FORM ERROR EVALUATION OF CIRCLES BASED ON A FINELY-DESIGNED GENETIC ALGORITHM

A genetic algorithm(GA)-based new method is designed to evaluate thecircularity error of mechanical parts. The method uses the capability of nonlinear optimization ofGA to search for the optimal solution of circularity error. The finely-designed GA (FDGA)characterized dynamical bisexual recombination and Gaussian mutation. The mathematical model of thenonlinear problem is given. The implementation details in FDGA are described such as the crossoveror recombination mechanism which utilized a bisexual reproduction scheme and the elitist reservationmethod; and the adaptive mutation which used the Gaussian probability distribution to determine thevalues of the offspring produced by mutation mechanism. The examples are provided to verify thedesigned FDGA. The computation results indicate that the FDGA works very well in the field of formerror evaluation such as circularity evaluation.

Modeling Method for Assembly Variation Propagation Taking Account of Form Error

The propagation of variations, such as fixture errors and datum errors resulting from assembly and machining processes, has been extensively studied. However, only a few studies that focus on form error propagation in assembly systems have been implemented. Machining errors, especially form errors, have great impact on assembly accuracy and accuracy stability of precision mechanical systems. With form errors being the research object, a method for calculating mating variation and specifying mating coordinate is proposed to improve the accuracy of the variation propagation model. Taking into account the form error of mating surfaces, the assembly variation propagation of a precision mechanical system is analyzed, and the brief derivation procedure of the variation propagation model is introduced afterwards. The variation propagation model involves a new concept of mating variation specified by the two mating surfaces. An innovative method, the difference surface search based method, is proposed to calculate the mating variation amongst the mating surfaces. The obtained mating variation is then utilized to specify the mating coordinate in the variation propagation model. Moreover, FEM is employed to simulate the contact state of the two mating surfaces to demonstrate effectiveness of the proposed method. Meanwhile, the mating variation and mating coordinate obtained are incorporated into the assembly variation propagation model, which is then verified by a following case study through a comparison between the calculated results and the experimental results. The comparing results indicate that the established model improves the prediction of assembly accuracy. The developed model enables the investigation of various fundamental issues in variation reduction, including variation analysis, process monitoring, accuracy prediction, and accuracy control.

Robustness and precision evaluation of the form error of micro-structured surfaces using real coded genetic algorithm

To obtain the form error of micro-structured surfaces robustly and accurately, a form er- ror evaluation method was developed based on the real coded genetic algorithm （RCGA）. The meth- od employed the average squared distance as the matching criterion. The point to surface distance was achieved by use of iterative method and the modeling of RCGA for the surface matching was also presented in detail. Parameter selection for RCGA including the crossover rate and population size was discussed. Evaluation results of series simulated surfaces without form error show that this method can achieve the accuracy of root mean square deviation （ Sq ） less than 1 nm and surface pro- file error （ St ） less than 4 nm. Evaluation of the surfaces with different simulated errors illustrates that the proposed method can also robustly obtain the form error with nano-meter precision. The e- valuation of actual measured surfaces further indicates that the proposed method is capable of pre- cisely evaluating micro-structured surfaces.

Variation analysis ofprecision mechanical assembly consideringform errors and local deformation

A method to analyze the effect of form errors and local deformation on the assembly accu- racy and its stability in a non-rigid assembly system is proposed. The contact finite element method was used to obtain local deformation of mating surfaces, which was superposed onto form errors to obtain real mating surface data of assemblies. Then mating variation was obtained by establishing vir- tual contact planes. Finally, an experiment of the assembly of two cylindrical components was car- ried out to verify the validity of the proposed method. By comparing the calculation accuracies of 3D assembly with and without taking into account local deformation, the results showed that the effects of local deformation of mating surfaces on calculation accuracy of mating variation was not neglect- able compared with form errors.

ANALYSIS OF TOOTH FORM ERROR OF EQUAL BASE CIRCLE BEVEL GEAR

The basic principle of equal base circle bevel gear (EBCBG) is illustrated simply Thetooth surface equation of EBCBG manufactured by end milling cutter with involute profile is de-rived. The tooth form error is analyzed on the basis of spherical involute

Least Squares Evaluations for Form and Profile Errors of Ellipse Using Coordinate Data

To improve the measurement and evaluation of form error of an elliptic section, an evaluation method based on least squares fitting is investigated to analyze the form and profile errors of an ellipse using coordinate data. Two error indicators for defining ellipticity are discussed, namely the form error and the profile error, and the difference between both is considered as the main parameter for evaluating machining quality of surface and profile. Because the form error and the profile error rely on different evaluation benchmarks, the major axis and the foci rather than the centre of an ellipse are used as the evaluation benchmarks and can accurately evaluate a tolerance range with the separated form error and profile error of workpiece. Additionally, an evaluation program based on the LS model is developed to extract the form error and the profile error of the elliptic section, which is well suited for separating the two errors by a standard program. Finally, the evaluation method about the form and profile errors of the ellipse is applied to the measurement of skirt line of the piston, and results indicate the effectiveness of the evaluation. This approach provides the new evaluation indicators for the measurement of form and profile errors of ellipse, which is found to have better accuracy and can thus be used to solve the difficult of the measurement and evaluation of the piston in industrial production.

