Technical Note · Shock Testing
Classical Shock Testing on a Shaker
Half-sine, sawtooth and trapezoid pulses: why a shaker needs compensation pulses to run them, how to check velocity and stroke before you test, and what compensation does to the shock response spectrum.
Key takeaways
- The classical shock pulses are the half-sine, the sawtooth and the trapezoid. Each is defined by its peak A and duration T.
- The number that decides whether a shaker can run a pulse is its velocity change, ΔV: the area under the pulse. A 30 g, 11 ms half-sine changes the velocity by 81 in/s.
- A shaker's armature must start and end at rest, within its stroke. So every shaker shock needs compensation pulses before and/or after the main pulse to cancel the velocity change.
- With symmetric compensation, the peak velocity is about ΔV/2. A shaker can therefore run pulses up to about twice its rated velocity in ΔV. Beyond that, use a shock machine.
- Compensation amplitude trades displacement against distortion: small compensation pulses are long and use a lot of stroke; large ones are short but change the low-frequency end of the SRS more.
The classical pulses
Before shock response spectra became the usual way to specify shock, shocks were specified as simple pulses: a shape, a peak acceleration and a duration. They remain in wide use in MIL-STD-810H Method 516.8, IEC 60068-2-27 and many product specifications, because they are easy to state, easy to verify and easy to reproduce from lab to lab (see MIL-STD-810H Vibration and Shock Methods Explained).
The half-sine is the most common, representing impacts against a resilient surface. The terminal-peak sawtooth ramps up and drops sharply; its shock response spectrum is flatter and less sensitive to small waveform errors, which is why standards often prefer it. The trapezoid holds its peak, and carries the most energy of the three for a given peak and duration.
Velocity change: the number that matters
Integrate acceleration over the pulse and you get the change in velocity. On a drop or pneumatic shock machine, the table is free to keep moving afterwards. On a shaker it is not: the armature is held by its suspension and must end the event at rest, inside its stroke.
| Pulse | Velocity change ΔV | 30 g, 11 ms example |
|---|---|---|
| Half-sine | (2/π) · A · T | 81.1 in/s |
| Terminal-peak sawtooth | A · T / 2 | 63.7 in/s |
| Initial-peak sawtooth | A · T / 2 | 63.7 in/s |
| Trapezoid (rise tr, fall tf) | A · (T − (tr + tf)/2) | 114.7 in/s (10% rise and fall) |
| Rectangular | A · T | 127.4 in/s |
A 30 g, 11 ms half-sine changes the velocity by 81.1 in/s. If the shaker simply delivered the pulse, the armature would still be moving at that speed when the pulse ended, and would run into its stops a few milliseconds later. Force is often not the limiting factor: the 100 lb moving mass needs 3,000 lbf at 30 g, which is within the shock rating of many shakers of this size, though it should be checked. Velocity and stroke usually are the limit.
Compensation: pre-pulses and post-pulses
The answer is to add small pulses of the opposite sign before and/or after the main pulse, so the total velocity change is zero. With symmetric pre- and post-pulses, the pre-pulse moves the table to −ΔV/2, the main pulse carries it through zero to +ΔV/2, and the post-pulse brings it back to rest.
Three consequences follow. The peak velocity is only half the pulse's ΔV, here 40.6 in/s. The table moves during the event: here 0.70 in, all on one side unless the start position is offset to center it. And the event is longer than the main pulse: 66 ms in total for an 11 ms pulse.
| Choice | What it does | Use it when |
|---|---|---|
| Pre- and post-pulses | Splits the velocity change between pulses before and after the main pulse | You want the lowest compensation amplitudes; a longer total event is acceptable |
| Pre-pulse only | All compensation happens before the main pulse; peak velocity is the full ΔV, not ΔV/2 | You need to see the article's residual response after the pulse undisturbed |
| Post-pulse only | All compensation happens after the main pulse; peak velocity is the full ΔV, not ΔV/2 | The specification allows no motion before the main pulse |
| Larger compensation amplitude | Shorter, stronger compensation pulses | Stroke is tight; the specification's tolerance band allows it |
| Displacement centering | Starts the event offset so the travel is split either side of center | The pulse needs most of the shaker's stroke |
Displacement and the compensation amplitude
The compensation pulses must carry the same velocity change as the main pulse, but at a lower amplitude, so they last longer. A 20% compensation pulse lasts 2.5 times as long as the main pulse; a 5% one lasts ten times as long. Longer compensation means the table keeps moving for longer, and needs more stroke.
