JPH07111321B2 - Surface roughness evaluation method and device - Google Patents
Surface roughness evaluation method and deviceInfo
- Publication number
- JPH07111321B2 JPH07111321B2 JP2048558A JP4855890A JPH07111321B2 JP H07111321 B2 JPH07111321 B2 JP H07111321B2 JP 2048558 A JP2048558 A JP 2048558A JP 4855890 A JP4855890 A JP 4855890A JP H07111321 B2 JPH07111321 B2 JP H07111321B2
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- frequency band
- roughness
- sectional curve
- fourier spectrum
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Description
【発明の詳細な説明】 （産業上の利用分野） 本発明は、機械部品、光学部品などの物体の表面の粗さ
を評価する方法および装置に関する。BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method and an apparatus for evaluating the surface roughness of objects such as mechanical parts and optical parts.
（従来の技術） 従来、表面粗さの評価方法として、接触式、非接触式な
どの測定方法で物体の表面形状を示す断面曲線を求め、
該断面曲線から物体の表面粗さの程度を規定する量とし
て最大高さRmaxを算出するものがある。また、最大高さ
Rmaxに代えて中心線平均粗さＲ（ａ）や２乗平均粗さR
rmsなどを算出する評価方法もある。(Prior Art) Conventionally, as a surface roughness evaluation method, a cross-sectional curve showing the surface shape of an object is obtained by a contact method, a non-contact measurement method, or the like,
There is a method in which the maximum height R max is calculated as an amount that defines the degree of surface roughness of an object from the sectional curve. Also the maximum height
Instead of R max , centerline average roughness R (a) and root mean square roughness R
There is also an evaluation method that calculates rms .
接触式測定方法には、触針で物体の表面をトレースし、
物体の表面の凹凸に対応する触針の上下動を電気量に変
換し、該電気量の変化量に基づき断面曲線を求める触針
方法がある。In the contact-type measurement method, trace the surface of the object with a stylus,
There is a stylus method in which the vertical movement of the stylus corresponding to the unevenness of the surface of the object is converted into an electric quantity, and the sectional curve is obtained based on the amount of change in the electric quantity.
非接触式測定方法には、レーザ光を対物レンズで集光
し、対物レンズの焦点付近に配置されている物体の表面
から反射される光と参照面から反射される光の干渉光を
検出し、光の変化量に基づき断面曲線を求める位相干渉
方法がある。The non-contact measurement method is to collect the laser light with an objective lens and detect the interference light of the light reflected from the surface of the object placed near the focal point of the objective lens and the light reflected from the reference surface. , There is a phase interference method for obtaining a sectional curve based on the amount of change in light.
（発明が解決しようとする課題） 物体の表面の凹凸には周期性が存在することから、断面
曲線を複数の周波数成分を有する空間波としてみなすこ
とができる。(Problems to be Solved by the Invention) Since the unevenness of the surface of the object has periodicity, the sectional curve can be regarded as a spatial wave having a plurality of frequency components.
しかし、触針法による測定方法では、縦方向分解能すな
わち表面の凹凸に対する分解能および横方向分解能すな
わち表面の凹凸の周期性に対する分解能が触針の先端の
径、触針の上下方向の追従性能などによって決定され
る。これに対し、位相干渉法による測定方法では、その
縦方向分解能および横方向分解能がレーザ光のスポット
径などによって決定される。その結果、各測定方法の特
性（縦分解能、横分解能）はそれぞれ異なり、同じ物体
の表面に対し、触針法による測定方法で得られた断面曲
線を用いるときと、位相干渉法による測定方法で得られ
た断面曲線を用いるときとでは、同じ表面に対する粗さ
の評価が異なることがある。However, in the measurement method by the stylus method, the vertical resolution, that is, the resolution for surface irregularities and the lateral resolution, that is, the resolution for the periodicity of surface irregularities, depend on the tip diameter of the stylus, the vertical tracking performance of the stylus, etc. It is determined. On the other hand, in the measurement method by the phase interferometry, the vertical resolution and the horizontal resolution are determined by the spot diameter of the laser light and the like. As a result, the characteristics (longitudinal resolution, lateral resolution) of each measurement method are different, and when the cross-section curve obtained by the stylus method is used for the same object surface and when the phase interferometry method is used. Roughness evaluation for the same surface may differ from when the obtained cross-section curve is used.
