On non-ideal and non-linear portal frame dynamics analysis using bogoliubov averaging method

We apply the Bogoliubov Averaging Method to the study of the vibrations of an elastic foundation, forced by a Non-ideal energy source. The considered model consists of a portal plane frame with quadratic nonlinearities, with internal resonance 1:2, supporting a direct current motor with limited power. The non-ideal excitation is in primary resonance in the order of one-half with the second mode frequency. The results of the averaging method, plotted in time evolution curve and phase diagrams are compared to those obtained by numerically integrating of the original differential equations. The presence of the saturation phenomenon is verified by analytical procedures.

Työstövärähtelyt metallin sorvauksessa ja jyrsinnässä: perusteet, ehkäiseminen ja matemaattinen mallintaminen

Tämä kandidaatintyö on tarkoitettu suomenkieliseksi selvitykseksi lastuavissa työstöprosesseissa esiintyvien työstövärähtelyjen luonteesta, syntymekanismeista ja välttämismenetelmistä. Erityisesti työssä keskitytään matemaattiseen mallintamiseen pohjautuviin välttämismenetelmiin.

Kiteen mekaanisten värähtelyjen vaimentaminen takaisinkytkennällä

Pulseri on laite, joka tuottaa noin 10 MHz:n taajuudella olevan sähköisen pulssin, joka ohjataan kiteeseen. Kide lähettää korkeataajuuksisen ääniaallon ja toimii samalla vastaanottimena kaikuna heijastuneille ääniaalloille. Kide ja membraanikalvo ovat vedessä. Ääniaalto heijastuu takaisin suodatusmembraanikalvosta, jolla on tarkoitus erotella epäpuhtauksia. Membraanikalvo ja kide ovat millimetrin etäisyydellä toisistaan ja ääniaalloilla kestää noin 1,3 mikrosekuntia kulkea kiteestä membraanikalvon pinnalle ja siitä kaikuna takaisin kiteeseen. Saadaksemme luotettavia tuloksia ääniaallon kulkuajasta, kiteen tulee olla värähtelemättömässä tilassa silloin, kun kaikuna palaava pulssi saapuu takaisin. Työssä keskitytään kiteen vaimentamiseen mahdollisimman nopeasti lähetetyn pulssin jälkeen ja siihen liittyviin ongelmiin.

Michelson interferometer with porch swing bearing for portable FTIR spectrometer

The interferometer for low resolution portable Fourier Transform middle infrared spectrometer was developed and studied experimentally. The final aim was a concept for a commercial prototype. Because of the portability, the interferometer should be compact sized and insensitive to the external temperature variations and mechanical vibrations. To minimise the size and manufacturing costs, Michelson interferometer based on plane mirrors and porch swing bearing was selected and no dynamic alignment system was applied. The driving motor was a linear voice coil actuator to avoid mechanical contact of the moving parts. The driving capability for low mirror driving velocities required by the photoacoustic detectors was studied. In total, four versions of such an interferometer were built and experimentally studied. The thermal stability during the external temperature variations and the alignment stability over the mirror travel were measured using the modulation depth of the wide diameter laser beam. Method for estimating the mirror tilt angle from the modulation depth was developed to take account the effect from the non-uniform intensity distribution of the laser beam. The spectrometer stability was finally studied also using the infrared radiation. The latest interferometer was assembled for the middle infrared spectrometer with spectral range from 750 cm−1 to 4500 cm−1. The interferometer size was (197 × 95 × 79) mm3 with the beam diameter of 25 mm. The alignment stability as the change of the tilt angle over the mirror travel of 3 mm was 5 μrad, which decreases the modulation depth only about 0.7 percent in infrared at 3000 cm−1. During the temperature raise, the modulation depth at 3000 cm−1 changed about 1 . . . 2 percentage units per Celsius over short term and even less than 0.2 percentage units per Celsius over the total temperature raise of 30 °C. The unapodised spectral resolution was 4 cm−1 limited by the aperture size. The best achieved signal to noise ratio was about 38 000:1 with commercially available DLaTGS detector. Although the vibration sensitivity requires still improving, the interferometer performed, as a whole, very well and could be further developed to conform all the requirements of the portable and stable spectrometer.

