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Measurement and analysis of thermo-elastic deviation of five-axis machine tool using dynamic R-test
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Procedia CIRP 00 (2018) 000–000
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Procedia CIRP 00 (2017) 000–000 Procedia CIRP 77 (2018) 521–524 www.elsevier.com/locate/procedia
8th CIRP Conference on High Performance Cutting (HPC 2018)
Measurement and28th deviation of five-axis machine CIRP Design Conference, May 2018, Nantes, France analysis of thermo-elastic tool using dynamic R-test A new methodology to analyze the functional and physical architecture of Christian Brecher, Michel Klatte, Tae Hun Lee*, Filippos Tzanetos existing products forJananBehrens, assembly oriented product family identification Fraunhofer Institute for Production Technology IPT, Steinbachstrasse 17, Aachen 52074, Germany
Paul Stief *, Jean-Yves Dantan, Alain Etienne, Ali Siadat
* Corresponding author. Tel.: +49-241-8904-394 ; fax: +49-241-8904-6394. E-mail address: [email protected]
École Nationale Supérieure d’Arts et Métiers, Arts et Métiers ParisTech, LCFC EA 4495, 4 Rue Augustin Fresnel, Metz 57078, France *Abstract Corresponding author. Tel.: +33 3 87 37 54 30; E-mail address: [email protected]
Thermal errors have a significant impact on machine tool accuracy. Due to their high expense, the conventional shop floors often have poor air conditioning. Even this environmental temperature variation can cause crucial thermo-elastic deviation for precise components. In this paper, a Abstract method based on dynamic R-test is presented for the measurement of thermo-elastic deviation of a five-axis machine tool under environmental temperature variation of a conventional shop floor. Due to short measuring time of under 8 minutes, the dynamic R-test enables geometric In today’s business environment, towards and customization is unbroken. Due to movement this development, the needtool of measurement of a thermal state ofthe thetrend machine tool.more The product advance variety in measuring speed is achieved by continuous of the machine agile and production For systems emergedthe to position cope with various products product families. To sensor design are andstored optimize production during thereconfigurable measurement procedure. this purpose, of machine axes andand measurement data of the synchronously. systems as well as to model, choose the the geometric optimal product matches, product analysis are needed. Indeed, of the known to With a mathematical errors are calculated including all methods location and orientation errorsmost and important errormethods motionsaim of the analyze oneThe product onare themodelled physical level. Different productoffamilies, however, may differThe largely in terms ofisthe number and five-axisa product machineortool. errorfamily motions as a B-spline function their related axis positions. measurement applied repeatnature of components. Thisenvironmental fact impedes temperature an efficient variation. comparison choice of appropriate product family combinations edly over three days under Theand results are presented with the measurement uncertainties for andthe the production correlation system. A new methodology is proposed to analyze existing products in view of their functional and physical architecture. The aim is to cluster of the measured errors and temperature. these products in new assembly product foropen the optimization existing lines and the creation of future reconfigurable © 2018 The Authors. Publishedoriented by Elsevier Ltd.families This is an access articleofunder the assembly CC BY-NC-ND license (http://creativecom© 2018 The Authors. Published by Elsevier Ltd. the physical structure of the products is analyzed. Functional subassemblies are identified, and assembly systems. Based on Datum Flow Chain, mons.org/licenses/by-nc-nd/3.0/) This is an open access under the International CC BY-NC-ND licenseCommittee (https://creativecommons.org/licenses/by-nc-nd/4.0/) aPeer-review functional analysis is article performed. a hybrid functional and physical graph (HyFPAG) is the output Cutting which depicts under responsibility of Moreover, the Scientific of the architecture 8th CIRP Conference on High Performance (HPC the Selection and peer-review under responsibility of the International Scientific Committee of the 8th CIRP Conference on High Performance similarity 2018). between product families by providing design support to both, production system planners and product designers. An illustrative Cutting (HPC 2018). example of a nail-clipper is used to explain the proposed methodology. An industrial case study on two product families of steering columns of thyssenkrupp Presta France is then thermal carried influence, out to give a firstR-test, industrial evaluation the proposed approach. Keywords: Thermo-elastic deviation, dynamic five-axis machineoftool © 2017 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the scientific committee of the 28th CIRP Design Conference 2018.
