A new slant on diagonal laser testing

Transcription

1 A new slant on diagonal laser testing T.J. Morris Cincinnati Machine U.K. Ltd., Birmingham, England Abstract In the early 1990s the Americans introduced diagonal laser tests as a quick method for evaluating the volumetric accuracy of machine tools. More recently, IS0 have started preparing a new standard based on this document. This paper examines what can be achieved with this type of test, and what advantages can be gained by carrying out the proposed additional face diagonal measurements in a three-dimensional domain. Of particular interest is the potential ability for checking squareness measurements on large machmes. 1 Different approaches to the measurement of accuracy When a customer asks a manufacturer how accurate his machine tool will be, what he really wants to know is, how accurately will the machine produce his components. For this, all he needs to know is how accurately the tool to workpiece relationship can be maintained. The manufacturer will probably evade the issue by producing a test document showing the accuracy of squareness between the axes, the positioning accuracy of each separate axis along a straight line, the run-out of the spindle and an impressive list of other similar test measurements. Furthermore, he will probably be able to quote chapter and verse of the standard that he has based his tests on. Users of machines do not usually confine themselves to single axis movements. If a work-piece has two holes in it that do not lie along a particular axis this will require a vector move involving two or even three axes. But the likely error in position here-the centre distance error-is not readily available from the results of the manufacturer's conventional machine tests. One of the problems of defining the accuracy of a machine tool is thus finding a measurement quantity that gives the customer precisely what he needs. The tests we derive-and subsequently create standards for-are, quite rightly,

2 becoming more scientific, more analytical, and more 'parametric'. This means that we are evaluating the fundamental components of a systematic error model based on the number of 'degrees of freedom' of the system. A three-axis machine tool has six degrees of freedom per axis and hence 18 'parameters' are needed to define the accuracy at any point in its work-zone. These parameters are all multi-valued, by which is meant that their values vary continuously from point to point along the relevant axis. The convenient addition of a further three single-valued parameters to define the alignment (or 'squareness') between the axes helps to rationalise the error model in accordance with the machine configuration. These twenty-one parameters (see section 4 for details) are all derived from the six degrees of freedom of the individual components. When all the parameters are known it is then feasible to synthesise the error in the distance between any pair of points in the work-zone-assuming that all the parameters remain constant. From this we can compute the 'Volumetric Accuracy' [l] of the machine, which is an honest attempt at producing a practical accuracy figure of merit applicable to all the points in the working volume. 2 The global approach There are times, however, when a different method can pay off: the 'global' approach. Here you measure just what you need to measure and ignore all the constituent parts. In a machine tool this simplifies down to measuring the requisite tool to work-piece relationship. Thls global error measurement is a function of all the constituent error parameters in the complex path linking the tool to the work-piece. The resultant error will be a displacement error in the position of either the tool or the work-piece-or, most probably, both. When we look at practical methods of accuracy measurement in use, we see that the distinction between an analytic and a global approach becomes blurred. An excellent example of this is the ball-bar. This is a linear transducer that measures variation in radius while attempting to follow a programmed circle. This is all it does: it measures a single composite quantity, the maximum value of which is designated 'circularity' [2]. The error at any point on the circle is a function of seven of the fundamental accuracy parameters: two errors of position, two of straightness, two of angle and one of squareness. Additionally, since the test is dynamic, further parameters are needed to define the path error (sew0 following errors), as well as accounting for the influence of external vibrations and velocity dependent hysteresis. Yet for all this, the ball-bar comes with analytical software that for the most part does a pretty good job at pigeon-holing the sources of error into a dozen or so 'functional' parameters. (These are generally different from the 21 geometric parameters.) All it needs are two contouring tests, one in each direction. It works well because 'intelligent' assumptions are made about how the machine tool is supposed to work.

