My mom and I had done considerable work about 20 years ago in the genealogy of the Ache/Achey's of Pennsylvania. The Bethlehem clan is pretty clear cut.
Unfortunately, I will quote from memory here as I do not have the primary source in front of me.
In September of the year 1752, three men with the surname of Ache arrived in Philadelphia, Pa. on the ship "Halifax" sailing from Amsterdam. Their names were Johannes Ache, Hermannius Ache and Johann Jakob Ache. These were not the first named Ache to appear in Pennsylvania, the clan in Lancaster and Lebanon Co. appear to have arrived earlier.
Anyhow, Johannes appears to have settled in Philadelphia and died young. Jakob was a bit of a mystery man to us. The early clan was primarily Calvinist (German Reform) in faith.
Hermannius was a farmer in what is now Montgomery Co. Pa, and lived a good long life dying in the early 1790's (you can find him on the 1790 Pa. census). His son, Ludwig, moved to Hellertown, Pa. and is the sire of the entire Bethlehem clan (buried at the old Union Church not far from I-78 in Hellertown, Northampton Co., Pa).
I relate to Hermannius through Ludwig of Hellertown, though his son Michael (of Bethlehem) and his grandson Charles (of Bethlehem, later of Reading, Pa.) who was my Great Grandfather.
Send me private e-mail so that I can get you in contact with my mom for further information.