曲面抛光平台几何误差分析与补偿研究

发布时间：2018-11-20 15:04

【摘要】：光学曲面零件在国防科技、航空航天、生物医学等领域有着广泛的应用。其特殊的几何特性、硬脆的材料性能以及较高的面型精度,对加工设备的精度提出了苛刻的要求。如何高精度、高效率、低成本的实现光学曲面的加工引起了国内外广大学者的深入研究。由于几何误差是机床误差的主要误差源,因此,通过分析光学曲面加工平台的几何误差,并进行补偿,对提升光学曲面零件的加工精度有着非常重要的意义。本文在国家重点基础研究发展计划(973计划)项目《光学自由曲面制造的基础研究》的子课题《光学自由曲面成形过程的物理解析及再构策略》(课题编号为2011CB706702)资助下,以四轴抛光平台为研究对象,系统地研究了包括旋转轴在内的四轴抛光平台的几何误差检测、建模和补偿等相关理论,分别采用多体系统理论与微分变换矩阵进行综合误差建模,最终获得了降低几何误差的曲面加工轨迹补偿值。对几何误差影响下运动轴移动部件与原部件的相对位置关系进行了表征,并最终得到了几何误差影响下,运动轴移动部件与理论位置的齐次坐标变换矩阵。采用雷尼绍激光干涉仪对四轴抛光平台进行了几何误差的测量,分别得到了轴间误差、直线轴的定位误差、直线度误差、俯仰及偏摆角误差和旋转轴的定位误差。在此基础上采用多体系统理论建立了几何误差的模型。通过多次测量和多项式拟合的方法,将热误差与几何误差进行分离,从测量数据中剔除热误差。研究了分离后的几何误差分布,通过求取数学期望的方法剔除了随机误差,最终得到了接近真实的几何误差测量数据。采用NURBS曲线对离散测量数据进行表征,优化后获得了满足精度要求且数据量较少的NURBS误差曲线,用于误差补偿的研究。采用多体系统理论及牛顿迭代法研究了四轴抛光平台综合误差补偿算法。建立了考虑几何误差的实验平台运动学模型,分析了刀具坐标系变换到工件坐标系的变换矩阵的非线性耦合特性,利用牛顿迭代法求解非线性方程组,通过采用理论运动学模型的雅克比矩阵代替考虑几何误差运动学模型的雅克比矩阵,简化了求解过程,提高了计算效率。由于基于多体系统理论的牛顿迭代误差补偿方法计算量不稳定,不便于在线实时补偿,因此本文提出了基于微分矩阵的综合误差建模与补偿方法,建立了各运动轴相对于工件坐标系的微分变换矩阵,获得了几何误差影响下的刀位轨迹变化。通过采用雅克比矩阵的伪逆矩阵计算几何误差补偿值,相对于牛顿迭代方法,所提出的微分方法便于实现实时误差补偿。
[Abstract]:Optical surface parts are widely used in the fields of national defense, aerospace, biomedicine and so on. Because of its special geometric characteristics, hard and brittle material properties and high surface precision, the precision of machining equipment is required harshly. How to achieve high precision, high efficiency and low cost of optical surface machining has caused the deep research of domestic and foreign scholars. Because geometric error is the main error source of machine tool error, it is very important to improve the machining accuracy of optical curved surface parts by analyzing the geometric error of optical surface machining platform and compensating it. This paper is supported by the National key basic Research and Development Program (973 Program) project "basic Research on Optical Free Surface Manufacturing", a subproject "physical Analysis and Reconstruction Strategy of Optical Free Surface forming process" (Project number 2011CB706702). Taking the four-axis polishing platform as the research object, the geometric error detection, modeling and compensation theory of the four-axis polishing platform, including the rotating axis, are systematically studied. The multi-body system theory and the differential transformation matrix are used to model the synthetic error respectively. Finally, the compensation value of the surface machining trajectory is obtained to reduce the geometric error. The relative position relationship between moving parts of moving axis and original parts is characterized under the influence of geometric errors, and the homogeneous coordinate transformation matrix between moving parts and theoretical positions of moving parts of moving axes is finally obtained under the influence of geometric errors. The geometric errors of the four-axis polishing platform were measured with Renishaw laser interferometer. The errors between axes, alignment errors, straightness errors, pitch and deflection angle errors and rotation axis positioning errors were obtained respectively. On this basis, the model of geometric error is established by using the theory of multi-body system. The thermal error is separated from the geometric error by means of multiple measurements and polynomial fitting, and the thermal error is eliminated from the measured data. The geometric error distribution after separation is studied, and the random error is eliminated by calculating the mathematical expectation. Finally, the real geometric error measurement data are obtained. The discrete measurement data are characterized by NURBS curve, and the NURBS error curve, which meets the precision requirement and has less data, is obtained after optimization, which can be used in the research of error compensation. The synthetic error compensation algorithm of four-axis polishing platform is studied by using multi-body system theory and Newton iteration method. The kinematics model of the experimental platform considering geometric errors is established. The nonlinear coupling characteristics of the transformation matrix from tool coordinate system to workpiece coordinate system are analyzed. Newton iteration method is used to solve the nonlinear equations. By using the Jacobian matrix of the theoretical kinematics model instead of the Jacobian matrix considering the geometric error kinematics model, the solving process is simplified and the computational efficiency is improved. Because the Newtonian iterative error compensation method based on the theory of multi-body system is unstable in calculation and is not convenient for on-line real-time compensation, a comprehensive error modeling and compensation method based on differential matrix is proposed in this paper. The differential transformation matrix of the moving axes relative to the workpiece coordinate system is established, and the change of the tool path under the influence of geometric errors is obtained. The geometric error compensation value is calculated by using the pseudo inverse matrix of Jacobian matrix. Compared with Newton iteration method, the proposed differential method is convenient to realize real-time error compensation.
【学位授予单位】：吉林大学
【学位级别】：博士
【学位授予年份】：2017
【分类号】：TH74

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