- Email: [email protected]
Thermal analysis of an LPV test-rig
Tribology International 32 (1999) 33–38
Thermal analysis of an LPV test-rig Ron A.J. van Ostayen *, Anton van Beek Laboratory of Tribology, Department of Mechanical Engineering, University of Technology, Delft, The Netherlands Received 2 September 1998; received in revised form 10 January 1999; accepted 27 January 1999
Abstract A material property which is often used in the comparison and selection of polymer based materials used for dry rubbing journal bearings is the Limiting Pressure-Velocity (LPV) value. In a large pressure and velocity range this value is determined by the maximum temperature and compressive strength in the contact area. The temperature is related to the amount of heat generated in the contact area between shaft and bearing and the total thermal resistance from that contact area to the ambient atmosphere. This thermal resistance is therefore not only determined by the bearing itself but also by the assembly as a whole in which that bearing has been used. The LPV-value for a particular material measured on a particular test-rig is therefore dependent on the thermal resistance of that test-rig and cannot be compared directly with an LPV curve for that same material measured on another test-rig which has a different thermal resistance. In this paper a thermal model is used to calculate the heat generation and transport in an LPV test-rig and the results of this model are verified with some experiments. Furthermore it is shown how the material properties such as friction coefficient and melting temperature obtained by another material testing method viz the so-called Finger Print (FP), in combination with the calculated thermal resistance of the test-rig, can be used to predict LPV-values for a material on that test-rig. 1999 Elsevier Science Ltd. All rights reserved. Keywords: Dry rubbing journal bearing; Material testing; Limiting pressure-velocity; Thermal network analysis
1. Dry rubbing journal bearing material testing Because of their easy design, lack of lubrication requirements and low initial and maintenance costs, dry rubbing bearings are the first choice in many bearing applications. A large group of these bearings is made of engineering plastics and in particular thermoplastics like PA, POM, PETP, PEEK, PEI and many others. Specific properties of these materials can be improved using a mix of fillers like glass to improve mechanical properties and geometric stability and carbon, PTFE and other lubricants to reduce friction. In order to select the best material for a specific bearing application, materials have to be tested and compared. This selection of a bearing material is among others based on a comparison of pertinent material and corre-
* Corresponding author. Fax: +31-015-278-7980. E-mail address: [email protected] (R.A.J. van Ostayen)
sponding bearing properties. An important selection property of a bearing is the Limiting Pressure-Velocity (LPV) curve [1,2]. The LPV-value of a bearing is the product of the load and speed at failure. The LPV-curve connects all the LPV-values for a bearing at different speeds and loads. In Fig. 1 an example of this LPVcurve of a journal bearing (material: POM) is given in which the maximum load per projected unit area W/LD is plotted against the sliding speed U. In this LPV-curve, two limiting lines corresponding to different failure mechanisms are present: 앫 Line I: The load cannot exceed the static load carrying capacity of the bearing. This limit is determined by the compressive strength of the bearing material. For the bearing in Fig. 1 this value is ⬇22.0·106 N/m2. 앫 Line II: The product of pressure (load per unit area) and speed (PV-value) cannot exceed some maximum value. This value is reached the moment that the maximum allowable wear-rate or the maximum
0301-679X/99/$ - see front matter. 1999 Elsevier Science Ltd. All rights reserved. PII: S 0 3 0 1 - 6 7 9 X ( 9 9 ) 0 0 0 0 6 - 7
34
R.A.J. van Ostayen, A. van Beek / Tribology International 32 (1999) 33–38 108
0.5 I
0.4
0.3 10
6
10
5
fw [-]
W/LD [N/m2]
107
0.2 II
0.1 4
10 0.001
0.01
0.1 U [m/s]
1
10
0 20
Fig. 1.
LPV curve for a POM bearing (Diameter: 20.0 mm, Length: 20.0 mm).