また、互いに異なる表面から求められた最大高さRmax、
中心線平均粗さＲ（ａ）、２乗平均粗さRrmsの値がそれ
ぞれ一致するとき、各表面に対する粗さの評価は一致す
るが、各表面の断面曲線はそれぞれ異なることがある。
その結果、最大高さRmax、中心線平均粗さＲ（ａ）、２
乗平均粗さRrmsなどで表面粗さを評価するだけでは、表
面粗さに対応する表面の凹凸の性質を評価することがで
きない。Also, the maximum height R max obtained from different surfaces,
When the values of the centerline average roughness R (a) and the root-mean-square roughness R rms match, the roughness evaluations for each surface match, but the cross-sectional curves of each surface may differ.
As a result, the maximum height R max , the center line average roughness R (a), 2
It is not possible to evaluate the property of surface irregularities corresponding to the surface roughness only by evaluating the surface roughness by using the root- mean-square roughness R rms or the like.
本発明の目的は、測定法の相違による表面粗さの評価の
違いをなくすことができ、表面粗さに対応する表面の凹
凸の性質を特徴づけることができる表面粗さ評価方法お
よび装置を提供することにある。An object of the present invention is to provide a surface roughness evaluation method and apparatus capable of eliminating the difference in the evaluation of the surface roughness due to the difference in the measurement method and characterizing the property of the surface roughness corresponding to the surface roughness. To do.
（課題を解決するための手段） 本発明の表面の粗さ評価方法は、機械部品などの物体の
表面形状を測定する表面形状測定手段で前記表面形状を
示す断面曲線を求め、該断面曲線を高速フーリエ変換に
よってフーリエスペクトルに展開し、該フーリエスペク
トルに応じて少なくとも２つの所定の周波数帯域を設定
し、前記各周波数帯域に対応するフーリエスペクトルの
逆フーリエ変換によって該各周波数帯域における断面曲
線をそれぞれ生成し、該各周波数帯域の断面曲線から物
体の表面の粗さを規定する量として中心線平均粗さＲ
（ａ）及び２乗平均粗さRrmsのうちの少なくとも一方を
該各周波数帯域ごとに算出する。(Means for Solving the Problem) The surface roughness evaluation method of the present invention obtains a cross-sectional curve showing the surface shape by a surface shape measuring means for measuring the surface shape of an object such as a machine part, and calculates the cross-sectional curve. The Fourier spectrum is expanded by the fast Fourier transform, at least two predetermined frequency bands are set according to the Fourier spectrum, and the cross-sectional curve in each frequency band is respectively calculated by the inverse Fourier transform of the Fourier spectrum corresponding to each frequency band. The center line average roughness R is generated as an amount that defines the roughness of the surface of the object from the cross-section curve of each frequency band.
At least one of (a) and the root mean square roughness R rms is calculated for each frequency band.
