Analysis of self-tapping screw joints in fibre glass reinforced PEI polymer used in the automotive industry

This article presents a study of the joining of polyetherimide (PEI) polymer parts reinforced with fibre glass which has great application in the automotive sector. A simulation model based on the finite element method is proposed. For the modelling of the polymeric material, the three-network viscoplastic (TNV) rheological model was used, with very adequate results and producing a good fit with the experimental data. In addition, a methodology is proposed that allows simplifying a three-dimensional to an axisymmetric model, which implies a notable reduction in computational cost. In addition, the work includes an experimental analysis that evaluates the tightening torque under conditions of assembly repetitiveness, relaxation over time and influence of thermal cycles. These scenarios have a different influence depending on the geometry of the self-tapping screw used. Regarding repetitiveness, it has been verified that PF-30 (CELOspArk (R)) loses 17.16% while in Delta-PT (DELTA PT (R)) it loses up to 41.93% in the tenth repetition. In contrast, in the relaxation over time scenario, the PF-30 loses 13.38% and the Delta-PT loses 17.82%. Finally, regarding the thermal cycles, cooling allows to slightly delay the loss of tightening torque in both screws in a similar way; however, in the heating stage, 36.89% is lost with PF-30 and only 14.66% with Delta-PT. This study represents an improvement in the knowledge of the joining processes of self-tapping screws with polymeric materials of an engineering nature. The simulation model can be easily adapted to other materials and other geometries, and the experimental study offers a vision of the evolution of tightening conditions in realistic operating scenarios

Meeting high precision requirements of additively manufactured components through hybrid manufacturing

A hybrid approach combining the laser powder bed fusion (LPBF) process and post-processing operations through 5-axis milling was employed to manufacture a Ti6Al4V aerospace component. From the design step, the requirements and needs in all the stages of the Hybrid Additive Manufacturing process were taken into account. A numerical simulation of distortions promoted by residual stresses during the additive process was employed to consider material allowance. The status of the as-built and post-processed component was analysed through scanning and CMM inspection and roughness measurements. The 3D scanned model of the as-built LPBF-ed component was used to understand the distortion behaviour of the component and compared to the numerical simulation. Finally, 5-axis milling operations were conducted in some critical surfaces in order to improve surface quality and dimensional accuracy of the as-built com- ponent. The inspection of the as-built and post-processed component showed the improvement achieved through the proposed hybrid approach. The work aims to provide the baselines needed to enable the metal Hybrid Additive Manufacturing of components with complex geometries where mandatory precision is required by integrating high accuracy machining operations as post-processing technique

Meeting high precision requirements of additively manufactured components through hybrid manufacturing

A hybrid approach combining the laser powder bed fusion (LPBF) process and post-processing operations through 5-axis milling was employed to manufacture a Ti6Al4V aerospace component. From the design step, the requirements and needs in all the stages of the Hybrid Additive Manufacturing process were taken into account. A numerical simulation of distortions promoted by residual stresses during the additive process was employed to consider material allowance. The status of the as-built and post-processed component was analysed through scanning and CMM inspection and roughness measurements. The 3D scanned model of the as-built LPBF-ed component was used to understand the distortion behaviour of the component and compared to the numerical simulation. Finally, 5-axis milling operations were conducted in some critical surfaces in order to improve surface quality and dimensional accuracy of the as-built com-ponent. The inspection of the as-built and post-processed component showed the improvement achieved through the proposed hybrid approach. The work aims to provide the baselines needed to enable the metal Hybrid Additive Manufacturing of components with complex geometries where mandatory precision is required by integrating high accuracy machining operations as post-processing technique.(c) 2022 The Author(s). This is an open access article under the CC BY license (http://creativecommons.org/ licenses/by/4.0/)

Modelling and analysis of surface topography generated in face milling operations.

