JPH0510751A - Evaluating method for measured value - Google Patents

Abstract

PURPOSE:To enable always correct evaluation of three-dimensionally measured values by removing the effect of errors in the installation of works on checking with design values even if such errors occur during measurement or machining. CONSTITUTION:The positional relationship of a design coordinate system (second coordinate system)G2 to an evaluation coordinate system (first coordinate system)G1 is found by the non-linear method of least squares using as an evaluation function (f) the shortest distance between a free curved surface S and each design point Q, the distance being specified by a measured coordinate value. The deviation of the design coordinate system G2 from the evaluation coordinate system G1 is corrected according to the found positional relationship and the measured value is checked with a design value.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a measurement value evaluation method for evaluating whether or not the three-dimensional measurement data of a free-form surface to be measured, which is measured by, for example, a three-dimensional measuring machine, is a value as designed. In particular, the present invention relates to preprocessing of measurement value matching processing.

[0002]

2. Description of the Related Art In recent years, CAD / CAM (Computer Aided)
With the improvement of design / processing efficiency by Design / Computer Aided Manufacturing) system and the high performance of NC machine tools, it has become possible to machine products with complicated shapes with high precision. Therefore, even in the measurement process of product evaluation, it is required to accurately measure a complicated three-dimensional shape including a free-form surface, and a high-precision three-dimensional measuring machine for that purpose has been developed. .

[0003]

However, the length,
It is relatively easy to evaluate the product by comparing the measured values in the one-dimensional coordinate system such as thickness and radius with the design values.
It is extremely difficult to evaluate whether or not the measured value obtained as the coordinate value of the three-dimensional coordinate system falls within the design tolerance range. This is because the coordinate system itself of the measured value deviates from the coordinate system to be evaluated due to a work mounting error or the like that occurs during measurement or machining. For this reason, conventionally, there has been a problem that the measured value obtained as the three-dimensional coordinate value cannot be correctly collated with the design value, and correct evaluation cannot be performed.

The present invention has been made in view of such a point, and even if a work mounting error occurs during measurement or machining, it is possible to eliminate the influence on design value verification due to the error. It is an object of the present invention to provide a design value evaluation method capable of evaluating a correct measured value.

[0005]

A design value evaluation method according to the present invention is a measurement value evaluation for evaluating an error between a measurement coordinate value obtained by measuring a free-form surface of a known shape and a design coordinate value. In the method, the shortest distance between the free-form surface specified by the measurement coordinate value and the design coordinate value is used as an evaluation function, and the first coordinate system and the design coordinate value of the measurement coordinate value at which this evaluation function converges to the minimum value. And a coordinate conversion process for matching one of the two coordinate systems with the other based on the obtained relative positional relationship between the two coordinate systems. After that, the error between the measured coordinate value and the design coordinate value is evaluated.

[0006]

According to the present invention, the shortest distance between the free-form surface specified by the measurement coordinate value and the design coordinate value is used as the evaluation function, and the measurement coordinate system (first measurement function) such that the evaluation function converges to the minimum value (first A relative positional relationship between the coordinate system) and the design coordinate system (second coordinate system) is obtained. Then, based on the obtained relative positional relationship between both coordinate systems, coordinate conversion of both coordinate values is performed so that one coordinate system matches the other coordinate system. As a result, according to the present invention, it is possible to eliminate the influence of a work attachment error during measurement or machining, and to correctly evaluate the measured value.

The free-form surface specified by the measured coordinate values is successively narrowed down to smaller patches, and the patch closest to the design coordinate values is selected, or a plurality of points are added to the inside of the selected patch. If you repeat the process of generating and selecting points close to the design coordinate value and the process of generating multiple points around the selected point, the amount of data to be processed will be greatly reduced. It is possible to increase the processing speed.

[0008]

Embodiments of the present invention will be described below with reference to the accompanying drawings. FIG. 1 shows an evaluation coordinate system (measurement coordinate system; first coordinate system) and a design coordinate system (second coordinate system), particularly prior to collation with a design value, in a measurement value evaluation method according to an embodiment of the present invention. 5 is a flowchart showing a part of coordinate system matching processing between the two. Specifically, the coordinate system matching process here calculates the shortest distance between each given design point Q and the free-form surface S, as shown in FIG. This is a process of obtaining the positional relationship of the design coordinate system G2 with respect to the system G1 and performing coordinate conversion of the design point Q based on the positional relationship.

First, prior to the description of the processing of this embodiment, a method of generating a free-form surface (probe center curved surface) from measurement data of a coordinate measuring machine will be briefly described.

