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The Physics of VSR

Whether choosing candidates for the VSR Process or deciding what equipment to acquire, it is important to understand how vibratory stress relief works:


  • Vibratory Stress Relief works by flexing the workpiece, by bending or twisting, with sufficient amplitude to combine the induced stresses caused by the flexure, with the trapped / residual stresses near the surfaces of the workpiece, which threaten the workpiece's dimensional integrity.  This causes plastic flow in the material, a common property of all forms of stress relief.


  • Merely causing mass oscillation, i.e., jumping up and down / no flexure, will cause little, if any, stress relief, since this produces little dynamic load. This means that the vibration speed or frequency range must be high enough to intercept the resonance. If not sufficiently high, only mass oscillation, which produces little or no flexure, will result. Thus one of the important VSR Equipment parameters is speed range.


  • Position of load cushions is important: They should NOT be under the corners of a rectangular part.   See graphic below, which shows the patterns of bend (on left) and torsional (on right) modes of vibration.   Corner cushion placement might allow the bend vibration mode, but would severely dampen the torsional or twisting vibration mode.  These are most often found at different frequencies / vibrator speeds.

Bend mode seen during VSR Treatment
Torsional mode seen during VSR Treatment

These are the chief modes of vibration seen with workpieces with an overall rectangular shape or envelope.   Structures with large amounts of open space, such as square tubing fabrications (e.g. automotive or aerospace tooling fixtures) will often display these modes.   Placing / spreading a dry powder on the workpiece, and tuning upon a resonance will allow the nodes, depicted as blue, hatched lines, to be seen.   The lines on top of the workpieces in the photos below are examples of such nodal lines.   


The nodal lines not only verify that a resonance is tuned upon, but also depict good locations for the vibrator, especially when a peak in the power curve occurs.    Advanced VSR pioneered plotting not only workpiece amplitude vs. vibrator speed, but also vibrator input power, an aid to achieving best vibrator position, orientation and unbalance setting.

Another mode of vibration, rarely seen in rectangular structures, but often with ring-shaped workpieces, is the ellipitical or "egg" mode.    Ring-shaped structures, whether hydroturbine discharge rings, or components of mining or tunneling systems, often have tight diameter tolerances.  "Fits" of mating surfaces or bolt or alignment pin hole patterns often must be exact for accurate assembly.    Here are the modes of vibration most often seen in rings, which include the bend and torsional, but also the elliptical mode.

Above left to right :  Ingersoll Machine Tools gantry being stress relieved, with arc-shaped node.

Stainless steel box beam with nodes.

Waterway gate with nodes defined by Oil Dry.

On right :  Video showing movement of powder defining a node, which regathers after being scattered.  

Bend mode of ring seen during VSR


Egg mode of vibration seen during VSR
Torsional vibe mode seen during VSR

A vibration mode almost unique to ring shapes is the ellipitical or "egg" mode, as shown in the plan view, above.  The rectangles represent the load cushions, used to isolate the workpiece from the floor.  Note that they have unequal spacing.  = spacing would dampen this vibration mode.    To drive this mode the vibrator must be oriented shaft vertical, so its output is almost entirely in the horizontal plane.    This is not possible with most vibrator designs, but can be easily and regularly accomplished using the Advanced VSR Model 8a System. 

Rings can undergo bend-mode vibration,  as shown above.

A ring can also display twisting or torsional mode vibration, as seen above.

  • Stress relief occurs chiefly by the incremental movement / migration of grains, often along what are called “slip lines” or “slip planes”.   Such movement also occurs during thermal stress relief, but also can occur during storage, accelerated further by incidental mechanical loading, such as by transport (see “fahrtbehandlung” on History of VSR page) or due to variations in temperature.


  • In the early 1980's, Advanced VSR's R&D team discovered a change in a workpiece's resonance pattern that occurred to workpieces that contained high levels of stress: The resonance peaks grew during vibration, both faster and further if the vibration was accurately tuned upon the resonance itself.


