An algorithm for CAD correction of the work pieces based on machine tool errors.

Anania, Florea Dorel ; Ispas, Constantin ; Mohora, Cristina 等

Abstract: In this paper is presented an algorithm for the correction of the 3D surfaces of the parts designed using CAD systems. This correction is realized depending of the tool machines' errors measured with performant measuring devices (Laser, Vibroport).The numerical command programs are realized based on the corrected surfaces of the part using CAD systems..

Key words: Machine tool errors, CAD-CAM, Algorithm, Operational coordinate.

1. INTRODUCTION

A tool machine, a produce of particular complexity is of quality if it can assure from a technical point of view the processing precision of the class it belongs to. So, the technical quality of a tool machine is appreciated by its dimensional precision, micro geometrical precision of the processed surfaces and the accuracy of the relative position of the generated surfaces, certain productivity conditions. (Ispas. 1998)

From all the components of the part processing process, the geometrical and cinematic errors of the tool machine can not be modified however much or whenever, but all the others can be compensated totally or partially. (Ispas.2006)

2. THE POSITION AND THE ORIENTATION IN THE OPERATIONAL CO-ORDINATES' SPACE

Most of the tool machines have in their structure prismatic clutches or rotation ones (specific for the machines with more than 3 axes). For the materialization of this clutches, kinematical chains with different levels of complexity are being used (the no. of elements, kinematical parameters, etc.) (Kersten 1983).

The general errors from these kinematical chains are cumulated in the tool machine's position general error. Such errors are being taken into consideration by the numerical command systems.

Indifferently of the programming system's complexity and command, the problem of a command, which consists in obtaining a large acceleration (short positioning time), of high positioning precisions, lack of vibrations, of an optimal proportion between the installed power and the weight, must be resolved in optimal conditions. (Rahman 2004.)

The movement's performances are mainly a result of the dynamical properties of the mechanical structure and of the quality of the movement command system. (Marinescu, 2002)

The tool's real position will vary of the ideal one, because the positioning precision measurements is obtained based on different kinematical chains and not exactly on the tool.

In figure 1 is presented the ideal position of the tool and the real one. The real position will be translated in three directions and rotated after the three axes because of the linearity and angular errors cumulated in the measured point.

The point that materializes the center of the tool will be translated on the x axis with [x.sub.r] (the linear errors cumulated on x axis), on y axis with yr (the linear errors cumulated on the y axis), on z axis with [z.sub.r] (the linear errors cumulated on z axis) and rotated with [PSI] (angular errors cumulated by the rotation around the x axis), with [phi] (angular errors cumulated by the rotation round the y axis) and with [theta] (angular errors cumulated by the rotation round the z axis). In fact, this position can not be measured by the machine tool command system, so it can not be corrected.

For the transformation from the Cartesian OXYZ into the O'X'Y'Z' the following unitary transformations have been used:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)

The transformation vector from O to O' is defined by the relation:

[T.sub.OO] = [R.sub.x] x [R.sub.y] x [R.sub.z] x [T.sub.r] (3)

The expressions to determine the position of the adjusted point depending on the ideal position are the following:

[x.sub.comp] = [x.sub.i] - (cos[psi] x cos[phi] - sin[psi] x cos[theta] x sin[phi]) x [r.sub.x] - - (cos[phi] x sin[phi] + sin[psi] x cos[theta] x cos[phi]) x [r.sub.y] - sin[psi] x sin[theta] x [r.sub.z] (4)

[y.sub.comp] = [y.sub.i] - (sin[psi] x cos[phi] + cos[psi] x cos[theta] x sin[phi]). [r.sub.x] + + (sin[psi] x sin[phi] - cos[psi] x cos[theta] x cos[phi]) x [r.sub.y] + cos[psi] x sin[theta] x [r.sub.z] (5)

[z.sub.comp] = [z.sub.i] - sin[theta] x sin[phi] x [r.sub.x] -sin[theta] x cos[phi] x [r.sub.y] - cos[theta] x [r.sub.z] (6)

where [x.sub.i], [y.sub.i], and [z.sub.i] are ideal coordinates for the studied point.

[FIGURE 1 OMITTED]

These relations are implemented in the CAD program for adjusting surfaces. Given the type of machine on which we apply the method of adjusting errors by modifying the surfaces of the CAD model, the mathematical relation 1, 2 and 3 can be modified.

