Planetary Gear Transmission Research Articles

Analysis of Inherent Characteristics of Two‐Speed Planetary Gear Transmission System

In the helicopter transmission system, because the two‐speed gear planetary transmission system without power interruption adopts the design of a double planetary gear system, the complexity of the structure leads to the time‐varying meshing stiffness, tooth surface friction and the interaction between components and other nonlinear factors are uncontrollable, and causes the helicopter transmission system vibration noise, unstable operation, and other problems. To solve the above problems, the inherent characteristics of the two‐speed planetary gear transmission system without power interruption were studied and analyzed to find out the influence law of its inherent characteristics. The inherent characteristics of a planetary gear drive system are mainly related to the integrated stiffness such as component mass, support stiffness, and meshing stiffness in the system. Based on the centralized mass method, the translation‐torsional coupling dynamics model of the double planetary gear drive system was established. According to the displacement coordination relationship between the components of the system, the dynamics equation of the double planetary gear drive system was constructed. The mass matrix and stiffness matrix were obtained using MATLAB, and the system’s natural frequency was obtained by solving the dynamics equation. The results show that the low‐order natural frequency is mainly the torsional vibration mode of the center component and the torsional vibration mode of the center component. The influence of the mass of the component on the natural frequency is more complex and has a certain influence on both the high‐ and low‐order natural frequency. The support stiffness in the system mainly affects the low‐order natural frequency and the meshing stiffness in the system mainly affects the high‐order natural frequency.

Review on power flow and efficiency of a closed differential planetary gear train

The closed differential planetary gear train transmits power in multiple paths, which has large power transmission and compact structure. It is widely used in high-power occasions such as ships. However, the closed differential planetary gear train has many power flow paths and complex structure. If the structural design is unreasonable, there will be power cycle (closed power) in the system, which will seriously reduce the efficiency of the system. There are many components of closed differential planetary gear train, and the uniform distribution of load is of great significance to improve the transmission quality and service life of the system.This paper mainly summarizes the research status of ordinary planetary gears, the power flow analysis status of closed differential planetary gear transmission and the efficiency analysis status of planetary gear transmission.

Use of sun gear orbits to obtain the load sharing in planetary transmissions and its impact in the tooth load

The present work assesses the possibility of using the orbits described by the sun gear in order to analyse the load sharing ratio in planetary gear transmissions. Furthermore, the current work is extended to observe the impact of the floatability and different tangential pinhole position errors in the load borne in a single contact between a pair of teeth in comparison to the load per planet. Therefore, it highlights the inaccuracy of the load sharing ratio (LSR) as an indicator of the overload in one tooth of the planet. Moreover, the use of the orbits represented with respect to a rotating reference provides helpful information to determine the overloads and underloads in the planets due to the existence of a tangential error in sequentially phased transmissions. Therefore, this proposal provides a simpler solution to the measurement of the LSR in planetary transmissions with different numbers of planets than the use of strain gauges.

Research on Root Strain Response Characteristics of Inner Ring of Planetary Gear Transmission System with Crack Fault

This paper established the system dynamics model for two kinds of tooth cracks of different depths of the sun gear and inner gear ring to study the influence mechanism of crack failure on the tooth root strain of the planetary gear transmission system. Combined with the finite element model of the inner gear ring, the tooth root strain of the ring was solved. Experiments verified the correctness of the solution method. The root strain under the crack fault of the sun gear and the tooth crack fault of the inner gear ring is analyzed, and the following conclusions are drawn: Periodic fault impact occurs in the strain signal of the tooth root of the inner gear ring during the crack fault of the sun gear root. The fault can be extracted by the fast spectral kurtosis method (FSK), and the fault components are used to determine whether the sun gear cracks. The Lempel-Ziv index showed a tendency to increase gradually during the process of solar wheel crack deepening, which could be used as the damage index of crack depth. The results can provide a basis and reference for fault diagnosis.

