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Testing the diagonal measuring technique
Precision Engineering 30 (2006) 132–144
Testing the diagonal measuring technique Ondrej Svoboda ∗ Faculty of Mechanical Engineering, Research Center for Manufacturing Technologies, Czech Technical University in Prague, Horska 3, 128 00 Prague 2, Czech Republic Received 10 February 2005; received in revised form 20 May 2005; accepted 17 June 2005 Available online 8 September 2005
Abstract This paper describes the results of a set of linear displacement accuracy measurements performed on two vertical CNC machining centers. The main scope of the work is to verify or disprove some of the recently claimed limitations of the conventional diagonal measurement method and of the “laser vector” or “sequential diagonal” method. Basically, we tested the effect of a large linear error deliberately introduced into one of the machine tool’s axes. It is concluded that the laser vector method has not correctly identified this error and distributed the error into the remaining axes of the machine tool. © 2005 Elsevier Inc. All rights reserved. Keywords: Laser diagonal; Vector diagonal; Machine error compensation; Machine calibration
1. Introduction Laser diagonal measurements of the geometric accuracy of machine tools are according to the standards [3,4] considered to be an estimation of the volumetric accuracy of CNC machine tools. Therefore, some manufacturers of laser measuring systems have tried to facilitate these types of measurements by offering extra components, e.g. swivel mirrors. Furthermore, the US company, Optodyne, Inc., has developed an add-on to the technique in order to enhance the quality of the results obtained from a conventional diagonal measurement [5]. The basic idea of their “laser vector” method is in a sequential step diagonal path performed by the machine tool instead of a simultaneous movement of all the machine axes (as suggested by the standards [3,4]). Hence, one measurement step of the continuous movement is replaced by three separate steps, first along the X-axis, subsequently along the Y-axis and finally along the Z-axis. By doing this three times more data points are obtained. Basically, each step of the sequential movement is affected by all the geometrical errors of the machine tool. As generally described in [5,6] the Optodyne software LDDMTM calculates the linear and ∗
Tel.: +420 221 990 934; fax: +420 221 990 999. E-mail address: [email protected].
0141-6359/$ – see front matter © 2005 Elsevier Inc. All rights reserved. doi:10.1016/j.precisioneng.2005.06.002
straightness errors according to a mathematical trajectory model. Additionally, it is noted that diagonal displacement tests can be used for the evaluation of the squareness errors. Thus, the three squareness errors in the individual machine coordinate planes are also obtained. In summary, it is claimed by Optodyne that with the help of the laser vector method one gets results of 12 error types from a measurement along the four body diagonals. Nevertheless Renishaw Plc. (UK) has published a paper [1] calling attention to a limitation of the diagonal measurement techniques and of the laser vector method in particular. It is the purpose of this paper to verify or disprove this limitation by a practical experience made by the Research center of manufacturing technology in Prague (RCMT), Czechia.
2. Motivation of the measurement As stated in [1], pages 4–6, the results of the laser vector method are affected by the misalignment errors of the mirror. This is due to the sequential step diagonal path, which involves a relatively large flat mirror, used as a target, to reflect the incoming laser beam back to the laser head for processing. Renishaw claims that from measurements made from the laser vector method, in isolation, it is not possible
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Table 1 Tested machine no. 1 Manufacturer Type
Bridgeport, UK VMC500XP
Axis stroke (mm)
650 X 500 Y 500 Z
Control system Measuring system Spindle characteristics Service hours
Heidenhein TNC410 Indirect 7000 rev/8.5 kW 892
Table 2 Tested machine no. 2
Fig. 1. Tested machine no. 1.
Manufacturer Type
Kovosvit MAS, Czechia MCV1270Power
Axis stroke (mm)
1270 X 610 Y 720 Z
Control system Measuring system Spindle characteristics Service hours
Heidenhein iTNC530 Direct (glass scales) 8000 rev/43 kW New
4. Performed measurements
Fig. 2. Tested machine no. 2.
to mathematically distinguish between progressive linear errors along the orthogonal axes of a machine and the errors introduced by the angularly misaligned plane mirror used in the vector method. Basically, if a machine comprised of two perfect axes and a third axis had a progressive linear error, say 10 m/m, the vector method would not be able to distinguish which axis contained the error and would distribute the error between the axes. The normalisation method adopted determines the distribution of the error between the axes. In order to experimentally prove, or disprove this theory, RCMT has performed a specific measurement on two mid-size CNC vertical milling machines (Figs. 1 and 2). The tested machine tools’ parameters, the description of the tests and the results are stated as follows.