allowable contact temperature is reached. For POM this PV-value is ⬇220.0·103 N/m2 m/s. For a bearing material, low wear and low friction are important material properties. Wear and friction data for a material can be obtained experimentally using different test geometries such as a block-on-ring or a pin-on-disc geometry. Some of these test geometries are outlined in a draft international standard [3, 4]. Unfortunately these test geometries are not defined in detail in this draft standard. Variations in test-piece and test-rig geometry and in test-rig material selection, and therefore in the thermal resistance of the test-rig are possible. These variations will result in different experimental results for the same material. Direct comparison of material properties from different sources is impossible because of this reason. In the Laboratory of Tribology at the University of Technology Delft, results obtained using a so-called Finger-Print test-rig and an LPV test-rig are combined. 1.1. Finger-print test The Finger-Print (FP) test-rig is a pin-on-disc geometry used to obtain a FP-curve of a material combination. The FP-curve gives the friction coefficient of a material combination for a given speed and load and contact temperature range [5]. In the FP test-rig, the disc temperature can be varied independently from the load and speed using external heating. Using the flash temperature theory [6] the difference between the measured and controlled bulk temperature of the disc and the actual contact temperature at the pin and disc interface can be estimated. For our FP test-rig the ratio between this temperature difference and the heat loss in the contact is ⬇0.295°C/W. Thus, for a measured heat loss of 30 W the actual contact temperature is ⬇9°C above the measured bulk temperature. In a typical FP experiment, after a running-in period,
40
60
80
100 o T [ C]
120
140
160
180
Fig. 2. FP-curve (Material: POM, Load: 106 N/m2, Speed: 0.5 m/s)
the load and speed are set and the temperature is increased slowly (8°C/h) from the ambient temperature (20°C) to a maximum temperature (200°C). The wear and friction are continuously recorded. The experiment is halted the moment excessive wear occurs (generally due to melting). In Fig. 2 the FP friction curve for a typical bearing material viz POM is given. The average friction coefficient for POM is 0.2 increasing to ⬇0.4 close to the melting point at 165°C. A number of these friction curves and wear curves at different speeds and loads can provide a complete picture of the friction and wear behaviour of a particular material combination. 1.2. Limiting pressure-velocity test-rig With the LPV test-rig, a radial bearing is tested with a constant angular shaft velocity and an increasing load. The load on the bearing is increased until failure occurs. The friction and bearing temperature are continuously recorded. This test-rig is used to obtain LPV data for bearing materials. The LPV test-rig (see Fig. 3) consists of a rotating
TEST BEARING
LOAD
Fig. 3.
LPV test-rig schematic, laboratory of Tribology, Delft.
R.A.J. van Ostayen, A. van Beek / Tribology International 32 (1999) 33–38
shaft supported by two deep-groove ball bearings. This shaft is made of stainless steel, all other major parts are made of aluminum. A test bearing (diameter 20 mm, lenght/diameter ratio 0.5…1.5) is mounted in a bearing holder and placed on the shaft (see Fig. 4 for a front view of the bearing holder on the shaft). This bearing holder can rotate freely around the shaft. A vertical load (W) is applied to the end of a rod fixed to the bearing holder. The friction torque (Mf) of the test bearing will force the bearing holder to rotate around the shaft until W is in equilibrium with Mf. The angle of the bearing holder is proportional with the friction coefficient of the bearing. This angle is measured using two displacement sensors. These sensors also measure the vertical displacement of the bearing due to wear of the test bearing and bending of the shaft. After a correction for the bending of the shaft, the wear of the bearing is obtained. The temperature is measured on the outer surface of the test bearing using a thermocouple probe. The load and speed, the friction and wear and the temperature are continuously recorded. In a typical experiment, after a running-in period, the speed is set (e.g. 0.5 m/s) and the load is increased slowly (40 N/h), from the minimal value (e.g. 0 N) to a preset maximal value (e.g. 400 N). The experiment is halted when this maximum value is reached or the moment excessive wear occurs.
Fig. 4. LPV test-rig, laboratory of Tribology, Delft.
35
The LPV-value is than equal to the PV-value at the moment bearing failure occurs, for example by a sharp increase in the friction coefficient or wear-rate. One of the possible failure mechanisms is thermal failure where the heat generated in the bearing leads to an increase in the contact temperature above some critical material temperature, e.g. the melting temperature. In Fig. 5 a number of failed partial journal bearings is presented. The contact temperature is related to the amount of heat generated in the contact area between bearing and shaft and the thermal resistance of not only the bearing but also of the assembly as a whole in which that bearing has been used. Therefore, the LPV-value must also be dependent on the amount of heat generated and the thermal resistance. Fig. 6 is an example of a friction curve and a temperature curve measured as function of the applied load on this test-rig for a POM bearing (diameter: 20 mm, length/diameter ratio: 1.0, bearing thickness: 2.35 mm, radial gap: 0.15 mm). In this experiment an increase in the friction coefficient occurs at 200 N. Therefore, the LPV-value for this material in this experiment becomes:
Fig. 5.