Research on a New Type of Low-Speed Water Flow Energy Turbine Pump

As the concept of Beautiful China is deeply rooted in the hearts of the people, most cities have developed riverside and waterfront areas into landscape leisure parks. At present, the vegetation in Jiangbin Park is irrigated with tap water. Flow energy has the characteristics of large reserves, wide distribution and renewable energy. Using this kind of energy to drive the water pump and realize the green irrigation of the vegetation in the riverside park will definitely open up a new way to expand the application of low-flow water flow energy. The project team plans to design a new type of turbine pump, adding a diversion cover and a collection device at the water inlet to reduce the start-up speed of the device and improve the utilization rate of water flow energy under small flow. The project team used planetary gear transmission to effectively improve the traditional hydraulic pump, increasing the torque transmitted to the pump shaft, enabling it to drive the impeller of the hydraulic pump to achieve energy-free pumping.

Similarity and experimental prediction on load sharing performance of planetary gear transmission system

The uneven load distribution among planetary gears will aggravate the vibration of the system, thus reducing the bearing capacity of the planetary gear transmission system (PGTS) and shortening the service life of the system. It is an effective method to predict and study the load sharing performance of the prototype through the scale model of PGTS. According to similarity theory, the similarity ratio of load sharing coefficient (LSC) of the dynamic model and LSC of the physical experiment model is derived. The LSC of PGTS is predicted and verified under different working conditions and structural flexibility. Based on the comprehensive tangential error similarity, the modified load method and the modified similarity ratio method are established to deal with position error distortion on planetary gear. Then, the dynamic model is used to verify the feasibility of the modification method. A scale model of PGTS is designed according to the similarity theory, and mechanical power closed test bench is established for the scale model. Finally, the load sharing performance of prototype PGTS is predicted through physical experiments under similar working conditions.

Analytical Investigation on Load Sharing Performance of Planetary Gear Transmission under Loop Maneuver

In order to explore the influence of airframe space motion on the load sharing performance (LSP) of planetary gear transmission (PGT) inside an aircraft, the combined influence of the rotation of the carrier (internal non-inertial system, INIS) and space motion of the fuselage (external non-inertial system, ENIS) is considered. Firstly, the motion equations of PGT members under the airframe loop maneuver are derived, and then the time-varying meshing stiffness, backlash, and tooth profile error are considered; a system-level dynamics model of PGT with casing is established and solved by numerical integration. The results show that the loop maneuver intensifies the fluctuation of the dynamic meshing force in the time domain and does not change its spectral distribution, but it will affect the peak value of the low frequency part. After considering the loop maneuver, there are differences in the load sharing coefficient (LSC) of each branch, and the fluctuation range of LSC increases. The interactive influence of working conditions, bearing stiffness, manufacturing eccentricity errors and loop motion parameters on the LSP is investigated and compared in depth. This research can be utilized to guide the design of aircraft’s drivetrain.

Influence of the eccentricity error on the vibrations of a planetary gear

Planetary gear systems are widely used in wind power, ships, aircraft, and construction machinery, etc. In the planetary gear system, when the eccentricity error exists in the planetary gear, the vibrations of the whole system should be affected. However, the influence of the eccentricity error was rarely considered in the previous dynamic models. To solve this problem, a planetary gear system with six planetary gears is established. The influence of the eccentricity error on the vibrations of the planetary gear system is analyzed. Different eccentricity error cases in the planetary gears are considered in the model, as well as the bearings with the radial clearance. The model with the eccentricity error is compared with the normal model. The statistics of dynamic responses of the ring gear and its variations are analyzed. Not that the vibrations of the planetary gear transmission system increase with the eccentricity error of planetary gear. This study can provide a new method for simulating and detecting the eccentricity errors in the planetary gear systems.

Early damage detection in planetary gear transmission in different operating conditions

Early damage detection in planetary gear transmission in different operating conditions

Triboelectric sensor for planetary gear fault diagnosis using data enhancement and CNN

The planetary gear transmission system is characterized by a complex structure and is often exposed to harsh working conditions, resulting in high failure damage rate. The self-powered sensing system based on the triboelectric nanogenerator provides an ideal scheme for online monitoring of the planetary gear operating condition. In this paper, a triboelectric planetary gear sensor (TPGS) is proposed for real-time monitoring of the speed and gear faults of the planetary reducer. The sensor is integrated at the tooth crest and root meshing gap of the planetary gear and the ring gear, which ensures the integrity of the gear structure and function. The results of the sensing experiment show that TPGS can be used to detect the speed of the planetary reducer in the range of 10–1000 rpm. Moreover, the speed detection error rate is less than 0.4%. To identify the gear faults, the stacked autoencoder (SAE) is used to enhance the data collected by TPGS, combined with convolutional neural network (CNN). The results show that the classification accuracy reached 100%. In this paper, a theoretical and experimental basis for development and online fault monitoring of a new intelligent gearbox with self-awareness and self-regulation is provided.

