This paper presents a study on the movement precision and accuracy of an extruder system related to the print bed on a 3D printer evaluated using the features of 2D circular trajectories generated by simultaneous displacement on x and y-axes. A computer-assisted experimental setup allows the sampling of displacement evolutions, measured with two non-contact optical sensors. Some processing procedures of the displacement signals are proposed in order to evaluate and to describe the circular trajectories errors (e.g., open and closed curves fitting, the detection of recurrent periodical patterns in x and y-motions, low pass numerical filtering, etc.). The description of these errors is suitable to certify that the 3D printer works correctly (keeping the characteristics declared by the manufacturer) for maintenance purpose sand, especially, for computer-aided correction of accuracy (e.g., by error compensation).

This paper presents some advances in condition monitoring for rotary machines (particularly for a lathe headstock gearbox) running idle with a constant speed, based on the behaviour of a driving three-phase AC asynchronous induction motor used as a sensor of the mechanical power via the absorbed electrical power. The majority of the variable phenomena involved in this condition monitoring are periodical (machines having rotary parts) and should be mechanically supplied through a variable electrical power absorbed by a motor with periodical components (having frequencies equal to the rotational frequency of the machine parts). The paper proposes some signal processing and analysis methods for the variable part of the absorbed electrical power (or its constituents: active and instantaneous power, instantaneous current, power factor, etc.) in order to achieve a description of these periodical constituents, each one often described as a sum of sinusoidal components with a fundamental and some harmonics. In testing these methods, the paper confirms the hypothesis that the evolution of the electrical power (instantaneous and active) has a predominantly deterministic character. Two main signal analysis methods were used, with good, comparable results: the fast Fourier transform of short and long signal sequences (for the frequency domain) and the curve fitting estimation (in the time domain). The determination of the amplitude, frequency and phase at origin of time for each of these components helps to describe the condition (normal or abnormal) of the machine parts. Several achievements confirm the viability of this study: a characterization of a flat driving belt condition and a beating power phenomenon generated by two rotary shafts inside the gearbox. For comparison purposes, the same signal analysis methods were applied to describe the evolution of the vibration signal and the instantaneous angular speed signal at the gearbox output spindle. Many similarities in behaviour among certain mechanical parts (including their electrical power, vibration and instantaneous angular speed) were highlighted.

This paper proposes a study in theoretical and experimental terms focused on the vibration beating phenomenon produced in particular circumstances: the addition of vibrations generated by two rotating unbalanced shafts placed inside a lathe headstock, with a flat friction belt transmission between the shafts. The study was done on a simple computer-assisted experimental setup for absolute vibration velocity signal acquisition, signal processing and simulation. The input signal is generated by a horizontal geophone as the sensor, placed on a headstock. By numerical integration (using an original antiderivative calculus and signal correction method) a vibration velocity signal was converted into a vibration displacement signal. In this way, an absolute velocity vibration sensor was transformed into an absolute displacement vibration sensor. An important accomplishment in the evolution of the resultant vibration frequency (or combination frequency as well) of the beating vibration displacement signal was revealed by numerical simulation, which was fully confirmed by experiments. In opposition to some previously reported research results, it was discovered that the combination frequency is slightly variable (tens of millihertz variation over the full frequency range) and it has a periodic pattern. This pattern has negative or positive peaks (depending on the relationship of amplitudes and frequencies of vibrations involved in the beating) placed systematically in the nodes of the beating phenomena. Some other achievements on issues involved in the beating phenomenon description were also accomplished. A study on a simulated signal proves the high theoretical accuracy of the method used for combination frequency measurement, with less than 3 microhertz full frequency range error. Furthermore, a study on the experimental determination of the dynamic amplification factor of the combination vibration (5.824) due to the resonant behaviour of the headstock and lathe on its foundation was performed, based on computer-aided analysis (curve fitting) of the free damped response. These achievements ensure a better approach on vibration beating phenomenon and dynamic balancing conditions and requirements.

In the technical literature there are some studies which use measured signals in order to compensate the errors caused by vibrations [1, 2], by the cutting force [3], by the deflections of the technological system [4], and others. Also, the technical literature presents some studies [6, which give few measurement techniques in order to measure the error which appears into the turning process and also, some methods to compensate or eliminate the consequences produced by those errors. In such conditions, this study propose to establish a possible methodology that can make the measurement of the radial deviation which corresponds to a work piece obtained into a turning process. The novelty of this study comes from the method of measurement used and from the measurement stand which provide the values of the radial deflection for the processed work piece, during the process. The experimental procedure assumes the existence of an experimental stand which allows to measure the distance between a sensor and the considered work piece. In such conditions, the mathematical algorithms used will transform the received electrical signal into a physical displacement. The obtained results suggest that the signal provided by the experimental stand and which it is used for measure the distance between a sensor and the considered work piece, allows to establish, with accuracy, the values for the radial deviations of the work piece. Also, this fact can offer a graphical representation of the shape which corresponds to the real profile of the processed work piece.