Chatter é uma vibração auto-excitada que ocorre durante usinagens e limita a produtividade do processo. Esta instabilidade causa qualidade superficial inaceitável, diminuição da vida da ferramenta e ruído. Estratégias para definição de modelos e controle desta vibração são importantes, devendo ser avaliadas e implementadas. Neste trabalho foram realizados experimentos e características como frequências naturais, respostas em frequência e respostas temporais foram obtidas. Analisando tais resultados é possível a visualização do acoplamento existente nas duas direções de vibração. Uma estratégia de redução de chatter foi implementada, através do uso de shunts passivos conectados ao sistema mecânico por meio de material piezoelétrico, e sua viabilidade foi verificada. A estratégia foi adaptada para ser utilizada nas duas direções de vibração e o resultado da redução da vibração se provou mais eficiente após esta adaptação. Diagramas de fase, respostas temporais e espectros foram obtidos durante a usinagem e um comportamento não-linear se mostrou presente. Após a validação do uso de material piezoelétrico para o controle de chatter, existe a necessidade de modelos numéricos para a descrição do fenômeno, para que controles ativos e mais efetivos possam ser desenvolvidos. Devido ao acoplamento entre as duas direções de vibração e ao comportamento não linear do fenômeno, modelos que contenham tais características foram estudados, modificados e adaptados. Os resultados numéricos obtidos pelos modelos estudados foram então comparados aos resultados experimentais e conclusões sobre similaridades foram apresentadas. Considerando os resultados obtidos, acredita-se que o modelo que melhor representa o sistema real pode ser utilizado para o desenvolvimento de controles ativos, que garantam uma redução mais efetiva do chatter. / Chatter is a self-excited vibration that leads to instability during ongoing machining, which affects productivity. Chatter instability causes poor surface quality, diminishes the tool\'s life and may cause clatter. Therefore, strategies to control chatter and chatter models are highly necessary, and must be evaluated and implemented. In an experimental campaign done during this work, characteristics such as natural frequencies, frequency responses and temporal responses were obtained. Trough these analysis, it was observed that the system presents a coupling in its two normal directions of vibration. One strategy for chatter reduction was then implemented, in which a passive shunt using piezoelectric material was used. The feasibility of this chatter reduction strategy for one direction could be verified. In addition, the strategy was adapted in order to be utilized in both main vibration directions and the results confirmed that this approach grants better results for the reduction of chatter. Phase-planes, temporal responses and spectras could also be derived from the turning experiments and a nonlinear behavior could be seen present. Being verified the possibility of using a piezoelectric material in chatter control, numerical models that describe the phenomena should be pursued, so that more effective active control could be developed. Because the experiments show the mode coupling between two directions and a nonlinear behavior, models that represent such characteristics were studied, modified and adapted. The numerical results from this models were then compared to the experiments and conclusions were drawn. Considering the obtained results, it is believed that the most similar model should be used in the development of active control that could guarantee a better chatter reduction.

