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Thermal characteristics of the spindle bearing system with a gear located on the bearing span
International Journal of Machine Tools & Manufacture 38 (1998) 1017–1030
Thermal characteristics of the spindle bearing system with a gear located on the bearing span Jin Kyung Choi, Dai Gil Lee* Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology, ME3221, Gusongdong, Yusong-gu, Taejon-shi, South Korea 305-701 Received 19 December 1996; in final form 9 October 1997
Abstract High cutting speeds and feeds are essential requirements of a machine tool structure to accomplish its basic function which is to produce a workpiece of the required geometric form with an acceptable surface finish at as high a rate of production as is economically possible. Since bearings in high speed spindle units are the main heat source of total cutting system, in this work, the thermal characteristics of the spindle bearing system with a tilting axis were investigated using finite element method to improve the performance of the spindle bearing system. Based on the numerical results, a specially designed prototype spindle bearing system was manufactured. Using the manufactured spindle bearing system, the thermal characteristics were measured and compared to the numerical results. From the comparison of the numerical results with the experimental results, it was found that the finite element method predicted well the thermal characteristics of the spindle bearing system. 1998 Elsevier Science Ltd. All rights reserved. Keywords: Machine tools; Spindle system; Thermal characteristics; Angular contact ball bearing
1. Introduction Recently in manufacturing fields, high-precision products as well as diversified small-quantity production have been demanded, and the production technologies involved have constantly been redeveloped to lower production costs. Hence there is a growing interest in shorter machining times with increasing cutting speeds [1]. However, the spindle speed increase of machine tools
* Corresponding author. 0890-6955/98/$19.00 1998 Elsevier Science Ltd. All rights reserved. PII: S 0 8 9 0 - 6 9 5 5 ( 9 7 ) 0 0 0 7 5 - 8
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for productivity improvement also incurs adverse effects such as chattering, noise and heat generation of spindle bearing systems [2]. During high speed machining, the excessive temperature increase in the spindle induces dissimilar thermal expansions between different machine elements, which causes friction and wear. Generally, the performance of machine tools is determined by the highest machining speed which is limited by the temperature increase in the spindle bearing system. Therefore, the structural optimization incorporating cooling and lubrication apparatuses to reduce heat generation of the spindle is required. Many studies on the thermal characteristics of spindle bearing systems have been performed through experiments and analyses, some of which are listed here. Clarke et al. investigated theoretically thermal characteristics of the float ring bearing by solving the Reynolds equation and the energy equation for the lubricant film thickness between the inner and outer surfaces [3]. Bergling and Gunnar developed a program for the thermal and lubricant statuses of bearings operated under adverse environments such as dry cleaning cylinders and paper manufacturing rollers [4]. Witig et al. investigated the effect of high rotational speed on the characteristics of the heat transfer and lubricant film thickness of airplane engine bearings [5]. Dunnuck et al. used FEM model to analyse the temperature distribution of train wheel roller bearings in steady state and investigated the frictional heat loss of the bearings under various loads and speeds [6]. Lee et al. formed the dynamic simulation model for a spindle bearing system and investigated the thermal behavior of the spindle bearing system with the thermal closed-loop system in which the thermal deformation and boundary condition of the spindle system were related [7]. For the temperature distribution of machine tools which employ special type bearings or cooling jackets, the transient state as well as the steady state of the temperature distribution should be investigated in order to obtain efficient cooling effects. Since the measurement of noise level of machine tools to check the proper mounting of bearings or normal operation is complex because of the noise superposition from different machine elements, the measurement of the temperature increase of spindle bearings is more effective for the diagnosis of spindle bearing systems. Recently, as complicated parts such as airplane frames, propellers and turbine blades have been widely used, the five-axis machining center equipped with a spindle tilting axis is increasingly employed and consequently its design and performance prediction have become important. In this paper, the thermal characteristics of the spindle bearing system with a gear located on the bearing span for a tilting axis were investigated experimentally and numerically, using finite element method (FEM). 2. Experimental set-up for the spindle bearing system For the development of the spindle bearing system, the type of bearings and material for the spindle should be selected first. The bearing arrangement and the spindle shape are then determined for the optimum performance of the spindle bearing system. In this work, the spindle bearing system for the five-axis, 22 kW machining center was designed. For the first stage of development, the experimental set-up for the prototype spindle bearing system as shown in Fig. 1 was designed and manufactured. The bearing mounting area of the spindle was ground and then plated with chrome. The front bearings were mounted on the
J.-K. Choi, D.G. Lee / International Journal of Machine Tools & Manufacture 38 (1998) 1017–1030
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Fig. 1. Experimental set-up for the prototype spindle bearing system.
