Reference
Formulas
Quick reference of all key equations across machining, forming, casting and welding.
Machining
8 formulas4 must-knowCutting Speed
Where: V = cutting speed (m/min), D = workpiece diameter (mm), N = spindle speed (RPM)
Material Removal Rate
Where: V = cutting speed, f = feed (mm/rev), d = depth of cut (mm)
Machining Time
Where: T = time (min), L = length of cut (mm), f = feed (mm/rev), N = RPM
Cutting Force
Where: Fc = cutting force (N), Ks = specific cutting force, A = uncut chip cross-section
Cutting Power
Where: P = power (kW), Fc = cutting force (N), V = cutting speed (m/min)
Taylor's Tool Life Equation
Where: V = cutting speed (m/min), T = tool life (min), n = exponent (HSS ≈ 0.1, carbide ≈ 0.2–0.4, ceramic ≈ 0.5–0.7), C = constant (≈ V at T = 1 min)
Chip Thickness Ratio
Where: t₀ = uncut (undeformed) chip thickness, tc = deformed chip thickness; used to find shear angle: tan φ = (r·cos α) / (1 − r·sin α)
Surface Roughness (Turning)
Where: Ra = arithmetic-mean roughness, f = feed (mm/rev), R = tool nose radius (mm)
Forming
11 formulas7 must-knowTrue Stress & Strain
Where: σₜ = true stress, εₜ = true strain, e = engineering strain
Flow Stress
Where: K = strength coefficient, n = strain-hardening exponent
Rolling Force
Where: Yf = flow stress, L = contact length, w = width, R = roll radius, Δh = draft
Maximum Draft (Rolling)
Where: μ = friction coefficient between roll and work, R = roll radius. Beyond this, rolls slip and cannot bite.
Reduction (Rolling)
Where: t₀ = entry thickness, tf = exit thickness
Drawing Force
Where: σ_d = drawing stress, A₀ = initial area, A_f = final area
Bend Allowance
Where: α = bend angle, R = inside radius, t = thickness, k = factor (0.33–0.5)
Deep-Drawing Ratio
Where: D₀ = blank diameter, Dp = punch diameter (LDR ≈ 2.0–2.2)
Sheet-Metal Clearance
Where: c = punch–die clearance, t = sheet thickness, a = allowance factor (4–8 % for cold-rolled steel)
Shearing / Punching Force
Where: L = perimeter of cut (mm), t = sheet thickness (mm), τ = shear strength of material (MPa)
Stamping Energy
Where: E = energy (ft·lb), F = punching force (lbf), p = punch penetration (fraction of t), t = sheet thickness (in). Empirical formula for press selection.
Casting
6 formulas4 must-knowChvorinov's Rule
Where: t = solidification time, B = mould constant, V/A = casting modulus
Riser Design
Where: Riser must solidify after the casting it feeds
Sprue Taper (Aspiration-free)
Where: A = cross-sectional area, h = height from sprue base
Pouring Time
Where: t = pouring time (s), W = casting weight (kg), K = empirical constant
Centrifugal Casting
Where: G = G-factor, ω = angular velocity, r = radius, N = RPM
Shrinkage Allowance
Where: L = pattern dimension (mm), s = linear shrinkage (mm/m). Typical: cast iron 10, Al alloys 15, brass 16, steel 21, lead 24.
Welding
4 formulas3 must-knowHeat Input
Where: H = heat input (kJ/mm), V = voltage, I = current, v = travel speed (mm/min)
Resistance Welding Heat
Where: Q = heat (J), I = current (A), R = joint resistance (Ω), t = time (s); k accounts for losses (≈ 40 % lost in spot welding).
Arc V–L Characteristic
Where: V = arc voltage, L = arc length (mm), a, b = electrode/process constants. Example (DC arc): V = 20 + 40·L.
Duty Cycle
Where: Relationship between welding current and duty cycle