JP3869811B2 - Machining state diagnosis method in cutting - Google Patents

Description

ここで、入力ｆによる工具１の変位ｘ_１は被削材２の変位ｘ_２に比較して、近似的にはｘ_１＞＞ｘ_２とおくことができる。したがって、［数１］は次式で表される。
【００２２】
【数２】

一方、被削材２の運動方程式は次式で表される。
【００２３】
【数３】

上記式［数２］、［数３］より、切削加工を表す力学モデルの運動方程式は次式となる。
【００２４】
【数４】

式［数４］はラプラス変換より、入力をｆ（ｔ）、出力を被削材２の変位ｘ_２（ｔ）の加速度とした力学モデルの伝達関数Ｈ（ｓ）は次式のように求まる。
【００２５】
【数５】

但し、力学モデルの伝達関数の係数Ａ_ｉ、Ｂ_ｉは力学パラメータｍ_ｉ、ｋ_ｉ、ｃ_ｉによって次式のように表される。
【００２６】
【数６】

次に、加速度信号の時系列モデルパラメータと上記モデルの力学パラメータｍ_ｉ、ｋ_ｉ、ｃ_ｉがどのような関係であるかを示すために力学モデルの離散時間モデルを導出する。
【００２７】
ここでは、以下のように力学モデルの離散化を行い、離散時間モデル伝達関数を導出した。
【００２８】
図１の力学モデルの伝達関数Ｈ（ｓ）は式［数５］で表され、次式に変換できる。
【００２９】
【数７】

ここで、Ｐ_１、Ｐ_２、Ｑ_１、Ｑ_２は定数である。
【００３０】
【数８】

とおくと、式［数７］の逆ラプラス変換より、伝達関数Ｈ（ｓ）のインパルス応答ｈ（ｔ）は次式で表される。
【００３１】
【数９】

ここで、ｔ＝ｎＴ（ｎ＝０，１，２，・・・）として離散化することにより、式［数９］は次式となる。
【００３２】
【数１０】

さらに、上式［数１０］のＺ変換より、力学モデルの離散時間モデル伝達関数Ｈ（ｚ）は次式で表される。
【００３３】
【数１１】

ここで、式［数８］より、
【００３４】
【数１２】

である。
【００３５】
次に、切削加工時に観測される被削材２の振動加速度を時系列モデルで表したときの時系列モデルパラメータと力学パラメータの関係を式［数１１］より求める。
【００３６】
前述のように、工作機械のような振動系への入力が未知で、振動系からの振動加速度の出力のみが入手可能な場合には、入力を白色信号とみなした時系列モデルによる解析が有効であり、その時系列信号は、一般に次式のような時系列モデルであるＡＲＭＡ（ｐ，ｑ）モデル（Auto Regressive Moving Average：自己回帰移動平均モデル）として表される。
【００３７】
【数１３】

ここで、ａ_ｉをＡＲパラメータ、ｂ_ｉをＭＡパラメータという。
【００３８】
一方、式［数１１］より力学モデルの離散時間モデルの伝達関数Ｈ（ｚ）は次のように表される。
【００３９】
【数１４】

ここで、
【００４０】
【数１５】

である。上式［数１５］は式［数６］より力学パラメータｍ_ｉ、ｋ_ｉ、ｃ_ｉを用いて次式で表される。
【００４１】
【数１６】

また、式［数１３］より、式［数１４］はＡＲＭＡ（ｐ，ｑ）モデルのＡＲＭＡ（４，３）モデルに相当し、次式で表される。
【００４２】
【数１７】

したがって、式［数１４］、式［数１７］より、時系列モデルパラメータであるＡＲパラメータと力学パラメータの関係式は次式で表される。
【００４３】
【数１８】

以上より、加工時に観測される加速度信号をＡＲＭＡ（４，３）モデルで表したときのＡＲパラメータａ_ｉは、図１の各力学パラメータと式［数１６］、式［数１８］のような関係がある。ここで、式［数１８］のＡＲパラメータａ_１、ａ_２、ａ_３、ａ_４には、ほとんど全ての力学パラメータが要素として含まれていることが分かる。即ち、ａ_ｉはｍ、ｋ、ｃの関数としてｆ（ｍ_ｊ，ｋ_ｊ，ｃ_ｊ）で表される。
【００４４】
次に、実際の切削加工状態に即して、ＡＲパラメータヘの加工状態の影響を図１における切削加工状態の良し悪しに一番影響する加工部３の力学パラメータｋ_３、ｃ_３に注目し、これらのパラメータを変化させることで、ＡＲパラメータの挙動をシミュレーションする。
【００４５】
本シミュレーションでは、図１の加工モデルにおける工具１、被削材２の各力学パラメータを実際の質量や、物性値を基に下記［表１］のように設定した。
【００４６】
【表１】

