Application of interpolation methods for the determination of position-dependent frequency response functions for the simulation of 5-axis milling processes

The occurrence of chatter vibrations in 5-axis milling processes is a common problem and can result in part failure, surface defects and increased wear of the cutting tool and the machine tool. In order to prevent process vibrations, machining processes can be optimized by utilizing geometric physically-based simulation systems. Since the modal parameters of the machine tool are dependent on the position of the linear and rotary axes, the dynamic behavior of milling processes can change along the NC path despite constant engagement conditions. In order to model the pose-dependent modal properties at the tool tip, the frequency response functions (FRFs) were measured at different locations of the workspace of the machine tool for various poses of the rotary axis of the spindle. To take the varying compliance within the workspace of a machine tool into account in a geometric physically-based milling process simulation, different interpolation methods for interpolating FRFs or parameter values of oscillator-based compliance models (OPV) were applied. For validation, the resulting models were analyzed and compared to measured data. In OPV interpolation, the individual oscillation modes were interpolated in their respective characteristics based on the oscillator parameters (eigenfrequencies, modal masses and damping values). In FRF interpolation, however, there was no differentiation between the modes, resulting in a wrong interpolation. It can therefore provide good results when only a small shift of the eigenfrequencies is expected, as in case of the analyzed machine tool, with only small movements of the translatory axes

Virtual Machining: Capabilities and Challenges of Process Simulations in the Aerospace Industry

AbstractMilling processes for the manufacturing of parts for aerospace applications can be influenced by various effects. When machining structural parts with high material removal rates, the stiffness of the machine tool can be a limiting factor because chatter vibrations. Additionally, vibrations of thin-walled structures, e. g., the blades of impellers or turbines, can lead to chatter vibrations and surface location errors. Thermo-mechanical deformations are another cause for violations of given shape tolerances. Geometric physically-based process simulations can be used to analyze milling processes with regard to these effects in order to optimize the process parameters. In this paper, an overview of several applications of a geometric physically-based simulation system for analyzing different effects during milling processes is presented. Depending on the relevant effects, process forces, the dynamic behaviour of the tool-spindle-machine system, vibrations of workpieces and fixture systems, as well as thermo-mechanical deformations are calculated

Virtual Machining: Capabilities and Challenges of Process Simulations in the Aerospace Industry

AbstractMilling processes for the manufacturing of parts for aerospace applications can be influenced by various effects. When machining structural parts with high material removal rates, the stiffness of the machine tool can be a limiting factor because chatter vibrations. Additionally, vibrations of thin-walled structures, e. g., the blades of impellers or turbines, can lead to chatter vibrations and surface location errors. Thermo-mechanical deformations are another cause for violations of given shape tolerances. Geometric physically-based process simulations can be used to analyze milling processes with regard to these effects in order to optimize the process parameters. In this paper, an overview of several applications of a geometric physically-based simulation system for analyzing different effects during milling processes is presented. Depending on the relevant effects, process forces, the dynamic behaviour of the tool-spindle-machine system, vibrations of workpieces and fixture systems, as well as thermo-mechanical deformations are calculated

Nonlinear Time-Frequency Control Theory with Applications

Nonlinear control is an important subject drawing much attention. When a nonlinear system undergoes route-to-chaos, its response is naturally bounded in the time-domain while in the meantime becoming unstably broadband in the frequency-domain. Control scheme facilitated either in the time- or frequency-domain alone is insufficient in controlling route-to-chaos, where the corresponding response deteriorates in the time and frequency domains simultaneously. It is necessary to facilitate nonlinear control in both the time and frequency domains without obscuring or misinterpreting the true dynamics. The objective of the dissertation is to formulate a novel nonlinear control theory that addresses the fundamental characteristics inherent of all nonlinear systems undergoing route-to-chaos, one that requires no linearization or closed-form solution so that the genuine underlying features of the system being considered are preserved. The theory developed herein is able to identify the dynamic state of the system in real-time and restrain time-varying spectrum from becoming broadband. Applications of the theory are demonstrated using several engineering examples including the control of a non-stationary Duffing oscillator, a 1-DOF time-delayed milling model, a 2-DOF micro-milling system, unsynchronized chaotic circuits, and a friction-excited vibrating disk. Not subject to all the mathematical constraint conditions and assumptions upon which common nonlinear control theories are based and derived, the novel theory has its philosophical basis established in the simultaneous time-frequency control, on-line system identification, and feedforward adaptive control. It adopts multi-rate control, hence enabling control over nonstationary, nonlinear response with increasing bandwidth ? a physical condition oftentimes fails the contemporary control theories. The applicability of the theory to complex multi-input-multi-output (MIMO) systems without resorting to mathematical manipulation and extensive computation is demonstrated through the multi-variable control of a micro-milling system. The research is of a broad impact on the control of a wide range of nonlinear and chaotic systems. The implications of the nonlinear time-frequency control theory in cutting, micro-machining, communication security, and the mitigation of friction-induced vibrations are both significant and immediate

