Proceedings of 2012 IEEE International Conference on Mechatronics and Automation August 5 - 8, Chengdu, China

Axial Thermal Error Compensation Method for the Spindle of a Precision Horizontal Machining Center Yang Li, Wanhua Zhao The State Key Lab for Manufacturing Systems Engineering Xi’an Jiaotong University Xi’an, Shaanxi Province, China [email protected] This method plans to compensate dimensional error introduced by thermal fluctuations[6-9]. The first two methods can reduce the thermal errors effectively. However, thermal error avoidance can only be implemented in the phase of machine designing and construction and building efficient cool system and heat pipe cost a lot. By contrast, thermal error compensation is more convenient and economical, as its principle is simple and can be easily executed in the factory with minimal cost. The tool spindle is the key part of the precision horizontal machining center. Its thermal deformation contributes greatly to the whole errors and has great influence on the performance of the machine tool. Thermal error compensation, as the convenient and cost-effective method for reducing the spindle thermal error, attracts attentions of scholars all over the world. By using of the finite element method, Zhao and Choi simulated the temperature field and the thermal error of the spindle of a CNC machine tool and a machining center respectively. Additionally, the test results showed that the simulation data fit well with the experimental results[10-11]. Creighton obtained the temperature and thermal deformation of the spindle under different spindle speed by thermal resistance sensors and capacitive sensors. Then the model of spindle thermal error was built based on the experimental data. Unfortunately, he did not implement the thermal compensation[12]. Wu developed a thermal error model by using genetic algorithm-based back propagation neural network and created a real-time thermal error compensation system consisting of additional software and hardware, such as temperature sensors, displacement sensors, amplifiers, A/D board and the computer. After employing this system, the diameter error was reduced from 27 m to 10 m. However, this compensation system called for additional devices and specialized persons to do software programming. It was not only complex but also expensive[13]. This work aims to develop an effective and simple method to compensate the spindle thermal error. At first, the finite element analysis is conducted to predict the temperature field and thermal deformation of the spindle system on a precision horizontal machining center. In order to increase the accuracy of the simulation analysis, the boundary conditions are set according to the measured parameters such as the speed of the spindle, temperatures of coolant oil, ambient temperature and so on. Secondly, magnetic temperature sensors are used respectively to obtain the temperature data and the non-contact tool setting system is used to test the axial

Abstract - Thermal error of spindle has great influence on the performance of the machine tool. In order to alleviate those impacts, an axial spindle thermal error compensation method is introduced in this paper. Firstly the temperature field and thermal deformation of the spindle system are simulated by finite element analysis (FEA) with a high accuracy, as the boundary conditions are set according to the measured parameters such as the speed of the spindle, temperatures of coolant oil, and ambient temperature etc. Secondly, magnetic temperature sensors and non-contact tool setting system are used to test the temperature data and axial thermal deformation respectively. Additionally Spearman’s rank correlation analysis is employed to determine the place and the number of critical temperature points which are closely correlated to spindle axial thermal deformation. By establishing a model between spindle temperature field and its axial thermal deformation and compensating the thermal error with predicted data which are sent to the CNC system directly, the axial thermal error at varying spindle speeds is effectively reduced up to 92 percent, from more than 225 microns to within 20 microns. Therefore, the spindle thermal error is reduced and the machining accuracy can be kept at a high level. Index Terms - Spindle thermal error, Thermal error compensation, Spearman’s rank correlation analysis, Critical temperature points, Precision horizontal machining center

I. INTRODUCTION Thermal error seriously affects the working accuracy of the precision horizontal machining center [1]. According to the research of Professor Peklenik of University of Birmingham in UK, the thermal error caused by the thermal deformation of machine tool accounts for 40% to 70% of the total error [2]. Compared with ball screw, guide ways and external thermal influences, such as solar radiation and ambient temperature, the tool spindle is the main thermal source[3]. In general, there are three techniques for reducing the thermal error, namely 1) Thermal error avoidance. This strategy tends to minimize thermal errors through better machine design, thermally insensitive materials and so on[4]. 2) Thermal error control This tactic attempts to equalize temperature field all over the structure by using cooling system or heat pipes [5]. 3) Thermal error compensation

978-1-4673-1278-3/12/$31.00 ©2012 IEEE

2319

spindle thermal deformation under different working conditions. Thirdly, according to experimental results, the place and the number of critical temperature points on the spindle which are closely correlated to its axial thermal deformation are determined by using Spearman’s rank correlation analysis. Then the model of thermal error compensation is developed based on the experimental temperature rise data of those critical points and axial thermal deformations. Finally, the values calculated from the model are sent to the CNC system of the machine tool directly for compensating and the effect of compensation are verified.

