Theoretical analysis of bearing considering elastic deformation – effects of the housing stiffness and bearing length on bearing performance

doi:10.1016/S0389-4304(98)00076-9

JSAE Review

Volume 20, Issue 2, April 1999, Pages 203-209

https://doi.org/10.1016/S0389-4304(98)00076-9 Get rights and content

Abstract

In recent high power, compact and light weight automotive engines, the bearing load has been increasing and housing stiffness has been decreasing. As a result, the bearing performance is greatly influenced by elastic deformations of both the housing and the bearing. The effects of changing both the housing stiffness and the bearing length on bearing performance were studied by using the elastohydrodynamic lubrication theory on connecting rod bearings for diesel engines.

Introduction

In recent years, the objective for automotive engine development has been to achieve lower fuel consumption, longer life, lower pollution and lower noise, while maintaining high output and high performance to meet the diversified requirements of the customers. The bearing loads in these engines have increased with higher power output due to the improvement of combustion and so on. Moreover, the reduction of housing stiffness has also added to the compactness and the light weight design, and as a result, the bearing is used under harsher conditions. Therefore, in order to make a bearing design with high reliability, it is essential to predict precisely the bearing performance at the initial stage of engine development.

For prediction of the performance on the engine bearings, the hydrodynamic lubrication theory, which assumes the bearing to be a rigid body, has been widely used. However, by applying the elastohydrodynamic lubrication theory (EHL) [1], [2] to consider the elastic deformations of both the bearing and the housing, a more accurate analysis can be expected under harsh conditions.

In the conventional studies, the designs of the housing and the bearing were treated separately, but EHL allows simultaneous study of both designs.

Fig. 1 shows the trend for the specific load of the connecting rod bearings in a diesel engine with a displacement of 7 to 9 l, particularly at high output power.

It is expected that the specific load of the connecting rod bearing will rise year by year, and will exceed 100 MPa in 2000 A.D.

The present study focused on the bearing specific load, which was increased by the rise of the cylinder pressure and the reduction of the bearing length, on the connecting rod bearings for diesel engines, and examination of the effects on the bearing performances with EHL.

Section snippets

Analysis method

A method of analysis of EHL, which was used in the present study, is described as follows:

Oil film characteristics under dynamic load are expressed by Reynolds equation (1) which is the fundamental formula for hydrodynamic lubrication: $∇ h^{3} η ∇ p −6 U R ∂h ∂θ + 2∂h ∂t =0,$ h: oil film thickness, R: shaft radius, p: oil film pressure, t: time, U: relative velocity between two surfaces and η: viscosity. Fig. 2 shows the coordinate system of the bearing.

The oil film pressure at the edge of the bearing was p=0,

Analysis model

The connecting rod bearing of a diesel engine with an engine displacement of 8 l was adopted in the present study. The main specifications of the engine and the bearing are shown in Table 1.

The connecting rod for analysis to obtain the compliance matrix is a half model excluding a portion of the small end as shown in Fig. 3, and is constrained at the rod upper end part completely. It is assumed that neither the connecting rod nor the bearing have a parting line and the big end bore and the

Effects of the cylinder pressure

As one effect of making a high power diesel engine, the cylinder pressure is increased. Moreover the trend is that the cylinder pressure increases every year. It is estimated that the maximum cylinder pressure will reach 20 MPa in the near future. Therefore, to confirm the effects of the connecting rod bearing on the higher specific load of the cylinder pressure, the cylinder pressure condition was changed, as shown in Table 2.

The oil film thickness distribution (bearing angle θ: 15°), the oil

Effects of the stiffness of housing and the bearing length

In a conventional design of stiff housing, the decrease of the bearing length was examined, and it was considered that an effective reduction of the power loss with decrease of the sliding area could be expected from the results of the rigid analysis, as shown in Fig. 7 (the calculated condition: Table 1). However, due to the requirement for low fuel consumption, the housing has been constrained into the compact and light weight design, and its stiffness is significantly reduced. The decrease

The maximum specific load and the bearing performance

The maximum load of the bearing divided by the projection area of the bearing is called the maximum specific load and has been used as a standard for severity in bearing design. By replacing the changes of the cylinder pressure and the dimension of the bearing length with that of the specific load, the bearing performance and the specific load were compared. Fig. 12 shows the relations between the maximum specific load and the bearing performance, including the minimum oil film thickness, the

Conclusions

On the connecting rod bearing for diesel engines, using the EHL analysis for the changes of the cylinder pressure and the bearing length which linked the housing stiffness, the following can be concluded:

(1)	The rise of cylinder pressure increases the bearing load and decreases the oil film thickness, and this increases the oil film pressure and the power loss.
(2)	By the decrease of the bearing length, the load capacity is reduced, the oil film thickness is reduced and the oil film pressure is

References (2)

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