Brake squeal is a common noise problem encountered in the automotive industry. Higherfriction coefficients and weight reduction recently led to higher vibration levels in the audiblefrequency range. This quality issue becomes economic due to penalties imposed to the brakesupplier although no robust design method exists. The industrial practice thus relies on costlyprototyping and adjustment phases. The evolution of computational power allows computationof large mechanical assemblies, but non-linear time simulations generally remain out of reach.In this context, the thesis objective is to provide numerical tools for squeal resolution at earlydesign stages.Parameterized reduction methods are developed, using system real modes as Rayleigh-Ritzvectors, and allow very compact reduced models with exact real modes. The proposed ComponentMode Tuning method uses the components free/free modes as explicit degrees of freedom.This allows very quick sensitivity computation and reanalyzes of an assembly as function oflocal component-wise parameters. Non-linear time simulations are made possible through twoingredients. A modified non-linear implicit Newmark scheme and a fixed Jacobian are adaptedfor contact vibrations. The brake is reduced keeping a superelement with exact real modes anda local non-linear finite element model in the vicinity of the pad/disc interaction.A set of design tools is illustrated for a full industrial brake model. First, instant stabilitycomputations and complex mode trajectories are studied. Modal interactions and non-linearphenomena inside the limit cycles are thus well understood. Time/frequency correlations areperformed using transient modal identification and space-time decomposition. A time domainmodal damping model is also shown to be very useful. The modification of a critical componentfor squeal resolution is finally tested and validated.

Le crissement de frein est une nuisance sonore classique dans l’automobile. L’augmentationdes coefficients de friction et la réduction de la masse mènent aujourd’hui à de hauts niveauxvibratoires dans les fréquences auditives, et ces problèmes de qualité se traduisent par des pénalités économiques aux équipementiers, bien qu’il n’existe pas de méthode robuste de conception.La pratique industrielle repose donc sur de coûteuses phases de prototypage et d’ajustement.L’évolution de la puissance de calcul permet le calcul de grands assemblages mécaniques mais lesétudes vibratoires non-linéaires restent généralement hors de portée. Dans ce contexte, l’objectifde la thèse est de fournir, dès les phases de conception, des outils de conception numérique d’aideà la résolution du crissement.Une méthode de réduction paramétrée utilisant comme base de Rayleigh-Ritz les modes réelsdu système assemblé permet la génération de modèles réduits très compacts, avec modes réelsexacts. La méthode proposée d’ajustement des modes de composants utilise les modes libresde composants comme degrés de liberté explicites. L’étude des sensibilités et la réanalyse d’unassemblage en fonction de modifications à l’échelle d’un composant deviennent possibles. Lesétudes temporelles non-linéaires sont rendues possibles par deux développements. Un schémade Newmark non-linéaire modifié et un Jacobien fixe adapté aux vibrations de contact sontintroduits. Le frein est réduit en un superélément avec modes réels exacts et une zone nonréduite au niveau du contact.Un ensemble d’outils de conception est illustré sur un modèle industriel de frein. La stabilitéinstantanée et les trajectoires de modes complexes sont étudiées. Les interactions modales et lesphénomènes non-linéaires au sein des cycles limites sont alors mieux compris. Des corrélationstemps/fréquence sont obtenues par l’identification modale instantanée et une décompositionespace-temps. La grande utilité d’un modèle temporel d’amortissement modal est illustrée.Enfin, la modification d’un composant critique au crissement est testée et validée. / Brake squeal is a common noise problem encountered in the automotive industry. Higherfriction coefficients and weight reduction recently led to higher vibration levels in the audiblefrequency range. This quality issue becomes economic due to penalties imposed to the brakesupplier although no robust design method exists. The industrial practice thus relies on costlyprototyping and adjustment phases. The evolution of computational power allows computationof large mechanical assemblies, but non-linear time simulations generally remain out of reach.In this context, the thesis objective is to provide numerical tools for squeal resolution at earlydesign stages.Parameterized reduction methods are developed, using system real modes as Rayleigh-Ritzvectors, and allow very compact reduced models with exact real modes. The proposed ComponentMode Tuning method uses the components free/free modes as explicit degrees of freedom.This allows very quick sensitivity computation and reanalyzes of an assembly as function oflocal component-wise parameters. Non-linear time simulations are made possible through twoingredients. A modified non-linear implicit Newmark scheme and a fixed Jacobian are adaptedfor contact vibrations. The brake is reduced keeping a superelement with exact real modes anda local non-linear finite element model in the vicinity of the pad/disc interaction.A set of design tools is illustrated for a full industrial brake model. First, instant stabilitycomputations and complex mode trajectories are studied. Modal interactions and non-linearphenomena inside the limit cycles are thus well understood. Time/frequency correlations areperformed using transient modal identification and space-time decomposition. A time domainmodal damping model is also shown to be very useful. The modification of a critical componentfor squeal resolution is finally tested and validated.

