Mechanical vibration characteristics of bell-type pump maintings

This thesis describes an analytical and experimental study to determine the mechanical characteristics of the pump mounting, bell housing type. For numerical purposes, the mount was modelled as a thin circular cylindrical shell with cutouts, stiffened with rings and stringers; the boundary conditions were considered to be either clamped-free or clamped-supporting rigid heavy mass. The theoretical study was concerned with both the static response and the free vibration characteristics of the mount. The approach was based on the Rayleigh-Ritz approximation technique using beam characteristic (axial) and trigonometric (Circumferential) functions in the displacement series, in association with the Love - Timoshenko thin shell theory. Studies were carried out to determine the effect of the supported heavy mass on the static response, frequencies and mode shapes; in addition, the effects of stringers, rings and cutouts on vibration characteristics were investigated. The static and dynamic formulations were both implemented on the Hewlett Packard 9845 computer. The experimental study was conducted to evaluate the results of the natural frequencies and mode shapes, predicted numerically. In the experimental part, a digital computer was used as an experiment controller, which allowed accurate and quick results. The following observations were made: 1. Good agreements were obtained with the results of other investigators. 2. Satisfactory agreement was achieved between the theoretical and experimental results. 3. Rings coupled the axial modal functions of the plain cylinder and tended to increase frequencies, except for the torsion modes where frequencies were reduced. Stringers coupled the circumferential modal functions and tended to decrease frequencies. The effect of rings was stronger than that of stringers. 4. Cutouts tended to reduce frequencies; in general, but this depends on the location of the cutouts; if they are near the free edge then an increase in frequencies is obtained. Cutouts coupled both axial and circumferential modal functions. 5. The supported heavy mass had similar effects to those of the rings, but in an exaggerated manner, particularly in the reduction of torsion frequencies. 6. The method of analysis was found to be a convenient analytical tool for estimating the overall behaviour of the shell with cutouts.

Updating finite element models using measured vibration data

The modelling of mechanical structures using finite element analysis has become an indispensable stage in the design of new components and products. Once the theoretical design has been optimised a prototype may be constructed and tested. What can the engineer do if the measured and theoretically predicted vibration characteristics of the structure are significantly different? This thesis considers the problems of changing the parameters of the finite element model to improve the correlation between a physical structure and its mathematical model. Two new methods are introduced to perform the systematic parameter updating. The first uses the measured modal model to derive the parameter values with the minimum variance. The user must provide estimates for the variance of the theoretical parameter values and the measured data. Previous authors using similar methods have assumed that the estimated parameters and measured modal properties are statistically independent. This will generally be the case during the first iteration but will not be the case subsequently. The second method updates the parameters directly from the frequency response functions. The order of the finite element model of the structure is reduced as a function of the unknown parameters. A method related to a weighted equation error algorithm is used to update the parameters. After each iteration the weighting changes so that on convergence the output error is minimised. The suggested methods are extensively tested using simulated data. An H frame is then used to demonstrate the algorithms on a physical structure.

Dynamic behaviour of rotary mechanical seals

This thesis covers both experimental and computer investigations into the dynamic behaviour of mechanical seals. The literature survey shows no investigations on the effect of vibration on mechanical seals of the type common in the various process industries. Typical seal designs are discussed. A form of Reynolds' equation has been developed that permits the calculation of stiffnesses and damping coefficients for the fluid film. The dynamics of the mechanical seal floating ring have been investigated using approximate formulae, and it has been shown that the floating ring will behave as a rigid body. Some elements, such as the radial damping due to the fluid film, are small and may be neglected. The equations of motion of the floating ring have been developed utilising the significant elements, and a solution technique described. The stiffness and damping coefficients of nitrile rubber o-rings have been obtained. These show a wide variation, with a constant stiffness up to 60 Hz. The importance of the effect of temperature on the properties is discussed. An unsuccessful test rig is described in the appendices. The dynamic behaviour of a mechanical seal has been investigated experimentally, including the effect of changes of speed, sealed pressure and seal geometry. The results, as expected, show that high vibration levels result in both high leakage and seal temperatures. Computer programs have been developed to solve Reynolds' Equation and the equations of motion. Two solution techniques for this latter program were developed, the unsuccesful technique is described in the appendices. Some stability problems were encountered, but despite these the solution shows good agreement with some of the experimental conditions. Possible reasons for the discrepancies are discussed. Various suggestions for future work in this field are given. These include the combining of the programs and more extensive experimental and computer modelling.

