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Effects of Journal Roundness Phase and Amplitude on Lubrication of Engine Bearings with Consideration of Straightness.

INTRODUCTION

The rotary motion joints of internal combustion engine are working under bad conditions characterized by large variations of dynamic loads and high peak loads, and high requirements are desired for components of the engine. Hydrodynamic journal bearings, with simple structures, low costs, and smooth operation at high speeds, are widely used in automotive engines to reduce the friction power loss. Most studies of dynamic performances of hydrodynamic journal bearing in literature did not take into account of manufacturing tolerances, which are inevitable during the manufacturing process and do affect the working performance of bearings. Unreasonable tolerance will lead to either a severe decline in quality or a substantial increase in the manufacturing and measuring costs. Therefore, it is necessary to study the effect of manufacturing tolerance on the working performance of bearings to provide guidance on designing the tolerances reasonably.

Some research have shown that the tolerances have an obvious effect on bearings lubrication. XU et al theoretically analyzed how manufacturing tolerances of the bearing width and the diameters of both the bearing shell and the journal affect the working performance of bearings based on Taguchi method [1]. In the studies of Wei et al, the effects of the friction power loss brought by the dimensional tolerances of the dynamic viscosity, bearing width, bearing diameter and journal diameter were analyzed [2]. Ogrodnik et al. found that the tolerance of a single dimension may not demonstrate a noteworthy effect on the system performance in isolation, but when it is coupled with other tolerances the effect can be signifcant, and the [2.sup.k] factor design was applied to study the coupling effects of different manufacturing tolerances on the bearings system [3]. Zhou et al discussed the relationship between the dimensional tolerances and friction power loss of the engine system and determined the optimal tolerance based on a Multi-Disciplinary optimization approach [4].

However, those studies only focus on the dimensional tolerances, and there is insuffcient understanding of how geometric tolerances of the journal may affect the bearing lubrication, especially the roundness coupled with straightness. The sizes of roundness and straightness tolerances are of the micron scale, which is the same with that of the bearings clearance, so it is large enough to generate remarkable effects on working performance of bearings. In the work of Dehart et al, the relationships between the roundness amplitude, the number of lobes and bearing wear are analyzed [5]. Mehenny et al discussed the effects of the number and the amplitudes of circumferential lobes on the operating parameters such as maximum lubricant pressure and minimum oil flm thickness, but the elastic deformation of the bearing shell is neglected [6]. Torii et al found that lubrication of a connecting rod journal bearing is signifcantly infuenced by the elastic deformation and shapes of a connecting rod bearing [7], so the elastic deformation of the journal and shell should be considered when analyzing the effect of roundness on bearing lubrication. Zeng et al presented a dynamics model of hydrodynamic bearing rotor system where roundness is considered, and effects of the eccentricity on friction power loss was studied [8]. Xu, et al theoretically discussed the effect of journal out-of-roundness on the dynamic performance of rotating machines supported by oil flm bearings [9].

Although the above-mentioned studies analyzed the effects of the number and the amplitudes of circumferential lobes on bearing lubrication with consideration of elastic deformation of the bearing shell and journal, the influence of the roundness phase (the angle of the roundness geometric shape along the journal circumferential direction) is ignored. As the load condition of the bearings is changing all the time during the 4-stroke cycle of an engine, the lubrication condition of the bearings with different roundness phases also changes accordingly. In addition, all of the above mentioned researches are under the assumption that the axial direction of the journal bearing is ideally straight (that is, the straightness amplitude is zero), and so the effect caused by the existence of straightness is neglected. This work aims to illustrate the effects of the roundness phase and amplitude on the bearing lubrication with the consideration of straightness. First, impacts of the roundness phase and amplitude on lubrication are analyzed, respectively. Then the coupling effects of roundness and straightness on friction loss of the bearing are analyzed and presented. It is shown that the roundness will increase or decrease the friction loss which is determined by the roundness phase, and the variation range of friction loss is determined by the roundness amplitude. It is also concluded that the coupling of roundness and straightness will increase the variation of friction loss.

The rest of the paper is organized as follows: Section 2 presents the background of this work. In Section 3, the individual effect of roundness phase and amplitude on friction loss is studied. The coupling effect of the roundness and straightness is given in Section 4, followed by the conclusion in Section 5.