Chatter é uma vibração auto-excitada que ocorre durante usinagens e limita a produtividade do processo. Esta instabilidade causa qualidade superficial inaceitável, diminuição da vida da ferramenta e ruído. Estratégias para definição de modelos e controle desta vibração são importantes, devendo ser avaliadas e implementadas. Neste trabalho foram realizados experimentos e características como frequências naturais, respostas em frequência e respostas temporais foram obtidas. Analisando tais resultados é possível a visualização do acoplamento existente nas duas direções de vibração. Uma estratégia de redução de chatter foi implementada, através do uso de shunts passivos conectados ao sistema mecânico por meio de material piezoelétrico, e sua viabilidade foi verificada. A estratégia foi adaptada para ser utilizada nas duas direções de vibração e o resultado da redução da vibração se provou mais eficiente após esta adaptação. Diagramas de fase, respostas temporais e espectros foram obtidos durante a usinagem e um comportamento não-linear se mostrou presente. Após a validação do uso de material piezoelétrico para o controle de chatter, existe a necessidade de modelos numéricos para a descrição do fenômeno, para que controles ativos e mais efetivos possam ser desenvolvidos. Devido ao acoplamento entre as duas direções de vibração e ao comportamento não linear do fenômeno, modelos que contenham tais características foram estudados, modificados e adaptados. Os resultados numéricos obtidos pelos modelos estudados foram então comparados aos resultados experimentais e conclusões sobre similaridades foram apresentadas. Considerando os resultados obtidos, acredita-se que o modelo que melhor representa o sistema real pode ser utilizado para o desenvolvimento de controles ativos, que garantam uma redução mais efetiva do chatter. / Chatter is a self-excited vibration that leads to instability during ongoing machining, which affects productivity. Chatter instability causes poor surface quality, diminishes the tool\'s life and may cause clatter. Therefore, strategies to control chatter and chatter models are highly necessary, and must be evaluated and implemented. In an experimental campaign done during this work, characteristics such as natural frequencies, frequency responses and temporal responses were obtained. Trough these analysis, it was observed that the system presents a coupling in its two normal directions of vibration. One strategy for chatter reduction was then implemented, in which a passive shunt using piezoelectric material was used. The feasibility of this chatter reduction strategy for one direction could be verified. In addition, the strategy was adapted in order to be utilized in both main vibration directions and the results confirmed that this approach grants better results for the reduction of chatter. Phase-planes, temporal responses and spectras could also be derived from the turning experiments and a nonlinear behavior could be seen present. Being verified the possibility of using a piezoelectric material in chatter control, numerical models that describe the phenomena should be pursued, so that more effective active control could be developed. Because the experiments show the mode coupling between two directions and a nonlinear behavior, models that represent such characteristics were studied, modified and adapted. The numerical results from this models were then compared to the experiments and conclusions were drawn. Considering the obtained results, it is believed that the most similar model should be used in the development of active control that could guarantee a better chatter reduction.

Self-excited vibration, known as chatter, limits material removal rate, surface finish and accuracy in machining, and may even cause structural damage to components of the machining system. Machining stability may be enhanced by a variety of methods, from moving machining parameters to stable regions, or using actively actuated tools specially designed to obstruct self-excitation, or even by passively enhancing the stiffness or damping of the system as to soften the critical mode of vibration. Although there are many approaches to reduce chatter, not all of them are always effective in every situation. Moving machining parameters is restricted by workpiece machinability. Active damping mechanisms require large contraptions to function and have limited effectiveness when dealing with high frequency chatter. Passive damping approaches have essentially entailed tuned mass dampers which require delicate finetuning and drastic alterations to the tool structure in order mount the vibration absorber system. This research presents an elegant and innovative application involving electrical discharge texturing for chatter suppression that takes advantage of frictional forces to passively damp self-excited vibrations. This technique proved effective in a frequency range from 100 to 4000 Hz achieving damping enhancements of more than 400% without the need of any tuning and showing repeatable damping values after subsequent assembly and disassembly cycles. When applied to a grooving operation the technique proved effective in increasing the limiting width of cut by more than 120%. / Thesis / Master of Applied Science (MASc)

Chatter, unstable vibration during machining, damages the tool and workpiece. A proper selection of spindle speed and depth of cut are required to prevent chatter during machining. Such proper cutting conditions are usually determined using vibration models of the machining process. Nonetheless, uncertainties in modeling or changes in dynamics during the machining operations can lead to unstable machining vibrations, and chatter may arise even when stable cutting conditions are used in the process planning stage. As a result, online chatter monitoring systems are key to ensuring chatter-free machining operations. Although various chatter monitoring systems are described in the literature, most of the existing methods are suitable for detecting chatter after vibrations become unstable. In order to prevent poor surface finish resulting from chatter marks during the finishing stages of machining, a new monitoring system that is capable of predicting the occurrence of chatter while vibrations are still stable is required. In this thesis, a new approach for predicting the loss of stability during stable turning operations is developed. The new method is based on the identification of the dynamics of self-excited vibrations during turning operations using Operational Modal Analysis (OMA). The numerical simulations and experimental results presented in this thesis confirm the possibility of using Operational Modal Analysis as an online chatter prediction method during stable machining operations. / Graduate

