- Email: [email protected]
Design optimization and development of CNC lathe headstock to minimize thermal deformation
CIRP Annals - Manufacturing Technology 58 (2009) 331–334
Contents lists available at ScienceDirect
CIRP Annals - Manufacturing Technology journal homepage: http://ees.elsevier.com/cirp/default.asp
Design optimization and development of CNC lathe headstock to minimize thermal deformation M. Mori (2)a,*, H. Mizuguchi a, M. Fujishima b, Y. Ido a, N. Mingkai b, K. Konishi b a b
Mori Seiki Co., Ltd., Nagoya, Japan Digital Technology Laboratory, Sacramento, USA
A R T I C L E I N F O
A B S T R A C T
Keywords: Thermal error Design method Accuracy
This paper has investigated an approach to reduce and compensate thermal displacement for high accuracy NC lathes. An efficient design and optimization method is proposed for a headstock structure design of NC lathes to minimize the thermal displacement of the spindle center position. Compared to the existing empirical methods, this method saves development time and cost. The Taguchi method and FEA method are used to identify the optimal headstock structure. The proposed method is verified by evaluating the spindle center transition of the headstock according to the optimization results. ß 2009 CIRP.
1. Introduction The demand for higher accuracy NC lathes has increased dramatically with respect to machining accuracy requirements. Thermal deformation has significant effects on the machining accuracy. Much research has been carried out on this topic. However, not many good results were gained in practice. The major studies on thermal deformation are summarized as follows. Moriwaki and Shamoto proposed an estimation compensation method for thermal displacement by using temperature sensor [1]. Brecher and Hirsche extended this work based on control internal data (e.g., axis feed and spindle speed) [2]. Spur et al. used non-metallic materials (e.g., carbon fiber reinforced plastics) to suppress thermal displacement [3]. Mitsuishi et al. applied the Finite Element Method (FEM) analysis on bearing preload and casting shape optimization to minimize displacement [4]. Jedrzejewski conducted compensation through a fin/fancoupled thermal actuator controlled by strain gage-based thermal distortion feedback [5]. Shimizu et al. developed an algorithm to estimate the total machine thermal deformation by fitting the deformation modes to data obtained from eddy current type displacement sensors [6]. Several machine tool manufacturers adopt the methods of using temperature information from sensors or internal NC controller to estimate thermal displacement and conduct compensation. For a NC lathe, the thermal displacement is usually affected by machine structure, ambient temperature, state of heat sources (servo motors or machining heat), airflow and coolant usage, etc. And, to estimate the displacement involves complex interplay of these parameters and needs a large number of combinatory experiments. While it is possible to conduct accurate compensation for linear thermal deformation along each axis, the compensation
* Corresponding author. 0007-8506/$ – see front matter ß 2009 CIRP. doi:10.1016/j.cirp.2009.03.033
accuracy drops dramatically as deformation is accompanied with twisting or warpage. Development of a new NC lathe involves modifying the structure of an existing machine and running experiments concurrently, which is usually time consuming and costly. In this paper, a novel approach is proposed to design a headstock for NC lathe immune to thermal deformation caused by random temperature deviation. By combining Taguchi method [7] with CAE analysis, an NC lathe spindle structure is determined and a headstock is manufactured based on the design result. The thermal deformation is evaluated to prove the efficiency of the proposed method.
2. Headstock structure and thermal displacement measurement Fig. 1 shows the internal structure of an NC lathe’s spindle associated with parameters of parts and ambient variables. The goal is to design a headstock with thermal displacement concentrated on the Y axis instead of X axis since the thermal error on Y axis is considerably smaller than that on X axis in terms of direct diametrical influence. The heat sources are front bearing housing, rear bearing housing and the motor. To measure thermal displacement, a hollow cylindrical workpiece was mounted into the spindle chuck while four eddy current displacement sensors were mounted on a fixture of cast iron with low thermal expansion. As shown in Fig. 2, the sensor fixture was attached to the machine body to measure the relative displacement between the body and the spindle [8]. Eqs. (1) and (2) were given as follows to calculate the thermal displacement on X and Y axis respectively.
dX ¼
dX1 dX2 2
(1)
M. Mori et al. / CIRP Annals - Manufacturing Technology 58 (2009) 331–334
332
Fig. 1. Headstock structure and thermal boundary conditions for the analysis model.
