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Teeth disengaging or back-side teeth meshing induced by backlash reduces the transmission quality and dynamic performance of gear systems, and accurate interpretation of multi-state meshing behavior can provide guidance for structural optimization and performance evaluation. Therefore, the multi-state meshing behavior of the gear system is elaborated. A new nonlinear dynamic model of a spur gear system with five-state meshing behavior is proposed based on time-varying backlash and contact ratio. The time-varying meshing stiffness and time-varying backlash considering the elastic contact of gear teeth, gear temperature rise and lubrication are included in the model. The five-state meshing behavior is clearly characterized by constructing five Poincaré maps, and its generation mechanism is studied using dynamic meshing force time history, teeth relative displacement time history and phase portrait. The bifurcation and evolution of five-state meshing behavior are analyzed under the effects of load factor, meshing frequency and error coefficient. The results show that the mutation in the direction of dynamic meshing force leads to teeth disengaging and back-side single or double teeth contact, forming multi-state meshing behavior. Bifurcation caused by parameter changes greatly affects the evolution of five-state meshing behavior, particularly grazing bifurcation can decrease the number of teeth disengagement. Chaotic behavior or trajectory expansion inspires multi-state meshing vibration of the system. Previous gear system models could not reveal these phenomena due to ignoring the multi-state meshing behavior.

Background: UVB radiation is an increasing threat to aquatic organisms, and also a potential driving force for zooplankton population dynamics. The bdelloid rotifer, for its parthenogenesis and high resistance to stress, can be used as an excellent model in ecology and evolutionary biology. Given the strong tolerance of bdelloid rotifer to stressors, we hypothesized that it could hold the ability to tolerate significant UV radiation, and this capacity may be associated with the trade-off strategies among life historic components. With this study, to estimate the ecological effects and responses of antioxidant system against UV radiation, the acute lethal, life history strategies, population growth, and antioxidant enzyme activities were assessed in the bdelloid Rotaria rotatoria after exposure to UV-B radiation. Results: The persistence of tolerance (evaluating by LT50) in rotifer to stress was playing a more vital role than the radiation dose (LD50) in survival, with a significant negative correlation between the radiation intensity and LT50. The larger the culture volume, the weaker the lethal effect. Rotifers prolonged their first reproductive time (JP), and shortened their reproductive period (RP) and longevity with the increasing of radiation dose, and the fecundity was significant inhibited by UV-B radiation. These responses can be taken as energy trade-off to retard their mortality. The population density of rotifers increased at the lowest dose of radiation, and then descended with the increasing of UVR dose, and this pattern was also corroborated by detecting the content of SOD and CAT, which suggested that hormesis also applies to R. rotatoria under UV-B radiation stress. The enzyme SOD has higher level of content and more sensitive to low UVR than CAT.Conclusions: The lethal effects of UV-B radiation to organisms depends not only on the conditions they exposed to, like as intensity and time of exposure, but also combination of factors namely, the type and effectiveness of the strategy they employ to cope with the changed environment. The species specificity, ages and physiological status also could be the regulating factors under the stresses, also in this case there was the strategy of energy trade-off between reproduction and survival in rotifers.