Operating Speed Range Research Articles

A Study on Ways to Expand the Speed Operation Range of Dental Laboratory Handpiece Motors Using Low-Cost Hall Sensors

In the dental prosthetics field, BLDC micro-motors are primarily used for implant procedures. As dental materials become increasingly harder, there is a growing demand for higher performance motors to precisely process these materials. However, difficulties in motor development arise due to price competitiveness. Dental motors require capabilities such as low-speed, high-torque for drilling operations and high-speed rotation for precise machining of high-strength dental materials. Additionally, there is a requirement to address thermal issues to prevent user burns due to motor-generated heat. Typically, motors requiring precision control utilize high-resolution position sensors like encoders or resolvers to acquire and control the rotor’s position. However, the high cost of these sensors and constraints such as increased device size pose challenges in maintaining price competitiveness. In this paper, we propose a control algorithm that satisfies the requirements for low-speed, high-torque and high-speed operation requirements for precision machining without hardware modifications using a BLDC micro-motor equipped with an inexpensive Hall sensor commonly used in the dental field. Furthermore, the algorithm is designed to ensure stable operation even in the event of Hall sensor failure or malfunction, and its effectiveness is validated through experiments.

Simulation and experimental analysis of traveling wave resonance of flexible spiral bevel gear system

Considering the traveling wave resonance (TWR) phenomenon of the spiral bevel gear system in the aero engine accessory casing, the flexible spiral bevel gear model is established by three-dimensional (3D) shell element and beam element. The dynamic model of flexible bevel gear system considering the change of meshing teeth pairs in the operating process is established by component mode synthesis (CMS) method and rotational modal projection method. The proposed model is verified by finite element (FE) solid model and experiment test results. On this basis, the TWR phenomenon of the bevel gear system is studied in combination with dynamic response and vibration stress experimental test. The results show that the bevel gear system has 3 nodal diameter resonance speeds within the actual operating speed range, which are one 1st nodal diameter resonance of pinion and two 1st nodal diameter resonance of gear. When the bevel gear system operates at TWR state, the amplitude corresponding to fm ± m·fr (fm is meshing frequency, m is nodal diameter number, fr is shaft rotational frequency) is larger than that corresponding to fm in the Fast Fourier transform (FFT) spectrum of the of the gear foundation vibration stress, and the vibration stress cloud map of the gear foundation shows the corresponding nodal diameter vibration shape. The research results provide a theoretical basis for feature recognition and influence law evaluation of TWR of bevel gear system.

Performing Magnetic Boundary Modulation to Broaden the Operational Wind Speed Range of a Piezoelectric Cantilever-Type Wind Energy Harvester

Small piezoelectric wind-induced vibration energy harvesting systems have been widely studied to provide long-term sustainable green energy for a large number of wireless sensor network nodes. Piezoelectric materials are commonly utilized as transducers because of their ability to produce high output power density and their simple structure, but they are prone to material fracture under large deformation conditions. This paper proposes a magnetic boundary modulated stepped beam wind energy harvesting system. On the one hand, the design incorporates a composite stepped beam with both high- and low-stiffness components, allowing for efficient vibration and electrical energy output at low wind speeds. On the other hand, a magnetic boundary constraint mechanism is constructed to prevent the piezoelectric sheet from breaking due to excessive deformation. Experiments have confirmed that the effective operational wind speed range of the harvester with magnetic boundary constraints is doubled compared to that of the harvester without magnetic boundary constraints. Furthermore, by adjusting the magnetic pole spacing of the boundary, the harvesting system can generate sufficiently high output power under high-wind-speed conditions without damaging the piezoelectric sheet.

