Planetary Transmission Research Articles

Dynamic Analysis of a Fault Planetary Gear System under Nonlinear Parameter Excitation

In order to facilitate lubrication and avoid the gear stuck due to thermal expansion, there needs to be a gap between the tooth profiles. As a strong nonlinear factor, the backlash will affect the motion state of the planetary gear system. When the gear failures occur, the motion state of the system will accordingly change. In this study, the meshing stiffness of the gear pair with tooth tip chipping fault is calculated by combining the analytic geometry method and the potential energy method. Then, a new nonlinear dynamic model including tooth backlash, time-varying mesh stiffness, and manufacturing error is established to study the dynamic response of the system. The equations of motion are derived by the Lagrangian method and solved by the numerical integration method. Taking the excitation frequency and tooth backlash as the variation parameters, respectively, the dynamic characteristics of the system are analyzed by comparing the global bifurcation diagrams between the health system and the fault system, and the path of the system into chaos is revealed. At the same time, the local characteristics of the system are revealed through the phase diagrams and Poincaré maps. The results show that with the variation of excitation frequency and tooth backlash, the fault system presents a more complex motion state. This study can provide the theoretical support for dynamic design and fault diagnosis of planetary gear transmission systems under the environment of gear fault-prone.

Semi-numerical analysis of a two-stage series composite planetary transmission considering incremental harmonic balance and multi-scale perturbation methods

Abstract. This study conducts an analytical investigation of the dynamic response characteristics of a two-stage series composite system (TsSCS) with a planetary transmission consisting of dual-power branches. An improved incremental harmonic balance (IHB) method, which solves the closed solution of incremental parameters passing through the singularity point of the analytical path, based on the arc length extension technique, is proposed. The results are compared with those of the numerical integration method to verify the feasibility and effectiveness of the improved method. Following that, the multi-scale perturbation (MsP) method is applied to the TsSCS proposed in this subject to analyze the parameter excitation and gap nonlinear equations and then to obtain the analytical frequency response functions including the fundamental, subharmonic, and superharmonic resonance responses. The frequency response equations of the primary resonance, subharmonic resonance, and superharmonic resonance are solved to generate the frequency response characteristic curves of the planetary gear system (PGS) in this method. A comparison between the results obtained by the MsP method and the numerical integration method proves that the former is ideal and credible in most regions. Considering the parameters of TsSCS excitation frequency and damping, the nonlinear response characteristics of steady-state motion are mutually converted. The effects of the time-varying parameters and the nonlinear deenthing caused by the gear teeth clearance on the amplitude–frequency characteristics of TsSCS components are studied in this special topic.

Data-driven dictionary design–based sparse classification method for intelligent fault diagnosis of planet bearings

Planet bearings have remained as the challenging components for health monitoring and diagnostics in the planetary transmission systems of helicopters and wind turbines, due to their intricate kinematic mechanisms, strong modulations, and heavy interferences from gear vibrations. To address intelligent diagnostics of planet bearings, this article presents a data-driven dictionary design–based sparse classification (DDD-SC) approach. DDD-SC is free of detecting the weak frequency features and can achieve reliable fault recognition performances for planet bearings without establishing any explicit classifiers. In the first step, DDD-SC implements the data-driven dictionary design with an overlapping segmentation strategy, which leverages the self-similarity features of planet bearing data and constructs the category-specific dictionaries with strong representation power. In the second step, DDD-SC implements the sparsity-based intelligent diagnosis with the sparse representation–based classification criterion and differentiates various planet bearing health states based on minimal sparse reconstruction errors. The effectiveness and superiority of DDD-SC for intelligent planet bearing fault diagnosis have been demonstrated with an experimental planetary transmission system. The extensive diagnosis results show that DDD-SC can achieve the highest diagnosis accuracy, strongest anti-noise performance, and lowest computation costs in comparison with three classical sparse representation–based classification and two advanced deep learning methods.

Dynamic characteristics analysis of planetary gear system with internal and external excitation under turbulent wind load.

According to the working characteristics of a 1.5 MW wind turbine planetary gear system under complex and random wind load, a two-parameter Weibull distribution model is used to describe the distribution of random wind speed, and the time-varying load caused by random wind speed is obtained. The nonlinear dynamic model of planetary gear transmission system is established by using the lumped parameter method, and the relative relations among various components are derived by using Lagrange method. Then, the relative relationship between the components is solved by Runge Kutta method. Considering the influence of random load and stiffness ratio on the planetary gear transmission system, the nonlinear dynamic response of cyclic load and random wind load on the transmission system is analyzed. The analysis results show that the variation of the stiffness ratio makes the planetary gear have abundant nonlinear dynamics behavior and the planetary gear can get rid of chaos and enter into stable periodic motion by changing the stiffness ratio properly on the premise of ensuring transmission efficiency. For the variable pitch wind turbine, the random change of external load increases the instability of the system.

