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Experimental investigation of air spindle unit thermal characteristics
Precision Engineering Journal of the International Societies for Precision Engineering and Nanotechnology 26 (2002) 49 –57
Experimental investigation of air spindle unit thermal characteristics Susumu Ohishi*, Yasushi Matsuzaki Department of Mechanical Engineering, Aoyama Gakuin University, Tokyo, Japan Received 16 January 2001; received in revised form 4 April 2001; accepted 31 May 2001
Abstract This paper presents a report on the first stage of a research on the thermal analysis of spindle units with aerostatic bearings and an experimental investigation of temperature distributions. The objective of the present paper is to provide background information for further analysis. A test machine was used running to a maximum rotational speed of 20000 min⫺1 with a 60 mm diameter spindle supported by aerostatic journal bearings of 20 m radial clearance, and the temperatures of the housing, bush and the interface between the bush and air film were measured. In addition, the inlet and outlet air temperatures, the air film pressures and the deformations of the housing and spindle were measured. The experimental results show that the heat flow pattern is essentially radial flow, although axial heat flow was observed. The circumferential temperature distribution can be considered to be uniform, and the temperatures are proportional to the square of the spindle speed. © 2001 Elsevier Science Inc. All rights reserved. Keywords: Aerostatic journal bearing; Temperature measurement
1. Introduction Although air lubricated bearings have been applied mainly to ultra precision machine tools so far, little information on the thermal aspects is available. The reason may be that the bearings have been considered to have little or no heat generation due to the low viscosity of air. With increasing demand for high speed machining, however, the effect of heat generation in the air film is no longer negligible, because the generated heat leads not only to thermal deformations of the machines but also to changes in the bearing clearance and therefore in the bearing characteristics. Spindle expansion due to centrifugal force also affects the change in clearance. Therefore, the bearing parameters determined at the design stage may no be longer optimal under actual high-speed conditions. This paper describes the first stage of a research project to develop design procedures for air film lubricated journal bearings. The main objective of this paper is to provide background information for a theoretical analysis to improve the design procedures.
* Corresponding author. Tel.: ⫹81-3-5384-3247; fax: ⫹81-3-53846300. E-mail address: [email protected] (S. Ohishi).
In contrast with air lubricated bearings, many researchers have studied thermal effects in oil lubricated hydrodynamic bearings, because lubricants undergo an increase in temperature due to viscous dissipation, which may significantly influence the viscosity and therefore the load carrying capacity. In a study of heat effects in journal bearings, Dowson et al. [1] conducted a major experimental investigation of temperature patterns and heat balance of steadily loaded journal bearings. They showed several important results, which have been referenced extensively. According to a survey of important theoretical, computational and experimental studies pertaining to thermal effects in journal bearings [2], the following six remarks have been experimentally verified for steadily loaded journal bearings. 1. The spindle can be treated as an isothermal component. 2. The axial temperature gradients within the bush are negligible. 3. Lubricant outlet temperature is a good representation of the mean temperature of the bush and spindle. 4. Significant circumferential temperature variation may occur on the surface of the bush next to the oil film. 5. The condition of the fluid at the inlet has pronounced effects on the thermal characteristics of the journal bearing.
0141-6359/02/$ – see front matter © 2001 Elsevier Science Inc. All rights reserved. PII: S 0 1 4 1 - 6 3 5 9 ( 0 1 ) 0 0 0 9 7 - 6
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S. Ohishi, Y. Matsuzaki / Precision Engineering 26 (2002) 49 –57
Fig. 1. Schematic representation and photograph of the test spindle unit
6. It is often important to consider how recirculating and fresh oil mix at the inlet. The above information is very useful in understanding the thermal aspects of air lubricated bearings, because the only difference is in the viscosity of the fluid. A test spindle unit with a 60 mm diameter spindle supported by aerostatic journal bearings of 20 m radial clearance was used, and the temperatures of the housing, bush and also the interface between the bush and air film were measured. In addition, the inlet and outlet air temperatures, the air film pressures and the deformations of the housing and spindle were measured.