Vibrações mecânicas oferecem grande limitação para a produtividade, qualidade ou mesmo viabilidade das operações de usinagem, especialmente quando se trata das autoexcitadas (chatter). Neste trabalho, foram desenvolvidas estratégias que tem como objetivo diminuir a intensidade de vibrações em processos de torneamento por meio do acoplamento de material piezelétrico ao suporte de ferramenta em conjunto com uso de shunts resistivo, indutivo e resistivo-indutivo em série ou em paralelo, criando assim estruturas eletromecânicas passivamente amortecidas. Para tanto, foram construídos modelos eletromecânicos de parâmetros distribuídos para mostrar a capacidade que tais estruturas eletromecânicas possuem em oferecer um maior amortecimento quando comparadas com estruturas mecânicas convencionais. Com os modelos construídos, foi possível verificar a influência causada pela espessura da camada de material piezelétrico bem como a influência dos shunts no comportamento da estrutura, sendo constatado que camadas mais espessas aumentam a capacidade de amortecimento da estrutura e que os shunts resistivo-indutivo, tanto em série quanto em paralelo, funcionam como um amortecedor dinâmico de vibrações amortecido e oferecem o melhor desempenho. A seguir, construiu-se o diagrama de lóbulos de estabilidade para comparar as estruturas com e sem shunts e observou-se que as estruturas com shunts resistivo-indutivo possuem um melhor desempenho. Também foram executados testes de impacto (tap tests) para a verificação experimental do comportamento da estrutura quando conectadas aos shunts e os resultados mostraram que há um maior amortecimento. Considerando os resultados obtidos, acredita-se que seja possível melhorar o desempenho de processos de torneamento usando material piezelétrico. / Mechanical vibrations offer great limitation for the productivity, quality or even feasibility of the machining operations when chatter is present. In this work it was developed strategies aiming to diminish the intensity of the vibration in turning processes. By coupling a piezoelectric material with a turning tool and by using different associations of resistive and inductive shunt (series or parallel) it was created electromechanical structures passively damped. Electromechanical models of distributed parameters were developed in order to show the capacity that these structures has to offer a greater dumping when compared with conventional mechanical structures. By using these constructed models it was possible to verify the influence of the thickness of the piezoelectric material as well as the influence of shunts in the behavior of structure. It was observed that thicker layers increase the damping capacity of the structure that resistive-inductive shunt (series or parallel) works as a damped dynamic vibration absorber which offer better performance. Latter was developed a stability lobes diagram in order to compare the structures with and without shunts and it was observed that structures connected to resistiveinductive shunt has a better performance. Tap tests were performed for the purpose of study the experimental behavior of the structure connected to shunt and results showed that there is a better damping in this situation. Considering the results obtained, is fair to believe that is possible to improve turning process by using piezoelectric materials.