spindle with interference tolerance, while the rear bearings were mounted with clearance tolerance to avoid the preload variation of the bearings due to temperature variation. Table 1 shows the assembly tolerances and arithmetic average surface roughnesses for the spindle bearing system. The angular contact ball bearings B70 series manufactured by FAG in Germany whose specifications are shown in Table 2 were selected for spindle bearings. For the high spindle stiffness, the front three bearings were mounted in T–O arrangement (complex arrangement) and the rear two bearings were arranged in O arrangement (back to back arrangement). Since the rotational accuracy and bearing stiffness of angular contact ball bearings are enhanced by preloading, the spindle bearings were preloaded by tightening the knuckle nuts. The lower friction grease, Arcanol 174 for high speed machine tools manufactured by FAG in Germany was used for bearing lubrication. After assembling, the eccentric force of the spindle bearing systems was removed for the Table 1 Fit tolerance and the arithmetical average roughnesses of the spindle Spindle diameter (mm) Tolerance (m) Circularity (m) Arithmetical averageroughness; Ra (m) Housing diamter (mm) Tolerance (m)
80 +3 1.2 2 120 Clearance fit +8
100 +3 1.5 2.5 150 Interference fit ⫺3
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Table 2 Specifications of the angular contact ball bearings (FAG, Germany) Bearing type
Inner diameter (mm)
Dynamic load rating (kN)
Static load rating (kN)
Limit speed (rpm)
Grease lubrication Oil-air lubrication B7020C B7016C
100 80
75 58.5
68 48
7000 9000
9500 13 000
rotational balance of the spindle shaft. Figure 2 shows the eccentric force of the spindle bearing system after balancing with respect to the spindle rotational speed. Figure 3 shows the photograph of the experimental set-up before assembling the power transmission gears. This set-up was used to measure the thermal characteristics of the spindle bearing system. 3. Measurement of the temperature increase of the spindle bearing system Although angular contact ball bearings for spindles should be pre-loaded to increase the rotational accuracy and stiffness of spindle bearing systems, excessive pre-loads often reduce the machining accuracy and bearing life of the spindle bearing system due to frictional heat [8]. In this work, the J-type thermocouples, which can be used in 0 苲 277°C and composed of iron (⫺) and constantan(+), were used to measure the heat generation of the spindle bearing system.
Fig. 2. Eccentric centrifugal force of the spindle with respect to rotational speed.
J.-K. Choi, D.G. Lee / International Journal of Machine Tools & Manufacture 38 (1998) 1017–1030
Fig. 3.
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Experimental set-up for measuring thermal characteristics of the spindle bearing system.
The electromotive force of the thermocouples was amplified by the temperature sensing chip (AQ594AQ, Analog Device) and the signal noises were removed by a low-pass filter. The analogue data from the low-pass filter was converted into digital form by the A/D converter (PCLabcard) and was saved in a personal computer. Figure 4 shows the experimental set-up for measuring the temperature of the spindle bearing system. Figure 5 shows the thermocouple locations inserted in the holes drilled in the housing to measure the temperature increases at the nearest point of bearings. Figure 6 shows the temperature rise of the front bearing with respect to time at the spindle rotational speed of 3500 rpm. In Fig. 6, the temperature of the front bearing increased at the early stage and gradually saturated to the final temperature when the amount of heat generation balanced with the heat dissipation into the atmosphere. The rising time (ts) and the temperature increase (␦Ts) up to the saturation temperature are two important factors for the cooling conditions of
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Fig. 4. Experimental set-up for measuring the temperature of the spindle bearing system.
Fig. 5. Locations of the thermocouples for measuring the thermal increases of the spindle bearing system.
machine tools. It is beneficial if the rising time (ts) is short and the temperature increase (␦Ts) is low. Figure 7 shows the temperature increases of the bearings with respect to the rotational speed. The polynomial fittings of the experimental temperature increases of Fig. 7 at the saturation state were expressed in terms of rotating speed as follow:
␦T1 = ⫺ 1.03 × 10⫺93 + 9.25 × 10⫺62 ⫺ 6.84 × 10⫺3 ⫺ 1.24 × 10⫺1
(1)
␦T2 = ⫺ 1.01 × 10⫺93 + 6.01 × 10⫺62 ⫺ 4.59 × 10⫺3 ⫺ 5.37 × 10⫺2 Where is the rotational speed of the spindle expressed in rpm, and ␦T1 and ␦T2 are the temperature increases of the front and rear spindle bearings expressed in Celsius, respectively. The rising time t up to the maximum temperature was expressed as follows: t = 8000 + [ ⫺6 + (1/432 ⫺ ( ⫺ 2600)/9)( ⫺ 1700)]( ⫺ 1400)
(2)
Where is the rotational speed of the spindle expressed in rpm, t is the rising time up to the saturation temperature expressed in seconds. Stone reported that the temperature increase of the
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Fig. 6. Temperature rise of the front bearing with respect to time when the spindle rotational speed was 3500 rpm.
Fig. 7.
Temperature increases of the bearings with respect to rotational speed.