以下に、シミュレーション結果である加工部３のパラメータをｋ_３＝０．８×１０^８〜１．６×１０^８（Ｎ／ｍ）、ｃ_３＝０．２×１０^６〜０．４×１０^６（Ｎｓ／ｍ）と変化させたときの式［数１８］のＡＲパラメータａ_１、ａ_２、ａ_３、ａ_４のそれぞれの変化の様子を図２に示す。
【００４７】
図２より、ａ_１に比べてａ_２、ａ_３、ａ_４は変化がない領域がほとんどであることより、ｋ_３、ｃ_３の変化は主にａ_ｉに現れると考えられる。図２においてｋ_３、ｃ_３の変化によって各ＡＲパラメータの増減がどのように変化しているか分かり易くするため、ｋ_３、ｃ_３両方を変化させたときの各ＡＲパラメータの挙動を下記［表２］にまとめる。
【００４８】
【表２】

図２及び［表２］より、ＡＲパラメータａ_１の変化する方向はｋ_３の増減によって支配されていることが分かり、ｋ_３とＡＲパラメータａ_１の関係は図３のようにリニアな関係になって、以下の近似式［数１９］で表される。
【００４９】
【数１９】

力学パラメータのｋ_３は切削抵抗に相当するパラメータであるので、ｋ_３の増加は切り込み深さの増加、送り速度の増加、または被削材２の硬さの増加といった条件に相当する。ｃ_３の増減はａ_１の変化の向きには影響を与えないが、ｃ_３が減少しているときはＡＲパラメータａ_１の変化する割合が大きい。また、このことは減衰係数ｃ_３が加工部３から散逸している熱エネルギー等に関係していると考えると、ｃ_３が減少している方が切削自体に用いられているエネルギーが大きいといえる。このようにＡＲパラメータａ_１を観測することでリアルタイムに切削加工状態を把握し予測することが可能になる。
【００５０】
次に、上記力学パラメータｋ_３、ｃ_３の変化が切削加工条件とどのような関係があるのか確かめるため、種々の切削加工条件の下で具体的な実施の形態の加工実験を図４に示される加工状態診断システム１０にて行った。
【００５１】
図４において、加工状態診断システム１０は、工作機械１１の主軸頭１９に取り付けられた工具１としてのエンドミル１２を用いて支持テーブル１３上のクランプ１４に固定された被削材２を種々の切削加工条件で加工したときに発生する振動の加速度を例えば前記被削材２の側面中央付近に取り付けられた加速度センサ１５により加速度信号として感知し、アンプ１６を通してスコープレコーダ１７に記録し、記録された加速度信号はパーソナルコンピュータ１８に取り込まれて上記式［数１］〜式［数１９］及び後述の式［数２０］〜式［数２４］等に基づいてパラメータ解析の信号処理を行うというシステム構成である。
【００５２】
被削材２として主に冷間金型用として使用される合金工具鋼ＳＫＤ１１を用いた例を示す。［表３］に切削加工条件を示す。基本的には切り込み深さを変化させ、加工により発生する振動の加速度を測定した。
【００５３】
【表３】

図５は（ａ）切り込み深さ１０ｍｍの場合、（ｂ）切り込み深さ３０ｍｍの場合、（ｃ）切り込み深さ４２ｍｍの場合のそれぞれに観測された振動加速度波形（時間領域）（左側）とそのパワースペクトル（周波数領域）（右側）である。加速度波形は切り込み深さがメーカー推奨条件の時、振幅が小さい傾向にある。
【００５４】
次に、この加速度波形を用いて、ＡＲＭＡ（ｐ，ｑ）モデルの次数をｐ＝１〜１０、ｑ＝１〜１０と変化させて時系列解析し、それぞれの時系列モデルのＡＩＣ（赤池情報基準）を算出した。この結果は図６のとおりであり、図６中の黒点で示される最適な振動加速度の時系列モデルはＡＲＭＡ（４，３）モデルで表されることがわかる。
【００５５】
図７は表３の切削加工条件で測定した加速度信号をＡＲＭＡ（４，３）モデルで解析し、切り込み深さの変化に伴う４つのＡＲパラメータａ_１（測定点■）、ａ_２（測定点●）、ａ_３（測定点▲）、ａ_４（測定点◆）の変化を示したものである。
【００５６】
ＡＲパラメータａ_１、ａ_２、ａ_３、ａ_４は切り込み深さがメーカー推奨値（３０ｍｍ）で最小値になる。切り込み深さの増加は切削抵抗の増加と比例するため、ＡＲパラメータの増加は切削抵抗の増加を表す。また、切り込み深さをメーカー推奨値より減少させると、工具１の先端に加工力が集中するようになり、工具１自体の振動が大きくなりＡＲパラメータは増加する。
【００５７】
図８は正常工具（測定点●）と摩耗した工具（測定点■）を使用した場合の各ＡＲパラメータａ_１、ａ_２、ａ_３、ａ_４の比較である。同じ切削加工条件でも４つのＡＲパラメータの絶対値は摩耗工具の方が正常工具より常に大きい。このことは同じ切削加工条件であれば観測される振動加速度をＡＲＭＡモデルで表したときのＡＲパラメータから工具の摩耗の程度を推定できることを示している。
【００５８】
図９の（ａ）は切り込み深さの変化による４つのＡＲパラメータとの関係を切り込み深さと４つのＡＲパラメータの平均値を用いて表したものである。図９の（ｂ）はＡＲパラメータの平均値に代わり、切り込み深さと加工面粗さ（最大高さＰｚ）との関係を示した。
【００５９】
図９の（ａ）と（ｂ）を比較すると明らかなように、切り込み深さの変化によるＡＲパラメータの平均値と加工面粗さを示すＰｚの変動は同様な傾向を示す。即ち、加工面粗さが悪ければＡＲパラメータの平均値も大きくなる傾向にあることが判る。これはＡＲパラメータの平均値から加工精度を表す加工面粗さが推定できることを示す。
【００６０】
そこで、次に、力学モデルパラメータに関与する時系列モデルパラメータと加工面粗さとの関係式の導出を検討する。
【００６１】
切削加工は加工物内部に高い応力を発生させて破壊、分離を起こさせる加工法であり、加工中に付加したエネルギの内、６０〜６５％が塑性変形に、３０〜３５％が表面エネルギーや摩擦熱となっている。これを、限界剪断応力τ_ｂ、ダッシュポットｃを用いて表現すると、切削加工時の加工部３の力学モデルは図１０の（ａ）のモデル１のように表される。一方、図１０の（ｂ）のモデル２は、図１に示された力学モデルにおける加工部３を切削抵抗の視点から表現したものである。
【００６２】
ここで、モデル１とモデル２の外力による変形エネルギーが等しいとすると、剛性ｋ_３と塑性変形で生じる加工表面積ΔＡとの関係は次式［数２０］で表される。
【００６３】
【数２０】