Negotiating home and belonging. Young Kurds in Finland

This study looks at negotiation of belonging and understandings of home among a generation of young Kurdish adults who were born in Iraq, Iran, and Turkey and who reached adulthood in Finland. The young Kurds taking part in the study belong to the generation of migrants who moved to Finland in their childhood and early teenage years from the region of Kurdistan and elsewhere in the Middle East, then grew to adulthood in Finland. In theoretical terms, the study draws broadly from three approaches: transnationalism, intersectionality, and narrativity. Transnationalism refers to individuals’ cross-border ties and interaction extending beyond nationstates’ borders. Young people of migrant background, it has been suggested, are raised in a transnational space that entails cross-border contacts, ties, and visits to the societies of departure. How identities and feelings of belonging become formed in relation to the transnational space is approached with an intersectional frame, for examination of individuals’ positionings in terms of their intersecting attributes of gender, age/generation, and ethnicity, among others. Focus on the narrative approach allows untangling how individuals make sense of their place in the social world and how they narrate their belonging in terms of various mechanisms of inclusion and exclusion, including institutional arrangements and discursive categorisation schemes. The empirical data for this qualitative study come from 25 semi-structured thematic interviews that were conducted with 23 young Kurdish adults living in Turku and Helsinki between 2009 and 2011. The interviewees were aged between 19 and 28 years at the time of interviewing. Interview themes involved topics such as school and working life, family relations and language-learning, political activism and citizenship, transnational ties and attachments, belonging and identification, and plans for the future and aspirations. Furthermore, data were collected from observations during political demonstrations and meetings, along with cultural get-togethers. The data were analysed via thematic analysis. The findings from the study suggest that young Kurds express a strong sense of ‘Kurdishness’ that is based partially on knowing the Kurdish language and is informed by a sense of cultural continuity in the diaspora setting. Collective Kurdish identity narratives, particularly related to the consciousness of being a marginalised ‘other’ in the context of the Middle East, are resonant in young interviewees’ narrations of ‘Kurdishness’. Thus, a sense of ‘Kurdishness’ is drawn from lived experiences indexed to a particular politico-historical context of the Kurdish diaspora movements but also from the current situation of Kurdish minorities in the Middle East. On the other hand, young Kurds construct a sense of belonging in terms of the discursive constructions of ‘Finnishness’ and ‘otherness’ in the Finnish context. The racialised boundaries of ‘Finnishness’ are echoed in young Kurds’ narrations and position them as the ‘other’ – namely, the ‘immigrant’, ‘refugee’, or ‘foreigner’ – on the basis of embodied signifiers (specifically, their darker complexions). This study also indicates that young Kurds navigate between gendered expectations and norms at home and outside the home environment. They negotiate their positionings through linguistic repertoires – for instance, through mastery of the Finnish language – and by adjusting their behaviour in light of the context. This suggests that young Kurds adopt various forms of agency to display and enact their belonging in a transnational diaspora space. Young Kurds’ narrations display both territorially-bounded and non-territorially-bounded elements with regard to the relationship between identity and locality. ‘Home’ is located in Finland, and the future and aspirations are planned in relation to it. In contrast, the region of Kurdistan is viewed as ‘homeland’ and as the place of origins and roots, where temporary stays and visits are a possibility. The emotional attachments are forged in relation to the country (Finland) and not so much relative to ‘Finnishness’, which the interviewees considered an exclusionary identity category. Furthermore, identification with one’s immediate place of residence (city) or, in some cases, with a religious identity as ‘Muslim’ provides a more flexible venue for identification than does identifying oneself with the (Finnish) nation.