3. The tested machine tools Two CNC vertical machining centers were chosen for the testing. A brief description is given in Tables 1 and 2.
The main idea of the tests was to simulate the effect of a large linear error in one of the machine tool’s axes by deliberately entering a selected error value into the machine’s compensation table. This compensation table would then be activated in the control system and the effect checked by measuring the linear displacement accuracy of the related axis. Additional geometric accuracy testing was done to get an overview of the volumetric accuracy of the machine and to further verify the conclusions drawn from the measurement results. The whole measurement scheme can be divided into two basic parts (Sections 4.1 and 4.2). All accuracy measurements were done bi-directionally (forward and backward) with at least three runs. Only detailed results from machine no. 1 will be presented in this paper. A short discussion on the results from machine no. 2 is given in Section 6. 4.1. Main measurement Before performing any measurements all the compensation tables for linear displacement accuracy were switched off. In the first step, the linear displacement errors of the X-, Y- and Z-axis were measured by a Renishaw ML10 laser system (Section 5.1). The results can be found in Figs. 3–5 for the X-, Y- and Z-axis, respectively. Measurement by the laser vector method was then performed, giving for each axis the linear displacement error and both straightness errors (Section 5.2). Figs. 6–8 show these errors for the individual
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Fig. 3. X-axis linear displacement accuracy without compensation.
Fig. 4. Y-axis linear displacement accuracy without compensation.
Fig. 5. Z-axis linear displacement accuracy without compensation.
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Fig. 6. Laser vector method: X-axis without compensation.
Fig. 7. Laser vector method: Y-axis without compensation.
axes. The diagonal displacement accuracy is shown in Fig. 9. Finally, the squareness errors were evaluated (Table 3). In the second step, a relatively large linear error in the Z-axis was deliberately entered into the control system (Section 5.4). In case of machine no. 1, the error reached 0.2 mm over the 500 mm stroke of the Z-axis. For machine no. 2, a 0.207 mm error was introduced on the stroke of 720 mm. The Table 3 Laser vector method: squareness errors (without compensation) XY (m/m) YZ (m/m) ZX (m/m)
35 53 45
effect of the new compensation tables was in both cases verified by a measurement of the linear displacement accuracy of the Z-axis as shown in Fig. 10 (machine no. 1). The next step was to perform the laser vector method measurement, this time with the large error in the Z-axis (Section 5.5). Results of this test are pointed out in Figs. 11–13 (X, Y- and Z-axis), Fig. 14 (diagonal displacement accuracy) and Table 4 (squareness errors). Based on these results, new compensation tables were generated and activated in the control system. Subsequently, another measurement by the laser vector method was done (Section 5.6) in order to check the effect of the compensations (Figs. 15–18 and Table 5). The last step was re-measurement of the linear displacement accu-
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Fig. 8. Laser vector method: Z-axis without compensation.
Fig. 9. Laser vector method: diagonal displacement accuracy.
racy in the individual axes by the Renishaw ML10 (Section 5.7; Figs. 19–21).
Besides the main measurements, other geometric accuracy tests were performed to get a global map of the
machine tool errors. Pitch and yaw angular errors of all the machine tool axes were measured with the Renishaw ML10 with angular optics. Roll angular errors of the X- and Y-axis were measured with Wyler electronic levels. Circular interpolation accuracy was tested in the individual coordinate planes with the Renishaw QC10 Ballbar.
Table 4 Laser vector method: 39 squareness errors (with deliberately entered error in Z-axis)
Table 5 Laser vector method: squareness errors (after compensation of deliberately entered error)
XY (m/m) YZ (m/m) ZX (m/m)
XY (m/m) YZ (m/m) ZX (m/m)
4.2. Additional measurements
39 56 46
1 7 8
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Fig. 10. Z-axis linear displacement accuracy: verification of deliberately entered error.
Fig. 11. Laser vector method: X-axis with deliberately entered error in Z-axis.
The influence of the ambient temperature is an important factor during all geometric accuracy measurements on CNC machine tools. Therefore, the ambient temperature was monitored during the whole measurement session. The result is stated in Fig. 22.
