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Calculations and Formulas used in Plastic Injection Molding

  • Posted On: February 9, 2025
  • Posted By: admin

1. Shot Size Calculation

Shot Size=Part Weight+Runner Weight\text{Shot Size} = \text{Part Weight} + \text{Runner Weight}

2. Clamping Force Calculation

Clamping Force (Tons)=Projected Area (cm²)×Cavity Pressure (kg/cm²)×11000\text{Clamping Force (Tons)} = \text{Projected Area (cm²)} \times \text{Cavity Pressure (kg/cm²)} \times \frac{1}{1000}

  • Typical cavity pressure: 300 – 800 kg/cm² (depends on material and part design)

3. Cooling Time Calculation

tc=d24×α×ln⁡(Tm−TeTs−Te)t_c = \frac{{d^2}}{{4 \times \alpha}} \times \ln \left( \frac{{T_m – T_e}}{{T_s – T_e}} \right)Where:
tct_c = Cooling time (seconds)
dd = Maximum wall thickness (mm)
α\alpha = Thermal diffusivity of material (mm²/s)
TmT_m = Melt temperature (°C)
TeT_e = Ejection temperature (°C)
TsT_s = Mold surface temperature (°C)

4. Injection Pressure Calculation

Injection Pressure=Viscous Resistance+Frictional Losses+Acceleration Pressure\text{Injection Pressure} = \text{Viscous Resistance} + \text{Frictional Losses} + \text{Acceleration Pressure}

5. Plasticizing Capacity (kg/hr)

Plasticizing Capacity=Screw Diameter (mm)×Screw Speed (rpm)×Material Factor\text{Plasticizing Capacity} = \text{Screw Diameter (mm)} \times \text{Screw Speed (rpm)} \times \text{Material Factor}

6. Mold Filling Time

tf=VQt_f = \frac{V}{Q}Where:
tft_f = Filling time (seconds)
VV = Volume of the part (cm³)
QQ = Flow rate (cm³/s)

7. Projected Area Calculation

Projected Area=Length×Width×Number of Cavities\text{Projected Area} = \text{Length} \times \text{Width} \times \text{Number of Cavities}

8. Shrinkage Calculation

Shrinkage (%)=Mold Dimension−Part DimensionMold Dimension×100\text{Shrinkage (\%)} = \frac{\text{Mold Dimension} – \text{Part Dimension}}{\text{Mold Dimension}} \times 100

9. Barrel Residence Time

Residence Time (min)=Shot Size (g)Plasticizing Rate (g/min)\text{Residence Time (min)} = \frac{\text{Shot Size (g)}}{\text{Plasticizing Rate (g/min)}}

10. Injection Speed (Linear Speed)

Injection Speed=Screw Movement (mm)Injection Time (s)\text{Injection Speed} = \frac{\text{Screw Movement (mm)}}{\text{Injection Time (s)}}

11. Cycle Time Calculation

Cycle Time (s)=tf+tc+to\text{Cycle Time (s)} = t_f + t_c + t_oWhere:
tft_f = Filling time
tct_c = Cooling time
tot_o = Other time (ejecting, mold open/close)

12. Melt Flow Index (MFI) Calculation

MFI (g/10 min)=Weight of Melted Plastic10\text{MFI (g/10 min)} = \frac{\text{Weight of Melted Plastic}}{10}

Injection Molding Parameters

  • Screw Rotation SpeedScrew Speed (m/min)=RPM×Screw Diameter×π\text{Screw Speed (m/min)} = \text{RPM} \times \text{Screw Diameter} \times \pi

 

  • Injection Timeti=VQt_i = \frac{V}{Q}Where:
    tit_i = Injection time (s)
    VV = Volume of the part (cm³)
    QQ = Injection flow rate (cm³/s)

 

  • Back Pressure CalculationBack Pressure (MPa)=Hydraulic Pressure (MPa)Area Ratio\text{Back Pressure (MPa)} = \frac{\text{Hydraulic Pressure (MPa)}}{\text{Area Ratio}}
  • Recovery Timetr=Shot Size (g)Plasticizing Rate (g/s)t_r = \frac{\text{Shot Size (g)}}{\text{Plasticizing Rate (g/s)}}
  • Injection VelocityInjection Velocity (mm/s)=Screw Stroke (mm)Injection Time (s)\text{Injection Velocity (mm/s)} = \frac{\text{Screw Stroke (mm)}}{\text{Injection Time (s)}}
  • Screw StrokeScrew Stroke (mm)=Shot Volume÷(π×(Screw Diameter2)2)\text{Screw Stroke (mm)} = \text{Shot Volume} \div \left( \pi \times \left( \frac{\text{Screw Diameter}}{2} \right)^2 \right)
  • Specific Energy ConsumptionEnergy (kWh/kg)=Power Consumption (kW)×Cycle Time (s)Part Weight (kg)\text{Energy (kWh/kg)} = \frac{\text{Power Consumption (kW)} \times \text{Cycle Time (s)}}{\text{Part Weight (kg)}}
  • Injection Unit CapacityInjection Capacity (g)=π4×d2×L×Material Density\text{Injection Capacity (g)} = \frac{\pi}{4} \times d^2 \times L \times \text{Material Density}Where dd = Screw diameter, LL = Screw length
  • Nozzle Pressure-Nozzle Pressure=Injection Pressure×Pressure Loss Factor\text{Nozzle Pressure} = \text{Injection Pressure} \times \text{Pressure Loss Factor}
  • Barrel Heat Transfer Rate

