Research on Instantaneous Angular Speed Signal Separation Method for Planetary Gear Fault Diagnosis

Planetary gear train is a critical transmission component in large equipment such as helicopters and wind turbines. Conducting damage perception of planetary gear trains is of great significance for the safe operation of equipment. Existing methods for damage perception of planetary gear trains mainly rely on linear vibration analysis. However, these methods based on linear vibration signal analysis face challenges such as rich vibration sources, complex signal coupling and modulation mechanisms, significant influence of transmission paths, and difficulties in separating damage information. This paper proposes a method for separating instantaneous angular speed (IAS) signals for planetary gear fault diagnosis. Firstly, this method obtains encoder pulse signals through a built-in encoder. Based on this, it calculates the IAS signals using the Hilbert transform, and obtains the time-domain synchronous average signal of the IAS of the planetary gear through time-domain synchronous averaging technology, thus realizing the fault diagnosis of the planetary gear train. Experimental results validate the effectiveness of the calculated IAS signals, demonstrating that the time-domain synchronous averaging technology can highlight impact characteristics, effectively separate and extract fault impacts, greatly reduce the testing cost of experiments, and provide an effective tool for the fault diagnosis of planetary gear trains.

Statistical Modification Analysis of Helical Planetary Gears based on Response Surface Method and Monte Carlo Simulation

Tooth modification technique is widely used in gear industry to improve the meshing performance of gearings. However, few of the present studies on tooth modification considers the influence of inevitable random errors on gear modification effects. In order to investigate the uncertainties of tooth modification amount variations on system＇s dynamic behaviors of a helical planetary gears, an analytical dynamic model including tooth modification parameters is proposed to carry out a deterministic analysis on the dynamics of a helical planetary gear. The dynamic meshing forces as well as the dynamic transmission errors of the sun-planet 1 gear pair with and without tooth modifications are computed and compared to show the effectiveness of tooth modifications on gear dynamics enhancement. By using response surface method, a fitted regression model for the dynamic transmission error（DTE） fluctuations is established to quantify the relationship between modification amounts and DTE fluctuations. By shifting the inevitable random errors arousing from manufacturing and installing process to tooth modification amount variations, a statistical tooth modification model is developed and a methodology combining Monte Carlo simulation and response surface method is presented for uncertainty analysis of tooth modifications. The uncertainly analysis reveals that the system＇s dynamic behaviors do not obey the normal distribution rule even though the design variables are normally distributed. In addition, a deterministic modification amount will not definitely achieve an optimal result for both static and dynamic transmission error fluctuation reduction simultaneously.

Design and Experimental Research on Seedling Pick-Up Mechanism of Planetary Gear Train with Combined Non-circular Gear Transmission

Currently, transplanting mechanisms for dryland plug seedlings in China are mainly semiautomatic and have low efficiency. The rotary seedling pick-up mechanism with a planetary gear train for non-uniform intermittent transmission, and a concave and convex locking arc device, has a large rigid impact. To solve these problems, according to the design requirements for a dryland plug seedling transplanting mechanism, a rotary seedling pick-up mechanism of a planetary gear train with combined non-circular gear transmission of incomplete eccentric circular and noncircular gears was proposed. This has the characteristics of two-times greater fluctuation of the transmission ratio in a cycle, and can achieve a non-uniform continuous drive. Through analysis of the working principle of the seedling pick-up mechanism, its kinematics model was established. The human–computer interaction optimization method and self-developed computer-aided analysis and optimization software were used to obtain a set of parameters that satisfy the operation requirements of the seedling pick-up mechanism. According to the optimized parameters, the structure of the seedling pick-up mechanism was designed, a virtual prototype of the mechanism was created, and a physical prototype was manufactured. A virtual motion simulation of the mechanism was performed, high-speed photographic kinematics tests were conducted, and the kinematic properties of the physical prototype were investigated, whereby the correctness of the theoretical model and the optimized design of the mechanism were verified. Further, laboratory seedling pick-up tests were conducted. The success ratio of seedling pick-up was 93.8% when the seedling pick-up efficiency of the mechanism was 60 plants per minute per row, indicating that the mechanism has a high efficiency and success ratio for seedling pick-up and can be applied to a dryland plug seedling transplanter.