一方、加工面粗さＰｚ（断面曲線の最大高さ）は、加工表面積に比例し、増加することから、Ｐｚ∝ΔＡと表される。よって、力学パラメータｋ_３と加工表面粗さＰｚの関係は近似的に次式で表される。
【００６４】
【数２１】

式［数２１］を用いて式［数１９］は次式で表される。
【００６５】
【数２２】

図１１は切削加工時の加速度信号をＡＲＭＡ（４，３）モデルで表したときのＡＲパラメータと、実際の加工面粗さＰｚの関係を調べた結果である。図１１から上式［数２２］の関係が認められる。
【００６６】
また、加工面粗さ波形による時系列モデルパラメータと加工面粗さとの関係式の導出を検討すると以下のようになる。
【００６７】
加工面粗さＰｚは、図１における被削材２の上下振動変位ｘ_２に関連して生成されると仮定すると、この伝達関数Ｈ′（ｓ）＝Ｘ_２（ｓ）／Ｆ（ｓ）は式［数５］より次式で表される。
【００６８】
【数２３】

このパルス伝達関数Ｈ′（ｚ）は、ＡＲＭＡ（４，１）モデルとして、次式で表される。
【００６９】
【数２４】

上式［数２４］より、加工面粗さＰｚはＡＲパラメータと関係することが分かる。
【００７０】
図１２は、加工面の粗さ波形をＡＲＭＡ（４，１）モデルで表したときのＡＲパラメータａ_１′と実際の加工面粗さＰｚの関係を調べた結果である。図１２においても、式［数２２］に示したような関係が認められることが分かる。
【００７１】
而して、上記関係から、図４における工作機械１１による切削加工中に前記被削材２に設置した加速度センサ１５の信号を測定して時系列モデルであるＡＲＭＡモデルとして表し、そのＡＲＭＡモデルのＡＲパラメータの変化から切削加工中の加工状態をリアルタイムに把握、推定し、予測することが可能となる。
【００７２】
【発明の効果】
本発明に係る切削加工における加工状態診断方法は、上記のように、切削加工中に発生する振動を加速度センサで測定し、その加速度信号を時系列モデルであるＡＲＭＡモデルとして表し、そのＡＲＭＡモデルの時系列モデルパラメータであるＡＲパラメータを加工診断システムでリアルタイムに監視することで加工異常や加工面粗さの良し悪しを把握し、予測し診断することができる。
【図面の簡単な説明】
【図１】切削加工を近似的に表現する力学モデルである。
【図２】加工部の力学パラメータｋ_３、ｃ_３を変化させたときのＡＲパラメータａ_１、ａ_２、ａ_３、ａ_４のそれぞれの変化の様子を示すシミュレーション結果である。
【図３】力学パラメータｋ_３とＡＲパラメータａ_１の関係を示すシミュレーション結果である。
【図４】本発明の切削加工における加工状態診断方法を実施する加工状態診断システムの構成図である。
【図５】３つの切り込み深さの切削加工で観測された振動加速度波形（時間領域）（左側）とそのパワースペクトル（周波数領域）（右側）の実測図である。
【図６】ＡＩＣによる時系列モデルの次数の算出結果を表す図である。
【図７】測定した加速度信号をＡＲＭＡ（４，３）モデルで解析し、切り込み深さの変化に伴う４つのＡＲパラメータの変化を示す図である。
【図８】正常工具と摩耗した工具を使用した場合の各ＡＲパラメータａ_１、ａ_２、ａ_３、ａ_４の比較を示す図である。
【図９】（ａ）は切り込み深さの変化による４つのＡＲパラメータとの関係を切り込み深さと４つのＡＲパラメータの平均値を用いて表した図であり、（ｂ）は切り込み深さと加工面粗さ（最大高さＰｚ）との関係を示す図である。
【図１０】（ａ）は切削加工時の加工部の力学モデルであり、（ｂ）は図１の力学モデルにおける加工部を切削抵抗の視点から表現した力学モデルである。
【図１１】切削加工時の加速度信号をＡＲＭＡ（４，３）モデルで表したときのＡＲパラメータと、加工面粗さＰｚの関係を調べた結果を示す図である。
【図１２】加工面粗さ波形をＡＲＭＡ（４，１）モデルで表したときのＡＲパラメータａ_１′と加工面粗さＰｚの関係を調べた結果を示す図である。
【符号の説明】
１ 工具
２ 被削材
３ 加工部
１０ 加工状態診断システム
１１ 工作機械
１２ エンドミル
１３ 支持テーブル
１４ クランプ
１５ 加速度センサ
１６ アンプ
１７ スコープレコーダ
１８ パーソナルコンピュータ
１９ 主軸頭
ａ_ｉ 加速度信号のＡＲＭＡ（４，３）モデルのＡＲパラメータ
ｂ_ｉ 加速度信号のＡＲＭＡ（４，３）モデルのＭＡパラメータ
ａ_１′ 加工面粗さ波形のＡＲＭＡ（４，１）モデルのＡＲパラメータ
ｍ_ｉ 質量（力学パラメータ）
ｃ_ｉ 減衰係数（力学パラメータ）
ｋ_ｉ 剛性（力学パラメータ）
Ｐｚ 加工面粗さ（断面曲線の最大高さ）[0001]
BACKGROUND OF THE INVENTION
The present invention relates to a method of diagnosing the machining state of the workpiece in machining by the machine tool of the milling machine or the like, and more particularly, represents the vibration of the workpiece to be observed as a time series model, the parameters of the time series model The present invention relates to a machining state diagnosis method for grasping and predicting a machining state such as a machining abnormality and a roughness of a machined surface in real time by estimating a machining state by observing a change in the above.
[0002]
[Prior art]
In order to automate and improve the accuracy of cutting, it is important to always keep the machining process in an optimum state.
[0003]
Currently, in order to keep the processing state optimal, the processing accuracy is confirmed by measuring the dimensions and surface roughness of the processed product with a precision meter such as a micrometer or surface roughness meter after processing. A method of feeding back the result of the navel, a method of grasping the machining state by observing vibrations during cutting, and the like are performed.
[0004]
Among them, the latter method based on the observation of the machining state by vibration measures signals such as vibration and AE (acoustic emission) as in the “abnormal diagnosis method in cutting” disclosed in [Patent Document 1] below. Then, the result is analyzed statistically and in time series, and when the calculated average value, peak value, etc. exceed a certain value set by a skilled engineer, it is a technique for making an abnormality.
[0005]
[Patent Document 1]
Japanese Patent Laid-Open No. 10-276749 [Problems to be Solved by the Invention]
However, with the above-described conventional abnormality diagnosis method, it is impossible to predict and grasp a processing abnormality or processing accuracy during cutting in real time.
[0006]
That is, in the conventional method based on the observation of vibration, when an average value or a peak value larger than a set value occurs, it is recognized as an abnormality, and it is possible to detect a minute change in the processed bear. In addition, the statistical or time series methods used in these analyzes do not set up a dynamic model that matches the actual processing, so the calculated value and the mechanical characteristic value are logical. It is not tied to.
[0007]
In an actual cutting work site, cutting conditions, dimensions, and the like are input to a machine tool as a program before machining, and machining is performed at once according to the program. The cutting conditions input at that time are the optimum cutting conditions, such as tool manufacturer's recommended values.
[0008]
However, since there are always changes in the machining environment such as the wear state of the tool, temperature, and humidity, even if the same cutting conditions are input as optimum, the machining accuracy varies depending on the machining environment at that time. That is, the optimum cutting conditions are slightly different depending on the working environment. The present situation is that such a minute change in the roughness of the machined surface is dealt with on the spot by relying on the five senses of a skilled worker.
[0009]
There has not yet been established a diagnostic method that evaluates in real time changes in the shape of a processed bear caused by fluctuations in the processing environment as described above, and automatically corrects the cutting processing conditions during processing.
[0010]
