 Open Access
 Authors : Lijun Yang , Yanshuang Wang , Erqiang Wang , Feilang Ning
 Paper ID : IJERTV9IS060883
 Volume & Issue : Volume 09, Issue 06 (June 2020)
 Published (First Online): 08072020
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Study on the Relationship Between Kinematic Viscosity, Density and Temperature of Lubricating Oil PAO
1Lijun Yang,2Yanshuang Wang,3Erqiang Wang,4Feilang Ning
1234Mechanical Manufacture and Automation 1234Tianjin University of Technology & Education 1234Tianjin, China
AbstractUsing the oil products kinematic viscosity tester and petroleum products density tester the kinematic viscosities and densities of five PAO oils with different initial viscosity were
measured in the range of 30Â°C~110Â°C. The relationship between viscosity, density and temperature of PAO oil was analyzed. The relation on viscositydensitytemperature of PAO oil was established. The results show that the viscosity and density of PAO lubricating oil decrease with the increase of temperature, and the higher the density of PAO oil, the higher the kinematic viscosity of PAO. The newly established viscositydensity temperature formula can better describe the relationship between viscosity, density and temperature of PAO oil in the range of 30Â°C110Â°C. This formula can be used to predict the viscosity of PAO oil in a certain range of temperature.
Keywords:PAO; kinematic viscosity; density; temperature

INTRODUCTION
PAO oil is widely used in all fields of industry because introduces an applied research method for viscosity conversion of lubricating oil at different temperatures, which can realize the rapid calculation of viscosity index of oil with pour point greater than 50Â°C[7].
Abroad, the Soviet union scholars .. studied the influence of viscositytemperature characteristics of lubricating oil on power loss of automobile transmission system[8].Seeton C J studied the relationship between fluid viscosity and temperature[9].D.Knezevic proposed a mathematical model for the dynamic viscosity of mineral oil in a hydraulic system, varying with temperature and pressure[10].Bair S studied the variation of the viscosity of various lubricating oils with temperature and pressure[11].
At present, the research on lubricating oil viscosity mainly focuses on the influence factors of lubricating oil viscosity, as well as the empirical formulas of temperature viscosity, temperaturedensity, temperature pressure viscosity.The relationship between viscositydensity temperature of lubricating oil has not been studied.In this paper, the viscosity and density of PAO oil and the relationship between viscosity and temperature are studied. The viscositydensitytemperature model of PAO aviation lubricating oil was established.
of its comprehensive high quality performance. As a quality index of lubricating oil, viscosity has influences on oil film thickness, bearing capacity, mechanical efficiency and friction heat generation, etc, and has become an important factor affecting the service life of equipment. Therefore, it is of great significance to study the viscosity of lubricating oil.
Domestic scholars have conducted many researches on the viscosity of lubricating oil[13].Li Xinghu analyzed the effects of temperature and pressure, molecular weight and molecular structure on viscosity of lubricating oil[4].Li Yong analyzed the influence of constant bath temperature, viscometer viscosity constant, viscometer cleanliness, viscometer installation state, sample cleanliness and other aspects on the measurement results of lubricating oil kinematic viscosity[5].In 2016, Cui Jinlei studied the relationship between lubricating oil density and viscosity, and proposed a new viscosity pressure relation formula based on density to obtain viscosity[6]. Reference 7

EXPERIMENTAL DEVICES AND METHODS The test samples were five PAO oil of different viscosity
provided by Sinopec Lubricant Company Tianjin Branch.The kinematic viscosity at 40Â°C is:32mm2/s, 48mm2/s,68mm2/s, 110mm2/s,125mm2/s.
In order to explore the relationship between kinematic viscosity, density and temperature of PAO oil, we first tested the kinematic viscosity and density of the above lubricating oil samples at different temperatures with petroleum product kinematic viscosity tester and petroleum product density tester.