Stochastic dynamic load-sharing analysis of the closed differential planetary transmission gear system by the Monte Carlo method

The closed differential planetary transmission system features a high speed-ratio, and a compact structure for transmitting power through a dual-path. Further, the power is usually shared unevenly among the planetary/star gears for manufacturing error. Furthermore, the dual-path causes power confluence aggravating uneven load distribution, and leading to transmission failure. In this regard, a widely used analysis method is adopting the maximum tolerance for critical parameters. However, manufacturing error are stochastic in engineering practice. Thus, this study investigates error randomness in dynamic load-sharing behavior. First, a stochastic multi-body dynamics model of a closed differential planetary transmission is established. Next, the sampled and stochastic distributions of the load-sharing behavior are obtained and compared with the Taguchi method. Then, the effect of manufacturing and assembling the tolerance zone on the load-sharing performance is investigated. Lastly, the experiment for the main gearbox of a MW wind turbine is used to verify the results determined using the stochastic errors. Notably, the method using the maximum errors overestimates the load-sharing coefficients by 92% for the differential stage, and by 100% for the closed stage.

Numerical calculation and experimental measurement for gear mesh force of planetary gear transmissions

In this paper, we propose a numerical method to calculate the dynamic mesh forces of planetary gear transmissions (PGTs). In this model, the effects of addendum modification are included in the time-varying mesh stiffness (TVMS) and then the influence of TVMS and relative mesh phase on the dynamic mesh forces are considered in the proposed model. To verify the proposed model, an experimental method is proposed to measure the dynamic ring-planet mesh forces by using gear tooth root-fillet strain signals. Static mesh experiments and dynamic mesh experiments are carried out to obtain the strain signals. To measure the dynamic mesh force, the loaded tooth contact analysis (LTCA) method and quasi-static experiments are carried to determine the coefficient matrix which is used to descript the relationship between the mesh force and tooth root-fillet strain. Finally, calculated mesh forces and measured forces are compared and discussed. Results indicate that the proposed experimental method can effectively measure the dynamic ring-planet mesh forces, and the numerical mesh forces agree well with the measured mesh forces.

A Bayesian-reliability based multi-objective optimization for tolerance design of mechanical assemblies

Tolerances significantly affect the assemblability of components, the product's performance, and manufacturing cost in mechanical assemblies. Despite the importance of product reliability assessment, the reliability-based tolerance design of mechanical assemblies has not been previously considered in the literature. In this paper, a novel method based on Bayesian modeling is proposed for the tolerance-reliability analysis and allocation of complex assemblies where the explicit assembly functions are difficult or impossible to extract. To reach this aim, a Bayesian model is developed for tolerance-reliability analysis. Then, a multi-objective optimization formulation is proposed for obtaining the optimum tolerances of components to minimize cost and maximize product performance. Subsequently, Non-dominated Sorting Genetic Algorithm II (NSGA-II) is employed for solving multi-objective optimization. Then, the enhanced TOPSIS is used to find the best optimum tolerances from the optimum Pareto solutions. Using the importance vector concept, a sensitivity analysis approach is used to determine the effects of design variables on the product reliability level and improve assembly reliability to the desired level. Finally, to exhibit the applicability of the proposed method, a transmission planetary gear system is considered, and the obtained results are compared and discussed for verification.

ARES.* V. No Evidence For Molecular Absorption in the HST WFC3 Spectrum of GJ 1132 b

Abstract We present a study on the spatially scanned spectroscopic observations of the transit of GJ 1132 b, a warm (∼500 K) super-Earth (1.13 R ⊕) that was obtained with the G141 grism (1.125–1.650 μm) of the Wide Field Camera 3 (WFC3) on board the Hubble Space Telescope. We used the publicly available Iraclis pipeline to extract the planetary transmission spectra from the five visits and produced a precise transmission spectrum. We analyzed the spectrum using the TauREx3 atmospheric retrieval code, with which we show that the measurements do not contain molecular signatures in the investigated wavelength range and are best fit with a flat-line model. Our results suggest that the planet does not have a clear primordial, hydrogen-dominated atmosphere. Instead, GJ 1132 b could have a cloudy hydrogen-dominated atmosphere, have a very enriched secondary atmosphere, be airless, or have a tenuous atmosphere that has not been detected. Due to the narrow wavelength coverage of WFC3, these scenarios cannot be distinguished yet, but the James Webb Space Telescope may be capable of detecting atmospheric features, although several observations may be required to provide useful constraints.

