Xmax

Why design for an excursion of Xmax + 10%.

The short answer is that by accepting a little distortion, a higher SPL is achievable.
Of course, there is always more to the story...

What is Xmax anyway?

Above is the cross section of a typical speaker voice coil assembly.
Shown in light yellow, is the zone between the pole piece and the magnet on the outside of the voil coil, where there is a uniform magnetic field
While ever the voice coil maintains a constant number of turns within this zone of constant magnetic field, the signal will be reproduced faithfully.

There comes a point where any further increase in excursion results in less turns on the voice coil being within this zone. Once this happens, the signal is no longer reproduced properly and distortion occurs.
Xmax is the amount by which the voice coil can move in one direction without it leaving the magnetic zone

If excursion is increased even further, the back of the voice coil former will eventually slam into the magnet, risking permanent damage to the driver.
Xlim is the amount by which the voice coil can move in one direction before this hard limit occurs. In other words it is the "excursion limit"

Xlim is always larger than Xmax but is often not published by the supplier.
Some unscrupulous suppliers actually state the value for Xmax as what should be Xlim so it is always wise to test carefully.
A good driver can have an Xlim that is Xmax * 2 although a posting at AVSForum suggets Xlim=Xmax + 25% is more realistic

The diagram shows what is known as an overhung design because the voice coil windings extend beyond the magnetic zone.
There is an underhung design where the voice coil is shorter than the zone and is intended to operate wholely within the magnetic field. This can be seen in the 3D cutaway image at the top of the page. The principles of Xmax and Xlim are the same.

So how far can we go?

There is a zone between Xmax and Xlim where we can operate without risk of physical damage but where distortion increases as we increase excursion.
Looking at discussions on various Audio forums, there is general consensus that, for a subwoofer, distortion becomes audible if you exceed Xmax + 10%. It is fairly safe to assume that you won't damage your driver.
When designing a sub for Home Theatre, which is primarily driven from the LFE channel, a little distortion is acceptable, so Xmax + 10% gives a better estimation of how the sub is likely to be used.