Planetary Gear Research Articles

Energy and Fuel Consumption of a New Concept of Hydro-Mechanical Tractor Transmission

Tractors equipped with hydro-mechanical transmissions (HMTs) typically deliver excellent fuel-saving performance but are expensive. To improve the fuel economy of cheaper tractors, the authors of this study have designed an HMT for a tractor that uses a simple, single planetary gear to merge the power and analyze its consumption of energy and fuel. First, we introduce the principle of transmission of the HMT and formulate a model to calculate its speed, torque, and efficiency. Second, we analyze the parasitic power of the HMT and simulate its characteristics of efficiency. Finally, we compare the efficiency of transmission and fuel consumption of HMTs with a single planetary gear and Simpson planetary gears. The results showed that parasitic power was obtained when the displacement of the variable pump was negative and the maximum ratio of hydrostatic power in each range was 45–46%. The highest efficiency of the proposed HMT in ranges RL (low range) and RH (high range) were 87% and 89%, respectively. It has a simpler structure than the HMT with Simpson planetary gears and consumes lower amounts of energy and fuel. These attributes make it suitable for use as a transmission system for large- and medium-power tractors with a continuously variable transmission.

An insight into the pass effect of the planet gear from an elastodynamics perspective

An insight into the pass effect of the planet gear from an elastodynamics perspective

INFLUENCE OF MANUFACTURING ERRORS ON THE BEHAVIOUR OF A TWO-STAGE PLANETARY GEAR TRAIN

Planetary gear train is widely used in large heavy-duty machineries such as helicopters and ships due to its large transmission ratio, strong bearing capacity, and small size. In this paper, and the load sharing ratio (LSR) and overall transmission error (TE) of a two-stage double-helical planetary gear train are studied. Firstly, the static balance equations of the double-helical planetary gear train are established. Then, the LSR under different mesh phasing and the overall TE are obtained by solving the equations. Finally, different errors such as pinhole position and eccentricity error are taken into consideration and the influence of errors on load sharing ratio and transmission error are analyzed. The results show that the excitation frequency of transmission error is related to the number of planet gears and mesh phasing and the LSR is related to the mesh phasing, especially to the sequentially phased transmission. It is also concluded that the excitation frequency of the output element of the two stages can be seen as the superposition of the mesh frequencies of each stage and that the studied errors have a significant impact on the LSR and the TE. Keywords: Double-helical planetary gear; Meshing phase; Load Sharing Ratio, Transmission Error.

Fault Diagnosis Method of Planetary Gearbox Based on ISSA-VME and Multi-scale Fuzzy Entropy

To solve the problem of noise interference and difficulty in feature extraction of vibration signals of planetary gearbox, propose a fault diagnosis method of planetary gearbox based on improved sparrow search algorithm optimized variational mode extraction (ISSA-VME) and multi-scale fuzzy entropy (MFE). The vibration signal was decomposed by ISSA-VME, and the multi-scale fuzzy entropy of the original signal was calculated according to the IMF component. The fault feature set composed of MFE was applied to the SVM classifier optimized by the improved sparrow search algorithm for fault pattern recognition. The experimental results demonstrate that compared with ICEEMDAN and VMD methods, ISSA-VME has a better effect and higher efficiency on vibration signal decomposition. The identification rate of missing teeth, cracks, wear, and other faults of planetary gearbox sun gear by the proposed method reaches 97.50%.

Equal Strength Optimal Design of Planetary Gear Transmission

In the design of planetary gear transmission, some gears are damaged during early use because of low strength, yet some are big structure sizes with high strength. In the paper, gears’ equal strength and minimum volume of the gearbox is regarded as optimization objective, and the exterior point penalty function method is used to solve them. Last, we obtain the design parameters under the condition of equal strength of the planetary transmission. Compared to the conventional design method, the weak strength of some gears is enhanced, the whole life is increased, and the overall volume is decreased. It shows we can get ideal results by equal strength optimization in the planetary transmission design.