Fig. 2. Mounting view of thermal displacement sensor.
dY ¼
dY1 dY2 2
Fig. 3. Selected features for model analysis.
(2)
where dX: thermal displacement in X axis direction; dY: thermal displacement in Y axis direction; dX1, dX2, dY1, dY2: distance between the sensors (X1, X2, Y1, Y2) and the workpiece.
under fixed ambient temperature of 22 8C with spindle speed of 1000 rpm. The analysis result shows a 3–12.5% difference of temperature compared to the experiment.
3. Thermal analysis model and boundary condition
4. Analysis model of headstock
A CAE model is built to conduct thermal analysis. This model includes the headstock, turret, tailstock and the lathe machine bed. The boundary conditions are given with initial temperature distribution, localized heat sources and external airflow. The initial temperature distribution was derived by using the commercial CFD (Computational Fluid Dynamics) software package, FLUENT. With this distribution, thermal strain was calculated and the results were further applied to determine the overall thermal displacements by using the CAE software, IDEAS. Heat values for sources of front bearing housing, rear bearing housing and the motor, were obtained in the following manner: the power output of spindle motor was acquired from the load meter of the spindle amplifier first; heat values of front and rear bearings were calculated using the bearing housing analysis program, BRAIN; then the heat values of spindle motor was calculated by subtracting the bearing housings’ heat values from the power output of spindle motor. Since the heat transmission from the spindle affects the thermal displacement of the whole machine, the machine bed, turret and tailstock were also included in the analysis model. In addition, the machine cover was added to model the airflow caused by spindle rotation more accurately. To verify analysis result, temperature change was measured at several points for comparison. The measurement was conducted
To design the headstock structure with minimal X axis thermal displacement, the critical features that affects headstock thermal displacement were investigated. Fig. 3 shows these features which are also called control factors: (A) rib shape and cast hole; (B) thickness of headstock cylinder; (C) thickness of front wall; (D) thickness of rear wall; (E) thickness of rib; (F) thickness of right wall; (G) thickness of left wall. Table 1 shows the control factor’s value at each level. The currently used headstock is referred as basic headstock. The bold values in Tables 1 and 2 are conditions of the basic headstock. For control factor A, 6 cases were studied, which are 3 cases with different rib shapes and 3 cases combined with cast Table 1 Value of control factor at each level. Control factor
Level 1
Level 2
Level 3
Level 4
Level 5
Level 6
A B C D E F G
I 20 15 15 20 20 20
I + hole 30 25 25 30 30 30
II 40 35 35 40 40 40
II + hole – – – – – –
III – – – – – –
III + hole – – – – – –
Unit for B–G is mm.
M. Mori et al. / CIRP Annals - Manufacturing Technology 58 (2009) 331–334
333
Table 2 L18 orthogonal array and result of analyses. Analysis model No.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Control factor A
B
C
D
E
F
G
1 1 1 2 2 2 3 3 3 4 4 4 5 5 5 6 6 6
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
1 2 3 1 2 3 2 3 1 3 1 2 2 3 1 3 1 2
1 2 3 2 3 1 1 2 3 3 1 2 3 1 2 2 3 1
1 2 3 2 3 1 3 1 2 2 3 1 1 2 3 3 1 2
1 2 3 3 1 2 2 3 1 2 3 1 3 1 2 1 2 3
1 2 3 3 1 2 3 1 2 1 2 3 2 3 1 2 3 1
X (mm)
Y (mm)
h (db)
S (mm)
0.023 0.030 0.024 0.022 0.029 0.030 0.022 0.004 0.023 0.017 0.001 0.014 0.028 0.014 0.011 0.004 0.019 0.017
0.162 0.160 0.144 0.141 0.149 0.147 0.167 0.171 0.157 0.157 0.162 0.153 0.174 0.157 0.164 0.164 0.154 0.156
35.7 33.6 35.5 36.3 33.9 33.6 36.2 50.1 35.6 38.4 59.8 40.1 34.0 40.2 42.1 51.6 37.5 38.6
0.012 0.015 0.012 0.011 0.014 0.015 0.011 0.002 0.012 0.009 0.001 0.007 0.014 0.007 0.006 0.002 0.009 0.008
X,Y: displacement value of each axis.
