Wang Yanshuang; Cheng Junwei; Cai Yujun

(1. Tianjin University of Technology and Education, Tianjin 300222; 2. School of Mechatronics Engineering, Henan University of Science and Technology, Luoyang 471003)

Study on Low-Temperature Traction Behavior of a Space Lubricating Oil No. 4116

Wang Yanshuang1,2; Cheng Junwei2; Cai Yujun1

(1. Tianjin University of Technology and Education, Tianjin 300222; 2. School of Mechatronics Engineering, Henan University of Science and Technology, Luoyang 471003)

The traction behavior of space lubricating oil No. 4116 was measured and analyzed at various oil inlet temperatures below 0 ℃ and various rolling speeds under normal loads by a test rig simulating the operating conditions of space bearings. A traction coefficient calculation model was presented. The rheological property and rheological parameters of the lubricant at a low oil inlet temperature were analyzed based on the Tevaarwerk-Johnson model. The results showed that the lubricating oil No. 4116 was sensitive to the rolling speed and had lower sensitivity to the normal load. This lubricating oil is more suitable for applications under high speed when it is used below 0 ℃. It behaves as an elastic-plastic fluid operating below 0 ℃. Both the average limiting shear stress and the average elastic shear modulus have a negative correlation with the rolling speed and oil inlet temperature and have a positive correlation with the normal load.

space bearing; space lubricating oil; traction behavior; low temperature; rheological property

1 Introduction

In the space technology, rolling bearings are widely used in many important rotating systems of spacecrafts. The statistical data from abroad show that poor lubrication can lead to galling of bearings that can cause the failure of spacecrafts. The traction behavior (also called the friction behavior) of lubricating oil film is a key parameter determining the lubrication property. It is also one of the basic parameters in rolling bearing design.

When a lubricated rolling bearing is operating, an elastohydrodynamic (EHD) film is developed. Because of the complex physical, chemical and rheological properties of the EHD film, the theoretic computation error has been significant for the traction force up to now. Therefore, the simulation experiments for traction behavior have been adopted widely all over the world. Over the years, the traction behavior of EHD lubrication film has been studied by many scholars at home and abroad[1-4]. Yang Boyuan measured the traction force of lubricating greases No. 7007 and No. 7008 at high speed[5]. Wang Yanshuang analyzed the traction characteristics of an aviation lubricating oil HKD at high temperature[6-7]. Quinchia L. A., et al. investigated the low-temperature flow behaviors of vegetable oils[8], which did not involve the traction properties of lubricants. The differences in traction behavior between the lubricating oil and grease were studied by Yamanak[9]. However, the above experimental researches were performed at room or high temperature and low speed. Till now the research on the traction behavior of space lubricating oil at low temperature has not been reported in any literature.

In this paper, the traction behavior of a domestic space lubricating oil was measured by a ball-disc test rig at low temperature and under various normal loads and rolling speeds. A model for calculating the low-temperature traction coefficient was presented. The rheological parameters and the rheological property of the lubricating oil were also analyzed. The research results have great significance to the design of rolling bearings, while laying the foundations for the further development on the rheology of lubricants.

2 Traction Test

2.1 The lubricating oil 4116 studied

The base oil for formulating the lubricating oil No. 4116is a chlorophenyl silicone oil. It is a kind of high and low temperature instrument oil, which has a good viscositytemperature property with low evaporation rate and high flash point. It has a good flow property even at -50 ℃. It is a popular lubricant used in high speed micro-motor bearings, low speed swing bearings and speed reducing gears. Its characteristic parameters are shown below:

Table 1 Parameters of lubricating oil No. 4116

2.2 Test rig and its working principle

The traction experiment was carried out on an improved ball-disc test rig, as shown in Figure 1. A new lowtemperature assembly was used to measure the traction characteristics of the lubricating oil at temperatures below 0 ℃. The working principle of the test rig is as follows: Firstly, the low temperature assembly is started to make the refrigerant Freon flow into the evaporator which is immersed in an alcohol bath. The temperature of the alcohol bath can be decreased via heat exchange between the alcohol and the refrigerant Freon. The lubricating oil to be tested is pumped into the oil pipe which is spiraled into the alcohol bath. The heat of the lubricating oil can be absorbed by the cold alcohol, resulting in a reduction in the temperature of the lubricating oil. The electric whisk is used to churn the alcohol to obtain the uniform temperature distribution in the alcohol bath. The low-temperature lubricating oil forms an oil jet at the end of the oil pipe. A temperature sensor is set up on the oil jet to transmit the oil temperature signal to a PID controller. The oil temperature signal is compared to the set value of the temperature by the PID temperature controller, which decides the on-off time of the heating rod immersed in the alcohol bath. The lubricating oil, the temperature of which has attained the set value T, is fed continually into the contact zone by the oil jet. The ball and the disc specimens are driven by the horizontal motor spindle I and the vertical motor spindle II, respectively, which are controlled by two frequency transformers. A hydrostatic shaft, which supports the motor spindle I, moves upward until the ball comes into contact with the disc, and then a normal load W is applied between them. The load is measured by a load sensor fixed under the hydrostatic shaft. The rolling speed of the ball and disc U = (U1+ U2)/2 droves the lubricant into the contact zone to develop a film with a certain thickness, where U1and U2are the linear velocities for the surfaces of ball and disc specimens, respectively. The sliding velocity ΔU=U2-U1, which is derived by adjusting the rotating speeds of motor spindle I and motor spindle II, sheers this oil film, resulting in a traction force. The traction force causes the ball together with motor spindle I to deflect around the axis of the hydrostatic shaft to oppress a traction sensor mounted on the machine frame so that the traction force can be picked up. Thus the traction force F can be measured at various slide-to-roll ratiosS=ΔU/U, and consequently, the curves describing the traction behavior of the lubricating oil can be obtained in the form of the traction coefficient μ=F/W against the slide-to-roll ratio S under various operating conditions.

