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.

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.

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.

Stability of motion state and bifurcation properties of planetary gear train

A nonlinear lateral-torsional coupled vibration model of a planetary gear system was established by taking transmission errors,time varying meshing stiffness and multiple gear backlashes into account.The bifurcation diagram of the system's motion state with rotational speed of sun gear was conducted through four steps.As a bifurcation parameter,the effect of rotational speed on the bifurcation properties of the system was assessed.The study results reveal that periodic motion is the main motion state of planetary gear train in low speed region when ns<2 350 r/min,but chaos motion state is dominant in high speed region when ns>2 350 r/min,The way of periodic motion to chaos is doubling bifurcation.There are two kinds of unstable modes and nine unstable regions in the speed region when 1 000 r/min<ns<3 000 r/min.

Dynamic load sharing behavior of transverse-torsional coupled planetary gear train with multiple clearances

A new nonlinear transverse-torsional coupled model with backlash and bearing clearance was proposed for planetary gear set. Meanwhile, sun gear and planet's eccentricity errors, static transmission error, and time-varying meshing stiffness were taken into consideration. The differential governing equations of motion were solved by employing variable step-size Rung-Kutta numerical integration method. The behavior of dynamic load sharing characteristics affected by the system parameters including input rate, sun gear's supporting stiffness and eccentricity error, planet's eccentricity error, sun gear's bearing clearance, backlashes of sun-planet and planet-ring meshes were investigated qualitatively and systematically. Some theoretical results are summarized at last which extend the current understanding of the dynamic load sharing behavior of planet gear train, enrich the related literature and provide references for the design of planetary gear train.

Efficiency Evaluation of Continuously Variable Transmissions Including a Planetary Gear Train

With their advantages, continuously variable transmissions have gained more popularity in the last decade by their use in mechanical transmission systems. The present paper aims to analysis the efficiency of the transmission based on the mechanical efficiency of the planetary gear train integrated in such transmission. In this analysis, we consider the mechanical efficiency of the transmission has been determined considering how the efficiency of the CVT members changes as a function of the operating conditions. The efficiency of the planetary gear train as a function of the configuration, speeds in his three input/output shafts, and also with respect to the power flow type. Results are compared with those obtained from other methods performance evaluation of the transmission, available in the literature.

Analytical geometry method of planetary gear trains

This paper presents an analytical geometry method for kinematics and efficiency of planetary gear trains (PGTs). The novel method which is capable of evolution and contrast analysis of mechanism kinematics, can be applied to any typical one-and two-degree-of-freedom plane PGTs containing any number of simple, compound or complex-compound planetary gear sets. The efficiency analysis of this method features a systematized and programmed process and its independence of the speed ratio. The primary contribution of this work lies in the integration of quantitative calculation, qualitative evolution and comparative analysis of kinematics of PGTs into one diagram, and in the integration of kinematics and efficiency analysis into a single method system. First, the analytical geometry method is defined, its basic properties are given, and the systematization procedure to perform kinematic analysis is demonstrated. As an application, analytical geometry diagrams of common PGTs are exhibited in the form of a list, whose kinematic characteristics and general evolution tendency are discussed. Then, with the mapping of PGTs onto the angular speed plane, the efficiency formula of analytical geometry, which has an extremely concise form, and a simple method for power flow estimation are put forward. Moreover, a general procedure is provided to analyze the efficiency and power flow. Finally, four numerical examples including a complicated eleven-link differential PGTs are given to illustrate the simpleness and intuitiveness of the analytical geometry method.

Optimization design and test of rice plug seedling transplanting mechanism of planetary gear train with incomplete eccentric circular gear and non-circular gears

In order to solve the problem of the high-speed mechanized transplanting of rice plug seedlings,the design requirements of transplanting mechanism for rice plug seedlings were analyzed and a kind of rice plug seedling transplanting mechanism of planetary gear train based on the drive with incomplete eccentric circular gear and non-circular gears was designed innovatively.The laboratory kinematics was examined.The working principle of the transplanting mechanism for rice plug seedlings was studied,kinematics analysis of the transplanting mechanism was carried out and its kinematic model was set up.A human-computer interaction optimization method was used to optimize the parameters of the transplanting mechanism.The computer aided analysis and optimization software of the transplanting mechanism based on Visual Basic 6.0 was developed.Through analyzing the influence of design variables on the optimization objectives of the transplanting mechanism,a set of parameters of the transplanting mechanism which meet the requirements of transplanting trajectory and posture for transplanting rice seedlings were obtained by means of human-computer interaction.The structure of the transplanting mechanism was designed according to this set of parameters,and its virtual prototype and physical prototype were set up and manufactured,respectively.The kinematic simulation test and high-speed photography kinematic test of the transplanting mechanism were conducted to obtain its kinematic performances,such as transplanting trajectory and posture.The results of bench test,simulation analysis and theoretical analysis were almost in agreement,which verified the correctness of the theoretical model and design results of the transplanting mechanism,indicating that the optimized transplanting mechanism can satisfy the requirements of transplanting rice seedlings and be applied in the rice plug seedling transplanter.