2. Experimental setup Fig. 1 shows the aerostatic spindle unit used, which was installed in a temperature controlled room. The spindle and housing materials are stainless steel and the bush is brass. The 60 mm diameter spindle supported on aerostatic journal and thrust bearings is driven by a built-in motor with water jacket. The cooling water is fed from a large tank installed adjacent to the test machine, which means that the water supply temperature is the same as the circumferential temperature. The air is provided through 12 feed holes with 0.5 mm diameter for each
S. Ohishi, Y. Matsuzaki / Precision Engineering 26 (2002) 49 –57
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Fig. 2. Sensor locations
journal bearing. The bearing axial length and radial clearance are 60 mm and 20 m, and the air supply pressure is 0.7 MPa.
Measurements were conducted on the front journal bearing. Ninety-four 1 mm diameter sheath type thermocouples (type T) were mounted in the housing, bush and
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S. Ohishi, Y. Matsuzaki / Precision Engineering 26 (2002) 49 –57
Fig. 3. Temperature variation with time (15000 min⫺1)
Fig. 4. Temperature variation with time (20000 min⫺1)
air film. The thermocouples were located in nine planes (A-A through I-I) at the radial and axial locations shown in Fig. 2. Fifty-four thermocouples to measure housing and bush temperatures were fixed in drilled holes of 1.5 mm diameter, and the nominal radial distances from the bush inner surface are indicated in Fig. 2. Thirty-six thermocouples for air film temperature measurements were mounted in plugs, which were assembled in the bush, the inner surface of which was then lapped. In addition to the locations shown in Fig. 2, ten adhesive type thermocouples were used for the housing outer surface temperature measurements, one sheath thermocouple for inlet air, one for outlet air, one for the circumference and one for motor cooling water. All thermocouples were calibrated in the range between 20 and 50° Celsius by using a platinum resistance thermometer with an accuracy of 0.02° Celsius as a calibration standard. In the C-C plane in Fig. 2, three semiconductor pressure transducers are embedded at 30, 150 and 210°, which is the region where the attitude angle was expected to be. The radial displacement of the spindle was measured with four capacitance type transducers located at the near end of the spindle. The transducers were configured as opposing pairs, one vertical pair and one horizontal pair. The signals from these pairs were combined to yield both spindle position and the expansion due to the centrifugal
force and temperature increase. The housing radial displacements were measured by four linear variable displacement transducers, and the spindle end displacement was also measured by a laser displacement meter.
3. Experimental procedure All 115-sensor outputs were connected to a digital volt meter via a scanner, and acquired by a computer at the rate of one per minute. At the same time, the output of the displacement transducers was recorded at 0.5 seconds intervals in order to obtain the spindle expansion due to the centrifugal force. It can be considered that the spindle expansion is caused mainly by the centrifugal force in the first 3 min, because the temperature rise is small in this time period. Measurements were conducted for the spindle rotational speeds of 5000, 10000, 15000 and 20000 min⫺1 with and without insulation of the ends of the spindle, bush and housing. The procedure was as follows: 1. 2. 3.
0 min. 1 min. 2 min.
4. 5.
3 min. 180, 360 min.
Start data acquisition Supply air and cooling water Start spindle rotation and increase speed to desired operating speed Reach desired steady speed Stop data acquisition
S. Ohishi, Y. Matsuzaki / Precision Engineering 26 (2002) 49 –57
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Fig. 7. Spindle end displacement due to centrifugal force
Fig. 5. Axial temperature distribution in the housing
4. Experimental results
are considered to be in steady state at 180 min for 5000 min⫺1 and 10000 min⫺1, and 300 min for 15000 min⫺1 and 20000 min⫺1. At a speed of 0 min⫺1, at which Poiseuille flow still exists, no temperature rise was measured. This means that the heat is generated mainly by the shearing in Couette flow. The lower figures in Figs. 3 and 4 are for the case where the spindle and housing ends were insulated by expanded polystyrene as shown in the upper figure of Fig. 5. The temperatures are generally higher than those without insulation. The housing axial temperature distribution shown in the lower figure of Fig. 5, however, indicates that the heat flows axially both with and without insulation, although the temperature gradients are small.
