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.

Research on stepless transmission utilizing noncircular gears

In view of the lack of systemic analysis for stepless transmission using noncircular gears, two basic noncircular gear units, an addition unit adopting differential mechanism and a multiplication unit applying a fixed gear train, are proposed. Then, the design methods of the noncircular gear pair of each unit, transmission ratio relationship, rotation angle relationship and key parameters with specific physical meanings are studied. The adjusting properties, composing strategy and varying range of transmission ratio etc. are investigated in detail for each unit. Following this, several examples of using a noncircular gear pair in the units and their manipulation technique are introduced.

CALCULATIONS OF THE INNER DISTURBANCE FREQUENCIES INSIDE THE EPICYCLIC GEARING

The forms of the vibration disturbances inside the epicyclic gear train are analyzed. Thefrequency equations for the inner disturbances of the epicyclic gearing with one or two degrees offreedom have been built. The latter of them is a 3-dimension problem and the range of the disturbance frequencies covers a series of planes inside the 3-dimension coordinates. As a result, thechances to lead to the system resonance are developed. The calculating results indicate that in thedesign process of the shaft system, the chances of resonance can be reduced by tunning the dynamicparameters and the structure of the system.

Method for Selecting the Optimal Solution for the Design of the Gear Train

Some researchers in mechanical engineering have developed systems for the design of gear transmission boxes, but almost no calculation methods exist for widespread synthesis. In this article, we outline methods for automatic determination of toothed helical gear trains and the selection criteria for the optimal choice of gear trains. In this work two methods were applied. As first design to use an expert system for the design and then optimize the design that is why we used Kappa PC and Catia for CAD.

Optimization design and experiment of the variable differential gear train planting mechanism

In order to improve the adaptability of the planting mechanism for different plant spacings,a variable differential gear train planting mechanism based on precise pose and trajectory control was proposed by combining the open chain 2R rod group and the variable differential gear train.According to the pose requirements of receiving seedling point,transporting seedling point and planting point,three precise pose points of constrained planting trajectory were determined.Through the three-position motion generation structural synthesis method,combined with computer-aided optimization design software,a set of mechanism parameters that meet the planting requirements were optimized.Based on the optimized mechanism parameters,by only changing the coordinates of two trajectory shape control points,three planting trajectories with key point position information adapted to 300 mm,400 mm and 500 mm plant spacing were obtained by interpolation,and three pairs of total transmission ratio of three groups of variable differential gear trains were calculated.When distributing the total transmission ratio of the mechanism,the fixed axis gear train and the differential gear train are combined.The fixed axis gear train included a pair of non-circular gear pairs and a pair of positive gear pairs,which were convenient for disassembly and assembly.The former drives the sun gear at variable speed,and the latter drives the planet carrier at uniform speed.Based on this structure,the transmission ratio of the positive gear pair is-1,and the transmission ratio of the differential gear train is 0.5.The sub-transmission ratio of the single-stage non-circular gear pair was calculated and the pitch curves of three pairs of noncircular gears were solved.Three pairs of non-circular gear pairs with different transmission ratios were replaced in turn and three sets of planting mechanisms were modeled in three dimensions.The virtual prototype motion simulation was completed by ADAMS software,and the physical prototype was built for vegetable pot seedling planting test.The theoretical solution was consistent with the attitude and trajectory of the actual test.When the test sample size was 100 plants,the actual average plant spacing was measured to be 303 mm,402 mm,and 503 mm,with errors of 1.3%,1.25%,and 1.88%.The width of the moving hole was 72 mm,70 mm,and 71 mm,and the planting success rate were 94%,96%,and 95%.The test results verified the correctness of the optimization design results of the mechanism,indicating that the variable differential gear train planting mechanism can adapt to a variety of plant spacing and has good planting effect.

Driving Mechanism of Cotton Comber's Detaching Roller Based on Time-Sharing Unidirectional Drive

The high-speed reciprocating motion of a detaching roller limits the velocity of a cotton comber and affects the quality of comber slivers. The article has proposed a controllable time-sharing unidirectional hybrid drive mechanism after analyzing detaching roller's current numerical control drive method. The analysis focuses on the detaching roller motion required according to cotton comber's velocity and process. The double-servo motors of the mechanism consists of differential gear trains. The mechanism addresses the problem of increased servo motor power,and failure of promptly responded to the positive inversion process of mechanism driven by servo motors. A velocity calculation model of the detaching roller controllable drive mechanism will be generated by using superposition method and design of differential gear trains. The accuracy of the model will be verified using the test platform. This study has presented a reliable and practical high-speed drive mechanism and can be a reference to future studies on high-speed reciprocating motion drive.

