Traditionally, the use of ferrite as a core of the linear variable differential transformer (LVDT) is suggested in its designs. Nevertheless, problems related to its brittleness and low tensile strength may be considered as important drawbacks for its use as a core material, especially when its geometry is likely to be modified. This work explores other alternatives related to soft magnetic materials, less used in applications of an LVDT core. By means of a decision matrix, from an assortment of different materials, three alternatives were selected. This proposal provides the identification of those materials with higher qualification values to be used as core material. In order to validate the performance of the selected materials, a prototype of LVDT was designed and fabricated. The design was carried out taking into consideration typical performance specifications. Finally, a comparison of the measurements of sensitivity and linearity of the proposed and traditional materials was made.

The motion of a particle that is projected into a resistant medium and subjected to a uniform gravitational field is considered. The drag force that acts upon the particle within the medium is proportional to the particle’s speed, the density of the medium, and the cross-section area of the projectile. We review the problem of a horizontal motion with a drag force that is linear in speed. The problem is formulated in terms of particle speed, mass, height, time, and expelled gas velocity. The equations of motion are solved analytically, and a case study is discussed. As a result, we obtain the deviation of the projectile as a function of time because of the expelled gases with or without drag force.

The design process of journal bearings of turbomachines is complex and time-consuming due to the many geometric and physical variables involved. This paper reports on the design of experiments (DOE) and the response surface design of experiments (RSDOE) methods employed on the design of the drive-end and free-end three-lobe journal bearings supporting a centrifugal compressor rotor. The suitability of each technique is discussed. The bearing design variables employed are bearing slenderness ratio, radial clearance, preload, and lubricant inlet temperature. The rotordynamic response variables selected were the critical speed location, the vibrations at critical speed and operating speed for both bearings, and the threshold speed of instability. The use of a nonlinear (quadratic) RSDOE model is justified. An optimization approach combining an SRDOE and rotordynamic finite element modeling is presented. This method leads to arrive to a multivariate model for multi-objective optimization with very few computations. Identification of the dominant design variables and their effects on several response variables allows establishing engineering feasible solutions with focus on manufacturing versus operating conditions tradeoff.

This paper proposes a methodology to analyze the resolution and variations in the positions of the 3RRR planar parallel mechanism driven by electrical actuators of discrete steps. This methodology consists of graphing and plotting all the possible combinations of angular movements of a three legs mechanism. This generates a “cloud of points” that will be the boundary of the control limits, so as to find the closest trajectory to a straight line. It was found that resolution, accuracy, and the approximation error improves when micro-steps are employed. For this purpose, it is necessary to determine direct and inverse kinematics, in order to calculate the workspace. A prototype was built to validate the methodology proposed.

Machine tool chatter causes machining instability, surface roughness, and tool wear in metal cutting processes. A stability lobe diagram based on the theory of regenerative vibration is an effective tool to predict and control the chatter. This paper presents the advances in the mechanical design of a parallel kinematic machine tool. The features that make it ideal for machining tasks, and that make unique in its own way, are highlighted. In addition, the description of the progress of this work will be focused on the analysis of the stability limitation for machining systems to derive the stability lobe diagram with modal analysis of the spindle. A vibratory model is developed by adding cutting forces and including analytical equations for the depth of cut and for the cutting speeds, both depending on the frequency of vibration. A step-by-step procedure provides a stability lobe diagram. The results show that it is relatively easy to provide a relationship between depth of cut and spindle speed. In turn, it makes it easy to compare machining processes under different cutting parameters and conditions.