本発明の表面粗さ評価装置は、機械部品などの物体の表
面形状を測定し、該表面形状を示す断面曲線を生成する
表面形状測定手段と、該表面形状測定手段から前記断面
曲線が与えられ、該断面曲線を高速フーリエ変換によっ
てフーリエスペクトルに展開する波形解析手段と、該波
形解析手段から各フーリエスペクトルが与えられ、該フ
ーリエスペクトルに応じて少なくとも２つの所定の周波
数帯域を設定する周波数帯域設定手段と、前記波形解析
手段から各フーリエスペクトルが与えられかつ前記周波
数帯域設定手段から前記所定の周波数帯域が与えられ、
前記各周波数帯域に対応するフーリエスペクトルの逆フ
ーリエ変換によって該各周波数帯域における断面曲線を
それぞれ生成する波形生成手段と、該波形生成手段から
前記各周波数帯域の断面曲線が与えられ、該各周波数帯
域の断面曲線から前記物体の表面の粗さを規定する量と
して中心線平均粗さＲ（ａ）及び２乗平均粗さRrmsのう
ちの少なくとも一方を該各周波数帯域ごとに算出する。The surface roughness evaluation device of the present invention measures the surface shape of an object such as a machine part, and a surface shape measuring means for generating a sectional curve showing the surface shape, and the surface shape measuring means provides the sectional curve. Waveform analysis means for expanding the cross-section curve into a Fourier spectrum by fast Fourier transform, and frequency band setting for setting at least two predetermined frequency bands in accordance with the Fourier spectrum given by the waveform analysis means Means, each Fourier spectrum is given from the waveform analysis means, and the predetermined frequency band is given from the frequency band setting means,
Waveform generating means for respectively generating a sectional curve in each frequency band by inverse Fourier transform of a Fourier spectrum corresponding to each frequency band, and a sectional curve of each frequency band is given from the waveform generating means, and each frequency band At least one of the center line average roughness R (a) and the root mean square roughness R rms is calculated for each frequency band as an amount that defines the roughness of the surface of the object from the cross-section curve.
（作用） 表面形状測定手段で求められた断面曲線は表面の凹凸の
高さを表わし、その凹凸には周期性が存在するから、前
記断面曲線を複数の周波数成分を有する空間波とみなす
ことがきでる。(Function) The cross-sectional curve obtained by the surface shape measuring means represents the height of the unevenness on the surface, and since the unevenness has periodicity, the cross-sectional curve can be regarded as a spatial wave having a plurality of frequency components. Out.
次に、前記断面曲線を処理する手順について説明する。
前記断面曲線を関数ｈ（ｘ）とすると、関数ｈ（ｘ）は
次の（１）式で表わされる。Next, a procedure for processing the section curve will be described.
The function h (x) is expressed by the following equation (1), where the section curve is the function h (x).
関数ｈ（ｘ）をフーリエスペクトルに展開すると、 ｈ（ｘ）＝a0cosω0x＋a1cosω1x＋… ＋ancosωnx＋b0sinω0x＋… ＋bnsinωnx ……（２） （２）式で表示されているｈ（ｘ）の周波数成分（スペ
クトル）の分布が求められる。 If you expand the function h (x) to Fourier spectrum, h (x) = a 0 cosω 0 x + a 1 cosω 1 x + ... + a n cosω n x + b 0 sinω 0 x + ... + b n sinω n x ...... (2) (2) The distribution of the frequency component (spectrum) of h (x) represented by the formula is obtained.
次いで、前記周波数成分の分布に応じて周波数帯域（ω
ｒ＜ωｍ＜ωｓ）を設定し、該周波数帯域におけるフー
リエスペクトルを（２）式から抽出する。抽出されたフ
ーリエスペクトルを用いて逆フーリエ変換すると、前記
周波数帯域における断面曲線hm（ｘ）が次の（３）式か
ら求められる。Then, depending on the distribution of the frequency components, the frequency band (ω
r <ω m <ω s ) is set, and the Fourier spectrum in the frequency band is extracted from the equation (2). When the inverse Fourier transform is performed using the extracted Fourier spectrum, the sectional curve h m (x) in the frequency band is obtained from the following equation (3).
（３）式で表わされる周波数帯域別の断面曲線からその
中心線平均粗さＲ′（ａ）、２乗平均粗さＲ′rmsなど
の周波数帯域別の量を算出することにより、各周波数帯
域別の量を用いて表面粗さを評価することができる。 By calculating the amount for each frequency band such as the center line average roughness R ′ (a) and the root mean square roughness R ′ rms from the cross sectional curve for each frequency band represented by the formula (3), Other amounts can be used to assess surface roughness.
