Planetary Gear Set Research Articles

Predictive energy management with engine switching control for hybrid electric vehicle via ADMM

This paper studies energy management (EM) of a power-split hybrid electric vehicle (HEV) equipped with planetary gear sets. We first formulate a mixed-integer global optimal control problem that includes a binary switching variable. Convex modeling, including the fuel model for a compound energy conversion unit, is then presented to reformulate the mixed-integer EM as a two-step program. For optimizing the engine switching and battery power decisions in the first step, we employ the alternating direction method of multipliers (ADMM) algorithm where the solution of the convex relaxation is used to initialize the non-convex problem. On the standard driving cycle, simulation results indicate that the ADMM based EM method saves 7.63% fuel compared to a heuristic method, and shows 99% optimality compared to a dynamic programming method, while saving three orders of magnitude in computing time. An ADMM combined model predictive control (ADMM-MPC) method is also developed that is suitable for receding horizon control scenarios. The ADMM-MPC method shows 5.28% fuel saving when implemented using a prediction horizon of 15 samples. Meanwhile, the mean computing time for MPC updates is 3.53ms. Our results demonstrate that the proposed ADMM is capable of real-time control.

Four window functions for simulation of vibration transmission effects in a planetary gear set

Analysis of vibration spectrum is one of the main investigation methods in the research filed for condition monitoring on planetary gear sets. However, such a gear set always exhibits complicated spectral structures in the vibration spectrum because of the planet carrier’s rotation, and the path distance from the fixed transducer to the moving meshing point will always be changed, which brings a modulation effect on the vibration signals received by a fixed transducer. Aiming to investigate the vibration transmission effects of planetary gear sets, four different window functions are introduced in this paper to simulate the transmission path changing with time i.e. the path between moving meshing position and a fixed transducer. Comparison results show that the Hamming window function may be a more suitable choice to model the transmission path changing with time in the planetary gear set.

A global iterative model for mesh stiffness and mesh force estimation of flexible internal meshing in spur planetary gear sets

A global iterative model for mesh stiffness and mesh force estimation of flexible internal meshing in spur planetary gear sets

Improved vibration AM-FM sideband phenomenon models of planetary gear set with distributed faults and fault-induced speed fluctuation

Vibration modulation features are the important indicators for the planetary gear set fault diagnosis. However, the modulation sidebands caused by the distributed faults of planetary gear set are complicated, especially the FM components related to fault-induced periodic speed fluctuation, which have not been clearly revealed. In this paper, the transfer path function, gear meshing force and measuring-direction projection function with FM components are combined to develop a series of phenomenon models when considering the distributed gear fault-induced speed fluctuation, which can theoretically deduce the vibration modulation sidebands. Field test of the wind turbine planetary gearbox and the fault simulation of experiment platform verify the high consistency of the vibration AM-FM sidebands obtained from the phenomenon models and the practical planetary gear sets. The proposed models contribute a clear explanation for the generation mechanism of vibration AM-FM sidebands even the sidebands with small amplitudes caused by the distributed faults of sun and planet gear, and provide the important and effective frequency features to confirm the condition of planetary gear set.

Seamless mode shift control for a new Simpson planetary gearset based dual motor powertrain in electric vehicles

This paper proposes a seamless mode shift control strategy for a Simpson planetary gearset based dual motor powertrain (SPGDMP) which has 6 driving modes. The dynamic model of SPGDMP is built, where the rotational inertia of transmission components, the flexibility of shafts, dynamic response of motor torque and brake pressure, and stick-slipping friction phenomenon of brake are considered. A seamless mode shift control strategy is proposed to avoid power interruption and reduce the vehicle jerk. The mode shift is decoupled to the torque transition process and speed transition process, which lowers the control difficulty. The step function is used to produce the smooth transition trajectories of torque and speed, which eliminates the large vehicle jerk induced by the unsmooth driving torque. In the speed transition process, a combination of speed feedback and torque feedforward control strategy is proposed to track the designed motor speed trajectory and the driver's input torque simultaneously. The simulation results demonstrate that the proposed mode shift control strategy can reduce the peak-to-peak value of vehicle jerk to a value below 2 m/s3.

Design of a Hybrid Electric Power-Split Transmission for Braking Energy Recovery in a Drilling Rig

Despite the promising potential of the hybrid electric power-split layout, its broader market penetration is prevented by the large number of feasible solutions and the constructive complexity, which overcomplicate the design process. Moreover, due to the lack of relevant literature references, the power-split transmissions design is even more difficult if concerning applications outside the automotive and agricultural sectors. In this paper, a general parametric model already available in the literature to design a single-mode power-split transmission with up to two planetary gear sets and six ordinary gear sets was applied to hybridize an oil drilling rig to recover energy braking during the gravity-driven lowering phases. This is the first power-split electric hybridization of a drilling rig. Two solutions differing in engine power size are presented. Thanks to the modularity of the model, the procedure enabled the optimization of the ICE, the electric machines, and the gear sets through decoupled design phases.

