五轴NURBS插补中的速度前瞻控制方法

为提高五轴非均匀有理B样条的插补精度,减轻段间转接时对机床的机械冲击,提出了一种速度前瞻控制处理方法.采用曲率圆逼近的方法建立了插补误差计算模型,并推导出满足插补误差要求的最小曲率半径与进给速度间的关系.采用数值分析方法预先计算出减速点的参数值,对样条插补进行了加减速前瞻规划处理.实时插补时对样条曲线上曲率半径较小的地方进行减速处理,以提高插补曲线的逼近精度.实例证明,该方法能有效降低插补误差和段间转接时的加速度,具有良好的实时性,可以应用到实际的数控系统中.     

位模式插补与位插补速度控制算法研究

为了给下位计算机的位插补运算提供精确的插补数据,避免下位机由于计算任务繁重而影响实时性,提出了一种基于上位计算机的误差可控的位插补数据牛成算法.首先,利用参数三次样条曲线拟合待加工曲线的关键型值点,获得加工曲线的刀位轨迹线;然后,根据推导出的最大允许误差与样条曲线离散段数之间的关系式,在给定的最大误差的约束下,对样条曲线进行离散化;最后,根据离散后的小线段计算生成位插补数据,传递给下位机.为了改善位插补加工效果,对位模式插补速度控制进行了研究,建立了位插补脉冲周期的数学模型.实际加工结果表明,给出的算法可行而且有效.     

Development of a real-time trajectory generator for NURBS interpolation based on the two-stage interpolation method

This paper deals with the real-time NURBS interpolation method in which the interpolation error between the ideal curve and the interpolated curve is compensated within the machine basic length unit (BLU). Parametric curve interpolation methods are based on the Taylor series expansion of curve parameters and an approximation. This approach enables effective feed command generation following the target curve. However, the interpolation error caused by the curve segmentation cannot be controlled.In this research, a two-stage interpolation method that compensates for interpolation errors within machine BLU is proposed. The interpolation result was filtered by an acceleration/jerk limitation equation. Through this two-stage interpolation, both the interpolation error condition and the motion dynamics can be satisfied.Using computer simulations in which interpolation results are revaluated by a numerical iteration method, it is shown that the two-stage interpolation algorithm can interpolate target curves precisely with geometric and dynamic contentment. The proposed algorithm was implemented in the CNC simulator system and an experimental run was conducted to identify the real-time adaptation.     

可配置型五坐标B样条插补控制器的研制

针对采用五轴联动数控机床的线性插补功能进行数控加工存在的不足,提出了一种B样条插补控制策略用于五轴联动数控机床以实现复杂曲面零部件的高速高精数控加工。参考开放式、模块化体系结构控制器(OMAC)标准,开发了具有B样条插补功能的五轴联动数控机床运动控制器。该控制器将控制任务按照实时性要求进行划分。人机交互、代码解析及参数映射关系构造等过程离线完成,插补运算、离散逻辑控制及逆运动学变换等过程由实时线程执行,保证了数控系统的硬实时性。为简化NC程序的编制过程,控制器设计为接收工件坐标系下的加工信息。通过开发适应各种形式数控机床的逆运动学变换模块,并将机床参数设计为可用户定制,使得控制器具有良好的通用性。在控制器内部建立NC程序文件中位置曲线和方位曲线间的参数映射关系,使得机床平动轴与转动轴间的运动规划符合实际加工要求,并可保证加工精度。实际加工实验中,在采用B样条插补算法的NC程序量降低为线性插补NC程序量15%倍时,其插补误差为线性插补误差的45%,控制器插补精度为0.68,表明该B样条插补控制器可以满足五坐标数控加工的要求。     

Development of a real-time look-ahead interpolation methodology with spline-fitting technique for high-speed machining