5 m/500 mm stroke. The worst situation is in the Yaxis, which has a progressive under-travel error reaching 30 m/350 mm. In case of the Z-axis a significant positive error of 25 m/500 mm was detected. 5.2. Laser vector method measurement result—machine without compensation
5. Measurement results and discussion 5.1. Linear displacement accuracy of the axes without compensation (measured in the traditional way by Renishaw ML10) Linear displacement accuracy of the machine was evaluated with the following results. The X-axis has a relatively small positive error of a magnitude of maximally
Based on the results of the laser vector method (machine without compensations) it can be stated that the X-axis positioning error and both straightness errors are 10 m in the whole axis stroke. The Y-axis has a relatively small linear displacement error and horizontal straightness error, whereas the most significant error here is the vertical straightness reaching 14 m. In the Z-axis, the maximal positioning error is 14 m, but more important are the straightness errors. Both of
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Fig. 12. Laser vector method: Y-axis with deliberately entered error in Z-axis.
them have got approximately the same magnitude of 23 m. The squareness errors vary from 35 to 53 m/m, the worst case was found in the YZ plane. The diagonal displacement accuracy characterised by the diagonal systematic deviation of positioning (according to [3]) is 34 m. In fact present are both diagonals with an over-travel and under-travel, therefore the maximal error evaluated from all the diagonals is 51 m. 5.3. Comparison of results obtained from the parallel to axis measurement and the vector method—machine without compensation It is clear that the results of linear displacement accuracy from both measurement methods vary in sign and magnitude.
The parallel to axis approach indicates a smaller error in the X-axis compared with the vector method. Furthermore, the parallel to X-axis measurement (Fig. 3) indicates a purely positive error, while the vector method results include both positive (up to +7 m) and negative errors (up to −5 m), as seen from Fig. 6. On the contrary in the Y- and Z-axis the vector method shows a significantly better linear displacement accuracy than the ordinary measurement results. Based on the laser vector method the Y-axis error oscillates around zero with a magnitude of +6 m/−5 m (Fig. 7), whereas the parallel to Y-axis measurement result is clearly linear reaching −30 m (Fig. 4). In case of Z-axis, linear displacement results from both methods indicate a positive error, nevertheless differences are found in the magnitude
Fig. 13. Laser vector method: Z-axis with deliberately entered error in Z-axis.
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Fig. 14. Laser vector method: diagonal displacement accuracy with deliberately entered error in Z-axis.
of the error: parallel to axis measurement result reaches 25 m (Fig. 5), laser vector method result reaches 14 m (Fig. 8). 5.4. Verification of the deliberately entered error into the Z-axis (measured in the traditional way by Renishaw ML10) The activated compensation table works as expected, a linear error value was measured with good repeatability. The maximal positioning error reaches 0.2 mm/500 mm. Linear displacement accuracy in the X- and Y-axis remained
unchanged compared with the state without any compensations. 5.5. Laser vector method measurement results—machine with a deliberately entered error in the Z-axis The linear displacement error of all the axes is now the most significant factor detected by the laser vector method. The straightness errors remain almost unchanged and so are the squareness errors. In case of the X-axis, the maximal positioning error is 64 m, in the Y-axis 43 m and in the Z-axis 60 m. In terms of the diagonal displacement accuracy all
Fig. 15. Laser vector method: X-axis after compensation of deliberately entered error.
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Fig. 16. Laser vector method: Y-axis after compensation of deliberately entered error.
the diagonals show significant positive errors, the worst case is 130 m (Ed ). 5.6. Laser vector method measurement results—machine after the compensation of the deliberately entered error The laser vector method measurement performed after the activation of the compensation tables generated by the LDDMTM software shows the following results. In the X-axis, the linear displacement errors and both straightness errors are below 10 m. The Y-axis geometric errors are even less significant, mostly below 6 m. The Z-axis linear displacement shows an under-travel of 14 m. Both straightness errors are
positive, horizontal +8 m, vertical +4 m. The squareness errors were also reduced to values below 10 m/m in all planes. The diagonal displacement error in the worst diagonal is 20 m. 5.7. Linear displacement accuracy of the axes after the compensation of the deliberately entered error by the vector method (measured in the traditional way by Renishaw ML10) A clear progressive under-travel error was found in the Xaxis (−60 m) and in the Y-axis (−30 m). The Z-axis has still a large progressive over-travel error reaching 125 m on the 500 mm stroke.
Fig. 17. Laser vector method: Z-axis after compensation of deliberately entered error.
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Fig. 18. Laser vector method: diagonal displacement accuracy after compensation of deliberately entered error.
