Only the lubrication performance at rated engine operating condition was generally analyzed in current design and research of engine connecting-rod and main bearing. However, the actual engine (especially vehicle engine) does not always operate in rated operating condition and its operating condition changes constantly. In this paper, a four-stroke four-cylinder engine is taken as the studying object, the load and lubrication of connecting-rod and main bearing in different operating conditions are analyzed. The load of connecting-rod bearing is calculated by the dynamic calculation method, the loads of all main bearings are calculated by the whole crankshaft beam-element finite element method, and the lubrication performance of connecting-rod and main bearings are analyzed by the dynamic method. The results show that there are major differences in the changes and numerical value at corresponding moment of the loads and lubrication performance of connecting-rod and main bearings in an engine operating cycle in different engine operating conditions; the most unfavorable case of the lubrication performance of connecting-rod and main bearings may not take place in the rated engine operating condition. There are also major differences between the lubrication performance of connecting-rod bearing and that of main bearing and between the lubrication performances of main bearings one another. Therefore, it will not be reasonable that the lubrication performance of a certain connecting-rod bearing or main bearing is analyzed in the design of the engine bearing. It is necessary to analyze simultaneously the lubrication performances of all bearings in different engine operating conditions.
1 Introduction
The connecting-rod or main bearing is one of main frictional pairs in engine. The operating condition of connecting-rod or main bearing affects directly the operational economy, reliability, durability and lifetime of engine. The capability and rationality of design are one of most essential factors to determine the performance of connecting-rod or main bearing. By the unremitting efforts of researchers and the progress of correlation technique, current design capability of engine connecting-rod and main bearing is improved continually, the factors considered in the design calculation of bearing are perfected increasingly, and the performance of bearing is predicted more accurately. Many researches on the lubrication of connecting-rod or main bearing have been done. For example, Liu analyzed the transient tribodynamic performance of crankshaft-main bearing system in engine starting up [1]. Zammit investigated the lubrication of crankshaft bearing during engine warm-up [2]. Inui, Jia and Galera et al. [3‐5] studied the factors affecting the lubrication of crankshaft bearing. Gu et al. [6] researched the performance of textured crankshaft bearing during an engine cycle. Mohammadpour, Mahdi, and Liu et al. [7‐9] analyzed the effect of cylinder deactivation on the tribo-dynamic-acoustic and thermo-hydrodynamic characteristics of crankshaft bearing. Francisco, Lavie and Zhang et al. [10‐12] studied the optimization of crankshaft bearing lubrication. Ozasa et al. [13] proposed a simplified estimation method of engine bearing lubrication. Shahmohamadi et al. [14] analyzed the mixed thermo-hydrodynamic lubrication of engine connecting rod bearing. Refs. [15‐18] study the thermo-elastohydrodynamic lubrication of engine crankshaft bearing. Tabrizi et al. [19] compared three kinds of simulation models of connecting rod bearing. Zhang et al. [20] researched the mixed lubrication performance of high power-density engine main bearing. Toshihiro et al. [21] analyzed the lubrication of gasoline engine connecting rod bearing. Bi and Chen et al. [22, 23] studied the lubrication of turbocharged engine main bearing. Choi et al. [24] analyzed the dynamically bearing elastohydrodynamic lubrication considering multi-flexible-body dynamics. Wei et al. [25‐27] investigated the thermo-elasto-hydrodynamic mixed lubrication of marine engine main bearing. Shao et al. [28] analyzed the lubrication performance of engine main bearing coupling cylinder block and crankshaft-connecting rod system. Zhao et al. [29] analyzed the lubrication performance of marine engine main bearing in typical operating conditions. Yang et al. [30] analyzed the lubrication of gasoline engine main bearing considering transient heat transfer. However, only the lubrication performance of connecting-rod and main bearing in rated engine operating condition was generally analyzed in current design and research. In actual use, the engine (especially used in vehicle) does not always operate in rated operating condition and its operating condition changes constantly. Therefore, it is necessary to study the lubrication performance of engine connecting-rod and main bearing in different operating conditions, which is helpful to perfect the lubrication analysis theory of engine bearing and can provide more comprehensive reference base for the design of connecting-rod and main bearing.
