Adaptive parametric interpolation scheme with limited acceleration and jerk values for NC machining

Parametric interpolation has many advantages over the traditional linear or circular interpolation in computer numerical control (CNC) machining. The existing work in this regard is reported to have achieved constant feedrate, confined chord error and limited acceleration/deceleration in one interpolator. However, the excessive jerk still exists due to abrupt change in acceleration profile, which will cause shock to the machine as well as deteriorate the surface accuracy. In this paper, an adaptive interpolation scheme incorporating machine’s dynamics capability consideration is proposed and illustrated in details. In the proposed algorithm, the commanded feedrate is maintained at most of the time and adaptively reduced in large curvature areas to meet the demand of the machining accuracy requirement, while at the same time, the acceleration and jerk values are limited within the machine’s capabilities during the whole interpolation process. It ensures a high machining accuracy, eliminates the phenomenon of overshoot/undershoot and reduces mechanical shock to the machine tools. The real-time performance of this interpolator is also measured to demonstrate its practical application. Two non-uniform rational B-spline (NURBS) curve interpolation experiments are provided to verify the feasibility and advantages of the proposed scheme.     

Design of jerk bounded feedrate with ripple effect for adaptive nurbs interpolator

A method for obtaining smooth, jerk bounded feedrate profile in high speed machining has been developed. This study proposes a NURBS interpolator based on adaptive feedrate control with a well developed lookahead algorithm. It is found that the values of the feedrate of the down stream sharp corner have profound effect on the feedrate of the upstream sharp corners causing a ripple effect (RE). By using a windowing scheme the feedrate profile obtained after lookahead is re-interpolated to obtain a continuous velocity and acceleration profiles which reduces the jerk related problems. This is compared with the adaptive NURBS interpolator to show the effectiveness of the proposed method. Simulation results indicate that the consideration of ripple effect is important in avoiding jerk and thereby increasing the machining accuracy.     

Design of a real-time adaptive interpolator with parameter compensation

The interpolator is the key part of a CNC system, which has strong effect on machining accuracy, tool motion smoothness, and machining efficiency. In this paper, a real-time adaptive interpolator is developed for non-uniform rational B-spline curves (NURBS) interpolation while considering the maximum acceleration/deceleration of the machine tool. In this proposed interpolator, both constant feedrate and high accuracy are achieved while the inconsistency of feedrate is dramatically reduced as well. In order to deal with the acceleration/deceleration around the feedrate-sensitive sharp corners, a look-ahead function is introduced to detect and adjust the feedrate adaptively. Furthermore, a parameter compensation scheme is proposed to eliminate the parametric truncation error which has been analyzed by several researchers but still not incorporated into any real-time interpolator so far. A case study was conducted to evaluate the feasibility of the developed interpolator.     

Efficient algorithm for time-optimal feedrate planning and smoothing with confined chord error and acceleration

In this paper, an efficient algorithm is proposed to generate a smooth near-time-optimal feedrate function along a parametric tool path for three-axis CNC machining under a feedrate bound, an acceleration bound for each axis, and a chord error bound. The algorithm first gives a discrete and computationally efficient algorithm to find a sequence of globally optimal velocity points under the feedrate, acceleration, and chord error bounds. A linear programming strategy is proposed to smooth the velocity points sequence. Finally, the velocity points sequence is fitted into a cubic spline to obtain a near-time-optimal and smooth feedrate function. Simulation and experiment results for Non-uniform rational basis spline curves are presented to illustrate the feasibility of the algorithm.     

Development of FPGA based NURBS interpolator and motion controller with multiprocessor technique

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.     

基于PLC的开放式数控NURBS插补功能的研究与实现

针对一种基于PLC的开放式数控系统,应用NURBS(Non-Uniform Rational B-Spline)曲线插补技术,对传统的自由曲线插补算法进行改进.同时根据STEP-NC标准对CAD/CAM/CNC一体化的新型数控插补方法进行研究,利用ActiveX技术实现了与CAD系统的数据交换,并在实验数控系统中加以应用.实验结果证明该插补算法可以有效地提高实时插补速度和精度,提高数控系统的工作效率.     

An optimal feedrate model and solution algorithm for a high-speed machine of small line blocks with look-ahead

In complex high-speed machining of consecutive small line blocks, the tool path segments can be so short that a machining center moving at a high feedrate cannot accelerate or decelerate fast enough to make direction changes accurately. Aiming at adjusting the feedrate automatically to achieve maximum productivity, this paper present a novel mathematical model considering the key and representative factors, and then based on it, propose an algorithm to seek the approximate optimal feedrate by evaluating the toolpath ahead. Simulation results demonstrate the machine using the proposed model and algorithm can go fast where possible and to slow down just enough where needed and the productivity can be improved dramatically .     

On robust stability of linear time invariant fractional-order systems with real parametric uncertainties

In this paper, the robust bounded-input bounded-output stability of a large class of linear time invariant fractional order families of systems with real parametric uncertainties is analyzed. The transfer functions contain polynomials in fractional powers of the Laplace variable s, possibly in combination with exponentials of fractional powers of s. Using the concept of the value set and a generalization of the zero exclusion condition theorem, a theorem to check the robust bounded-input bounded-output stability of these families of systems is presented. An upper cutoff frequency for drawing the value sets is provided as well. Finally, two numerical examples are given to illustrate results obtained by the lemma and theorems presented in the paper.     

