JP2004132944A - System and method for evaluating manufacturing error and program for the same - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a system for evaluating manufacturing errors for surely feeding back to manufacturing/working equipment with information for modifying the errors by quantitatively evaluating the shape errors in 3-D space accompanied by the manufacturing for the equipment composed of various parts of complicated shape. <P>SOLUTION: This system for evaluating manufacturing errors uses a 3-D fluoroscopic image. Each pixel of CAD perspective image is moved in 3-D (spatially) using a specified arithmetic expression. A simulation is continued till the image after moving the CAD perspective image coincide with the actual fluoroscopic image, while altering coefficients of the arithmetic expression. When the CAD perspective image after moving and actual fluoroscopic image are nearly coincident in each pixel distribution having similar gradation, each coefficient of the arithmetic expression is extracted. Based on these coefficients, errors of each pixel in the actual fluoroscopic image is calculated. Based on the amount of the errors, information for reducing errors in various parts is fed back to the manufacturing/working equipment. <P>COPYRIGHT: (C)2004,JPO

Description

【数２】

【数３】

【００２９】
この各々の式において、各大括弧のなかの第１項（中括弧の項）は被試験体１４の誤差の周期性を示すフーリエ級数であり、第２項はべき乗的な誤差の量を示しており、第３項は上記定数である。
上記第１項のフーリエ級数は、被試験体１４の誤差の周期性に対応している。上述した各係数及び定数の仮の値とは、同様な材料及び加工形状の部品の誤差評価によって、以前に求められた値などの、ある程度実際に近い（上記誤差関数に対応可能）と考えられる値が用いられる。
【００３０】
次に、ステップＳ３において、誤差量演算部４は、（１），（２），（３）式の誤差関数による演算（所定の演算）から求められた誤差量ｕ（ｘ，ｙ，ｚ），ｖ（ｘ，ｙ，ｚ），ｗ（ｘ，ｙ，ｚ）に基づき、各々のピクセルを移動させる。この座標変換による移動により、各々の座標値が変位した数値を誤差量としている。
すなわち、上記誤差量ｕ，ｖ，ｗに基づき、ｐ（ｘ，ｙ，ｚ）を移動させることにより、（ｘ，ｙ，ｚ）の位置に合ったピクセルは、（ｘ＋ｕ，ｙ＋ｖ，ｚ＋ｗ）の位置に移動し、すなわち、ｐ（ｘ，ｙ，ｚ）がｐ（ｘ＋ｕ，ｙ＋ｖ，ｚ＋ｗ）となる。
【００３１】
このピクセル値ｐ（ｘ＋ｕ，ｙ＋ｖ，ｚ＋ｗ）を、ピクセル値ｐ^＊（Ｘ，Ｙ，Ｚ）とする。ここで、Ｘ＝ｘ＋ｕ，Ｙ＝ｙ＋ｖ，Ｚ＝ｚ＋ｗである。
そして、誤差量演算部４は、上述したピクセルの３次元座標における移動の処理を、ＣＡＤボクセルモデルを構成する各ピクセルに対して行う。
ここで、ピクセル値ｐ^＊（Ｘ，Ｙ，Ｚ）は、誤差量演算部４により求められた仮想の加工後の試料のボクセルモデル、すなわち、シミュレーション結果としての、移動後のＣＡＤボクセルモデル（シミュレーションボクセルモデル）である。
【００３２】
次に、ステップＳ４において、誤差量演算部４は、実ボクセルモデルにおける座標値（Ｘ，Ｙ，Ｚ）におけるピクセル値Ｐ（Ｘ、Ｙ、Ｚ）と、上記ピクセル値ｐ^＊（Ｘ，Ｙ，Ｚ）との数値の比較を、実ボクセルモデルにおける各座標値において行う。
すなわち、誤差量演算部４は、実ボクセルモデルの各座標値におけるピクセル値Ｐ（Ｘ、Ｙ、Ｚ）の数値と、移動後のＣＡＤボクセルモデルの各座標値におけるピクセル値ｐ^＊（Ｘ，Ｙ，Ｚ）の数値とが一致（または所定の範囲を有していて、略一致する場合も含む）するか否かの判定を行う。
【００３３】
ここで、誤差量演算部４は、実ボクセルモデルの各座標値におけるピクセル値Ｐ（Ｘ、Ｙ、Ｚ）の数値と、移動後のＣＡＤボクセルモデルの各座標値におけるピクセル値ｐ^＊（Ｘ，Ｙ，Ｚ）の数値とが一致した場合（このＣＡＤボクセルモデルピクセルの移動量が誤差量に対応する）、各係数ａ_ｕｎ〜ｊ_ｗｍ及び定数ｐ_ｕ〜ｒ_ｗを出力して処理を終了するが、一致しない場合、処理をステップＳ５へ進める。
このとき、誤差量演算部４は、差分関数である下記に示す（４）式により、ボクセルモデル全体のピクセル値に対して、ピクセル値Ｐ（ｘ，ｙ，ｚ）が移動されたピクセル値Ｐ（Ｘ，Ｙ，Ｚ）と、ｐ^＊（Ｘ，Ｙ，Ｚ）との差分を合計して、２５５（階調度）×Ｍにより正規化して、差分関数ｆとして出力する。
【数４】

