Narrative:

We departed ZZZ 2.5 hours late after extensive on gate and taxi delays due to thunderstorms impacting the field and departure corridors. A crew critical offtime (cco) extension was required on our duty day in order to depart. A take off go around [power] takeoff with wind shear precautions was planned and executed. On climb out we remained IMC to cruise altitude; encountering rain and turbulence throughout the climb. No airframe icing was noted; but engine anti ice was turned on as total air temperature (tat) dropped to 10C. Engine ai was turned off at -40C tat. Rate of climb was very low as we passed FL300; and ATC was advised due to less than 500 FPM climb rate. As we leveled at FL340; the engine ECAM page appeared with a 6.3 N1 vibration indication flashing. The first officer (first officer) retrieved the vibration checklist in the QRH and we reviewed it. With auto throttle off I cycled the thrust from idle to climb thrust. The vibration indicated 3.4 at idle and 8.0 at climb thrust. I sent this information to maintenance. Dispatch immediately sent a suggestion to divert. We descended to FL270 (for more airspeed envelope) and I continued to try other power settings with the same result. At high vibration both the first officer and I noticed a distinct smell in the aircraft. The smell was also noted by a flight attendant in the aft galley.I requested a phone patch with maintenance. After discussing the issue with maintenance and dispatch I made the decision to divert. Dispatch sent landing performance and I gave the flight attendants a briefing. I made an announcement to the passengers and the first officer coordinated a turn to ZZZ1. I decided to land overweight rather than remain airborne with an engine problem. We ran the overweight landing checklist and landed uneventfully.as we descended to warm air; the vibration indication returned to normal (0.0) so I suspect engine icing as the cause.maintenance write-ups were entered for both the engine vibration and the overweight landing.

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Original NASA ASRS Text

Title: A320 flight crew reported that they had a very slow climb rate above FL300 and the engine ECAM page appeared with a very high N-1 vibration indication.

Narrative: We departed ZZZ 2.5 hours late after extensive on gate and taxi delays due to thunderstorms impacting the field and departure corridors. A Crew Critical Offtime (CCO) extension was required on our duty day in order to depart. A Take Off Go Around [power] takeoff with wind shear precautions was planned and executed. On climb out we remained IMC to cruise altitude; encountering rain and turbulence throughout the climb. No airframe icing was noted; but engine anti ice was turned on as Total Air Temperature (TAT) dropped to 10C. Engine AI was turned off at -40C TAT. Rate of climb was very low as we passed FL300; and ATC was advised due to less than 500 FPM climb rate. As we leveled at FL340; the engine ECAM page appeared with a 6.3 N1 vibration indication flashing. The First Officer (FO) retrieved the vibration checklist in the QRH and we reviewed it. With Auto Throttle off I cycled the thrust from idle to climb thrust. The vibration indicated 3.4 at idle and 8.0 at climb thrust. I sent this information to maintenance. Dispatch immediately sent a suggestion to divert. We descended to FL270 (for more airspeed envelope) and I continued to try other power settings with the same result. At high vibration both the FO and I noticed a distinct smell in the aircraft. The smell was also noted by a flight attendant in the aft galley.I requested a phone patch with maintenance. After discussing the issue with maintenance and dispatch I made the decision to divert. Dispatch sent landing performance and I gave the flight attendants a briefing. I made an announcement to the passengers and the FO coordinated a turn to ZZZ1. I decided to land overweight rather than remain airborne with an engine problem. We ran the overweight landing checklist and landed uneventfully.As we descended to warm air; the vibration indication returned to normal (0.0) so I suspect engine icing as the cause.Maintenance write-ups were entered for both the engine vibration and the overweight landing.

Data retrieved from NASA's ASRS site and automatically converted to unabbreviated mixed upper/lowercase text. This report is for informational purposes with no guarantee of accuracy. See NASA's ASRS site for official report.