Poisson's ratio Specific heat ( J /( Kg < DC ) )

0.28

0.25

0.28

0.3

465

470

460

434

Thermal conductivity ( W /( m< K ) )

32.6

39.2

40.1

60.5

Thermal expansivity ( 1/ DC )

1.17x10-5

1.10x10-5

1.30x10-5

1.20x10-5

In order to guarantee the high accuracy of simulation, parameters such as the speed of the spindle, the temperature of coolant oil, the ambient temperature and so on, are measured and the heat load of heat sources and boundary conditions at varying spindle rate applied to the model are computed on the basis of those experimental data. Equation (1) [14-15] is the formula which is used to calculate the heat load of heat sources. H f = 1.047 ×10−4 nM (1)

II. FINITE ELEMENT ANALYSIS (FEA) The FEA herein is conducted using ANSYS Workbench software to predict the temperature field and the thermal deformation of a spindle. In order to reducing the time of calculation, the geometric model of the spindle system is simplified, shown in Fig. 1. There are three sets of bearings labeled as 1#, 2#, 3#, which are considered as the heat sources. The 1# and 2# bearings are angular contact bearings. They are respectively located near the spindle nose and in the middle of the spindle system. The 3# bearing is the ball bearing that is close to the encoder placed at the end of the spindle system. Outside the spindle, there is a cooling jacket to prevent the spindle system from overheating.

Where, H f (W) is the heat output of the bearing which is the main heat source, n (r/min) is rotational speed of the bearing, M is the friction torque ( N < mm ). Equation (2) is the function applied for the calculation of heat convection[16]. h = ( Nu < λ ) / l (2) Where, h ( W / m 2 < DC ) is the convection heat-transfer coefficient, Nu is the Nusselt number, λ ( W / m < DC ) is the thermal conductivity of the fluid, l (m) is the characteristic dimension which is decided according to the size and structure of different parts. The calculation results are showed in the table II. It easily finds that the heat loads are raised along with the increase of the spindle speed, because the higher the speed is, the more heat will be generated. Similarly, the increase of the spindle speed will lead to the increase of the convective heat transfer. TABLE II HEAT LOAD OF HEAT SOURCES AND CONVECTIVE HEAT TRANSFER COEFFICIENTS UNDER DIFFERENT SPINDLE SPEED Spindle speed (r/min)

Fig.1 Simplified geometrical model of the spindle

By using sweep method, patch conforming method and automatic method according to the structures of different parts in the spindle system, the model is meshed into 40895 elements. The element size is determined considering both the simulation accuracy and the time of calculation. The spindle, spindle box and bearings are assumed to be made of 38CrMoALA, gray cast iron and bearing steel, while other parts are assumed to be steel #45. Table I shows the properties of those different materials of different parts in the spindle system. In the process of analyzing, the effect of thermal contact resistance is neglected. Material Density ( kg / m3 ) Modulus of elasticity (GPa)

Table I MATERIAL PROPERTIES gray cast 38CrMoALA GCr15 iron 7600

7800

7850

208

140

208

200

1# 2# 3# Spindle bearing bearing bearing box

Encoder

Spindle

Cooling jacket

2000

279.8

280.0

105.8

2.65

3.37

56.24

12.3

3000

364.0

364.2

138.7

2.93

3.72

72.66

12.5

4000

439.1

439.4

168.0

3.27

3.93

86.85

12.8

Fig. 2 and Fig.3 show the predict temperature field and thermal deformation of the spindle when the spindle speed is 2000r/min. The latter is determined by the former. From Fig.2 it can be concluded that the 3# bearing generates more heat (its temperature is approximately 50ć when the spindle speed is 2000r/min) than other two bearings (46ć and 43ć). This is because that there is a cooling jacket working outside of 1# and 2# bearing but there is not any cooling system located near the 3# bearing. Consequently, it is the main heat source in the spindle system. From Fig.3 it can

steel #45

7800

Convective heat transfer coefficient(W/(m2·K))

Heat load(W)

2320

be deduced that the non-uniform temperature distribution produces severe thermal distortion. Compared with the radial thermal deformation (approximately 10 m at 2000r/min), the axial deformation (more than 50 m at 2000r/min) is much more severe.

error of the spindle is obtained by counting the gap between the two positions tested before and after the spindle heated.