Q=U×A×(Tb−Ts)Q = U \times A \times (T_b – T_s)Where:
QQ = Heat transfer rate (W)
UU = Heat transfer coefficient
AA = Barrel surface area
TbT_b = Barrel temperature, TsT_s = Surface temperature

Mold Design and Cooling

  • Runner Diameter Calculation

D=(4×Vπ×L)1/2D = \left( \frac{4 \times V}{\pi \times L} \right)^{1/2}Where VV = Volume of runner, LL = Length of runner

  1. Gate Size Calculation

Ag=QvA_g = \frac{Q}{v}Where AgA_g = Gate area, QQ = Flow rate, vv = Velocity

  1. Cooling Channel Length

Lc=π×dNL_c = \frac{\pi \times d}{N}Where dd = Diameter of channel, NN = Number of channels

  1. Heat Dissipation Rate

Q=m×Cp×ΔTQ = m \times C_p \times \Delta TWhere QQ = Heat dissipation (J), mm = Mass of part, CpC_p = Specific heat, ΔT\Delta T = Temperature difference

  1. Mold Temperature Difference

ΔTm=Tmax−Tmin\Delta T_m = T_{max} – T_{min}

  1. Ejection Force Calculation

Fe=Ae×PeF_e = A_e \times P_eWhere AeA_e = Ejection area, PeP_e = Ejection pressure

  1. Mold Life Cycle Calculation

Mold Life=Total CyclesCycles per Day\text{Mold Life} = \frac{\text{Total Cycles}}{\text{Cycles per Day}}

Material Properties

  1. Density of Melted Plastic

ρm=mV\rho_m = \frac{m}{V}Where ρm\rho_m = Melt density, mm = Mass, VV = Volume

  1. Viscosity Calculation

η=τγ˙\eta = \frac{\tau}{\dot{\gamma}}Where η\eta = Viscosity, τ\tau = Shear stress, γ˙\dot{\gamma} = Shear rate

  1. Thermal Expansion Coefficient

α=ΔLL0×ΔT\alpha = \frac{\Delta L}{L_0 \times \Delta T}

  1. Tensile Strength

σ=FA\sigma = \frac{F}{A}Where σ\sigma = Tensile strength, FF = Force, AA = Cross-sectional area

  1. Flexural Modulus

Ef=L3×F4×d3×ΔyE_f = \frac{L^3 \times F}{4 \times d^3 \times \Delta y}

  1. Moisture Absorption Rate

M=Ww−WdWd×100M = \frac{W_w – W_d}{W_d} \times 100Where WwW_w = Wet weight, WdW_d = Dry weight

Cycle Time Optimization

  1. Total Cycle Time

tcycle=tf+tc+te+tot_{cycle} = t_f + t_c + t_e + t_o

  1. Mold Open Time

to=Machine Setting for Mold Open/Closet_o = \text{Machine Setting for Mold Open/Close}

  1. Mold Venting Area

Av=Lv×WvA_v = L_v \times W_v

  1. Flash Calculation

Flash (mm)=Parting Line Mismatch+Material Overflow\text{Flash (mm)} = \text{Parting Line Mismatch} + \text{Material Overflow}

Energy and Cost Calculation

  1. Machine Hour Rate

Hourly Rate=Annual Machine CostTotal Annual Operating Hours\text{Hourly Rate} = \frac{\text{Annual Machine Cost}}{\text{Total Annual Operating Hours}}

  1. Production Cost per Part

C=M+L+ENC = \frac{M + L + E}{N}Where MM = Material cost, LL = Labor cost, EE = Energy cost, NN = Number of parts

  1. Energy Consumption per Shot

Es=P×t3600E_s = \frac{P \times t}{3600}

Shrinkage and Warpage

  1. Linear Shrinkage

S=Lm−LpLm×100S = \frac{L_m – L_p}{L_m} \times 100Where LmL_m = Mold length, LpL_p = Part length

  1. Volumetric Shrinkage

Sv=Vm−VpVmS_v = \frac{V_m – V_p}{V_m}

  1. Warpage Calculation

W=Δd/LW = \Delta d / L

Advanced Formulas

  1. Cavity Balance Ratio

B=Longest Flow LengthShortest Flow LengthB = \frac{\text{Longest Flow Length}}{\text{Shortest Flow Length}}

