Planetary Gear Transmission Research Articles

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.

A numerical method for calculating the misalignments of planetary gears

Because misalignments derived from the deflections of transmission systems have significant effects on the load capacity of planetary gears, these misalignments should be accurately considered in the analysis of planetary gears. Here, we develop a new approach for misalignment calculations of cylindrical planetary gears. A nonlinear model of a planetary gear transmission system is built based on the finite element method and nonlinear bearing theory for misalignment calculations that can precisely simulate the structural characteristics and mechanical properties of a planetary gear system. The nonlinear static equation of a planetary system is solved efficiently using the Newton–Raphson method. Gear misalignments of all the planet branches are determined by the results of the system static analysis. The reliability and advantages of the proposed method are discussed via case studies. The effects of including the variation of the planet positions and the nonlinearity of the bearing stiffness on the planetary gear misalignments under different load conditions are studied. The misalignments can be reliably determined using the proposed method for calculating the load capacity of planetary gears.

Efficiency comparison of electric vehicles powertrains with dual motor and single motor input

Two novel dual motor input powertrains are proposed to improve the energy efficiency of electric vehicles (EVs). The first powertrain is based on a dual motor with planetary gear transmission (DMPGT), which connects two motors to the sun gear and ring gear respectively, and the carrier is engaged with output shaft. Two band brakes equipped on the sun gear and ring gear can realize three driving modes. The second powertrain is based on a dual motor with parallel axle transmission (DMPAT). It also provides three driving modes through switching on and off the two motors. To evaluate the two proposed powertrains, they will be compared with the widely adopted single motor with 1-speed and with 2-speed powertrains. The gear ratios of the powertrains are selected aiming at the vehicle dynamic performance, while the gear or mode shifting is designed to maximize the efficiency of EVs through an instantaneous optimization algorithm. The simulation results of the two proposed powertrains in three typical driving cycles demonstrate that the EVs equipped with both DMPGT and DMPAT have a higher overall efficiency than the EVs equipped with single motor input powertrain.

Study on nonlinear bifurcation characteristics of multistage planetary gear transmission for wind power increasing gearbox

In order to study the nonlinear dynamic characteristics of multistage gear transmission system of wind power increasing gearbox, a three degree of freedom dynamic model of high speed gear pair of wind power increasing box is established. The nonlinear bifurcation characteristics of the gear pair in high-speed level of the wind turbine gearbox are analyzed by numerical analysis method. The research shows that the high speed gear pair of the multistage planetary transmission system of the wind power increasing box shows significant dynamic non-linearity in the process of dynamic meshing. By controlling the value of internal and external excitation parameters, the influence of the nonlinear bifurcation response of the system is discussed, which can provide a useful reference for the parameter selection and nonlinear dynamic behavior analysis of the gear system.

Transmission Design and Kinematics Simulation of Fixed Gear and Planetary Gear

Based on the theory of 2K-H planetary gear ransmission, a fixed-axis gear planetary gear transmission scheme is designed, the gear meshing parameters are determined, and the theoretical transmission ratio and output speed are calculated. The 3D model software UG NX8.0 is used to build the solid model, and the virtual prototype model is built based on ADAMS 2013 and the kinematics simulation is carried out. The simulation results are compared with the theoretical values. The results show that the errors of speed and gear ratio are 0.43% and 0.50%. The correctness of the design parameters and the credibility of the virtual prototype model are validated, which lays the foundation for further research on the dynamic characteristics of the planetary gear mechanism.

Influence of Time-varying Mesh Stiffness Excitation on Vibration of Planetary Automatic Transmission

Based on the energy method, the time-varying mesh stiffness models of the internal and external meshing of the planetary gears are established. The translationrotation coupled dynamics differential equation of the planetary transmission system is established through the concentrated mass method. Analyze the influence of time-varying mesh stiffness excitation on the vibration of planetary gear transmission. The results show that the vibration response of the planetary gear sets is mainly related to the connection form under the excitation of the time-varying mesh stiffness. The time-varying mesh stiffness has the greatest influence on the vibration of the planet gear. The vibration of the planet gear is obviously more serious than the other components of the same planetary. When multiple planetary gear sets are connected, the vibration of the output component is smaller than the other components. Moreover the vibration of the input planetary set is generally greater than the rear planetary set except the planet gear.

