Accepted Manuscript Friction torque in rolling bearings lubricated with axle gear oils Maroua Hammami, Ramiro Martins, Carlos Fernandes, Jorge Seabra, Mohamed Slim Abbes, Mohamed Haddar PII:
S0301-679X(17)30533-9
DOI:
10.1016/j.triboint.2017.11.018
Reference:
JTRI 4958
To appear in:
Tribology International
Received Date: 20 August 2017 Revised Date:
6 November 2017
Accepted Date: 11 November 2017
Please cite this article as: Hammami M, Martins R, Fernandes C, Seabra J, Abbes MS, Haddar M, Friction torque in rolling bearings lubricated with axle gear oils, Tribology International (2017), doi: 10.1016/j.triboint.2017.11.018. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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Friction Torque in Rolling Bearings Lubricated with Axle Gear Oils Maroua Hammamia,c,∗, Ramiro Martinsa , Carlos Fernandesa , Jorge Seabrab , Mohamed Slim Abbesc , Mohamed Haddarc a INEGI,
Universidade do Porto, Campus FEUP, Rua Dr. Roberto Frias 400, 4200-465 Porto, Portugal Universidade do Porto, Rua Dr. Roberto Frias s/n, 4200-465 Porto, Portugal c Unit of Mechanics, Modelling and Manufacturing, National Engineers School of Sfax, University of Sfax, Sfax W-3038, Tunisia
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b FEUP,
Abstract
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As a part of the main research project within the aim of increasing significantly drive axle efficiency, this work focuses on rolling bearing friction torque lubricated with five fully formulated axle gear oils with different viscosity and different formulations. The lubricant tribological behaviour in different rolling bearings was analyzed. A modified Four-Ball Machine was used to test the rolling bearings. The effect of speed, temperature and axial load on rolling bearing friction torque was assessed. Experimental results for the internal friction torque were validated with an SKF model. Direct comparisons in terms of friction torque between axle gear oils when they are lubricating different rolling bearing types are presented and discussed. Keywords: Axle gear oils, Tribological behaviour, Rolling bearings, Friction torque, Axle efficiency
1. Introduction
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Power losses in automotive drive trains have become an important field of investigation in automotive industry [1–5]. So far, the federal standards and the state government regulations in vehicle fuel economy combined with limits imposed by Environmental Protection Agency (EPA) rules on CO2 emissions into the atmosphere have traditionally been the main reason for this focus in drive train power losses [6–9]. The looming energy crisis and increasing fuel prices have also added to the motivation to reduce such losses. It has been well settled that the automotive axle-differential is considered as a significant contributor to power loss in the drive line [10]. Axle efficiency values were reported to be as low as 90 to 95 % depending on the type of vehicle and on the applied torque and speed [2, 11, 12]. Therefore, any tangible improvement to the axle efficiency has a significant impact on the carbon emissions and the energy consumption [3, 11].
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The axle transmission is a key component of the vehicle powertrain. It is a very compact mechanical system, consisting generally of a hypoid bevel geared transmission, tapered roller bearings, seals, shafts and an axle gear oil [13]. The axle transmission requires a very high reliability, since failures are not accepted by consumers [14–16]. As any power transmission system, axle power losses are divided into several energy loss mechanisms as proposed in a number of papers by Hohn et al. [17–19]. The sources of the major axle power losses were dissipated mainly in friction loss between the meshing teeth of hypoid gears [12, 20–23], friction loss in the bearings [24–26], friction loss in the seals [27] and spin losses due to lubricant pumping and churning, and windage [5, 28]. Axle power losses mainly originated in two type of losses. No-load losses or churning losses generated by gears, rolling bearings and seals that are related to the input speed, the operating conditions and mainly ∗ Corresponding
author Email address:
[email protected] (Maroua Hammami )
Preprint submitted to Tribology International
November 13, 2017
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related to the lubricant properties such as viscosity and density of the oil [6–8, 15] as well as immersion depth of the components in a sump lubricated axle [29]. Rolling bearing losses depend on its type and size, bearing arrangement, lubricant viscosity and supply [19]. These losses are relevant but they are outside the scope of this research. Load dependent losses generated by gears and rolling bearings are related to the transmitted torque, coefficient of friction and sliding velocity in the contact area of the components. Load dependent rolling bearing losses also dependent on type and size, rolling and sliding conditions and lubricant type [30]. In order to have a good prediction of the power losses of the system, each component should be tested separately.