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B7211 bearing whose DN value was 110 000 was 7°C after 30 min operation [9]. In this work, the temperature increase was 3°C when the similar bearings of B7020 whose DN value was 110 000 were rotated at 1100 rpm. It is well known that the temperature increase of the spindle bearing system should be less than 10°C when the spindle is operated at the 2/3 speed of the maximum rotational speed for 1 h. Therefore, it was concluded that the maximum rotational speed of the spindle bearing spindle in this work was 2700 rpm because the temperature increase of the spindle front bearing was about 10°C from Fig. 7 when the rotational speed was 1800 rpm. 4. Thermal characteristics of the spindle bearing system Although the thermal analysis of rotating spindles is not easy because the heat transfer coefficient of the air cannot be obtained precisely due to the geometric complexity of spindles, the quantitative analysis of the temperature distribution in spindle bearing systems and the amount of heat dissipation of bearings are frequently required in the design stage of a cooling unit for spindle bearing systems. The major heat generation of the spindle bearing system is caused by the friction between the ball and race of the bearing. Since the heat generation due to friction is much dependent on bearing surroundings and drive conditions, it is difficult to express the characteristics of the heat generation in a general equation. The heat generation of bearings is usually assessed by assuming three modes of generation [8]. The following equations depict the three modes of heat generation: Htot = Hs + H1 + Hv Hs = 1.05 × 10⫺4 n Ms
(3)
HI = 1.05 × 10⫺4 n MI Hv = 1.05 × 10⫺4 n Mv Where Hs is the heat generation due to the moment Ms from the spinning motion of the bearing balls, HI the heat generation due to the moment MI from the applied load on the bearing and Hv the heat generation due to the moment Mv from the lubricant in the bearing cage. Htot is the total heat generation and n is the rotational speed (rpm). For B70 type bearings with grease lubrication, the total heat generations of the front three bearings (B7020) and the two rear bearings (B7016) were 216 W and 71 W, respectively when the rotational speed was 3500 rpm without applied bearing load. Kreith suggested the heat transfer coefficient for the rotational spindle with the assumption of uniform diameter and little temperature differences along the axial direction by the following equation under the forced convection condition [10]: NuD = 0.133 ReD2/3Pr1/3 (ReD ⬍ 4.3 × 105, 0.7 ⬍ Pr ⬍ 670) h = NuD/D
(4)
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Where NuD is the Nusselt number based on diameter, ReD and Pr are the Reynolds and the Prandtl numbers, respectively. In these assumptions, when the spindle was rotated at 3500 rpm, NuD and the heat transfer coefficient (h) were 423 and 115 W m⫺2 K⫺1, respectively. However, as this spindle bearing system had a gear located on the bearing span, the convection of heat from the spindle was more activated. Since the exact value of the heat transfer coefficient was not known, the temperature distributions of the spindle as well as the temperature rises of the bearings were calculated with respect to time when the range of the heat transfer coefficient was from 115 W m⫺2 K⫺1 to 400 W m⫺2 K⫺1 to compare the numerical results with the experimental results. The heat transfer coefficient of the fixed housing was assumed to be 80 W m⫺2 K⫺1 for the forced convection condition [11]. In order to assess the temperature rise with respect to time as well as the temperature distribution at the steady state, the thermal characteristics of the spindle bearing system was analysed using ANSYS, which is a commercial finite element analysis software package. Figure 8 shows the three dimensional model in which the cooling apparatus was optimally positioned for the above boundary conditions. Figure 9 shows the temperature rise with respect time when the heat transfer coefficients of the rotational spindle were 115 W m⫺2 K⫺1 and 400 W m⫺2 K⫺1. In Fig. 9, when the heat transfer coefficient of the rotating spindle was 115 W m⫺2 K⫺1 the rising time (ts) and the temperature increase (␦Ts) up to the saturation temperature were 1590 s and 60°C, respectively. However, these numerical results were different from the experimental results because too low value of the heat transfer coefficient was chosen. Therefore, the temperature distributions were calculated by varying the heat transfer coefficient of the spindle. Table 3 shows the rising times (ts) and the
Fig. 8.
Three dimensional FEM modeling for the thermal analysis of the spindle bearing system.
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Fig. 9. Temperature rise of the bearings with respect to time when the heat transfer coefficients of the rotational spindle were 115 W m⫺2 K⫺1 and 400 W m⫺2 K⫺1, respectively. Table 3 Rising times and temperature increases of the front bearings with respect to the heat transfer coefficients of the rotational spindle at 3500 rpm Heat transfer coefficients of the rotational spindle (W m⫺2 K⫺1)
Rising time ts Temperature increase ␦Ts°
115
200
300
400
1590 60
1480 56
1330 51
1200 46
Experimental result 1180 46
temperature increases (␦Ts) up to the saturation temperature with respect to the heat transfer coefficient. When the heat transfer coefficient was assumed to be 400 W m⫺2 K⫺1, the rising time (ts) 1200 s and the temperature increase (␦Ts) were 1200 s and 46°C, respectively, which were similar to the experimental results. Figure 10 shows the temperature distribution in the spindle bearing system for these boundary conditions. Since the temperature increase of the whole spindle bearing system is governed by the heat generation of the bearings, the means for the control of the thermal behavior of the bearings should be considered in the design step. In order to dissipate the heat generated in the spindle bearing system effectively, the cooling jacket of the helical coil shape with the square cross-section was provided, as shown in Fig. 11. To make the analysis simple, it was assumed that the coolant flow through the housing duct had small temperature difference and the secondary flow by the centrifugal force was negligible. When the inlet mass flux and temperature of the coolant were 0.02 kg s⫺1 and 15°C, respect-
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1027
Fig. 10. Temperature distribution of the spindle bearing system at 3500 rpm after 20 minutes.