Chatter is unwanted since it causes deteriorating effects on the milling process. Stability lobe diagrams are developed in order to determine the stable cutting conditions at which chatter-free machining can be made. The need of cutting away more chips to make milling operations quicker has brought the concept of high-speed milling. This increased the importance of estimating stability lobe diagrams of the milling process more accurately. The state-of-art chatter and spindle-toolholder-tool models predict the stability lobe diagram for milling process quite effectively. However, sometimes chatter might occur even at cutting conditions selected using theoretically obtained stability lobe diagrams. One of the reasons for that may be nonlinearities in the system. This being the motivation, in this work, nonlinearities at the bearings of spindle-toolholder-tool system are investigated. In this thesis, cubic nonlinearity is assumed to represent stiffness of a bearing in a spindle-toolholder-tool system. Effects of nonlinearity on stability lobe diagram of a milling process are studied by using the mathematical model developed for such a system. Frequency response function of spindle-toolholder-tool system without bearings is obtained using Timoshenko beam model. Then, bearings are modeled by using describing function theory and coupled to the dynamics of spindle-toolholder-tool modeled. Solution of the equations of motion of the system in frequency domain is obtained via Newton&#039 / s method with ALC. It is an effective frequency domain method in which turning points on frequency response function are traced. This is important for the system studied, as bearing nonlinearity may introduce turn backs in the response of the system. Case studies are carried out to study the effects of bearing nonlinearity on stability lobe diagram. The effects of the following factors are studied: Magnitude of cutting force, degree of nonlinearity and number of teeth on cutter. Displacement amplitude dependent stiffness of bearings affects the dynamic response due to rigid body modes of the system. It is observed that an increase in cutting force magnitude or in coefficient of bearing nonlinearity results in increase of natural frequencies, thus showing hardening behavior. Shifting of frequencies in the response curve shifts stability lobes related to the affected modes, to the right. For increased number of flutes on cutter, effect of nonlinearity at bearings on stability of the milling process becomes lower. Experimental studies to determine the changes in dynamics of a system during cutting are also carried out in this thesis. Inverse chatter analysis is conducted to obtain modal parameters of a single-degree-of-freedom system using the experiment data. Decrease in natural frequency is observed at high cutting speeds for the particular spindle used. This shift may be due to speed-dependent bearing dynamics and real time adjustment of preload on bearings.

The aim of the thesis is to propose active damping as a potential control strategy for chatter instability in machine tools. The regenerative process theory explains chatter as a closed loop interaction between the structural dynamics and the cutting process. This is considered to be the most dominant reason behind machine tool chatter although other instability causing mechanisms exist. The stability lobe diagram provides a quantitative idea of the limits of stable machining in terms of two physical parameters: the width of contact between tool and the workpiece, called the width of cut and the speed of rotation of the spindle. It is found that the minimum value of the stability limit is proportional to the structural damping ratio for turning operations. This important finding provides the motivation of influencing the structural dynamics by active damping to enhance stability limits of a machining operation. A direct implementation of active damping in an industrial environment may be difficult. So an intermediate step of testing the strategy in a laboratory setup, without conducting real cutting is proposed. Two mechatronic "Hardware in the Loop" simulators for chatter in turning and milling are presented, which simulate regenerative chatter experimentally without conducting real cutting tests. A simple cantilever beam, representing the MDOF dynamics of the machine tool structure constitutes the basic hardware part and the cutting process is simulated in real time on a DSP board. The values of the cutting parameters such as spindle speed and the axial width of cut can be changed on the DSP board and the closed loop interaction between the structure and the cutting process can be led to instability. The demonstrators are then used as test beds to investigate the efficiency of active damping, as a potential chatter stabilization strategy. Active damping is easy to implement, robust and does not require a very detailed model of the structure for proper functioning, provided a collocated sensor and actuator configuration is followed. The idea of active damping is currently being implemented in the industry in various metal cutting machines as part of the European Union funded SMARTOOL project (www.smartool.org), intended to propose smart chatter control technologies in machining operations.

