CMfgE cheat sheet

Machining: cutting speed V = πDN/12 (ft/min, D in inches); material removal rate in turning MRR = V·f·d, where f is feed and d is depth of cut.

Taylor tool life: V·T^n = C, so doubling speed cuts tool life by factor 2^(1/n); n ≈ 0.1–0.15 for HSS, 0.2–0.3 for carbide, 0.4–0.5 for ceramic.

Chip thickness ratio r = t0/tc = sin φ / cos(φ − α); shear plane angle φ rises with rake angle α and falls with friction.

Specific cutting energy u = F_c/V·t0·w; it rises sharply as undeformed chip thickness falls (size effect), so light cuts are less efficient per volume.

Casting: Chvorinov's rule solidification time t = B(V/A)^2, so risers must have a higher V/A modulus than the section they feed.

Fluidity in casting falls with wider freezing range, lower superheat, and higher thermal conductivity of the mold.

Welding energy: heat input H = ηEI/v (J/mm); arc efficiency ≈ 0.6–0.9 for arc processes, higher for submerged arc, lower for GTAW losses.

Bulk forming: forging force F ≈ Y_f·A·K_f, where K_f (1.0–1.5 typical) accounts for friction and redundant work; flow stress rises with strain hardening.

Sheet metal: minimum bend radius rises with thickness and falls with ductility; bend allowance = θ(R + K·t) with K ≈ 0.33–0.5 depending on neutral axis shift.

Little's Law: WIP = throughput × flow time; it holds for any stable system and links inventory, rate, and lead time.

Utilization ρ = arrival rate / service rate; for a single server, queue time grows nonlinearly as ρ → 1, roughly proportional to ρ/(1−ρ).

OEE = Availability × Performance × Quality; Availability = run time / planned production time, Performance = ideal cycle time × count / run time.

Takt time = available production time / customer demand; line balancing assigns tasks so each station cycle time stays at or below takt.

EOQ = sqrt(2DS/H); reorder point = demand during lead time plus safety stock, with safety stock = z·σ_LT.

Kanban count = (demand × replenishment lead time × (1 + safety factor)) / container size.

Theory of Constraints: system throughput is set by the bottleneck; drum-buffer-rope schedules the constraint and buffers it with time, not inventory.

Cellular layout groups dissimilar machines into cells by part family (group technology), cutting setup and transport time versus a functional layout.

Cost of quality splits into prevention, appraisal, internal failure, and external failure; external failure typically costs the most per defect.

ASTM/ISO 52900 classifies processes into seven families: vat photopolymerization, material extrusion, material jetting, binder jetting, powder bed fusion, directed energy deposition, and sheet lamination.

Laser powder bed fusion energy density E = P/(v·h·t) (J/mm³), where P is laser power, v scan speed, h hatch spacing, t layer thickness.

Resolution trade-off: thinner layers and finer hatch spacing improve surface finish and density but raise build time roughly as 1/(layer thickness).

Powder bed fusion needs support structures mainly to conduct heat away and anchor overhangs; material extrusion needs them for geometric support of overhangs.

Residual stress and warping in metal powder bed fusion scale with thermal gradients; preheating the build plate and scan-strategy rotation reduce them.

Binder jetting is not a melting process, so parts are green and require sintering; sintering shrinkage is typically 15–25% linear for metal systems.

Vat photopolymerization cures layer-by-layer with UV; overcure between layers controls interlayer bond strength and dimensional accuracy.

Design for AM: consolidate assemblies into one part, use lattice and topology optimization, and accept anisotropy because Z-direction properties are usually weakest.

Build time estimate for extrusion ≈ (part volume / extrusion rate) + layer count × travel time per layer.

ISA-95 hierarchy levels: 0 process, 1 sensing/actuation, 2 control, 3 MES, 4 ERP; data integration typically crosses levels 2–4.

OPC UA provides platform-independent, secure, structured data exchange and an information model; it is not tied to a single fieldbus.

MQTT is a lightweight publish/subscribe protocol with a broker; QoS levels 0, 1, 2 trade delivery guarantee against overhead.

Digital twin maturity: descriptive (as-is data), predictive (simulation), prescriptive (optimization); a twin needs a live data link to stay synchronized.

Predictive maintenance uses condition signals (vibration, current, temperature); vibration bearing faults show characteristic frequencies at BPFO, BPFI, and 1× running speed.

Edge computing reduces latency and bandwidth by filtering and preprocessing at the machine; cloud handles long-term analytics and model training.

Cybersecurity: IEC 62443 zones and conduits segment OT networks; the Purdue model separates enterprise IT from control networks with a DMZ.

Statistical process control: control limits at ±3σ of the process, not specification limits; Cpk = min(USL−μ, μ−LSL)/(3σ).

Overall equipment data for analytics requires time-stamped, synchronized tags; unsynchronized clocks corrupt OEE and root-cause analysis.