That is, in the measuring process using the coordinate measuring machine, as shown in FIG. 3, probe center point group data (hereinafter referred to as "measurement point group data") D is obtained for each measurement cross section MS. At this time, the measurement pitch and the number of measurement points may be arbitrary. Therefore, the measurement point group data D obtained from the coordinate measuring machine has various intervals.

A first free curve C ₁ fitting process is then performed on this measurement point group data D. The fitting process of the first free curve C ₁ is performed for each measurement point sequence of each measurement cross section. As shown in FIG. 4, the first free curve C ₁ is composed of a plurality of curves that do not extend the range of the minute value ε between the measurement points, and adjacent curves are tangents at their connecting points. Decide to be common.

Next, the first free-form curve C ₁ corresponding to each of the obtained measurement point sequences is divided into n equal parts (n is an arbitrary integer) based on, for example, the chord length, and the obtained equal parts are obtained. The first free-form curve is calculated again so as to smoothly pass through the points. here,
The vector data of the i-th ((i is 0 to n) division point in the j-th measurement point sequence is P _ij .

Next, as shown in FIG. 5, a free curve passing through a division point having a common i, that is, the first free curve C ₁ (the first free curve C ₁ obtained by the above process A second free curve C ₂ (hereinafter, the direction of the _second free curve C ₂ is hereinafter referred to as the v direction) is determined. The second free curve C ₂ is passed through the pass point P _ij, tangent in the pass point P _ij is determined as a condition to become in common. As an algorithm for determining the free curve, for example, an algorithm for generating a cubic Bezier curve of class C ¹ connection or class C ² connection can be used.

Next, a free-form surface having a common tangent plane in a range surrounded by free-form curves generated by such an algorithm is generated. In order to generate a patch stretched so that the tangent planes are common, for example, two patches having a common boundary curve and satisfying the condition that the tangent planes match at both end points may be generated. If this condition is met,
The tangent planes match at all points on the boundary curve.
By the above processing, unit free-form surfaces are generated, and the probe center curved surface can be generated by a set of these unit free-form surfaces.

For the obtained probe center curved surface,
Although a real curved surface can be calculated by performing offset processing for the probe radius, the free curved surface targeted in this processing may be the real curved surface or the probe center curved surface.

When the free-form surface is obtained, the shortest distance between the free-form surface and each design point is obtained as an evaluation function.
The position P on the free-form surface closest to the design point is calculated (S
1). Here, in order to reduce the data amount and speed up the calculation, the entire patch is divided into several patch groups as shown in FIG. Next, as shown in FIG.
Extract the n patch groups that are closest to the specified design point,
As shown in FIG. 8, m patches closest to the design point are extracted from the patches included in the extracted patch group. Next, as shown in FIG. 9, an internal point is generated in the extracted patch, and only one point, which is the closest to the designated design point, is extracted. Then, as shown in FIG. 10, the periphery of the extracted inner point is further divided, and only the closest k points are extracted. By repeating this k-point extraction processing s times, one point closest to the design value is obtained. Here,
n, m, l, k, and s are tuning parameters, which can be arbitrarily set in consideration of processing efficiency and accuracy.

After the position P on the free-form surface is calculated, the evaluation function f is then calculated (S2). The evaluation function f is shown in FIG.
As shown in, each design point Q is calculated from the obtained position P of each point.
It is represented by the shortest distance L to. If the free curved surface is the probe center curved surface, the free curved surface may be corrected by the radius r of the probe tip sphere. FIG. 12A shows
When the design point Q exists on the real surface side with respect to the probe center curved surface S, FIG. 12B shows the case where the design point Q exists on the opposite side to the probe center curved surface S with respect to the real surface. ing.

Then, the optimum position and orientation of the design reference coordinate system are obtained by the nonlinear least squares method (S3). Variable parameters of the nonlinear least squares method include a translational parameter of the origin (Δx, Δy, Δz) [FIG. 13 (a)] and a tilt amount parameter of the Z axis (Δl, Δm) [FIG. 13 (b)].
And the Z-axis rotation parameter (Δω) [Fig. 13 (c)]. That is, the directions of the Z-axis, the X-axis, and the Y-axis can be calculated by Δl and Δm as shown in Equation 1.

[0019]

[Equation 1]

The parameters are (Δx, Δy, Δz),
(Δl, Δm) and Δω are applied to the coordinate system in this order. However,
The values in parentheses apply at the same time. To calculate the optimum position, a non-linear least squares method is used which repeatedly applies the following equation.

[0021]

[Equation 2]

Here, Δx, Δy, and Δz are tuning parameters. Δl, Δm, and Δω are set according to the following equation 3 according to the average distance R from the origin of the design reference coordinate system to each design point, and L, M, and Ω are used as tuning parameters.

