本文選題：二次曲面輪廓度誤差 + 最小區(qū)域原則　； 參考：《哈爾濱工業(yè)大學(xué)》2016年博士論文

【摘要】：二次曲面因其特殊的幾何或者物理意義,在科研生產(chǎn)的諸多領(lǐng)域擁有廣泛的應(yīng)用。包括二次曲面輪廓度誤差評定和二次曲面空間位置姿態(tài)求取的二次曲面的測量評定技術(shù)也越發(fā)受到關(guān)注。很多二次曲面零件的輪廓度誤差和其空間位置姿態(tài)都與這些零件的幾何和物理意義息息相關(guān)。例如,在航天工程中,星載天線的面形誤差和空間位置姿態(tài)就直接關(guān)系到天線的電性能。為準(zhǔn)確地評定拋物面天線等二次曲面的輪廓度誤差及求取其空間位置姿態(tài),特對以下的相關(guān)技術(shù)進(jìn)行研究探索。首先,依據(jù)目前國際和國家標(biāo)準(zhǔn)中的輪廓度誤差和形狀誤差的定義,借鑒平面度、圓柱度誤差定義和二次曲面輪廓度誤差評定的研究資料,對球度、圓錐度、橢球面、拋物面和雙曲面輪廓度誤差進(jìn)行定義。建立了基于最小區(qū)域原則或者基于最小二乘原則的空間任意位置姿態(tài)二次曲面輪廓度誤差評定模型,以解決工程中空間二次曲面的評定問題。為提高測量評定的準(zhǔn)確性和效率,給出基于初始測量點(diǎn)三坐標(biāo)數(shù)據(jù)的二次曲面類別歸算方法、模型初值的計(jì)算公式和各類二次曲面的面型約束條件公式。對模型最優(yōu)解的存在性進(jìn)行了分析。提出了角度分割逼近算法結(jié)合改進(jìn)的粒子群算法(IPSO)求解空間任意位置姿態(tài)二次曲面的測量評定模型。在評定中采用角度分割逼近算法計(jì)算測量點(diǎn)到空間二次曲面的法向偏差,再根據(jù)輪廓度誤差定義得到模型中的目標(biāo)函數(shù)。分析了角度分割逼近算法成立的兩條前提假設(shè),并根據(jù)假設(shè)給出合理的算法網(wǎng)格布局遞推公式。根據(jù)模型中目標(biāo)函數(shù)的特點(diǎn),提出主要以最優(yōu)化解析法結(jié)合PSO算法求解評定模型的IPSO算法,并分析了模型的收斂性和算法的時間復(fù)雜度。根據(jù)幾何特性對空間二次曲面輪廓度誤差評定模型進(jìn)行計(jì)算簡化,并給出簡化模型的初值計(jì)算公式。通過實(shí)驗(yàn),采用基于最小二乘原則、基于最小區(qū)域原則的二次曲面輪廓度誤差評定模型、基于最小區(qū)域原則的空間二次曲面輪廓度誤差評定的計(jì)算簡化模型和SA(Spatial Analyzer)軟件進(jìn)行各類二次曲面輪廓度誤差評定并對比結(jié)果,證明各個模型都能對空間二次曲面準(zhǔn)確地完成輪廓度誤差評定,同時計(jì)算簡化模型更有效率。根據(jù)國際和國家標(biāo)準(zhǔn)及以往的研究,定義了基于最小區(qū)域原則或者基于最小二乘原則的空間二次曲面位置姿態(tài),并給出其相應(yīng)的求取模型和初值求取公式。根據(jù)拋物面天線電性能研究采用面形誤差概念,同時給出拋物面法向均方根、軸向均方根誤差的位置姿態(tài)求取模型。通過實(shí)驗(yàn)驗(yàn)證了二次曲面位置姿態(tài)求取模型被驗(yàn)證。在空間二次曲面輪廓度誤差評定模型基礎(chǔ)上,提出一種使用三坐標(biāo)測量儀時的直接半徑補(bǔ)償方法。最后采用Faro三坐標(biāo)測量儀對某型號拋物面天線進(jìn)行測量評定實(shí)驗(yàn),通過實(shí)驗(yàn)表明幾類典型空間二次曲面輪廓度評定模型及簡化模型、二次曲面空間位置姿態(tài)求取模型、角度分割逼近算法、直接半徑補(bǔ)償方法可以有效的完成二次曲面測量評定的任務(wù)。
[Abstract]:Two surfaces are widely used in many fields of scientific research and production because of their special geometric or physical meaning. The measurement and evaluation techniques for the measurement and evaluation of the two surfaces, including the profile error assessment of two surfaces and the position and pose of two surfaces, have also been paid more attention. The profile error and its space position of many two surface parts For example, in space engineering, the surface error of the Spaceborne Antenna and the position of the space position are directly related to the electrical performance of the antenna. In order to accurately assess the profile error of the two surface of the paraboloid antenna and to obtain the position of its space position, the following related techniques are made. First of all, according to the definition of contour error and shape error in international and national standards, by reference to the research data of flatness, cylindricity error definition and two surface profile error assessment, the definition of sphericity, conic, ellipsoid, paraboloid and double surface profile error is defined. In order to improve the accuracy and efficiency of the measurement evaluation, a method for the classification of the two surface categories based on the three coordinate data of the initial measurement points is given, and the calculation of the initial value of the model is given. The formula and the face type constraint condition formula of all kinds of two surfaces are analyzed. The existence of the optimal solution of the model is analyzed. An angle segmentation approximation algorithm combined with improved particle swarm optimization (IPSO) is proposed to solve the measurement evaluation model of the two curved surface of a space arbitrary position. The normal deviation of the two curved surface is obtained, and then the objective function in the model is obtained by the definition of the contour error. The two premise assumptions of the angle segmentation approximation algorithm are analyzed, and a rational algorithm of the recursive formula of the algorithm grid layout is given according to the hypothesis. Based on the characteristics of the objective function in the model, the optimization method is proposed to combine the PSO algorithm with the optimization method. The IPSO algorithm of the evaluation model is solved, and the convergence of the model and the time complexity of the algorithm are analyzed. According to the geometric characteristics, the estimation model of the space two surface profile error is simplified, and the formula of the initial value calculation of the simplified model is given. Through the experiment, the two times curve based on the minimum two multiplying principle and the minimum region principle is adopted. The error assessment model of surface profile degree, the simplified model and SA (Spatial Analyzer) software based on the minimum area principle for evaluating the profile error of the two surface profile, and the comparison results of the profile error evaluation of various two surfaces, prove that each model can accurately evaluate the contour error of the space two surfaces. The simplified model is more efficient. According to the international and national standards and previous studies, the position and posture of the space two order surface based on the minimum region principle or the least square principle are defined, and the corresponding calculation model and the initial value formula are given. The paraboloid method is used to calculate the position and attitude of the root mean square root error in the axial mean square root error. Through the experiment, it is proved that the position and attitude model of the two curved surface is verified. On the basis of the spatial profile error assessment model of the two curved surface, a direct half path compensation method using the three coordinate measuring instrument is proposed. Finally, the Faro three coordinate measurement is used. The measurement and evaluation experiment of a type of parabolic antenna is carried out by the instrument. Through the experiment, several types of typical space two surface profile evaluation model and simplified model, two curved surface positions pose model, angle segmentation approximation algorithm, and the direct radius compensation method can effectively complete the task of two surface measurement and evaluation.
【學(xué)位授予單位】：哈爾濱工業(yè)大學(xué)
【學(xué)位級別】：博士
【學(xué)位授予年份】：2016
【分類號】：TG806

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