ively, the coolant flow in the duct was laminar. In this case, the Nusselt number was 2.98 and the heat transfer coefficient was 220 W m⫺2 K⫺1 [11]. Figure 12 shows the temperature increase in the transient period with the cooling jacket and Fig. 13 shows the temperature distribution in the steady state with the cooling jacket. The rising time (ts) and the temperature increase (␦Ts) were reduced by 70 s and 2°C, respectively, compared to those without the cooling jacket. Table 4 shows the rising times (ts) and the temperature increases (␦Ts) of the bearing with respect to the heat transfer coefficient. 5. Conclusions In this work, a prototype spindle bearing system with a tilting gear on the bearing span for a five axis machining center, was designed and manufactured to investigate the thermal characteristics of the spindle bearing system. The prototype spindle was used for the measurement of the temperature increase. The temperature increase of the spindle bearing system was also analysed by the finite element method and compared to the experimental results. The calculated heat generation of the bearings of B70 series of FAG was 216 W at 3500 rpm and the heat transfer coefficient of 400 W m⫺2 K⫺1 of the rotational spindle was used to calculate the temperature distribution of the spindle bearing system. The calculated rising time (ts) and the temperature increase (␦Ts) were 1200 s and 46°C, respectively, which were similar to the experi-
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Fig. 11. FEM modeling of the coolant jacket with square cross-section in the spindle housing.
mental results. Therefore, it was concluded that the finite element analysis was a suitable tool for the thermal analysis of the spindle bearing system if the suitable value of the heat transfer coefficient of the spindle was chosen. When a cooling jacket was implemented to the spindle bearing system, the rising time (ts) and the temperature increase (␦Ts) were reduced by 70 s and 2°C compared to the spindle bearing system without the cooling jacket.
Table 4 Rising times and temperature increases of the front bearings with respect to the heat transfer coefficients of the coolant flow at 3500 rpm Heat transfer coefficients of the coolant flow (W m⫺2 K⫺1) no coolant flow Rising time ts (second) Temperature increase ␦Ts (°C)
220
400
600
800
1200
1130
1050
960
920
46
44
40
36
33
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Fig. 12.
Temperature rise of the spindle bearing system with cooling jacket with respect to time.
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Fig. 13. Temperature distribution of the spindle bearing system with cooling jacket at 3500 rpm after 20 minutes.
References [1] M. Weck, A. Koch, Spindle-bearing systems for high-speed applications in machine tools, Ann. CIRP 42 (1993) 445. [2] K.J.H. Al-Shareef, J.A. Brandon, On the effect of variations in the design parameters on the dynamic performance of machine tool spindle bearing systems, Int. J. Mach Tools Manufact. 30 (1990) 431. [3] D.M. Clarke, C. Fall, G.N. Hayden, T.S. Wilkinson, Steady-state model of a floating ring bearing including thermal effects, J. Tribology Trans. ASME 114 (1992) 141. [4] Bergling, Gunnar, Accurate estimates needed for bearing heat, lube conditions, J. Pulp & Paper 65 (1991) 56. [5] S. Witig, A. Glahn, J. Himmerlsbach, Influence of high rotational speeds on heat transfer and oil film thickness in aero engine bearing chamber, Internal Gas Turbine and Aeroengine Congress and Exposition of ASME 8 (1993). [6] L. Dunnuck, D.T.F. Conry, C. Cusano, Steady-state temperature and stack-up force distributions in a railroad roller bearing assembly, RTD Trans. ASME 5 (1992) 89. [7] L. Sunkyu, S. Hidenori, I. Yoshimi, Thermal behavior of bearing surrounding in machine tool spindle system, JSME 57 (1991) 3612. [8] A. Harris, Rolling Bearing Analysis, 3rd ed, p. 330 and Chap. 15, Wiley, New York, 1991. [9] B.J. Stone, The state of the art in the measurement of the stiffness and damping of rolling element bearings, Ann. CIRP 32 (1982) 529. [10] F. Kreith, Convection heat transfer and flow phenomena of rotating spheres, Int. J. Heat Mass Transfer 6 (1963) 881. [11] F.M. White, Heat Transfer, Chap. 6. Addison-Wesley, MA, 1984.
