Compound Planetary Gear Set Research Articles

Vibration-shock behavior analysis of compound planetary gear set based on harmonic balance method

Due to the clearance between the mating gears, a dynamic load rises and causes tooth impact and vibration. In the compound planetary gear set, under the interaction of transmission error, meshing stiffness, support stiffness and backlash, the unilateral tooth impact could evolve into bilateral tooth impact, resulting in a worse dynamic behavior. This work reveals the influence of internal excitations and external excitations on vibration-shock behavior, and, for this purpose, a “purely torsional” lumped parameter dynamics model of compound planetary gear set is built and combined with a harmonic balance method. The steady dynamics response under the frequency domain and time domain is given by the numerical solving method, and the results indicated that the bilateral impact occurs due to the transmission error. To avoid the influence of transmission error on the impact at the resonance peak, the input speed of the compound planetary gear set should avoid the resonance range and harmonious response range. To improve the tooth surface contact by increasing the backlash, it is recommended to decrease the initial velocity to below ωmesh = 0.8.

Influence of floating support on the dynamic characteristics of compound planetary gear set

Due to a large number of components, complex meshing relations and high requirements for assembly accuracy, the dynamic characteristic of compound planetary gear, such as vibration, impact, periodic motion and load sharing, are more easily affected by internal excitation than those of simple planetary gear set and parallel shafting gear set. To improve the load sharing behavior and the resistance of Chaos motions in the compound planetary gear set, in this work, by introducing the floating support into the center gear and planet gear, a lumped-parameter dynamic model of the compound planetary gear set is built based on the lumped parameter method and Lagrange kinematics equation. The steady response is calculated by numeric method to investigate the influence of floating support from different components on loading sharing behavior and periodic motion. The results indicate that, the increase of the floating value of all components improves the instantaneous load-sharing behavior, and single floating of planet gear reduces the load sharing behavior. To avoid the system being in quasi-periodic motion and Chaos motions under the condition of floating support, the input speed should be avoided away from the range of 3201 r/min-5069 r/min.

Modelling of time-varying meshing stiffness under tooth wear condition for nonlinear dynamics in compound planetary gear set

Under tooth profile wear condition, with running time increasing, the tooth chord length of the gear tooth is thinner and the tooth profile is not involute profile any more, which results in the changes in amplitude and fluctuation of time-varying meshing stiffness. In this work, in order to reveal the influence of tooth profile wear on time-varying meshing stiffness, an analytical model for calculating the time-varying meshing stiffness under tooth wear condition is built and incorporated with a “translational-rotational” dynamic model of compound planetary gear set. Poincare section, the phase trajectory and bifurcation diagram are employed for analysis of periodic and chaotic motion. The results indicate that, tooth wear accumulation result in the reduction in the amplitude of meshing stiffness at the meshing region of double-pair teeth, but makes no difference in meshing stiffness for the meshing region of single-pair teeth. In order to avoid the system being in Chaos motions, under large tooth wear condition, the input speed should be avoided away from 3700 r/min-6725 r/min, so as to keep the system in a stable periodic motion state.

A dynamic tooth wear prediction model for reflecting “two-sides” coupling relation between tooth wear accumulation and load sharing behavior in compound planetary gear set

In planetary gear set, load sharing behavior determines the average amplitude of meshing force, so determines the tooth wear. Meanwhile, tooth wear accumulation increases the backlash, so affects the load sharing behavior. As a result, a “two-sides” coupling relation appears between load sharing behavior and tooth wear. In order to reveal this coupling relation, a static tooth wear prediction model for compound planetary gear set is employed to describe the wear distribution along tooth profile and backlash generated by tooth wear accumulation. Then, a “translational-rotational” lumped-parameter dynamic model of compound planetary gear set is built to calculate the eccentric load coefficient for each meshing pair, under the excitation from the backlash generated by tooth wear accumulation, transmission error, and other excitation. Based on the aforementioned two models, a dynamic tooth wear prediction model is put forward to reflect “two-sides” coupling relation between tooth wear accumulation and load sharing behavior in compound planetary gear set. Lastly, in order to improve the reliability, a 3D-diformable model is built to study the influence of tooth wear on load sharing. The results indicated that, with the system running and tooth wear increasing, under the condition of no-initial transmission error, tooth wear accumulation decreases the load sharing at meshing engagement and disengagement, and under the condition of initial transmission error, tooth wear accumulation improves load sharing behavior slightly.

