JPH0719856A - Shape measuring apparatus - Google Patents

Abstract

PURPOSE:To make it possible to obtain the measured shape data at a constant pitch by efficiently correcting circular distortion based on the data of the displacement amount of a stylus. CONSTITUTION:In a measuring part 1, a stylus 5, which is operated in a circular pattern, is moved along the surface of a work 7, and the dispalcement amount data (z) of the stylus 5 are sampled at a specified interval and outputted. In a circular-distortion correcting part 2, the circular distortion caused by the circular action of the stylus is corrected based on the displacement amount data (z). In a constant-pitch processing part 3, a specified straight line or curve is applied on the corrected data z' and x' after the correction of the circular distortion, and re-sampling is performed at the constant pitch. In a trend removing part 4, a straight line or curve along the surface shape of the work 7 is applied on the displacement amount data z'', which are obtained by re-sampling, and the component of the applied straight line or curve is removed from the data z''.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a shape measuring machine for measuring a surface roughness of a work by moving a stylus operating in an arc along the surface of the work.

[0002]

2. Description of the Related Art This type of shape measuring machine measures the trajectory shape drawn by the tip of the stylus as the surface shape by detecting the vertical displacement of the stylus while sliding the stylus along the surface of the work. When the stylus operates in an arc with a predetermined point as a reference, if the vertical displacement of the stylus is large, it will be between the sliding contact position and displacement obtained as the measured value and the actual sliding contact position and displacement of the stylus tip. There is an error. This error is usually called arc distortion, and in the conventional shape measuring machine composed of an analog electronic circuit, the arc distortion is corrected using an arithmetic circuit.

[0003]

However, when such a conventional shape measuring apparatus converts a detected value into a digital value for use in subsequent data processing, it has the following problems. That is, since the circular arc distortion largely appears in the sliding contact direction of the stylus, even if the output after correcting the circular arc distortion through the arithmetic circuit is sampled at a constant time interval, the measured value should be sampled at a constant interval in the sliding contact direction. I can't.

The present invention has been made in order to solve such a problem, and a shape measuring machine capable of efficiently correcting an arc distortion from data of a displacement amount of a stylus to obtain shape measurement data of a constant pitch. The purpose is to provide.

[0005]

The shape measuring machine according to the present invention is a measuring means for sampling and outputting data of the displacement amount of the stylus at a predetermined interval while moving the arc-operated stylus along the surface of the work. And an arc distortion correction means for correcting the arc distortion of the stylus caused by the arc operation of the stylus based on the displacement amount of the stylus output from the measuring means, and the arc distortion correction means for correcting the arc distortion. A constant pitch processing means for applying a predetermined straight line or a curve to the sampling data of the displacement amount of the stylus afterwards and re-sampling at a constant pitch is provided.

Further, the shape measuring machine according to the present invention applies a straight line or a curve along the surface shape of the work to the data of the displacement amount obtained by re-sampling by the constant pitch processing means, and re-sampling. It is characterized by further comprising trend removing means for removing the fitted straight line or curved line component from the obtained displacement amount data.

[0007]

According to the present invention, the stylus displacement amount data is sampled at predetermined intervals, and the stylus arc distortion is digitally erased from the displacement amount data. When the circular arc distortion is removed, the corrected data shifts in the sliding contact direction and the displacement direction of the stylus. Therefore, the constant pitch processing means applies a straight line or a curve to the corrected data and resamples it at a constant pitch. Convert to data. This facilitates subsequent data processing, such as removal of trend curves.

[0008]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS A shape measuring machine according to an embodiment of the present invention will be described below with reference to the accompanying drawings. FIG. 1 is a block diagram showing a schematic configuration of the shape measuring machine of this embodiment. This measuring machine includes a measuring unit 1, an arc distortion correcting unit 2, a constant pitch processing unit 3, and a trend removing unit 4.