For this pulse, 20% compensation needs 0.70 in peak-to-peak, comfortably inside a 2 in stroke. At 5% it needs 2.4 in, which this shaker does not have. Raising the compensation amplitude reduces the stroke, but the compensation pulses then become a larger part of what the test article feels. Specifications limit how large they may be, through the tolerance band around the pulse.
Center the travel. The compensated pulse moves the table one way and back. Starting the event with the table offset to the other side splits the travel either side of center, so a pulse that needs 0.70 in peak-to-peak only needs ±0.35 in from center.
Can this shaker run this pulse?
Because the peak velocity with symmetric compensation is about ΔV/2, a quick check is to compare half the pulse's velocity change with the shaker's rated velocity. The example below uses the illustrative 70 in/s shaker from Shaker Performance Limits.
| Pulse | Amplitude, duration | ΔV (in/s) | Peak velocity ≈ ΔV/2 (in/s) | On this shaker? |
|---|---|---|---|---|
| Half-sine | 30 g, 11 ms | 81.1 | 40.6 | Within velocity limit |
| Half-sine | 100 g, 6 ms | 147.5 | 73.7 | Exceeds 70 in/s: use a shock machine |
| Terminal-peak sawtooth | 20 g, 11 ms | 42.5 | 21.2 | Within velocity limit |
| Terminal-peak sawtooth | 40 g, 11 ms | 84.9 | 42.5 | Within velocity limit |
| Half-sine | 50 g, 11 ms | 135.2 | 67.6 | Marginal: 97% of the velocity limit; check the shock force rating (5,000 lbf at 100 lb) |
Pulses that pass the velocity check still need a stroke check, which depends on the compensation chosen, and a force check against the shaker's shock rating. High-velocity-change pulses, such as many crash-hazard shocks, belong on a drop or pneumatic shock machine.
| Electrodynamic shaker | Drop or pneumatic shock machine | |
|---|---|---|
| Velocity change | Limited: about twice the rated velocity with symmetric compensation | Large: set by drop height or pressure |
| Waveform control | Closed loop: any classical pulse, SRS synthesis, measured transients | Shaped by programmers or pads; limited control |
| Repeatability | High: the controller equalizes and corrects | Depends on programmer wear and setup |
| Pre- and post-pulses | Always present, by physics | None: the table is free to move |
| Also does vibration | Yes, on the same setup | No |
What compensation does to the shock response spectrum
A shock's damage potential is usually judged by its shock response spectrum: the peak response of a set of single-degree-of-freedom oscillators to the pulse (see Shock Response Spectrum (SRS)).
At high frequencies the SRS of each pulse settles to about its peak acceleration. At low frequencies an uncompensated pulse's SRS is set by its velocity change. Compensation cancels that net velocity change, so it lowers the SRS at the lowest frequencies. The compensation pulses also have their own frequency content, which raises the SRS noticeably in the band they occupy: for this pulse, by about 3 dB around 20 to 30 Hz. For test articles whose important modes are well above both, this changes little. For low-frequency articles, it is worth comparing the compensated pulse's SRS with what the specification intends, or specifying the test as an SRS in the first place.
Running the test
- Equalize at a reduced level. The controller measures the system with low-level pulses, then corrects the drive so the control waveform matches the reference before full-level pulses are applied.
- Check the dynamic limits before the first full-level pulse. Peak velocity, peak displacement and force for the compensated pulse, against the shaker's limits.
