In this work, the stability of a flexible thin cylindrical workpiece in turning is analyzed. A process model is derived based on a finite element representation of the workpiece flexibility and a nonlinear cutting for...In this work, the stability of a flexible thin cylindrical workpiece in turning is analyzed. A process model is derived based on a finite element representation of the workpiece flexibility and a nonlinear cutting force law. Repeated cutting of the same surface due to overlapping cuts is modeled with the help of a time delay. The stability of the so obtained system of periodic delay differential equations is then determined using an approximation as a time-discrete system and Floquet theory. The time-discrete system is obtained using the semi-discretization method. The method is implemented to analyze the stability of two different workpiece models of different thicknesses for different tool positions with respect to the jaw end. It is shown that the stability chart depends on the tool position as well as on the thickness.展开更多
In this contribution, inside turning of a thin-walled cylinder is investigated in simulation. Self-excited vibrations can arise due to repeated cutting of the same surface, that lead to instability.A flexible multibod...In this contribution, inside turning of a thin-walled cylinder is investigated in simulation. Self-excited vibrations can arise due to repeated cutting of the same surface, that lead to instability.A flexible multibody system model of the system is the basis for a subsequent analysis of the stability of the process. Stability analysis is done using an approximation as a time-discrete system via the semi-discretization method. An adaptronic turning chisel comprising a piezo actuator and sensors is then used in combination with different control concepts to improve the stability of the process. The effectiveness of the different strategies is compared based on the influence on the stability charts. A classic H∞ controller based on a model of the coupled system of workpiece and tool can only yield some improvements, when an additional measurement of the workpiece displacement is added. Incorporating knowledge on the cutting process coupling workpiece and tool using a gain scheduled H∞ controller allows further improvements. However, robustness with respect to model uncertainties, notably concerning the force law, remains an issue. C 2013 The Chinese Society of Theoretical and Applie-d Mechanics. [doi：10.1063/2.1301308]展开更多
A high-order full-discretization method （FDM） using Hermite interpolation （HFDM） is proposed and implemented for periodic systems with time delay. Both Lagrange interpolation and Hermite interpolation are used to ...A high-order full-discretization method （FDM） using Hermite interpolation （HFDM） is proposed and implemented for periodic systems with time delay. Both Lagrange interpolation and Hermite interpolation are used to approximate state values and delayed state values in each discretization step. The transition matrix over a single period is determined and used for stability analysis. The proposed method increases the approximation order of the semidiscretization method and the FDM without increasing the computational time. The convergence, precision, and efficiency of the proposed method are investigated using several Mathieu equations and a complex turning model as examples. Comparison shows that the proposed HFDM converges faster and uses less computational time than existing methods.展开更多
基金partially done while Arnab Chanda visited the University of Stuttgart from September 2010 to May 2011 under DAAD-IIT Sandwich Master Program funded by a DAAD M.Sc.ScholarshipThe doctoral research of Achim Fischer was funded since 2010 by the Baden-Wrttemberg Stiftung and the Stuttgart Cluster of Excellence Simtech
文摘In this work, the stability of a flexible thin cylindrical workpiece in turning is analyzed. A process model is derived based on a finite element representation of the workpiece flexibility and a nonlinear cutting force law. Repeated cutting of the same surface due to overlapping cuts is modeled with the help of a time delay. The stability of the so obtained system of periodic delay differential equations is then determined using an approximation as a time-discrete system and Floquet theory. The time-discrete system is obtained using the semi-discretization method. The method is implemented to analyze the stability of two different workpiece models of different thicknesses for different tool positions with respect to the jaw end. It is shown that the stability chart depends on the tool position as well as on the thickness.
基金funded by the Baden-Württemberg Stiftung and the Stuttgart Cluster of Excellence in Simulation Technology,SimTech
文摘In this contribution, inside turning of a thin-walled cylinder is investigated in simulation. Self-excited vibrations can arise due to repeated cutting of the same surface, that lead to instability.A flexible multibody system model of the system is the basis for a subsequent analysis of the stability of the process. Stability analysis is done using an approximation as a time-discrete system via the semi-discretization method. An adaptronic turning chisel comprising a piezo actuator and sensors is then used in combination with different control concepts to improve the stability of the process. The effectiveness of the different strategies is compared based on the influence on the stability charts. A classic H∞ controller based on a model of the coupled system of workpiece and tool can only yield some improvements, when an additional measurement of the workpiece displacement is added. Incorporating knowledge on the cutting process coupling workpiece and tool using a gain scheduled H∞ controller allows further improvements. However, robustness with respect to model uncertainties, notably concerning the force law, remains an issue. C 2013 The Chinese Society of Theoretical and Applie-d Mechanics. [doi：10.1063/2.1301308]
基金partially supported by a scholarship from the China Scholarship Councilthe German Research Foundation (DFG) for financial support within the Cluster of Excellence in Simulation Technology (EXC 310) at the University of Stuttgart
文摘A high-order full-discretization method （FDM） using Hermite interpolation （HFDM） is proposed and implemented for periodic systems with time delay. Both Lagrange interpolation and Hermite interpolation are used to approximate state values and delayed state values in each discretization step. The transition matrix over a single period is determined and used for stability analysis. The proposed method increases the approximation order of the semidiscretization method and the FDM without increasing the computational time. The convergence, precision, and efficiency of the proposed method are investigated using several Mathieu equations and a complex turning model as examples. Comparison shows that the proposed HFDM converges faster and uses less computational time than existing methods.
