A problem with the rear tub bearing or the spin basket could be causing this problem. With the washer empty, check for forward/backward play in the stainless steel spin basket in relation to the plastic outer tub. Also check for upward play. Push up of the top front edge of the spin basket. Spin the basket a few degrees and check it again for upward play. Continue to check the basket around the whole 360 degrees. If you find a section where you detect significant upward play, then you likely have a bad spin basket and may also have a bad rear tub bearing.
I recommend that you check your owner's manual for warranty information if you suspect that you have a bad spin basket and or failed rear tub bearing. The spin basket normally has a limited parts warranty that is longer than the 1 year full warranty. The out tub has a 10 year warranty on some HE3 models. The owner's manual for your washer will have the details of warranties on these parts if they are covered. You would have to pay for the labor (around $150) for the diagnosis and replacement of the parts. If you don't have your manual, you can normally find an online copy through the owner's manual search feature on our Manage My Life website. Click on the "Manuals" link at the top of this web page.
Based on the cost of these parts and the complicated repair involved in replacing them yourself, I recommend that you call Sears for service if the parts mentioned above are covered and you suspect that one or both have failed.
A component that could be causing a buzzing noise in the rinse and spin cycle is the drain pump. You can
unplug the washer
and check the drain pump using the procedure shown in the image below. When you pull the large item filter out of the pump, you may find debris or foreign objects that are in the drain pump housing.
These tips may help you with this HE3 washer problem. If you need more assistance, reply with additional details and the full model number of your washer.