  1. Pressure Drop Calculation

ΔP=8×η×L×Qπ×d4\Delta P = \frac{8 \times \eta \times L \times Q}{\pi \times d^4}

  1. Melt Compressibility

C=ΔVV×ΔPC = \frac{\Delta V}{V \times \Delta P}

  1. Fill Pattern Ratio

FPR=Part VolumeTotal Shot VolumeFPR = \frac{\text{Part Volume}}{\text{Total Shot Volume}}

  1. Pack and Hold Pressure

Ph=Pi×RP_h = P_i \times RWhere RR = Holding pressure ratio

  1. Deformation Under Load

δ=F×L33×E×I\delta = \frac{F \times L^3}{3 \times E \times I}

  1. Mold Deflection

δm=Fm×Lm33×Em×Im\delta_m = \frac{F_m \times L_m^3}{3 \times E_m \times I_m}

Advanced Mold Design

  • Runner Volume CalculationVr=π×(d2)2×LV_r = \pi \times \left( \frac{d}{2} \right)^2 \times LWhere:
    VrV_r = Runner volume (cm³)
    dd = Diameter of runner (cm)
    LL = Length of runner (cm)
  • Gate Volume CalculationVg=π×d2×h4V_g = \frac{\pi \times d^2 \times h}{4}Where dd = Gate diameter, hh = Gate height
  • Part Weight from VolumePart Weight (g)=Part Volume (cm³)×Material Density (g/cm³)\text{Part Weight (g)} = \text{Part Volume (cm³)} \times \text{Material Density (g/cm³)}
  • Cooling Channel Pressure LossΔP=f×Ld×ρ×v22\Delta P = f \times \frac{L}{d} \times \frac{\rho \times v^2}{2}
  • Cavity Filling RatioFr=VfVc×100F_r = \frac{V_f}{V_c} \times 100Where VfV_f = Filled volume, VcV_c = Cavity volume
  • Number of CavitiesNc=Clamping Force (kN)Required Force per Cavity (kN)N_c = \frac{\text{Clamping Force (kN)}}{\text{Required Force per Cavity (kN)}}
  • Cooling Channel AreaAc=π×r2A_c = \pi \times r^2
  • Gate Velocityvg=QAgv_g = \frac{Q}{A_g}Where vgv_g = Gate velocity, AgA_g = Gate area
  • Mold Thermal ResistanceRm=ΔTQR_m = \frac{\Delta T}{Q}
  • Heat Loss through Cooling Channel
  • Q=m×Cp×(Tin−Tout)Q = m \times C_p \times (T_{in} – T_{out})
  • Material Properties and Rheology
  1. Specific Heat Capacity
  • Cp=Qm×ΔTC_p = \frac{Q}{m \times \Delta T}
  1. Shear Rate Calculation
  • γ˙=4Qπr3\dot{\gamma} = \frac{4Q}{\pi r^3}
  1. Shear Stress
  • τ=η×γ˙\tau = \eta \times \dot{\gamma}
  1. Melt Elasticity
  • Em=σϵE_m = \frac{\sigma}{\epsilon}
  1. Poisson’s Ratio
  • ν=−Δd/dΔL/L\nu = -\frac{\Delta d/d}{\Delta L/L}
  1. Thermal Conductivity
  • k=Q×LA×ΔTk = \frac{Q \times L}{A \times \Delta T}
  1. Thermal Expansion Volume Change
  • ΔV=V0×β×ΔT\Delta V = V_0 \times \beta \times \Delta T
  1. Viscoelastic Modulus
  • G=σγG = \frac{\sigma}{\gamma}
  1. Melt Flow Rate (MFR)
  • MFR=Weight of Extruded Material (g)10 minMFR = \frac{\text{Weight of Extruded Material (g)}}{10 \, \text{min}}
  1. Shrinkage in Thickness
  • St=Tm−TpTmS_t = \frac{T_m – T_p}{T_m}

Part Quality and Dimensional Accuracy

  1. Surface Finish Depth
  • Df=2QπrD_f = \sqrt{\frac{2Q}{\pi r}}
  1. Part Flatness
  • Fp=ΔhLF_p = \frac{\Delta h}{L}
  1. Warping Rate
  • Wr=ΔLL0×100W_r = \frac{\Delta L}{L_0} \times 100
  1. Sink Mark Depth
  • Ds=PED_s = \frac{P}{E}
  1. Residual Stress
  • σr=E×ϵr\sigma_r = E \times \epsilon_r
  1. Part Thickness Uniformity
  • Ut=Tmax−TminTavg×100U_t = \frac{T_{max} – T_{min}}{T_{avg}} \times 100
  1. Reinforcement Factor
  • Rf=σreinforcedσunreinforcedR_f = \frac{\sigma_{reinforced}}{\sigma_{unreinforced}}
  1. Gloss Level
  • G=IrIi×100G = \frac{I_r}{I_i} \times 100
  1. Impact Strength
  • I=EAI = \frac{E}{A}
  1. Toughness
  • T=∫0ϵfσdϵT = \int_0^{\epsilon_f} \sigma d\epsilon
  • Cycle Time Optimization
  1. Ejector Stroke Calculation
  • Se=Hp+10 mm (Safety Margin)S_e = H_p + 10 \, \text{mm (Safety Margin)}
  1. Heating Time
  • th=L24αt_h = \frac{L^2}{4\alpha}
  1. Preheating Energy
  • Eh=m×Cp×ΔTE_h = m \times C_p \times \Delta T
  1. Holding Time
  • th=3×tct_h = 3 \times t_c
  1. Mold Open Time
  • to=te+tmt_o = t_e + t_m
  1. Cavity Fill Time for Thin Walls
  • tf=Lvt_f = \frac{L}{v}
  1. Cooling Rate
  • Rc=ΔTtcR_c = \frac{\Delta T}{t_c}
  1. Optimal Cycle Time
  • topt=tf+tc+tet_{opt} = t_f + t_c + t_e

