System Chain Analysis Guide

Why "Whole Chain" Is the Right Frame

Walk into any plant and you will find calculators on phones for everything: wire sizing, motor FLA lookup, sheave ratio, gearbox torque, pump affinity, vibration severity. Each one tells you something true about one link of a rotating-equipment chain. None of them tell you which link is the problem.

Real maintenance work is the opposite of single-link work. The complaint is "the fan is loud and pulling more amps than it used to." The cause is a sheave that someone swapped six months ago to "speed it up", which raised the head ratio (head scales with speed squared, so a 15 percent speed bump = 32 percent head rise), which pushed the operating point further to the right of the fan curve into the high-amp region. The fix is not bigger amps, it is putting the original sheave back. But you cannot see that without holding all four links — electrical, motor, transmission, driven — at once and noticing the one that does not match.

The System Chain Analyzer is built around that frame. You enter what you can measure, the analyzer evaluates each link, and the system verdict tells you which link is most likely the cause. The dedicated single-purpose calculators dive deeper after you know where to look.

Link 1: Electrical Supply

The electrical link covers everything from the source breaker to the motor terminals: voltage, phase, breaker size, wire gauge, run length, and conductor type (copper vs aluminum). The analyzer checks four things against NEC 2023:

Wire ampacity vs Table 430.250 FLA × 1.25 (NEC 430.22)

The branch circuit conductor for a single motor must have an ampacity of at least 125 percent of the motor full-load current from Table 430.250 (3-phase) or Table 430.248 (1-phase), not from the nameplate. This is a critical and counterintuitive code rule: a high-efficiency motor often has a nameplate FLA lower than the table value, and using nameplate would under-size the wire. The analyzer always uses the table value for the 125 percent ampacity check (NEC 430.22) and only uses nameplate for overload-relay sizing (NEC 430.32). The two paths are deliberately separate.

If you only have a nameplate FLA and no HP, the analyzer falls back to the nameplate value for the conductor calculation but surfaces a CAUTION explaining that the strict NEC 430.22 reference (which requires the table value) was missing — that lets the wire check still produce a meaningful DANGER on a clearly-undersized conductor instead of silently returning OK.

Breaker rating per NEC 430.52(C)(1)

For an inverse-time circuit breaker on a NEMA Design B / C / D motor, the maximum breaker rating is 250 percent of the NEC Table 430.250 FLA (3-phase) or Table 430.248 FLA (1-phase), with Exception 1 allowing the next standard size up, and Exception 2(c) allowing up to 400 percent only when 250 percent will not carry the starting current. Below about 175 percent, a breaker will routinely nuisance-trip on locked-rotor inrush. The analyzer flags the typical 175 to 250 percent band as OK, 250 to 400 percent as CAUTION (verify the engineering justification), and above 400 percent as DANGER (the breaker no longer protects). The breaker basis is the same NEC table FLA used for wire ampacity — never the nameplate, which would artificially inflate the percentage on high-efficiency motors and generate false DANGER warnings.

Voltage drop vs NEC 210.19 / 215.2 informational target

NEC 210.19 (branch) and 215.2 (feeder) informational notes recommend max 3 percent on either, 5 percent combined. The analyzer triggers CAUTION at 5 percent and DANGER at 8 percent. Above 8 percent, a NEMA Design B motor will not develop rated torque (NEMA MG-1 §12.44 allows operation at ±10 percent nameplate voltage with derated torque, and the utility tolerance plus this drop puts you at the edge). The voltage drop formula is V_drop = √3 × I × L × R / 1000 for three-phase, or 2 × I × L × R / 1000 for single-phase, where I is the FLA, L is the one-way length in feet, and R is the resistance per 1000 ft from NEC Chapter 9 Table 8.

Aluminum conductor warning

The analyzer uses copper resistance values. Aluminum has roughly 60 percent more resistance per ohm-foot, requires AL-rated terminations (NEC 110.14(B)), and uses a different ampacity column. If you tell the analyzer you have aluminum, it surfaces a CAUTION reminder; verify against the NEC Table 310.16 aluminum column directly, or use the dedicated Wire Sizing Calculator.

Field check: If the electrical link is showing CAUTION or DANGER, the most useful next measurement is to clamp-meter the motor at normal load. If the motor is drawing well below FLA, the wire and breaker may not actually be limiting; the motor might be lightly loaded for some other reason. If the motor is at or above FLA, you have the additional question of whether the wire was always undersized or whether the load grew.