BACKGROUND

In this section, the background information of this work is presented. First the bearing model based on elastohydrodynamic (EHD) theory is introduced briefly, and then the roundness model defined in terms of roundness phase and the roundness amplitude is presented.

Bearing Model

The elastic deformation of the bearing shell is of a micron scale, which is comparable with the amplitude of roundness, thus it is necessary to take account of elastic deformation when establishing the bearing model for a more accurate analysis of how tolerances may affect the friction power loss. Therefore, AVL Excite PowerUnit, which is proved to be able to provide accurate results for the engine bearings [10]. is applied to build the bearing model based on the elastohydrodynamic (EHD) theory which takes the elastic deformation into consideration.

The differential equation applied in the EHD model describes the pressure variation of the oil film between the shaft and the bearing shell, as shown in Eq. (1) [11]:

[mathematical expression not reproducible] (1)

where P is the oil film pressure, h is the modified thickness of oil film, [rho] is the oil density, [eta] is the dynamic viscosity of the oil, [v.sub.t] is the tangential velocity, and t is time. The effects of fill ratio, represented by [[[theta].sub.r], on bearing lubrication are taken into account as well.

The modified oil film thickness h concerning the elastic deformation, roughness, and roundness error is computed by the following equation:

h([theta]) = [h.sub.0]([theta]) + [h.sub.E]([theta]) + [h.sub.R]([theta]) + [h.sub.z]([theta])+[h.sub.s]([theta]) (2)

where [h.sub.0]([theta]) is the oil film thickness with the assumption of rigid journals and a rigid bearing shell, [h.sub.E]([theta]) is the thickness variation caused by the elastic deformation of the journals and bearing shell, [h.sub.R]([theta]) is the variation resulted from the roughness of the journals and bearing shell, [h.sub.z]([theta]) is the variation due to the existence of roundness, and [h.sub.S]([theta]) is the variation caused by the existence of straightness.

The boundary condition of JFO (Jakobsson, Floberg, Olsson) theory is adopted to ensure mass conservation at the boundary of the oil film. The crankshaft and connecting rod in this model are taken as flexible bodies, both of which are meshed into hexahedral units by finite element software (Hypermesh).

The calculated oil film thickness is taken into the extended Reynolds equation (Eq. (1)). which is then solved via the finite difference method with the bearing surface divided by hydrodynamic (HD) mesh [12]. The pressure variation across the entire bearing surface computed from Reynolds equation is utilized as the load condition for the finite element (FE) mesh of the connecting-rod. Then the elastic deformation throughout the journal surface under that load condition will be calculated and plugged into Eq. (2) to get the oil film thickness. After that the newly obtained oil film thickness will replace the old one in the Reynolds equation, and the pressure variation across the bearing surface will again be calculated. The HD mesh and FE mesh will be computed repeatedly until the pressure and fill ratio converge, that is, the differences of both values between the last two consecutive iterations are less than 0.1%.

Roundness Model

Most profiles of crankpins are similar to ellipse in geometry [7,8], and roundness tolerance in shape of an ellipse is studied in this work to investigate the effects of roundness tolerance on bearing lubrication. The geometry of an ellipse roundness tolerance is shown in Figure 1.

The roundness phase is defined as the angle between [O.sub.0]C and z axis when the piston is at TDC during exhaust stroke, and it is denoted by a as shown in Figure 1. z axis in Figure 1 is along the direction of the piston cylinder liner, O is the center of the bearing, [O.sub.0] is the center of the journal, and [OMEGA] is the angle that journal has rotated. AC in Figure 1 is the major axis of the ellipse, and [O.sub.0]B is the semi-minor axis of the ellipse. The amplitude of the ellipse roundness is defined as [delta] = [delta]1 + [delta]2 where [delta]1 is the distance between the major axis endpoint Ato the ideal circular profile and [delta]2 is the distance between the minor axis endpoint B and the ideal circular profile. Then the ellipse can be described by

[mathematical expression not reproducible] (3)

where [y.sub.r] and [z.sub.r] are the axes along the minor axis and the major axis of the ellipse, respectively, and [r.sub.0] is the mean radius of the ellipse calculated by the least squares method. Then the variation of oil film thickness caused by the ellipse roundness can be computed from the following equation.

