JP2576007B2 - Surface roughness measuring device - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a surface roughness measuring device, and more particularly to an improvement of a low-pass filter for extracting a undulating curve segment from a sectional curve.

[0002]

2. Description of the Related Art A surface roughness measuring device used for evaluating the surface processing accuracy of various machined products is shown in FIG. 13 (a) or (b).
It is configured as follows. These are examples of the stylus type. FIG. 13A shows a stylus 1 for tracing the surface of an object to be measured, a detector 2 for converting the vibration detected by the stylus 1 into an electric signal and amplifying it, and filtering the output of the detector 2. It comprises an analog filter 3, an A / D converter 4 for converting a filtered signal into a digital signal, and a data processing unit 5 for processing the converted digital data. FIG. 13B shows a case where a filtering process is performed digitally in the data processing unit 4 without using an analog filter.

The signal waveform detected by the detector 2 is called a cross-sectional curve shown in FIG. 14 (a), and this cross-sectional curve has a low frequency as shown in FIGS. 14 (b) and 14 (c). Includes undulation curves and high frequency roughness curves. A roughness curve corresponds to a small uneven component corresponding to the surface roughness.
A low-pass filter is used to determine the undulation curve from the cross-sectional curve, and a high-pass filter is used to determine the surface roughness. When a low-pass filter for obtaining a undulation curve is used, the surface roughness curve can also be obtained by subtracting the output of the low-pass filter from the original signal. The analog filter 3 shown in FIG. 13A is for performing such a filtering process.
In (b), this is performed digitally in the data processing unit 4.

As described above, the surface roughness curve is obtained by cutting a waviness curve component longer than a certain wavelength, and the wavelength is called a cutoff value. Regarding the characteristics of a low-pass filter for obtaining a waviness curve for performing surface roughness measurement, standards are defined both domestically and internationally.
That is, since the spatial distribution of the cross-sectional curve amplitude is statistically represented by a Gaussian distribution, the case where the filter characteristic (window function) represented in the spatial domain takes the same form as this is defined as an ideal state (Gaussian filter). The standard requires that the error from the Gaussian filter be within a certain range.

In the analog filter system shown in FIG. 13 (a), it is conventionally known that, when RC filters having the same time constant are connected in cascade infinitely, the filter characteristics approach an ideal Gaussian filter without limit. On the other hand, recently, digital filtering processing in computer software using the method shown in FIG. 13B has become mainstream. Specifically, a method has been proposed in which a Gaussian filter is realized approximately by connecting two-stage filters in cascade.

[0006]

However, as a secondary filter, for example, a normal infinite impulse response filter (I
In a method of obtaining a window function of a triangle approximation using an IR filter, an error still remains. When a finite impulse response filter (FIR filter) is used, the error can be further reduced. However, in that case, the number of operations becomes extremely large, and therefore, an extremely long operation time is required. The present invention
An object of the present invention is to provide a surface roughness measuring device including a low-pass filter capable of performing a filtering process with a relatively short operation time and a small error with respect to a Gaussian filter.

[0007]

According to the present invention, a surface roughness is obtained by obtaining a swelling curve component from a cross-sectional curve of an object to be measured by a low-pass filter and subtracting the swelling curve component from an original signal to extract a roughness curve component. In the measuring device, the low-pass filter is configured by cascading two filters represented by a transfer function of the following equation (1) having an adjustment coefficient in a range of ζ = 0.7134 to 1.1083. It is characterized by. G (s) = 1 / {(αs / ωc) ² +2 (αs / ωc) +1} (1) s = jω ω = 2πf (f: frequency) ωc = 2πfc (fc: cutoff frequency) α = constant

In the present invention, more preferably, the adjustment coefficient 調整 is set in the range of ζ = 0.770 to 0.8918. In order to set the absolute value of the transfer function to 0.5 as the cutoff value (ω = ωc), that is, to set the amplitude transmissibility to 50%, the constant α satisfies the following expression (2). It is preferable to set. α ² = ｛(2ζ ² -1) ² +1｝ ^1/ 2-(2ζ ² -1) ... (2)

