Planetary Gear Transmission Research Articles

Dynamical Analysis of Planetary Gear Transmission System Under Support Stiffness Effects

The transverse-torsional nonlinear model of multistage gear transmission system which is comprised of a planetary gear set and two parallel gear stages is proposed with time-varying meshing stiffness, comprehensive gear errors and gear backlash. The nonlinear dynamic responses are analyzed by applying excitation frequency and support stiffness as the bifurcation parameters. The motions of the system are identified through global bifurcation diagram, largest Lyapunov exponent (LLE) and Poincaré map. The numerical results demonstrate that the support stiffness affects the system, especially on planetary gear set. The motions of the system with the changes of the support stiffness are diverse including some different multiperiodic motions. Also, the state of the system undergoes 2T-periodic motion, chaos, quasi-periodic behavior and multiperiodic motion. For the support stiffness or other nonlinear factors of the gear system, the suitable range of working frequencies could make the system stable. Correspondingly, parameters of the system should be designed properly and controlled for the better operation and enhancing the life of the system.

Design of three speed planetary gear hub system with gear shifting mechanism

Today’s 21st century has come a long way in the evolution of transmission systems. This paper aims in keen understanding and conceptual learning of Epi-cyclic gear drive system for transmission of power. The results of planetary gear transmission system yields the key characteristics such as high power density and compact design. To improve the detailed understanding of multi speed planetary gear hub systems, the work in this research will primarily guide through the utilization of these unique systems via the design of 3-speed planetary gear transmission system. Further to better predict the very potential and economical manufacturing process of planetary gears, first, the traditional manufacturing of gears is to be understood and thereby, speculating the creation of 3-D printed metal gears that will more accurately react to changing revolutionary manufacturing technologies and transmission systems, and make more effective use of these basic principles of gear system. The main objective, being, to brief the designers and manufacturers to rapidly conceptualize these basic ideas in to physically possible innovative models for the sake of revolution of the present gear technology.

Dynamic modeling of planetary gear set with tooth surface wear

Wear commonly occurs in planetary gear transmission systems. Fundamentally, the tooth wear could cause tooth profile deviation, which would increase the vibration and noise of gearbox. In order to monitor and forecast the wear condition of gears via vibration-based methods, it is necessary to establish the dynamics model of a planetary gear set with tooth surface wear, which can provide a prior about the vibration characteristics of gear wear. In this study, a purely torsional dynamics model of a planetary gear set with tooth surface wear is proposed to analyze the fault mechanism of tooth surface wear. The tooth surface wear is incorporated into the dynamics model through unloaded static transmission error (USTE) and time-varying mesh stiffness (TVMS), which are evaluated by Archard’s wear equation. Subsequently, the vibration responses of the planetary gear set with tooth surface wear are analyzed. It is revealed that tooth wear would change the vibration responses in both time- and frequency-domain and the condition indicators present different trends.

Analysis of Load-Sharing Behavior of the Multistage Planetary Gear Train Used in Wind Generators: Effects of Random Wind Load

Load-sharing behavior is very important for power-split gearing systems. Taking the multistage planetary gear train transmission of an Million Watt (MW) wind generator as the investigation object, and based on the gear transmission system of a wind generator in a complex and changing load environment, a random wind model of a wind farm is built by using the two-parameter Weibull distribution. According to the realistic working region of the wind generator, the random wind speed is changed into time-varying input speed of the wind generator gear box. Considering the internal excitation, such as mesh stiffness, mesh damping of gear pairs and the meshing error, a dynamic model for a multistage planetary gear transmission system is built by using the lumped parameter method. The load-sharing coefficients are obtained for each planet gear pair in the same meshing period of the transmission system that is under the interaction of time-varying input speed and internal excitation. It is shown that the degree of load-sharing coefficient fluctuation for each planet gear pair of the first- and second-stage planetary gear train is significantly affected by time-varying input speed. The research results can lay a theoretical foundation for optimization and reliability of planetary gear transmission systems of wind generators.

Research on gear crack diagnosis of the planet gear transmission

Objected to the planetary gear transmission, research on the fault diagnosis of gear cracks is mainly carried out with method of EEMD decomposition and Envelope demodulation. During the process, EEMD decomposition is used to the experiment data and continuously parameters of the root mean square (RMS) value, peak-to-peak (PtP) value, kurtosis (Kr), and other parameters of the IMF components are computed. According those parameters, the signal is reconstructed and after band-pass filtering the Hilbert transform and the envelope demodulation are carried out. The results showed that the power spectrum information obtained by using the EEMD decomposition and Hilbert transform could effectively response fault characteristics of the gear crack in the planetary transmission. The research is beneficial to the gear meshing fault diagnosis of the planetary transmission quickly and accurately and has a positive engineering value.

