Compound Planetary Gear Research Articles

Influence of eccentricity error on the orbit of a two-stage double-helical compound planetary gear train with different mesh phasing configurations

The eccentricity error is an unavoidable error during the manufacturing and mounting process and has a significant influence on the response of gear systems, especially for planetary gear train. First, based on the most basic quasi-static model, pressure angle, contact ratio and meshing stiffness are considered to be the time-varying parameters due to the eccentricity error. Then, a new quasi-static model of a two-stage compound planetary gear train with eccentricity error is established, and the accuracy of the established model is verified by analyzing the orbit result of healthy gear. Furthermore, the influence of eccentricity error on the response in the time-domain (orbit) under various error combinations is studied and discussed. Finally, it is found that the orbit of the component with eccentricity error is very different from that without eccentricity error, and the formation law of orbit for gear with eccentricity error is revealed in this paper. The results of the quasi-static model could provide a fundamental understanding to the dynamic model for the studied compound planetary gear train.

Study on nonlinear dynamics characteristics of dual speed dual clutch transmission system based on bond graph

The variable speed transmission system employs compound planetary gear trains and clutches. Compared to traditional aviation transmission systems, the added control parts in the variable transmission system result in a stronger coupling between components and more complex dynamic response characteristics. Modeling using the central mass method is complex and abstract. This study proposes a bond graph-based method for modeling and analyzing the dynamic behavior of the variable transmission system. The transmission system is divided into multiple component-level real-time dynamic models, and obtain a nonlinear multi-energy domain shift dynamic models based on energy flow paths coupling. The mathematical model is numerically solved using the Runge-Kutta method. Simulation results show that there is a delay in the speed response during the shifting process. Further analysis reveals that this “give and take” phenomenon is related to the mechanical structure and passive working principle of the one-way clutch. Subsequently, the time-domain response of the output speed under the hydraulic loading characteristic curves of linear, exponential, S-shaped, and composite functions, as well as the clutch torque, were studied. The impact of different hydraulic loading durations based on the exponential curve on component speed and torque was also analyzed. The simulation results provide a theoretical basis for designing low-shift impact, high-reliability, and high-performance variable transmission systems.

Optimal Design of a Compound Planetary Reducer Using a Nonlinear Optimization Method

The growth of the robotics industry has led to rising demand for reducers that increase torque efficiently while reducing motor speed. Among them, compound planetary reducers can be effectively used in robots because they can achieve high gear ratios with smaller volume. The design of conventional reducers comprises the method of setting a gear ratio to design the gear dimensions and calculating efficiency through dynamic analysis. However, this method suffers from repeated designing and analysis, which makes it very time-consuming. Therefore, this study defines the problem of reducer design as the problem of optimization by setting an objective function, constraints, and boundary conditions, and proposes to obtain the results in a short period of time using the Sequential Least Squares Programming(SLSQP) method. Using the SLSQP method, optimization results can be obtained as real numbers, making it suitable for use in compound planetary friction reducers with no constraints on the selection of gear dimension. For the design problem of the conventional compound planetary gear reducer in which the module value exists, an additional optimal design method considering the module is proposed. To compare the optimal results, we have made a 30:1 compound planetary friction reducer and a 50:1 compound planetary gear reducer using 3D printing. A gear ratio evaluation experiment was conducted to evaluate the performance of the actual manufactured prototype reducers.

Vibration-shock behavior analysis of compound planetary gear set based on harmonic balance method

Due to the clearance between the mating gears, a dynamic load rises and causes tooth impact and vibration. In the compound planetary gear set, under the interaction of transmission error, meshing stiffness, support stiffness and backlash, the unilateral tooth impact could evolve into bilateral tooth impact, resulting in a worse dynamic behavior. This work reveals the influence of internal excitations and external excitations on vibration-shock behavior, and, for this purpose, a “purely torsional” lumped parameter dynamics model of compound planetary gear set is built and combined with a harmonic balance method. The steady dynamics response under the frequency domain and time domain is given by the numerical solving method, and the results indicated that the bilateral impact occurs due to the transmission error. To avoid the influence of transmission error on the impact at the resonance peak, the input speed of the compound planetary gear set should avoid the resonance range and harmonious response range. To improve the tooth surface contact by increasing the backlash, it is recommended to decrease the initial velocity to below ωmesh = 0.8.