（実施例） 第１図は本発明の表面粗さ評価装置の一実施例を示すブ
ロック図、第２図は第１図の表面粗さ評価装置に用いら
れている表面形状測定手段の検知部の概要を示す図であ
る。(Embodiment) FIG. 1 is a block diagram showing an embodiment of the surface roughness evaluation device of the present invention, and FIG. 2 is a detection unit of the surface shape measuring means used in the surface roughness evaluation device of FIG. It is a figure which shows the outline | summary.
表面粗さ評価装置は、第１図に示すように、表面形状測
定手段10を備える。表面形状測定手段10は、第２図に示
すように、触針12でスキッド14に対する表面16の高さの
変化を測定し、表面16の凹凸に対応する触針12の上下動
をそれに対応する電気信号に変換する検知部18を有す
る。検知部18の電気信号は処理部20に与えられ、処理部
20は前記電気信号に基づき表面16の凹凸を示す断面曲線
を生成する。The surface roughness evaluation device is provided with a surface shape measuring means 10 as shown in FIG. As shown in FIG. 2, the surface shape measuring means 10 measures changes in the height of the surface 16 with respect to the skid 14 with the stylus 12, and corresponds to the vertical movement of the stylus 12 corresponding to the unevenness of the surface 16. It has a detection unit 18 for converting into an electric signal. The electric signal of the detection unit 18 is given to the processing unit 20,
20 generates a cross-sectional curve showing the unevenness of the surface 16 based on the electric signal.
表面形状測定手段10の処理部20で生成された断面曲線
は、波形解析手段22に与えられる。波形解析手段22は、
前記断面曲線を高速フーリエ変換によってフーリエスペ
クトルに展開する。The sectional curve generated by the processing unit 20 of the surface shape measuring unit 10 is given to the waveform analyzing unit 22. The waveform analysis means 22 is
The cross section curve is developed into a Fourier spectrum by a fast Fourier transform.
前記断面曲線を表わす関数をｈ（ｘ）とするとき、前記
断面曲線は複数の周波数成分を含む空間波とみなされる
ことにより、前記断面曲線を表わす関数ｈ（ｘ）は高速
フーリエ変換によって次の（４）式で、示されるから、 （４）式よりｈ（ｘ）の周波数成分の分布を得ることが
できる。When the function representing the cross section curve is h (x), the cross section curve is regarded as a spatial wave including a plurality of frequency components, and thus the function h (x) representing the cross section curve is given by the following fast Fourier transform. Since it is shown by the equation (4), The distribution of the frequency component of h (x) can be obtained from the equation (4).
波形解析手段22で得られた周波数成分の分布は、周波数
帯域設定手段24および波形生成手段26に与えられる。周
波数帯域設定手段24は波形解析手段22で得られた周波数
成分の分布に応じて少なくとも１つの周波数帯域を設定
し、該周波数帯域に対応する帯域情報を出力する前記断
面曲線から表面うねりのようにピッチの大きい波の成分
を除去するために、周波数帯域設定手段24に周波数帯域
の下限値を定める下限周波数ωLLを予め設定することが
好ましい。The distribution of frequency components obtained by the waveform analysis means 22 is given to the frequency band setting means 24 and the waveform generation means 26. The frequency band setting means 24 sets at least one frequency band according to the distribution of the frequency components obtained by the waveform analysis means 22, and outputs the band information corresponding to the frequency band from the cross-section curve like a surface waviness. In order to remove a wave component having a large pitch, it is preferable to preset the lower limit frequency ω LL that determines the lower limit value of the frequency band in the frequency band setting means 24.
