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As the key components of wind turbine, the weight of gear transmission system becomes larger and larger with the increasing power of wind turbine. Lightweight and high reliability has been the developing tendency for planetary gear transmission system for working reliability and reducing costs. A coupled nonlinear dynamics modeling for planetary ge...
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... to ISO 81400-4-2005: Wind turbines-Part 4 Design and Specification of Gearboxes, life expectancy is 20 years under the circumstance of meeting design reliability requirement of 0.99. Application factor and dynamic load factor are shown in Figure 6-15 under the circumstance when system reliability requirement is 0.99. ...
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Abstract
Gearboxes are widely used in wind turbine applications. Planet ge...
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Citations
... In this context, some authors have been interested in implementing the concept of robustness and reliability in the design phase [5,6]. The work presented by Y. M. Zhang et al [5] consists of analyzing the reliability of a pair of gears using the numerical perturbation method and reliability-based design theory. ...
Gear trains are widely used for power transmission in industrial mechanical systems. Taking into account uncertainties in the engineering design process represents a considerable industrial stake in controlling the robustness and reliability. This work consists of minimizing the weight of a pair of gears train by considering the different sources of uncertainty. An optimization technique based on a specific Particle Swarm Optimization algorithm (PSO) is developed to identify the optimal configuration that combines reliability with robustness. The propagation of uncertainty in the proposed method is performed with the Monte Carlo simulation. The design of a pair of gears is a compromise between weight, reliability, and robustness. Therefore, the developed algorithm allows optimization by taking into account the uncertain parameters constituting the pair of gears model while ensuring an acceptable compromise between reliability stability, and performance. In comparison to the concept generally used, the proposed approach offers lower weight and provides superior performance.KeywordsRobustnessReliabilityUncertaintyOptimization
... Xiang et al. [2020] further improved the dynamics model of a single-stage planetary gear plus two-stage parallel shaft gear system and focused on the effect of the support stiffness on the dynamic characteristics of the system. It can be found that the multistage planetary gear transmission (MPGT) system, as a gear transmission method widely used in high-power wind turbine, the current research is limited to the inherent characteristics and load sharing characteristics [Han et al., 2017;Dong et al., 2016;Ji et al., 2012;Wei et al., 2013], and there is still a lack of theoretical research on its chaos and impact characteristics. In addition, the vibration mechanism of the MPGT is complex and it is closely related to nonlinear dynamical behavior. ...
A dynamic modeling method for Multistage Planetary Gear Transmission (MPGT) is proposed based on the concept of integral planetary gearbox modeling. The integrated interaction of multiple nonlinear parameters is considered in the dynamic model. The time-varying mesh stiffness of each gear pair is calculated by the energy method. The effects of input torque, gear backlash, and meshing damping on the chaos and impact characteristics of the system are analyzed in detail. The results show that the dynamic behavior of the system is closely related to the Dynamic Meshing Force (DMF). When the system is in the states of chaos, bifurcation, and jumping, the DMF fluctuates violently, and the stability and reliability of the system are seriously affected. With the increase of input torque and meshing damping, the system exits chaos through the inverse period-doubling bifurcation path, which indicates that increasing the input torque and meshing damping can suppress the chaotic motion and enhance the stability of the system. The backlash has a significant effect on the nonlinear behavior and meshing impact characteristics of the system. When the backlash is small, the system is in bilateral impact, and the meshing impact tends to be stable as the backlash increases. In order to improve the vibration characteristics of the system, a slightly larger backlash is necessary. The results can be used to guide the dynamic characteristics design and vibration control of the MPGT.
... However, as the control mechanisms may be delayed in responding to the weaknesses that occur in case of sudden changes in the wind, this loading condition is considered more critical than the other condition [23]. Therefore, one of the objectives of this study is to create a wind profile and examine the gearbox weaknesses that may arise from this profile. ...
