Natural weapons operate under different rules than do manufactured weapons, which are covered in the Universal Monster Rules and in the Combat Rules. The short version is, you get to attack once with each natural weapon, regardless of how many iterative attacks you have from high BAB.
So if your BAB was +6/+1, you would get to attack once with each claw, each at +6 BAB. Total of two attacks, not four, and you would never make the claw attacks (or any other attacks) at +1 BAB.
You could combine these natural attacks with manufactured weapons as long as they don’t use the same limb. For example, say your barbarian wore spiked armor: you could attack with both the spiked armor and the claws. When you do so, you take all your regular attacks from BAB with the manufactured weapon, and then also take any natural attacks you have, but treated as secondary. In this case, this would be spiked armor +6, spiked armor +1, claw +1, claw +1. That way you do get four attacks. Note that secondary natural attacks also add only half your Strength bonus to their damage.