This paper presents a model for predicting the surface topography generated in face milling operations. In these operations, when the face mill inserts remove the workpiece material, they leave marks on the machined surfaces. The marks depend on the face mill geometry, the geometry and runout of the face mill inserts, and cutting conditions, e.g. feed and step over. In order to predict the surface topography, the geometry of the face mill cutting edges must first be modelled. The modelling of the cutting edge geometry is for round insert face mills and for square shoulder face mills. Due to the influence of insert runout on the final surface topography, axial and radial runouts of the face mill inserts are also taken into account in the modelling of the cutting edge geometry. Next, the equations expressing the trajectory of any cutting edge point are derived as a function of the feed value, the rotation angle of the face mill, its axial position, and its radial position with respect to the face mill axis. Finally, given the cutting edge geometry and the trajectory of cutting edge points, a methodology based on the discretization of the milled surface in a grid with a finite number of points is developed in this paper for the simulation of the surface topography. The methodology is based on the fact that at each grid point, the final height of the topography will be the height of the workpiece material remaining at this point after many face mill revolutions. For this reason, the procedure initially estimates the rotation angles of the face mill for which the face mill cutting edges in their front-cutting and back-cutting motion pass by the grid point being considered. In order to achieve this, a transcendental equation that is only dependent on the rotation angle is derived from the cutting edge trajectory equations. This equation is transformed into an equivalent polynomial equation by means of Chebyshev expansions. The transformed equation is solved for the rotation angle using a standard root finder that does not require a starting value. Then, by means of the estimated rotation angles and the cutting edge trajectory equations, the radial positions of the cutting edge points passing by the grid point are obtained. Finally, based on these radial positions and the cutting edge geometry, the heights of cutting edge points, which can generate the surface topography at this grid point, are estimated. The final height of the surface topography will correspond to the lowest value among the estimated height values. The methodology can be easily extended and applied to face mills with other insert geometries or to face mills with central and peripheral inserts. In addition, the simulation of the surface topography generated by lateral passes in face milling operations is simplified. The procedure allows the influence of the face mill geometry, the feed value and the step over between passes to be analysed and the roughness values to be predicted. In order to validate the model predictions, a series of face milling tests are carried out. Predicted surface topographies are compared with measured topographies and a good agreement between them is observed

Modelización de las vibraciones laterales de baja frecuencia en procesos de taladrado.