LPV test bearing: Examples of thermal failure.
36
R.A.J. van Ostayen, A. van Beek / Tribology International 32 (1999) 33–38
Th Ts Tmax Th data Ts data
150
50
100 W [N]
150
200
o
0
T [ C]
o
T [ C]
200 80 70 60 50 40 30 20
0.5
100
fw [-]
0.4 0.3
50
0.2 0.1 0.0 0
50
100 W [N]
150
200
0 0
Fig. 6. LPV experiment for a POM bearing (Speed: 0.5 m/s). Friction coefficient fw and bearing temperature T as function of the load W.
LPV⫽
W 200.0 ·U⫽ ·0.5⫽250.0·103N/m2m/s LD 0.02·0.02
(1)
This value is close to the LPV-curve in Fig. 1. Note that the temperature presented in Fig. 6 is not the contact temperature in the bearing but the temperature of the outer surface of the bearing. 1.3. Comparison LPV and FP test methods Comparing the FP and LPV test methods, the following observations can be made: both methods are useful when comparing and selecting materials. An advantage of the FP test-rig is the fact that load, speed and contact temperature can be set independently. This implies that all major parameters are controlled and thus the same results can be obtained on a test-rig with a different construction. The LPV value is useful particularly in case of material selection for a journal bearing application. However the contact temperature is dependent on the load and speed and this complicates the prediction of material behaviour in a different application. The FP curve is more difficult to translate to a practical application. In the following section, a model derived using the thermal network method will be used to predict the contact temperature and LPV value in the LPV test-rig using the FP curve obtained on the FP test-rig.
Fig. 7.
50
100 W [N]
150
200
LPV experiment (Fig. 6) compared with the thermal model (sliding speed: 0.5 m/s).
heat sources, heat resistors and heat capacitors analog to an electrical network. The LPV test-rig described in the previous section is modeled with this so-called thermal network method [7]. Using this model the temperatures in the test-rig and in particular the contact temperature in the bearing can be calculated for any given material. The results of these calculations show an accurate agreement between the measured and the calculated contact temperature in the test bearing. In Fig. 7 the results from the model are compared with the temperature on the outside of the bearing (see also Fig. 6) (Th) and the temperature measured at the end of the shaft (Ts). The calculated contact temperature Tmax in Fig. 7 reaches the melting temperature of 165°C at a load of 201 N, very close to the point where the bearing in the experiment failed! In Fig. 8 a summary of a large number of LPV experiments is presented. The sliding speed for all these experiments was equal to 0.5 m/s. In this figure the measured (dots) and calculated (dotted line) test bearing temperature are plotted as function of the heat loss in the test bearing. The thermal network seems to model the 300
Tbearing data Tbearing Tcontact
250
2. Thermal model of the LPV test-rig The thermal behaviour of a machine or construction is a complex combination of several modes of heat generation and heat transport. Heat is generated in heat sources like bearings, seals, gears etc. and transported from and through these heat sources by heat conduction, heat convection and radiation. A possible method to model this thermal behaviour is to build a network of
T [oC]
200
150
100
50
0 0
Fig. 8.
10
20
30 P [W]
40
50
LPV experiments compared with TNM model.
60
R.A.J. van Ostayen, A. van Beek / Tribology International 32 (1999) 33–38 30
37
ture and therefore the LPV-value demonstrates the influence of the test-rig design on the measured LPVvalue.
Q Qs Qb
25
Q [W]
20
3. Conclusion 15
10
5
0 0
50
Fig. 9.
100 W [N]
150
200
Heat distribution in the test-rig.