hole either presence or absence. From the spindle motor, bearing housing to each part of the headstock, different rib shapes were analyzed to predict the changes in thermal conduction route which contribute to thermal deformation. Three variations of wall thickness are also investigated, whose change causes thermal capacity balance between the front and rear part of the headstock, which contributes to different thermal displacement. To identify the optimum design by analyzing each possible combination of the control factors and levels is time consuming, for instance, the case study of Table 1 requires a total of 4374 analyses, which is far beyond practical. Therefore, the Taguchi method is applied to reduce the total analysis number. For above case with 7 control factors and 6 levels, it is possible to determine the optimal combination by analyzing only 18 conditions using Taguchi method, as explain in the following section. 5. Optimization of headstock structure Table 2 shows the 18 analysis models of headstock structure for design optimization using Taguchi method. The SN ratio h and the sensitivity S are expressed in Eq. (3) and (4) respectively. The thermal displacement result from CAE analysis at the spindle speed of 2000 rpm was used for the calculation.
h ¼ 10 log
S¼
1 Ve
combination with the smallest deviation of thermal displacement at different spindle speed. To verify this combination, the thermal displacement in X direction with spindle speed at 500, 1000, 1500 and 2000 rpm was analyzed respectively. Fig. 5 shows the results: thermal displacement in X axis was 0.0005, 0.0001 and 0.0005 mm correspondingly at speed 500, 1000 and 1500 rpm, which confirms the small deviation. Note: No. 11 was selected with control factors of (4, 2, 1, 1, 3, 3, 2) even though the best combination was (4, 2, 1, 2, 3, 3, 2) considering the biggest SN ratio. This means the control factor D, thickness of rear wall is 15 mm instead of 25 mm. The reasons behind are two: the SN ratio difference between value 1 and 2 of D was very small as shown in Fig. 4; better thermal conductivity can be gained by using same thickness for the front wall (C) and real wall (D). Accordingly, Fig. 6 is the factorial effect graph of sensitivity. As shown in Eq. (4), the sensitivity is calculated as the average of thermal displacement. The effect and the direction of thermal displacement for each control factor were also shown in Fig. 6. It is clear that the Rib II, control factor A with level 3 and 4, has large effect on thermal displacement. As it affects the thermal displacement in negative direction, this is an important factor to minimize the displacement amount.
(3)
n 1X x n i¼1 i
(4)
where Ve ¼
St ¼
1 ðSt SmÞ n1 n X x2i ; i¼1
Sm ¼
n 1 X x n i¼1 i
!2
Fig. 4. Factorial effect graph of SN ratio.
xi: thermal displacement result from CAE analysis in X axis direction at each spindle speed (mm). Fig. 4 is the factorial effect graph derived from the SN ratio results in Table 2. It can be observed that the smaller the deviation of thermal displacement in X axis direction is, the bigger the SN ratio is. This is because that the SN ratio is the inverse number of the variance Ve shown in Eq. (3). As shown in Fig. 4, each control factor is paired with a biggest SN ratio, for example, level 4 to the control factor A and level 2 to the control factor B. Finally, the analysis model No. 11 of headstock structure is determined as the
Fig. 5. Analysis result of the displacement in X axis direction.
M. Mori et al. / CIRP Annals - Manufacturing Technology 58 (2009) 331–334
334
Fig. 9. Comparison of front and rear wall temperature change. Fig. 6. Factorial effect graph of sensitivity.