Accurate Evaluation of Free-form Surface Profile Error Based on Quasi Particle Swarm Optimization Algorithm and Surface Subdivision

Although significant progress has been made in precision machining of free-form surfaces recently, inspection of such surfaces remains a difficult problem. In order to solve the problem that no specific standards for the verification of free-form surface profile are available, the profile parameters of free-form surface are proposed by referring to ISO standards regarding form tolerances and considering its complexity and non-rotational symmetry. Non-uniform rational basis spline（NURBS） for describing free-form surface is formulated. Crucial issues in surface inspection and profile error verification are localization between the design coordinate system（DCS） and measurement coordinate system（MCS） for searching the closest points on the design model corresponding to measured points. A quasi particle swarm optimization（QPSO） is proposed to search the transformation parameters to implement localization between DCS and MCS. Surface subdivide method which does the searching in a recursively reduced range of the parameters u and v of the NURBS design model is developed to find the closest points. In order to verify the effectiveness of the proposed methods, the design model is generated by NURBS and the measurement data of simulation example are generated by transforming the design model to arbitrary position and orientation, and the parts are machined based on the design model and are measured on CMM. The profile errors of simulation example and actual parts are calculated by the proposed method. The results verify that the evaluation precision of freeform surface profile error by the proposed method is higher 10%-22% than that by CMM software. The proposed method deals with the hard problem that it has a lower precision in profile error evaluation of free-form surface.

Hyperbolic Error Analysis and Parametric Optimization of Round Body Form Tool

with the merits of the easy manufacture and the long service life and the processing the inside or outside form surface, round body form tool is extensive use in large scales production. Its main demerit is the big hyperbolic error which is caused in the process of processing cone, but about the discussion of hyperbolic error, there are two drawbacks in the current books and documents: (1) The error measuring plane is established on the rake face of tool, which doesn’t coincide with the actual measuring plane (axial plane) of work piece; (2) When the influential elements of error are analyzed, single parameter is only discussed. In order to overcome these demerits, the mathematical model of hyperbolic error on the axial plane of work piece is built in this paper when round body form tool processes cone. The fundamental reason which causes hyperbolic error when round body form tool processes cone is that the line profile replaces the curve profile of theory in the radial cut plane of tool in the design and manufacture of tool. In order to evaluate the mathematical formula of its error, firstly, the equation of cone of work piece must be established, secondly, the equation of cutting lip in the rake face is established, then, the profile equation of the radial plane of tool is evaluated on the condition that coordinate is changed, at last, the hyperbolic error is derived according to the equation and the substitutional line equation, and the error is converted to the axial plane of work piece which is coincided with the measuring plane. The actual calculation and the theory analysis indicated that if the cone length and the coning of the cone of work piece are fixed, the main elements which affect the hyperbolic error in the axial plane of work piece are the outside diameter R of round body form tool, the rake angle and the rear angle in "base point". If these three parameters are combined rationally, the hyperbolic error is minimum when round body form tool process cone, and the machining precision of work piece can be improved, on the condition that neither the work capacity of the tool design nor the manufacture cost of tool increases.

3DP工艺中阶梯误差与渗透误差相互作用研究

3DP工艺中影响零件成型精度的原理性误差主要来源于阶梯误差和黏结剂渗透误差,并且在误差测量结果中难以区分.本文基于黏结剂在砂床中的流动状态,建立了黏结剂从喷射到渗透过程的数值仿真模型,分析了在二维平面不同角度三角面片打印时理想模型边界和实际黏结砂粒边界之间的位置误差,研究了阶梯误差和渗透误差之间的相互作用.在此基础上,针对不同角度三角面片打印过程中阶梯误差与黏结剂渗透误差相互作用关系也不相同的问题,提出了基于三角面片法向量方向与成型方向夹角的三角面片偏移误差公式用于表达这两种误差对成型质量的综合影响.结果表明:在向上三角面片中,渗透误差与阶梯误差相互补偿,三角面片偏移误差随着斜面与水平面夹角角度的减小而减小;在向下三角面片中,阶梯误差与渗透误差相互叠加,三角面片偏移误差随着斜面与水平面夹角角度的减小而增大.将三角面片偏移误差的公式计算值与其实际测量值进行对比,公式计算误差最大为0.060 mm,最小为0.002 mm,表明三角面片偏移误差公式用于表达阶梯误差与黏结剂渗透误差综合作用的有效性.

