LiMin Zhu

Shanghai Jiao Tong University, Shanghai, Shanghai Shi, China

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Publications (70)96.66 Total impact

  • [Show abstract] [Hide abstract]
    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.
    International Journal of Machine Tools and Manufacture 02/2015; 130. · 2.74 Impact Factor
  • 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.
    Computer-Aided Design 02/2015; 59:43–49. · 1.52 Impact Factor
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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.
    International Journal of Machine Tools and Manufacture 01/2014; · 2.74 Impact Factor
  • 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.
    International Journal of Machine Tools and Manufacture 12/2013; 75:1–8. · 2.74 Impact Factor
  • 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.
    IEEE Transactions on Automation Science and Engineering 10/2013; 10(4):1166-1172. · 2.16 Impact Factor
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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.
    Chinese Journal of Mechanical Engineering 09/2013; 26(5):940-947. · 0.45 Impact Factor
  • 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.
    International Journal of Machine Tools and Manufacture 05/2013; 68:75–80. · 2.74 Impact Factor
  • 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.
    Nonlinear Dynamics 04/2013; 76(1):289-304. · 2.42 Impact Factor
  • 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.
    International Journal of Machine Tools and Manufacture 02/2013; 65:88-98. · 2.74 Impact Factor
  • 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.
    Computer-Aided Design 12/2012; 44(12):1229–1234. · 1.52 Impact Factor
  • Source
    Han Ding, Ye Ding, LiMin Zhu
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    ABSTRACT: As a basic and advanced machining technique, the high-speed milling process plays an important role in realizing the goal of high performance manufacturing. From the viewpoint of machining dynamics, obtaining chatter-free machining parameters is a prerequisite to guaranteeing machining accuracy and improving machining efficiency. This paper gives an overview on recent progress in time domain semi-analytical methods for chatter stability analysis of milling processes. The state of art methods of milling stability prediction in milling processes and their applications are introduced in detail. The bottlenecks involved are analyzed, and potential solutions are discussed. Finally, a brief prospect on future works is presented.
    Chinese Science Bulletin 11/2012; 57(33). · 1.37 Impact Factor
  • Xu Zhang, Youfu Li, Limin Zhu
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    ABSTRACT: The 3D scene acquisition is becoming increasingly crucial in practical application. In this paper, a new method is proposed to measure the surface of objects, which just require one color pattern image. In our decoding method, advancements are made at two steps. First, color identification is modeled as an unsupervised classification problem and K-means are adopted on a new color feature, called regularized color. It is insensitive to surface orientation, illumination direction and illumination intensity for matte, dull surfaces. Second, a discontinuity-preserving method is proposed in the sequence matching, which is based on the window voting to judge correct correspondences and potential borders.In the experiments, this new color feature is compared with RGB, normalized color, HSI. Their class separability measurements are evaluated by scattering criteria and Bhattacharyya distance. The results show that regularized color has much higher discriminating power than RGB and equivalent performance with HSI. Our matching method is also compared with the traditional local matching methods. The results affirm that ours has higher accuracies on six different objects.
    Optics and Lasers in Engineering 10/2012; 50(10):1416–1422. · 1.70 Impact Factor
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    ABSTRACT: This work is motivated by the fact that the conventional cutting parameters optimization in milling process has been widely investigated based on the assumption that the dynamics of the milling system is deterministic. Since there are many uncertain factors in a practical milling process, nominal cutting parameters derived from the deterministic cutting parameters optimization formulation cannot guarantee the stability of milling process and cannot lead to actual maximization of material removal rate and minimization of surface location error at the shop floor level. We develop a robust spindle speed optimization formulation, in which the upper bound of surface location error and lower bound of Lobe diagram are adopted as the optimization object and the constraint condition, respectively. For a comparison, we also give a deterministic spindle speed optimization formulation, without uncertainties. Time finite element approach is employed as the conventional deterministic model to obtain the Lobe diagram and surface location error. The upper and lower bounds of Lobe diagram and surface location error due to the model parameters uncertainties are calculated using the sensitivity analysis. The optimization problems are solved by an augmented Lagrangian function method. Experiments of milling of blades with spindle speeds derived from the deterministic and robust optimization results are implemented. The robust optimization result leads to stable milling process, while the deterministic one does not. The experimental results validate the proposed method. The robust optimization formulation given in this paper is helpful to the decision making in a practical milling process.
    International Journal of Machine Tools and Manufacture. 10/2012; 61:9-19.
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    ABSTRACT: As one of the bases of gradient-based optimization algorithms, sensitivity analysis is usually required to calculate the derivatives of the system response with respect to the machining parameters. The most widely used approaches for sensitivity analysis are based on time-consuming numerical methods, such as finite difference methods. This paper presents a semi-analytical method for calculation of the sensitivity of the stability boundary in milling. After transforming the delay-differential equation with time-periodic coefficients governing the dynamic milling process into the integral form, the Floquet transition matrix is constructed by using the numerical integration method. Then, the analytical expressions of derivatives of the Floquet transition matrix with respect to the machining parameters are obtained. Thereafter, the classical analytical expression of the sensitivity of matrix eigenvalues is employed to calculate the sensitivity of the stability lobe diagram. The two-degree-of-freedom milling example illustrates the accuracy and efficiency of the proposed method. Compared with the existing methods, the unique merit of the proposed method is that it can be used for analytically computing the sensitivity of the stability boundary in milling, without employing any finite difference methods. Therefore, the high accuracy and high efficiency are both achieved. The proposed method can serve as an effective tool for machining parameter optimization and uncertainty analysis in high-speed milling.