Multi-Speed Transmission Mechanism Using a Compound Planetary Gear Set and Brakes

Today, the use of electric vehicles (EVs) is increasing. Electric motors, which are used as the power source in EVs, have better torque-speed characteristics than traditional engines. However, electric motors also have a low speed torque limitation; moreover, their energy efficiency at low speed is not very high, resulting in severe heat generation when climbing steep slopes. While it is better to use multi-speed transmissions in EVs, the complex structure of conventional multi-speed transmissions decreases the advantages of EVs. This paper proposes a multi-speed transmission mechanism that uses a compound planetary gear set and brakes; its simple structure and lack of a synchronizer make it suitable for EVs. The electric motor’s high controllability makes high-speed gear shifting possible because the motor’s teeth are always engaged. It is also possible to throw the motor out of gear or to put the brake on the output shaft. General equations for the reduction ratios are derived and a design possibility for the arbitrary reduction ratio is mentioned. A simple experimental setup is presented, demonstrating that the proposed multi-speed transmission mechanism is effective.

Robust optimisation of dynamic and NVH characteristics for compound power-split hybrid transmission

In this paper, vibro-acoustic characteristics of a power-split hybrid transmission including a compound planetary gear set are investigated by numerical procedure and refined system dynamics modelling. For validation of the numerical predictions, bench tests are performed for dynamic and acoustic responses of the hybrid transmission, contribution rates of acoustic radiation power induced due to the planetary gears, support bearings, transmission shafts and the gearbox housing are estimated. In improving the noise, vibration and harshness (NVH) performance of the transmission during hybrid vehicle acceleration, traction torques of the motors against the planetary gear parametric resonance are formulated and an optimal control strategy is proposed. By real road NVH test results acquired on board of the midsize hybrid car, it is demonstrated that a significant reduction of the planetary gear whine noise is achieved. As a result, numerical approaches applied to establish relationships between torques of the two traction motors and parametric excitations of the compound planetary gear train are experimentally validated.

Numerical and Experimental Investigations of Noise and Vibration Characteristics for a Dual-Motor Hybrid Electric Vehicle

This paper investigates the abnormal noise and vibration of a hybrid electric vehicle during the electric-only driving mode. The sources of the noise and vibration are first identified through the frequency analysis, and then several measures are implemented to reduce the noise and vibration level. The experimental results have identified the gear meshing in the compound planetary gear set is the main source of the noise and vibration. The theoretical analysis demonstrates that gear pairs of the short planet-small sun gear and short planet-long planet in the compound planetary gear set contribute to the main noise and vibration of the hybrid system in the electric-only driving mode. This research also shows that the gear-meshing noise level in the compound planetary gear set can be decreased significantly by matching the engagement parameters, such as meshing stiffness, tooth error, and pitch error. The observation results in this paper are able to provide a practical reference for improving the ride comfort of hybrid electric vehicles in the future study.

Backlash Analysis of Compound Planetary Gear Set in Rotary Actuators

This paper proposes a model for backlash analysis of compound planetary gear set in rotary actuators. Three main types of errors in the compound planetary gear set are analysed, that is, manufacturing errors, assembly errors and deformation errors. Due to the randomness of the errors, the backlash model of the gear set was established based on probability theory to improve the backlash estimation for the practical applications. Finally, the backlash of a compound planetary gear set was calculated and the influences of main errors to the backlash were also investigated.

Model-based analysis and fault diagnosis of a compound planetary gear set with damaged sun gear

The vibration properties of compound planetary gears are more complicated than that of simple ones. This paper aims to investigate the fault properties of a compound planetary gear set in chipped sun gear conditions using model-based method. A three-dimensional lumped-parameter nonlinear dynamic model for the compound planetary gear set is established. This model considers the time-varying mesh stiffness (TVMS), the mesh phase relations, and gear chipping defects. The analytical equations are derived to quantify the TVMS reduction induced by the chipped gear based on the improved potential energy method. Further, the simulations are performed to demonstrate the fault features of sun gears with single or multiple chipped teeth in different gear stages. Moreover, the theoretical derivations are validated through the experimental signals analysis.

Fault features analysis of a compound planetary gear set with damaged planet gears

The fault properties of compound planetary gear set are much more complicated than the simple planetary gear set. A damaged planet will induce two periodic transient impulses in the raw signals and generates modulation sidebands around the mesh harmonics. This paper aims to investigate the fault properties of a compound planetary gear set in damaged planet conditions. A dynamic model is proposed to simulate the vibration signals. The time interval between the fault-induced close impulses in the time domain is used as a significant feature to locate the faulty planet. Considering the phase relations, the time-varying mesh stiffness is obtained. Then, the fault properties are demonstrated in the simulation, and the theoretical derivations are experimentally verified.

