Multibody dynamics model of the cycloidal gearbox with uniform discretization of the cycloidal wheel profile

In a modern wind turbine, the gearbox is an expensive and fault-prone subsystem. Currently, condition monitoring, based on comparison of data of healthy baseline measurement and online measurement, followed by feature analysis and decision making, is the main approach of diagnosis and prognosis. Although having been employed in many practical implementations, such methods have limitations. For example, a huge database is needed when operating conditions change and normal variations are significant. Traditionally, first-principle-based modeling of gearboxes is considered very challenging, primarily due to their dynamic characteristics that exhibit time-periodicity and encompass a very wide frequency range. In this research, aiming at achieving the predictive modeling capability, a lumped-parameter model of a two-stage laboratory gearbox testbed is constructed based on the assumed mode method. This model can characterize the gearbox dynamic effects including the time-varying mesh stiffness and backlash. The Floquet theory and harmonic balance method are then applied to analytically investigate the system dynamics, where the eigenvalues of the time-periodic gearbox are extracted and correlated to the spectral analysis results of the time-domain response prediction. This modeling approach and the associated analysis lay down a foundation for establishing hybrid dynamic model of complex gearbox systems which will further be utilized in model-based diagnosis and prognosis.

This paper focuses on creating a virtual model of mechanical gearbox used in medium-sized terrain vehicle using MSC.Adams software. This software is regarded as the most common and effective tool to simulate the gearbox as multibody system and to record and analyse the vibration signal from the gearbox. The paper makes an overview of modelling and simulation and performs an analysis with frequency spectrum. The paper demonstrates that it is possible to simulate vibration signals through the model of the gearbox created in 3D CAD software and then analyse in multi-body dynamics software MSC.Adams. Successful application of the virtual model not only help us decrease the cost of design work, but also help us identify the patterns of the vibration signal and the relations between the signal and the technical condition of the gearbox. The goal is to create a virtual model of a mechanical gearbox. In MSC.Adams, the vibration values of the rotating components can be detected in different gears. These values are then analysed and evaluated. The result is a simulation of fault states and identification of vibration frequencies for practical applications.

The cycloid drive usually has a cycloidal wheel meshing with pins to achieve transmission. The profile of the cycloidal wheel is generally a curve derived from an epitrochoid. This paper presents two design types of cycloid drive, the cycloidal wheel profile of one is internal offset of epicycloid and the other is external offset of hypocycloid. Parametric 3-D models of the two design types are constructed in AutoCAD. Dynamics simulation is carried out using machinery system dynamics simulation technology, and the correctness of the dynamics model is verified by the motion curve. The dynamic meshing force between the cycloidal wheel and the pins of the two design types is solved, and transmission characteristics are compared. The results show that the hypocycloidal drive design produces more stable output speed, and can improve meshing force.

Planetary gearbox is a complex power transmission system which contains a large number of nonlinear contact interfaces and coupled vibration transfer paths. The vibration mechanism of planetary gearbox is very complicated and it's difficult to accurately describe its running state by vibration signals. In this paper, a nonlinear multibody dynamic model of planetary gearbox is proposed. Based on the bearing's parameters, the simulated response signal of Inner ring fault is calculated and transformed into fault excitation force. Based on SIMPACK software, the vibration responses of the gearbox model with bearing fault excitation force are obtained. To verify the simulation results, vibration signals at 4 different monitoring points of an actual planetary gearbox with bearing inner ring fault are analysed. The bearing fault characteristic frequency on medium-speed shaft is detected. Finally, the vibration responses of the actual planetary gearbox and the multibody dynamic model are compared. It shows that the main frequency components of the simulated vibration response agree well with the experimental results. The dynamic model of gearbox in this paper can provide guideline for the fault diagnose of planetary gearbox.

