LiMin Zhu

Shanghai Jiao Tong University, Shanghai, Shanghai Shi, China

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Publications (82)116.06 Total impact

  • Ye Ding · Jinbo Niu · LiMin Zhu · Han Ding
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    ABSTRACT: A semi-analytical method is presented in this paper for stability analysis of milling with a variable spindle speed (VSS), periodically modulated around a nominal spindle speed. Taking the regenerative effect into account, the dynamics of the VSS milling is governed by a delay-differential equation (DDE) with time-periodic coefficients and a time-varying delay. By reformulating the original DDE in an integral-equation form, one time period is divided into a series of subintervals. With the aid of numerical integrations, the transition matrix over one time period is then obtained to determine the milling stability by using Floquet theory. On this basis, the stability lobes consisting of critical machining parameters can be calculated. Unlike the constant spindle speed (CSS) milling, the time delay for the VSS is determined by an integral transcendental equation which is accurately calculated with an ordinary differential equation (ODE) based method instead of the formerly adopted approximation expressions. The proposed numerical integration method is verified with high computational efficiency and accuracy by comparing with other methods via a two-degree-of-freedom milling example. With the proposed method, this paper details the influence of modulation parameters on stability diagrams for the VSS milling.
    No preview · Article · Sep 2015 · Journal of Vibration and Acoustics
  • Jinbo Niu · Ye Ding · Limin Zhu · Han Ding
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    ABSTRACT: This paper presents an eigenvalue assignment method for the time-delay systems with feedback controllers. A new form of Runge-Kutta algorithm, generalized from the classical fourth-order Runge-Kutta method, is utilized to stabilize the linear delay differential equation (DDE) with a single delay. Pole placement of the DDEs is achieved by assigning the eigenvalue with maximal modulus of the Floquet transition matrix obtained via the generalized Runge-Kutta method (GRKM). The stabilization of the DDEs with feedback controllers is studied from the viewpoint of optimization, i.e., the DDEs are controlled through optimizing the feedback gain matrices with proper optimization techniques. Several numerical cases are provided to illustrate the feasibility of the proposed method for control of linear time-invariant delayed systems as well as periodic-coefficient ones. The proposed method is verified with high computational accuracy and efficiency through comparing with other methods such as the Lambert W function and the semidiscretization method (SDM).
    No preview · Article · Sep 2015 · Journal of Dynamic Systems Measurement and Control
  • YaoAn Lu · Ye Ding · LiMin Zhu
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    ABSTRACT: The two additional rotational motions of five-axis machining make the determination of the optimal feed direction and tool orientation a challenging task. A new model to find the optimal feed direction and tool orientation maximising the machining width and avoiding local gouging at a cutter contact (CC) point with a flat-end cutter considering the tool path smoothness requirement is developed in this paper. The machining error is characterised by a signed distance function defined from a point on the bottom tool circle of the cutter to the design surface. With the help of the differential evolution approach, the optimisation model can be resolved to determine the optimal tool orientation and feed direction at a given CC point, and generate the smooth tool paths following the optimal feed direction. Simulation examples demonstrate the developed techniques can improve the tool orientation and feed direction at a CC point to increase the machining width, improving the efficiency of freeform surface machining.
    No preview · Article · Jul 2015 · International Journal of Production Research
  • Huan Zhao · LiMin Zhu · Han Ding
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    ABSTRACT: The cross-coupled control (CCC) is widely applied to reduce contour errors in contour-following applications. In such situation, the contour error estimation plays an important role. Traditionally, the linear or second-order estimation approach is adopted for biaxial motion systems, whereas only linear approach is available for triaxial systems. In this paper, the second-order contour error estimation, which was presented in our previous work, is utilized to determine the variable CCC gains for motion control systems with three axes. An integrated stable motion control strategy, which combines the feedforward, feedback and CCC controllers, is developed for multiaxis CNC systems. Experimental results on a triaxial platform indicate that the CCC scheme based on the second-order estimation, compared with that based on the linear one, significantly reduces the contour error even in the conditions of high tracking feedrate and small radius of curvature.