ここで、Ｍは総ボクセル数であり、Σは画像内の全ボクセルに対して総和を取ることを表している。
そして、誤差量演算部４は、差分関数ｆの差分関数値が求められる毎に、順次前回のｆの数値と比較して、上記差分関数値の谷（最も差分関数値の小さい点、すなわち最小値）を検出し、この点をボクセルモデル全体の各ピクセル値の階調度の一致した点とする。
【００３４】
次に、ステップＳ５において、誤差量演算部４は、各係数ａ_ｕｎ〜ｊ_ｗｍ及び定数ｐ_ｕ〜ｒ_ｗの変更量を、非線形計画法などの最適化手法によって、このアルゴリズに従った演算により、上記係数及び定数の数値を逐次変更する。
そして、誤差量演算部４は、変更された各係数ａ_ｕｎ〜ｊ_ｗｍ及び定数ｐ_ｕ〜ｒ_ｗにより、新たな誤差量ｕ（ｘ，ｙ，ｚ），ｖ（ｘ，ｙ，ｚ），ｗ（ｘ，ｙ，ｚ）を求めるため、処理をステップＳ２へ戻す。
【００３５】
上述したように、誤差量演算部４は、実ボクセルモデルの各座標値におけるピクセル値Ｐ（Ｘ、Ｙ、Ｚ）の数値と、移動後のＣＡＤボクセルモデルの各座標値におけるピクセル値ｐ^＊（Ｘ，Ｙ，Ｚ）の数値とが一致するまで、ステップＳ２からステップＳ５の処理を繰り返して行う。
そして、誤差量演算部４は、最終的に、実ボクセルモデルの各座標値におけるピクセル値Ｐ（Ｘ、Ｙ、Ｚ）の数値と、移動後のＣＡＤボクセルモデルの各座標値におけるピクセル値ｐ^＊（Ｘ，Ｙ，Ｚ）の数値とが一致（階調度が一致）すると、このときの各係数ａ_ｕｎ〜ｊ_ｗｍ及び定数ｐ_ｕ〜ｒ_ｗを出力する。
【００３６】
これにより、誤差量演算部４は、（１）式から（３）式において、各係数ａ_ｕｎ〜ｊ_ｗｍ及び定数ｐ_ｕ〜ｒ_ｗが求まることにより、この（１）式から（３）式を各ＣＡＤボクセルモデルと実ボクセルモデルとの各々の座標値における誤差量を求める誤差関数として用いることとなる。
すなわち、上記誤差関数は、図５に示す加工面において、○印と□印（実ボクセルモデル）との座標値の差（誤差量）が、○印の点（ＣＡＤボクセルモデル）の座標値の関数として表される。
【００３７】
次に、ステップＳ６において、誤差量演算部４は、所定のＣＡＤボクセルモデルの座標値（ｘ、ｙ、ｚ）に基づき、各座標値に対応する誤差量の演算を行う。これにより、誤差量演算部４は、上記誤差関数により、任意に入力されるＣＡＤボクセルモデルにおける座標値に基づいて、ＣＡＤボクセルモデルと実ボクセルモデルとの誤差量を、３次元的に求めることができる。
【００３８】
ここで、任意に入力される座標値のデータは、３次元ＣＡＤデータにおける座標値である。
そして、誤差量演算部４は、各座標値毎に得られた誤差量に対して「−１」を乗じて、この乗算の結果を、ＣＡＤシステム５に入力する、ＣＡＤボクセルモデルの座標値修正データとして出力する。
ここで、「−１」を誤差量に対して乗算する理由は、３次元ＣＡＤデータの座標値に加算することにより、加工後に発生する誤差量を、あらかじめ打ち消すために行われる。
【００３９】
次に、ステップＳ７において、誤差量演算部４は、上記座標修正データをＣＡＤシステム５に対して出力する。
これにより、ＣＡＤシステム５は、入力される座標修正データに基づいて、対応する部品の３次元ＣＡＤデータの修正を行う。
すなわち、ＣＡＤシステム５は、３次元ＣＡＤデータにおける対応する座標値に対して、入力される座標修正データを加算することで、３次元ＣＡＤデータの修正を行う。
【００４０】
そして、ＣＡＤシステム５は、誤差量に基づいた上述した修正処理により、修正された３次元ＣＡＤデータを、ＮＣ加工機６へ出力する。
これにより、ＮＣ加工機６は、部品の加工に使用していた３次元加工データを、入力される修正された３次元ＣＡＤデータと置き換え、この修正された３次元データを用い、以降の部品の加工を行う。
【００４１】
したがって、修正された３次元ＣＡＤデータにより、加工された部品の加工面の形状が、ＣＡＤシステム５において元々の設計で生成された（誤差量による修正前の）３次元ＣＡＤデータ、すなわち加工したい面に近い形状に加工されることになる。
また、図３のフローチャートの処理を複数回繰り返すことにより、誤差関数の誤差量算出の精度がより向上し、ＮＣ加工機による加工後の部品の形状を、当初ＣＡＤにより設計された形状に近づけることが可能となる。
【００４２】
上記ステップＳ３において、誤差量演算部４の行う各ピクセル値Ｐ^＊（Ｘ，Ｙ，Ｚ）の値の求め方について、以下に説明する。
まず、誤差量演算部４は、図６（ａ）に示すボクセルモデルにおいて、各画素に対応して空間格子を作成し、図６（ｂ）に示すように、各ピクセル値を対応する格子の重心に各々割り付ける。
そして、誤差量演算部４は、演算した「ｕ，ｖ，ｗ」により上記重心を、図６（ｃ）に移動させる（重心を変形写像により移動させる、（Ｍａｐｐｉｎｇ，ｘ＝Ｄ（Ｘ））。移動後の重心（以下、移動点（Ｍａｐｐｅｄ　Ｐｏｉｎｔｓ）：黒丸）と、変形画像を構成する空間固定格子の重心（以下、対応点（Ｆｉｘｅｄ　Ｐｏｉｎｔｓ）：白丸）とは、図６（ｃ）で分かるように一般的には一致しない。
次に、誤差量演算部４は、最終的に、各空間固定格子毎に、移動点のピクセル値を、対応点に割り付けることにより、図６（ｄ）に示すように、シミュレーションボクセルモデルを生成する。
【００４３】
このため、以下の条件により、各移動点のピクセル値から、各空間固定格子の対応点のピクセル値を決定する。
基本的に、本実施形態においては、各対応点に対して最も近傍に存在する移動点のピクセル値を、この対応点のピクセル値とする、最近隣内挿法を基礎とした８近傍最近隣近似法を用いている。
すなわち、誤差量演算部４は、移動点が、対応点を含む空間固定格子内へ移動したとき、移動点がこの空間固定格子内に１つの場合、移動点のピクセル値を対応点のピクセル値とし、移動点が空間固定格子内に複数ある場合、これら移動点のピクセル値の平均値を演算し、この平均値を対応点のピクセル値とする。
【００４４】
また、対応点の空間固定格子内に移動点が存在しない場合、その周囲３×３格子内の８近傍格子内の探索を行う。
このとき、周囲３×３格子内に移動点が存在しない場合、ピクセル値を「０」とし、移動点が存在する場合、その移動点のなかから対応点の位置に最も近傍にある移動点のピクセル値を、この対応点のピクセル値とする。
上述の説明は説明を簡略化するために２次元で行ったが、三次元の場合には、その空間固定格子内に移動点が無い場合、近接格子周囲３×３×３格子内の２６格子として移動点の探索を行い、８近傍格子の場合と同様の手法により対応点の格子点を決定する。
【００４５】
次に、ステップＳ５における各係数及び定数各々の数値の求め方について説明する。
すでに述べたように、ステップＳ５において、誤差量演算部４は、上述したように、各係数ａ_ｕｎ〜ｊ_ｗｍ及び定数ｐ_ｕ〜ｒ_ｗの変更量を、非線形計画法などの最適化手法によって、このアルゴリズに従った演算により、上記係数及び定数の数値を逐次変更する。
ここで、ボクセル値は離散値であるため、また最近隣近似に基づいて離散的な画像処理を行うため、目的関数の感度情報（各係数及び定数の変化量に対応する数値ｆの変化の度合い）を得ることができない。
【００４６】
このため、本実施形態において、誤差量演算部４は、遺伝的アルゴリズム（Ｇｅｎｅｔｉｃ　Ａｌｇｏｒｉｔｈｍ）等（以下説明するａ）及びｂ）のアルゴリズム）の離散的最適化方法により差分関数ｆの最小化処理を行う。
ａ）遺伝的アルゴリズムを用いる場合
誤差量演算部４は、例えば、変数及び定数のデータ容量として、各々８ビットバイナリを割り当て、各変数及び定数毎に２５６段階の数値を有しているとする。
この２５６段階の数値は、予め変形の範囲（探索範囲として）として想定される所定の範囲（ボクセルモデルのピクセル数や寸法など）を、２５５分割したものである。
そして、遺伝的アルゴリズムのシミュレーションの条件として、各個体は、誤差量演算部４において、上記各変数及び定数の数値から選択されて、１０００個の組み合わせとして構成される。
各個体の組み合わせを変更する遺伝子操作としては、一様交叉（交叉率７５％），線形ランキング選択，エリート戦略及び突然変異（突然変異率１．０％）などを用いた。
【００４７】
ｂ）ＳＣＥ−ＵＡ（Ｓｈｕｆｆｌｅｄ　Ｃｏｍｐｌｅｘ　Ｅｖｏｌｕｔｉｏｎ　Ｍｅｔｈｏｄ　ｄｅｖｅｌｏｐｅｄ　ａｔ　ｔｈｅ　ＵｎｉｖｅｒｓｉｔｙＡｒｉｚｏｎａ）法
このＳＣＥ−ＵＡ方法は、遺伝的アルゴリズム類似の進化手法を取り入れ、物理的な意味を持つ解の探索領域を設定できることと、計算の途中で、複数の個体群で独立に進化させるため、最終的に解を得る場合、計算不能や発散などが発生せず、必ず解が求まることを特徴としている。
すなわち、ＳＣＥ−ＵＡ法は、競争進化及び集団混合の概念を組み合わせた帯域探索による最適化手法である。以下に計算手順を簡単に示す。
▲１▼　決定変数（（１）〜（３）式における係数ａ_ｕｎ〜ｊ_ｗｍ及び定数ｐ_ｕ〜ｒ_ｗ、または（１’）〜（３’）式における変数ａ_ｕ１３（ｋ_１，ｋ_２，ｋ_３）等）の個数ｎ，集団数ｐ，各集団内の個体数ｍ（＝２ｎ＋１）を設定し、各個体を決定変数を座標値とするｎ次元空間上の点とみなす。
例えば、係数および定数の数が合計ｎ個ある場合、ｐ個の集団に、各々「２ｎ＋１」個の個体群を振り分ける。
▲２▼　初期世代として、各決定変数値をランダムに与え、例えば、（４）式の差分関数の差分関数値が低い順に個体を並べる。
▲３▼　▲２▼において並べた順に、先頭の個体から、１番目の個体を第１集団に含め、２番目の個体を第２集団へ、…、ｐ番目の個体を第ｐ集団へ、ｐ＋１番目の個体を第１番目の集団へ、２ｐ（すなわち、ｐ＋ｐ）番目の個体を第ｐ集団へ、…と、全ての集団へ順次個体を振り分ける。
すなわち、この振り分け方法は、ｐ（Ｘ，Ｙ，Ｚ）と、このピクセル値に対応する各係数および定数を選択して組み合わせて演算されたｐ^＊（Ｘ，Ｙ，Ｚ）とにより、差分関数ｆを求めて、差分関数値が小さい順にｐ個の各集団に順次振り分けていく。
例えば、係数および定数の数が合計ｎ個ある場合、ｐ個の集団に、各々「２ｎ＋１」個の個体群を振り分ける。
▲４▼　各集団毎に独立させて、ＣＣＥ（Ｃｏｎｄｉｔｉｏｎａｌ　Ｃｌａｓｓ　Ｅｎｔｒｏｐｙ）アルゴリズムにより、個体群の進化を行わせる。
上記ＣＣＥアルゴリズムにおいては、差分関数ｆの差分関数値が高い個体を、より差分関数値の低い個体とするよう、係数および定数を変化させて、各個体を進化させてゆく。
▲５▼　最終的に、ｐ個の集団を、すなわち全集団を１つにまとめて、全集団に含まれていた全個体を、再度、差分関数値の低い順番に並べ替えて、この全個体の内の最も優れた個体の差分関数値が、予め設定された収束判定値の範囲内になるか、または、係数および定数の最適化処理の繰り返し回数が予め設定された繰り返し設定値となるか、のいずれかに対応するまで、▲３▼〜▲５▼を繰り返して、係数および定数の最適化処理を行う。
【００４８】
次に、誤差量演算部４が誤差量ｕ，ｖ，ｗの算出に用いている（１），（２）及び（３）式を、下記に示す各々（１’），（２’）及び（３’）に換えて、誤差量ｕ，ｖ，ｗを算出する場合について説明する。
【数５】