Study of Control Methods of a High-Frequency Cycloconverter for Domestic Induction Heating Appliances

A high-frequency cyclonverter acts as a direct ac-to-ac power converter circuit that does not require a diode bidge rectifier. Bridgeless topology makes it possible to remove forward voltage drop losses that are present in a diode bridge. In addition, the on-state losses can be reduced to 1.5 times the on-state resistance of switches in half-bridge operation of the cycloconverter. A high-frequency cycloconverter is reviewed and the charging effect of the dc-capacitors in ``back-to-back'' or synchronous mode operation operation is analyzed. In addition, a control method is introduced for regulating dc-voltage of the ac-side capacitors in synchronous operation mode. The controller regulates the dc-capacitors and prevents switches from reaching overvoltage level. This can be accomplished by variating phase-shift between the upper and the lower gate signals. By adding phase-shift between the gate signal pairs, the charge stored in the energy storage capacitors can be discharged through the resonant load and substantially, the output resonant current amplitude can be improved. The above goals are analyzed and illustrated with simulation. Theory is supported with practical measurements where the proposed control method is implemented in an FPGA device and tested with a high-frequency cycloconverter using super-junction power MOSFETs as switching devices.

Teollisuuspuhaltimien runkorakenteiden ja siipipyörien suunnittelu

Tämä diplomityö tehtiin Voikkaalla Dust Control Systems Oy:lle. Työ on osa teollisuuspuhaltimien tuotekehitystä yrityksen olemassaolevan puhallinratkaisujen, sekä suunnitteluprosessin kautta. Työn tavoitteena oli tutkia puhaltimen toiminnasta aiheutuvan värähtelyn vaikutusta puhaltimen rakenteisiin nykyisillä puhallinmalleilla, sekä tutkia eri rakenneratkaisujen käyttöä yrityksen normaalista tuotelinjasta suuremmilla puhaltimilla. Työ toteutettiin kahden toteutuneen puhallinprojektin yhteydessä, joiden rakenteellisia ominaisuuksia pyrittiin arvioimaan normaalin suunnitteluprosessin ohella puhallinkomponenttien mitoituksen suhteen. Molemmat projektit olivat yrityksen mittakaavassa huomattavan suuria sekä suunnittelultaan haastavia, joten ne sopivat diplomityön toteutukseen hyvin. Suunnittelussa käytettiin FE-mallinnukseen Femap ja COMSOL-ohjelmistoja, sekä värähtelyn simulointiin yliopistolla kehitettyä RoBeDyn – laskentaohjelmaa. Työn aikana todettiin, että tarkempi FE-mallinnus yrityksen valmiista 3D-malleista on varsin hankala toteuttaa ja vaatisi mallien suunnittelun erityisesti lujuuslaskentaa varten. Laskennassa päädyttiin käyttämään yksinkertaistettuja malleja, joiden avulla saatiin johdonmukaisia arvioita puhaltimien toiminnasta eri materiaalivahvuuksilla. Käytännössä tuloksien oikeellisuutta päästään arvioimaan kesällä 2015 puhaltimien valmistuttua.

Emission, kinetic and magnetic phenomena in rare-earth and transition metal doped ZnSe single crystals