In this paper, a four-stroke four-cylinder engine is taken as the studying object, the loads and lubrication characteristics of its connecting-rod bearing and all main bearings in different engine operating conditions are calculated, and the effects of engine operating condition on the lubrication performances of connecting-rod and main bearings are researched. The parameters of the engine and its bearings are shown in Table 1.
Table 1
Parameters of engine and bearings
Parameter
Value
Cylinder diameter D (mm)
105
Stroke S (mm)
118
Rated power Pe (kW)
76
Rated speed n (r/min)
3200
Width of connecting-rod bearing Ll (mm)
30
Diameter of connecting-rod bearing Dl (mm)
66
Clearance of connecting-rod bearing cl (mm)
0.152
Width of main bearing Lz (mm)
27
Diameter of main bearing Dz (mm)
80
Clearance of main bearing cz (mm)
0.146
Dynamic viscosity of lubricating oil η (Pa·s)
0.014347
Oil inlet pressure p0 (Pa)
2000
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2 Calculation of the Loads of Bearing in Different Engine Operating Conditions
The load of connecting-rod bearing is calculated by the dynamic calculation method [31], which is obtained by analyzing the applied forces on the engine crank-rod mechanism based on the engine cylinder pressure indicator diagram (some shown in Figure 1) measured in engine bench test and configuration parameters. The loads of all main bearings are calculated by the finite element method of whole crankshaft beam-element [31]. The beam-element finite element model of whole crankshaft is shown in Figure 2.
Figure 1
Indicator diagram
Figure 2
Beam-element finite element model of whole crankshaft
×
×
The loads of connecting-rod bearing and No. 2 main bearing under full engine load at 1200 r/min and 3200 r/min are shown in Figures 3 and 4, respectively. There are great differences of the change rule and numerical value of bearing load at corresponding moment in an engine operating cycle in different engine operating conditions.
Figure 3
Load of connecting-rod bearing
Figure 4
Load of No. 2 main bearing
×
×
The maximum loads of connecting-rod bearing and all main bearings in an engine operating cycle under full engine load at 1200, 1600, 1800, 2000, 2200, 2400, 2800 and 3200 r/min are shown in Table 2. The maximum load of connecting-rod bearing in an engine operating cycle reduces with the increase of engine speed under same engine load.
Table 2
Maximum loads of connecting-rod bearing and all main bearings at full load and different speed
Speed (r/min)
Connecting-rod bearing (N)
No. 1 main bearing (N)
No. 2 main bearing (N)
No. 3 main bearing (N)
No. 4 main bearing (N)
No. 5 main bearing (N)
1200
53331
20274
31468
25552
33835
18590
1600
51170
17201
28939
18793
30635
15926
1800
50427
19345
33061
20407
34978
17910
2000
46949
19203
33030
18699
34949
17772
2200
47620
19815
34587
17938
36581
18336
2400
47059
19605
35388
15776
36803
18131
2800
37376
15911
34085
24240
34355
14690
3200
27491
11903
29118
26126
29529
10882
The maximum value of the maximum load of connecting-rod bearing in an engine operating cycle appears at low engine speed (1200 r/min), and the numerical value of the maximum load of connecting-rod bearing in an engine operating cycle at high engine speed (3200 r/min, rated engine operating condition) is small. The main reason is that the load of connecting-rod bearing is decided by the actual condition of the movement and applied force of engine crank-rod mechanism. The maximum load of connecting-rod bearing in an engine operating cycle appears near to the combustion top dead center. Based on the applied force analysis of engine crank-rod mechanism, the load of connecting-rod bearing is the resultant force of the forces resulted from the cylinder pressure, the reciprocating inertial force and the rotational inertial force. The reciprocating inertial force and the rotational inertial force will be increased with the increase of engine speed, but the acting directions of the reciprocating inertial force and the rotational inertial force at the combustion top dead center are opposite to the direction of force resulted from the cylinder pressure, so the higher the engine speed the more the reduction of the maximum load of connecting-rod bearing. The change situation of the maximum load of one main bearing in an engine operating cycle against the engine speed is different from that of another main bearing under same engine load. The loads of No. 1 and No. 5 main bearing are affected mainly by the force on single crank, and the maximum loads of No. 1 and No. 5 main bearing happen at the lower engine speed (1200 r/min). The loads of No. 2, No. 3 and No. 4 main bearing are decided by the forces of adjacent two cranks, and the maximum loads of No. 2, No. 3 and No. 4 main bearing happen at the higher engine speed.