Design of clamping-pot-type planetary gear train transplanting mechanism for rice wide-narrow-row planting

To design a clamping-pot-type wide-narrow-row pot seedling transplanting(WPST)mechanism with desired spatial beak-shaped trajectory and working posture,a new design method of planetary gear train transplanting mechanism(PGTM)with non-circular gears based on several key spatial poses(position and posture)was proposed.The PGTM was simplified to a spatial open-loop chain with two-revolute(2R)joints.The geometric constraint equations containing only the structural parameters of the chain were then established on the basis of the three key spatial poses,and the homotopy algorithm was used to obtain all the required parameters of the mechanism.In accordance with the parameters obtained,the relative angular displacement relation between the planet carrier and the transplanting arm was optimized,the trajectory of the mechanism was replayed,and the total transmission ratio was determined.The degree of freedom of the spatial 2R mechanism was reduced by attaching to the unequal gear pair,and the transmission ratio was distributed in accordance with the gear type to realize the design of a non-circular gear pitch curve.Lastly,a clamping-pot-type PGTM for rice WPST driven by the combination of planar non-circular and non-conical gears was designed,and virtual simulation and prototype test were conducted.Results showed that the simulation and prototype test trajectories were consistent with the desired trajectory.Under the operating speeds of 50 r/min and 90 r/min,the success rates of seedling picking were 95.32%and 90.15%,respectively,which verified the feasibility of the theoretical method.This method could provide a reference for the design of a spatial PGTM with nonuniform transmission.

A multi-criteria fusion feature selection algorithm for fault diagnosis of helicopter planetary gear train

Planetary gear train is a prominent component of helicopter transmission system and its health is of great significance for the flight safety of the helicopter.During health condition monitoring,the selection of a fault sensitive feature subset is meaningful for fault diagnosis of helicopter planetary gear train.According to actual situation,this paper proposed a multi-criteria fusion feature selection algorithm (MCFFSA) to identify an optimal feature subset from the highdimensional original feature space.In MCFFSA,a fault feature set of multiple domains,including time domain,frequency domain and wavelet domain,is first extracted from the raw vibration dataset.Four targeted criteria are then fused by multi-objective evolutionary algorithm based on decomposition (MOEA/D) to find Proto-efficient subsets,wherein two criteria for measuring diagnostic performance are assessed by sparse Bayesian extreme learning machine (SBELM).Further,Fmeasure is adopted to identify the optimal feature subset,which was employed for subsequent fault diagnosis.The effectiveness of MCFFSA is validated through six fault recognition datasets from a real helicopter transmission platform.The experimental results illustrate the superiority of combination of MOEA/D and SBELM in MCFFSA,and comparative analysis demonstrates that the optimal feature subset provided by MCFFSA can achieve a better diagnosis performance than other algorithms.

Design and experimental study of a planetary gearing mechanism based on twice unequal amplitude transmission ratio

To obtain the optimal seedling taking trajectory,this study proposed the adjustment of the total transmission ratio curve by using human-computer interaction.On the basis of this design method,a planetary non-circular gear mechanism was designed that can realize the twice unequal amplitude transmission ratio to meet the seedling harvesting requirements.The cubic non-uniform B-spline curve was used to fit the twice unequal amplitude transmission ratio curve,and the transmission ratio was freely distributed in two levels.The seedling pick-up mechanism was designed by controlling the seedling taking track and the corresponding attitude directly through the local section of the total transmission ratio,and the gear pitch curve was directly controlled by the transmission ratio.The kinematics model of the seedling pick-up mechanism was also established.Furthermore,the influence of the total transmission ratio on the seedling picking track,the ratio of the wave crest to the amplitude,and the mechanism parameters were discussed.A human-computer interactive optimization software was developed using Matlab,and a set of optimal parameters for the seedling pick-up mechanism was obtained to meet the transplanting requirements.By using the Adams software,the virtual prototype simulation of the seedling pick-up mechanism was completed,and the idle experiment for the track and attitude of the prototype was conducted through high-speed camera technology.The theoretical,simulated,and experimental trajectories were consistent with each other.Results revealed that the success rate of the seedling picking exceeded 90%when the rotation speeds were 40 r/min,50 r/min,and 60 r/min,and the qualified rate of the matrix decreased with the increase in rotating speed.Moreover,the number of damaged plants increased with the increase in rotating speed.The experimental results showed that the seedling pick-up mechanism designed using the proposed method demonstrated a good effect and met the required seedling picking performance.

Design of flower transplanting mechanisms based on double planet carrier non-circular gear train with complete rotation kinematic pair

In view of the problems of the existing mechanisms based on 2R open-chain planetary gear train for seedling transplanting,such as the bad tracking flexibility,low positioning accuracy,and high structure design difficulties of the mechanisms based on 3R open-chain planetary gear train for seedling manipulation.In this paper,a transplanting mechanism based on the solution domain synthesis of a 3R open-chain-based complete rotation kinematic pair,a gear train with a single cycle integral rotating pair,is designed.The Burmester curve equation is derived from the given transplanting trajectory and four exact poses corresponding to each other on the rotation center.Then,the open-chain road model of the 3R complete rotation kinematic pair is obtained under the constraint governed by the judgment condition of the hinge integral rotating pair.Meanwhile,combined with our developed in-house optimization software,the solution to the optimal parameters for the transplanting mechanism can be optimized according to the target trajectory.Finally,the feasibility of the design method is verified by transplanting testing,where kale seedlings with ages of about 20 d and heights of about 80-120 mm are used.The experimental results show that the actual motion trajectory of the prototype is basically identical to the theoretical trajectory,validating the feasibility of transplanting mechanism design,parts processing,and test-bed construction.Through the statistical analysis,the average success rate of transplanting is 90.625%,and the reliability of designed mechanism is satisfied.This study provides a promising solution for the seedling transplanting of two-planet scaffold pots.