Limitations of laser diagonal measurements

Transcription

1 Precision Engineering 27 (2003) Limitations of laser diagonal measurements Mark A.V. Chapman Laser and Calibration Products Division, Renishaw Plc., Old Town, Wotton-under-Edge, Glos GL12 7DW, UK Received 11 March 2003; accepted 14 March 2003 Abstract The introduction of B5.54 and ISO230-6 machine tool performance measurement standards is increasing the popularity of laser interferometer diagonal, step diagonal and vector methods for the evaluation and compensation of machine tool errors. This is due to the potential reduction in calibration time, these methods can provide over the more conventional laser interferometer-based linear, angle and straightness measurements taken along lines parallel to the machine s X, Y and Z axes. This paper highlights limitations in the results produced by diagonal-based measurements and by the more recently introduced vector or step diagonal methods. The purpose of this paper is to alert potential users of these methods to their limitations so they can make informed decisions as to whether the reduction in calibration time they can provide outweighs the loss of accuracy and detail in the results. It also indicates some of the dangers in using laser diagonal data alone for the compensation of machine tool errors Elsevier Science Inc. All rights reserved. Keywords: Laser interferometer; Machine calibration; Laser diagonal; Step diagonal test; Vector diagonal; B5.54; ISO230-6; Volumetric accuracy; Machine error compensation 1. Laser diagonal measurement In laser diagonal measurements (as described in B5.54 and ISO230-6 Standards), a laser interferometer is used to measure the positioning accuracy of a machine tool as it moves along each of the machine s four body diagonals in turn. These four body diagonals are shown schematically in Fig. 1. The American B5.54 Standard [1] states that the volumetric accuracy of a machine may be rapidly estimated by measuring the displacement accuracy of the machine along body diagonals. The International ISO230-6 Standard [2] states that diagonal displacement tests allow the estimation of the volumetric performance of a machine tool and also that diagonal displacement tests may be used for acceptance purposes and as reassurance of machine performance where parameters of the test are used as a comparison index. However, recent work has highlighted that, under certain conditions, a machine can achieve a good result on ISO230-6 and B5.54 diagonal tests, even though it has a poor volumetric performance. This is because changes in the lengths of the body diagonals caused by one source of error in the machine can be cancelled out by the changes due to another source of error. Fax: This effect is easily illustrated by considering a simple 2m 1m 0.5 m machine tool. If the machine has no errors, the body diagonal measurement will show that, to the nearest micrometre, all four body diagonals are m long. (From Pythagoras theorem = ( ).) Now suppose the same machine has a 25 m/m over-travel error (positive linear error) in the motion of the X axis, a 100 m/m under-travel (negative linear error) in the Y axis motion and no error in the Z axis. Under these conditions the laser diagonal test will show the diagonal lengths have changed by less than 0.1 um and so, to the nearest micrometre, they are still m long. (From Pythagoras theorem = ( ).) The B5.54 and ISO230-6 diagonal tests will, therefore, indicate that the machine is still good, when clearly this is not the case. The machine has a volumetric error of over 100 m. (Note: Volumetric error is defined here as the length of the worst case error vector between the target and the actual machine position anywhere within the machine volume.) A similar effect is shown by the square and rectangle in Fig. 2, both of which have diagonals of the same length, even though their shapes are clearly different. It might be imagined that these are special cases, which will only give concerns under very unique circumstances. However, this is not so. In fact, if any axis (or axes) show an over-travel error whilst any another axis (or axes) show an /$ see front matter 2003 Elsevier Science Inc. All rights reserved. doi: /s (03)

