machining-economics

name	machining-economics
description	Machining economics — Taylor's tool life equation, minimum cost cutting speed, maximum production rate speed, tool cost per edge, economic tool life, cycle time, machine hourly rate, setup cost, scrap cost, total cost per part, process selection economics, make vs. buy analysis, overall equipment effectiveness (OEE).
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Machining Economics — Complete Skill

Taylor's Tool Life Equation

Taylor equation: V × T^n = C [V = cutting speed [m/min]; T = tool life [min]; n = Taylor exponent; C = constant at T=1 min]

Extended Taylor equation (with feed and depth): V × T^n × f^a × d^b = C₁ [f = feed rate [mm/rev]; d = depth of cut [mm]; a, b = empirical exponents]

Typical n values: HSS tools in steel: n = 0.10–0.15 (very speed sensitive) Carbide tools in steel: n = 0.25–0.35 Ceramic/CBN in hardened steel: n = 0.40–0.70 (less speed sensitive; longer life at high speed)

Tool life prediction: Given V₁, T₁: V₂ = V₁ × (T₁/T₂)^n Example: carbide (n=0.3); at 200 m/min life = 20 min; at what speed for T₂=60 min? V₂ = 200 × (20/60)^0.3 = 200 × 0.333^0.3 = 200 × 0.693 = 138.6 m/min

Machinability ratio: MR = C_material / C_reference × 100% [relative to AISI 1212 = 100% reference] Free-machining steel (12L14): MR ≈ 160%; 304 SS: MR ≈ 45%; Ti-6Al-4V: MR ≈ 25%

Economic Cutting Speed Analysis

Cost Components per Part

C_part = C_machining + C_tool + C_setup + C_nonproductive

Machining time per part: t_m = (L + L_approach + L_overrun) / (f × n) × (1/N_passes) [min; L = feature length; f = feed; n = spindle speed; N_passes = number of passes] t_m = π × D × L / (1,000 × V × f) [turning; D = part diameter [mm]; V in m/min]

Cutting (machining) cost: C_machining = t_m × M_rate [M_rate = machine hourly rate including operator [$/ min]] M_rate = ($60–$300/hr) / 60 = $1–$5/min [typical CNC machining center]

Tool cost per part: C_tool = (C_edge / n_parts_per_edge) [C_edge = cost per cutting edge; n_parts = number of parts per tool edge] n_parts = T / t_m [number of parts machined per tool life T] C_tool = C_edge × t_m / T [C_tool = C_edge × t_m / T]

C_edge (cost per cutting edge): Insert cost divided by edges per insert: Carbide insert: $5–$25 each; 2–8 edges → C_edge = $1–$12 HSS drill bit: $3–$50; single edge → C_edge = $3–$50 Diamond/CBN: $100–$500 each; 1–4 edges → C_edge = $50–$500

Tool change time cost: Each tool change takes t_c = 1–5 min → cost: C_change = t_c × M_rate Distributed over parts: C_change_per_part = C_change × t_m / T = M_rate × t_c × t_m / T

Total variable machining cost per part: C_var = t_m × M_rate × (1 + t_c/T) + C_edge/T × t_m [$/part]

Minimum Cost Cutting Speed (V_opt)

Objective: minimize total cost C_part by choosing optimal V Optimization: dC_var/dV = 0:

Optimal tool life for minimum cost: T_opt = (1/n - 1) × (t_c + C_edge/M_rate) [min; n = Taylor exponent]

Example: n = 0.25; t_c = 3 min; C_edge = $5; M_rate = $3/min T_opt = (1/0.25 - 1) × (3 + 5/3) = 3 × (3 + 1.67) = 14 min

Optimal cutting speed: V_opt = C / T_opt^n [from Taylor equation; C from known (V₁, T₁)] If at V₁=200 m/min, T₁=20 min, n=0.25: C = 200 × 20^0.25 = 200 × 2.115 = 423 V_opt = 423 / 14^0.25 = 423 / 1.934 = 219 m/min

Maximum Production Rate Speed (V_max_prod)

When cycle time is critical (minimize machining time, not cost): T_opt_prod = (1/n - 1) × t_c [no tool cost term; only tool change time] T_opt_prod = 3 × 3 = 9 min (using above example without C_edge/M_rate) V_max_prod = 423 / 9^0.25 = 423 / 1.732 = 244 m/min

V_max_prod > V_min_cost: maximum productivity runs faster with shorter tool life; acceptable if tool cost negligible relative to machine time

Operating window: V_min_cost ≤ V_operation ≤ V_max_prod (typical; balance cost and productivity)

Cycle Time Analysis

CNC Machining Cycle Time

Total cycle time per part: t_cycle = t_load + t_setup_per_part + t_cut + t_rapid_traverse + t_tool_change_per_part + t_unload

Load/unload time: 0.5–3 min depending on part size and automation Setup time (amortized): t_setup_per_part = T_setup / N_batch_size [T_setup = total setup hours; N_batch = number of parts] Typical: T_setup = 1–4 hr for CNC turning/milling; amortize over 50–500 parts per batch

