Formula Sheet
Quick reference for manufacturing process calculations
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All Units
Casting Processes
Welding Processes
Drilling Operations
Bulk Deformation
Surface Finishing
🏭
Casting Processes
Shrinkage Allowance
ΔL = L × α × ΔT
Variables:
L = original length, α = coefficient of expansion, ΔT = temperature change
Units:
mm
Example Calculation:
For steel: ΔL = 100 × 12×10⁻⁶ × 1000 = 1.2mm
Volume of Casting
V = l × w × h
Variables:
l = length, w = width, h = height
Units:
mm³ or cm³
Example Calculation:
V = 50 × 30 × 20 = 30,000 mm³
Surface Area of Casting
SA = 2(lw + lh + wh)
Variables:
l = length, w = width, h = height
Units:
mm² or cm²
Example Calculation:
SA = 2(50×30 + 50×20 + 30×20) = 6,200 mm²
Pattern Size with Shrinkage
Lp = Lc × (1 + S/100)
Variables:
Lp = pattern length, Lc = casting length, S = shrinkage %
Units:
mm
Example Calculation:
Lp = 100 × (1 + 2/100) = 102 mm
Solidification Time
t = K × (V/A)²
Variables:
t = time, K = constant, V = volume, A = surface area
Units:
seconds
Example Calculation:
t = 2 × (1000/500)² = 8 seconds
Chvorinov's Rule
t = B × (V/A)ⁿ
Variables:
t = solidification time, B = mold constant, V = volume, A = surface area, n = exponent (≈2)
Units:
seconds
Example Calculation:
t = 3 × (500/250)² = 12 seconds
Pouring Time
tp = K × W^(2/3)
Variables:
tp = pouring time, K = constant, W = weight of casting
Units:
seconds
Example Calculation:
tp = 1.5 × 10^(2/3) = 6.9 seconds
Gating Ratio
Sprue : Runner : Gate = 1 : 2 : 4
Variables:
Cross-sectional areas in ratio
Units:
dimensionless
Example Calculation:
If sprue = 10mm², runner = 20mm², gate = 40mm²
⚡
Welding Processes
Heat Input
H = (V × I × 60) / S
Variables:
H = heat input, V = voltage, I = current, S = welding speed
Units:
J/mm
Example Calculation:
H = (25 × 150 × 60) / 300 = 750 J/mm
Arc Power
P = V × I
Variables:
P = power, V = voltage, I = current
Units:
Watts
Example Calculation:
P = 25 × 150 = 3,750 W
Welding Speed
S = L / T
Variables:
S = speed, L = length, T = time
Units:
mm/min
Example Calculation:
S = 300 / 5 = 60 mm/min
Deposition Rate
DR = (I × DE) / 1000
Variables:
DR = deposition rate, I = current, DE = deposition efficiency
Units:
kg/hr
Example Calculation:
DR = (200 × 85) / 1000 = 17 kg/hr
Thermal Efficiency
η = (Heat in weld) / (Total heat input)
Variables:
η = efficiency, dimensionless ratio
Units:
%
Example Calculation:
η = 2000 / 3000 = 66.7%
Penetration Depth
P = K × I^a × V^b × S^c
Variables:
P = penetration, K = constant, I = current, V = voltage, S = speed
Units:
mm
Example Calculation:
P = 0.1 × 200^1.5 × 25^0.5 × 60^(-0.5) = 8.2 mm
Dilution Ratio
D = (Ab / (Ab + Aw)) × 100
Variables:
D = dilution %, Ab = base metal area, Aw = weld metal area
Units:
%
Example Calculation:
D = (15 / (15 + 10)) × 100 = 60%
🔧
Drilling Operations
Cutting Speed
V = πDN / 1000
Variables:
V = cutting speed, D = drill diameter, N = spindle speed
Units:
m/min
Example Calculation:
V = π × 10 × 1500 / 1000 = 47.1 m/min
Spindle Speed
N = 1000V / (πD)
Variables:
N = spindle speed, V = cutting speed, D = drill diameter
Units:
rpm
Example Calculation:
N = 1000 × 30 / (π × 8) = 1194 rpm
Feed Rate
f = mm/rev per cutting edge
Variables:
f = feed rate per revolution
Units:
mm/rev
Example Calculation:
f = 0.2 mm/rev for 10mm drill in steel
Material Removal Rate
MRR = (πD²fN) / 4
Variables:
MRR = material removal rate, D = diameter, f = feed, N = speed
Units:
mm³/min
Example Calculation:
MRR = (π × 10² × 0.2 × 1000) / 4 = 15,708 mm³/min
Drilling Time
T = L / (f × N)
Variables:
T = time, L = hole depth, f = feed rate, N = speed
