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Thermal behavior of a machine tool equipped with linear motors
International Journal of Machine Tools & Manufacture 44 (2004) 749–758 www.elsevier.com/locate/ijmactool
Thermal behavior of a machine tool equipped with linear motors Jong-Jin Kim a, Young Hun Jeong b, Dong-Woo Cho b, a
b
iCurie-Lab, 5F Daewon Building 946-18, Daechi-dong, Kangnam-gu, Seoul 135-846, South Korea Department of Mechanical Engineering, Pohang University of Science and Technology, San 31 Hyoja-dong, Nam-gu, Pohang, Kyungbuk 790-784, South Korea Received 30 October 2003; received in revised form 22 January 2004; accepted 2 February 2004
Abstract Development of a feed drive system with high speed and accuracy has been a major issue in the machine tool industry. Linear motors can be used as efficient tool to achieve the high speed and accuracy. However, a high speed feed drive system with linear motors, in turn, can generate heat problems. Also, frictional heat is produced at the ball or roller bearing of LM block when driven at high speed. It can affect the thermal deformation of the linear scale as well as that of the machine tool structure. In this paper, important heat sources and resulting thermal errors in a machine tool equipped with linear motors were investigated when it was operated at high speed. The thermal deformation characteristics were identified through measuring the thermal error caused from thermal deformation of the linear scale and the machine tool structure. The dominant thermal error components were identified from the thermal error analysis using finite element method. It was shown that the proposed analysis scheme is efficient in identifying the dominant thermal error components and its magnitudes such as the thermal expansion and movement of the linear scale, thermal deformation of the machine tool slide. # 2004 Elsevier Ltd. All rights reserved. Keywords: Thermal deformation; Machine tool; Linear motor; Linear scale; Linear guideway; FEM
1. Introduction Enhancing the productivity and accuracy of manufacturing systems has become increasingly important for modern industry. Linear motors are efficient tools that offer high speed and accuracy. By eliminating mechanical transmission mechanisms, much higher speeds and greater acceleration can be achieved without suffering from backlash or excessive friction [1,2]. Therefore, linear motors are one way to overcome the limits on velocity and positional accuracy that are inherent in ball-screw feed drive systems [1–4]. One obstacle to the application of linear motors is heat. The motor coil generates heat, and the temperav ture can increase by over 100 C [5]. As a linear motor operates in direct combination with a machine tool slide, the heat generated in the linear motor can affect Corresponding author. Tel.: +82-54-279-2171; fax: +82-54-2795899. E-mail address: [email protected] (D.-W. Cho).
0890-6955/$ - see front matter # 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijmachtools.2004.02.006
the machine tool’s structure. Machine tools equipped with linear motors usually operate at high speed, so the balls or rollers in the block of the linear motion (LM) guideway also rotate at high speed, generating considerable frictional heat, which can be transferred to machine tool structure through the slide. Previous studies have examined the thermal behavior of machine tools equipped with ball-screws [6,7], and a few papers have dealt with the thermal behavior and optimization of the linear motor itself [3,5]. However, there has been little research on the thermal behavior of machine tools equipped with linear motors. This study investigated the thermal behavior of a machine tool equipped with linear motors when operated at high speed. To identify the thermal behavior of this type of machine tool, we measured the temperature and temperature variation at various points, and used the results to analyze the important heat sources and thermal behavior. Various thermal error components, such as thermal expansion of linear scales and thermal deformation of each part of a machine tool’s structure
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affect the positional accuracy of a machine tool, either individually or in combination [8,9]. If the thermal deformation has compound effects on the machine tool slide and linear scale, then differentiating the contribution of each component experimentally is a formidable task. Therefore, the finite element method (FEM) was adopted to analyze the contribution of each component to thermal error. Consequently, it was found that the proposed scheme was efficient in identifying the dominant thermal error components and their magnitudes. Until recently, most machine tools equipped with linear motors have been of the horizontal type, with a box-in-box structure, and the machine tool that we studied was typical in these respects. Therefore, the scheme proposed in this study is applicable to many other machine tools equipped with linear motors. This study used the proposed scheme to analyze the typical thermal behavior of a machine tool equipped with linear motors. Thermal deformations of the linear scale and machine tool parts were identified in detail and the effects of thermal deformation on thermal error were investigated. In addition, we show that linear motors’ cooling systems can significantly affect the thermal behavior of machine tools.
2. Thermal error measurement 2.1. Temperature sensor locations and experimental setup
Table 1 Temperature sensor locations Temperature sensor locations Linear motor Primary part Secondary part Linear scale Linear guideway LM block LM guide Y-frame Column Spindle Room temperature
Sensor number X
Y
Z
1, 2 3 4, 5, 6
10, 11 12 13, 14, 15
19 20 21, 22
9 7, 8 29 30 26, 27 31, 32
18 16, 17
25 23, 24
movement. The position feedback is done using linear scales (LC481, Heidenhein). Temperatures were measured every 20 s during motion, using 32 T-type thermocouples that were attached to the machining center, as shown in Fig. 1 and Table 1. The experimental setup that was used to measure thermal error is shown in Fig. 2. The resultant thermal error was measured at the end of the spindle, which was considered the cutting point. Thermal error in the feed direction was measured using a laser interferometer (ML10, Renishaw). Two gap sensors (AEC5505, Applied Electronics) and a photo sensor (F1RH, Takenaka) were used to identify thermal errors in the remaining axes. 2.2. Experimental conditions
In this study, thermal error measuring experiments were conducted on a horizontal machining center (FH500) that was developed by Daewoo Heavy Industries and Machinery, Ltd. Two linear motors (1FN3, SIEMENS) are used for X- and Y-axis movement and one linear motor (1FN1, SIEMENS) is used for Z-axis
This paper investigated the thermal behavior of a machine tool equipped with linear motors operating at high speed. The spindle and its cooler were left off to eliminate the effect of thermal deformation of the spindle itself. The experimental conditions are listed in Table 2. As shown in Table 2, experiments for each axis were performed separately to eliminate combined effects on thermal error when operating on multiple axes. The machine tool was operated at various feed rates along each axis, within the maximum stroke and during a given time. Under the experimental conditions shown in Table 2, ‘arbitrary’ means that the feedrate was changed every 20 min.