Fig.2 Temperature field of the spindle at 2000r/min

Fig.4 Spindle temperature tests setup

Fig.3 The axial thermal deformation of the spindle at 2000r/min

III. EXPERIMENTAL TEST AND ESTABLISHMENT OF THERMAL ERROR MODEL

In order to provide enough measured data for determining the place and number of critical points, a preliminary experiment is conducted. The set-up of the experimental tests is shown in Fig.4 and 5. It is showed in Fig.4 that temperature sensors are placed at points which are closed to the heat source (bearings) and distributed evenly over the entire spindle system. Sensors are used to test the temperature profiles of the spindle. They are made of magnet thermal resistor, which can be installed and demounted easily on and off the spindle. The outputs of them are sent to a multi-channel parameter measurement system. Those analog quantities gathered by temperature sensors can be transferred into digital quantities, then recorded and displayed promptly with this system. Renishaw non-contact tool setting system (NC 4) which is showed in Fig. 5 is generally a tool providing highspeed/high-precision measurement of cutting tools on a machining center. It can also be applied for testing the spindle axial thermal deformation. It consists of transmitter and receiver units. The former is able to emit a beam of laser which is supposed to be accepted by the latter. When the front of the spindle moves through the laser beam, the laser beam is broken and the system can detect the position of the spindle in the Z direction at that moment. Therefore, the axial thermal

Fig.5 Spindle axial thermal error tests setup

Spearman’s rank correlation coefficient  is one of the standard nonparametric statistical coefficients. It represents the closeness of two random variables (X and Y) and its formula is showed as follows. The more close to 1 the  is, the more tightly the two variables are considered to relate to each other [17-18]. ρ = 1 − (6 d 2 ) /(n3 − n) (3)

¦

Where, d is the difference of the X’s rank and Y’s rank, n is the number of the variables. Based on the preliminary test results, different  between temperatures and thermal errors are calculated and named after the number of the temperature sensors. It means that the Spearman’s rank correlation coefficient between temperature data obtained from 1# sensors and axial thermal error is labeled as the 1# . It turns out that 1#  is 0.85, 2#~9#  is 0.95 and both 10# and 11#  is 1(Table III). That is because

2321

10# and 11# sensors are both placed at the end of the spindle system close to the main heat source (3# bearing). Compared with 11# sensor, 10# sensor’s data is higher. Therefore, 10# sensor is selected as the critical point.

and the system is going to automatically search for the corresponding values in the table. Then thermal error compensation is conducted directly without additional compensation system consisted of external hardware and software devices. Verification test is also implemented and the result is showed in Fig.7-9. It can be deduced that the axial thermal errors of the spindle when its speed is 2000r/min, 3000r/min and 4000/min can be reduced from 75m, 140m, 225m to less than 13m. The ratios of them are 85%, 90% and 94% respectively. By using the method presented in this paper, the axial thermal error of the spindle on a precision horizontal machining center will be reduced distinctly and the machining accuracy can be warranted effectively.

TABLE III SPERMAN’S RANK CORRELATION COEFFICIENTS () BETWEEN DEFFERENT TEMPERATURE DATA AND THERMAL ERRORS 1# 2# 3# 4# 5# 6# 7# 8# 9# 10# 11#  0.85

0.95

0.95

0.95

0.95

0.95

0.95

0.95

0.95

1

1

Thermal deformation (m)

In order to obtain the temperature data at critical point and the axial thermal deformation under different spindle speed to establish the model of spindle thermal error, another experiment is conducted. Base on the test data, the model is developed using the least square method. Equation (4) is the function of the model. f ( x) = 0.1386 x 2 + 5.103 x + 2.779 (4) Where, x ( DC ) is temperature rise of critical point, f(x) (m) is the value of thermal error. Fig.6 shows the comparison between the predicted axial thermal errors and the test data. It can be concluded that the model fits the axial thermal error of the spindle well.

Thermal deformation (m)

Thermal deformation (m)

Temperature rise ( DC ) Fig.7 Spindle axial error of precision horizontal machining center with and without compensation at spindle speed of 2000r/min

Temperature rise ( DC ) Fig.8 Spindle axial error of precision horizontal machining center with and without compensation at spindle speed of 3000r/min

Temperature rise ( DC ) Fig.6 Predicted axial thermal errors versus test data

Thermal deformation (m)

IV. THERMAL ERROR COMPENSATION Differing from other thermal error compensation strategies, the method introduced in this paper is implemented directly using CNC system of the precision horizontal machining center. Considering the operational capability of the CNC system, a table of thermal error compensation shown as Table IV is established according to the model and then planted into the system. TABLE IV THERMAL ERROR COMPENSATION TABLE IN CNC SYSTEM Temperature Rise ( DC )

0.0

0.5

1.0

1.5

2.0

2.5

3.0

Value of Compensationΰmα

0

5

8

11

14

16

19

Temperature Rise ( DC )

...

27

27.5

28

28.5

29

29.5

Value of Compensationΰmα

…

242

248

254

261

267

274

Temperature rise ( DC ) Fig.9 Spindle axial error of precision horizontal machining center with and without compensation at spindle speed of 4000r/min V.

