This thesis presents models and algorithms necessary to simulate the five-axis flank milling of jet-engine impellers in a virtual environment. The impellers are used in the compression stage of the engine and are costly, difficult to machine, and time-consuming to manufacture. To improve the productivity of the flank milling operations, a procedure to predict and optimize the cutting process is proposed. The contributions of the thesis include a novel cutter-workpiece engagement calculation algorithm, a five-axis flank milling cutting mechanics model, two methods of optimizing feed rates for impeller machining tool paths and a new five-axis chatter stability algorithm. A semi-discrete, solid-modeling-based method of obtaining cutter-workpiece engagement (CWE) maps for five-axis flank milling with tapered ball-end mills is developed. It is compared against a benchmark z-buffer CWE calculation method, and is found to generate more accurate maps. A cutting force prediction model for five-axis flank milling is developed. This model is able to incorporate five-axis motion, serrated, variable-pitch, tapered, helical ball-end mills and irregular cutter-workpiece engagement maps. Simulated cutting forces are compared against experimental data collected with a rotating dynamometer. Predicted X and Y forces and cutting torque are found to have a reasonable agreement with the measured values. Two offline methods of optimizing the linear and angular feeds for the five-axis flank milling of impellers are developed. Both offer a systematic means of finding the highest feed possible, while respecting multiple constraints on the process outputs. In the thesis, application of these algorithms is shown to reduce the machining time for an impeller roughing tool path. Finally, a chatter stability algorithm is introduced that can be used to predict the stability of five-axis flank milling operations with general cutter geometry and irregular cutter-workpiece engagement maps. Currently, the new algorithm gives chatter stability predictions suitable for high speed five-axis flank milling. However, for low-speed impeller machining, these predictions are not accurate, due to the process damping that occurs in the physical system. At the time, this effect is difficult to model and is beyond the scope of the thesis.

This thesis presents models and algorithms necessary to simulate the five-axis flank milling of jet-engine impellers in a virtual environment. The impellers are used in the compression stage of the engine and are costly, difficult to machine, and time-consuming to manufacture. To improve the productivity of the flank milling operations, a procedure to predict and optimize the cutting process is proposed. The contributions of the thesis include a novel cutter-workpiece engagement calculation algorithm, a five-axis flank milling cutting mechanics model, two methods of optimizing feed rates for impeller machining tool paths and a new five-axis chatter stability algorithm. A semi-discrete, solid-modeling-based method of obtaining cutter-workpiece engagement (CWE) maps for five-axis flank milling with tapered ball-end mills is developed. It is compared against a benchmark z-buffer CWE calculation method, and is found to generate more accurate maps. A cutting force prediction model for five-axis flank milling is developed. This model is able to incorporate five-axis motion, serrated, variable-pitch, tapered, helical ball-end mills and irregular cutter-workpiece engagement maps. Simulated cutting forces are compared against experimental data collected with a rotating dynamometer. Predicted X and Y forces and cutting torque are found to have a reasonable agreement with the measured values. Two offline methods of optimizing the linear and angular feeds for the five-axis flank milling of impellers are developed. Both offer a systematic means of finding the highest feed possible, while respecting multiple constraints on the process outputs. In the thesis, application of these algorithms is shown to reduce the machining time for an impeller roughing tool path. Finally, a chatter stability algorithm is introduced that can be used to predict the stability of five-axis flank milling operations with general cutter geometry and irregular cutter-workpiece engagement maps. Currently, the new algorithm gives chatter stability predictions suitable for high speed five-axis flank milling. However, for low-speed impeller machining, these predictions are not accurate, due to the process damping that occurs in the physical system. At the time, this effect is difficult to model and is beyond the scope of the thesis.