Kinematic Modeling and Characteristic Analysis of Eccentric Conjugate Non-circular Gear & Crank-Rocker & Gears Train Weft Insertion Mechanism

A novel weft insertion mechanism named eccentric conjugate non-circular gear & crank-rocker & gears train weft insertion mechanism was proposed in order to better meet the requirements of rapier loom's weft insertion mechanism as well as reduce the manufacturing difficulty. Meanwhile, based on the working principle of this mechanism, kinematical mathematic models of this mechanism were established and an aided analysis and simulation software was compiled. The influences of eccentricity ratio, deformation coefficient, and other important parameters on the kinematics characteristics of this mechanism were analyzed by using the software. A group of preferable parameters which could meet the requirements of weft insertion technology were obtained by means of human-computer interactive optimization method. The maximum velocity, maximum acceleration, and variation of acceleration of this mechanism are smaller than those of the conjugate cam weft insertion mechanism applied on TT96 rapier loom under the conditions of the same unilateral total stroke of rapier head and the same rotary speed of loom spindle; meanwhile the other demands of weaving technology can be met by this novel weft insertion mechanism.

Calculating method of contact stress for non-circular gears

According to Hertz theory, the difference of contact stress for non-circular gears and equivalent gears is compared in the paper, a calculating method of contact stress for non-circular gears by using equivalent gears is researched, and computing formulas of power and rotation speed for equivalent gears are deduced. A numerical simulation of contact stress for non-circular gears has also been conducted based on the finite element method. By the comparison of fitting curves, the feasibility of using equivalent gears instead of non-circular gears to calculate the contact stress is testified.

Crack Fault Classification for Planetary Gearbox Based on Feature Selection Technique and K-means Clustering Method

During the condition monitoring of a planetary gearbox, features are extracted from raw data for a fault diagnosis.However, different features have different sensitivity for identifying different fault types, and thus, the selection of a sensitive feature subset from an entire feature set and retaining as much of the class discriminatory information as possible has a directly effect on the accuracy of the classification results. In this paper, an improved hybrid feature selection technique(IHFST) that combines a distance evaluation technique(DET), Pearson’s correlation analysis, and an ad hoc technique is proposed. In IHFST, a temporary feature subset without irrelevant features is first selected according to the distance evaluation criterion of DET, and the Pearson’s correlation analysis and ad hoc technique are then employed to find and remove redundant features in the temporary feature subset, respectively, and hence,a sensitive feature subset without irrelevant or redundant features is selected from the entire feature set. Further, the k-means clustering method is applied to classify the different kinds of health conditions. The effectiveness of the proposed method was validated through several experiments carried out on a planetary gearbox with incipient cracks seeded in the tooth root of the sun gear, planet gear, and ring gear. The results show that the proposed method can successfully distinguish the different health conditions of a planetary gearbox, and achieves a better classification performance than other methods. This study proposes a sensitive feature subset selection method that achieves an obvious improvement in terms of the accuracy of the fault classification.

Planetary Gear Profile Modification Design Based on Load Sharing Modelling

In order to satisfy the increasing demand on high performance planetary transmissions, an important line of research is focused on the understanding of some of the underlying phenomena involved in this mechanical system. Through the development of models capable of reproduce the system behavior, research in this area contributes to improve gear transmission insight, helping developing better maintenance practices and more efficient design processes. A planetary gear model used for the design of profile modifications ratio based on the levelling of the load sharing ratio is presented. The gear profile geometry definition, following a vectorial approach that mimics the real cutting process of gears, is thoroughly described. Teeth undercutting and hypotrochoid definition are implicitly considered, and a procedure for the incorporation of a rounding arc at the tooth tip in order to deal with corner contacts is described. A procedure for the modeling of profile deviations is presented, which can be used for the introduction of both manufacturing errors and designed profile modifications. An easy and flexible implementation of the profile deviation within the planetary model is accomplished based on the geometric overlapping. The contact force calculation and dynamic implementation used in the model are also introduced, and parameters from a real transmission for agricultural applications are presented for the application example. A set of reliefs is designed based on the levelling of the load sharing ratio for the example transmission, and finally some other important dynamic factors of the transmission are analyzed to assess the changes in the dynamic behavior with respect to the non-modified case. Thus, the main innovative aspect of the proposed planetary transmission model is the capacity of providing a simulated load sharing ratio which serves as design variable for the calculation of the tooth profile modifications.