Kinematic viscosity testing device and method
The measurement of kinematic viscosity is performed by SYP10036 petroleum products kinematic viscosity tester.Figure 1 is the device diagram of petroleum products kinematic viscometer, which is mainly composed of temperature control box, constant temperature cylinder, constant temperature medium, heater, agitator, stopwatch and viscometer.
FIG. 1 Motion viscometer for petroleum products
During the test, pour the constant temperature medium into the constant temperature cylinder, turn on the heater and set the test temperature.When the temperature of the constant temperature medium reaches the test temperature, the viscometer loaded into the sample is placed vertically in the constant temperature medium for 15 minutes to measure the time of a certain amount of lubricating oil sample flowing
through the capillary tube of the viscometer.Repeat the measurement 4 timesthe kinematic viscosity of the sample
at the set temperature can be obtained by multiplying the average value of the time obtained at least 3 times by the viscometer constant of the selected viscometer. The kinematic viscosity data of the lubricating oil measured by the above device is shown in Table 1.
TABLE I. KINEMATIC VISCOSITY OF PAO OILS AT DIFFERENT TEMPERATURES
Sample
Temperature
PAO
32mm2/s
PAO
48mm2/s
PAO
68mm2/s
PAO
110mm2/s
PAO
125mm2/s
30Â°C
40.7
73.7
85.83
182.67
208.38
50Â°C
20.3
32.09
44
72.36
80.44
70Â°C
11.06
16.81
22.73
33.49
38.02
90Â°C
6.82
9.91
12.85
18.93
21.17
110Â°C
4.46
6.4
8.11
11.83
13.01

Density test device and method
The determination of the lube oil sample density is done by the petroleum product density tester.The structure of the density tester for petroleum products is shown in FIG. 2,
FIG. 2 Density tester for petroleum products
During the test, the constant temperature medium glycerol is poured into the constant temperature cylinder, and the constant temperature is set through the temperature control box.Pour the sample into the sample bucket, put the sample bucket into the constant temperature medium, make the liquid level of the sample lower than that of the constant temperature
which is mainly made up of a sample barrel of a constant temperature stirrer and a set of measuring range is composed of 600~650Kg/m3, 650~700Kg/m3, 700~750 Kg/m3,
800~800Kg/m3, 800~900Kg/m3
900~950Kg/m3,950~1000Kg/m3 densitometer.
medium, and maintain the constant temperature for a certain time.When the temperature of the lubricating oil sample measured by the thermometer reaches the set temperature, select the appropriate densitometer and place it into the sample in the sample bucket.After the densitometer stabilizes, Read the scale on the densitometer that is tangent to the liquid level of the samle. This reading value is the density of the sample at this temperature.See Table 2
TABLE II. DENSITY OF POLYOLEFIN LUBRICANTS AT DIFFERENT TEMPERATURES(UNITS:Kg/m3)
Temperature
Sample
30Â°C
50Â°C
70Â°C
90Â°C
110Â°C
PAO(32)
816.3
806.2
794.1
780.5
767.2
PAO(48)
822.6
812.3
800.2
787.8
774.1
PAO(68)
826.7
816.5
805.5
792.2
780.1
PAO(110)
830.2
818.3
806.1
795
782.3
PAO(125)
831.3
820.0
807.3
796.1
783.2


ANALYSIS OF TEST RESULTS
After collating the experimental data, the density
viscosity relationship of PAO lubricating oil at 30Â°C,50Â°C,70Â°C,90Â°C,110Â°C was obtained, as shown in FIG. 3
840
30OC
50OC
70OC
90OC
110OC
30OC
50OC
70OC
90OC
110OC
830
820
Density (Kg /m3)
Density (Kg /m3)
810
800
790
780
770
760
20 30 40 50 60 70 80 90 100 110 120 130 140
Kinematic viscosity (mm2/ s)
FIG. 3 Relationship between dynamic viscosity and temperature of lubricating oil with different viscosities
As can be seen from the figure, the density of lubricating oil with the same kinematic viscosity gradually decreases with the increase of temperature, and the trend of density reduction is approximately linearly correlated with the trend of temperature increase.At the same temperature, the lubricating oil with high kinematic viscosity has higher density, and with the increase of kinematic viscosity, the trend of density increase gradually decreases.