    No preview · Article · Jul 2015 · Science China Technological Sciences
  • Ye Ding · Jinbo Niu · Limin Zhu · Han Ding
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    ABSTRACT: This paper proposes a semi-analytical solution via the differential quadrature method (DQM) for stability analysis of linear multi-degree-of-freedom second-order systems with multiple delays. The vibration systems are reformulated as a delayed differential equation (DDE) in state-space form. With the derivative of the state vector with respect to time at an arbitrary discrete-time point being expressed as a linear weighted sum of the values of the state vector, the original DDE is approximated by a set of algebraic equations, leading to the Floquet transition matrix. Based on Floquet theory, the stability of the systems is then determined by checking the eigenvalues of the transition matrix. The computational accuracy and efficiency are demonstrated through comparison with existing methods via numerical examples. As an application, the proposed method is employed to predict chatter stability in simultaneous machining operations, providing a reference for the choice of machining parameters.
    No preview · Article · Apr 2015 · Journal of Vibration and Acoustics
  • Meiju Yang · Chunxia Li · Guoying Gu · Limin Zhu
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    ABSTRACT: In this paper, a novel rate-dependent Prandtl-Ishlinskii (P-I) model is proposed to characterize the rate-dependent hysteresis nonlinearity of piezoelectric actuators. The new model is based on a modified rate-dependent play operator, in which a dynamic envelope function is introduced to replace the input function of the classical play operator. Moreover, a dynamic density function is utilized in the proposed P-I model. The parameters of the proposed model are identified by a modified particle swarm optimization algorithm. Finally, experiments are conducted on a piezo-actuated nanopositioning stage to validate the proposed P-I model under the sinusoidal inputs. The experimental results show that the developed rate-dependent P-I model precisely characterize the rate-dependent hysteresis loops up to 1000 Hz.
    No preview · Article · Mar 2015 · Frontiers of Mechanical Engineering
  • QingZhen Bi · Jing Shi · YuHan Wang · LiMin Zhu · Han Ding
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    ABSTRACT: A novel analytical five-axis path-smoothing algorithm is developed for the high speed machining of a linear five-axis tool path. Segment junctions of the linear tool path in the machine tool coordinate system, which are tangent-discontinuous points, are all blended by two transition cubic Bézier curves. One cubic Bézier curve is used to smooth the segment junction of the translational path, and the other Bézier curve is used to smooth the segment junction of the rotational path. The tangency and curvature continuities are both guaranteed in the new path. The dual-Bézier transition algorithm has three advantages: (1) Compared with the path-smoothing method in the workpiece coordinate system, the new dual-Bézier transition method directly and simultaneously smooths the machine tool axis trajectories of both translational path and rotational path. The feed speed and stability will both be improved because the tool path discontinuities are the most important source of feed fluctuation. (2) The constraints of approximation error and the synchronization of parametrization of two smoothed curves, which are the most challenging problems in the smoothing of 5-axis tool path, are both considered. (3) The transition cubic Bézier curve pair has an analytical solution and can be easily integrated in the real-time interpolator. Computational examples and the cutting experiment of an impeller blade show that the novel path-smoothing method has obvious advantages in both feed smoothness and cutting efficiency over the original linear interpolator.
    No preview · Article · Feb 2015 · International Journal of Machine Tools and Manufacture
  • LiMin Zhu · YaoAn Lu
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    ABSTRACT: By representing the swept envelope of a generic rotary tool as a sphere-swept surface, the necessary and sufficient conditions for tangent continuity of swept tool envelopes are derived. They can be applied to sequentially generate tool paths for radially tangential multi-pass flank milling of complex surfaces. It is shown that the position vector of the tool tip is uniquely determined while the unit vector representing the tool orientation should satisfy a linear constraint. This constraint function can be readily incorporated into the existing tool path optimization models and algorithms for single pass flank milling. An example is given to confirm the validity of the proposed approach for the radially tangential multi-pass five-axis flank milling.
