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Purpose This paper aims to provide efficient methods to calculate the friction coefficients and film thickness ratios in mixed lubrication (ML) regime for water lubricated bearings. Mathematical models consider influence of micro-asperities contacts which is based on the Gauss random distribution. Design/methodology/approach Effects of external loads, rotating speeds and radial clearances are obtained. Algorithm shown here is applied to a class of common industrial problems. Calculated Stribeck values are given and evaluated. The calculated and experimental results agree well which proves the correctness of the model. Findings In Part I, the authors believe that the paper presents the following for the first time: universal methods are developed for the calculation of friction coefficients and film thickness ratios (lambda) in ML regime; effects of different external loads, rotating speeds and radial clearances on friction coefficients and film thickness ratios are presented in detail; comparisons are made between the results predicted by the model and experimental results, and they agree rather well which proves the correctness of the model. Originality/value Present work successfully develops universal methods for predicting the friction coefficients and film thickness ratios.

Purpose As the companion paper of Part I, this paper aims to get more insight into the essence of lambda and to reveal its nature and role in the transition of lubrication states. Mixed lubrication (ML) model with micro-asperities contacts has been discussed in details in Part I. Design/methodology/approach Mimetic algorithm is used to get numerical solutions. Relationships between film thickness ratios and lubrication states transition with different external loads, rotating speeds, radial clearances, elastic modulus, surface hardness and roughness parameters are obtained. Findings The characteristic parameters of transitions from boundary lubrication (BL) to ML and ML to hydrodynamic lubrication (HL) are studied to determine how these parameters change with above factors. Finally, the essence and major influencing factors of lambda are summarized for such bearings. Originality/value In Part II, the authors believe that the paper presents for the first time: further insight into the essence of the lambda ratio, and its role in the lubrication states transition are given; the determinations of the characteristic parameters of transition from BL to ML and ML to HL are investigated for the first time; the characteristic parameters of transitions from BL to ML and ML to HL are also studied to determine how parameters (external load, rotating speed, radial clearance, elastic modulus, surface hardness and roughness parameter) change with above factors; a summary of the essence and major influencing factors of lambda for such bearings is given.

-Researches of the nature of friction coefficient of water lubricated bearing are carried out in this paper. Based on the experimental results of composite material bearing under hydrodynamic lubrication by water, we calculate the Stribeck curves as the function of load and speed, deviate the modified Reynolds equation considering wall slip effects in Cartesian coordinate system, put forward the essential model of friction coefficient, the composition of friction coefficient and essential changing correlation between them. Numerical results are in good agreement with experimental results, which verifies existence of wall slip. Researches indicate that there is always an appropriate working condition which friction coefficient is minimum. Comparison of the theoretical and experimental results shows that they are consistent on the overall trend but still exist some deviations under certain operating conditions. Reasonable explanations are given to illustrate the correctness of theoretical model. Key words:Water lubricated bearing / nature of friction coefficient / wall slip effect / solid contact effect and fluid viscous effect / experimental research

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