Will a pulse fit on the shaker

A shaker can deliver a shock pulse only if it can deliver three things at once: the force for the peak, the velocity the pulse leaves the table with, and the travel the whole event needs, compensation included. The three are spent by different parts of the pulse. The peak acceleration costs force, the moving mass times the peak. The duration costs stroke, because displacement grows with the peak times the duration squared. The velocity sits between them. So the check is done before the first pulse, against the shaker's shock ratings, and visualdynamics.core.stroke makes it: from a record, or from a nominal pulse with the compensation chosen.

The nominal pulse

compensated_half_sine(peak, duration, sample_rate, share=0.2) builds the pulse a stroke is usually first estimated on. The half-sine sits between a half-sine pre-pulse and post-pulse of the opposite sign, each at share times the peak (a fifth by default, the share test documents commonly allow) and each lasting duration / (2 * share), so each carries back half the main pulse's velocity change. The table starts and ends at rest: the pre-pulse takes it to minus half the velocity change, the main pulse to plus half, the post-pulse back to zero. So the peak velocity is half the velocity change, 2AT/π, and at a fifth the whole event lasts six durations; at a tenth it lasts eleven, and the table travels 1.80 times as far before it is brought back.

Why the integration is raw

read_stroke integrates the acceleration twice by the trapezoid rule with nothing removed, from rest at the record's first sample: the same filters.integrate the Integrate act uses, called with drift_corner=None. The default 2 Hz drift high-pass is no longer transparent here, because the displacement of a compensated pulse is content at a few hertz. With it, a 50 g, 11 ms pulse reads 1.212 in peak to peak instead of 1.166 in, 3.9 % high, and its displacement no longer starts and ends at rest. A stroke estimate is integrated raw.

What it reports

read_stroke(history, channel, stroke=, velocity=, force=, moving_mass=, body_mass=) returns a StrokeReading. Every rating is optional and in SI (visualdynamics.units.to_si converts), and a rating not given is reported without a verdict. The channel must be acceleration in a declared unit, and a channel with a sample that is not a number is refused. The ratings are judged by the rules in visualdynamics.core.shaker, the same ones the replication fit uses.

Reading	What it is
peak_acceleration, peak_velocity, velocity_change	the largest acceleration and table velocity either way, and the span of the velocity
relative_velocity	the peak velocity with the shaker body counted, the coil's velocity against the body
peak_to_peak, lowest, highest	the table's displacement from rest
travel, travel_down, travel_up	the travel with the shaker body counted, peak to peak and each way from center: the table's displacement times one plus the moving mass over the body's mass
rule	the half-sine rule for the record's own peak and velocity change: A T² / 2, about 193 A T² inches with A in g
force	the moving mass times the peak acceleration
shares(), fits	each demand as a share of its rating, and whether every rating given holds
fits_stroke	whether the travel stays inside half the stroke each way from center, where the stops are

The body is counted because the ratings are the armature's motion relative to the body, and a body on isolation mounts moves the other way by the ratio of the moving mass to its own. The stops are on the body, and the back voltage the amplifier works against comes from the coil's velocity through the body's magnet, so the travel and the velocity both count it when both masses are given. The compensation is low in frequency, where the body moves most. A body bolted to a seismic mass or a rigid floor barely moves: leave body_mass out for it, and the travel and the velocity are the table's own.

The stroke share is the larger travel each way from center over half the stroke, because the armature rests at center, held there by its suspension, so the stops are half the stroke away on each side. The symmetric arrangement travels one way only, to its full peak to peak and back, so it can be inside the stroke peak to peak and still reach a stop. The peak to peak is reported as a number and not judged. When it fits the stroke and the travel one way does not, the reading says that centering the travel would fit; centering is the controller's compensation, an asymmetric pre- and post-pulse.

The half-sine rule is reported beside the integration as the first check it is. On the nominal pulse it reads 0.16 % high on every pulse (a 100 g, 6 ms pulse needs 0.694 in, the rule says 0.695 in; a 20 g, 30 ms one needs 3.47 in). On a record of any other shape the difference between the two is what the shape and the compensation are worth. A controller that shapes its compensation for least displacement does better than the symmetric arrangement, so a pulse the reading passes with room fits, and one it puts near a rating sends the operator to the controller's own prediction and to a measurement.

An example

The 40 g, 13 ms half-sine compensated at a fifth, on a shaker with a 2.5 in shock stroke, a 70 in/s shock velocity and a 6,000 lbf shock force, with 100 lb moving on a body of 3,000 lb:

from visualdynamics.core.stroke import compensated_half_sine, read_stroke
from visualdynamics.plot import plot_stroke
from visualdynamics.units import to_si

pulse = compensated_half_sine(40.0, 0.013, 102400.0, unit='g')
ratings = {'stroke': float(to_si(2.5, 'in')),
           'velocity': float(to_si(70.0, 'in/s')),
           'force': float(to_si(6000.0, 'lbf')),
           'moving_mass': float(to_si(100.0, 'lb')),
           'body_mass': float(to_si(3000.0, 'lb'))}
reading = read_stroke(pulse, **ratings)
print('\n'.join(reading.describe()))
plot_stroke(pulse, **ratings, path='stroke.png')

The table moves 1.30 in peak to peak and the body adds a thirtieth, so the travel against the body is 1.35 in. It runs 1.35 in down from center and none up, against 1.25 in to the stop each way: 108 % of the room, so the pulse as compensated here reaches a stop. The 1.35 in peak to peak is inside the 2.5 in stroke, so compensation that centers the travel would put about 0.67 in each way, inside the stops. The table's velocity peaks at 63.9 in/s, and the coil moves 66.0 in/s against the body, 94 % of the 70 in/s rating; the force is 4,000 lbf, 67 % of its own. So the pulse fits once the controller centers its travel. With the body bolted down and body_mass left out, the travel is 104 % of the room and the velocity 91 % of its rating.

To check the force at the top of a tolerance band, build the nominal pulse at the band's upper edge (1.2 times the peak for a band of plus 20 %); the stroke grows with it, as it would on the shaker.

In the app

Select a time history that holds acceleration in a declared unit and choose Stroke on the bar. The plot shows the first selected acceleration channel in three rows, each rating on the row it limits: the shock velocity either side of zero, and the stops half the stroke either side of center. The panel beside it takes the ratings in the window's units (zero is no rating) and reads out the peaks, the peak to peak beside the half-sine rule, the travel with the body, peak to peak and each way from center, the force, and each demand against its rating in words. Every edit redraws at once. The ratings are kept when another record is selected, since a shaker's ratings do not change with the record, and the reading is journaled as its plot_stroke call.

Where judgment lives

• The record's length. The integration runs over the whole record from its first sample, so a record should open at rest before the event and close after the compensation. A record whose velocity does not come back to rest carries a zero shift or an offset, and its stroke is not to be believed until that is found.
• The ratings. Many shaker sheets give a shock velocity and a shock stroke above the continuous figures; where only continuous figures are given, those are the ratings.
• The body's mass, and the compensation the controller will actually build, which the symmetric arrangement only stands in for. Where the reading puts a pulse close to the stroke, measure the displacement on a calibration load before the article goes on.