Ok. If the dryer currently has a 4 wire connection, you will see a small wire connected to the center terminal that disappears into the dryer. This is the bonding wire. Since your new three wire cord does not have a separate ground, you need to take that small wire and screw it into the existing ground terminal - where the existing ground wire in the 4 conductor cord is attached.
A drawing may help.....take the wire that is on the center terminal and ground it to the dryer case like this:
Then connect your new three wire cable.
Make sure you do this. Failure to do this is dangerous and not to code.
Again, a 4 wire is preferable.
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Thanks very much.