[0009]

According to the present invention, an adjustment coefficient ζ is introduced into the transfer function of a general second-order filter as shown by the equation (1), and this is set in the range of ζ = 0.7134 to 1.1083. By cascading two stages, it is possible to perform phase compensation and suppress an error from the Gaussian filter to 10% or less. Further, when ζ is set in the range of 0.7760 to 0.8918, the error can be suppressed to 5% or less. In particular, if the low-pass filter having the transfer function represented by the equation (1) is realized by the IIR filter, the filtering process with a small error from the Gaussian filter can be performed in a short calculation time.

[0010]

Embodiments of the present invention will be described below in detail. FIG. 1A shows a surface roughness measuring apparatus according to one embodiment. As shown in the figure, the apparatus comprises a stylus 11 for tracing the surface of a device under test, a detector 12 for converting a signal detected by the stylus 11 into an electric signal and amplifying the signal, and a digital output of the detector 12. An A / D converter 13 converts the digital data into a signal, and a data processing unit 14 processes the converted digital data. The digital processing unit 14 is, for example, a microcomputer, and two-stage IIR filters 151 and 152 are firstly configured in the software, and a swell curve component is extracted from the cross-sectional curve data detected here. Further, by performing data processing of subtracting the undulation component from the original signal, a roughness curve is obtained.

The digital filtering performed by the IIR filters 151 and 152 is the same as that performed by an analog filter represented by a transfer function in which an adjustment coefficient ζ is introduced as shown in the above equation (1). Prior to the specific digital processing, the filter characteristics of the embodiment will be described. First, when a filter having a transfer function in which the adjustment coefficient よ う な as described above is introduced is cascaded in two stages, the absolute value (amplitude transfer rate) of the transfer function becomes | G (ω) | ² = 1 / [｛1- ( αω / ωc) ^2} becomes ^{2 + 4ζ 2 (αω / ωc} ) 2] ... (3). From the equation (3), the relationship between α and に shown in the above equation (2) is obtained as a condition for setting the absolute value of the transfer function to 0.5 with the cutoff value ω = ωc.

Next, an error of this transfer function from the Gaussian filter is obtained by calculating the transfer function of equation (1) while variously changing the adjustment coefficient ζ. The calculation data will be specifically shown. FIGS. 2A and 2B show the relationship between the absolute error value | E | max and the adjustment coefficient ζ. (b) is an enlarged view of (a). From this calculation result, the error is 0.05 (ie, 5%) or less in the range of ζ = 0.770 to 0.8918. Also, ζ =
In the range of 0.7134 to 1.1083, the error is 0.1.
0 (ie, 10%) or less. Further, when the minimum error is obtained, ζ = 0.8133 and the minimum error is 0.029065.

FIGS. 3A and 3B show the relationship between the maximum value Emax of the error and the adjustment coefficient ζ, and FIGS. 4A and 4B show the minimum value Emin of the error.
5 (a) and 5 (b) show the relationship between the error width Emax−
This is the relationship between Emin and the adjustment coefficient ζ. In these figures, (b) is an enlarged view of (a). From the results of FIG. 5, the minimum value of the error width 0.037055 can be obtained by giving the adjustment coefficient ζ = 0.8256.

FIGS. 6A and 6B show the relationship between the mean value of the error and the adjustment coefficient 、, and FIGS. 7A and 7B show the relationship between the mean square value of the error and the adjustment factor ζ. In these figures, (b) is an enlarged view of (a).

From the above calculation results, it is assumed that, for example, an adjustment coefficient に す る = 0.8133 that minimizes the maximum value of the absolute error value is selected. At this time, the maximum value of the error is 0.008419, the minimum value of the error is −0.029062, the width of the error is 0.037481, the average value of the error is −0.005670, and the root mean square value of the error is 0.010937.