中低英语水平学习者书面语错误动态变化特征

以某高职英语专业普高、职高生源各一个班级学生为研究对象,以前后两次限时有效英语书面作文语料自建语料库。采用错误分析理论,对作文中词形、词汇及句法错误进行共时与历时比较分析,试图发现产生的变化规律。研究表明,两类研究对象英语书面语作文改善和句法错误变化统计显著,书面作文成绩、词汇及句法错误差异显著。初次英语书面作文成绩与词形、词汇、句法错误均显著负相关;后次作文中普高班学生的成绩与句法错误中等负相关,职高班学生作文成绩与词汇及句法错误显著负相关。研究结果为深入研究中国中低英语水平学习者书面写作动态发展特征、能力提升途径及写作教学实践提供了有益启示。

微分形式新安江模型

现有新安江模型数学上是代数方程并限于一阶差分方法求解,不可避免存在数值误差,探索数值求解误差控制新途径,对于提高模型计算精度具有重要意义。基于微分系统框架,识别新安江模型的状态变量和通量,推导其控制方程和本构方程,提出微分形式的新安江模型(ODE-XAJ),并采用四阶显式Runge Kutta法求解。数值实验结果显示,以解析解为基准,ODE-XAJ绝对误差处于或小于10^(-4)mm量级,可实现对解析解的高阶近似;以ODE-XAJ结果为基准,按归一化平均绝对误差评价,现有新安江模型的数值求解误差约为8.7%。典型流域应用结果显示,ODE-XAJ确定性系数提升0.02,洪量相对误差降低4.3%。研究表明,ODE-XAJ理论上分离了模型的数学方程与具体解法,可有效控制数值求解误差,提升模型模拟精度。

RESIDUAL A POSTERIORI ERROR ESTIMATE TWO-GRID METHODS FOR THE STEADY (NAVIER-STOKES) EQUATION WITH STREAM FUNCTION FORM

Residual based on a posteriori error estimates for conforming finite element solutions of incompressible Navier-Stokes equations with stream function form which were computed with seven recently proposed two-level method were derived. The posteriori error estimates contained additional terms in comparison to the error estimates for the solution obtained by the standard finite element method. The importance of these additional terms in the error estimates was investigated by studying their asymptotic behavior. For optimal scaled meshes, these bounds are not of higher order than of convergence of discrete solution.

基于全概率公式的M-APSK误码率分析模型

为有效评估加性白高斯噪声信道中M-APSK的性能,提出了一种基于全概率公式的理论误码率分析模型。首先根据星座点分布及其编码特点对星座平面进行区域划分,然后由接收符号落在相应区域的概率推导出各比特的判决错误概率表达式,最后得到理论误码率的精确闭式解。以16APSK和32APSK为例,推导出了其各类星座图的理论误码率计算公式,与Monte Carlo仿真结果非常吻合。模型具有通用性,PSK、QAM、PAM、APSK等调制方式均可利用该模型得到理论误码率的精确闭式解。相较于依赖大量数值计算的复杂二维概率积分方法,所提模型能够更方便地给出M-APSK的误码率性能。

超大跨鱼腹式轮辐索桁架结构施工成型方法与结构敏感性研究

超大跨鱼腹式轮辐索桁架结构形式新颖,施工成型难度大,受加工误差和施工偏差影响大。为此,需通过大量仿真计算分析,找到合理可行的施工成型方法;对各种误差和偏差进行研究,找到敏感性较强的拉索、耳板等构件,为施工过程控制提供依据。以卢赛尔体育场超大跨鱼腹式轮辐索桁架结构为研究对象,通过施工过程数值仿真,对3种施工成型方法进行结构内力、变形等力学响应分析与比选;通过施工监测结果验证选择的最优成型方法的合理性和可行性;通过在计算模型中引入一定缺陷的方法,研究了拉索长度误差和节点板施工偏差对结构内力的影响。研究结果表明,采用优选方案后,在模拟提升过程中各榀索桁架索力接近且变化一致,环索径向位移控制在800mm以内;径向索索力监测值和模拟值偏差在10%以内;加工误差和施工偏差对本榀索桁架索力影响较大,对间隔1榀的索桁架索力几乎无影响。

Wheel Setting Error Modeling and Compensation for Arc Envelope Grinding of Large-Aperture Aspherical Optics

Precision grinding is a key process for realizing the use of large-aperture aspherical optical elements in laser nuclear fusion devices,large-aperture astronomical telescopes,and high-resolution space cameras.In this study,the arc envelope grinding process of large-aperture aspherical optics is investigated using a CM1500 precision grinding machine with a maximum machinable diameter ofΦ1500 mm.The form error of the aspherical workpiece induced by wheel setting errors is analytically modeled for both parallel and cross grinding.Results show that the form error is more sensitive to the wheel setting error along the feed direction than that along the lateral direction.It is a bilinear function of the feed-direction wheel setting error and the distance to the optical axis.Based on the error function above,a method to determine the wheel setting error is proposed.Subsequently,grinding tests are performed with the wheels aligned accurately.Using a newly proposed partial error compensation method with an appropriate compensation factor,a form error of 3.4μm peak-to-valley(PV)for aΦ400 mm elliptical K9 glass surface is achieved.