4.1. Temperature rise Fig. 3 and 4 show the temperature variations with time in the B-B plane at spindle rotational speeds of 15000 min⫺1 and 20000 min⫺1 respectively. Temperatures of air film, bush, housing, exhaust air and housing outer surface increase rapidly within about 60 min. As may be easily expected, air film temperature is highest, followed by bush and housing temperatures. The cooling water temperature increases gradually. In the present experiments, temperatures
Fig. 6. Bearing pressure variation with time
4.2. Spindle behavior The spindle radial displacements were measured, as mentioned above, in order to know the spindle center loci during the operations. In general, it is very difficult to identify the spindle center, because the spindle is not necessary located in the bottom of the bush before supplying air and there is not sufficient evidence that the spindle center is
Fig. 8. Thermal expansion of spindle end
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S. Ohishi, Y. Matsuzaki / Precision Engineering 26 (2002) 49 –57
Fig. 9. Circumferential temperature distribution in steady state (without insulation)
on the vertical center line of the bush when the spindle is stationary after supplying air. Fig. 6 shows the pressure variation with time at three points in the bearing, and the pressures are almost equal. Judging from this, it seems that the spindle is floating in the middle of the bush. The decrease in pressures with time may be due to the increase in the bearing clearance, because the thermal expansion coefficient of the bush material is about 1.8 times larger than that of the spindle material. During the first few minutes, the spindle end recedes due to centrifugal force as indicated in Fig. 7 and after that advanced due to thermal expansion. As shown in Fig. 8, the displacements become steady in a shorter time than the temperatures shown in Figs. 3 and 4. This suggests that the spindle reaches thermal equilibrium faster than the bush and housing. Gradual decreases in the displacements after 120 min for without insulation may be due to the effects of the thermal deformations of the bush and housing, although it is not verified experimentally or analytically. 4.3. Temperature distribution Circumferential temperature distributions of the air film, bush and housing are presented in Fig. 9 for without insulation and in Fig. 10 for with insulation. In contrast to
Fig. 10. Circumferential temperature distribution in steady state (with insulation)
temperature distributions in hydrodynamic journal bearings, the temperature distributions along the circumference are uniform. Needless to say, the air film temperatures are highest. Small variations can be observed, particularly at a spindle speed of 20000 min⫺1. As far as air film temperatures are concerned, Fig. 11 demonstrates that the circumferential distributions are almost identical regardless of the location in the bearing. 5. Discussion As mentioned above, there is a small change in temperature along the circumference, which can be attributed to the method of feeding air to the bearing. The air supply system employed in the test unit is shown in Fig. 12, which is in common use. Air is supplied from two holes drilled on the housing, flows within a slot and is then fed to the bearing clearance space through feed holes. Effects of cooler air flowing into the slot are clearly shown in Figs. 13 (A-A plane), 14 (B-B plane) and 15 (C-C and D-D plane), where bold arrows indicate the air inlet positions. The housing temperatures are affected more because the housing is cooled with fresh air, and the air film less due to the effect of the mixing of recirculating air and fresh air.
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Fig. 13. Effect of cooler air flow (A-A plane)
the distance from the thrust bearing to the spindle end as shown in Fig. 1. The calculated values are consistent with the measured ones, especially in the first 60 min, suggesting that the spindle can be approximately treated as an isothermal component. The difference at 20000 min⫺1 may be responsible for the effect of the thermal deformation of the housing.