En esta tesis se desarrolla un modelo para la predicción de la estabilidad del proceso de taladrado frente a vibraciones laterales de baja frecuencia. El taladrado es una de las operaciones más frecuentes en el sector aeronáutico y en el sector de automoción, en los que los requerimientos de tolerancias y acabados superficiales son exigentes. El taladrado es a menudo una de las últimas operaciones en realizarse en el proceso de fabricación de una pieza, cuando dicha pieza tiene incorporada la mayor parte de su valor añadido. En consecuencia, si uno o varios agujeros no cumplen con las tolerancias de dimensión, de forma o de integridad superficial, la penalización económica que supone la rectificación de dichos errores es muchas veces muy alta y la pieza puede ser desechada, lo cual, a su vez, implica un alto coste extra. Por ello, es de gran interés estudiar las posibles fuentes de error en taladrado, que dan lugar a la generación de agujeros con errores de forma que no cumplan con los requerimientos deseados. Una de las principales fuentes de error en taladrado es la aparición de vibraciones durante el proceso de corte. Las vibraciones que se generan en estas operaciones se pueden clasificar en dos grupos: (1) vibraciones de chatter (lateral y de torsión-axial), que se excitan a frecuencias cercanas a la frecuencia natural del sistema y (2) vibraciones laterales de baja frecuencia, conocidas como whirling en la bibliografía, que se excitan a frecuencias relacionadas con la frecuencia de giro de la broca. Las vibraciones de chatter provocan la generación de agujeros en los que la superficie del fondo es ondulada y una disminución de la calidad superficial de los agujeros. En cambio, la aparición de las vibraciones de whirling tiene como consecuencia la generación de agujeros con perfiles de forma lobulada. El presente trabajo se centra en el estudio y modelización de las vibraciones laterales de baja frecuencia (whirling) en taladrado y en la predicción de la estabilidad del proceso frente a dichas vibraciones de whirling en función de las condiciones de corte (avance, velocidad de giro y profundidad de corte). La modelización del proceso permite determinar las condiciones de corte para las cuales no se producen vibraciones de baja frecuencia sin tener que recurrir al método de prueba y error. La modelización de las vibraciones de baja frecuencia en taladrado se ha llevado a cabo a partir de la deducción de la ecuación del movimiento lateral del centro de la broca y de la predicción de las fuerzas que actúan sobre la herramienta. En cuanto a las fuerzas de taladrado que actúan sobre la herramienta, en esta tesis se considera la aplicación simultánea de fuerzas en dos zonas diferentes de la broca: (1) los filos principales y (2) el filo transversal. Las fuerzas generadas en cada región se pueden descomponer a su vez en: (1) fuerzas de corte debidas al arranque de material de la pieza de trabajo y (2) fuerzas de amortiguamiento del proceso. Para la predicción de las fuerzas de corte aplicadas en los filos principales, se propone un modelo de fuerzas de corte que tiene en cuenta la variación de la geometría de la broca y de las fuerzas de corte específicas a lo largo de los filos principales. Se lleva a cabo una discretización de la zona del filo involucrada en el corte, que se divide en elementos de corte discretos de igual tamaño. En base a las expresiones de los ángulos de corte y teniendo en cuenta la influencia del efecto regenerativo de la vibración en la variación del área de corte, se predicen las fuerzas de corte que actúan sobre cada elemento de la discretización empleando un modelo de corte oblicuo. Con objeto de calcular la fuerza de corte total que se aplica sobre la broca, se lleva a cabo un sumatorio de las fuerzas de corte aplicadas sobre cada elemento de cada filo de la herramienta. Con objeto de calcular las fuerzas de amortiguamiento del proceso, en esta tesis se emplea un modelo que tiene en cuenta la variación de la geometría de la cara de incidencia a lo largo de los filos principales. En base a dicha geometría, se calcula el volumen de material de pieza comprimido bajo la cara de incidencia y, a su vez, las fuerzas de amortiguamiento del proceso, que se consideran proporcionales a dicho volumen. Para la predicción de las fuerzas actuantes en el filo transversal, se considera también la generación de fuerzas debidas al corte y al fenómeno de amortiguamiento del proceso. Para el cálculo de las fuerzas de corte en el filo transversal, se modeliza esta zona de la herramienta como una cuña rígida y se emplea un modelo de corte ortogonal. Por su parte, las fuerzas de amortiguamiento del proceso en el filo transversal se predicen en base a un modelo de la bibliografía. La predicción de los límites de estabilidad del proceso de taladrado frente a vibraciones laterales de baja frecuencia se basa en el análisis de la ecuación del movimiento lateral de la broca. En esta tesis, se proponen dos metodologías para llevar a cabo dicho análisis. En primer lugar, se presenta una nueva metodología basada en el estudio de la ecuación del movimiento en el dominio de la frecuencia. Esta metodología es aplicable al análisis de la estabilidad del taladrado con agujero previo. La segunda metodología se basa en la teoría de semi-discretización temporal de ecuaciones diferenciales con retardo. Esta metodología es aplicable al estudio de la estabilidad en los casos de taladrado enterizo y con agujero previo. Las dos metodologías propuestas permiten predecir la aparición de vibraciones de baja frecuencia en función de las condiciones de corte (avance, velocidad de giro y profundidad de corte). Finalmente, la modelización de las vibraciones laterales