Identifying cracks in the incipient state is essential to prevent the failure of engineering structures. Detection methods relying on the analysis of the changes in modal parameters are widely used because of the advantages they present. In our previous research, we found that eigenfrequencies were capable of indicating the position and depth of damage when sufficient vibration modes were considered. The damage indicator we developed was based on the relative frequency shifts (RFS). To calculate the RFSs for various positions and depths of a crack, we established a mathematical relation that involved the squared modal curvatures in the healthy state and the deflection of the healthy and damaged beam under dead mass, respectively. In this study, we propose to calculate the RFS for beams with several cracks by applying the superposition principle. We demonstrate that this is possible if the cracks are far enough from each other. In fact, if the cracks are close to each other, the superposition method does not work and we distinguish two cases: (i) when the cracks affect the same beam face, the frequency drop is less than the sum of the individual frequency drops, and (ii) on the contrary, cracks on opposite sides cause a decrease in frequency, which is greater than the sum of the frequency drop due to individual damage. When the RFS curves are known, crack assessment becomes an optimization problem, the cost function being the distance between the measured RFSs and all possible RFSs for several vibration modes. Thus, the RFS constitutes a benchmark that characterizes damage using only the eigenfrequencies. We can accurately locate multiple cracks and estimate their severity through experiments and thus prove the reliability of the proposed method.

Nowadays, the damage severity evaluation in mechanical structures is mostly performed by analyzing the natural frequency shift. The non-isotropic materials, as the multi-layered ones, are wide-spread in industrial applications, due to their interesting physic-mechanical properties. Thus, a deeper approach of multi-layered beams becomes an important request in the research domain. This paper introduces a damage severity estimator by expressing the crack evolution as a function of stored energy. It is well known that the energy stored in a beam without damage is greater than the energy of that damaged beam. As a consequence, the beam deflection can be related to the stored energy. In this regard, the possibility to split the damage localization and the damage severity assessment has been proven, and also the graphical evolution of the natural frequency shift has been achieved as a function of the crack depth. The results achieved by the finite element method (FEM) and experimental tests are given in tables and graphics. For the first five vibration modes, a comparison was made between frequencies accomplished by analytical, numerical and experimental analyses, in order to give more credibility to the accuracy of the research data presented in this paper.

Starting with the last century, a lot of enthusiastic researchers have invested significant time and energy in proposing various drives capable to generate linear propulsion force. Regrettably, only a few of these devices passed the patent phase and have been practically materialized. The aim of this paper was to simulate the dynamic behavior of an inertial propulsion drive (IPD) developed by the authors, to demonstrate its functionality. The core of the IPD consists of two symmetric drivers that each performs rotation of eight steel balls on an eccentric path. We propose three solutions for the element which maintain the off-center trajectory of the balls. For the simulation, we used the multibody system approach and determine the evolution of the displacement, velocity, and power consumption. Further, we analyze the collisions between the elements of the system and the influence of this phenomenon on the dynamic behavior of the IPD. We found that collisions generate impact forces which affect the ball acceleration values achieved by simulation. We have concluded that the developed system is capable to generate linear movement. In addition, in terms of velocity and power consumption, the best constructive version of the retaining disk is that which has a cylindrical inner bore placed eccentric relative to the rotation center of the balls.

Identifying cracks in the incipient state is essential to prevent the failure of engineering structures. Detection methods relying on the analysis of the changes in modal parameters are widely used because of the advantages they present. In our previous research, we have found that eigenfrequencies were capable of indicating the position and depth of damage when sufficient vibration modes were considered. The damage indicator we developed was based on the relative frequency shifts (RFS). To calculate the RFSs for various positions and depths of a crack, we established a mathematical relation that involved the squared modal curvatures in the healthy state and the deflection of the healthy and damaged beam under dead mass, respectively. In this study, we propose to calculate the RFS for beams with several cracks by applying the superposition principle. We demonstrate that this is possible if the cracks are far enough from each other. In fact, if the cracks are close to each other, the superposition method does not work and we distinguish two cases: (i) when the cracks affect the same beam face, the frequency drop is less than the sum of the individual frequency drops, and (ii) on the contrary, cracks on opposite sides cause a decrease in frequency, which is greater than the sum of the frequency drop due to individual damage. When the RFS curves are known, crack assessment becomes an optimization problem, the cost function being the distance between the measured RFSs and all possible RFSs for several vibration modes. Thus, the RFS constitutes a benchmark that characterizes damage using only the eigenfrequencies. We can accurately locate multiple cracks and estimate their severity trough experiments and thus prove the reliability of the proposed method.

In the current energy landscape, efficiency is a critical topic. Therefore, even in the case of geared transmissions, it is essential to predict and calculate power losses as accurately as possible from the design phase. There are mainly three categories of losses in a gear unit: friction—the power losses due to the contact between teeth in rotation on the one hand and the seals with the spindles on the other hand; churning—the power losses generated by the air–lubricant mixture compression around teeth roots during rotation; and windage—the power losses due to the teeth aerodynamic trail in the air–lubricant mixture. While the first two categories of losses are intensively studied in the literature, the papers focusing on windage power losses are less representative. An estimation of windage power losses can be performed by numerical simulation, and the accuracy of the results depends on the mesh density and the available computing power. The present study discusses the influence of meshing on the windage torque of an orthogonal face gear immersed in air and compares numerical results generated by SolidWorks 2025 Flow Simulation software with experimental data measured on a test rig.