I enjoy cuddling and displaying affection towards someone I am in a relationship with, but I don't have much of a desire to be intimate with that person.

If it's normal for you, it's normal.

You might want to look up information on asexuality and demisexuality. Asexuality.org has a lot of good information.

Have you ever been intimate with anyone else?
If this person has a problem with your lack of intimacy, you need to leave this person alone..

May I ask how old you are? Also, do you have any health issues or take any medications (including self-medicating?)

Heath is right that what is 'normal' for is 'normal'.

"Normal" is a relative term. It changes with the individual, their age, their health, the place they are in their life, etc.