de baja frecuencia se ha validado experimentalmente a través de ensayos de taladrado enterizo y con agujero previo. En base a la comparación entre los resultados obtenidos en dichos ensayos y las predicciones del modelo propuesto, se puede concluir que el modelo predice de forma adecuada la aparición de vibraciones de whirling en función de las condiciones de corte, así como las frecuencias a las que se excitan dichas vibraciones.In this thesis, a model to predict the stability of drilling process against low-frequency lateral vibrations is developed. Drilling is one of the most common machining operations in the aerospace and automotive industries, in which tough tolerances and surface finish are required. Drilling is usually one of the last operations conducted in the manufacturing process of a workpiece. Hence, it is usually accomplished once that the part has a high added value. Consequently, if one or more holes do not fulfill the dimension, shape or surface integrity requirements, the economic cost of rectifying errors in drilling can be very high. In addition, the part can also be thrown away, which in turn implies a high extra cost. Therefore, the study of mechanisms and conditions that may cause the appearance of errors during drilling and lead to the formation of holes that are out of tolerance is highly important. One of the main sources of error formation during drilling is related to vibration appearance. During drilling operations, two main types of vibration can occur: (1) chatter vibrations, that are excited at frequencies near the natural frequency of the system and (2) lowfrequency vibrations, known as whirling in the literature, in which excited frequency values are related to the rotation frequency of the tool. Chatter vibrations lead to the formation of holes with undulated bottom surface, whereas whirling vibration appearance during drilling leads to the generation of lobed-shape holes. The present work focuses on the study and modeling of low-frequency lateral vibrations (whirling) in drilling and on the process stability prediction against those whirling vibrations as function of cutting conditions (feed, rotation speed and depth of cut). Process modeling allows the determination of cutting conditions for which no whirling vibrations appear, so that the errortrial method can be avoided. Low-frequency lateral vibration modeling in drilling is based on the development of the lateral motion equation of the drill center and on the prediction of the forces that act on the tool. With regard to the drilling forces that act on the drill, in this thesis it is assumed that during drilling operation forces arise in two different regions of the drill: (1) main cutting edge region and (2) chisel edge region. Furthermore, forces generated along each region are decomposed into: (1) cutting forces, that are related to the material removal process and (2) process damping forces. In order to predict cutting forces that arise at the main cutting edges, a model is proposed that considers the drill geometry and specific cutting force variation along the main cutting edges. The cutting edge section involved in the cutting is divided into discrete elements, each of them having the same size. In order to predict cutting forces, an oblique cutting force model is applied on each discrete element. The model considers both the cutting angle equations and the influence of the regenerative effect of the vibration on the cutting area variation. So as to obtain the overall cutting force acting on the main cutting edges, cutting forces acting at each element contained in each cutting edge must be added. With the aim of predicting process damping forces, in this thesis, a model is developed that considers clearance face geometry variation along the main cutting edges. Based on this geometry, the volume of workpiece material that is compressed under the clearance face of the drill is calculated. In turn process damping forces, that are assumed to be proportional to the compressed material volume, are predicted. According to the forces that arise in the chisel edge region, both cutting and process damping forces are assumed to appear in this region during drilling. For the prediction of cutting forces on the chisel edge, this region is modelled as a rigid wedge and an orthogonal cutting model is employed. For the calculation of process damping forces in the chisel edge a model from the literature is employed. The prediction of low-frequency lateral vibrations in drilling is based on the analysis of the lateral motion equation of the drill. In this thesis, two methodologies are proposed to accomplish the mentioned analysis. Firstly, a new methodology is presented that is based on a frequency domain analysis of the motion equation. This methodology can be applied for the analysis of the stability of drilling with pilot hole. The second methodology is based on the semi-discretization theory of delayed differential equations. This methodology can be applied for the stability prediction of drilling with and without pilot hole. Both methodologies allow the prediction of low-frequency lateral vibration in drilling process as function of cutting conditions (feed, rotation speed and depth of cut). Finally, low-frequency lateral vibration modeling is experimentally validated by means of drilling tests with and without pilot hole. In comparing the results obtained in the experimental tests and the model predictions, it can be concluded that the model is able to predict the appearance of low-frequency lateral vibrations as function of cutting conditions. In addition, the proposed model can also predict the frequencies at which those vibrations are excited