【数６】

【数７】

【００４９】
これら（１’），（２’）及び（３’）式は、（１），（２），（３）式各々に対して、フーリエ級数の項に、複数の座標軸における誤差の影響を含ませたものである。
（１’），（２’）及び（３’）式各々において、Ｍｕ，Ｍｖ，Ｍｗ及びＮｕ，Ｎｖ，Ｎｗは各々整数値で問題により適宜設定する定数であり、ωは基本周波数であり、同様に問題により適宜設定する定数である。
また、α_ｉｊｋ，β_ｉｊｋ，γ_ｉｊｋは、ｉ，ｊ，ｋが異なれば、異なる変数として定義され、ＧＡ等の最適化アルゴリズムにより、差分関数から求められる差分関数値が最小となるように決定される変数である。
そして、ａ_ｕ１３（ｋ１，ｋ２，ｋ３），ａ_ｖ１３（ｋ１，ｋ２，ｋ３），ａ_ｗ１３（ｋ１，ｋ２，ｋ３）等も、ｋ１，ｋ２，ｋ３が異なれば、異なる変数として定義され、ＧＡ等の最適化アルゴリズムにより、差分関数から求められる差分関数値が最小となるように決定される変数である。
このため、（１’），（２’）及び（３’）式を用いることにより、各々の座標軸方向の変位に対して、他座標軸方向からの影響、すなわち補正量を含ませることとなり、（１），（２），（３）式を用いた場合に比較して、誤差量ｕ，ｖ，ｗを算出する際に、より精度の高いシミュレーションが行える。
【００５０】
上述した本願発明の製造誤差評価システムを用いることにより、従来、ＮＣ加工機６で切削加工を行った部品の誤差評価が長さの単位でしか行えず、複雑な加工形状を有する部品の加工において、高い精度で各座標値における誤差量を得ることができなかったものが、座標値に対応した誤差量を演算する誤差関数を用いることにより、３次元ＣＡＤデータの任意の座標値において、加工の結果生じる誤差量を高い精度で演算して得ることができ、この誤差量を３次元ＣＡＤデータにフィードバックすることにより、予め発生する誤差量を予測した３次元ＣＡＤデータを生成することが可能となり、従来に比較して高い精度で部品の加工及び製造を行うことが可能となる。
【００５１】
すなわち、本願発明の製造誤差評価システムを用いることにより、複雑な加工形状をした部品について、その加工及び製造に付随する形状の誤差を、Ｘ線ＣＴ装置１から得られた実透視画像に基づく３次元の実ボクセルモデルと、ＣＡＤシステム５の３次元ＣＡＤデータから得られるＣＡＤボクセルモデルとの比較により、誤差量演算部４が座標値に対応した誤差量を演算する誤差関数を求め、座標値毎に数値的に誤差量を評価することができるので、部品の各部における誤差量を３次元空間で定量的に表すことが可能となり、その誤差量を修正するためのフィードバック情報として座標値修正データを、ＣＡＤシステム５に戻し、設計時の３次元ＣＡＤデータと誤差量とから加工時に発生する誤差をあらかじめ推定した３次元ＣＡＤデータを新たに生成し、この推定した３次元ＣＡＤデータをＮＣ加工機６へ出力して、的確に誤差量をフィードバックさせることで、ＣＡＤシステム５で設計した部品の形状（実際に必要な寸法として設計されたＣＡＤデータ；つまり、設計時のＣＡＤデータ）に、ＮＣ加工機６による部品の加工形状を高い精度で近づけることができる。
【００５２】
なお、上記した本発明の実施形態においては、製造誤差評価システムにおいて実行される手順をコンピュータ読取り可能な記録媒体に記録し、この記録媒体に記録されたプログラムをコンピュータシステムに読み込ませ、実行することにより本発明の製造誤差評価システムが実現されるものとする。ここでいうコンピュータシステムとは、ＯＳや周辺機器等のハードウアを含むものである。
【００５３】
更に、「コンピュータシステム」は、ＷＷＷシステムを利用している場合であれば、ホームページ提供環境（あるいは表示環境）も含むものとする。
また、「コンピュータ読取り可能な記録媒体」とは、フレキシブルディスク、光磁気ディスク、ＲＯＭ、ＣＤ−ＲＯＭ等の可搬媒体、コンピュータシステムに内蔵されるハードディスク等の記憶装置のことをいう。さらに「コンピュータ読取り可能な記録媒体」とは、インターネット等のネットワークや電話回線等の通信回線を介してプログラムが送信された場合のシステムやクライアントとなるコンピュータシステム内部の揮発性メモリ（ＲＡＭ）のように、一定時間プログラムを保持しているものも含むものとする。
【００５４】
また、上記プログラムは、このプログラムを記憶装置等に格納したコンピュータシステムから、伝送媒体を介して、あるいは、伝送媒体中の伝送波により他のコンピュータシステムに伝送されてもよい。ここで、プログラムを伝送する「伝送媒体」は、インターネット等のネットワーク（通信網）や電話回線等の通信回線（通信線）のように情報を伝送する機能を有する媒体のことをいう。
また、上記プログラムは、前述した機能の一部を実現するためのものであっても良い。さらに、前述した機能をコンピュータシステムにすでに記録されているプログラムとの組み合わせで実現できるもの、いわゆる差分ファイル（差分プログラム）であっても良い。
【００５５】
以上、本発明の一実施形態を図面を参照して詳述してきたが、具体的な構成はこの実施形態に限られるものではなく、本発明の要旨を逸脱しない範囲の設計変更等があっても本発明に含まれる。
【００５６】
【発明の効果】
本発明の製造誤差評価システムによれば、複雑な加工形状をした部品について、その加工及び製造に付随する形状の誤差を、Ｘ線ＣＴから得られた３次元ボクセルモデルと、３次元ＣＡＤデータから得られる３次元ボクセルモデルとのピクセルの階調度の分布状態の比較を数値的に評価することができ、部品の各部における誤差量を３次元空間で定量的に表すことが可能となるため、その誤差量をフィードバック情報として、製造・加工機器に的確に供給することができるので、加工後の部品の形状を、ＣＡＤで設計した３次元ＣＡＤデータに、高い精度で近づけることができる。
【図面の簡単な説明】
【図１】本発明の一実施形態による製造誤差評価システムの構成例を示すブロック図である。
【図２】図１のＸ線ＣＴ装置１の構成を示す概念図である。
【図３】図１における誤差量演算部４の誤差量算出の動作例を示すフローチャートである。
【図４】実透視画像とＣＡＤ透視画像とにより、設計時の部品の形状と加工された部品の形状の比較を示す概念図である。
【図５】実透視画像とＣＡＤ透視画像とにより、設計時の部品の形状と加工された部品の形状の比較を示す概念図である。
【図６】誤差量演算部４における各ピクセル値Ｐ^＊（Ｘ，Ｙ，Ｚ）の値の算出方法の説明を行う概念図である。
【符号の説明】
１　Ｘ線ＣＴ装置
２　画像処理装置
３　画像記憶部
４　誤差量演算部
５　ＣＡＤシステム
６　ＮＣ加工機
１１　Ｘ線管
１２　Ｘ線
１３　Ｘ線検出装置
１４　被試験体[0001]
TECHNICAL FIELD OF THE INVENTION
The present invention reduces processing and manufacturing errors based on an error amount obtained by comparing three-dimensional CAD (Computer Aided Design) data at the time of design with a three-dimensional perspective image obtained by X-rays and the like after processing and manufacturing. Also, the present invention relates to a manufacturing error evaluation system for performing processing corresponding to a design.
[0002]
[Prior art]
2. Description of the Related Art In recent years, when processing and manufacturing equipment, a design drawing is converted into three-dimensional data, that is, received as a so-called three-dimensional CAD data by a processing machine (for example, an NC (Numerical Control) machine tool) and a manufacturing machine (for example, a plastic molding machine). The processing and manufacturing are automatically performed, and the efficiency of the processing and manufacturing operations is improved.
However, in the actually processed and manufactured product, the dimensions of each part of the manufacturing and processing result are different from the three-dimensional CAD data, that is, processing errors and manufacturing errors in various processing and manufacturing always occur.
[0003]
Therefore, in order to improve the processing and manufacturing accuracy of the product, it is necessary to feed back the processing error and the manufacturing error, and adjust the setting of the processing dimensions of the processing machine and the manufacturing machine in accordance with each error.
Here, the conventional method of evaluating processing and manufacturing errors numerically evaluates how much the distance between two points differs between a dimension on a design drawing and a dimension of an actually processed and manufactured product. (A different amount is referred to as an error amount).
[0004]
For example, in FIG. 4, a solid line represents a surface to be machined as a design value (data of a machining dimension of CAD), and a broken line represents a surface actually machined by cutting with an NC machine.
The CAD data input to the NC processing machine is coordinate values of points set by discrete circles, and the intervals between the circles are sufficiently small in order to increase the processing accuracy. Needs to be set in fine units.
Further, the results of measuring the processed surface using X-ray CT or moiré after cutting by the NC processing machine are indicated by □ (for example, see Non-Patent Document 1).
[0005]
From the measurement results indicated by the □ marks, the amount of error is calculated by calculating the difference from the 印 marks, and the CAD data input to the NC processing machine is corrected for each coordinate value indicated by the 印 marks to process. Accuracy can be improved.
However, in order to correct the CAD data indicated by the 印 mark, it is necessary to associate the coordinate value of each □ mark with the coordinate value of the □ mark after processing.
Here, when a square part shown in FIG. 4 is machined and a machined surface is formed as shown by a broken line, it is possible to easily associate a circle with a square and evaluate an error with respect to thickness and width. Can be performed easily (part shape that can be evaluated for error by length).
[0006]
[Non-patent document 1]
Shizuka Kodo, Shino Himei, Hiroshi Arita, et al., Prceeding of 6th Symposium on "Microjoining and Assembly Technology in Electronics", 85-90.
[0007]
[Problems to be solved by the invention]
As described above, even in the conventional error evaluation regarding the length, if the component or product has a simple shape such as a square shown in FIG. 4, a processing error and a manufacturing error (hereinafter, the two are collectively regarded as a shape error) ) Can be quantitatively fed back to a manufacturing machine or a processing machine to some extent quantitatively.
However, in a part or product having a complicated shape, the distance between the two points differs depending on the selection of the two coordinate values, and a large numerical difference occurs in the shape error as an error amount. It cannot be easily used as a reference.
[0008]
For example, when processing a curved surface (or a complicated three-dimensional curved surface) shown in FIG. 5, which of the coordinate values of the 印 marks designated by the CAD data corresponds to the coordinate values of the □ marks after the processing. Identification cannot be performed easily.
In other words, in the conventional method of evaluating an error using a length, it is easy to specify which of two adjacent □ marks is the coordinate value after displacement as the coordinate value after displacement when the shape becomes complicated. Therefore, it is not possible to obtain an accurate error amount for each mark, and it is not possible to appropriately correct the coordinate value of the mark, ie, the CAD data.