Dynamic modeling and analysis of the planetary gear under pitching base motion

Planetary gear transmission is subjected to base motions in many industrial applications such as wind turbines and automobiles, and its dynamic behavior will be affected by base motions. To develop a dynamic model more suitable for the planetary gear under base motions, the general modeling procedures are illustrated in detail from the perspective of energy. A rotational-translational-axial dynamic model of the planetary gear under pitching base motion is proposed and validated. Pitching base motion causes additional damping, stiffness and forced excitation, which disrupts the force symmetry of the planetary gear and results in unequal load sharing. Dynamic responses of the planetary gear are obtained by numerical integration, and spectrum analysis is conducted using the Fourier transform. Spectra of the rotational and translational vibrations of the central components show completely different characteristics because of the structure symmetry of the planetary gear. The influences rules of parameters on response spectra and load sharing conditions are derived, including the amplitude and the frequency of the pitching base motion, and the carrier rotating speed. When the base excitation frequency approaches half the translational natural frequencies, the load sharing condition of the planetary gear will deteriorate rapidly. The load sharing factor increases by the square of the base excitation amplitude.

A METHOD FOR DETERMINING THE DISTRIBUTION OF LOADS IN ROLLING PAIRS IN CYCLOIDAL PLANETARY GEAR

The power transmission system in the cycloidal planetary gear is created by a serial connection of three rolling pairs: central cylindrical roller bearings, a set of rolling pins in the straight-line mechanism, and cycloidal meshing. The paper presents the numerical method for determining the distribution of forces acting on each rolling pair of this gear. Unlike analytical methods, numerical methods allow one to find that distribution in corrected meshing. Geometrical dimensions used in the equations of balance for the planetary gear transmission Palmgren`s dependences for the deformation line contact were used to calculate forces between co-operating elements. Once the distribution of load is known, one can predict the fatigue life of Cyclo’s gears in rolling pairs. The fatigue of rolling pairs is a very good criterion to optimize geometrical parameters of the power transmission system.

Multi-body Dynamic Analysis of Wind Power Gearbox

Using multi-body dynamics theory, we establish a multi-body system model of a 1.5WM wind power gearbox. Based on Hertz contact theory, The meshing force calculation method of gear meshing transmission is presented. This paper makes a simulation study about the time domain characteristics and frequency spectrum characteristics of meshing forces in planetary transmission, analysis the variation curves with time of dynamic load coefficients of multistage planetary transmission. The results show that the contact force in time domain has obvious dynamic characteristics when planetary gear transmission and its frequency domain showed modulation phenomenon. The carrier is the gear meshing frequency and modulation wave frequency is gear rotation frequency.

Design principle and modeling method of asymmetric involute internal helical gears

In the field of mechanical engineering, involute helical gears are widely used. Compared with the involute spur gear, helical gears have a high bearing strength, more smooth transmission, less impact and less noise. The internal gear pairs have the features of large transmission ratio, low vibration, low noise and low wear and hence are widely used in planetary gear transmission systems. In order to meet the requirements of high strength, high speed of the modern gear transmission systems, a new type of asymmetric involute internal helical gears is designed based on conventional involute gears. This paper discusses the gear shaper cutter modeling for machining this new gear, analyzes the formation principle of asymmetric tooth profile and establishes a three-dimensional modeling by SolidWorks. Through MATLAB simulation, pressure angle, tooth number, coefficient of displacement and contact ratio of conventional and asymmetric gear are compared and analyzed. Using ANSYS, two types of gears are compared on strength in order to demonstrate superiority of asymmetric tooth and further study about the asymmetric internal helical gears.