An investigation into vibration criteria for rotating machinery

Concern had been expressed by engineers of the Shell Chemical Company regarding the validity of existing vibration criteria for rotating machinery. A survey showed that existing criteria were based solely on the amplitude of vibration, normally of the bearing housings, with no allowance being made for the dynamic properties of the support1ng structure. The feasibility of measuring the mechanical impedance of bearing supports in order to assess the severity of vibration generated by a machine has been investigated. It is suggested that in many cases the oscillatory bearing force levels obtained for these measurements will provide a quantitative indication of severity. Theoretical and experimental work has been conducted on a model rig, comprising a flexible shaft running in journal bearings housed in flexible, asymmetric supports. The accuracy with which the system behaviour could be predicted using measured support impedances is discussed together with the extraction of uncoupled support impedances from measurements on the complete rotating system. Access was available to several industrial centrifugal compressors. To enable the bearing support impedances of these machines to be measured on site considerable attention has been paid to the evolution of a technique involving the use of transient excitation. To develop this technique the model rig and a large rotary converter have been used as test structures. Methods have also been devised and developed for the analysis of the transient impedance data.

Leg muscles motion during whole body linear frequency sweep vibration

Whole body vibration (WBV) aims to mechanically activate muscles by eliciting stretch reflexes. Mechanical vibrations are usually transmitted to the patient body standing on a oscillating plate. WBV is now more and more utilized not only for fitness but also in physical therapy, rehabilitation and in sport medicine. Effects depend on intensity, direction and frequency of vibration; however, the training frequency is one of the most important factors involved. A preliminary vibratory session can be dedicated to find the best vibration frequency for each subject by varying, stepwise, the stimulation frequency and analyzing the resulting EMG activity. This study concentrates on the analysis of muscle motion in response to a vibration frequency sweep, while subjects held two different postures. The frequency of a vibrating platform was increased linearly from 10 to 60 Hz in 26 s, while platform and single muscles (Rectus Femoris, Biceps Femoris - long head and Gastrocnemius Lateralis) motions were monitored using tiny, lightweight three-axial MEMS accelerometers. Displacements were estimated integrating twice the acceleration data after gravity contribution removal. Mechanical frequency response (amplitude and phase) of the mechanical chains ending at the single muscles was characterized. Results revealed a mechanical resonant-like behavior at some muscles, very similar to a second-order system in the frequency interval explored; resonance frequencies and dumping factors depended on subject and its positioning onto the vibrating platform. Stimulation at the resonant frequency maximizes muscle lengthening, and in turn muscle spindle solicitation, which produce muscle activation. © 2009 Springer-Verlag.

Analysis and modelling of muscles motion during whole body vibration

The aim of the study is to characterize the local muscles motion in individuals undergoing whole body mechanical stimulation. In this study we aim also to evaluate how subject positioning modifies vibration dumping, altering local mechanical stimulus. Vibrations were delivered to subjects by the use of a vibrating platform, while stimulation frequency was increased linearly from 15 to 60Hz. Two different subject postures were here analysed. Platform and muscles motion were monitored using tiny MEMS accelerometers; a contra lateral analysis was also presented. Muscle motion analysis revealed typical displacement trajectories: motion components were found not to be purely sinusoidal neither in phase to each other. Results also revealed a mechanical resonant-like behaviour at some muscles, similar to a second-order system response. Resonance frequencies and dumping factors depended on subject and his positioning. Proper mechanical stimulation can maximize muscle spindle solicitation, which may produce a more effective muscle activation. © 2010 M. Cesarelli et al.

