The answer is three.

As often happens in real situations, this problem has plenty of extraneous, irrelevant and useless data. All that is needed is the balance beam scale and the pistons.  Because the balance beam compares two items it is often viewed as binary device when in fact it is a tristate device where  the three states are less than, greater than and equal. With this in mind, the 27 pistons are divided into three groups of nine. Two groups are placed on the scale where an imbalance will indicate the group containing the heavy piston and a balance will indicate the heavy piston is part of the group not on the scale. The heavy group of 9 is divided into three groups of three and the weighing process is repeated, identifying the group of three containing the heavy piston. For the third and final measurement, two of the three pistons from the heavy group are compared on the balance. The balance will indicate the heavy piston or, if it indicates balance, the heavy piston will be the one not on the balance.

Wishing all a joyous Independence Day!

Regards
Brent Regan