Conceptual design of planetary gearbox system for constant generator speed in hydro power plant

Micro Hydro Power Plant (MHPP) is emerging as one of the most clean, renewable and reliable energy technology for harnessing power. In MHPP hydro governors are avoided, that results in turbine speed fluctuation. MHPP requires either speed or torque amplification of generator for constant power generation. To achieve this, planetary gear transmission system is explored for MHPP due to its higher efficiency and compact size. A conceptual planetary gearbox system is developed for MHPP to maintain constant generator speed. The conceptual gearbox is designed, modelled and analysed using ADAMS software. Simulation results are found to be in close agreement with analytical results. Hence, conceptual design of planetary gearbox can be used to govern constant generator speed. In this paper, a MHPP which generate constant power of 5 kW at constant generator speed of 1490 rpm is analysed and validated

Dynamic analysis of planetary gear train system with double moduli and pressure angles

The planetary gear transmission with double moduli and pressure angles gearing is proposed for meeting the low weight high reliability requires. A dynamic differential equation of the NGW planetary gear train system with double and pressure angles is established. The 4-Order Runge-Kutta numerical integration method is used to solve the equations from which the result of the dynamic response is got. The dynamic load coefficients are formulated and are compared with those of the normal gear train．The double modulus planetary gear transmission is designed and manufactured. The experiment of operating and vibration are carried out and provides.

Analysis and design exploration of single stage compound stepped planetary gear transmissions

High-ratio compound stepped planetary transmissions are typically characterised by poor overall efficiencies, even if the individual mesh efficiencies are high, because of the very high sliding velocities imposed by the kinematics of their topologies. Here, a parametric exploration of the design space is presented for a stepped transmission topology, which is assessed in terms of transmission ratio, efficiency, and power density. It is confirmed that high ratio per (compound) stage is accompanied by low mechanical efficiency and/or large volume for the most part of the parametric design space, as is also anticipated by prior research. At the same time, specific niche regions of particular importance are identified that combine high-ratio, high-efficiency, and good power density.

Dynamic characteristics of a planetary gear system based on contact status of the tooth surface

Studies on the planetary gear have attracted considerable attention because of its advantages, such as compactness, large torque-to-weight ratio, vibrations, and high efficiency, which have resulted in its wide applications in industry, wind turbine, national defense, and aerospace fields. We have established a novel dynamic model of the planetary gear transmission by using Newton’s theory, in which some key factors such as time-variant meshing stiffness, phase relationships, and tooth contact characteristics are considered. The influences of gear axial tipping, operating conditions, and the meshing phase on the contact characteristics and the dynamic characteristics were researched systematically. It was found that the contact area of the tooth surface was moved due to the axial gear tipping, which obviously affected the meshing stiffness. With the increase in the inclination angle of the sun gear, the meshing stiffness decreases, which produces an evident influence on the high natural frequency in the planetary transmission system. In terms of the dynamic characteristics of the system, the component of rotating frequency appeared in the dynamic meshing force of the sun gear and the planetary gear. Moreover, the floating track of the center wheel varied significantly and exhibited an oval distribution as the inclination angle of the sun gear changed. When the inclination angle of the sun gear increased, the rotating frequency component increased significantly, but the other meshing frequency components remained unchanged; meanwhile, the deformation of the floating track also increased. If the inclination angle of the sun gear changes, the vibration state of the system and the collision impact could become more serious, and the lifetime of the planetary transmission system will reduce. Furthermore, when the load was increased, we found that the gear-tooth contact zone transformed from line contact to surface contact, the meshing stiffness increased, the effect of high natural frequency on the planetary transmission system became more evident, but its low-order natural frequency remained stable. With regard to the dynamic characteristics of the system, the components of the major frequency at the external gearing remained unchanged, but the rotation frequency of the sun gear and the meshing frequency amplitude increased linearly with the increase in load. In conclusion, the variation in the meshing stiffness of the planetary gear system had minor impact on the low-order natural frequency, but had a significant impact on the high natural frequency of the planetary transmission system due to the phase variation of the gear.