The present invention is intended to solve the problem that the conventional method for grasping the machining state has, and it is possible to cut the work material in real time from the vibration of the work material observed during the cutting work. realizing the machining state diagnosis method which allows Rukoto to be grip the machining state bunch an object.
[0011]
[Means for Solving the Problems]
The present invention for achieving the above object, a time series model vibration generated from a pressurized Engineering system cutting ARMA (p, q) model: expressed by (Auto Regressive Moving Average autoregressive moving average model), the ARMA grasping the machining status by observing the model AR parameters are estimated Teisu shall.
[0012]
Furthermore, those that understand a fine machined surface roughness observing the AR parameters obtained by representing monitoring the vibration acceleration in the switching cutting machining ARMA model, estimates, predicts.
[0013]
As a specific solution, the present invention
(1) A step of inputting vibrations generated from a work material during cutting into a computer as an acceleration signal by an acceleration sensor, and a step of expressing a waveform obtained from the acceleration signal by the computer as an ARMA model which is a time series model. It is possible to grasp the machining state of the work material in real time by monitoring the variation of the AR parameter of the ARMA model that is involved in the mechanical parameters in the cutting process and changes according to the waveform obtained from the acceleration signal. Provided is a machining state diagnosis method in cutting processing characterized by the above.
(2) The waveform obtained from the acceleration signal is an acceleration waveform, and the time series model is an ARMA (4, 3) model having first to fourth order AR parameters and first to third order MA parameters. , by monitoring the variation of the AR parameters of ARMA (4,3) model that varies with the acceleration waveform, knowing the quality of surface finish of the workpiece which is proportional to the first-order AR parameters in real time The machining state diagnosis method in the cutting process according to the above (1) , characterized in that:
(3) The ARMA (4, 1) model in which the waveform obtained from the acceleration signal is the vertical vibration displacement of the work material, and the time-series model has a first-order to fourth-order AR parameter and a first-order MA parameter. By monitoring the fluctuation of the AR parameter of the ARMA (4, 1) model that changes due to vertical vibration displacement, the quality of the work surface roughness of the work material that is proportional to the primary AR parameter can be determined in real time. A method of diagnosing a machining state in the cutting process according to the above (1) , characterized by grasping .
(4) In the cutting process according to the above (1), by monitoring the variation of the AR parameter of the ARMA model, the processing state of the work material is grasped in real time and the degree of wear of the tool used for the cutting process is estimated. A machining state diagnosis method is provided.
[0014]
DETAILED DESCRIPTION OF THE INVENTION
Embodiments of a machining state diagnosis method in cutting according to the present invention will be described with reference to tables and drawings.
[0015]
First, in cutting with a machine tool, in order to grasp (monitor or control) the cutting state in real time, a vibration system at the time of cutting consisting of the tool 1, the work material 2, etc. is modeled, and the vibration It is considered to be extremely effective to observe the variation of the time series model parameters obtained by monitoring the factors governing the system, that is, the acceleration signal of vibration and performing the time series analysis using the time series model.
[0016]
Therefore, here, a dynamic machining model is set and its equation of motion is derived, and the relationship between the mechanical parameters of the machining model and the time series model parameters is derived.
[0017]
First, a transfer function by setting a dynamic model representing the changeover cutting machining as follows.
[0018]
As shown in FIG. 1, a mechanical model representing cutting of a work material 2 by a tool 1 in a machine tool 11 is a two-degree-of-freedom vibration system including a tool 1, a work material 2, and a machining part 3 representing a cutting process. It can be expressed approximately. Here, symbols m _i , c _i , and k _i represent mass, damping coefficient, and rigidity, respectively, and subscripts i 1, 2, and 3 represent a tool, a work material, and a processed part, respectively. Here, c ₃ of the processing portion 3 is attenuation coefficient including thermal, etc., k ₃ is equivalent to cutting resistance. The cutting resistance is represented by three combined forces of a main component force, a feed component force, and a back component force. Generally, the harder the workpiece 2 is, the greater the feed rate and the depth of cut are. Wherein _{m i,} c _{i, k} i is that dynamic parameters.
[0019]
The machine tool during cutting has complicated elements, and the cutting force f (t), which is an input to the vibration system of the dynamic model, is unknown. Therefore, the dynamic model is formulated with the input f (t) to the unknown tool 1 as white noise and the vibration acceleration observed from the work material 2 as an output.
[0020]
The equation of motion of the tool 1 in FIG.
[0021]
[Expression 1]