基于拼接技术的大量程绝对式直线时栅位移传感器自校准方法研究

针对大量程直线位移传感器扩展测量范围和实现绝对定位互相矛盾的问题,在其应用场合缺乏高效安装高精度参考器件的条件,导致难以频繁在线校准以保持其测量精度,基于拼接技术提出一种适用于直线时栅位移传感器的误差延拓自校准新方法。,将复杂的大量程绝对式测量拆分为单段栅尺上的绝对位移测量和栅尺拼接后的绝对位置判断;将绝对位置数据作为位置判断依据并构建双测头结构,实现接缝处感应信号的平滑过渡;利用原生的双测头结构获得定距测量序列,结合误差延拓法构建周期误差函数,再使用快速傅里叶变换获得测量序列幅度谱重构误差函数。为了验证上述方法的可行性和有效性,制作了单段栅尺长度为600 mm的传感器样机进行实验。结果表明,2段栅尺拼接后在量程903 mm内能够实现绝对位置测量;采用自校准方法后传感器单周期内平均误差峰值从2.00μm降至0.59μm,误差补偿效果为70.50%;大量程误差峰值从18.93μm降至0.75μm,误差补偿效果为96.04%;此外,通过校准效果对比实验证明了误差延拓自校准方法优于基于傅里叶谐波补偿的比较校准法,误差校准效果提升约76.20%。

Geometric Approximation Technique for Minimum Zone Sphericity Error

The mathematical modeling for evaluation of the sphericity error is proposed with minimum radial separation center. To obtain the minimum sphericity error from the form data, a geometric approximation technique was devised. The technique regarded the least square sphere center as the initial center of the concentric spheres containing all measurement points, and then the center was moved gradually to reduce the radial separation till the minimum radial separation center was got where the constructed concentric spheres conformed to the minimum zone condition. The method was modeled firstly, then the geometric approximation process was analyzed, and finally,the software for data processing was programmed. As evaluation example, five steel balls were measured and the measurement data were processed with the developed program. The average iteration times of the approximation technique is 4.2, and on average the obtained sphericity error is 0. 529μm smaller than the least square solution,with accuracy increased by 7. 696%.

气浮垫的误差均化能力研究

为探究小孔节流气浮轴承的误差均化能力的主要影响因素,建立单个气浮垫的误差运动模型,并利用所定义的均化系数研究气浮垫误差运动、导轨条形状误差和气浮垫结构参数三者之间的定量关系。研究表明:对于长波长的导轨条形状误差(波数为0~1),当波数逐渐增加时,均化系数从1逐渐降低到接近0;对于短波长的导轨条形状误差(波数为1~10),当波数靠近或者等于正整数时,均化系数取接近于0的最小值;当波数靠近或者等于正整数加0.5时,均化系数取小于0.25的局部最大值;结构参数中,封气边宽度对误差均化能力有很大影响,气垫间隙和小孔节流器孔径对误差均化能力基本无影响;当移动速度小于10 000 mm/s时,移动速度对误差均化能力的影响微弱。

基于工程数据的行为形成因子权重确定方法

针对行为形成因子影响人员行为的问题,提出一种行为形成因子权重的确定方法。评述现有的行为形成因子权重确定方法,指出存在的缺陷和不足,构建一种基于工程数据的行为形成因子权重确定方法。结果表明:该方法能得到不同人为差错类型所对应行为形成因子的权重,更具客观性,可为人为差错的管理提供有效指导,为人为差错概率量化提供支持。

维吾尔语语法教学思考——以能动式为例

维吾尔语动词有人称、数、时、语态、体、式等语法范畴,维吾尔语动词能动式是初级维吾尔语精读教学中的语法重点。本文认为学生在学习过程中,由于对维吾尔语动词能动式构成成分记忆不扎实,出现了附加不正确的现象;对元音弱化等内容掌握不牢,在使用过程中出现了书写错误;没能掌握其在汉语中的对应表达,在句子是否使用能动式判断时出现了错误,最终不能正确使用能动式翻译句子。因此,教师在教学过程中要加强学生基础知识的训练,在讲授维吾尔语语法时适当采用对比的方法,引导学生充分利用母语对第二语言习得的正向迁移,使学生理解汉语与维吾尔语的共同点与不同点。学生在学习过程中要充分发挥主观能动性,端正学习态度,利用母语对二语习得的有利影响学好维吾尔语语法。