Thermal characteristics of the spindle bearing system with a gear located on the bearing span Jin Kyung Choi, Dai Gil Lee* Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology, ME3221, Gusongdong, Yusong-gu, Taejon-shi, South Korea 305-701 Received 19 December 1996; in final form 9 October 1997
Abstract High cutting speeds and feeds are essential requirements of a machine tool structure to accomplish its basic function which is to produce a workpiece of the required geometric form with an acceptable surface finish at as high a rate of production as is economically possible. Since bearings in high speed spindle units are the main heat source of total cutting system, in this work, the thermal characteristics of the spindle bearing system with a tilting axis were investigated using finite element method to improve the performance of the spindle bearing system. Based on the numerical results, a specially designed prototype spindle bearing system was manufactured. Using the manufactured spindle bearing system, the thermal characteristics were measured and compared to the numerical results. From the comparison of the numerical results with the experimental results, it was found that the finite element method predicted well the thermal characteristics of the spindle bearing system. 1998 Elsevier Science Ltd. All rights reserved. Keywords: Machine tools; Spindle system; Thermal characteristics; Angular contact ball bearing
1. Introduction Recently in manufacturing fields, high-precision products as well as diversified small-quantity production have been demanded, and the production technologies involved have constantly been redeveloped to lower production costs. Hence there is a growing interest in shorter machining times with increasing cutting speeds [1]. However, the spindle speed increase of machine tools
* Corresponding author. 0890-6955/98/$19.00 1998 Elsevier Science Ltd. All rights reserved. PII: S 0 8 9 0 - 6 9 5 5 ( 9 7 ) 0 0 0 7 5 - 8
1018
J.-K. Choi, D.G. Lee / International Journal of Machine Tools & Manufacture 38 (1998) 1017–1030
for productivity improvement also incurs adverse effects such as chattering, noise and heat generation of spindle bearing systems [2]. During high speed machining, the excessive temperature increase in the spindle induces dissimilar thermal expansions between different machine elements, which causes friction and wear. Generally, the performance of machine tools is determined by the highest machining speed which is limited by the temperature increase in the spindle bearing system. Therefore, the structural optimization incorporating cooling and lubrication apparatuses to reduce heat generation of the spindle is required. Many studies on the thermal characteristics of spindle bearing systems have been performed through experiments and analyses, some of which are listed here. Clarke et al. investigated theoretically thermal characteristics of the float ring bearing by solving the Reynolds equation and the energy equation for the lubricant film thickness between the inner and outer surfaces [3]. Bergling and Gunnar developed a program for the thermal and lubricant statuses of bearings operated under adverse environments such as dry cleaning cylinders and paper manufacturing rollers [4]. Witig et al. investigated the effect of high rotational speed on the characteristics of the heat transfer and lubricant film thickness of airplane engine bearings [5]. Dunnuck et al. used FEM model to analyse the temperature distribution of train wheel roller bearings in steady state and investigated the frictional heat loss of the bearings under various loads and speeds [6]. Lee et al. formed the dynamic simulation model for a spindle bearing system and investigated the thermal behavior of the spindle bearing system with the thermal closed-loop system in which the thermal deformation and boundary condition of the spindle system were related [7]. For the temperature distribution of machine tools which employ special type bearings or cooling jackets, the transient state as well as the steady state of the temperature distribution should be investigated in order to obtain efficient cooling effects. Since the measurement of noise level of machine tools to check the proper mounting of bearings or normal operation is complex because of the noise superposition from different machine elements, the measurement of the temperature increase of spindle bearings is more effective for the diagnosis of spindle bearing systems. Recently, as complicated parts such as airplane frames, propellers and turbine blades have been widely used, the five-axis machining center equipped with a spindle tilting axis is increasingly employed and consequently its design and performance prediction have become important. In this paper, the thermal characteristics of the spindle bearing system with a gear located on the bearing span for a tilting axis were investigated experimentally and numerically, using finite element method (FEM). 2. Experimental set-up for the spindle bearing system For the development of the spindle bearing system, the type of bearings and material for the spindle should be selected first. The bearing arrangement and the spindle shape are then determined for the optimum performance of the spindle bearing system. In this work, the spindle bearing system for the five-axis, 22 kW machining center was designed. For the first stage of development, the experimental set-up for the prototype spindle bearing system as shown in Fig. 1 was designed and manufactured. The bearing mounting area of the spindle was ground and then plated with chrome. The front bearings were mounted on the
J.-K. Choi, D.G. Lee / International Journal of Machine Tools & Manufacture 38 (1998) 1017–1030
1019
Fig. 1. Experimental set-up for the prototype spindle bearing system.