Fig. 11. Circumferential air film temperature distribution in A-A, B-B, C-C and D-D planes
Fig. 16 shows a comparison between measured spindle end displacements and calculated values. In the calculations, it was assumed that the spindle had a uniform temperature equal to the mean of air film temperatures measured at different locations and that the effective length was
Fig. 14. Effect of cooler air flow (B-B plane)
Fig. 12. Air feeding system
Fig. 15. Effect of cooler air flow (C-C and D-D planes)
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S. Ohishi, Y. Matsuzaki / Precision Engineering 26 (2002) 49 –57
Fig. 16. Comparison between measured and calculated spindle expansion
The exhaust air temperatures are closely related to the mean air film temperatures, which can be seen clearly in Fig. 17. Therefore the exhaust air temperature is a good representation of the mean temperature of the air film and spindle. It can be considered that the heat is generated mainly by Couette flow. According to Petroff’s equation [3], which can evaluate the friction loss in journal bearings under the condition of concentricity, the amount of heat generated is proportional to the square of the spindle
Fig. 18. Relation between temperature and spindle rotational speed
speed. Fig. 18 presents the relation of the temperature of air film and housing outer surface to the spindle rotational speeds. The results demonstrate that Petroff’s equation is applicable to aerostatic journal bearings. This suggests that the heat partition, which is unknown at present, is invariable independent of the spindle speed.
6. Conclusions The main objective of the present experimental study is to identify the thermal characteristics of aerostatic journal bearings for further theoretical analysis. The results are summarized as follows: 1. Although the temperature gradient is small, axial heat flow is observed. 2. Temperature distribution along circumference is uniform. 3. The spindle can be approximately treated isothermal. 4. Temperatures are proportional to the square of spindle rotational speed. Fig. 17. Relation between exhaust air and air film temperature
The above information may provide the background necessary for the development of thermal models of air
S. Ohishi, Y. Matsuzaki / Precision Engineering 26 (2002) 49 –57
spindle units and for the progress in adequate design procedures. Acknowledgments The authors acknowledge the contribution of Mr. Katsutoshi Tanaka, Toshiba Machine Co. Ltd, for his helpful discussions and support.
57
References [1] Dowson D, Hudson JD, Hunter B, March CN. An experimental investigation of the thermal equilibrium of steadily loaded journal bearings. Proc Instn Mech Engrs 1966 – 67;181(3B):70 – 80. [2] Khonsari MM. A review of thermal effects in hydrodynamic bearings. Part II: Journal bearings. ASLE Trans.;30(1);1987:26 –33. [3] Fuller DD. Theory and practice of lubrication for engineers. John Wiley & Sons 1963.
Experimental investigation of air spindle unit thermal characteristics Susumu Ohishi*, Yasushi Matsuzaki Department of Mechanical Engineering, Aoyama Gakuin University, Tokyo, Japan Received 16 January 2001; received in revised form 4 April 2001; accepted 31 May 2001
Abstract This paper presents a report on the first stage of a research on the thermal analysis of spindle units with aerostatic bearings and an experimental investigation of temperature distributions. The objective of the present paper is to provide background information for further analysis. A test machine was used running to a maximum rotational speed of 20000 min⫺1 with a 60 mm diameter spindle supported by aerostatic journal bearings of 20 m radial clearance, and the temperatures of the housing, bush and the interface between the bush and air film were measured. In addition, the inlet and outlet air temperatures, the air film pressures and the deformations of the housing and spindle were measured. The experimental results show that the heat flow pattern is essentially radial flow, although axial heat flow was observed. The circumferential temperature distribution can be considered to be uniform, and the temperatures are proportional to the square of the spindle speed. © 2001 Elsevier Science Inc. All rights reserved. Keywords: Aerostatic journal bearing; Temperature measurement
1. Introduction Although air lubricated bearings have been applied mainly to ultra precision machine tools so far, little information on the thermal aspects is available. The reason may be that the bearings have been considered to have little or no heat generation due to the low viscosity of air. With increasing demand for high speed machining, however, the effect of heat generation in the air film is no longer negligible, because the generated heat leads not only to thermal deformations of the machines but also to changes in the bearing clearance and therefore in the bearing characteristics. Spindle expansion due to centrifugal force also affects the change in clearance. Therefore, the bearing parameters determined at the design stage may no be longer optimal under actual high-speed conditions. This paper describes the first stage of a research project to develop design procedures for air film lubricated journal bearings. The main objective of this paper is to provide background information for a theoretical analysis to improve the design procedures.
