There are a couple mistakes (I believe) in your note. MJG is right, this is fatigue (I recognize the MIL-HNDBK-5 equation). So we need to be careful about how we treat this, and about what the definition of cycles is. Please look at the attached Prime 3.0 sheet.
Borrowing on Fred's idea how about
seems to work fine. Does anybody see a problem with this?
Well, Hz = 1/sec
so Hz sec is unitless.
Because (for fft's) I need Hz for frequency of vibration due to a rotating shaft, I set "RPM = Hz/60" (note the caps!) Then I get the correct numerical value for the fft resolved frequency. I like this answer:
I prefer 1 RPM = 2 Pi / 60 Hz and 1 rev = 2 Pi.
so RPM = rpm (already built-in)
And rev is a built-in and equals 2 pi.
For cycle I guess that cycle = 1. Because then for the electrical alternating current you have that 60 cycles/seg = 60 Hz which agrees with the usual frequency.
cycle = 1
cycle + % = 2 but must be an error
In Mathcad 11
rad + sr = error (!!!)
In Mathcad 15 and Prime
rad + sr = 2 (???)