本文關(guān)鍵詞：基于幾何要素控制點(diǎn)變動(dòng)的公差數(shù)學(xué)模型，由筆耕文化傳播整理發(fā)布。

第49卷第5期

2013年3月 機(jī) 械 工 程 學(xué) 報(bào) JOURNAL OF MECHANICAL ENGINEERING

Vol.49 No.5 Mar. 2013

DOI：10.3901/JME.2013.05.138

基于幾何要素控制點(diǎn)變動(dòng)的公差數(shù)學(xué)模型*

吳玉光1 張根源2

(1. 杭州電子科技大學(xué)機(jī)械工程學(xué)院 杭州 310018；

2. 浙江傳媒學(xué)院電子信息學(xué)院 杭州 310018)

摘要：提出采用幾何要素的控制點(diǎn)位置變動(dòng)表示尺寸和幾何公差的方法。定義點(diǎn)線面幾何要素的尺寸誤差、位置誤差和方向誤差的控制點(diǎn)分別為點(diǎn)、直線的兩個(gè)端點(diǎn)、平面的矩形包圍盒的三個(gè)頂點(diǎn)，定義直線和平面的形狀誤差的控制點(diǎn)分別為直線和平面的內(nèi)部組成點(diǎn)。根據(jù)目標(biāo)要素和基準(zhǔn)要素的幾何類型、相互位置和基準(zhǔn)優(yōu)先順序建立公差坐標(biāo)系，根據(jù)公差坐標(biāo)系建立平面要素的矩形包圍盒，對(duì)幾何要素的自由度進(jìn)行分類和定義，以平移自由度方向作為控制點(diǎn)的變動(dòng)方向，通過(guò)控制點(diǎn)變動(dòng)的各種組合模擬幾何要素的各種誤差形式。根據(jù)幾何要素的誤差概率分布作為控制點(diǎn)的變動(dòng)規(guī)律，控制點(diǎn)變動(dòng)參數(shù)的定義域就是公差帶，目標(biāo)要素的控制點(diǎn)變動(dòng)參數(shù)之間的相互制約關(guān)系可以表示方向公差和位置公差的相互作用關(guān)系，而目標(biāo)要素和基準(zhǔn)要素之間的控制點(diǎn)變動(dòng)參數(shù)關(guān)系則可以表示各種公差原則。該公差數(shù)學(xué)模型既符合公差標(biāo)準(zhǔn)和實(shí)際慣例，又能夠適用于公差分析、設(shè)計(jì)、檢測(cè)等應(yīng)用領(lǐng)域的各種數(shù)學(xué)分析方法。

關(guān)鍵詞：幾何公差 控制點(diǎn) 自由度 數(shù)學(xué)模型

中圖分類號(hào)：TP39

Tolerance Mathematical Model Based on the Variation of Control Points of Geometric Element

WU Yuguang1 ZHANG Genyuan2

(1. School of Mechanical Engineering, Hangzhou Dianzi University, Hangzhou 310018;

2. School of Electronic & Information, Zhejiang University of Media and Communications, Hangzhou 310018) Abstract：A new tolerance model by representing the position variation of control points of geometric element is proposed. The control points of point, line and plane geometric element are defined as point itself, two end points of line, any three vertices of bounding box of plane and the interior constituting points of line and plane, which are used to present the dimensional error, the position error, the orientation error and the form error. The tolerance coordinate system of target geometric element is established according to the geometric type of target geometry and datum geometry, the relative position between target geometry and datum geometry, and the precedence of datum reference frames. The degree of freedoms (DOFs) of geometry element are classified and defined under the tolerance coordinate system. The bounding box of plane is set up at the tolerance coordinate system and the variation direction of control points is defined along translational DOF of geometry element, and the variation combination of all control points are used to represent various error of geometric element. The variation of control points is controlled to follow the error probability distribution of geometric element and the definitional domain of variation parameter of control point is the tolerance zone, the restrict relationship among the control points of target element are used to represent the interaction relationship between position and orientation tolerance, and the relationship between the variation parameters of control point of target and datum element are used to represent the tolerance principles. The model is compatible with the tolerance standards and practice rules, it also suits the mathematical analysis method of many applications such as tolerance analysis, tolerance allocation and verification.

Key words：Geometric tolerance Control point Degree of freedom Mathematical model

0 前言?

零件的公差控制目標(biāo)幾何要素在尺寸、位置和?形狀上偏離理想狀態(tài)的程度，公差數(shù)學(xué)模型是公差信息的數(shù)學(xué)描述與表示，通過(guò)公差的數(shù)學(xué)模型一致地解釋公差信息的每一個(gè)成員的意義，獲得基準(zhǔn)要素和被測(cè)要素之間的幾何尺寸變動(dòng)和形狀變動(dòng)的數(shù)值關(guān)系等，公差的數(shù)學(xué)模型是公差分析、公差設(shè)計(jì)、公差檢驗(yàn)等相關(guān)技術(shù)的基礎(chǔ)。 * 國(guó)家自然科學(xué)基金(51175132)和浙江省自然科學(xué)基金(Y1080379)資助

項(xiàng)目。20120705收到初稿，20130105收到修改稿 ?

  本文關(guān)鍵詞：基于幾何要素控制點(diǎn)變動(dòng)的公差數(shù)學(xué)模型，，由筆耕文化傳播整理發(fā)布。