DE102008007127A1 - Method for measuring components - Google Patents

Abstract

The invention relates to a method for measuring components, which is suitable for determining the exact position of a component in a three-dimensional Cartesian coordinate system. For this purpose, an open algorithm is used, the method determines the movements of translational and rotational nature necessary for the best possible match of both layers quickly and as accurately as possible from the desired and actual position of a component. The unknowns q1 to q5 necessary for the description of the transfer of the actual coordinates to the desired coordinates are obtained by minimizing the Gaussian error square and by setting the partial derivative of the function $ I1 to zero.

Description

Field of the invention

The The invention relates to a method for measuring components in a Cartesian measuring or Machine tool, which is suitable for the exact position of a Component in a three-dimensional Cartesian coordinate system determine.

method for measuring components are then applied, inter alia, when components are manufactured using CNC machine tools. For this the position of a semi-finished product must if possible before starting the processing be determined exactly. Likewise, such methods are used if a component, such as a milled part, before or after manufacturing to be measured. The survey serves, for example, the review of manufacturing quality and thus the determination of the manufacturing error. The lower this one fails, the higher is the production quality. Around the deviation between the actual and the desired shape of the component to determine, before the beginning of the actual measurement first the Actual position of the component as possible be determined exactly. If necessary, then the position of the component successively be corrected until a possible Good match the body boundaries of Target and actual component or a match of Target and actual position is reached. Only then can the actual Determination of the manufacturing error.

The Determination of the position of a component is in the context described above also referred to as calibration.

State of the art

A often used possibility to achieve high manufacturing accuracies or a correct one Control the same while avoiding reorienting the clamped component offers the use of highly accurate clamping devices. In this case it is assumed that the tensioning device itself has such a high accuracy that the component in this is sufficiently accurately stored at all times and not reoriented must be before, for example, a further processing or a Quality control is done.

Such However, procedures normally prohibit removal and re-clamping of the component, because this produces a directly after the production Actual position of the component, which naturally close to that by the CNC control predetermined target position comes close, is changed. When reloading the Component will not hit the previous location again. from that There is the disadvantage that the manufacturing and the Meßspannvorrichtung must be identical and the component must remain at all times in the clamping device. In case of unavoidability of a change of the tensioning device, for example, for backside processing of the component, the geometric quality of the jig must be very high be high, resulting in corresponding costs.

alternative can however, simply constructed clamping devices can also be used, wherein the manufacturing and the Meßspannvorrichtung is present separately. The determination of the position of a clamped component then takes place usually with the help of three-dimensional recording measuring systems, for example 3D probes. Within the work space recording takes place a fixed number of measuring points, which on the workpiece surface of lie to be measured component. In practice, has a number proved advantageous from six measuring points; especially easy or however, particularly complex geometries may suffice a different number or be necessary.

To determine the position of the measuring points serve the six degrees of freedom of a body in space, so the translation in the X, Y and Z direction and rotation about the X, Y and Z axis. With knowledge of the location of a sufficient number of known points of the workpiece surface arranged in space, the position of the associated body can be determined exactly. One criterion in choosing the location of these points is, among other things, the distance of the points from each other. The larger the distance, the lower the measurement error that occurs during the measurement of the component. Also, three points spanning a plane spanning a parallel plane to the coordinate plane may not be collinear. The determination of the measuring points is generally determined by the designer or a quality engineer depending on the respective component geometry. From this component geometry, often accessible from CAD drawings or CNC control data sets, the corresponding n set points p _{iSoll are} known, where i runs from 1 to n and n is the number which is at least necessary to clearly describe the component position.

By means of the probe are then determined on the surface of the component, the associated n actual points p _iIst . Here, too, i runs from 1 to n.

To obtain the necessary set points p _ISOLL with the Istpunkten p _Iact in accordance, an algorithm is used which calculates the translations and rotations that the component to Achieve the best possible match.

