Didier Remond

Practical performances of high-speed measurement of gear transmission error or torsional vibrations with optical encoders

We evaluated in this paper an improved technique for measuring gear transmission error (GTE) at high speed, by using low pulse per revolution optical encoders. The originality of this technique lies in the fact that highly precise, completely digital measurements of torsional vibration or transmission error (TE) at high speed are achievable by the use of low-price, basic optical components. The lengths of encoder pulses are estimated with a high-frequency timer (100 MHz): thus, it appears that the theoretical precision of this device depends only on the angular speed of shafts, not on the number of pulses per revolution of the encoder. In practice, the intrinsic encoder accuracy (namely the grating or electronic signal processing precision) directly affects precision measurements. Alternatively, the number of pulses per revolution of the encoder specifies the resolution. We examined the possibility of calibrating encoders through using a specific test rig. The determination of corrective data assigned to each grating leads to an insignificant improvement of the precision measurement. The coherence from one revolution to another does not present any significant deterministic component. The overall precision achieved is less than 0.03 second of arc for each frequency of the power spectral density. This calibration device only gives a good assessment of eccentricity induced by mechanical mounting of optical discs on a shaft, compared with the direct measurement on grating discs. The correlation between the two measurements is less than 3% of the magnitude of the relative eccentricity. Thus, the encoder technique seems to be a cheap and easy way to implement transmission error measurement on real mechanical systems with high precision and sufficient reliability.

Conservation of the links between gene transcription and chromosomal organization in the highly reduced genome of Buchnera aphidicola

BackgroundGenomic studies on bacteria have clearly shown the existence of chromosomal organization as regards, for example, to gene localization, order and orientation. Moreover, transcriptomic analyses have demonstrated that, in free-living bacteria, gene transcription levels and chromosomal organization are mutually influenced. We have explored the possible conservation of relationships between mRNA abundances and chromosomal organization in the highly reduced genome of Buchnera aphidicola, the primary endosymbiont of the aphids, and a close relative to Escherichia coli.ResultsUsing an oligonucleotide-based microarray, we normalized the transcriptomic data by genomic DNA signals in order to have access to inter-gene comparison data. Our analysis showed that mRNA abundances, gene organization (operon) and gene essentiality are correlated in Buchnera (i.e., the most expressed genes are essential genes organized in operons) whereas no link between mRNA abundances and gene strand bias was found. The effect of Buchnera genome evolution on gene expression levels has also been analysed in order to assess the constraints imposed by the obligate symbiosis with aphids, underlining the importance of some gene sets for the survival of the two partners. Finally, our results show the existence of spatial periodic transcriptional patterns in the genome of Buchnera.ConclusionDespite an important reduction in its genome size and an apparent decay of its capacity for regulating transcription, this work reveals a significant correlation between mRNA abundances and chromosomal organization of the aphid-symbiont Buchnera.

Numerical and Experimental Study of the Loaded Transmission Error of a Spiral Bevel Gear

The design of spiral bevel gears in aeronautical gear boxes requires very precise and realistic numerical simulations. One important criteria is the loaded transmission error (LTE) that gear designers attempt to reduce at the nominal torque. This paper presents a numerical tool that simulates the loaded meshing of spiral bevel gears and experimental tests carried out on a real helicopter gear box. Tooth profile is defined by the Gleason cutting process and tooth bending effects and contact deformations are both taken into account. The bending effect computation uses a three-dimensional finite element model, while the contact deformations are obtained by using Boussinesq’s theory. Experimental measurements of the LTE were performed using magnetic and optical encoders rigidly connected with the pinion and gear shafts, giving access to the records of the instantaneous angular positions. The numerical simulations fit quite well the experimental results.

Semi-adaptive modal control of on-board electronic boards using an identification method

Modal active control, based on a state model, is an efficient method of increasing the lifetime of electronic boards by using piezoelectric components. In the case of industrial mass production, dispersions lead to changes in mechanical and electromechanical properties. Moreover, initial operating conditions such as boundary conditions can change during the lifetime of the control and modify its efficiency and stability. Therefore, a semi-adaptive modal control strategy in deferred time is proposed to attenuate these problems. Firstly modal control gains are calculated by using a classical linear quadratic Gaussian algorithm with the nominal model including mode shapes. Then control I/O data are collected by an identification system that uses on-board piezoelectric components. A subspace method is implemented to estimate modal matrices in order to update the controller. The sensitivity of control performance to modal parameter variation is presented. Estimated control frequencies and modal damping are finally used to update modal control gains. The effectiveness of the proposed method is examined through numerical simulation and experimental tests in the case of boundary condition modifications. This adaptive modal control/identification design greatly increases the nominal robustness of the controller in the case of frequency shifts.