Methodologies for converting short line segments into parametric curves were proposed in the past. However, most of the algorithms only consider the position continuity at the junctions of parametric curves. The discontinuity of the slope and curvature at the junctions of the parametric curve might cause feedrate fluctuation and velocity discontinuous. This paper proposes a look-ahead interpolation scheme for short line segments. The proposed interpolation method consists of two modules: spline-fitting and acceleration/deceleration (acc/dec) feedrate-planning modules. The spline-fitting module first looks ahead several short line segments and converts them into parametric curves. The continuities of the slope and curvature at each junctions of the spline curve are ensured. Then the acc/dec feedrate-planning module proposes a new algorithm to determine the feedrate at the junction of the fitting curve and unfitted short segments, and the corner feedrate within the fitting curve. The chord error and acceleration of the trajectory are bounded with the proposed algorithm. Simulations are performed to validate the tracking and contour accuracies of the proposed method. The computational efforts between the proposed algorithm and the non-uniform rational B-spline (NURBS)-fitting technique are compared to demonstrate the efficiency of the proposed method. Finally, experiments on a PC-based control system are conducted to demonstrate that the proposed interpolation method can achieve better accuracy and reduce machining time as compared to the approximation optimal feedrate interpolation algorithm.     

A NURBS interpolation algorithm with continuous feedrate

The high-speed precision machining of a part requires minimal feedrate fluctuation and contour error, and parametric spline interpolations have proven to be superior over linear and circular interpolations. However, parametric spline interpolations may result in large feedrate fluctuation due to an inaccurate mapping between the spline parameter u and the displacement S. This paper presents a non-uniform rational B-spline interpolation algorithm with compensatory parameter to minimize feedrate fluctuation and contour error. Since the cubic or quintic polynomials expressing the u-S mapping are acquired, they can be calculated by two consecutive interpolation points with the continuity condition. Thus, the parameter u can be calculated quickly and accurately by substituting the desired displacement S into the cubic or quintic polynomials. Simulation shows that the feedrate fluctuation of the proposed algorithm is much smaller than that of Taylor interpolation algorithms and Feed correction algorithm.     

An interpolation method for the open CNC system based on EPM

A typical open computer numerical control (CNC) system should own the capability of being redeveloped easily and effectively, and any improvements of interpolation algorithm or machining technique could be put into practice by users conveniently. However, this is not always available in the current open CNC systems. To solve this problem, an interpolation method based on external profile mode (EPM) is introduced to improve the universality and the performance of an open CNC system in this paper. The method is realized with a rough interpolation in the PC host and a fine interpolation in the slave motion controller. With this method, various interpolation algorithms can be easily realized in the rough interpolation when machining complex contours. Meanwhile, the machining parameters during each interpolation cycle can be wholly determined by the host, so a real-time adjustment of machining parameters can be accomplished during the interpolation. The working principal of EPM is presented in this paper, and the realization of interpolation algorithms with the proposed method is described. A look-ahead algorithm for determining the machining parameters of each segment is implemented based on the length of segments in the rough interpolation. An acceleration/deceleration strategy with confined jounce is proposed in the look-ahead algorithm. The experimental results of specific profile interpolation show that the interpolation method based on EPM can make the open CNC system more universality and high performance.     

面向高速加工的样条曲线实时插补算法

数控加工追求更高的加工效率和光洁的加工表面,但大多数样条曲线插补算法是根据进给速度、最大合加/减速度和合加加速度来设计的,并没有考虑如何充分利用单轴的最大加减速能力。提出一种时间近似最优的样条曲线实时插补算法,它面向数控系统对高速加工的需求,在考虑机床动态性能的基础上,充分利用单轴的最大加减速能力,以达到理论上近似最优的加工效率。同时该算法通过预处理求速度限制曲线、速度曲线反向链接和平滑处理三个步骤求出满足加工精度以及机床单轴的最大加速度、加加速度等约束条件的加工速度曲线,能有效提高加工表面的粗糙度。仿真结果表明,该算法在有效提高加工效率的同时,能实现对减速点的精确定位,得到光滑的加工速度曲线。     

A simple point cloud data reduction method based on Akima spline interpolation for digital copying manufacture

Point cloud data acquisition is the first key step in digital copying manufacture. In order to reduce extremely dense acquired data while maintaining data accuracy, this paper presents a simple and practical on-line point cloud data reduction method for digital copying manufacture, which is based on Akima spline interpolation. The basic idea of this method is similar to sketch painting: Outline the broad contour of the curve first and then revise local details until the interpolated curve satisfies the required accuracy. In this method, Akima spline interpolation is adopted to connect acquired points for CNC machining in digital copying process. It obtains a smaller data reduction ratio and a smoother machined surface than conventional methods. Experimental results indicate that the proposed Akima reduction method is able to eliminate redundant data effectively under different required accuracy. The reduction performance of this method is superior to equal ATCD reduction method obviously under the same required accuracy. The proposed method can be used in the real-time data acquisition process of digital copying manufacture to replace traditional methods.     