周波数帯域設定手段24から出力される帯域情報は波形生
成手段26に与えられる。波形生成手段26は、前記帯域情
報に基づき関数ｈ（ｘ）の周波数成分の分布から前記帯
域情報が示す周波数帯域に含まれる周波数成分を抽出
し、該抽出された周波数成分を逆にフーリエ変換するこ
とによって前記帯域情報が示す周波数帯域における周波
数帯域別断面曲線を生成する。例えば、周波数帯域設定
手段24が次の（５）式で示される周波数帯域を設定する
とき、 ωｒ＜ωｍ＜ωｓ 波形生成手段26が生成する周波数帯域別の断面曲線を表
わす関数hm（ｘ）は次の（６）式で示される。The band information output from the frequency band setting means 24 is given to the waveform generating means 26. The waveform generating means 26 extracts frequency components included in the frequency band indicated by the band information from the distribution of frequency components of the function h (x) based on the band information, and inversely Fourier transforms the extracted frequency components. As a result, a sectional curve for each frequency band in the frequency band indicated by the band information is generated. For example, when the frequency band setting means 24 sets the frequency band represented by the following equation (5), ω r <ω m <ω s The function h m representing the sectional curve for each frequency band generated by the waveform generation means 26 (X) is expressed by the following equation (6).
波形生成手段26で生成された周波数帯域別の断面曲線お
よびその周波数帯域に対応する帯域情報は演算手段28に
与えられる。演算手段28は、前記周波数帯域別の断面曲
線に基づき表面16の粗さを規定する周波数帯域別の量を
算出する。例えば、前記周波数帯域における中心線平均
粗さRm（ａ）、２乗平均粗さRmrmsなどが前記周波数帯
域別断面曲線から算出される。前記周波数帯域別の断面
曲線、その周波数帯域に対応する帯域情報および前記周
波数帯域別の粗さ量は演算手段28から表示部30へ出力さ
れる。 The sectional curve for each frequency band generated by the waveform generating means 26 and the band information corresponding to the frequency band are given to the calculating means 28. The calculating means 28 calculates the amount for each frequency band that defines the roughness of the surface 16 based on the cross-sectional curve for each frequency band. For example, the center line average roughness R m (a), the root mean square roughness R mrms, and the like in the frequency band are calculated from the frequency band-based sectional curves. The section curve for each frequency band, the band information corresponding to the frequency band, and the roughness amount for each frequency band are output from the calculating unit 28 to the display unit 30.
表示部30は、前記周波数帯域別の断面曲線、周波数帯域
に対応する帯域情報および前記周波数帯域別の粗さ量を
表示する。The display unit 30 displays the sectional curve for each frequency band, band information corresponding to the frequency band, and the roughness amount for each frequency band.
表面粗さ評価装置を用いてシリコンウェハーの表面の凹
凸を測定し、その表面粗さを評価するとき、第３図〜第
５図に示すように、各周波数帯域における周波数帯域別
の断面曲線および周波数帯域別の粗さ量が求められる。
第３図は第１図の表面粗さ評価装置によって得られたシ
リコンウェハーの表面の所定の周波数帯域における断面
曲線を示す図、第４図は第３図の周波数帯域と異なる他
の周波数帯域における断面曲線を示す図、第５図は第３
図の周波数帯域と異なるさらに他の周波数帯域における
断面曲線を示す図である。When measuring the unevenness of the surface of a silicon wafer using a surface roughness evaluation device and evaluating the surface roughness, as shown in FIGS. 3 to 5, cross-sectional curves for each frequency band in each frequency band and The amount of roughness for each frequency band is obtained.
FIG. 3 is a diagram showing a sectional curve in a predetermined frequency band of the surface of the silicon wafer obtained by the surface roughness evaluation apparatus of FIG. 1, and FIG. 4 is another frequency band different from the frequency band of FIG. Figure showing the cross-section curve, Figure 5 is the third
It is a figure which shows the cross-section curve in another frequency band different from the frequency band of a figure.
第３図に示す断面曲線32、第４図に示す断面曲線34およ
び第５図に示す断面曲線36から算出される周波数帯域別
の粗さ量を第１表に示す。Table 1 shows the roughness amount for each frequency band calculated from the sectional curve 32 shown in FIG. 3, the sectional curve 34 shown in FIG. 4 and the sectional curve 36 shown in FIG.