Controlling temperature is still a very complex problem combined with high cost which lead to most industrial shop floors Five-axis machining is a key technology for broad manufachaving poor air conditioning. The environmental temperature turing processes such as molds, turbine components in aviation variation can already cause crucial machine tool deviations. A and engine in the automotive sector. Compared to three-axis very good overview of the current state of thermal issues in ma1. Introduction of the product range and characteristics manufactured and/or machine tools, five-axis machine tools are capable of manufacchine tools is available in [1]. The volumetric error measureassembled in this system. In this context, the main challenge in turing complex components with a higher automation level. ment technique is especially advantageous for five-axis maDue to the fast development in the domain of modelling and analysis is now not only to cope with single However, due to their complex kinematics, five-axis machine chine tools due to their complex kinematics. The current state communication and an ongoing trend of digitization and products, a limited product range or existing product families, of error measurement techniques is presented in [2]. tools have more origins of error which can often cause workdigitalization, manufacturing enterprises are facing important but also to be able to analyze and to compare products to define piece deviations larger than the required tolerances. AdditionFor the characterization of machine tool thermo-elastic bechallenges in today’s market environments: a continuing new product families. It can be observed that classical existing ally, the ever-increasing demands of metal-cutting industry for havior, the measurement method has to be very fast because of tendency towards reduction of product development times and product families are regrouped in function of clients or features. more productive and more precise machine tools cannot be met the rapidly changing thermal state. Recent researches show that shortened product lifecycles. In addition, there is an increasing However, assembly oriented product families are hardly to find. without considering thermal issues. It has been estimated that measurement methods based on so called ‘R-test’ [3] can calidemand of customization, being at the same time in a global On the product family level, products differ mainly in two up to 75% of geometrical workpiece errors can be traced to therbrate the five-axis machine tool completely in relatively short competition with competitors all over the world. This trend, main characteristics: (i) the number of components and (ii) the mal issues in machine tools [1]. measurement duration. Mayer [4] developed a measurement which is inducing the development from macro to micro type of components (e.g. mechanical, electrical, electronical). The source of machine tool thermal deviation can be classimethod based on R-test which measures all location and orienmarkets, results in diminished lot sizes due to augmenting Classical methodologies considering mainly single products fied into internal and environmental temperature variation. tation errors and three positioning errors of a five axis machine product varieties (high-volume to low-volume production) [1]. or solitary, already existing product families analyze the To cope with this augmenting variety as well as to be able to product structure on a physical level (components level) which 2212-8271 possible © 2018 The Authors. Publishedpotentials by Elsevier Ltd. open access causes article under the CC BY-NC-ND license an efficient definition and identify optimization in This theis an existing difficulties regarding (http://creativecommons.org/licenses/by-nc-nd/3.0/) production system, it is important to have a precise knowledge comparison of different product families. Addressing this 1. Introduction
Keywords: Assembly; Design method; Family identification
Peer-review under of the International ScientificLtd. Committee of the 8th CIRP Conference on High Performance Cutting (HPC 2018).. 2212-8271 © 2018responsibility The Authors. Published by Elsevier This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Selection © and peer-review under responsibility of the International Scientific Committee of the 8th CIRP Conference on High Performance Cutting 2212-8271 2017 The Authors. Published by Elsevier B.V. (HPC 2018). Peer-review under responsibility of the scientific committee of the 28th CIRP Design Conference 2018. 10.1016/j.procir.2018.08.244
Christian Brecher et al. / Procedia CIRP 77 (2018) 521–524 Author name / Procedia CIRP 00 (2018) 000–000
522 2
tool. The method required 30 minutes of measurement time and is also applied for the measurement of thermo-elastic deviation. Ibaraki et al. [5, 6] proposed a new thermal test based on R-test which measures the error motions of the rotary table. Gebhardt [7] applied R-test for measurement and compensation of location and orientation errors using phenomenological model. In previous works [8, 9], a measurement method based on R-test is developed to identify all necessary errors of a five-axis machine tool with a rotary swivelling table using B-spline interpolation method, which can model the error motions more precisely and robustly. With dynamic R-test, measurement was applied continuously along the measurement path. The measurement procedure took 10 minutes to measure the defined errors. This paper applies the further developed dynamic R-test which requires 8 minutes of measuring time for geometric errors including all location and orientation errors and important error motions of a five-axis machine tool with a rotary swivelling table (Fig. 1). The measurement is applied repeatedly at the target machine under environmental temperature variation in a conventional shop floor. T emperature sensors Y
error motions (9 error motions of the linear axes and 2 of the rotary axes) are defined as in ISO 230-1 for the target five axis machine tools [10]. The bottle of the measurement time of the static R-test is the stand still duration of the machine at each measurement position. This duration is required to stabilize the machine dynamic behavior when the machine stops for the measurement. Thus, further reduction of the time is limited. Dynamic R-test applies continuous measurement during the machine movement which can reduce the measurement time drastically. For the precise measurement, two important additional conditions are required: 1. Sufficiently low machine inaccuracy during simultaneous five-axis movement, 2. Synchronizing the machine position data and sensor data. The parameters are optimized in machine control before the experiment to reduce the dynamical machine inaccuracy. The sensor values and the machine positions are gathered synchronously during the continuous measurement with a developed data acquisition tool which enables the connection with the sensor via WLAN and with the machine control via Ethernet. This approach is validated as in [9] for the sufficiently low measurement uncertainties. 3. Experimental Setup and Procedure
X Z A C
Fig. 1. Investigated five-axis machine tool with a rotary swivelling table and environmental temperature sensors
2. Measurement Method As an indirect measurement method, R-test requires a mathematical model of the machine and the errors of axes. Thus, the TCP/machine deviations can be described as a combination of all errors and their influences. The mathematical model of the machine and B-spline interpolation method of error motions are applied as in [8, 9]. For the measurement of thermo-elastic behavior, the geometric errors in Table 1 are applied in this paper. Table 1. Applied geometric errors for the target five-axis machine tools. Error Class
Considered Errors
Error motions of the linear axes
EXX, EYX, EZX, EXY, EYY, EZY, EXZ, EYZ, EZZ
Error motions of the rotary axes
EAA, ECC
Perpendicularity errors of the linear axes
C0X, A0Z, B0Z
Location and orientation errors of the rotary axes
Y0A, Z0A, B0A, C0A, X0C, Y0C, A0C, B0C
11 constant errors (3 perpendicular errors of the linear axes and 8 location and orientation errors of the rotary axes) and 11
For the measurement strategy of R-test, four ball positions and a length measurement are applied. The measurement positions are defined so that the relevant machine volume is utilized as in table 2, and the measurement uncertainties of each error coefficient are sufficient. For the additional length measurement, a rod of invar with two balls is calibrated before the measurement. Table 2. Applied axes travel for the R-test measurement and maximum axes travel of the machine Axis
X [mm]
Y [mm]
Z [mm]
A [°]
Appl.
