I think you already know...vibrations that affect sensitive equipment. The below is an extract from Groundborne vibration caused by mechanised construction works - Transport Research Laboratory (UK).
There are currently two British Standards which offer advice on acceptable levels of vibrations in structures. BS 7385 : Part 1 : 1990, Mechanical vibration and shock - vibration of buildings - guidelines for the measurement of vibrations and evaluation of their effects on buildings, discusses the principles for carrying out vibration measurements and processing the data. Part 2 of the Standard, Evaluation and measurement for vibration in buildings. Guide to damage levels from groundborne vibration (BSI, 1993), suggests levels at which the following three categories of damage might occur.As for what would be acceptable limits:
Cosmetic The formation of hairline cracks on drywall surfaces, or the growth of existing cracks in plaster or drywall surfaces; in addition, the formation of hairline cracks in mortar joints of brick/concrete block construction.
Minor The formation of large cracks or loosening and falling of plaster or drywall surfaces, or cracks through bricks/concrete blocks.
Major Damage to structural elements of the building, cracks in support columns, loosening of joints, splaying of masonry cracks, etc.
As for your issue, you are dealing with equipment. The above recommendations are for buildings. Only the equipment manufacturer will be able to tell you the acceptable peak particle velocity. I image they will likely say zero.
You should be looking at using a press piler which is nearly vibration free. See GIKEN -