第１表からシリコンウェハーの測定表面を長い波長帯域
（低い周波数帯域）で粗い面であり、短い波長帯域（高
い周波数帯域）で滑かな面であると評価しまた特徴づけ
ることができる。 From Table 1 it can be evaluated and characterized that the measurement surface of the silicon wafer is a rough surface in the long wavelength band (low frequency band) and a smooth surface in the short wavelength band (high frequency band).
なお、本実施例では触針式の表面形状測定手段10を用い
ているが、それに代えて光学式などの表面形状測定手段
を用いることができる。光学式の表面形状測定手段で得
られた断面曲線を、触針式の表面形状測定手段10で得ら
れた断面曲線と同様に、高速フーリエ交換によってフー
リエスペクトルに展開することにより、逆フーリエ変換
によって所定の周波数帯域に対応するフーリエスペクト
ルから該周波数帯域における断面曲線が生成されるか
ら、前記周波数帯域別の断面曲線から算出される周波数
帯域別の粗さ量を用いて表面粗さを評価することができ
る。Although the stylus type surface shape measuring means 10 is used in the present embodiment, an optical type surface shape measuring means can be used instead. The cross-sectional curve obtained by the optical surface shape measuring means, similarly to the cross-sectional curve obtained by the stylus type surface shape measuring means 10, by developing into a Fourier spectrum by fast Fourier exchange, by the inverse Fourier transform Since the cross-section curve in the frequency band is generated from the Fourier spectrum corresponding to the predetermined frequency band, the surface roughness is evaluated using the roughness amount for each frequency band calculated from the cross-section curve for each frequency band. You can
同一の表面を触針式の表面形状測定手段10および光学式
の表面形状測定手段でそれぞれ測定するとき、触針式の
表面形状測定手段10の縦方向分解能および横方向分解能
は触針12の先端の径、触針12の上下方向の追従性能など
によって決定され、光学式の表面形状測定手段の縦方向
分解能および横方向分解能はレーザ光のスポット径など
によって決定されることにより、各表面形状測定手段か
ら得られる断面曲線は互いに異なる。しかし、各断面曲
線に対して同じ周波数帯域を設定し、同一周波数帯域に
おける断面曲線のそれぞれを求めることにより、一方の
断面曲線から算出されたRmmax、Rm（ａ）,Rmrmsと他方
の断面曲線から算出されたＲ′mmax、Ｒ′ｍ（ａ）、
Ｒ′mrmsとを同一の周波数帯域において比較することが
できるから、その比較結果に基づき測定方法の相違に起
因する各分解能の差をなくすることができる。その結
果、表面形状測定手段の測定方法の相違による表面粗さ
の評価結果の違いをなくすことができる。When measuring the same surface with the stylus type surface shape measuring means 10 and the optical type surface shape measuring means respectively, the longitudinal resolution and the lateral resolution of the stylus type surface shape measuring means 10 are the tip of the stylus 12. Diameter, the vertical tracking performance of the stylus 12, etc., and the longitudinal resolution and lateral resolution of the optical surface profile measuring means are determined by the spot diameter of the laser beam, etc. The cross-section curves obtained from the means are different from each other. However, by setting the same frequency band for each section curve and obtaining each section curve in the same frequency band, R mmax , R m (a), R mrms calculated from one section curve and the other section curve are calculated. calculated from the cross section curve the R 'mmax, R' m ( a),
Since R ′ mrms can be compared with each other in the same frequency band, it is possible to eliminate the difference in each resolution due to the difference in the measuring method based on the comparison result. As a result, it is possible to eliminate the difference in the evaluation result of the surface roughness due to the difference in the measuring method of the surface shape measuring means.
