In this paper, a multi-delay milling system considering helix angle and run-out effects is firstly established. An exponential cutting force model is used to model the interaction between a work-piece and a cutting tool, and a new approach is presented for accurately calibrating exponential cutting force coefficients and cutter run-out parameters. Furthermore, based on an implicit multi-step Adams formula and an improved precise time-integration algorithm, a novel stability prediction method is proposed to predict the stability of the system. The involved time delay term and periodic coefficient term are integrated as a comprehensive state term in the integral response which is approximated by the Adams formula. Then, a Floquet transition matrix with an arbitraryorder form is constructed by using a series of matrix multiplication, and the stability of the system is determined by the Floquet theory. Compared to classical semi-discretization methods and fulldiscretization methods, the developed method shows a good performance in convergence, efficiency,accuracy, and multi-order complexity. A series of cutting tests is further carried out to validate the practicability and effectiveness of the proposed method. The results show that the calibration process needs a time of less than 5 min, and the stability prediction method is effective.
In some applications,there are signals with piecewise structure to be recovered.In this paper,we propose a piecewise_ISS(P_ISS)method which aims to preserve the piecewise sparse structure(or the small-scaled entries)of piecewise signals.In order to avoid selecting redundant false small-scaled elements,we also implement the piecewise_ISS algorithm in parallel and distributed manners equipped with a deletion rule.Numerical experiments indicate that compared with alSS,the P_ISS algorithm is more effective and robust for piecewise sparse recovery.
Rational Bézier surface is a widely used surface fitting tool in CAD. When all the weights of a rational Bézier surface go to infinity in the form of power function, the limit of surface is the regular control surface induced by some lifting function, which is called toric degenerations of rational Bézier surfaces. In this paper, we study on the degenerations of the rational Bézier surface with weights in the exponential function and indicate the difference of our result and the work of Garc′?a-Puente et al. Through the transformation of weights in the form of exponential function and power function, the regular control surface of rational Bézier surface with weights in the exponential function is defined, which is just the limit of the surface.Compared with the power function, the exponential function approaches infinity faster, which leads to surface with the weights in the form of exponential function degenerates faster.
Isoparametric quadrilateral elements are widely used in the finite element method, but the accuracy of the isoparametric quadrilateral elements will drop obviously deteriorate due to mesh distortions. Spline functions have some properties of simplicity and conformality. Two 8-node quadrilateral elements have been developed using the triangular area coordinates and the B-net method, which can exactly model the quadratic field for both convex and concave quadrangles. Some appropriate examples are employed to evaluate the performance of the proposed elements. The numerical results show that the two spline elements can obtain solutions which are highly accurate and insensitive to mesh distortions.