Quantitative Damage Detection for Planetary Gear Sets Based on Physical Models

Planetary gear set is the critical component in helicopter transmission train, and an important problem in condition monitoring and health management of planetary gear set is quantitative damage detection. In order to resolve this problem, an approach based on physical models is presented to detect damage quantitatively in planetary gear set. A particular emphasis is put on a feature generation and selection method, which is used for sun gear tooth breakage damage detection quantitatively in planetary gear box of helicopter transmission system. In this feature generation procedure, the pure torsional dynamical models of 2K-H planetary gear set is established for healthy case and sun gear tooth-breakage case. Then, a feature based on the spectrum of simulation signals of the dynamical models is generated. Aiming at selecting the best feature suitable for quantitative damage detection, a two-sample Z-test procedure is used to analyze the performance of features on damage evolution tracing. A feature named SR, which had better performance in tracking damage, is proposed to detect damage in planetary gear set. Meanwhile, the sun gear tooth-chipped seeded experiments with different severity are designed to validate the method above, and then the test vibration signal is picked up and used for damage detection. With the results of several experiments for quantitative damage detection, the feasibility and the effect of this approach are verified. The proposed method can supply an effective tool for degradation state identification in condition monitoring and health management of helicopter transmission system.

Dynamic characteristics of the planetary gear train excited by time-varying meshing stiffness in the wind turbine

Wind power has attracted increasing attention as a renewable and clean energy. Gear fault frequently occurs under extreme environment and complex loads. The time-varying meshing stiffness is one of the main excitations. This study proposes a 5 degree-of-freedom torsional vibration model for the planetary gear system. The influence of some parameters(e.g., contact ratio and phase difference) is discussed under different conditions of a single teeth pair and double pairs of teeth. The impact load caused by the teeth face fault, ramped load induced by the complex wind conditions, and the harmonic excitation are investigated. The analysis of the time-varying meshing stiffness and the dynamic meshing force shows that the dynamic design under different loads can be made to avoid resonance, can provide the basis for the gear fault location of a wind turbine, and distinguish the fault characteristics from the vibration signals.

EFFICIENCY ANALYSIS OF DOUBLE CRANK RING-PLATE-TYPE PIN-CYCLOIDAL GEAR PLANETARY DRIVE

From the general formula for calculating the efficiency of planetary geartrains, the efficiency of the double crank ring-plate-type pin-cycloidal gear planetary drive isderived. To prove the theory, an experimental study has been conducted. The tested value of theefficiency of a sample set of the new-type drive in the experiment agrees with the calculated one.It shows that the new-type drive is of not merely high bearing capacity, but also quite highefficiency.

Design of Vegetable Pot Seedling Pick‑up Mechanism with Planetary Gear Train

It has been challenging to design seedling pick-up mechanism based on given key points and trajectories,because it involves dimensional synthesis and rod length optimization.In this paper,the dimensional synthesis of seedling pickup mechanism with planetary gear train was studied based on the data of given key points and the trajectory of the endpoint of seedling pick-up mechanism.Given the positions and orientations requirements of the five key points,the study first conducted a dimensional synthesis of the linkage size and center of rotation.The next steps were to select a reasonable solution and optimize the data values based on the ideal seedling trajectory.The link motion was driven by the planetary gear train of the two-stage gear.Four pitch curves of noncircular gears were obtained by calculating and distributing the transmission ratio according to the data.For the pitch curve with two convex points,the tooth profile design method of incomplete noncircular gear was applied.The seedling pick-up mechanism was tested by a virtual prototype and a physical prototype designed with the obtained parameter values.The results were consistent with the theoretical design requirements,confirming that the mechanism meets the expected requirements for picking seedlings up.This paper presents a new design method of vegetable pot seedling pick-up mechanism for an automatic vegetable transplanter.