（発明の効果） 本発明の表面粗さ評価方法および装置によれば、各周波
数帯域別の断面曲線から各周波数帯域における表面粗さ
を規定する量を算出することにより、各周波数帯域別の
量を用いて表面粗さを評価することができるから、表面
形状測定手段の測定方式の相違による表面粗さの評価の
違いをなくすことができ、表面粗さに対応する表面の凹
凸の性質を特徴づけることができる。(Effect of the Invention) According to the surface roughness evaluation method and apparatus of the present invention, the amount for each frequency band is calculated by calculating the amount that defines the surface roughness in each frequency band from the sectional curve for each frequency band. Since it is possible to evaluate the surface roughness using, it is possible to eliminate the difference in the evaluation of the surface roughness due to the difference in the measurement method of the surface shape measuring means, and to characterize the nature of the unevenness of the surface corresponding to the surface roughness. Can be attached.
第１図は本発明の表面粗さ評価装置の一実施例を示すブ
ロック図、第２図は第１図の表面粗さ評価装置に用いら
れている表面形状測定手段の検知部の概要を示す図、第
３図は第１図の表面粗さ評価装置によって得られたシリ
コンウェハーの表面の周波数帯域における断面曲線を示
す図、第４図は第３図の周波数帯域と異なる他の周波数
帯域における断面曲線を示す図、第５図は第３図の周波
数帯域と異なるさらに他の周波数帯域における断面曲線
を示す図である。 10……表面形状測定手段、22……波形解析手段、24……
周波数帯域設定手段、26……波形生成手段、28……演算
手段。FIG. 1 is a block diagram showing an embodiment of the surface roughness evaluation apparatus of the present invention, and FIG. 2 shows an outline of the detection unit of the surface shape measuring means used in the surface roughness evaluation apparatus of FIG. 3 and FIG. 3 are diagrams showing cross-sectional curves in the frequency band of the surface of the silicon wafer obtained by the surface roughness evaluation apparatus of FIG. 1, and FIG. 4 is another frequency band different from the frequency band of FIG. FIG. 5 is a diagram showing a sectional curve, and FIG. 5 is a diagram showing a sectional curve in yet another frequency band different from the frequency band in FIG. 10 …… Surface shape measuring means, 22 …… Waveform analyzing means, 24 ……
Frequency band setting means, 26 ... Waveform generating means, 28 ... Computing means.
Claims (2)
表面形状測定手段で前記表面形状を示す断面曲線を求
め、該断面曲線を高速フーリエ変換によってフーリエス
ペクトルに展開し、該フーリエスペクトルに応じて少な
くとも２つの所定の周波数帯域を設定し、前記各周波数
帯域に対応するフーリエスペクトルの逆フーリエ変換に
よって該各周波数帯域における断面曲線をそれぞれ生成
し、該各周波数帯域の断面曲線から物体の表面の粗さを
規定する量として中心線平均粗さＲ（ａ）及び２乗平均
粗さRrmsのうちの少なくとも一方を該各周波数帯域ごと
に算出する表面粗さ評価方法。1. A surface profile measuring means for measuring the surface profile of an object such as a machine part is used to obtain a sectional curve showing the surface profile, the sectional curve is developed into a Fourier spectrum by a fast Fourier transform, and the Fourier spectrum is determined according to the Fourier spectrum. At least two predetermined frequency bands are set, and a cross-sectional curve in each frequency band is generated by inverse Fourier transform of the Fourier spectrum corresponding to each frequency band. A surface roughness evaluation method for calculating, for each frequency band, at least one of a center line average roughness R (a) and a root mean square roughness R rms as an amount defining the roughness.