Modelización de las vibraciones laterales de baja frecuencia en procesos de taladrado.

En esta tesis se desarrolla un modelo para la predicción de la estabilidad del proceso de taladrado frente a vibraciones laterales de baja frecuencia. El taladrado es una de las operaciones más frecuentes en el sector aeronáutico y en el sector de automoción, en los que los requerimientos de tolerancias y acabados superficiales son exigentes. El taladrado es a menudo una de las últimas operaciones en realizarse en el proceso de fabricación de una pieza, cuando dicha pieza tiene incorporada la mayor parte de su valor añadido. En consecuencia, si uno o varios agujeros no cumplen con las tolerancias de dimensión, de forma o de integridad superficial, la penalización económica que supone la rectificación de dichos errores es muchas veces muy alta y la pieza puede ser desechada, lo cual, a su vez, implica un alto coste extra. Por ello, es de gran interés estudiar las posibles fuentes de error en taladrado, que dan lugar a la generación de agujeros con errores de forma que no cumplan con los requerimientos deseados. Una de las principales fuentes de error en taladrado es la aparición de vibraciones durante el proceso de corte. Las vibraciones que se generan en estas operaciones se pueden clasificar en dos grupos: (1) vibraciones de chatter (lateral y de torsión-axial), que se excitan a frecuencias cercanas a la frecuencia natural del sistema y (2) vibraciones laterales de baja frecuencia, conocidas como whirling en la bibliografía, que se excitan a frecuencias relacionadas con la frecuencia de giro de la broca. Las vibraciones de chatter provocan la generación de agujeros en los que la superficie del fondo es ondulada y una disminución de la calidad superficial de los agujeros. En cambio, la aparición de las vibraciones de whirling tiene como consecuencia la generación de agujeros con perfiles de forma lobulada. El presente trabajo se centra en el estudio y modelización de las vibraciones laterales de baja frecuencia (whirling) en taladrado y en la predicción de la estabilidad del proceso frente a dichas vibraciones de whirling en función de las condiciones de corte (avance, velocidad de giro y profundidad de corte). La modelización del proceso permite determinar las condiciones de corte para las cuales no se producen vibraciones de baja frecuencia sin tener que recurrir al método de prueba y error. La modelización de las vibraciones de baja frecuencia en taladrado se ha llevado a cabo a partir de la deducción de la ecuación del movimiento lateral del centro de la broca y de la predicción de las fuerzas que actúan sobre la herramienta. En cuanto a las fuerzas de taladrado que actúan sobre la herramienta, en esta tesis se considera la aplicación simultánea de fuerzas en dos zonas diferentes de la broca: (1) los filos principales y (2) el filo transversal. Las fuerzas generadas en cada región se pueden descomponer a su vez en: (1) fuerzas de corte debidas al arranque de material de la pieza de trabajo y (2) fuerzas de amortiguamiento del proceso. Para la predicción de las fuerzas de corte aplicadas en los filos principales, se propone un modelo de fuerzas de corte que tiene en cuenta la variación de la geometría de la broca y de las fuerzas de corte específicas a lo largo de los filos principales. Se lleva a cabo una discretización de la zona del filo involucrada en el corte, que se divide en elementos de corte discretos de igual tamaño. En base a las expresiones de los ángulos de corte y teniendo en cuenta la influencia del efecto regenerativo de la vibración en la variación del área de corte, se predicen las fuerzas de corte que actúan sobre cada elemento de la discretización empleando un modelo de corte oblicuo. Con objeto de calcular la fuerza de corte total que se aplica sobre la broca, se lleva a cabo un sumatorio de las fuerzas de corte aplicadas sobre cada elemento de cada filo de la herramienta. Con objeto de calcular las fuerzas de amortiguamiento del proceso, en esta tesis se emplea un modelo que tiene en cuenta la variación de la geometría de la cara de incidencia a lo largo de los filos principales. En base a dicha geometría, se calcula el volumen de material de pieza comprimido bajo la cara de incidencia y, a su vez, las fuerzas de amortiguamiento del proceso, que se consideran proporcionales a dicho volumen. Para la predicción de las fuerzas actuantes en el filo transversal, se considera también la generación de fuerzas debidas al corte y al fenómeno de amortiguamiento del proceso. Para el cálculo de las fuerzas de corte en el filo transversal, se modeliza esta zona de la herramienta como una cuña rígida y se emplea un modelo de corte ortogonal. Por su parte, las fuerzas de amortiguamiento del proceso en el filo transversal se predicen en base a un modelo de la bibliografía. La predicción de los límites de estabilidad del proceso de taladrado frente a vibraciones laterales de baja frecuencia se basa en el análisis de la ecuación del movimiento lateral de la broca. En esta tesis, se proponen dos metodologías para llevar a cabo dicho análisis. En primer lugar, se presenta una nueva metodología basada en el estudio de la ecuación del movimiento en el dominio de la frecuencia. Esta metodología es aplicable al análisis de la estabilidad del taladrado con agujero previo. La segunda metodología se basa en la teoría de semi-discretización temporal de ecuaciones diferenciales con retardo. Esta metodología es aplicable al estudio de la estabilidad en los casos de taladrado enterizo y con agujero previo. Las dos metodologías propuestas permiten predecir la aparición de vibraciones de baja frecuencia en función de las condiciones de corte (avance, velocidad de giro y profundidad de corte). Finalmente, la