- Use the specification's tolerance band. The pulse, its compensation and the residual motion after it must all stay inside the tolerance the specification defines.
- Count pulses and directions. Many specifications ask for several pulses in each direction along each axis; reversing polarity repeats the test in the opposite direction.
Common misconceptions
| Misconception | Reality |
|---|---|
| "A shaker can reproduce any pulse within its force rating." | Force is often not the limit for shock. Velocity change and stroke usually are, because the armature must end at rest within its travel. |
| "The compensation pulses spoil the test." | They are required by physics and allowed by the standards within the tolerance band. They change the low-frequency end of the SRS, lowering it at the very bottom and raising it in the band where the compensation pulses act. |
| "A shorter pulse is always easier." | A shorter pulse at the same peak has less velocity change, yes; but a shorter pulse at a much higher peak, as in many specifications, can have more. |
| "Half-sine and sawtooth pulses are interchangeable." | Their SRS differ. The terminal-peak sawtooth has a flatter, more symmetric spectrum and is less sensitive to waveform details, which is why it is often preferred. |
| "If the controller accepts the pulse, the shaker can run it." | Check the pulse's peak velocity and displacement against the shaker's limits; the controller's displayed dynamic limits make this easy. |
Quick reference
| Quantity | Formula or rule | Example |
|---|---|---|
| Half-sine velocity change | ΔV = (2/π)·A·T | 30 g, 11 ms → 81.1 in/s |
| Sawtooth velocity change | ΔV = A·T/2 | 20 g, 11 ms → 42.5 in/s |
| Peak velocity, symmetric pre/post | ≈ ΔV / 2 | 40.6 in/s |
| Largest ΔV a shaker can run | ≈ 2 × rated velocity | 70 in/s shaker → about 140 in/s |
| Displacement | Falls as compensation amplitude rises | 20%: 0.70 in pk-pk |
| Center the travel | Offset the start so travel is split ± | 0.70 in pk-pk → ±0.35 in |
| SRS effect of compensation | Lowers the lowest-frequency SRS; can raise it about 3 dB where the compensation pulses act | Check against the specification's SRS if one is given |
How Panther helps
- Every classical pulse: Panther Shock generates half-sine, trapezoidal, rectangular, initial-peak sawtooth and terminal-peak sawtooth pulses, or imports a pulse from a UFF file.
- Compensation your way: choose pre- and post-pulses, pre-pulse only or post-pulse only; optimize for displacement or use symmetric or non-symmetric acceleration compensation; set the compensation amplitude from 5 to 100%; and allow single- or double-sided displacement to make full use of the shaker's stroke.
- Dynamic limits shown before you run: the pulse's dynamic limits are displayed during setup, and shaker limits on acceleration, velocity, displacement and drive voltage abort the test if reached.
- Tolerances built in: pulse tolerance bands can follow MIL-STD-810 or be set as custom limits on the pre-pulse, main pulse and post-pulse.
- Accurate reproduction: adaptive equalization corrects for shaker and fixture response, equalization can start well below full level, and a non-linear adjustment factor corrects for known gain non-linearity without extra equalization pulses.
- SRS in the same application: Shock Response Analysis computes the SRS of the pulse with selectable damping, and SRS Shock Synthesis runs SRS-specified shocks directly.
- Fast transients captured: simultaneous sampling at up to 262,144 samples/s with 24-bit resolution.
References and further reading
- MIL-STD-810H, Method 516.8, Shock.
- IEC 60068-2-27, Environmental testing — Part 2-27: Tests — Test Ea and guidance: Shock.
- C. M. Harris and A. G. Piersol (eds.), Harris' Shock and Vibration Handbook, 5th ed., McGraw-Hill.
- D. O. Smallwood, "An Improved Recursive Formula for Calculating Shock Response Spectra," Shock and Vibration Bulletin 51, 1981.
- Spectral Dynamics Technical Library: Shock Response Spectrum (SRS); Shaker Performance Limits.