5.8. Additional measurements Angular motion errors were measured with the following results: in the X-axis the most significant is the pitch error of 60 rad. The yaw and roll angular errors are 20 rad each. In the Y-axis only the yaw error of 16 rad is significant. The Z-axis linear displacement is affected by a pitch error of 18 rad. 5.9. Ambient temperature Particular attention was paid to the ambient temperature situation during all measurements. According to the results stated in Fig. 22 the temperature variation from 9 a.m. to 17
p.m. (one-day measurement session) is below 1 ◦ C, which is good enough to maintain a reasonably small uncertainty of the geometric error measurements. 5.10. Discussion of measurement results from machine no. 1 At this point, based on the results presented in Sections 5.1–5.9, it can be stated that by applying a 200 m positioning error into the machine’s Z-axis the laser vector method distributes the error into the remaining axes. This process resulted in a 60 m under-travel error in the X-axis, a 30 m under-travel error in the Y-axis and a 120 m over-travel error in the Z-axis with respect to the “parallel to axes” measure-
Fig. 19. X-axis linear displacement accuracy after compensation of deliberately entered error.
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Fig. 20. Y-axis linear displacement accuracy after compensation of deliberately entered error.
Fig. 21. Z-axis linear displacement accuracy after compensation of deliberately entered error.
ments. On the other hand, the straightness and squareness errors evaluated by the LDDMTM software remained almost unchanged after the introduction of the large error in the Zaxis, which is a reasonable result.
6. Discussion of measurement results from machine no. 2 Linear displacement errors of this machine, without compensations, are significant only in the Z-axis, where the error reaches 27 m. The X- and Y-axis linear displacement errors are below 10 m. On the other hand, extensive angular errors were found in the X-axis. The pitch error is 49 rad and the yaw error is 32 rad. The laser vector method results (machine without compensations) are as follows. The diagonal displacement accuracy is
rather poor. Diagonal “npp” has a maximum error of −55 m, the maximal positive error of +24 m is in the “ppp” diagonal. The largest linear displacement error of 15 m is in the X-axis. Straightness errors are significant in the X-axis (horizontal straightness error: 21 m) and in the Z-axis (horizontal straightness error: 29 m, vertical straightness error: 23 m). Squareness errors vary from 36 to 46 m/m in the individual coordinate planes. The deliberately entered error into the Z-axis linear displacement compensation table reached 0.207 mm/720 mm with good repeatability and was verified by a “parallel to axis” measurement. The laser vector method results with the deliberately entered large error in the Z-axis indicate a maximum diagonal displacement error of 116 m for diagonal “ppp”. All the diagonals have positive errors. The straightness errors in all axes remain practically the same. The linear displacement
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Fig. 22. Ambient temperature during measurements.
error in the X-axis is now 66 m, in the Y- and Z-axis 34 m. The squareness errors remain the same in the XY and ZXplane. A reduction of 12 m/m is present in the YZ-plane compared to the situation without compensations. At this point, it is clear that the results of the testing are basically the same as in case of machine no. 1. Common conclusions can therefore be drawn based on all the measurement data.
displacement error, then this error will not be correctly identified by the sequential diagonal measurement method. In fact, the large error in one axis will be distributed into the remaining axes, thus causing the degradation of their accuracy. This fact is extremely important if the sequential diagonal measurement results are intended to be used for machine error correction. The problem is illustrated by the results from machine no. 1 in Section 5.7.
7. Additional LDDMTM software feature
Acknowledgements
The new version of the LDDMTM software includes the possibility to enter the linear errors from a “parallel to axis” measurement into the vector method analysis. By doing this, the straightness and squareness errors remain unchanged whilst the linear displacement errors are replaced by the “parallel to axis” data. For a three axes machine, two linear displacement measurements are needed.
The author wishes to express thanks to the following people for their contributions during the preparation and review of this paper: Dr. Ray Chaney (Renishaw) and Dr. Charles Wang (Optodyne). This research has been supported by the Czech Ministry of Education under the Grant LN00B128.
8. Conclusion
References
The tests performed on two vertical CNC machining centers at the Research Center for Manufacturing Technologies show that if one of the machine tool axes has a large linear
[1] Chapman MAV. Limitations of laser diagonal measurements. Precision Eng 2003;27(4). [3] ISO 230-6, 2002. Test code for machine tools—Part 6. Determination of linear displacement accuracy on body and face diagonals (Diago-
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nal Displacement Tests)”, an International Standard, by International Standards Organization; 2002. [4] ASME—American Society of Mechanical Engineers, B5.541992 Methods for performance evaluation of computer numerically controlled machining centres, An American National Standard.
[5] Wang C. Laser vector measurement technique for the determination and compensation of volumetric positioning errors. Part 1. Basic theory. Rev Sci Instrum 2000;71(10). [6] Wang C. A theoretical analysis of 4 body diagonal displacement measurement and sequential step diagonal measurement. In: Proceedings of the Lamdamap 2003 Conference. 2003.