Design and Testing of Electric Drive System for Maize Precision Seeder

To improve the expandability, seeding accuracy, and operating speed range of the electric drive system (EDS) of precision seeders, this study constructed an EDS based on a controller area network (CAN) bus and designed a motor controller based on a field-orientated control (FOC) algorithm. Full-factorial bench and field tests based on seed spacing (0.1, 0.2, and 0.3 m) and operating speed (3, 6, 9, 12, and 15 km/h) were carried out to evaluate the performance of the EDS. The results of bench tests showed that seeding quality varied inversely with operating speed and positively with seed spacing. The average quality of feed index (QFI) at 0.1, 0.2, and 0.3 m seed spacing in bench tests was 88.38%, 96.67%, and 97.36%, with the average coefficient of variation (CV) being 20.13%, 16.27%, and 13.20%. Analysis of variance confirmed that both operating speed and seed spacing had a significant effect on QFI and CV (p < 0.001). The analysis of motor rotational speed accuracy showed that the relative error of motor rotational speed above 410 rpm did not exceed 2.24%, and the relative error had less influence on the seeding quality. The average QFI was 85.93%, 95.91%, and 96.24%, with the average CV being 21.12%, 15.50%, and 16.49% at 0.1, 0.2, and 0.3 m seed spacing in field tests. The methods and results of this study can provide a reference for the design and optimization of the EDS in a maize precision seeder and provide an effective solution for the improvement of maize yields.

Review of linear flux-switching machines for variable speed applications

Purpose This paper aims to present an overview of permanent magnet linear flux-switching machines (PMLFSM), field excited LFSM and hybrid excited LFSM (HELFSM) topologies as presented in literature for transportation systems such as high-speed trains and maglev systems. Design/methodology/approach The structural designs of different configurations are thoroughly investigated, and their respective advantages and disadvantages are examined. Based on the geometry and excitation sources, a detailed survey is carried out. Specific design and space issues, such as solid and modular structures, structure strength, excitation sources placement, utilization of PM materials, and flux leakage are investigated. Findings PMLFSM provide higher power density and efficiency than induction and DC machines because of the superior excitation capability of PMs. The cost of rare-earth PMs has risen sharply in the past few decades because of their frequent use, so the manufacturing cost of PMLFSM is increasing. Owing to the influence of high-energy PMs and magnetic flux concentration, the efficiency and power density are higher in such machines. PM is the only excitation source in PMLFSM and has constant remanence, limiting its applications in a wide speed operation range. Therefore, the field winding is added in the PMLFSM to flexibly regulate the magnetic field, making it a hybrid excited one. The HELFSM possess better flux linkage, high thrust force density and better flux controlling ability, leading to a wide speed range. However, the HELFSM have problems with the crowded mover, as PM, field excited and armature excitation are housed on a short mover. So, for better performance, the area of each excitation component has to compete with each other. Originality/value Transportation of goods and people by vehicles is becoming increasingly prevalent. As railways play a significant role in the transportation system and are an integral part of intercity transportation. So, this paper presents an overview of various linear machines that are presented in literature for rail transit systems to promote sustainable urban planning practices.

Technology and technical means for the implementation of reproduction methods for soil fertility

Soil fertility is determined by the presence of humus as the main part of organic matter. The extended reproduction of soil fertility is ensured by the introduction of organic and mineral fertilizers, the cultivation of sidereal crops and the decomposition of plant residues. (Research purpose) The research purpose is developing the technologies and means of mechanization for extended reproduction of fertility. (Materials and methods) For the joint application of liquid organic fertilizers and the cultivation of siderates, a unit has been developed that implements a hose technology for transporting liquid organic fertilizers. Fertilizers are fed through pressure hose lines to the working parts deep into the soil layer. The combined unit consists of a tractor K-744 Kirovets and an adapter for deep tillage with liquid fertilizers, as well as a seeder for small-seeded crops. To level the surface of the field after the passage of the unit and the sealing of the sown seeds of the sideral culture, the unit is equipped with a tooth roller. (Results and discussion) Formulas for determining the critical processing depth are given, the power calculation of the unit is performed. The design of the tillage tool allows to install flat-cutting working parts with a grip of 0.80 meters and slits with a grip of 0.45 meters. Tests of the combined unit were carried out. The depth of tillage was 36±1 centimeters, the seeding rate of the sideral crop (oilseed radish) was 25 kilograms per hectare, the operating speed range of the unit was from 0.4 to 0.8 meters per second. (Conclusions) The uniformity of the subsurface distribution of organic fertilizers was 90-95 percent. The specific energy intensity of the technological process of the combined unit based on the K-744 tractor for intra-soil fertilization is 40-65 kilowatt hours per hectare (excluding the capacity for pumping fertilizers). Energy consumption depends on the depth of cultivation and resistivity of the soil. The proposed method allows preventing water and wind erosion of the soil, improving its agronomically valuable properties. Reducing the pesticide load on the soil and its microflora contributes to the transition to a model of sustainable agroecosystems, improving and improving crop quality. The proposed technology provides extended reproduction of soil fertility.

