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Planetary gears are widely used in automobiles, helicopters, heavy machinery, etc., due to the high speed reductions in compact spaces; however, the gear fault and early damage induced by the vibration of planetary gears remains a key concern. The time-varying parameters have a vital influence on dynamic performance and reliability of the gearbox. An analytical model is proposed to investigate the effect of gear tooth crack on the gear mesh stiffness, and then the dynamical model of the planetary gears with time-varying parameters is established. The natural characteristics of the transmission system are calculated, and the dynamic responses of transmission components, as well as dynamic meshing force of each pair of gear are investigated based on varying internal excitations induced by time-varying parameters and tooth root crack. The effects of gear tooth root crack size on the planetary gear dynamics are simulated, and the mapping rules between damage degree and gear dynamics are revealed. In order to verify the theoretical model and simulation results, the planetary gear test rig was built by assembling faulty and healthy gear separately. The failure mechanism and dynamic characteristics of the planetary gears with tooth root crack are clarified by comparing the analytical results and experimental data.

Planetary transmissions are an important form of mechanical transmission. Because of its advantages of high transmission ratio, high bearing capacity, and compact structure, it is widely used in complex mechanical equipment such as aerospace, wind power generation equipment, and mining machinery. Due to the influence of time-varying parameters, the planetary gear system always has the problem of nonlinear dynamics and excessive vibration. The planetary transmission system has a high failure rate, and the root crack is one of the most important forms of gear failure, due to complicated internal structure and large load during operation. When the root of the transmission system is cracked, the vibration of the system will be intensified and, in serious cases, the equipment will be damaged. Therefore, the dynamic study of the planetary gear transmission system with tooth root crack failure and analysis of the fault mechanism has an important theoretical significance and engineering application value for improving the reliability and service life of the gear. Mathematical modeling and analysis are important methods to solve the nonlinear dynamics of planetary gear transmission systems. The control of nonlinear dynamic systems is a widely recognized challenging issue. It is promising to develop vibration reduction design of the planetary gear system based on U-model, because of the unique advantages of U-model in nonlinear control [1, 2]. Some scholars have carried out a lot of work on the dynamics of gear systems by mathematical modeling. Bonori and Pellicano [3] presented a dynamic model of a single pair of gear transmission systems and analyzed the effects of random manufacturing errors on the dynamic response of the system. Chaari et al. [4] established an analytical model of time-varying gear meshing stiffness based on the analytical method and analyzed the variation of crack to gear stiffness under two different parameters. Guo and Parker [5] established a dynamic model of the planetary gear train based on the lumped parameter method and solved the dynamic model to obtain the dynamic response of the transmission system. Chen and Shao [6] studied the effects of internal ring cracks on the time-varying mesh stiffness and dynamic response of planetary gear trains. Some scholars have also carried out a lot of research on the dynamics of planetary transmission systems. Zhou [7] studied the influence of crack parameters on dynamic characteristics by establishing a finite element model. Wan [8] proposed a meshing stiffness correction method based on the potential energy method. The dynamic model of a gear transmission system with tooth root crack was established by using the lumped parameter method, and the dynamic equation was solved to obtain the dynamic response. In previous planetary transmission dynamics analysis, the bearing was simplified to the ideal constraint boundary, and the bearing was simplified to a constant stiffness coefficient spring, also ignoring the influence of the bearing time-varying stiffness on the dynamic characteristics of the transmission system. Bearings and gears are the key components of the planetary transmission system. The dynamic characteristics of the bearings have an important influence on the stability and service life of the transmission system. Walters [9] proposed the dynamic analysis model of the rolling bearing. The dynamic model of the rolling bearing was established, and the drag force between the rolling element and the ferrule was obtained by considering the four degrees of freedom of the rolling element and the six degrees of freedom of the cage. Harris and Kotzalas [10] considered the effect of elastohydrodynamics on the basis of quasi-static analysis and improved the pseudostatic analysis method of rolling bearings. In establishing the balance equations of the rolling element, the cage, and the inner ring, the rolling element's revolution and bearing deformation parameters are obtained.

Zhou [11] considered the time-varying stiffness of rolling bearings, established the coupled dynamics model of MW-class wind turbine gear transmission system by using the lumped parameter method, obtained the inherent characteristics of the transmission system, and solved the dynamics of each bearing contact stress, but it does not consider the influence of the centrifugal force of the roller on the bearing stiffness. Mohammed et al. [12] presents an investigation of the performance of crack propagation scenarios, to compare these scenarios from a fault diagnostics point of view. Park et al. [13] proposes a variance of energy residual (VER) method, for planetary gear fault detection under variable-speed conditions.

In the planetary gear transmission system, the dynamic meshing excitation of the gear teeth is transmitted to the casing through the bearing, causing vibration and noise of the casing. The dynamic characteristics of the bearing have an important influence on the performance of the entire transmission system. In the past, the scholars neglected the influence of the mass of the rolling element and the centrifugal force of the roller on the time-varying stiffness of the bearing when studying the gear-bearing coupling dynamic system. At the same time, the dynamic characteristics of the faulty planetary transmission system were not studied. In this paper, the planetary transmission system with tooth root crack is taken as the research object. According to the Hertz contact theory, considering the mass of the rolling element and the effect of centrifugal force, the time-varying bearing stiffness model is established. At the same time, the time-varying bearing stiffness, the transmission error, and the time-varying meshing stiffness of the cracked gear are introduced. The gear-bearing coupling dynamics model with crack is established. The influence of time-varying bearing stiffness on the dynamic characteristics of the gear transmission system is analyzed. The influence of crack failure on the dynamic characteristics of the gear is explored, which provides a more detailed mathematical method for the fault diagnosis and vibration control of the planetary gear transmission system.