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The maximum loads of connecting-rod bearing and all main bearings in an engine operating cycle at 2200 r/min under 20%, 40%, 60%, 80% and full engine load are shown in Table 3. Under the same engine speed, the maximum loads of connecting-rod bearing and all main bearings in an engine operating cycle increase basically with the increase of engine load, and the maximum loads of connecting-rod bearing and all main bearings in an engine operating cycle take place at full engine load.
Table 3
Maximum loads of connecting-rod bearing and all main bearings at 2200 r/min and different load percentage
Load percentage (%)
Connecting-rod bearing (N)
No. 1 main bearing (N)
No. 2 main bearing (N)
No. 3 main bearing (N)
No. 4 main bearing (N)
No. 5 main bearing (N)
20
28691
12184
23992
11477
24135
11259
40
29087
12720
23306
16483
24858
11757
60
40858
17392
30918
14547
32491
16089
80
44273
18675
32765
16334
34650
17277
100
47620
19815
34587
17938
36581
18336
3 Lubrication Analysis of Connecting-Rod and Main Bearing in Different Engine Operating Condition
3.1 Method and Formulation
The journal axis orbits of all bearings are calculated by the dynamic method in the lubrication analyses of all connecting-rod or main bearings [32].
where p is the oil film pressure, h is the oil film thickness, η is dynamic viscosity of lubricating oil, u = uj + ub, uj is the velocity of journal surface and uj = Rjωj, Rj is the journal radius, ωj is the angular velocity of journal, ub is the velocity of bearing surface and ub = Rbωb, Rb is the bearing radius, ωb is the angular velocity of bearing.
Reynolds’ equation is solved by the finite difference method.
where c is the radial clearance of bearing, e is the journal eccentric distance of bearing, ψ is the attitude angle of bearing, δ is the change of oil film thickness caused by elastic deformation of bush surface of bearing under oil film pressure, and the elastic deformation of bush surface of bearing under oil film pressure is calculated by the compliance matrix method.
3.1.3 Load Equilibrium Equation
If the effect of the oil film inertia is not considered, the motion of the journal axes of bearing conforms to the Newton second law, that is,
where P is the load vector of bearing, F is the resultant oil film force vector of bearing, v is the velocity vector of journal axes.
3.1.4 End Leakage Flow-Rate of Bearing
The lubricating oil flow-rate Q1 from the front-end plane of bearing and the lubricating oil flow-rate Q2 from the rear-end plane of bearing are given by
The journal axes orbits, maximum oil film pressures, minimum oil film thicknesses, end leakage flow-rates and frictional coefficients of connecting-rod bearing and No. 2 main bearing in an engine operating cycle under full engine load at 1200 r/min and 3200 r/min are shown in Figures 5, 6, 7, 8, 9, 10, 11, 12, 13, 14. In different engine operating conditions, there are major differences of the lubrication performance of bearings, and there are obvious differences in the changes and numerical values of the journal axes orbits, maximum oil film pressures, minimum oil film thicknesses, end leakage flow-rates and frictional coefficients of bearings in an engine operating cycle.
Figure 5
Journal axis orbit of connecting-rod bearing
Figure 6
Journal axis orbit of No. 2 main bearing
Figure 7
Maximum oil film pressure of connecting-rod bearing
Figure 8
Maximum oil film pressure of No. 2 main bearing
Figure 9
Minimum oil film thickness of connecting-rod bearing
Figure 10
Minimum oil film thickness of No. 2 main bearing
Figure 11
End leakage flow-rate of connecting-rod bearing
Figure 12
End leakage flow-rate of No. 2 main bearing
Figure 13
Frictional coefficient of connecting-rod bearing
Figure 14
Frictional coefficient of No. 2 main bearing
×
×
×
×
×
×
×
×
×
×
The maximum oil film pressures, minimum oil film thicknesses and average frictional power losses of connecting-rod bearing and all main bearings in an engine operating cycle under full engine load and at 1200, 1600, 1800, 2000, 2200, 2400, 2800 and 3200 r/min respectively are shown in Tables 4, 5, 6.