Cost and Production Analysis

  1. Material Cost per Part
  • Cm=Part Weight (g)×Material Cost per gramC_m = \text{Part Weight (g)} \times \text{Material Cost per gram}
  1. Energy Cost per Shot
  • Ce=Es×Cost per kWhC_e = E_s \times \text{Cost per kWh}
  1. Labor Cost per Part
  • Cl=Hourly Labor CostParts per HourC_l = \frac{\text{Hourly Labor Cost}}{\text{Parts per Hour}}
  1. Total Production Cost
  • Ct=Cm+Ce+Cl+CdC_t = C_m + C_e + C_l + C_dWhere CdC_d = Depreciation cost
  1. Machine Utilization Efficiency
  • Eu=Actual Production TimeTotal Available Time×100E_u = \frac{\text{Actual Production Time}}{\text{Total Available Time}} \times 100
  1. Scrap Rate
  • Sr=Scrap WeightTotal Material Weight×100S_r = \frac{\text{Scrap Weight}}{\text{Total Material Weight}} \times 100
  1. Return on Investment (ROI)
  • ROI=Net ProfitInitial Investment×100ROI = \frac{\text{Net Profit}}{\text{Initial Investment}} \times 100
  1. Production Throughput
  • Tp=Total Parts ProducedTotal TimeT_p = \frac{\text{Total Parts Produced}}{\text{Total Time}}
  1. Cycle Efficiency
  • Ec=tidealtactual×100E_c = \frac{t_{ideal}}{t_{actual}} \times 100
  1. Payback Period
  • Pp=Investment CostAnnual Net SavingsP_p = \frac{\text{Investment Cost}}{\text{Annual Net Savings}}
  1. Break-Even Analysis
  • BEP=Fixed CostsPrice per Part−Variable Cost per PartBEP = \frac{\text{Fixed Costs}}{\text{Price per Part} – \text{Variable Cost per Part}}
  1. Annual Output Capacity
  • Ac=Cycle Time (s)×Total Annual Operating HoursA_c = \text{Cycle Time (s)} \times \text{Total Annual Operating Hours}

Thermal Dynamics (Cooling and Heating)

  1. Heat Transfer Rate (Mold to Coolant)Q=U×A×ΔTQ = U \times A \times \Delta T
  2. Mold Temperature GradientΔTm=Tc−Tw\Delta T_m = T_c – T_w
  3. Time for Heat Transferth=m×Cp×ΔTQt_h = \frac{m \times C_p \times \Delta T}{Q}
  4. Thermal Diffusivityα=kρ×Cp\alpha = \frac{k}{\rho \times C_p}
  5. Cooling Time for Semi-Crystalline Plasticstc=d24×αt_c = \frac{d^2}{4 \times \alpha}
  6. Cooling EfficiencyEc=Tin−ToutTmax−Tmin×100E_c = \frac{T_{in} – T_{out}}{T_{max} – T_{min}} \times 100
  7. Heat Fluxq=QAq = \frac{Q}{A}
  8. Steady-State Heat TransferQ=k×A×ΔTdQ = k \times A \times \frac{\Delta T}{d}
  9. Melt Cooling RateRc=ΔTtR_c = \frac{\Delta T}{t}
  10. Reynolds Number (Coolant Flow)

Re=ρ×v×dμRe = \frac{\rho \times v \times d}{\mu}

Material Behavior and Rheology

  1. Melt Flow Index (MFI)

MFI=Mass of Melt (g)10 minMFI = \frac{\text{Mass of Melt (g)}}{10 \, \text{min}}

  1. Shear Rate for Circular Channels

γ˙=8Qπr3\dot{\gamma} = \frac{8Q}{\pi r^3}

  1. Shear Stress (Circular Channel)

τ=ΔP×r2L\tau = \frac{\Delta P \times r}{2L}

  1. Stress Relaxation

σ(t)=σ0×e−tτ\sigma(t) = \sigma_0 \times e^{-\frac{t}{\tau}}

  1. Creep Strain

ϵ=σE+β×t\epsilon = \frac{\sigma}{E} + \beta \times t

  1. Dynamic Viscosity (Newtonian Flow)

η=τγ˙\eta = \frac{\tau}{\dot{\gamma}}

  1. Specific Volume Change (Due to Shrinkage)

ΔV=ΔLL×100\Delta V = \frac{\Delta L}{L} \times 100

  1. Elastic Recovery Rate

Er=ΔLelasticΔLtotal×100E_r = \frac{\Delta L_{elastic}}{\Delta L_{total}} \times 100