3. Thermal behavior modeling using FEM
Fig. 1. Thermocouple locations on the machine tool.
Separate FEM models were constructed for the linear scale and a machine tool equipped with linear motors. They were modeled separately for several reasons: first, in many cases, the thermal deformation of a linear scale is the dominant thermal error component,
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so using only an FEM model for the linear scale allows simple and fast simulation that is easy to analyze. Second, the results of a separate model can be used to analyze the compound error measured experimentally. Finally, a linear scale apparatus that is not deformed by the thermal deformation of the machine tool structure has already been devised. 3.1. FEM model of the linear scale A detailed FEM model of a linear scale was constructed, including the shape of the cross-section using parabolic tetrahedral type elements. For realism, the material properties of the linear scale cover and scale were those of aluminum alloy and glass, respectively. Moreover, motion was constrained by fixing the linear scale in the transverse direction, as though it was affixed to the machine tool. The thermal behavior was analyzed by measuring the temperature variation of the linear scale, to model the heat transfer from the machine tool structure. The geometric modeling and solution of the FEM were performed using SOLIDWORKS 2001 and COSMOS/ WORKS 7.0, respectively. 3.2. FEM model of a machine tool equipped with linear motors The FEM mesh model for the machine tool used is shown in Fig. 3. The elements were generated in the Fig. 2.
The experimental setup for measuring thermal errors.
Table 2 Experimental conditions Experiment no.
Axis
Feedrate (m/min)
Stroke (mm)
Time (min)
1 2 3 4 5 6 7 8a 9 10 11 12 13 14
X X X X Y Y Y Y Y Y Z Z Z Z
60 36 12 Arbitrary 60 60 36 36 12 Arbitrary 60 36 12 Arbitrary
60 560 60 560 60 560 60 560 50 550 50 300 50 550 50 550 50 550 50 550 100 430 100 430 100 430 100 430
150 150 150 220 120 120 120 120 180 220 150 150 150 220
a All the experiments except for Experiment 8 were conducted with both the power cooler and precision cooler of the linear motors being operated. For Experiment 8, the precision cooler was turned off during the experiment to investigate influence of the cooling system on the thermal deformation of the machine tool structure.
Fig. 3.
Mesh model of the machine tool for FEM thermal analysis.
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error of the precision cooler in the linear motors’ cooling systems were also checked.
Table 3 The materials of the machine tool Component
Material
X-slide, Y-slide, Y-frame Z-slide Column Linear motor—secondary part Etc.
SS41 (stainless steel) SCMn2A (stainless steel) AGC45C (cast carbon steel) Magnet SS41 (stainless steel)
same way as for the linear scale mesh model. A total of 192,913 nodes and 110,265 elements were used. The material properties of the model are listed in Table 3. The non-linear characteristics of the material properties that might occur with an increase in temperature were not considered, since the variation in temperature was not significant. The following assumptions and boundary conditions were used to perform the thermal error analysis using FEM. A steady state during the analysis was assumed. Moreover, machining was not considered, so there was no heat generation due to machining. In the thermal deformation analysis, displacement of the nodes comprising the bottom surface of the machine tool was assumed to be zero. Heat flux was input to represent the heat generated by the roller friction at the X-, Yand Z-axis LM guideways. The effect of a precision cooler was represented by a negative heat flux. The primary part of the linear motor is too complex to model. However, the analysis was fast and easy using the simplified model. The primary part of the linear motor was replaced by an attractive force in the perpendicular direction, because there is an air space between the primary and secondary parts, where an electromagnetic attractive force acts. This confirmed that although there was thermal expansion, the gap changed with expansion without causing any significant thermal error. In addition, the primary parts were fixed in the feed direction because they served to fix the slide. Heat generated in the primary part of the linear motor was replaced by heat fluxes, which were calculated from the measured temperatures.
4. Thermal error analysis The thermal behavior was identified from the measured and FEM results. The important heat sources were summarized. The thermal error caused by deformation of the linear scale was analyzed. Then, the combined effects of thermal deformation of the linear scale and of the machine tool slide were investigated. Also investigated were the thermal expansion and bending of the machine tool as a result of the heat generated by the linear motors. The effects on thermal
4.1. Heat sources The experiments showed that the important heat sources could be divided into two types: internal and external heat sources. Three important internal heat sources were identified. First, the linear motors generated a large amount of heat. Second, frictional heat was produced at the LM guideways by the high speed rotation of the balls or rollers in the block of the LM guideway. Third, the thermal behavior of the machine tool depended on the setup of the cooling systems for the linear motors, which consisted of power and precision coolers [10]. A power cooler was used to cool the primary part of the linear motor, while a precision cooler prevented the heat generated in the linear motor from being transferred to the machine tool structure. The start-up condition for the power and precision v coolers was 18 and 19 C, respectively. Nevertheless, the linear motors generated a lot of heat, some of which was transferred to the machine tool structure. By contrast, the only important external heat source identified was the ambient temperature, as the effects of the heat generated by other machine tools, the operator, and lighting apparatus had already been eliminated from the experimental environment. 4.2. Thermal expansion of linear scales The thermal error caused by the thermal expansion of a linear scale was examined. Fig. 4(a),(b) illustrates the temperature variations and subsequent thermal error, respectively, in Experiment 5, which is presented in Table 2. The temperature increased in the linear motor, the block of the LM guideway, and the linear scale due to travel in the Y-direction. Fig. 4(b) shows that the thermal error measured in the Y-direction differed in magnitude and direction at different positions. In another experiment, the feedrates were changed arbitrarily to precisely identify the main causes of thermal error. Fig. 5(a) shows the arbitrary changes in the feedrate in the Y-direction used in Experiment 10. Fig. 5(b),(c) shows the measured temperature variations and the respective thermal error. Fig. 5(b) shows that the temperature variations of the Y-axis linear motor were similar to the feedrate variation seen in Fig. 5(a). Nevertheless, this pattern cannot explain the measured thermal error shown in Fig. 5(c), which plots the temperatures measured in the block of the Y-axis LM guideway, linear scale, and points in between, and the Y-direction thermal error. The temperature variations in the three cases corresponded almost perfectly. Therefore, the frictional heat generated in the block of
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Fig. 4.