Here, the displacement _{x 1} of the tool 1 by input f is compared to the displacement _{x 2} of the workpiece 2 can be placed between _x 1 >> _{x 2} in approximately. Therefore, [Equation 1] is expressed by the following equation.
[0022]
[Expression 2]

On the other hand, the equation of motion of the work material 2 is expressed by the following equation.
[0023]
[Equation 3]

From the above equations [Equation 2] and [Equation 3], the equation of motion of the dynamic model representing the cutting work is as follows.
[0024]
[Expression 4]

Expression [Equation 4] is obtained from Laplace transform, and the transfer function H (s) of the dynamic model with the input as f (t) and the output as the acceleration of the displacement x ₂ (t) of the work material 2 is obtained as follows: .
[0025]
[Equation 5]

However, the coefficients A _i and B _i of the transfer function of the dynamic model are expressed by the following equations by the dynamic parameters m _i , k _i , and c _i .
[0026]
[Formula 6]

Then, to derive a discrete-time model of the dynamic model to show dynamic parameter m _i of time-series model parameters and the model of the acceleration _signal, k _i, or c _i is any relationship.
[0027]
Here, the dynamic model was discretized as follows, and a discrete-time model transfer function was derived.
[0028]
The transfer function H (s) of the dynamic model in FIG. 1 is expressed by the equation [Equation 5] and can be converted into the following equation.
[0029]
[Expression 7]

Here, P ₁ , P ₂ , Q ₁ and Q ₂ are constants.
[0030]
[Equation 8]

In other words, the impulse response h (t) of the transfer function H (s) is expressed by the following equation from the inverse Laplace transform of Equation [7].
[0031]
[Equation 9]

Here, by discretizing as t = nT (n = 0, 1, 2,...), Expression [Equation 9] becomes the following expression.
[0032]
[Expression 10]

Furthermore, the discrete time model transfer function H (z) of the dynamic model is expressed by the following equation from the Z transformation of the above equation [Equation 10].
[0033]
[Expression 11]