The temperature rises in the table are the differences between the measured values on the critical point and the ambient temperature. These data are straightly input into CNC

CONCLUSION

This paper presents an axial thermal error compensation method for the spindle of a precision horizontal machining center. The results of the initial finite element analysis show

2322

[14]T. Y. Chen, W. J. Wei, J.C. Tsai, “Optimum design of headstocks of precision lathes,” International Journal of Machine Tool & Manufacture, vol. 39, no. 12, pp. 1961-1977, December 1999. [15]T. A. Harris, Rolling Bearing Analysis, 3rd ed., New York: John Wiley and Sons, 1991, pp. 540-560. [16]J. P. Holman, Heat Transfer, 9rd ed., New York: McGraw-Hill Companies, Inc., 2002, pp. 205-253. [17]C. B. Borkowf, “A new nonparametric method for variance estimation and confidence interval construction for Spearman’s rank correlation,” Computational Statistics & Data Analysis, vol. 34, no. 2, pp. 219-241, August 2000. [18]T. D. Gauthier, “Detecting Trends Using Spearman’s rank correlation coefficient,” Environmental forensics, vol. 2, no. 4, pp. 359-362, December 2001.

that the 3# bearing placed close to the encoder is the main heat source and the axial thermal deformation is more severe than the radial one. In order to select the critical point and develop the thermal error model, several experimental tests are conducted. The predicted axial thermal errors obtained from the model fit the experimental data well. The compensation strategy in this paper is implemented using a thermal compensation table which is established based on the model and planted in the CNC directly. This compensation scheme reduces the effect of the thermal error more than 85% under various spindle operating speeds successfully. ACKNOWLEDGMENT First and the most, the author would like to thank Prof. Zhao, a respectable and responsible supervisor, for his valuable guidance. The author would also like to thank Dr. Wenming Wei for his help in implementing experiments. In addition, it is gratefully acknowledged that the work has been supported by the State Key Laboratory for Manufacturing System Engineering and the special foundation for State major key projects (2012ZX04005-011). Finally, sincere appreciation is extended to the reviewers of this paper for their helpful recommendations. REFERENCES [1] J. Mou, “A Systematic Approach to Enhance Machine Tool,” International Journal of Machine Tool & Manufacture, vol. 37, no. 5, pp. 1669-685, 1997. [2] J. Peklenik, Untersuchung der Genauigkeitsfragen in der automatisierten Fertigung, Koln: Westdeutscher Verlag, 1961. [3] Y. C. Wang, M. Kao, C. P. Chang, “Investigation on the spindle thermal displacement and its compensation of precision cutter grinders,” Measurement, vol. 44, no. 6, pp. 1183-1187, July 2011. [4] R. Ramesh, M. A. Mannan, A.N. Poo, “Error compensation in machine tools-a review Part 2: Thermal errors,” International Journal of Machine Tool & Manufacture, vol.40, no. 9, pp. 1257-1284, July 2000. [5] M. Weck, P. McKeown, “Reduction and Compensation of Thermal Errors in Machine Tools,” Annals of the CIRP, vol. 44, no. 2, pp. 589598, 1995. [6] Y. Wang, G. Zhang, S. M. Kee, J. W. Sutherland, “Compensation for the thermal error of a multi-axis machining center,” Journal of Materials Processing Technology, vol. 75, no. 1, pp. 45-53, March 1998. [7] S. Li, Y. Zhang, G. Zhang, “A study of pre-compensation for thermal errors of NC machine tools,” International Journal of Machine Tool & Manufacture, vol. 37, no. 12, pp. 1715-1719, December 1997. [8] S. Yang, J. Yan, J. Ni, “Accuracy enhancement of a horizontal machining center by real-time compensation,” Journal of Manufacturing Systems, vol. 15, no. 2, pp. 113-124, 1996. [9] S. C. Veldhuis, M. A. Elbestawi, “A strategy for the compensation of errors in five-axis maching,” Annals of the CIRP, vol. 44, no. 1, pp. 373377, 1995. [10] H. Zhao, J. Yang, J. Shen, “Simulation of thermal behaviour of a CNC machine tool spindle,” International Journal of Machine Tool & Manufacture, vol. 47, no. 6, pp. 1003-1010, May 2007. [11]J. K. Choi, D.G. Lee, “Thermal characteristics of the spindle bearing system with a gear located on the bearing span,” International Journal of Machine Tool & Manufacture, vol. 38, no. 9, pp. 1017-1030, September 1998. [12] E. Creighton, A. Honegger, A. Tulsian, D. Mukhopadhyay, “Analysis of thermal errors in a high-speed micro-milling spindle,” International Journal of Machine Tool & Manufacture, vol. 50, no. 4, pp. 386-393, April 2010. [13]H. Wu, H. Zhang, Q. Guo, X. Wang, J. Yang, “Thermal Error Optimization modelling and real-time compensation on a CNC turning center,” Journal of Materials Processing Technology, vol. 207, no. 1, pp. 172-179, October 2008.

2323