Parametric Instability of an Axially Moving Belt Subjected to Multifrequency Excitations: Experiments and Analytical Validation

This paper experimentally investigates the parametric instability of an industrial axially moving belt subjected to multifrequency excitation. Based on the equations of motion, an analytical perturbation analysis is achieved to identify instabilities. The second part deals with an experimental setup that subjects a moving belt to multifrequency parametric excitation. A data acquisition technique using optical encoders and based on the angular sampling method is used with success for the first time on a nonsynchronous belt transmission. Transmission error between pulleys, pulley/belt slip, and tension fluctuation are deduced from pulley rotation angle measurements. Experimental results validate the theoretical analysis. Of particular note is that the instability regions are shifted to lower frequencies than the classical ones due to the multifrequency excitation. This experiment also demonstrates nonuniform belt characteristics (longitudinal stiffness and friction coefficient) along the belt length that are unexpected sources of excitation. These variations are shown to be sources of parametric instability.

From transmission error measurements to angular sampling in rotating machines with discrete geometry

The benefits of angular sampling when measuring various signals in rotating machines are presented and discussed herein. The results are extracted from studies on transmission error measurements with optical encoders in the field of power transmissions and can be broadened to include phase difference measurements, such as torsional vibrations, and applied to control, monitoring and measurement in rotating machines with discrete geometry. The main conclusions are primarily that the use of angular sampling enables the exact location of harmonics and, consequently, the obtaining of spectral amplitude components with precision. This is always true even if the resolution of encoders is not directly related to the studied discrete geometry. It then becomes possible to compare these harmonics under different operating conditions, especially when speed varies, without changing any parameters in spectral analysis (window length, spectral resolution, etc.). Moreover, classical techniques of improving signal to noise ratio by averaging become fully efficient in the detection of defective elements. This study has been made possible thanks to the technique of transmission error measurement with optical encoders that allows the comparison of sampling procedures, based on the same raw data.

On the use of the Instantaneous Angular Speed measurement in non-stationary mechanism monitoring

Power transmission faults are one important cause of machine downtime many production activities are working to prevail. Vibration monitoring tools have achieved this role on the assumption that the stationary condition hypothesis is maintained. Several industries, including wind energy production, are however demanding to observe mechanical or electrical rotating components behaviour at variable speeds. Instantaneous angular speed measurement has been recently proven able to detect localized faults in bearings using only an encoder close from the source of the defect. This paper presents the results obtained from a large span experiment on a 2MW wind turbine. The uniqueness of the sensor used to monitor the whole line shafting along with the continuous non stationary conditions are so many difficulties cumulated on this attempt. Two basic signal processing tools are theoretically defined and experimentally applied in an original way on the Instantaneous Angular Speed measurement to efficiently tackle these practical issues.Copyright

Contribution of angular measurements to intelligent gear faults diagnosis

Currently, work on the automation of vibration diagnosis is mainly based on indicators extracted from Time sampled Acceleration signals. There are other attractive alternatives such as those based on Angle synchronized measurements, which can provide a considerable number of more relevant and diverse indicators and, thus, lead to better performance in gear fault classification. The diversity of angular measurements (Instantaneous Angular Speed, Transmission Error and Angular sampled Acceleration) represents potential sources of relevant information in fault detection and diagnosis systems. These complementary measurements of existing signals or new relevant signals allow the construction of Feature Vector (FV) offering robust and effective classification methods even for different or non-stationary running speed conditions. In this paper, we propose to build several FVs based on indicators derived from the angular techniques to compare them to the ones calculated from the time signals, proving their superior performance in detection and identification of gear faults. It will be a question to demonstrate the effectiveness of angular indicators in increasing classification performances, using a supervised classifier based on Artificial Neural Networks and thus determining the most suitable signals.

Electrical Modeling for Faults Detection Based on Motor Current Signal Analysis and Angular Approach

Recently, Motor Current Signal Analysis (MCSA) appears as an effective tool for fault diagnosis in rotating machinery and proved to be sufficient for detecting localized mechanical faults in electromechanical systems operating in stationary conditions. In the case of non-stationary conditions, speed variations must be distinguished from angular velocity perturbation caused by the presence of a defect. In the framework of diagnosis of rotating machinery, angular approaches are well suited to make monitoring resistive to speed disturbances. This paper proposes a reformulation of the MCSA associated with angular approach in modeling multiphysic behavior. The resulting model described in this paper can be used to investigate of the influence of the Instantaneous Angular Speed (IAS) variations on the electrical responses of the whole rotating system.

Modal Behavior Monitoring of a Discrete Evolutive Structure

Abstract The proposed paper takes part in a general project of behavior monitoring of structures or rotating machines, particularly with the characterization of modal changes. The study presented here focuses on implementation of an integrated modal identification method in time domain allowing the monitoring of mode shapes. A three degrees of freedom system is designed as three pendulums, one of them offering the possibility to move its mass. Changes in position of this moving mass introduce small changes on natural frequencies but significant changes in modal shapes under controlled operating conditions. A corresponding analytical model is achieved for simulation and characterization of the proposed identification method. The latter is based on classical identification tools (N4SID) in association with modal reconstruction methodology. An experimental validation is performed by comparing the results obtained with a nonparametric traditional identification (swept sine and characterization of the modal displacements by harmonic excitation at the resonance frequencies). Then, with the validation of the model by the experimental setup, it is shown that the modal reconstruction remains effective for rapid changes in behavior of the studied system.