[mathematical expression not reproducible] (4)

ANALYSIS OF ROUNDNESS PHASE AND AMPLITUDE ON FRICTION LOSS AND LUBRICATION

The parameters of the bearing studied in this work are listed in Table 1.

As we all know the friction power loss is an important output performance of the bearing. In this section, the friction power loss, peak oil film pressure (POFP) and minimum oil film thickness (MOFT) of the bearing under different roundness phases and amplitudes are analyzed to show the effects of roundness on the friction loss and bearing lubrication. Single-factor analysis is performed to show how the phase and the amplitude of roundness could affect the lubrication of the bearing, respectively.

Effects of Roundness Phase on Bearing Lubrication

Results of the friction loss, POFP and MOFT of the bearing at different roundness phases with the same roundness amplitude (5 urn) are shown in Figure 2. For a 4-stroke engine, from the intake stage to the exhaust stage within which the crank angle rotates 720 degrees, the load conditions of the bearing is changing all the time, and as a result the lubrication state of bearings varies with different roundness phases even with the same roundness amplitude. Since the ellipse roundness is axisymmetric, the roundness phase in this paper is set to vary from 0[degrees] to 180[degrees]. The dashed lines in Figure 2 show the corresponding result of an ideal journal, that is, the cross section of the journal is ideally circular.

It can be concluded from Figure 2 that the roundness phase of the journal has an obvious influence on the lubrication condition and friction loss of the bearing. With the increase of the roundness phase, the friction power loss also increases, and the maximum friction loss appears at the roundness phase of 67[degrees]. Then the power loss decreases until the minimum friction loss appears at the roundness phase of 157[degrees]. On the other hand, when compared with the ideal journal case, it is indicated that the roundness phase could increase the friction power loss, and it is also able to decrease the friction power loss of the bearing. So the existence of roundness will help to reduce the friction loss under some conditions.

The variation of POFP with respect to the roundness phase is contrary to that of the friction loss, as shown in Figure 2(b). This indicates that different roundness phases result in different oil pressure distributions and lubrication conditions. With the roundness amplitude of 5um, different roundness phases may lead to an increased or decreased POFP.

As for the MOFT, although in most cases the existence of roundness results in a reduced MOFT, but some roundness phases may lead to an increased MOFT with the variation range less than 0.1mm. It is noted that the variation of MOFT is different with that of the friction loss and POFP in that it has two peaks. The position of MOFT with respect to roundness phase along with the MOFT are presented in Figure 2 (c), which shows that roundness phase also changes the position where MOFT appears and the occurrence of the two peaks is resulted from this position change of MOFT.

Next the lubrication states for the cases when the friction loss reaches its maximum (at 67[degrees]CA) and minimum (at 157[degrees]CA) values are presented, and this is to show how roundness phases could affect the friction loss under these two roundness phases. The eccentric displacements of journal center for the two roundness phases are shown in Figure 3(a) for a complete 4-stroke cycle. As shown in Figure 3(a), during the 720-degree rotational movement process, the bearing with the roundness of 67[degrees] has a larger eccentricity than that of the roundness phase of 157[degrees], which means it has a thinner oil film thickness, and this leads to an increase of the transient friction power loss as illustrated in Figure 3(b).

From Figure 3(b) it is also shown that at the crank angle of 47CA, the friction losses of the two cases have the largest gap, so the oil film pressure of roundness phase at 67[degrees] and 157[degrees] at 47CA is presented as shown in Figures 4(a) and 4(b). The case of an ideal journal with zero roundness tolerance is also presented in Figure 4(c) for comparison.

Compared with the ideal journal case shown in Figure 4(c), the case of 67[degrees] roundness phase has a larger loading area which ranges from 150[degrees] to 300[degrees] of the circumferential angle. Although the pressure peaks of the 67[degrees] roundness phase are smaller, there are three load peaks, and the total friction loss is larger as shown previously in Figure 2(a). The case of 157[degrees] roundness phase, compared with the ideal journal case, has a narrower loading area and larger pressure peaks, and comprehensively the total friction loss is reduced as shown previously in Figure 2(a). Thus it is concluded that the existence of roundness changes the pressure distribution of the bearing, and thus affects the friction loss. A well-controlled roundness is able to reduce the total friction loss.

