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Geometry compensation of coordinate measurement machines

Section carried out with the technical advice of Hexagon Metrology, S.A.15/08/2005

Take a point on the surface of the object to measure technically means register three Cartesian coordinates of the center of the tip of the measurement transducer. These coordinates are taken from trasductores which "read them" in the optical rules along the axes of the machine. In this way means that the tip of the tool is only the tip of a complex mechanical components and links kinematic chain, and a series of static type errors are joining the chain because of structural deformations and Assembly. In order to obtain, through several readings, results measurement as accurate as possible is necessary to use sophisticated techniques to determine the error and its correction.

Premise

First and foremost has to remember that before the advance of compensation systems software errors in geometry, the accuracy of the machines was achieved through laborious calibrations mechanical, whose effectiveness depended on highly specialized technicians. Currently, the use of mathematical algorithms for the correction of errors makes no necessary mechanics so that the characteristics of repeatability and linearity of geometric errors are acceptable within certain values. This is achieved thanks to the results of high quality that offers geometry compensation, best of which were mechanically, on condition that the positions of head of measurement are very repeatable.

Geometric errors

Bridge machines

Fundamental errors (parameters) which dealt with compensation algorithms are a total of 21 bridge machines: 9 errors of translation (6 of linearity, positioning 3), 9 errors of rotation and 3 errors in quadrature.

Figure 1a

Figure 1b

Figure 1 c

LXX, Lyy, Lzz	Errors in positioning of the axes, due to the response of the ópti cas rules and the rotation of the axes.	Fig. 1A
Lxy Lxz LyX, Lyz LZX Lzy	Errors of linearity of the axes on the transverse axes. Due to the imperfect of the routes of displacement linearity and the effects of rotation of the axes.	Fig. 1A
Rxx, Rxy Rxz Ryx, Ryy Ryz Rzx, Rzy Rzz	Errors of rotation of the axes environment to each of the 3 axes. With the provisions of a vessel are called rool, pitch and jaw. Due to the imperfect of the routes of displacement linearity and structural deformations produced during the Assembly.	Fig. 1B
Qxy, Qyz, Qzx	Mistakes of balancing between pairs of axes. Due to the imperfections of assembling of the structure.	Fig. 1 c

Gantry machines

Between large gantry machines that use a second translator position along the longitudinal axis, the positioning error takes into account even the value reads the translator that works in the secondary, pro rata to the position of the transversal carriage. The rest of errors are treated as in bridge machines.

Horizontal arm machines

All parameters that have been described for bridge machines are applied and are managed on the horizontal arm machines. In this type of machines to be take into account three parameters which are due to subsidence caused by the weight of the horizontal arm that deformed, depending on its size, the geometry of the amount and some components to which it is linked.

The first parameter, called Rcx, takes into account the rigid rotation of the amount with respect to the longitudinal axis caused by the deformation of the structure to which is the amount (Fig.2).

The other two parameters, known as Fzy and Rmx, correcting the effects of the deformation of the amount with respect to the longitudinal axis (fig. 2).

These 3 components of correction completed, for the horizontal arm machines, the model of compensation already described for vertical arm machines.

In the case of horizontal double arm machines are valid, separately, all the foregoing considerations. Errors due to the correlation of the two arms are offset in the management of the system of reference common to the two volumes of measurement.

Measurement errors and its compensation

When run the operations of the machine Assembly, after having made the appropriate verifications of functionality and correct dynamic behavior, is done measurement to determine geometric errors.

These operations are applied to the head of machine tools appropriate instruments which will make it possible to measure errors of rotation and translation of each of the axes. Each process is divided in steps, which depend on the type of machine and precision to fetch.

Then describes the main phases of compensation. At the end of each phase values obtained are entered into the map of compensation and accountability in order to correct the effect of these errors.

1st phase: Rotation errors

Electronic precision levels mounted on the head of the machine are used to measure rotation Rxx errors, Ryy. These values can be measured in differential form with respect to that obtained from other levels (reference levels) in the table.

An interferometric laser is used to measure the rest of rotation errors.

The relative rotation between the retroreflector (optical that, in this case is mounted on the machine head) and the Interferometer (reference optical) reads the laser through the different steps of compensation that are achieved through the shaft which is measuring.

As well as by the level of reference, including the optical reference will have to be solid with the Bureau of the pieces.

2nd phase: Roll of the Z axis error

This phase is sensitive and complex. This rotation cannot be measured with methods that we have already described.

The linearity is usually measured laser (this is described further below). The optical mounted on the head of the machine applies to jumps, something that can be more or less long. Thus, the differential reading between two measurements obtained with spacing (offset) appropriate optic will provide the values that are searched.

3rd phase: errors of linearity (linearity)

They are measured with Laser interferometric. Optical components which allow take transverse deviations mobile optical (mounted on the head of the machine) in compliance with respect to a reference optical during movements by the axis of measurement are used to detect them. The fixed optical (retroreflector) is usually located on the opposite side of the laser head.

4th phase: positioning errors and errors in quadrature

Positioning errors are normally detected the interferometric laser. Similarly to rotations, the retroreflector is mounted in the head of the machine and the Interferometer will be the optical reference. This is situated close to the laser head.

In the detection of errors in positioning phase, it is important to take into account the temperature of the optical rules, because of its thermal expansion. The procedure of compensation expected the temperature to which the machine made correct measurements is 20 ° c. When she is measuring positioning errors be counted the different temperatures of the optical rules and its coefficient of thermal expansion.

Quadrature errors are obtained from differential measurements of a caliber to be put in two positions for each of the 3 plans coordinated by the volume of measurement. The caliber is measured with a diagonal of the plane and then doing a diagonal opposite at the same level.

Verification of the formula of the uncertainty of measurement

Once completed the phase of correction of the Quadratures and activated the last part of the algorithm of set-off, are repeated measurements of the volumetric diagonals in the calibers of reference. Through these operations are verified the performance of the machine of measurement on the formula of expected measurement uncertainty.

Periodic verification of metrological system benefits

With the rules of certification of the quality of each company says that measuring instruments be checked periodically and if it is necessary that they fix up. This includes measuring machines by coordinates, as a reference tool to control parts of production. They not only have to follow the regulations, but above all the normal rules of common sense, this is the basis to manage well all the measurement and production teams.

DEA recommends that measuring machines be checked and are repaired annually. Given the few mechanical needs of measuring machines, intervention is resolved in the most cases with a normal benefits verification, unless there are structural or functional variations which occurred during the use of the machine because of:

Subsidence of the mechanical structure (improbable unless there are accidental collisions)
Improper use of the machine
Neglect of preventive peacekeeping operations
Sinking of the pavement
Effects of vibration caused by the environment (machines in operation, the passage of conveyor lanes, etc.). The machine is not well insulated.
Use of the rollers of displacement when they are present
Impairment of the benefits of the sensors or optical rules.
The periodic calibration is a series of operations of maintenance and functional checks and metrological:
Control of the State of the mechanical and structural bodies
General conditions of operation of the machine verification
Cleaning of travel guides
Cleaning of optical rules
Transmission belts tension
Damage control and repair
Verification of benefits metrological (see paragraph "Verification of the formula of uncertainty of measurement")

Only in the event of a significant difference with regard to the last check is the repair of the machine with the necessary instruments