Dynamic characteristics of the floating non-loaded ring gear with external spline teeth in Ravigneaux planetary gear sets

When analyzing the dynamic characteristics of Ravigneaux planetary gear sets, the vibration of loaded parts is often paid more attention than non-loaded part since that it is theoretically believed to transfer no power. However, a failure problem is found that the non-loaded part does vibrate seriously and so causes the crack in the middle zone between two spline tooth roots when driving the clutch friction plates to rotate synchronously. The finite element method is applied to model the whole Ravigneaux planetary gear set with two ring gears. The simulated result proves that the floating non-loaded ring gear burdens transient high-frequency acceleration and deceleration impact from planet gears. The sectional stress distribution is analyzed for the floating ring gear under the impact. The middle zone between two internal tooth roots has large stress, and the same characteristics exists for the external spline teeth. This vibration of the floating non-loaded ring gear is the final excitation source for the clutch friction plates driven by the floating ring gear. This work is of high value for controlling the vibration level of the floating ring gear and solving the fracture fatigue problem of its matching friction plates in Ravigneaux planetary gear sets.

Energy efficiency optimization of Simpson planetary gearset based dual-motor powertrains for electric vehicles

The improvement of powertrain energy efficiency is of great significance to improve the driving range of electric vehicles. This paper proposes four configurations of Simpson planetary gearset-based dual-motor powertrain (SPGDMP) and optimizes their parameters. The powertrain energy efficiency is obtained through the scalable motor model and the gear ratio-dependent transmission efficiency model. The influence of powertrain parameters is then analyzed to determine the design variables. An improved economic performance indicator with less computational cost is proposed, which can reduce the computational time by 98.82% compared with the conventional economic indicator calculated by the dynamic programming (DP) algorithm. Considering the trade-off between dynamic and economic performance, the multi-objective optimization model is proposed, which gains the discrete Pareto front by the NSGA-Ⅱ and makes the discrete Pareto front continuous by neural network fitting (NNF). The optimization results show that compared with a widely studied torque coupled dual-motor powertrain (TCDMP), SPGDMPs can reduce the energy consumption and motors power by at least 5.02% and 14.56%, respectively. The energy efficiency of SPGDMPs has a little improvement when the powertrain equips with more brakes.

A Novel Electronic Wedge Brake Based on Active Disturbance Rejection Control

The electronic wedge brake system (EWB) used in the automotive industry is a new structure designed for brake-by-wire systems. This paper proposes a novel EWB system which is mainly composed of a screw-driven wedged inner brake pad, a fixed outer brake pad, a fixed caliper-flexible brake rotor and a hybrid stepper motor. The proposed EWB system does not have a planetary gear set or a ball screw mechanism, it simplified the existing EWB systems. The proposed EWB system is designed to take advantage of the self-interlocking ability of the screw mechanism to hold the brakes with zero-overhauling and the self-energizing ability of the wedge brake pad to reduce the braking effort. In the braking phase, the screw driven wedge inner brake pad forces the flexible rotor against a fixed flat brake pad. The rotor is elastically deformed to make the contact against the fixed pad. Except for the applied force, the friction force between the brake rotor and the wedge pad exerts additional force as the wedge is pulled along the direction of rotation, thus requiring a lower brake actuation force. In this paper, the active disturbance rejection control (ADRC) algorithm is introduced to improve the response ability and stability of the proposed EWB. Simulations are performed to demonstrate the effectiveness of the ADRC controller in the proposed EWB system.

Vibration signal modeling of planetary gearbox based on dynamics and finite element method for tooth crack diagnosis

Planetary gear set contains many kinds of nonlinear factors, such as time-varying meshing stiffness, bearing support, backlash, and comprehensive transmission error, which will deeply affect the gearbox response behaviors and vibration characteristics. During the operation of planetary gear set, there are several gear pairs meshing simultaneously, which will lead to multiple vibration sources and complicate vibration transmission. The revolution of the planet gears makes the meshing force of the gear pairs vary periodically, and the continuous motion of the meshing point also changes the length of vibration transmission path. This study aims to establish a hybrid model that can simulate the vibration signals of gearbox measuring points through fusing the dynamic model of planetary gear set and the transmission path model. Through the simulation analysis, the vibration characteristics of the measuring point signal of the planetary gearbox are revealed, and the crack fault of the planet gear tooth is effectively isolated. Finally, the availability and validity of the presented model are experimentally verified, and the magnitude match is up to 78%. The model can not only provide a theoretical basis for data-driven fault diagnosis methods, but also solve the pain point of diagnostic samples scale and balance by simulation means.