Link 2: Motor

The motor link covers the nameplate (HP, FL RPM, poles, FLA, service factor) and the present clamp-meter reading. The analyzer computes synchronous RPM from pole count, slip from the difference between sync and nameplate RPM, torque from HP and RPM, and runs a present-amps overload check against the service factor.

Synchronous RPM and slip

Synchronous RPM = 7200 / poles at 60 Hz (or 6000 / poles at 50 Hz). 4-pole = 1800 sync, 2-pole = 3600 sync, 6-pole = 1200 sync, 8-pole = 900 sync. Real induction motors run slightly slower because of slip — typically 1 to 5 percent for NEMA Design B motors. So a 4-pole nameplate of 1750 RPM at 1800 sync is 2.78 percent slip, which is normal. NEMA Design D motors run higher slip (5 to 13 percent) for high-inertia loads like punch presses.

The analyzer infers pole count automatically from a nameplate RPM. Enter 1750 and it picks 4-pole. Enter 3450 and it picks 2-pole. If you enter both and they conflict, you get a CAUTION because one of them is wrong.

Service-factor overload check

NEMA service factor 1.15 means the motor can run continuously at 115 percent of nameplate FLA without exceeding the temperature class. Above 115 percent, the motor is past nominal SF and the temperature rise will eat insulation life rapidly. The analyzer treats the SF envelope correctly: present amps past the SF ceiling (e.g. above 115 percent on a 1.15 SF motor) flags DANGER; present amps between 100 and 115 percent on a 1.15 SF motor flags CAUTION because the motor is operating in its rated envelope but accelerating insulation aging; present amps between 90 and 100 percent flags CAUTION for no headroom; below 90 percent is OK. A 1.0 SF motor (no envelope) flags DANGER at 100 percent because there is no headroom to give back.

Torque and HP

Torque in lb-ft = HP × 5252 / RPM. The constant 5252 comes from 33,000 ft-lb/min per HP divided by 2π. A 10 HP motor at 1750 RPM produces 30 lb-ft of nameplate torque. The analyzer surfaces this so the transmission link can multiply or divide through the gearbox or belt drive.

Field check: If the motor link is showing CAUTION because of present amps, the next move is to figure out what changed in the load. Did someone change a sheave? Did a damper close upstream? Is a bearing failing? The "What Probably Changed" panel reads the cross-link evidence and surfaces the most likely culprit with a confidence chip.

Link 3: Transmission

The transmission link covers how torque and speed get from the motor to the driven equipment. The analyzer supports four types: direct (1:1, no transmission), V-belt, gearbox (helical, bevel, or worm), and chain.

V-belt drive math

Speed ratio = driven OD / driver OD. Driven RPM = motor RPM × (driver OD / driven OD), with a typical 2 percent slip baked in for downstream displays. Belt speed in FPM = π × driver OD × motor RPM / 12. Wrap angle on the small sheave = 180° − 2·arcsin((D−d) / 2C), where D is the larger sheave OD, d is the smaller, and C is the center distance.

The analyzer flags four belt-specific risks:

• Geometry impossibility: if center distance is at or below (D + d) / 2, the sheaves overlap. The analyzer returns 0 for wrap angle and surfaces a DANGER.
• Belt FPM ceiling: classical V-belts on cast-iron sheaves are limited to 6,500 FPM by rim-speed fragmentation risk (Gates / MPTA). Narrow V-belts (3V, 5V, 8V) in ductile iron with dynamic balance can run to 10,000 FPM. The analyzer reads your belt section and applies the correct ceiling so a properly engineered narrow drive does not false-flag DANGER.
• Wrap angle: below 120° is DANGER (belt cannot grip the small sheave). Below 150° is CAUTION (drive capacity reduced). The 120° boundary is inclusive.
• Single-stage ratio cap: above 8:1 single-stage is impractical for V-belts (Gates / RMA design data). Above 8:1 surfaces a CAUTION with a recommendation to size up the small sheave or use a two-stage drive.

Gearbox math and the worm-efficiency trap

Gearbox output RPM = motor RPM / ratio. Output torque = motor torque × ratio × efficiency. A 30:1 reducer at 95 percent efficiency takes 30 lb-ft motor input and produces 855 lb-ft output. Helical and bevel single-stage runs 95 percent efficient up to about 8:1. Single-stage worms run 50 to 70 percent efficient at 60:1 — and the math breaks badly if you use 95 percent for a worm.

