An efficient construction of equal-area fabric diagrams

Fabric analysts are confronted by massive computerization requirements to process and synthesize efficiently the vast volume of accumulating fabric data. The efficient application of the computer to density-contour and plot-fabric data in an equal-area projection is given by the method which presents the most economical, reproducible, and accurate fabric diagram. Optimizing these features requires a new technique which unifies the construction of the fabric diagram completely in terms of the geometry of the reference sphere. In effect the new method determines the fabric diagram on the surface of the reference sphere and projects it, subsequently, onto the meridial plane. Although the procedure is not feasible to perform manually, it can be performed readily by digital computer to yield highly economic, reproducible, and accurate fabric diagrams. A simple computer program of the procedure, as well as an application, illustrate the capabilities of the method.     

A three-dimensional triangular vision-based contouring error detection system and method for machine tools

Contouring error detection for machine tools can be used to effectively evaluate their dynamic performances. A triangular vision-based contouring error detection system and method is proposed in this paper, realizing the three-dimensional error measurement of an arbitrary trajectory in conditions of a high feed rate and wide motion range. First, a high-precision measurement fixture, which consists of high-precision circular coded markers and a highly uniform light source, is designed to accurately characterize the motion trajectory of a machine tool and realize the high-quality collection of an image sequence. Then, to improve the contouring error detection accuracy, a coded marker decoding and center location method for the automatic recognition and high-precision center positioning of the circular coded markers are applied. Using image preprocessing and matching, the markers’ three-dimensional coordinates in the camera coordinate system can be constructed. Moreover a data transformation method induced by the orthogonal motion of machine tools is proposed to obtain the three-dimensional trajectory in the machine tool coordinate frame and the contouring error can be calculated. Finally, a three-dimensional contouring error detection study of an equiangular spiral interpolation at different feed rates is performed in the laboratory. It is shown that the average contouring error for a feed rate of 1000 mm/min is about 3 µm, which verifies the vision measurement accuracy and feasibility.     

基于PMAC的快速成形轮廓运动控制研究

从快速成形的工作原理出发,提出以PMAC多轴运动控制器、PC机以及伺服电机为主体的运动控制方案,研究了轮廓数据向PMAC格式的数据转换方法以及将数据下载到PMAC数据缓冲区驱动数控平台来实现快速成形轮廓运动过程,设计实现了基于PMAC的快速成形轮廓运动控制体系的软、硬件体系.     

Fuzzy logic cross-coupling controller for precision contour machining

This paper introduces a new cross-coupling controller with a rule-based fuzzy logic control. It is asserted that (i) fuzzy logic controllers provide a better transient response (which is essential for better contour accuracy during transient motions) than the conventional controllers, such as PID controllers, and (ii) cross-coupling controllers perform better than axial controllers in trajectory tracking by machine tools. In this paper, a fuzzy logic controller and a cross-coupling controller are combined to reduce contour errors. A simulation of the FLCCC was performed and the FLCCC was implemented on a CNC milling machine. The simulation and the experimental results show improved contour accuracy over the conventional cross-coupling controller.     

<Emphasis Type="Bold">Accurate Machining of Freeform Surfaces by Restraining Cutter Contouring Errors</Emphasis>

Machined parts having sculptured surfaces pose challenges in the field of CAD/CAM. Sculptured surfaces are essential in the manufacture of components with curved geometry, which are demanded mostly in the aerospace and die and mould industries. This paper presents an adaptive cutter path restraining method for freeform surface machining and its implementation in milling. The ultimate goal is to achieve high contouring accuracy for sculptured parts machining which is a principal index for the performance evaluation of CNC machines. The proposed method is robust in achieving the desired surface cutting with the capability of satisfying pre-specified tolerance requirements using certain adaptive laws. The given tolerance is measured as the angular deviation by which the generated cutter path differs from the desired path. Since the feedrate is considered to be the most significant cutting parameter, only feedrate variations from 5 mm s^-1 to 30 mm s ^-1 are applied in this system. The tool paths generated with and without the adaptive mechanism are compared. The proposed methodology has been tested on a CNC milling system with an open-architecture controller. The experimental results demonstrate that the proposed tolerance feedback mechanism is very effective for producing parts with sculptured surfaces.     

A contouring program based on dual kriging interpolation

For contouring very large data sets, such as those arising from 3-D finite element computations, for instance, or in numerical cartography, a computer program based on dual kriging interpolation was developed at École Polytechnique for the Castor project (a multidisciplinary research and development work in computational software for hydroelectric projects). The dual kriging technique presented here simplifies considerably the handling of interpolated data and is especially useful for 3-D applications. It also containsspline interpolation as a particular case and theleast squares method as a limit case. In order to minimize the computational effort, several original features have been incorporated in this program: (1) the concept ofdistance of influence was introduced to allow the algorithm, when evaluating the interpolation value at a given location, to discard data points that are situated too far apart; (2)arbitrary geometric domains are decomposed into simpler regions, inside which the requested contours are drawn directly by scanning vertical slices from left to right, instead of building each contour line sequentially as in direct contouring; (3) contour lines may also be stored in arandom access database (this last feature was added to enable the automatic assembly of isovalue surfaces in 3-D applications such as stress analysis); and (4) contours can be smoothed by interpolating separately the sequences ofX andY coordinates for each contour line. This process, calledparametric kriging, permits the efficient compression of the number of data points necessary to record contours.     