thermal behaviour of the test-rig fairly accurately. The calculated contact temperature (solid line) is also presented in Fig. 8. The slope of this curve is the thermal resistance of the test-rig and this resistance largely determines the LPV value measured for a particular material. This curve can be used, given the friction coefficient and the melting temperature of the material, to predict the LPV-value for a speed of 0.5 m/s for this material on this particular LPV test-rig. If this curve is known for two different LPV test-rigs it can be used to compare LPV values obtained on both test-rigs and to translate the results from one test-rig to another. Fig. 9 shows the heat distribution of the heat generated in the test bearing. It is clear that the major (⬇80%) portion of the total heat Q is transported through the shaft Qs. The rest of the heat is transported through the bearing and the bearing holder Qb. If the heat resistance of the shaft is changed the contact temperature and therefore the LPV-value will change accordingly. In Fig. 10 the contact temperature is plotted as a function of the heat conduction coefficient of the shaft. The large variation of the contact tempera-
It has been shown that the LPV value of a material obtained on a test-rig is strongly influenced by the thermal resistance of that test-rig. It is therefore difficult to compare LPV values given by different bearing material suppliers. Using the thermal resistance of a test-rig it is possible to predict the LPV-value for a given material, if the friction coefficient of that material is known. This friction coefficient can be obtained using a FP test-rig. In order to effectively standardize the LPV experiment it is necessary to dictate a thermal resistance for the standardized LPV test-rig. A possible value for this thermal resistance could be 6.25°C/W, the thermal resistance of the test-rig used in this study. The FP test provides a complete picture of the friction and wear behaviour of a material combination because of the possibility to set load, speed and contact temperature independently.
References [1] ESDU. Dry rubbing bearings—a guide to design and material selection. Item No. 68018, Engineering Sciences Data Unit Ltd., London, England, 1968. [2] Neale MJ. Tribology handbook. In: London: Butterworths, 1973. [3] Draft International Standard. Plain bearings—testing of the tribological behaviour of bearing materials—part i: Testing of metallic bearing materials. ISO/DIS 7148-1, International Organization for Standardization, 1994. [4] Draft International Standard. Plain bearings—testing of the tribological behaviour of bearing materials—part ii: Testing of polymer-based bearing material. ISO/DIS 7148-2, International Organization for Standardization, 1994. [5] Honselaar ACM, de Gee AWJ. Dynamic loadability of polymer-
300
250
o
T [ C]
200
150
100
50
0 1
Fig. 10.
10 k [W/moC]
100
Influence of the heat conduction coefficient of the shaft k on the contact temperature.
38
R.A.J. van Ostayen, A. van Beek / Tribology International 32 (1999) 33–38
metal friction couples. In: Proceedings of the 5th International Congress on Tribology, Helsinki, May 1989. [6] Bos J. Frictional Heating of Tribological Contacts. PhD thesis, University of Technology Twente, 1995.
[7] van Ostayen RAJ, van Beek A. Thermal network modeling of an LPV test-rig. Trib Int 1999;32: 39–43.
Thermal analysis of an LPV test-rig Ron A.J. van Ostayen *, Anton van Beek Laboratory of Tribology, Department of Mechanical Engineering, University of Technology, Delft, The Netherlands Received 2 September 1998; received in revised form 10 January 1999; accepted 27 January 1999
Abstract A material property which is often used in the comparison and selection of polymer based materials used for dry rubbing journal bearings is the Limiting Pressure-Velocity (LPV) value. In a large pressure and velocity range this value is determined by the maximum temperature and compressive strength in the contact area. The temperature is related to the amount of heat generated in the contact area between shaft and bearing and the total thermal resistance from that contact area to the ambient atmosphere. This thermal resistance is therefore not only determined by the bearing itself but also by the assembly as a whole in which that bearing has been used. The LPV-value for a particular material measured on a particular test-rig is therefore dependent on the thermal resistance of that test-rig and cannot be compared directly with an LPV curve for that same material measured on another test-rig which has a different thermal resistance. In this paper a thermal model is used to calculate the heat generation and transport in an LPV test-rig and the results of this model are verified with some experiments. Furthermore it is shown how the material properties such as friction coefficient and melting temperature obtained by another material testing method viz the so-called Finger Print (FP), in combination with the calculated thermal resistance of the test-rig, can be used to predict LPV-values for a material on that test-rig. 1999 Elsevier Science Ltd. All rights reserved. Keywords: Dry rubbing journal bearing; Material testing; Limiting pressure-velocity; Thermal network analysis
