4
Measurement Uncertainty and Machine Tool Testing W. Knapp(2) Institute for Machine Tools and Manufacturing (IWF), Swiss Federal Institute of Technology (ETH), Zurich, Switzerland Abstract According to international standards measurement uncertainties have to be stated with all measurements, including results from machine tool testing. For average industrial conditions measurement uncertainties are estimated for positioning measurements with laser interferometers and linear scales, for straightness measurements with laser interferometer and straightedge, and for pitch measurements. The results, i.e. the test uncertainties, are discussed and compared with average tolerances given in IS0 standards for the corresponding test procedures. Uncertainties are not estimated for optimum conditions in order to make more people aware, that the alignment of the measurement device, temperature effects and repeatability of the machine tool and the measurement device might cause larger uncertainties than the uncertainty of the device alone. Keywords: Machine tool, test uncertainty, tolerance 1 INTRODUCTION Measurement uncertainties have been of much concern for many years within the ClRP community [1,2]. Today the estimation of measurement uncertainties and their use for proving the conformance with specifications is laid down in international guides and standards [3,4,5]. Measurement uncertainty is often understood as the standard deviation observed, when measurements are repeated. Such an understanding collides with the concept of deterministic thinking [6], best formulated as Porta's law: Random results are the consequence of random procedures [7]. However, the measurement uncertainty is large, if the repeatability of a measurement is bad, but also becomes large, if the knowledge of relevant parameters is poor, parameters like the calibration of the measurement device, the temperature when measuring, the alignment or set-up of the instrument. The measurement uncertainty is just a numerical statement on how sure we are on the measurement result. The measurement uncertainty strongly depends on the contributors we look at [2] and on the assigned magnitude of the contributors used. Therefore the contributors to the measurement uncertainty taken into account will be stated clearly. Many statements on measurement uncertainties are based on best practice, especially if a new device and its capabilities are described in a paper or in a brochure, often assuming a near perfect environment. When looking at machine tool tests in a workshop best practice is sometimes not available, nor a near perfect environment. Therefore in this paper we are looking at measurement uncertainties in an industrial environment, in order to obtain real machine tool test uncertainties. It is also the aim to make more people aware that tiny things count, and that we should not just believe in small digital numbers printed on measurement reports. 2 CONTRIBUTORS TO THE MEASUREMENT For the machine tool test uncertainty the following contributors are looked at: UNCERTAINTY FOR MACHINE TOOL TESTS the uncertainty of the calibration of the measurement device, the alignment of the device on the machine tool, the compensation of the machine tool temperature when measuring at temperatures other than 20"C, the environmental temperature variation error (ETVE or drift), and the repeatability of the set up of the measurement device. The typical industrial environment for machine tool tests is characterised by the following parameters, although sometimes tests have to be carried out in worse conditions: environmental temperature 25°C difference in machine surface temp. 2°C 1 pm angular drift in 15 minutes 3 pm/m 5 pm roll, pitch, yaw (according to [9]) 60 pm/m out-of-straightness (according to [9]) 20 pm nominal thermal expansion coefficient 12 pm/m"C Furthermore we assume, that a knowledgeable person is carrying out the test. In particular this means, that the measurement device is used correctly according to the guidelines of the manufacturer/supplier, all necessary compensations, like compensation for temperature influences, for the measurement device and the machine tool are carried out, the measurement device is mounted statically and dynamically stiff and without any backlash, and the machine components holding the device behave as rigid bodies. If these assumptions do not correspond to the real test conditions, additional contributors to the measurement uncertainty have to be taken into account. drift (test according to [8]) in 15 min. drift (test according to [8]) in 60 min.