modelización de las vibraciones laterales de baja frecuencia se ha validado experimentalmente a través de ensayos de taladrado enterizo y con agujero previo. En base a la comparación entre los resultados obtenidos en dichos ensayos y las predicciones del modelo propuesto, se puede concluir que el modelo predice de forma adecuada la aparición de vibraciones de whirling en función de las condiciones de corte, así como las frecuencias a las que se excitan dichas vibraciones.In this thesis, a model to predict the stability of drilling process against low-frequency lateral vibrations is developed. Drilling is one of the most common machining operations in the aerospace and automotive industries, in which tough tolerances and surface finish are required. Drilling is usually one of the last operations conducted in the manufacturing process of a workpiece. Hence, it is usually accomplished once that the part has a high added value. Consequently, if one or more holes do not fulfill the dimension, shape or surface integrity requirements, the economic cost of rectifying errors in drilling can be very high. In addition, the part can also be thrown away, which in turn implies a high extra cost. Therefore, the study of mechanisms and conditions that may cause the appearance of errors during drilling and lead to the formation of holes that are out of tolerance is highly important. One of the main sources of error formation during drilling is related to vibration appearance. During drilling operations, two main types of vibration can occur: (1) chatter vibrations, that are excited at frequencies near the natural frequency of the system and (2) lowfrequency vibrations, known as whirling in the literature, in which excited frequency values are related to the rotation frequency of the tool. Chatter vibrations lead to the formation of holes with undulated bottom surface, whereas whirling vibration appearance during drilling leads to the generation of lobed-shape holes. The present work focuses on the study and modeling of low-frequency lateral vibrations (whirling) in drilling and on the process stability prediction against those whirling vibrations as function of cutting conditions (feed, rotation speed and depth of cut). Process modeling allows the determination of cutting conditions for which no whirling vibrations appear, so that the errortrial method can be avoided. Low-frequency lateral vibration modeling in drilling is based on the development of the lateral motion equation of the drill center and on the prediction of the forces that act on the tool. With regard to the drilling forces that act on the drill, in this thesis it is assumed that during drilling operation forces arise in two different regions of the drill: (1) main cutting edge region and (2) chisel edge region. Furthermore, forces generated along each region are decomposed into: (1) cutting forces, that are related to the material removal process and (2) process damping forces. In order to predict cutting forces that arise at the main cutting edges, a model is proposed that considers the drill geometry and specific cutting force variation along the main cutting edges. The cutting edge section involved in the cutting is divided into discrete elements, each of them having the same size. In order to predict cutting forces, an oblique cutting force model is applied on each discrete element. The model considers both the cutting angle equations and the influence of the regenerative effect of the vibration on the cutting area variation. So as to obtain the overall cutting force acting on the main cutting edges, cutting forces acting at each element contained in each cutting edge must be added. With the aim of predicting process damping forces, in this thesis, a model is developed that considers clearance face geometry variation along the main cutting edges. Based on this geometry, the volume of workpiece material that is compressed under the clearance face of the drill is calculated. In turn process damping forces, that are assumed to be proportional to the compressed material volume, are predicted. According to the forces that arise in the chisel edge region, both cutting and process damping forces are assumed to appear in this region during drilling. For the prediction of cutting forces on the chisel edge, this region is modelled as a rigid wedge and an orthogonal cutting model is employed. For the calculation of process damping forces in the chisel edge a model from the literature is employed. The prediction of low-frequency lateral vibrations in drilling is based on the analysis of the lateral motion equation of the drill. In this thesis, two methodologies are proposed to accomplish the mentioned analysis. Firstly, a new methodology is presented that is based on a frequency domain analysis of the motion equation. This methodology can be applied for the analysis of the stability of drilling with pilot hole. The second methodology is based on the semi-discretization theory of delayed differential equations. This methodology can be applied for the stability prediction of drilling with and without pilot hole. Both methodologies allow the prediction of low-frequency lateral vibration in drilling process as function of cutting conditions (feed, rotation speed and depth of cut). Finally, low-frequency lateral vibration modeling is experimentally validated by means of drilling tests with and without pilot hole. In comparing the results obtained in the experimental tests and the model predictions, it can be concluded that the model is able to predict the appearance of low-frequency lateral vibrations as function of cutting conditions. In addition, the proposed model can also predict the frequencies at which those vibrations are excited