Performances of a Balanced Hydraulic Motor with Planetary Gear Train

The current research of a balanced hydraulic motor focuses on the characteristics of the motor with three planet gears.References of a balanced hydraulic motor with more than three planet gears are hardly found.In order to study the characteristics of a balanced hydraulic motor with planetary gear train that includes more than three planet gears,on the basis of analysis of the structure and working principle of a balanced hydraulic motor with planetary gear train,formulas are deduced for calculating the hydraulic motor＇s primary performance indexes such as displacement,unit volume displacement,flowrate fluctuation ratio,etc.Influences of the gears＇ tooth number on displacement and flowrate characteristics are analyzed.In order to guarantee the reliability of sealing capability,the necessary conditions that tooth number of the sun gear and the planet gears should satisfy are discussed.Selecting large unit volume displacement and small displacement fluctuation ratio as designing objectives,a balanced hydraulic motor with three planet gears and a common gear motor are designed under the conditions of same displacement,tooth addendum coefficien and clearance coefficient.By comparing the unit volume displacement and fluctuation ratio of the two motors,it can be seen that the balanced hydraulic motor with planetary gear train has the advantages of smaller fluctuation ratio and larger unit volume displacement.The results provide theoretical basis for choosing gear tooth-number of this kind of hydraulic motor.

Finite Element Analysis of Internal Gear in High-Speed Planetary Gear Units

The stress and the elastic deflection of internal ring gear in high-speed spur planetary gear units are investigated. A rim thickness parameter is defined as the flexibility of internal ring gear. Six evenly spaced linear springs are used to describe the fitting status between internal ring gear and the gearcase. The finite element model of the whole internal ring gear is established by means of Pro/E and ANSYS. The loads on meshing teeth of internal ring gear are applied according to the contact ratio and the load-sharing coefficient. With the finite element analysis (FEA), the influences of flexibility and fitting status on the stress and elastic deflection of internal ring gear are predicted. The simulation reveals that the principal stress and deflection increase with the decrease of rim thickness of internal ring gear. Moreover, larger spring stiffness helps to reduce the stress and deflection of internal ring gear. Therefore, the flexibility of internal ring gear must be considered during the design of high-speed planetary gear transmissions.

Dynamic load sharing characteristics and sun gear radial orbits of double-row planetary gear train

A new non-linear bending-torsional coupled model for double-row planetary gear set was proposed, and planet's eccentricity error, static transmission error, and time-varying meshing stiffness were taken into consideration. The solution of differential governing equation of motion is determined by applying the Fourier series method. The behaviors of dynamic load sharing characteristics affected by the system parameters including gear eccentricities error, ring gear's supporting stiffness, planet's bearing stiffness, torsional stiffness of first stage carrier and input rotation rate were investigated qualitatively and systematically, and sun gear radial orbits at first and second stage were explored as well. Some theoretical results are summarized as guidelines for further research and design of double-row planetary gear train at last.

Translational - torsional coupled model based nonlinear dynamic analysis of an NGW planetary gear train

This paper aims to investigate the nonlinear dynamic behaviors of an NGW planetary gear train with multi-clearances and manufacturing/assembling errors. For this purpose, an analytical translational- torsional coupled dynamic model is developed considering the effects of time-varying stiffness, gear backlashes and component errors. Based on the proposed model, the nonlinear differential equations of motion are derived and solved iteratively by the Runge-Kutta method. An NGW planetary gear reducer with three planets is taken as an example to analyze the effects of nonlinear factors. The results indicate that the backlashes induce complicated nonlinear dynamic behaviors in the gear train. With the increment of the backlashes, the gear system has experienced periodic responses, quasi-periodic response and chaos responses in sequence. When the planetary gear system is in a chaotic motion state, the vibration amplitude increases sharply, causing severe vibration and noise. The present study provides a fundamental basis for design and parameter optimization of NGW planetary gear trains.

Bifurcation and chaos study on transverse-torsional coupled 2K-H planetary gear train with multiple clearances

A new non-linear transverse-torsional coupled model was proposed for 2K-H planetary gear train, and gear's geometric eccentricity error, comprehensive transmission error, time-varying meshing stiffness, sun-planet and planet-ring gear pair's backlashes and sun gear's bearing clearance were taken into consideration. The solution of differential governing equation of motion was solved by applying variable step-size Runge-Kutta numerical integration method. The system motion state was investigated systematically and qualitatively, and exhibited diverse characteristics of bifurcation and chaos as well as non-linear behavior under different bifurcation parameters including meshing frequency, sun-planet backlash, planet-ring backlash and sun gear's bearing clearance. Analysis results show that the increasing damping could suppress the region of chaotic motion and improve the system's stability significantly. The route of crisis to chaotic motion was observed under the bifurcation parameter of meshing frequency. However, the routes of period doubling and crisis to chaos were identified under the bifurcation parameter of sun-planet backlash; besides, several different types of routes to chaos were observed and coexisted under the bifurcation parameter of planet-ring backlash including period doubling, Hopf bifurcation, 3T-periodic channel and crisis. Additionally, planet-ring backlash generated a strong coupling effect to system's non-linear behavior while the sun gear's bearing clearance produced weak coupling effect. Finally, quasi-periodic motion could be found under all above–mentioned bifurcation parameters and closely associated with the 3T-periodic motion.