3 3 Diagonal laser test Another test that does this is the diagonal laser test. This was first introduced in the early 1990's by the Americans as a 'cheap and cheerful' alternative to a fullblown volumetric analysis. This was part of their comprehensive ANSIiASME [3] standard for testing machine tools. Their standard states "Complete testing of the volumetric performance of machine tools is a difficult and time-consuming process. This Standard has attempted to reduce the time and cost associated with such testing by using diagonal displacement measurements...". The laser test has long been established as the most effective way of determining the accuracy of positioning of a single axis. Its popularity over other methods is no doubt due to the fact that its cost is independent of the length of measurement. Over the years, standards have appeared detailing how this test should be carried out. The latest of these is IS : 1997 [4]. The new diagonal test involves moving three axes simultaneously in order to measure the accuracy of the length of the four principal diagonals that define the work-zone. (See fig. 1.) The laser is used in a method similar to the conventional single axis method, and the same software can be used for simple processing of the data. These diagonals are the maximum straight-line travels achievable within the working volume. The accuracy values, together with reversal errors are reported for each separate diagonal, and that is all. From the laser's viewpoint a diagonal test is no different from any other straight-line test. Figure 1: The four principal 'body' diagonals of a 3D work-zone A renewed interest in these tests by the larger users of machine tools in the aerospace industry (on both sides of the Atlantic) has now prompted the IS0 to develop its own version of this standard [5] for diagonal measurement. Although ISO's new standard is based on the ANSIiASME document, it takes on board some of the experience and ideas gained by users in the interim period.

4 As thls standard is not finalised yet, it is timely to examine some of the relevant issues, including, specifically, the proposal to introduce 'face' diagonals. Although the American standard refers only to 'body' diagonals, it is now becoming evident that the measurement of face diagonals has something to offer. (Face diagonals are of course the only option for a 2D turning machine, where they define the working plane just as the body diagonals do in a 3D domain.) 4 Machine tool accuracy parameters Before examining diagonal tests in detail, we need to take a closer look at the factors influencing the accuracy of the machine, particularly the accuracy parameters and the way these affect the overall volumetric accuracy and, by extension, the diagonals. These parameters cover the scale errors for each axis (1-31, straightness errors in two planes for each axis (4-9), angular errors (pitch, roll and yaw) of each axis about the principal directions (10-18) and squareness errors between pairs of axes (19-21). Of these, we should note that the parameters for positioning (or scale) have quite different properties from the other essentially 'geometric' parameters. All measurements, in whatever field, have a degree of uncertainty associated with them owing to the limitations of the equipment and the test conditions prevailing. Laser positioning tests are no exception. But, unllke the other eighteen parameters, positioning values have an additional uncertainty associated with them because they are dynamic: their errors are in the direction of travel and occur as a result of this travel. They are also influenced by external random processes outside the tester's control, such as friction and heating. Furthermore, the machine has to be operating before the measurements can have any meaning. Because of this, positioning tests usually carry additional qualifying parameters for 'Repeatability' based on statistical evaluation [6]. We may need to decide how uncertainty applies to the diagonal test. The remaining 'static' geometric error parameters are generally independent of the machine operation, but not of each other, being derived from the same error source: the basic straightness of the axis guide rails. Any given point on a rail can depart from its 'true' position in each of the three dimensional directions and thus has three degrees of freedom. Errors along the length, however, are not meaningful in this context. Rail errors in the other two directions, perpendicular to the length, will confer straightness errors on the bearing that runs on the rail. Generally, a moving slide or carriage is supported by a number of bearings running on at least two rails. The path of the carriage reflects the resultant or combined straightness of the individual rails and bearings. A computer model can be created to simulate a carriage running along rails with straightness errors. This has to take into account the number and separation of the bearings and rails. The carriage exhibits five degrees of freedom as it moves along the rails, since it now has three additional errors of orientation as well as the two of straightness imparted to it by the bearings. The simulations show that, luckily,

