REF-THY-HYS-VIZ

Hysteresis in Lever-Type DTIs — Error Modalities, Interactive Module DRAFTMODULE

REV A candidate · 2026-08-04 · Companion module to the hysteresis dossier (docType/docId ruling pending). Section numbers are module-scoped (V1–V4) to avoid collision with parent-doc numbering.

Unmarked claims are Established. Simulator curves are pedagogical models, not measured data.

Hysteresis is the difference in indicated reading at the same true stylus position depending on direction of approach. Plot true position on one axis and indicated reading on the other: the ascending pass and the descending pass trace two different paths instead of one, and together those two paths form a closed loop. A wider loop means a bigger disagreement between the two approach directions at that point; no gap between the passes means no loop at all. This module isolates each error modality visually, then combines them in a loop simulator whose fault presets mirror the diagnostic signature table.

ascending (loading) descending (unloading) ideal, indicated = true

§V1 — Error modalities: definition and causes

Three shapes cover everything below: a loop (direction changes the answer), a consistent offset (same wrong answer either direction), or scatter (no consistent answer at all — just noise). Which shape you're looking at narrows the search before you even read the causes.

Loop

Direction changes the reading. Hysteresis, dead-band.

Consistent offset

Same wrong answer either direction. Linearity, cosine error.

Scatter

No consistent shape — a cloud. Repeatability error.

Each block plots indicated reading against true displacement for one error modality, with its causes alongside. Only the first two are direction-dependent; the rest are distinct error classes that get misdiagnosed as hysteresis at the bench. "Common" reflects frequency at this bench and in the repair literature (Meyer); "potential" covers mechanisms that are real but rarer, or only confirmed once.

Dead-band is not a separate physics — it is hysteresis expressed entirely at reversal, where the hand holds still until lost motion is consumed. The r_deadband branch of REF-SVC-IAP-DX diagnoses this localized case. Cosine error is the one modality that is operator/setup error — the instrument itself is healthy, and no teardown will remove it; every other modality above is a service question.

§V2 — Loop simulator

The stylus cycles through a full stroke and back. Sliders inject each physical mechanism; the loop traces indicated vs true. Presets reproduce the diagnostic signatures of §V4 — or click a row in the table there.

true displacement (micrometer head) — 0 to 10 grad

Cycle running — conclusion appears once both passes are traced.

take-up preload pivot / mesh friction oil drag (viscous) cycle speed

localized snag stiction after dwell one-way fault

hysteresis err, mid-range— dead-band at reversal— rate-dependent?—

Hover any curve, the marker, or the loop-width bracket on the plot — and any control label — for what it represents.

Diagnostic separation trick: true hysteresis (friction, backlash) is rate-independent — the loop holds its width when you change cycle speed. A loop that widens with speed is viscous oil drag, not hysteresis. Try it: raise oil drag, then move the speed slider.

§V3 — Force hysteresis: the same physics in force units

Measuring force vs deflection, both directions (milligram-scale-under-stylus method). The vertical gap ΔF between rising and falling curves is friction + preload deficit expressed in force units; divided by the effective spring gradient it predicts the positional loop of §V2. Interapid nominal: 0.12 N (≈12 gf) for .0005″ models.

friction force F_f spring gradient k

ΔF (loop gap)— predicted positional hys.— mean force @ mid—

§V4 — Diagnostic signatures

Click a row to load its loop in §V2. For the component-level suspects behind each signature, see the causes columns in §V1.

Loop signature	Points to
Uniform gap, both directions, whole range	Friction — dry pivots, dirt, drag
Gap concentrated at reversal (dead-band)	Insufficient preload — backlash unmasked
Localized snag at one position	Damaged tooth, cracked crown jewel, debris
Loop widens with cycle speed	Viscous oil drag — not true hysteresis
Worse after dwell, clears with cycling	Stiction — aged or excess lubricant
Responds one direction only	Lever mis-mating — mechanism fault, beyond hysteresis