Design and experimental verification of hybrid excitation magnetic field modulation machine for electric vehicle propulsion

As one sort of flux modulation machine based on magnetic gear effect, field-modulated machine features with low speed large torque. A novel hybrid excitation field-modulated machine (HEFMM) is proposed by introducing the concept of hybrid excitation, the flux modulation poles (FMPs) and excitation winding of which are emplaced in stator teeth and the adjacent FMPs. It can be maintained wide speed range operation through the processes of flux-enhancing and flux-weakening with no increasing machine bulk, as well as the numbers of stator and rotor slot. The working principle of proposed machine is deeply studied, as well as basic electromagnetic characteristics are calculated by finite element method, including no-load magnetic flux linkage, no-load back electromotive force, cogging torque and output torque. In addition, the processes of flux-enhancing and flux-weakening are analyzed. Finally, one prototype with one kilowatt was built and its static characteristics were tested. The results show that the proposed HEFMM has the features of high torque density, small cogging torque and wide speed range, which is promising candidate for electric vehicle direct drive field.

Sustainable Sea of Internet of Things: Wind Energy Harvesting System for Unmanned Surface Vehicles.

Harvesting wind energy from the environment and integrating it with the internet of things and artificial intelligence to enable intelligent ocean environment monitoring are effective approach. There are some challenges that limit the performance of wind energy harvesters, such as the larger start-up torque and the narrow operational wind speed range. To address these issues, this paper proposes a wind energy harvesting system with a self-regulation strategy based on piezoelectric and electromagnetic effects to achieve state monitoring for unmanned surface vehicles (USVs). The proposed energy harvesting system comprises eight rotation units with centrifugal adaptation and four piezoelectric units with a magnetic coupling mechanism, which can further reduce the start-up torque and expand the wind speed range. The dynamic model of the energy harvester with the centrifugal effect is explored, and the corresponding structural parameters are analyzed. The simulation and experimental results show that it can obtain a maximum average power of 23.25 mW at a wind speed of 8 m/s. Furthermore, three different magnet configurations are investigated, and the optimal configuration can effectively decrease the resistance torque by 91.25% compared with the traditional mode. A prototype is manufactured, and the test result shows that it can charge a 2200 μF supercapacitor to 6.2 V within 120 s, which indicates that it has a great potential to achieve the self-powered low-power sensors. Finally, a deep learning algorithm is applied to detect the stability of the operation, and the average accuracy reached 95.33%, which validates the feasibility of the state monitoring of USVs.

Dynamic Performance Evaluation of a Brushless AC Motor Drive Using Different Sensorless Schemes

The presented study concerns with evaluating the dynamic performance of an isotropic sinusoidal brushless motor drive while utilizing different sensorless schemes. Three estimation algorithms are considered: the first depends on extracting the speed and position via comparing two values of motor's voltage in two co-ordinate systems; the second extracts the speed and position signal via comparing two different values of motor's current defined in two co-ordinates; while the third depends on estimating the motor's flux and use it to get the speed and position. The vector control is adopted to manage the drive dynamics. The detailed mathematical derivations for all system components are presented to facilitate the performance analysis. The theoretical base of each sensorless scheme is also described in detail. The target of the provided comparative analysis is to outline the weakness and strength points of each adopted sensorless schemes while estimating the speed and rotor position for a wide operating speed range. The judgment is measured in terms of the speed and rotor position estimation errors and the dynamic response as well. The performance evaluation process is carried out using MATLAB/Simulink software in which all system parts are simulated using their mathematical models. The findings from the study state that when it comes to dynamic speed behaviour, the voltage-based sensorless technique dominates, while the current-based sensorless approach gives stability in speed estimate priority. Alternatively, the third adopted sensorless scheme offers an acceptable high-speed performance and respectable performance at lower speeds. Statistically, it is found that the voltage-based estimation technique gives respectively lower speed and position estimation errors with percentages of 35% and 10% lower than their values under the current-based estimation technique, and with percentages of 35% and 30% lower than their values under the third adopted scheme.