The comprehensive analysis of milling stability and surface location error with considering the dynamics of workpiece

Cutting movement is still one of the main means to obtain the desired machined surface. As the most representative cutting method in subtractive manufacturing, milling is widely used in industrial production. However, the chatter induced by the dynamic interaction between machine tool and process not only reduces the accuracy of the machined workpiece, but also increases the tool wear and affects the rotary accuracy of the spindle. The stability lobe diagram can provide stable machining parameters for the technicians, and it is currently an effective way to avoid chatter. In fact, the dynamic interaction between the machine tool and process is very complicated, which involves the machine tool, milling tool, workpiece and fixture. The induced mechanism of chatter depends on different machining scenarios and is not entirely dependent on the vibration modes of milling tool. Therefore, it is important to obtain stable machining parameters and to know the dynamic surface location error distribution, which can ensure machining quality and improve machining efficiency. In this dissertation, two methods for constructing stability lobe diagram are first introduced, and then two machining scales, macro milling and micro milling, are studied. For the macro-milling scale, the dynamic response of the in-process workpiece with time-varying modal parameters during the material removal process is analyzed. The stability lobe diagrams for thin-walled workpiece and general workpiece with continuous radial immersion milling are established respectively. Besides, the cumulative surface location error distribution is also studied and verified for the general workpiece. For the micro-milling scale, the dynamics at the micro-milling tool point is obtained by means of the receptance coupling substructure analysis method. The stability lobe diagram and surface location error distribution are analyzed under different restricted/free tool overhang lengths. The relationship between measurement results and burrs is further explained by cutting experiments, and the difference between the two milling scales is compared in the end

Nonlinear Time-Frequency Control Theory with Applications

Nonlinear control is an important subject drawing much attention. When a nonlinear system undergoes route-to-chaos, its response is naturally bounded in the time-domain while in the meantime becoming unstably broadband in the frequency-domain. Control scheme facilitated either in the time- or frequency-domain alone is insufficient in controlling route-to-chaos, where the corresponding response deteriorates in the time and frequency domains simultaneously. It is necessary to facilitate nonlinear control in both the time and frequency domains without obscuring or misinterpreting the true dynamics. The objective of the dissertation is to formulate a novel nonlinear control theory that addresses the fundamental characteristics inherent of all nonlinear systems undergoing route-to-chaos, one that requires no linearization or closed-form solution so that the genuine underlying features of the system being considered are preserved. The theory developed herein is able to identify the dynamic state of the system in real-time and restrain time-varying spectrum from becoming broadband. Applications of the theory are demonstrated using several engineering examples including the control of a non-stationary Duffing oscillator, a 1-DOF time-delayed milling model, a 2-DOF micro-milling system, unsynchronized chaotic circuits, and a friction-excited vibrating disk. Not subject to all the mathematical constraint conditions and assumptions upon which common nonlinear control theories are based and derived, the novel theory has its philosophical basis established in the simultaneous time-frequency control, on-line system identification, and feedforward adaptive control. It adopts multi-rate control, hence enabling control over nonstationary, nonlinear response with increasing bandwidth ? a physical condition oftentimes fails the contemporary control theories. The applicability of the theory to complex multi-input-multi-output (MIMO) systems without resorting to mathematical manipulation and extensive computation is demonstrated through the multi-variable control of a micro-milling system. The research is of a broad impact on the control of a wide range of nonlinear and chaotic systems. The implications of the nonlinear time-frequency control theory in cutting, micro-machining, communication security, and the mitigation of friction-induced vibrations are both significant and immediate