Vibration analysis could be used to find the cause behind the presence of debris in oil, in other words, it could be used to locate a fault already detected by oil analysis. it is also possible to use Oil analysis as a confirmation tool, after detecting signs of fault in vibration analysis.
The bearing or roller bearing vibration is related mostly with the oil condition. as iniitial values the viscosity, temperature and density are very important. During the operation, the water content, and the metal chips content is very very important. Also temperature and viscosity is importat too. I agree with Ahmed Guerine about the references
It is a multivariate problem. It could be interesting to put the obtained parameters together and try to find the correlation between them. If you find any trends, it could open perspectives to make a link between vibration and oil analysis. I think that if a vibration is detected, the metal content in oil could be high.
The oil analysis deals with the characteristics of the oil (i.e. viscosity, heat conductivity,density,...), to connect it with the vibration analysis, these characteristics must be involved in the vibration equations.
In order to connect this analysis, there must be an intermediate equation, take the journal bearing as an example, you have Reynolds equation which contains the viscosity term (as oil property), after solving this equation (include the dynamic term), and integrating the resulting pressure, you can estimate the stiffness and damping for the oil lubricant. For the vibration analysis, you will use the above results in the vibration's equation (i.e. equation of motion). And by any change in the oil, there is a changed in the resulting vibration.