This Algorithm is generally from the manufacturers of the corresponding device controllers firmly implemented in the respective control program and externally neither accessible still changeable and is often not exactly known. That means, that the user does not have precise knowledge about the algorithm for determination the position correction possesses, so that he also no information about possibly resulting from the algorithm resulting measurement or calculation error. As well it is withheld from the user, own additions or algorithms for Determination of the position correction to implement.

Of Furthermore, the known methods for determining the position are relatively time-consuming, because the calculation methods are complex and / or the number of Iterations from measuring and traversing movement is too high, which is too Achieving a sufficiently low target-actual position deviation are necessary.

Object of the invention

The The object of the invention is therefore to provide a method for measuring components using an open algorithm, the process being performed quickly and as accurately as possible from the target and actual position of a component to the best possible agreement of both layers necessary movements of translational and rotational nature determined.

The The object is achieved by the method proposed in claim 1. Accordingly, will an implicit, over-determined, Nonlinear system of equations whose solution sought Position correction in a very good approximation provides.

Further preferred embodiments are the dependent claims as well as the following detailed description.

description

The Method for measuring components in a Cartesian measuring or machine tool is based on the solution of a system of equations of n equations with five Unknown, whereby this system of equations implicitly, (in the case of n ≥ 6) and is nonlinear. With sufficient consideration of kinematic Boundary conditions is the solution of the equation system, the position correction sought in a very good approximation ready.

The The following description gives a preferred order of the ones to be performed Steps on. However, it is obvious that also other orders or the parallel processing of certain steps conceivable and in particular, for example, to save time also useful could be. It's just to make sure that a particular procedural step each can only be processed if all necessary data that must be available for its execution, too available.

In order to carry out the method according to the invention, first of all n setpoints p _{iSoll are read in,} for example, from a drawing, a CAD program or an NC data set. An index i runs from 1 to n and each point has three coordinates; one each for the position in the x, y and z directions.

Subsequently, n actual points p _{iIst are} read, which were previously detected by means of a suitable measuring device such as a 3D probe. The index i again runs from i = 1 ... n. The assignment is made in the same way as in the previous step.

Now a set of coordinates q _{k is} determined which uniquely describes a Cartesian measuring or machine tool. Preferably, these coordinates clearly describing the machine are selected such that their number is as small as possible (minimum coordinates). In the case of a five-axis machine, this results in a maximum of five coordinates or parameters.

Then a first term of the form f ₁ = Trans (q ₁ , q ₂ , q ₃ ) is set up, which describes the translation in the x, y and z directions.

Subsequently and analogously to the previous step, a second or a third term f ₂ = red (q ₄ ) or f ₃ = red (q ₅ ) is determined, which describes the rotation about a B or C axis. It should be noted that the B and C axes do not necessarily have to be identical to the x, y or z axis or direction.

In the case of a lack of corresponding movement possibilities of the machine, the respective coordinates or parameters, for example, permanently set to zero. For example, if the machine has only translational axes, q ₄ and q ₅ could be set to zero.

Then a system of equations can be set up, in which the following applies to the correct positioning of the component: p jSoll = Trans (q 1 , q 2 , q3) + red (q 4 ) · Red (q 5 ) · P jist (1)

In this case, j again runs from 1 to n, so that there are 3 · n equations with five unknowns, namely q ₁ to q ₅ .

The desired transfer by Translation and rotation of the component in the desired position could be now by loosening of the equation system with 3 · n Get equations and 5 unknowns. With sufficient consideration kinematic boundary conditions is the solution of the equation system then the desired position correction in a very good approximation ready.

