Dynamic modeling and analysis of a split-torque transmission with a tooth crack fault

Dynamic modeling and analysis are generally regarded as effective tools to investigate the vibration characteristics and fault mechanisms of planetary gear systems with a tooth crack fault. In actual gearboxes, the tooth crack is always a three-dimensional spatial surface, but it was usually simplified as a two-dimensional domain in most previous studies. In this paper, the tooth crack is modeled as a spatial shape that propagates along the crack depth, length and height directions simultaneously. Based on the potential energy principle, an improved analytical method is proposed to calculate the time-varying mesh stiffness (TVMS) of a planetary gear system with a spatial tooth crack. Furthermore, a coupled translational–torsional dynamic model is established for a planetary gear system including time-varying parameters and nonlinear factors. Numerical simulations are conducted to reveal the influences of the spatial crack propagation on the TVMS and vibration responses. In addition, an experimental study is carried out on a gear transmission test rig to verify the proposed analytical method and dynamic model. The mesh stiffness calculation method of the spatial cracked tooth and corresponding analysis results in this study might provide references to detect tooth crack faults in planetary gear systems.

Dynamic modeling and analysis of multistage planetary gear system considering tooth crack fault

Hilbert-Huang Transform (HHT) has been renowned for its capacity to reveal fault indicating information issue from vibration signals. It uses Empirical Mode Decomposition (EMD) to decompose a signal accordingly to its contained information into a set of Intrinsic Mode Functions (IMFs). Then, the instantaneous frequencies are performed of each IMF using Hilbert Transform (HT). However, the HHT has some disadvantages which are caused by the EMD technique. The EMD has the mode mixing problem that may occur between IMFs, it causes the End Effect phenomenon, which leads to a wrong instantaneous values at both sides of the signal. Furthermore, its lack of mathematical basis. To overcome the HHT inherent problems, we propose the use of the Empirical Wavelet Transform (EWT) which designs an appropriate wavelet filter bank fully depends on the processed signal with HT in the early detection and condition monitoring of tooth crack fault. In this paper, we develop a dynamic model describing a single stage spur gear in normal and abnormal functioning. Results of analyzing the pinion’s vibration displacement show that the proposed approach denoted (HEWT) successfully detect the tooth crack at a much earlier stage of damage development even though in noisy environment. Performance evaluation and comparison between HEWT and HHT methods show that the HEWT is better sensitive to tooth crack fault detection in gearbox systems.

Crack in gears impacts the dynamic response of wind turbine multistage gear system, which also influences the safe operation of wind turbine. A translational–torsional nonlinear dynamic model of the multistage gear system is proposed with root crack fault. The model considers the effects of sun gear support, time-varying mesh stiffness, gear backlash and other factors. The mesh stiffness with root crack is analyzed by using potential energy method. Based on the Runge–Kutta method, the system responses are obtained with multiple parameters changing. The nonlinear dynamic features of the cracked and normal system are compared by bifurcation diagram, time series, phase trajectory, Poincaré map, spectrum diagram and corresponding three-dimensional diagrams. The analyses show the effects of input torque, backlash, crack occurrence and evolution on the system dynamic behaviors, and the effect of crack fault on the gear system response is further verified by experiment. The results provide a theoretical basis for the cognition of fault mechanism and fault diagnosis of wind turbine gearbox.

Detection of gear tooth crack fault through vibration analysis relies on extracting the fault induced periodic impulses. Singular value decomposition (SVD)-based methods have been used for periodic impulse extraction. Reported reweighted SVD-based method did not consider interferences from non-fault related vibration components on the periodic modulation intensity (PMI) criteria, leading to the selection of incorrect signal component(s) for reconstruction. This paper proposes an improved SVD-based method by adopting autoregression model-based baseline removal approach. SVD is applied to decompose the residual signal, instead of the raw signal. The interferences from non-fault related vibration components on the PMI are therefore eliminated. Simulation study has shown that the improved method outperforms the reported method in detecting early tooth crack fault.

Fault feature analysis of cracked gear based on LOD and analytical-FE method

Nonlinear characteristics analysis of encased differential gear train containing tooth crack fault

This paper focuses on the vibration analysis for tooth crack detection of split-torque transmission system. Firstly, on the basis of the potential energy principle, a healthy tooth model and a cracked tooth model are established respectively. Corresponding mathematical equations of gear mesh stiffness are derived. Then, the dynamic model of a split-torque transmission system is established considering the translational and torsional motions. By implanting the tooth crack into different gears, the vibration responses of the split-torque transmission system are simulated and analyzed, and vibration signals of various conditions can be obtained to provide basis for the development of feature extraction and fault diagnosis methods.