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The rolling bearings are a major contributor to axle system power loss [25] and their main function in axles is to support the pinion and the differential gear under high load carrying capacity and high stiffness. To achieve high efficiency in axle differentials, the reduction of internal friction torque in rolling bearings is of major concern. Thus, the importance of understanding internal friction in rolling bearings becomes relevant. The energy saving and bearings performance optimization are required [31]. The energy consumption due to rolling bearing power loss is becoming more and more important when taking into account the focus of science and industry on this issue. Recently, automotive manufacturers and the rolling bearings manufacturers are trying to improve rolling bearing designs in order to reduce the power loss generated, the energy consumption and the operating temperatures and improve the lubrication conditions. At the same time, they ask the lubricant manufacturers to provide new products that increase rolling bearing life, while reducing the energy dissipated [25, 26].
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Only a limited number of studies focused on developing the axle rolling bearings friction torque. Spindler and von Petery (2003) [24] reported that INA (Industrie-NAdellager) has developed a new bearing design, where the tapered roller bearings on the pinion shaft are replaced by double row angularcontact ball bearing and the tapered roller bearings of the ring gear shafts are replaced by single-row angular ball bearings. The benefits of the rolling bearing substitution are no preload loss during operation with 50 % reduction of friction torque meeting the requirements for high rigidity and long life. Matsuyama et al. (2004) [25] published results when the super-low friction torque tapered roller bearing supporting the pinion was used in rear axle differentials. This study achieved a friction torque reduction of 80 % compared to standard bearings. Petery et al. (2004) [32] reported that INA and FAG in collaboration with BMW conducted power loss measurements of the original bearing design of a BMW axle with cross-locating taper roller bearing arrangement and an alternative design with crosslocating double- and single-row angular ball bearing arrangement. For medium load and speed and low temperatures, relevant in the New European Driving Cycle (NEDC), the bearing loss reduction for the alternative design was over 50 per cent [19]. Hoshokawa et al. (2009) [26] proposed a new bearing concept which is the double row angular contact ball bearing-so-called Tandem Ball Bearings for rear axle drives. Through a comparative testing between a new bearing design and standard bearing used in axles a relevant reduction of 50 % in friction torque can be achieved. This bearing concept not only increases the service life but also make significant contribution to lower fuel consumption by up 1.5 % in every driving. The motivation behind this study is conducting an accurate measurement of internal friction torque of different rolling bearing types which is challenging since experimental measurements must be determined precisely. A modified Four-Ball Machine (Cameron-Plint TE 82/7752) was suited. The tests were performed under a wide range of operating conditions (load, speed, temperature and lubricant). Then, the power loss of rolling bearings can be predicted using models based on a large number of measurements and they have been developed by bearing manufacturers such as SKF and FAG. For this work, the model selected to analyze the results obtained is the SKF Friction Torque Model [33]. This model will be calibrated using the experimental results from tests performed with the selected rolling bearing types, lubricated with several axle gear oils having different formulations. A better understanding of the influence of the oil’s formulation in the rolling bearing’s power loss after the calibration of the model is expected. 2
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The present work provides new knowledge about torque loss in different rolling bearings types lubricated with axle gear oils. Extensive tests were performed and a considerable amount of experimental results of power loss in rolling bearings, difficult to find in literature, were obtained. The model calibration allows a better understanding of the influence of the rolling bearing geometry and the oil’s formulation in the bearing’s power loss for different loads and speeds. The rolling bearing power loss model will be relevant for the global axle differential power loss model predictions. 2. Axle gear oils properties
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Five multigrade axle gear oils, available on the market and with large range of kinematic viscosity, were selected. All the lubricants are fully synthetic oils except for the 80W90-A product which is a semi synthetic oil. Three among them (75W90-A, 80W90-A and 75W140-A), are reference (A) oils and labelled as “Fuel Efficient”, and the other two products (75W85-B and 75W90-B) are candidate (B) oils, as presented in Table 1. Several experimental analyses were performed to characterize the chemical, physical, rheological and tribological properties of the selected axle oil formulations and the measured properties are displayed in Table 1. A detailed presentation of those analysis and properties measured can be found in [34]. 3. Materials and methods
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3.1. Rolling bearing assembly Rolling bearing tests were performed on a modified Four-Ball Machine where the four-ball arrangement was replaced by a rolling bearing assembly as shown in Figure 1. This assembly allows to test several rolling bearings and to obtain reliable friction torque measurements at different operating temperature. Additional details of this assembly can be found in [31]. The rolling bearing assembly is composed mainly of two parts. The first part is bearing lower race (3) which is fitted in the spacer (2) and this set is fitted on the bearing housing (1). These parts of the group (A) are tight clamped to ensure that there is no relative motion between them. The second part is the bearing upper race (5) is mounted on the shaft adapter (6). In operation, the load (P) is applied on the lower plate (13) and the rotational speed (n) is transmitted to the shaft adapter (6), which is connected to the drive shaft of the machine (see Figure 1). In order to measure the internal bearing torque, a piezoelectric torque cell KISTLER 9339A was used, ensuring high accuracy measurements (∓ 1 Nmm) even when the friction torque generated in the bearings was very low compared to the measurement range available. During the test, the temperature at different points is recorded. Five thermocouples (I-V) are positioned in strategic locations in order to measure the lubricant and bearing housing temperatures. This assembly is also monitored with two other thermocouples used to measure the temperatures of the room and of the air flowing around the bearing housing. The rolling bearing assembly is submitted to continuous forced air convection by two fans, having 38 mm in diameter and running at 2000 rpm, evacuating the heat generated during bearing operation. Also, to control the temperature during the tests, the bearing assembly is mounted with two heaters which are controlled with a PID control system with feedback given by thermocouple III (see Figure 2). The control system can assure a temperature variation always lower than ∓ 1 ◦ C. The rolling bearing assembly presented above is suitable for ball and roller bearings whose dimensions are limited by the bearing housing and the machine itself.