5 the magnitude of the resultant errors is generally much less than the individual errors of rail straightness because of averaging effects. (This is a phenomenon that, over the years, has enabled us to produce increasingly more accurate machines from less accurate ones.) Lateral movement can be conveniently split into a trend line (the line of travel) at a particular angle plus a deviation about this line. This gives rise to the concepts of straightness and squareness, which are so important in machine tool metrology. As parameters, these will require proper definitions, which we shall come to shortly. The effect that the various parameters have on volumetric accuracy is very much dependent upon the machine configuration, i.e., the way the axes act together. So far, we have considered just one axis, where errors in the rails generate straightness and angular errors in the carriage. For an individual single axis, angular errors in orientation do not affect position, and, since they are usually quite small, have little effect on the performance of the machine. To give a machine three-dimensional capability, however, it is always necessary to compound two or three of the axes, i.e., one axis is required to support another. This is where angular errors start to become important. It is these errors in orientation of the supporting axis that affect the supported axis. The amount of error imparted varies with the position of the supported axis, depending on the size of the Abbe offsets. Thus if a Y axis supports an X axis, the X axis yaw will have little affect on the (X) positional accuracy, but Y axis yaw, which varies arbitrarily with the Y position, will produce a linear error in the Y direction proportional to the X position. When three axes are compounded the effect is even more pronounced. As soon as we start adding axes we also have to consider the alignment between them. Quite often (but with the notable exception of slant bed lathes) axes are positioned orthogonally and thls naturally introduces the concept of squareness. But squareness is closely bound up with straightness. (It should be noted that the calibration of an axis with a laser will remove all angular effects along the line of the laser beam and effectively re-define the rotation point for angular errors to lie on the beam. It therefore makes sense to ensure that laser beams are always close to the spindlelwork-piece zone.) 5 Straightness and squareness: least-squares and end-points The IS0 definition of straightness [7] is the deviation from the general 'trend line'. The best trend line (according to the standard) is the one that 'minimises straightness errors', and this can be based either on end-points or on leastsquares. The least-squares value is always more 'scientific', being derived from a larger data sample; but in practice results may not always be much different. (An alternative definition uses a polynomial. This is the way some proprietary ball-bar diagnostic software computes straightness. It is defined by a single parameter that comes out of the calculation for the least-squares circular analysis of the contouring plot. Its practical significance is that the shape, when turned upside down, approximates to the typical gravitational sag (catenary) of a

6 machine element between supports. It is quite common to see a shape of this kind even in the horizontal mode where the errors of the larger machine that produced the subject machine become inherited. For this reason, some CNC controllers are now available with compensation software that covers not only errors in axis positioning but also errors in squareness and straightness. Some of these permit compensation for straightness defined in this way. The problem is, of course, much more complex for long machines having multiple points of support.) We find that the current IS0 definition for squareness doesn't clearly separate it fiom straightness. It certainly does not describe an intrinsic geometrical parameter of the machine. The principle used follows closely the traditional shop-floor practice of measuring a square artefact with a dial gauge. Here, squareness is measured as the range of deviation of the dial gauge over the length of the square. A squareness error of,050 mm in lm does not necessarily mean a slope of,050 mm in lmetre. Despite this confusion, we now understand squareness to be an angular measurement between the mean lines of travel of two orthogonal axes. This will appear in the next revision of the IS0 standard. The lines of travel are the trend lines through the measured points using either end-points or least squares. The straightness definition remains valid. In the previous section we saw how straightness of the rails controls all the other errors except dynamic positioning accuracy. If squareness is defined by end-points, then squareness and straightness errors are eliminated from the equations for the diagonals connecting the end-points. But plots of positioning error at intermediate points on the diagonal will still show errors that include the local straightness errors. If squareness is defined by least-squares, the plots will then show straightness error values at the end-points. 6 Body diagonals We have seen that the effect these errors have on accuracy depends very much on the way the machine axes are compounded. This applies to the accuracy of the diagonals, too. Some general results are shown in table 1. Scale errors affect all diagonals equally, so that the difference between any pair remains constant. Each squareness error will affect a different pair of diagonals by equal and opposite amounts, the other pair remaining constant. Straightness errors, if measured by end-points, do not come into the equation. Angular errors depend on configuration and their effects are worse for doubly compounded axes.