spindle with interference tolerance, while the rear bearings were mounted with clearance tolerance to avoid the preload variation of the bearings due to temperature variation. Table 1 shows the assembly tolerances and arithmetic average surface roughnesses for the spindle bearing system. The angular contact ball bearings B70 series manufactured by FAG in Germany whose specifications are shown in Table 2 were selected for spindle bearings. For the high spindle stiffness, the front three bearings were mounted in T–O arrangement (complex arrangement) and the rear two bearings were arranged in O arrangement (back to back arrangement). Since the rotational accuracy and bearing stiffness of angular contact ball bearings are enhanced by preloading, the spindle bearings were preloaded by tightening the knuckle nuts. The lower friction grease, Arcanol 174 for high speed machine tools manufactured by FAG in Germany was used for bearing lubrication. After assembling, the eccentric force of the spindle bearing systems was removed for the Table 1 Fit tolerance and the arithmetical average roughnesses of the spindle Spindle diameter (mm) Tolerance (m) Circularity (m) Arithmetical averageroughness; Ra (m) Housing diamter (mm) Tolerance (m)
80 +3 1.2 2 120 Clearance fit +8
100 +3 1.5 2.5 150 Interference fit ⫺3
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Table 2 Specifications of the angular contact ball bearings (FAG, Germany) Bearing type
Inner diameter (mm)
Dynamic load rating (kN)
Static load rating (kN)
Limit speed (rpm)
Grease lubrication Oil-air lubrication B7020C B7016C
100 80
75 58.5
68 48
7000 9000
9500 13 000
rotational balance of the spindle shaft. Figure 2 shows the eccentric force of the spindle bearing system after balancing with respect to the spindle rotational speed. Figure 3 shows the photograph of the experimental set-up before assembling the power transmission gears. This set-up was used to measure the thermal characteristics of the spindle bearing system. 3. Measurement of the temperature increase of the spindle bearing system Although angular contact ball bearings for spindles should be pre-loaded to increase the rotational accuracy and stiffness of spindle bearing systems, excessive pre-loads often reduce the machining accuracy and bearing life of the spindle bearing system due to frictional heat [8]. In this work, the J-type thermocouples, which can be used in 0 苲 277°C and composed of iron (⫺) and constantan(+), were used to measure the heat generation of the spindle bearing system.
Fig. 2. Eccentric centrifugal force of the spindle with respect to rotational speed.
J.-K. Choi, D.G. Lee / International Journal of Machine Tools & Manufacture 38 (1998) 1017–1030
Fig. 3.
1021
Experimental set-up for measuring thermal characteristics of the spindle bearing system.
The electromotive force of the thermocouples was amplified by the temperature sensing chip (AQ594AQ, Analog Device) and the signal noises were removed by a low-pass filter. The analogue data from the low-pass filter was converted into digital form by the A/D converter (PCLabcard) and was saved in a personal computer. Figure 4 shows the experimental set-up for measuring the temperature of the spindle bearing system. Figure 5 shows the thermocouple locations inserted in the holes drilled in the housing to measure the temperature increases at the nearest point of bearings. Figure 6 shows the temperature rise of the front bearing with respect to time at the spindle rotational speed of 3500 rpm. In Fig. 6, the temperature of the front bearing increased at the early stage and gradually saturated to the final temperature when the amount of heat generation balanced with the heat dissipation into the atmosphere. The rising time (ts) and the temperature increase (␦Ts) up to the saturation temperature are two important factors for the cooling conditions of
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Fig. 4. Experimental set-up for measuring the temperature of the spindle bearing system.
Fig. 5. Locations of the thermocouples for measuring the thermal increases of the spindle bearing system.
machine tools. It is beneficial if the rising time (ts) is short and the temperature increase (␦Ts) is low. Figure 7 shows the temperature increases of the bearings with respect to the rotational speed. The polynomial fittings of the experimental temperature increases of Fig. 7 at the saturation state were expressed in terms of rotating speed as follow:
␦T1 = ⫺ 1.03 × 10⫺93 + 9.25 × 10⫺62 ⫺ 6.84 × 10⫺3 ⫺ 1.24 × 10⫺1
(1)
␦T2 = ⫺ 1.01 × 10⫺93 + 6.01 × 10⫺62 ⫺ 4.59 × 10⫺3 ⫺ 5.37 × 10⫺2 Where is the rotational speed of the spindle expressed in rpm, and ␦T1 and ␦T2 are the temperature increases of the front and rear spindle bearings expressed in Celsius, respectively. The rising time t up to the maximum temperature was expressed as follows: t = 8000 + [ ⫺6 + (1/432 ⫺ ( ⫺ 2600)/9)( ⫺ 1700)]( ⫺ 1400)
(2)
Where is the rotational speed of the spindle expressed in rpm, t is the rising time up to the saturation temperature expressed in seconds. Stone reported that the temperature increase of the
J.-K. Choi, D.G. Lee / International Journal of Machine Tools & Manufacture 38 (1998) 1017–1030
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Fig. 6. Temperature rise of the front bearing with respect to time when the spindle rotational speed was 3500 rpm.
Fig. 7.
Temperature increases of the bearings with respect to rotational speed.