Fig. 7. Thermal displacement in X axis direction 10 h after spindle start rotation.
wall is approximately 2.4 8C higher than the rear wall. This means the headstock will tilt backward, resulting in an X displacement shift into the positive direction. At the front wall, headstock No. 11 was 0.4 8C lower than the basic headstock, while the rear wall was 0.6 8C warmer, resulting in an approximately 1 8C difference reduction between the front and rear walls compared to the basic headstock’s case. This means that headstock No. 11 will tilt relatively forward compared to the tilting degree of the basic headstock’s case. This results in a displacement reduction for headstock at the steady state condition when is mounted on an actual machine. For headstock No. 9, the rear wall temperature was approximately 0.2 8C higher than the front wall, and the tendency of tilting forward was stronger than headstock No. 11, resulting in displacement shift into the minus direction of X. 7. Conclusions
Fig. 8. Thermal displacement in Y axis direction 10 h after spindle start rotation.
6. Experiment results The analysis result shows that headstock structure of No. 11 will produce the best result with smallest thermal displacement and No. 9 will cause the largest displacement in minus direction of X. To verify this result, two headstocks are manufactured correspondingly and installed on the real NC lathes. The experiments were performed with spindle speed at 500, 1000, 1500 and 2000 rpm. The thermal displacement was measured for 10 h to ensure displacement stabilization was reached after spindle start rotation. Fig. 7 shows X axis displacement of the headstock in three cases: basic structure, structure of No. 11 and No. 9 at different spindle speed. While the basic headstock shows a proportional increase in thermal displacement with spindle speed, the No. 11 displaced less than 0.001 mm even at full spindle speed. Also in conformity with the above analysis results, structure of No. 9 contributed large displacement in minus direction of X. Fig. 8 shows the three cases’ comparison of thermal displacement in Y axis. All three headstock structures have the same tendency of enlarging thermal displacement in Y direction as the spindle speed increases. Fig. 9 shows the three cases’ comparison results of front and rear wall temperature change. For the basic headstock, the front
A novel method is proposed for designing the headstock structure for NC lathe with minimized thermal displacement in X direction using CAE techniques and Taguchi Method. With the proposed design method, an optimal headstock design immune to thermal displacement was possible after analyzing only 18 patterns, which dramatically reduces development time and costs comparing to the traditional trial and error approach. An optimal headstock is determined from the analysis results and manufactured with Full Mold Casing method. The thermal displacement of the headstock in X direction at spindle speed of 500, 1000, 1500 and 2000 rpm was measured respectively. The result was less than 0.001 mm, showing the consistency between the analysis and actual experiment result, which confirms the efficiency of the proposed method.
References [1] Moriwaki T, Shamoto E (1998) Analysis of Thermal Deformation of an Ultraprecision Air Spindle System. Annals of the CIRP 47(1):315–319. [2] Brecher C, Hirsche B (2004) Compensation of Thermo-elastic Machine Tool Deformation Based on Control internal Data. Annals of the CIRP 53(1):299–304. [3] Spur G, Hoffmann E, Paluncic Z, Benzinger K, Nymoen H (1988) Thermal Behavior Optimization of Machine Tools. Annals of the CIRP 37(1):401–405. [4] Mitsuishi M, Warisawa S, et al, (2001) Development of an Intelligent HighSpeed machining Center. Annals of the CIRP 50(1):275–278. [5] Jedrzejewski J (1990) Numerical Optimization of Thermal Behavior of Machine Tools. Annals of the CIRP 39(1):379–382. [6] Shimizu S, Ooi G, Yagyu S (2006) New Measuring Method for Thermal Deviation Caused by Liner Axis Motion in Multi-Task Machine, JSME International Journal Series. The Japan Society of Mechanical Engineers 49(2):316–321. [7] Taguchi G (1993) Taguchi on Robust Technology Development: Bringing Quality Engineering Upstream. ASME Press. [8] Mizuguchi H, Iwakiri M, Shinno H (2008) In-process Measurement of Spindle Center Transition in NC Lathe During Machining. International Symposium On Flexible Automation, JS021, .