Vibrações mecânicas oferecem grande limitação para a produtividade, qualidade ou mesmo viabilidade das operações de usinagem, especialmente quando se trata das autoexcitadas (chatter). Neste trabalho, foram desenvolvidas estratégias que tem como objetivo diminuir a intensidade de vibrações em processos de torneamento por meio do acoplamento de material piezelétrico ao suporte de ferramenta em conjunto com uso de shunts resistivo, indutivo e resistivo-indutivo em série ou em paralelo, criando assim estruturas eletromecânicas passivamente amortecidas. Para tanto, foram construídos modelos eletromecânicos de parâmetros distribuídos para mostrar a capacidade que tais estruturas eletromecânicas possuem em oferecer um maior amortecimento quando comparadas com estruturas mecânicas convencionais. Com os modelos construídos, foi possível verificar a influência causada pela espessura da camada de material piezelétrico bem como a influência dos shunts no comportamento da estrutura, sendo constatado que camadas mais espessas aumentam a capacidade de amortecimento da estrutura e que os shunts resistivo-indutivo, tanto em série quanto em paralelo, funcionam como um amortecedor dinâmico de vibrações amortecido e oferecem o melhor desempenho. A seguir, construiu-se o diagrama de lóbulos de estabilidade para comparar as estruturas com e sem shunts e observou-se que as estruturas com shunts resistivo-indutivo possuem um melhor desempenho. Também foram executados testes de impacto (tap tests) para a verificação experimental do comportamento da estrutura quando conectadas aos shunts e os resultados mostraram que há um maior amortecimento. Considerando os resultados obtidos, acredita-se que seja possível melhorar o desempenho de processos de torneamento usando material piezelétrico. / Mechanical vibrations offer great limitation for the productivity, quality or even feasibility of the machining operations when chatter is present. In this work it was developed strategies aiming to diminish the intensity of the vibration in turning processes. By coupling a piezoelectric material with a turning tool and by using different associations of resistive and inductive shunt (series or parallel) it was created electromechanical structures passively damped. Electromechanical models of distributed parameters were developed in order to show the capacity that these structures has to offer a greater dumping when compared with conventional mechanical structures. By using these constructed models it was possible to verify the influence of the thickness of the piezoelectric material as well as the influence of shunts in the behavior of structure. It was observed that thicker layers increase the damping capacity of the structure that resistive-inductive shunt (series or parallel) works as a damped dynamic vibration absorber which offer better performance. Latter was developed a stability lobes diagram in order to compare the structures with and without shunts and it was observed that structures connected to resistiveinductive shunt has a better performance. Tap tests were performed for the purpose of study the experimental behavior of the structure connected to shunt and results showed that there is a better damping in this situation. Considering the results obtained, is fair to believe that is possible to improve turning process by using piezoelectric materials.

<p>Predmet istraživanja prikazanih u okviru doktorske diseracije su samopobudne vibracije pri obradi glodanjem. Na osnovu detaljne analize zakonitosti nastanka samopobudnih vibracija uspostavljena je određena paralela između glodanja i mikrogkodanja, za slučajeve kada je dubina rezanja veća od radijusa rezne ivice alata. Za tako usvojene pretpostavke, razvijeni su modeli unapređene numeričke simulacije procesa glodanja i mikroglodanja. Razvijeni modeli su svestrano verifikovani, s jedne strane, u segmentima gde postoje podaci u literaturi; poređenjem sa rezultatima drugih autora, a sa druge strane poređenjem sa sopstvenim eksperimentalnim ispitivanjima. Za eksperimentalno definisanje granične dubine rezanja pri glodanju predložena je inovativna metoda tangenti, a pri mikroglodanju, imajući u vidu raspoloživu mernu opremu, metoda hrapavosti obrađene površine. Matematički modeli i eksperimentalne metode su verifikovani pri obradi tri karakteristične vrste materijala i na dva obradna sistema pri glodanju, odnosno jednom materijalu i jednom obradnom sistemu pri mikroglodanju. Rezultati istraživanja su prezentovani kroz dvanaest poglavlja čiji sadržaj se navodi u nastavku.</p><p>U prvom, uvodnom poglavlju, ukazano je na značaj istraživanja samopobudnih vibracija pri makro i mikroglodanju. Prikazana je i aktuelnost istraživanja analizom broja naučnih radova koji se bave problematikom samopobudnih vibracija u periodu od poslednjih dvadeset pet godina.<br />Kroz drugo poglavlje detaljno su prikazana dosadašnja istraživanja samopobudnih vibracija pri makroglodanju, dok su u trećem poglavlju prikazana istraživanja samopobudnih vibracija pri mikroglodanju. Izvršena je analiza uticajnih parametri na graničnu dubinu rezanja, koja predstavlja osnovni pokazatelj dinamičke stabilnosti kako makro, tako i mikroobradnih sistema.