137 to 693
148 to 705
-610 to 332
-60 to 60
C [°] 0 to 360
Max.
24 to 825
15 to 815
-615 to -15
Over ±90
0 to 360
The fully automated measurement procedure shortens the measurement time additionally to under 8 minutes. This enables to measure the geometric errors of a thermal state. For the measurement of the thermo-elastic behavior, the measurement procedure is applied repeatedly. The first measurement is defined as a reference thermal state to consider just the thermo-elastic behavior of the machine tool. Thus, the first raw measurement values are subtracted from other following measurements before error calculation. The target machine’s environment has a simple air conditioning system which is activated from 05:00 to 18:00 and controls the environmental temperature with a set point of 20 °C. The developed dynamic R-test is applied on the target machine repeatedly five times between 08:00 and 22:00 approximately every 3 hours over three days. Except for the measuring procedure, the machine is in standstill at all times with all axes in control. Dynamic R-test is applied within a fully automated procedure.
Christian Brecher et al. / Procedia CIRP 77 (2018) 521–524 Author name / Procedia CIRP 00 (2018) 000–000
For the measurement of temperature variation, two air temperature sensors are applied on the machine tool (in Fig. 1). The temperature measurement began one day before the first R-test measurement. 4. Experiment Result and Analysis
23 22 21 20
24
Sensor 1Sensor 1 Sensor 2Sensor 2 Measurement Measurement
measurements is calculated from the dynamic R-test. In the following section, important geometric errors are depicted for the analysis of the measurement method and the thermo-elastic behavior. Fig. 4 and Fig. 5 show the variation of the constant errors (perpendicularity errors of linear axes and locations errors of the rotary axes) over 15 measurements in three days respectively. The errors are recorded for each time of the measurement and begin with zero at the first measurement of Aug 16 as the reference thermal state. Due to the repeatedly similar air temperature variation at the nights and mornings, the errors of the first measurement at each days (09:00 of Aug 17 and 08:30 of Aug 18) are nearly zero. The three perpendicularity errors and X0C follow a trend similar to the air temperature variation in Fig. 2. However, for the location errors of Z-axis (Z0A, Y0A), the errors have high leap at the second measurement of the first measurement of each day. This may be an indication that this error is very sensitive to internal heat sources. Since the measurement procedure itself requires movement of all machine axes, it may act as a thermal load on the machine.
23 22 21 20 Aug 16 Aug 16 Aug 17 Aug 17 Aug 18 Aug 18
2 20 1 10
2 0
0 8: 11 : 14 : 1 8 : 2 1: 09 : 12 : 1 5: 1 8: 21 : 08 : 1 1: 1 4: 18 : 21 : 3 0 30 30 3 0 3 0 0 0 00 0 0 0 0 0 0 30 3 0 3 0 30 30
Aug 16
Aug 17
Aug 18
Fig. 4. Change of the perpendicularity errors of the linear axes
20 Y0A Z0A X0C Y0C
10
0
-10 0 8 11 14 1 8 2 1 09 12 1 5 1 8: 21 08 1 1: 1 4: 18 : 21 : :3 0 :30 :30 :3 0 :3 0 :0 0 :00 :0 0 0 0 :0 0 :30 3 0 3 0 30 30
C0 AX 0 B Z EY0Z E X Z EXX E ZY E XY E YZ EX Z EYX EZY Y0 Z ZA 0 XA 0 YC 0 B 0C C 0A AA B00C E C A E A CC
ECC EAA B0C A0C C0A B0A Y0C X0C Z0A Y0A EZZ EYY EXX EYZ EXZ EZY EXY EZX EYX B0Z A0Z C0X
00
4
-4
Error value [µm]
Maximum error value [µrad or µm] Max. uncertainty (µm, µrad )
3 30
B0Z
6
-2
Fig. 2. Environmental temperature change during the experiment and time of R-test measurements
The measurement uncertainties of the error coefficients (k=2) are estimated with Monte Carlo simulation. For the calculation, the sensor values of each measurement position are varied with a normal distributed function of sensor measurement uncertainties (0.5 – 0.7 µm, k=2). The maximum measurement uncertainty of the angular error coefficient does not exceed 2.3 µm and that of the translational error coefficient 2 µm (Fig. 3).