On-Line Production Control of Tandem Systems with Finite Inter-Stage Storage, Using a Dynamic Maximum Cycle Time Algorithm

For a tandem manufacturing system with finite interstage storage and asynchronous operations, stage cycle times are allowed to vary from cycle to cycle and from stage to stage. Owing to the nature of the operation and the occurrences of blocking and starvation, the relationship between the time each stage spends on each job and the output rate of the system is not directly observable. In order to operate the system so that it meets the demand without over-producing or under-producing, it would be helpful to know the time limit available for each stage to operate on each job. This paper describes a method for calculating such cycle time limits for each stage at each cycle on a real-time basis. The calculated cycle time limits are always bounded below, approximately by the expected time between outputs of the system. The value of a cycle time limit is a function of the current system state, performance history of the stages and the interrelationship among the stages. Emulation examples (with 3-stage and 10- stage systems) will show that while cycle times are allowed to vary, as long as they do not exceed their calculated limits throughout the production, system output will be very close to a predefined expected amount.     

常用弹簧二维三维参数化造型技术研究与系统开发

弹簧是机械设计的常用零件之一,广泛用于机器和仪表中。弹簧的种类复杂多样、形状各异,无论手工还是CAD交互制图均比较繁琐。系统以AutoCAD系统为开发平台,运用了Visual Lisp、Visual Basic编程语言、Access数据库技术及对话框开发技术,对各种常用弹簧类型几何图形及标准数据表等内容进行详细研究与参数化造型系统开发。该系统只需用户点击鼠标或键入参数便能够方便、准确、快捷地给出正确的弹簧二维或三维图形,成功解决了弹簧设计建模过程中绘图修改繁琐、设计周期过长、设计质量难以保证等难题,从而对机械CAD技术向数字化、集成化发展具有重要意义。     

Development of the precision planar motor stage using a new magnet array and robust control with the parametric uncertainty model

This paper discusses the development of a new precision motor stage, where a new magnet array is proposed and a new robust controller is implemented. Several planar motor parameters, such as the air gap flux density and flux linkage, are analytically evaluated by the scalar potential, and, thus, about a 5–8% increase is observed for the proposed magnet array. A new robust controller is also proposed using the parametric uncertainty model, which can effectively control the movement during both stable and cogging positions. The performance of the robust controller is evaluated, and it shows much higher robustness and about a 200% higher position accuracy when compared with the conventional PID controller. Therefore, the developed planar motor stage is successfully designed and implemented, and, thus, proposes great potential for most of the positioning applications in the field of semiconductor equipment and machine tools.     

汽车变速箱性能检测系统的设计

随着汽车工业的迅猛发展 ,变速箱作为汽车的重要传动部件 ,其操作性、传动性与安全性日显重要 ,因此本研究所研制和开发了“汽车变速箱性能检测系统”。本文首先从整体上介绍了该系统的构成 ,其次详细论述了信号测试系统的测试参数和测试原理 ,最后详细介绍了软件系统的体系结构以及各子系统的功能 ,并对子系统间并发性的解决方案进行了讨论     

On the design and development of hybrid journal bearings: a review

This paper presents a comprehensive review of developments in the design and application of hydrostatic and hybrid journal bearing systems during the last few decades. Revolutionary changes have taken place in the applications of hydrostatic and hybrid journal bearings, from very low‐speed radar to very high‐speed turbo‐machinery and ultra‐precision machine tools requiring high stiffness to improve accuracy. Hydrostatic and hybrid bearings are of interest because of their potential at very high operating speed and heavy load‐carrying capacity. This paper also outlines the analyses done of these types of journal bearings in practical application, which has led to improved bearing design. This review critically discusses the parameters that significantly affect the static and dynamic performance of a journal bearing. This review includes coverage of recent publications in the literature pertaining to hydrostatic and hybrid journal bearings focusing on the influence of parameters such as bearing geometry, supply pressure, flow control devices, fluid compressibility, fluid inertia, journal misalignment, bearing flexibility, surface roughness, and thermal effects. Copyright © 2006 John Wiley & Sons, Ltd.     

考虑动态刚度、传递误差及齿侧间隙的齿轮系统谐振分析

在所建立的考虑啮合动态刚度、传递误差、齿侧间隙等多种非线性因素的直齿圆柱齿轮系统非线性动力学分析模型中,将时变啮合刚度按5次谐波展开,齿侧间隙按3次多项式拟合,运用多尺度法对该模型进行了分析,推导了系统主共振和谐波共振响应下的频率响应方程,绘制了相应的频率响应曲线,分析了系统中的静态栽荷和动态栽荷以及阻尼对谐振响应幅值和频率的不同影响作用。     

Estimation of the section thickness and optical disector height with a simple calibration method

The distance between the upper and lower surfaces of a section (i.e. the section thickness) can be measured with a microcator or a shaft encoder. In the present report, an alternative simple method is described for estimating the section thickness where such equipment is not available. The basic principle of the method is based on a calibration method already described in the literature. The main difference is that it enables one to make more precise measurements. Provided that the calibration and measurements are made properly, this method can be used in estimating the section thickness, optical disector heights, and in particular in the determination of the thickness sampling fraction for the optical fractionator.     