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Page 1: Measurement Uncertainty and Machine Tool Testing

Measurement Uncertainty and Machine Tool Testing

W. Knapp(2) Institute for Machine Tools and Manufacturing (IWF), Swiss Federal Institute of Technology (ETH),

Zurich, Switzerland

Abstract According to international standards measurement uncertainties have to be stated with all measurements, including results from machine tool testing. For average industrial conditions measurement uncertainties are estimated for positioning measurements with laser interferometers and linear scales, for straightness measurements with laser interferometer and straightedge, and for pitch measurements. The results, i.e. the test uncertainties, are discussed and compared with average tolerances given in IS0 standards for the corresponding test procedures. Uncertainties are not estimated for optimum conditions in order to make more people aware, that the alignment of the measurement device, temperature effects and repeatability of the machine tool and the measurement device might cause larger uncertainties than the uncertainty of the device alone.

Keywords: Machine tool, test uncertainty, tolerance

1 INTRODUCTION Measurement uncertainties have been of much concern for many years within the ClRP community [1,2]. Today the estimation of measurement uncertainties and their use for proving the conformance with specifications is laid down in international guides and standards [3,4,5]. Measurement uncertainty is often understood as the standard deviation observed, when measurements are repeated. Such an understanding collides with the concept of deterministic thinking [6], best formulated as Porta's law: Random results are the consequence of random procedures [7]. However, the measurement uncertainty is large, if the repeatability of a measurement is bad, but also becomes large, if the knowledge of relevant parameters is poor, parameters like the calibration of the measurement device, the temperature when measuring, the alignment or set-up of the instrument. The measurement uncertainty is just a numerical statement on how sure we are on the measurement result. The measurement uncertainty strongly depends on the contributors we look at [2] and on the assigned magnitude of the contributors used. Therefore the contributors to the measurement uncertainty taken into account will be stated clearly. Many statements on measurement uncertainties are based on best practice, especially if a new device and its capabilities are described in a paper or in a brochure, often assuming a near perfect environment. When looking at machine tool tests in a workshop best practice is sometimes not available, nor a near perfect environment. Therefore in this paper we are looking at measurement uncertainties in an industrial environment, in order to obtain real machine tool test uncertainties. It is also the aim to make more people aware that tiny things count, and that we should not just believe in small digital numbers printed on measurement reports.

2 CONTRIBUTORS TO THE MEASUREMENT

For the machine tool test uncertainty the following contributors are looked at:

UNCERTAINTY FOR MACHINE TOOL TESTS

the uncertainty of the calibration of the measurement device,

the alignment of the device on the machine tool, the compensation of the machine tool temperature when measuring at temperatures other than 20"C,

the environmental temperature variation error (ETVE or drift), and the repeatability of the set up of the measurement device.

The typical industrial environment for machine tool tests is characterised by the following parameters, although sometimes tests have to be carried out in worse conditions:

environmental temperature 25°C

difference in machine surface temp. 2°C

1 pm angular drift in 15 minutes 3 pm/m

5 pm roll, pitch, yaw (according to [9]) 60 pm/m out-of-straightness (according to [9]) 20 pm

nominal thermal expansion coefficient 12 pm/m"C Furthermore we assume, that a knowledgeable person is carrying out the test. In particular this means, that

the measurement device is used correctly according to the guidelines of the manufacturer/supplier,

all necessary compensations, like compensation for temperature influences, for the measurement device and the machine tool are carried out,

the measurement device is mounted statically and dynamically stiff and without any backlash, and the machine components holding the device behave as rigid bodies.

If these assumptions do not correspond to the real test conditions, additional contributors to the measurement uncertainty have to be taken into account.

drift (test according to [8]) in 15 min.

drift (test according to [8]) in 60 min.

Page 2: Measurement Uncertainty and Machine Tool Testing

2.1 The uncertainty of the calibration of the

The calibration certificate states that uncertainty, but in many cases a calibration of the device has not been carried out. For industrial practice the statement of uncertainty given by the manufacturer/supplier of the device has to be taken. Therefore just these numbers are used for the uncertainty estimates in the following examples.