Frequency-Domain Analysis and Joint Torque Vibration Suppression Control on Two-Input-Two-Output Torque Difference Amplification Motor Drive System of Electrified Vehicles

<div>To improve the cornering performance, a torque vectoring differential (TVD) that generates a torque difference between the left and right wheels has been developed. Particularly, the use of multiple electric traction motors can easily achieve this. A TVD with a two-motor-torque difference amplification mechanism (TDA-TVD), which employs a unique alignment of planetary gears, has been studied and it can generate a larger torque difference compared to an individual-wheel-drive (IWD) system in the case of using the equal torque output from the traction motors. However, due to the mechanically complicated driving force transmission system including driveshafts and planetary gears, TDA-TVD is prone to cause torsional vibrations of the driveshaft, and the yaw rate of the vehicle body while differential torque is generated. A previous study derived a dynamic model TDA-TVD and designed a vibration suppression feedforward controller. While the study demonstrated a certain vibration suppression performance, it did not strictly consider the load side characteristics during the yaw motion. In addition, there was no frequency-domain analysis either. On the other hand, this study will analyze TDA-TVD in the frequency domain and propose a novel modeling method to construct vibration suppression controllers that deal with both longitudinal motion and yaw motion simultaneously. First, this article shows a theoretical frequency-domain analysis using matrices and obtains resonance frequencies of TDA-TVD. Second, TDA-TVD is modeled based on a summation-differential mode transformation (SDMT). Third, simulations and experimental evaluations of vibration suppression controls using a real vehicle equipped with the TDA-TVD are demonstrated.</div>

Dynamic modeling and vibration analysis of planetary gear sets concerning mesh phasing modulation

This paper studies the changes in behavior, in terms of mesh phasing modulation, of planetary gear transmissions (PGTs) due to various gear pinhole position errors. An advanced model of the spur PGT is established to explore the effects of the position errors on mesh phasing relations and an analytical determination of the relative mesh phasing variation is derived. Furthermore, the vibration performance of planetary gears is investigated by developing a novel dynamic model and components of the vibration signals are clarified using the proposed model. Additionally, we further perform several experiments to measure the mesh phasing variations using strain gauges and collect the gear vibration signals using accelerometers. Finally, simulation and experimental results are compared to verify the proposed models, and the results indicate that the presented models provide the opportunity for the researchers to quantify the mesh phasing relations relative to the gear position errors as well as clarify the frequency modulation mechanism of gear vibrations in PGTs.

Tooth root crack detection of planet gear in industrial robot RV reducer

The windowed synchronous averaging (WSA) is widely utilized for planetary structures. However, it cannot be applied for the fault detection of the planetary structure in the industrial robot rotate vector (RV) reducer. The robot usually works within a specified angle range, which causes the RV reducer rotates incompletely. To address this issue, an angle compensation local synchronous fitting scheme is proposed. To detect the localized planet gear fault in the RV reducer, the observed vibration is equi-angle resampled. And the synchronous interference contained in the resampled vibration is constructed and removed according to the angle compensation strategy. The residual data is used to construct the synthetic vibration of the planet gear. Then, the fault feature of the planet gear can be detected. Experiments on the RV reducer test rig under the robot running conditions support the effectiveness of the proposed scheme positively.

Load sharing performance analysis of planetary gear system considering the coupling effects of gear pair and journal bearing

In this paper, a load-sharing performance analysis method of the planetary gear system is proposed considering the coupling effects of double-helical gear and journal bearing. Firstly, the coupling effects between the meshing characteristics of the double-helical gear pair and the dynamic characteristics of journal bearing under the actual operation state are studied, the dynamic model of the double-helical gear planetary transmission system is established, and the load sharing coefficient before and after considering the coupling effects are calculated; secondly, the load sharing characteristic test rig of planetary transmission system is built, and the load sharing coefficient of gear system under the test condition is measured to verify the accuracy of the proposed method; finally, the effects of operating parameters and structural parameters on the load sharing characteristic of gear system are discussed.