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Table 1. Axle gear oils properties. Unit
75W85-B
75W90-A
75W90-B
candidate
reference
candidate
reference
reference
Mineral
PAO
GL-4/GL-5 /MT-1
GL-5
97 936 1436 26947 23
33 1093 1686 22784 12
[-]
PAO
PAO
PAO
API/standard
[-]
-
GL-4/GL-5 /MT-1
-
[ppm] [ppm] [ppm] [ppm] [ppm] [ppm]
0 1795 6 783 2954 899
18 1087 1622 23262 7
81 2891 17 958 3271 1120
Physical properties Density @ 15 ◦ C Thermal expansion coefficient (αt × 10−4 ) Viscosity @ 40 ◦ C Viscosity @ 70 ◦ C Viscosity @ 100 ◦ C
[g/cm 3 ] [/] [cSt] [cSt] [cSt]
aA nA mA
[/] [/] [/]
s @ 0.2 GPa [35] t @ 0.2 GPa [35]
Tribofilm characterization C 1s Fe 2p O 1s Ca 2p Mg 1s P 2p S 2p Zn 2p3
0.861 -7.6
0.886 -7.7
0.885 -6.8
68.95 23.86 11.44
112.35 36.7 16.37
114.42 38.14 17.18
123.3 34.86 14.38
200.7 61.86 26.21
7.6655 2.9663
7.5833 2.9133
0.7 7.407 2.842
8.5027 3.2783
7.1537 2.7211
40.2
44.3
43.3
50.7
46.3
D
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VI
0.87 -7.3
[K −1 ]
28.5
31.3
30.9
34.8
33.2
[K −1 ]
21.1
23.1
22.9
25
24.7
[/] [/]
0.7382 0.1335
0.7382 0.1335
0.7382 0.1335
0.9904 0.139
0.7382 0.1335
[P a−1 ]
1.291
1.387
1.39
1.934
1.498
[P a−1 ]
1.128
1.194
1.2
1.623
1.28
[P a−1 ]
1.022
1.072
1.079
1.435
1.142
[/]
162
147
163
118
169
38.87 0.83 40.37 7.68 8.75 1.21 2.3
48.83 0.52 40.47 2.58 7.15 0.45 -
35.01 1.29 44.24 10.23 5.91 2.01 1.32
39.11 0.39 47.41 0.39 3.88 7.58 0.6 0.07
53.79 37.07 2.24 6.38 0.5 -
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Piezoviscosity @ 40 ◦ C (αGold ×10−8 ) [35] Piezoviscosity @ 70 ◦ C (αGold ×10−8 ) [35] Piezoviscosity @ 100 ◦ C (αGold ×10−8 ) [35]
[K −1 ]
75W140-A
0.853 -8.1
TE
Thermoviscosity @ 40 ◦ C (β×103 ) Thermoviscosity @ 70 ◦ C (β×103 ) Thermoviscosity @ 100 ◦ C (β×103 )
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Chemical composition Boron (B) Calcium (Ca) Magnesium (Mg) Phosphorus (P) Sulphur (S) Zinc (Zn)
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Base oil
80W90-A
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Parameter
[At [At [At [At [At [At [At [At
%] %] %] %] %] %] %] %]
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Figure 1. Schematic view of the rolling bearing assembly.
Figure 2. Rolling bearing housing with heaters controlled by a PID system.