1. Dry rubbing journal bearing material testing Because of their easy design, lack of lubrication requirements and low initial and maintenance costs, dry rubbing bearings are the first choice in many bearing applications. A large group of these bearings is made of engineering plastics and in particular thermoplastics like PA, POM, PETP, PEEK, PEI and many others. Specific properties of these materials can be improved using a mix of fillers like glass to improve mechanical properties and geometric stability and carbon, PTFE and other lubricants to reduce friction. In order to select the best material for a specific bearing application, materials have to be tested and compared. This selection of a bearing material is among others based on a comparison of pertinent material and corre-
* Corresponding author. Fax: +31-015-278-7980. E-mail address: [email protected] (R.A.J. van Ostayen)
sponding bearing properties. An important selection property of a bearing is the Limiting Pressure-Velocity (LPV) curve [1,2]. The LPV-value of a bearing is the product of the load and speed at failure. The LPV-curve connects all the LPV-values for a bearing at different speeds and loads. In Fig. 1 an example of this LPVcurve of a journal bearing (material: POM) is given in which the maximum load per projected unit area W/LD is plotted against the sliding speed U. In this LPV-curve, two limiting lines corresponding to different failure mechanisms are present: 앫 Line I: The load cannot exceed the static load carrying capacity of the bearing. This limit is determined by the compressive strength of the bearing material. For the bearing in Fig. 1 this value is ⬇22.0·106 N/m2. 앫 Line II: The product of pressure (load per unit area) and speed (PV-value) cannot exceed some maximum value. This value is reached the moment that the maximum allowable wear-rate or the maximum
0301-679X/99/$ - see front matter. 1999 Elsevier Science Ltd. All rights reserved. PII: S 0 3 0 1 - 6 7 9 X ( 9 9 ) 0 0 0 0 6 - 7
34
R.A.J. van Ostayen, A. van Beek / Tribology International 32 (1999) 33–38 108
0.5 I
0.4
0.3 10
6
10
5
fw [-]
W/LD [N/m2]
107
0.2 II
0.1 4
10 0.001
0.01
0.1 U [m/s]
1
10
0 20
Fig. 1.
LPV curve for a POM bearing (Diameter: 20.0 mm, Length: 20.0 mm).
allowable contact temperature is reached. For POM this PV-value is ⬇220.0·103 N/m2 m/s. For a bearing material, low wear and low friction are important material properties. Wear and friction data for a material can be obtained experimentally using different test geometries such as a block-on-ring or a pin-on-disc geometry. Some of these test geometries are outlined in a draft international standard [3, 4]. Unfortunately these test geometries are not defined in detail in this draft standard. Variations in test-piece and test-rig geometry and in test-rig material selection, and therefore in the thermal resistance of the test-rig are possible. These variations will result in different experimental results for the same material. Direct comparison of material properties from different sources is impossible because of this reason. In the Laboratory of Tribology at the University of Technology Delft, results obtained using a so-called Finger-Print test-rig and an LPV test-rig are combined. 1.1. Finger-print test The Finger-Print (FP) test-rig is a pin-on-disc geometry used to obtain a FP-curve of a material combination. The FP-curve gives the friction coefficient of a material combination for a given speed and load and contact temperature range [5]. In the FP test-rig, the disc temperature can be varied independently from the load and speed using external heating. Using the flash temperature theory [6] the difference between the measured and controlled bulk temperature of the disc and the actual contact temperature at the pin and disc interface can be estimated. For our FP test-rig the ratio between this temperature difference and the heat loss in the contact is ⬇0.295°C/W. Thus, for a measured heat loss of 30 W the actual contact temperature is ⬇9°C above the measured bulk temperature. In a typical FP experiment, after a running-in period,
40
60
80
100 o T [ C]
120
140
160
180
Fig. 2. FP-curve (Material: POM, Load: 106 N/m2, Speed: 0.5 m/s)
the load and speed are set and the temperature is increased slowly (8°C/h) from the ambient temperature (20°C) to a maximum temperature (200°C). The wear and friction are continuously recorded. The experiment is halted the moment excessive wear occurs (generally due to melting). In Fig. 2 the FP friction curve for a typical bearing material viz POM is given. The average friction coefficient for POM is 0.2 increasing to ⬇0.4 close to the melting point at 165°C. A number of these friction curves and wear curves at different speeds and loads can provide a complete picture of the friction and wear behaviour of a particular material combination. 1.2. Limiting pressure-velocity test-rig With the LPV test-rig, a radial bearing is tested with a constant angular shaft velocity and an increasing load. The load on the bearing is increased until failure occurs. The friction and bearing temperature are continuously recorded. This test-rig is used to obtain LPV data for bearing materials. The LPV test-rig (see Fig. 3) consists of a rotating
TEST BEARING
LOAD
Fig. 3.
LPV test-rig schematic, laboratory of Tribology, Delft.