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Temperature variations and thermal errors in Experiment 5. (a) Temperature variations and (b) thermal errors in the Y-direction.
the LM guideway was conducted to the linear scale via the machine tool structure. In fact, the pattern of thermal error is similar to that of the temperature variations shown in Fig. 5(c). Now, the cause of the thermal error that occurred in Experiment 5 can be inferred more clearly, as follows: the temperature increase in the linear scale induces thermal expansion. Fig. 6 shows the structure of the Yaxis linear scale. When the linear scale expands towards the two sides from the center position, which is at 390 mm in this case, the amount of thermal expansion increases with the distance of the measured position from the center. Since the Y-axis experiments were performed for the range from 50 to 550 mm, the largest thermal error in the Y-axis was observed at the 50-mm position, which was the position farthest from the center. At the 550-mm position, the direction of deformation was reversed and the deformation was less than that at the 50-mm position.
To verify these results, the thermal behavior of the linear scale was simulated using FEM. The thermal expansion of the linear scale was simulated, using the temperature variation measured in Experiment 5 as the boundary conditions. Fig. 7 shows the results of the simulation and the corresponding experimental results. The deformation in the Y-direction during travel in the Y-axis in Experiment 5 shows very close agreement with the thermal expansion of the Y-axis linear scale. Moreover, this implies that thermal expansion of the linear scale was the dominant thermal error component in this case. This procedure can also be applied to the X-direction thermal error in the X-axis experiments. When traveling in the X-direction, the frictional heat generated in the X-axis LM guideway block is conducted to the linear scale through the machine tool structure. Therefore, thermal behavior similar to those described above, was obtained via the same route.
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Fig. 6. Thermal expansion of the Y-axis linear scale.
Fig. 5. Measurement results in Experiment 10. (a) Arbitrary feed rate condition, (b) temperature variations of Y-axis linear motor, and (c) temperature variations and thermal error.
4.3. Thermal behavior in a machine tool slide with a linear scale Generally, a linear scale is attached to a machine tool slide. Consequently, thermal deformation of the machine tool slide can affect the linear scale. This section investigates the combined effects of the thermal deformation of the linear scale and of the machine tool slide.
Fig. 8(a),(b) shows the temperature variations and the Z-direction thermal error measured in Experiment 11, respectively. The temperature increased in the Zaxis linear motor, LM guideway, and linear scale. The temperature variation of the Z-axis linear motor was less than that of the other linear motors, but this was because the thermocouple was attached to the side of the linear motor because of the cover on the machine tool. When traveling in the Z-direction, the thermal behavior differed from the results for X- or Y-direction travel described in Section 4.2. The magnitude of the thermal error differed at each different Z-position; this can be thought to have resulted from the thermal expansion of the linear scale. However, regardless of position, the general tendency was for the thermal error to increase in one direction. Therefore, the thermal error can be explained by the increased offset in one direction added to the thermal expansion of the linear scale. Two types of offset, which are explained below, were combined in one direction and increased thermal error. Fig. 9 shows the two types of offset that increased in one direction. The first was the thermal expansion of the Z-slide due to the heat generated by the Z-axis linear motor and the LM guideway block. For each v 1 C increase in temperature, a thermal error of a few micrometer was generated in the Z-slide because of the length of the Z-slide in the feed direction. The second offset was the movement of the Z-axis linear scale, located on the hind part of the Z-slide, due to thermal expansion of the Z-slide. When the linear scale was moved backward, the Z-slide was pushed forward an equivalent distance, increasing the position error. An FEM was used for an in-depth analysis, and the magnitude of each thermal error component was calcu-
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Fig. 7.
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Comparison between the FEM analysis and the experimentally measured results in Experiment 5.
lated. Fig. 10(a)–(c) shows the FEM results for the Zdirection thermal error in Experiment 11 when traveling in the Z-direction. Fig. 10(a) shows the temperature distribution. The temperature of the Z-slide increased with Z-axis movement, causing thermal deformation,
Fig. 8. Temperature variations and thermal errors in Experiment 11. (a) Temperature variations and (b) thermal errors in the Z-direction.
as shown in Fig. 10(b). Thermal expansion of the Zslide amounted to approximately 15.2 lm in the negative direction with respect to the mirror of the laser interferometer. In addition, the thermal expansion of the Z-slide shifted the Z-axis linear scale approximately 4.6 lm in the positive Z-direction. These offset values were added to the FEM analysis results for the linear scale computed by inputting the temperature variation condition in Experiment 11, and are shown in Fig. 10(c). The predicted error was within 8.5% when the combined effects of the thermal error components were separated using the FEM thermal error analysis.
Fig. 9. Two types of offsets in Experiment 11.