The measuring unit 1 is provided with a stylus arm 6 having a stylus 5 attached to its tip. The stylus arm 6 is driven in the X-axis direction in the figure by the drive device 8 so that the tip of the stylus 5 slides along the surface of the work 7. The position of the stylus arm 6 in the X-axis direction is detected by the linear encoder 9, and is output as position data x in the X-axis direction at regular time intervals. Further, the stylus arm 6 operates in an arc around the fulcrum P on the base end side in accordance with the displacement of the tip of the stylus 5 in the Z-axis direction in the figure. The amount of displacement in the Z-axis direction is detected by the differential transformer 10 that works together with the stylus arm 6. The output of the differential transformer 10 is synchronously detected by the synchronous detection circuit 11,
The A / D converter 12 samples at a constant time interval, converts the displacement amount data z into a digital value, and outputs the displacement amount data z.

The arc correction unit 2 corrects the position data x and the displacement amount data z output from the measuring unit 1 on the basis of the displacement amount data z, and outputs corrected data x ', z'. The constant pitch processing unit 3 executes a straight line or curve fitting process from the correction data x ′, z ′ from the circular arc correction unit 2,
The obtained straight line or curve is resampled at a constant pitch to generate and output constant pitch correction data z ″. The trend removing unit 4 uses the correction data z ″ output from the constant pitch processing unit 3 and the range curve. Are removed to output surface roughness data Δz.

Next, the processing of the circular arc correction unit 2 in the shape measuring apparatus configured as described above will be described. Figure 2
FIG. 6 is a diagram for explaining arc distortion of the stylus 5. If the length of the stylus 5 is H and the length from the fulcrum P of the stylus arm 6 to the base end of the stylus 5 is L, X when the stylus arm 6 is tilted by an angle θ from the state parallel to the X axis. The error dx in the axial direction and the error dz in the Z-axis direction can be expressed by the following formula 1.

[0012]

## EQU1 ## dx = L (1-cos θ) -H sin θ dz = H (1-cos θ)

Here, dx can be modified as follows.

[0014]

[Expression 2] dx = L {1-√ (1-sin ² θ)} − H sin θ √ (1-sin ² θ) = √ (1-X) = f (X), f (X) ≈ f (0) + {f '(0) / 1! } X + {f ″ (0) /
2! } X ² f '(X) = ( ^-1/2 ) (1-X) ^-1/2 f "(X) = (-1/4) (1-X) ^-3/2 f' (0) = -1 / 2 f "(0 ) = - 1/4 ∴f (X) ≒ 1-X / 2-X 2/8 = 1- sin 2 θ / 2- sin 4 θ / 8 ∴dx ≒ L { 1-√ (1-sin ² θ / 2-sin ⁴ θ /
8)}-H sin θ = L sin ² θ / 2-L sin ⁴ θ / 8-H sin θ

Since sin θ = z / L, the following equation 2
If the first-order term of is taken, dx can be expressed as in the following Expression 3.

[0016]

## EQU00003 ## dx = z (z-2H) / 2L

Similarly, dz can be expressed by the following equation 4.

[0018]

Dz = H {1-√ (1-sin ² θ)} ≈H {1- (1-sin ² θ / 2-sin ⁴ θ / 8)} = H sin ² θ / 2-H sin ⁴ θ / 8 ∴dz = Hz ² / 2L ²

Therefore, the arc distortion correction unit 2 calculates dx and dz based on the input displacement amount data z to obtain dx and dz, and then calculates the following Formula 5. The correction data x ', z'corrected for the arc distortion is output.

[0020]

## EQU5 ## x '= x + dx z' = z + dz

As described above, dx and dz can be obtained by a simple bit shift or addition / subtraction / multiplication / division operation. Further, these calculations may be performed using a ROM table or the like.

When the arc distortion correction is performed, the correction data x ', z'does not have a constant pitch as shown by the white circles in FIG. Interpolation is performed with a quadratic curve, a cubic curve, and the like, and the interpolated curve is resampled at a constant pitch as indicated by black circles in the figure. For the interpolation curve, an optimal method may be selected in consideration of the interpolation accuracy and the calculation time.

Next, the trend removing section 4 will be described. When measuring and analyzing the surface of a work having a curvature, it is necessary to remove the waviness component of the work as a preprocessing such as parameter calculation. A curve suitable for the surface shape of the work is referred to as a trend curve here, but the trend removing unit 4 removes the trend curve suitable for the work shape selected in advance by the operator of the measuring instrument from the correction data x ″, z ″. , The residual data is output as surface roughness data Δz.