Rapid traverse time: t_rapid = L_rapid / V_rapid [V_rapid = 40–60 m/min for CNC machining center; negligible for large batches]

Tool change time (cumulative per part): t_change_per_part = t_c × (t_cut / T) [tool change time × fraction of tool life consumed per part]

Spindle Speed and Feed Rate

Spindle speed: n = (V × 1,000) / (π × D) [rpm; V = cutting speed [m/min]; D = diameter [mm]] CNC machines: n_max = 4,000–40,000 rpm; choose n ≤ n_max

Material removal rate (MRR): MRR = V × f × d [mm³/min; V [m/min] × 1,000 → mm/min; f = feed [mm/rev × n (rpm) = mm/min]; d = depth [mm]]

Machine Hourly Rate

Machine hourly rate (M_rate) components: M_rate = (depreciation + maintenance + overhead + energy + operator_labor) / productive_hours_per_year

Depreciation: Machine cost: $100k–$2M; life = 10–15 years; depreciation = $7k–$200k/yr Per hour (2,000 productive hrs/yr): $3.5–$100/hr

Labor: Operator: $25–$60/hr (+ benefits: 30–40%) = $35–$85/hr total CNC machines with minimal supervision: reduce to 20–50% of operator cost per machine

Overhead: Facility: 80–150% of direct labor (floor space, electricity, coolant, supervisors, etc.)

Typical M_rate ranges: Simple lathe/mill: $50–$80/hr = $0.83–$1.33/min CNC turning center: $80–$150/hr = $1.33–$2.50/min 5-axis machining center: $150–$300/hr = $2.50–$5.00/min Grinding (cylindrical precision): $100–$200/hr EDM: $80–$200/hr

Overall Equipment Effectiveness (OEE)

OEE = Availability × Performance × Quality

Availability: A = (Operating time) / (Scheduled time) [unplanned downtime + scheduled maintenance] A = (Scheduled time - Downtime) / Scheduled time [target A > 90%]

Performance: P = (Actual output) / (Ideal output at design speed) [speed losses; target P > 95%] P = (Parts per hour actual) / (Parts per hour design)

Quality: Q = Good parts / Total parts produced [rejects + rework; target Q > 99%]

OEE target: OEE > 85%: world class; OEE 60–85%: typical US manufacturing; OEE < 60%: poor

Example: Scheduled 8 hr shift; 0.5 hr planned maintenance; 0.8 hr downtime A = (8 - 0.5 - 0.8)/8 = 83.8% Design: 60 parts/hr; actual: 52 parts/hr → P = 52/60 = 86.7% Rejected: 3 of 416 total → Q = 413/416 = 99.3% OEE = 0.838 × 0.867 × 0.993 = 72.1%

Make vs. Buy Analysis

Make decision justified when: Total manufactured cost per part (TMCPC) < supplier price × (1 + inventory/logistics burden) Strategic component → IP protection, quality control, supply security Spare capacity on existing machines

TMCPC calculation: TMCPC = (direct material + direct labor + variable overhead) + (fixed overhead × burden rate) Fixed overhead amortized over volume → TMCPC decreases with volume (learning curve)

Learning curve: Cost decreases by constant percentage each time cumulative production doubles Learning rate 85%: 15% cost reduction each doubling → 4× volume → 0.85² = 72.3% of original cost TMCPC_N = TMCPC_1 × N^(log(learning_rate)/log(2)) [N = cumulative production]

Break-even analysis: Fixed investment (tooling, machine) + variable cost per part vs. buy price Break-even quantity = Fixed investment / (Buy price - Variable cost)

Scrap and Rework Cost

Cost of scrap per part: C_scrap = C_material + C_machining_to_date [labor + machine time already spent] Scrap rate = defective / total; typical target < 0.5% for precision machining

Cost of quality (COQ): COQ = (Prevention + Appraisal + Internal failure + External failure) costs Typical COQ: 5–30% of sales revenue; excessive COQ → process improvement investment justified

Standards and References

Source	Scope
Taylor (1906) ASME Trans.	Original tool life equation
ASTM E618	Machinability evaluation standard
ISO 3685	Tool life testing in turning (establishes VB wear criteria)
Machining Data Handbook (Metcut)	Comprehensive cutting speed/feed data by material
SME Handbook of Metal Cutting	Process economics formulas

Output

Provide: material and machining operation (turning/milling/drilling), Taylor constants (n, C) with source, machining time per part t_m [min] (formula and calculation), tool life T_opt [min] (minimum cost criterion), optimal cutting speed V_opt [m/min], tool cost per part C_tool [$/part], machine rate M_rate [$/min], total variable cost C_var [$/part], cycle time breakdown (cut/load/unload/tool change [min]), OEE calculation (A × P × Q [%]) if production data given, make vs. buy break-even quantity (if applicable), learning curve factor (rate and doubling), scrap cost per part [$/part], and applicable standard (ISO 3685, Taylor equation with n and C values).