Table 4
Maximum film pressures of connecting-rod bearing and main bearings at full load and different speed
Speed (r/min)
Connecting-rod bearing (MPa)
No. 1 main bearing (MPa)
No. 2 main bearing (MPa)
No. 3 main bearing (MPa)
No. 4 main bearing (MPa)
No. 5 main bearing (MPa)
1200
372.52
47.70
94.41
88.91
143.88
43.51
1600
221.53
37.71
109.10
38.33
147.12
34.24
1800
153.78
38.55
87.20
36.47
91.72
35.28
2000
136.71
37.00
92.38
30.46
91.92
32.29
2200
129.58
36.04
94.06
33.27
95.51
32.75
2400
120.20
34.70
97.56
43.17
98.58
31.49
2800
136.22
39.39
75.86
115.56
71.16
38.46
3200
92.74
50.10
73.14
115.79
73.07
45.26
Table 5
Minimum film thicknesses of connecting-rod bearing and main bearings at full load and different speed
Speed (r/min)
Connecting-rod bearing (μm)
No. 1 main bearing (μm)
No. 2 main bearing (μm)
No. 3 main bearing (μm)
No. 4 main bearing (μm)
No. 5 main bearing (μm)
1200
2.34
4.35
3.08
4.31
3.01
5.04
1600
3.05
3.63
3.51
5.08
3.27
3.84
1800
3.13
3.23
3.38
4.30
3.20
3.39
2000
2.65
3.20
3.39
4.11
3.16
3.56
2200
2.58
2.96
3.34
3.47
3.08
3.39
2400
2.39
2.81
3.30
3.07
3.06
3.33
2800
2.48
2.56
4.48
1.83
3.31
3.61
3200
1.97
2.09
3.12
1.42
3.01
2.90
Table 6
Average friction power losses of connecting-rod bearing and main bearings at full load and different speed
Speed (r/min)
Connecting-rod bearing (W)
No. 1 main bearing (W)
No. 2 main bearing (W)
No. 3 main bearing (W)
No. 4 main bearing (W)
No. 5 main bearing (W)
1200
43.74
56.53
49.53
55.55
50.73
57.45
1600
83.55
98.02
95.14
114.62
98.54
97.20
1800
102.09
118.07
124.11
145.81
129.42
117.84
2000
132.33
161.82
144.88
180.93
155.34
153.26
2200
150.77
201.86
189.04
218.17
201.40
185.02
2400
177.09
242.79
226.87
255.20
244.85
216.11
2800
245.28
293.11
252.78
463.87
290.62
248.65
3200
271.30
413.43
392.23
515.31
442.73
382.44
When the engine load is same, the maximum oil film pressure of connecting-rod bearing in an engine operating cycle is decreased generally with the increase of engine speed, and the maximum oil film pressure (372.52 MPa) of connecting-rod bearing at 1200 r/min is as 4.02 times as that (92.74 MPa) at 3200 r/min, which shows that the maximum oil film pressure of connecting-rod bearing at lower engine speed is larger remarkably than the one at higher engine speed under the same engine load. The main reason why the maximum oil film pressure of connecting-rod bearing at lower engine speed is larger than the one at higher engine speed under the same engine load is that, when the engine load is same, the maximum load of connecting-rod is decreased basically with the increase of engine speed, and the maximum load of connecting-rod at 1200 r/min is larger remarkably than the one at 3200 r/min.
When the engine load is same, the changes of the maximum oil film pressures of all main bearings in an engine operating cycle is different one another with the change of engine speed. The maximum oil film pressures of No. 1 and No. 5 main bearings do not have obvious change at different engine speed, the maximum oil film pressures of No. 2 and No. 4 main bearings are larger at lower engine speed, and the maximum oil film pressure of No. 3 main bearings is larger at higher engine speed.