[0009]
Therefore, it is difficult to obtain an error amount of each part having a complicated shape in the error evaluation regarding the length, and necessary and appropriate information (errors) for reducing the processing and manufacturing errors in processing and manufacturing the entire shape. ) Cannot be fed back to an NC machine or the like.
[0010]
The present invention has been made under such a background. With respect to parts and products having complicated shapes, dimensions in CAD data of design drawings and parts and products actually processed / manufactured by an NC processing machine or the like are described. It is possible to improve the machining and manufacturing accuracy by quantitatively evaluating the shape error (error amount) with the dimensions of each part in a three-dimensional space and feeding back the error evaluation result to the manufacturing / processing machine. A manufacturing error evaluation system is provided.
[0011]
[Means for Solving the Problems]
A manufacturing error evaluation system according to the present invention includes an X-ray CT apparatus that has an X-ray source and a plurality of X-ray detectors and collects X-ray data on a cross section of a test object. An image processing unit that generates a three-dimensional perspective image of the body; three-dimensional CAD data that is design data of the test object; and a three-dimensional perspective image of the test object that is processed based on the three-dimensional CAD data. The image storage unit and each pixel of the three-dimensional CAD data are moved by a predetermined operation, the shapes of the three-dimensional CAD data and the three-dimensional perspective image are matched, and the displacement due to the movement of the pixels of the three-dimensional CAD data is changed by an error. And an error amount calculating unit for obtaining the amount.
[0012]
In the manufacturing error evaluation system according to the present invention, the error amount calculation unit moves each pixel of the three-dimensional CAD data while sequentially changing a coefficient and a constant of the predetermined calculation expression, thereby obtaining the three-dimensional CAD. The data and the three-dimensional perspective image are matched in shape.
In the manufacturing error evaluation system according to the present invention, the error amount calculation unit compares the gradient of each pixel between the three-dimensional perspective image and the three-dimensional CAD data after the movement, and determines whether the distribution of the gradient is the same. It is characterized in that it is determined whether the shapes of the three-dimensional CAD data and the three-dimensional perspective image match.
[0013]
A manufacturing error evaluation method according to the present invention includes a data collection step of collecting X-ray data relating to a cross section of a test object from an X-ray CT apparatus having an X-ray source and a plurality of X-ray detectors; An image processing process in which a three-dimensional perspective image of the test object is generated based on the three-dimensional CAD data, three-dimensional CAD data that is design data of the test object, and the three-dimensional CAD data processed based on the three-dimensional CAD data The image storing process in which the three-dimensional perspective image is stored in the image storage unit, and moving each pixel of the three-dimensional CAD data by a predetermined operation to match the shapes of the three-dimensional CAD data and the three-dimensional perspective image, And calculating an error amount in manufacturing based on the pixel movement amount.
[0014]
In the manufacturing error evaluation method of the present invention, the three-dimensional CAD data and the three-dimensional perspective image can be obtained by moving each pixel while sequentially changing coefficients and constants of the predetermined arithmetic expression in the error amount calculating process. Are matched.
In the manufacturing error evaluation method according to the present invention, the three-dimensional CAD data and the three-dimensional CAD data are associated with each other in the three-dimensional perspective image and the three-dimensional CAD data after the movement in the error amount calculation process based on each gradient. It is characterized in that the matching of the shape with the perspective image is determined.
[0015]
A manufacturing error evaluation program according to the present invention includes a data collection process for collecting X-ray data relating to a cross section of a test object from an X-ray CT apparatus having an X-ray source and a plurality of X-ray detectors; Image processing for generating a three-dimensional perspective image of the test object based on the three-dimensional CAD data, which is design data of the test object, and three-dimensional CAD data processed based on the three-dimensional CAD data. An image storage process in which a three-dimensional perspective image is stored in an image storage unit, and each pixel of the three-dimensional CAD data is moved by a predetermined operation so that the shapes of the three-dimensional CAD data and the three-dimensional perspective image are matched to each other. And an error amount calculation process for obtaining an error amount in manufacturing based on the movement amount of the computer.
A recording medium of the present invention is a computer-readable recording medium on which the above-described manufacturing error evaluation program is recorded.
[0016]
BEST MODE FOR CARRYING OUT THE INVENTION
The present invention provides a three-dimensional fluoroscopic image (hereinafter referred to as a CAD fluoroscopic image) of a test object (a part or product designed by CAD) based on CAD data in which a design drawing is three-dimensionalized in advance, and an X-ray CT image from an X-ray CT apparatus. An actually processed (manufactured) three-dimensional perspective image (hereinafter referred to as an actual perspective image) of the test object generated from X-ray data based on the transmission intensity of the line is prepared.
Hereinafter, the manufacturing error evaluation system of the present invention will be described using a three-dimensional fluoroscopic image obtained by using an X-ray CT apparatus.
However, the present invention is not limited to the X-ray CT apparatus, and it is also possible to use a three-dimensional perspective image of a processed part by an MRI (magnetic resonance image) or an ultrasonic apparatus. Here, a CAD voxel model and a real voxel model are generated as three-dimensional voxel models of the CAD fluoroscopic image and the real fluoroscopic image, respectively.
Then, the error amount calculation unit 4 described later performs coordinate conversion of each pixel using a predetermined calculation expression, and converts each pixel of the CAD voxel model to a distribution shape similar to the real voxel model, that is, a pixel of a gradient. Move three-dimensionally (spatially) until the distribution shapes match.
[0017]
At this time, until the CAD voxel model after the movement of the pixels by the coordinate transformation and the actual voxel model have the same pixel distribution shape with the same gradient, the numerical values of the coefficients and the constants of the arithmetic expression are sequentially changed. Simulation (three-dimensional movement of pixels by coordinate transformation based on a predetermined arithmetic expression) is performed.