一种三次插值样条曲线的插补方法研究

针对复杂轮廓零件数控加工的实际需求,基于数据采样插补原理,对一种三次插值样条曲线的插补算法进行了研究.样条曲线进行参数化运算插补,先使用一系列首尾相接的微小直线段来逼近给定的插值样条曲线轮廓,再利用轨迹空间与参变量空间的对应关系,控制参变量,求取插补点坐标,得到整个离散化插补轨迹.此算法加工速度稳定性高,有利于高速高精地生成插补轨迹.     

An improvement EMD method based on the optimized rational Hermite interpolation approach and its application to gear fault diagnosis

A demodulation technique based on improvement empirical mode decomposition (EMD) is investigated in this paper. Firstly, the problem of the envelope line in EMD is introduced and the drawbacks of two classic interpolation methods, cubic spline interpolation method and cubic Hermite interpolation method are discussed; then a new envelope interpolation method called optimized rational Hermite interpolation method (O-EMD) is proposed, which has a shape controlling parameter compared with the cubic Hermite interpolation algorithm. At the same time, in order to improve the envelope approximation accuracy of local mean, the parameter determining criterion is put forward and an optimization with Genetic Algorithm (GA) is applied to automatic select the suitable shape controlling parameter in each sifting process. The effectiveness of O-EMD method is validated by the numerical simulations and an application to gear fault diagnosis. Results demonstrate that O-EMD method can improve the reliability and accuracy significantly compared with traditional EMD method.     

Correcting and compressing interpolation algorithm for free-form surface machining

The existing interpolation algorithm cannot meet the need of high-speed and high-accuracy machining of a free-form surface. So this paper proposed a correcting and compressing interpolation algorithm. Depending on the distance and angle evaluated from the adjacent command points, the machining path of free form can be divided into two machining types. For those regions where the accurate figure is critical such as corners, the convention linear interpolation is performed exactly between the adjacent command points. For those regions having a large radius of curvature where the smooth figure is critical, firstly, the interior point selection method based on circle transition is derived to reduce the tolerance between the machining path and the original surface; secondly, the interior point correction method based on the least-square method is proposed to reduce the calculation error and round-off error in the interior point and estimate the first- and second-order derivative vectors of the interior point; thirdly, the shape-defining point is selected by the bend direction of the machining path and fitted to a quintic spline curve which has the C2 continuity; fourthly, the fitting accuracy controlling method is proposed to ensure the machining accuracy; lastly, the curve interpolation is performed on the fitted smooth curve. Machining tests carried out on a vertical machining center show that the proposed algorithm can improve the machining efficiency and machining quality of a free-form surface.     

用于加工弧面凸轮轮廓曲面的NURBS插补方法

在分析弧面凸轮轮廓曲面上加工刀痕产生的原因,以及对分度机构性能影响的基础上,提出了用NURBS样条插补凸轮从动件运动规律曲线的思想方法.通过对NURBS样条插补改进算法的深入分析,得出了进一步校正满足加工步长条件的NURBS样条参数增量的算式.同时对插补前弧面凸轮从动件运动规律曲线的修正、NURBS插补误差和插补过程的实现进行了计算与分析.结果表明,采用文中给出的方法,能显著提高弧面凸轮轮廓面的加工精度.     

基于Newton-Rapson迭代法的NURBS插补算法的研究

一阶、二阶Taylor展开式求解NURBS曲线插补坐标点ui+1,存在计算量大、插补时间长等问题,该文提出了一种基于Newton-Rapson迭代法的NURBS插补算法。仿真和实验结果表明:该算法计算过程简单有效,具有可行性和实用性,可以减少插补计算量和插补时间,提高插补精度和加工效率,满足了数控系统实时、高速、高效率插补的要求,对其他数控插补的过程具有很强的借鉴意义。     

High accurate interpolation of NURBS tool path for CNC machine tools

Feedrate fluctuation caused by approximation errors of interpolation methods has great effects on machining quality in NURBS interpolation, but few methods can efficiently eliminate or reduce it to a satisfying level without sacrificing the computing efficiency at present. In order to solve this problem, a high accurate interpolation method for NURBS tool path is proposed. The proposed method can efficiently reduce the feedrate fluctuation by forming a quartic equation with respect to the curve parameter increment, which can be efficiently solved by analytic methods in real-time. Theoretically, the proposed method can totally eliminate the feedrate fluctuation for any 2nd degree NURBS curves and can interpolate 3rd degree NURBS curves with minimal feedrate fluctuation. Moreover, a smooth feedrate planning algorithm is also proposed to generate smooth tool motion with considering multiple constraints and scheduling errors by an efficient planning strategy. Experiments are conducted to verify the feasibility and applicability of the proposed method. This research presents a novel NURBS interpolation method with not only high accuracy but also satisfying computing efficiency.     