According to a particularly preferred embodiment of the method according to claim 2 follow after the determination of the setpoints p _jSoll , and the actual points p _jIst two intermediate steps (z ₁ , z ₂ ) for generating two coordinate vectors r _Soll and r _Istl , by eliminating excess coordinates from the Vectors p _jSoll and p _{jIst are} generated. The conditions for the possible reductions are derived from kinematic, constructive, quality-oriented and / or component-specific features. As a rule, r _Soll and r _{Ist represent} 6 × 1 vectors. In this embodiment, analogously to (1), the reduced equation system results: r Should = Trans (q 1 , q 2 , q 3 ) + Red (q 4 ) · Red (q 5 ) * R is (2)

For the frequent case that n = 6 or greater, this is an equation system that is at least simply overdetermined (six or more equations, five unknowns). Furthermore, it is a nonlinear system of equations, since sine and cosine terms occur due to the equations of rotation. Finally, it is an implicit system of equations which is given by a form corresponding to F (x, y (x)) = 0, and which therefore can not be resolved explicitly according to the unknowns q ₁ to q _{5 as a} rule.

According to a preferred embodiment of the method according to claim 3 takes place after setting up the desired coordinate vector r _Soll , as well as the actual coordinate vector r _actual, a further intermediate step (z ₃ ) in which the excess coordinates in r _setpoint or r _{actual are set} to zero , According to a particularly preferred embodiment, both the surplus coordinates in r _Soll and r _{Ist are set} to zero.

• (i) q₁ = Translation in die x-Richtung
• (ii) q₂ = Translation in die y-Richtung
• (iii) q₃ = Translation in die z-Richtung
• (iv) q₄ = Rotation um die B-Achse
• (v) q₅ = Rotation um die C-Achse

According to a further preferred embodiment of the method according to the invention, the assignment of the abovementioned measuring machine or machine tool coordinates takes place in accordance with the following rule:

• (i) q ₁ = translation in the x direction
• (ii) q ₂ = translation in the y direction
• (iii) q ₃ = translation in the z direction
• (iv) q ₄ = rotation around the B axis
• (v) q ₅ = rotation around the C axis

There the B and C axes are not aligned with the x, y, or z axes have to be identical to describe the transformation five instead of six unknowns (For example, the rotation about an A-axis, which is identical to the x-direction is) off.

According to another preferred embodiment, the terms f ₁ , f ₂ and f _{3 are} formed such that the term f ₁ = Trans (q ₁ , q ₂ , q ₃ ) in the form of a 3 × 1 matrix, and the terms f ₂ = Red (q ₄ ) and f ₃ = red (q ₅ ) are each noted in the form of a 3 × 3 matrix. According to a particularly preferred embodiment, the positional shift is calculated from the corresponding data. According to a further particularly preferred embodiment, in an additional step (i) the equation systems (1) or (2) are converted into another system of equations, which reduces the number of unknowns to the number of equations. As a result, the system of equations to be solved is no longer overdetermined and thus easier to solve.

According to another preferred embodiment, the reduction of the number of unknowns to be achieved in the additional step (i) is such that the requirement for a minimization of the Gaussian error square is established according to the following equations: residuum j = (Trans (q 1 , q 2 q 3 ) + Red (q 4 ) · Red (q 5 ) · P jist ) - p jSoll (I) residuum T f ·residuum j = Σ (f (q 1 , q 2 , q 3 , q 4 , q 5 ) - p jSoll ) 2 =: F (q) (ii)

By partially deriving the above equations and zeroing according to the formula ∂F (q) / ∂ (q i ) = 0 Now a system of five equations with five unknowns q _i with i = 1 ... 5 is generated, which after solution yields the searched translations q ₁ to q ₃ and rotations q ₄ and q ₅ .

To a further embodiment Now the system of the resulting five equations will be on relevant numerical Procedure solved. To a further embodiment the equation system is solved analytically, if such a solution found can be.

According to a further preferred embodiment, the reduction of the number of unknowns to be achieved in the additional step (i) takes place in such a way that the requirement for a minimization of the Gaussian error square according to FIGS following equations: residuum = (Trans (q 1 , q 2 , q 3 ) + Red (q 4 ) · Red (q 5 ) * R is ) - r Should (I) residuum T · Residuum = Σ (f (q 1 , q 2 , q 3 , q 4 , q 5 ) - r Should ) 2 =: F (q) (ii)

By partially deriving the above equations and zeroing according to the formula ∂F (q) / ∂ (q i ) = 0 Now a system of five equations with five unknowns q _i with i = 1 ... 5 is generated, which after solution yields the searched translations q ₁ to q ₃ and rotations q ₄ and q ₅ .