That is, when the distribution shape of the pixels having the same gradient in the CAD voxel model after the movement and the actual voxel model match or substantially match, the error amount calculation unit 4 calculates the actual voxel model and each pixel. Is assumed to match the shape of the CAD fluoroscopic image to which is moved.
Here, “substantially coincident” means that, in advance, in the CAD voxel model and the actual voxel model, the ratio of pixels that have been matched by coordinate transformation with respect to the number of pixels in each image is set. It will be shown.
[0018]
Hereinafter, embodiments of the present invention will be described with reference to the drawings. FIG. 1 is a block diagram illustrating a configuration example of a manufacturing error evaluation system according to an embodiment of the present invention. In this figure, the manufacturing error evaluation system of the present invention includes at least an X-ray CT apparatus 1, an image processing unit 2, an image storage unit 3, and an error amount calculation unit 4.
The X-ray CT apparatus 1 irradiates an X-ray to the device under test and outputs X-ray data based on the intensity of the X-ray transmitted through the device under test, that is, the transmission intensity.
[0019]
Next, the configuration of the X-ray CT apparatus 1 will be briefly described with reference to FIG. FIG. 2 is a conceptual diagram illustrating a configuration example of the X-ray CT apparatus.
The X-ray CT apparatus 1 has an X-ray tube 11 that emits X-rays and an X-ray detector 13 that detects the intensity of the X-rays at opposing positions, and a test object 14 (according to three-dimensional CAD data). The parts processed by the NC processing machine 6) are fixed between the X-ray tube 11 and the X-ray detector 13 by a fixing device (not shown).
[0020]
The fixing device is capable of rotating the device under test along the body axis of the device under test 14 in the R direction within an angle range of 360 °.
Here, since the X-ray tube 11 radiates the X-rays 12 spreading in a fan shape, the fixing device controls the X-ray tube 11 and the X-rays so that the X-rays 12 spreading in the fan shape become the width of the test object 14. The position of the detector 13 is adjusted.
The X-ray detector 13 measures, for example, the X-ray intensity of the X-rays 12 transmitted through the DUT 14 at the section 14 n of the DUT 14.
[0021]
The fixing device is movable in the Z1 direction or the Z2 direction along the body axis.
The X-ray CT apparatus 1 controls the rotation and the vertical movement of the fixing device, and measures the X-ray intensity of the X-rays 12 transmitted through the DUT 14 while rotating and moving the DUT 14. Do.
At this time, the X-ray CT apparatus 1 measures the X-ray intensity of the X-rays 12 transmitted through the DUT 14 with respect to the DUT 14.
The X-ray CT apparatus may have any configuration as long as a three-dimensional fluoroscopic image can be obtained.
[0022]
Returning to FIG. 1, with the configuration described above, the X-ray CT apparatus 1 outputs the X-ray data of the cross section of the test object (the test object 14 in FIG. 2).
Then, the image processing unit 2 accumulates the X-ray data (X-ray fluoroscopic image) output from the X-ray CT apparatus 1 during the rotation of the device under test by 360 °, and reproduces the accumulated X-ray data. By performing the configuration calculation, a cross section of the test object, that is, a tomographic image of the test object perpendicular to the body axis is generated.
[0023]
Further, the image processing unit 2 superimposes the tomographic images obtained by synchronously moving the tomographic images along the body axis in the Z1 direction or the Z2 direction at minute intervals in the body axis direction, and A two-dimensional perspective image (that is, an actual perspective image) is generated.
At this time, the X-ray CT apparatus causes the image processing unit 2 to generate a real fluoroscopic image by the above-described processing.
Further, the image processing 2 stores the obtained real fluoroscopic image in the image storage unit 3 and displays the real fluoroscopic image on a display screen of an image display device (not shown).
[0024]
The CAD system 5 generates three-dimensional CAD data, which is three-dimensional design data of a part, used for processing of the part by the NC processing machine 6 by an operator's design process.
Further, the CAD system 5 generates a CAD fluoroscopic image, which is a three-dimensional image showing the shape of the part at the time of completion from the three-dimensional CAD data, and transmits the CAD fluoroscopic image to the image storage unit 3 together with the three-dimensional CAD data. Write and register (store). The NC processing machine 6 reads the three-dimensional CAD data from the image storage unit 3 and performs, for example, cutting of a part based on the three-dimensional CAD data.
[0025]
Hereinafter, the arithmetic expression and algorithm of the arithmetic performed by the error amount arithmetic unit 4 will be described with reference to FIG. FIG. 3 is a flowchart showing an operation example of the error amount calculation of the error amount calculation unit 4.
In step S1, the image processing unit 2 reads the CAD perspective image and the actual perspective image from the image storage unit 3, and converts each three-dimensional perspective image to a predetermined image size (for example, “ The gradient of each pixel is extracted with the resolution expressed by “number of pixels / unit volume”, and a three-dimensional image (three-dimensional voxel model) composed of a distribution of pixel values indicating the gradient of each pixel is generated. .
[0026]
At this time, in each of the CAD perspective image and the actual perspective image, the image processing unit 2 normalizes the gradient of the pixels of the entire image using the gradient of the maximum value in the contour and the like.
For example, when the gradient is r and the standardization is 0 ≦ r ≦ 1, the maximum gradient is expressed as “1”.
Thereby, the pixels of the CAD voxel model are moved, and the distribution of the gradient of each pixel is compared with the distribution of the gradient of the pixels of the actual voxel model. In, it becomes easy to associate each pixel.
[0027]
Here, in the three-dimensional voxel model generated from the CAD perspective image (hereinafter, CAD voxel model), the gradient of each pixel at the position indicated by the coordinates of x, y, and z is represented by a pixel value p (x, y, z). ), And in a three-dimensional voxel model generated from an actual perspective image (hereinafter, an actual voxel model), the gradient of each pixel at a position indicated by x, y, and z coordinates is represented by a pixel value P (x, y, z).
[0028]
Next, in step S2, the error amount calculation unit 4 calculates the error amount u in each of the x, y, and z directions of each pixel by using the following Expressions (1), (2), and (3). (X, y, z), v (x, y, z), and w (x, y, z) are obtained.
At this time, the coefficient a used in each of the equations (1), (2), and (3) (error function) _um ~ J _wm , Constant p _u ~ R _w Is a temporary value.
Here, the tentative value is a coefficient a in the above-described equations (1) to (3) obtained for a part that is considered to have a similar shape among other parts for which error evaluation has already been completed. _um ~ J _wm , Constant p _u ~ R _w Is a substitute value.
(Equation 1)