    No preview · Article · Feb 2015 · Computer-Aided Design
  • YaoAn Lu · QingZhen Bi · LiMin Zhu
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    ABSTRACT: Based on the Rayleigh–Ritz method, this article proposes an indicator to quantify the stiffness of a conical cutter for flank milling of impellers. Its validity is verified by the finite element analysis. A mathematical model is then developed to optimize the geometry of the conical cutter. The objective is to improve the stiffness of the cutter. Three kinds of geometric constraints are considered. First, the ball end of the cutter should be tangential to the hub surface. Second, the cutter should be interference-free with the adjacent blade. Finally, the machining error should satisfy the precision requirements. All these geometric constraints are characterized by the signed point-to-surface distance function. Based on the differential property of the distance function, a sequential linear programming method is applied to obtain the optimal geometry of the cutter along with the tool path. Simulation results confirm the effectiveness of the proposed model and algorithm.
    No preview · Article · Oct 2014 · Proceedings of the Institution of Mechanical Engineers Part B Journal of Engineering Manufacture
  • Huan Zhao · YaoAn Lu · LiMin Zhu · Han Ding
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    ABSTRACT: In this study, a real-time look-ahead interpolation methodology with B-spline curve fitting technique using the selected dominant points is proposed. First, an improved scheme for selecting the dominant points is proposed to reduce the numbers of control points and iterations. Second, a point-to-curve distance function is defined, and its Taylor’s expansion is investigated for curve fitting. Finally, a real-time look-ahead interpolation function, which consists of spline fitting, feedrate scheduling and parametric interpolation modules, is developed to obtain smooth tool path and feedrate profile simultaneously. Experiments on an X-Y-Z platform are conducted with a three-dimensional tool path, and the results demonstrate the feasibility and efficiency of the present algorithms.
    No preview · Article · Aug 2014 · Proceedings of the Institution of Mechanical Engineers Part B Journal of Engineering Manufacture
  • Ye Ding · LiMin Zhu · Han Ding
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    ABSTRACT: This paper presents a semi-analytical wavelet-based approach for stability analysis of time-periodic delay-differential equations (DDEs) with a single discrete time delay. By using the autocorrelation functions of compactly supported Daubechies scaling functions, the DDE is discretized to a set of algebraic equations, employing the wavelet collocation method. The state transition matrix over a single period is constructed to determine the stability based on Floquet theory. Stability charts for the one-degree-of-freedom milling model and time-delayed Mathieu equation are obtained, illustrating both the efficiency and accuracy of the proposed approach.
    No preview · Article · Jan 2014 · Nonlinear Dynamics
  • Jing Shi · QingZhen Bi · LiMin Zhu · YuHan Wang
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    ABSTRACT: The widespread linear five-axis tool path (G01 blocks) is usually described by two trajectories. One trajectory describes the position of the tool tip point, and the other one describes the position of the second point on the tool axis. The inherent disadvantages of linear tool path are tangential and curvature discontinuities at the corners in five-axis tool path, which will result in feedrate fluctuation and decrease due to the kinematic constraints of the machine tools. In this paper, by using a pair of quintic PH curves, a smoothing method is proposed to round the corners. There are two steps involved in our method. Firstly, according to the accuracy requirements of the tool tip contour and tool orientation tolerances, the corner is rounded with a pair of PH curves directly. Then, the control polygon lengths of PH curves are adjusted simply to guarantee the continuous variation of the tool orientation at the junctions between the transition curves and the remainder linear segments. Because the PH curves for corner rounding can be constructed without any iteration, and those two rounded trajectories are synchronized linearly in interpolation, which makes this smoothing method can be applied in a high efficiency way. Its high computational efficiency allows it to be implemented in real-time applications. This method has been integrated into a CNC system with an open architecture to implement on-line linear five-axis tool path smoothing. Simulations and experiments validate its practicability and reliability.
    No preview · Article · Jan 2014 · International Journal of Machine Tools and Manufacture
  • Huan Zhao · LiMin Zhu · Han Ding
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    ABSTRACT: Traditionally, approximation methods are utilized in the parametric interpolation because of the nonanalytic relationship between the spline parameter and the arc length. The approximation error has been considered as the source of the feedrate fluctuation. This paper shows that the discrepancy between the desired tool path and the target trajectory of the motion system is another primary source, and presents a feedback interpolator to eliminate the feedrate fluctuation. To evaluate the initial parameter value for the interpolator, an arc-length based Taylor's expansion with arc-length compensation is proposed, which alleviates greatly the feedrate command error caused by the trajectory deviation. Then, a feedback correction scheme is developed to further reduce the feedrate command error that results from the approximation error. Both computational load analysis and numerical simulations are conducted, and the results show that the present interpolator has very good performance in both efficiency and accuracy, thus is a good choice for high speed and high precision CNC machines.