Compared with other speed reducers, the two-stage cycloidal planetary one also known as RV reducer has higher precision, higher mechanical efficiency, higher loading capacity as well as long service life. These characteristics make it attractive for industrial applications, especially for robotics applications and machine tools, where high precision and large torque transmission are required. The traditional RV reducer uses cycloidal drive which is comprised of the cycloidal wheel and the pins. It has some disadvantages in the pin design, because of small clearance between the pin and the cycloidal wheel, the collision between the pin and the cycloidal wheel may lead to unstable stress in the key parts and output velocity fluctuation. This paper presents an innovative cycloidal planetary reducer using internal meshing principle instead of external meshing between cycloidal wheel and pins in traditional RV reducer. In the new design of the reducer, the internal teeth with cycloidal profile are processed inside the reducer housing, meshing with two pin holders which are placed at the inner side of the cycloidal teeth to achieve transmission. The pin holder is a new integral structure of pins integrated on a round plate. Then a comparison study is conducted through establishment of system dynamics analysis. The transmission characteristics and meshing force of both the new type of reducer and the traditional RV reducer are analyzed under the same condition of reduction ratio. The results show the new reducer improves on these shortcomings, its transmission performance is competitive as compared to traditional RV reducer. What’s even better is that its output speed is more stable, and the contact force between the pin position on the pin holder and the internal cycloidal teeth inside the reducer housing is smaller, as well as the contact frequency is obviously decreased.

In this paper a versatile analysis of the cycloidal gearbox vibrations and the resonance phenomenon was performed. The objective of this work was to show resonance phenomenon and vibrations study in the multibody dynamics model and in the finite element model of the cycloidal gearbox. The output torque was analyzed as a function of the external sleeves stiffness. The results from the multibody dynamics model were verified in the finite element model using natural frequency with load stiffening, direct frequency response and direct transient response analyses. It was shown that natural frequencies of the cycloidal gearbox undergo changes during motion of the mechanism. The gearbox passes through the thresholds of the increased vibration amplitudes, which lead to excessive wear of the external sleeves. The analysis in the multibody dynamics model showed, that the increase in the external sleeves stiffness increases frequency of the second-order fluctuation at the output shaft. Small stiffness of the external sleeves guarantees lower frequency of the second order vibrations and higher peak-to-peak values of the output torque. The performed research plays important role in the cycloidal gearbox design. This work shows gearbox dynamics problems which are associated with wear of the external sleeves.

Dynamics simulations with faults can elucidate fault vibration characteristics, yet the vibrational properties of the quay crane lifting gearboxes under dynamic load excitation remain unclear. Based on multi-body dynamics theory, a multi-body dynamical model of the quay crane gearbox is established, simulating dynamic load excitation caused by cables and containers during the operation of a quay crane. The vibration responses under various working conditions and load types of different gear states are analyzed, and the corresponding fault frequency features are extracted by envelope spectrum. Simulations indicate that local gear faults enlarge the amplitude of gearbox vibrations, inducing the phenomenon of gear mesh frequency and its harmonics modulated by gear fault frequency. Based on these studies, a testbed for the quay crane gearbox is constructed. The experiment verifies the accuracy of the dynamic model and reveals that the simulation signal of load-as-dynamic-load is more consistent with reality than static load. The results provide a basis for fault diagnosis of quay crane lifting gearboxes under dynamic load, and can offer simulation data support for intelligent diagnosis models lacking fault samples.

In the following investigation the modeling of a shaft machine system is discussed for the hybrid propulsion of a Ship. The system consists of an Internal Combustion Engine (ICE), a Doubly Fed Induction Machine (DFIM) serving as motor (whereas capable of working in four quadrants), and a planetary gear box which connects the ICE and the DFIM to the propeller for hybrid propulsion. The full dynamic model of the planetary gear box is taken into account, comprising both rotational and translational modes for the gears. The dynamic model of the planetary gear box is being solved by employing dimensionless parameters in order to mitigate the problem related to the difference of the magnitude between stiffness and damping coefficients. The total approach and the mathematical models adopted in this study, particularly for the mechanical system aspires to the development of a well established basis for studying the interactions between the electrical and mechanical subsystems. In the future the dynamics of roller elements and thrust bearings will also be included.

Multibody dynamical modeling of the FPSO soft yoke mooring system and prototype validation

The combat vehicle gearbox, during the operation, generates vibration signals being related to the technical condition of gearbox. The analysis of the vibration signal could be used to determine accurately the behaviour of gearbox. Along with the development of the computer technology, the multi-body dynamic solution has been used widely to simulate, analyse, and determine the technical condition of gearbox. The purpose of this paper is to introduce the dynamic model of combat vehicle gearbox, and the simulation process based on the multi-body dynamic software, namely MSC.ADAMS. This proposed model allows the detection of failure conditions of individual gears and bearings in the gearbox. In this way, the fault conditions of the individual transmission components are identified. In the future, we would like to include a material wear module in the model, and we would like to model the life of the gearbox. We assume that we would also carry out accelerated tests of the gearbox to verify validity.