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3.2. Rolling bearings tested A wide range of rolling bearing geometries might be used in axle differentials. Generally, the axle contains eight bearings. Two taper rolling bearings that support the input pinion and two more to support the hypoid gear wheel. The two half shafts are also supported by two rolling bearings. Given that, these outer bearings are physically remote from the main drive unit they are considered thermally distinct and their contribution was neglected [28]. The modified Four-Ball Machine permits the friction torque measurements with specific types of rolling bearings whose dimensions are limited by a maximum outer diameter of 56 mm and a maximum width of 16 mm. With such limitations, it is crucial to understand the behaviour of different rolling element bearings, understand the lubrication capabilities of different axle gear oils and try to reduce the power loss in rolling bearings, knowing the influence of several parameters such as speed, load, oil formulation and bearing geometry. The experimental tests were performed with three types of rolling bearing geometries, lubricated with the selected axle gear oils. The rolling bearings selected are the Thrust Ball Bearing (TBB, ref. 51107 SKF), the Cylindrical Roller Thrust Bearing (RTB, ref. 81107 SKF) and the Taper Roller Bearing (TRB, ref. 320/28 X/Q. SKF). The dimensions and characteristics of the selected geometries are reported in Figure 3 and Table 2.
(a) TBB 51107.
(b) RTB 81107 TN.
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Figure 3. TBB 51107, RTB 81107 TN and TRB 320/28 X/Q geometries.
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(c) TRB 320/28 X/Q.
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Table 2. Characteristics of TBB 51107, RTB 81107 TN and TRB 320/28 X/Q.
Thrust Ball Bearing TBB 51107
28 16
Dynamic C Static C0
kN kN
19.9 51
29 93
31.9 38
Reference speed Limiting speed
rpm rpm
5600 7500
2800 5600
9500 13000
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mm mm mm
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Speed ratings
35 12
Taper Roller Bearing TRB 320/28 X/Q
d H D
Principal dimensions
Basic load ratings
Roller Thrust Bearing RTB 81107 TN
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3.3. Operating conditions The oil level should reach the center of the lowest rolling element as indicated by the manufacturer [33] and the oil volume required is approximately 14 ml for TBB and RTB and 8 ml for TRB as indicted by Cousseau et al. [31]. A new rolling bearing is mounted for each oil test, in order to avoid the possible chemical interactions between oils and even to reduce the influence of the surface finish. The surface roughness of all rolling bearing raceways was measured, using an absolute stylus probe in a HommelWereke T4000 device. The measurements confirm that the surface roughness of all raceways tested with the different axle gear oils was very similar. The test machine allows a maximum inner raceway speed of 1500 rpm. However, above 1200 rpm all axle gear oils promote full-film lubrication regime. Once this condition is reached the EHL coefficient of friction is defined. Measurements above 1200 rpm will not provide additional data useful for the torque loss model of rolling bearings. For that, the tests were performed for different rotational speed between 75 and 1200 rpm, allowing to cover all lubrication regimes, from boundary to full-film lubrication. The friction torque was measured for different rotational speeds, in the range 75 up to 1200 rpm. This speed range is within the limits of the test machine, allowing to cover all lubrication regimes, from boundary to full-film lubrication. According to the axle lubricant temperatures measured during an EPA (Environmental Protection Agency) driving cycle including both city and highway cycles, the operating temperature of 70 ◦ C was selected [36]. All rolling bearings were submitted to an axial load of 7000 N, assuring a sufficiently high bearing rigidity [24, 26]. The characteristics of the contact between the rolling elements (ball or roller) and the raceway were displayed in Tables 3 and 4 for TBB 51107 and RTB 81107, respectively. For TBB and RTB the normal load is equal to the applied axial load.
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Table 3. Ball-raceway contact parameters for TBB 51107 rolling bearing.
Unit
Axial load a Ac p0 δ
∞ 3×10−3 −3 -3.38×10 3×10−3 −3 6×10 53.4×10−3 0.18
[N]
4000
7000
[µm] [mm2 ] [GPa] [µm]
102.8 0.14 2.06 5.22
123 0.198 2.47 7.48
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[m] [m] [m] [m] [µm]
Ball
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RXi RY i RX RY σc
Raceway
RXi RX l σc
Raceway
Roller
[m] [m] [m] [µm]
∞
[N]
4000
7000
[µm] [mm2 ] [GPa]
33.22 0.332 0.766
43.5 0.435 1.004
2.5×10−3 5×10−3 5×10−3 0.14
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a Ac p0
Unit
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Axial load
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Table 4. Roller-raceway contact parameters for RTB 81107 TN rolling bearing.
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3.4. Test procedure Before starting each test, a running-in period is always required for each rolling bearing and is carried under an axial load of 1000 N and increasing rotational speed from 75 to 1200 rpm during 10 minutes. For each test with the selected rolling bearing, the axial load is applied and the rotational speed set to the required value and the operating temperature is imposed. When the machine reaches the stabilized temperature (thermal equilibrium) due to the heaters, four friction torque measurements were performed. Three values were kept and the most dispersed one was disregarded. The torque measurement should be made in short periods of time (120 s) at stabilized temperatures (±2 ◦ C) in order to avoid the drift effect of the torque cell [31]. Measurements during longer periods (above 120 s) show a decay of the applied torque due to temperature gradients and are intrinsic to piezo-electric torque cells. So, the friction torque value (for each rotational speed and load) is the average value of the three closest measurements.