* Corresponding author. Tel.: ⫹81-3-5384-3247; fax: ⫹81-3-53846300. E-mail address: [email protected] (S. Ohishi).
In contrast with air lubricated bearings, many researchers have studied thermal effects in oil lubricated hydrodynamic bearings, because lubricants undergo an increase in temperature due to viscous dissipation, which may significantly influence the viscosity and therefore the load carrying capacity. In a study of heat effects in journal bearings, Dowson et al. [1] conducted a major experimental investigation of temperature patterns and heat balance of steadily loaded journal bearings. They showed several important results, which have been referenced extensively. According to a survey of important theoretical, computational and experimental studies pertaining to thermal effects in journal bearings [2], the following six remarks have been experimentally verified for steadily loaded journal bearings. 1. The spindle can be treated as an isothermal component. 2. The axial temperature gradients within the bush are negligible. 3. Lubricant outlet temperature is a good representation of the mean temperature of the bush and spindle. 4. Significant circumferential temperature variation may occur on the surface of the bush next to the oil film. 5. The condition of the fluid at the inlet has pronounced effects on the thermal characteristics of the journal bearing.
0141-6359/02/$ – see front matter © 2001 Elsevier Science Inc. All rights reserved. PII: S 0 1 4 1 - 6 3 5 9 ( 0 1 ) 0 0 0 9 7 - 6
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S. Ohishi, Y. Matsuzaki / Precision Engineering 26 (2002) 49 –57
Fig. 1. Schematic representation and photograph of the test spindle unit
6. It is often important to consider how recirculating and fresh oil mix at the inlet. The above information is very useful in understanding the thermal aspects of air lubricated bearings, because the only difference is in the viscosity of the fluid. A test spindle unit with a 60 mm diameter spindle supported by aerostatic journal bearings of 20 m radial clearance was used, and the temperatures of the housing, bush and also the interface between the bush and air film were measured. In addition, the inlet and outlet air temperatures, the air film pressures and the deformations of the housing and spindle were measured.
2. Experimental setup Fig. 1 shows the aerostatic spindle unit used, which was installed in a temperature controlled room. The spindle and housing materials are stainless steel and the bush is brass. The 60 mm diameter spindle supported on aerostatic journal and thrust bearings is driven by a built-in motor with water jacket. The cooling water is fed from a large tank installed adjacent to the test machine, which means that the water supply temperature is the same as the circumferential temperature. The air is provided through 12 feed holes with 0.5 mm diameter for each
S. Ohishi, Y. Matsuzaki / Precision Engineering 26 (2002) 49 –57
51
Fig. 2. Sensor locations
journal bearing. The bearing axial length and radial clearance are 60 mm and 20 m, and the air supply pressure is 0.7 MPa.
Measurements were conducted on the front journal bearing. Ninety-four 1 mm diameter sheath type thermocouples (type T) were mounted in the housing, bush and
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S. Ohishi, Y. Matsuzaki / Precision Engineering 26 (2002) 49 –57
Fig. 3. Temperature variation with time (15000 min⫺1)
Fig. 4. Temperature variation with time (20000 min⫺1)
air film. The thermocouples were located in nine planes (A-A through I-I) at the radial and axial locations shown in Fig. 2. Fifty-four thermocouples to measure housing and bush temperatures were fixed in drilled holes of 1.5 mm diameter, and the nominal radial distances from the bush inner surface are indicated in Fig. 2. Thirty-six thermocouples for air film temperature measurements were mounted in plugs, which were assembled in the bush, the inner surface of which was then lapped. In addition to the locations shown in Fig. 2, ten adhesive type thermocouples were used for the housing outer surface temperature measurements, one sheath thermocouple for inlet air, one for outlet air, one for the circumference and one for motor cooling water. All thermocouples were calibrated in the range between 20 and 50° Celsius by using a platinum resistance thermometer with an accuracy of 0.02° Celsius as a calibration standard. In the C-C plane in Fig. 2, three semiconductor pressure transducers are embedded at 30, 150 and 210°, which is the region where the attitude angle was expected to be. The radial displacement of the spindle was measured with four capacitance type transducers located at the near end of the spindle. The transducers were configured as opposing pairs, one vertical pair and one horizontal pair. The signals from these pairs were combined to yield both spindle position and the expansion due to the centrifugal
force and temperature increase. The housing radial displacements were measured by four linear variable displacement transducers, and the spindle end displacement was also measured by a laser displacement meter.