When the engine load is same, the minimum oil film thicknesses of connecting-rod bearing and all main bearings in an engine operating cycle do not have the same change one another with the change of engine speed. The minimum oil film thicknesses of connecting-rod bearing and all main bearings in an engine operating cycle at higher engine speed (3200 r/min) are generally smaller in addition to the individual circumstances.
When the engine load is same, the average frictional power losses of connecting-rod bearing and all main bearings increase with the increase of engine speed, and the average frictional power losses of connecting-rod bearing and all main bearings are the largest at higher engine speed (3200 r/min).
The maximum oil film pressures, minimum oil film thicknesses and average frictional power losses of connecting-rod bearing and all main bearings in an engine operating cycle at 2200 r/min under 20%, 40%, 60%, 80% and full engine load are shown in Tables 7, 8, 9.
Table 7
Maximum film pressures of connecting-rod bearing and main bearings at 2200 r/min and different load percentage
Load percentage (%)
Connecting-rod bearing (MPa)
No. 1 main bearing (MPa)
No. 2 main bearing (MPa)
No. 3 main bearing (MPa)
No. 4 main bearing (MPa)
No. 5 main bearing (MPa)
20
70.48
21.19
37.00
37.84
62.98
19.00
40
68.20
21.21
58.90
45.69
64.49
19.00
60
106.24
30.36
83.19
33.71
84.43
27.59
80
118.66
33.35
89.35
32.96
90.63
30.32
100
129.58
36.04
94.06
33.27
95.51
32.75
Table 8
Minimum film thicknesses of connecting-rod bearing and main bearings at 2200 r/min and different load percentage
Load percentage (%)
Connecting-rod bearing (μm)
No. 1 main bearing (μm)
No. 2 main bearing (μm)
No. 3 main bearing (μm)
No. 4 main bearing (μm)
No. 5 main bearing (μm)
20
2.96
2.97
3.20
3.48
3.68
3.63
40
2.92
2.98
3.82
3.24
3.64
3.65
60
2.79
2.97
3.46
3.42
3.26
3.45
80
2.70
2.97
3.40
3.49
3.18
3.60
100
2.58
2.96
3.34
3.47
3.08
3.39
Table 9
Average friction power losses of connecting-rod bearing and main bearings at 2200 r/min and different load percentage
Load percentage (%)
Connecting-rod bearing (W)
No. 1 main bearing (W)
No. 2 main bearing (W)
No. 3 main bearing (W)
No. 4 main bearing (W)
No. 5 main bearing (W)
20
136.99
196.14
188.14
212.51
200.18
173.85
40
134.66
195.25
188.04
176.99
188.04
173.10
60
145.50
198.77
190.54
214.24
203.35
178.23
80
150.90
201.64
189.76
216.54
203.03
179.63
100
150.77
201.86
189.04
218.17
201.40
185.02
When the engine speed is same, the maximum oil film pressures of connecting-rod bearing and all main bearings in an engine operating cycle are increased generally with the increase of engine load, but the maximum value of the maximum oil film pressures of No. 3 main bearing is appeared at the smaller engine load (40%).
When the engine speed is same, the minimum oil film thickness of connecting-rod bearing is decreased with the increase of engine load, and the maximum value appears at the full engine load (100%). The minimum oil film thicknesses of all main bearings do not have the same change with the change of engine load, the minimum values of the minimum oil film thicknesses of Nos. 1, 4, 5 main bearings all appear at the full engine load (100%), and the minimum values of the minimum oil film thicknesses of Nos. 2, 3 main bearings appear at the smaller engine load.
When the engine speed is same, the average frictional power losses of connecting-rod bearing and all main bearings in an engine operating cycle do not change obviously with the change of engine load. The average frictional power losses of connecting-rod bearing and all main bearings in an engine operating cycle are generally increased slightly with the increase of engine load in addition to the individual engine loads.
In addition, the corresponding comparisons between the lubrication performance of connecting-rod bearing and the one of main bearings at same engine operating condition (shown in Tables 4, 5, 6, 7, 8, 9) show that, the maximum oil film pressure of connecting-rod bearing in an engine operating cycle is larger than those of all main bearings, the minimum oil film thickness of connecting-rod bearing in an engine operating cycle is smaller than those of all main bearings, and the average frictional power losses of connecting-rod bearing in an engine operating cycle is smaller than those of all main bearings. Also, there is the corresponding difference between the lubrication performances (the maximum oil film pressure, minimum oil film thickness and average frictional power loss in an engine operating cycle) of all main bearings one another at same engine operating condition, and some difference is larger.