Figure 1 Test rig

The ball and disc specimens were made of GCr15 steel, and they were ground and polished to give a surface roughness σ of less than 0.02 μm. The minimum film thickness hminworked out by the Hamrock-Dowson formula is more than 0.1 μm under all operating conditions. Then the roughness parameter λ=hmin/σ>5, while the surface roughness has no contribution to the traction force between the ball and the disc.

2.3 Operating conditions

The operating conditions simulated by the test rig are shown below:

Rolling speed U: 3 m/s, 5 m/s, 7 m/s, 9 m/s, 15 m/s, and 20 m/s;

Normal load W: 40N, 69N, 98N, and 135N;

Maximum Hertz contact pressure P0: 1.0 GPa, 1.2 GPa, 1.35 GPa, and 1.5 GPa;

Oil inlet temperature T: 0 ℃, -10 ℃, and -20 ℃;

Slide-to-roll ratio S: 0—0.2.

2.4 Test results and analysis

A total of 72 curves of the space lubricating oil No. 4116 describing the traction coefficient μ versus the slide-toroll ratio S were obtained. Several representative traction curves are plotted in Figs. 2—4, where the points represent the experimental data.

Figure 2 Variation in traction coefficient versus slide-toroll ratio at different oil inlet temperatures

Figure 3 Variation in traction coefficient versus slide-toroll ratio at different rolling speeds

Figure 4 Variation in traction coefficient versus slide-toroll ratio at different maximum Hertz contact pressures

The apparently similar characteristics of the traction curves can be observed from Figs. 2 to 4. Namely, at low slide-to-roll ratio, the traction coefficient increases approximately linearly. However, a continuous increase in the slide-to-roll ratio can give rise to a nonlinear increase in traction coefficient. After reaching a maximum value of traction coefficient, it remains constant with a further increase in slide-to-roll ratio.

It can be seen from Figure 2 that a traction coefficient gradually increases with the decrease in the oil inlet temperature under a constant normal load and rolling speed. The increase in the amplitude of the traction coefficient when the oil inlet temperature decreases from 0 ℃ to -10 ℃ is smaller than the case with oil temperature decreasing from -10 ℃ to -20 ℃. This can be explained by the reason that the lower the temperature is, the worse the viscosity-temperature property would be.

Figure 3 suggests that when the oil inlet temperature andnormal load remain constant, the higher the rolling speed is, the smaller the traction coefficient would be. The rolling speed that exceeds 15 m/s has a significant impact on the traction coefficient. Therefore the lubricating oil No. 4116 is sensitive to the rolling speed, since it is more suitable for operating at high speed when it is used below 0 ℃. The variation in the traction coefficient versus the maximum Hertz contact pressure is shown in Figure 4. The increase in the Hertz contact pressure or the normal load gives rise to an increasing traction coefficient. The lubricating oil No. 4116 shows a lower sensitivity to the normal load when the load increases.

3 Model for Calculation of Traction Coefficient

On the basis of the low temperature traction curves, the relationship of the traction coefficient μ and the slide-toroll ratio S can be described by

where A, B, and C are parameters varying according to the normal load, rolling speed and inlet oil temperature. For the purpose of convenience in application, the normal load, the rolling speed and the inlet oil temperature can be non-dimensionalized as follows:

Then the coefficients A, B and C can be expressed by the following equations:

Formulae (5)—(7) may be transformed into linear equations by taking logarithm on both sides. The values of coefficients A0~A3, B0~B3and C0~C3can be obtained by multiple linear regression analysis as shown in Table 2. Then the formula for calculating the traction coefficient of lubricating oil No. 4116 at low temperature is obtained:

The correlation coefficients are all greater than 0.9 as shown in Table 2. It suggests that it is feasible to adopt the equations (5)—(7). It can be seen from Figs. 2 to 4 that a good agreement exists between the experimental traction coefficient and the traction coefficient computed by the above model. It is illustrated that the low temperature traction coefficient model which is established in this article is accurate and available.