三次NURBS样条曲线插补加工螺旋转子建模与加工研究

提出在螺旋转子加工制造过程中,采用三次NURBS样条曲线插补替代通常的微直线段插补;建立了螺旋转子端面摆线段三次NURBS样条曲线方程.在Pro/E软件上比较了三次样条插补曲线和理论摆线之间的精度误差.最后通过在立式加工中心上比较了采用三次NURBS样条插补和采用微直线段插补的加工精度和加工效率,采用三次NURBS样条插补加工取得了理想的效果.     

珩磨机运动控制卡的三次B样条曲线插补算法

数控珩磨机在加工复杂曲线曲面时,控制系统通常以TMS320F2812芯片为核心,设计DSP运动控制卡的定时器控制中断控制伺服电动机来完成插补。介绍了一种利用DSP运动控制卡进行三次B样条曲线的插补方法,该方法不仅可以缩短插补时间,也可以通过控制运动控制卡定时器中断来调整插补轨迹。最后实例表明,该插补算法不仅满足运动控制的要求,而且也满足了高速高精度插补的要求。     

A new envelope algorithm of Hilbert–Huang Transform

The algorithm to compute the envelope-line in Hilbert–Huang Transform (HHT) has major drawbacks. This paper first introduces the problem of an envelope-line algorithm in HHT, analyses the shortcomings of two classic algorithms, cubic spline interpolation algorithm and the Akima interpolation algorithm, and then proposes an important theory called the Segment Slide Theory in light of the principle of parabola parameter spline interpolation method and proves it. Based on the theory we proposed and with intuitive geometric meaning, a new envelope algorithm, the segment power function method, is put forward. The new algorithm is superior to existing algorithms because in most situations it is more flexible than the cubic spline interpolation algorithm and smoother than the Akima interpolation algorithm as shown in the experimental examples, and it is less likely to introduce a false frequency when applied to HHT.     

Fast NURBS interpolation based on the biarc guide curve

In parametric spline interpolation, the real-time parameter update is a crucial step which will directly affect the processing performance such as the feed rate fluctuation, the contour error, the online computational effort, etc. The use of Taylor approximation interpolation method to identify the next interpolate point will cause large feed rate fluctuation due to the accumulation error and the truncation error, which will affect the machining quality. As there is no accurate analytic expression between the parameter u and arc length S and the mapping between them is nonlinear, and in order to reduce the feed rate fluctuation and light computation requirement for online interpolation, the paper first samples the tool path with step parameter and Gauss integration, with the sampled points being in the coordinate system defined by parameter u and arc length S. Then, the sampled points are fitted into the guide curve with the use of the biarc fitting method, and the analytic expression between parameter u and arc length S is established. The biarc so derived can be used to realize a fast NURBS interpolation and the simulation results validate the reliability and effectiveness of the proposed method.     

Variable-period feed interpolation algorithm for high-speed five-axis machining

To alleviate the feed fluctuation and to maintain a smooth feed in conventional five-axis machining, an optimal feed interpolation algorithm (look-ahead) is proposed. However, the problem arises where the segment usually cannot be interpolated exactly in an integer period because of the nonzero joint feed at the junction. To overcome this problem, and to achieve faster machining speed and higher quality parts, this paper presents an optimal feed interpolation algorithm for high-speed, five-axis machining having the function of “look-ahead”, i.e., variable-period linear interpolation algorithm. In real applications, the proposed algorithm results in: (1) constant speed; (2) high machining accuracy. Moreover, in this paper, an efficient method for acceleration and deceleration control is presented to achieve the highest-quality feed profiles and to shorten machining times. The precision and speed of machining is improved greatly. Experimental results verify the effectiveness of the proposed method.