Model for the prediction of whirling vibrations in drilling processes through semi-discretization of the drill motion equation

In this work, a model for the prediction of drilling stability against low-frequency lateral vibrations, named as whirling in the literature, is proposed. These vibrations are lateral displacements of the tool that arise at frequencies near multiples of the rotation frequency of the drill. The appearance of whirling vibrations leads to the generation of lobe-shaped holes. In order to predict whirling vibrations, the motion equation of the drill is deduced taking into account the modal characteristics of the drill and the cutting and process damping forces that act on it. In this paper, forces that arise in two different regions of the drill are considered: (1) forces on the main cutting edges and (2) forces on the chisel edge. Different force models are presented for each region that include both the regenerative effect of the vibration on the cutting area and the process damping. An oblique cutting model and an orthogonal model are employed for the calculation of cutting forces acting on the main cutting edges and on the chisel edge, respectively. The cutting force model for the main cutting edges takes into account the cutting angle (inclination angle, rake angle, and chip flow angle) variation along the main cutting edges. For the chisel edge region, where the feed speed is no longer negligible with respect to the cutting speed, the dynamic cutting angles are employed for the force model development. Concerning the process damping force model, previous works in the literature consider a constant value of the clearance angle for the calculation of the process damping coefficient. However, in this work, the variation of the normal clearance angle along the main cutting edges is considered. It is shown that, depending on the clearance face grinding parameters employed, the clearance angle can double its value along the main cutting edges. Considering the force models and through the semi-discretization of the motion equation of the drill, the appearance of low-frequency lateral vibrations is predicted regarding the drill geometry and cutting conditions such as drill rotation speed and feed. In addition, given cutting conditions at which whirling vibrations are expected to occur, the model is able to predict the vibration frequencies that are excited. The drilling model and the stability predictions are experimentally validated by means of drilling tests with different drill diameters and cutting conditions. In comparing the experimentally obtained results and the predictions obtained by the model, it is concluded that the model can reasonably predict the appearance of whirling vibrations as a function of drill geometry and cutting conditions. Generated hole shape is also analyzed through the measurement of hole roundness and bottom surface geometry. It is observed that, when drilling in the presence of whirling vibrations, holes with lobed shape and polygonal bottom surface are generated. It is also noticed that both the number of lobes and the number of sides of the polygonal bottom surface are directly related to the vibration frequencies that arise

Analysis of self-tapping screw joints in fibre glass reinforced PEI polymer used in the automotive industry

This article presents a study of the joining of polyetherimide (PEI) polymer parts reinforced with fibre glass which has great application in the automotive sector. A simulation model based on the finite element method is proposed. For the modelling of the polymeric material, the three-network viscoplastic (TNV) rheological model was used, with very adequate results and producing a good fit with the experimental data. In addition, a methodology is proposed that allows simplifying a three-dimensional to an axisymmetric model, which implies a notable reduction in computational cost. In addition, the work includes an experimental analysis that evaluates the tightening torque under conditions of assembly repetitiveness, relaxation over time and influence of thermal cycles. These scenarios have a different influence depending on the geometry of the self-tapping screw used. Regarding repetitiveness, it has been verified that PF-30 (CELOspArk (R)) loses 17.16% while in Delta-PT (DELTA PT (R)) it loses up to 41.93% in the tenth repetition. In contrast, in the relaxation over time scenario, the PF-30 loses 13.38% and the Delta-PT loses 17.82%. Finally, regarding the thermal cycles, cooling allows to slightly delay the loss of tightening torque in both screws in a similar way; however, in the heating stage, 36.89% is lost with PF-30 and only 14.66% with Delta-PT. This study represents an improvement in the knowledge of the joining processes of self-tapping screws with polymeric materials of an engineering nature. The simulation model can be easily adapted to other materials and other geometries, and the experimental study offers a vision of the evolution of tightening conditions in realistic operating scenarios