2.2 The alignment of the device on the machine tool Mechanical devices are easily aligned within 0.5 mm parallel over the travel of the machine tool axis under test. Knowledge and devices for the alignment are available in an average industrial environment. The alignment of optical devices, like laser interferometers, is time consuming, especially if personnel is carrying out the alignment, that does not use the laser interferometer regularly, but just from time to time. In these cases the alignment procedure is often stopped as soon as the device produces a measurement signal. And for positioning measurements signals are already produced, if the non parallelism is still 4 mm over the travel of the axis under test.

2.3 The compensation of the machine tool temperature when measuring at temperatures other than 20°C

The uncertainty of the compensation of the temperature of machine tools [10,11,12] and of coordinate measuring machines [13,21] has been widely discussed. The estimation of the uncertainty due to thermal effects is now described in an IS0 draft report [14]. The main contributors are the uncertainty of the temperature measurement and the uncertainty of the thermal expansion coefficient. For the uncertainty of the temperature measurement we take a range of M.35”C, assuming a correct mounting of the sensor at a relevant position on the machine tool. This value is typical for material sensors used with laser interferometers. The uncertainty of the thermal expansion coefficient is taken as a range of 2 pm/m”C for steel, as suggested in [14]. We take the expansion coefficient of steel, as we want to show the effects between the tool and a workpiece out of steel.

2.4 The environmental temperature variation error (ETVE or drift)

measu rement device

Drift due to temperature differences in space and time can be checked by drift tests and given as ETVE values [10,11,14]. Typical values for an industrial environment are ranges of 1 pm, respectively 3 pm/m in 15 minutes, and 5 pm in 60 minutes. Sudden changes in the environment do not effect the machine tool and mechanical measurement devices immediately, they react with their thermal time constants. Therefore the ETVE values mentioned above can be taken as average values in an industrial environment. If optical measurement devices are used, sudden changes in the environment have an immediate influence on the measurement device, because they show no time constants [15]. Such influences should be taken into account in the uncertainty estimates, or by drift tests with the measurement device on the machine tool. Figure 1 shows the influence from an experiment with a laser straightness set up [16], where a change in the surface temperature near the laser beam is simulated by placing a bottle with warm water near the beam. The range of the signal - the laser is operated in dynamic

Pm +2.5

0

-2.5

0 t 1

t 2

300 seconds

Figure 1 : Dynamic straightness measurement with laser interferometer in vertical plane, no movement of machine tool axis, at time 1 bottle with warm water (57°C) is placed below laser beams, at time 2 bottle is withdrawn.

mode - changes from 0.5 pm to 5 pm, when a bottle with warm water of 57°C is placed below the two laser beams. The length of the warm surface is 22% of the distance between the Wellastone prism and the straightness reflector. The averaged standard uncertainty (coverage factor k=l) caused by this effect is 0,4 pm/”C for a distance of 1 m between the optics. A similar effect appears for a laser angular set up [16]. Here the standard uncertainty (k=l) is 2.4 pm/m/”C for a distance of 1 m between the optics. If no special drift test on the machine tool is carried out, which is not recommended, then the geometric measurement should be repeated at least five times, as demanded in IS0 230-2 [17]. The repeatability of the measurements, expressed as a range or as a standard deviation, includes the repeatability of the machine tool axis under test and the influence of temperature variations during the five runs. If the geometric test is carried out under typical environmental conditions, the repeatability value can be taken as an estimate for the environmental temperature variation error, ETVE, and the repeatability of the machine tool axis under test.