3.5. Taper Rolling Bearings - Assembly, operating conditions and test procedure Several modifications were introduced into the test assembly, the operating conditions and the test procedure in order to measure the internal friction torque in Taper Rolling Bearings (TRB). A different shaft adapter (see Figure 4), minimizing the misalignment of the TRB, and a lower race support were manufactured. Instead of a cone Morse connection, the superior part of the shaft adapter is a hollow shaft design to assemble on the machine input shaft. Furthermore, both pieces have a hole across their sections and perpendicular to their rotational axles with a screw applied to prevent the sliding effect among the two parts. 8
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Figure 4. Schematic view of the TRB assembly.
Table 5. Roller-raceway contact parameters for TRB 320/28 X/Q rolling bearing.
Unit
[m] [m] [m] [µm]
17.26×10 2.95×10−3 5.9×10−3 12.16×10−3 0.25
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Axial load [N]
[µm] [mm2 ] [GPa]
4000
7000
41.79 1.016 0.957
55.28 1.345 1.266
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a Ac p0
Roller
−3
D
RXi RX l σc
Raceway
where
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Fa / sin(ψ) z
(1)
e (2) 1.5 It was necessary to take into account that tapered roller bearings should have a long running-in period, which is characterized by a significant amount of friction between the rolling elements and the raceways, and it can be identified by the temperature spike shown in Figure 6. After reaching the maximum operating temperature, a gradual decrease of the temperature is observed until a stabilized value is achieved. The time necessary to reach the stabilization temperature depends on the lubricant formulation and, consequently, the running-in time is not pre-defined. Instead, the running-in period is complete when the temperature variation is lower than 1 ◦ C per hour. ψ = arctan
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Figure 5. Simplified inter geometry for TRB [37].
75
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70 65 60
50
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θ [ºC]
55
45 40 35 30 25
0
2
4
6
8
10
12
14
t [hours]
Figure 6. Temperature variation (θ) of tapered roller bearings during the running-in period (t).
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4. Film thickness inside rolling bearings
Λ=
h0c σc
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The film thickness (h0 ) of the rolling element/raceway contact is calculated using the Hamrock and Dowson [38] equation (see Appendix A) for elliptical contacts (TBB) and Dowson and Higginson [39] equation (see Appendix B) for line contacts (RTB and TRB). The corrected film thickness (h0C ) is given in Equation (A.6) which is the product of the central film thickness with the thermal correction factor (φT ), as shown in Equation (A.7). The concept of specific film thickness (Λ) is usually used to determine the lubrication regime. The specific film thickness is calculated with Equation (3). (3)
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ν ν1
(5)
This parameter depends essentially on the mean diameter dm of the rolling bearing without selecting the type of rolling bearing. For that reason, the viscosity ratio can be related to the specific film thickness, as it is shown in Equation (6).
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k∼ = Λ1.3
(6)
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Figure 7 (a) presents the viscosity ratio, calculated using the SKF catalogue [33], for TBB under constant temperature of 70 ◦ C and a load of 7000 N. Using this concept it is possible to observe that the viscosity ratio increases when the speed increases. The five axle oils are classified according to their viscosity at the operating temperature. The 75W140-A oil has the highest viscosity generating the highest viscosity ratio while 75W85-B oil has the lowest viscosity and promotes the lowest viscosity ratio. The viscosity ratio values of oils 75W90-B, 75W90-A and 80W90-A are placed between the previous two, depending directly on their viscosity. In general [33], a rolling bearing operates under boundary film regime for a viscosity ratio 0.4 < k < 1, under mixed-film lubrication regime for 1.0 < k < 2.0 and under full-film lubrication regime for 2.0 < k < 4.0. From 75 rpm up-to 1200 rpm, and for all axle gear oil formulations, boundary and mixed-film lubrication are the dominant lubrication regimes. At 1200 rpm full-film lubrication regime is achieved for all lubricants except for the 75W85-B oil. Figure 7 (b) shows the variation of viscosity ratio in roller-raceway contact of RTB with the rotational speed under the applied loads of 7000 N and at 70 ◦ C. It is possible to observe that the viscosity ratio increases when the speed increases up to 600 rpm. Axle gear oils share a similar behaviour as TBB tests for the speed range before 600 rpm since the temperature is maintained constant. The 75W85-B oil with the lowest viscosity and piezo-viscosity had an opposite behaviour of the 75W140-A oil, promoting the lowest viscosity ratio. The viscosity ratio values of oils 75W90-B, 75W90-A and 80W90-A are placed between the previous two, depending directly on their kinematic viscosity (see Table 1).
