Actuator Safety Margin Calculation Audit

Actuator Safety Margin Calculation Audit

Ada re-derives this chapter’s own numbers step by step, at full precision

ADA · CALCULATION AUDIT

Actuator Safety Margin Calculation Audit

Switching off a 100 mH relay coil carrying 80 mA in a microsecond looks harmless, yet the chapter’s own figures put the un-clamped flyback spike at 8000 V — enough to punch a transistor rated for 60 V. The chapter also sizes a 20 A relay for a 12.5 A heater and trips a watchdog when a logging delay stretches the 80 ms control loop past its 100 ms limit. This audit re-derives each of those margins and asks whether the numbers really support the rule that safety is a bounded chain, not a single part.

Companion to the chapter Actuator Safety and Protection — every number here comes from that chapter.

— flyback, isolation, timing, and snubbers, ~4 minutes

The safety story is physical: stored magnetic energy, timeout margins, relay current ratings, and RC time constants all need numbers. Use the chapter values already on the page and round only after the arithmetic is complete.

See the relationship before changing it

The figure reads from left to right. The blue card is measured control-loop time. The middle card applies this page's rule. The green card is watchdog time margin. Walk the arrows once: set the input, apply the rule, then read the result with its unit.

The retained audit below checks several chapter fixtures. This model keeps those stated values fixed and changes only measured control-loop time, so the numeric fixture does not switch without explanation.

Walk the arrows. A longer control loop consumes watchdog margin until the bounded safety response must trip.

Derive the baseline in four named moves

1. 1

   Name the input. The chapter baseline is 80 ms.

2. 2

   Name the relationship. watchdog margin = 100 ms limit - measured loop time

3. 3

   Substitute with units. 100 ms - 80 ms = 20 ms

4. 4

   Read the result. Keep the unit beside the value. Use it only inside the technical boundary on this page.

Predict, then change measured control-loop time

Try Predict the direction of watchdog margin = 100 ms limit - measured loop time. Test another measured control-loop time, then compare watchdog time margin.

Measured control-loop time

80 ms

Chapter baseline

Watchdog time margin

Observe A longer control loop consumes watchdog margin until the bounded safety response must trip. Reset measured control-loop time to 80 and compare watchdog time margin.

Explain A longer control loop consumes watchdog margin until the bounded safety response must trip.

Check yourself

What should you do before trusting a moved-control result?

Answer: Predict its direction, apply the shown relationship, keep the units, and reset to the worked baseline.

What does this small model leave out?

Answer: Only measured control-loop time moves here. Field effects named in the technical boundary stay fixed.

Honesty note. This teaching model changes only measured control-loop time. It is not a field prediction.

The chapter's values

Use only the chapter values above and below: a 100 mH relay coil, 80 mA coil current, 1 microsecond switch-off, 0.7 V diode clamp, 10 ms dissipation interval, an 80 ms control loop, 100 ms watchdog, 150 ms delayed iteration, a 12.5 A heater load, a 1.5x relay-rating rule, a 20 A relay, a 15 A fuse, and a 100 ohm + 100 nF snubber.

V = L x dI/dt; E = 0.5 x L x I^2; P = E / t; rating = load x safety_factor; tau = R x C

The worked checks

Check	Arithmetic	Review meaning
Flyback spike without a clamp	100 mH = 0.100 H; 80 mA = 0.080 A; 1 us = 0.000001 s; 0.100 x (0.080 / 0.000001) = 8000 V	The stored field can force a transistor far past a 60 V rating if the design gives it no safe path.
Stored coil energy	0.5 x 0.100 H x 0.080^2 A^2 = 0.00032 J = 0.32 mJ	The energy is small, but it is concentrated at switch-off and must go somewhere controlled.
Diode dissipation check	0.00032 J / 0.010 s = 0.032 W = 32 mW	A 10 ms clamp interval turns the spike into a modest heat pulse instead of an uncontrolled voltage stress.
Watchdog timing margin	100 ms - 80 ms = 20 ms; 150 ms - 100 ms = 50 ms late	The normal loop has only a 20 ms margin; a 150 ms logging delay correctly trips the watchdog.
Relay current selection	12.5 A x 1.5 = 18.75 A; 20 A - 18.75 A = 1.25 A	The 20 A relay clears the stated minimum by 1.25 A, while the 15 A fuse remains below the relay rating.
Snubber time constant	100 ohm x 100 nF = 100 x 0.000000100 F = 0.000010 s = 10 us	The RC path acts on microsecond switching transients, not on slow actuator logic or software timeouts.

Audit conclusion: the chapter's own values support the design rule: safety is not one component. It is a bounded chain of current ratings, stored-energy paths, timeout margins, isolation, and independent fallback behavior.

Every number above is taken from the chapter’s own examples and re-derived step by step.

TryChoose Check audit and recompute the 8000 V flyback case, 12.5 A heater load, and 100 ms watchdog bound.

ObserveThe results demand a 20 A relay while the electrical transient and 100 ms timing limit remain separate safeguards.

ExplainSafety requires all 3 margins because flyback containment, contact derating, and watchdog response interrupt different failure paths.

Technical boundaries. The audit uses ideal inductance, stated derating, and deterministic loop times. It does not perform hazard analysis, model clamp dynamics, contact welding probability, thermal cycling, software concurrency, watchdog coverage, common-cause failure, or safety certification.

Audit result

Each arithmetic margin checks one premise only; the combined system still needs measured fault response and an independent safety case.