As the trend curve, a straight line, a circle, a conic curve (ellipse, parabola, hyperbola), an nth degree polynomial curve or the like is used. The parameters of these curves are calculated from the correction data x ", z" by the least squares method. Can be found at.
FIG. 4 is a diagram showing a case where a straight line is fitted as a trend curve. The equation of the curve is shown in the following equation 6, and a and b are obtained by the least square method. This example is effective for removing an error when a flat work has an inclination.

[0025]

## EQU6 ## z = ax + b

FIG. 5 is a diagram showing a case where a circle or a conic curve is fitted as the trend curve. When the shape of the work is an accurate circular shape, it is desirable to fit a circle, and when it is a distorted circular shape, it is desirable to fit a conic curve. The equation of the conic curve is shown in the following Expression 7, and k, r, the parallel movement amount, and the rotation movement amount are obtained by the least square method. When this curve is selected, it is equivalent to correction with the smallest sum of residuals among ellipse, parabola, and hyperbola.

[0027]

(7) kx ² −2rx + z ² = 0

FIG. 6 is a diagram showing a case where an n-th degree polynomial curve is fitted as a trend curve. The equation of the curve is
It is shown in the following formula 8 and by the method of least squares, a _n , a _n-1 ,
..., a ₁ , a ₀ are obtained.

[0029]

## EQU00008 ## z = a _n x ⁿ + a _n-1 x ^(n-1) + ... + a ₁ x + a ₀

By this trend removal processing, the contour component of the cross-sectional shape of the work can be removed.
The surface roughness can be accurately evaluated.

[0031]

As described above, according to the present invention, the stylus displacement amount data is sampled at predetermined intervals, the circular distortion of the stylus is eliminated from the displacement amount data, and then the constant pitch processing is performed. As a result, it is possible to obtain accurate displacement amount data at a constant pitch, and thus it is possible to accurately evaluate the surface roughness and the like of the painting powder.

[Brief description of drawings]

FIG. 1 is a block diagram showing a schematic configuration of a shape measuring machine according to an embodiment of the present invention.

FIG. 2 is a diagram for explaining arc distortion of a stylus in the same measuring machine.

FIG. 3 is a diagram for explaining constant pitch processing in the same measuring machine.

FIG. 4 is a diagram for explaining straight line correction in the trend removal processing of the measuring instrument.

FIG. 5 is a diagram for explaining a circle or conic curve correction in the trend removal processing of the measuring instrument.

FIG. 6 is a diagram for explaining an nth-order polynomial curve correction in the trend removal processing of the measuring machine.

[Explanation of symbols]

1 ... Measuring unit, 2 ... Arc distortion correction unit, 3 ... Constant pitch processing unit,
4 ... Trend removing unit, 5 ... Stylus, 6 ... Stylus arm, 7 ... Work, 8 ... Driving device, 9 ... Linear encoder, 10 ... Differential transformer, 11 ... Synchronous detection circuit, 12
... A / D converter.

 ─────────────────────────────────────────────────── ─── Continuation of the front page (72) Inventor Tsukasa Kojima, 1-1-2, Kita 7-jo Nishi, Kita-ku, Sapporo-shi, SE Yamakyo Building, 11th floor, System Technology Institute Inc.

Claims (2)

[Claims] 1. A measuring means for sampling and outputting data of displacement of the stylus at predetermined intervals while moving the stylus operating in a circular arc along the surface of the work, and the stylus generated by the circular operation of the stylus. Arc distortion correction means for correcting the arc distortion of the stylus based on the displacement amount of the stylus output from the measuring means, and the predetermined sampling data of the displacement amount of the stylus after the arc distortion is corrected by the arc distortion correction means. A shape measuring machine, comprising: a constant pitch processing means for applying a straight line or a curve and re-sampling at a constant pitch. 2. A displacement amount data obtained by re-sampling by the constant pitch processing means is fitted with a straight line or a curve along the surface shape of the work, and the displacement amount data obtained by the re-sampling is applied. The shape measuring machine according to claim 1, further comprising trend removing means for removing a component of the fitted straight line or curved line.