Removing noise from accelerometer data
From the looks of this data you could simply clamp any samples between 0.7 and 1.3 to 1.0 so that you get a flat line until the machine starts operating. Alternatively (or additionally) only enable data collection when you see a short series of samples above a particular threshold.

Looking at your frequency plot, you show that the noise floor is wideband and spans all the way across your target range. This means there's no frequency-based filter (e.g. low pass) that you can use in this scenario.