Precise model-based simulation for a deep hybrid transmission with compound planetary gear set

Establishing a precise system level model for transmission system is quite necessary and feasible for today’s computer technology. Taking into account of the exact parameters and actual working condition, an accurate model for a new deep hybrid transmission with compound planetary gear set is constructed, which in consideration of the gravity and centrifugal effect. The system level model contains the gears, shafts, bearings, clutches, electric motors and the housings. Few studies are found to investigate structure influence in system level for noise, vibration and harshness performance. Validation for the simulation results with test in three typical working conditions is carried out, which shows a quite well agreement. Furthermore, some parameters for this compound planetary gear set are investigated. The results show that for radial clearance between the ratchet and ring gear the smaller the better, while the axial clearance between the ratchet and ring gear requires cautious consideration to realize a better vibration performance for different planetary gear set. In the case of carrier, the radius of the connection pawl and the thickness of the carrier input shaft have remarkable influence on vibration characteristics. The vibration amplitude is the lowest when these two values equaling to 55 and 7 mm, respectively. Other than that, it is interesting to notice that the carrier position has a significant influence on the system vibration in pure electric drive mode. It is shown that if the planet carrier is fixed and sun gear rotates as input, the position of carrier should keep planet gears at high gravity center and symmetrical distribution on both sides of carrier centerline in the gravitational direction. The vibrational magnitude is the smallest as the carrier rotating 50° along z axis for this compound planetary gear set.

Vibration and acoustic investigation for a deep hybrid transmission with power-split compound planetary gear set

A new compound planetary gear set was produced for hybrid transmission with advantages superior to classical Ravigneaux planetary gears. However, vibration and noise problems need more attention in order to meet the market demand. Vibration characteristics of the new power-split hybrid transmission with a four-shaft compound planetary gear set are investigated. An equivalent method for stepped shaft is proposed to simplify the motor E1 shaft. Based on six degrees of freedom of helical gear pair model and shaft-bearing model, a dynamic model for the planetary mechanism is established in pure electric driving mode. The numerical analysis of the distinctive natural frequencies and corresponding vibration modes is produced. Moreover, in order to identify the noise source, noise and vibration experiments are carried out on test rig. By comparing the numerical results and test data, the noise and vibration at a frequency of 696 Hz are evidently caused by the transverse vibration of motor E1 shaft, and the rotational vibration of ring gear exacerbates the vibration and noise. Not only the impact of torques from motors E1, E2 and semi-shaft but also the influences of carrier speed and preload on differential bearings are investigated.

Influence of the backlash generated by tooth accumulated wear on dynamic behavior of compound planetary gear set

Backlash is a key internal excitation on the dynamic response of planetary gear transmission. After the gear transmission running for a long time under load torque, due to tooth wear accumulation, the backlash between the tooth surface of two mating gears increases, which results in a larger and irregular backlash. However, the increasing backlash generated by tooth accumulated wear is generally neglected in lots of dynamics analysis for epicyclic gear trains. In order to investigate the impact of backlash generated by tooth accumulated wear on dynamic behavior of compound planetary gear set, in this work, first a static tooth surface wear prediction model is incorporated with a dynamic iteration methodology to get the increasing backlash generated by tooth accumulated wear for one pair of mating teeth under the condition that contact ratio equals to one. Then in order to introduce the tooth accumulated wear into dynamic model of compound planetary gear set, the backlash excitation generated by tooth accumulated wear for each meshing pair in compound planetary gear set is given under the condition that contact ratio equals to one and does not equal to one. Last, in order to investigate the impact of the increasing backlash generated by tooth accumulated wear on dynamic response of compound planetary gear set, a nonlinear lumped-parameter dynamic model of compound planetary gear set is employed to describe the dynamic relationships of gear transmission under the internal excitations generated by worn profile, meshing stiffness, transmission error, and backlash. The results indicate that the introduction of the increasing backlash generated by tooth accumulated wear makes a significant influence on the bifurcation and chaotic characteristics, dynamic response in time domain, and load sharing behavior of compound planetary gear set.

Fault Diagnosis for a Multistage Planetary Gear Set Using Model-Based Simulation and Experimental Investigation

The gear damage will induce modulation effects in vibration signals. A thorough analysis of modulation sidebands spectral structure is necessary for fault diagnosis of planetary gear set. However, the spectral characteristics are complicated in practice, especially for a multistage planetary gear set which contains close frequency components. In this study, a coupled lateral and torsional dynamic model is established to predict the modulation sidebands of a two-stage compound planetary gear set. An improved potential energy method is used to calculate the time-varying mesh stiffness of each gear pair, and the influence of crack propagation on the mesh stiffness is analyzed. The simulated signals of the gear set are obtained by using Runge-Kutta numerical analysis method. Meanwhile, the sidebands characteristics are summarized to exhibit the modulation effects caused by sun gear damage. At the end, the experimental signals collected from an industrial SD16 planetary gearbox are analyzed to verify the theoretical derivations. The results of experiment agree well with the simulated analysis.