Here, from the equation [Equation 8],
[0034]
[Expression 12]

It is.
[0035]
Next, the relationship between the time series model parameter and the dynamic parameter when the vibration acceleration of the work material 2 observed at the time of cutting is represented by a time series model is obtained from the formula [Equation 11].
[0036]
As described above, when the input to the vibration system such as a machine tool is unknown and only the output of vibration acceleration from the vibration system is available, analysis using a time series model that considers the input as a white signal is effective , and the time series signal is typically a time-series model as follows ARMA (p, q) model: expressed as (Auto Regressive moving average autoregressive moving average model).
[0037]
[Formula 13]

Here, a _{i is referred} to as an AR parameter, and b _{i is referred} to as an MA parameter.
[0038]
On the other hand, the transfer function H (z) of the discrete time model of the dynamic model is expressed as follows from the formula [Equation 11].
[0039]
[Expression 14]

here,
[0040]
[Expression 15]

It is. Mechanical parameters from the above equation [Expression 15] is the formula [Formula 6] _{m i,} k _i, using a _{c i} is expressed by the following equation.
[0041]
[Expression 16]

Further, from the equation [Equation 13], the equation [Equation 14] corresponds to the ARMA (4, 3) model of the ARMA (p, q) model, and is expressed by the following equation.
[0042]
[Expression 17]

Therefore, the relational expression between the AR parameter , which is a time series model parameter , and the dynamic parameter is expressed by the following expression from Expression [Expression 14] and Expression [Expression 17].
[0043]
[Formula 18]

As described above, the AR parameter a _i when the acceleration signal observed at the time of processing is expressed by the ARMA (4, 3) model is the same as the dynamic parameters shown in FIG. 1 and the equations [Equation 16] and Equation [Equation 18]. There is a relationship. Here, it can be seen that almost all dynamic parameters are included as elements in the AR parameters a ₁ , a ₂ , a ₃ , and a ₄ in Expression [18]. That is, a _i is expressed as f (m _j , k _j , c _j ) as a function of m, k, and c.
[0044]
In the following, with reference to the actual cutting conditions, focusing on dynamic parameter k _3, c ₃ of the processing unit 3 that most influence the effect of the processing conditions of the AR parameters f in good or bad cutting state shown in FIG. 1 The behavior of the AR parameter is simulated by changing these parameters.
[0045]
In this simulation, the mechanical parameters of the tool 1 and the work material 2 in the machining model of FIG. 1 were set as shown in [Table 1] below based on the actual mass and physical property values.
[0046]
[Table 1]

In the following, parameters of the processed part 3 as simulation results are k ₃ = 0.8 × 10 ^{8 to} 1.6 × 10 ⁸ (N / m), c ₃ = 0.2 × 10 ^{6 to} 0.4 × 10. FIG. 2 shows how the AR parameters a ₁ , a ₂ , a ₃ , and a ₄ in the equation [Equation 18] change when ⁶ (Ns / m) is changed.
[0047]
From FIG. 2, it is considered that changes in k ₃ and c ₃ mainly appear in a _i because a ₂ , a ₃ , and a ₄ have almost no change compared to a ₁ . K _3, since the increase or decrease of the AR parameters by a change in c ₃ is clarity how the change in FIG. 2, the behavior of the following Table of the AR parameters when changing both k _3, c ₃ 2].
[0048]
[Table 2]

From the figure 2 and Table 2, the direction of change of the AR parameters a ₁ is found that is dominated by the increase or decrease of k _3, the relationship of k ₃ and AR parameter a ₁ is a linear relationship as shown in FIG. 3 Thus, it is expressed by the following approximate expression [Equation 19].
[0049]
[Equation 19]

Since the mechanical parameter k ₃ is a parameter corresponding to the cutting resistance, an increase in k ₃ corresponds to a condition such as an increase in the cutting depth, an increase in the feed rate, or an increase in the hardness of the work material 2. Although increase and decrease of c ₃ does not affect the orientation of the change of a _1, when the c ₃ is decreasing greater rate of change of the AR parameters a _1. This also considering that the attenuation coefficient c ₃ are related to thermal energy or the like which is dissipated from the processing unit 3, an energy who c ₃ is reduced is used for the cutting itself is large I can say that. Thus it is possible to predict and understand the cutting state in real time by observing the AR parameters a _1.
[0050]
Next, in order to ascertain how the changes in the mechanical parameters k ₃ and c ₃ are related to the cutting conditions, machining experiments of specific embodiments under various cutting conditions are shown in FIG. The machining state diagnosis system 10 was used.
[0051]
In FIG. 4, the machining state diagnosis system 10 performs various cutting operations on the workpiece 2 fixed to a clamp 14 on a support table 13 using an end mill 12 as a tool 1 attached to a spindle head 19 of a machine tool 11. Acceleration of vibration generated when machining under machining conditions is detected as an acceleration signal by an acceleration sensor 15 attached near the center of the side surface of the work material 2, for example, and recorded in a scope recorder 17 through an amplifier 16 and recorded. A system configuration in which the acceleration signal is taken into the personal computer 18 and signal processing for parameter analysis is performed based on the above-described equations [Equation 1] to [Equation 19] and equations [Equation 20] to [Equation 24] described later. It is.
[0052]
An example using alloy tool steel SKD11 mainly used for a cold mold as the work material 2 will be shown. [Table 3] shows the cutting conditions. Basically, the depth of cut was changed, and the acceleration of vibration generated by machining was measured.
[0053]
[Table 3]

