motor single phasing or double phasing

If you are referring to a low voltage (440V) motor, the most effective protection against single-phasing is to use a thermal O/L relay with SP protection. Less than $ 10. Mechanically operated thermobimetal device. Awesome accuracy at this price.

If it is an expensive motor of high HP or at medium voltage, electronic relays are available.

Hmmm... some potentially dangerous generalization here...

Bi-metal thermal overload relays are NOT a good way to protect a motor from single phasing. This has been grossly over sold by the IEC motor control manufacturers. It only works if the motor is almost fully loaded when the single phasing occurs, and only if it is already running. If the motor is not running when a phase is lost, it has no idea and will allow you to attempt to start. By the time it trips, damage may already happen.

It works via a system called a "differential trip bar" in the trip mechanism that relies upon equal force being applied by all 3 bi-metal strips. If one is "cold" because no current is flowing through it, the bar moves slightly against the other two bi-metal strips so they will trip QUICKER under a loaded condition. But if the motor is not fully loaded to where the other two bi-metal strips are bending in the first place, the overload will NOT trip at all! Unfortunately when you single phase a 3 phase motor, it creates a lot of what is called "negative sequence current" as a result of one of the phases being un-powered for portions of each cycle. Those negative sequence currents cause anti-torque pulsations in the rotor, so in essence the rotor begins to "fight itself" and heat up. Than means you often will get rotor damage even though the overall current going to the motor stator (as seen by the remaining 2 bi-metal strips) is still below the tripping threshold.

And by the way, this "differential trip bar" ONLY is found in IEC thermal overload relays. NEMA style OLRs do NOT have that feature at all, so they do NOTHING to protect against single phasing. The same is true for eutectic melting alloy OLRs.

As waross pointed out, the best way to do it is to use a Phase Monitor Relay. Of those, the best are ones sensing current, not voltage, because the voltage type can be fooled by regeneration off of a spinning motor, i.e. if the phase is lost while the motor is running, it may not detect it. Current based Phase Monitors look at the total current in each phase. It is not only fool proof, but they usually also provide phase current imbalance protection. Some solid state OLRs now have this kind of protection built-in, that's another good way to go.

........and also motors draw much more current than no load current when single phasing (making the application for phase loss protection of the simple IEC thermal overload or motor starter / cb more likely to offer some protection).