3. Experimental procedure All 115-sensor outputs were connected to a digital volt meter via a scanner, and acquired by a computer at the rate of one per minute. At the same time, the output of the displacement transducers was recorded at 0.5 seconds intervals in order to obtain the spindle expansion due to the centrifugal force. It can be considered that the spindle expansion is caused mainly by the centrifugal force in the first 3 min, because the temperature rise is small in this time period. Measurements were conducted for the spindle rotational speeds of 5000, 10000, 15000 and 20000 min⫺1 with and without insulation of the ends of the spindle, bush and housing. The procedure was as follows: 1. 2. 3.
0 min. 1 min. 2 min.
4. 5.
3 min. 180, 360 min.
Start data acquisition Supply air and cooling water Start spindle rotation and increase speed to desired operating speed Reach desired steady speed Stop data acquisition
S. Ohishi, Y. Matsuzaki / Precision Engineering 26 (2002) 49 –57
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Fig. 7. Spindle end displacement due to centrifugal force
Fig. 5. Axial temperature distribution in the housing
4. Experimental results
are considered to be in steady state at 180 min for 5000 min⫺1 and 10000 min⫺1, and 300 min for 15000 min⫺1 and 20000 min⫺1. At a speed of 0 min⫺1, at which Poiseuille flow still exists, no temperature rise was measured. This means that the heat is generated mainly by the shearing in Couette flow. The lower figures in Figs. 3 and 4 are for the case where the spindle and housing ends were insulated by expanded polystyrene as shown in the upper figure of Fig. 5. The temperatures are generally higher than those without insulation. The housing axial temperature distribution shown in the lower figure of Fig. 5, however, indicates that the heat flows axially both with and without insulation, although the temperature gradients are small.
4.1. Temperature rise Fig. 3 and 4 show the temperature variations with time in the B-B plane at spindle rotational speeds of 15000 min⫺1 and 20000 min⫺1 respectively. Temperatures of air film, bush, housing, exhaust air and housing outer surface increase rapidly within about 60 min. As may be easily expected, air film temperature is highest, followed by bush and housing temperatures. The cooling water temperature increases gradually. In the present experiments, temperatures
Fig. 6. Bearing pressure variation with time
4.2. Spindle behavior The spindle radial displacements were measured, as mentioned above, in order to know the spindle center loci during the operations. In general, it is very difficult to identify the spindle center, because the spindle is not necessary located in the bottom of the bush before supplying air and there is not sufficient evidence that the spindle center is
Fig. 8. Thermal expansion of spindle end
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S. Ohishi, Y. Matsuzaki / Precision Engineering 26 (2002) 49 –57
Fig. 9. Circumferential temperature distribution in steady state (without insulation)
on the vertical center line of the bush when the spindle is stationary after supplying air. Fig. 6 shows the pressure variation with time at three points in the bearing, and the pressures are almost equal. Judging from this, it seems that the spindle is floating in the middle of the bush. The decrease in pressures with time may be due to the increase in the bearing clearance, because the thermal expansion coefficient of the bush material is about 1.8 times larger than that of the spindle material. During the first few minutes, the spindle end recedes due to centrifugal force as indicated in Fig. 7 and after that advanced due to thermal expansion. As shown in Fig. 8, the displacements become steady in a shorter time than the temperatures shown in Figs. 3 and 4. This suggests that the spindle reaches thermal equilibrium faster than the bush and housing. Gradual decreases in the displacements after 120 min for without insulation may be due to the effects of the thermal deformations of the bush and housing, although it is not verified experimentally or analytically. 4.3. Temperature distribution Circumferential temperature distributions of the air film, bush and housing are presented in Fig. 9 for without insulation and in Fig. 10 for with insulation. In contrast to
Fig. 10. Circumferential temperature distribution in steady state (with insulation)
temperature distributions in hydrodynamic journal bearings, the temperature distributions along the circumference are uniform. Needless to say, the air film temperatures are highest. Small variations can be observed, particularly at a spindle speed of 20000 min⫺1. As far as air film temperatures are concerned, Fig. 11 demonstrates that the circumferential distributions are almost identical regardless of the location in the bearing. 5. Discussion As mentioned above, there is a small change in temperature along the circumference, which can be attributed to the method of feeding air to the bearing. The air supply system employed in the test unit is shown in Fig. 12, which is in common use. Air is supplied from two holes drilled on the housing, flows within a slot and is then fed to the bearing clearance space through feed holes. Effects of cooler air flowing into the slot are clearly shown in Figs. 13 (A-A plane), 14 (B-B plane) and 15 (C-C and D-D plane), where bold arrows indicate the air inlet positions. The housing temperatures are affected more because the housing is cooled with fresh air, and the air film less due to the effect of the mixing of recirculating air and fresh air.