Planetary gear sets are utilized in various critical applications. Being one of these applications, investigation of wind turbine systems is essential to improve sub-systems such as planetary gearbox, yaw gear, and pitch system under different conditions. In this study, a new finite element model is proposed for obtaining the transient load on the gears of a planetary gearset, and examining the failure types. As an improvement, determination of critical loading scenario for gearset, modeling the blades as a link between the gearset and wind load, and differences between two different beam models are investigated. The model is simulated under reverse load condition which is caused by the sudden change of direction of the wind. The outcome of the simulations shows that the beam model, which takes into account shear deformation, performs within the expected levels according to the literature. Besides, by comparing the outputs of the simulation results, the failure of the gears under an extreme condition is estimated to be due to bending moment on the gear root rather than pitting on the gear tooth surface. As a recommendation for further research, it is suggested to consider reverse load condition in gear designs for wind turbines in order to better understand their behaviour.
... [1][2][3] Kubur et al. 4 proposed a dynamic model of a multi-shaft helical gear reduction unit formed by N flexible shafts, and studied the influence of bearing stiffness, shaft size, and other parameters on the vibration of the gearbox. Later, Wei et al. 5 established the coupled nonlinear dynamics model of a wind turbine planetary gear transmission system, and proposed a lightweight and reliability constrained optimization design method according to the sequential quadratic programming algorithm. Subsequently, Chang et al. 6 proposed a comprehensive coupled gearbox system dynamics model of a gear-shaft-bearing-shell system, which improved the accuracy of bearing response and thus more accurately estimated the radiation noise of the gearbox. ...
Aiming at noise problem of two-stage gearbox, this paper uses the panel acoustic contribution analysis (PACA) and response surface methodology to conduct structural-borne acoustics analysis and multi-objective optimization of gearbox. Using this optimization, optimal layout and parameters of the added ribs can be determined. The dynamic model of a spur gear-shaft-bearing system is built in consideration of the time-varying mesh stiffness, the time-varying bearing stiffness, and the flexibility of the shaft, while dynamic load of the bearing is obtained through solving the model. The dynamic load of bearings is considered as excitation to analyze the vibration and noise radiation characteristics of housing. Furthermore, acoustic transfer vector, modal acoustic contribution and PACA are used to select the region with the most acoustic contribution. The variable ribs structure model (VRSM) is established in this region. Finally, the VRSM are adopted to optimize the housing. The optimization model based on the peak sound pressure level (PSPL) and the ribs mass (R m ) is established by using response surface method. Through multi-objective optimization, the variable in VRSM can be modified or deleted to reduce the radiated noise of the gearbox. The optimization results demonstrate that the PSPL after optimization is decreased by 4.88 dB at frequency of 3130 Hz. At the same mass, the noise reduction effect of VRSM is 12% higher than that of standard rib. Therefore, the optimization effect of the housing structure is obvious. PACA-VRSM-RSM- NSGA-II technology provides a new research scheme for reducing the vibration and noise of the gearbox.
... Dong et al. [2016] discussed the load sharing behavior of two-stage planetary gear train plus one-stage parallel shaft gear transmission system and carried out experimental verification. Wei et al. [2013] established a coupled nonlinear dynamic model of two-stage planetary gear train plus one-stage parallel shaft gear transmission, induced the load factors of the system, and proposed an optimal design method for planetary gear transmission system. Ji et al. [2012] discussed the inherent characteristics of two-stage planetary gear train plus one-stage parallel shaft gear system. ...
A nonlinear dynamic model for a multistage planetary gear transmission system, which consists of two-stage planetary gear plus one-stage parallel shaft gear, is proposed. The time-varying meshing stiffness, comprehensive meshing errors and backlash between gear pairs are taken into account in the model, and the connections between the gear stages are characterized by coupling stiffness. The dimensionless vibration differential equations of the system are derived and solved numerically. By means of global bifurcation diagram, largest Lyapunov exponent (LLE), phase diagram and Poincaré map, the stability of the system is studied with the bifurcation parameters variation including excitation frequency and comprehensive meshing errors. The results demonstrate that the system presents strange attractors with rich forms under different parameter combinations. With the increase of the excitation frequency, the meshing state of the system changes, showing a complex motion and indicating the sensitivity of the system to external excitation. Under the variation of the bifurcation parameter of comprehensive meshing error, the complex dynamic behavior of the system is observed, it is found that the increase of comprehensive meshing error has a negative impact on the stability of the system.
