Don't look at the voltage.
Imagine the solinoid as a large inductor smoothing the PWM waveforem. When a pulse is applied, a current will start to flow in the inductor, when the pulse is removed, it will continiue to flow thought the freewheel diode until it decays to 0. If the PWM frequency is high enough (the time per cycle needs to be many times smaller than the RL time constant for this to work), then the current will never return to 0. Imagine that the PWM is at 50% duty, the current through the inductor will average out to be half the maximum current, ingnoring the ripple.
Use a Schotky diode as a they have lower on voltages and are much faster than Si.