Matrix-Based Operation Method for Detecting Structural Isomorphism of Planetary Gear Train Structures

AbstractPlanetary gear sets (PGSs) have been widely used in automatic transmissions (AT) and dedicated hybrid transmissions (DHTs). In this paper, a novel isomorphic detection method for planetary gear transmission structure is proposed based on matrix operation. The isomorphic detection process includes two main parts. In the first part, various components of the transmission structure are classified. In the second part, isomorphic structures of the numerous structures are detected. Through the application of the proposed detection approach, the structures obtained by different synthesis algorithms can be greatly reduced. Furthermore, by the analysis and transformation of the hybrid configuration to conventional transmission configuration, the scope of use of the algorithm can be expanded through the method. The proposed detection approach is capable of automatically detecting the isomorphic structure of the potential structures obtained by synthesis algorithm.

Modeling and Dynamic Characteristics of Planetary Gear Transmission in Non-inertial System of Aerospace Environment

Abstract The traditional research on the dynamics of planetary gear transmission (PGT) is based on the assumption that the support is on the ground. However, the PGT inside the aircraft is spatially moved along with the airframe, which is not only subject to gravity, but also to additional inertia forces. These loads should affect the dynamic characteristics of the PGT. The PGT itself is a non-inertial system (NIS) and is called the internal non-inertial system (INIS). By contrast, an airframe in the aerospace environment is named an external non-inertial system (ENIS). In order to investigate the dynamic behavior of the PGT in a compound NIS, the kinematic equations of various components in arbitrary spatial motion state of the airframe are deduced. Subsequently, the coupled dynamics model of PGT in NIS is improved. The dynamic responses of PGT in different non-inertial conditions are compared based on the hovering motion of the airframe. The results indicate that INIS is the main factor affecting the trajectory of planet gear, while ENIS is the force source changing the trajectory of the central component. The aircraft’s hovering motion makes the gravity effect become a relatively time-varying excitation, but the dominant factor is still the additional inertial forces. The non-inertial effect during aerospace operation can significantly affect the bearing force, vibration and load sharing performance. It will lead to serious errors if the traditional research method is still used to obtain the dynamic behavior of PGT in the aerospace environment.

M-band flexible wavelet transform and its application to the fault diagnosis of planetary gear transmission systems

Abstract The fault diagnosis of planetary gear transmission systems is crucial for the safety of machineries and equipment. To identify the underlying fault features in measured signals, a novel M-band flexible wavelet transform is constructed. This transform provides a denser sampling of the time–frequency plane and preserves tunable filter parameters and dilation factors. A perfect reconstruction condition of the proposed transform is established, and its corresponding wavelet filter bank is designed to satisfy the perfect reconstruction condition. A numerical implementation algorithm of M-band flexible wavelet transform is investigated using a multirate filter bank and fast Fourier transform. Denoising the simulation signals demonstrates that the proposed transform exhibits better performance than analytic flexible wavelet transform, orthogonal wavelet transform, and biorthogonal wavelet transform. A new fault diagnosis method for planetary gear transmission systems is proposed on the basis of M-band flexible wavelet transform and spectral negentropy. Experimental and comparative results show that the proposed method can be more effectively and accurately applied to the fault diagnosis of planetary gear transmission systems compared with typical fault diagnosis methods based on analytic flexible wavelet transform, Morlet wavelet transform, and infograms.

Efficiency modelling and analysis for a novel double-arc bevel gear nutation transmission system for pure electric vehicles

Since more attention has been paid to the development of pure electric vehicles, small and high efficiency of transmission system is the trend. The paper proposes a novel double-arc bevel gear nutation transmission system with two inputs and one output for pure electric vehicles. Compared with the traditional planetary gear transmission, the designed system has advantages of compact structure, small radial dimension and low cost. The nutation transmission of double-arc bevel gears is transformed into a spur planetary gear transmission mechanism with few teeth difference when the inclination angle is equal to zero. Based on kinetic and gear meshing analysis, it is found that the transmission efficiency of the model is related to the nutation gear ratio and the speed ratio of two power sources. The approach of analyzing the efficiency proposed in this paper can provide theoretical basis for the efficiency analysis of the nutation transmission in the future.