該表面形状を示す断面曲線を生成する表面形状測定手段
と、該表面形状測定手段から前記断面曲線が与えられ、
該断面曲線を高速フーリエ変換によってフーリエスペク
トルに展開する波形解析手段と、該波形解析手段から各
フーリエスペクトルが与えられ、該フーリエスペクトル
に応じて少なくとも２つの所定の周波数帯域を設定する
周波数帯域設定手段と、前記波形解析手段から各フーリ
エスペクトルが与えられかつ前記周波数帯域設定手段か
ら前記所定の周波数帯域が与えられ、前記各周波数帯域
に対応するフーリエスペクトルの逆フーリエ変換によっ
て該各周波数帯域における断面曲線をそれぞれ生成する
波形生成手段と、該波形生成手段から前記各周波数帯域
の断面曲線が与えられ、該各周波数帯域の断面曲線から
前記物体の表面の粗さを規定する量として中心線平均粗
さＲ（ａ）及び２乗平均粗さRrmsのうちの少なくとも一
方を該各周波数帯域ごとに算出する演算手段とを有する
表面粗さ評価装置。2. A surface shape of an object such as a mechanical part is measured,
Surface shape measuring means for generating a sectional curve showing the surface shape, and the sectional curve is given from the surface shape measuring means,
Waveform analysis means for expanding the cross-section curve into a Fourier spectrum by fast Fourier transform, and frequency band setting means for giving each Fourier spectrum from the waveform analysis means and setting at least two predetermined frequency bands in accordance with the Fourier spectrum And each Fourier spectrum is given from the waveform analysis means and the predetermined frequency band is given from the frequency band setting means, and a sectional curve in each frequency band is obtained by inverse Fourier transform of the Fourier spectrum corresponding to each frequency band. And a centerline average roughness as an amount that defines the roughness of the surface of the object from the sectional curve of each frequency band given from the waveform generating means. R (a) and the mean square respective frequency bands at least one of the roughness R rms Surface roughness evaluation device and a calculating means for calculating each time.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| JP2048558A JPH07111321B2 (en) | 1990-02-28 | 1990-02-28 | Surface roughness evaluation method and device |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| JP2048558A JPH07111321B2 (en) | 1990-02-28 | 1990-02-28 | Surface roughness evaluation method and device |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| JPH03251701A JPH03251701A (en) | 1991-11-11 |
| JPH07111321B2 true JPH07111321B2 (en) | 1995-11-29 |
Family
ID=12806713
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| JP2048558A Expired - Lifetime JPH07111321B2 (en) | 1990-02-28 | 1990-02-28 | Surface roughness evaluation method and device |
Country Status (1)
| Country | Link |
|---|---|
| JP (1) | JPH07111321B2 (en) |
Families Citing this family (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP4445215B2 (en) * | 2003-06-06 | 2010-04-07 | 住友ゴム工業株式会社 | Method for inspecting unevenness of tire side |
| JP2005344928A (en) * | 2004-05-07 | 2005-12-15 | Koyo Seiko Co Ltd | Oil seal and sealing structure including this oil seal |
| JP4850486B2 (en) * | 2005-11-07 | 2012-01-11 | 公益財団法人鉄道総合技術研究所 | Method for calculating actual shape of vehicle travel path and method for calculating repair amount of vehicle travel path |
| JP4737099B2 (en) * | 2007-01-26 | 2011-07-27 | トヨタ自動車株式会社 | Robot and robot control apparatus and control method |
| JP2018013445A (en) * | 2016-07-22 | 2018-01-25 | 株式会社ミツバ | Shape evaluation method of vertebra |
| JP7186109B2 (en) * | 2019-02-21 | 2022-12-08 | 中国塗料株式会社 | Roughness profile evaluation method, roughness analysis device, roughness analysis program, roughness measurement method and roughness measurement device |
| EP4074999A4 (en) * | 2019-12-12 | 2022-12-28 | Sumitomo Electric Industries, Ltd. | Sliding member and method for producing same |
Family Cites Families (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JPS5912309A (en) * | 1982-07-12 | 1984-01-23 | Kawasaki Steel Corp | Method for detecting abnormal part of profile of belt shaped body |
-
1990
- 1990-02-28 JP JP2048558A patent/JPH07111321B2/en not_active Expired - Lifetime
Also Published As
| Publication number | Publication date |
|---|---|
| JPH03251701A (en) | 1991-11-11 |
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