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Figure 7 (c) displays the viscosity ratio values for TRB under the same operating conditions. It was observed that the lubricants were ranked with a similar trend as the viscosity ratio values in TBB tests. Generally, the viscosity ratio values in TRB are slightly lower than the viscosity ratio values in TBB. For the given range of rotational speeds and for all the axle oil formulations, boundary and mixed film lubrication are the dominant lubrication regimes (k ≤ 2), except at 1200 rpm.
2.5
3.5 2 3
1.5
2
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k [-]
k [-]
2.5
1
1.5 1
0
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0.5 0.5
0
0
200
400
600
800
1000
1200
n [rpm]
(a) TBB.
4 3.5
1400
0
200
400
600
800
1000
1200
1400
n [rpm]
(b) RTB.
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3
k [-]
2.5
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2
1.5
1
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0.5
0
200
400
600
800
1000
1200
1400
n [rpm]
(c) TRB.
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Figure 7. Viscosity ratio for TBB, RTB and TRB under 70 ◦ C and 7000 N operating conditions.
5. Friction torque model In order to understand the experimental results as well as to predict the power loss in rolling bearings lubricated with axle gear oils, a friction torque model is required. For that SKF proposed a detailed model [33] which divides the total friction torque in its true physical components. It takes into account four different torque losses as shown in the following equation: 12
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0 Mt = Mrr + Msl + Mseal + Mdrag
(7)
TBB 51107
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Since the rolling bearings tested do not have seals, the Mseal component was disregarded in the calculation. The drag losses are very small because the operating speeds and the mean diameter of the rolling bearings are also small (dm = 43.5 mm for TBB and RTB), consequently, the drag torque loss term was also disregarded. Figure 8 presents the usual drag torque loss for two different rolling bearings, respectively TBB 51107 and RTB 81107. The results show that the drag torque losses are negligible for these rolling bearings, when compared with the other torque loss mechanisms. RTB 81107
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Mdrag[Nmm]
80
50 40 30 20 10 0 0
200
400
600
800
1000
1200
1400
D
n [rpm]
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Figure 8. Drag losses for different rolling bearing geometries TBB 51107 and RTB 81107 under lubricated with 75W90-A at 70 ◦ C.
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Therefore, the total friction torque of the rolling bearings had only two contributions: the rolling and 0 and Msl , as presented in the following equation: sliding torques, respectively, Mrr 0 Mt = Mrr + Msl
(8)
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Assuming that the friction torque obtained from experimental measurements was equal to the total torque loss predicted by the SKF model (Mt = Mtexp ) and the rolling torque was accurately calculated, the sliding torque can be directly determined (see Equation (9)). 0 0 Msl = Mt − Mrr = Mtexp − Mrr
(9)
All the following Equations (10)-(15) are necessary to calculate the rolling and sliding torques. 0 Mrr = φish · φrs · [Grr · (n · υ)0.6 ]
φish =
1 1 + 1.84 · 10−9 · (n · dm )1.28 · ν 0.64
φrs =
1 p
Krs ·ν·n·(d+D)·
e
Msl = Gsl · µsl 13
Kz 2·(D−d)
(10) (11) (12) (13)
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µsl = φbl · µbl + (1 − φbl ) · µEHL φbl =
(14)
1
(15)
e2.6·10−8 ·(n·ν)1.4 ·dm
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The equations related to the geometry of each rolling bearings used are presented in Appendix C.
0 Msl M exp − Mrr = t Gsl Gsl
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The rolling torque (Equation (10)) depends on the bearing type, rotational speed, oil viscosity and two factors, namely the inlet shear heating φish , and the kinematic replenishment reduction factor φrs . The sliding torque (Equation (13)) was highly influenced by the bearing type, the coefficient of friction and the lubrication regime. The lubrication regime on the model is quantified by the φbl quantity where the coefficient of friction under full film (µEHL ) and boundary (µbl ) lubrication were presented. Knowing the value of the sliding friction torque determined using Equation (13), it is possible to calculate the sliding coefficient of friction using Equation (16). The sliding coefficient of friction (µexp ) is now sl considered as an experimental coefficient of friction determined through rolling bearing tests.
Furthermore, the sliding coefficient of friction can be effectively predicted by this model using Equation (14) once the boundary film coefficient of friction-µbl and the full-film coefficient of friction-µEHL values are known. The coefficients of friction µbl and µEHL are calculated minimizing the difference between µsl and µexp sl through Equations (14) and (16). 6. Experimental and model results
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6.1. Thrust ball bearings experimental results (TBB 51107) The tests of TBB lubricated with axle oils were carried out under a constant temperature of 70 ◦ C and an axial load of 7000 N. Figure 9 (a) shows that, in general, the measured total friction torque of the TBB decreases when the operating speed increases from 75 rpm to 1200 rpm, except in the case of oil 75W140-A, for which the friction torque increased as the speed increases. It is clear that, for low rotational speeds, the two candidate (B) oils generated higher values of the total friction torque than the reference (A) oils (see Figure 9 (a)) due to the significant differences between them in terms of the additive packages present in their formulations.