To a further embodiment Now the system of the resulting five equations will be on relevant numerical Procedure solved. To a further embodiment the equation system is solved analytically, if such a solution found can be.

To a preferred embodiment of the Method, the data of the calculated actual position are sent to a measuring or handed over machine tool control. Then, based on these data, a position correction of the workpiece Change the workpiece position or a position correction of the tool causes, so that the workpiece subsequently in as possible optimal agreement with the actual situation is located.

To another embodiment of the method become cylindrical coordinates instead of Cartesian coordinates used and used the procedure mutatis mutandis.

To a further embodiment is the number of target coordinates and the actual coordinates is exactly 6. In this case receives one first according to the inventive method simply overdetermined Equation system, which is in a system of equations with five equations and five unknowns is convicted.

To again another embodiment the number of target coordinates and the actual coordinates are smaller or larger than 6. This can be particularly useful if the situation is particularly simple or particularly complex geometries to be measured, and / or if the expected position deviation only in very specific directions and / or angle can be made, or if the position deviations especially are big.

To a further embodiment The process will take some or all of those steps can be processed in parallel, also processed in parallel. hereby can be achieved a further time advantage, in particular at long individual measuring times come to fruition.

By Application of the method according to the invention can achieved in practice up to about 30% time savings compared to conventional Einmessverfahren become. The reason for that is mainly due to that the processing of the method according to the invention sequentially and not iteratively, provided that by the number the measuring points disregards predetermined iterations. In addition or in addition can by a use of the method according to the invention simple clamping devices to be used; the use of complex devices is not more necessary. As a result, a significant cost savings can be achieved.

Finally is the algorithm proposed here is freely accessible and can easily be changed from User adjusted by correction factors, otherwise supplemented or be further developed.

Prefers is the inventive method deposited in the form of a computer program. A calculator, which the corresponding data, in particular the desired and actual coordinates gets is thus enabled, the calculations of the invention perform.

Especially preferred is the corresponding program on a disk such a compact disc (CD), a floppy disk or a magnetic tape. Accordingly, this data carrier comprises a program according to the inventive method.

figure description

The single figure shows schematically a flow chart of a preferred Embodiment of the inventive method.

First, the read-in of the setpoint and actual points p _iSoll or p _{iIst takes place} . (Step (a) and Step (b).

Steps (a) and (b) are shown side by side. This means that the corresponding process steps are to be processed in parallel. The setpoints p _iSoll as well as the actual points p _iIst are read or acquired in parallel at the same time. In an alternative, not shown embodiment, these and / or all steps are executed exclusively sequentially.

The diagram also includes a first and a second intermediate step (z ₁ and z ₂ ) for generating a desired or actual coordinate vector r _set or r _actual . Also, a third intermediate step z ₃ for zeroing supernumerary coordinates of these vectors are shown. While steps z ₁ and z ₂ can be carried out selectively, this only makes sense for z ₃ if z ₁ and z ₂ were previously executed. Therefore, the dashed line branches below z ₂ to the left and right.

In each case, the determination of the coordinates q _k describing a measuring or machine tool follows (step c).

In Steps (d) to (f) are used to determine the terms that govern translation or describe the rotations of the machine coordinates.

Finally done forming a system of equations (step (g)) which is then in Step (h) is solved for example by means of a computer.

To a preferred embodiment here in addition a function as described in step (i) used (minimization the Gaussian square).

To clarify the input and output data, the corresponding parts of the diagram are drawn in bold lines. These are the desired and actual coordinates as well as the translations and rotations q ₁ to q ₅ sought.