  1. Glass Transition Temperature

Tg=Tm+Tf2T_g = \frac{T_m + T_f}{2}

  1. Flow Stress in the Melt

σf=k×γ˙n\sigma_f = k \times \dot{\gamma}^n

Injection Pressure and Velocity

  1. Maximum Injection Pressure

Pmax=FAP_{max} = \frac{F}{A}

  1. Pressure Drop in Runner System

ΔP=128×η×L×Qπ×d4\Delta P = \frac{128 \times \eta \times L \times Q}{\pi \times d^4}

  1. Injection Speed

vi=ΔVtv_i = \frac{\Delta V}{t}

  1. Injection Force

F=P×AF = P \times A

  1. Melt Front Velocity

vm=Ltfv_m = \frac{L}{t_f}

  1. Pressure Loss in Cavity

ΔP=k×L×ηd2\Delta P = k \times L \times \frac{\eta}{d^2}

  1. Injection Specific Energy

E=P×VηE = \frac{P \times V}{\eta}

  1. Screw Back Pressure Calculation

Pb=FAsP_b = \frac{F}{A_s}

  1. Screw Rotation Speed (RPM)

Screw Speed=Qπd2\text{Screw Speed} = \frac{Q}{\pi d^2}

  1. Shot Size in Screw Injection

Vs=π4×d2×hV_s = \frac{\pi}{4} \times d^2 \times h

Cooling Optimization

  1. Cooling Channel Reynolds Number

Re=ρ×v×DμRe = \frac{\rho \times v \times D}{\mu}

  1. Nusselt Number for Cooling

Nu=0.023×Re0.8×Pr0.3Nu = 0.023 \times Re^{0.8} \times Pr^{0.3}

  1. Cooling Channel Volume

Vc=π×r2×LV_c = \pi \times r^2 \times L

  1. Heat Removal Efficiency

ηh=QremovedQtotal×100\eta_h = \frac{Q_{removed}}{Q_{total}} \times 100

  1. Wall Temperature at Cooling Channel

Tw=Tc−Qh×AT_w = T_c – \frac{Q}{h \times A}

Mechanical Properties

  1. Young’s Modulus

E=σϵE = \frac{\sigma}{\epsilon}

  1. Yield Stress

σy=FyA\sigma_y = \frac{F_y}{A}

  1. Flexural Strength

σf=3FL2bd2\sigma_f = \frac{3FL}{2bd^2}

  1. Impact Energy

E=12mv2E = \frac{1}{2}mv^2

  1. Toughness Calculation

T=∫0ϵfσdϵT = \int_0^{\epsilon_f} \sigma d\epsilon

Clamping Force and Mold Design

  1. Clamping Force

Fc=P×AF_c = P \times A

  1. Projected Area Calculation

Ap=L×WA_p = L \times W

  1. Mold Deflection

δm=F×L33EI\delta_m = \frac{F \times L^3}{3EI}

  1. Gate Cross-sectional Area

Ag=π4×d2A_g = \frac{\pi}{4} \times d^2

  1. Mold Cavity Pressure

Pc=FAP_c = \frac{F}{A}

Process Efficiency and Cost Analysis

  1. Production Rate

R=1tcycle×60R = \frac{1}{t_{cycle}} \times 60

  1. Scrap Cost

Cs=Scrap Weight×Material Cost per kgC_s = \text{Scrap Weight} \times \text{Material Cost per kg}

  1. Overall Equipment Efficiency (OEE)

OEE=A×P×QOEE = A \times P \times QWhere AA = Availability, PP = Performance, QQ = Quality

  1. Energy Consumption per Shot

Es=P×tE_s = P \times t

  1. Labor Cost per Part

Cl=Hourly Labor RateParts per HourC_l = \frac{\text{Hourly Labor Rate}}{\text{Parts per Hour}}

Advanced Thermal and Mechanical Formulas

  1. Thermal Stress

σt=α×E×ΔT\sigma_t = \alpha \times E \times \Delta T

  1. Thermal Expansion (Linear)

ΔL=α×L×ΔT\Delta L = \alpha \times L \times \Delta T

  1. Material Hardness Calculation

H=FAH = \frac{F}{A}

  1. Fatigue Strength

σf=σ0×(Nf)−b\sigma_f = \sigma_0 \times (N_f)^{-b}

  1. Resilience

Ur=σ22EU_r = \frac{\sigma^2}{2E}

Mechanics and Part Filling
  1. Volumetric Flow Rate

Q=A×vQ = A \times v

  1. Flow Front Advancement

Lf=v×tL_f = v \times t

  1. Pressure Drop across the Mold

ΔP=128×η×L×Qπ×d4\Delta P = \frac{128 \times \eta \times L \times Q}{\pi \times d^4}