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Figure 9 (b) shows that when the speed increased the specific film thickness inside the TBB increased from 0.22/0.46 up to 1.30/2.75, depending on the tested oil, meaning that boundary and mixed lubrication regimes prevail under these operating conditions as indicated by Figure 9 (f) as well. The results of the rolling friction torque inside the thrust ball bearing are displayed in Figure 9 (c). As 0 expected, at constant temperature (70 ◦ C) the rolling torque increases when the speed increases (Mrr ∝(n · 0.6 υ) ). Comparing the behaviour of the different oil formulations, the 75W140-A oil, with the highest operating viscosity, generated the highest rolling torques, while 75W85-B oil, with the lowest viscosity, generated the lowest rolling torques. The rolling torques of the other three oil formulations follow the trend of their viscosities. So the main parameter that differentiates the lubricants in the calculation of the rolling torque is the viscosity at the operating temperature. As expected the sliding torque, presented in Figure 9 (d), was higher than the rolling torque, presented in Figure 9 (c). The sliding torque curves present the same trend of the total friction torque curves.
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In fact, under constant operating temperature, the film thickness increases as the operating speed increases, the specific film thickness also increases thus generating lower sliding torque loss, as shown in Figure 9 (b). In a real application, without temperature control, when the speed increases the temperature also increases. Higher speeds promote higher film thickness and lower torque loss, while higher temperature promotes a reduction of oil viscosity, and consequently a decrease of film thickness and an increase on sliding torque loss. However, a real application under full-film lubrication and without temperature control tends to reach a constant specific film thickness no matter the rotational speed [40]. These counter effects are in general in favour of speed increase up to a certain thermal limit, above which, there will be no benefits in increasing the operating speed. This is well demonstrated by the inlet shear heating effect on film thickness. The experimental sliding torques can be used to determine the experimental sliding coefficient of friction, using Equation (16), as presented in Figure 9 (e). The sliding coefficient of friction µsl follows the trend of the sliding torque.
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Figure 9 (f) shows the weighting factor φbl , which is always between 0 and 1. This parameter decreases when the speed increases. The 75W85-B presents the highest values while the 75W140-A presents the lowest values. Other formulations have values in between. The weighting factor is inversely proportional to the viscosity of the lubricant, explaining this behaviour. The weighting factor presents a direct influence on the sliding coefficient of friction µsl presented in Figure 9 (e). It should also be noticed that the values of φbl for each oil formulation almost cover the whole range of values (0≤φbl ≤1), meaning that the operating conditions represent all the lubrication regimes, from boundary to full-film lubrication.
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6.2. Cylindrical roller thrust bearings experimental results (RTB 81107) The experimental tests with cylindrical roller thrust bearings, lubricated with axle gear oils, were carried out under the same constant operating temperature (70 ◦ C) and a high axial load (7000 N). However, it was not possible to keep a constant operating temperature of 70 ◦ C above 600 rpm, as shown in Figure 10. In those cases, it was necessary to cool the bearing housing, and that was not achieved. At 1200 rpm, the maximum temperature reached 135 ◦ C with 75W90-A oil. Figure 11 (a) displays the total friction torque measured for RTB in all operating conditions. The total friction torque decreases with increasing speed, up to 600 rpm and T =70 ◦ C. Above 600 rpm, it is interesting to notice that the reference (A) oils generated significantly higher operating temperatures than the candidate (B) oils, whose operating temperature remained constant (70 ◦ C) at 900 rpm and reached 85 ◦ C at 1200 rpm. Up to 600 rpm, 80W90-A oil generally produced the lowest values of the total friction torque while 75W90-A oil usually generated the highest corresponding values. Oils 75W140-A, 75W85-B and 75W90B presented intermediate values. Above 600 rpm the candidate (B) oils generated the lowest friction torques. Figure 11 (b) shows that when the operating speed increases from 75 rpm to 600 rpm the specific film thickness inside the RTB increases from 0.21-0.45 up to 0.87-1.81, meaning that mixed film lubrication prevails. All axle gear oils share the same trend, where 75W140-A oil produced the highest Λ because of its high viscosity at 70 ◦ C and 75W85-B oil generated the lowest Λ because of its low viscosity. Above 600 rpm the specific film thickness is not constant and strongly dependent on the test temperature. The rolling torque calculated for RTB under the operating conditions is presented in Figure 11 (c). It is observed that when the speed increases the rolling torque increases. This figure also shows that oils 75W90-B, 75W90-A and 80W90-A generated very similar rolling torques, because they have similar viscosities at 70 ◦ C. Equation (9) was used to obtain the sliding friction torque (see Figure 11 (d)). This figure shows that the sliding torque decreases with the increase of speed for all operating conditions. The lubricant behaviour presents the same trend of their total friction torque. However, it is not possible to compare the sliding 15
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Figure 9. Results of TBB 51107 lubricated with axle gear oils at constant temperature of 70 ◦ C under an axial load of 7000 N.