  • Furthermore, if the vibration was allowed to continue, often requiring finding more than one resonance to drive, until the entire resonance pattern was stable, this stability indicated that the workpiece would behave dimensionally stable during machining, i.e., STABILITY OF THE VIBRATION DATA  =  STABILITY OF THE WORKPIECE'S DIMENSIONS.


  • In the event that a great deal of material was removed during machining (which can occur during “rough” machining), a second treatment after this machining, in prep for the final machining, can further improve achievable dimensional accuracy. See Ingersoll 18 m VSR Report, which shows an 18 meter / 59.5 foot long milling machine gantry that was machined to within + / - 0.05 mm / 0.002 of an inch straight over its full length.

  • Several independent researchers have verified that resonance is more effective than near / approximate resonance (sometimes called “subresonance”) to stress relieve, although this approximate resonant approach might be easier on the vibration equipment.   Three such works can be seen in the VSR Technical Library.


  • Many resonance peaks of structures are narrow: They only span a small portion of the speed range of the vibrator. To be detectable, and later to be tuned upon and then driven / held / tracked, tight speed regulation is required.

VSR Chart shows narrow peak at ~ 3700 RPM, measuring only 30 RPM wide.  To detect and tune upon such peaks, the vibrator motor must have tight speed regulation.  Note that the peak grew ~ 20% during treatment (green before / after red).  If not tuned directly upon the peak, this treatment progress could NOT be seen.  In other words, if the vibrator was tuned off the peak, how can the peak growth, which is the treatment progress, be seen?   Hence, the importance of using resonant vibration, both to stress relieve AND monitor treatment progress.

  • Thus the second important VSR Equipment parameter is speed regulation, which can be expressed as a percent of actual speed, or an absolute ( + / - ) variation from actual speed, similar to a tolerance spec. Tight speed regulation or tolerance is determined by a combination of vibrator motor and motor drive design choices.   Advanced VSR Vibrators have tight speed regulation, in the range of 0.1 - 0.02% depending on model.

  • INSTRUMENTATION / RECORDING of the key vibration data is critical, especially for rigid, heavy-plate structures with narrow resonance peaks.  The VSR Chart on the left shows documentation of ~ 20% peak growth, with very little or no peak shifting.    Made on a Model 7.5 VSR System, this document is saved in PDF format, and shows both the original, base-line resonance pattern (green) and the final, stable resonance pattern (red) superimposed upon it. 

To gauge the performance of a VSR System, three parameters / features are crucial:

-  Vibrator speed range, the higher / the better.

-  Vibrator speed regulation, the tighter (smaller) / the better

-  Vibration data display & instrumentation:  Automatic plotting and graphic display of workpiece amplitude and vibrator power, both plotted vs. vibrator speed, will supply the most comprehensive data to assist the operator, allow monitoring of treatment progress, and then record the change in resonance pattern that accompanies stress relief.

Vibratory stress relief vs. thermal stress relief

The VSR Technical Library contains several research works that show that vibratory stress relief under laboratory conditions, is as effective as thermal stress relief.    But a real-world comparison of vibratory vs. thermal often is of more value to manufacturing managers.   There are many examples of structures that were machined to required tolerances after being stress relieved with Advanced VSR's equipment and process, but a test designed by Voith Hydro is even further illuminating.  In this test a mild steel block measuring 36 X 12 X 8 inches had welded to it a 1 inch thick plate.   Welding two members with large variations in wall thickness is one of the most common sources of residual stress, due to unequal cooling that occurs. 

During test a Model 8 vibratory stress relief system was used, in the right photo, the vibrator has a red arrow, the accelerometer a green arrow, and one of the cushions has a blue arrow. 

If no stress relief is done, the plate will warp / distort 1/8"  /  3 mm when the braces are removed.

If thermally stress relieved, the plate will warp / distort 0.04"  /  1 mm, or three times less than no stress relief.

Voith found that if VSR Processed, the plate distorted only 0.02"  /  0.5 mm, or six times less than no stress relief  . . . . .


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