(Equation 2)

[Equation 3]

[0029]
In each of the equations, the first term (braces) in each square bracket is a Fourier series indicating the periodicity of the error of the device under test 14, and the second term indicates the power-like error amount. And the third term is the above constant.
The Fourier series of the first term corresponds to the periodicity of the error of the device under test 14. The above-described provisional values of the coefficients and constants are considered to be somewhat close to actual values (corresponding to the above-described error function), such as values previously obtained by error evaluation of parts having similar materials and processed shapes. The value is used.
[0030]
Next, in step S3, the error amount calculator 4 calculates the error amount u (x, y, z) obtained from the operation (predetermined operation) using the error function of the equations (1), (2), and (3). , V (x, y, z), w (x, y, z) to move each pixel. A numerical value in which each coordinate value is displaced by the movement by the coordinate conversion is set as an error amount.
In other words, by moving p (x, y, z) based on the error amounts u, v, w, the pixel matching the position of (x, y, z) becomes (x + u, y + v, z + w) Move to the position, that is, p (x, y, z) becomes p (x + u, y + v, z + w).
[0031]
This pixel value p (x + u, y + v, z + w) is converted to a pixel value p ^* (X, Y, Z). Here, X = x + u, Y = y + v, and Z = z + w.
Then, the error amount calculation unit 4 performs the above-described process of moving the pixel in the three-dimensional coordinates for each pixel constituting the CAD voxel model.
Where the pixel value p ^* (X, Y, Z) is a virtual voxel model of the sample after processing obtained by the error amount calculation unit 4, that is, a CAD voxel model (simulation voxel model) after movement as a simulation result.
[0032]
Next, in step S4, the error amount calculator 4 calculates the pixel value P (X, Y, Z) at the coordinate value (X, Y, Z) in the real voxel model and the pixel value p. ^* Comparison of the numerical value with (X, Y, Z) is performed for each coordinate value in the actual voxel model.
That is, the error amount calculator 4 calculates the pixel value P (X, Y, Z) at each coordinate value of the real voxel model and the pixel value p at each coordinate value of the CAD voxel model after the movement. ^* It is determined whether or not the numerical value of (X, Y, Z) matches (or has a predetermined range and includes substantially the same).
[0033]
Here, the error amount calculation unit 4 calculates the pixel value P (X, Y, Z) at each coordinate value of the actual voxel model and the pixel value p at each coordinate value of the CAD voxel model after movement. ^* When the numerical value of (X, Y, Z) matches (the movement amount of the CAD voxel model pixel corresponds to the error amount), each coefficient a _un ~ J _wm And the constant p _u ~ R _w Is output and the process ends, but if they do not match, the process proceeds to step S5.
At this time, the error amount calculation unit 4 calculates the pixel value P (x, y, z) by shifting the pixel value P (x, y, z) with respect to the pixel value of the entire voxel model by the following equation (4) which is a difference function. (X, Y, Z) and p ^* The difference from (X, Y, Z) is summed, normalized by 255 (gradation) × M, and output as a difference function f.
(Equation 4)