7 Table 1 : Effects of errors on body diagonals WYIZ Linear scale errors XYIXZIYZ Squareness errors X/Y/Z Pitch, roll, yaw errors WYIZ Straightness errors All affected equally; difference between any 2 unchanged One pair of diagonals unaffected; one pair will alter by equal and opposite amounts Effect on diagonals dependent on configuration. Only supporting axes have an effect. Affects local values, but not diagonals if endpoints used Volumetric accuracy (however defined-and this is a separate issue) is the result of the combination of all twenty-one machine error parameters. Using diagonals to replace true volumetric analysis makes the assumption that the worst errors always occur at the extremes of travel. If this is so then the diagonal error is a suitable substitute for volumetric accuracy. (It may be numerically different, but this is only a matter of definition.) Volumetric tests carried out on a full parameter evaluation can generate 3D plots of error and it is quite common for these to show worst values at the extremes of travel, thus lending support for the use of diagonals in this way. Diagonal errors, llke their volumetric equivalents are also a function of the twenty-one parameters. Attempting to solve the four simultaneous equations for the body diagonal errors in order to evaluate these parameters is impossible since there are too many 'unknowns'. Diagonal testing cannot therefore be a complete replacement for individual parameter evaluation. But since many of the actual errors are, in practice, quite small, they may often be ignored It turns out that measuring diagonal accuracy is not particularly difficult, and that the test appears in many ways to have the same attributes as the ball-bar test: useful 'pointers' may be obtained even when the analysis is not entirely rigorous. In other words, although the goal of the test is a composite, or synthetic quantity, which is function of many parameters, it is still possible to get some useful information from it. As with the ball-bar we are stuck with a set of equations with too many unknowns. Interestingly, the American standard also recommends that diagonal tests be supplemented by ball-bar tests. 7 Face diagonals The 'New Slant' on diagonals is a two dimensional one: the introduction of face diagonals in a three-dimensional work-zone. Here it is clear that there are no unique face diagonals defining the work-zone as with the body diagonals (or with face diagonals in a 2D space). So. why introduce face diagonals at all?

8 For one thing, the planar performance of a machine is, it seems, quite important. We started by looking at what the customer needed. Quite often he restricts his operations to two dimensions, working in planar mode. A vertical machining centre, drilling and tapping plate-like work-pieces, is a typical example. Such a machine would require much greater accuracy in the horizontal plane than vertically. Many machines function in this way and are found to have scale feedback for X and Y, but only (less accurate) resolver feedback for Z. In fact, this is probably the most popular specification for a VMC. Its customers are looking for two-dimensional accuracy. And this is what this test gives them. But more significantly, this test emulates an age-old process for checking squareness. In any true rectangle the diagonals must always be equal, a fact well-known to the ancient Egyptians. Furthermore, the difference in the diagonals gives a precise measure of the squareness error. As with body diagonals, all end-point straightness errors are eliminated and scale errors act equally on both diagonals. Only errors of squareness show up. Even errors out of the plane of measurement have a negligibly small contribution-at least for machine tool applications. Referring to fig. 2, derivation of squareness error (6X/Y), based on end-points, is simply obtained. This requires the lengths of the two diagonals to be measured (by laser), from which the following formulae can be applied: -- 6x Do (D, -D,) for a rectangle of sides X, Y Y 2XY -- 6x - (D,-D,) for a square of sides L (L=X=Y) L Do D, and D2 are the measured diagonals; Do is the nominal; SX is the error in X. Figure 2: Computing squareness from 'face' diagonals

9 Table 2: Effects of errors on face diagonals Scale errors in X and Y / Both affected eauallv: difference unchanged " i Scale errors in Z 1 No effect X & Y Straightness errors / Affects local values, but not diagonals if / Pitch, roll, yaw errors in X Pitch, roll, yaw errors in Y (l)* Pitch, roll errors in Y (2)* Yaw errors in Y (2)* Pitch, roll, yaw errors in Z XIY Squareness errors X/Z Squareness errors YiZ Squareness errors end-points used No effect No effect 2nd order changes to diagonals Behaves like squareness, but very much less No effect Both affected equally in opposite direction; difference proportional to squareness error Both affected equally and to 2nd order; difference unchanged Both affected equally and to 2nd order; difference unchanged *Note: In case (1) the two axes are independent. In case (2) the X-axis is supported by the Y. For completeness, a summary of all the effects that error parameters can have on face diagonals is given in table 2 above. Note that there are very slight differences according to whether or not the two axes are compounded. Of course, a simple ball-bar plot can also be used to generate end-point squareness by measuring the difference in the major and minor diameters of the generated ellipse. Evaluation using the relevant software gives you the leastsquares value. The working range of the ball-bar is, of course, generally much smaller than that achievable with a diagonal laser test, and differences in measured squareness may occur as a consequence. Moving the ball-bar to different positions on the table produces a similar effect. Although the least-squares method of evaluating squareness is undoubtedly a 'better' (i.e. more 'scientific') method, we should not lose sight of the reason for testing. If a machine has an unacceptable squareness error, as evinced by the quality of the work-pieces being machined, this will be shown up by both the least-squares and the end-point methods. Each test will give results of similar, but not identical, magnitude. Although the face diagonal test is based on end-point squareness, conversion to a least-squares value can actually be accomplished quite easily. This is done by measuring squarenesses over a set of rectangles starting from the centre. The squareness for each smaller square has then to be weighted by the square of the nominal diagonal. To carry out the test two face diagonals are required per plane and, while it certainly takes longer than a ball-bar test, it does offer the following advantages: Almost all the working plane can be covered by one test.