<br />Na osnovu saznanja prikazanih u okviru drugog i trećeg poglavlja u četvrtom poglavlju su definisani ciljevi i hipoteze istraživanja.<br />Matematičke metode za definisanje karte stabilnosti obradnog sistema, prikazane su u petom poglavlju. Prikazana su dva matematička modela za definisanje karte stabilnosti pri makroglodanju, model srednjeg ugla kontakta alata u zahvatu i model Furijeovih redova. Prezentovana je numerička simulacija procesa obrade glodanjem, namenjena prvenstveno za simulaciju sila rezanja. Polazeći od prethodno prikazane ideje u okviru ovog poglavlja je razvijena nova matematička metoda predikcije granične dubine rezanja - unapređena numerička simulacija procesa glodanja.<br />U okviru šestog poglavlja prikazane su eksperimentalne metode identifikacije vibracija mašina alatki, odnosno eksperimentalno određivanje modalnih parametara obradnih sistema kao i metode detekcije samopobudnih vibracija pri glodanju. U cilju definisanja granične dubine rezanja, prikazana je metoda frekventne analize vibracija pri glodanju, kao metoda koja se često koristi u savremenim eksperimentalnim istraživanjima. Međutim, i matematičke i eksperimentalne metode analize vibracija pri glodanju imaju određena ograničenja. Polazeći od prethodnog, razvijena je inovativna metoda tangenti, bazirana na ranije korišćenoj metodi u okviru Laboratorije za mašine alatke Instituta za proizvodno mašinstvo FTN u Novom Sadu, i primeni savremenih mernih sistema. Pored toga, u ovom poglavlju je eksperimentalno potvrđen uticaj samopobudnih vibracija na kvalitet obrađene površine i geometrijsku tačnost obratka.<br />Metodologija sprezanja matematički i eksperimentalno definisanih funkcija frekventnog odziva elemenata mašine alatke prikazana je u sedmom poglavlju. Prezentovane su jednačine sprezanja pomerajnih odziva matematmički definisanih funkcija frekventnog odziva alata i držača alata, bazirane na Ojlerovoj teoriji grede, sa eksperimentalno definisanom funkcijom frekventnog odziva sklopa glavnog vretena mašine alatke.<br />U okviru osmog poglavlja razvijen je matematički model sila rezanja pri mikroglodanju. Predloženi model sila rezanja, koji uzima u obzir silu trenja između leđne površine alata i obrađene površine, implementiran je u unapređenu numeričku simulaciju glodanja čime je omogućena njena primena za definisanje graničnih dubina rezanja pri mikroglodanju.</p><p>Verifikacija razvijenih numeričkih i eksperimentalnih metoda za ispitivanje vibracija pri makroglodanju je prikazana u devetom poglavlju. Sproveden je niz eksperimentalnih ispitivanja, pri kojima su određivane granične dubine glodanja pri obradi tri različita materijala obratka (Al7075, 42CrMo4 i Ti-6Al-4V) na dva obradna sistema. Na osnovu ovih ispitivanjima izvršena je verifikacija unapređene numeričke simulacije glodanja i inovativne metode tangenti.<br />U desetom poglavlju prikazana je verifikacija metoda analize samopobudnih vibracija pri mikroglodanju. Primenom metodologije sprezanja pomerajnih odziva, definisani su modalni parametri obradnog sistema za mikroobradu, potrebni za definisanje graničnih dubina rezanja, tj. karte stabilnosti, unapređenom numeričkom simulacijom mikroglodanja. Karta stabilnosti definisana razvijenom unapređenom numeričkom simulacijom, verifikovana je eksperimentalno i poređenjem sa literaturnim izvorima.<br />U jedanaestom poglavlju data su zaključna razmatranja, kritički osvrt na ostvarene rezultate, i pravci budućih istraživanja.<br />Dvanaesto poglavlje prikazuje pregled korišćene literature, koju čini 218 referenci većim delom citirane u samom radu, a u zasebnom poglavlju dati su prilozi.</p> / <p>The subject of research presented in the doctoral dissertation are self-excited vibrations in milling. Based on a detailed analysis of the self-excited vibrations occurrence, a certain parallel has been established between macro and micromilling, for cases when the depth of cut is greater than the cutting edge radius of the tool. For such adopted assumptions, models of advanced numerical simulation of macro and micromilling processes were developed. The developed models were comprehensively verified, on the one hand, by comparison with the results of other authors, and on the other hand by comparison with own experimental results. An innovative tangent method has been proposed for the experimental definition of the cutting depth limit in milling, and the method of machined surface roughness has been proposed for micromilling, having in mind the available measuring equipment. Mathematical models and experimental methods were verified by machining three characteristic types of materials on two machining systems in macromilling, and one material on one machining system in micromilling. The results of the research are presented through twelve chapters, the content of which is listed below.</p><p>In the first, introductory chapter, the importance of the research of self - excited vibrations in macro and micromilling is pointed out. The topicality of the research is also presented by analyzing the number of scientific papers dealing with the issue of self - excited vibrations in the period of the last twenty - five years.