2.5 The repeatability of the set up of the

If the set up of the measurement device is not known exactly, the influence of the Abbe offsets has to be taken into account for the measurement of the positioning accuracy, the straightness and the squareness. With mechanical measurement devices the set up in general can be repeated easily: The device is aligned in the centre of the table, the device is laying on the table, respectively known fixtures are used. With optical devices magnetic sockets and adjustable fixtures are used in order to simplify the alignment of the device, respectively the beam. The final position of the beam relative to the table or the spindle is seldom documented, we just know, that the position of the beam in the working volume is within f 25 mm

2.6 Calculation of the measurement uncertainty Most of the single contributors are estimated as ranges. Each range is transferred to a standard uncertainty assuming a rectangular distribution within the range [3]. The combined standard uncertainty is calculated assuming uncorrelated contributors [3], if not stated otherwise. The measurement or test uncertainty is stated for a coverage factor k of 2.

measurement device

Page 3: Measurement Uncertainty and Machine Tool Testing

3

3.1 Positioning accuracy test The positioning measurement is based on five measurements upwards and five measurements downwards, the parameters are calculated according to

IS0 230-2 is currently under revision, mainly in order to include the estimation of the measurement uncertainty as an informative annex. The following estimations are based on this annex [I71 and are applied for a measurement with a laser interferometer and for a linear scale. Laser interferometer and linear scale have been already compared as axes measurement devices built in machine tools under optimum conditions [15]. Here we want to look at the two devices for testing a machine tool axis under average industrial conditions.

3.2 Test uncertainty for positioning The test uncertainties for laser interferometer and linear steel scale are given in Table 1 together with the estimates of the single contributors and their standard uncertainties. Table 1 also includes the comparison of the uncertainty (coverage factor k=2) with the tolerance for the unidirectional systematic deviation €?, the range of the mean values from upwards or downwards positioning, according to the IS0 standard for machining centres [ I 81. The accuracy statement for the laser interferometer includes the compensation of the air temperature, therefore no additional uncertainty has to be calculated for the temperature compensation for the laser. For the steel scale the uncertainty of the thermal expansion coefficient has to taken into account, because the accuracy statement does not include that influence

TEST UNCERTAINTY FOR POSITIONING TEST

IS0 230-2 [17].

contributor device measuring length accuracy, 1525°C accuracy wavelength accuracy u (device) alignment beam alignment scale alignment u(a1ignment) compensation of temper temp. measurement Atemperature scalehable nominal expansion coeff. u(exp.coeff) of table u(exp.coeff.) of scale u( tern perat u re) repeatability of 5 runs u( repeatability) repeatability of set up offset between 2 set ups maxi m u m pitch/yaw u(set up)

U(E?) ( k 2 ) Tolerance for E? UlTolerance

laser

1000 mm 3.4 ppm

0.2 ppm 1.0 pm

4 mm

2.3 pm :ure (25°C) M.35 "C

12 pm/m"C 2 pm/m"C

3.8 pm

0.7 pm

50 mm 60 pm/m 1.2 pm

9 Pm 15 pm 60%

scale

1000 mm

2 Pm

0.6 pm

0.5 mm 0.0 pm

0.1 "C 12 pm/m"C 2 pm/m"C 2 pm/m"C

4.1 pm

0.7 pm

0.5 mm 60 pm/m 0.0 pm

The machine table is taken as representative for the steel workpiece. Therefore for the laser the temperature of the table is measured, and the uncertainty of the temperature measurement and the uncertainty of the expansion coefficient of the table contribute to the test uncertainty. For the steel scale no temperature measurement is necessary, as the nominal expansion of the steel table and the steel scale compensate. The only influences are the uncertainty of the expansion coefficient of the table and the temperature difference between table and scale, which is 0.1"C after 10 minutes according to an experiment, where the scale is just laid on the table. The test uncertainty (k=2) for laser and linear scale both take more than 50% of the tolerance for the unidirectional systematic deviation of positioning. The situation is often worse, because machine tool manufacturers state much smaller tolerances than the IS0 standard [18].