Testing the diagonal measuring technique Ondrej Svoboda ∗ Faculty of Mechanical Engineering, Research Center for Manufacturing Technologies, Czech Technical University in Prague, Horska 3, 128 00 Prague 2, Czech Republic Received 10 February 2005; received in revised form 20 May 2005; accepted 17 June 2005 Available online 8 September 2005
Abstract This paper describes the results of a set of linear displacement accuracy measurements performed on two vertical CNC machining centers. The main scope of the work is to verify or disprove some of the recently claimed limitations of the conventional diagonal measurement method and of the “laser vector” or “sequential diagonal” method. Basically, we tested the effect of a large linear error deliberately introduced into one of the machine tool’s axes. It is concluded that the laser vector method has not correctly identified this error and distributed the error into the remaining axes of the machine tool. © 2005 Elsevier Inc. All rights reserved. Keywords: Laser diagonal; Vector diagonal; Machine error compensation; Machine calibration
1. Introduction Laser diagonal measurements of the geometric accuracy of machine tools are according to the standards [3,4] considered to be an estimation of the volumetric accuracy of CNC machine tools. Therefore, some manufacturers of laser measuring systems have tried to facilitate these types of measurements by offering extra components, e.g. swivel mirrors. Furthermore, the US company, Optodyne, Inc., has developed an add-on to the technique in order to enhance the quality of the results obtained from a conventional diagonal measurement [5]. The basic idea of their “laser vector” method is in a sequential step diagonal path performed by the machine tool instead of a simultaneous movement of all the machine axes (as suggested by the standards [3,4]). Hence, one measurement step of the continuous movement is replaced by three separate steps, first along the X-axis, subsequently along the Y-axis and finally along the Z-axis. By doing this three times more data points are obtained. Basically, each step of the sequential movement is affected by all the geometrical errors of the machine tool. As generally described in [5,6] the Optodyne software LDDMTM calculates the linear and ∗
Tel.: +420 221 990 934; fax: +420 221 990 999. E-mail address: [email protected].
0141-6359/$ – see front matter © 2005 Elsevier Inc. All rights reserved. doi:10.1016/j.precisioneng.2005.06.002
straightness errors according to a mathematical trajectory model. Additionally, it is noted that diagonal displacement tests can be used for the evaluation of the squareness errors. Thus, the three squareness errors in the individual machine coordinate planes are also obtained. In summary, it is claimed by Optodyne that with the help of the laser vector method one gets results of 12 error types from a measurement along the four body diagonals. Nevertheless Renishaw Plc. (UK) has published a paper [1] calling attention to a limitation of the diagonal measurement techniques and of the laser vector method in particular. It is the purpose of this paper to verify or disprove this limitation by a practical experience made by the Research center of manufacturing technology in Prague (RCMT), Czechia.
2. Motivation of the measurement As stated in [1], pages 4–6, the results of the laser vector method are affected by the misalignment errors of the mirror. This is due to the sequential step diagonal path, which involves a relatively large flat mirror, used as a target, to reflect the incoming laser beam back to the laser head for processing. Renishaw claims that from measurements made from the laser vector method, in isolation, it is not possible
O. Svoboda / Precision Engineering 30 (2006) 132–144
133
Table 1 Tested machine no. 1 Manufacturer Type
Bridgeport, UK VMC500XP
Axis stroke (mm)
650 X 500 Y 500 Z
Control system Measuring system Spindle characteristics Service hours
Heidenhein TNC410 Indirect 7000 rev/8.5 kW 892
Table 2 Tested machine no. 2
Fig. 1. Tested machine no. 1.
Manufacturer Type
Kovosvit MAS, Czechia MCV1270Power
Axis stroke (mm)
1270 X 610 Y 720 Z
Control system Measuring system Spindle characteristics Service hours
Heidenhein iTNC530 Direct (glass scales) 8000 rev/43 kW New
4. Performed measurements
Fig. 2. Tested machine no. 2.
to mathematically distinguish between progressive linear errors along the orthogonal axes of a machine and the errors introduced by the angularly misaligned plane mirror used in the vector method. Basically, if a machine comprised of two perfect axes and a third axis had a progressive linear error, say 10 m/m, the vector method would not be able to distinguish which axis contained the error and would distribute the error between the axes. The normalisation method adopted determines the distribution of the error between the axes. In order to experimentally prove, or disprove this theory, RCMT has performed a specific measurement on two mid-size CNC vertical milling machines (Figs. 1 and 2). The tested machine tools’ parameters, the description of the tests and the results are stated as follows.