Muscle motion and EMG activity in vibration treatment

The aim of this study is to highlight the relationship between muscle motion, generated by whole body vibration, and the correspondent electromyographic (EMG) activity and to suggest a new method to customize the stimulation frequency. Simultaneous recordings of EMG and tri-axial accelerations of quadriceps rectus femoris from fifteen subjects undergoing vibration treatments were collected. Vibrations were delivered via a sinusoidal oscillating platform at different frequencies (10-45 Hz). Muscle motion was estimated by processing the accelerometer data. Large EMG motion artifacts were removed using sharp notch filters centred at the vibration frequency and its superior harmonics. EMG-RMS values were computed and analyzed before and after artifact suppression to assess muscular activity. Muscles acceleration amplitude increased with frequency. Muscle displacements revealed a mechanical resonant-like behaviour of the muscle. Resonance frequencies and dumping factors depended on subject. Moreover, RMS of artifact-free EMG was found well correlated (R 2 = 0.82) to the actual muscle displacement, while the maximum of the EMG response was found related to the mechanical resonance frequency of muscle. Results showed that maximum muscular activity was found in correspondence to the mechanical resonance of the muscle itself. Assuming the hypothesis that muscle activation is proportional to muscle displacement, treatment optimization (i.e. to choose the best stimulation frequency) could be obtained by simply monitoring local acceleration (resonance), leading to a more effective muscle stimulation. Motion artifact produced an overestimation of muscle activity, therefore its removal was essential. © 2009 IPEM.

Whole body vibration training:analysis and characterization

The aim of this work is to contribute to the analysis and characterization of training with whole body vibration (WBV) and the resultant neuromuscular response. WBV aims to mechanically activate muscle by eliciting stretch reflexes. Generally, surface electromyography is utilized to assess muscular response elicited by vibrations. However, EMG analysis could potentially bring to erroneous conclusions if not accurately filtered. Tiny and lightweight MEMS accelerometers were found helpful in monitoring muscle motion. Displacements were estimated integrating twice the acceleration data after gravity and small postural subject adjustments contribution removal. Results showed the relevant presence of motion artifacts on EMG recordings, the high correlation between muscle motion and EMG activity and how resonance frequencies and dumping factors depended on subject and his positioning onto the vibrating platform. Stimulations at the resonant frequency maximize muscles lengthening and in turn, muscle spindle solicitation , which may produce more muscle activation. Local mechanical stimulus characterization (Le, muscle motion analysis) could be meaningful in discovering proper muscle stimulation and may contribute to suggest appropriate and effective WBV exercise protocols. ©2009 IEEE.

Muscle movement and electrodes motion artifact during vibration treatment

Vibration treatment by oscillating platforms is more and more employed in the fields of exercise physiology and bone research. The rationale of this treatment is based on the neuromuscular system response elicited by vibration loads. surface Electromyography (EMG) is largely utilized to assess muscular response elicited by vibrations and Root Mean Square of the electromyography signals is often used as a concise quantitative index of muscle activity; in general, EMG envelope or RMS is expected to increase during vibration. However, it is well known that during surface bio-potential recording, motion artifacts may arise from relative motion between electrodes and skin and between skin layers. Also the only skin stretch, modifying the internal charge distribution, results in a variation of electrode potential. The aim of this study is to highlight the movements of muscles, and the succeeding relevance of motion artifacts on electrodes, in subjects undergoing vibration treatments. EMGs from quadriceps of fifteen subjects were recorded during vibration at different frequencies (15-40 Hz); Triaxial accelerometers were placed onto quadriceps, as close as possible to muscle belly, to monitor motion. The computed muscle belly displacements showed a peculiar behavior reflecting the mechanical properties of the structures involved. Motion artifact related to the impressed vibration have been recognized and related to movement of the soft tissues. In fact large artifacts are visible on EMGs and patellar electrodes recordings during vibration. Signals spectra also revealed sharp peaks corresponding to vibration frequency and its harmonics, in accordance with accelerometers data. © 2008 Springer-Verlag.