用骨架折弯进行蜗轮建模及其齿廓成型

讨论了利用骨架折弯进行蜗轮建模的可能性,并根据对蜗轮齿面成型原理分析设计出一个较合理的方案,最终实现了以相对较简单的方式完成蜗轮建模的构想。     

The saucor, a new stereological tool for analysing the spatial distributions of cells, exemplified by human neocortical neurons and glial cells

The 3D spatial arrangement of particles or cells, for example glial cells, with respect to other particles or cells, for example neurons, can be characterized by the radial number density function, which expresses the number density of so-called 'secondary' particles as a function of their distance to a 'primary' particle. The present paper introduces a new stereological method, the saucor, for estimating the radial number density using thick isotropic uniform random or vertical uniform random sections. In the first estimation step, primary particles are registered in a disector. Subsequently, smaller counting windows are drawn with random orientation around every primary particle, and the positions of all secondary particles within the windows are recorded. The shape of the counting windows is designed such that a large portion of the volume close to the primary particle is examined and a smaller portion of the volume as the distance to the primary object increases. The experimenter can determine the relation between these volumina as a function of the distance by adjusting the parameters of the window graph, and thus reach a good balance between workload and obtained information. Estimation formulae based on the Horvitz-Thompson theorem are derived for both isotropic uniform random and vertical uniform random designs. The method is illustrated with an example where the radial number density of neurons and glial cells around neurons in the human neocortex is estimated using thick vertical sections for light microscopy. The results indicate that the glial cells are clustered around the neurons and the neurons have a tendency towards repulsion from each other.     

机械摆随机同步跟踪机构的原理分析与设计

在一些机械设备中,受货位常常随俯仰机构作俯仰运动。要使机械摆及时准确地供货到位,就需要按照受货位的俯仰位置,同步调整机械摆的供摆动角,本文采用机械反馈机构,把系统的末端状态反馈到中间机构（调整杠杆支点）,实现了机械摆随机同步跟踪,在某一工程机械设备中成功地实现自动接货,供货功能。     

Studies on the importance of sympathetic innervation, adrenergic receptors, and a possible local catecholamine production in the development of patellar tendinopathy (tendinosis) in man

Changes in the patterns of production and in the effects of signal substances may be involved in the development of tendinosis, a chronic condition of pain in human tendons. There is no previous information concerning the patterns of sympathetic innervation in the human patellar tendon. In this study, biopsies of normal and tendinosis patellar tendons were investigated with immunohistochemical methods, including the use of antibodies against tyrosine hydroxylase (TH) and neuropeptide Y, and against alpha1-, alpha2A-, and beta1-adrenoreceptors. It was noticed that most of the sympathetic innervation was detected in the walls of the blood vessels entering the tendon through the paratendinous tissue, and that the tendon tissue proper of the normal and tendinosis tendons was very scarcely innervated. Immunoreactions for adrenergic receptors were noticed in nerve fascicles containing both sensory and sympathetic nerve fibers. High levels of these receptors were also detected in the blood vessel walls; alpha1-adrenoreceptor immunoreactions being clearly more pronounced in the tendinosis tendons than in the tendons of controls. Interestingly, immunoreactions for adrenergic receptors and TH were noted for the tendon cells (tenocytes), especially in tendinosis tendons. The findings give a morphological correlate for the occurrence of sympathetically mediated effects in the patellar tendon and autocrine/paracrine catecholamine mechanisms for the tenocytes, particularly, in tendinosis. The observation of adrenergic receptors on tenocytes is interesting, as stimulation of these receptors can lead to cell proliferation, degeneration, and apoptosis, events which are all known to occur in tendinosis. Furthermore, the results imply that a possible source of catecholamine production might be the tenocytes themselves     

On the unique solvability of a direct dynamics problem for mechanisms with redundant constraints and Coulomb friction in joints

The uniqueness of simulated motion of an overconstrained rigid body mechanism with joint friction is studied. The investigated issue originates in the problem of joint reactions solvability. It is known that in case of redundant constraints existence the constraint reaction forces cannot be — in general — uniquely determined. It can be proved, however, that — under certain conditions — selected reactions can be specified uniquely. Analytical and numerical methods for reactions solvability analysis are available. It is shown in this paper that indeterminacy of normal reactions results in indeterminacy of friction forces, and moreover, non-uniqueness of friction forces results in non-uniqueness of simulated motion. A method of finding these joints, for which friction forces are unique, is presented. It is also proved that if only uniquely solvable friction effects are introduced, then simulated motion of the mechanism is unique, otherwise it is not. Finally, examples of dynamic analysis of overconstrained mechanisms with joint friction are presented; unique and non-unique results are obtained.