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4.4. Thermal deformation of the machine tool This section describes the thermal deformation of the machine tool structure that is caused by the frictional heat generated in the LM guideway and linear motors. Fig. 11 shows the thermal error that occurred in the Zdirection in Experiment 5. The thermal error was 17 lm, despite the fact that the travel was in the Y-direction. As shown in Fig. 11, the temperature variation in the Z-axis linear scale was small and the ambient temperature remained constant. By contrast, the temperature variation of the Y-axis linear motor was about v 25 C. The heat produced by the Y-axis linear motor was conducted to the machine tool structure, inducing thermal expansion and affecting the Z-axis linear scale. That is, the result shown in Fig. 11 resulted from a combination of the thermal error components: the thermal expansion of the Z-slide, and the movement and thermal expansion of the Z-axis linear scale. These results were verified using FEM, and results similar to those in Section 4.3 were obtained. Thermal expansion of the Z-slide in the negative Z-direction was 11.84 lm. Moreover, the Z-axis linear scale moved 2.14 lm in the positive Z-direction with the thermal expansion of the Z-slide. The thermal expansion of the Z-axis linear scale at this position was 1.5 lm. Therefore, the estimated total thermal error was 15.48 lm in the Z-axis direction, which was close to the measured value (17 lm), with a 8.9% prediction error. Fig. 12 shows the temperature variations and thermal error that occurred in the X-direction in Experiment 9. There was no temperature variation in the X-axis linear scale, and thus no effect on structural deformation. In the experimental situation, therefore, the deformation consisted only of bending of the Y-frame and Z-slide, as a result of the thermal imbalance, which was equivalent to the temperature difference between the linear motors, shown in Fig. 12.
Fig. 10. FEM analysis and comparison results in Experiment 11. (a) Temperature distribution, (b) thermal deformation in the Z-direction, and (c) comparison between the FEM analysis and the experimentally measured results.
Fig. 11. Temperature variations and thermal error in Experiment 5.
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Fig. 12. Temperature variations and thermal error in Experiment 9.
Using the FEM, the computed error was 6.2 lm, which was close to the measured value of 6.6 lm. 4.5. Effects of the linear motors’ cooling systems If no precision cooler is used, the heat generated in a linear motor is conducted to the machine tool structure, causing thermal deformation. This effect was analyzed in this section.
Fig. 13. The effect of precision cooler. (a) Y directional thermal errors in Experiment 7 and (b) Y directional thermal errors in Experiment 8.
Fig. 14. FEM analysis results in Experiment 8. (a) Thermal distribution, (b) thermal deformation in the Y-direction, and (c) comparison the results between the FEM analysis and the experimentally measured results.
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The effects of a precision cooler on thermal error were observed in Experiments 7 and 8, and the measured thermal errors are shown in Fig. 13(a) and (b), respectively. The results of Experiment 7 can be interpreted as showing the effects of thermal expansion of the linear scale discussed in Section 4.2. However, the thermal behavior differed in Experiment 8, in which the precision cooler was turned off. Fig. 13(b) shows that other thermal error components increased with time, as well as the linear scale expansion included in the observed results. In this case, the heat produced in the linear motors was very likely conducted directly to the machine tool structure. Fig. 14(a) shows the simulated temperature distribution of the machine tool when Y-axis feed drive traveled with the precision cooler off. Heat produced in the linear motor was transmitted to the X-slide, increasing the temperature measured at the sides of the X-slide. Fig. 14(b) shows the thermal deformation caused by this temperature distribution. The X-slide expanded markedly in the upward direction. Moreover, the Y-axis linear scale attached to the X-slide moved upward accordingly. From the simulated FEM results, it was calculated that the linear scale moved up by 34 lm. This value was added to the calculated thermal expansion of the Y-axis linear scale and gave the results depicted in Fig. 14(c). As a result, the discrepancy between the two experiments was clarified.
5. Conclusions This paper investigated the thermal behavior of a machine tool equipped with linear motors operating at high speed. The dominant thermal error components and their magnitudes were identified from experimentally measured and FEM results. Heat loss in the linear motor, frictional heat from the LM block, and the cooling system for the linear motor were considered the important internal heat factors, whereas the ambient temperature was the only meaningful external heat source. The thermal error caused by the thermal expansion of the linear scale was identified based on the FEM and experimental analyses. In addition, the combined effects of the thermal deformation of the machine tool structure, the associated movement of the linear scale, and the thermal expansion of the linear scale itself were analyzed. When no precision cooler was
used, the heat generated in the linear motor was conducted to the machine tool structure, causing thermal deformation. The results of this thermal behavior analysis of a machine tool equipped with linear motors provide data that can be used in design optimization and compensation, thus enhancing the accuracy of this type of machine tool.
Acknowledgements This research was funded by Daewoo Heavy Industries and Machinery, Ltd., and many of the experiments were conducted using machine tools in their plant. The authors sincerely thank the persons concerned.
References [1] B. Yao, L. Xu, Adaptive robust motion control of linear motors for precision manufacturing, Mechatronics 12 (2002) 595–616. [2] D. Renton, M.A. Elbestawi, Motion control for linear motor feed drives in advanced machine tools, International Journal of Machine Tools and Manufacture 42 (2001) 479–507. [3] G. Abdou, W. Tereshkovich, Performance evaluation of a permanent magnet brushless DC linear drive for high-speed machining using finite element analysis, Finite Elements in Analysis and Design 35 (2000) 169–188. [4] Daewoo Heavy Industries and Machinery, Ltd., Development of a horizontal type machining center with the linear motor for high speed and accuracy, Ministry of Commerce, Industry and Energy in S. Korea, 2001. [5] C. Jang, J. Kim, Y. Kim, Thermal resistance modeling of linear motor driven stages for chip mounter applications, Inter Society Conference on Thermal Phenomena, 2002, pp. 77–84. [6] R. Ramesh, M.A. Mannan, A.N. Poo, Error compensation in machine tools—a review. Part II: Thermal errors, International Journal of Machine Tools and Manufacture 40 (2000) 1257–1284. [7] J. Ni, CNC machine accuracy enhancement through real-time error compensation, ASME Journal of Manufacturing Science and Engineering 119 (1997) 717–725. [8] J. Yang, J. Yuan, J. Ni, Thermal error mode analysis and robust modeling for error compensation on a CNC turning center, International Journal of Machine Tools and Manufacture 39 (1999) 1367–1381. [9] W.S. Yun, S.K. Kim, D.W. Cho, Thermal error analysis for a CNC lathe feed drive system, International Journal of Machine Tools and Manufacture 39 (1999) 1087–1101. [10] Linear motors 1FN1/1FN3 (Overview), Order No. 6ZB54110BD02-0BA0, 2002, Siemens.