[0023]

[Formula 3] Δl = L / R Δm = M / R Δω = Ω / R

The following expression 2 is solved by the modified Cholesky method to obtain a1 to a6 (S4). Next, a convergence determination process of the nonlinear least squares method is performed (S5). In the convergence determination, the number 3 of 4
Use one of the two conditions to determine if this is met.

[0025]

[Equation 4]

If the conditions are satisfied, the process is terminated, and if not, a new coordinate system position and orientation are obtained by the following equation 5, and the same process is executed again (S).
5).

[0027]

[Expression 5] x = x + a1 y = y + a2 z = z + a3 l = l + a4 m = m + a5 ω = ω + a6

By repeating this process until convergence, the optimum position and orientation of the design coordinate system based on the evaluation coordinate system can be finally calculated. In the above embodiment, the position and orientation of the design coordinate system (second coordinate system) with respect to the evaluation coordinate system (first coordinate system) are obtained.
Obtain the position and orientation of the evaluation coordinate system with respect to the design coordinate system,
You may make it coordinate-convert the measured value. However, in this case, since it is necessary to perform coordinate conversion on the free-form surface, the amount of data processing will be slightly increased compared to the previous embodiment.

[0029]

As described above, according to the present invention, the shortest distance between the free-form surface specified by the measurement coordinate value and the measurement coordinate value is used as the evaluation function, and this evaluation function converges to the minimum value. While the relative positional relationship between the measurement coordinate system (first coordinate system) and the design coordinate system (second coordinate system) is obtained,
Based on the obtained relative positional relationship between both coordinate systems, the coordinate conversion of both coordinate values is performed so that the one coordinate system matches the other coordinate system. The influence of mounting error etc. is eliminated, and it becomes possible to evaluate the measured value correctly.

[Brief description of drawings]

FIG. 1 is a flowchart of coordinate system matching processing in a measurement / evaluation method according to an embodiment of the present invention.

FIG. 2 is a schematic diagram for explaining an outline of coordinate system matching processing according to the present embodiment.

FIG. 3 is a schematic diagram showing measurement point cloud data obtained from a coordinate measuring machine.

FIG. 4 is a schematic diagram showing a state in which measured point cloud data is fitted with a first free curve.

FIG. 5 is a schematic diagram showing a state in which a first free curve is equally divided and respective equally divided points are smoothly connected by a second free curve.

FIG. 6 is a schematic diagram showing a state in which a plurality of patches are grouped for the process of obtaining the shortest free-form surface position at a design point.

FIG. 7 is a schematic diagram showing how patch groups are narrowed down in the same process.

FIG. 8 is a schematic diagram showing patches finally narrowed down in the same process.

FIG. 9 is a schematic diagram showing a state in which inner points are generated in a patch selected in the same process.

FIG. 10 is a schematic diagram showing how a plurality of points are generated around the selected point in the same process.

FIG. 11 is a schematic diagram showing the distance between a selected point on the free-form surface and the design point.

FIG. 12 is a schematic diagram showing a distance between a point on a free-form surface and a design point when the probe radius is offset.

FIG. 13 is a schematic diagram showing an evaluation coordinate system and a design coordinate system for explaining variable parameters in the nonlinear least squares method.

[Explanation of symbols]

MS ... measurement section, D ... measurement point group data, C1 ... first free curve, C2 ... second free curve, S ... probe center curved surface, Q ... design point.

   ─────────────────────────────────────────────────── ─── Continued front page    (72) Inventor Kozo Ariga             1-3-4 Yushima, Bunkyo-ku, Tokyo KT             Chanomizu Seihashi Building 6th floor Systemte Co., Ltd.             In the kunology in status

Claims (3)

[Claims] 1. In a measurement value evaluation method for evaluating an error between a measurement coordinate value obtained by measuring a free-form surface of a known shape and a design coordinate value, a free-form surface specified by the measurement coordinate value is used. The shortest distance from the design coordinate value is used as an evaluation function, and the relative positional relationship between the first coordinate system of the measurement coordinate value and the second coordinate system of the design coordinate value at which the evaluation function converges to the minimum value is obtained. Between the measured coordinate value and the design coordinate value after performing a coordinate conversion process for matching one of the coordinate systems with the other based on the obtained relative positional relationship between the coordinate systems. A measurement value evaluation method characterized by evaluating the error of. 2. The evaluation function is calculated by sequentially narrowing down the free-form surface specified by the measurement coordinate value into smaller patches and selecting the patch closest to the design coordinate value. Claim 1
Measured value evaluation method described. 3. A process of generating a plurality of points inside a selected patch, a process of selecting a point closest to the design coordinate value, and a process of generating a plurality of points around the selected point. The measurement value evaluation method according to claim 2, wherein the evaluation function is calculated by repeating and a plurality of times.