Next, when the adjustment coefficient ζ is selected as described above, the coefficient when the filter represented by this transfer function is actually constituted by an analog filter is obtained as follows. Drive speed v = 0.5 mm / sec Cutoff value (wavelength) λc = 0.8 mm Amplitude transmissivity at cutoff value 50% Number of sampling points per cutoff value 1000, Cutoff frequency fc = 0.625 Hz Sampling The interval is 1.6 msec.

When the transfer function of the analog filter is transformed to G (s) = G / (s ² + b 1 · s + b 0), its coefficients G, b 1 and b 0 are obtained as follows. G = ωc ² / α ² = 22.22827993 b1 = ωc / α = 7.8150663 b0 = ωc ² / α ² = 22.222827993

In this embodiment, the analog low-pass filter thus designed is digitally realized by software as described above. FIG. 2 shows a filtering processing flow at that time. First, when the above low-pass filter is approximated by a recursive digital filter (IIR filter), the calculation formula is as follows. y / x = G (a0 + a1z- ¹ + a2z- ² ) / (b0 + b1z- ¹ + b2z- ² ) (4) In this equation, x is input data of the filter, and y is output data of the filter. is there. Further, z ^-ix indicates i-th previous x. G, a0, a1, a2, b0, b1, b2 are constants.

From the coefficients of the analog filter designed above, the coefficients of the digital filter are obtained by the input impulse invariant method as follows. a0 = 0 a1 = 1.590023199 a2 = 0 b0 = 1.0 b1 = -1.987517195 b2 = 9.8857745G = 3.5564654

When an actual filter calculation is performed from equation (4), as described above, since a0 = a2 = 0, yi = G.a1.xi-1 -b1.yi-1 -b2.yi- 2… (5) Steps S1 to S7 in FIG. 2 correspond to the processing of the first stage IIR filter 151 in which n pieces of input data are x and intermediate output data are y.
First, in step S1, coefficients k1 (= G.a1) and k2 (=
b1) and k3 (= b2) are calculated. Step S2, S
The first, second and third terms on the right side of equation (5) are calculated in steps 3 and S4, respectively, and in step S5 intermediate output data yi based on equation (5) is obtained. The above calculation is repeated in order from the beginning up to the number of data n (S7). Steps S8 to S13 correspond to the processing of the IIR filter 152 in the second stage. The output data sequence zi is obtained by sequentially performing the data obtained above similarly from the end in accordance with the equation (5). This is the output of the low-pass filter with phase compensation.

The two-stage IIR filter 151 described above
, 152, the undulation curve is obtained as described above. Further, by subtracting the output of the low-pass filter from the original data in the data processing unit 14, the phase-compensated high-pass filter processing is performed, and the surface roughness is obtained.

In the above-described embodiment, a digital filter in which two-stage secondary filters are assembled by software is used. However, the present invention is not limited to this. The two-stage connection of the secondary filter represented by the above transfer function can be implemented digitally or analogly by hardware.
Such an embodiment will be specifically described below.

FIG. 9 shows an example of the configuration of a digital filter using bilinear transformation. a delay unit represented by z ⁻¹ , a 0,
It is composed of weighting circuits denoted by a1, a2, b1, and b2, and an adder / subtractor. The cutoff wavelength is λc,
Assuming that the sampling interval is λs, an adjustment coefficient ζ is introduced into each weight coefficient, and the following equation is obtained. However, A in the following equation is A = λs ² + 4ζαλcλs + (2αλc) ² . ^{a0 = λs 2 / A a1 =} 2a0 a2 = a0 b1 = {2λs 2 -2 (2αλc) 2} / A b2 = {λs 2 -4ζαλc λs + (2αλc) 2} /
A