Lightweight design of the planetary gear reducer of reduction drive hub motors

Hub motor is the development direction of new energy vehicles in the future. Usually, the reduction drive hub motor is directly arranged in the narrow rim space, so there are strict restrictions on the volume and weight of its reducer. This paper presents a highly integrated transmission scheme which can improve the working life of the reducer. For the planetary gear reducer integrated by the reduction drive hub motor, a multi-objective optimization function with minimum volume and large coincidence degree is constructed. In terms of constraints, the necessary conditions of planetary gear transmission are fully considered, the gear module meets the requirements of national standards, and the strength conditions of gear transmission. Using genetic optimization algorithm, the optimal solution satisfying the constraints is obtained. The optimization results show that the coincidence degree of the engagement between the sun gear and the planetary gear increases by 67% and the equivalent volume decreases by 31%, which can reduce the volume and reduce the transmission noise at the same time.

Analysis of Planetary Gear Transmission Characteristics Based on ANSYS

Planetary gear transmission is widely used in roadhead, crane and other transmission equipment, its reliability and stability are related to the service life and work efficiency of equipment, but the current research on planetary gear transmission device is not comprehensive, lack of accurate analysis of gear meshing process load. Therefore, in this paper, ANSYS software as a platform, through the construction of dynamics module, to solve the gear teeth surface, gear teeth root and gear teeth tip stress analysis and deformation and displacement, the finite element analysis. The research results provide necessary technical support for the design and production of planetary gear transmission.
 Aims: Through finite element analysis of planetary gear transmission, the dynamic parameters of planetary gear transmission are solved, and the reliability and stability of planetary gear transmission equipment are improved.
 Study Design: By constructing the dynamics module of planetary gear, the stress analysis, deformation and displacement of gear tooth surface, gear tooth root and gear tooth top are solved, and the finite element analysis is carried out.
 Place and Duration of Study: North China University of Water Resources and Electric Power, from March to July 2022.
 Methodology: The finite element analysis was carried out on the model of planetary gear transmission mechanism, and the model was established and simplified by using SolidWorks software. The modal analysis and dynamic analysis were carried out by using ANSYS software, and the meshes were divided and constraints were added. Finally, the parameters such as stress, strain and displacement of the meshing position were solved.
 Results: The result of model meshes is 357575 units and 204871 nodes. The algorithm has 219 iterations and 15 convergence points. The experimental results show that there is a meshing position with the worst contact fatigue strength in the contact area between the outer ring gear and the planetary gear tooth surface. At this position, the contact stress value of the tooth surface is 22626Pa.
 Conclusion: In this paper, the planetary gear device is modeled by SolidWorks software, and the finite element analysis is carried out by ANSYS software to obtain the stress and strain parameters in the transmission process of the device, as well as the worst meshing point of the gear, the most vulnerable point of fatigue and other dangerous points. It lays a certain technical foundation for the optimization and improvement of gear and the design and production of planetary gear transmission device.

Nonlinear Dynamics Analysis of a Multistage Planetary Gear Transmission System

A nonlinear dynamic model for a multistage planetary gear transmission system, which consists of two-stage planetary gear plus one-stage parallel shaft gear, is proposed. The time-varying meshing stiffness, comprehensive meshing errors and backlash between gear pairs are taken into account in the model, and the connections between the gear stages are characterized by coupling stiffness. The dimensionless vibration differential equations of the system are derived and solved numerically. By means of global bifurcation diagram, largest Lyapunov exponent (LLE), phase diagram and Poincaré map, the stability of the system is studied with the bifurcation parameters variation including excitation frequency and comprehensive meshing errors. The results demonstrate that the system presents strange attractors with rich forms under different parameter combinations. With the increase of the excitation frequency, the meshing state of the system changes, showing a complex motion and indicating the sensitivity of the system to external excitation. Under the variation of the bifurcation parameter of comprehensive meshing error, the complex dynamic behavior of the system is observed, it is found that the increase of comprehensive meshing error has a negative impact on the stability of the system.