2 402 M.A.V. Chapman / Precision Engineering 27 (2003) Fig. 3. Machine with X axis yaw error. Fig. 1. The four body diagonals. under-travel error, their combined effect on the body diagonal result will, to some extent, cancel. This can lead to some confusing results. Consider two further examples: Machine A has a 1 m 1m 1 m operating volume with a +50 m/m over-travel error in the X axis and no error in the Y and Z axes. This machine will achieve a B5.54 and ISO230-6 diagonal test result of 28.9 m. Its volumetric accuracy is 50 m. Machine B is a similar 1 m 1m 1 m machine, but has a 100 m/m over-travel error in X, a50 m/m under-travel error in Y and 25 m/m under-travel error in Z. This machine will achieve a B5.54 and ISO230-6 diagonal test result of 14.4 m, which is better than machine A. However, its volumetric accuracy is 115 m, which is worse than machine A. Machine B has achieved a B5.54 and ISO diagonal tests result which is twice as good as machine A, even though its volumetric performance is twice as bad. Fig. 3 shows another interesting combination of errors. In this case the machine (shown by the shaded area) has a bent X Fig. 2. Square and rectangle with same length diagonals. axis causing a gross yaw error in its motion. (The dotted lines indicate a perfect machine.) The machine has been adjusted with a laser so that the linear X and Y motions have no error when measured through the centre of the machine volume. In this example the overall diagonal lengths are also almost perfect. However, in this instance, providing measurements are also taken at multiple positions along the diagonal (as required by B5.54 and ISO230-6) the effect of the yaw error will be detected. Clearly laser measurement of overall diagonal lengths and the results of B5.54 and ISO230-6 laser diagonal tests do not always give reliable indication of volumetric performance, and therefore need interpreting with caution. Diagonal tests cannot be used, in isolation, to compare the volumetric performance of machines. In order to provide reliable results it is essential to also carry out additional tests such as linear accuracy and pitch and yaw tests parallel to the X, Y and Z axes and perhaps a telescoping ballbar test. (ISO230-6 suggests supplementing the body diagonal tests with tests on face diagonals, tests parallel to the machine axes and by circular or telescoping ballbar tests.) These tests are all clearly described elsewhere in the B5.54 and ISO230 series of standards, but are sometimes ignored to minimize test times. 2. Step diagonal and vector diagonal methods Recently, it has been proposed in a number of technical papers [3,4], that the original laser diagonal test can be enhanced by using a special step sequence to move between target positions on the body diagonals. This method is often called a step diagonal or vector method. In the original laser diagonal tests (as described in B5.54 and ISO230-6 Standards), the machine moves its X, Y and Z axes simultaneously to move in a straight line between the target positions along each body diagonal. This is illustrated in Fig. 4, which shows the target positions (as dots) along one

3 M.A.V. Chapman / Precision Engineering 27 (2003) Fig. 4. B5.54 and ISO230-6 diagonal test target positions. Fig. 6. Step diagonal test set-up. of the body diagonals. Laser data is recorded at each target position using a laser linear interferometer, aligned along the diagonal and striking a retroreflector optic. In the step diagonal test or vector test, the X, Y and Z axes are moved one at a time with laser data recorded after the movement of each axis. This generates three times as much data. This is illustrated in Fig. 5, which shows the additional target positions. It has been claimed that, in addition to the original diagonal displacement error results, the step diagonal method can also provide results for the linear accuracy, straightness and squareness of the X, Y and Z axes. To carry out this test, the laser system is usually operated with a plane mirror reflector mounted on the machine s spindle. This mirror ensures that the laser beam is always returned into the laser s return port as the machine zig-zags along the diagonal. The test set-up is illustrated in Fig. 6, which shows the side view of a laser aligned along a machine body diagonal. The laser beam is reflected back to the laser by a plane mirror. Notice that, as the machine zig-zags along the diagonal, the mirror moves from side to side relative to the laser beam. Fig. 5. Step diagonal test target positions. This causes the point at which the laser strikes the mirror to change. If the laser beam and mirror are aligned perfectly and there are no pitch, yaw and roll errors in the machine, then the theory of operation is as follows. When the X axis moves the laser will measure the combined effect of errors in the linear and straightness motion of the X axis. When the Y axis moves the laser will record the combined effect of errors in the linear and straightness motion of the Y axis. Then, when the Z axis moves, the laser will measure the combined effect of errors in the linear and straightness motion of the Z axis. By repeating the measurement along all four body diagonals it is mathematically possible to identify the individual contributions from the linear and straightness errors of each axis, and also to identify the squareness errors between the three orthogonal axes. However, there are two fundamental problems with this approach. Firstly, the vast majority of machines do have roll, pitch and yaw errors which will contaminate the results and introduce additional terms which the mathematics cannot identify. Secondly, (and more importantly), errors in the alignment of the plane mirror and laser beam will introduce additional errors which cannot be separated from linear displacement errors in the X, Y and Z axes of the machine. The effect of mirror misalignment is illustrated in Fig. 7, which shows the side view of the laser aligned to a body diagonal of a 1:1:1 aspect ratio machine. The movement of a misaligned mirror (shaded) is compared with that of a perfectly aligned mirror (outline). The mirror has been misaligned by a small angle about the machine s Y axis. (The mirror misalignment has been grossly exaggerated in the figure for clarity.) When the mirror moves along the X axis, the laser beam will travel across the mirror surface and, because the mirror is not perfectly perpendicular to the laser beam, this will introduce a measurement error (as shown in the figure). In