In this work emission, optical, electrical and magnetic properties of the d- and f- elements doped zinc selenide crystals were investigated within a wide temperature range. Doping was performed in various technological processes: during the growth by chemical vapor transport method; by thermal diffusion from the Bi or Zn melt. Concentration of the doping impurity in the crystals was controlled by amount of the dopant in the source material or by its concentration in the doping media. Special interest in the work was paid to the influence of the different concentrations of Cr and Yb impurities on ZnSe crystals’ properties, correlations between observed effects and similarities with the Ni, Mn and Gd dopants are analysed. Possibility of formation of the excitons bound to the doping d-ions was shown. In contrast to this, it was observed that f-elements do not bound excitons, but prevent formation of excitons bound to some uncontrolled impurities. A mechanism of Cr doping impurity interaction with background impurities and zinc selenide structural defects was proposed based on experimental data. An assumption about resonant energy transfer between double charged chromium ions and complexes based on crystals’ vacancy defects was made. A correlation between emission and magnetic properties of the d- ions doped samples was established. Based on this correlation a mechanism explaining the concentration quench of the emission was proposed. It was found that f-ions bind electrically active shallow and deep donor and acceptor states of background impurity to electrically neutral complexes. This may be observed as “purification” of ZnSe crystals by doping with the rare-earth elements, resulting i tendency of the properties of f-ion doped crystals to the properties of intrinsic crystals, but with smaller concentration of uncontrolled native and impurity defects. A possible interpretation of this effect was proposed. It was shown that selenium substituting impurities decrease efficiency of the Yb doping. Based on this experimental results an attempt to determine ytterbium ion surroundings in the crystal lattice was made. It was shown that co-doping of zinc selenide crystals with the d- and f- ions leads to the combination of the impurities influence on the material’s properties. On the basis of obtained data an interaction mechanism of the d- and f-elements co-dopants was proposed. Guided by the model of the ytterbium ion incorporation in the selenide sublattice of the ZnSe crystals, an assumption about stabilization of single charged chromium ions in the zinc sublattice crystal nodes, by means of formation of the local charge compensating clusters, was made.

Sähkökoneessa esiintyvien voimien yksityiskohtainen mittausjärjestelmä

Hissiteollisuudessa nostokoneistoina käytettyjen sähkömoottoreiden laatuvaatimukset ovat tiuken-tuneet viime vuosina. Erityisesti koneistojen tuottama ääni ja mekaaninen värähtely ovat olleet jat-kuvasti tiukentuneen tarkastelun alaisena. Hissikoriin ja hissiä ympäröiviin rakenteisiin välittyvästä värähtelystä johtuva ääni on yksi hissin laatuvaikutelmaan merkittävimmin vaikuttavia tekijöitä. Nostokoneisto on yksi tärkeimmistä äänen ja värähtelyn lähteistä hissijärjestelmässä. Koneiston suunnittelulla edellä mainittuja tekijöitä voidaan minimoida. Sähkökoneiden suunnittelussa finiit-tielementtimenetelmien (FEM) käyttö on vakiintunut haastavimmissa sovelluksissa. Kone Oyj:llä nostokoneistoina käytetään aksiaalivuokestomagneettitahtikoneita (AFPMSM), joiden FEM simu-lointiin käytetään yleisesti kolmea eri tapaa. Kukin näistä vaihtoehdoista pitää sisällään omat hyö-tynsä, että haittansa. Suunnittelun kannalta tärkeää on oikean menetelmän valinta ai-ka/informatiivisuus suhteen maksimoimiseksi. Erittäin tärkeää on myös saatujen tulosten oikeelli-suus. Tämän diplomityön tavoite on kehittää järjestelmä, jonka avulla AFPMS-koneen voimia voidaan mitata yksityiskohtaisella tasolla. Järjestelmän avulla voidaan tarkastella käytössä olevien FE-menetelmien tulosten oikeellisuutta sekä äänen että värähtelyn syntymekanismeja. Järjestelmän tarkoitus on myös syventää Kone Oyj tietotaitoa AFPMS-koneiden toiminnasta. Tässä työssä esitellään AFPMS-koneen epäideaalisuuksia, jotka voivat vaikuttaa mittajärjestelmän suunnitteluun. Myös koneen epäideaalisuuksiin lukeutuvaa ääntä on tarkasteltu tässä työssä. Jotta työn tavoitteiden mukaista FE-menetelmien vertailua ja tulosten oikeellisuuden tarkastelua voitai-siin tehdä, myös yleisimpiä AFPMS-koneen FE-menetelmiä tarkastellaan. Työn tuloksena on mittajärjestelmän suunnitelma, jonka avulla voidaan toteuttaa kuuden vapausas-teen voimamittaus jokaiselle koneistomagneetille alle 1N resoluutiolla. Suunnitellun järjestelmän toimivuutta on tarkasteltu FE-menetelmiä käyttäen ja järjestelmässä käytettävän voima-anturin ky-vykkyyttä on todennettu referenssimittauksin. Suunniteltu mittajärjestelmä mahdollistaa sähkömoottorin useiden eri epäideaalisuuksien tarkaste-lun yksityiskohtaisella tasolla. Mittausajatuksen soveltaminen myös muiden koneiden tutkimiseen tarjoaa mahdollisuuksia jatkotutkimuksille.

