Sensitivity and Efficiency of the Frequency Shift Coefficient Based on the Damage Identification Algorithm: Modeling Uncertainty on Natural Frequencies

Health surveillance in industries is an important prospect to ensure safety and prevent sudden collapses. Vibration Based Structure Health Monitoring (VBSHM) is being used continuously for structures and machine diagnostics in industry. Changes in natural frequencies are frequently used as an input parameter for VBSHM. In this paper, the Frequency Shift Coefficient (FSC) is used for the assessment of various numerical damaged cases. An FSC-based algorithm is employed in order to estimate the positions and severity of damages using only the natural frequencies of healthy and unknown (damaged) structures. The study focuses on cantilever beams. By considering the minimization of FSC, damage positions and severity are obtained. Artificially damaged cases are assessed by changes in its positions, the number of damages and the size of damages along with the various parts of the cantilever beam. The study is further investigated by considering the effect of uncertainty on natural frequencies (0.1%, 0.2% and 0.3%) in damaged cases, and the algorithm is used to estimate the position and severity of the damage. The outcomes and efficiency of the proposed FSC based method are evaluated in order to locate and quantify damages. The efficiency of the algorithm is demonstrated by locating and quantifying double damages in a real cantilever steel beam using vibration measurements.

A Novel VBSHM Strategy to Identify Geometrical Damage Properties Using Only Frequency Changes and Damage Library

Vibration-based structural health monitoring is an efficient way to diagnose damage and structural integrity at the earliest stage. In this paper, a new strategy is developed for damage localization and estimation, as well as damage properties identification for a rectangular geometry damage using only eigenfrequencies of the healthy and damaged structure. This strategy is applied to a cantilever beam. In this framework, a damage library is built by correlating 2D and 3D finite element models. The correlation is done by minimizing a so-called frequency shift coefficient. The proposed strategy also uses the frequency shift coefficient to correlate a 2D damaged model with an unknown beam case. The 2D damage, represented by a bending stiffness reduction, is then associated to a 3D damage by employing the damage library. Numerical cases with single and double damage of varying position and severity are tested and used to validate the approach. Finally, experimental results are proposed that show the relevance of the strategy.

The Kinematic Design of 2K Type Planetary Gear Reducers with High Reduction Ratio

3K type and 2K-2H type planetary gear trains can be designed to have high reduction ratios. Due to the reason of power circulation, these two kinds of planetary gear trains with high reduction ratios have low meshing efficiencies. The 2K type planetary gear reducer only contain two ring gears and one carrier, hence it will not have the problem of power circulation and will have better meshing efficiency than 3K type and 2K-2H type planetary gear reducers. Also, in general, the gear reducers with high reduction ratio are compound gear system. The purpose of this paper is to propose 2K type planetary simple gear reducers with high reduction ratios. Based on the concept of train value equation, the kinematic design of 2K type planetary gear trains with high reduction ratio are synthesized. Six 2K type planetary gear reducers are designed to illustrate the kinematic design process. Three of the examples are 2K type planetary gear reducers with simple planet gears. For the 2K type planetary simple gear reducer, there is a problem that is the simple planet gear engages to two ring gears with different tooth number. One example is used to illustrate how to design the two ring gears with different shift coefficient to engage the same planet gear. Based on the proposed process, all 2K type planetary simple gear reducers with high reduction ratios can be synthesized.

Feasible Solution of Profile-Shift Coefficient for Involute Internal Gear Pair in Zero-Tooth-Difference Mechanism

Zero-tooth-difference internal gear mechanism is applied in thrust-eccentric gear coupling designed particularly for oil-submerged motor driven progressing cavity pumping system. The petroleum output of pump depends on the distance (eccentricity) between the canters of external and internal gears proportionally, while the eccentricity is affected by the profile-shift coefficient (abbreviated hereafter as PSC). Larger PSC can increase the amount of eccentricity but decrease the strength of gear, especially for small numbers of teeth. The optimum coupling relationship of radial and tangential PSC is just what to be found here. The work presented in this paper focuses on a method for determining the PSC of gears in the mechanism. The domain of initial values is prepared at first based on developed mathematical model. Then, according to tooth profile engagement equation and additional constraint conditions, a reasonable set of PSC is approached for different eccentricities. Moreover, the PSC can be modified and readjusted with optimum method until satisfied result is obtained finally.