Tool chatter in longitudinal turning is addressed with a new perspective using a complex machining model describing the coupled tool-workpiece dynamics subject to nonlinear regenerative cutting forces, instantaneous depth-of-cut (DOC) and workpiece whirling due to material imbalance. The workpiece is modeled as a system of three rotors: unmachined, being machined and machined, connected by a flexible shaft. The model enables workpiece motions relative to the tool and tool motions relative to the machining surface to be three-dimensionally established as functions of spindle speed, instantaneous DOC, rate of material removal and whirling. Excluding workpiece vibrations from the cutting model is found improper. A rich set of nonlinear behaviors of both the tool and the workpiece including period-doubling bifurcation and chaos signifying the extent of machining instability at various DOCs is observed. Presented numerical results agree favorably with physical experiments reported in the literature. It is found that whirling is non-negligible if the fundamental characteristics of machining dynamics are to be fully understood. The 3D model is explored along with its 1D counterpart, which considers only tool motions and disregards workpiece vibrations. Numerical simulations reveal diverse behaviors for the 3D coupled and 1D uncoupled equations of motion for the tool. Most notably, observations made with regard to the inconsistency in describing stability limits raise the concern for using 1D models to obtain stability charts. The nonlinear 3D model is linearized to investigate the implications of applying linear models to the understanding of machining dynamics. Taylor series expansion about the operating point where optimal machining conditions are desired is applied to linearize the model equations of motion. Modifications are also made to the nonlinear tool stiffness term to minimize linearization errors. Numerical experiments demonstrate inadmissible results for the linear model and good agreement with available physical data in describing machining stability and chatter for the nonlinear model. Effects of tool geometry, feed rate, and spindle speed on cutting dynamics are also explored. It is observed that critical DOC increases with increasing spindle speed and small DOCs can induce cutting instability -- two of the results that agree qualitatively well with published experimental data.

Tool chatter in longitudinal turning is addressed with a new perspective using a complex machining model describing the coupled tool-workpiece dynamics subject to nonlinear regenerative cutting forces, instantaneous depth-of-cut (DOC) and workpiece whirling due to material imbalance. The workpiece is modeled as a system of three rotors: unmachined, being machined and machined, connected by a flexible shaft. The model enables workpiece motions relative to the tool and tool motions relative to the machining surface to be three-dimensionally established as functions of spindle speed, instantaneous DOC, rate of material removal and whirling. Excluding workpiece vibrations from the cutting model is found improper. A rich set of nonlinear behaviors of both the tool and the workpiece including period-doubling bifurcation and chaos signifying the extent of machining instability at various DOCs is observed. Presented numerical results agree favorably with physical experiments reported in the literature. It is found that whirling is non-negligible if the fundamental characteristics of machining dynamics are to be fully understood. The 3D model is explored along with its 1D counterpart, which considers only tool motions and disregards workpiece vibrations. Numerical simulations reveal diverse behaviors for the 3D coupled and 1D uncoupled equations of motion for the tool. Most notably, observations made with regard to the inconsistency in describing stability limits raise the concern for using 1D models to obtain stability charts. The nonlinear 3D model is linearized to investigate the implications of applying linear models to the understanding of machining dynamics. Taylor series expansion about the operating point where optimal machining conditions are desired is applied to linearize the model equations of motion. Modifications are also made to the nonlinear tool stiffness term to minimize linearization errors. Numerical experiments demonstrate inadmissible results for the linear model and good agreement with available physical data in describing machining stability and chatter for the nonlinear model. Effects of tool geometry, feed rate, and spindle speed on cutting dynamics are also explored. It is observed that critical DOC increases with increasing spindle speed and small DOCs can induce cutting instability -- two of the results that agree qualitatively well with published experimental data.