РЕМОНТ КОРЕННЫХ И ШАТУННЫХ ШЕЕК КОЛЕНЧАТЫХ ВАЛОВ ДИЗЕЛЬНЫХ ДВИГАТЕЛЕЙ ПРИ ПОМОЩИ ДИСКРЕТНОГО УПРОЧНЕНИЯ

Studies to assess the effect of discrete hardening of the crankshaft journals on its fatigue strength have been carried out. For this purpose, fatigue tests were carried out on two control parts of the D80 type crankshaft. It was established that the destruction of control part No. 1 occurred after 322,000 cycles, control part No. 2 after 201,000 cycles. The destruction zone of both control parts passes along the R8 mm transition fillet of the connecting rod journals. This allows us to conclude that the discrete hardening factor is not associated with fatigue failure of the control parts. In order to determine the service life of the crankshaft of the KamAZ 740 engine, strengthened in a discrete way (shaft of the fourth repair size), it was installed on a KamAZ 5320 vehicle. As a result of the tests, it was found that during the entire testing cycle the vehicle's mileage was 109,000 km. Moreover, at the time of completion of the tests, all parameters of the car’s engine met the technical requirements. The KamAZ 5320 vehicle is in operation to this day. Its mileage was 269,000 km without stopping for major repairs. To conduct operational tests of a cast iron crankshaft with discrete hardening of a D80 type engine, a 1D80B diesel generator engine was taken, which after assembly was subjected to full-scale testing. These tests included a 100-hour engine run-in, determination of the vibration level and amplitudes of torsional vibrations of the diesel generator shaft line in the operating speed range. The analysis of the vibration state of the engine showed that in all test modes the vibration level at the points under study does not exceed the norms (0.350 mm on the turbocharger housing and 0.150 mm on the generator foot). The maximum stresses from torsional vibrations were: 8, about 17.5 MPa; 4, 5 order 10.5 MPa; 1.5 order 10.0 MPa. The resulting stress levels are significantly lower than permissible. Tests of the 1D80B diesel generator showed its full compliance with the technical requirements for the operation of this engine.

Multi‐objective hierarchical optimisation design and experimental verification of an alterable‐magnetic‐circuit variable‐flux memory machine

AbstractRare‐earth permanent magnet synchronous machines face challenges in manipulating their magnetic fields, which hinders the ability to extend the operation speed range. Moreover, this inflexibility leads to reduced efficiency in high‐speed scenarios when the machine is under flux‐weakening control and increases the risk of the magnets becoming demagnetised. The authors propose an alterable‐magnetic‐circuit variable‐flux memory machine (AMC‐VFMM) and a multi‐objective hierarchical optimisation method is conducted to optimise the machine. Firstly, the topology and alterable‐magnetic‐circuit principle of the proposed AMC‐VFMM are introduced. Then, optimisation objectives including torque production capability, flux regulation capability, and resisting unintentional demagnetisation capability are defined, and the hierarchical optimisation approach is established by stratifying the optimisation objectives and variables through the sensitivity analysis. Finite element analysis indicates that electromagnetic performances of the optimised design scheme are significantly enhanced. The bench test of the prototype demonstrates the superiority of the proposed AMC‐VFMM and validates the effectiveness of the optimisation design method.

Comparative analysis of dual stator machines

Electromagnetic performance of three different types of double stator permanent magnet machine is analyzed and compared in this study. The analyzed machines in this study are Machine 1, Machine 2 and Machine 3. These machines are designated as: M 1, M 2 and M 3, respectively. The studies are implemented using two-dimensional and three-dimensional finite element analysis (2D-FEA and 3D-FEA) methods. The predicted performance indices are: total harmonic distortion of the voltage, torque ripple, cogging torque, winding inductances, output torque and unbalanced magnetic force (UMF). The studies show that the investigated machine types have negligible reluctance torque and thus, similar axes inductance values. Therefore, the machines’ bulk torque components are contributed mainly by the magnets while the armature excitation sources yield lesser torque components. Amongst the compared machines, M 3 type has an outstanding performance in almost all the performance metrics, compared to M 2 and M 1 types. Nevertheless, M 1 machine type has some good attributes, particularly, with respect to its high output torque per applied magnet volume, in addition to its widest operating speed range ability. Low-speed high-torque applications are most suitable for the investigated machines in practice.

