JP3098213B2 - Circular contour measuring method and system - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for detecting a difference between a circular contour such as an ellipse and a circle measured using a roundness measuring device or the like and a circular contour defined by design data. The present invention relates to a method and a system for measuring a circular contour, which can be quantitatively evaluated.

[0002]

2. Description of the Related Art A roundness measuring device or the like is conventionally used for evaluating the contour shape of a cylindrical part such as a piston. In the measurement by the roundness measuring machine, the tip of the stylus when the rotary table is rotated once while the stylus of the measuring machine is pressed against the side of the cylindrical work placed on the rotary table The shake amount is obtained as measurement data as shown in FIG. In this type of surface shape measurement, since the unevenness of the measurement surface is detected in a high range, the moving radius of the work itself cannot be obtained as measurement data, but the measurement is performed as a deviation from a given reference measurement radius R. Data is required. On the other hand, as shown in FIG. 9, the design reference radius R (with “＾” at the top; hereinafter referred to as “ΔR”) in consideration of the elliptical shape and the design reference It is given in the form of a list of deviation data ΔRj (j is the number of the measurement point) from ＾ R. In this case, ΔRj is all 0 for a perfect circle.

[0003]

When the contour data is collated with the design data for the deviation data obtained by the roundness measuring machine, there are the following problems. That is, since an alignment error occurs when the work is set on the table in the measurement data, the design value coordinate system X, Y and the measurement value coordinate system x, Y
10 (a) and 10 (b), the parallel movement amounts ΔX and ΔY of the center of the measurement coordinate system x and y with respect to the center of the design coordinate system X and Y as shown in FIGS. And the amount of deviation Δθ in the rotational direction of the measurement reference with respect to the design reference as shown in FIG.
Also, the measurement data does not include true radial information,
Since it is represented by an amount of deviation from an appropriately determined reference measurement radius R, it is necessary to consider a radial error ΔR between the design data and the measurement data as shown in FIG. Workpiece alignment errors can be canceled to some extent by fine adjustment on the measuring instrument side, but fine adjustment has its limitations. In addition, the error ΔR in the radial direction cannot be avoided due to the nature of the measurement. For this reason,
Conventionally, there has been a problem that quantitative contour matching cannot be performed.

The present invention has been made in view of the above points, and provides a circular contour measuring method and system capable of performing quantitative contour matching by canceling a workpiece alignment error and a radial error during measurement. The purpose is to do.

[0005]

SUMMARY OF THE INVENTION A circular contour measuring system according to the present invention has a circular contour measuring means for measuring a circular contour of an object to be measured, and a circular contour measuring means for measuring a circular contour measured by the measuring means. Calculation processing means for executing processing for quantitative contour matching evaluation between the measured contour shape and the design contour shape based on the measurement data and the design data given by the deviation from the design reference radius; The arithmetic processing means calculates an approximate curve of the measurement data from the measurement data, and calculates a translation amount, a rotation amount, and a design reference between the design data and the calculated approximate curve of the measurement data. A best-fit processing means for calculating a best-fit parameter based on a radial error, based on the best-fit parameter calculated by the best-fit processing means; Characterized by comprising a contour matching processing means for executing the contour matching processing of the measurement data to the meter data.

The circular contour measuring method of the present invention provides measurement data obtained as a deviation from a measurement reference radius by a circular contour measuring means for measuring a circular contour to be measured, and deviation from a design reference radius. In the measuring method for measuring a circular contour based on the obtained design data, an approximate curve of the measured data is calculated from the measured data, and an approximate curve of the calculated measured data is calculated with respect to the design data. Calculating a best-fit parameter based on the amount of translation, rotation, and error in the radial direction of the design reference, and then performing contour matching of measured data with respect to design data based on the calculated best-fit parameter. To be

[0007] The circular contour measuring program recorded on the medium according to the present invention comprises a circular contour measuring means for measuring a circular contour of an object to be measured, from the measured data obtained as a deviation from a measurement reference radius. Is calculated based on the translation amount, the rotational movement amount, and the error in the design reference radial direction between the design data given by the deviation from the design reference radius and the calculated measurement data approximate curve. The method includes a step of calculating a best fit parameter, and a step of executing contour matching processing of measured data with respect to design data based on the calculated best fit parameter.

According to the present invention, an approximate curve thereof is calculated from the measurement data, and a translation amount, a rotational movement amount, and an error in the radial direction of the design reference between the design data and the calculated approximate curve are calculated. Since the best fit parameter is calculated and the error is canceled based on this parameter to execute the contour matching process of the measured data with the design data, not only the alignment error of the measured data but also the radial error The contour matching is performed in a state in which the contour is also removed, and the quantitative evaluation of the contour shape becomes possible.