Oak Ridge National Laboratory researchers used the nation's fastest supercomputer to map the molecular vibrations of an important but little-studied uranium compound produced during the nuclear fuel cycle for results that could lead to a cleaner, safer world. googletag.cmd.push(function() { googletag.display('div-gpt-ad-1449240174198-2'); }); The study by researchers from ORNL, Savannah River National Laboratory and the Colorado School of Mines used simulations conducted on ORNL's Summit supercomputer and state-of-the-art neutron spectroscopy experiments conducted at the Spallation Neutron Source to identify key spectral features of uranium tetrafluoride hydrate, or UFH, a little-studied byproduct of the nuclear fuel cycle. The findings may enable better detection of this environmental pollutant and better understanding of how environmental conditions influence the chemical behavior of fuel cycle materials."In this kind of work, we don't have the luxury of choosing what kinds of materials we work with," said Andrew Miskowiec, an ORNL physicist and lead author of the study, published in The Journal of Physical Chemistry C. "We're often dealing with small quantities or even just particles of byproducts and degraded material that no one intended to make of compounds that we don't know much about. We need to know: If we found this material in the field, how would we recognize it?"UFH forms when uranium tetrafluoride, a radioactive salt routinely used in producing uranium metal, begins to break down after immersion in water for 12 hours or longer. Even though scientists have studied uranium and its power to split the atom for nearly a century, most of those studies have focused on intentional results rather than unintended byproducts like UFH."From World War II through the Cold War, we have decades of study, but the main concern was making things work from a production standpoint, like building bombs and powering reactors," Miskowiec said. "UFH wasn't considered valuable for those purposes. That means it hasn't been studied as closely and isn't as well understood. We need to know as much as we can about these materials in order to know what to look for when we discover them in the wild."Each of uranium's various molecular forms undergoes a unique set of vibrations, created by the dynamic motion of its atoms, that can act as a signature if scientists know what to look for. The research team used VISION, the world's highest-resolution inelastic neutron scattering spectrometer at the SNS, to bombard samples with neutrons, monitor the energy lost or gained, and capture the full range of UFH's vibrations. (adsbygoogle = window.adsbygoogle || []).push({}); "For other common characterization techniques, we would have had to dissolve or otherwise destroy the sample to study it," said Ashley Shields, an ORNL computational chemist and co-author of the study. "If we don't have a big sample to start with, we definitely don't want to destroy it before extracting as much information as possible. Spectroscopy gives us a way to gather data and preserve the sample for further analysis."Conventional scattering methods rely on photons or electrons, which interact with an atom's outer shell and capture only a limited portion of the wide range of vibrations between atoms in a uranium compound. That's not a problem for neutrons, which penetrate all the way to an atom's nucleus."Neutrons are sensitive to all the atoms in the compound's structure, so we get the entire vibrational spectrum," Miskowiec said. "These extraordinary instruments at SNS gave us a huge amount of data, and now we needed a way to interpret it."The team received an allocation of time on Summit, the Oak Ridge Leadership Computing Facility's 200-petaflop IBM AC922 supercomputing system, via the U.S. Department of Energy's Advanced Scientific Computing Research's Leadership Computing Challenge. They used density functional theory, a quantum-mechanical approach to estimating materials' structure, to model UFH's properties.The combination of detail captured by VISION and the interpretation of large-scale, highly accurate density functional theory calculations made possible by Summit yielded the first complete picture of UFH's full vibrational spectrum for new insights into the compound's atomic structure."These are extremely large, intricate structures with a lot of atoms constantly vibrating in all directions with very little symmetry," Shields said. "Every break in the symmetry requires more calculations, increasing the compute time required to determine the vibrational properties. These computations allow us to visualize what kinds of vibrations these are, what the motion looks like, which atoms are participating in and causing each vibration, and at what frequency."The team used the data to compare the calculated vibrational spectrum to the experimental one measured at the SNS, allowing for atomic-level identification of spectral features in the experimental data. The study required more than 115,000 node hours to render the results."Without Summit, these calculations couldn't have been done," Shields said. "There's a diversity of motion happening in the atomic structure we can tease out computationally that we just can't capture any other way."Future studies will build on the findings to explore UFH's stability."We now have a better ability to identify this material in the field, and the results will be foundational for understanding other environmental aspects of the fuel cycle," Miskowiec said. More information:Andrew Miskowiec et al, Inelastic Neutron Spectra of Uranium Tetrafluoride Hydrate, UF4(H2O)2.5, The Journal of Physical Chemistry C (2021). DOI: 10.1021/acs.jpcc.1c05747Journal information:Journal of Physical Chemistry C 2b1af7f3a8