Study on kinematic characteristics of planetary multistage face gears transmission

A planetary gear transmission system with multistage face gears combinations as core component can easily realize the variable speed in differential transmission ratios with structural advantages. In order to improve the transmission stability and loading capacity, it is necessary to set up a reasonable kinematic model for multistage face gears pair. This study focuses on the kinematic characteristics of multistage face gears structure with double crown surface by the methods of numerical calculation and experimental verification. The transmission error and efficiency solving models are established by numerical calculation method to analyze the influences of each factor in detail. Then the correctness of the above numerical models are verified with transmission error and efficiency experiment. In addition, the numerical results are compared with the experimental results to further indicate the important influences of the multistage face gears components on the transmission error and efficiency of whole transmission system. The results can provide references for the dynamic and experimental study of multistage face gears in some degree.

High power density design for planetary gear transmission system

Planetary gear transmission system has been widely used in the field of aerospace equipment, automobiles, ships, etc. High power density design is an important development direction for transmission machinery, but there is a lack of systematic and deepening research in planetary gear transmission system field. Taken the most widely used 2K–H-type planetary gear transmission system as research object, a design method of high power density considering volume and efficiency is put forward. First, the transmission efficiency model of 2K–H-type planetary gear transmission system is built on the basis of calculation of single gear pair meshing efficiency instead of the look-up table method. Second, the volume model of 2K–H-type planetary gear transmission system is built according to the structure of gear. Finally, the smallest volume and the minimum power loss of 2K–H-type planetary gear transmission system are the target of optimization, and the linear-weighted combination method is used to construct target function. Taken a 2K–H-type planetary gear reducer in some machine tool as an example, the optimization is carried out. The results show that the power loss of optimized system is reduced by 11.42%, and the volume of system is reduced by 25.2%.

Dynamic Analysis of Planetary Gear Transmission System Considering the Flexibility of Internal Ring Gear

A rigid-flexible coupled dynamic model of the planetary gear transmission system was developed considering the flexibility of the internal ring gear (flexible internal ring gear) and the sun shaft based on the shell theory and Timoshenko beam theory, respectively. For the dynamic modeling, the time-varying meshing stiffness and static transmission error excitations were considered and the Runge–Kutta numerical algorithm was applied to calculate the dynamic response. The results indicate that the flexibility of internal ring gear sharply decreases the dynamic factor between the internal ring gear and the planet gear, and it also shows significant positive influences on the system load-sharing performance. For the fixed internal ring gear, the maximum stress is located on the midpoint along the axial direction. The maximum dynamic deformations appear at the ends of the tooth surface along width direction, and the dynamic deformation shows a decremental trend from the tooth top edge to the tooth root edge. The load-sharing coefficient decreases rapidly with the increase in the thickness, as the support stiffness is small. The misalignment of one of the planet pins and various static transmission errors have a negative influence on the load-sharing coefficient of the planetary gear transmission system.

Research Progress in Dynamics of Planetary Gear Transmission System

Research Progress in Dynamics of Planetary Gear Transmission System

采煤机牵引部两级行星齿轮传动系统刚柔耦合动力学分析

采煤机牵引部两级行星齿轮传动系统刚柔耦合动力学分析

The Analysis and Modeling of the Synthetical Meshing Stiffness of Inner Gearing considering the Flexible Inner Ring Gear

As a key part of vibration generation and transmission of planetary gear transmissions, thin‐walled inner ring gear deforms under the influence of meshing excitation and seriously affects the reliability and fatigue life of the transmission system. The effect of the flexibility of the inner ring gear on the transmission system is ignored in the calculation of making the inner ring gear as a rigid body in the lumped parameter model, while the calculation amount of the finite element model is too large. Therefore, it is very important to establish an accurate and reasonable model to solve the flexibility of the inner ring gear. In this paper, according to the supporting mode, supporting quantity, thickness, and sectional shape of the inner ring gear, the inner ring gear is reasonably separated into the form of multisection curved beam. The displacement of the gear teeth in the meshing line caused by the flexibility of the inner ring gear is obtained rapidly and accurately. It lays an important theoretical foundation for the dynamic analysis of planetary gear transmission.

