I have a Kenmore Elite HE3 that has plastic pieces

Mine had the same problem. It also loudly vibrated at high speed spin. I took it apart and found the basket support that bolts to the back of the basket(this is what drives the basket) had corroded and broke one of the three arms off. It would work normally but at high speed it wobles. This is what causes the basket to rub the plastic and chew it up. I have to replace the front outer tub and the basket, about 500.00 in parts. if you have it done much more.

I can't solve the problem, but my HE3 42824 has done the exact same thing...the kenmore subcontractor repair people have been less than helpful and want to charge 180 just to come out and service it. We were told on the phone that it MAY be the plastic tub, and it MAY be covered under warranty. After waiting 5 days for a maintenance appointment, only to have them cancel it for 5 days, we had enough...I we bought a Samsung last night! I don't think the Kenmore cleans well, anyhow, and it adds a bit of a musty smell to my clothes, so I am glad to be rid of it!