Effects of Roundness Amplitude on Bearing Lubrication

In addition to roundness phase, the effects of roundness amplitude on friction loss and lubrication of the bearing is also analyzed.

Simulation results of the friction loss, POFP and MOFT of the bearings with different roundness amplitudes at the roundness phase of 67[degrees] and 157[degrees] are shown in Figure 5. The roundness amplitudes is set to range from 0.5 to 5 [micro]m. The dashed lines in these figures indicate the case of an ideal bearing with zero roundness tolerance.

From Figure 5(a) it is shown that at the roundness phase of 67[degrees], the friction loss gets larger with the increase of roundness amplitude. However, at the roundness phase of 157[degrees], the friction loss decreases with the increase of roundness amplitude. This indicates that the roundness with a "right" phase could lead to reduction of the friction loss even when the roundness amplitude may be large, but a "wrong" roundness phase will increase the friction loss even when the roundness phase is small and it becomes more severe when the amplitude gets larger. The results also indicate that variations of the roundness phase and amplitudes will indeed result in variations of the bearing performance, e.g., the variation of the friction loss may reach 40W for one bearing and could be larger for the entire engine. Thus the proper design and control of roundness tolerance is quite necessary for performance consistency of the bearings from the same production line. It is shown that the roundness amplitude determines the lubrication state of the bearing, that is, it determines the variation range of friction loss.

The variation of POPF with respect to the roundness amplitude is contrary to that of the friction loss for both cases, as shown in Figure 5(b). That is, at 67[degrees] CA, a larger roundness amplitude leads to a smaller POFP, and at 157[degrees]CA a larger roundness amplitude leads to a larger POFP.

Figure 5(c) shows that the MOFT for the case with the roundness phase of 67[degrees] decreases with the increase of roundness amplitude, which is always smaller than that of the ideal journal. For the roundness phase of 157[degrees], the MOFT increases with the increase of roundness amplitude until the amplitude reaches 2um, and then the MOFT decreases. This phenomenon could be explained by Figure 5(d) which shows that the position of MOFT along the circumferential direction of the shell changes with the roundness amplitude and thus leads to the change of MOFT. It is concluded that MOFT is affected by roundness phase and amplitude simultaneously. At the same roundness phase, by controlling the roundness amplitude, a larger MOFT may be obtained.

The eccentric displacements of the journal center for the two roundness amplitudes at two roundness phases during a complete 4-stroke cycle of the engine are shown in Figure 6(a). As expected, the (5um, 67[degrees]) roundness has the largest displacement and the (5um, 157[degrees]) roundness has the smallest displacement. The displacement for the cases with 157[degrees] is always smaller than that of the 67[degrees]. The friction losses for the four cases are presented in Figure 6(b). The roundness with the largest/smallest displacements also leads to the largest/smallest friction loss, respectively.

The pressure distributions for the two roundness phases with the roundness amplitude of 0.5um are shown in Figure 7. If we compare Figure 7(a) with Figure 4(a). we can see that the decrease of roundness amplitude at the roundness phase of 67[degrees] is able to decrease the loading area but increase the pressure peaks. If we compare Figure 7(b) with Figure 4(b). it can be seen that the decrease of roundness amplitude releases the pressure peak for the roundness phase of 157[degrees] but at the same time expands the loading area.

It can be concluded from the above discussion that the roundness phase determines whether the existence of roundness would increase or decrease the friction loss of the bearing, and the roundness amplitude determines to what extent the friction loss is increased or decreased.

EFFECTS OF ROUNDNESS ON FRICTION LOSS IN CONSIDERATION OF STRAIGHTNESS

In reality, the journal of the bearing has manufacturing tolerances not only along the circumferential direction represented by the roundness, but also along the axial direction represented by the straightness. Consequently, it is also necessary to analyze the effects of the roundness on bearing lubrication in consideration of the straightness of the journal. In this section, first two forms of straightness tolerances, that is, one resulting in an increase of the friction loss (straightness form 1) and the other leading to a decrease in the friction loss of the bearing (straightness form 2), are considered. Then the coupling effects of roundness and straightness regarding their amplitudes and phases respectively are analyzed and discussed.