    No preview · Article · Dec 2013 · International Journal of Machine Tools and Manufacture
  • Source
    Chen Luo · Limin Zhu · Han Ding
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    ABSTRACT: Fixtures are used in almost all modern manufacturing operations. In practice, there is a wide range of specifications on the manufacturing precision and thus different requirements on workpiece locating accuracy during each production process. In view of that, this paper developed a unified signed distance function framework. Under this framework, three systems of sensitivity equations, which link the locator source errors to the resulting workpiece localization error, were derived. Accordingly, unique linear, one-sided quadratic, and two-sided quadratic models have been developed. These three models, distinguished by whether or not taking into account workpiece and/or locator curvature effects, provide a range of locating precision analysis which is illustrated and verified by several examples. The developed modeling technique can handle general fixture locating rather than being limited to certain locating schemes. The proposed models are of practical relevance and have great potential to be applied towards locating scheme evaluation, fixture design, fault diagnosis, and tolerance analysis.
    Full-text · Article · Oct 2013 · IEEE Transactions on Automation Science and Engineering
  • Huan Zhao · Limin Zhu · Zhenhua Xiong · Han Ding
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    ABSTRACT: The high-speed computational performance is gained at the cost of huge hardware resource, which restricts the application of high-accuracy algorithms because of the limited hardware cost in practical use. To solve the problem, a novel method for designing the field programmable gate array(FPGA)-based non-uniform rational B-spline(NURBS) interpolator and motion controller, which adopts the embedded multiprocessor technique, is proposed in this study. The hardware and software design for the multiprocessor, one of which is for NURBS interpolation and the other for position servo control, is presented. Performance analysis and experiments on an X-Y table are carried out, hardware cost as well as consuming time for interpolation and motion control is compared with the existing methods. The experimental and comparing results indicate that, compared with the existing methods, the proposed method can reduce the hardware cost by 97.5% using higher-accuracy interpolation algorithm within the period of 0.5 ms. A method which ensures the real-time performance and interpolation accuracy, and reduces the hardware cost significantly is proposed, and it’s practical in the use of industrial application.
    No preview · Article · Sep 2013 · Chinese Journal of Mechanical Engineering
  • Ye Ding · LiMin Zhu · XiaoJian Zhang · Han Ding
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    ABSTRACT: This paper presents a time-domain semi-analytical method for stability analysis of milling in the framework of the differential quadrature method. The governing equation of milling processes taking into account the regenerative effect is formulated as a linear periodic delayed differential equation (DDE) in state space form. The tooth passing period is first separated as the free vibration duration and the forced vibration duration. As for the free vibration duration, the analytical solution is available. As for the forced vibration duration, this time interval is discretized by sampling grid points. Then, the differential quadrature method is employed to approximate the time derivative of the state function at a sampling grid point within the forced vibration duration by a weighted linear sum of the function values over the whole sampling grid points. The Lagrange polynomial based algorithm (LPBA) and trigonometric functions based algorithm (TFBA) are employed to obtain the weight coefficients. Thereafter, the DDE on the forced vibration duration is discretized as a series of algebraic equations. By combining the analytical solution of the free vibration duration and the algebraic equations of the forced vibration duration, Floquet transition matrix can be constructed to determine the milling stability according to Floquet theory. Simulation results and experimentally validated examples are utilized to demonstrate the effectiveness and accuracy of the proposed approach.