Dynamic Responses of the Planetary Gear Mechanism Considering Dynamic Wear Effects

Gear wear is unavoidable and results in vibrations and decreased performance in a planetary gear system. In this work, the wear phenomenon of the gear teeth surface and the dynamic responses of the planetary gear mechanism are investigated through a computational methodology. Dynamic responses are presented by considering the dynamic wear effects. First, the model of the planetary gear mechanism dynamics is established by considering the nonlinear stiffness and friction of gear surfaces. The dynamic wear model of the gear is then established based on Archard’s wear model. Further, the coupling between the dynamics and wear characteristics of the planetary gear mechanism is presented by considering the dynamic wear effects. Finally, a numerical investigation is conducted. The simulation results reveal severe wear between the sun and planet gears. The wear depth and meshing vibration responses exhibit prominent nonlinear characteristics. The low-order resonance of the meshing frequency becomes more marked as the mesh times and wear increase.

Research on the Coupled Phase-Tuning Vibration Characteristics of a Two-Stage Planetary Transmission System

Mesh phasing has a dramatic impact on the static and dynamic behaviours of planetary gear systems. This research investigates the coupled phase-tuning mechanism of two-stage planetary gear systems and the corresponding relationship with the coupled vibration of the system. Due to the inherent meshing symmetry of the system, the phase-coupled tuning mechanism of the two-stage planetary system is derived based on meshing force relationships and coupling characteristics between different stages. The excitation and suppression relationships associated with the teeth number, harmonic order, and coupling vibration of the coupled system are clearly described. To study the effect of coupled phase tuning on the vibration response of a two-stage planetary gear system, a nonlinear dynamic model was established. The vibration responses under different tuning modes were calculated, and a coupled phase-tuning law for two-stage planetary systems was verified. Model 3 was used as a research tool to build a two-stage planetary transmission experimental platform, and the transverse vibration and torsional vibration of the first stage sun gear were analysed to further verify the correctness of the phase-coupling tuning law.

Research of the deformability of the cantilever axis of the satellite of a multi-satellite planetary gear and its influence on the load distribution over power flows

A mathematical model of the axis of the satellite, cantilevered in the cheek of the carrier of the planetary gear, is presented. The axis of the satellite is presented in the form of a beam on an elastic base. The influence of the flexibility of the axle and the drive elements mated with it on the distribution of the load over power flows is considered. The Leibniz formulas and the Euler method were used to obtain the model. The coefficient of uneven load distribution over power flows is obtained by solving a system of displacement compatibility equations, including deformations of the wheel teeth, rolling bearing, satellite axle and mating parts, taking into account the initial non-adherence of the teeth due to gear manufacturing errors. The load capacity of a planetary gear with cantilever axes of satellites is analyzed depending on the number of power flows. Keywords: planetary gear, deformation, cantilever axle, load distribution. fplehanov@list.ru, alexandrsun4009@gmail.com

Modeling and Analysis of Novel Space Disc Planet Motor With Multi-Port Output

A novel space disc planet motor (NSDPM) is proposed by combining planetary gear drive and permanent magnet disc motor, which integrates advantages of disc motor and permanent magnet planetary gears. It can realize output with multiple ports in different directions and improve the compactness of power drive system. In this paper, the driving mechanism and design requirements of the novel space motor have been analyzed. The analytical models of space magnetic field generated by disc rotor and planet stator are derived, respectively. The effectiveness of analytical models is verified by finite element model (FEM). The driving torque of disc rotor is deduced by Maxwell stress tensor method, and the validity of analytical model is verified by FEM of its equivalent 2D model. The influences of electromagnetic parameters on driving torque of disc rotor are discussed. In addition, the transmission ratio and driving torque experiment are conducted. The experimental results prove the validity of driving principle and stability of torque output. The research results are of great significance to further study of electromagnetic structure optimization.