Effects of Roundness on Bearing Friction Loss under Two Straightness Forms

The friction loss of the bearing with the roundness amplitude of 5um at different roundness phases for two different forms of straightness are shown in Figure 8. It is shown that at the same roundness phase, different straightness values lead to different friction losses. It is also noted that the existence of straightness changes the variation range of the friction loss with respect to the roundness phase. Besides, as can be seen from Figure 8. the maximum and minimum friction losses caused by the roundness phase have been altered compared with the case when the journal is ideally straight.

The friction loss of the bearing with respect to roundness amplitude under two roundness phases (80[degrees] and 160[degrees]) as well as two straightness forms are shown in Figure 9. It is shown that at the same roundness amplitude, different straightness amplitudes lead to different friction losses. It is also noted that the straightness changes the variation range of the friction loss. But unlike the case of roundness phase, the straightness does not change the trend of friction loss with respect to the roundness amplitude.

When comprehensively considering the roundness phase and amplitude, the maximum variations of friction loss caused by roundness (amplitude and phase) under the two straightness forms are given in Figure 10. It is concluded that the existence of straightness indeed affects the variation of friction loss caused by roundness. Next how to consider the coupling effect of roundness and straightness with the coupling results are presented.

Coupling Effects of Roundness and Straightness on Friction Loss of Bearing

In this section, the coupling effects of roundness and straightness on the variation of friction loss is systematically studied and analyzed, which will provide useful guidance on how to simultaneously design and control the two geometrical tolerances of the bearing.

A surrogate model based on simulation data is built to assist the analysis. First sample points in terms of the amplitudes and phases of both roundness and straightness are obtained using LHS (Latin Hyper-cubic Sampling) [13], one of the widely applied DoE (Design of Experiment) techniques. Different sets of values correspond to different combinations of roundness and straightness forms. These samples are given to the bearing model as inputs and the friction losses for each case are obtained. The samples points together with their corresponding outputs are used to build the surrogate model and Kriging modeling approach [14] is applied. Based on the Kriginig model, optimization is performed to search for the combinations of straightness and roundness forms that lead to the maximum and minimum friction losses, respectively, to determine the variation of the friction loss caused by the coupling of these two geometrical tolerances.

The results are presented in Figure 12. It is shown that the friction variation caused by the coupling of the two geometrical tolerances is larger than the sum of the friction loss caused by individual geometrical tolerance, which shows that the coupling of the tolerances will indeed lead to a larger variation of friction loss. It is also confirmed that friction loss caused by roundness will be significantly affected by the existence of straightness, thus, for future studies of how roundness may affect the friction loss and lubrication of the bearing, more factors should be considered.

CONCLUSION

In this work, the effects of roundness amplitude and phase on friction loss and lubrication are analyzed and presented. It is shown that the existence of roundness will lead to increase or decrease of friction loss which is determined by the roundness phase and the variation range is determined by the roundness amplitude. For POFP, similar but opposite conclusions is obtained. However, MOFT will be decreased in most cases, and be increased sometimes, which depends on the roundness amplitude and phase simultaneously.

The effect of roundness on friction loss under the existence of straightness is also studied. It is concluded that different forms of straightness have different impacts on friction loss caused by roundness in terms of the variation range as well as the maximum and minimum friction loss values. What's more, the coupling of roundness and straightness leads to a larger variation of friction loss compared with their individual effects, which proves that there do exist coupling effects between straightness and roundness.

The conclusion shows that geometrical tolerances will also affect the system performances and should be paid more attention to. Besides, the coupling of different geometrical tolerances should not be ignored, and the systematic analysis should be further researched.

REFERENCES

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[2.] Wei Y, Chen Z., Jiao Y, "Effects of Dimensional Tolerances on the Friction Power Loss of Hydrodynamic Journal Bearing System." Journal of Donghua University (English Edition), 31.3 (2014): 266-271.

[3.] Ogrodnik, P., Xu, W., Goodwin, M. J., Bancroft, G. A., "A theoretical investigation of the use of 2 k factorial analysis to determine the effects of dimensional manufacturing tolerances on the stability of hydrodynamic journal bearing systems," Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology (2011): 1350650111408180.