Semi-analytic semi-numerical analysis of dynamic characteristics of a two-stage coupled series PGT based on IHB and MsP methods

This paper conducts an analytical investigation of the dynamic response characteristics of a two-stage coupled series system (TsCSS) with a planetary gear transmission (PGT), consisting of dual-power branches. An improved incremental harmonic balance (IHB) method, based on the arc length extension technique, is proposed. The results are compared with those of the numerical integration method, in order to verify the feasibility and efficiency of the improved method. Afterwards, the multi-scale perturbation (MsP) method is applied to the proposed TsCSS. The frequency response equations of the primary resonance, subharmonic resonance and superharmonic resonance, are solved in order to generate the frequency response characteristic curves of the planetary transmission system. A comparison between the results obtained by the MsP method and the numerical integration method demonstrates that the former is ideal and credible in most of the regions. Considering the parameters of TsCSS excitation frequency and damping, the nonlinear response characteristics of steady-state motion are mutually converted. The impact of the time-varying parameters and nonlinear deenthing caused by the gear teeth clearance on the amplitude–frequency characteristics of the TsCSS components, is finally studied.

Dynamic Modeling and Analysis of Nonlinear Compound Planetary System

In the vehicle composite planetary gear transmission system, nonlinear excitations such as time-varying meshing stiffness, backlash and comprehensive error would lead to large vibration and noise, uneven load distribution, unstable operation and other problems. To address these issues, this work focuses on compound planetary gears and develops the bending-torsion coupling nonlinear dynamic model of the system based on the Lagrange equation. There are internal and external multi-source excitations applied to the system. This model is used to study the bending-torsion coupling meshing deformation relationship of each meshing pair along with the translational and torsional directions. The natural frequencies and vibration modal characteristics of the system are extracted from the model, and the influence of rotational inertia and meshing stiffness on the inherent characteristics of the system are studied. The coupling vibration characteristics of the system under operating condition are analyzed in terms of the inherent characteristics and time–frequency characteristics of the system. The simulation results exhibit that the planetary gear system has three modes. The change in natural frequency trajectory has two phenomena: modal transition and trajectory intersection. The main frequencies include engine rotating frequency, meshing frequency and its double frequency, and the rotation frequency and harmonic frequency of the engine have a great influence on the vibration response of the system. Finally, the virtual prototype of the composite planetary system is used to verify the accuracy of the established model from speed, inherent characteristics, meshing force and frequency composition.

Effects of three types of bearing misalignments on dynamic characteristics of planetary gear set-rotor system

Bearing misalignment may be one of the causes of cage fracture fault. However, the research of bearing misalignment on vibration characteristics of the rotating machinery system has not been paid enough attention. In this paper, the effects of axial, radial and tilt misalignments of the rotor support bearing on the dynamic characteristics of the planetary gear set-rotor system are analyzed. Firstly, based on the Hertz contact theory, a nonlinear restoring force model of the ball bearing is proposed under axial, radial, and inner/outer ring tilt misalignments. Secondly, taking the planetary gear transmission system of a tracked vehicle as the research object. The dynamic model of the planetary gear set is established through the lumped parameter method. The rotor is established by the Timoshenko beam element. Finally, the dynamic model of the planetary gear set-ball bearing-rotor system is obtained by coupling these three parts. Based on the proposed model, the dynamic responses are analyzed considering bearing misalignment. The results showed that the three types of misalignments reduce the vibration amplitude due to the strengthened constraint of the bearing on the system, but increase the load-bearing area and contact load. Radial and tilt misalignments increase the varying compliance (VC) frequency amplitude of the bearing. On the contrary, axial misalignment reduces the VC frequency amplitude. The sensitive evaluation indexes of three misalignment states are given. The research results can provide a theoretical basis for fault diagnosis and identification of bearing misalignment in complex rotating machinery system.