Integrated direct/indirect adaptive robust contouring control of a biaxial gantry with accurate parameter estimations

This paper presents an integrated direct/indirect adaptive robust contouring controller (DIARC) for an industrial biaxial high-speed gantry that achieves not only excellent contouring performance but also accurate parameter estimations for secondary purposes such as machine health monitoring and prognosis. Contouring control problem is first formulated in a task coordinate frame. A physical model-based indirect-type parameter estimation algorithm is then developed to obtain accurate on-line estimates of unknown model parameters. A DIARC controller possessing dynamic-compensation-like fast adaptation is subsequently constructed to preserve the excellent transient and steady-state contouring performance of the direct adaptive robust controller (DARC) designs. The proposed DIARC along with previously developed DARC contouring controllers are implemented on a high-speed industrial biaxial gantry to test their achievable performance in practice. Comparative experimental results verify the improved contouring performance and the accurate physical parameter estimates of the proposed DIARC algorithm.     

Biaxial contouring control with friction dynamics using a contour index approach

In conventional designs, contouring control is usually decomposed into independent tracking tasks of axes. Its success relies on good tracking performance of each axis, which is difficult to achieve when the dynamics of each axis is different from each other and subjected to nonlinear frictions and load variations. Additionally, another difficulty in contouring control is the formulation of a contouring error model and real-time estimation of contouring error. Therefore, in this paper, a contour following strategy was developed to improve contouring accuracy without depending on axial tracking performance. The proposed contouring error model is formulated systematically based on the coordinated transformation scheme. A contour index (CI) is evaluated geometrically, which can be treated as an equivalent contour error such that a reduction in CI implies a reduction in contour error. With the proposed approach, the resulting contour performance will not be degraded if the tracking task of each axis is not carried out precisely. Experiments were conducted using a bi-axial linear stage and the results demonstrate that the contouring qualities were still maintained at high feed-rates even in the presence of undesirable tracking lags.     

Dynamics and contouring control of a 3-DoF parallel kinematics machine

In machining applications, instead of tracking error (the difference between the actual position and the desired position), contouring error (the minimum distance from the actual position to the desired trajectory) characterizes product quality. In this paper, we propose a generalized moving task coordinate frames based contouring control for parallel kinematics machines, whose dynamics is in general coupled and strongly nonlinear. The Orthopod, a 3 degree-of-freedom purely translational parallel kinematics machine, is introduced as a control plant. The Lagrange-D’Alembert formulation is used to model the system dynamics. The developed dynamic model in Cartesian space is transformed and parametrized by tangential error, normal error, and binormal error in moving task coordinate frames. The contouring error is then approximated by the normal error and the binormal error, which is the projection of tracking error to the normal plane at the desired position. By employing the structural properties of the transformed dynamics, a special feedback linearization, the computed torque control is applied. It leads to a stabilization problem for a second-order linear time-invariant system. Coulumb plus viscous friction model is used to compensate friction effects. Friction parameters are identified by least-squares approach. For comparison purpose, the tracking error based computed torque control is also carried out. Experiments demonstrate that the proposed control scheme not only leads to improved contouring accuracy, but also produces smaller and smoother control input torques, which may contribute to smaller vibration.     

A novel curvature circle iterative algorithm for contour error control of multi-axis CNC machine tools

High-precision real-time estimation of contouring errors is a prerequisite for contouring errors control of multi-axis CNC machine tools. This paper focuses on developing a nearest point projection curvature circle iterative (NPP–CCI) algorithm to achieve real-time estimation of multi-axis contouring errors. It is found that the traditional curvature circle iterative (CCI) method has two major shortcomings. The first is that the iterative process may terminate incorrectly at the local contour position, and the other is that the actual tool position and local curvature circle are not necessarily coplanar in three-dimensional space, which would lead to inaccurate calculation of the delay time parameter and eventually affect the estimation accuracy. In order to address the problem of false termination, an index method is used to find the closest reference position with respect to the actual position. At the same time, the projection technology is proposed to overcome the problem met in extending the planar curvature circle iterative method to the spatial applications. The proposed NPP-CCI algorithm is more suitable for spatial contouring errors estimation in tracking complex trajectories and has higher estimation accuracy than the traditional CCI algorithm. Various experiments with different tool paths are conducted on an in-house developed multi-axis experimental platform to verify the effectiveness of the proposed algorithm. The experimental results show that the NPP-CCI algorithm can estimate the contouring errors with higher accuracy than the traditional CCI algorithm, and with the help of real-time computation and compensation, the contouring errors are reduced by more than 44% in terms of the MAX and RMS values.