LiMin Zhu

Shanghai Jiao Tong University, Shanghai, Shanghai Shi, China

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Publications (67)88.75 Total impact

  • 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
  • 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
  • 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: 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
  • International Journal of Machine Tools and Manufacture. 01/2012; 61:9-19.
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    ABSTRACT: In this paper, a new type of decoupled 2-DOF translational parallel micro-positioning stage is designed to realize the 2-DOF ultra-precision linear motion. The stage consists of two piezoelectric actuators (PZTs) and a monolithic compliant mechanism. The monolithic compliant mechanism adopts two types of compound double parallel four-leaf flexures and a mirror symmetric structure to reduce the input and output cross coupling and parasitic motion. Based on the stiffness matrix method and screw theory, a mathematical model is constructed to analyze the compliant mechanism. The optimal design is performed in view of performance constraints. The design results show good static and dynamic performances of the stage, which are well validated by the simulation of finite-element-analysis (FEA) and experimental results. The experimental results show that the proposed stage has a full range of 40μm × 40μm when the full voltage(100V) is applied on the two PZTs. Besides, the stage only has the maximum cross coupling of -50dB between the two axes, low enough to utilize single-input-single-out(SISO) control strategies for positioning and tracking.
    Robotics and Automation (ICRA), 2011 IEEE International Conference on; 06/2011
  • Xu Zhang, Limin Zhu, Youfu Li
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    ABSTRACT: Determining the correspondence in coded structured light is challenging, but it is very important in one-shot techniques for 3D shape reconstruction. The problem of decoding stripe patterns can be modeled as matching two code sequences. We propose decoding edges indirectly based on the property of the stripe pattern, which can be represented as edge code, color code, or mixed code sequences. While traditional methods match two edge code sequences, indirect decoding matches two color sequences or mixed code sequences. The advantages of the proposed method, including a higher Hamming distance, enforced local coherence, and more code information, make indirect decoding excellent in performance. Previously, the lack of ground truth has prevented direct comparisons of different decoding algorithms. Here we obtain six benchmark datasets using the robust space-time analysis. Five decoding methods are quantitatively evaluated using the ground truth. The comparison results show that our method is robust for complex code situations and that it outperforms the state-of-the-art technique in this area.
    Journal of the Optical Society of America A 04/2011; 28(4):651-61. · 1.67 Impact Factor
  • Source
    GuoYing Gu, LiMin Zhu
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    ABSTRACT: In this paper, a new ellipse-like mathematic model is proposed to describe the rate-dependent hysteresis in piezoelectric actuators. Since the expressions of the model are completely analytical and can be determined only by a set of parameters, this method simplifies the modeling of complicated hysteresis behaviors. To represent the hysteresis effects, experiments are performed with designed sinusoidal excitations under different frequencies in the range 0.5–300 Hz. The rate-dependent hysteresis is characterized as increasing maximum hysteresis error (MHE) and decreasing peak-to-peak output amplitude (PPOA) phenomenons with the increase of input frequencies. Then, the parameters of the developed model are extracted from the experimental data using the direct least square method through MATLAB offline. The simulation results well correspond to the measured data and demonstrate that the developed model can precisely predict the rate-dependent hysteresis. We also investigate the parameters’ properties with hysteresis characteristics. In the developed model, the length of the minor radius describes the MHE varying with the input frequencies and amplitudes, while the length of major radius and the orientation of the ellipses represent the decreasing PPOA phenomenon. Finally, a real-time feedforward controller with an inverse model is designed to compensate for the rate-dependent hysteresis under different input frequencies. The experimental results show that the hysteresis effects are obviously reduced at both the lower and higher frequencies.
    Sensors and Actuators A Physical 02/2011; 165(2):303-309. · 1.94 Impact Factor
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    ABSTRACT: In this paper, a NURBS hardware interpolator based on FPGA is designed to perform the feedrate profile scheduling, de-Boor Cox calculation and second-order Talor expansion to realize real-time interpolation. Look-ahead algorithm including curve-scanning, feedrate adjustment and acceleration/deceleration planning is implemented in the computer to release the computational load of the interpolator, whereas a motion control card with DSP+FPGA architecture receives the pre-processed results from the look-ahead circuit through PCI bus, and sequently performs the interpolation task in the FPGA and position servo control in the DSP. Experiments are carried out to verify the feasibility of this interpolator. The results imply the FPGA can finish the interpolation within 0.5ms, meanwhile its resource utilization and the calculation speed can compromise to satisfy the practical application.
    Intelligent Robotics and Applications - 4th International Conference, ICIRA 2011, Aachen, Germany, December 6-8, 2011, Proceedings, Part II; 01/2011
  • Xu Zhang, Limin Zhu
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    ABSTRACT: The probabilistic algorithms are effective and widely used to recognize the curves in machine vision and image processing. In this paper, a novel algorithm for detecting circles is presented. It is based on the observation that the connectivity can help to alleviate the computational load of the probabilistic algorithm. A graph model is introduced to express connectivity in the detected edges, and a modified depth-first-search algorithm is developed to segment the whole graph into connected subgraphs and then partition the complex subgraph into simple paths. Then, four pixels are randomly selected from the sampling set, consisting of one proper path or several consecutive paths, to detect circles. The connectivity constraint is further employed to verify the candidates of circles to eliminate the pseudo ones. The experiments, comparing the proposed algorithm with the randomized Hough transform and the efficient randomized circle detection algorithm, show that it has the advantages of computational efficiency and robustness. KeywordsCircles detection–Random sampling–Connectivity–Graph
    Machine Vision and Applications 01/2011; 22(4):651-662. · 1.44 Impact Factor