Contents lists available at ScienceDirect
CIRP Annals - Manufacturing Technology journal homepage: http://ees.elsevier.com/cirp/default.asp
Design optimization and development of CNC lathe headstock to minimize thermal deformation M. Mori (2)a,*, H. Mizuguchi a, M. Fujishima b, Y. Ido a, N. Mingkai b, K. Konishi b a b
Mori Seiki Co., Ltd., Nagoya, Japan Digital Technology Laboratory, Sacramento, USA
A R T I C L E I N F O
A B S T R A C T
Keywords: Thermal error Design method Accuracy
This paper has investigated an approach to reduce and compensate thermal displacement for high accuracy NC lathes. An efficient design and optimization method is proposed for a headstock structure design of NC lathes to minimize the thermal displacement of the spindle center position. Compared to the existing empirical methods, this method saves development time and cost. The Taguchi method and FEA method are used to identify the optimal headstock structure. The proposed method is verified by evaluating the spindle center transition of the headstock according to the optimization results. ß 2009 CIRP.
1. Introduction The demand for higher accuracy NC lathes has increased dramatically with respect to machining accuracy requirements. Thermal deformation has significant effects on the machining accuracy. Much research has been carried out on this topic. However, not many good results were gained in practice. The major studies on thermal deformation are summarized as follows. Moriwaki and Shamoto proposed an estimation compensation method for thermal displacement by using temperature sensor [1]. Brecher and Hirsche extended this work based on control internal data (e.g., axis feed and spindle speed) [2]. Spur et al. used non-metallic materials (e.g., carbon fiber reinforced plastics) to suppress thermal displacement [3]. Mitsuishi et al. applied the Finite Element Method (FEM) analysis on bearing preload and casting shape optimization to minimize displacement [4]. Jedrzejewski conducted compensation through a fin/fancoupled thermal actuator controlled by strain gage-based thermal distortion feedback [5]. Shimizu et al. developed an algorithm to estimate the total machine thermal deformation by fitting the deformation modes to data obtained from eddy current type displacement sensors [6]. Several machine tool manufacturers adopt the methods of using temperature information from sensors or internal NC controller to estimate thermal displacement and conduct compensation. For a NC lathe, the thermal displacement is usually affected by machine structure, ambient temperature, state of heat sources (servo motors or machining heat), airflow and coolant usage, etc. And, to estimate the displacement involves complex interplay of these parameters and needs a large number of combinatory experiments. While it is possible to conduct accurate compensation for linear thermal deformation along each axis, the compensation
* Corresponding author. 0007-8506/$ – see front matter ß 2009 CIRP. doi:10.1016/j.cirp.2009.03.033
accuracy drops dramatically as deformation is accompanied with twisting or warpage. Development of a new NC lathe involves modifying the structure of an existing machine and running experiments concurrently, which is usually time consuming and costly. In this paper, a novel approach is proposed to design a headstock for NC lathe immune to thermal deformation caused by random temperature deviation. By combining Taguchi method [7] with CAE analysis, an NC lathe spindle structure is determined and a headstock is manufactured based on the design result. The thermal deformation is evaluated to prove the efficiency of the proposed method.
2. Headstock structure and thermal displacement measurement Fig. 1 shows the internal structure of an NC lathe’s spindle associated with parameters of parts and ambient variables. The goal is to design a headstock with thermal displacement concentrated on the Y axis instead of X axis since the thermal error on Y axis is considerably smaller than that on X axis in terms of direct diametrical influence. The heat sources are front bearing housing, rear bearing housing and the motor. To measure thermal displacement, a hollow cylindrical workpiece was mounted into the spindle chuck while four eddy current displacement sensors were mounted on a fixture of cast iron with low thermal expansion. As shown in Fig. 2, the sensor fixture was attached to the machine body to measure the relative displacement between the body and the spindle [8]. Eqs. (1) and (2) were given as follows to calculate the thermal displacement on X and Y axis respectively.
dX ¼
dX1 dX2 2
(1)
M. Mori et al. / CIRP Annals - Manufacturing Technology 58 (2009) 331–334
332
Fig. 1. Headstock structure and thermal boundary conditions for the analysis model.