DETERMINATION OF VISCOSITYDENSITY TEMPERATURE RELATIONSHIP
Use First Optimization softwareregression analysis of
the above experimental data was carried out by using Macquarie method.The fitting formula between kinematic viscosity density and temperature is obtained as follows:
1
1
1 1
p p
p
p
7
7
p
p
1 2 1 T p
5 1 p
8 1 T p
1 p
4
4
p3
p6
p3
4 7
6
1
In the formula:
T is temperature, is the density of PAO oil at T: p1= 40.168;
p2= 12.869;
p3= 7.905;
p4= 23.451;
p5= 8.01868G102;
p6= 7.741;
p7= 1.09197G102; p8= 1.6955976G104;
Formula (1) reflects the relationship between PAO lubricating oil kinematic viscosity, density and temperature,Population correlation coefficient R= 0.99205,The relationship of the three is shown in Figure 4.
FIG. 4 Comparison of calculated and tested values of kinematic viscositydensitytemperature relationship
In the figure, the grid represents the predicted value of formula (1), and the white squares represent the test data points.

ERROR ANALYSIS
Table 3~7 shows the comparison between the calculated value and the test value of Formula (1) when the temperature is 30Â°C, 50Â°C, 70Â°C, 90Â°C and 110Â°C, respectively.
TABLE III. COMPARISON OF CALCULATED VALUES AND TEST VALUES(TEMPERATURE OF 30Â°C)
DensityKg/m3
Test valuemm2/s
calculated value
mm2/s
relative error%
816.3
40.7
33.859
16.80
822.6
73.7
64.95
11.87
826.7
85.83
104.65
21.93
830.2
182.67
173.8
4.86
831.3
208.38
211.63
1.56
TABLE IV. COMPARISON OF CALCULATED VALUES AND TEST VALUES(TEMPERATURE OF 50Â°C)
DensityKg/m3
Test valuemm2/s
calculated value
mm2/s
relative error%
806.2
20.3
22.288
9.79
812.3
32.09
37.30
16.24
816.5
44
52.71
19.80
818.3
72.36
61.37
15.19
820
80.44
71.188
11.50
TABLE V. COMPARISON OF CALCULATED VALUES AND TEST VALUES(TEMPERATURE OF 70Â°C)
DensityKg/m3
Test value
mm2/s
calculated value
mm2/s
relative error%
794.1
11.06
12.43
12.39
800.2
16.81
20.96
24.69
805.5
22.73
31.02
36.47
806.1
33.49
32.37
3.34
807.3
38.02
35.24
7.31
TABLE VI. COMPARISON OF CALCULATED VALUES AND TEST VALUES(TEMPERATURE OF 90Â°C)
DensityKg/m3
Test valuemm2/s
calculated value
mm2/s
relative error%
780.5
6.82
4.82
29.33
787.8
9.91
11.38
14.83
792.2
12.85
16.35
27.24
795
18.57
20.05
7.97
796.1
20.17
21.64
7.29
TABLE VII. COMPARISON OF CALCULATED VALUES AND TEST VALUES(TEMPERATURE OF 110Â°C)
DensityKg/m3
Test value
mm2/s
calculated value
mm2/s
relative error%
767.2
4.46
0.21
104.71
774.1
6.4
4.11
35.78
780.1
8.11
8.70
7.27
782.3
11.83
10.63
10.14
783.2
13.01
11.47
11.84
It can be seen from the above table that the calculated value of viscositydensity temperature relation is close to the experimental value.

CONCLUSION
In this paper, the kinematic viscosity and density of PAO oil samples with different initial viscosities were measured at different temperatures and the experimental data were analyzed.A functional reationship between PAO oil viscositydensitytemperature was obtained by fitting test data.The following conclusions can be drawn:

The viscosity and density of lubricating oil decrease with the increase of temperature. At the same temperature, the density increases with the increase of kinematic viscosity, but the increase trend decreases gradually.

The equation of viscositydensity temperature function is obtained.It can describe the relationship between viscosity density and temperature of PAO oil.The kinematic viscosity of PAO lubricating oil in the range of 30Â°C110Â°C can be predicted using this relation.
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