FIG. 10 shows an example of the configuration of a digital filter using an impulse response invariant conversion. At this time, the weighting factor of each weighting circuit is as follows under the condition that the adjustment factor ζ ≦ 1. a1 = 1 + b1 + b2 b1 = -2 exp (-ζλs / αλc) · cos {(1- ζ 2) 1/2 λs / αλc} b2 = exp (-2 ζλs / αλc)

FIG. 11 shows a configuration example using an RC analog circuit. The values of each resistor and capacitor are set as follows by introducing the adjustment coefficient ζ. R1 = R2 = R (appropriate value) C1 = αλc / ζR C2 = αζλc / R

FIG. 12 shows an example of a configuration using another analog circuit. In this case, the values of each resistor and capacitor are set as follows. R1 = R2 = R3 = R (suitable value) C1 = 2αζλc / 3R C2 = 3αλc / 2ζR

Further, according to the present invention, as shown in FIG. 1 (b), a secondary filter of the first stage is constituted by an analog filter 16 and placed before the A / D converter 13, and the second stage is provided in the digital processing unit 14. May be assembled as the IIR filter 15. In the above, the case where the adjustment coefficient の of the first-stage filter and the adjustment coefficient の of the second-stage filter are equal has been described. However, these need not always be completely matched. In addition, the present invention can be variously modified and implemented without departing from the spirit thereof.

[0028]

As described above, according to the present invention, by using a low-pass filter in which a predetermined adjustment coefficient is introduced into a transfer function, it is possible to extract a waviness curve component with high accuracy in a short calculation time. A roughness measuring device can be provided.

[Brief description of the drawings]

FIG. 1 is a diagram showing a configuration of a surface roughness measuring device according to an embodiment of the present invention.

FIG. 2 is a flowchart of a filtering process of the embodiment of FIG. 1 (a).

FIG. 3 is a diagram illustrating a relationship between a maximum value of a filter characteristic error absolute value and an adjustment coefficient.

FIG. 4 is a diagram illustrating a relationship between a maximum value of a filter characteristic error and an adjustment coefficient.

FIG. 5 is a diagram illustrating a relationship between a minimum value of a filter characteristic error and an adjustment coefficient.

FIG. 6 is a diagram illustrating a relationship between a width of a filter characteristic error and an adjustment coefficient.

FIG. 7 is a diagram illustrating a relationship between an average value of a filter characteristic error and an adjustment coefficient.

FIG. 8 is a diagram illustrating a relationship between a root mean square value of a filter characteristic error and an adjustment coefficient.

FIG. 9 is a digital filter configuration according to another embodiment of the present invention.

FIG. 10 is a digital filter configuration according to another embodiment of the present invention.

FIG. 11 is an analog filter configuration according to another embodiment of the present invention.

FIG. 12 is an analog filter configuration according to another embodiment of the present invention.

FIG. 13 is a diagram showing a configuration of a conventional surface roughness measuring device.

FIG. 14 is an explanatory diagram of the principle of surface roughness measurement.

[Explanation of symbols]

11: stylus, 12: detector, 13: A / D converter, 14
... Digital data processing unit, 15 ... IIR filter, 1
6 ... Analog filter.

Claims (2)

(57) [Claims] 1. A surface roughness measuring device for obtaining a undulation curve component from a cross-sectional curve of an object to be measured by a low-pass filter and extracting the undulation curve component from an original signal to extract a roughness curve component. , Ζ = 0.7
A surface roughness measuring apparatus, comprising: a filter having an adjustment coefficient in a range of 134 to 1.1083 and represented by the following transfer function and cascaded in two stages. G (s) = 1 / {(αs / ωc) ² +2} (αs / ωc
) +1｝ s = jω ω = 2πf (f: frequency) ωc = 2πfc (fc: cutoff frequency) α = constant 2. The surface roughness measuring apparatus according to claim 1, wherein the constant α is set so as to satisfy the following equation. Serial ^{α 2 = {(2ζ 2 -1} ) 2 +1} 1/2 - (2ζ 2 -1)