Fig. 2. Mounting view of thermal displacement sensor.
dY ¼
dY1 dY2 2
Fig. 3. Selected features for model analysis.
(2)
where dX: thermal displacement in X axis direction; dY: thermal displacement in Y axis direction; dX1, dX2, dY1, dY2: distance between the sensors (X1, X2, Y1, Y2) and the workpiece.
under fixed ambient temperature of 22 8C with spindle speed of 1000 rpm. The analysis result shows a 3–12.5% difference of temperature compared to the experiment.
3. Thermal analysis model and boundary condition
4. Analysis model of headstock
A CAE model is built to conduct thermal analysis. This model includes the headstock, turret, tailstock and the lathe machine bed. The boundary conditions are given with initial temperature distribution, localized heat sources and external airflow. The initial temperature distribution was derived by using the commercial CFD (Computational Fluid Dynamics) software package, FLUENT. With this distribution, thermal strain was calculated and the results were further applied to determine the overall thermal displacements by using the CAE software, IDEAS. Heat values for sources of front bearing housing, rear bearing housing and the motor, were obtained in the following manner: the power output of spindle motor was acquired from the load meter of the spindle amplifier first; heat values of front and rear bearings were calculated using the bearing housing analysis program, BRAIN; then the heat values of spindle motor was calculated by subtracting the bearing housings’ heat values from the power output of spindle motor. Since the heat transmission from the spindle affects the thermal displacement of the whole machine, the machine bed, turret and tailstock were also included in the analysis model. In addition, the machine cover was added to model the airflow caused by spindle rotation more accurately. To verify analysis result, temperature change was measured at several points for comparison. The measurement was conducted
To design the headstock structure with minimal X axis thermal displacement, the critical features that affects headstock thermal displacement were investigated. Fig. 3 shows these features which are also called control factors: (A) rib shape and cast hole; (B) thickness of headstock cylinder; (C) thickness of front wall; (D) thickness of rear wall; (E) thickness of rib; (F) thickness of right wall; (G) thickness of left wall. Table 1 shows the control factor’s value at each level. The currently used headstock is referred as basic headstock. The bold values in Tables 1 and 2 are conditions of the basic headstock. For control factor A, 6 cases were studied, which are 3 cases with different rib shapes and 3 cases combined with cast Table 1 Value of control factor at each level. Control factor
Level 1
Level 2
Level 3
Level 4
Level 5
Level 6
A B C D E F G
I 20 15 15 20 20 20
I + hole 30 25 25 30 30 30
II 40 35 35 40 40 40
II + hole – – – – – –
III – – – – – –
III + hole – – – – – –
Unit for B–G is mm.
M. Mori et al. / CIRP Annals - Manufacturing Technology 58 (2009) 331–334
333
Table 2 L18 orthogonal array and result of analyses. Analysis model No.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Control factor A
B
C
D
E
F
G
1 1 1 2 2 2 3 3 3 4 4 4 5 5 5 6 6 6
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
1 2 3 1 2 3 2 3 1 3 1 2 2 3 1 3 1 2
1 2 3 2 3 1 1 2 3 3 1 2 3 1 2 2 3 1
1 2 3 2 3 1 3 1 2 2 3 1 1 2 3 3 1 2
1 2 3 3 1 2 2 3 1 2 3 1 3 1 2 1 2 3
1 2 3 3 1 2 3 1 2 1 2 3 2 3 1 2 3 1
X (mm)
Y (mm)
h (db)
S (mm)
0.023 0.030 0.024 0.022 0.029 0.030 0.022 0.004 0.023 0.017 0.001 0.014 0.028 0.014 0.011 0.004 0.019 0.017
0.162 0.160 0.144 0.141 0.149 0.147 0.167 0.171 0.157 0.157 0.162 0.153 0.174 0.157 0.164 0.164 0.154 0.156
35.7 33.6 35.5 36.3 33.9 33.6 36.2 50.1 35.6 38.4 59.8 40.1 34.0 40.2 42.1 51.6 37.5 38.6
0.012 0.015 0.012 0.011 0.014 0.015 0.011 0.002 0.012 0.009 0.001 0.007 0.014 0.007 0.006 0.002 0.009 0.008
X,Y: displacement value of each axis.
