data recover from damaged hard disk

If the data on the disk are extremely important and you don't have backups, then you should hire a professional. It will be expensive, but it is preferable to risking further damage to the data by trying to recover it yourself.

Sometimes damaged external hard drives perform inconsistently. You might try waiting a while an plugging it back in, or even trying it on a different computer. That doesn't usually work, but sometimes it does.

An external hard drive is an internal disk inside an enclosure, though often the enclosure is not designed to be easily user-serviceable. If the enclosure (for example, its power or data connectors, or the circuitry in the enclosure that is not part of the drive itself) is what's damaged, then you may be able to use the disk by removing it from the enclosure and putting it inside a new enclosure (or directly inside a computer). You may be able to search the web to find out what interface (e.g. SATA, EIDE) your external drive uses internally, but you'll find out for sure when you open it up and see. Furthermore, it's possible that the only "damage" is that a data or power connection has been broken or loosened. If that is the case, you can firmly seat the connection, and the drive may work again.

If the internal drive is itself damaged and unusable, then it is still typically possible to recover the data. However, doing so involves taking it to data recovery specialists with special equipment, and would be extremely costly.