Analytical thermal model of orthogonal cutting process for predicting the temperature of the cutting tool with temperature-dependent thermal conductivity

High temperatures generated in cutting processes significantly affect the surface integrity of machined parts and tool wear, leading to workpiece thermal damage, tensile residual stresses in the workpiece and a reduction in tool life. In recent years, different analytical thermal models to predict cutting temperatures have been developed in literature based on 2D modeling of the cutting process and the assumption that thermal conductivities of work piece and chip are not dependent on temperature. However, this dependence of conductivity on temperature may have a significant influence on predicted temperatures and must be taken into account. In this paper, a thermal model of the orthogonal cutting process that considers thermal conductivity of materials (chip and tool) to be dependent on temperature is developed. A linear variation of thermal conductivity with temperature is assumed for chip (workpiece) and tool materials. The model is based on application of: (1) the Kirchhoff transformation in order to convert the nonlinear heat conduction problem into a linear one, (2) the theory of moving and stationary heat sources in semi-infinite and infinite mediums in order to model primary and secondary deformation zones and (3) imaginary heat sources to meet adiabatic boundary conditions in the chip and tool. Imaginary heat sources were defined in the thermal model proposed in this paper in such a way that the effect of the tool-chip interface dimensions and of cutting tool width on the tool temperature could be taken into account. This allows the temperature on the rake face and lateral faces of the tool to be predicted. To this end, a new methodology that considers the temperature-dependent thermal conductivity of materials was developed in order to estimate heat partition ratio along the secondary heat source (tool-chip interface), which is assumed to be non-uniform. Orthogonal cutting tests were also performed in order to verify model predictions by comparing them to tool temperature distributions measured using an IR camera

Modelling of elliptical dimples generated by five-axis milling for surface texturing.

Surface texturing processes that improve workpiece surface properties such as the friction of textured surfaces, the lubrication of sliding surfaces and the adhesion of workpiece surfaces are of increasing interest in industry. The most frequently employed processes for surface texturing are based on laser methods and on chemical etching processes. A widespread application of surface texturing is the improvement of tribological properties in terms of friction and load capacity. In these applications, surface texturing usually consists of generating dimples that are uniformly distributed on the workpiece surface. Five-axis milling with a ball-end mill can be an effective and productive option for these processes in these applications, as it is able to generate surface texturing that consists of periodic elliptical dimples if the tool geometry and the cutting conditions (feed, depth of cut and yaw and tilt angles defining tool axis orientation) are appropriately selected. In this paper, a model that predicts the geometry (shape, dimensions and orientation) of elliptical dimples machined by five-axis milling on flat surfaces for given cutting conditions is developed. In order to achieve this, equations expressing the trajectory followed by the cutting edges in five-axis milling are derived. The model takes into account the effect of tool parallel axis offset on dimple geometry. Next, the influence of cutting conditions on dimple geometry is analysed in order to define the cutting conditions that generate a given dimple geometry. From this analysis, a significant influence of the tools tilt angle on the elliptical shape of the dimples and a linear dependence of the yaw angle on dimple orientation are observed. In order to mill elliptical-shaped dimples, tilt angles larger than 30 degrees and feed, step over and depth of cut values that avoid interference between the dimples generated by different cutting edges of the ball-end mill are required. Finally, a series of five-axis milling tests was carried out in order to validate model predictions. A low dispersion in the dimensions and area of milled dimples was obtained. The shape and dimensions of predicted and measured dimples are compared and good correspondence between them is observed, the largest error being 7%