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VSR Process Monitoring: Resonance Detection and Verification of Stress Relief

Vibratory stress relief (VSR) produces a measurable process record that documents what happened during treatment — the natural frequencies of the part before vibration, the resonant modes selected and held during treatment, and the shift in those frequencies after stress redistribution. UTEC Industrial provides in-house induction hardening, through-hardening, and quench-and-temper heat treating services for industrial components in the Pacific Northwest, with integrated CNC machining and reverse-engineering capability. Unlike thermal stress relief, where the evidence is a time-temperature chart, VSR evidence is a frequency-response dataset. This article covers how automated VSR equipment performs resonance detection, how the scan-vibrate-scan sequence works, what acceptance criteria engineers use to confirm treatment effectiveness, and what the delivered process record contains.

How does automated VSR equipment detect resonance in a part?​

Automated VSR equipment detects resonance by performing a controlled frequency sweep with an eccentric-mass exciter and recording the structural response at accelerometers clamped to the part. The exciter is a variable-speed motor driving an unbalanced rotating mass; at motor speed N revolutions per minute, it produces a sinusoidal force at frequency N/60 Hz. A typical industrial VSR sweep runs the exciter from about 15 Hz (900 RPM) up to 100–120 Hz (6,000–7,200 RPM) over 2–5 minutes, while the controller samples accelerometer output at 10–100 Hz sample rate. When the exciter frequency coincides with a natural frequency of the structure, the accelerometer amplitude rises sharply — often 5x to 20x above the off-resonance baseline — producing a peak on the amplitude-vs-frequency plot. Damping ratio for typical welded steel structures is around 0.5–2%, which produces peaks with half-power bandwidth of 0.3–2 Hz — narrow enough to pick out cleanly on a swept-sine plot. The controller identifies peaks algorithmically by finding local amplitude maxima above a threshold (commonly 2–4x the baseline), records the peak frequency, peak amplitude, and phase angle, and presents the sweep as a numbered list of candidate resonant modes for the operator or program to select for treatment (Walker, C.A., Waddell, A.J., and Johnston, D.J. (1995). Proceedings of the Institution of Mechanical Engineers, Part E; Wozney, G.P. (1957). Welding Engineer).

What is the scan-vibrate-scan sequence?​

Scan-vibrate-scan is the standard VSR treatment sequence: a pre-treatment frequency scan to identify resonant modes, a vibration phase at one or more selected modes, and a post-treatment frequency scan to document changes. The pre-scan sweeps the exciter across the programmable range (typically 15–120 Hz) and produces the baseline frequency-response plot. The operator or automated program reviews the pre-scan, selects the resonant modes with the highest amplitudes at the accelerometers near high-stress regions of the part — typically two to four modes for a complex weldment — and sets the treatment parameters. The vibrate phase holds the exciter at the first selected resonant frequency for a programmed time (typically 15–45 minutes per mode), with the controller tracking the peak as the part's dynamic response evolves. Because the resonant frequency drifts as stress redistributes, the controller adjusts the exciter speed within a narrow band (usually ±0.5 to ±2 Hz) to stay on the moving peak — without this tracking, the exciter would walk off resonance and treatment effectiveness would drop. After each mode is treated, the cycle either moves to the next mode or enters the post-scan. The post-scan repeats the frequency sweep and produces the post-treatment response plot. Comparison of the pre-scan and post-scan is the primary in-process evidence that treatment achieved stress redistribution (ASM Handbook, Vol. 4A, ASM International, 2013; Walker et al. (1995). Proceedings of the Institution of Mechanical Engineers, Part E).

