Ingeniero Civil Mecánico / La aplicación de la dinámica estructural en la manufactura tradicional (torneado, fresado, entre otros ) ha permitido predecir la ocurrencia de vibraciones catastróficas o chatter en la herramienta durante un proceso de corte. Esto posibilita mejorar los parámetros de corte de manera de incrementar la tasa de remoción de material (MRR) sin que dañe a la herramienta o a la pieza trabajada. El Process Damping corresponde al amortiguamiento que se agrega al sistema debido a las fuerzas de fricción que se generan en la interacción entre una de las caras de la herramienta y la superficie ondulada de la pieza de trabajo. Este amortiguamiento permite aumentar la estabilidad durante el proceso de corte a bajas velocidades. El objetivo del presente trabajo es incorporar este fenómeno a modelos numéricos de un proceso de torneado a través de parámetros de la herramienta y condiciones de operación dadas (velocidad de corte y profundidad de corte). En la primera parte de este reporte se presentan las bases teóricas para los dos modelos dinámicos desarrollados: la simulación de las vibraciones y fuerzas de corte en el dominio temporal; y un modelo en el dominio de frecuencias que permita la obtención de los diagramas de estabilidad. La principal contribución del trabajo corresponde a la incorporación de Process Damping a los dos modelos dinámicos desarrollados para el proceso de torneado. El método usado se basó en la energía disipada durante el corte, donde los dos factores más importantes para la modelación de Process Damping fueron el coeficiente de indentación y la identificación del área de penetración durante el proceso de corte. Se realizó un análisis de sensibilidad del fenómeno de Process Damping ante distintas condiciones de operación y propiedades del material y herramienta. Luego, se analizó los dos modelos para tres tests declarados desde la literatura. Por último, se estudió que las simulaciones en el dominio temporal se complementaran con el diagrama de estabilidad generado por la simulación en el dominio de frecuencias. Para cada test se analizaron los diagramas de estabilidad obtenidos, y los gráficos de desplazamiento de la herramienta y fuerzas de corte para casos específicos, donde se observó gráficamente la influencia de la fuerza de Damping en el corte. Entre el Test #1 y Test #2 se identificó el efecto del radio de punta de la herramienta en el diagrama de estabilidad, y entre el Test #3 y los otros dos Tests se analizó la diferencia del efecto de Process Damping entre el aluminio y el acero, respectivamente. Finalmente, a partir de los resultados exhibidos se validaron los dos modelos dinámicos propuestos que incluyen los efectos del Process Damping en el torneado, permitiendo predecir las zonas de estabilidad a bajas velocidades de corte para condiciones de operación dadas. El presente trabajo de investigación se realizó en el Centro de Manufactura Avanzada de la Universidad de Sheffield, en el grupo de Machining Dynamics del área de proyectos tecnológicos.

Although a considerable amount of research exists on geometrical aspects of 5-axis flank milling, the dynamics of this efficient milling operation have not yet been given proper attention. In particular, investigating machining chatter in 5-axis flank milling remains as an open problem in the literature. The axial depth of cut in this operation is typically quite large, which makes it prone to machining chatter. In this thesis, chatter in 5-axis flank milling is studied by developing analytical methods of examining vibration stability, generating numerical simulations of the process, and conducting experimental investigations. The typical application of 5-axis milling includes the machining of thermal resistant steel alloys at low cutting speeds, where the process damping dominates the machining vibration. The results of experimental study in this thesis showed that the effect of process damping is even stronger in flank milling due to the long axial engagement. Accordingly, the first part of the thesis is devoted to studying process damping, and in the second part, the modeling of chatter in flank milling is presented. Linear and nonlinear models have been reported in the literature that account for process damping. Although linear models are easier to implement in predicting stability limits, they could lead to misinterpretation of the actual status of the cut. On the other hand, nonlinear damping models are difficult to implement for stability estimation analytically, yet they allow the prediction of “finite amplitude stability” from time domain simulations. This phenomenon of “finite amplitude stability” has been demonstrated in the literature using numerical simulations. In this thesis, that phenomenon is investigated experimentally. The experimental work focuses on uninterrupted cutting, in particular plunge turning, to avoid unduly complications associated with transient vibration. The experiments confirm that, because of the nonlinearity of the process damping, the transition from fully stable to fully unstable cutting occurs gradually over a range of width of cut. The experimental investigation is followed by developing a new formulation for process damping based on the indentation force model. Then, the presented formulation is used to compute the stability lobes in plunge turning, taking into account the effect of nonlinear process damping. The developed lobes could be established for different amplitudes of vibration. This is a departure from the traditional notion that the stability lobes represent a single boundary between fully stable and fully unstable cutting conditions. Moreover, the process damping model is integrated into the Multi-Frequency Solution and the Semi Discretization Method to establish the stability lobes in milling. The basic formulations are presented along with comparisons between the two approaches, using examples from the literature. A non-shallow cut is employed in the comparisons. Assessing the performance of the two methods is conducted using time domain simulations. It is shown that the Semi Discretization Method provides accurate results over the whole tested range of cutting speed, whereas higher harmonics are required to achieve the same accuracy when applying the Multi Frequency Solution at low speeds. Semi Discretization method is modified further to calculate the stability lobes in flank milling with tools with helical teeth. In addition to the tool helix angle and long axial immersion, the effect of instantaneous chip thickness on the