Research on Hybrid Input Mechanical Press Driven by Two Motors

Given the speed requirements of a mechanical press slider, a differential gear train is adopted instead of the belt and gear drive of a general mechanical press. Two electric motors are used to drive the differential gear train with hybrid input. Based on the working principle of a differential gear train, the angular speed equations and the power dis- tribution equations of the input-output system are established. By controlling the angular speeds of the two motors, the slider can move at different speeds. Taken a JH23-100 type mechanical press as example, the driving system is designed and the power of two motors determined. The simulated results show that the highest slider speed in the mechanical press approaches 39 mm/s only at the forging-punching stage, far less than the 232 mm/s of a general JH23-100 type mechanical press. This provides a new scheme to realize low-speed forging-punching technology from a mechanical press.

Decoding the Moon Phase Display Device over the Front Dial of the Antikythera Mechanism

The Antikythera mechanism is the most famous ancient astronomical calculator. The damaged excavation is a critical constraint for decoding the mechanism completely. By the systematic reconstruction design methodology, all feasible designs of the moon phase display device, which is one of the unclear mechanisms of the Antikythera mechanism, are reconstructed. These designs, including ordinary gear trains and epicyclic gear trains, are the simplest designs and satisfy the surviving evidence. The Antikythera mechanism and its reconstruction designs presented by LIN and YAN are introduced first. Three pointer types of the Antikythera mechanism are concluded based on their display motions and the orientation of the mechanism. In accordance with the analysis of the available interior reconstruction designs and the surviving evidence, four feasible designs of the moon phase display device are generated. All of them utilize the ball pointer with black and white that rotates around the radial axis to show cyclic moon phase. Two of these four feasible reconstruction designs are driven by one input source, and their bronze disks are fixed and rotatable respectively. Both of the remaining reconstruction designs are driven by two input sources, and their bronze disks are rotatable. Therefore, the four reconstruction designs of the moon phase display device reveal all possible display conditions of the moon phase pointers and the possible purposes of the bronze disk.

Configuration Synthesis and Performance Analysis of 9‑Speed Automatic Transmissions

Current research of automatic transmission(AT)mainly focuses on the improvement of driving performance,and configuration innovation is one of the main research directions.However,finding new configurations of ATs is one of the main limitations of configuration innovation.In the present study,epicyclic gear trains(EGTs)are applied to investigate mechanisms of 9-speed ATs.Then four kinematic configurations are proposed for automatic transitions.In order to evaluate the performance of proposed mechanisms,the lever analogy method is applied to conduct kinematic and mechanical analyses.The power flow analysis is conducted,and then transmission efficiencies are calculated based on the torque method.The comparative analysis between the proposed and existing mechanisms is carried out where obtained results show that proposed mechanisms have reasonable performance and can be used in ATs.The prototype of an AT is manufactured and the speed test is conducted,which proves the accuracy of analysis and the feasibility of proposed mechanisms.

System Life and Reliability Modeling of a Multiple Power Takeoffs Accessory Gearbox Transmission

A mathematical model for system life and reliability of a multiple power takeoffs aeroengine accessory gearbox transmission is presented.The geometry model of gear train is distributed into several subsystems by different transmitted powers.The lives of each component are combined to determine the units,subsystems and entire system lives sequentially according to a strict series probability model.The unit and subsystem interface models are defined to dispose the loads of common components.The algorithm verification is presented and a numerical example is given to illustrate the use of this program.The initial design could not fulfill the life requirement.A design modification shows that the gear train has a more balanced life distribution by strengthening the weak parts,and the overall life of entire system is increased above the design requirement.This program can help the designer to approach an optimal accessory gearbox transmission design efficiently.

Assessment of the curving performance of heavy haul trains under braking conditions

To study the curving performance of trains, 1D and 3D dynamic models of trains were built using nu- merical methods. The 1D model was composed of 210 simple wagons, each allowed only longitudinal motion; whereas the 3D model included three complicated wagons for which longitudinal, lateral, and vertical degrees of freedom were considered. Combined with the calculated results from the 1D model under braking conditions, the behavior of draft gears and brake shoes were added to the 3D model. The assessment of the curving performance of trains was focused on making comparisons between idling and braking conditions. The results indicated the following： when a train brakes on a curved track, the wheel-rail lateral force and derailment factor are greater than under idling conditions. Because the yawing movement of the wheelset is limited by brake shoes, the zone of wheel contact along the wheel tread is wider than under idling conditions. Furthermore, as the curvature becomes tighter, the traction ratio shows a nonlinear increasing trend, whether under idling or braking conditions. By increasing the brake shoe pressure, train steering becomes more difficult.

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.

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.

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.