  1. Flow Length to Thickness Ratio

FL/TH=Lt\text{FL/TH} = \frac{L}{t}

  1. Hydraulic Diameter

Dh=4APD_h = \frac{4A}{P}Where AA = Cross-sectional area, PP = Wetted perimeter

  1. Mold Filling Velocity

vf=Fill VolumeFill Timev_f = \frac{\text{Fill Volume}}{\text{Fill Time}}

  1. Laminar Flow Criterion

Re<2300Re < 2300

  1. Critical Flow Rate for Laminar to Turbulent Transition

Qc=Re×μ×dρQ_c = \frac{Re \times \mu \times d}{\rho}

  1. Cavity Balancing Ratio

Rb=ΔPmaxΔPminR_b = \frac{\Delta P_{max}}{\Delta P_{min}}

Cycle Time Optimization and Machine Parameters

  1. Total Cycle Time

tcycle=tf+tc+te+tot_{cycle} = t_f + t_c + t_e + t_oWhere:
tft_f = Fill time
tct_c = Cooling time
tet_e = Ejection time
tot_o = Mold open/close time

  1. Fill Time for Thin Walls

tf=L22v×ht_f = \frac{L^2}{2v \times h}

  1. Cooling Time with Biot Number

tc=Bik×ΔTt_c = \frac{\text{Bi}}{k \times \Delta T}Where Bi\text{Bi} = Biot number

  1. Machine Downtime Percentage

Dt=Downtime (min)Total Time (min)×100D_t = \frac{\text{Downtime (min)}}{\text{Total Time (min)}} \times 100

  1. Mold Open/Close Time Calculation

tm=2Lvmt_m = \frac{2L}{v_m}

  1. Optimal Cooling Channel Diameter

dc=4×Acπd_c = \sqrt{\frac{4 \times A_c}{\pi}}

Material Shrinkage and Dimensional Accuracy

  1. Overall Shrinkage

S=Dm−DpDm×100S = \frac{D_m – D_p}{D_m} \times 100

  1. Linear Shrinkage

Sl=Lm−LpLm×100S_l = \frac{L_m – L_p}{L_m} \times 100

  1. Volumetric Shrinkage

Sv=Vm−VpVm×100S_v = \frac{V_m – V_p}{V_m} \times 100

  1. Post-Molding Dimensional Change

Dc=Do+ΔDtD_c = D_o + \Delta D_t

  1. Tolerance Calculation

T=±(Nominal Dimension×Tolerance Percentage)T = \pm (\text{Nominal Dimension} \times \text{Tolerance Percentage})

  1. Warp Prediction Formula

W=C×ΔTW = C \times \Delta T

Part Quality and Defect Diagnosis

  1. Deflection under Load

δ=FL33EI\delta = \frac{FL^3}{3EI}

  1. Sink Mark Depth Prediction

Ds=k×(Tm−Tp)D_s = k \times (T_m – T_p)

  1. Part Flatness Deviation

Fd=ΔhLF_d = \frac{\Delta h}{L}

  1. Residual Stress

σr=E×ΔLL\sigma_r = \frac{E \times \Delta L}{L}

  1. Mold Surface Roughness

Ra=1n∑i=1n∣yi∣R_a = \frac{1}{n} \sum_{i=1}^n |y_i|

  1. Stress Concentration Factor

Kt=σmaxσnomK_t = \frac{\sigma_{max}}{\sigma_{nom}}

  1. Impact Strength of Molded Part

I=EAI = \frac{E}{A}

Cost and Production Efficiency

  1. Total Cost per Part

Ct=Cm+Ce+Cl+CdC_t = C_m + C_e + C_l + C_d

  1. Annual Production Capacity

Ap=3600×Operating HourstcycleA_p = \frac{3600 \times \text{Operating Hours}}{t_{cycle}}

  1. Cost per Shot

Cs=Total CostNumber of ShotsC_s = \frac{\text{Total Cost}}{\text{Number of Shots}}

  1. Break-Even Production Quantity

BEP=Fixed CostsSelling Price−Variable CostBEP = \frac{\text{Fixed Costs}}{\text{Selling Price} – \text{Variable Cost}}

  1. Material Utilization Efficiency

Em=Net Material UsedTotal Material Input×100E_m = \frac{\text{Net Material Used}}{\text{Total Material Input}} \times 100

  1. Labor Productivity

Pl=Total Parts ProducedLabor HoursP_l = \frac{\text{Total Parts Produced}}{\text{Labor Hours}}

  1. Cost of Poor Quality (COPQ)

COPQ=Rework Cost+Scrap Cost+Inspection CostCOPQ = \text{Rework Cost} + \text{Scrap Cost} + \text{Inspection Cost}