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B7211 bearing whose DN value was 110 000 was 7°C after 30 min operation [9]. In this work, the temperature increase was 3°C when the similar bearings of B7020 whose DN value was 110 000 were rotated at 1100 rpm. It is well known that the temperature increase of the spindle bearing system should be less than 10°C when the spindle is operated at the 2/3 speed of the maximum rotational speed for 1 h. Therefore, it was concluded that the maximum rotational speed of the spindle bearing spindle in this work was 2700 rpm because the temperature increase of the spindle front bearing was about 10°C from Fig. 7 when the rotational speed was 1800 rpm. 4. Thermal characteristics of the spindle bearing system Although the thermal analysis of rotating spindles is not easy because the heat transfer coefficient of the air cannot be obtained precisely due to the geometric complexity of spindles, the quantitative analysis of the temperature distribution in spindle bearing systems and the amount of heat dissipation of bearings are frequently required in the design stage of a cooling unit for spindle bearing systems. The major heat generation of the spindle bearing system is caused by the friction between the ball and race of the bearing. Since the heat generation due to friction is much dependent on bearing surroundings and drive conditions, it is difficult to express the characteristics of the heat generation in a general equation. The heat generation of bearings is usually assessed by assuming three modes of generation [8]. The following equations depict the three modes of heat generation: Htot = Hs + H1 + Hv Hs = 1.05 × 10⫺4 n Ms
(3)
HI = 1.05 × 10⫺4 n MI Hv = 1.05 × 10⫺4 n Mv Where Hs is the heat generation due to the moment Ms from the spinning motion of the bearing balls, HI the heat generation due to the moment MI from the applied load on the bearing and Hv the heat generation due to the moment Mv from the lubricant in the bearing cage. Htot is the total heat generation and n is the rotational speed (rpm). For B70 type bearings with grease lubrication, the total heat generations of the front three bearings (B7020) and the two rear bearings (B7016) were 216 W and 71 W, respectively when the rotational speed was 3500 rpm without applied bearing load. Kreith suggested the heat transfer coefficient for the rotational spindle with the assumption of uniform diameter and little temperature differences along the axial direction by the following equation under the forced convection condition [10]: NuD = 0.133 ReD2/3Pr1/3 (ReD ⬍ 4.3 × 105, 0.7 ⬍ Pr ⬍ 670) h = NuD/D
(4)
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Where NuD is the Nusselt number based on diameter, ReD and Pr are the Reynolds and the Prandtl numbers, respectively. In these assumptions, when the spindle was rotated at 3500 rpm, NuD and the heat transfer coefficient (h) were 423 and 115 W m⫺2 K⫺1, respectively. However, as this spindle bearing system had a gear located on the bearing span, the convection of heat from the spindle was more activated. Since the exact value of the heat transfer coefficient was not known, the temperature distributions of the spindle as well as the temperature rises of the bearings were calculated with respect to time when the range of the heat transfer coefficient was from 115 W m⫺2 K⫺1 to 400 W m⫺2 K⫺1 to compare the numerical results with the experimental results. The heat transfer coefficient of the fixed housing was assumed to be 80 W m⫺2 K⫺1 for the forced convection condition [11]. In order to assess the temperature rise with respect to time as well as the temperature distribution at the steady state, the thermal characteristics of the spindle bearing system was analysed using ANSYS, which is a commercial finite element analysis software package. Figure 8 shows the three dimensional model in which the cooling apparatus was optimally positioned for the above boundary conditions. Figure 9 shows the temperature rise with respect time when the heat transfer coefficients of the rotational spindle were 115 W m⫺2 K⫺1 and 400 W m⫺2 K⫺1. In Fig. 9, when the heat transfer coefficient of the rotating spindle was 115 W m⫺2 K⫺1 the rising time (ts) and the temperature increase (␦Ts) up to the saturation temperature were 1590 s and 60°C, respectively. However, these numerical results were different from the experimental results because too low value of the heat transfer coefficient was chosen. Therefore, the temperature distributions were calculated by varying the heat transfer coefficient of the spindle. Table 3 shows the rising times (ts) and the
Fig. 8.
Three dimensional FEM modeling for the thermal analysis of the spindle bearing system.
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Fig. 9. Temperature rise of the bearings with respect to time when the heat transfer coefficients of the rotational spindle were 115 W m⫺2 K⫺1 and 400 W m⫺2 K⫺1, respectively. Table 3 Rising times and temperature increases of the front bearings with respect to the heat transfer coefficients of the rotational spindle at 3500 rpm Heat transfer coefficients of the rotational spindle (W m⫺2 K⫺1)
Rising time ts Temperature increase ␦Ts°
115
200
300
400
1590 60
1480 56
1330 51
1200 46
Experimental result 1180 46
temperature increases (␦Ts) up to the saturation temperature with respect to the heat transfer coefficient. When the heat transfer coefficient was assumed to be 400 W m⫺2 K⫺1, the rising time (ts) 1200 s and the temperature increase (␦Ts) were 1200 s and 46°C, respectively, which were similar to the experimental results. Figure 10 shows the temperature distribution in the spindle bearing system for these boundary conditions. Since the temperature increase of the whole spindle bearing system is governed by the heat generation of the bearings, the means for the control of the thermal behavior of the bearings should be considered in the design step. In order to dissipate the heat generated in the spindle bearing system effectively, the cooling jacket of the helical coil shape with the square cross-section was provided, as shown in Fig. 11. To make the analysis simple, it was assumed that the coolant flow through the housing duct had small temperature difference and the secondary flow by the centrifugal force was negligible. When the inlet mass flux and temperature of the coolant were 0.02 kg s⫺1 and 15°C, respect-
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Fig. 10. Temperature distribution of the spindle bearing system at 3500 rpm after 20 minutes.