What specific changes in the resonance signal indicate stress relief occurred?​

Two specific signal changes are accepted industry-wide as evidence that VSR produced stress redistribution: an upward shift in resonant frequency and a change in peak amplitude and shape. Frequency shift: as residual stresses relax, the stiffness distribution in the part changes slightly — tensile residual stresses effectively reduce the structure's modal stiffness, so as they relax, modal stiffness rises and natural frequencies shift upward by about 0.5–5 Hz for a mode in the 20–80 Hz range (proportionally, roughly 0.5–5% of the mode's pre-treatment frequency). The shift is subtle but reproducible, and the controller records it directly on the pre-scan/post-scan overlay. Amplitude and peak-width change: the peak at the treated resonant mode typically broadens and drops in amplitude during treatment, reflecting increased modal damping from the plastic deformation work performed at stress concentration sites. A peak that was 15x baseline in the pre-scan may be 8–12x baseline in the post-scan, with a broader half-power bandwidth. Secondary indicators include a decrease in acceleration amplitude required to hold a given displacement and a shift in the phase angle between exciter force and accelerometer response. None of these indicators are absolute numerical acceptance thresholds — they are qualitative evidence that the part responded to vibration in the way a part undergoing stress relief would respond. Parts that show no frequency shift and no peak-shape change typically did not experience stress redistribution, and the treatment should be investigated (exciter placement, amplitude, mode selection) rather than recorded as complete (Walker et al. (1995). Proceedings of the Institution of Mechanical Engineers, Part E; Wozney (1957). Welding Engineer).

What dynamic stress amplitude does the equipment target during treatment?​

The controller and operator target a dynamic (alternating) stress amplitude at critical stress locations of approximately 20–40% of the material's yield strength — large enough to push the combined stress (residual + dynamic) above yield at the highest-stress sites, but well below the endurance limit to avoid fatigue damage. For a welded carbon steel structure with yield strength near 50 ksi and weld residual stresses approaching 40–50 ksi at critical weld toes, a dynamic stress of 10–20 ksi superimposed on the residual stress brings peak stress above the 50 ksi yield and drives local micro-plastic deformation. The dynamic stress amplitude is not measured directly — it is inferred from the accelerometer displacement amplitude, the mode shape, and the material properties. Operators typically scale the exciter mass setting (the unbalance) and the motor speed to achieve a displacement in the target range — a common rule of thumb is accelerometer displacement of 0.001–0.005 inch (0.025–0.125 mm) at resonance for medium-size weldments, scaled up or down by part size. Higher-stiffness or higher-strength materials (alloy steels, quenched and tempered grades with yield above 100 ksi) require more exciter force but should still target the 20–40% of yield ratio, which keeps treatment below the material's endurance limit (typically around 40–50% of tensile strength for wrought steel in reversed loading). Over-amplitude treatment risks initiating fatigue cracks at weld toe stress concentrations — the primary failure mode associated with misapplied VSR (ASM Handbook, Vol. 4A, ASM International, 2013; Walker et al. (1995). Proceedings of the Institution of Mechanical Engineers, Part E).

What acceptance criteria does an engineer use to judge a VSR treatment effective?​

For routine non-code VSR — the majority of industrial stress relief — acceptance is based on three in-process criteria evaluated against the recorded pre-scan and post-scan data. First, resonant frequency shift: a measurable upward shift (typically 1–5 Hz on a mode in the 20–80 Hz band) at the treated modes indicates stiffness redistribution consistent with stress relief. Second, peak amplitude or shape change: a reduction in peak amplitude or broadening of the half-power bandwidth at treated modes indicates increased modal damping consistent with micro-plastic work. Third, treatment time and power: the integrated exciter time at each treated mode must meet the specification (for example, 30 minutes minimum per mode) and the exciter amplitude must have been held within the target range. If all three indicators are satisfied, the treatment is accepted. For applications with tighter acceptance requirements, quantitative residual stress measurement by X-ray diffraction (ASTM E915, ASTM E837 for hole-drilling) before and after treatment provides direct evidence — but this is reserved for quality-critical work (aerospace-grade fabrications, precision machine tool castings, nuclear-adjacent structures) because the measurement cost is significant. Dimensional stability verification — remeasuring the part after 24–72 hours to confirm no residual growth or distortion — is sometimes added for parts being stress-relieved specifically to prevent post-machining distortion. The combination of in-process resonance evidence plus post-treatment dimensional measurement covers most industrial acceptance requirements (ASTM E837; ASTM E915; Walker et al. (1995). Proceedings of the Institution of Mechanical Engineers, Part E).