Wear prediction and meshing characteristics for the planetary gear set considering angular misalignment and rotating carrier

This paper focuses on the effect of angular misalignment on wear prediction of the planetary gear set with the rotating carrier, which is more complex than that of the parallel-axis gear due to the position changing of the planet gears. The wear depth is calculated based on the Archard’s wear theory, the load distribution is obtained by the three dimensional loaded tooth contact analysis (3D-LTCA) method, and the effect of angular misalignment is considered by introducing the change in meshing clearance between the two engaged tooth flanks. The load distribution, the time-varying mesh stiffness (TVMS) and the backlash of gear pairs are presented under different wear levels. The results show that, with the combined effect of angular misalignment and rotating carrier, the wear depth on both sides of the face width is larger than that in the middle, and the difference is the greatest at the root. Moreover, TVMS is affected not only by the tooth wear, but also by the rotating carrier, and the cycle of TVMS and the backlash is half of that of the carrier rotation.

A Generalized Dynamic Model and Coupling Meshing Force Analysis for Planetary Gear Set Transmissions

The dynamics analysis of a planetary gear set transmissions requires the creation of completely different models for different gears, which is very tedious. In this paper, a generalized dynamics modeling process is proposed for a three planetary gear set transmissions, and a generalized dynamic model for multiple gears is established by using the lumped mass method. The analysis of meshing force characteristics is carried out for the second gear position, and the meshing frequency coupling phenomenon between the meshing forces of the three planetary gear sets is investigated. The results show that, for the current gear set of meshing force, the meshing frequency components of other gear sets only appear in a part of the speed, and with the increase in speed, certain low-frequency components of other sets that exist at low speed will decrease or even disappear, and the coupling relationship between the meshing forces of different planetary gear sets is not symmetrical.

Increasing Safety in Ultralight Aviation with a Wankel-Based Series/Parallel Hybrid Electric Power System

The goal of this investigation is to propose a series/parallel hybrid electric power system for ultralight aviation designed to improve safety and, possibly, reduce fuel consumption. The power system consists of a Wankel engine, two electric machines, a battery, and a planetary gear set, all acquired from the automotive market. After a preliminary design based on takeoff power, the system is simulated over a typical flight mission and in case of engine failure for a first validation of the proposed powertrain. The investigation also shows a comparison in terms of performance and fuel consumption between the initial configuration (reciprocating piston engine), a non-hybrid Wankel arrangement, and the proposed hybrid electric configurations by using in-house simulation software. A heuristic energy management strategy is proposed as well. During a typical mission, the new powertrain works as a parallel hybrid during takeoff and climb, thus ensuring high performance and safety. During the cruise, the system behaves like a parallel hybrid with a continuously variable transmission that makes the engine work always at high efficiency. The battery is partially recharged during the descent by the extra power of the engine. The preliminary results reported in this work predict an improvement in fuel consumption by about 20% compared with the initial piston engine configuration and 28% compare with the non-hybrid Wankel powertrain, despite the larger takeoff weight.

Efficiency analysis of dual motor powertrain with planetary gear set

Abstract This paper focuses on electric vehicles with dual motors combined with a planetary gear train. The combination of sun and ring motor allows for achieving higher efficiencies and satisfying power demands as compared to single motor powertrains. Primarily dual motor drive with planetary gear train is proposed and simulated with different drive cycles. Secondarily by extracting the motor efficiency maps working area of different modes, speed and efficiency are determined. Finally, an optimization algorithm was developed to automatically change speed and torque as per load demand. In this way, our work could represent a framework for improving efficiency performances and load demands of an electric vehicle.

Dynamic modeling of the planetary gear set considering the effects of positioning errors on the mesh position and the corner contact

Dynamic modeling of the planetary gear set considering the effects of positioning errors on the mesh position and the corner contact

Nonlinear dynamic modeling and analysis of a helicopter planetary gear set for tooth crack diagnosis

Planetary gearset is a vital dynamic component in helicopter transmission. In the planetary gearbox, there are many nonlinear dynamic factors, such as time-varying meshing stiffness, bearing support stiffness, comprehensive transmission error and tooth backlash. These nonlinear factors will deeply affect the vibration response characteristics of the gearbox system, and bring new challenges to the crack fault detection and diagnosis. To unveil the nonlinear properties of planetary gear set, a 21 degrees of freedom translational-torsional model of the planetary gear set is established by integrating above-mentioned nonlinear factors. Analysis of the fault influence on natural frequency and statistical indicators of simulation responses, the optimal indicators for fault detection are found. Then, nonlinear dynamic characteristics of gear system under fault state are conducted, and crack fault symptoms are pointed out using time-domain waveform analysis and power spectrum analysis of response signals, which actively illustrates the system fault mechanism and achieves fault isolation. Finally, the effectiveness of the model for planetary gear set with tooth crack is verified by experiments.