Pyörivän keskiökärjen rakenteen kehittäminen työstövärähtelyjen välttämiseksi sorvauksessa

Tässä diplomityössä käsitellään sorvauksen työstövärähtelyjen ja sorvin keskiökärjen rakenteen yhteyttä. Työ on osa Lappeenrannan teknillisen yliopiston VMAX-projektia, ja sen taustalla on pyrkimys uudenlaisen, sorvin kärkipylkän puristusvoiman ajonaikaiseen säätämiseen perustuvan työstövärähtelyjen välttämismenetelmän kehittämiseen. Tämän menetelmän toiminnan todentaminen oli työn ensimmäinen tavoite. Menetelmän toteuttaminen asettaa kuitenkin käytetyn keskiökärjen rakenteelle tiettyjä vaatimuksia. Työn toisena tavoitteena oli nämä vaatimukset täyttävän keskiökärjen prototyypin kehittäminen. Tutkimus eteni seuraavasti. Ensimmäiseksi ongelma määriteltiin tutustumalla työn teoreettiseen taustaan ja aiheeseen liittyvään tutkimukseen Lappeenrannan teknillisestä yliopistosta ja muualta. Myös keskiökärkiä valmistavien yritysten tuotekatalogeja tarkasteltiin. Seuraavaksi siirryttiin alustavaan suunnitteluvaiheeseen, jossa verifioitiin menetelmän toiminta ja luotiin konsepteja keskiökärjen rakenteen kehittämistä varten. Tämän alustavan vaiheen jälkeen suoritettiin suunnitteluprosessi keskiökärjen prototyypille. Lopuksi, suunnitellun prototyypin rakenteen käyttäytymistä arvioitiin tietokonemallinnuksen avulla. Lisätuloksena tutkimuksen aikana johdettiin yksinkertaistettu elementtimenetelmään perustuva laskentamalli järjestelmän ominaistaajuuksien selvittämiseksi. Laskentamallin tarkkuutta arvoitiin. Suunnitteluprosessin tuloksena saatiin kaikki menetelmän toiminnan sekä normaalin käytön asettamat vaatimukset täyttävä rakenne keskiökärjen prototyypille. Myös johdetun laskentamallin tulokset ovat varsin lähellä 3D-elementtimallinnuksen antamia tuloksia. Tutkimuksen tavoitteiden voidaan siis sanoa toteutuneen. Koska prototyyppiä ja laskentamallia ei kuitenkaan ole vielä kokeellisesti verifioitu, tämä ei ole täysin varmaa.

Studies of rotor dynamics using a multibody simulation approach

The non-idealities in a rotor-bearing system may cause undesirable subcritical superharmonic resonances that occur when the rotating speed of the rotor is a fraction of the natural frequency of the system. These resonances arise partly from the non-idealities of the bearings. This study introduces a novel simulation approach that can be used to study the superharmonic vibrations of rotor-bearing systems. The superharmonic vibrations of complex rotor-bearing systems can be studied in an accurate manner by combining a detailed rotor and bearing model in a multibody simulation approach. The research looks at the theoretical background of multibody formulations that can be used in the dynamic analysis of flexible rotors. The multibody formulations currently in use are suitable for linear deformation analysis only. However, nonlinear formulation may arise in high-speed rotor dynamics applications due to the cenrrifugal stiffening effect. For this reason, finite element formulations that can describe nonlinear deformation are also introduced in this work. The description of the elastic forces in the absolute nodal coordinate formulation is studied and improved. A ball bearing model that includes localized and distributed defects is developed in this study. This bearing model could be used in rotor dynamics or multibody code as an interface elements between the rotor and the supporting structure. The model includes descriptions of the nonlinear Hertzian contact deformation and the elastohydrodynamic fluid film. The simulation approaches and models developed here are applied in the analysis of two example rotor-bearing systems. The first example is an electric motor supported by two ball bearings and the second is a roller test rig that consists of the tube roll of a paper machine supported by a hard-bearing-type balanceing machine. The simulation results are compared to the results available in literature as well as to those obtained by measuring the existing structure. In both practical examples, the comparison shows that the simulation model is capable of predicting the realistic responses of a rotor system. The simulation approaches developed in this work can be used in the analysis of the superharmonic vibrations of general rotor-bearing systems.