hole either presence or absence. From the spindle motor, bearing housing to each part of the headstock, different rib shapes were analyzed to predict the changes in thermal conduction route which contribute to thermal deformation. Three variations of wall thickness are also investigated, whose change causes thermal capacity balance between the front and rear part of the headstock, which contributes to different thermal displacement. To identify the optimum design by analyzing each possible combination of the control factors and levels is time consuming, for instance, the case study of Table 1 requires a total of 4374 analyses, which is far beyond practical. Therefore, the Taguchi method is applied to reduce the total analysis number. For above case with 7 control factors and 6 levels, it is possible to determine the optimal combination by analyzing only 18 conditions using Taguchi method, as explain in the following section. 5. Optimization of headstock structure Table 2 shows the 18 analysis models of headstock structure for design optimization using Taguchi method. The SN ratio h and the sensitivity S are expressed in Eq. (3) and (4) respectively. The thermal displacement result from CAE analysis at the spindle speed of 2000 rpm was used for the calculation.
h ¼ 10 log
S¼
1 Ve
combination with the smallest deviation of thermal displacement at different spindle speed. To verify this combination, the thermal displacement in X direction with spindle speed at 500, 1000, 1500 and 2000 rpm was analyzed respectively. Fig. 5 shows the results: thermal displacement in X axis was 0.0005, 0.0001 and 0.0005 mm correspondingly at speed 500, 1000 and 1500 rpm, which confirms the small deviation. Note: No. 11 was selected with control factors of (4, 2, 1, 1, 3, 3, 2) even though the best combination was (4, 2, 1, 2, 3, 3, 2) considering the biggest SN ratio. This means the control factor D, thickness of rear wall is 15 mm instead of 25 mm. The reasons behind are two: the SN ratio difference between value 1 and 2 of D was very small as shown in Fig. 4; better thermal conductivity can be gained by using same thickness for the front wall (C) and real wall (D). Accordingly, Fig. 6 is the factorial effect graph of sensitivity. As shown in Eq. (4), the sensitivity is calculated as the average of thermal displacement. The effect and the direction of thermal displacement for each control factor were also shown in Fig. 6. It is clear that the Rib II, control factor A with level 3 and 4, has large effect on thermal displacement. As it affects the thermal displacement in negative direction, this is an important factor to minimize the displacement amount.
(3)
n 1X x n i¼1 i
(4)
where Ve ¼
St ¼
1 ðSt SmÞ n1 n X x2i ; i¼1
Sm ¼
n 1 X x n i¼1 i
!2
Fig. 4. Factorial effect graph of SN ratio.
xi: thermal displacement result from CAE analysis in X axis direction at each spindle speed (mm). Fig. 4 is the factorial effect graph derived from the SN ratio results in Table 2. It can be observed that the smaller the deviation of thermal displacement in X axis direction is, the bigger the SN ratio is. This is because that the SN ratio is the inverse number of the variance Ve shown in Eq. (3). As shown in Fig. 4, each control factor is paired with a biggest SN ratio, for example, level 4 to the control factor A and level 2 to the control factor B. Finally, the analysis model No. 11 of headstock structure is determined as the
Fig. 5. Analysis result of the displacement in X axis direction.
M. Mori et al. / CIRP Annals - Manufacturing Technology 58 (2009) 331–334
334
Fig. 9. Comparison of front and rear wall temperature change. Fig. 6. Factorial effect graph of sensitivity.