... e latter was used in order to simplify the calculations in the reliability model of gears. Also Jing Wei et al. [ 9 ] presented an optimum design approach for the planetary gear transmission and included lightweight and reliability as constraints. eir results showed that the reliability of the optimized parameters was lower than that of the original one. ...
Uncertainties in design represent a considerable industrial stake. Controlling the reliability and robustness of a mechanical system at the level of design has become necessary in order to control these uncertainties. Using the theory of probabilistic design optimization, the present work reports on the application of the concept of reliability-based robustness on minimizing the weight of a planetary gear train (PGT). The optimum combination of reliability and robustness for the minimum weight of the PGT was found using an optimization algorithm based on Particle Swarm Optimization (PSO) and Monte Carlo Simulation (MCS). The algorithm was developed by combining the propagation of uncertainties with the optimization of the function objective within a single probabilistic model. The results show that a reliability-based robust design o ers a better alternative to the traditional deterministic design models. An equivalence between the proposed method and the deterministic method is established and approved.
... Gear transmission is the most important and widely used transmission in mechanical transmission. In particular, long-life precision gears are widely used in mechanical transmission systems with high reliability requirements, such as wind turbine gearboxes [1] and aero engines [2]. As the requirements Metals 2020, 10 for long-life precision gears are increasing, the requirements of machining accuracy, assembly accuracy and gear tooth modification are also growing, and these factors have a great influence on the tooth surface contact stress (TSCS) of gears. ...
Based on the three-dimensional (3D) finite element method (FEM) and Taguchi method (TM), this paper analyzes the tooth surface contact stress (TSCS) of spur gears with three different influence factors: tooth profile deviations (TPD), meshing errors (ME) and lead crowning modifications (LCM), especially researching and analyzing the interactions between TPD, ME and LCM and their degree of influence on the TSCS. In this paper, firstly, a 3D FEM model of one pair of engaged teeth is modeled and the mesh of the contact area is refined by FEM software. In the model, the refined area mesh and the non-refined area mesh are connected by multi-point constraint (MPC); at the same time, in order to save the time of the FEM solution on the premise of ensuring the solution’s accuracy, the reasonable size of the refined area is studied and confirmed. Secondly, the TSCS analyses of gears with one single influence factor (other factors are all ideal) are carried out. By inputting the values of different levels of one single factor into the FEM model, especially using the real measurement data of TPD, and conducting the TSCS analysis under different torques, the influence degree of one single factor on TSCS is discussed by comparing the ideal model, and it is found that when the influence factors exist alone, each factor has a great influence on the TSCS. Finally, through TM, an orthogonal test is designed for the three influence factors. According to the test results, the interactions between the influence factors and the influence degree of the factors on the TSCS are analyzed when the three factors exist on the gear at the same time, and it is found that the TPD has the greatest influence on the TSCS, followed by the lead crowning modified quantity. The ME is relatively much small, and there is obvious interaction between ME and LCM. In addition, the optimal combination of factor levels is determined, and compared with the original combination of a gear factory, we see that the contact fatigue performance of the gear with the optimal combination is much better. The research of this paper has a certain reference significance for the control of TPD, ME and LCM when machining and assembling the gears.
... The application factor K A and dynamic factor K V are usually used to determine the extent to which the actual load of the gear pair deviates from the nominal load. The expressions can be defined as [23] ...
For the better design and monitoring of gearboxes operating under nonstationary conditions, the dynamic interaction behavior of an electric motor drive multistage gear set is investigated in this study. Initially, dynamic mathematical models of an asynchronous motor and a multistage gear set are established by using the equivalent circuit method and the lumped parameter method, respectively. An electromechanical model coupling the asynchronous motor and the gearbox is subsequently developed, which is suitable for nonstationary conditions. The system transient responses under an impact external load are analyzed, and the mechanical torsional-vibration and electric current response are compared. Finally, the dynamic load propagation mechanism and the interaction effect on different gears are examined. The results demonstrate that the vibration frequencies of the multistage gearbox in steady and transient states both can be captured in the current. Electric current can be applied to reflect the external load variation and the internal vibration status of the driven gearbox under stationary or nonstationary conditions. The mutual excitation effects between adjacent gear pairs change the respective dynamic characteristics of the gears, and gears with small nominal loads are susceptible.