10 Rectangular areas are not a problem, even of high aspect ratio. Large machines accommodated as easily as small ones. Results of practical tests often show squareness values gradually increasing with the area of measurement-see table 3. (In section 6 we saw that volumetric errors also often increase towards the axis limits.) Similar results are obtained with ball-bar checks when then the ball-bar radius is increased or the ball-bar is moved to the extremities of the table. It is sometimes reported that squareness measured with a ball-bar does not always agree with values obtained using traditional squares and dial gauges. Since the parameter 'squareness' is a single value defined by end-points or least-squares, local divergences should now be classed as angular errors. (This is aside from the confusion of squareness definitions discussed in section 5.) Measuring such 'local' values of squareness by square or ball-bar can thus give rise to significant errors. Table 3 shows interesting results of a practical test on a VMC (see photograph in fig. 3) measuring squareness with ball-bar and diagonals at different locations. 8 Practicalities The American standard describes a laser set up procedure where the test program is modified to suit the placement of the optics. This means that there is some departure from using the true end-points, and, consequently, the full length of the diagonals. Thls set up procedure is, however, a tremendous advantage and dramatically reduces the number of iterations required to get good beam strength over the full length of travel. With horizontal machining centres a restriction in the diagonal length may occur as a result of interference between spindle carrier and beam, and the optics often have to be therefore offset from the gauge point. Table 3: Practical results of face diagonal test Method 1 Radius or '/2 diag / Squareness pmlm l location Laser diagonal 1 47 mm / centre The overall least-squares value was,0247 mdm Laser manufacturers have made available the requisite additional optical equipment for some years. The so called 'turning mirror' is a general piece of

11 equipment for bending laser beams, which can be used for this purpose, as well as for negotiating the non-orthogonal axes found on slant-bed lathes. Figure 3: XY face diagonal set up on a vertical machining centre Figure 3 shows a simple set up on a vertical machining centre for carrying out an XY face diagonal test. It can be seen that the laser, interferometer and turning mirror are merely placed on the table with the turning mirror at the right hand corner of the table. Note that the actual path is determined by the location of the interferometer, not the mirror. The 'dead path' will always be longer than for simple laser tests. With suitable software the initial programming of the machine and the subsequent evaluation of the laser data files can be carried out efficiently and accurately. Computation of least-squares values over a range of working areas can then easily be accommodated. 9 Summary of conclusions Body diagonals can often provide a quick substitute for full volumetric tests, because maximum errors tend naturally to occur at the extremities. Face diagonals provide a measure of planar accuracy, which finds application in the work place. Face diagonals also provide an effective alternative method for evaluating squareness, which is particularly relevant to large machines and areas of high aspect ratio. In these respects it probably surpasses other methods.

12 References [l] Postlethwaite, S.R. & Ford, D.G., LAMDAMAP '97: "Geometric error analysis software for CNC machine tools", Laser Metrology and Machine Performance 111, pp , 1997 [2] IS Circular tests for numerically controlled machine tool, and IS see below in ref. 7. [3] ANSIIASME B5.54 Methods for Performance Evaluation of CNC Machining Centers. [4] IS : Test code for machine tools-part 2: Determination of accuracy and repeatability of positioning of numerically controlled machine tools. [5] IS0 DIS Diagonal displacement test [6] Morris, T.J., LAMDAMAP199: "The importance of being repeatable", Laser Metrology and Machine Performance. IV, pp , 1999 [7] IS Geometric accuracy of machines operating under no load or finishing conditions Acknowledgment: The test work associated with this paper was supported by hnding from EU Craft Project, contract no: SMT4-CT