One of the challenges for the fault feature extraction of a planetary gearbox is that the weak gear fault related vibration feature is often buried by the strong background noise in the gearbox. The minimum entropy deconvolution (MED) method for weak impulsive feature enhancement has been successfully applied to the feature extraction of gears and bearings in fixed-axis gearboxes. However, it is often failed if the result is converged to a single pulse rather than a periodic pulse sequence which corresponding to the gear or the bearing localized fault. In order to address this issue, the multipoint optimal minimum entropy deconvolution adjusted (MOMEDA) is employed in this paper to extract the vibration feature related to an individual planet gear with tooth-crack fault in a planetary gearbox. The effectiveness and advantages of the method are verified by experiments.

In order to solve the dynamic vibration characteristics of the power-split transmission system, the system of the dynamic mechanical model is established. Firstly, according to the theoretical analysis method of the tooth contact analysis (TCA) and loaded tooth contact analysis (LTCA), the actual meshing process of each gear pair is simulated, and the time-varying mesh stiffness excitation is obtained, which can improve the numerical precision. Next, by using the lumped mass method, the bending-torsional coupling three-dimensional dynamical model of the power-split transmission is established. The identical dimensionless equations are deduced by eliminating the effect of rigid displacement and the method of dimensional normalization. Next, the frequency domain and time domain responses of this system are obtained. The dynamic load change characteristics of each gear pair are analyzed. The results show that establishment, solution, and analysis of the system dynamics model could provide a basis for the dynamic design and have an important significance for the dynamic efficiency analysis and dynamic performance optimization design of the power-split transmission. Through theoretical data compared with the experimental data, we verified the correctness of the method proposed.

KOMPUTASI, Juli 2006, Vol.3, No.6, Hal 1-11 In general, any geographic phenomena are visually depicted as ‘static’ spatial model. This thesis presents how some variable can be combined t o give more information to the spatial analysis model and how to implement the dynamic map and the dynamic spatial model.. Conceptually, there are six steps to implement the dynamic spatial model for Upper Ciliwung Watershed including data compilation and preparation, data analysis, spatial model development, interfacing, spatial database programing, simulation and verification. Microsoft Visual Basic V.6.0 and Map Object Version 2.1 were used to implement. T he application program developed is generally interactive with a few tools and dialog interface. User can flexibly set up different land use change scenarios for knowing the hydrology responses to support the decision maker. The outputs of the dynamic spatial analysis model are: peak runoff rate [m 3 /s]. runoff volume [m 3 ], and percentage of each contributing area. This dynamic spatial analysis model is able to determine of contributing area of runoff water by tracking the flow direction of its watershed characteristic from the study area. The result of this dynamic spatial analysis model will be useful to be use for controlling the impact of the land use changes od Upper Ciliwung Watershed. Key Word: Spatial analysis, dynamic model, land use change, scenario, peak run off rate, debit, watershed