    No preview · Article · Aug 2013 · Journal of Manufacturing Science and Engineering
  • LiMin Zhu · Huan Zhao · Han Ding
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    ABSTRACT: To reduce contour error in contour-following tasks, a common approach is to design a controller based on the contour error information. Hence, real-time contouring error estimation plays an important role in contour-following control. However, the available second-order estimation formulas only apply to biaxial motion systems, and cannot be generalized to handle arbitrary contours tracked by multi-axis motion systems. In this paper, a point-to-curve distance function is defined, and its properties are investigated, especially, its second-order Taylor approximant is derived. On this basis, a novel second-order approach for calculating contour errors of arbitrary contours in real time is proposed. The inter-correlations between the present approach and four commonly used ones are classified. Simulation and experimental results demonstrate the effectiveness of the proposed contour error estimation algorithm.
    No preview · Article · May 2013 · International Journal of Machine Tools and Manufacture
  • JinBo Niu · Ye Ding · LiMin Zhu · Han Ding
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    ABSTRACT: On the basis of Runge–Kutta methods, this paper proposes two semi-analytical methods to predict the stability of milling processes taking a regenerative effect into account. The corresponding dynamics model is concluded as a coefficient-varying periodic differential equation with a single time delay. Floquet theory is adopted to predict the stability of machining operations by judging the eigenvalues of the state transition matrix. This paper firstly presents the classical fourth-order Runge–Kutta method (CRKM) to solve the differential equation. Through numerical tests and analysis, the convergence rate and the approximation order of the CRKM is not as high as expected, and only small discrete time step size could ensure high computation accuracy. In order to improve the performance of the CRKM, this paper then presents a generalized form of the Runge–Kutta method (GRKM) based on the Volterra integral equation of the second kind. The GRKM has higher convergence rate and computation accuracy, validated by comparisons with the semi-discretization method, etc. Stability lobes of a single degree of freedom (DOF) milling model and a two DOF milling model with the GRKM are provided in this paper.
    No preview · Article · Apr 2013 · Nonlinear Dynamics
  • Huan Zhao · LiMin Zhu · Han Ding
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    ABSTRACT: Straight lines, or G01 blocks, are the most widespread representation form for the tool path in CNC machining. At the junctions between consecutive segments, the tangency and curvature discontinuities may lead to feedrate fluctuation and acceleration oscillation, which would deteriorate the machining efficiency and quality. To solve this problem, a real-time path-smoothing method is proposed, which adopts a curvature-continuous B-spline with five control points to blend the adjacent straight lines. The advantage of the transition scheme is that, G2 continuity, analytical calculation of the curvature extrema, approximation error control and real-time performance are considered simultaneously. Then, a bidirectional scanning algorithm for jerk limited S-shape feedrate profile is proposed to evaluate the feedrate constraints. On this basis, a real-time look-ahead scheme, which comprises of path-smoothing, bidirectional scanning and feedrate scheduling, is developed to acquire a feedrate profile with smooth acceleration. Also, an arc-length based interpolation algorithm for mixed linear and parametric segments is proposed to overcome the difficulty of crossing different segments. With these schemes, the smoothness of both tool path and feedrate is guaranteed. Simulation and experiments on an X–Y–Z platform are conducted. The results demonstrate the feasibility and efficiency of the present algorithms.
    No preview · Article · Feb 2013 · International Journal of Machine Tools and Manufacture
  • LiMin Zhu · Han Ding · YouLun Xiong
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    ABSTRACT: By representing the swept envelope of a generic rotary cutter as a sphere-swept surface, our previous work on distance function based tool path optimization is extended to develop the model and algorithm for simultaneous optimization of the tool path and shape for five-axis flank milling. If the tool path is fixed, a novel tool shape optimization method is obtained. If the tool shape is fixed, a tool path optimization method applicable to any rotary cutter is obtained. The approach applies to non-ruled surfaces, and also finds applications in cutter dimension optimization and flank millable surface design. Numerical examples are given to confirm its validity.
    No preview · Article · Dec 2012 · Computer-Aided Design

Publication Stats

754 Citations
116.06 Total Impact Points


  • 2004-2015
    • Shanghai Jiao Tong University
      • • Department of Mechanical Engineering (ME)
      • • State Key Laboratory of Mechanical Systems and Vibration
      • • Institute of Robotics
      Shanghai, Shanghai Shi, China
  • 2010-2011
    • Shanghai University
      • Department of Precision Mechanical Engineering
      Shanghai, Shanghai Shi, China