Existing studies on the dynamic characteristics of planetary gearboxes are generally based on traditional modeling methods. The models were idealized because of various uncertain factors that affect the dynamic characteristics of the planetary gearbox. The influence of non-mechanical components, such as driving motors, on dynamic analysis, is often ignored. Digital twin technology can not only simulate the data characteristics of physical entities to realize the real-time state evaluation and fault diagnosis of complex equipment but also reflect the entity characteristics of the modeled object completely. Therefore, a digital twin multi-body dynamic model of a planetary gearbox is established for detecting the combined fault of the sun gear missing teeth and the planetary gear missing teeth or pitting under different working conditions. The dynamic characteristics of a planetary gearbox subjected to electromechanical coupling were studied. The sun gear fault frequency, planetary gear fault frequency, and both related modulation frequencies appear in the experiment, and the corresponding fault characteristic frequencies also appear in the digital twin simulation. The validity of the proposed model was experimentally verified. Finally, the root-mean-square index was used to analyze the fault sensitivity of the traditional and digital twin models. The results show that the fault diagnosis effect of the digital twin model has a significant advantage, thus verifying the necessity of considering the effect of electromechanical coupling on the dynamic characteristics of the planetary gearbox.

Vibration-based methods has been widely used for diagnosing tooth root crack fault in planetary gearbox. Compared to the traditional transverse vibration signal, the torsional vibration signal is theoretically free from the modulation effect by time-varying transfer paths, so it has simple frequency contents to extract fault signature easily. In this paper, torsional vibration signal which is extracted in dynamic simulation models, is analyzed to diagnose tooth root crack fault. Firstly, a rigid-flexible coupling model of a healthy planetary gearbox is constructed and verified. The model can obtain a fairly accurate result with much low time cost. Then, based on model of healthy planetary gearbox, three typical crack fault models are constructed. This is aimed at extracting dynamic response of fault planetary gearboxes. Finally, transverse signals and torsional signals are analyzed to diagnose tooth root crack fault. The results obtained indicate that it is an effective method to diagnose planetary gearbox crack fault via torsional vibration signal analysis, and provide a theoretical reference for diagnosis of tooth root crack failure in planetary gearbox.

In this paper the analysis of backlash influence on the spectrum of torque at the output shaft of a cycloidal gearbox has been performed. The model of the single stage cycloidal gearbox was designed in the MSC Adams. The analysis for the excitation with the torque and the analysis with constant angular velocity of the input shaft were performed. For these analyses, the amplitude spectrums of the output torque for different backlashes was solved using FFT algorithm. The amplitude spectrums of the combined sine functions composed of the impact to impact times between the cycloidal wheel and the external sleeves were computed for verification. The performed studies show, that the backlash has significant influence on the output torque amplitude spectrum. Unfortunately the dependencies between the components of the spectrum and the backlash could not be expressed by linear equations, when vibrations of the output torque in the range of (350 Hz – 600 Hz) are considered. The gradual dependence can be found in the spectrum determined for the combined sine functions with half-periods equal impact-to-impact times. The spectrum is narrower for high values of backlash.

ABSTRACTThe application of stochastic modelling for learning the behaviour of a multibody dynamics (MBD) models is investigated. Post-processing data from a simulation run are used to train the stochastic model that estimates the relationship between model inputs (suspension relative displacement and velocity) and the output (sum of suspension forces). The stochastic model can be used to reduce the computational burden of the MBD model by replacing a computationally expensive subsystem in the model (suspension subsystem). With minor changes, the stochastic modelling technique is able to learn the behaviour of a physical system and integrate its behaviour within MBD models. The technique is highly advantageous for MBD models where real-time simulations are necessary, or with models that have a large number of repeated substructures, e.g. modelling a train with a large number of railcars. The fact that the training data are acquired prior to the development of the stochastic model discards the conventional sampling plan strategies like Latin Hypercube sampling plans where simulations are performed using the inputs dictated by the sampling plan. Since the sampling plan greatly influences the overall accuracy and efficiency of the stochastic predictions, a sampling plan suitable for the process is developed where the most space-filling subset of the acquired data with number of sample points that best describes the dynamic behaviour of the system under study is selected as the training data.Results indicated that the stochastic modelling technique is effective in improving the computational efficiency of the MBD model without compromising the accuracy of the predictions, although the improvements in the computational efficiency of the technique could not be quantified due to the inefficiencies associated with transferring the data between multiple software packages (SIMPACK, SIMULINK).

Modelling of gearbox dynamics under time-varying nonstationary load for distributed fault detection and diagnosis