Sellumassan varastosäiliön rakenneanalyysi

Tämä työ käsittelee valkaistun ja valkaisemattoman sellumassan varastosäiliön tärinää ja värähtelyä. Värähtelyn seurauksena säiliön seinämän jäykisterenkaan hitsausliitokseen on syntynyt särö. Työn tavoitteena on selvittää, mikä johtaa särön syntyyn ja miten kestäväm-piä varastosäiliöitä voidaan rakentaa materiaali-, valmistus- tai rakennemuutoksien avulla. Työ alkoi tutkimalla rakennemateriaalina olevan duplex-teräksen mikrorakenteen ominai-suuksia, sekä sen hitsattavuutta ja seostamista kirjallisuustutkimuksena. Kirjallisuustutki-musta jatkettiin selvittämällä mahdollisia vaurion syntymekanismeja seinämän särölle. Työssä analysoitiin myös tehtaalla mitattuja värähtelyarvoja. Lopuksi laskettiin FE-analyysillä tyhjän varastosäiliön ominaismuodot ja -taajuudet moodianalyysillä, sekä selvi-tettiin harmonisella analyysillä pinnankorkeuden vaihtelun vaikutus siirtymävasteeseen ja kriittisiin värähtelytaajuuksiin. Varastosäiliöön kohdistuvaa värähtelyä ei ole mahdollista poistaa kokonaan, mutta väräh-telyn aiheuttamia seurauksia kyetään rajaamaan useilla keinoilla. Toimenpiteinä voivat olla ainakin seinämän materiaalin paksuuden lisääminen, jäykisteripojen lisääminen ja kriittisten sellun pinnankorkeuksien välttäminen. Kriittiseksi pinnankorkeudeksi havaittiin 40–45 %:n täyttöaste ja turvalliseksi korkeudeksi 35–38 %:n täyttöaste. Varastosäiliölle kriittisen ominaistaajuuden katsotaan syntyvän taajuuksilla 3,3–3,8 Hz ja 5,8–6,4 Hz. Sellumassa putoaa varastosäiliöön noin 2 Hz taajuudella.