Correspondence between muscle motion and EMG activity during whole body vibration

The aim of this study is to highlight the relation between muscle motion and electromyographyc activity during whole body vibration. This treatment is accounted for eliciting a reflex muscle activity in response to vibratory stimulation. Simultaneous recordings from quadriceps Rectus Femoris EMG and 3D muscle accelerations on fifteen subjects undergoing vibration treatments were collected. In our study vibrations were delivered via a sinusoidal oscillating platform at different frequencies (10-45 Hz), with a constant amplitude. Muscle motion was estimated by processing accelerometer data. Displacements revealed a mechanical resonant-like behaviour of the muscle; resonance frequencies and dumping factors depended on subject. Large EMG motion artifacts were removed using sharp notch filters centred at the vibration frequency and its superior harmonics. RMS values of artifact-free EMG were found correlated to the actual muscle displacement. The results were in accordance to the hypothesis of a proprioceptive response during vibration treatment. Nevertheless, motion artifacts produced an overestimation of muscle activity, therefore its removal was essential. © 2009 Springer Berlin Heidelberg.

Outer rotor mechanical and dynamic performance analysis for high-speed machine

Due to high-speed rotation, the problems about rotor mechanics and dynamics for outer rotor high-speed machine are more serious than conventional ones, in view of above problems the mechanical and dynamics analysis for an outer rotor high-speed permanent magnet claw pole motor are carried out. The rotor stress analytical calculation model was derived, then the stress distribution is calculated by finite element method also, which is coincided with that calculated by analytical model. In addition, the stress distribution of outer rotor yoke and PMs considering centrifugal force and temperature effect has been calculated, some influence factors on rotor stress distribution have been analyzed such as pole-arc coefficient and speed. The rotor natural frequency and critical speed were calculated by vibration mode analysis, and its dynamics characteristics influenced by gyroscope effect were analyzed based on Campbell diagram. Based on the analysis results above an outer rotor permanent magnet high-speed claw pole motor is design and verified.

Whole body vibration treatments in postmenopausal women can improve bone mineral density:results of a stimulus focussed meta-analysis

Whole body vibration treatment is a non-pharmacological intervention intended to stimulate muscular response and increase bone mineral density, particularly for postmenopausal women. The literature related to this topic is controversial, heterogeneous, and unclear despite the prospect of a major clinical effect. The aim of this study was to identify and systematically review the literature to assess the effect of whole body vibration treatments on bone mineral density (BMD) in postmenopausal women with a specific focus on the experimental factors that influence the stimulus. Nine studies fulfilled the inclusion criteria, including 527 postmenopausal women and different vibration delivery designs. Cumulative dose, amplitudes and frequency of treatments as well as subject posture during treatment vary widely among studies. Some of the studies included an associated exercise training regime. Both randomized and controlled clinical trials were included. Whole body vibration was shown to produce significant BMD improvements on the hip and spine when compared to no intervention. Conversely, treatment associated with exercise training resulted in negligible outcomes when compared to exercise training or to placebo. Moreover, side-alternating platforms were more effective in improving BMD values than synchronous platforms and mechanical oscillations of magnitude higher than 3 g and/or frequency lower than 25 Hz were also found to be effective. Treatments with a cumulative dose over 1000 minutes in the follow-up period were correlated to positive outcomes. Our conclusion is that whole body vibration treatments in elderly women can reduce BMD decline.However, many factors (e.g. amplitude, frequency and subject posture) affect the capacity of the vibrations to propagate to the target site; the adequate level of stimulation required to produce these effects has not yet been defined. Further biomechanical analyses to predict the propagation of the vibration waves along the body and assess the stimulation levels are required.