Here, M is the total number of voxels, and Σ indicates that the sum is calculated for all the voxels in the image.
Each time the difference function value of the difference function f is obtained, the error amount calculation unit 4 sequentially compares the difference function value with the previous value of f to determine the valley of the difference function value (the point where the difference function value is the smallest, that is, ) Is detected, and this point is defined as a point where the gradient of each pixel value of the entire voxel model matches.
[0034]
Next, in step S5, the error amount calculation unit 4 sets each coefficient a _un ~ J _wm And the constant p _u ~ R _w Is changed sequentially by an optimization method such as a non-linear programming method by an operation according to the algorithm.
Then, the error amount calculation unit 4 calculates the changed coefficient a _un ~ J _wm And the constant p _u ~ R _w Then, the process returns to step S2 to obtain new error amounts u (x, y, z), v (x, y, z), and w (x, y, z).
[0035]
As described above, the error amount calculation unit 4 calculates the pixel value P (X, Y, Z) at each coordinate value of the real voxel model and the pixel value p at each coordinate value of the CAD voxel model after movement. ^* Until the numerical value of (X, Y, Z) matches, the processing from step S2 to step S5 is repeated.
Then, the error amount calculation unit 4 finally calculates the pixel value P (X, Y, Z) at each coordinate value of the actual voxel model and the pixel value p at each coordinate value of the CAD voxel model after the movement. ^* When the numerical values of (X, Y, Z) match (the gradations match), each coefficient a at this time is _un ~ J _wm And the constant p _u ~ R _w Is output.
[0036]
Accordingly, the error amount calculation unit 4 calculates each coefficient a in the equations (1) to (3). _un ~ J _wm And the constant p _u ~ R _w Is obtained, the equations (1) to (3) are used as an error function for calculating an error amount in each coordinate value between each CAD voxel model and the actual voxel model.
That is, in the above-mentioned error function, the difference (error amount) between the coordinate values of the mark and the mark (actual voxel model) on the machined surface shown in FIG. Expressed as a function.
[0037]
Next, in step S6, the error amount calculation unit 4 calculates an error amount corresponding to each coordinate value based on the coordinate value (x, y, z) of the predetermined CAD voxel model. Thus, the error amount calculation unit 4 can three-dimensionally calculate the error amount between the CAD voxel model and the actual voxel model based on the arbitrarily input coordinate values in the CAD voxel model by the error function. it can.
[0038]
Here, the coordinate value data arbitrarily input is coordinate values in the three-dimensional CAD data.
Then, the error amount calculation unit 4 multiplies the error amount obtained for each coordinate value by “−1” and inputs the result of the multiplication to the CAD system 5 to correct the coordinate value of the CAD voxel model. Output as data.
Here, the reason why the error amount is multiplied by “−1” is that the error amount generated after machining is canceled in advance by adding the coordinate value to the coordinate value of the three-dimensional CAD data.
[0039]
Next, in step S7, the error amount calculator 4 outputs the coordinate correction data to the CAD system 5.
Thus, the CAD system 5 corrects the three-dimensional CAD data of the corresponding component based on the input coordinate correction data.
That is, the CAD system 5 corrects the three-dimensional CAD data by adding the input coordinate correction data to the corresponding coordinate values in the three-dimensional CAD data.
[0040]
Then, the CAD system 5 outputs the corrected three-dimensional CAD data to the NC processing machine 6 by the above-described correction processing based on the error amount.
Thus, the NC processing machine 6 replaces the three-dimensional processing data used for processing the part with the input corrected three-dimensional CAD data, and uses the corrected three-dimensional data to perform subsequent parts processing. Perform processing.
[0041]
Therefore, based on the corrected three-dimensional CAD data, the shape of the processed surface of the processed part is generated by the original design in the CAD system 5 (before correction by the error amount), that is, the surface to be processed. It will be processed into a shape close to.
In addition, by repeating the processing of the flowchart of FIG. 3 a plurality of times, the accuracy of calculating the error amount of the error function is further improved, and the shape of the part processed by the NC processing machine is made closer to the shape originally designed by CAD. Becomes possible.
[0042]
In the above step S3, each pixel value P ^* A method for obtaining the value of (X, Y, Z) will be described below.
First, the error amount calculation unit 4 creates a spatial grid corresponding to each pixel in the voxel model shown in FIG. 6A, and, as shown in FIG. Assign each to the center of gravity.
Then, the error amount calculation unit 4 moves the center of gravity to the state shown in FIG. 6C by using the calculated “u, v, w” (move the center of gravity by deformation mapping, (Mapping, x = D (X))). The center of gravity after movement (hereinafter referred to as “moved points (Mapped Points): black circles)” and the center of gravity of the spatial fixed grid constituting the deformed image (hereinafter referred to as “corresponding points (Fixed Points): white circles)” are shown in FIG. As you can see, they generally do not match.
Next, the error amount calculation unit 4 finally generates a simulation voxel model as shown in FIG. 6D by allocating the pixel value of the moving point to the corresponding point for each spatial fixed grid. I do.
[0043]
Therefore, the pixel value of the corresponding point of each spatial fixed grid is determined from the pixel value of each moving point under the following conditions.
Basically, in the present embodiment, the pixel value of the moving point that is closest to each corresponding point is set as the pixel value of the corresponding point, and the eight nearest neighbors based on the nearest neighbor interpolation method are used. The approximation method is used.
That is, when the moving point moves into the spatial fixed grid including the corresponding point and the moving point is one in the spatial fixed grid, the error amount calculating unit 4 determines the pixel value of the moving point as the pixel value of the corresponding point. When there are a plurality of moving points in the spatial fixed grid, the average value of the pixel values of these moving points is calculated, and this average value is set as the pixel value of the corresponding point.
[0044]
If there is no moving point in the space fixed grid of the corresponding point, a search is performed in eight neighboring grids in a 3 × 3 grid around the moving point.
At this time, if there is no moving point in the surrounding 3 × 3 grid, the pixel value is set to “0”. If there is a moving point, the moving point closest to the position of the corresponding point among the moving points is set. Let the pixel value be the pixel value of this corresponding point.
The above description has been made in two dimensions for the sake of simplicity, but in the case of three dimensions, if there is no moving point in the space fixed grid, 26 grids in the 3 × 3 × 3 grid around the neighboring grid Then, a search for a moving point is performed, and the grid point of the corresponding point is determined by the same method as that for the 8-neighbor grid.
[0045]
Next, a description will be given of how to calculate the numerical values of each coefficient and each constant in step S5.
As described above, in step S5, the error amount calculation unit 4 determines, as described above, each coefficient a _un ~ J _wm And the constant p _u ~ R _w Is changed sequentially by an optimization method such as a non-linear programming method by an operation according to the algorithm.
Here, since the voxel values are discrete values and the discrete image processing is performed based on the nearest neighbor approximation, the sensitivity information of the objective function (the degree of change of the numerical value f corresponding to the amount of change of each coefficient and constant) ) Can not get.
[0046]
Therefore, in the present embodiment, the error amount calculation unit 4 performs the minimization processing of the difference function f by a discrete optimization method such as a genetic algorithm (Genetic Algorithm) or the like (algorithms a) and b) described below). Do.
a) When using a genetic algorithm
For example, it is assumed that the error amount calculation unit 4 assigns an 8-bit binary as the data capacity of a variable and a constant, and has 256 levels of numerical values for each variable and constant.
The 256-step numerical value is obtained by dividing a predetermined range (the number of pixels and dimensions of the voxel model, etc.), which is assumed as a deformation range (as a search range) in advance, into 255.
Then, as conditions for the simulation of the genetic algorithm, each individual is selected from the above variables and constants in the error amount calculation unit 4 and configured as 1000 combinations.
Genetic manipulation to change the combination of each individual included uniform crossover (crossover rate 75%), linear ranking selection, elite strategy, and mutation (mutation rate 1.0%).
[0047]
b) SCE-UA (Shuffled Complex Evolution Method developed at the University Arizona) method
This SCE-UA method adopts an evolution method similar to a genetic algorithm, and can set a search area for a solution having a physical meaning. In addition, during the calculation, it evolves independently in a plurality of populations. When a solution is obtained, it is characterized in that no solution or divergence occurs and a solution is always obtained.
That is, the SCE-UA method is an optimization method based on band search that combines the concepts of competitive evolution and group mixing. The calculation procedure is briefly described below.
(1) Decision variable (coefficient a in equations (1) to (3)) _un ~ J _wm And the constant p _u ~ R _w Or the variable a in the equations (1 ′) to (3 ′) _u13 (K ₁ , K ₂ , K ₃ )), The number n of groups, the number p of groups, and the number m of individuals in each group (= 2n + 1) are set, and each individual is regarded as a point on an n-dimensional space having coordinate values of decision variables.
For example, when there are a total of n coefficients and constants, “2n + 1” individual groups are assigned to p groups.
{Circle around (2)} As the initial generation, each decision variable value is given at random, and for example, individuals are arranged in ascending order of the difference function value of the difference function of the equation (4).
(3) In the order arranged in (2), from the first individual, the first individual is included in the first group, the second individual is included in the second group, ..., the p-th individual is included in the p-th group, and p + 1 Individuals are sequentially allocated to all groups, such as the second individual to the first population, the 2p (ie, p + p) th individual to the p-th population, and so on.
That is, in this sorting method, p (X, Y, Z) and p, calculated by selecting and combining each coefficient and constant corresponding to this pixel value, are used. ^* With (X, Y, Z), a difference function f is obtained, and is sequentially allocated to each of the p groups in ascending order of the difference function value.
For example, when there are a total of n coefficients and constants, “2n + 1” individual groups are assigned to p groups.
{Circle around (4)} The population is independently evolved by the CCE (Conditional Class Entropy) algorithm independently for each group.
In the above CCE algorithm, each individual is evolved by changing coefficients and constants so that an individual having a higher differential function value of the differential function f is an individual having a lower differential function value.
{Circle around (5)} Finally, the p groups, that is, all the groups are put together into one, and all the individuals included in the entire group are rearranged again in ascending order of the difference function value. Is the difference function value of the best individual within the range of the preset convergence determination value, or the number of repetitions of the optimization process of the coefficient and the constant is the preset repeat set value And (3) to (5) are repeated until the coefficients correspond to any of the above.
[0048]
Next, the equations (1), (2) and (3) used by the error amount calculator 4 for calculating the error amounts u, v and w are expressed by the following equations (1 ′), (2 ′) and (2 ′), respectively. The case of calculating the error amounts u, v, w instead of (3 ′) will be described.
(Equation 5)

(Equation 6)

(Equation 7)

