解:$(1)$原式$=2x²-\frac {1}{2}+3x-4x+4x²-2=6x²-x-\frac {5}{2}$
∵$x=\frac {1}{2}$,∴原式$=6×\frac {1}{4}-\frac {1}{2}-\frac {5}{2}=-\frac {3}{2}$
$(2)$原式$=2a²-(2a²-\frac {1}{2}ab+8ab)-\frac {1}{2}ab=2a²-2a²+ \frac {1}{2}ab-8ab-\frac {1}{2}ab=-8ab$
当$a=1$,$b=\frac {1}{4}$时,原式$=-8×1×\frac {1}{4}=-2$