Mold Wear and Maintenance

  1. Wear Rate

Wr=ΔMΔtW_r = \frac{\Delta M}{\Delta t}

  1. Surface Hardness Reduction

Hr=H0−ΔHH_r = H_0 – \Delta H

  1. Lubrication Film Thickness

h=2ηvPh = \frac{2\eta v}{P}

  1. Mold Life Estimation

Lm=Number of CyclesWear per CycleL_m = \frac{\text{Number of Cycles}}{\text{Wear per Cycle}}

  1. Corrosion Rate

Cr=K×WA×tC_r = \frac{K \times W}{A \times t}

  1. Crack Propagation Rate

dadN=C×(ΔK)m\frac{da}{dN} = C \times (\Delta K)^m

  1. Fatigue Life of Mold Components

Nf=(σfσ)1bN_f = \left( \frac{\sigma_f}{\sigma} \right)^{\frac{1}{b}}

  1. Thermal Fatigue Factor

Tf=ΔT×E2(1−ν)T_f = \frac{\Delta T \times E}{2(1-\nu)}

  1. Preventive Maintenance Frequency

Fm=Total RuntimePM Cycle TimeF_m = \frac{\text{Total Runtime}}{\text{PM Cycle Time}}

  1. Downtime Reduction Ratio

Dr=Initial Downtime−Current DowntimeInitial Downtime×100D_r = \frac{\text{Initial Downtime} – \text{Current Downtime}}{\text{Initial Downtime}} \times 100

 

Thermal Management and Cooling Optimization

(101 – 120)

  1. Thermal Conductivity

k=Q×dA×ΔTk = \frac{Q \times d}{A \times \Delta T}

  1. Heat Capacity

C=m×cpC = m \times c_p

  1. Time to Reach Steady-State Temperature

ts=m×cp×ΔTQt_s = \frac{m \times c_p \times \Delta T}{Q}

  1. Heat Loss through Mold Wall

Q=h×A×(Tm−Tw)Q = h \times A \times (T_m – T_w)

  1. Fourier’s Law (Heat Transfer in 1D)

Q=−k×dTdxQ = -k \times \frac{dT}{dx}

  1. Cooling Channel Flow Rate

Qf=v×AQ_f = v \times A

  1. Critical Cooling Channel Length

Lc=π×DNuL_c = \frac{\pi \times D}{Nu}

  1. Specific Heat Ratio

γ=cpcv\gamma = \frac{c_p}{c_v}

  1. Heat Transfer Coefficient (Cooling System)

h=kLh = \frac{k}{L}

  1. Temperature Rise in Cooling Water

ΔTw=Qm×cp\Delta T_w = \frac{Q}{m \times c_p}

Rheology and Melt Behavior

(121 – 140)

  1. Viscosity at Shear Rate

η=η0×(1+(λ×γ˙)2)n−12\eta = \eta_0 \times (1 + (\lambda \times \dot{\gamma})^2)^{\frac{n-1}{2}}

  1. Power-Law Model for Viscosity

η=k×γ˙n−1\eta = k \times \dot{\gamma}^{n-1}

  1. Newtonian Viscosity Calculation

η=τγ˙\eta = \frac{\tau}{\dot{\gamma}}

  1. Volumetric Flow Rate of Melt

Q=v×AQ = v \times A

  1. Frictional Heating in Melt

Qf=μ×v2×ρQ_f = \mu \times v^2 \times \rho

  1. Shear Rate in Rectangular Channel

γ˙=6Qwh2\dot{\gamma} = \frac{6Q}{wh^2}

  1. Relaxation Time

λ=ηG\lambda = \frac{\eta}{G}

  1. Retention Time of Polymer in Barrel

tr=VbQt_r = \frac{V_b}{Q}

  1. Shear Stress in Circular Channel

τ=4×Q×ηπ×r3\tau = \frac{4 \times Q \times \eta}{\pi \times r^3}

  1. Dynamic Modulus

G′=σγG’ = \frac{\sigma}{\gamma}

Mechanical Properties and Stress Analysis

(141 – 160)

  1. Tensile Stress

σt=FA\sigma_t = \frac{F}{A}

  1. Compressive Stress

σc=FA\sigma_c = \frac{F}{A}

  1. Poisson’s Ratio

ν=−ϵlϵt\nu = -\frac{\epsilon_l}{\epsilon_t}

  1. Flexural Modulus

Ef=FL34bh3ΔE_f = \frac{FL^3}{4bh^3\Delta}

  1. Bulk Modulus

K=E3(1−2ν)K = \frac{E}{3(1-2\nu)}

  1. Shear Modulus

G=E2(1+ν)G = \frac{E}{2(1+\nu)}

  1. Stress Intensity Factor

KI=σπaK_I = \sigma \sqrt{\pi a}

  1. Fatigue Strength

σf=σ0×(N)−b\sigma_f = \sigma_0 \times (N)^{-b}

  1. Von Mises Stress

σv=σx2−σxσy+σy2+3τ2\sigma_v = \sqrt{\sigma_x^2 – \sigma_x\sigma_y + \sigma_y^2 + 3\tau^2}