A novel mathematical model for analysis of the cracked planet gear

The crack fault often appears in the complicated gear system, and even causes tooth broken. To solve this problem, an improved model is proposed in this paper, which considers the coupling effect of cracks on both gear tooth and gear foundation, and a 2D finite element model is established to verify the proposed method. The influences of crack size and inclination angle on meshing stiffness are investigated. The results are used to simulate the situation of the crack occurring at the sun gear in an 18 degrees of freedom dynamic model of the planetary gear set, so as to obtain the dynamic responses of the crack gear system both in time domain and frequency domain. Finally, two different methods are used to process the original vibration signals to obtain the residual signals. Combining the residual signals, several statistical indicators are employed to characterize the evolution of crack propagation.

An Energy Management Strategy of Power-Split Hybrid Electric Vehicles Using Reinforcement Learning

With the rapid development of science and technology, the automobile industry is also gradually expanding due to which energy security and ecological security are seriously threatened. This paper was aimed at studying the energy organization strategy of power-split hybrid electric vehicles based on a reinforcement learning algorithm. A power-split hybrid electric vehicle (HEV) combines the advantages of both series and parallel hybrid vehicle architectures by using a planetary gear set to split and combine the power generated by electric machines and a combustion engine. This improves the fuel economy to some extent. However, to increase the fuel economy to a greater extent. This study primarily introduces the hybrid electric vehicle’s structure and presents a reinforcement learning-based management of energy approach for hybrid electric vehicles. It constructs the vehicle power model of HEV and Markov probability transfer model, then designs the energy control strategy based on reinforcement learning, and finally compares it with the energy control strategy based on PID (Proportional-Integral-Derivative). Using MATLAB/Simulink, the cycle conditions of NEDC (New European Driving Cycle) and FTP-75 (Federal Test Procedure) are selected to carry out simulation experiments. The energy management technique suggested in this study, which is based on reinforcement learning, may efficiently enhance the usage rate of automotive gasoline. The replication results show that the fuel consumption per 100 km (kilometers) based on reinforcement learning management strategy is 4.6% and 2.7% lower than the PID management strategy under two working conditions. The economy of fuel of the hybrid electric vehicle is also effectively improved.

DNA Assembly of Modular Components into a Rotary Nanodevice.

The bacterial flagellar motor is a rotary machine composed of functional modular components, which can perform bidirectional rotations to control the migration behavior of the bacterial cell. It resembles a two-cogwheel gear system, which consists of small and large cogwheels with cogs at the edges to regulate rotations. Such gearset models provide elegant blueprints to design and build artificial nanomachinery with desired functionalities. In this work, we demonstrate DNA assembly of a structurally well-defined nanodevice, which can carry out programmable rotations powered by DNA fuels. Our rotary nanodevice consists of three modular components, small origami ring, large origami ring, and gold nanoparticles (AuNPs). They mimic the sun gear, ring gear, and planet gears in a planetary gearset accordingly. These modular components are self-assembled in a compact manner, such that they can work cooperatively to impart bidirectional rotations. The rotary dynamics is optically recorded using fluorescence spectroscopy in real time, given the sensitive distance-dependent interactions between the tethered fluorophores and AuNPs on the rings. The experimental results are well supported by the theoretical calculations.

Prognostics of Gear Manufacturing Errors for Planetary Gear Systems Based on Power Flow Theory

Abstract Gear manufacturing errors are key parameters in planetary gear trains and have effects on load sharing, tooth stress, and so on. Accurate estimation of manufacturing errors can help monitor the conditions of planetary gear systems. This study investigates the dynamic response sensitivity to model parameters for a nonlinear single-stage planetary gear set with coupled lateral and torsional motions. Power flow theory is introduced to assess the gear vibration and the parameter sensitivity. The response sensitivity equations are deduced with the direct method (DM). The influence of the rotating speed is considered in the sensitivity analysis. Then, the identifiability of the parameter estimation is investigated based on the sensitivity results. The Gauss-Newton method is applied to estimate the manufacturing errors. Gear meshing is a primary factor in gear vibration, so the sensitivities of its vibration power to the parameters are analyzed in this paper. The estimated results are accurate when the collected data contain a lower noise signal. The sensitivity and parameter estimation make it possible to provide support for the design and diagnosis of a planetary gear set.