Summary A new model technique is described for comprehensive dynamic stress and displacement analysis of wellbore-completion tubulars, including friction loads with history. A dynamic model of tubing forces is necessary to predict local pipe velocity, which in turn determines the magnitude and direction of localized frictional contact. By tracking dynamic changes in axial force starting from the initial running state, a complete load history can be simulated for the installed casing and tubing through the service life of the well. The dynamic friction model subdivides the casing or tubing string joint by joint and uses an elastic pipe-momentum balance. Pipe velocity is related to axial force by the elasticity equation. Dynamically determined velocity is necessary to predict the magnitude and orientation of local node-friction vectors. Damping for the dynamic analysis is provided by annular fluid viscosity. The elastic equations are solved as a set of algebraic equations in terms of past and future values of pipe axial force and velocity. Key model inputs such as pressure, temperature, fluid, and wellbore-friction coefficients can be changed at each successive load step. Running loads and packer setting with slackoff or pickup loads determine the initial tubing-stress configuration. Given the initial configuration, each subsequent load case is calculated starting from the prior load and resultant friction state, allowing for full history dependence. The surface velocity profile of running individual stands is a key input. Unexpected magnitudes of downhole transfer of surface load are demonstrated. A change in the operation-load sequence is shown to produce significant differences in tubular axial loads, indicating that special attention to load history should be considered when performing a tubular-stress analysis. For slackoff, overpull, or packer-setting events, the model can track dynamic load response at downhole points, such as a packer or cement top. An example well with a deviated profile and a planned sequence of life-cycle operations including stimulation, production, and shut-in was simulated for a variety of load sequences. The model has been validated against field data using the actual hookload plot during installation of a single-trip, multizone intelligent completion in an offshore highly deviated extended-reach-drilling (ERD) well. Example calculations are given for a high-pressure/high-temperature (HP/HT) subsea well and a horizontal unconventional well. The dynamic friction model allows for the seamless integration of running loads with friction into a fully sequential stress analysis of subsequent well life-cycle loads for landed completion strings. Although dynamic analysis has been extensively applied to complex drilling phenomena such as drillstring vibration or bottomhole-assembly design, current industry models for completion tubulars such as casing and tubing separate the installation state from the in-service life envelope or attempt to solve the problem with a static analysis. This represents a critical deficiency in the current industry state of the art for completion tubulars, which the present work proposed herein strives to address. From a comparison with appropriate static analytic solutions and industry-standard drag-and stress-models, dynamics were found to affect friction-force directions and magnitudes, suggesting that tubular dynamics cannot be neglected.

Historical records of childhood disease incidence reveal complex dynamics. For measles, a simple model has indicated that epidemic patterns represent attractors of a nonlinear dynamic system and that transitions between different attractors are driven by slow changes in birth rates and vaccination levels. The same analysis can explain the main features of chickenpox dynamics, but fails for rubella and whooping cough. We show that an additional (perturbative) analysis of the model, together with knowledge of the population size in question, can account for all the observed incidence patterns by predicting how stochastically sustained transient dynamics should be manifested in these systems.

Considerable research attentions have recently been paid toward a mobile manipulator (a robot arm standing on a mobile platform) due to its extended workspace beyond the manipulator reach. Mobile manipulators have a wide range of potential applications where it is desirable to achieve higher degree of flexibility in transport and handling task. However, a vast number of research publications only focus on trajectory planning. This preliminary research work presents dynamic modeling and analysis of a mobile flexible robot arm with aims to provide insights for the design and control of such mobile robot manipulators. In this work, the dynamic model is developed using a computationally efficient method: Discrete Time Transfer Matrix Method (DT-TMM). The concepts and principle of DT-TMM are briefly overviewed, and then are applied to a mobile flexible robot arm for dynamic modeling with the detailed procedure. Numerical simulations and dynamic analyses are performed to illustrate the effectiveness of the proposed dynamic modeling method, and to provide the clues for our ongoing research work in the design and control of mobile robot manipulators.

In order to further reduce the incisions of laparoscopic surgery and the possibility of infection, the organic combination of single-incision laparoscopic surgery (SILS) and robotics has made the degree of minimally invasive surgery further improved. A new 5-DOF single-incision laparoscopic surgery robot was designed based on Axiomatic Design Theory, whose structure consisting of the movement mechanism, the endoscope and the position and pose adjustment mechanism. The robot parts are connected in series and parallel, allowing a pivotal motion of the endoscope in the center of the robot for realizing the incision. In order to achieve a performance optimization and a dynamic control of the single-incision laparoscopic surgical robot, the kinematics and dynamic modeling and dynamic stiffness analysis of the robot are especially important. The forward kinematics equation, inverse kinematics equation and Jacobian matrix of the SILS robot are derived based on D-H method and geometric method, and the kinematics numerical simulation is carried out by Matlab. The dynamic equation of the robot is derived by Kane method. Subsequently, a numerical simulation of the robot dynamics equation is performed, with its virtual prototype utilized to set the motion plan of the robot mechanism. After robot’s dynamic simulation, the numerical changes of the driving force and torque for each robot’s moving mechanism are obtained. The performed simulation results further verify the correctness of the established robot’s dynamic model. Finally, utilizing the above methods, the dynamic stiffness model and evaluation index of the robot are determined, and the dynamic stiffness of the robot is analyzed and evaluated. The results of the kinematics, dynamic and stiffness analysis of the SILS robot further validate that the 5-DOF SILS robot has a reasonable structure, motion and sufficient stability to meet the needs of single-incision laparoscopic surgery.