The document provides specific guidance for assessing the severity of radial vibration measured on the shafts of coupled industrial machines with fluid-film bearings in situ. The criteria provided in this document apply to coupled industrial machines, having maximum continuous rated speeds in the range 1000 r/min to 30000 r/min and not limited by size and power, comprising - steam turbines, - turbocompressors, - turbogenerators, - turbofans, - electric drives and associated gears, where relevant, - rotodynamic pumps (turbopumps); however, the information provided in this part of ISO 7919-3 complements that given in ISO 10816-7. Two criteria are provided for assessing the machine vibration when operating under steady state conditions. One criterion considers the magnitude of the observed vibration; the second considers changes in the magnitude. In addition, different criteria are provided for transient operating conditions, such as run-up and coast-down. The evaluation procedures presented in this part of ISO 7919 are based on broad-band measurements. This part of ISO 7919 does not apply to land-based steam turbine-generator sets for power stations with outputs greater than 50 MW (see ISO 7919-2), nor to machine sets in hydraulic power generating and pumping plants with outputs of 1 MW or greater (see ISO 7919-5).