    Chinese Journal of Mechanical Engineering 09/2012; 25(5). · 0.45 Impact Factor
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    ABSTRACT: The conventional prediction of milling stability has been extensively studied based on the assumptions that the milling process dynamics is time invariant. However, nominal cutting parameters cannot guarantee the stability of milling process at the shop floor level since there exists many uncertain factors in a practical manufacturing environment. This paper proposes a novel numerical method to estimate the upper and lower bounds of Lobe diagram, which is used to predict the milling stability in a robust way by taking into account the uncertain parameters of milling system. Time finite element method, a milling stability theory is adopted as the conventional deterministic model. The uncertain dynamics parameters are dealt with by the non-probabilistic model in which the parameters with uncertainties are assumed to be bounded and there is no need for probabilistic distribution densities functions. By doing so, interval instead of deterministic stability Lobe is obtained, which guarantees the stability of milling process in an uncertain milling environment. In the simulations, the upper and lower bounds of Lobe diagram obtained by the changes of modal parameters of spindle-tool system and cutting coefficients are given, respectively. The simulation results show that the proposed method is effective and can obtain satisfying bounds of Lobe diagrams. The proposed method is helpful for researchers at shop floor to making decision on machining parameters selection.
    Chinese Journal of Mechanical Engineering 09/2012; 25(5). · 0.45 Impact Factor
  • Xu Zhang, Youfu Li, Limin Zhu
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    ABSTRACT: Color code is widely employed in coded structured light to reconstruct the three-dimensional shape of objects. Before determining the correspondence, a very important step is to identify the color code. Until now, the lack of an effective evaluation standard has hindered the progress in this unsupervised classification. In this paper, we propose a framework based on the benchmark to explore the new frontier. Two basic facets of the color code identification are discussed, including color feature selection and clustering algorithm design. First, we adopt analysis methods to evaluate the performance of different color features, and the order of these color features in the discriminating power is concluded after a large number of experiments. Second, in order to overcome the drawback of K-means, a decision-directed method is introduced to find the initial centroids. Quantitative comparisons affirm that our method is robust with high accuracy, and it can find or closely approach the global peak.
    Applied Optics 08/2012; 51(22):5340-56. · 1.69 Impact Factor
  • Chen Luo, LiMin Zhu, Han Ding
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    ABSTRACT: This paper presents a new method to analyze frictionless grasp immobility based on defined surface-to-surface signed distance function. Distance function's differential properties are analyzed and its second-order Taylor expansion with respect to differential motion is deduced. Based on the non-negative condition of the signed distance function, the first- and second-order free motions are defined and the corresponding conditions for immobility of frictionless grasp are derived. As one benefit of the proposed method, the second-order immobility check can be formulated as a nonlinear programming problem. Numerical examples are used to verify the proposed method.
    Robotica 07/2012; 30(04). · 0.88 Impact Factor
  • Xu Zhang, Limin Zhu, Youfu Li, Dawei Tu
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    ABSTRACT: Gamma distortion is a dominant error source of phase measuring profilometry. It makes a single frequency for the ideal sinusoidal waveform an infinite width of spectrum. Besides, the defocus of the projector-camera system, like a spatial low-pass filter, attenuates the amplitudes of the high-frequency harmonics. In this paper, a generic distorted fringe model is proposed, which is expressed as a Fourier series. The mathematical model of the harmonic coefficients is derived. Based on the proposed model, a robust gamma calibration method is introduced. It employs the multifrequency phase-shifting method to eliminate the effect of defocus and preserve the influence of gamma distortion. Then, a gamma correction method is proposed to correct the gamma distortion with the calibrated gamma value. The proposed correction method has the advantage of high signal-to-noise ratio. The proposed model is verified through experiments. The results confirm that the phase error is dependent on the defocus and the pitch. The proposed gamma calibration method is compared with the state of the art and proves to be more robust to pitch and defocus variations. After adopting the proposed gamma correction method, the phase precision is much enhanced with higher quality in the measured surfaces.
    Journal of the Optical Society of America A 06/2012; 29(6):1047-58. · 1.67 Impact Factor
  • Robotica 01/2012; 30(4):613-625. · 0.89 Impact Factor
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    ABSTRACT: This paper focuses on the development of an efficient semi-analytical solution of chatter stability in milling based on the spectral method for integral equations. The time-periodic dynamics of the milling process taking the regenerative effect into account is formulated as a delayed differential equation with time-periodic coefficients, and then reformulated as a form of integral equation. On the basis of one tooth period being divided into a series of subintervals, the barycentric Lagrange interpolation polynomials are employed to approximate the state term and the delay term in the integral equation, respectively, while the Gaussian quadrature method is utilized to approximate the integral term. Thereafter, the Floquet transition matrix within the tooth period is constructed to predict the chatter stability according to Floquet theory. Experimental-validated one-degree-of-freedom and two-degree-of-freedom milling examples are used to verify the proposed algorithm, and compared with existing algorithms, it has the advantages of high rate of convergence and high computational efficiency.
    Science China Technological Sciences 12/2011; 54(12). · 1.11 Impact Factor

Publication Stats

378 Citations
96.66 Total Impact Points


  • 2004–2015
    • Shanghai Jiao Tong University
      • • Department of Mechanical Engineering (ME)
      • • State Key Laboratory of Mechanical Systems and Vibration
      • • School of Mechanical Engineering
      • • Institute of Robotics
      Shanghai, Shanghai Shi, China
  • 2012
    • Elsevier B.V.
      Filadelfia, Pennsylvania, United States
  • 2010–2011
    • Shanghai University
      • Department of Precision Mechanical Engineering
      Shanghai, Shanghai Shi, China