Establishment and analysis of nonlinear frequency response model of planetary gear transmission system

Abstract. Based on the lumped parameter theory, a nonlinear bending torsion coupling dynamic model of planetary gear transmission system was established by considering the backlash, support clearance, time-varying meshing stiffness, meshing damping, transmission error and external periodic excitation. The model was solved by the Runge–Kutta method, the dynamic response was analyzed by a time domain diagram and phase diagram, and the nonlinear vibration characteristics were studied by the response curve of the speed vibration displacement. The vibration test of the planetary gearbox was carried out to verify the correctness of frequency domain response characteristics. The results show that the vibration response in the planetary gear system changes from a multiple periodic response to a single periodic response with the increase in input speed. Under the action of the backlash, time-varying meshing stiffness and meshing damping, the speed vibration displacement response curves of internal and external meshing pairs appear to form a nonlinear jump phenomenon and have a unilateral impact area, and the system presents nonlinear characteristics. The nonlinear vibration of the system can be effectively suppressed by decreasing the mesh stiffness or increasing the mesh resistance, while the vibration response displacement of the system increases by increasing the external exciting force, and the nonlinear characteristics of the system remain basically unchanged. The backlash is the main factor affecting the nonlinear frequency response of the system, but it can restrain the resonance of the system in a certain range. The spectrum characteristics of the vibration displacement signal of the planetary gearbox at different speeds are similar to the simulation results, which proves the validity of the simulation analysis model and the simulation results. It can provide a theoretical basis for the system vibration and noise reduction and a dynamic structural stability design optimization.

Optimized design and experiment of the three-arm transplanting mechanism for rice potted seedlings

The transplanting arm of two-arm transplanting mechanism is easy to cause seedlings injury and missing due to its faster speed relative to the seedlings. In order to solve the existed problems, a three-arm transplanting mechanism for rice potted seedlings was developed in this study. The developed three-arm transplanting mechanism for rice potted seedling can make the transplanting arm realize special trajectory and attitude through the unequal planetary gear transmission. The kinematic model of three-arm transplanting mechanism for rice potted seedling was established, and the optimal design software was developed. Based on the heuristic optimization algorithm named “parameter guide”, a set of satisfied mechanism parameters required by the rice potted seedling transplanting were obtained. The trajectory and attitude of three-arm transplanting mechanism used for the rice potted seedling were analyzed. Besides, the virtual simulation results were basically consistent with the optimization software results, and the correctness of theoretical analysis and virtual simulation were also verified by each other. When the developed transplanting mechanism picked up the seedling, the velocity of transplanting arm relative to the seedling was reduced by about 30%. The results showed that the injury rate of rice potted seedling transplanting mechanism was 0.04%, the missing rate of seedling was 1.4%, the integrity rate of seedling pot matrix was 96%, and the success rate of picking seedling was 99.92%. Keywords: agricultural machinery, transplanting mechanism, rice potted seedling, three-arm, optimal design DOI: 10.25165/j.ijabe.20211405.6844 Citation: Yin J J, Wang Z L, Zhou M L, Wu L N, Zhang Y. Optimized design and experiment of the three-arm transplanting mechanism for rice potted seedlings. Int J Agric & Biol Eng, 2021; 14(5): 56–62.

Electromechanical Dynamic Analysis of the Integrated System of Switched Reluctance Motor and Planetary Gear Transmission

Electromechanical Dynamic Analysis of the Integrated System of Switched Reluctance Motor and Planetary Gear Transmission

Reliability modeling for planetary gear transmission system considering dependent failure processes

AbstractMany mechanical systems are subject to degradation and random shock processes, which are dependent and competing. The two processes are soft failure process and hard failure process, either of which occurs will cause the system to fail. In this paper, a hard failure model of the gear system is established based on the Stress‐Strength Interference model, and a soft failure model of the system is also proposed. To consider the dependence between the two failure processes, the copula function is adopted. Then, the reliability model of the system subject to degradation and shocks is developed, and an expression of the system reliability is derived. Finally, a planetary gear transmission system is taken as a numerical example to demonstrate the effectiveness of the proposed model, which is considered a k‐out‐of‐n system experiencing the processes of degradation and random shocks. Moreover, the effect of model parameters on reliability is evaluated through sensitivity analysis.