R.A.J. van Ostayen, A. van Beek / Tribology International 32 (1999) 33–38
shaft supported by two deep-groove ball bearings. This shaft is made of stainless steel, all other major parts are made of aluminum. A test bearing (diameter 20 mm, lenght/diameter ratio 0.5…1.5) is mounted in a bearing holder and placed on the shaft (see Fig. 4 for a front view of the bearing holder on the shaft). This bearing holder can rotate freely around the shaft. A vertical load (W) is applied to the end of a rod fixed to the bearing holder. The friction torque (Mf) of the test bearing will force the bearing holder to rotate around the shaft until W is in equilibrium with Mf. The angle of the bearing holder is proportional with the friction coefficient of the bearing. This angle is measured using two displacement sensors. These sensors also measure the vertical displacement of the bearing due to wear of the test bearing and bending of the shaft. After a correction for the bending of the shaft, the wear of the bearing is obtained. The temperature is measured on the outer surface of the test bearing using a thermocouple probe. The load and speed, the friction and wear and the temperature are continuously recorded. In a typical experiment, after a running-in period, the speed is set (e.g. 0.5 m/s) and the load is increased slowly (40 N/h), from the minimal value (e.g. 0 N) to a preset maximal value (e.g. 400 N). The experiment is halted when this maximum value is reached or the moment excessive wear occurs.
Fig. 4. LPV test-rig, laboratory of Tribology, Delft.
35
The LPV-value is than equal to the PV-value at the moment bearing failure occurs, for example by a sharp increase in the friction coefficient or wear-rate. One of the possible failure mechanisms is thermal failure where the heat generated in the bearing leads to an increase in the contact temperature above some critical material temperature, e.g. the melting temperature. In Fig. 5 a number of failed partial journal bearings is presented. The contact temperature is related to the amount of heat generated in the contact area between bearing and shaft and the thermal resistance of not only the bearing but also of the assembly as a whole in which that bearing has been used. Therefore, the LPV-value must also be dependent on the amount of heat generated and the thermal resistance. Fig. 6 is an example of a friction curve and a temperature curve measured as function of the applied load on this test-rig for a POM bearing (diameter: 20 mm, length/diameter ratio: 1.0, bearing thickness: 2.35 mm, radial gap: 0.15 mm). In this experiment an increase in the friction coefficient occurs at 200 N. Therefore, the LPV-value for this material in this experiment becomes:
Fig. 5.
LPV test bearing: Examples of thermal failure.
36
R.A.J. van Ostayen, A. van Beek / Tribology International 32 (1999) 33–38
Th Ts Tmax Th data Ts data
150
50
100 W [N]
150
200
o
0
T [ C]
o
T [ C]
200 80 70 60 50 40 30 20
0.5
100
fw [-]
0.4 0.3
50
0.2 0.1 0.0 0
50
100 W [N]
150
200
0 0
Fig. 6. LPV experiment for a POM bearing (Speed: 0.5 m/s). Friction coefficient fw and bearing temperature T as function of the load W.
LPV⫽
W 200.0 ·U⫽ ·0.5⫽250.0·103N/m2m/s LD 0.02·0.02
(1)
This value is close to the LPV-curve in Fig. 1. Note that the temperature presented in Fig. 6 is not the contact temperature in the bearing but the temperature of the outer surface of the bearing. 1.3. Comparison LPV and FP test methods Comparing the FP and LPV test methods, the following observations can be made: both methods are useful when comparing and selecting materials. An advantage of the FP test-rig is the fact that load, speed and contact temperature can be set independently. This implies that all major parameters are controlled and thus the same results can be obtained on a test-rig with a different construction. The LPV value is useful particularly in case of material selection for a journal bearing application. However the contact temperature is dependent on the load and speed and this complicates the prediction of material behaviour in a different application. The FP curve is more difficult to translate to a practical application. In the following section, a model derived using the thermal network method will be used to predict the contact temperature and LPV value in the LPV test-rig using the FP curve obtained on the FP test-rig.
Fig. 7.