Life Distribution Transformation Model of Planetary Gear System

Planetary gear systems have been widely used in transportation, construction, metallurgy, petroleum, aviation and other industrial fields. Under the same condition of power transmission, they have a more compact structure than ordinary gear train. However, some critical parts, such as sun gear, planet gear and ring gear often suffer from fatigue and wear under the conditions of high speed and heavy load. For reliability research, in order to predict the fatigue probability life of planetary gear system, detailed kinematic and mechanical analysis for a planetary gear system is firstly completed. Meanwhile, a gear bending fatigue test is carried out at a stress level to obtain the strength information of specific gears. Then, a life distribution transformation model is established according to the order statistics theory. Transformation process is that, the life distribution of test gear is transformed to that of single tooth, and then the life distribution of single tooth can be effectively transformed to that of the planetary gear system. In addition, the effectiveness of the transformation model is finally verified by a processing method with random censoring data.

Analysis and Simulation for Planetary Gear Fault of Helicopter Based on Vibration Signal

Fault diagnosis for helicopter's main gearbox based on vibration signals by experiments always requires high costs. To solve this problem,a helicopter's planetary gear system is taken as an example. Firstly,a simulation model is established by McFadden,and analyzed under ideal condition. Then this model is developed and improved as the delay-time model of the vibration signal which determines the phase-change of sidebands when the system is running. The cause and change-rules of planetary gear system's vibration signal are analyzed to establish the fault diagnosis model.At the same time,the vibration signal of fault condition is simulated and analyzed. This simulation method can provide a reference for fault monitoring and diagnosis for planetary gear system.

Configuration design and control of hybrid tracked vehicle with three planetary gear sets

The hybrid tracked vehicles(HTV)usually adopt series hybrid powertrain with extra steering mechanism,which has relatively low transmission efficiency and reduces the flexibility of structural arrangement.To overcome the disadvantages,a new kind of single-mode powertrain has been proposed.The power-split hybrid powertrain is composed of three planetary gear(PG)sets connected to one engine,left and right track outputs,and three motors.The proposed powertrain can realize steering while going forward by controlling the output torque on each side without extra steering mechanism or steering shaft.Due to the diversity of the connection way between components and planetary gear sets,a rapid configuration design approach is proposed for the design selection of HTV.The automated dynamic modelling method can show the one-to-one correspondence with the selected feasible groups by establishing two characteristic matrices,which is more simple than other researches.The analytically-based method is proposed to classify all possible connection designs into several groups to decrease the searching scope with improved design efficiency.Finally,the optimal control strategy is used to find the design with optimal fuel economy under typical condition of HTV.The case study is implemented by the proposed design approach which demonstrates better design performances compared with the existing series-hybrid HTV.

Design and Experiment of Non-circular Combined Gear Train Beating-up Mechanism

The most important performance of a beating-up mechanism is that the dwelling time of the sley must ensure the completion of the weft insertion. To meet this requirement, a new non-circular combined gear train beating-up mechanism which is composed of two-stage planetary gear trains is proposed. The first-stage is a Fourier planetary gear train and the second-stage is a non-circular planetary gear train. For designing of this new mechanism, the ideal kinematic equations of the sley are constructed first. Then the kinematic model of the first-stage Fourier planetary gear train is established and the reverse solution for the pitch curves of the second-stage non-circular gears is deduced. With a computer-aided design program, the influences of several important parameters on the pitch curves of the second-stage non-circular gears are analyzed, and a set of preferable structural parameters are obtained. Finally, a test bed of this mechanism is developed and the experimental results show that this new beating-up mechanism can achieve the designed dwelling time, namely it can meet the requirements of beating-up process.