Fig. 7. Thermal displacement in X axis direction 10 h after spindle start rotation.
wall is approximately 2.4 8C higher than the rear wall. This means the headstock will tilt backward, resulting in an X displacement shift into the positive direction. At the front wall, headstock No. 11 was 0.4 8C lower than the basic headstock, while the rear wall was 0.6 8C warmer, resulting in an approximately 1 8C difference reduction between the front and rear walls compared to the basic headstock’s case. This means that headstock No. 11 will tilt relatively forward compared to the tilting degree of the basic headstock’s case. This results in a displacement reduction for headstock at the steady state condition when is mounted on an actual machine. For headstock No. 9, the rear wall temperature was approximately 0.2 8C higher than the front wall, and the tendency of tilting forward was stronger than headstock No. 11, resulting in displacement shift into the minus direction of X. 7. Conclusions
Fig. 8. Thermal displacement in Y axis direction 10 h after spindle start rotation.
6. Experiment results The analysis result shows that headstock structure of No. 11 will produce the best result with smallest thermal displacement and No. 9 will cause the largest displacement in minus direction of X. To verify this result, two headstocks are manufactured correspondingly and installed on the real NC lathes. The experiments were performed with spindle speed at 500, 1000, 1500 and 2000 rpm. The thermal displacement was measured for 10 h to ensure displacement stabilization was reached after spindle start rotation. Fig. 7 shows X axis displacement of the headstock in three cases: basic structure, structure of No. 11 and No. 9 at different spindle speed. While the basic headstock shows a proportional increase in thermal displacement with spindle speed, the No. 11 displaced less than 0.001 mm even at full spindle speed. Also in conformity with the above analysis results, structure of No. 9 contributed large displacement in minus direction of X. Fig. 8 shows the three cases’ comparison of thermal displacement in Y axis. All three headstock structures have the same tendency of enlarging thermal displacement in Y direction as the spindle speed increases. Fig. 9 shows the three cases’ comparison results of front and rear wall temperature change. For the basic headstock, the front
A novel method is proposed for designing the headstock structure for NC lathe with minimized thermal displacement in X direction using CAE techniques and Taguchi Method. With the proposed design method, an optimal headstock design immune to thermal displacement was possible after analyzing only 18 patterns, which dramatically reduces development time and costs comparing to the traditional trial and error approach. An optimal headstock is determined from the analysis results and manufactured with Full Mold Casing method. The thermal displacement of the headstock in X direction at spindle speed of 500, 1000, 1500 and 2000 rpm was measured respectively. The result was less than 0.001 mm, showing the consistency between the analysis and actual experiment result, which confirms the efficiency of the proposed method.
References [1] Moriwaki T, Shamoto E (1998) Analysis of Thermal Deformation of an Ultraprecision Air Spindle System. Annals of the CIRP 47(1):315–319. [2] Brecher C, Hirsche B (2004) Compensation of Thermo-elastic Machine Tool Deformation Based on Control internal Data. Annals of the CIRP 53(1):299–304. [3] Spur G, Hoffmann E, Paluncic Z, Benzinger K, Nymoen H (1988) Thermal Behavior Optimization of Machine Tools. Annals of the CIRP 37(1):401–405. [4] Mitsuishi M, Warisawa S, et al, (2001) Development of an Intelligent HighSpeed machining Center. Annals of the CIRP 50(1):275–278. [5] Jedrzejewski J (1990) Numerical Optimization of Thermal Behavior of Machine Tools. Annals of the CIRP 39(1):379–382. [6] Shimizu S, Ooi G, Yagyu S (2006) New Measuring Method for Thermal Deviation Caused by Liner Axis Motion in Multi-Task Machine, JSME International Journal Series. The Japan Society of Mechanical Engineers 49(2):316–321. [7] Taguchi G (1993) Taguchi on Robust Technology Development: Bringing Quality Engineering Upstream. ASME Press. [8] Mizuguchi H, Iwakiri M, Shinno H (2008) In-process Measurement of Spindle Center Transition in NC Lathe During Machining. International Symposium On Flexible Automation, JS021, .