A New Methodology for Multistage Multispeed Planetary Transmission Design Based on Geometry

Abstract In the planetary automatic transmission design, efficiency is one of the primary performance indicators determining the final selection from multiple candidates. However, efficiency evaluation is the last step of conceptual design, thereby causing the trial result is often known at the end of the design. A new methodology based on geometry is presented for multistage planetary automatic transmission design, ranging from clutching sequence synthesis to efficiency evaluation. The emphasis is placed on a unified model for design steps with different analysis principles to predict power transfer characteristics earlier. Some new results and improvements are also presented, such as general speed ratio (SR) change law, simultaneous traversal of different shift types, and the efficiency formula. An example is provided to illustrate the applicability to a 3-DOF planetary automatic transmission and shows that early identification of power transfer characteristics can lock in necessary subsequent calculations, thereby eliminating unnecessary analysis and speeding up the design process.

Semi-numerical analysis of a two-stage series composite planetary transmission considering IHB and MsP methods

This study conducts an analytical investigation of the dynamic response characteristics of a two-stage series composite system (TsSCS) with a planetary transmission 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 to verify the feasibility and effectiveness of the improved method. Following that, the multi-scale perturbation (MsP) method is applied to the TsSCS proposed in this paper. The frequency response equations of the primary resonance, subharmonic resonance, and superharmonic resonance are solved to generate the frequency response characteristic curves of the planetary transmission system in this method. A comparison between the results obtained by the MsP method and the numerical integration method proves that the former is ideal and credible in most regions. Considering the parameters of TsSCS excitation frequency and damping, the nonlinear response characteristics of steady-state motion are mutually converted. The effects of the time-varying parameters and the nonlinear deenthing caused by the gear teeth clearance on the amplitude-frequency characteristics of TsSCS components are studied in this special topic.

Analysis of Dynamic Characteristics of the Multistage Planetary Gear Transmission System with Friction Force

Multistage planetary gear transmission system has been widely utilized in engineering practice due to the salient characteristics, such as high bearing load and large speed ratio. This paper addresses a two-stage planetary gearbox and establishes a system coupling torsional dynamical model which considers the time-varying mesh stiffness, friction forces, and interstage coupling factors. Meanwhile, the friction and lubrication states are classified to comprehensively analyze the calculation of friction coefficients under different conditions. Considering the time-varying influence of friction on the tooth surface under the condition of fluid lubrication, the vibration response under parametric excitation is solved by a numerical method. A multistage planetary transmission test bench is built in the back-to-back form so as to test the vibration of the two-stage planetary gearbox. It shows that the simulation results of the dynamical model are consistent with the test data. Consideration of the calculation of friction on the tooth surface and the friction coefficients is helpful for the establishment of the more accurate dynamical model and lays the foundation for the structural design, fault diagnosis, and dynamic optimization of the multistage planetary gear transmission system.

Planetary gear transmissions load sharing measurement from tooth root strains: Numerical evaluation of mesh phasing influence

The present work proposes a numerical approach to the problem of the calculation of the load sharing in planetary transmissions by measuring the strains in the root of the sun gear teeth, a rather common experimental procedure. The approach to model the virtual strain gauges is described in detail. This technique is modelled mimicking the experimental measuring procedure. The presented technique is employed in different simulation scenarios including in-phase and sequentially phased transmissions. Moreover, various tangential position errors are included. These configurations cover the most common scenarios in industrial applications. From these scenarios, the results show discrepancies between the real load sharing and the measured data. The nature of these discrepancies is studied in depth from the geometrical point of view.

Down shift control with power of planetary-type automatic transmission for a heavy-duty vehicle

Gear-shift with power belongs to one of the most important advantages of the planetary transmission for heavy-duty vehicles. However, there is no power transmitted from the engine to the driving wheels since the accelerator pedal is released completely in the most down shifts, and the previous research mainly focused on up shift with power corresponding. In contrast, down shift with power can be useful for the improvement of shift quality as well as vehicular safety and drivability for heavy-duty vehicles. The model of power train is build and a control methodology for down shift with power is presented based on the modelling dynamic analysis. Adaptive sliding mode control for better robustness is formulated and the turbine speed with fixed changing rate is chosen to be the controlling ideal reference trajectory. Finally, heavy-duty vehicle with full load based tests of climbing in mountains are conducted, and the results indicate that the proposed down shift with power control strategy can improve the shift quality and the vehicular performance.