cutting force coefficients is considered in the modified formulation of Semi Discretization as well. Considering the effect of chip thickness variation on the cutting force coefficients is even more important in the modeling of 5-axis flank milling, where the feedrate, and consequently the chip thickness, varies at each cutter location. It also varies along the tool axis due to the additional rotary and tilt axis. In addition to the feedrate, the tool and workpiece engagement geometry varies at each cutter location as well. The actual feedrate at each cutter location is calculated by the dynamic processing of the toolpath. The tool and workpiece engagement geometry is calculated analytically using the parametric formulation of grazing surface at the previous and current passes. After calculating the instantaneous chip thickness and tool/workpiece engagement geometry, they are integrated into the Semi Discretization Method in 5-axis flank milling to examine the stability of vibration at each cutter location. While the presented chatter analysis results in establishing stability lobes in 3-axis flank milling, it results in developing a novel approach in presenting the stability of the cut in 5-axis flank milling. The new approach, namely “stability maps”, determines the unstable cutter locations of the toolpath at each spindle speed. The accuracy of established 3-axis flank milling stability lobes and 5-axis stability maps is verified by conducting a set of cutting experiments and numerical simulations.

Although a considerable amount of research exists on geometrical aspects of 5-axis flank milling, the dynamics of this efficient milling operation have not yet been given proper attention. In particular, investigating machining chatter in 5-axis flank milling remains as an open problem in the literature. The axial depth of cut in this operation is typically quite large, which makes it prone to machining chatter. In this thesis, chatter in 5-axis flank milling is studied by developing analytical methods of examining vibration stability, generating numerical simulations of the process, and conducting experimental investigations. The typical application of 5-axis milling includes the machining of thermal resistant steel alloys at low cutting speeds, where the process damping dominates the machining vibration. The results of experimental study in this thesis showed that the effect of process damping is even stronger in flank milling due to the long axial engagement. Accordingly, the first part of the thesis is devoted to studying process damping, and in the second part, the modeling of chatter in flank milling is presented. Linear and nonlinear models have been reported in the literature that account for process damping. Although linear models are easier to implement in predicting stability limits, they could lead to misinterpretation of the actual status of the cut. On the other hand, nonlinear damping models are difficult to implement for stability estimation analytically, yet they allow the prediction of “finite amplitude stability” from time domain simulations. This phenomenon of “finite amplitude stability” has been demonstrated in the literature using numerical simulations. In this thesis, that phenomenon is investigated experimentally. The experimental work focuses on uninterrupted cutting, in particular plunge turning, to avoid unduly complications associated with transient vibration. The experiments confirm that, because of the nonlinearity of the process damping, the transition from fully stable to fully unstable cutting occurs gradually over a range of width of cut. The experimental investigation is followed by developing a new formulation for process damping based on the indentation force model. Then, the presented formulation is used to compute the stability lobes in plunge turning, taking into account the effect of nonlinear process damping. The developed lobes could be established for different amplitudes of vibration. This is a departure from the traditional notion that the stability lobes represent a single boundary between fully stable and fully unstable cutting conditions. Moreover, the process damping model is integrated into the Multi-Frequency Solution and the Semi Discretization Method to establish the stability lobes in milling. The basic formulations are presented along with comparisons between the two approaches, using examples from the literature. A non-shallow cut is employed in the comparisons. Assessing the performance of the two methods is conducted using time domain simulations. It is shown that the Semi Discretization Method provides accurate results over the whole tested range of cutting speed, whereas higher harmonics are required to achieve the same accuracy when applying the Multi Frequency Solution at low speeds. Semi Discretization method is modified further to calculate the stability lobes in flank milling with tools with helical teeth. In addition to the tool helix angle and long axial immersion, the effect of instantaneous chip thickness on the cutting force coefficients is considered in the modified formulation of Semi Discretization as well. Considering the effect of chip thickness variation on the cutting force coefficients is even more important in the modeling of 5-axis flank milling, where the feedrate, and consequently the chip thickness, varies at each cutter location. It also varies along the tool axis due to the additional rotary and tilt axis. In addition to the feedrate, the tool and workpiece engagement geometry varies at each cutter location as well. The actual feedrate at each cutter location is calculated by the dynamic processing of the toolpath. The tool and workpiece engagement geometry is calculated analytically using the parametric formulation of grazing surface at the previous and current passes. After calculating the instantaneous chip thickness and tool/workpiece engagement geometry, they are integrated into the Semi Discretization Method in 5-axis flank milling to examine the stability of vibration at each cutter location. While the presented chatter analysis results in establishing stability lobes in 3-axis flank milling, it results in developing a novel approach in presenting the stability of the cut in 5-axis flank milling. The new approach, namely “stability maps”, determines the unstable cutter locations of the toolpath at each spindle speed. The accuracy of established 3-axis flank milling stability lobes and 5-axis stability maps is verified by conducting a set of cutting experiments and numerical simulations.