Key characteristics of generic bond graphs for planetary gears

This paper deals with generalized power flow models of compound planetary gear trains based on standard planetary gears. In this context, the Bond Graph approach provides an optimal tool for a large variety of structures. Starting with compound gears based on two standard planetary gears, two kinds of parameter definitions are discussed and two specifications for power ratio and efficiency are compared. Next, the influence of elastic shaft connections is clarified. Essential methods for these findings are the use of symmetry and the definition of sub-systems and, if applicable, of scalar or vectorial models. The second part deals with the effect of the number of constraints on constructions based on three standard planetary gears. Typical consequences, such as the number of free running elements, of complete Willis equations or of self-locking impacts, are systemized and illustrated by means of reference instances. It is shown by example that constructions featuring five external shafts would avoid such effects. Corresponding outcomes for the equivalent dynamic system equations, the parameter definitions and the Bond Graph modelling are given.

Bond Graph-Based Approach to Modeling Variable-Speed Gearboxes with Multi-Type Clutches

The modeling and simulation of gearboxes is important for analyzing the dynamic characteristics and designing control strategies of transmission systems. Variable-speed gearboxes include compound planetary gear trains and clutches, which complicates dynamic modeling. Here, a procedural bond graph-based modeling method that considers many uncertainties is proposed. The proposed method yields a constant system–structure model. First, bond graph models of the two most common planetary gears were summarized, and were used as sub-models of a compound planetary gear train. Then, the Karnopp friction sub-model of the friction clutch and a relative angular displacement sub-model of the one-way clutch were constructed. Based on the dynamic coupling between the sub-models, the modeling steps of the gearbox, including the compound planetary gear train friction clutch one-way clutch coupling system, are described in detail. Next, the main sources of uncertainties of gearbox were analyzed and the simulation methods were given. Finally, the novel uncertain bond graph model was used to simulate the double planetary gearbox; the transmission ratio before and after the shift was 2.42 and 1.72, compared with the design values of 2.41 and 1.71, respectively; the deviation is within 5.8%; The average rotating speeds of the output shaft fluctuated by 6 and 2.5% respectively, which was within a reasonable range, so the effectiveness of the method is verified.

Influence of floating support on the dynamic characteristics of compound planetary gear set

Due to a large number of components, complex meshing relations and high requirements for assembly accuracy, the dynamic characteristic of compound planetary gear, such as vibration, impact, periodic motion and load sharing, are more easily affected by internal excitation than those of simple planetary gear set and parallel shafting gear set. To improve the load sharing behavior and the resistance of Chaos motions in the compound planetary gear set, in this work, by introducing the floating support into the center gear and planet gear, a lumped-parameter dynamic model of the compound planetary gear set is built based on the lumped parameter method and Lagrange kinematics equation. The steady response is calculated by numeric method to investigate the influence of floating support from different components on loading sharing behavior and periodic motion. The results indicate that, the increase of the floating value of all components improves the instantaneous load-sharing behavior, and single floating of planet gear reduces the load sharing behavior. To avoid the system being in quasi-periodic motion and Chaos motions under the condition of floating support, the input speed should be avoided away from the range of 3201 r/min-5069 r/min.

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.

Analysis of nine-speed planetary change-gears through the torque method

An alternative method for kinematic and power analysis of compound gear train is presented, which uses the torques and lever analogy of a given gear train. The method combines the accuracy of the Willis analytical method with the clarity of the graphic method of Kutzbach. Unlike these methods, the torque method allows determining not only the gear ratio, but the magnitude and direction of power flows, and hence the determination of efficiency of a given compound planetary gear train. The application of the method is illustrated with example of novel arrangement of complex nine-speed change-gear. Structural, kinematic, and power (efficiency) analysis are made. A software for these analysis facilitation is developed. A numerical example is presented and discussed.