3. The tested machine tools Two CNC vertical machining centers were chosen for the testing. A brief description is given in Tables 1 and 2.
The main idea of the tests was to simulate the effect of a large linear error in one of the machine tool’s axes by deliberately entering a selected error value into the machine’s compensation table. This compensation table would then be activated in the control system and the effect checked by measuring the linear displacement accuracy of the related axis. Additional geometric accuracy testing was done to get an overview of the volumetric accuracy of the machine and to further verify the conclusions drawn from the measurement results. The whole measurement scheme can be divided into two basic parts (Sections 4.1 and 4.2). All accuracy measurements were done bi-directionally (forward and backward) with at least three runs. Only detailed results from machine no. 1 will be presented in this paper. A short discussion on the results from machine no. 2 is given in Section 6. 4.1. Main measurement Before performing any measurements all the compensation tables for linear displacement accuracy were switched off. In the first step, the linear displacement errors of the X-, Y- and Z-axis were measured by a Renishaw ML10 laser system (Section 5.1). The results can be found in Figs. 3–5 for the X-, Y- and Z-axis, respectively. Measurement by the laser vector method was then performed, giving for each axis the linear displacement error and both straightness errors (Section 5.2). Figs. 6–8 show these errors for the individual
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Fig. 3. X-axis linear displacement accuracy without compensation.
Fig. 4. Y-axis linear displacement accuracy without compensation.
Fig. 5. Z-axis linear displacement accuracy without compensation.
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Fig. 6. Laser vector method: X-axis without compensation.
Fig. 7. Laser vector method: Y-axis without compensation.
axes. The diagonal displacement accuracy is shown in Fig. 9. Finally, the squareness errors were evaluated (Table 3). In the second step, a relatively large linear error in the Z-axis was deliberately entered into the control system (Section 5.4). In case of machine no. 1, the error reached 0.2 mm over the 500 mm stroke of the Z-axis. For machine no. 2, a 0.207 mm error was introduced on the stroke of 720 mm. The Table 3 Laser vector method: squareness errors (without compensation) XY (m/m) YZ (m/m) ZX (m/m)
35 53 45
effect of the new compensation tables was in both cases verified by a measurement of the linear displacement accuracy of the Z-axis as shown in Fig. 10 (machine no. 1). The next step was to perform the laser vector method measurement, this time with the large error in the Z-axis (Section 5.5). Results of this test are pointed out in Figs. 11–13 (X, Y- and Z-axis), Fig. 14 (diagonal displacement accuracy) and Table 4 (squareness errors). Based on these results, new compensation tables were generated and activated in the control system. Subsequently, another measurement by the laser vector method was done (Section 5.6) in order to check the effect of the compensations (Figs. 15–18 and Table 5). The last step was re-measurement of the linear displacement accu-
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Fig. 8. Laser vector method: Z-axis without compensation.
Fig. 9. Laser vector method: diagonal displacement accuracy.
racy in the individual axes by the Renishaw ML10 (Section 5.7; Figs. 19–21).
Besides the main measurements, other geometric accuracy tests were performed to get a global map of the
machine tool errors. Pitch and yaw angular errors of all the machine tool axes were measured with the Renishaw ML10 with angular optics. Roll angular errors of the X- and Y-axis were measured with Wyler electronic levels. Circular interpolation accuracy was tested in the individual coordinate planes with the Renishaw QC10 Ballbar.
Table 4 Laser vector method: 39 squareness errors (with deliberately entered error in Z-axis)
Table 5 Laser vector method: squareness errors (after compensation of deliberately entered error)
XY (m/m) YZ (m/m) ZX (m/m)
XY (m/m) YZ (m/m) ZX (m/m)
4.2. Additional measurements
39 56 46
1 7 8
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Fig. 10. Z-axis linear displacement accuracy: verification of deliberately entered error.
Fig. 11. Laser vector method: X-axis with deliberately entered error in Z-axis.
The influence of the ambient temperature is an important factor during all geometric accuracy measurements on CNC machine tools. Therefore, the ambient temperature was monitored during the whole measurement session. The result is stated in Fig. 22.