Thermal behavior of a machine tool equipped with linear motors Jong-Jin Kim a, Young Hun Jeong b, Dong-Woo Cho b, a
b
iCurie-Lab, 5F Daewon Building 946-18, Daechi-dong, Kangnam-gu, Seoul 135-846, South Korea Department of Mechanical Engineering, Pohang University of Science and Technology, San 31 Hyoja-dong, Nam-gu, Pohang, Kyungbuk 790-784, South Korea Received 30 October 2003; received in revised form 22 January 2004; accepted 2 February 2004
Abstract Development of a feed drive system with high speed and accuracy has been a major issue in the machine tool industry. Linear motors can be used as efficient tool to achieve the high speed and accuracy. However, a high speed feed drive system with linear motors, in turn, can generate heat problems. Also, frictional heat is produced at the ball or roller bearing of LM block when driven at high speed. It can affect the thermal deformation of the linear scale as well as that of the machine tool structure. In this paper, important heat sources and resulting thermal errors in a machine tool equipped with linear motors were investigated when it was operated at high speed. The thermal deformation characteristics were identified through measuring the thermal error caused from thermal deformation of the linear scale and the machine tool structure. The dominant thermal error components were identified from the thermal error analysis using finite element method. It was shown that the proposed analysis scheme is efficient in identifying the dominant thermal error components and its magnitudes such as the thermal expansion and movement of the linear scale, thermal deformation of the machine tool slide. # 2004 Elsevier Ltd. All rights reserved. Keywords: Thermal deformation; Machine tool; Linear motor; Linear scale; Linear guideway; FEM
1. Introduction Enhancing the productivity and accuracy of manufacturing systems has become increasingly important for modern industry. Linear motors are efficient tools that offer high speed and accuracy. By eliminating mechanical transmission mechanisms, much higher speeds and greater acceleration can be achieved without suffering from backlash or excessive friction [1,2]. Therefore, linear motors are one way to overcome the limits on velocity and positional accuracy that are inherent in ball-screw feed drive systems [1–4]. One obstacle to the application of linear motors is heat. The motor coil generates heat, and the temperav ture can increase by over 100 C [5]. As a linear motor operates in direct combination with a machine tool slide, the heat generated in the linear motor can affect Corresponding author. Tel.: +82-54-279-2171; fax: +82-54-2795899. E-mail address: [email protected] (D.-W. Cho).
0890-6955/$ - see front matter # 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijmachtools.2004.02.006
the machine tool’s structure. Machine tools equipped with linear motors usually operate at high speed, so the balls or rollers in the block of the linear motion (LM) guideway also rotate at high speed, generating considerable frictional heat, which can be transferred to machine tool structure through the slide. Previous studies have examined the thermal behavior of machine tools equipped with ball-screws [6,7], and a few papers have dealt with the thermal behavior and optimization of the linear motor itself [3,5]. However, there has been little research on the thermal behavior of machine tools equipped with linear motors. This study investigated the thermal behavior of a machine tool equipped with linear motors when operated at high speed. To identify the thermal behavior of this type of machine tool, we measured the temperature and temperature variation at various points, and used the results to analyze the important heat sources and thermal behavior. Various thermal error components, such as thermal expansion of linear scales and thermal deformation of each part of a machine tool’s structure
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J.-J. Kim et al. / International Journal of Machine Tools & Manufacture 44 (2004) 749–758
affect the positional accuracy of a machine tool, either individually or in combination [8,9]. If the thermal deformation has compound effects on the machine tool slide and linear scale, then differentiating the contribution of each component experimentally is a formidable task. Therefore, the finite element method (FEM) was adopted to analyze the contribution of each component to thermal error. Consequently, it was found that the proposed scheme was efficient in identifying the dominant thermal error components and their magnitudes. Until recently, most machine tools equipped with linear motors have been of the horizontal type, with a box-in-box structure, and the machine tool that we studied was typical in these respects. Therefore, the scheme proposed in this study is applicable to many other machine tools equipped with linear motors. This study used the proposed scheme to analyze the typical thermal behavior of a machine tool equipped with linear motors. Thermal deformations of the linear scale and machine tool parts were identified in detail and the effects of thermal deformation on thermal error were investigated. In addition, we show that linear motors’ cooling systems can significantly affect the thermal behavior of machine tools.