Study on QEMF Model and Adaptive Full-Order Observer Design for Universal Sensorless Control of IPMSMs

Quadratic extended electromotive force (QEMF) model enabled the use of traditional high-speed adaptive estimation methods combined to high-frequency signal injection (HFSI) for full-range sensorless position control of interior permanent magnet synchronous motors (IPMSMs). However, the first QEMF model presented in literature only works with HFSI in the q-axis, due to the QEMF being a function of the q-axis current derivative. The q-axis HFSI is known to produce undesired torque ripple. Furthermore, q-axis signal injection can be insufficient for low-speed position estimation in IPMSMs with low salience. A recent study demonstrated that the QEMF concept can be modeled as a function of the d-axis current derivative. In this paper, the influence of d-axis HFSI on QEMF is investigated and compared to the q-axis HFSI method. Furthermore, the electromotive force based observers are usually designed for medium to high-speed operation. Here, the adaptive full-order observer is adapted in order to achieve universal sensorless control through QEMF based d-axis HFSI. The state observer and adaptive law are designed by a cascade methodology, which guarantees accurate EEMF estimation and robustness throughout the entire operating speed range. Experimental results are presented in order to validate the proposed method and analysis under full-range sensorless control.

Segmented layered bistable piezoelectric laminates for enhanced energy harvesting from wind‐induced vibration

AbstractIn this study, a segmented layered bistable piezoelectric energy harvester (SBPEH) has been developed and thoroughly investigated for its wind energy harvesting capabilities. The SBPEH's performance was comprehensively evaluated through the creation of a detailed 3D finite element model using Abaqus and XFlow software, and further validated via rigorous wind tunnel experiments. The results of this research demonstrate the SBPEH's remarkable potential for wind energy harvesting. With a wide operational wind speed range, it achieved a maximum measured power output of 5.476 mW, coupled with an outstanding power density of 68.45 mW/cm3, both of which were realized at a wind speed of 13 m/s. It is worth noting that as the wind speed surpasses a specific threshold, the energy harvesting efficiency of the SBPEH experiences a decline, emphasizing the importance of identifying the optimal operational wind speed range for maximizing energy output. These findings offer valuable insights for the enhancement and application of SBPEHs, contributing to the advancement of renewable energy technologies and providing an eco‐friendly solution for power generation.Highlights The study introduces a new segmented layered bistable piezoelectric energy harvester (SBPEH) design for wind energy harvesting, addressing the limitations of traditional harvesters. Performance is evaluated through 3D finite element modeling, ABAQUS, Xflow simulations, and wind tunnel experiments. The SBPEH operates efficiently across a broad wind speed range (6–14 m/s), showcasing optimal output power of 5.476 mW at 13 m/s.

Modification of rotor modal properties based on structural changes in the stiffness of its bearings and shaft

The rotor structures are fundamental mechanical systems that realize the transfer of rotary motion in technical devices and systems. In some operating regimes, the rotor systems are often subjected to undesirable and damaging phenomena resulting in resonant state. The ability to prevent or reduce the level of unwanted rotor vibrations in the given operating mode is an important task in the process of structural design of rotor structures. In general, the dynamic properties of rotor systems depend on their spatial properties - geometric parameters and material properties, i.e. distribution of mass and stiffness properties of rotor structures. For the structural design of the rotor or its structural modification, which will allow the redistribution of its spatial properties (mass and stiffness), two approaches based on changing the bearing stiffness and also on the shaft stiffness are presented in this paper. The main goal for modifying the spatial properties of the rotor is to get the critical rotor speed out of the operating speed range.

Dynamic response and wave motion of a periodically supported beam under an ultra-high-speed load: Wave dispersion and critical velocities

Vacuum tube transportation system is an attractive transportation mode due to the ultra-high-speed (over 1000 km/h) it can reach. Most vacuum tube transportation systems, e.g., the Hyperloop operate in elevated tube structure on periodical supports. When the speed of the vehicle reaches certain critical values, the periodical supporting structure experiences resonance-like response whose vibrational magnitude is significantly amplified. The amplification of the response has an adverse impact on the safety of the vehicle operation and severability of the supporting structures. This work aims to boost the fundamental understanding of the underlying physical mechanism of wave motions and critical velocities in the “moving load on periodical structure” problem utilizing an ultra-high-speed Hyperloop-type transportation system as an example. In this work, an ultra-high-speed moving load on a periodically supported beam is used to model the dynamic response of the supporting structure under an ultra-high-speed travelling vehicle. The steady-state response of the periodically supported beam is solved analytically and illustrated for sub- and trans-critical speeds. The dispersion relation is obtained while deriving the steady-state response. The relation between wave propagation in a periodical structure and critical speeds of the moving load on it is established. It is shown that the critical speeds could be within the operational speed range of ultra-high-speed transportation system. The number and magnitude of critical speeds are closely related to wave motions in the periodically supported structure. It is found that the primary critical speeds associated with largest beam responses may not exist, depending on the relative flexibility of the supports. The optimal structural parameters are associated with wave motion transition (between Local Resonance and Bragg Scattering) in the supporting structure. With this simplified model, wave motions in a periodical structure and critical speeds of the moving load on it is explained in a general physical sense. This work provides theoretical basis for the structural design and operation of the ultra-high-speed transportation system, as well as other engineering applications in which ultra-high-speed moving load is involved.