5 m/500 mm stroke. The worst situation is in the Yaxis, which has a progressive under-travel error reaching 30 m/350 mm. In case of the Z-axis a significant positive error of 25 m/500 mm was detected. 5.2. Laser vector method measurement result—machine without compensation
5. Measurement results and discussion 5.1. Linear displacement accuracy of the axes without compensation (measured in the traditional way by Renishaw ML10) Linear displacement accuracy of the machine was evaluated with the following results. The X-axis has a relatively small positive error of a magnitude of maximally
Based on the results of the laser vector method (machine without compensations) it can be stated that the X-axis positioning error and both straightness errors are 10 m in the whole axis stroke. The Y-axis has a relatively small linear displacement error and horizontal straightness error, whereas the most significant error here is the vertical straightness reaching 14 m. In the Z-axis, the maximal positioning error is 14 m, but more important are the straightness errors. Both of
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Fig. 12. Laser vector method: Y-axis with deliberately entered error in Z-axis.
them have got approximately the same magnitude of 23 m. The squareness errors vary from 35 to 53 m/m, the worst case was found in the YZ plane. The diagonal displacement accuracy characterised by the diagonal systematic deviation of positioning (according to [3]) is 34 m. In fact present are both diagonals with an over-travel and under-travel, therefore the maximal error evaluated from all the diagonals is 51 m. 5.3. Comparison of results obtained from the parallel to axis measurement and the vector method—machine without compensation It is clear that the results of linear displacement accuracy from both measurement methods vary in sign and magnitude.
The parallel to axis approach indicates a smaller error in the X-axis compared with the vector method. Furthermore, the parallel to X-axis measurement (Fig. 3) indicates a purely positive error, while the vector method results include both positive (up to +7 m) and negative errors (up to −5 m), as seen from Fig. 6. On the contrary in the Y- and Z-axis the vector method shows a significantly better linear displacement accuracy than the ordinary measurement results. Based on the laser vector method the Y-axis error oscillates around zero with a magnitude of +6 m/−5 m (Fig. 7), whereas the parallel to Y-axis measurement result is clearly linear reaching −30 m (Fig. 4). In case of Z-axis, linear displacement results from both methods indicate a positive error, nevertheless differences are found in the magnitude
Fig. 13. Laser vector method: Z-axis with deliberately entered error in Z-axis.
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Fig. 14. Laser vector method: diagonal displacement accuracy with deliberately entered error in Z-axis.
of the error: parallel to axis measurement result reaches 25 m (Fig. 5), laser vector method result reaches 14 m (Fig. 8). 5.4. Verification of the deliberately entered error into the Z-axis (measured in the traditional way by Renishaw ML10) The activated compensation table works as expected, a linear error value was measured with good repeatability. The maximal positioning error reaches 0.2 mm/500 mm. Linear displacement accuracy in the X- and Y-axis remained
unchanged compared with the state without any compensations. 5.5. Laser vector method measurement results—machine with a deliberately entered error in the Z-axis The linear displacement error of all the axes is now the most significant factor detected by the laser vector method. The straightness errors remain almost unchanged and so are the squareness errors. In case of the X-axis, the maximal positioning error is 64 m, in the Y-axis 43 m and in the Z-axis 60 m. In terms of the diagonal displacement accuracy all
Fig. 15. Laser vector method: X-axis after compensation of deliberately entered error.
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Fig. 16. Laser vector method: Y-axis after compensation of deliberately entered error.
the diagonals show significant positive errors, the worst case is 130 m (Ed ). 5.6. Laser vector method measurement results—machine after the compensation of the deliberately entered error The laser vector method measurement performed after the activation of the compensation tables generated by the LDDMTM software shows the following results. In the X-axis, the linear displacement errors and both straightness errors are below 10 m. The Y-axis geometric errors are even less significant, mostly below 6 m. The Z-axis linear displacement shows an under-travel of 14 m. Both straightness errors are
positive, horizontal +8 m, vertical +4 m. The squareness errors were also reduced to values below 10 m/m in all planes. The diagonal displacement error in the worst diagonal is 20 m. 5.7. Linear displacement accuracy of the axes after the compensation of the deliberately entered error by the vector method (measured in the traditional way by Renishaw ML10) A clear progressive under-travel error was found in the Xaxis (−60 m) and in the Y-axis (−30 m). The Z-axis has still a large progressive over-travel error reaching 125 m on the 500 mm stroke.
Fig. 17. Laser vector method: Z-axis after compensation of deliberately entered error.
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Fig. 18. Laser vector method: diagonal displacement accuracy after compensation of deliberately entered error.