S. Ohishi, Y. Matsuzaki / Precision Engineering 26 (2002) 49 –57
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Fig. 13. Effect of cooler air flow (A-A plane)
the distance from the thrust bearing to the spindle end as shown in Fig. 1. The calculated values are consistent with the measured ones, especially in the first 60 min, suggesting that the spindle can be approximately treated as an isothermal component. The difference at 20000 min⫺1 may be responsible for the effect of the thermal deformation of the housing.
Fig. 11. Circumferential air film temperature distribution in A-A, B-B, C-C and D-D planes
Fig. 16 shows a comparison between measured spindle end displacements and calculated values. In the calculations, it was assumed that the spindle had a uniform temperature equal to the mean of air film temperatures measured at different locations and that the effective length was
Fig. 14. Effect of cooler air flow (B-B plane)
Fig. 12. Air feeding system
Fig. 15. Effect of cooler air flow (C-C and D-D planes)
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Fig. 16. Comparison between measured and calculated spindle expansion
The exhaust air temperatures are closely related to the mean air film temperatures, which can be seen clearly in Fig. 17. Therefore the exhaust air temperature is a good representation of the mean temperature of the air film and spindle. It can be considered that the heat is generated mainly by Couette flow. According to Petroff’s equation [3], which can evaluate the friction loss in journal bearings under the condition of concentricity, the amount of heat generated is proportional to the square of the spindle
Fig. 18. Relation between temperature and spindle rotational speed
speed. Fig. 18 presents the relation of the temperature of air film and housing outer surface to the spindle rotational speeds. The results demonstrate that Petroff’s equation is applicable to aerostatic journal bearings. This suggests that the heat partition, which is unknown at present, is invariable independent of the spindle speed.
6. Conclusions The main objective of the present experimental study is to identify the thermal characteristics of aerostatic journal bearings for further theoretical analysis. The results are summarized as follows: 1. Although the temperature gradient is small, axial heat flow is observed. 2. Temperature distribution along circumference is uniform. 3. The spindle can be approximately treated isothermal. 4. Temperatures are proportional to the square of spindle rotational speed. Fig. 17. Relation between exhaust air and air film temperature
The above information may provide the background necessary for the development of thermal models of air
S. Ohishi, Y. Matsuzaki / Precision Engineering 26 (2002) 49 –57
spindle units and for the progress in adequate design procedures. Acknowledgments The authors acknowledge the contribution of Mr. Katsutoshi Tanaka, Toshiba Machine Co. Ltd, for his helpful discussions and support.
57
References [1] Dowson D, Hudson JD, Hunter B, March CN. An experimental investigation of the thermal equilibrium of steadily loaded journal bearings. Proc Instn Mech Engrs 1966 – 67;181(3B):70 – 80. [2] Khonsari MM. A review of thermal effects in hydrodynamic bearings. Part II: Journal bearings. ASLE Trans.;30(1);1987:26 –33. [3] Fuller DD. Theory and practice of lubrication for engineers. John Wiley & Sons 1963.