基于新一代GPS的几何特征数学建模及三维公差分析方法研究

发布时间：2018-03-14 17:39

本文选题：产品几何技术规范　切入点：三维偏差数学模型　出处：《大连理工大学》2015年硕士论文　论文类型：学位论文

【摘要】：产品的设计质量可以赋予产品质量“先天性优劣”的本质特性。公差设计是一项保证产品质量的重要技术,也是决定产品加工成本的关键性因素。然而,在传统的公差设计理论中,尺寸、形位公差及载荷的协同作用并没有得到足够的重视。本文基于新一代产品几何技术规范(GPS)标准体系,以数字化的方法进行三维偏差数学建模,通过齐次坐标变换法,提出一种综合考虑尺寸、形位公差及零件受载协同作用的三维公差分析方法。主要研究内容如下：(1)利用矢量坐标描述空间物体的位置和姿态,推导出物体空间位姿变动的表达式。通过引入4维列矢量描述物体空间位姿的方法,建立三维偏差空间传递模型的表达式。(2)将新一代GPS标准体系的几何形体恒定度作为切入点,结合小位移旋量(SDT)理论,利用公差边界与位姿旋量的数学关系作为约束条件,建立平面尺寸和圆柱尺寸三维公差数学模型；依据ASME中形位公差的定义,建立了平行度、平面度等形位公差的数学模型。(3)基于新一代GPS标准体系的认证表面模型,利用有限元法提取零件变形表面的节点数据,通过特定的数学准则拟合变形信息,获取零件的拟合变形要素,建立零件受载变形的三维偏差数学模型。(4)利用齐次坐标变换法把零件的制造及变形偏差嵌入到三维公差耦合累积模型中。在产品的设计阶段,开展了零件刚性及柔性条件下三维公差分析方法的研究。(5)降低零件的制造成本,同时提高产品质量是公差分析的重要目的。本文提出以田口方法正交表作为零件制造偏差分组的依据,通过零件偏差匹配控制试验,选出最优的偏差匹配组合方案,实现保证产品质量的目的。
[Abstract]:The essential characteristics of the design quality of the product can give the product quality "congenital quality". Tolerance design is an important technology to ensure product quality, is the key factor to the processing cost of the products. However, in the traditional theory of size tolerance design, shape, synergistic effect of tolerance and load and did not get enough pay attention. In this paper, based on the new generation geometrical product specification (GPS) standard system, 3D deviation mathematical modeling based on the digital method, the homogeneous coordinate transformation method, proposed a comprehensive consideration of the size, shape and position tolerances of parts and three-dimensional tolerance load synergy analysis method. The main contents are as follows: (1) the use of vector coordinates to describe the position and posture of spatial objects, spatial expressions derived object pose changes. The space position of objects is described through the introduction of the 4 dimensional column vector, three-dimensional partial The expression difference of spatial transfer model. (2) a new generation of GPS standard system of geometric constant degree as a starting point, combined with small displacement torsors (SDT) theory, using the mathematical relationship between the tolerance boundary and position of the screw as a constraint condition, a plane size and the size of cylindrical three dimensional mathematical model of tolerance basis; the definition of shape and position tolerance in ASME, established the mathematical model of parallelism, flatness and other tolerances. (3) certification of surface model in the new generation GPS standard system based on the extraction of surface deformation of parts node data using the finite element method, the deformation information through specific mathematical criterion fitting, fitting to get the deformation of the part elements of three-dimensional deviation mathematical model set up the part deformation under load. (4) by using the homogeneous coordinate transformation method of parts manufacturing and deformation into 3D tolerance deviation coupling model. In the accumulation stage of product design, carry out parts Study on the analytical method of rigid and flexible under the condition of three-dimensional tolerance. (5) reduce the manufacturing cost of parts, and improve the quality of products is an important objective of tolerance analysis. In this paper, by using Taguchi method of orthogonal table as manufacturing deviation are grouped on the basis, through the parts to control the experiment, deviation, deviation, the optimum combination scheme. Ensure the quality of the products.

【学位授予单位】：大连理工大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：TG801

【共引文献】