FIG. 5 shows vibration acceleration waveforms (time domain) (left side) and their observed values for (a) when the cutting depth is 10 mm, (b) when the cutting depth is 30 mm, and (c) when the cutting depth is 42 mm. It is a power spectrum (frequency domain) (right side). The acceleration waveform tends to have a small amplitude when the depth of cut is the manufacturer's recommended condition.
[0054]
Next, using this acceleration waveform, the order of the ARMA (p, q) model is changed from p = 1 to 10 and q = 1 to 10 to perform time series analysis, and the AIC (Akaike information of each time series model). Standard) was calculated. This result is as shown in FIG. 6, and it can be seen that the time series model of the optimum vibration acceleration indicated by the black dots in FIG. 6 is represented by the ARMA (4, 3) model.
[0055]
FIG. 7 shows an analysis of the acceleration signal measured under the cutting conditions shown in Table 3 using the ARMA (4, 3) model, and shows four AR parameters a ₁ (measurement points ■) and a ₂ (measurement points) associated with changes in the cutting depth. ●), a ₃ (measurement point ▲), a ₄ (measurement point ◆) changes are shown.
[0056]
The AR parameters a ₁ , a ₂ , a ₃ , and a ₄ have minimum cutting depths as recommended by the manufacturer (30 mm). Since an increase in the cutting depth is proportional to an increase in cutting force, an increase in AR parameter represents an increase in cutting force. Further, when the cutting depth is decreased from the manufacturer's recommended value, the machining force is concentrated on the tip of the tool 1, the vibration of the tool 1 itself is increased, and the AR parameter is increased.
[0057]
FIG. 8 is a comparison of the AR parameters a ₁ , a ₂ , a ₃ , and a ₄ when using a normal tool (measurement point ●) and a worn tool (measurement point ■). Under the same cutting conditions, the absolute values of the four AR parameters are always greater for worn tools than for normal tools. This indicates that the degree of wear of the tool can be estimated from the AR parameter when the observed vibration acceleration is expressed by the ARMA model under the same cutting conditions.
[0058]
FIG. 9A shows the relationship between the four AR parameters according to the change of the cutting depth, using the cutting depth and the average value of the four AR parameters. FIG. 9B shows the relationship between the cutting depth and the machined surface roughness (maximum height Pz) instead of the average value of the AR parameter.
[0059]
As is clear from a comparison of FIGS. 9A and 9B, the average value of the AR parameter and the variation of Pz indicating the processed surface roughness due to the change of the cutting depth show the same tendency. That is, it can be seen that the average value of the AR parameter tends to increase if the processed surface roughness is poor. This indicates that the machined surface roughness representing the machining accuracy can be estimated from the average value of the AR parameter.
[0060]
Then, next, the derivation of the relational expression between the time series model parameter related to the mechanical model parameter and the machined surface roughness is examined.
[0061]
Cutting is a processing method that generates high stress inside the workpiece to cause destruction and separation. Of the energy added during processing, 60 to 65% is plastic deformation, 30 to 35% is surface energy, It becomes frictional heat. If this is expressed by using the limit shear stress τ _b and the dashpot c, the mechanical model of the machined part 3 at the time of cutting is expressed as model 1 in FIG. On the other hand, the model 2 in FIG. 10B represents the machining portion 3 in the dynamic model shown in FIG. 1 from the viewpoint of cutting resistance.
[0062]
Here, the model 1 and the deformation energy due to external forces of the model 2 are equal, the relationship between the working surface area ΔA occurring stiffness k ₃ and plastic deformation is expressed by the following equation: [Equation 20].
[0063]
[Expression 20]

On the other hand, the processed surface roughness Pz (maximum height of the cross-sectional curve) increases in proportion to the processed surface area, and is expressed as Pz∝ΔA. Therefore, the relationship between the dynamic parameters k ₃ machining surface roughness Pz is approximately expressed by the following equation.
[0064]
[Expression 21]

Using the equation [Equation 21], the equation [Equation 19] is expressed by the following equation.
[0065]
[Expression 22]

FIG. 11 shows the result of examining the relationship between the AR parameter when the acceleration signal at the time of cutting is expressed by the ARMA (4, 3) model and the actual machined surface roughness Pz. From FIG. 11, the relationship of the above equation [Equation 22] is recognized.
[0066]
Further, derivation of the relational expression between the time series model parameter and the machined surface roughness based on the machined surface roughness waveform is as follows.
[0067]
Assuming that the machined surface roughness Pz is generated in relation to the vertical vibration displacement x ₂ of the work material 2 in FIG. 1, this transfer function H ′ (s) = X ₂ (s) / F (s) Is expressed by the following equation from Equation [5].
[0068]
[Expression 23]

This pulse transfer function H ′ (z) is expressed by the following equation as an ARMA (4, 1) model.
[0069]
[Expression 24]