[0049]
Equations (1 ′), (2 ′), and (3 ′) include, for each of equations (1), (2), and (3), the effects of errors in a plurality of coordinate axes in the terms of the Fourier series. It was not.
In each of the equations (1 ′), (2 ′) and (3 ′), Mu, Mv, Mw and Nu, Nv, Nw are integer values, and are constants appropriately set according to a problem, ω is a fundamental frequency, Similarly, the constant is appropriately set depending on the problem.
Also, α _ijk , Β _ijk , Γ _ijk Is a variable that is defined as a different variable when i, j, and k are different, and is determined by an optimization algorithm such as GA so as to minimize the difference function value obtained from the difference function.
And a _u13 (K1, k2, k3), a _v13 (K1, k2, k3), a _w13 (K1, k2, k3) and the like are defined as different variables when k1, k2, and k3 are different, and are determined by an optimization algorithm such as GA so that the difference function value obtained from the difference function is minimized. Variable.
Therefore, by using the equations (1 ′), (2 ′) and (3 ′), the displacement in each coordinate axis direction includes the influence from other coordinate axis directions, that is, the correction amount. Compared to the case where the equations (1), (2) and (3) are used, a more accurate simulation can be performed when calculating the error amounts u, v and w.
[0050]
By using the above-described manufacturing error evaluation system of the present invention, it is possible to evaluate an error of a part that has been cut by the NC processing machine 6 only in units of length, and to process a part having a complicated processing shape. Although the error amount in each coordinate value could not be obtained with high accuracy, the processing of the arbitrary coordinate value of the three-dimensional CAD data was performed by using the error function for calculating the error amount corresponding to the coordinate value. The resulting error amount can be calculated and obtained with high accuracy, and by feeding back this error amount to the three-dimensional CAD data, it becomes possible to generate three-dimensional CAD data in which the error amount generated in advance is predicted. Processing and manufacturing of parts can be performed with higher precision than before.
[0051]
That is, by using the manufacturing error evaluation system of the present invention, for a component having a complicated processing shape, the error of the shape accompanying the processing and manufacturing is calculated based on the actual fluoroscopic image obtained from the X-ray CT apparatus 1. By comparing the three-dimensional real voxel model with the CAD voxel model obtained from the three-dimensional CAD data of the CAD system 5, the error amount calculator 4 calculates an error function for calculating the error amount corresponding to the coordinate value, and Since the error amount can be evaluated numerically, the error amount in each part of the component can be quantitatively represented in a three-dimensional space, and coordinate value correction data is used as feedback information for correcting the error amount. , Returning to the CAD system 5, and three-dimensional CAD data in which an error generated during machining is estimated in advance from the three-dimensional CAD data at the time of design and the amount of error. By newly generating and outputting the estimated three-dimensional CAD data to the NC processing machine 6 and accurately feeding back the error amount, the shape of the part designed by the CAD system 5 (designed as an actually required dimension) (Ie, CAD data at the time of design), the machining shape of the part by the NC machine 6 can be approximated with high accuracy.
[0052]
In the embodiment of the present invention described above, the procedure executed in the manufacturing error evaluation system is recorded on a computer-readable recording medium, and the program recorded on the recording medium is read and executed by the computer system. As a result, the manufacturing error evaluation system of the present invention is realized. The computer system here includes an OS and hardware such as peripheral devices.
[0053]
Further, the "computer system" includes a homepage providing environment (or display environment) if a WWW system is used.
The “computer-readable recording medium” refers to a portable medium such as a flexible disk, a magneto-optical disk, a ROM, a CD-ROM, and a storage device such as a hard disk built in a computer system. Further, the “computer-readable recording medium” is a system such as a volatile memory (RAM) in a computer system which is a client when a program is transmitted through a network such as the Internet or a communication line such as a telephone line. In addition, those that hold programs for a certain period of time are also included.
[0054]
Further, the above program may be transmitted from a computer system storing the program in a storage device or the like to another computer system via a transmission medium or by a transmission wave in the transmission medium. Here, the “transmission medium” for transmitting a program refers to a medium having a function of transmitting information, such as a network (communication network) such as the Internet or a communication line (communication line) such as a telephone line.
Further, the program may be for realizing a part of the functions described above. Furthermore, what can implement | achieve the function mentioned above in combination with the program already recorded on the computer system, and what is called a difference file (difference program) may be sufficient.
[0055]
As described above, one embodiment of the present invention has been described in detail with reference to the drawings. However, the specific configuration is not limited to this embodiment, and there are design changes and the like within a range not departing from the gist of the present invention. Are also included in the present invention.
[0056]
【The invention's effect】
According to the manufacturing error evaluation system of the present invention, for a part having a complicated processing shape, a shape error accompanying the processing and manufacturing is calculated from a three-dimensional voxel model obtained from X-ray CT and three-dimensional CAD data. The comparison of the distribution state of the gradient of the pixel with the obtained three-dimensional voxel model can be numerically evaluated, and the error amount in each part of the component can be quantitatively represented in the three-dimensional space. Since the error amount can be accurately supplied to the manufacturing / processing equipment as feedback information, the shape of the processed part can be brought close to the three-dimensional CAD data designed by CAD with high accuracy.
[Brief description of the drawings]
FIG. 1 is a block diagram illustrating a configuration example of a manufacturing error evaluation system according to an embodiment of the present invention.
FIG. 2 is a conceptual diagram showing a configuration of the X-ray CT apparatus 1 of FIG.
FIG. 3 is a flowchart illustrating an example of an operation of calculating an error amount by an error amount calculation unit 4 in FIG.
FIG. 4 is a conceptual diagram showing a comparison between the shape of a part at the time of design and the shape of a processed part using an actual perspective image and a CAD perspective image.
FIG. 5 is a conceptual diagram showing a comparison between the shape of a part at the time of design and the shape of a processed part using an actual perspective image and a CAD perspective image.
FIG. 6 shows each pixel value P in the error amount calculation unit 4. ^* It is a conceptual diagram explaining the calculation method of the value of (X, Y, Z).
[Explanation of symbols]
1 X-ray CT system
2 Image processing device
3 Image storage unit
4 Error calculation unit
5 CAD system
6 NC processing machine
11 X-ray tube
12 X-ray
13 X-ray detector
14 DUT

Claims (8)

An X-ray CT apparatus having an X-ray source and a plurality of X-ray detectors, and collecting X-ray data on a cross section of the test object;
An image processing unit that generates a three-dimensional perspective image of the test object based on the X-ray data;
An image storage unit that stores three-dimensional CAD data that is design data of the test object and a three-dimensional perspective image of the test object that is processed based on the three-dimensional CAD data;
Each pixel of the three-dimensional CAD data is moved by a predetermined operation, the shape of the three-dimensional CAD data is matched with the shape of the three-dimensional perspective image, and an error amount for obtaining a displacement due to the movement of the pixel of the three-dimensional CAD data as an error amount. A manufacturing error evaluation system, comprising: a calculation unit. The error amount calculation unit moves each pixel of the three-dimensional CAD data while sequentially changing the coefficients and constants of the predetermined calculation expression, so that the three-dimensional CAD data and the three-dimensional perspective image are compared. 2. The manufacturing error evaluation system according to claim 1, wherein the shapes are matched. The error amount calculation unit compares the gradient of each pixel between the three-dimensional perspective image and the three-dimensional CAD data after moving, and determines whether or not the distribution of the gradient is the same. The manufacturing error evaluation system according to claim 1, wherein the matching of the shape with the image is determined. A data acquisition step of acquiring X-ray data on a cross section of the test object from an X-ray CT apparatus having an X-ray source and a plurality of X-ray detectors;
An image processing step of generating a three-dimensional perspective image of the test object based on the X-ray data;
An image storage process in which three-dimensional CAD data as design data of the test object and a three-dimensional perspective image of the test object processed based on the three-dimensional CAD data are stored in an image storage unit;
Each pixel of the three-dimensional CAD data is moved by a predetermined operation, the shape of the three-dimensional CAD data and the shape of the three-dimensional perspective image are matched, and an error amount calculating process for obtaining an error amount in manufacturing based on the movement amount of each pixel. And a manufacturing error evaluation method. In the error amount calculation step, the shape of the three-dimensional CAD data and the shape of the three-dimensional perspective image are matched by sequentially moving each pixel while sequentially changing the coefficients and constants of the predetermined calculation expression. The method for evaluating a manufacturing error according to claim 4. In the error amount calculation step, each pixel in the three-dimensional perspective image and the three-dimensional CAD data after movement are made to correspond to each other based on the respective gradients, and the shape coincidence between the three-dimensional CAD data and the three-dimensional perspective image is determined. The manufacturing error evaluation method according to claim 4, wherein the method is performed. A data collection process of collecting X-ray data on a cross section of a test object from an X-ray CT apparatus having an X-ray source and a plurality of X-ray detectors;
Image processing for generating a three-dimensional perspective image of the test object based on the X-ray data;
Image storage processing in which three-dimensional CAD data as design data of the test object and a three-dimensional perspective image of the test object processed based on the three-dimensional CAD data are stored in an image storage unit;
Each pixel of the three-dimensional CAD data is moved by a predetermined calculation, the shape of the three-dimensional CAD data and the shape of the three-dimensional perspective image are matched, and an error amount calculation process for obtaining an error amount in manufacturing based on the movement amount of each pixel. And a computer-executable manufacturing error evaluation program. A computer-readable recording medium on which the manufacturing error evaluation program according to claim 7 is recorded.

Images