<br />The second chapter presents in detail the previous research on self-excited vibrations during macromilling, while the third chapter presents research on self-excited vibrations during micromilling. An analysis of the influential parameters on the cutting depth limit was performed, which is a basic indicator of the dynamic stability of both macro and micromachining systems.<br />Based on the findings presented in the second and third chapters, the fourth chapter defines the goals and hypotheses of the research.<br />Mathematical methods for defining the stability lobe diagram of the machining system are presented in the fifth chapter. Two mathematical models for defining the stability lobe diagram for macromachining are presented, the model of the tool&rsquo;s mean contact angle and the model of Fourier series. Numerical simulation of the milling process is presented, intended primarily for the simulation of cutting forces. Starting from the previously presented idea, a new mathematical method for predicting the cutting depth limit has been developed within this chapter - an improved numerical simulation of the milling process.<br />In the sixth chapter, experimental methods of machine tools vibration identification are presented, ie experimental determination of machining systems modal parameters as well as methods of self - excited vibrations detection during milling. In order to define the cutting depth limit, the method of vibrations frequency analysis during milling is presented, as a method that is often used in modern experimental research. However, both mathematical and experimental methods of milling vibration analysis have certain limitations. Starting from the previous one, an innovative tangent method was developed, based on the previously developed method, used within the Laboratory for Machine Tools, Institute of Production Engineering Facultz of Technical Sciences in Novi Sad, and the application of modern measuring systems. In addition, in this chapter, the influence of self - excited vibrations on the machined surface quality and the geometric accuracy of the workpiece is experimentally confirmed.<br />The methodology of machine tool elements mathematically and experimentally defined frequency response functions coupling is presented in the seventh chapter. The displacement responses coupling equations of mathematically defined tools and tool holders FRF&#39;s (based on Euler &#39;s beam theory) with the experimentally defined FRF of the machine tool main spindle assembly are presented.<br />Within the eighth chapter, a mathematical model of cutting forces in micromilling was developed. The proposed cutting forces model, which takes into account the friction force between the reliefe tool surface and the machined surface, is implemented in an advanced numerical micromilling simulation, which enables its application to define cutting depth limit in micromilling.</p><p>Verification of the developed numerical and experimental methods for vibrations analysis during macromachining is presented in the ninth chapter. A series of experimental tests were performed, during which the cutting depth limits were determined during the milling of three different workpiece materials (Al7075, 42CrMo4 and Ti-6Al-4V) on two machining systems.<br />In the tenth chapter, the verification of the methods of analysis of self-excited vibrations during micromilling is presented. Using the methodology of coupling displacement responses, the modal parameters of the machining system for micromachining are defined, needed to define the cutting depth limits, ie. stability lobe diagram, by advanced numerical micromilling simulation The stability lobe diagram, defined by the developed advanced numerical simulation, was verified experimentally and by comparison with literature sources.<br />The eleventh chapter provides concluding remarks, a critical review of the achieved results, and directions for future research.<br />The twelfth chapter presents an overview of the used literature, which consists of 218 references, mostly cited in the paper itself.</p>

Les bruits automobiles induits par le frottement sont à l’origine de nombreuses plaintes clients et occasionnent des coûts de garantie considérables pour les constructeurs automobiles. Les objectifs de la thèse consistent à comprendre la physique à l’origine de ces bruits et proposer des méthodologies de simulation afin de les éradiquer. Un système générique est tout d’abord étudié. Ce système discret met en jeu un contact entre deux masses et une loi de frottement de Coulomb présentant une discontinuité à vitesse relative nulle. Des calculs de valeurs propres complexes de ce système linéarisé autour de sa position d’équilibre glissant sont menés et montrent la présence d’instabilités par flottement voire par divergence. Les simulations temporelles montrent quant à elles que les non-linéarités de contact permettent de stabiliser les niveaux vibratoires en cas d’instabilité selon quatre régimes distincts. De plus, malgré ses trois degrés de liberté, ce système est capable de reproduire les mécanismes de stick-slip, sprag-slip et couplage modal ainsi que les bruits de crissement, grincement et craquement rencontrés sur les systèmes automobiles. Des études paramétriques sont également présentées et mettent en avant des bifurcations de Hopf