Analysis and design exploration of single stage compound stepped planetary gear transmissions

Analysis and design exploration of single stage compound stepped planetary gear transmissions

Rigid-flexible coupling dynamics simulation of planetary gear transmission based on MFBD

This paper deals with the problem of getting dynamic characteristics in complex mechanical multi-body system. Based on the MFBD (Multi-Flexible-Body Dynamics) technology, the rigid-flexible coupling dynamic simulation method is proposed, and then the method is applied to the planetary gear transmission. The results show that the dynamic stress distribution of planetary gear can be obtained to determine the dangerous location, and the dynamic response characteristics are more obvious. Then the simulation model of planetary gear transmission with broken tooth is established, the fault feature extraction in time-frequency domain is carried out using the acceleration signal. In addition, industrial data is also used to validate the effectiveness of the proposed method.

Effect of load and meshing stiffness variation on modal properties of planetary gear

Modal analysis of mechanical transmissions allows identification of critical frequencies and corresponding vibration modes. Major research works are done under constant loading conditions. However, load fluctuation can lead to variability in stiffness characteristics. Also, in the case of gear transmission, the fluctuation of mesh stiffness is rarely considered in the modal analysis. In this paper, a modal analysis of planetary gear transmission is investigated for different loading conditions and under mesh stiffness fluctuation. Hammer impact tests are carried out and the vibrations on fix ring are measured with different levels of load. During each test, natural frequencies are identified through frequency response function. The obtained results are correlated against the corresponding tridimensional lumped parameter of the test rig. Distributions of modal strain and kinetic energy for different loading conditions are studied as well as the effect of mesh stiffness variation on the natural frequencies.

Physics-based integrated vehicle health management system for predicting the remaining useful life of an aircraft planetary gear transmission

PurposeIntegrated vehicle health management has been developed for several years in different industries, to be able to provide the required inputs to determine the optimal maintenance operations depending on the actual health status of the system. The purpose of this paper is to demonstrate the potential of a physics-based model (PbM) for prognostics with a real case study, based on the detection of incipient faults and estimate the remaining useful life of a planetary transmission of an aircraft system.Design/methodology/approachMost of the research in the area of health assessment algorithms has been focused on data-driven approaches that are not based on the knowledge of the physics of the system, while PbM approaches rely on the understanding of the system and the degradation mechanisms. A physics-based modelling approach to represent metal-metal contact and fatigue in the gears of the planetary transmission of an aircraft system is applied.FindingsBoth the failure mode caused by metal-metal contact as caused by fatigue in the gears is described. Furthermore, the real-time application that retrieves the results from the simulations to assess the health of the system is described. Finally the decision making that can be executed during flight in the aircraft is incorporated.Originality/valueThe paper proposes an innovative prognostics health management system that assesses two important failure modes of the planetary transmission that regulates the speed of the generators of an aircraft. The results from the models have been integrated in an application that emulates a real system in the aircraft and computes the remaining useful life in real time.

Study on Nonlinear Dynamic Characteristics of 2K-H Planetary Gear System

A 2K-H type planetary gear reducer with involute spur gear is adopted as the research object. Considering the time-varying meshing stiffness, the time-varying backlash of the gear meshing and the time varying pressure angle and other nonlinear factors, the lateral-torsional-swing coupled nonlinear dynamic model of the planetary gear transmission system is established. According to the equations of Lagrange, the dynamic differential equations are derived. By introducing the state variable, the second-order differential equation of the coupled system is reduced to the first-order differential equation. The fifth-order step-varying adaptive Runge-Kutta numerical integration method is used to solve the dynamic equation. Compared with the previous dynamic models, this nonlinear dynamic model for the planetary gear transmission system is more closely to the practical operating conditions of the transmission system, which has laid a foundation for further evaluating the dynamic characteristics of the planetary gear transmission system in the future