Origami Pump Based on Planetary Gear System for Pneumatic Pressure

In this article, an origami pump system based on a planetary gear for operating a soft actuator is introduced. The proposed system consists of three main parts: planetary gear system, origami pump, and soft pneumatic chamber. A planetary gear system operated by dc motors supplies torque to an origami pump. The origami pump with the Kresling pattern can be contracted and expanded only by rotation from the torque. As the pump contracts, pressure is transmitted to the soft chamber, causing it to bend in a particular direction. The performance of the proposed system is analyzed in terms of two aspects: pump displacement and internal pressure. The change in performance according to input frequency and rotation angle is theoretically modeled and compared with the experimental results.

Analysis and simulation of the influence of initial liquid level on lubricating flow state and oil-churning resistance moment of planetary reducer

In order to study the influences of the initial liquid level on lube characteristics and oil-churning resistance moment of gear reducer, the heat generating power of one special kind of planet gear reducer under the special working condition is calculated. The fluid temperature at different initial liquid levels is calculated by FEA method. According to the relation between the physical parameters of the lube and the fluid temperature, the corresponding relation between the physical parameters of the lube and the initial liquid level is deduced. Based on the FEA results, the physical parameters of the lube are set to conduct the co-simulation of the oil-churning process of the planetary reducer under different initial liquid levels by MPS method. Depend on the simulation results, the influence of initial liquid level on lubricating flow state and oil-churning resistance moment of planetary reducer is analysed, and the initial liquid level is sifted. These studies provide methods and reference for lubrication medium set in transmission boxes, such as planet gear reducer and so on.

Simulation study of active vibration control of planetary gear: Theoretical and numerical analysis using pole placement

This paper presents analytical and numerical studies on the active assignment of poles to a planetary gear system for vibration control in order to avoid resonance. This involves feeding back the displacement and velocity to add active stiffness and damping, respectively. A rotating frame of reference has been adopted in order to describe the dynamics over a broad range of rotational speed. As an illustration, the closed loop poles were assigned to the translational directions of the sun gear first and thereafter the carrier. This can be achieved by placing the actuators on the outer race of their bearings mounted onto their shafts. The controller was designed such that the closed loop poles can be assigned considering the rotational speed. In this way, it is possible to apply a robust pole-placement that is insensitive to the rotational speed. Numerical examples, where sensors and actuators were collocated, are presented to demonstrate the feasibility of the method when applied to a physical system. The results shows that the active control force and power required for the system, when rotating, can be determined using a rotating frame of reference and transformed for practical implementation. In addition, the same conjugate poles were assigned to the carrier and sun gear and the optimal place to apply control forces was discovered. This depends upon the control power required to shift the poles from one location to another. The results show that more control power will be required to shift the poles of the system when poles were assigned to the sun gear, where higher active bearing stiffness was required. Therefore, the optimal place to assign poles in this case is the carrier due to lower control power required to shift the system poles.

Torques and Moments of Inertia Models for Horizontal Axis Hydrokinetic Turbine Driveline

The quantification of torques and moments of inertia of horizontal axis hydrokinetic turbine driveline is important to precisely predict the dynamic behavior of the complete system. Initially, this paper presents different models used in the literature for describing torques and moments of inertia of turbine components. A dynamic model of a small hydrokinetic turbine using belt transmission is developed. The model uses the Blade Element Momentum (BEM) for determining the power coefficient of the turbine rotor and considers the inertial effects and dissipative torques of whole system using some of the torque models and moments of inertia described previously. The results for the dynamical behavior of the turbine model are compared with experimental data, showing good agreement. In order to numerically analyze a more efficient drivetrain, the belt transmission is replaced by a planetary gearbox in the dynamic model, and the new results are also assessed. As a result, it was found that with planetary gears, a more compact transmission can be used, reducing the inertial effects, which brings a better efficiency in the starting of the machine and shortening the transient regime time.