Coordinated Torque, Energy and Clutch Control Strategy for Downshifts in P2 Parallel xHEV Powertrains

<div class="section abstract"><div class="htmlview paragraph">This paper describes a methodology for investigating the controls coordination of clutch and propulsion torque sources relative to clutch energy, electrification energy consumption and output torque profile for offgoing controlled downshifts in P2 parallel xHEV powertrain configurations. The focus is on an 8 speed planetary automatic transmission, but the approach is equally applicable to any powerflow design with clutch-to-clutch shifting. The modeling technique is for an overall control strategy relative to achieving a targeted transmission input speed profile. A reduced order model of the transmission system is presented that accounts for input shaft acceleration and compensation of inertial contributions to offgoing clutch torque and transmission output torque. The coordinated control of offgoing clutch, engine and P2 electric motor torques are explored in the context of power on and off downshifts for clutch energy, P2 energy consumption and output torque trajectory that directly translates to responsiveness and/or perceived shift quality. The presence of a torque converter and lockup clutch and the influence of the lockup clutch state control on downshifting coordination and torque disturbance is also incorporated in the analysis. Potential improvements in downshift response, clutch controllability and output torque trajectory are provided for the particular 8 speed transmission powerflow considered. The methodology presented can easily be applied to any clutch-to-clutch transmission architecture and powerflow, whether planetary, dual clutch or other.</div></div>

A New Health Condition Detection Method for Planetary Gears Based on Modified Distributed Compressed Sensing and Multiscale Symbol Dynamic Entropy

Planetary gear transmission system is an important transmission part of large machinery and is prone to failure. Aiming at the problem of how to extract fault information from vibration signals of nonlinear and nonstationary planetary gearboxes, a performance degradation evaluation index of planetary gearboxes based on improved distributed compressed sensing and modified multiscale symbolic dynamic entropy (DCSMDE) is proposed. DCSMDE combines distributed compression sensing with modified multiscale symbol dynamic entropy and solves the problem of strong nonlinearity and strong vibration signal coupling of the planetary transmission system from the homologous signals of multiple sensors. A distributed compression sensing parameter optimization algorithm based on Rényi entropy is proposed, which uses improved distributed compression sensing technology to simultaneously sample, compress, and denoise the multisource vibration data of rotating machinery. DCSMDE is used to calculate the reconstructed signal, extract the features with higher recognition characteristics, and use the change trend of the DCSMDE value to judge the working status of the planetary gearbox. Experimental results show that DCSMDE can be applied to dynamic evolution and fault identification of mechanical systems and accurately classify actual fault signals. It provides a new idea for the classification of planetary gear faults and the recognition of performance degradation.

Characteristics analysis of the new flexible ring gear for helicopter reducer

As a key component of the vibration generation and transmission of planetary transmission system, the design of ring gear will directly affect the vibration of the system. After considering the advantages and disadvantages of the traditional ring gear structure, the new flexible ring gear was designed by scholars and applied to helicopter reducer. There is a dearth of reported analysis in the meshing characteristics of the new flexible ring gear, which leads to the blind selection of the ring gear. By building an accurate parametric finite element model, the meshing characteristics of the new flexible ring gear and the difference in dynamic characteristics between the new flexible ring gear and the traditional ring gear are obtained. The analysis shows that the new ring gear is superior to the traditional ring gear in many aspects, but it also has the characteristic of unbalance loading on the tooth surface. In addition, a test method is proposed to accurately measure the load sharing coefficient and dynamic load factor of planetary transmission and the simulation results of flexible ring gear are verified by comparison.

Dual-Motor Planetary Transmission to Improve Efficiency in Electric Vehicles

Electric cars are typically subject to highly variable operational conditions, especially when they drive in urban environments. Consequently, the efficiency of the electric motors may degrade significantly, possibly leading to lower autonomy and higher running costs. Latest advances in power electronics and motion control have paved the way to the development of novel architectures of full electric power transmissions. In this paper, a dual-motor solution is proposed where two smaller motors are coupled via a planetary gear, in contrast to the standard configuration that uses one larger motor directly connected to the drive wheels with a fixed ratio reducer. The dual-motor architecture guarantees that both motors operate in the vicinity of their optimal working range, resulting in a higher overall energy efficiency. The technical requirements and the control strategy of the dual-motor system are selected through a parametric optimization process. Results included were obtained from extensive simulations performed over different standard driving cycles, showing that the dual-motor power transmission generally outperforms the single-motor counterpart with an average efficiency improvement of about 9% that is reached in both the power delivery and regeneration stage.