2. Thermal error measurement 2.1. Temperature sensor locations and experimental setup
Table 1 Temperature sensor locations Temperature sensor locations Linear motor Primary part Secondary part Linear scale Linear guideway LM block LM guide Y-frame Column Spindle Room temperature
Sensor number X
Y
Z
1, 2 3 4, 5, 6
10, 11 12 13, 14, 15
19 20 21, 22
9 7, 8 29 30 26, 27 31, 32
18 16, 17
25 23, 24
movement. The position feedback is done using linear scales (LC481, Heidenhein). Temperatures were measured every 20 s during motion, using 32 T-type thermocouples that were attached to the machining center, as shown in Fig. 1 and Table 1. The experimental setup that was used to measure thermal error is shown in Fig. 2. The resultant thermal error was measured at the end of the spindle, which was considered the cutting point. Thermal error in the feed direction was measured using a laser interferometer (ML10, Renishaw). Two gap sensors (AEC5505, Applied Electronics) and a photo sensor (F1RH, Takenaka) were used to identify thermal errors in the remaining axes. 2.2. Experimental conditions
In this study, thermal error measuring experiments were conducted on a horizontal machining center (FH500) that was developed by Daewoo Heavy Industries and Machinery, Ltd. Two linear motors (1FN3, SIEMENS) are used for X- and Y-axis movement and one linear motor (1FN1, SIEMENS) is used for Z-axis
This paper investigated the thermal behavior of a machine tool equipped with linear motors operating at high speed. The spindle and its cooler were left off to eliminate the effect of thermal deformation of the spindle itself. The experimental conditions are listed in Table 2. As shown in Table 2, experiments for each axis were performed separately to eliminate combined effects on thermal error when operating on multiple axes. The machine tool was operated at various feed rates along each axis, within the maximum stroke and during a given time. Under the experimental conditions shown in Table 2, ‘arbitrary’ means that the feedrate was changed every 20 min.
3. Thermal behavior modeling using FEM
Fig. 1. Thermocouple locations on the machine tool.
Separate FEM models were constructed for the linear scale and a machine tool equipped with linear motors. They were modeled separately for several reasons: first, in many cases, the thermal deformation of a linear scale is the dominant thermal error component,
J.-J. Kim et al. / International Journal of Machine Tools & Manufacture 44 (2004) 749–758
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so using only an FEM model for the linear scale allows simple and fast simulation that is easy to analyze. Second, the results of a separate model can be used to analyze the compound error measured experimentally. Finally, a linear scale apparatus that is not deformed by the thermal deformation of the machine tool structure has already been devised. 3.1. FEM model of the linear scale A detailed FEM model of a linear scale was constructed, including the shape of the cross-section using parabolic tetrahedral type elements. For realism, the material properties of the linear scale cover and scale were those of aluminum alloy and glass, respectively. Moreover, motion was constrained by fixing the linear scale in the transverse direction, as though it was affixed to the machine tool. The thermal behavior was analyzed by measuring the temperature variation of the linear scale, to model the heat transfer from the machine tool structure. The geometric modeling and solution of the FEM were performed using SOLIDWORKS 2001 and COSMOS/ WORKS 7.0, respectively. 3.2. FEM model of a machine tool equipped with linear motors The FEM mesh model for the machine tool used is shown in Fig. 3. The elements were generated in the Fig. 2.
The experimental setup for measuring thermal errors.
Table 2 Experimental conditions Experiment no.
Axis
Feedrate (m/min)
Stroke (mm)
Time (min)
1 2 3 4 5 6 7 8a 9 10 11 12 13 14
X X X X Y Y Y Y Y Y Z Z Z Z
60 36 12 Arbitrary 60 60 36 36 12 Arbitrary 60 36 12 Arbitrary
60 560 60 560 60 560 60 560 50 550 50 300 50 550 50 550 50 550 50 550 100 430 100 430 100 430 100 430
150 150 150 220 120 120 120 120 180 220 150 150 150 220
a All the experiments except for Experiment 8 were conducted with both the power cooler and precision cooler of the linear motors being operated. For Experiment 8, the precision cooler was turned off during the experiment to investigate influence of the cooling system on the thermal deformation of the machine tool structure.
Fig. 3.
Mesh model of the machine tool for FEM thermal analysis.
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error of the precision cooler in the linear motors’ cooling systems were also checked.
Table 3 The materials of the machine tool Component
Material
X-slide, Y-slide, Y-frame Z-slide Column Linear motor—secondary part Etc.
SS41 (stainless steel) SCMn2A (stainless steel) AGC45C (cast carbon steel) Magnet SS41 (stainless steel)
same way as for the linear scale mesh model. A total of 192,913 nodes and 110,265 elements were used. The material properties of the model are listed in Table 3. The non-linear characteristics of the material properties that might occur with an increase in temperature were not considered, since the variation in temperature was not significant. The following assumptions and boundary conditions were used to perform the thermal error analysis using FEM. A steady state during the analysis was assumed. Moreover, machining was not considered, so there was no heat generation due to machining. In the thermal deformation analysis, displacement of the nodes comprising the bottom surface of the machine tool was assumed to be zero. Heat flux was input to represent the heat generated by the roller friction at the X-, Yand Z-axis LM guideways. The effect of a precision cooler was represented by a negative heat flux. The primary part of the linear motor is too complex to model. However, the analysis was fast and easy using the simplified model. The primary part of the linear motor was replaced by an attractive force in the perpendicular direction, because there is an air space between the primary and secondary parts, where an electromagnetic attractive force acts. This confirmed that although there was thermal expansion, the gap changed with expansion without causing any significant thermal error. In addition, the primary parts were fixed in the feed direction because they served to fix the slide. Heat generated in the primary part of the linear motor was replaced by heat fluxes, which were calculated from the measured temperatures.