50
100 W [N]
150
200
LPV experiment (Fig. 6) compared with the thermal model (sliding speed: 0.5 m/s).
heat sources, heat resistors and heat capacitors analog to an electrical network. The LPV test-rig described in the previous section is modeled with this so-called thermal network method [7]. Using this model the temperatures in the test-rig and in particular the contact temperature in the bearing can be calculated for any given material. The results of these calculations show an accurate agreement between the measured and the calculated contact temperature in the test bearing. In Fig. 7 the results from the model are compared with the temperature on the outside of the bearing (see also Fig. 6) (Th) and the temperature measured at the end of the shaft (Ts). The calculated contact temperature Tmax in Fig. 7 reaches the melting temperature of 165°C at a load of 201 N, very close to the point where the bearing in the experiment failed! In Fig. 8 a summary of a large number of LPV experiments is presented. The sliding speed for all these experiments was equal to 0.5 m/s. In this figure the measured (dots) and calculated (dotted line) test bearing temperature are plotted as function of the heat loss in the test bearing. The thermal network seems to model the 300
Tbearing data Tbearing Tcontact
250
2. Thermal model of the LPV test-rig The thermal behaviour of a machine or construction is a complex combination of several modes of heat generation and heat transport. Heat is generated in heat sources like bearings, seals, gears etc. and transported from and through these heat sources by heat conduction, heat convection and radiation. A possible method to model this thermal behaviour is to build a network of
T [oC]
200
150
100
50
0 0
Fig. 8.
10
20
30 P [W]
40
50
LPV experiments compared with TNM model.
60
R.A.J. van Ostayen, A. van Beek / Tribology International 32 (1999) 33–38 30
37
ture and therefore the LPV-value demonstrates the influence of the test-rig design on the measured LPVvalue.
Q Qs Qb
25
Q [W]
20
3. Conclusion 15
10
5
0 0
50
Fig. 9.
100 W [N]
150
200
Heat distribution in the test-rig.
thermal behaviour of the test-rig fairly accurately. The calculated contact temperature (solid line) is also presented in Fig. 8. The slope of this curve is the thermal resistance of the test-rig and this resistance largely determines the LPV value measured for a particular material. This curve can be used, given the friction coefficient and the melting temperature of the material, to predict the LPV-value for a speed of 0.5 m/s for this material on this particular LPV test-rig. If this curve is known for two different LPV test-rigs it can be used to compare LPV values obtained on both test-rigs and to translate the results from one test-rig to another. Fig. 9 shows the heat distribution of the heat generated in the test bearing. It is clear that the major (⬇80%) portion of the total heat Q is transported through the shaft Qs. The rest of the heat is transported through the bearing and the bearing holder Qb. If the heat resistance of the shaft is changed the contact temperature and therefore the LPV-value will change accordingly. In Fig. 10 the contact temperature is plotted as a function of the heat conduction coefficient of the shaft. The large variation of the contact tempera-
It has been shown that the LPV value of a material obtained on a test-rig is strongly influenced by the thermal resistance of that test-rig. It is therefore difficult to compare LPV values given by different bearing material suppliers. Using the thermal resistance of a test-rig it is possible to predict the LPV-value for a given material, if the friction coefficient of that material is known. This friction coefficient can be obtained using a FP test-rig. In order to effectively standardize the LPV experiment it is necessary to dictate a thermal resistance for the standardized LPV test-rig. A possible value for this thermal resistance could be 6.25°C/W, the thermal resistance of the test-rig used in this study. The FP test provides a complete picture of the friction and wear behaviour of a material combination because of the possibility to set load, speed and contact temperature independently.
References [1] ESDU. Dry rubbing bearings—a guide to design and material selection. Item No. 68018, Engineering Sciences Data Unit Ltd., London, England, 1968. [2] Neale MJ. Tribology handbook. In: London: Butterworths, 1973. [3] Draft International Standard. Plain bearings—testing of the tribological behaviour of bearing materials—part i: Testing of metallic bearing materials. ISO/DIS 7148-1, International Organization for Standardization, 1994. [4] Draft International Standard. Plain bearings—testing of the tribological behaviour of bearing materials—part ii: Testing of polymer-based bearing material. ISO/DIS 7148-2, International Organization for Standardization, 1994. [5] Honselaar ACM, de Gee AWJ. Dynamic loadability of polymer-
300
250
o
T [ C]
200
150
100
50
0 1
Fig. 10.
10 k [W/moC]
100
Influence of the heat conduction coefficient of the shaft k on the contact temperature.
38
R.A.J. van Ostayen, A. van Beek / Tribology International 32 (1999) 33–38
metal friction couples. In: Proceedings of the 5th International Congress on Tribology, Helsinki, May 1989. [6] Bos J. Frictional Heating of Tribological Contacts. PhD thesis, University of Technology Twente, 1995.
[7] van Ostayen RAJ, van Beek A. Thermal network modeling of an LPV test-rig. Trib Int 1999;32: 39–43.