ainsi que l’effet déstabilisant potentiellement induit par l’amortissement. Des méthodologies permettant de catégoriser les réponses en termes de bruit et de mécanisme sont par la suite proposées. Les occurrences et risques de ces derniers sont alors analysés et des tendances sont dégagées. Enfin, la relation entre les bruits et les mécanismes est établie. L’attention est ensuite portée sur un système automobile particulier. Afin d’étudier son comportement crissant, les analyses de stabilité et les simulations temporelles sont désormais menées sur des modèles éléments-finis. Les simulations temporelles permettent d’observer l’établissement de vibrations auto-entretenues et d’identifier, parmi tous les modes instables prédits lors des analyses de stabilité, celui qui est réellement à l’origine de l’instabilité. L’effet du coefficient de frottement sur les motifs de coalescence et les cycles limites est également investigué. Le risque de crissement est ensuite évalué pour des conditions d’utilisation variées du système. La méthodologie, basée sur des analyses de stabilité, permet de retrouver les principaux constats expérimentaux obtenus sur banc d’essai. Le rôle des géométries et des matériaux constituant le système est également discuté. Enfin, une solution permettant de réduire de façon significative le risque de crissement est proposée. / Automotive friction-induced noises are the source of many customer complaints and lead to hugewarranty costs for car manufacturers. The objectives of the thesis are to improve the understanding ofthe physics at the origin of these noises and to propose numerical methodologies to eradicate them.A generic system is first investigated. This discrete system includes a contact between two masses anda Coulomb friction law with a discontinuity at zero relative velocity. Calculations of complex eigenvaluesof the linearized system around its sliding equilibrium position are carried out and show the presence offlutter and even divergence instabilities. Time simulations show that contact non-linearities permit tostabilize the vibrational levels in case of instability according to four distinct behaviors. Furthermore,despite its three degrees of freedom, this system is able to reproduce the stick-slip, sprag-slip and modecouplingmechanisms as well as the squeal, squeak and creak noises encountered in automotive systems.Parametric studies are also presented and highlight Hopf bifurcations as well as the destabilizing effectpotentially induced by damping. Methodologies allowing the categorization of the responses in termsof noise and mechanism are then proposed. Occurrences and risks of these noises and mechanismsare thus analyzed and trends are highlighted. The relationship between noises and mechanisms is alsoestablished.A specific automotive system is then considered. In order to study its squeal behavior, stabilityanalysis and time simulations are now carried out on finite element models. Time simulations allowto observe the establishment of self-excited vibrations and to identify, among all the unstable modespredicted by the stability analysis, the one which is actually the source of the instability. The effectof friction on the coalescence patterns and limit cycles is also investigated. The risk of squeal is thenevaluated in different operating conditions. The methodology, based on stability analysis, leads toresults in good agreement with the experimental observations. The role of geometries and materialsconstituting the system is also discussed. Finally, a solution with significantly low risk of squeal isproposed.

This thesis deals with computational modeling of curve squeal noise phenomena which occurs during cornering tight curves by trams. Lateral creep between rail and wheel and slip-stick phenomena leads to self-excited vibrations of the wheel which, therefore, emits unpleasant high-pitched noise. Two FEM models in frequency domain are carried out. First model is based on prestressed modal analysis. Due to unsymmetric stiffness matrix, unstable eigenvalues can occur. It is assumed that self-excited vibrations occurs on frequencies corresponding to that eigenvalues. Second model uses harmonic response analysis. It examines vibrations of the wheel excited by lateral creep force acting in contact region. This force is obtained externally by simple time-domain model. Results from harmonic response are used consequently for noise radiation computation.

This diploma thesis deals with the design of a two-axis multi-spindle lathe carriage. In the first part, there is made a research, and its aim is to find possible variants of design solutions. After the best rated variant was selected, the thesis further continues with the necessary technical calculations of the main design nodes such as a synchronous servomotor, ball screw, linear guide and bearing. The design itself was carried out with regard to calculations and the resulting model was examined in terms of dynamic stability. The subject of examination was to find the natural frequencies of the assembly and to determine the amplitudes of the oscillations which arise from the harmonic excitation force. Finally, Lobe diagrams for grooving and longitudinal turning operations were drawn.