4. Thermal error analysis The thermal behavior was identified from the measured and FEM results. The important heat sources were summarized. The thermal error caused by deformation of the linear scale was analyzed. Then, the combined effects of thermal deformation of the linear scale and of the machine tool slide were investigated. Also investigated were the thermal expansion and bending of the machine tool as a result of the heat generated by the linear motors. The effects on thermal
4.1. Heat sources The experiments showed that the important heat sources could be divided into two types: internal and external heat sources. Three important internal heat sources were identified. First, the linear motors generated a large amount of heat. Second, frictional heat was produced at the LM guideways by the high speed rotation of the balls or rollers in the block of the LM guideway. Third, the thermal behavior of the machine tool depended on the setup of the cooling systems for the linear motors, which consisted of power and precision coolers [10]. A power cooler was used to cool the primary part of the linear motor, while a precision cooler prevented the heat generated in the linear motor from being transferred to the machine tool structure. The start-up condition for the power and precision v coolers was 18 and 19 C, respectively. Nevertheless, the linear motors generated a lot of heat, some of which was transferred to the machine tool structure. By contrast, the only important external heat source identified was the ambient temperature, as the effects of the heat generated by other machine tools, the operator, and lighting apparatus had already been eliminated from the experimental environment. 4.2. Thermal expansion of linear scales The thermal error caused by the thermal expansion of a linear scale was examined. Fig. 4(a),(b) illustrates the temperature variations and subsequent thermal error, respectively, in Experiment 5, which is presented in Table 2. The temperature increased in the linear motor, the block of the LM guideway, and the linear scale due to travel in the Y-direction. Fig. 4(b) shows that the thermal error measured in the Y-direction differed in magnitude and direction at different positions. In another experiment, the feedrates were changed arbitrarily to precisely identify the main causes of thermal error. Fig. 5(a) shows the arbitrary changes in the feedrate in the Y-direction used in Experiment 10. Fig. 5(b),(c) shows the measured temperature variations and the respective thermal error. Fig. 5(b) shows that the temperature variations of the Y-axis linear motor were similar to the feedrate variation seen in Fig. 5(a). Nevertheless, this pattern cannot explain the measured thermal error shown in Fig. 5(c), which plots the temperatures measured in the block of the Y-axis LM guideway, linear scale, and points in between, and the Y-direction thermal error. The temperature variations in the three cases corresponded almost perfectly. Therefore, the frictional heat generated in the block of
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Fig. 4.
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Temperature variations and thermal errors in Experiment 5. (a) Temperature variations and (b) thermal errors in the Y-direction.
the LM guideway was conducted to the linear scale via the machine tool structure. In fact, the pattern of thermal error is similar to that of the temperature variations shown in Fig. 5(c). Now, the cause of the thermal error that occurred in Experiment 5 can be inferred more clearly, as follows: the temperature increase in the linear scale induces thermal expansion. Fig. 6 shows the structure of the Yaxis linear scale. When the linear scale expands towards the two sides from the center position, which is at 390 mm in this case, the amount of thermal expansion increases with the distance of the measured position from the center. Since the Y-axis experiments were performed for the range from 50 to 550 mm, the largest thermal error in the Y-axis was observed at the 50-mm position, which was the position farthest from the center. At the 550-mm position, the direction of deformation was reversed and the deformation was less than that at the 50-mm position.
To verify these results, the thermal behavior of the linear scale was simulated using FEM. The thermal expansion of the linear scale was simulated, using the temperature variation measured in Experiment 5 as the boundary conditions. Fig. 7 shows the results of the simulation and the corresponding experimental results. The deformation in the Y-direction during travel in the Y-axis in Experiment 5 shows very close agreement with the thermal expansion of the Y-axis linear scale. Moreover, this implies that thermal expansion of the linear scale was the dominant thermal error component in this case. This procedure can also be applied to the X-direction thermal error in the X-axis experiments. When traveling in the X-direction, the frictional heat generated in the X-axis LM guideway block is conducted to the linear scale through the machine tool structure. Therefore, thermal behavior similar to those described above, was obtained via the same route.
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Fig. 6. Thermal expansion of the Y-axis linear scale.
Fig. 5. Measurement results in Experiment 10. (a) Arbitrary feed rate condition, (b) temperature variations of Y-axis linear motor, and (c) temperature variations and thermal error.
4.3. Thermal behavior in a machine tool slide with a linear scale Generally, a linear scale is attached to a machine tool slide. Consequently, thermal deformation of the machine tool slide can affect the linear scale. This section investigates the combined effects of the thermal deformation of the linear scale and of the machine tool slide.
Fig. 8(a),(b) shows the temperature variations and the Z-direction thermal error measured in Experiment 11, respectively. The temperature increased in the Zaxis linear motor, LM guideway, and linear scale. The temperature variation of the Z-axis linear motor was less than that of the other linear motors, but this was because the thermocouple was attached to the side of the linear motor because of the cover on the machine tool. When traveling in the Z-direction, the thermal behavior differed from the results for X- or Y-direction travel described in Section 4.2. The magnitude of the thermal error differed at each different Z-position; this can be thought to have resulted from the thermal expansion of the linear scale. However, regardless of position, the general tendency was for the thermal error to increase in one direction. Therefore, the thermal error can be explained by the increased offset in one direction added to the thermal expansion of the linear scale. Two types of offset, which are explained below, were combined in one direction and increased thermal error. Fig. 9 shows the two types of offset that increased in one direction. The first was the thermal expansion of the Z-slide due to the heat generated by the Z-axis linear motor and the LM guideway block. For each v 1 C increase in temperature, a thermal error of a few micrometer was generated in the Z-slide because of the length of the Z-slide in the feed direction. The second offset was the movement of the Z-axis linear scale, located on the hind part of the Z-slide, due to thermal expansion of the Z-slide. When the linear scale was moved backward, the Z-slide was pushed forward an equivalent distance, increasing the position error. An FEM was used for an in-depth analysis, and the magnitude of each thermal error component was calcu-
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Fig. 7.