In theoretical part, this master´s thesis deals with vibrations in cutting machine and description of creation of self-excited vibrations theory. In practical part, there is problem of chatter in cutting machine solved with using simulation program Adams and computing program MATLAB. Gradually, Multi body system of cutting machine and model of cutting tool with features flexible body are analyzed. At the end all both models were used to create complex model of the cutting machine .

O chatter é o principal problema de instabilidade nos processos de usinagem, e é causado pelas ondulações deixadas na superfície durante cortes sucessivos, ou chamado processo de regeneração, e é caracterizado pelo ruído e qualidade superficial ruim nas superfícies usinadas. Portanto, a comunidade científica tem se preocupado em desenvolver ações, tanto para a predição do fenômeno, como para desenvolver estratégias para sua redução. Neste trabalho avalia-se numérica e experimentalmente, a utilização de pastilhas piezelétricas acopladas no suporte da ferramenta, e aplicando estratégias de controle passivo e ativo, procurando a redução do chatter em processos de torneamento. A solução passiva consiste em conectar os terminais das pastilhas piezelétricas a um circuito elétrico dissipador de energia. A solução ativa propõe usar uma das pastilhas como sensor e a outra como atuador para aplicar leis de controle de realimentação. Na avaliação numérica foi considerado um modelo eletromecânico de parâmetros distribuídos usando a teoria de viga engastada de Euler-Bernoulli, e as equações constitutivas elétricas e mecânicas do material piezelétrico. A comparação das funções de resposta em frequência (FRFs) do sistema, obtidas numericamente, mostra uma adição de amortecimento ao sistema quando é usado um circuito de dissipação com uma resistência e uma indutância como solução passiva. A avaliação numérica da solução ativa indica que o controle de realimentação de velocidade adiciona amortecimento do sistema. A melhora da estabilidade no processo de torneamento destas duas estratégias é comprovada num diagrama de lóbulos de estabilidade. Na parte experimental foram obtidas as funções de resposta em frequência do sistema suporte da ferramenta, usando um sistema de aquisição de dados, com o fim de comparar as magnitudes da resposta, e foram feitos testes de torneamento com o fim de comparar qualitativamente as qualidades superficiais obtidas nas peças usinadas. A medição das FRFs com circuitos de dissipação indicou uma atenuação da resposta para um sistema com circuito em série, estratégia que foi avaliada em testes de torneamento, e mostrando uma melhora no acabamento superficial. / Chatter is the main problem of instability in machining processes, caused by the modulations left on the surface during the successive cuts, called regeneration process, and is characterized by violent vibrations, noise and poor surface quality on machined surfaces. Thus, the scientific community has been concerned with developing actions for both the phenomenom prediction, and developing strategies to reduce them. This work evaluates numerically and experimentally the use of piezoelectric layers embedded to the tool-holder, and applying active and passive strategies trying to reduce the chatter in turning processes. For the passive case, the conductive electrode pairs of the piezoelectric layers are connected to a shunt circuit which modifies the system dynamics. The active solution proposes to use one of the piezoelectric layers as sensor an the other one as actuator, in order to apply feedback control laws. A numerical evaluation considers an electromechanical distributed parameter model based on Euler- Bernoulli cantilever beam theory, and the electrical and mechanical constitutive equations of the piezoelectric material. A comparison of the system frequency response functions (FRFs), numerically obtained, shows an increase of system damping when a resistive-inductive shunt circuit is used as a passive solution. The numerical evaluation of the active solution shows that the velocity feedback control increases the system damping. The turning process stability improvement using both strategies, is shown in a stability lobe diagram. Frequency response functions of the tool-holder system were obtained experimentally using a data acquisition system, in order to compare the response amplitudes. Turning tests were performed in order to compare surface qualities obtained of machined parts. Measurement of FRFs using series resistive-inductive shunt circuits shows a system response attenuation, later this strategy was evaluated in turning tests, showing an improvement in surface finish.