What data record does the VSR equipment generate for each job?​

Automated VSR equipment produces a per-job data record that serves the same documentation function as the furnace chart on a thermal stress relief job. The standard record includes: the part identification and job number; the exciter mounting location and accelerometer positions (photographed or diagrammed); the pre-treatment frequency sweep plot showing all resonant peaks identified between the lower and upper frequency limits; the list of resonant modes selected for treatment with each peak frequency and amplitude; the treatment profile at each mode showing exciter frequency vs. time, accelerometer amplitude vs. time, and total integrated time per mode; the post-treatment frequency sweep plot; a pre-scan/post-scan overlay showing frequency shift and amplitude change at each treated mode; the exciter speed and unbalance settings used; the total treatment time; operator identification; and date and time stamps. UTEC Industrial's automated VSR equipment generates this record for every job and archives the digital file, with a printed summary included in the shipping documentation. For customers requiring additional detail — pre-treatment residual stress measurement, dimensional inspection before and after, specific mode-shape documentation — these items are added per the customer's quality plan at quote stage (Walker et al. (1995). Proceedings of the Institution of Mechanical Engineers, Part E; AMS 2750).

Can the VSR equipment record be used as quality evidence for non-code applications?​

Yes — the VSR process record is the standard quality evidence for non-code stress relief work, and it is accepted by most industrial customers whose quality plans require documented stress relief. The record demonstrates (a) that the specified treatment program was executed, (b) that resonance was achieved at the selected modes, and (c) that the frequency-response signatures characteristic of stress redistribution — frequency shift and peak-shape change — appeared during treatment. For engineer-specified non-code work on structural weldments, machine bases, cast components for dimensional stability, and similar applications, this record satisfies most customers' documentation requirements. It is not accepted as a substitute for ASME Section VIII Division 1 UW-40 thermal PWHT records, AWS D1.1 Clause 5.8 PWHT records, or API 650 thermal cycle records — these codes specifically require thermal cycle documentation, and VSR does not satisfy the code regardless of the record quality. Where the customer's internal quality plan or a purchase-order requirement calls for "documented stress relief" without invoking a specific code, the VSR record is normally adequate. For borderline cases — critical non-code work, first-article approval on a new fabrication, a customer new to VSR — supplementing the resonance record with a pre/post X-ray diffraction residual stress measurement (per ASTM E915) or hole-drilling measurement (per ASTM E837) provides quantitative evidence. The scan-vibrate-scan resonance record, combined with the process profile and operator sign-off, is the standard quality artifact for routine industrial VSR work, and customers with more stringent documentation requirements should specify the additional evidence at quote stage rather than after treatment is complete (ASTM E915; ASTM E837; AWS D1.1, Clause 5.8; ASME Section VIII Div 1, UW-40).

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References​

  • ASM International. (2013). ASM Handbook, Volume 4A: Steel Heat Treating Fundamentals and Processes. ASM International.
  • Walker, C.A., Waddell, A.J., and Johnston, D.J. (1995). "Vibratory stress relief — an investigation of the underlying processes." Proceedings of the Institution of Mechanical Engineers, Part E: Journal of Process Mechanical Engineering, 209(1), 51–58.
  • Wozney, G.P. (1957). "Resonant-vibration fatigue practice." Welding Engineer, 42(2), 41–46.
  • ASTM E837: Standard Test Method for Determining Residual Stresses by the Hole-Drilling Strain-Gauge Method. ASTM International.
  • ASTM E915: Standard Test Method for Verifying the Alignment of X-Ray Diffraction Instrumentation for Residual Stress Measurement. ASTM International.
  • ASME Boiler and Pressure Vessel Code, Section VIII Division 1 (current edition). American Society of Mechanical Engineers.
  • AWS D1.1: Structural Welding Code — Steel (current edition). American Welding Society.
  • AMS 2750: Pyrometry. SAE Aerospace.

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