C0X A0Z
8
Error value [µrad]
24
Environ mental temperature [°C]
Environ mental temperature [°C]
The temporal variation of air temperature over the experiment duration is shown in Fig. 2. Due to the sensor positions, the measurement results are slightly different. Nevertheless, the air temperature varies between 21 °C to 24.5 °C during the experiment. The variation shows a periodical trend of air conditioning which turns on before the first measurement and turns off before fourth measurement every day. Due to the relatively higher temperature of outside in summer, the air conditioning cools down the air temperature.
523 3
Fig. 3. Maximum measurement uncertainties of identified coefficients for each error
The first measurement of Aug 16 is defined as reference state. The change of error coefficients over the following 14
Aug 16
Aug 17
Aug 18
Fig. 5. Change of the location errors of the rotary axes
The following figures Fig. 6 and Fig. 7 show two error motions EXX and ECC over the respective axis positions during the experiment. The errors are modelled as a B-Spline function over the axis positions for each time of the measurement (bold black
Christian Brecher et al. / Procedia CIRP 77 (2018) 521–524 Author name / Procedia CIRP 00 (2018) 000–000
lines). Between the measurements, the error functions are linearly interpolated with the colour gradation. The color varies from blue to red with increasing error value. The maximum values at each measurement of both errors follow a trend similar to the environmental air temperature (compared with Fig. 2). EXX
10
0 2
Fig. 8. Maximum change of each measured errors during the experiment
0 -2 600
00 2 1:0 0 1 8: 00 1 5 ::00 12 :0 0 09
30 21 :3 0 1 8: 0 3 1 4:3 0 11::3 0 08
200
30 2 1:3 0 1 8: 30 1 4 ::30 11 3 0 0 8:
400
Fig. 6. Change of the positioning error EXX over axis position
ECC
6
Errorvalue value[µrad] [µrad] Error
20
ECC EAA B0C A0C C0A B0A Y0C X0C Z0A Y0A EZZ EYY EXX EYZ EXZ EZY EXY EZX EYX B0Z A0Z C0X
Errorvalue value[µm] [µm] Error
4
30
Maximum error value [µrad or µm]
524 4
4 2 0 -2
Experiments with a machine tool in standstill under variable environmental condition over three days show that the development of these errors can be identified. For some errors, a clear correlation to the environmental temperature is evident. Other errors, notably the location error of the Z-axis (Z0A) seem to be strongly correlated with internal heat sources of the machine tool, which are activated during the measurement procedure. Accordingly, future research should focus on the refinement of the method. Further experiments are required in order to assess the measurement uncertainty of the thermo-elastically induced errors, since some heat sources may be relevant to blur the results over the eight-minute measurement period. The usecase shown in this paper needs further investigations in order to identify the influence of the measuring procedure itself on the result. References
200
30 21 :3 0 18 :3 0 1 4:3 0 1 1::30 08
00 21 ::0 0 18 00 1 5::00 12 0 0 09 :
30 21 ::3 0 18 0 3 1 4 ::30 11 3 0 08 :
0
Fig. 7. Change of the positioning error ECC over axis position
Fig. 8 shows a bar plot with the maximum of each error obtained during the experiment. It is evident that the maximum errors can differ significantly and therefore have a different sensitivity to thermal loads. Again, the location error Z0A shows a significant behavior. With almost 30 µm, it is the error most sensitive to the applied thermal loads. As mentioned above, the influencing heat source of Z0A may originate from machineinternal sources due to the measurement procedure. In order to identify the main influencing heat source, further research is necessary. 5. Conclusion and outlook In this paper, it has been demonstrated that the R-test is qualified as a measurement of the thermo-elastic behavior of fiveaxis machine tools. This has been achieved by automation and optimizations of the measurement procedure, which result in a measurement time of under eight minutes for the identification of 22 geometric errors.