Dynamically Balanced Pointing System for CubeSats: Study and 3D Printing Manufacturing

The increasing presence of additive manufacturing (AM) in the space sector prompted us to investigate the feasibility of a single degree of freedom (DoF) pointing system (PS) made by means of a compound planetary gear train system (C-PGTS) integrating a dynamic balancing system (DBS) and entirely realized in AM. We analyzed in detail the dynamics of the system dealing with the design and the realization of the prototype. Of fundamental importance for this paper is the careful selection of materials for AM suitable for the prohibitive conditions of space. The results, deriving from the comparison between the experimental part and the simulations, underline the correct dimensioning of the PS and the fundamental importance of DBS in maintaining the satellite attitude. The results also confirm the capabilities of AM in the production of complex mechanical systems, allowing high precision, combined with interesting mechanical properties and low weight.This suggests the potential of AM in the space domain, both for structural parts and active components, such as those listed in this work.

Development of an Agile Omnidirectional Mobile Robot With GRF Compensated Wheel-leg Mechanisms for Human Environments

Wheeled mobile robots have been receiving continuous attention in various fields because of their stability, efficiency, and simple mechanisms. However, most of them require significantly larger occupied space than humans and have limited maneuverability in the environment for humans, such as crowded corridors, floor thresholds, ramps, and elevators. This letter presents a new wheel-leg mobile robot that combines the legs for changeable support polygon and mecanum wheels for holonomic motion. The robot has a human-like slim shape with 4 wheel-leg mechanisms, each of which has one 2-DOF leg frame and one mecanum wheel. To allow 2-DOF leg motion while maintaining the orientation of the mecanum wheels, a unique parallel link mechanism was devised. In order to achieve agile motion and impact and vibration absorption capability, a back-drivable high payload compound planetary gear was developed. The ground reaction force (GRF) compensation mechanism in each leg reduces the required payload of the actuators. The letter describes the detailed mechanical design of the robot and the actuators. The effectiveness of the proposed robot was verified in various experiments, fast omnidirectional motion test, a climbing test of a single step, and a motion test in the elevator with people.

Modelling of time-varying meshing stiffness under tooth wear condition for nonlinear dynamics in compound planetary gear set

Under tooth profile wear condition, with running time increasing, the tooth chord length of the gear tooth is thinner and the tooth profile is not involute profile any more, which results in the changes in amplitude and fluctuation of time-varying meshing stiffness. In this work, in order to reveal the influence of tooth profile wear on time-varying meshing stiffness, an analytical model for calculating the time-varying meshing stiffness under tooth wear condition is built and incorporated with a “translational-rotational” dynamic model of compound planetary gear set. Poincare section, the phase trajectory and bifurcation diagram are employed for analysis of periodic and chaotic motion. The results indicate that, tooth wear accumulation result in the reduction in the amplitude of meshing stiffness at the meshing region of double-pair teeth, but makes no difference in meshing stiffness for the meshing region of single-pair teeth. In order to avoid the system being in Chaos motions, under large tooth wear condition, the input speed should be avoided away from 3700 r/min-6725 r/min, so as to keep the system in a stable periodic motion state.

A Novel Wolfrom-Based Gearbox for Robotic Actuators

In many robotic applications, high torque density and highly efficient actuators are required to handle the high torque motion without hampering mobility through excessive weight and footprint. Traditionally, engineers designing actuators for these types of applications use high-speed electrical motors in combination with high-ratio speed reducers such as harmonic and cycloid drives or lever arms in order to achieve the required torques. However, these systems are not ideal since they suffer from one or more of the following limitations: high cost, load hysteresis, nonlinear behavior, and torque ripple. An alternative to achieving the required torque increase is using an interesting type of compound planetary gear trains (C-PGTs). In this article, a novel type of such a C-PGT, based on the Wolfrom topology, is presented. An extra degree of freedom is created, which can be used to increase the performance of the overall gearbox, i.e., increase its efficiency, reduce its inertia, increase its torque capability, etc. This modified Wolfrom is discussed in detail by deriving a general framework for the design of such a transmission system. This framework consists of listing the specific fitting conditions for such a Wolfrom planetary gear train, the derivation of an efficiency model based on the Rolling Power concept, and a load analysis to determine the weakest gearing element. Finally, a prototype is built to demonstrate the design framework and the feasibility of the Wolfrom variant. Additionally, the trend of the efficiency model is confirmed.