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Comparison between the FEM analysis and the experimentally measured results in Experiment 5.
lated. Fig. 10(a)–(c) shows the FEM results for the Zdirection thermal error in Experiment 11 when traveling in the Z-direction. Fig. 10(a) shows the temperature distribution. The temperature of the Z-slide increased with Z-axis movement, causing thermal deformation,
Fig. 8. Temperature variations and thermal errors in Experiment 11. (a) Temperature variations and (b) thermal errors in the Z-direction.
as shown in Fig. 10(b). Thermal expansion of the Zslide amounted to approximately 15.2 lm in the negative direction with respect to the mirror of the laser interferometer. In addition, the thermal expansion of the Z-slide shifted the Z-axis linear scale approximately 4.6 lm in the positive Z-direction. These offset values were added to the FEM analysis results for the linear scale computed by inputting the temperature variation condition in Experiment 11, and are shown in Fig. 10(c). The predicted error was within 8.5% when the combined effects of the thermal error components were separated using the FEM thermal error analysis.
Fig. 9. Two types of offsets in Experiment 11.
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4.4. Thermal deformation of the machine tool This section describes the thermal deformation of the machine tool structure that is caused by the frictional heat generated in the LM guideway and linear motors. Fig. 11 shows the thermal error that occurred in the Zdirection in Experiment 5. The thermal error was 17 lm, despite the fact that the travel was in the Y-direction. As shown in Fig. 11, the temperature variation in the Z-axis linear scale was small and the ambient temperature remained constant. By contrast, the temperature variation of the Y-axis linear motor was about v 25 C. The heat produced by the Y-axis linear motor was conducted to the machine tool structure, inducing thermal expansion and affecting the Z-axis linear scale. That is, the result shown in Fig. 11 resulted from a combination of the thermal error components: the thermal expansion of the Z-slide, and the movement and thermal expansion of the Z-axis linear scale. These results were verified using FEM, and results similar to those in Section 4.3 were obtained. Thermal expansion of the Z-slide in the negative Z-direction was 11.84 lm. Moreover, the Z-axis linear scale moved 2.14 lm in the positive Z-direction with the thermal expansion of the Z-slide. The thermal expansion of the Z-axis linear scale at this position was 1.5 lm. Therefore, the estimated total thermal error was 15.48 lm in the Z-axis direction, which was close to the measured value (17 lm), with a 8.9% prediction error. Fig. 12 shows the temperature variations and thermal error that occurred in the X-direction in Experiment 9. There was no temperature variation in the X-axis linear scale, and thus no effect on structural deformation. In the experimental situation, therefore, the deformation consisted only of bending of the Y-frame and Z-slide, as a result of the thermal imbalance, which was equivalent to the temperature difference between the linear motors, shown in Fig. 12.
Fig. 10. FEM analysis and comparison results in Experiment 11. (a) Temperature distribution, (b) thermal deformation in the Z-direction, and (c) comparison between the FEM analysis and the experimentally measured results.
Fig. 11. Temperature variations and thermal error in Experiment 5.
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Fig. 12. Temperature variations and thermal error in Experiment 9.
Using the FEM, the computed error was 6.2 lm, which was close to the measured value of 6.6 lm. 4.5. Effects of the linear motors’ cooling systems If no precision cooler is used, the heat generated in a linear motor is conducted to the machine tool structure, causing thermal deformation. This effect was analyzed in this section.
Fig. 13. The effect of precision cooler. (a) Y directional thermal errors in Experiment 7 and (b) Y directional thermal errors in Experiment 8.
Fig. 14. FEM analysis results in Experiment 8. (a) Thermal distribution, (b) thermal deformation in the Y-direction, and (c) comparison the results between the FEM analysis and the experimentally measured results.
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The effects of a precision cooler on thermal error were observed in Experiments 7 and 8, and the measured thermal errors are shown in Fig. 13(a) and (b), respectively. The results of Experiment 7 can be interpreted as showing the effects of thermal expansion of the linear scale discussed in Section 4.2. However, the thermal behavior differed in Experiment 8, in which the precision cooler was turned off. Fig. 13(b) shows that other thermal error components increased with time, as well as the linear scale expansion included in the observed results. In this case, the heat produced in the linear motors was very likely conducted directly to the machine tool structure. Fig. 14(a) shows the simulated temperature distribution of the machine tool when Y-axis feed drive traveled with the precision cooler off. Heat produced in the linear motor was transmitted to the X-slide, increasing the temperature measured at the sides of the X-slide. Fig. 14(b) shows the thermal deformation caused by this temperature distribution. The X-slide expanded markedly in the upward direction. Moreover, the Y-axis linear scale attached to the X-slide moved upward accordingly. From the simulated FEM results, it was calculated that the linear scale moved up by 34 lm. This value was added to the calculated thermal expansion of the Y-axis linear scale and gave the results depicted in Fig. 14(c). As a result, the discrepancy between the two experiments was clarified.
5. Conclusions This paper investigated the thermal behavior of a machine tool equipped with linear motors operating at high speed. The dominant thermal error components and their magnitudes were identified from experimentally measured and FEM results. Heat loss in the linear motor, frictional heat from the LM block, and the cooling system for the linear motor were considered the important internal heat factors, whereas the ambient temperature was the only meaningful external heat source. The thermal error caused by the thermal expansion of the linear scale was identified based on the FEM and experimental analyses. In addition, the combined effects of the thermal deformation of the machine tool structure, the associated movement of the linear scale, and the thermal expansion of the linear scale itself were analyzed. When no precision cooler was
used, the heat generated in the linear motor was conducted to the machine tool structure, causing thermal deformation. The results of this thermal behavior analysis of a machine tool equipped with linear motors provide data that can be used in design optimization and compensation, thus enhancing the accuracy of this type of machine tool.
Acknowledgements This research was funded by Daewoo Heavy Industries and Machinery, Ltd., and many of the experiments were conducted using machine tools in their plant. The authors sincerely thank the persons concerned.
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