From the above equation [Equation 24], it can be seen that the machined surface roughness Pz is related to the AR parameter.
[0070]
FIG. 12 shows the result of examining the relationship between the AR parameter a ₁ ′ and the actual machined surface roughness Pz when the roughness waveform of the machined surface is represented by the ARMA (4, 1) model. Also in FIG. 12, it can be seen that the relationship shown in the formula [Equation 22] is recognized.
[0071]
Thus, from the above relationship, the signal of the acceleration sensor 15 installed on the work material 2 is measured during the cutting by the machine tool 11 in FIG. 4 and expressed as an ARMA model which is a time series model. It is possible to grasp, estimate and predict the machining state during the cutting process in real time from the change of the AR parameter.
[0072]
【The invention's effect】
In the machining state diagnosis method in cutting according to the present invention, as described above, vibration generated during cutting is measured by an acceleration sensor, and the acceleration signal is expressed as an ARMA model that is a time series model. when the AR parameters a series model parameter to grasp the good or bad of abnormal working and surface finish by monitoring in real time process diagnostic system can predict and diagnose.
[Brief description of the drawings]
FIG. 1 is a dynamic model that approximately represents cutting.
FIG. 2 is a simulation result showing changes in AR parameters a ₁ , a ₂ , a ₃ , and a ₄ when dynamic parameters k ₃ and c ₃ of the processed part are changed.
3 is a simulation result showing a relationship between the dynamic parameters k ₃ and AR parameters a _1.
FIG. 4 is a configuration diagram of a machining state diagnosis system for implementing a machining state diagnosis method in cutting according to the present invention.
FIG. 5 is an actual measurement diagram of a vibration acceleration waveform (time domain) (left side) and its power spectrum (frequency domain) (right side) observed by cutting with three depths of cut.
FIG. 6 is a diagram illustrating a calculation result of the order of a time series model by AIC.
FIG. 7 is a diagram showing changes in four AR parameters accompanying changes in the cutting depth by analyzing measured acceleration signals using an ARMA (4, 3) model.
FIG. 8 is a diagram showing a comparison of AR parameters a ₁ , a ₂ , a ₃ , and a ₄ when a normal tool and a worn tool are used.
FIG. 9A is a diagram showing the relationship between four AR parameters due to changes in the cutting depth, using the cutting depth and the average value of the four AR parameters, and FIG. It is a figure which shows the relationship with roughness (maximum height Pz).
10A is a mechanical model of a machined part at the time of cutting, and FIG. 10B is a mechanical model expressing the machined part in the mechanical model of FIG. 1 from the viewpoint of cutting resistance.
FIG. 11 is a diagram showing a result of examining a relationship between an AR parameter and an machining surface roughness Pz when an acceleration signal at the time of cutting is expressed by an ARMA (4, 3) model .
FIG. 12 is a diagram showing a result of examining a relationship between an AR parameter a ₁ ′ and a processed surface roughness Pz when a processed surface roughness waveform is expressed by an ARMA (4, 1) model .
[Explanation of symbols]
DESCRIPTION OF SYMBOLS 1 Tool 2 Work material 3 Machining part 10 Machining state diagnostic system 11 Machine tool 12 End mill 13 Support table 14 Clamp 15 Acceleration sensor 16 Amplifier 17 Scope recorder 18 Personal computer 19 Spindle head a _i ARMA (4,3) model of acceleration signal of AR parameters b _i acceleration signal ARMA (4,3) model MA parameters a ₁ 'surface finish waveform ARMA (4, 1) model AR parameters m _i mass (inertial parameters)
c _i damping coefficient (mechanical parameter)
k _i stiffness (mechanical parameter)
Pz Machining surface roughness (maximum height of cross-section curve)

Claims (4)

A step of inputting a vibration generated from a work material during cutting into a computer as an acceleration signal by an acceleration sensor, and a step of expressing a waveform obtained from the acceleration signal by the computer as an ARMA model which is a time series model, It is possible to grasp the machining state of the work material in real time by monitoring the change of the AR parameter of the ARMA model that is related to the mechanical parameters in the cutting process and changes according to the waveform obtained from the acceleration signal. A machining state diagnosis method in the cutting process. The waveform obtained from the acceleration signal is an acceleration waveform, and the time series model is an ARMA (4, 3) model having first to fourth order AR parameters and first to third order MA parameters, and an acceleration waveform. It is characterized in that the quality of the machined surface roughness of the work material that is proportional to the primary AR parameter can be grasped in real time by monitoring the fluctuation of the AR parameter of the ARMA (4, 3) model that varies depending on The machining state diagnosis method in cutting according to claim 1 . The waveform obtained from the acceleration signal is the vertical vibration displacement of the work material, and the time-series model is an ARMA (4, 1) model having a first-order to fourth-order AR parameter and a first-order MA parameter, By monitoring changes in the AR parameter of the ARMA (4, 1) model that changes due to vertical vibration displacement, it is possible to grasp in real time whether the work surface roughness of the work material is proportional to the primary AR parameter. The machining state diagnosis method in cutting according to claim 1 . 2. The machining state diagnosis method in machining according to claim 1, wherein the machining condition of the work material is grasped in real time and the degree of wear of the tool used for the machining is estimated by monitoring the fluctuation of the AR parameter of the ARMA model. .

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