The analyzer defaults to 95 percent for gearbox ratios up to 30:1 (assumed helical or bevel) and drops to 70 percent above 30:1 (assumed worm). If you have the actual nameplate efficiency, override the default. A single-stage gearbox above 60:1 also surfaces a CAUTION reminder to verify nameplate.

Chain drive

Chain drives use the same gearbox math (output RPM = input RPM / ratio, output torque = input torque × ratio × η) but with a default 97 percent efficiency for well-lubricated roller chain (ANSI B29). Single-stage chain ratios above 7:1 are unusual; ANSI B29 recommends below 7:1 single, below 10:1 with an idler.

Field check: The strobe-tach reading is the ground truth for transmission slip. If the calculated driven RPM (no slip) is 800 and the strobe reads 760, you have 5 percent slip — beyond the typical 1 to 2 percent V-belt slip. The analyzer compares against the no-slip theoretical RPM (not the displayed 2-percent-slip value) so the actual slip is reported correctly without the typical-slip baseline cancelling itself out.

Link 4: Driven Equipment

The driven link is what the rotating chain is actually doing — pumping water, blowing air, conveying coal, mixing slurry, cutting metal. The analyzer supports ten common types and applies the right physical model to each:

Centrifugal cube law

Centrifugal pumps, fans, blowers, and mixers follow the affinity laws: flow Q is proportional to speed N, head H is proportional to N squared, power P is proportional to N cubed (Hydraulic Institute and AMCA 201). A 10 percent speed bump produces a 21 percent head rise and a 33 percent power rise. The analyzer flags head ratios above 1.21 (CAUTION) and 1.50 (DANGER), and HP ratios above 1.15 (CAUTION, motor service factor) and 1.40 (DANGER, motor cannot absorb).

For pumps, NPSH required also scales with N squared, so any speed increase above 5 percent surfaces a CAUTION about cavitation that may show up at the new operating point even if it was acceptable at the old speed. For fans, head ratios above 1.21 trigger a ductwork-stall reminder per AMCA 201; the fan-stall region is on the left of the peak pressure point of the fan curve.

Linear (positive-displacement) law

PD pumps (gear, lobe, progressive cavity), reciprocating compressors, and screw compressors scale flow linearly with speed. Head and pressure are set by the system back-pressure (relief valve, regulator, or sump pressure), not by speed. So a 20 percent speed bump on a PD pump produces a 20 percent flow rise but does not change discharge pressure unless the system curve also moves. Power scales roughly linearly with speed at constant pressure.

None (no affinity)

Conveyors, augers, and machine tools do not follow affinity laws. Conveyor power is set by load × speed × friction; auger torque depends on bridging and material density; machine tool spindle power depends on cutting parameters. The analyzer applies an overspeed check against the equipment-type max RPM but does not project flow, head, or HP for these categories. It does, however, surface a CAUTION when the calculated driven RPM differs from the expected RPM by more than 5 percent — that level of drift on a non-affinity load means a sprocket got swapped, a gearbox got rebuilt with the wrong ratio, or a belt got changed without correcting for it.

Overspeed check

Each driven equipment type has a default max RPM. Centrifugal pumps default to 3600 (most pumps), centrifugal fans to 3600 (small fans run higher), reciprocating compressors to 1200, machine tools to 12,000 (modern HSM spindles). The analyzer flags calculated driven RPM above 92 percent of max as CAUTION and above max as DANGER. If you have a specific nameplate max RPM, enter the override; otherwise the type default applies.

How the Verdict and Risk Score Combine

The system verdict is the single OK / CAUTION / DANGER reading at the top. It combines all four chain segment tiers plus the symptom-matcher results:

• Any DANGER warning in any segment → system DANGER
• Any CAUTION warning (no DANGER) → system CAUTION
• No warnings, no missing inputs → system OK
• No warnings, but required inputs missing → system CAUTION ("Inputs incomplete — cannot certify safe")

The last bullet is a deliberate safety bias: the analyzer never returns OK if any required check could not be evaluated. Missing wire gauge means the voltage drop check did not run, which means the analyzer cannot certify the chain safe regardless of how good the rest looks.

The Risk Score is a separate 0 to 100 triage number that reflects how stacked the cautions and dangers are. Each segment contributes 0 to 25 points: about 5 for OK, 5 to 10 for UNKNOWN with missing inputs, 12 to 18 for CAUTION, 22 to 25 for DANGER. The total below 45 is low triage risk, 45 to 69 is moderate, 70 and up is high. The score is for triage prioritization across multiple machines, not safety certification of one machine.