Dynamic Response Analysis for NW Planetary Gear Transmission Used in Electric Wheel Hub

Taking the NW planetary gear transmission of an electric wheel hub as the research object, the mesh model was developed to calculate the mesh parameters using Masta. Then the lump parameter method was used to establish the dynamic model of the NW planetary transmission system considering the time-varying mesh stiffness, transmission error and bearing stiffness. The impacts of the torque load on the dynamic characteristics including the dynamic mesh force, center trajectory, offsets and load sharing coefficients were investigated. Results show that the dynamic mesh force waveform and spectral characteristics of each planetary gear at high and low speeds under the rated and maximum torque load are almost identical. Compared to the peak response at speed 485 rpm and 1770 rpm, both the magnitude and location of the third response at relative high speed about 4300 rpm are increased due to the load increasing. The mean and fluctuation range of the offsets in the radial direction are both larger than the tangential direction. As the load increases, the mean value of the radial offset increases and the magnitude decreases significantly. The mean value of the tangential offset decreases significantly, but the magnitude increases first and then decreases. The load sharing characteristics of the low-speed stage of the NW planetary gear is better than the first stage. With the increase of the load, the load sharing performance of a two-stage planetary transmission gets better and the difference in load sharing between the high-speed and low-speed stages also decreases.

Modeling and Dynamic Characteristics of Planetary Gear Transmission in Non-inertial System of Aerospace Environment

Modeling and Dynamic Characteristics of Planetary Gear Transmission in Non-inertial System of Aerospace Environment

Load-sharing analysis of two-stage three-branch star gearing based on deformation compatibility

A load-sharing analysis methodology was proposed for the multiple-branch star gear transmission which is composed of a number of closed-loop power flows. The moment equilibrium and deformation compatibility equations for the two-stage star gearing were derived, which are clearly different from that used in planetary gear transmission. Then the load-sharing analysis model was established and employed to systematically study the load-sharing behavior of the two-stage three-branch star gearing, some untouched aspects were investigated. Results show that the most sensitive directions of the central and star gear assembly errors on load-sharing are along the meshing line. The effects of the size and direction of the central gear–manufacturing errors on load sharing are the same for each branch, the initial directions of the central or a certain star gear–manufacturing errors will have no effect on the load-sharing coefficient of the system, but the initial directions of the assembly errors will. The conditions in which the load distribution curves repeat the first track were also obtained. Finally, a numerical example of a three-branch star gear aviation reducer was adopted to verify the feasibility of this proposed method, and the calculation results show good agreement with a previously published and validated model.

Dynamic Characteristics and Load Sharing of Herringbone Wind Power Gearbox

In this study, the dynamic model for the herringbone planetary gear transmission system is established by the lumped parameter method based on the system dynamics and the Lagrange equation, and the impact of the support stiffness and the torsional stiffness on dynamic characteristics is studied. The research results have a guiding significance for the design of the herringbone gear transmission system. In this model, the herringbone gear is treated as a special gear coupled by 2 opposite helical gears, where the stagger angle, comprehensive meshing error, support stiffness, support damping, and load inertia are considered in the analysis of dynamics. Moreover, the dynamic characteristic of the carrier is considered as well. By calculating the meshing force curve of the transmission system, the impact of the stagger angle, supporting stiffness, and the torsional stiffness on meshing force and load sharing coefficient is analyzed. The results show that the stagger angle has an obvious impact on load sharing coefficient while it has little impact on maximum meshing force. And the support stiffness has a more obvious impact on the dynamic characteristics of the system. The recommendary support stiffness of the system is that all of the support stiffness of the sun gear, planetary gear, ring gear, and carrier is 107 N/m. The torsional stiffness has little impact on the dynamic characteristics of transmission system, except the torsional stiffness of planetary gear, and carrier has an obvious impact on load sharing coefficient. The commercial software ADAMS carried out dynamics analysis of the transmission system to verify the necessity validity of the theoretical analysis.

Research on vibration characteristics of multistage gears transmission system driven by internal and external excitation

In order to accurately describe the complex transmission systems and clarify the effects of internal and external excitation on the vibration characteristics for large complex transmission systems, a dynamics model considering gear meshing error and time-varying meshing stiffness is established at two-stage planetary gears systems. The coupling model is established by matrix set method for two-stage planetary gears and multistage spur gears transmission systems. The random load excitation verified by experiments is the external excitation in the system, and the excitation caused by the time-varying meshing stiffness and meshing error is the internal excitation. The research on the response of the vibration systems shows that the internal excitation caused by gear meshing stiffness and gear meshing error has important influence on the dynamic load behavior of spur gears transmission in complex systems. For the planetary system with heavy external load, the dynamic behavior mainly depends on the external load, and the influence of internal excitation on the dynamic meshing force is less than that of the external excitation for the planetary system. The external excitation mainly affects the low-frequency region of the dynamic meshing force for the system, and the internal excitation affects the high-frequency region of the dynamic force for the system. The frequency influence interval of the internal excitation is much larger than that of the external excitation.