Investigation of a PM Flux-Modulated Motor With Mechanical Flux-Weakening Solution for Wide Speed-Range Operation in Traction Applications

Investigation of a PM Flux-Modulated Motor With Mechanical Flux-Weakening Solution for Wide Speed-Range Operation in Traction Applications

Drag reduction characteristics of recirculation flow at rocket base in an RBCC engine under ramjet/scramjet mode

To reduce the drag generated by the recirculation flow at the rocket base in a Rocket-Based Combined Cycle (RBCC) engine operating in the ramjet/scramjet mode, a novel annular rocket RBCC engine based on a central plug cone was proposed. The performance loss mechanism caused by the recirculation flow at the rocket base and the influence of the plug cone configuration on the thrust performance were studied. Results indicated that the recirculation flow at the rocket base extended through the entire combustor, which creates an extensive range of the “low-kinetic-energy zone” at the center and leads to an engine thrust loss. The plug cone serving as a surface structure had a restrictive effect on the internal flow of the engine, making it smoothly transit at the position of the large separation zone. The model RBCC engine could achieve a maximum thrust augmentation of 37.6% with a long plug cone that was twice diameter of the inner isolator. However, a shorter plug cone that was half diameter of the inner isolator proved less effective at reducing the recirculation flow for a supersonic flow and induced an undesirable flow fraction that diminished the thrust performance. Furthermore, the effectiveness of the plug cone increased with the flight Mach number, indicating that it could further broaden the operating speed range of the scramjet mode.

Maximum Torque per Ampere Technique for Switched Reluctance Motor Drive

Numerous researchers have investigated switched reluctance motors (SRMs) as a competitor to other electrical motors for usage in electric and hybrid vehicle appliances. SRMs are fault-tolerant and have a broad operating speed range. However, they have numerous drawbacks, such as high nonlinearity in machine models, complex control, and torque ripple. This study aims to improve the SRM drive system to attain maximum torque per ampere in a wide speed range. In the design and control of SRMs, maximizing torque per ampere (MTPA) is a crucial objective. MTPA refers to the strategy of achieving the maximum possible torque output for a given current input (amperes). This is essential for enhancing the efficiency and performance of the motor. The paper focuses on achieving MTPA in an SRM drive system-based commutation angle control. Utilizing a bacterial foraging optimization algorithm (BFOA), the suitable commutation angles at each operation point are determined. The intended technique is straightforward to realize and does not require complex algorithms. Simulation comparisons on an 8/6 SRM are also presented to validate the intended control technique. The results indicate that the MTPA has been enhanced by 6.961% compared to the conventional method.

Dynamic modeling and analysis of planetary gear system for tooth fault diagnosis

This study concentrates on the dynamic modeling and analysis of a planetary gear system with tooth broken faults. Firstly, a systematic calculation method of time-varying mesh stiffness (TVMS) for the planetary gear system is developed. Analytical models are established for both external-external and external-internal gear pairs under both healthy and tooth broken conditions. Then, a translational-torsional nonlinear dynamic model is established for a planetary gear system and coupled with the TVMS calculation method, to achieve dynamic simulations with tooth broken faults on the sun, planet and ring gears. The influences of tooth broken faults at different gears and at different damage degrees on the vibration responses are revealed. In addition, 15 condition indicators are chosen to assess their sensitivity to the tooth broken faults in a wide range of operational speed rather than a specific operational speed, in order to provide comprehensive information for evaluating the vibration characteristics and health conditions. Finally, experimental vibration signals from a gear transmission test rig are applied to verify the proposed dynamic model. The modeling method and analysis results here could provide some suggestions for the vibration analysis and fault diagnosis of planetary gear systems, and further provide data basis for the development of fault diagnosis methods.