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6.3. Comparison between TBB and RTB It is interesting to compare the friction behaviours of the TBB and RTB rolling bearings. Under constant temperature (70 ◦ C) and constant load (7000 N), the total friction torque decreases when the speed increases, both for TBB and RTB. However, the maximum torques measured for each type of bearing at 75 rpm are 370 N.mm and 1060 N.mm for TBB and RTB, respectively, showing the major role and influence of the rolling bearing type and geometry on the total friction torque Mt . When the speed increases, the rolling torque, Mrr , shows a small increase in the case of TBB and a large increase in the case of RTB (see Figures 9 (c) and 11 (c)). The maximum rolling torques calculated for each type of bearing are 92 N.mm for TBB and 142 N.mm for RTB, showing again the influence of the rolling bearing geometry on the rolling torque. The reduction of the sliding torque, Msl , with increasing speeds, is much more significant in a RTB than in a TBB, as may be noticed comparing Figures 9 (d) and 11 (d). These differences in the internal friction torque (Mt , Mrr and Msl ) between TBB and RTB are related to the geometry of the contact area, an elliptical contact in the case of TBB and a line (rectangular) contact in the case of the RTB, and to the sliding speed inside the contact, which is higher in the case of the RTB. These differences are reflected also on the values of Grr and Gsl ), which are significantly higher in the case of RTB. As mentioned in section 5, the minimization of the difference between experimental and model values of the sliding coefficient of friction allows the calculation of the µbl and µEHL values. In this case, the values of µbl and µEHL were determined for each type of rolling bearing (TBB and RTB) and for each type of axle gear oil formulation according to three groups (group I: 75W85-B and 75W90-B, group II: 75W90-A and 80W90-A and group III: 75W140-A), as presented in Table 6. 17
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Figure 11. Results of RTB 81107 lubricated with axle gear oils at constant temperature of 70 ◦ C with an axial load of 7000 N.
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The boundary coefficient of friction, µbl , depends on the gear oil formulation and rolling bearing type, as shown in Table 6. For all the lubricant formulations (A and B), the boundary coefficient of friction µTblBB B is larger than µRT . In the case of the TBB, µbl for the candidate (B) oils reached a high value (µTblBB bl = 0.124), meaning that the formulations containing Zinc generate very high sliding torque under boundary film lubrication. This behaviour was not observed with RTB. The full-film coefficient of friction, µEHL , also depends on the gear oil formulation and rolling bearing type. The reference and the candidate oils have similar behaviours when lubricating the two rolling bearing BB B types (µTEHL > µRT EHL ). In general, the candidate (B) oils, which have lower viscosities also generated lower µEHL coefficients. The Stribeck curves of the five axle gear oils lubricating the two rolling bearing types are presented in Figures 12 and 13, for TBB and RTB, respectively. Those figures present the experimental results with the error bar for each value shown with markers and the model simulations shown by the continuous lines, in function of the modified Hersey parameter Sp = U r · η · α0.5 · F n−0.5 .
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In general, the approximation of the sliding coefficient of friction µsl , predicted by the model, is quite good, whatever the axle gear oil formulation and rolling bearing type. It is also clear that there is a better approximation at high speeds and high viscosities (larger values of Sp). At low speed, under boundary film lubrication conditions, the scatter of the µsl values is larger.
Table 6. Values of the coefficients µbl and µEHL for TBB 51107 and RTB 81107, under 7 kN and at 70 ◦ C.
Valid for 3262.5 < n · dm < 52200 Bearing type Lubricant Parameter TBB RTB µbl 0.124 0.073 75W85-B and 75W90-B µEHL 0.056 0.032 µbl 0.097 0.071 75W90-A and 80W90-A µEHL 0.064 0.036 µbl 0.078 0.073 75W140-A µEHL 0.063 0.040 19
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6.4. Tapered roller bearings experimental results (TRB 320/28 X/Q) The results of the total friction torque measurements carried out on TRB, under a 7 kN axial load and at 70 ◦ C, are presented in Figure 14. Mt decreases with the increase of the rotational speed, while the corresponding specific film thickness increased from 0.22-0.45 up to 1.29-2.46, that is from boundary film lubrication up to mixed film lubrication, (see Figure 14 (b)).
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