Units:
minutes
Example Calculation:
T = 50 / (0.2 × 1000) = 0.25 min
Thrust Force
F = K × f^a × D^b
Variables:
F = thrust force, K = constant, f = feed, D = diameter
Units:
N
Example Calculation:
F = 500 × 0.2^0.8 × 10^1.2 = 2,850 N
Torque
T = K × f^a × D^b
Variables:
T = torque, K = constant, f = feed, D = diameter
Units:
N⋅m
Example Calculation:
T = 50 × 0.2^0.8 × 10^1.8 = 1,420 N⋅m
Power Required
P = (MRR × Specific Energy) / 60
Variables:
P = power, MRR = material removal rate, SE = specific energy
Units:
kW
Example Calculation:
P = (15,708 × 2.5) / 60 = 654 W
🔨
Bulk Deformation
True Stress
σ = F / A
Variables:
σ = true stress, F = force, A = instantaneous area
Units:
MPa or N/mm²
Example Calculation:
σ = 10,000 / 50 = 200 MPa
True Strain
ε = ln(l / l₀)
Variables:
ε = true strain, l = current length, l₀ = original length
Units:
dimensionless
Example Calculation:
ε = ln(120 / 100) = 0.182
Flow Stress
σf = K × εⁿ
Variables:
σf = flow stress, K = strength coefficient, ε = strain, n = strain hardening exponent
Units:
MPa
Example Calculation:
σf = 500 × 0.2^0.3 = 350 MPa
Forging Force
F = σf × A × Kf
Variables:
F = force, σf = flow stress, A = area, Kf = shape factor
Units:
N
Example Calculation:
F = 200 × 1000 × 1.5 = 300,000 N
Rolling Force
F = μ × R × w × Δh × Qp
Variables:
F = force, μ = friction coefficient, R = roll radius, w = width, Δh = reduction, Qp = mean pressure
Units:
N
Example Calculation:
F = 0.3 × 250 × 100 × 5 × 150 = 5,625,000 N
Extrusion Pressure
P = σf × ln(A₀ / Af)
Variables:
P = pressure, σf = flow stress, A₀ = initial area, Af = final area
Units:
MPa
Example Calculation:
P = 300 × ln(100 / 25) = 416 MPa
Drawing Force
F = σf × Af × ln(A₀ / Af)
Variables:
F = force, σf = flow stress, Af = final area, A₀ = initial area
Units:
N
Example Calculation:
F = 250 × 50 × ln(100 / 50) = 8,664 N
Reduction Ratio
r = ((t₀ - tf) / t₀) × 100
Variables:
r = reduction %, t₀ = initial thickness, tf = final thickness
Units:
%
Example Calculation:
r = ((10 - 8) / 10) × 100 = 20%
✨
Surface Finishing
Grinding Ratio
G = Volume of work removed / Volume of wheel wear
Variables:
G = grinding ratio, dimensionless
Units:
dimensionless
Example Calculation:
G = 50 / 2 = 25
Material Removal Rate
MRR = v × f × d
Variables:
MRR = removal rate, v = work speed, f = feed rate, d = depth of cut
Units:
mm³/s
Example Calculation:
MRR = 30 × 0.01 × 0.05 = 0.015 mm³/s
Specific Energy
u = P / MRR
Variables:
u = specific energy, P = power, MRR = material removal rate
Units:
J/mm³
Example Calculation:
u = 1000 / 0.015 = 66,667 J/mm³
Surface Speed
vs = πDsNs / 1000
Variables:
vs = surface speed, Ds = wheel diameter, Ns = wheel speed
Units:
m/s
Example Calculation:
vs = π × 200 × 3000 / 1000 = 1,885 m/s
Contact Length
lc = √(d × D)
Variables:
lc = contact length, d = depth of cut, D = wheel diameter
Units:
mm
Example Calculation:
lc = √(0.05 × 200) = 3.16 mm
Surface Roughness (Ra)
Ra = (1/n) × Σ|yi|
Variables:
Ra = average roughness, n = number of points, yi = height deviation
Units:
μm
Example Calculation:
Ra = (2 + 3 + 1 + 4) / 4 = 2.5 μm
Grinding Time
T = (L × N) / (f × vs)
Variables:
T = time, L = length, N = number of passes, f = feed rate, vs = table speed
Units:
minutes
Example Calculation:
T = (100 × 20) / (0.01 × 500) = 400 min
Quick Reference Guide
Common Units
Force: N (Newtons)
Pressure: MPa, N/mm²
Speed: m/min, rpm
Power: W, kW
Temperature: °C, K
Conversion Factors
1 MPa = 1 N/mm²
1 kW = 1000 W
1 m/min = 16.67 mm/s
°C = K - 273.15
1 inch = 25.4 mm
Constants
π ≈ 3.14159
e ≈ 2.71828
ln(2) ≈ 0.693
√2 ≈ 1.414
√3 ≈ 1.732