5.8. Additional measurements Angular motion errors were measured with the following results: in the X-axis the most significant is the pitch error of 60 rad. The yaw and roll angular errors are 20 rad each. In the Y-axis only the yaw error of 16 rad is significant. The Z-axis linear displacement is affected by a pitch error of 18 rad. 5.9. Ambient temperature Particular attention was paid to the ambient temperature situation during all measurements. According to the results stated in Fig. 22 the temperature variation from 9 a.m. to 17
p.m. (one-day measurement session) is below 1 ◦ C, which is good enough to maintain a reasonably small uncertainty of the geometric error measurements. 5.10. Discussion of measurement results from machine no. 1 At this point, based on the results presented in Sections 5.1–5.9, it can be stated that by applying a 200 m positioning error into the machine’s Z-axis the laser vector method distributes the error into the remaining axes. This process resulted in a 60 m under-travel error in the X-axis, a 30 m under-travel error in the Y-axis and a 120 m over-travel error in the Z-axis with respect to the “parallel to axes” measure-
Fig. 19. X-axis linear displacement accuracy after compensation of deliberately entered error.
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Fig. 20. Y-axis linear displacement accuracy after compensation of deliberately entered error.
Fig. 21. Z-axis linear displacement accuracy after compensation of deliberately entered error.
ments. On the other hand, the straightness and squareness errors evaluated by the LDDMTM software remained almost unchanged after the introduction of the large error in the Zaxis, which is a reasonable result.
6. Discussion of measurement results from machine no. 2 Linear displacement errors of this machine, without compensations, are significant only in the Z-axis, where the error reaches 27 m. The X- and Y-axis linear displacement errors are below 10 m. On the other hand, extensive angular errors were found in the X-axis. The pitch error is 49 rad and the yaw error is 32 rad. The laser vector method results (machine without compensations) are as follows. The diagonal displacement accuracy is
rather poor. Diagonal “npp” has a maximum error of −55 m, the maximal positive error of +24 m is in the “ppp” diagonal. The largest linear displacement error of 15 m is in the X-axis. Straightness errors are significant in the X-axis (horizontal straightness error: 21 m) and in the Z-axis (horizontal straightness error: 29 m, vertical straightness error: 23 m). Squareness errors vary from 36 to 46 m/m in the individual coordinate planes. The deliberately entered error into the Z-axis linear displacement compensation table reached 0.207 mm/720 mm with good repeatability and was verified by a “parallel to axis” measurement. The laser vector method results with the deliberately entered large error in the Z-axis indicate a maximum diagonal displacement error of 116 m for diagonal “ppp”. All the diagonals have positive errors. The straightness errors in all axes remain practically the same. The linear displacement
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Fig. 22. Ambient temperature during measurements.
error in the X-axis is now 66 m, in the Y- and Z-axis 34 m. The squareness errors remain the same in the XY and ZXplane. A reduction of 12 m/m is present in the YZ-plane compared to the situation without compensations. At this point, it is clear that the results of the testing are basically the same as in case of machine no. 1. Common conclusions can therefore be drawn based on all the measurement data.
displacement error, then this error will not be correctly identified by the sequential diagonal measurement method. In fact, the large error in one axis will be distributed into the remaining axes, thus causing the degradation of their accuracy. This fact is extremely important if the sequential diagonal measurement results are intended to be used for machine error correction. The problem is illustrated by the results from machine no. 1 in Section 5.7.
7. Additional LDDMTM software feature
Acknowledgements
The new version of the LDDMTM software includes the possibility to enter the linear errors from a “parallel to axis” measurement into the vector method analysis. By doing this, the straightness and squareness errors remain unchanged whilst the linear displacement errors are replaced by the “parallel to axis” data. For a three axes machine, two linear displacement measurements are needed.
The author wishes to express thanks to the following people for their contributions during the preparation and review of this paper: Dr. Ray Chaney (Renishaw) and Dr. Charles Wang (Optodyne). This research has been supported by the Czech Ministry of Education under the Grant LN00B128.
8. Conclusion
References
The tests performed on two vertical CNC machining centers at the Research Center for Manufacturing Technologies show that if one of the machine tool axes has a large linear
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nal Displacement Tests)”, an International Standard, by International Standards Organization; 2002. [4] ASME—American Society of Mechanical Engineers, B5.541992 Methods for performance evaluation of computer numerically controlled machining centres, An American National Standard.
[5] Wang C. Laser vector measurement technique for the determination and compensation of volumetric positioning errors. Part 1. Basic theory. Rev Sci Instrum 2000;71(10). [6] Wang C. A theoretical analysis of 4 body diagonal displacement measurement and sequential step diagonal measurement. In: Proceedings of the Lamdamap 2003 Conference. 2003.