In the best-fit processing means, a Fourier series curve of the measured data is calculated from the measured data by a linear least squares method, and can be used as an approximate curve. The best fit parameter is
The one that minimizes the diameter difference between each design data and the approximate curve obtained from the measurement data can be calculated by the nonlinear least squares method.

[0010]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS A circular contour measuring system 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 this system. This system controls the operation of the circularity / cylindrical shape measuring device 1 and the circularity / cylindrical shape measuring device 1 and inputs measurement data and design data to perform quantitative contour matching evaluation. And a computer 2 for outputting the evaluation result.

A rotary table holder 12 is provided on a base 11 of the roundness / cylindrical shape measuring device 1, and a rotary table 13 is rotatably mounted on the rotary table holder 12. On the turntable 13, a cylindrical work 14 to be measured is placed.
The work 14 is driven to rotate together with the turntable 13 that is driven to rotate by a driving means such as a motor (not shown). The rotary table holding table 12 is provided with a fine adjustment knob 15 for finely adjusting the position of the rotary table 13 in the x and y directions in the figure.

On the other hand, a column 16 is provided upright on the base 11 and a slider 17 is provided along the column 16 so as to be vertically drivable. An arm 18 is provided on the slider 17 so as to be drivable in the horizontal direction. A stylus 19 is attached to the tip of the arm 18, and the rotary table 13 makes one rotation while the tip of the stylus 19 is in contact with the outer peripheral surface of the work 15. Is obtained as measurement data.

On the other hand, the computer 2 comprises a computer main body 21, a keyboard 22, a mouse 23, and a display device 24. The computer 2 has measurement data obtained by the roundness / cylindrical shape measuring device 1 and design data previously given from a CAD system or the like. After performing a best fit process for canceling an alignment error or a radial error between the two, a contour matching process for matching the contour between the measured data and the design data is performed. These processes are executed by a circular contour measuring program installed in the computer main body 21, and the program is provided via an appropriate medium such as a CD-ROM or a communication medium.

Next, a procedure of a measuring operation using the system configured as described above will be described. FIG. 2 is a flowchart showing the measurement procedure. First, the work 14 is set as a measuring operation in the roundness / cylindrical shape measuring machine 1 (S1). At this time, the work 14
As shown in FIGS. 10A, 10B, and 10C, the parallel movement amounts ΔX, ΔX in the X and Y directions with respect to the reference coordinates of the design data.
Y and the movement amount Δθ in the rotation direction appear as alignment errors. For this reason, in the setting, the adjustment work of the rotary table 14 by the fine adjustment knob 15 and the adjustment work using the auxiliary tool are performed to minimize the alignment error.

Next, a measurement process is executed (S2). While the stylus 19 of the roundness / cylindrical shape measuring device 1 is in contact with the work 14, the contour of the work 14 for one rotation is measured. As the measurement reference radius R, the design reference radius ＾ R or its value when the system has a function of indicating an approximate radius may be used. At this time, as described above, a radial error ΔR occurs between the design data and the measurement data as shown in FIG. 10D.

Subsequently, a best fit process is executed inside the computer 2, where the errors ΔX, ΔY,
Δθ and ΔR are canceled (S3). In this processing, V (parallel movement amount), Θ (rotational movement amount), ΔR (radial direction error) so that the measured data and the design data have the same effect as the conventional subjective alignment operation.
Is the best fit parameter, and is realized by software.

Finally, based on the optimal alignment between the measured data and the design data obtained in the best fit process (S3), contour matching for quantitatively evaluating the difference in the contour shape of the measured data with respect to the design data is executed ( S4).

FIG. 3 is a flowchart showing details of the best fit process (S3). In the best fit process, first, a Fourier series approximation curve of the measured data is obtained from the measured data using the linear least squares method (S11). That is, as shown in FIG. 4, the measurement data obtained by the roundness / cylindrical shape measuring device 1 is obtained from the deviation Δri from the measurement reference radius at each angle θi, and is expressed as follows.

[0019]

(Equation 1)

Here, assuming that the measurement reference radius is R, the two-dimensional coordinates of each measurement point p are represented by the following equation (2).

[0021]

(Equation 2)

Similarly, the design data is, as shown in FIG.
Since it is obtained as the deviation amount ΔRj from the design reference radius at each angle 求 め j, the two-dimensional coordinates of each design point P are also obtained as shown in Expression 3.

[0023]

(Equation 3)

Here, j is the design point number (1 to N) and ΔR is the design reference radius. Since the two-dimensional coordinate values of the measurement data and the design data are used to perform the best fit process, the above equations (2) and (3) are required. However, in the roundness / cylindrical shape measuring device 1, the radius of movement itself cannot be measured due to accuracy, so that an appropriate value input by the user is used as the measurement reference radius R. Therefore, appropriate processing can be performed by taking into account the error ΔR between the measurement reference radius R and the design reference radius 可能 R.