Reliability Design of Two-Stage Planetary Gear Wheel Hub Reducer based on Multi-Objective Optimization

The mining dump truck has a large load capacity, low running speed, and the characteristics of low speed and high torque. The planetary wheel reducer can meet this demand, which is widely used in such vehicles. According to the structural characteristics of a 170-ton vehicle two-stage planetary gear reducer, the reliability of planetary gear transmission at all levels was analysed, and the system parameters were optimized on this basis. The multi-objective optimization design method was used to transform the maximum reliability of the system into the maximum reliability of the gears at all levels, and the constraints are established based on the actual processing, operation, installation, assembly and other working conditions. The MATLAB multi-objective optimization module was used to solve the analysis, and the best gear design parameters were obtained after rounding. Under different operating conditions, the planetary reducer before and after optimization was compared and analysed to obtain the reliability and service life of the entire deceleration system after optimization. The analysis results show that: after the parameter optimization of the planetary reducer, the transmission efficiency is 0.946, and the transmission ratio of the system is 30.54, which meets the actual use requirements. The reliability coefficient of the contact strength of the tooth surface of the secondary sun gear is 2.52, the reliability coefficient of the bending fatigue strength of the root of the secondary inner ring gear is 2.59, and the reliability of the secondary gear is 0.989. The reliability is obviously improved. The safety factor of the main parts is high. The service life of each gear of the whole secondary reduction system meets the design requirements. The analysis content and results provide reference for the optimization design and reliability analysis of similar planetary gear systems.

Artificial ecosystem optimization by means of fitness distance balance model for engineering design optimization

Optimization techniques have contributed to significant strides in complex real-world engineering problems. However, they must overcome several difficulties, such as the balance between the capacities for exploitation and exploration and avoiding local optimum. An enhanced Artificial Ecosystem Optimization (AEO) is proposed incorporating Fitness Distance Balance Model (FDB) for handling various engineering design optimization problems. In the proposed optimizer, the combined FDB design aids in selecting individuals who successfully contribute to population-level searches. Therefore, the FDB model is integrated with the AEO algorithm to increase the solution quality in nonlinear and multidimensional optimization situations. The FDBAEO is developed for handling six well-studied engineering optimization tasks considering the welded beam, the rolling element bearing, the pressure vessel, the speed reducer, the planetary gear train, and the hydrostatic thrust bearing design problems. The simulation outcomes were evaluated compared to the systemic AEO algorithm and other recent meta-heuristic approaches. The findings demonstrated that the FDBAEO reached the global optimal point more successfully. It has demonstrated promising abilities. Also, the proposed FDBAEO shows greater outperformance compared to several recent algorithms of Atomic Orbital Search, Arithmetic-Trigonometric, Beluga whale, Chef-Based, and Artificial Ecosystem Optimizers. Moreover, it declares great superiority compared to various reported optimizers.

Research on electro-hydraulic ratios for a novel mechanical-electro-hydraulic power coupling electric vehicle

In the context of globalization where new energy vehicles are widely used, this paper proposes a novel mechanical-electro-hydraulic power coupling system for electric vehicles (MEHV). The planetary gear mechanism (PDCM) is integrated with the accumulator, hydraulic pump/motor, battery and motor to realize the mutual conversion of mechanical energy, electric energy and hydraulic energy. Subsequently, a rule-based energy management strategy is established to distribute energy and realize smooth switching in real time. Then, further analysis is carried out on the electro-hydraulic torque distribution. The results illustrate that, the peak torque of the drive motor (DM) can be decreased, and the hydraulic energy can be fully utilized to improve the state of charge (SOC) under appropriate ratio. Simultaneously, to ensure the appropriate electro-hydraulic ratio under complicated conditions, this paper adopts the fuzzy rule-based energy management strategy of multi-parameter input. Ultimately, the actual driving conditions are established using the actual driving data and the strategy. Consequently, the peak torque is significantly lower than pure electric vehicle, the battery energy consumption is reduced by 19.06%. Therefore, the approach proposed in this paper notably improves the running state of the motor, the energy utilization rate, as well as the economy and stability of the vehicle.