[1] Mayr J, Jedrzejewski J, Uhlmann E, Donmez MA, Knapp W, et al. Thermal issues in machine tools. CIRP Annals - Manufacturing Technology, 2012;61(2):771-791. [2] Schwenke H, Knapp W. Geometric error measurement and compensation of machines – An update. CIRP Annals - Manufacturing Technology, 2008;57(2):660-675. [3] Weikert S. R-test, a new device for accuracy measurements on five axis machine tools. CIRP Annals - Manufacturing Technology, 2004;53(1):429-432. [4] Mayer J. Five-axis machine tool calibration by probing a scale enriched reconfigurable uncalibrated master balls artefact. CIRP Annals Manufacturing Technology, 2012;61(1):515-518. [5] Ibaraki S, Hong C. Thermal test for error maps of rotary axes by R-test. Key Engineering Materials, 2012;523-524:809-814. [6] Ibaraki S, Ota Y. A machining test to calibrate rotary axis error motions of five-axis machine tools and its application to thermal deformation test. Internation Journal of Machine tools and Manufacture, 2014;86:81-88. [7] Gebhardt M. Thermal behaviour and compensation of rotary axes in 5axis machine tools. Dissertation ETH Zürich, 2014. [8] Brecher C, Behrens J, Lee TH, Charlier S. Calibration of five-axis machine tool using R-test procedure. Proceedings of the 12th International Conference, Exhibition on Laser Metrology, CMM & Machine Tool Performance (LAMDAMAP), 2017. [9] Brecher C, Behrens J, Lee TH. Rapid geometric calibration of five-axis machine tool using dynamic R-test. The 7th International Conference of Asian Society for Precision Engineering and Nanotechnology (ASPEN), 2017. [10] ISO 230-1:2012. Test code for machine tools - Part 1: Geometric accuracy of machines operating under no-load or quasistatic condition.
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Procedia CIRP 00 (2018) 000–000
www.elsevier.com/locate/procedia
Procedia CIRP 00 (2017) 000–000 Procedia CIRP 77 (2018) 521–524 www.elsevier.com/locate/procedia
8th CIRP Conference on High Performance Cutting (HPC 2018)
Measurement and28th deviation of five-axis machine CIRP Design Conference, May 2018, Nantes, France analysis of thermo-elastic tool using dynamic R-test A new methodology to analyze the functional and physical architecture of Christian Brecher, Michel Klatte, Tae Hun Lee*, Filippos Tzanetos existing products forJananBehrens, assembly oriented product family identification Fraunhofer Institute for Production Technology IPT, Steinbachstrasse 17, Aachen 52074, Germany
Paul Stief *, Jean-Yves Dantan, Alain Etienne, Ali Siadat
* Corresponding author. Tel.: +49-241-8904-394 ; fax: +49-241-8904-6394. E-mail address: [email protected]
École Nationale Supérieure d’Arts et Métiers, Arts et Métiers ParisTech, LCFC EA 4495, 4 Rue Augustin Fresnel, Metz 57078, France *Abstract Corresponding author. Tel.: +33 3 87 37 54 30; E-mail address: [email protected]
Thermal errors have a significant impact on machine tool accuracy. Due to their high expense, the conventional shop floors often have poor air conditioning. Even this environmental temperature variation can cause crucial thermo-elastic deviation for precise components. In this paper, a Abstract method based on dynamic R-test is presented for the measurement of thermo-elastic deviation of a five-axis machine tool under environmental temperature variation of a conventional shop floor. Due to short measuring time of under 8 minutes, the dynamic R-test enables geometric In today’s business environment, towards and customization is unbroken. Due to movement this development, the needtool of measurement of a thermal state ofthe thetrend machine tool.more The product advance variety in measuring speed is achieved by continuous of the machine agile and production For systems emergedthe to position cope with various products product families. To sensor design are andstored optimize production during thereconfigurable measurement procedure. this purpose, of machine axes andand measurement data of the synchronously. systems as well as to model, choose the the geometric optimal product matches, product analysis are needed. Indeed, of the known to With a mathematical errors are calculated including all methods location and orientation errorsmost and important errormethods motionsaim of the analyze oneThe product onare themodelled physical level. Different productoffamilies, however, may differThe largely in terms ofisthe number and five-axisa product machineortool. errorfamily motions as a B-spline function their related axis positions. measurement applied repeatnature of components. Thisenvironmental fact impedes temperature an efficient variation. comparison choice of appropriate product family combinations edly over three days under Theand results are presented with the measurement uncertainties for andthe the production correlation system. A new methodology is proposed to analyze existing products in view of their functional and physical architecture. The aim is to cluster of the measured errors and temperature. these products in new assembly product foropen the optimization existing lines and the creation of future reconfigurable © 2018 The Authors. Publishedoriented by Elsevier Ltd.families This is an access articleofunder the assembly CC BY-NC-ND license (http://creativecom© 2018 The Authors. Published by Elsevier Ltd. the physical structure of the products is analyzed. Functional subassemblies are identified, and assembly systems. Based on Datum Flow Chain, mons.org/licenses/by-nc-nd/3.0/) This is an open access under the International CC BY-NC-ND licenseCommittee (https://creativecommons.org/licenses/by-nc-nd/4.0/) aPeer-review functional analysis is article performed. a hybrid functional and physical graph (HyFPAG) is the output Cutting which depicts under responsibility of Moreover, the Scientific of the architecture 8th CIRP Conference on High Performance (HPC the Selection and peer-review under responsibility of the International Scientific Committee of the 8th CIRP Conference on High Performance similarity 2018). between product families by providing design support to both, production system planners and product designers. An illustrative Cutting (HPC 2018). example of a nail-clipper is used to explain the proposed methodology. An industrial case study on two product families of steering columns of thyssenkrupp Presta France is then thermal carried influence, out to give a firstR-test, industrial evaluation the proposed approach. Keywords: Thermo-elastic deviation, dynamic five-axis machineoftool © 2017 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the scientific committee of the 28th CIRP Design Conference 2018.