3.3 Improvements Significant improvements can be achieved for the laser interferometer, if the laser is calibrated (u(device)=0.5 prn), if the alignment is made on the return beam at the laser head (beam alignment = I mm over travel, u(a/ignment)=O.l pm), if the temperature is at 21°C and the temperature measurement within a range of 0.2"C (u(temperature)=0.9 prn), if a drift test is carried out (€TV€=l pm), and if the set up is know to a range of 1 mm (u(set up)=O,O pm). Then the test uncertainty for the unidirectional systematic deviation, U(€?, k=2), becomes 2.1 pm or 14% of the IS0 tolerance [18]. For the linear scale improvements are made, if the tests are carried out at 21 "C and at a temperature difference between table and scale of less than 0.05"C (u(temperature)=0.8 pm), and if a drift test is carried out (€TV€=l pm). The resulting test uncertainty for E? and k=2 is then 2.0 pm or 13% of the IS0 tolerance [18].

4 TEST UNCERTAINTY FOR STRAIGHTNESS TEST

4.1 Straightness test Straightness tests with a mechanical straightedge and the laser interferometer are compared in respect to the test uncertainties. For the mechanical straightedge the reversal method according to [I91 is also looked at.

4.2 Test uncertainty for straightness Table 2 shows the relevant contributors and the test uncertainty, compared to the tolerances in IS0 [9]. The out-of-straightness of the straightedge is according to IS0 [5]. The improvement for the straightedge is by the straightedge reversal, although a longer test period and the repeatability of the machine tool have to be taken into account. The improvement for the laser could be a reversal according to [19], or a better alignment of the optics in order to reduce the measuring range.

5 TEST UNCERTAINTY FOR LASER PITCH TEST For the pitch test with laser interferomerter we look at the following contributors: device (u(device)=0.2 pm/m), thermal drift (u(drift)=0.7 pm/m), cross talk according to [20] based on 1 mm non- alignment cross ta/k)=0.3 pm/m), and air disturbance as described in chapter 2.4 for a surface temperature difference of 2°C (u(air disturbance)=4.7 pm/m). This results in a test uncertainty (k=2) of 10 pm/m or 17% of the tolerance for machining centres stated in [9].

Table 1: Test uncertainty for positioning measurement

Page 4: Measurement Uncertainty and Machine Tool Testing

contributor

device measuring range dial gauge acc. straightedge acc. u(device) u(a1ignrnent) thermal drift in 15 minutes in 60 minutes u(drift) air disturbance Asurface temp. u(air)

straightedge

1 mm

12 pm 3.6 prn 0.0 prn

2 pm

1 pm

0.3 prn

repeatability of machine range u(repeatabi1ity)

U (k=2) Tolerance 20 prn Ufrolerance 35%

straightedge reversal

1 mm 2 pm 0 pm

0.8 prn 0.0 prn

5 pm 1.4 prn

2 pm 0.6 prn

4 Pm 20 prn 20%

laser

1 mm

3.0 prn 0.0 prn

1 pm

0.3 prn

2°C 0.7 prn

Table 2: Test uncertainty for straightness

6 SUMMARY Classical tests for machine tool testing are characterised by short measuring lengths, simple artefacts and simple set ups, e.g. a dial gauge with a test mandrel. For classical tests the largest uncertainty contributor is the measuring device, the other influences are in general of no importance, moreover people and knowledge capable of understanding correct classical measurements are available in an industrial environment. Here the uncertainty of the device defines the test uncertainty. Advanced tests are characterised by long measuring lengths, by need of experience for set up and alignment, or by complex procedures. For advanced tests in an industrial environment the uncertainty due to the measuring device is in the same magnitude as the influence from set up and alignment, and much smaller than the influence of the environment. Here the estimation of the test uncertainty is essential and cannot be derived from the uncertainty of the measurement device alone.

7 ACKNOWLEDGMENTS Research work for this contribution was financed by KTI, Switzerland, the European Commission, and industrial partners from Austria, Belgium, Finland, Germany, the Netherlands, and Switzerland (projects KTI 51 52.3, SMT4-CT97-2171 'Multibeam').

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