Verdict and score are intentionally different. A single DANGER lights up the verdict (binary safety) but only contributes 22 to 25 points to the score. Two danger segments stacked plus minor cautions elsewhere will move the score into the 70+ range without changing the binary verdict. Use both: the verdict tells you whether to stop and act now; the score tells you whether this machine is the worst of your morning rounds.

How the Symptom Matcher Routes Complaints

The Symptoms step accepts plain-English text — "breaker trips on start", "motor frame hot", "belt squealing", "pump rattling like marbles", "fan airflow dropped" — and scores each phrase against a library of common chain-failure modes. Each library entry carries:

• Segment tag: electrical, motor, transmission, driven, or system. Tells the verdict aggregator which chain link the symptom is pointing at.
• Severity: OK, CAUTION, or HIGH. Drives the contribution to the system verdict.
• Likely causes: a short list of root causes ranked by frequency.
• Action: the next field measurement or check that resolves the symptom, with a citation to NEMA, Gates, AMCA 201, ISO 10816, NEC, or Hydraulic Institute as appropriate.
• Keywords: a comma-separated list of plain-text matches, weighted higher for strong-signal terms like "squeal", "trip", "cavitation", "single-phase".

The matcher rejects stop-words ("the", "and", "this", "with", "motor", "pump", "fan"), accepts tokens of 4 or more characters, and lets short strong-signal words ("hot", "amp", "amps") through the length filter. Each match is shown with its segment tag and severity, and the chain diagram shows up to four matched-symptom chips below the chain so you can see at a glance which link is being implicated.

The matcher does not interpret photos, vibration spectra, or audio. It is a keyword-routing layer, not a diagnostic AI. When the symptom matches nothing, the empty state suggests stronger keywords to try ("trips", "hot", "squeal", "vibration", "rattling", "humming"). The matcher never returns false matches just to fill space.

When to Jump to a Single-Purpose Calculator

The Related ToolGrit Calculators panel groups cross-links by chain segment and includes a one-line "why this tool" explanation. Each link carries query-string state so the destination can prefill from the chain analysis. The most common jumps:

• Wire Sizing Calculator when the electrical link is borderline and you want the full NEC ampacity table with derating factors.
• Motor Slip Calculator or Motor Nameplate Decoder when the motor link is showing inferred-pole conflicts or you want to decode the rest of the nameplate.
• Sheave & Belt Field Calculator when the transmission is a V-belt drive and you suspect a sheave change is the cause; this gives you belt section ID, part-number decoding, bushing identification, and field cheat codes.
• Belt Drive Calculator for engineering-grade belt design with service factors and HP rating per belt.
• Pump Affinity Laws Calculator when the driven equipment is centrifugal and you need to project flow, head, and HP at the new speed (or trim the impeller instead of changing the sheave).
• Coupling Alignment Calculator when symptoms point to vibration at the coupling and you need dial-indicator tolerances.
• Vibration Severity Checker for ISO 10816 zone interpretation when you have a vibration reading.

The System Chain Analyzer does not replace these tools. It tells you which one to open next.

Recommended Field Workflow

For a typical service call:

1. Read the nameplates first. Motor HP, FL RPM, FLA, SF; voltage at the panel; breaker rating. Enter these in steps 1 and 2 before you touch a tool.
2. Identify the transmission. Direct, belt, gearbox, or chain. For belts, measure both sheave ODs with a tape rule. For gearboxes and chains, read the ratio off the nameplate or count teeth.
3. Identify the driven equipment. Centrifugal pump, centrifugal fan, PD pump, conveyor, etc. Look up the expected RPM from the pump curve, fan nameplate, or maintenance log if you have it.
4. Take present-state readings. Clamp-meter the motor at normal load. Strobe-tach the driven shaft. Note any audible or visible symptoms.
5. Read the verdict. Look at the chain diagram for the worst-tier segment. Read the System Status card and the Chain Summary table.
6. Read "What Probably Changed." The inference panel surfaces the most likely root cause with a confidence chip. High-confidence inferences are reasonably actionable; medium and low confidence are starting points for further measurement.
7. Take the next step. The "What to Check Next" panel lists the specific measurement to take, why it matters, and how to take it in the field. Cycle back to the analyzer once you have the new reading.
8. Cross-link if needed. If the chain analysis points to one segment as the problem, open the dedicated single-purpose calculator from the Related Tools panel for the deep dive.
9. Export the PDF. The PDF includes the verdict, chain summary, calculated results, warnings, what changed, symptom matches, next steps, and a NEC FLA reference table. Hand it to the customer or attach it to the work order.