train with floating spline structure. The effects of input torque, spline clearance, spline shaft stiffness and spline friction coefficient on the load sharing performance of gear pairs were analyzed. The results show that the differential stage system has a better load sharing performance than the encased stage system. The increase of input torque helps to improve the load sharing performance of the system, and the improvement of the encased stage system is more obvious. The floating spline of sun gear of the encased stage has a greater impact on the load sharing performance of the system. Furthermore, increasing the floating spline clearance, reducing spline shaft stiffness or increasing the friction coefficient of the spline can improve the load sharing performance of the system overall.

A matrix-based method for synthesizing planetary gear trains to facilitate the creation of transmission systems

The structural synthesis of planetary gear trains (PGTs) lays an important foundation for creating new mechanisms of transmission systems. Most existing studies focused on the synthesis of single degree-of-freedom (DOF) PGTs, while the synthesis of multi-DOF PGTs is very limited. This paper presents a matrix-based method for the automatic synthesis of non-fractionated PGTs with both single and multiple DOFs. First, the concept of a modified dual graph is proposed, based on which a new and simple method is presented to efficiently detect fractionated graphs. Then, the concepts of vertex adjacency index and moment matrix are defined, and a reliable algorithm is proposed to detect isomorphic graphs. Finally, a matrix-based method for the automatic synthesis of non-fractionated PGTs is presented, and the complete databases of non-fractionated PGTs with 3–9 links and 1–3 DOFs are generated for the first time. The creative design of mechanisms of 6-speed automatic transmission (AT) is taken for instance to illustrate how to design new transmission systems based on our databases.