For the best fit calculation, it is necessary to interpolate the measured data and approximate with some curve.
The algorithm needs to satisfy the conditions that it has appropriate accuracy and that it is fast (it is desirable to find a solution instantly for use in leveling, etc.). Here, an algorithm using a Fourier approximation curve is exemplified as a method for satisfying the above, but another approximation curve may be used. Although it is conceivable to approximate the design data with a curve, the number of design points (for example, 16 points) is generally smaller than the number of measurement points (for example, 7,200 points at maximum). It is desirable to approximate the data with a curve.

As the Fourier series approximation curve, for example, the following equation 4 is used.

[0027]

(Equation 4)

Here, α and β are real numbers, and what values are used as these values are determined by the data shape, and are fixed thereafter. Therefore, f (θ) is not always a periodic function in the angle range of the measurement data.

To obtain the Fourier series approximation curve of Equation 4 from the measured data (θi, Δri) by the linear least squares method, the following processing is executed. Now

[0030]

(Equation 5)

In other words, s is c _k (k = 0 to m), s _k
(K = 1 to m) Sum 2m + 1 pieces of c _k of the quadratic equation s _k. Therefore, hereinafter, c _k, a s _k by using a serial number e _k
And That is,

[0032]

(Equation 6)

At this time, Equation 5 can be expressed as Equation 7 below.

(Equation 7)

Here, A is a (2m + 1,2m + 1) symmetric matrix, B is a (1,2m + 1) matrix, and C is a constant. To find the minimum of Equation 7,

[0035]

(Equation 8)

Can be solved. From Equation 8,

[0037]

(Equation 9)

Is obtained, and e ₀ to e _2m are obtained by solving this.

Next, the best fit parameters Θ (rotation angle), V (parallel movement amount), and ΔR (reference radius adjustment amount) with the Fourier series approximation curve obtained for the design data are calculated using the nonlinear least squares method. It is calculated (S12). Now, as shown in FIG. 6, the point P is the j-th design point, and the point Q is the j-th design point P is the best fit parameter Θ, V =
Assuming that the point is moved by (v ₁ , v ₂ ), ΔR, the coordinates of P and Q are as follows.

[0040]

(Equation 10)

[0041] Here in polar coordinates the _{Q r Q, Θ Q, j} ; and expressed using (with the "~" above both in the following text "~r _Q", "~Θ _{Q, j"} is referred to as),

[0042]

[Equation 11]

Is as follows. When sj ′ in FIG. 6 is a distance (radial difference) from the point Q to the Fourier series approximation curve at the corresponding angle, and sj is a value adjusted by the adjustment amount ΔR in the radial direction, sj ′ and sj are Each is represented by the following Equation 12.

[0044]

(Equation 12)

Here, the best fit parameters Θ, V, ΔR are calculated by the nonlinear least squares method as shown in FIG. 7 using the above sj as an evaluation function. First, the initial values of the parameters Θ, V, ΔR are determined to be appropriate values (S21).
Next, the first-order partial differential Ds of the evaluation function s and Hessian (He
ssian) is calculated (S22). That is, focusing on the fact that ~ r _Q and ~ Θ _{Q, j} are functions of Θ and V, partial differentiation of _Q in Equation 10 with parameters Θ and V gives
Equation 13 is obtained.

[0046]

(Equation 13)

Next, the partial differentiation of Equation 11 gives

[0048]

[Equation 14]

Therefore,

[0050]

(Equation 15)

Here, t indicates one of the parameters Θ, v ₁ and v ₂ . {Q / ∂ on the right side of Equation 15
the t, by substituting the number _{13, ~r Q, ~Θ Q,} j is determined.

Next, the evaluation function sj is defined as Θ, v1, v2, Δ
Partially differentiate with R. The partial derivative with respect to ΔR is immediately obtained from Expression 11,

[0053]

(Equation 16)

Is obtained as follows. Assuming that t is one of the parameters Θ, v ₁ , and v ₂ as described above,

[0055]

[Equation 17]

Is as follows. ∂ (~ Θ _{Q, j} ) of Equation 17 /
Since ∂t, ∂ (〜r _Q ) / ∂t can be calculated from Equation 15, the partial differential of sj is obtained from this. The final Ds,
DDs is calculated as follows. tα (α = 1, 2,
Let 3, 4) be v ₁ , v ₂ , Θ, and ΔR, respectively.