4 404 M.A.V. Chapman / Precision Engineering 27 (2003) Fig. 7. The effect of mirror misalignment. Fig. 8. The effect of mirror misalignment. this example, the change in laser reading, recorded as the machine s X axis moves forward, is too large. If the plane mirror is misaligned by an angle of just 40 arcseconds or 0.2 mm/m (a typical alignment tolerance) and the X axis step size is 50 mm, then the laser will record an extra 7 m of displacement during the movement of the X axis. This measurement error will occur during every step of the X axis and will thus accumulate to 140 m/m of X axis travel. This error is significant and, although it can be removed by performing a linear regression (slope removal) on the resulting X axis data, this process will also remove any information about any overall under-travel or over-travel errors in the machine s X axis. When the mirror moves along the Z axis, the laser beam will travel back across the mirror to the original position. So, in this example, the laser will record a measurement that is 7 m too small. Note how this error is opposite (or complimentary) to the error introduced on the X axis. Again this error will accumulate to 140 m/m of Z axis travel, and although this can be removed by performing a linear regression (slope removal), this process will also remove any information about any overall under-travel or over-travel errors in the machine s Z axis. It has been suggested that this problem can be overcome by repeating the measurement in the reverse direction using the opposite axis movement sequence. However, it is easy to demonstrate that the errors introduced onto the measurements in both forward and reverse directions are identical. Fig. 8 shows that, even though the laser beam has travelled onto the opposite side of the mirror, the change in laser reading, recorded as the machine s X axis moves back, is still too large. The error is identical to that shown in Fig. 7 when the X axis moved forward. The net result of this is that step diagonal method cannot produce accurate data about overall linear under-travel or over-travel errors in the machine s X, Y and Z axes. Therefore, the method cannot produce reliable linear accuracy data. It is possible to use the four body diagonal lengths to determine if the overall machine volume is too large, or too small, but it is not possible to determine which of the machine s linear axes is responsible for any error. It also important to realise that, if the alignment of the mirror changes during the test (as it will if the machine has a pitch or yaw error), then the error due to mirror misalignment will not accumulate linearly, and hence cannot be completely removed by linear regression. Therefore, linear data obtained from the laser step diagonal method, for the machine s X, Y and Z axes, should not be used for the linear error compensation of those axes. Although such compensation may appear to produce an improvement in a machine s performance on B5.54 and ISO230-6 diagonal tests, these tests cannot reliably identify the effects of complimentary errors in the linear motions of the X, Y and Z axes. Therefore, any improvement in the B5.54 and ISO230-6 body diagonal test results, following such compensation, cannot be taken as evidence that the machine s volumetric accuracy has actually been improved to a corresponding degree. This is covered in more detail below. 3. The sensitivity of squareness results to machine aspect ratio Although the step diagonal data does not produce overall linear accuracy data, the measurement of body diagonal lengths (by either step diagonal or regular diagonal measurements) can yield information about the squareness errors between the machine s X, Y and Z axes. In theory, if all diagonals are of the same length, then the X, Y and Z axes will be orthogonal to one another, and if the diagonals are not equal in length, then it is possible to calculate the non-squareness between the X Y, Y Z and Z X axes. However, the quality of these calculated squareness results is very dependent on the aspect ratio of the machine and the

5 M.A.V. Chapman / Precision Engineering 27 (2003) Fig. 9. Uncertainty in calculated squareness results from body diagonal measurements. stability/accuracy of the laser diagonal readings. It is typically recommended that such measurements should not be carried on machine volumes with an aspect ratio of >3:1. Fig. 9 shows the uncertainty in the calculated squareness results for laser body diagonal measurement uncertainties of 1 and 5 ppm when measuring diagonals on machines with differing aspect ratios. (A machine with an aspect ratio of 3 is taken as having an X axis which is three times longer than the Y and Z axes, and the uncertainty is calculated for the Y Z squareness.) Uncertainties in the laser diagonal length measurements are typically caused by changes in machine temperature that occur over the time it takes to measure the four diagonals. An uncompensated change in machine temperature of just 0.1 C will typically cause a diagonal measurement error of 1 ppm. A change of 0.5 C will typically cause a diagonal measurement error of 5 ppm. Fig. 9 clearly illustrates the difficulty in obtaining high accuracy squareness results in unstable environments and on machines with unfavourable aspect ratios. The step diagonal method of capturing data can exacerbate this difficulty by almost trebling the time it takes to capture the data (due to the step sequence and the extra data points) and by reducing the range of Z axis travel available (due to the size of the angled plane mirror). On long thin machines, it is possible to measure the machine in two or three separate sections, each with a more favourable aspect ratio, but this increases calibration time dramatically. If axis squareness is to be measured using laser diagonal measurements, it is strongly recommended that measurements are carried out on face rather than body diagonals. This has the advantage of reducing the test time (thereby minimising any thermal changes) and improves the aspect ratio. 4. Machine error compensation using diagonal or step diagonal data 4.1. Squareness correction It is accepted that B5.54 and ISO230-6 body diagonal test results can be used to identify machine squareness errors and that this data may be used to improve machine accuracy. However, special care needs to be taken to maintain the relative accuracy of the laser body diagonal measurements, especially on machines with unequal axis lengths or in unstable environments. To overcome these limitations it is strongly recommended that X Y, Y Z and Z X squareness are measured independently using any one of the following test methods. Reference square and dial indicator (clock gauge). Laser interferometer face diagonal measurement. Telescoping ballbar test. Alignment laser with an optical square (penta-prism). Laser interferometer straightness measurement with optical square. Note that before performing any squareness corrections or compensations, the alignment of the work-surface (table) to the machine s X, Y and Z axes must also be considered. Failure to do this may result in a table surface that is not parallel to the plane defined by the compensated motions of the machine s X and Y axes.