This thesis presents models and algorithms necessary to simulate the five-axis flank milling of jet-engine impellers in a virtual environment. The impellers are used in the compression stage of the engine and are costly, difficult to machine, and time-consuming to manufacture. To improve the productivity of the flank milling operations, a procedure to predict and optimize the cutting process is proposed. The contributions of the thesis include a novel cutter-workpiece engagement calculation algorithm, a five-axis flank milling cutting mechanics model, two methods of optimizing feed rates for impeller machining tool paths and a new five-axis chatter stability algorithm. A semi-discrete, solid-modeling-based method of obtaining cutter-workpiece engagement (CWE) maps for five-axis flank milling with tapered ball-end mills is developed. It is compared against a benchmark z-buffer CWE calculation method, and is found to generate more accurate maps. A cutting force prediction model for five-axis flank milling is developed. This model is able to incorporate five-axis motion, serrated, variable-pitch, tapered, helical ball-end mills and irregular cutter-workpiece engagement maps. Simulated cutting forces are compared against experimental data collected with a rotating dynamometer. Predicted X and Y forces and cutting torque are found to have a reasonable agreement with the measured values. Two offline methods of optimizing the linear and angular feeds for the five-axis flank milling of impellers are developed. Both offer a systematic means of finding the highest feed possible, while respecting multiple constraints on the process outputs. In the thesis, application of these algorithms is shown to reduce the machining time for an impeller roughing tool path. Finally, a chatter stability algorithm is introduced that can be used to predict the stability of five-axis flank milling operations with general cutter geometry and irregular cutter-workpiece engagement maps. Currently, the new algorithm gives chatter stability predictions suitable for high speed five-axis flank milling. However, for low-speed impeller machining, these predictions are not accurate, due to the process damping that occurs in the physical system. At the time, this effect is difficult to model and is beyond the scope of the thesis. / Applied Science, Faculty of / Mechanical Engineering, Department of / Graduate

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.

In this dissertation, a numerical method to design a curved surface for accurately flank milling with a general tool of revolution is presented. Instead of using the ruled surface as the design surface, the flank millable surface can better match the machined surface generated by flank milling techniques, and provide an effective tool to the designer to control the properties and the specifications of the design surface. A method using the least squares surface fitting to design the flank millable surface is first discussed. Grazing points on the envelope of the moving tool modeled by the grazing surface are used as the sample points and a NURBS surface is used to approximate the given grazing surface. The deviation between the grazing surface and the NURBS surface can be controlled by increasing the number of the control points. The computation process for this method is costly in time and effort. In engineering design, there is a need for fast and effortless methods to simplify the flank millable surface design procedure. A technique to approximate the grazing curve with NURBS at each tool position is developed. Based on the characteristics of the grazing surface and the geometries of the cutting tool, these NURBS representations at a few different tool positions, namely at the start, interior and end, are lofted to generate a NURBS surface. This NURBS surface represents the grazing surface and is treated as the design surface. Simulation results show that this design surface can accurately match the machined surface. The accuracy of the surface can be controlled by adding control points to the control net of the NURBS surface. A machining test on a 5-axis machine was done to verify the proposed flank millable surface design method. The machined surface was checked on a CMM and the obtained results were compared with the designed flank millable surface. The comparison results show that the machined surface closely matches the design surface. The proposed flank millable surface design method can be accurately used in the surface design.

In this dissertation, a numerical method to design a curved surface for accurately flank milling with a general tool of revolution is presented. Instead of using the ruled surface as the design surface, the flank millable surface can better match the machined surface generated by flank milling techniques, and provide an effective tool to the designer to control the properties and the specifications of the design surface. A method using the least squares surface fitting to design the flank millable surface is first discussed. Grazing points on the envelope of the moving tool modeled by the grazing surface are used as the sample points and a NURBS surface is used to approximate the given grazing surface. The deviation between the grazing surface and the NURBS surface can be controlled by increasing the number of the control points. The computation process for this method is costly in time and effort. In engineering design, there is a need for fast and effortless methods to simplify the flank millable surface design procedure. A technique to approximate the grazing curve with NURBS at each tool position is developed. Based on the characteristics of the grazing surface and the geometries of the cutting tool, these NURBS representations at a few different tool positions, namely at the start, interior and end, are lofted to generate a NURBS surface. This NURBS surface represents the grazing surface and is treated as the design surface. Simulation results show that this design surface can accurately match the machined surface. The accuracy of the surface can be controlled by adding control points to the control net of the NURBS surface. A machining test on a 5-axis machine was done to verify the proposed flank millable surface design method. The machined surface was checked on a CMM and the obtained results were compared with the designed flank millable surface. The comparison results show that the machined surface closely matches the design surface. The proposed flank millable surface design method can be accurately used in the surface design.

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.