Spikes in raw acceleration data from AC motor
The spikes seem to have a few common heights that are roughly related by factors of 2, which strongly suggests that they are noise-induced single-bit errors in the binary data.

One good way to address this is to take the standard deviation of all the data, and then simply throw away any samples that are more than, say, 2&sigma; from the mean.

Another technique is to use a median-value filter, which looks at a sliding window of, say, 3 or 5 samples, and replaces the middle sample with the median value of the samples in the window. I've used this technique to remove "salt and pepper noise" (same problem) in video data.



Simply post-processing the data as described above might be adequate for your purposes of monitoring equipment health, etc. But if you want to find and fix the root cause of the bit errors, you'll need to focus on the digital communications paths in the system:


between the accelerometer and the MCU
between the MCU and the system where you're analyzing the data


Switching the plastic box to a metal one might be a good first step, especially for the upper bullet item. Shielded cable (if you're not already using it) would help with the second item.