Made available in DSpace on 2016-12-12T20:25:12Z (GMT). No. of bitstreams: 1 Everton Ruggeri.pdf: 24321266 bytes, checksum: d9116328281ce8d4d01d557335e3d70b (MD5) Previous issue date: 2014-09-09 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / In recent years, the study of chatter vibrations has been intensifying in the machining of materials, however, the analysis of chatter vibration has been conducted only for machining of ductile materials and few studies analyzing these vibrations in machining of brittle materials are found in the literature. The chatter vibrations in machining process can considerably compromise the workpiece surface finish, tool wear and in some cases provide severe damage to the machine-tool. Thus there is an imminent need to expand the theory of chatter vibrations for the class of brittle materials. To analyze the vibrations of the process and zones where the process is stable, and where it is unstable, the stability lobes diagram was used. This diagram is constructed in most cases for applications at high speed cutting. In this work, the analysis of the stability lobe diagram was made for application at low cutting speed, where the phenomenon of damping arises. The damping is a crucial factor in the process, it increases system stability. The phenomenon of damping was considered in the formulation of chatter vibrations using the indentation model of Wu. Apart from consideration of the damping effect, an analysis of dynamic stiffness on the mechanical system adopted was made by means of a simulation using the peak to peak method of passing of the tool in the workpiece. For experiments validations, the signals of force and acceleration were acquired and an analysis was conducted in time and frequency domain to identify where the vibrations emerged. The workpiece surface finish and RMS value of the signals were checked and compared with the stability conditions of the process. The results demonstrated perfectly the consequences that the chatter vibrations present in machining of grey cast iron and proved that the stability lobe diagram shows good results to detect the vibrations in machining of brittle materials, determining the areas where the material removal should be avoid. / Nos últimos anos, o estudo das vibrações regenerativas tem-se intensificando na usinagem de materiais, entretanto, a análise das vibrações regenerativas vem sendo conduzidas apenas para a usinagem de materiais dúcteis e poucos trabalhos analisando essas vibrações na usinagem de materiais frágeis são encontrados na literatura. As vibrações regenerativas no processo de usinagem podem comprometer consideravelmente o acabamento superficial da peça, o desgaste da ferramenta e em alguns casos proporcionar danos severos à máquina-ferramenta. Por isso, há uma necessidade eminente de expandir a teoria das vibrações regenerativas para a classe de materiais frágeis. Para analisar as vibrações no processo e regiões onde se possui um corte estável e onde há um corte instável, foi utilizado o diagrama de lóbulos de estabilidade. Este diagrama é construído na grande maioria dos casos para aplicações em alta velocidade de corte. Neste trabalho, a análise do diagrama de lóbulos de estabilidade foi feita para ensaios em baixa velocidade de corte, onde o fenômeno de amortecimento surge. O amortecimento é um fator crucial no processo, pois aumenta a estabilidade do sistema. O fenômeno de amortecimento foi considerado na formulação das vibrações regenerativas utilizando o modelo de indentação de Wu. Além da consideração do amortecimento, uma análise da influência da rigidez no sistema mecânico adotado foi realizada por uma simulação utilizando o método pico a pico, da passagem da ferramenta no corpo de prova. Para validação dos experimentos realizados, os sinais de força e de aceleração foram adquiridos e uma análise foi conduzida no domínio do tempo e no domínio da frequência para identificar onde as vibrações surgiram. O acabamento superficial da peça e valor RMS dos sinais também foram verificados e comparados com as condições de estabilidade do processo. Os resultados demonstraram perfeitamente as consequências que as vibrações regenerativas apresentam na usinagem do ferro fundido cinzento e comprovam que o diagrama de lóbulos de estabilidade mostra bons resultados para identificação das vibrações na usinagem de materiais frágeis, determinando as zonas onde se deve evitar a remoção de material.