A three-dimensional matrix of points defines, mathematically, the machine's work space. For more than 2000 mm for the work space the distance between measured points should be 100 mm; for less than 2000 mm, it should be 50 mm.

For each of these points it should be measure the linear and angular positioning errors obtained for the machine tool systematic errors in normal functioning state.

3. COMPENSATION OF THE MACHINE TOOL ERRORS BY CAD-CAM MODELLING

The main idea of this method is, base on the machine's errors, to modify the 3D model of the piece's surfaces in a CAD system (computer aided design). This modified model will be used for generating numeric command program in a CAM system (computer aided manufacturing).

The program is structured in a number of 17 functions for calculating and generating external files type CatScript. The program is modularly structured and easy to follow and read, facilitated by the comments inside the program.

The input data will be errors' values measured with a LASER interferometer. These errors are for linear positioning precision measured in specific points in the work space, in micrometers, and angular, in the same point, measured in degrees. At the same time, there can be introduced global errors after studying the machine's dynamic behaviour at different work rates.

As a result there will be 3 type of files CatScript: ideal.CATScript- for generating points and/or curves and/or surfaces which materialize ideal surface; real.CATScript- for generating points and/or curves and/or surfaces which materialize the real surface; compensat.CATScript- for generating points and/or curves and/or surfaces which materialize the adjusted surface.

The functions used:

* calcul_er()--function for calculating the work space's point coordinates depending on the errors.

* deschide_catia(""); -function for opening ideal.catscript; real.catscript; compensat.catscript files where will be written specific CATIA commands for drawing point and/or curves and/or ideal surfaces;

* scrie_p_ideale(ref); scrie_p_reale(ref); scrie_p_adjust(ref)--functions for generating drawing command sequences for each ideal, real and adjusted point in the work space. This function has as an argument ref--the number of points in the work space;

* traseaza_linii()--function for generating the commands for drawing lines between the coordinates of the two adjacent points into direction of the Cartesian system;

* linii_ref()--function which defines lines generated with traseaza_linii() in order to use them as a reference element in drawing plane surfaces;

* traseaza_plan(1)--function which draws plane surfaces between four adjacent curves (lines) that form a closed contour;

* Inchide_catia()--function which close all the opened filse of CATIA.

[FIGURE 2 OMITTED]

As a result of running the program we obtain real and compensated 3D surfaces for the parts to be processed, used for generating the CAM program. In the figure 2 is presented a particular case for a plane surface.

4. CONCLUSION

This paper is based on the research developed into doctorate thesis Research regarding the dynamic of the manufacturing systems with high speed machining into Univeristy POLITEHNICA of Bucharest

This method can be applied on any type of machine tool, having high speeds or not. It has to have implemented a numerical command system.

In order to improve the performances of a numerical command tool machine it isn't necessary to modify the machine, only to determine the errors (geometrical, thermal, dynamical errors, etc.) and to modify the numerical command programs implemented on the machine according to them. For this a CAD-CAM system is necessary and a compensation program (like the one presented in this paper) that is much easier to realize from an economic point of view and also of the necessary time.

The purpose of the present researches presented was the realization of an algorithm utilizable for the total or partial compensation of the machine tool global errors during the milling operations on numerical command machines.

5. REFERENCES

Ispas C., Predincea N., Zapciu M., Mohora C., Boboc D., (1998)--Machines-Tools Tests and Reception -, Editura Tehnica,Bucuresti,

Ispas C. (2006)--Machine tools for HSM. 1. Context, 2.Particularites, 3. Conception 4. Research in Romania, 4-emes Assies Machines et Usinage Grand Vitesse, 8,9 juin 2006, ENSAM, Aix-en-Provence, www.lsis.org/AssisesMUGV2006

Kersten, A,. (1983)--Geometrical Machine-tool comportment among static and thermal loads.--Doctorate thesis, Fakultat fur Maschinenwessen de rheinsch-westfalischen technischen hochschule aachen (1983)

Marinescu I., Ispas C., Boboc D. (2002)--Handbook of Machine Tool Analysis, United States of America, ISBN 0-8247-0704-4,

Rahman M. (2004)--Modelling and measurement of multi-axis machine tools to improve positioning accuracy in a software way--doctorate thesis University of Oulu.