Step-down transformer AC to DC voltage conversion problem?
It's quite possible that the 18V reading is the RMS value when given an input of 110V, and you're inputting 117V and reading the peak value.
The conversion factor between RMS and peak for a sinusoidal waveform is sqrt(2); add the 110:117 increase in voltage and that's pretty close to what you're seeing.

You should also note that a bridge of diodes is not sufficient to get a clean DC signal -- there will still be a 120 Hz signal (with lots of overtones) after rectification, and you need to filter and regulate this to the voltage you need.
Add a couple of 470 uF or 1000 uF capacitors across the rectified signal (low ESR, and rated for 2x your expected input voltage!) and a linear regulator with sufficient current capacity, set to the actual output voltage you want, and you'll probably have a reasonable power supply.

An alternative is of course to build a switching power converter.