A magnetorheological fluid based planetary gear transmission for mechanical power-flow control

Power transmission for mechanical systems often involves the use of clutching- or dissipative-elements to protect drive systems and provide steady output power. As standard implementations in motor-driven systems, these devices operate passively or in discrete states, providing limited controllability to the power output. This paper presents a magnetorheological-fluid-based differential (planetary) gear transmission which serves to variably couple motor power through a sun gear input to a load affixed to a planet carrier output. This is achieved both rapidly and continuously through controlled slippage between the ring gear of the device and its casing. Compared to conventional MR clutches, the unique functionality of the differential gearbox enables use of an MR brake with lower inertia than an in-line clutch. Through control of current supplied to the energizing electromagnet of brake component of the transmission, simple and reversible governing of output torque and speed is achieved. This behaviour is modelled and verified through testing, showing a 349% variation in brake torque for constant speed tests from the off state to the maximum capacity of the device, with a 262% variation in brake torque under a harmonic input displacement also observed. The versatility of the device demonstrated through PID speed and torque control.

The atmosphere of HD 209458b seen with ESPRESSO

We observed two transits of the iconic gas giant HD 209458b between 380 and 780 nm, using the high-resolution ESPRESSO spectrograph. The derived planetary transmission spectrum exhibits features at all wavelengths where the parent star shows strong absorption lines, for example, Na I, Mg I, Fe I, Fe II, Ca I, V I, Hα, and K I. We interpreted these features as the signature of the deformation of the stellar line profiles due to the Rossiter-McLaughlin effect, combined with the centre-to-limb effects on the stellar surface, which is in agreement with similar reports recently presented in the literature. We also searched for species that might be present in the planetary atmosphere but not in the stellar spectra, such as TiO and VO, and obtained a negative result. Thus, we find no evidence of any planetary absorption, including previously reported Na I, in the atmosphere of HD 209458b. The high signal-to-noise ratio in the transmission spectrum (~1700 at 590 nm) allows us to compare the modelled deformation of the stellar lines in assuming different one-dimensional stellar atmospheric models. We conclude that the differences among various models and observations remain within the precision limits of the data. However, the transmission light curves are better explained when the centre-to-limb variation is not included in the computation and only the Rossiter-McLaughlin deformation is considered. This demonstrates that ESPRESSO is currently the best facility for spatially resolving the stellar surface spectrum in the optical range using transit observations and carrying out empirical validations of stellar models.

PERSPECTIVES OF CYCLOID TRANSMISSION

In modern mechanical engineering, transmissions with the use of an involute tooth profile are widespread. However, one of the main disadvantages of these transmissions is that they exposure to wear. In this study, research on the cycloid profile is conducted as an alternative option. Cycloid profiles are one of the profiles applied to the teeth in order to transmit motion. Although cycloid profiles are mainly used in instrumentation, satellites are made of cycloid profile in planetary gears. Cycloid profile teeth are less exposed to wear during operation. Practically, the shape of cycloidal teeth does not allow them to break, so there is no bending deformation in the teeth. In planetary gear transmission, the satellites are usually made of a cycloid profile. Cycloid profile teeth are exposed to less wear. Currently, planetary gear reducers are widely used mainly in the oil industry, drilling equipments, in the lifting mechanisms, gearboxes, on chain conveyors, rotary tables, in robotics, manufacturing, mechanical and chemical engineering fields and so on. The increased load capacity of the cycloid pinion gears is due to the multi-pair contact surface and it has a superior adhesion profile than the involute profile. The loading schemes of cycloidal and evolvent profile teeth shows that the normal force in contact Fn and its dangerous section on the tooth of the cycloidal profile is much less than in the case when the tooth has an involute profile. This is due to the fact that with cycloid profile transmission the number of teeth simultaneously transmitting the load is significantly greater than when implementing the same transmission with involute teeth. Cycloid profile gear reducers can be considered as a modern solution to current requirements such as high efficiency, smooth and quiet work, ability to accept short-term maximum loads, small overall size, minimum technical requirements etc. The simulation of the real load conditions and interference generated during the rotation of the shaft was developed in Solidworks in order to determine the contact stresses and the contact areas resulting from these stresses of the teeth of the gear and satellites of cycloid profile planetary gear reducers. This simulation determines the values of the teeth involved in the contact, the interference of those teeth, the contact areas and the contact stresses generated in these areas, depending on the angle of rotation of the shaft. The profile of the proposed teeth allows to achieve the minimum size with the maximum transmission ratio. Keywords: cycloid profile, cycloid transmission, planetary reducer, interference, simulation, contact area.