I've noticed that some tefillin have very sharp edges at the base of the titura. As many people may have noticed, this can become highly uncomfortable while davening.
Does anyone have a solution for this problem which won't passul tefillin?
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I understand to what you are referring and know from my own experience how painful (and pinching) the edges of the titura can be. It distracts from kawannah and tefillah.
The only requirement for square angles and corners in with regard to the bayith itself (whether of the shel yadh or the shel rosh), the shape of the stitching around the base, and the four corners which are stitched in order to create the tovar (ma'abarta). See Mishneh Torah, Hilkhoth Tefillin 3:1-19.
Further, none of the items listed in the reference above with regard to what causes pesiluth in tefillin relate to the edge around the bottom of the tefillin.
This being the case, it is my suggestion that you take your tefillin to a sofer who is willing and have them use a small sanding or grinding tool (frequently used by soferim who manufacture tefillin) and ever-so-slightly round the sharp edge around the bottom of the titura (i.e. the unpainted part that rest against the arm). Doing so will do absolutely no damage to the squareness of the corners on your shel yadh and will most likely not even be noticeable to anyone but you.
Le`aniyuth da'ati, this is a fairly simple solution that will in no way posul your tefillin.
[NOTE: I would warn against attempting to make any alteration whatsoever on one's own tefillin. All such changes - with the possible exception of touching up the paint on the batim - should ONLY be made by a qualified sofer.]
Hope this helps. Kol tuv.