4 Conclusions
(1)
In different engine operating conditions, there are great differences of the loads of connecting-rod and main bearings. When the engine load is same, the maximum load of connecting-rod bearing appears at the lower engine speed, the maximum loads of some main bearings appear at the lower engine speed but the others appear at the higher engine speed. When the engine speed is same, the maximum loads of connecting-rod bearing and all main bearings appear at the full engine load.
(2)
In different engine operating conditions, there are obvious difference of the lubrication performance of connecting-rod and main bearing.
When the engine load is same, the maximum oil film pressure of connecting-rod bearing at lower engine speed is larger obviously than the one at higher engine speed; the change of the maximum oil film pressure of each main bearing with the engine speed is not the same; the smaller values of the minimum oil film thicknesses of connecting-rod bearing and all main bearings appear generally at higher engine speed; the maximum average frictional power losses of connecting-rod bearing and all main bearings happen at higher engine speed.
When the engine speed is same, the maximum oil film pressures of connecting-rod bearing and main bearings increase generally with the increase of engine load; the minimum oil film thickness of connecting-rod bearing happens at the full engine load, the minimum oil film thicknesses of some main bearings happen at the full engine load but some other happen at the lower engine load; the average frictional power losses of connecting-rod bearing and all main bearings do not have evident change with the change of engine load.
(3)
Under the same engine operating condition, the maximum oil film pressure of connecting-rod bearing is larger than the one of main bearing; the minimum oil film thickness of connecting-rod bearing is smaller than the one of main bearing; the average frictional power loss of connecting-rod bearing is smaller than the one of main bearing.
(4)
There are the larger difference between the lubrication performances of main bearings one another under same engine operating condition.
Therefore, it is not comprehensive and reasonable that only the lubrication performance of a certain connecting-rod bearing or main bearing at rated engine operating condition is analyzed. It is necessary to analyze simultaneously the lubrication performance of connecting-rod bearing and all main bearings in different engine operating conditions in the design of engine.
Authors’ Contributions
JS was in charge of the whole trial; BL wrote the manuscript; SZ and EM assisted with the lubrication analyses of bearing; HW and XZ assisted with the finite element analysis; QT assisted with the measurement of engine cylinder pressure. All authors read and approved the final manuscript.
Authors’ Information
Jun Sun, born in 1960, is currently a professor at School of Automotive and Transportation Engineering, Hefei University of Technology, China. He received his PhD degree from Hefei University of Technology, China, in 2005. His research interests include tribology and modern design theory and method.
Biao Li, born in 1991, is currently a PhD candidate at School of Mechanical Engineering, Hefei University of Technology, China. He received his master degree from Anhui University of Technology, China, in 2016.
Shaoyu Zhu, born in 1994, is currently a PhD candidate at School of Automotive and Transportation Engineering, Hefei University of Technology, China. He received his bachelor degree from Hefei University of Technology, China, in 2015.
Enming Miao, born in 1971, is currently a professor at School of Instrument Science and Opto-electronics Engineering, Hefei University of Technology, China. He received his PhD degree from Hefei University of Technology, China, in 2004.
Hu Wang, born in 1972, is currently a professor at School of Mechanical Engineering, Hefei University of Technology, China. He received his PhD degree from Hefei University of Technology, China, in 2010.
Xiaoyong Zhao, born in 1962, is currently a professor at School of Mechanical Engineering, Hefei University of Technology, China.
Qin Teng, born in 1962, is currently a professor at School of Automotive and Transportation Engineering, Hefei University of Technology, China. He received his PhD degree from Hefei University of Technology, China, in 2007.
Competing Interests
The authors declare that they have no competing interests.
Funding
Supported by Science Fund of State Key Laboratory of Engine Reliability of China (Grant No. skler-201708) and National Natural Science Foundation of China (Grant No. 51490660/51490661).
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