Controlling temperature is still a very complex problem combined with high cost which lead to most industrial shop floors Five-axis machining is a key technology for broad manufachaving poor air conditioning. The environmental temperature turing processes such as molds, turbine components in aviation variation can already cause crucial machine tool deviations. A and engine in the automotive sector. Compared to three-axis very good overview of the current state of thermal issues in ma1. Introduction of the product range and characteristics manufactured and/or machine tools, five-axis machine tools are capable of manufacchine tools is available in [1]. The volumetric error measureassembled in this system. In this context, the main challenge in turing complex components with a higher automation level. ment technique is especially advantageous for five-axis maDue to the fast development in the domain of modelling and analysis is now not only to cope with single However, due to their complex kinematics, five-axis machine chine tools due to their complex kinematics. The current state communication and an ongoing trend of digitization and products, a limited product range or existing product families, of error measurement techniques is presented in [2]. tools have more origins of error which can often cause workdigitalization, manufacturing enterprises are facing important but also to be able to analyze and to compare products to define piece deviations larger than the required tolerances. AdditionFor the characterization of machine tool thermo-elastic bechallenges in today’s market environments: a continuing new product families. It can be observed that classical existing ally, the ever-increasing demands of metal-cutting industry for havior, the measurement method has to be very fast because of tendency towards reduction of product development times and product families are regrouped in function of clients or features. more productive and more precise machine tools cannot be met the rapidly changing thermal state. Recent researches show that shortened product lifecycles. In addition, there is an increasing However, assembly oriented product families are hardly to find. without considering thermal issues. It has been estimated that measurement methods based on so called ‘R-test’ [3] can calidemand of customization, being at the same time in a global On the product family level, products differ mainly in two up to 75% of geometrical workpiece errors can be traced to therbrate the five-axis machine tool completely in relatively short competition with competitors all over the world. This trend, main characteristics: (i) the number of components and (ii) the mal issues in machine tools [1]. measurement duration. Mayer [4] developed a measurement which is inducing the development from macro to micro type of components (e.g. mechanical, electrical, electronical). The source of machine tool thermal deviation can be classimethod based on R-test which measures all location and orienmarkets, results in diminished lot sizes due to augmenting Classical methodologies considering mainly single products fied into internal and environmental temperature variation. tation errors and three positioning errors of a five axis machine product varieties (high-volume to low-volume production) [1]. or solitary, already existing product families analyze the To cope with this augmenting variety as well as to be able to product structure on a physical level (components level) which 2212-8271 possible © 2018 The Authors. Publishedpotentials by Elsevier Ltd. open access causes article under the CC BY-NC-ND license an efficient definition and identify optimization in This theis an existing difficulties regarding (http://creativecommons.org/licenses/by-nc-nd/3.0/) production system, it is important to have a precise knowledge comparison of different product families. Addressing this 1. Introduction
Keywords: Assembly; Design method; Family identification
Peer-review under of the International ScientificLtd. Committee of the 8th CIRP Conference on High Performance Cutting (HPC 2018).. 2212-8271 © 2018responsibility The Authors. Published by Elsevier This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Selection © and peer-review under responsibility of the International Scientific Committee of the 8th CIRP Conference on High Performance Cutting 2212-8271 2017 The Authors. Published by Elsevier B.V. (HPC 2018). Peer-review under responsibility of the scientific committee of the 28th CIRP Design Conference 2018. 10.1016/j.procir.2018.08.244
Christian Brecher et al. / Procedia CIRP 77 (2018) 521–524 Author name / Procedia CIRP 00 (2018) 000–000
522 2
tool. The method required 30 minutes of measurement time and is also applied for the measurement of thermo-elastic deviation. Ibaraki et al. [5, 6] proposed a new thermal test based on R-test which measures the error motions of the rotary table. Gebhardt [7] applied R-test for measurement and compensation of location and orientation errors using phenomenological model. In previous works [8, 9], a measurement method based on R-test is developed to identify all necessary errors of a five-axis machine tool with a rotary swivelling table using B-spline interpolation method, which can model the error motions more precisely and robustly. With dynamic R-test, measurement was applied continuously along the measurement path. The measurement procedure took 10 minutes to measure the defined errors. This paper applies the further developed dynamic R-test which requires 8 minutes of measuring time for geometric errors including all location and orientation errors and important error motions of a five-axis machine tool with a rotary swivelling table (Fig. 1). The measurement is applied repeatedly at the target machine under environmental temperature variation in a conventional shop floor. T emperature sensors Y