ively, the coolant flow in the duct was laminar. In this case, the Nusselt number was 2.98 and the heat transfer coefficient was 220 W m⫺2 K⫺1 [11]. Figure 12 shows the temperature increase in the transient period with the cooling jacket and Fig. 13 shows the temperature distribution in the steady state with the cooling jacket. The rising time (ts) and the temperature increase (␦Ts) were reduced by 70 s and 2°C, respectively, compared to those without the cooling jacket. Table 4 shows the rising times (ts) and the temperature increases (␦Ts) of the bearing with respect to the heat transfer coefficient. 5. Conclusions In this work, a prototype spindle bearing system with a tilting gear on the bearing span for a five axis machining center, was designed and manufactured to investigate the thermal characteristics of the spindle bearing system. The prototype spindle was used for the measurement of the temperature increase. The temperature increase of the spindle bearing system was also analysed by the finite element method and compared to the experimental results. The calculated heat generation of the bearings of B70 series of FAG was 216 W at 3500 rpm and the heat transfer coefficient of 400 W m⫺2 K⫺1 of the rotational spindle was used to calculate the temperature distribution of the spindle bearing system. The calculated rising time (ts) and the temperature increase (␦Ts) were 1200 s and 46°C, respectively, which were similar to the experi-
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Fig. 11. FEM modeling of the coolant jacket with square cross-section in the spindle housing.
mental results. Therefore, it was concluded that the finite element analysis was a suitable tool for the thermal analysis of the spindle bearing system if the suitable value of the heat transfer coefficient of the spindle was chosen. When a cooling jacket was implemented to the spindle bearing system, the rising time (ts) and the temperature increase (␦Ts) were reduced by 70 s and 2°C compared to the spindle bearing system without the cooling jacket.
Table 4 Rising times and temperature increases of the front bearings with respect to the heat transfer coefficients of the coolant flow at 3500 rpm Heat transfer coefficients of the coolant flow (W m⫺2 K⫺1) no coolant flow Rising time ts (second) Temperature increase ␦Ts (°C)
220
400
600
800
1200
1130
1050
960
920
46
44
40
36
33
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Fig. 12.
Temperature rise of the spindle bearing system with cooling jacket with respect to time.
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Fig. 13. Temperature distribution of the spindle bearing system with cooling jacket at 3500 rpm after 20 minutes.
References [1] M. Weck, A. Koch, Spindle-bearing systems for high-speed applications in machine tools, Ann. CIRP 42 (1993) 445. [2] K.J.H. Al-Shareef, J.A. Brandon, On the effect of variations in the design parameters on the dynamic performance of machine tool spindle bearing systems, Int. J. Mach Tools Manufact. 30 (1990) 431. [3] D.M. Clarke, C. Fall, G.N. Hayden, T.S. Wilkinson, Steady-state model of a floating ring bearing including thermal effects, J. Tribology Trans. ASME 114 (1992) 141. [4] Bergling, Gunnar, Accurate estimates needed for bearing heat, lube conditions, J. Pulp & Paper 65 (1991) 56. [5] S. Witig, A. Glahn, J. Himmerlsbach, Influence of high rotational speeds on heat transfer and oil film thickness in aero engine bearing chamber, Internal Gas Turbine and Aeroengine Congress and Exposition of ASME 8 (1993). [6] L. Dunnuck, D.T.F. Conry, C. Cusano, Steady-state temperature and stack-up force distributions in a railroad roller bearing assembly, RTD Trans. ASME 5 (1992) 89. [7] L. Sunkyu, S. Hidenori, I. Yoshimi, Thermal behavior of bearing surrounding in machine tool spindle system, JSME 57 (1991) 3612. [8] A. Harris, Rolling Bearing Analysis, 3rd ed, p. 330 and Chap. 15, Wiley, New York, 1991. [9] B.J. Stone, The state of the art in the measurement of the stiffness and damping of rolling element bearings, Ann. CIRP 32 (1982) 529. [10] F. Kreith, Convection heat transfer and flow phenomena of rotating spheres, Int. J. Heat Mass Transfer 6 (1963) 881. [11] F.M. White, Heat Transfer, Chap. 6. Addison-Wesley, MA, 1984.