A modified mathematical model for simulating gear crack from root with linear growth path in a pinion is developed, in which an improved potential energy method is used to calculate the time-varying meshing stiffnesses of the meshing gear pair while we also take the deformation of gear-body into consideration. The formulas for the meshing stiffness are deduced when the crack grows as the linear growth path in the pinion. A 16DOF dynamic model of a one-stage spur gear system is used to study the response from the system considering time-varying meshing stiffnesses and different levels of crack growing in the pinion. As vibration signals induced by the tooth crack are buried in normal vibration signals which are induced by the normal gear pair in meshing at the early stage of crack growth, the algorithm combined autoregressive modeling method and demodulation method is proposed to process the signals to investigate the response characteristics as the crack grows, and the comparison of the relationship between indicators and the crack levels from different simulation methods are given.
Summary
Prefabricated steel structures have certain obvious advantages, that is, rapid construction, industrial production, and environmental protection. Although prefabricated structures have been applied in a number of countries in the world, in most cases, these structures are suitable only for low‐rise buildings, and their applications in high‐rise buildings are nota\bly rare. This paper proposes a new type of prefabricated steel structure called the modular‐prefabricated high‐rise steel frame structure with diagonal braces. Based on the T30 building, which is a hotel building with 30 storeys above the ground, the mechanical properties, failure mode, failure mechanism, and elastic–plastic development laws of the structure were studied via elastic and elastic–plastic design and analyses under various load cases and combinations. The analysis of the internal force and displacement response with frequent earthquakes was performed using the response spectrum and elastic time‐history methods, and an analysis under rare earthquakes is performed via static elastic–plastic pushover analysis. This paper summarizes the elastic and elastic–plastic structural design methods and process. This study provides important references for the design of this kind of modular‐prefabricated high‐rise steel structure, and the design method has been compiled into a design specification named Technical Specifications for Prefabricated Steel Frame Structure with Diagonal Bracing Joints.
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