There is a burnt odor around a grease lubricated bearing. Is that a concern?

A burnt odor may indicate overheating of the bearing.  A burnt odor suggests that the grease may have been oxidized or thermally degraded.  It is prudent to investigate the source of a burnt odor, and to determine its cause.  If the source of the odor is a grease lubricated bearing, the equipment should be shut down and the problematic bearing checked.