Table 2 Regression values of the parameters A, B and C

4 Rheological Property

4.1 Rheological model

Although the formula (8) for calculating the traction coefficient of lubricating oil No. 4116 can be conveniently used to compute the traction coefficient under each operating condition of space bearings at low temperature, there is no parameter in formula (8) which can illustrate the microscopic essence of the traction behavior. The traction behavior is governed by the rheological property of the lubricant in the contact zone, which may be illustrated by a rheological model or a constitutive model. The rheological model may relate the shear stress τ developed in the lubricant film to the shear strain rate γwhich is imposed on the elements of the fluid by the action of slidingbetween the ball and the disc specimens.

The lubricating oil No. 4116 behaves as a linear elastic fluid or a linear viscous fluid at small slide-to-roll ratios depending on the Deborah number D=ηU/Ga, where η is the dynamic viscosity at the contact pressure, G is the elastic shear modulus of the lubricant and a is the radius of the contact circle. Each computed Deborah number for the lubricating oil No. 4116 under all operating conditions in this paper is larger than 20. It suggests that the lubricating oil No. 4116 behaves as a linear elastic fluid at small slide-to-roll ratios. The Tevaarwerk-Johnson elasticplastic rheological model may describe the rheological property that the lubricant behaves as linear elastic fluid until the shear stress arrives at the limiting shear strength and then undergoes plastic change. The lubricating oil No. 4116 has the similar rheological property as shown in Figs. 2—4, which can be illustrated by the Tevaarwerk-Johnson elastic-plastic rheological model.

In general the shear stress components in the coordinate directions, denoted as τxand τy, satisfy the following pair of coupled differential equations:

where ΔU is the sliding speed in the rolling direction x, ΔV is the lateral sliding speed in the y direction which is transverse to the rolling direction, h is the film thickness of lubricant, ω is the ball spin velocity, and X=x/a is the dimensionless coordinate in the rolling direction. The elastic shear modulus G is assumed to be constant at its average value

In equation (9), the local equivalent shear stress is:

when τe<τc, F(τe)=0; and when

where τcis the limiting shear strength.

Tevaarwerk and Johnson assumed that τcis proportional to the local Hertz pressure written as the following equation:

where τcis the average limiting shear stress.

The isothermal film thickness hisocan be computed by the central film thickness at the point contact proposed by Hamrock and Downson.

In our test rig, the rigid traction measurement system was made to eliminate the lateral sliding and spin as shown in literature[10]. So only the shear component in the rolling direction x is considered. The shear stress can be obtained by integrating the formula (9), and the traction force by integrating the shear stress in the contact circle is then expressed in the following form as:

4.2 R heological parameters

In terms of a traction curve in which the traction coefficient μ=F/W is proportional to the slide-to-roll ratio S=ΔU/U for small values of S, this equation becomes

where m is the slope of the traction curve. For small values of S, F(τe)=0, and upon integrating the formula (9a) to get the shear stress, followed by integrating the shear stress all over the contact circle, the traction force reduces to

Based on the equations (16) and (17), the mean shear modulus takes the form of

One may solve the mean shear modulus G using equation (18) by measuring the slope m at low slide-to-roll ratios on a test traction curve.

For large values of S, the shear stress approaches the lim-iting shear stress and F approaches the maximum value

The maximum traction coefficient is then

The maximum traction coefficient may be obtained by experimental measurement, so one may solveby means of the following equation:

It is found out that both Gandincrease with an increasing normal load, and decrease with an increasing rolling speed and inlet oil temperature. The average elastic shear modulus and the average limiting shear stress may be expressed as the following forms by three dimensionless parameters referred to in Eqs. (2)—(4).

5 Conclusions

Based on the improved ball-disc test rig with a new low temperature assembly, the traction characteristics of the lubricating oil No. 4116 have been measured successfully at temperatures below 0 ℃.

The traction coefficient of lubricating oil No. 4116 increases with a decreasing oil inlet temperature and rolling speed, and it increases with an increasing normal load. The lower the temperature decrease is, the bigger the increasing amplitude of the traction coefficient would be. The lubricating oil No. 4116 is sensitive to the rolling speed and shows lower sensitivity to the normal load. It is more suitable for high speed operation when it is used below 0 ℃.

A new low-temperature traction coefficient model for lubricating oil No. 4116 has been established, and the correlation coefficient is not less than 0.9.

The lubricating oil No. 4116 behaves as a linear elastic fluid until the shear stress reaches a limiting shear strength and then undergoes a plastic change at low temperature. Increasing rolling speed, increasing inlet oil temperature and decreasing normal load may result in lower average elastic shear modulus G and average limiting shear stressthe computed formulae of which have been presented in this paper.

Acknowledgements: This research is supported by the National Science Foundation of China (Nos. 51105131 and 51475143), the Henan Provincial Key Scientific and Technological Project (No. 142102210110) and the Tianjin Science and Technology Support Program.

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date: 2015-01-06; Accepted date: 2015-04-09.

Wang Yanshuang, E-mail: hkd_wang_ yan_shuang@126.com.