A nonlinear dynamic model for analysis of the combined influences of nonlinear internal excitations on the load sharing behavior of a compound planetary gear set

Nonlinear internal excitations, which include meshing stiffness, backlash, and bearing clearance, may cause nonuniform load distribution in compound planetary gear transmission. To quantify the influence of nonlinear internal excitations on load sharing behavior, and to study the combined effects of meshing stiffness, backlash, and bearing clearance on load sharing behavior, this paper develops a nonlinear dynamic model of a Ravigneaux compound planetary gear set with all members possessing translational and torsional vibration degrees of freedom, as an extend dynamic model to the prior research for compound planetary gear set. In detail, the dynamic model is derived on the basis of the second Lagrange equations, and the load sharing coefficients for different meshing pairs are defined and calculated. Single factor analysis is introduced to investigate the influence of each nonlinear internal excitation on load sharing coefficient ( LSC). On the basis of single factor analysis, Taguchi method is incorporated with the nonlinear dynamic model to study the combined effects of nonlinear internal excitation and figure out the most significant control factor affecting LSC among meshing stiffness, backlash, and bearing clearance. The calculation results are evaluated by using signal-to-noise ( S/ N) analysis and ANOVA method. The results indicate that backlash affects the load sharing behavior most significantly, compared with mean value of meshing stiffness and bearing clearance.

Harmonic balance method implementation of nonlinear dynamic characteristics for compound planetary gear sets

In this paper, the harmonic balance method has been extended to investigate the nonlinear dynamics of a compound planetary gear sets. The lumped parameter dynamic model, incorporating parametric gear mesh stiffness fluctuations, transmission errors and gear backlash, is established. The responses of the system, mesh stiffness, transmission error, and gear backlash have all been represented by harmonic functions, which have been utilized to derive the algebraic equations via Galerkin process. The nonlinear dynamic characteristics of the gear sets are researched, and the effect of nonlinearities on the frequency response characteristic has been investigated by changing the value of the non-dimensional backlash, mesh stiffness, and amplitude of error excitations. The multiple value, jump and discontinuities phenomena have been revealed in the presented frequency response curves. The formulation derived here can also be extended to incorporate incremental harmonic balance method and parameter continuation scheme for further nonlinear dynamics investigation.

Accounting of power loss in differential mechanism while design of multithreaded hybrid powerplants

The paper discusses the issue of power loss accounting in compound planetary gear sets used in design of multithreaded hybrid powerplants known also as Power-Split or PGHP. The method of determining these losses is offered.

Impact of Mesh Errors on Dynamic Load Sharing Characteristics of Compound Planetary Gear Sets

Impact of Mesh Errors on Dynamic Load Sharing Characteristics of Compound Planetary Gear Sets

The Research on Natural Characteristic and Eigensensitivity of Ravingneaux Compound Planetary Gear Sets

The dynamic model of Ravingneaux compound planetary gear sets has been built. Then the Natural frequency and vibration model have been solved in the Ravingneaux compound planetary gear sets. The eigensensitivity to parameters have been researched based on the dynamical model. The varying trend of natural frequency according to the varying of parameters have been researched, which include gear mass (sun gear, ring gear , or planet gear), the moment of inertia of gears, the support stiffness , the torsional stiffness.

Torsional vibration and acoustic noise analysis of a compound planetary power-split hybrid electric vehicle

Theoretical and experimental analyses of torsional vibrations and acoustic noise for a deep hybrid electric vehicle driveline including an electric, continuously variable transmission are carried out. The dynamic and mathematical models with 16 degrees of freedom in a matrix form are developed for the torsional vibration characteristics of the hybrid driveline. On the other hand, the noise sources of the hybrid electric vehicle powertrain excited in the pure electric mode and the hybrid drive mode are tested and measured using acoustic and speed sensors. The noise orders and the frequency domain responses are constructed using signal treatment and torsional vibration analysis. The theoretical predictions for the natural frequencies and the corresponding vibration modes of the hybrid driveline are presented. The noise test results are also given in accordance with the torsional vibration modes of the hybrid driveline in the pure electric mode and the hybrid drive mode. The noise sources due to the self-excited and frequency-multiplied vibrations are found, focusing on the compound planetary gear set in the power-split electric, continuously variable transmission.