error motions (9 error motions of the linear axes and 2 of the rotary axes) are defined as in ISO 230-1 for the target five axis machine tools [10]. The bottle of the measurement time of the static R-test is the stand still duration of the machine at each measurement position. This duration is required to stabilize the machine dynamic behavior when the machine stops for the measurement. Thus, further reduction of the time is limited. Dynamic R-test applies continuous measurement during the machine movement which can reduce the measurement time drastically. For the precise measurement, two important additional conditions are required: 1. Sufficiently low machine inaccuracy during simultaneous five-axis movement, 2. Synchronizing the machine position data and sensor data. The parameters are optimized in machine control before the experiment to reduce the dynamical machine inaccuracy. The sensor values and the machine positions are gathered synchronously during the continuous measurement with a developed data acquisition tool which enables the connection with the sensor via WLAN and with the machine control via Ethernet. This approach is validated as in [9] for the sufficiently low measurement uncertainties. 3. Experimental Setup and Procedure
X Z A C
Fig. 1. Investigated five-axis machine tool with a rotary swivelling table and environmental temperature sensors
2. Measurement Method As an indirect measurement method, R-test requires a mathematical model of the machine and the errors of axes. Thus, the TCP/machine deviations can be described as a combination of all errors and their influences. The mathematical model of the machine and B-spline interpolation method of error motions are applied as in [8, 9]. For the measurement of thermo-elastic behavior, the geometric errors in Table 1 are applied in this paper. Table 1. Applied geometric errors for the target five-axis machine tools. Error Class
Considered Errors
Error motions of the linear axes
EXX, EYX, EZX, EXY, EYY, EZY, EXZ, EYZ, EZZ
Error motions of the rotary axes
EAA, ECC
Perpendicularity errors of the linear axes
C0X, A0Z, B0Z
Location and orientation errors of the rotary axes
Y0A, Z0A, B0A, C0A, X0C, Y0C, A0C, B0C
11 constant errors (3 perpendicular errors of the linear axes and 8 location and orientation errors of the rotary axes) and 11
For the measurement strategy of R-test, four ball positions and a length measurement are applied. The measurement positions are defined so that the relevant machine volume is utilized as in table 2, and the measurement uncertainties of each error coefficient are sufficient. For the additional length measurement, a rod of invar with two balls is calibrated before the measurement. Table 2. Applied axes travel for the R-test measurement and maximum axes travel of the machine Axis
X [mm]
Y [mm]
Z [mm]
A [°]
Appl.
137 to 693
148 to 705
-610 to 332
-60 to 60
C [°] 0 to 360
Max.
24 to 825
15 to 815
-615 to -15
Over ±90
0 to 360
The fully automated measurement procedure shortens the measurement time additionally to under 8 minutes. This enables to measure the geometric errors of a thermal state. For the measurement of the thermo-elastic behavior, the measurement procedure is applied repeatedly. The first measurement is defined as a reference thermal state to consider just the thermo-elastic behavior of the machine tool. Thus, the first raw measurement values are subtracted from other following measurements before error calculation. The target machine’s environment has a simple air conditioning system which is activated from 05:00 to 18:00 and controls the environmental temperature with a set point of 20 °C. The developed dynamic R-test is applied on the target machine repeatedly five times between 08:00 and 22:00 approximately every 3 hours over three days. Except for the measuring procedure, the machine is in standstill at all times with all axes in control. Dynamic R-test is applied within a fully automated procedure.
Christian Brecher et al. / Procedia CIRP 77 (2018) 521–524 Author name / Procedia CIRP 00 (2018) 000–000
For the measurement of temperature variation, two air temperature sensors are applied on the machine tool (in Fig. 1). The temperature measurement began one day before the first R-test measurement. 4. Experiment Result and Analysis
23 22 21 20
24
Sensor 1Sensor 1 Sensor 2Sensor 2 Measurement Measurement
measurements is calculated from the dynamic R-test. In the following section, important geometric errors are depicted for the analysis of the measurement method and the thermo-elastic behavior. Fig. 4 and Fig. 5 show the variation of the constant errors (perpendicularity errors of linear axes and locations errors of the rotary axes) over 15 measurements in three days respectively. The errors are recorded for each time of the measurement and begin with zero at the first measurement of Aug 16 as the reference thermal state. Due to the repeatedly similar air temperature variation at the nights and mornings, the errors of the first measurement at each days (09:00 of Aug 17 and 08:30 of Aug 18) are nearly zero. The three perpendicularity errors and X0C follow a trend similar to the air temperature variation in Fig. 2. However, for the location errors of Z-axis (Z0A, Y0A), the errors have high leap at the second measurement of the first measurement of each day. This may be an indication that this error is very sensitive to internal heat sources. Since the measurement procedure itself requires movement of all machine axes, it may act as a thermal load on the machine.