Multibody models for examination of touchdown bearing systems

Increased rotational speed brings many advantages to an electric motor. One of the benefits is that when the desired power is generated at increased rotational speed, the torque demanded from the rotor decreases linearly, and as a consequence, a motor of smaller size can be used. Using a rotor with high rotational speed in a system with mechanical bearings can, however, create undesirable vibrations, and therefore active magnetic bearings (AMBs) are often considered a good option for the main bearings, as the rotor then has no mechanical contact with other parts of the system but levitates on the magnetic forces. On the other hand, such systems can experience overloading or a sudden shutdown of the electrical system, whereupon the magnetic field becomes extinct, and as a result of rotor delevitation, mechanical contact occurs. To manage such nonstandard operations, AMB-systems require mechanical touchdown bearings with an oversized bore diameter. The need for touchdown bearings seems to be one of the barriers preventing greater adoption of AMB technology, because in the event of an uncontrolled touchdown, failure may occur, for example, in the bearing’s cage or balls, or in the rotor. This dissertation consists of two parts: First, touchdown bearing misalignment in the contact event is studied. It is found that misalignment increases the likelihood of a potentially damaging whirling motion of the rotor. A model for analysis of the stresses occurring in the rotor is proposed. In the studies of misalignment and stresses, a flexible rotor using a finite element approach is applied. Simplified models of cageless and caged bearings are used for the description of touchdown bearings. The results indicate that an increase in misalignment can have a direct influence on the bending and shear stresses occurring in the rotor during the contact event. Thus, it was concluded that analysis of stresses arising in the contact event is essential to guarantee appropriate system dimensioning for possible contact events with misaligned touchdown bearings. One of the conclusions drawn from the first part of the study is that knowledge of the forces affecting the balls and cage of the touchdown bearings can enable a more reliable estimation of the service life of the bearing. Therefore, the second part of the dissertation investigates the forces occurring in the cage and balls of touchdown bearings and introduces two detailed models of touchdown bearings in which all bearing parts are modelled as independent bodies. Two multibody-based two-dimensional models of touchdown bearings are introduced for dynamic analysis of the contact event. All parts of the bearings are modelled with geometrical surfaces, and the bodies interact with each other through elastic contact forces. To assist in identification of the forces affecting the balls and cage in the contact event, the first model describes a touchdown bearing without a cage, and the second model describes a touchdown bearing with a cage. The introduced models are compared with the simplified models used in the first part of the dissertation through parametric study. Damages to the rotor, cage and balls are some of the main reasons for failures of AMB-systems. The stresses in the rotor in the contact event are defined in this work. Furthermore, the forces affecting key bodies of the bearings, cage and balls can be studied using the models of touchdown bearings introduced in this dissertation. Knowledge obtained from the introduced models is valuable since it can enable an optimum structure for a rotor and touchdown bearings to be designed.

Investigation of molecular polarizabilities and derivatives in halomethanes

The research undertaken was to obtain absolute Raman intensities for the symmetric stretching vibrations of the methyl halides, CH3X with (X=F, CI, Br), by experiment and theory. The intensities were experimentally measured using the Ar+ ion gas laser as excitation source, a Spex 14018 double monochromator and a RCA C-31034 photomultiplier tube as detector. These intensities arise from changes in the derivative of the polarizability (8 a'), with respect to vibration along a normal coordinate (8qi). It was intended that these derivatives obtained with respect to normal coordinates would be converted to derivatives with respect to internal coordinates, for a quantitative comparison with theory. Theoretical numerical polarizability derivatives for the stretching vibrations are obtained using the following procedure. A vibration was simulated in the molecule by increasi.ng and decreasing the respective bond by the amount ±o.oosA for the C-H bonds and ±o.oIA for the C-X (X=F, CI, Br) bond. The derivative was obtained by taking the difference in the polarizability for the equilibrium geometry and the geometry when a particular bond is changed. This difference, when divided by the amount of change in each bond and the number of bonds present results in the derivative of the polarizability with respect to internal coordinate i.e., !1u/!1r. These derivatives were obtained by two methods: I} ab initio molecular orbital calculation and 2} theory of atoms in molecules (AIM) analysis. Due to errors in the experimental setup only a qualitative analysis of the results was undertaken relative to the theory. Theoretically it is predicted that the symmetric carbonhalogen stretch vibrations are more intense than the respective carbon-hydrogen stretch, but only for the methyl chloride and bromide. The carbon fluorine stretch is less intense than the carbon-hydrogen stretch, a fact which is attributed to the small size and high electronegativity of the fluorine atom. The experimental observations are seen to agree qualitatively with the theory results. It is hoped that when the experiment is repeated, a quantitative comparison can be made. The analysis by the theory of atoms in molecules, along with providing polarizabilities and polarizability derivatives, gives additional information outlined below. The theory provides a pictorial description of the main factors contributing to the molecular polarizability and polarizability derivative. These contributions are from the charge transfer and atomic dipole terms i.e., transfer of charge from one atom to another and the reorganization of atomic electronic charge distribution due to presence of an electric field. The linear relationship between polarizability and molecular volume was also observed.