[4.] Zhou, Jianhua, Mian Li., and Min Xu., "Multi-Disciplinary Tolerance Optimization for Internal Combustion Engines Using Gaussian Process and Sequential MDO Method," SAE International Journal of Materials and Manufacturing 9.2016-01-0303 (2016): 410-418.

[5.] DeHart, A. and Smiley, J., "Imperfect Journal Geometry - Its Effect on Sleeve Bearing Performance," SAE Technical Paper 640837. 1964, doi:10.4271/640837.

[6.] Mehenny, D., Taylor, C, Jones, G., and Xu, H., "The Influence of Circumferential Waviness of the Journal on the Lubrication of Dynamically Loaded Journal Bearings," SAE Technical Paper 970216. 1997, doi:10.4271/970216.

[7.] Torii, H., Nakakubo, T., and Nakada, M., "Elastohydrodynamic Lubrication of a Connecting Rod Journal Bearing in Consideration of Shapes of the Bearing," SAE Technical Paper 9204851992 doi:10.4271/920485.

[8.] Zeng H, Xu W., and Wei Y, "Effects of the roundness error on the friction power loss," China Mechanical Engineering 2012, 23(8)

[9.] Xu, W., Ogrodnik, P. J., Li, B., Zhang, H., and Gao, S., "Effect of journal out-of-roundness on stability of a symmetric hydrodynamic journal bearing system. Part 1: Theoretical analysis," Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology (2015): 1350650115579211.

[10.] Resch, T., Schweiger, C, Offner, G., and Miyauchi, Y, "Numerical Investigation in Rotor Motion and Elasto-Hydrodynamic Rotor Bearing Behavior of a Rotary Engine Using Flexible Multi-Body Dynamics," SAE Technical Paper 2007-01-1459. 2007, doi:10.4271/2007-01-1459.

[11.] Excite Powerunit Theory Manual, Version v2014, AVL List GmBH, Austria, 2014

[12.] Gulwadi, S. and Shrimpling, G., "Journal Bearing Analysis in Engines Using Simulation Techniques," SAE Technical Paper 2003-01-0245. 2003, doi:10.4271/2003-01-0245.

[13.] McKay, Michael D., Beckman Richard J., and Conover William J. "A comparison of three methods for selecting values of input variables in the analysis of output from a computer code." Technometrics42.1 (2000): 55-61.

[14.] Speckhart, F. H., "Calculation of Tolerance Based on A Minimum Cost Approach," Journal of the Engineering Industry, 94 (2): 447-453, 1972.

CONTACT INFORMATION

Bao Wang

Institute of Automotive Engineering

National Engineering Laboratory for Automotive Electronic Control Technology

Shanghai Jiao Tong University

Shanghai, China 200240

wangbao_john@sjtu.edu.cn

Jianhua Zhou

Institute of Automotive Engineering

National Engineering Laboratory for Automotive Electronic Control Technology

Shanghai Jiao Tong University

Shanghai, China 200240

zhoujhjane@sjtu.edu.cn

Min Xu

Institute of Automotive Engineering

National Engineering Laboratory for Automotive Electronic Control Technology

Shanghai Jiao Tong University

Shanghai, China 200240

mxu@sjtu.edu.cn

ACKNOWLEDGMENTS

The work presented here is supported in part by National Natural Science Foundation of China through Grant No. 51605286 and Shanghai automotive industry science and technology development foundation under the project No. 1614. Such support does not constitute an endorsement by the funding agency of the opinions expressed in the article.

Bao Wang, Jianhua Zhou, and Min Xu

Shanghai Jiao Tong University
Table 1. Parameters of the bearing

Terms                     Nominal sizes

Bearing/Journal diameter  38mm
Bearing shell width       16.2 mm
Oil type                  SAE 5W-10
Shaft rotational speed    6000rpm
Roundness Tolerance       5micron
Straightness Tolerance    5micron
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Author:Wang, Bao; Zhou, Jianhua; Xu, Min
Publication:SAE International Journal of Passenger Cars - Mechanical Systems
Article Type:Technical report
Date:Jul 1, 2017
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