... Helical gear-shaft systems are ubiquitously used in the automobile [1] , wind energy [2] and robotics industries [3] due to their characteristics of stable transmission, high load capacity, and long life cycles. Compared with spur gears, the teeth of helical gears are set at an angle and take the shape of a helix, which allows two or three teeth of each gear to always be in contact with the pinion. ...
... The meshed-out tooth-face pair needs to be replaced by the meshing-in tooth-face pair to accurately capture the contacts between the gear pair. tc (1) tout (2) tc (2) tout (3) tc (3) tout (4) tc (4) tc (1) tc (2) Meshing-in moment ...
... The meshed-out tooth-face pair needs to be replaced by the meshing-in tooth-face pair to accurately capture the contacts between the gear pair. tc (1) tout (2) tc (2) tout (3) tc (3) tout (4) tc (4) tc (1) tc (2) Meshing-in moment ...
The dynamics of helical gear-shaft systems are characterized by three-dimensional (3D) meshing contacts that have significant variations in the location and size of the contact area, resulting in noise that is unavoidably transmitted to the gearbox through the shaft. Accurate and efficient predictions of the dynamic behaviors of helical gear and shaft are indispensable in reliable and cost-effective gearbox design. Available analytical methods, though computationally feasible, cannot consider multi-point contacts and uneven tooth-load distribution. In contrast, the finite element (FE) method provides a high-fidelity approach to compute the dynamic behaviors of a general gear-shaft system at high expenses of computation. This paper aims to establish a high-efficiency multibody dynamic model for 3D contacts in helical gear-shaft systems, in which the helical gear is pertinently represented under the framework of Arbitrary Lagrangian Eulerian formulation and the shaft is discretized by 3D Timoshenko beam elements. The computational efficiency is greatly improved through the following four steps. First, the low-frequency approximation technique is adopted to reduce the degrees of freedom (DOFs) resulting from the fixed boundary normal modes. Second, under the framework of ALE formulation, only the FE nodes of three meshing tooth-faces are defined as boundary nodes. Then, the dynamic equations and Jacobian matrix are simplified by ignoring the inertial forces associated with deformation. Finally, a two-step algorithm is adopted to accelerate the contact detection process. The accuracy and efficiency of the proposed method are demonstrated through five numerical tests with correlation to commercial nonlinear finite element software.
... Kubo and Kiyono [16] analyzed the effect of tooth form errors on the helical gear dynamics, and they assume a composite tooth form error with four types of shape. Wei et al. [17] established a coupled nonlinear dynamics model which is used for planetary gear transmission systems in wind turbines and incorporates the effects of the time-varying mesh stiffness, dynamic transmission error, gear mesh impact, and input varying load; thus, the transmission error changes as a sine wave with time. Case three: the errors are shown as random processes. ...
In the research of gear transmission, the vibration and noise problem has received many concerns all the times. Scholars use tooth modification technique to improve the meshing state of gearings in order to reduce the vibration and noise. However, few of researchers consider the influence of measured manufacturing errors when they do the study of tooth modification. In order to investigate the efficiency of the tooth modification in the actual project, this paper proposes a dynamic model of a helical gear pair including tooth modification and measured manufacturing errors to do a deterministic analysis on the dynamical transmission performance. In this analysis, based on the measured tooth deviation, a real tooth surface (including modification and measured tooth profile error) is fitted by a bicubic B-spline. With the tooth contact analysis (TCA) and loaded tooth contact analysis (LTCA) on the real tooth surface, the loaded transmission error, tooth surface elastic deformation, and load distribution can be determined. Based on the results, the time-varying mesh stiffness and gear mesh impact are computed. Taking the loaded transmission error, measured cumulative pitch error, eccentricity error, time-varying mesh stiffness, and gear mesh impact as the internal excitations, this paper establishes a 12-degree-of-freedom (DOF) dynamic model of a helical gear pair and uses the Fourier series method to solve it. In two situations of low speed and high speed, the gear system dynamic response is analyzed in the time and frequency domains. In addition, an experiment is performed to validate the simulation results. The study shows that the proposed technique is useful and reliable for predicting the dynamic response of a gear system.