[0057]

(Equation 18)

As the Hessian approximate matrix DDs, an expression excluding the second term on the right side of Expression 18 is used. That is,

[0059]

[Equation 19]

When Ds and DDs are obtained in this way, next,

[0061]

[Equation 20] DDs · dp = −Ds

Is solved to calculate the best fit parameter increment dp (S23). The best fit parameters Θ, V, and ΔR are updated (S24), and the above processing is repeated until the parameter increment dp becomes sufficiently small (S2).
5). When the parameter increment dp is sufficiently small,
The parameters Θ, V, ΔR are determined. Then, after the error between the design data and the measurement data is canceled using the obtained parameters, the contour matching processing (S5)
Is executed, quantitative evaluation of the contour shape becomes possible.

[0063]

As described above, according to the present invention, the approximate curve thereof is calculated from the measured data, and the amount of translation, rotation and rotation between the design data and the calculated approximate curve is calculated. The best fit parameter based on the error in the design reference radial direction is calculated, and based on this parameter, the error is canceled and the contour matching process of the measured data with the design data is executed. Instead, contour matching is performed in a state where errors in the radial direction have been removed, and quantitative evaluation of the contour shape becomes possible.

[Brief description of the drawings]

FIG. 1 is an external view of a circular contour measuring system according to an embodiment of the present invention.

FIG. 2 is a flowchart showing a procedure for measuring a circular contour in the system.

FIG. 3 is a flowchart of a best fit process in the same procedure.

FIG. 4 is a diagram for explaining measurement data in the system.

FIG. 5 is a diagram for explaining design data in the system.

FIG. 6 is a diagram showing a relationship between design data and design data in which alignment errors have been canceled in the same system.

FIG. 7 is a flowchart showing a procedure for calculating a best fit parameter in the best fit process.

FIG. 8 is a diagram for explaining the contents of measurement data.

FIG. 9 is a diagram for explaining the contents of design data.

FIG. 10 is a diagram for explaining an alignment error and a radial error between measurement data and design data.

[Explanation of symbols]

1 ... roundness / cylindrical shape measuring machine, 2 ... computer, 11
... Base, 13 ... Rotary table, 14 ... Work, 19 ...
Stylus.

────────────────────────────────────────────────── ─── Continuation of the front page (72) Inventor Kozo Umeda 1-20-1 Sakado, Takatsu-ku, Kawasaki-shi, Kanagawa Pref. JP-A-8-122050 (JP, A) JP-A-6-294643 (JP, A) JP-A-6-282633 (JP, A) JP-A-8-285570 (JP, A) JP-A-6-126597 (JP, A) (58) Fields investigated (Int. Cl. ⁷ , DB name) G01B 21/00-21/32 G01B 11/00-11/30 102 G01B 5/00-5/30 G06T 7/00 G06T 7/60

Claims (5)

(57) [Claims] 1. A circular contour measuring means for measuring a circular contour of an object to be measured, a measurement data obtained by the measuring means as a deviation from a measurement reference radius, and a design given by a deviation from a design reference radius. An arithmetic processing means for performing a process for quantitative contour matching evaluation between the measured contour shape and the design contour shape based on the data, the arithmetic processing means comprising: Best-fit processing for calculating an approximation curve, and calculating a best-fit parameter based on an error in the translational direction, the amount of rotational movement, and the error in the design reference radial direction between the design data and the approximation curve of the calculated measurement data. Means for executing contour matching processing of measured data with respect to design data based on the best fit parameter calculated by the best fit processing means. Circular profile measuring system characterized by comprising a contour matching process unit. 2. The circular contour according to claim 1, wherein the best-fit processing means calculates a Fourier series curve of the measured data as an approximate curve from the measured data by a linear least squares method. Measurement system. 3. The method according to claim 1, wherein the best-fit processing means calculates the best-fit parameter that minimizes the difference in diameter between each design data and the approximate curve obtained from the measurement data by a nonlinear least squares method. The circular contour measuring system according to claim 1 or 2, wherein: 4. Based on measurement data obtained as a deviation from a measurement reference radius by circular contour measurement means for measuring a circular contour of a measurement object, and design data given as a deviation from a design reference radius. In a measurement method for measuring a circular contour, an approximate curve of the measurement data is calculated from the measurement data, and a translation amount and a rotation amount between the design data and the approximation curve of the calculated measurement data are calculated. And calculating a best fit parameter based on an error in a design reference radial direction, and then performing contour matching processing of measured data with respect to the design data based on the calculated best fit parameter. 5. An approximation curve of the measurement data is calculated from the measurement data obtained as a deviation from the measurement reference radius by a circular contour measurement means for measuring a circular contour of a measurement target, and the deviation from the design reference radius is calculated. Calculating a best-fit parameter based on a translation amount, a rotational movement amount, and an error in a design reference radial direction between the given design data and the approximate curve of the calculated measurement data; Executing a contour matching process of the measured data with the design data based on the fit parameters.