We are a builder of vibratory stress relief systems, which we recommend be used as a post-weld or mid-term machining means of rendering precision components dimensionally stable. This equipment (and also that made by our competitors, who are great aspousers of vibration during welding) is also used by our customers to minimize welding distortion. It is most commonly used in situations where very high shrink occurs, such as with stainless, aluminum, or other metals that tend to distort more than mild steel during welding. We also have heard from shops that perform weld repairs, esp. on castings, which are quite tricky to weld-repair, that they see benefits from this method. Let's make a distinction between vibratory stress relief (VSR), which is the post-weld method of enhancing dimensional stability, and vibration during welding (VDW), which is what your question is about.
We have NOT found welding during vibration to be either a very predictable or repeatable process, based on feedback from both our customers and those of our competitors. We do not believe that a parameter or group of parameters have been identified which allow adjustment of aspects of the vibration, such as vibrator speed, vibrator unbalance, etc. One frequent comment/complaint we do get from those who do biz with our competitors is the disappointing results they obtained from efforts to use VDW. Thus, we do not recommend VDW, and we do not raise the subject in our lit or support material.
That being said, I have seen some interesting demonstrations that would indicate that there might be some positive effect from VDW. If have seen a plasma cutter used to cut a 24 inch wide, 8 foot long, 1" thick mild steel plate down the middle, lengthwise, resulting in two pieces slightly less than 12" wide. The cut widens and separates, due to shrinkage of the material, as the cutting head moves down the length of the plate.
If the plate is vibrated gently (a vibrator with adjustable unbalance up to 3 in-lbs, adjusted to 20%, and turning at 2500 RPM, with the AOR [axis of rotation] aligned with the length of the plate), the separation, which one could liken, or consider analogous, to some degree with welding distortion, was reduced by more than 75%.
To perform mere VDW, a full blown vibratory stress relief system is NOT needed. Indeed, a better choice from an equipment reliability standpoint, rather than using an electric vibrator, might well be a pneumatic vibrator, condsidering the heat the vibrator might be subjected to. Speed control can be done with control of the air supply.
What material are you welding, how much distortion are you suffering, and what target distortion level do you hope to achieve?? There might well be other means, or a combination of methods available, such as pre-heat (I do not claim to be a welding expert) that would solve your problem.
BK