Effects of Vibration Isolator on Compound Planetary Gear Train with Marine Twin-Layer Gearbox Case: a Dynamic Load Analysis

This study aims to take the compound planetary gear train as an example to investigate how the vibration isolator affects the dynamic characteristics of the gear system. The dynamic parameters are obtained from the finite element model of the gearbox case with the vibration isolators by the substructure method. The lumped mass method is used to construct the systematic coupled dynamic model of the compound planetary gear train with the marine twin-layer gearbox case. The dynamic response of the coupled system is calculated by the numerical calculation method of the Fourier series. The number of vibration isolators negatively affects the bearing forces of the input shaft, output shaft, and planets. The influence of the number of vibration isolators on LSCs is different in the differential stage and the encased stage. When the vibration isolators stiffness is less than 200 N/μm, the stiffness of the vibration isolator has a significant effect on the bearing forces of the input shaft, output shaft, and planets. The increase in the stiffness of the vibration isolator would increase the LSCs of the differential stage and decrease the LSCs of the encased stage. The number and stiffness of the vibration isolator have influences on the bearing forces and the LSCs. Compared with the LSCs in the differential stage, the LSCs in the encased stage are more sensitive to the number and stiffness of vibration isolators.

Development of a Simulation Model for HMT of a 50 kW Class Agricultural Tractor

This study was conducted to develop a simulation model of a 50 kW class hydro mechanical transmission (HMT) tractor and to verify the model by comparing the measured and simulated data, including the axle torque, rotational speed, and power transmission efficiency. The platform of the HMT was composed of the engine, hydrostatic unit (HSU), compound planetary gear, range shift, spiral bevel gear, and final reduction gear. The HMT had three gear stages and a maximum forward speed of 40 km/h. To evaluate the performance of the HTM, a test bench was installed based on the engine of the HMT platform, and a simulation model was developed using 3D simulation software. To compare the results of the simulation, a bench test using the platform was performed according to the gear stages. The similarities between the measured and simulated data were analyzed using the t-test. As a result, there were no significant differences for the axle torque, rotational speed, and power transmission efficiency. Finally, the power transmission efficiency between the measured and simulated results was compared and analyzed using linear regression analysis to validate the accuracy of the simulation model. The trend of the power transmission efficiency between the measured and simulated results appeared to be similar in all sections, and we obtained a simulation model with the accuracy of an R-squared value of more than 0.97. In conclusion, the measured and simulated results were similar to each other. Considering the results of this study, it will be useful to develop the HMT tractor and to improve the power transmission efficiency for the optimal design.

A New Approach to Understanding Planetary Gear Train Efficiency and Powerflow

<div class="section abstract"><div class="htmlview paragraph">Understanding planetary gear efficiency is more involved than understanding efficiency of external gears because of the recirculating power that is inherent in planetary gear operation. There have been several publications going back several decades on this topic. However, many of these publications are mathematical in their approach and tend to be overlooked by practicing engineers. This paper brings a new, more visual and more intuitive approach to the problem. It uses lever diagrams, which have been a standard tool in the transmission engineer’s arsenal for almost four decades, to visualize the power flow and develop analytical expressions for the efficiency of simple and compound planetary gears. It then extends the approach to more complex gear trains.</div></div>

A dynamic tooth wear prediction model for reflecting “two-sides” coupling relation between tooth wear accumulation and load sharing behavior in compound planetary gear set