23 22 21 20 Aug 16 Aug 16 Aug 17 Aug 17 Aug 18 Aug 18
2 20 1 10
2 0
0 8: 11 : 14 : 1 8 : 2 1: 09 : 12 : 1 5: 1 8: 21 : 08 : 1 1: 1 4: 18 : 21 : 3 0 30 30 3 0 3 0 0 0 00 0 0 0 0 0 0 30 3 0 3 0 30 30
Aug 16
Aug 17
Aug 18
Fig. 4. Change of the perpendicularity errors of the linear axes
20 Y0A Z0A X0C Y0C
10
0
-10 0 8 11 14 1 8 2 1 09 12 1 5 1 8: 21 08 1 1: 1 4: 18 : 21 : :3 0 :30 :30 :3 0 :3 0 :0 0 :00 :0 0 0 0 :0 0 :30 3 0 3 0 30 30
C0 AX 0 B Z EY0Z E X Z EXX E ZY E XY E YZ EX Z EYX EZY Y0 Z ZA 0 XA 0 YC 0 B 0C C 0A AA B00C E C A E A CC
ECC EAA B0C A0C C0A B0A Y0C X0C Z0A Y0A EZZ EYY EXX EYZ EXZ EZY EXY EZX EYX B0Z A0Z C0X
00
4
-4
Error value [µm]
Maximum error value [µrad or µm] Max. uncertainty (µm, µrad )
3 30
B0Z
6
-2
Fig. 2. Environmental temperature change during the experiment and time of R-test measurements
The measurement uncertainties of the error coefficients (k=2) are estimated with Monte Carlo simulation. For the calculation, the sensor values of each measurement position are varied with a normal distributed function of sensor measurement uncertainties (0.5 – 0.7 µm, k=2). The maximum measurement uncertainty of the angular error coefficient does not exceed 2.3 µm and that of the translational error coefficient 2 µm (Fig. 3).
C0X A0Z
8
Error value [µrad]
24
Environ mental temperature [°C]
Environ mental temperature [°C]
The temporal variation of air temperature over the experiment duration is shown in Fig. 2. Due to the sensor positions, the measurement results are slightly different. Nevertheless, the air temperature varies between 21 °C to 24.5 °C during the experiment. The variation shows a periodical trend of air conditioning which turns on before the first measurement and turns off before fourth measurement every day. Due to the relatively higher temperature of outside in summer, the air conditioning cools down the air temperature.
523 3
Fig. 3. Maximum measurement uncertainties of identified coefficients for each error
The first measurement of Aug 16 is defined as reference state. The change of error coefficients over the following 14
Aug 16
Aug 17
Aug 18
Fig. 5. Change of the location errors of the rotary axes
The following figures Fig. 6 and Fig. 7 show two error motions EXX and ECC over the respective axis positions during the experiment. The errors are modelled as a B-Spline function over the axis positions for each time of the measurement (bold black
Christian Brecher et al. / Procedia CIRP 77 (2018) 521–524 Author name / Procedia CIRP 00 (2018) 000–000
lines). Between the measurements, the error functions are linearly interpolated with the colour gradation. The color varies from blue to red with increasing error value. The maximum values at each measurement of both errors follow a trend similar to the environmental air temperature (compared with Fig. 2). EXX
10
0 2
Fig. 8. Maximum change of each measured errors during the experiment
0 -2 600
00 2 1:0 0 1 8: 00 1 5 ::00 12 :0 0 09
30 21 :3 0 1 8: 0 3 1 4:3 0 11::3 0 08
200
30 2 1:3 0 1 8: 30 1 4 ::30 11 3 0 0 8:
400
Fig. 6. Change of the positioning error EXX over axis position
ECC
6
Errorvalue value[µrad] [µrad] Error
20
ECC EAA B0C A0C C0A B0A Y0C X0C Z0A Y0A EZZ EYY EXX EYZ EXZ EZY EXY EZX EYX B0Z A0Z C0X
Errorvalue value[µm] [µm] Error
4
30
Maximum error value [µrad or µm]
524 4
4 2 0 -2
Experiments with a machine tool in standstill under variable environmental condition over three days show that the development of these errors can be identified. For some errors, a clear correlation to the environmental temperature is evident. Other errors, notably the location error of the Z-axis (Z0A) seem to be strongly correlated with internal heat sources of the machine tool, which are activated during the measurement procedure. Accordingly, future research should focus on the refinement of the method. Further experiments are required in order to assess the measurement uncertainty of the thermo-elastically induced errors, since some heat sources may be relevant to blur the results over the eight-minute measurement period. The usecase shown in this paper needs further investigations in order to identify the influence of the measuring procedure itself on the result. References
200
30 21 :3 0 18 :3 0 1 4:3 0 1 1::30 08
00 21 ::0 0 18 00 1 5::00 12 0 0 09 :
30 21 ::3 0 18 0 3 1 4 ::30 11 3 0 08 :
0
Fig. 7. Change of the positioning error ECC over axis position
Fig. 8 shows a bar plot with the maximum of each error obtained during the experiment. It is evident that the maximum errors can differ significantly and therefore have a different sensitivity to thermal loads. Again, the location error Z0A shows a significant behavior. With almost 30 µm, it is the error most sensitive to the applied thermal loads. As mentioned above, the influencing heat source of Z0A may originate from machineinternal sources due to the measurement procedure. In order to identify the main influencing heat source, further research is necessary. 5. Conclusion and outlook In this paper, it has been demonstrated that the R-test is qualified as a measurement of the thermo-elastic behavior of fiveaxis machine tools. This has been achieved by automation and optimizations of the measurement procedure, which result in a measurement time of under eight minutes for the identification of 22 geometric errors.
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