6 406 M.A.V. Chapman / Precision Engineering 27 (2003) Linear correction It has also been reported [3,4] that laser step diagonal measurements can be used to provide linear compensation data. Unfortunately, the calculations used to remove the mirror alignment errors also remove information about the overall linear error in the X, Y and Z axes. This makes reliable linear error correction impossible. It is possible to make a correction so that the machine passes the B5.54 and ISO230-6 body diagonal tests, by applying equal compensation to all three axes, but there is a danger that this will actually make the machine s accuracy worse. Consider the following example. Machine C is a 1 m 1m 1 m machine which has perfect X and Y axes, but the Z axis over-travels by 100 m/m. The axes are all square to one another. The step diagonal results will show that all four body diagonals are too long (each diagonal is m long instead of m, an error of +58 m). However, the linear regression calculations used to remove errors due to plane mirror alignment will also destroy any information about which of the machine s axes is responsible for the fault. To circumvent this problem it is possible to simply apply a 33.3 m/m correction to each axis. This will produce a good diagonal test result, but it hasn t fixed the machine. The Z axis is left with a linear error of m/m. The X and Y axes (which were perfect), now have a linear error of 33.3 m/m. After compensation the machine s accuracy in the X Y plane has been seriously degraded, even though the B5.54 and ISO body diagonal results indicate that the machine has been improved! 5. Conclusion This paper has demonstrated that machines with significant errors in the motions of their axes can still achieve good results on the B5.54 and ISO230-6 body diagonal tests. It is, therefore, recommended that future versions of these standards be modified to emphasise that diagonal tests, in isolation, do not give a reliable indication of a machine s volumetric accuracy or performance, but only detect changes in position along diagonals. The standards should more clearly emphasise that in order to reliably assess overall volumetric performance, it is essential to combine body diagonal tests with conventional linear displacement, and angular pitch and yaw tests parallel to the machine s X, Y and Z axes. This paper has also demonstrated that the step diagonal or vector method cannot provide reliable linear accuracy data for a machine s X, Y and Z axes. It has shown the dangers of using such data for linear error compensation and of relying on a subsequent B5.54 or ISO230-6 body diagonal test to prove such compensation has been effective. It is recommended that linear error compensation should only be performed based on data obtained from conventional linear displacement accuracy tests made parallel to the machine s X, Y and Z axes. It is also recommended that pitch and yaw measurements are performed to confirm the validity of the linear data before compensation is performed. Potential users of the diagonal and step diagonal test methods should, therefore, consider whether the potential savings in test time justify the reductions in accuracy that may result. Acknowledgments The author wishes to express thanks to the following people for their contributions during the preparation and review of this paper. Dr. Ray Chaney and Pascal Malesinski, Renishaw Plc. James Bryan, Bryan Associates, Pleasanton, CA, USA. Wolfgang Knapp, Chairman ISO/TC39, Machine Tools, Engineering Office Dr. W. Knapp, Tim Morris, Cincinnati Machine UK Ltd., Hans Soons & Alkan Donmez, NIST, USA. References [1] American Society of Mechanical Engineers (ASME). B methods for performance evaluation of computer numerically controlled machining centres. An American National Standard. [2] International Standards Organisation (ISO). ISO 230-6: 2002 test code for machine tools, Part 6. Determination of positioning accuracy on body and face diagonals (diagonal displacement tests). An International Standard. [3] Wang C. Laser vector measurement technique for the determination and compensation of volumetric positioning errors, Part 1. Basic theory. Review of Scientific Instruments, vol. 71, No. 10, October [4] Wang C, Liotto G. A laser non-contact measurement of static positioning and dynamic contouring accuracy of a CNC machine tool. In: Proceedings of the Measurement Science Conference, Los Angeles, January 24 25, 2002.