In planetary gear set, load sharing behavior determines the average amplitude of meshing force, so determines the tooth wear. Meanwhile, tooth wear accumulation increases the backlash, so affects the load sharing behavior. As a result, a “two-sides” coupling relation appears between load sharing behavior and tooth wear. In order to reveal this coupling relation, a static tooth wear prediction model for compound planetary gear set is employed to describe the wear distribution along tooth profile and backlash generated by tooth wear accumulation. Then, a “translational-rotational” lumped-parameter dynamic model of compound planetary gear set is built to calculate the eccentric load coefficient for each meshing pair, under the excitation from the backlash generated by tooth wear accumulation, transmission error, and other excitation. Based on the aforementioned two models, a dynamic tooth wear prediction model is put forward to reflect “two-sides” coupling relation between tooth wear accumulation and load sharing behavior in compound planetary gear set. Lastly, in order to improve the reliability, a 3D-diformable model is built to study the influence of tooth wear on load sharing. The results indicated that, with the system running and tooth wear increasing, under the condition of no-initial transmission error, tooth wear accumulation decreases the load sharing at meshing engagement and disengagement, and under the condition of initial transmission error, tooth wear accumulation improves load sharing behavior slightly.

Application of decision–making parametric structures in the analysis of a compound planetary gear

The design process of planetary gears can be divided into two main stages, i.e. conceptual design and construction, that is the preparation of construction documentation. In the first stage, the constructor has a very limited number of project data. In the case of a reduction or multiplier transmission these are usually output parameters (torque and speed), characteristics of the driving and the driven machine, Therefore, the stage of gearbox design must be supported by preliminary calculations, which supports the selection of the correct technical solution, leading to the stage of the structural design preparation. In the method of systematic search, we used an algorithm for generating induction decision trees, based on entropy growth as a method related to machine learning. In the next step, the decision-making parametric structures were employed. In the future, the presented solution will allow further analyses and syntheses such as checking the isomorphism of the proposed solutions, determining the validity of constructions and/or operating parameters of the analysed gears.

Mesh Phase Analysis of Encased Differential Gear Train for Coaxial Twin-Rotor Helicopter

Dynamic excitation caused by time-varying meshing stiffness is one of the most important excitation forms in gear meshing process. The mesh phase relations between each gear pair are an important factor affecting the meshing stiffness. In this paper, the mesh phase relations between gear pairs in an encased differential gear train widely used in coaxial twin-rotor helicopters are discussed. Taking the meshing starting point where the gear tooth enters contact as the reference point, the mesh phase difference between adjacent gear pairs is analyzed and calculated, the system reference gear pair is selected, and the mesh phase difference of each gear pair relative to the system reference gear pair is obtained. The derivation process takes into account the modification of the teeth, the processing, and assembly of the duplicate gears, which makes the calculation method and conclusion more versatile. This work lays a foundation for considering the time-varying meshing stiffness in the study of system dynamics, load distribution, and fault diagnosis of compound planetary gears.

Multi-Speed Transmission Mechanism Using a Compound Planetary Gear Set and Brakes

Today, the use of electric vehicles (EVs) is increasing. Electric motors, which are used as the power source in EVs, have better torque-speed characteristics than traditional engines. However, electric motors also have a low speed torque limitation; moreover, their energy efficiency at low speed is not very high, resulting in severe heat generation when climbing steep slopes. While it is better to use multi-speed transmissions in EVs, the complex structure of conventional multi-speed transmissions decreases the advantages of EVs. This paper proposes a multi-speed transmission mechanism that uses a compound planetary gear set and brakes; its simple structure and lack of a synchronizer make it suitable for EVs. The electric motor’s high controllability makes high-speed gear shifting possible because the motor’s teeth are always engaged. It is also possible to throw the motor out of gear or to put the brake on the output shaft. General equations for the reduction ratios are derived and a design possibility for the arbitrary reduction ratio is mentioned. A simple experimental setup is presented, demonstrating that the proposed multi-speed transmission mechanism is effective.