Reference numerals and abbreviations

• n

  Number of tactile points or coordinates

  p _iSoll

  Set points - with i = 1 ... n

  p _iIst

  Actual points with i = 1 ... n

  r _Soll

  n × 1 nominal coordinate vector r _Is n × 1 actual coordinate vector q _k (minimum) coordinates of the measuring or machine tool

  Trans (q ₁ , q ₂ , q ₃ )

  Term or 3 × 1 matrix Translation in an x, y and z direction

  Red (q ₄ )

  Term or 3 × 3 matrix to describe the rotation about a B-axis

  Red (q ₅ )

  Term or 3 × 3 matrix to describe the rotation about a C-axis

  q ₁

  Translation into the x-direction

  q ₂

  Translation into the y-direction

  q ₃

  Translation into the z-direction

  q ₄

  Rotation around the B axis

  q ₅

  Rotation around the C-axis

Claims (14)

Method for measuring components in a Cartesian measuring machine or machine tool, comprising the following steps: (a) reading in n setpoints p _iSoll from a drawing with i = 1 ... n; (b) reading in n detected by means of a suitable measuring device actual points p _iIst with i = 1 ... n; (c) determining a set of coordinates q _k which uniquely describes a Cartesian measuring or machine tool. (d) determining a first term f ₁ = Trans (q ₁ , q ₂ , q ₃ ) which describes the translation in an x, r and z direction; (e) determining a second term f ₂ = red (q ₄ ) describing the rotation about a B axis; (f) determining a third term f ₃ = red (q ₅ ) describing the rotation about a C axis; (g) Setting up a system of equations p jSoll = Trans (q 1 , q 2 , q 3 ) + Red (q 4 ) · Red (q 5 ) · P jist . where j = 1 ... n, (h) solution of the equation system with 3 * n equations and 5 unknowns from (g), (i) position correction of the component using the solution from step h). The method of claim 1, wherein after determining the desired or actual points and before setting up the equation system, a desired coordinate vector r _Soll and an actual coordinate vector r _{Ist is} determined. Method according to Claim 2, in which the surplus coordinates in r _set and / or r _{actual are set} to zero. Method according to Claims 1 to 3, in which the assignment of the coordinates from step (c) takes place according to the following rule: (i) q ₁ = translation in the x-direction (ii) q ₂ = translation in the y-direction (iii) q ₃ = translation in the z-direction (iv) q ₄ = rotation about the B-axis (v) q ₅ = rotation around the C-axis Method according to one of the preceding claims, in which the terms f ₁ , f ₂ and f _{3 are} formed such that f ₁ = Trans (q ₁ , q ₂ , q ₃ ) in the form of a 3 × 1 matrix, and the terms f ₂ = red (q ₄ ) and f ₃ = red (q ₅ ) in the form of a 3 × 3 matrix. The method of claim 1, wherein in an additional Step (i) the system of equations is transferred to another equation system, which is the number of unknowns on the number of equations reduced. The method of claim 1, 2 and 6, wherein in the additional step (i) the reduction of the number of unknowns is performed such that the Requirement for a minimization of the Gaussian error square according to the equations residuum j = (Trans (q 1 , q 2 , q 3 ) + Red (q 4 ) · Red (q 5 ) · P jist ) - p jSoll (I) residuum T j ·residuum j = Σ (f (q 1 , q 2 , q 3 , q 4 , q 5 ) - p jSoll ) 2 = F (q) (ii) ∂F (q) / ∂ (q i ) = 0 (iii) to a system of equations consisting of five equations according to (iii) with five unknowns q _i with i = 1 ... 5. The method of claim 7, wherein the system the resulting five Equations about solved numerical methods becomes. Method according to one of the preceding claims, in which the calculated actual situation handed over to a machine control is and / or causes a position correction by changing the workpiece position becomes. Method according to one of the preceding claims, in which used instead of Cartesian cylindrical coordinate systems become. Method according to one of claims 1 to 7, wherein the Number of target coordinates and the actual coordinates is exactly 6. Method according to one of the preceding claims, in which some or all of those steps that work in parallel are also processed in parallel. Computer program for execution on a computer, which the implementation the method according to the invention according to claims 1 to 12 allowed. disk, the a computer program according to claim 13 includes.