  1. Creep Compliance

J(t)=ϵ(t)σJ(t) = \frac{\epsilon(t)}{\sigma}

Clamping Force and Mold Design

(161 – 180)

  1. Required Clamping Force

Fc=P×AF_c = P \times A

  1. Projected Area of Part

Ap=L×WA_p = L \times W

  1. Cavity Pressure at Fill

Pc=FcAP_c = \frac{F_c}{A}

  1. Gate Cross-sectional Area

Ag=πd24A_g = \frac{\pi d^2}{4}

  1. Runner Volume Calculation

Vr=πd2L4V_r = \frac{\pi d^2 L}{4}

  1. Mold Opening Stroke

Sm=Hp+He+CS_m = H_p + H_e + C

  1. Mold Base Thickness

tm=Fk×At_m = \frac{F}{k \times A}

  1. Cooling Channel Spacing

Sc=2×rS_c = 2 \times r

  1. Ejection Force

Fe=P×ApnF_e = \frac{P \times A_p}{n}

  1. Mold Parting Line Pressure

Pp=FApP_p = \frac{F}{A_p}

Process Optimization and Diagnostics

(181 – 200)

  1. Cycle Time Efficiency

Et=tidealtactual×100E_t = \frac{t_{ideal}}{t_{actual}} \times 100

  1. Energy Consumption per Cycle

Ec=P×tcycleE_c = P \times t_{cycle}

  1. Overall Process Yield

Y=Good PartsTotal Parts×100Y = \frac{\text{Good Parts}}{\text{Total Parts}} \times 100

  1. Defect Rate

Dr=Defective PartsTotal Parts×100D_r = \frac{\text{Defective Parts}}{\text{Total Parts}} \times 100

  1. First Pass Yield (FPY)

FPY=Accepted PartsTotal PartsFPY = \frac{\text{Accepted Parts}}{\text{Total Parts}}

  1. Quality Index (Cpk)

Cpk=min⁡(USL−μ3σ,μ−LSL3σ)Cpk = \min \left( \frac{USL – \mu}{3\sigma}, \frac{\mu – LSL}{3\sigma} \right)

  1. Machine Utilization Rate

Um=Operating TimeTotal Time×100U_m = \frac{\text{Operating Time}}{\text{Total Time}} \times 100

  1. Scrap Rate

Sr=Scrap WeightTotal Input Material×100S_r = \frac{\text{Scrap Weight}}{\text{Total Input Material}} \times 100

  1. Tool Life Estimation

Tl=CvnT_l = \frac{C}{v^n}

  1. Preventive Maintenance Interval

PMI=Operating HoursFailuresPMI = \frac{\text{Operating Hours}}{\text{Failures}}

Advanced Mold Design & Structural Analysis (Formulas 201-240)

  1. Mold Deflection Calculation

δ=FL33EI\delta = \frac{F L^3}{3 E I}

  1. Moment of Inertia for Rectangular Cross-section

I=bh312I = \frac{b h^3}{12}

  1. Mold Cavity Pressure

Pc=FcAP_c = \frac{F_c}{A}

  1. Runner Balance Ratio

Rb=L1L2R_b = \frac{L_1}{L_2}

  1. Gate Area

Ag=πd24A_g = \frac{\pi d^2}{4}

  1. Cooling Channel Layout Efficiency

Ec=LeffectiveLtotalE_c = \frac{L_{effective}}{L_{total}}

  1. Ejection Force Calculation

Fe=P×AF_e = P \times A

  1. Parting Line Misalignment Tolerance

Tp=dmax−dmin2T_p = \frac{d_{max} – d_{min}}{2}

  1. Mold Thickness Optimization

tm=FkAt_m = \frac{F}{k A}

  1. Core Pin Deflection

δpin=4FL3πEd4\delta_{pin} = \frac{4 F L^3}{\pi E d^4}

  1. Mold Surface Temperature Gradient

ΔT=QkA\Delta T = \frac{Q}{k A}

  1. Thermal Expansion of Mold

ΔL=αLΔT\Delta L = \alpha L \Delta T

  1. Aspect Ratio of Molded Part

AR=LtAR = \frac{L}{t}

  1. Mold Stress at High Pressure

σ=P×d2t\sigma = \frac{P \times d}{2t}

  1. Cooling Channel Diameter for Optimal Heat Removal

dc=4Aπd_c = \sqrt{\frac{4 A}{\pi}}

  1. Part Volume Estimation

V=L×W×HV = L \times W \times H

  1. Draft Angle Calculation

θ=tan⁡−1(d1−d2h)\theta = \tan^{-1} \left( \frac{d_1 – d_2}{h} \right)

  1. Gate Freeze Time

tg=d24αt_g = \frac{d^2}{4\alpha}

  1. Mold Venting Area

Av=n×πr2A_v = n \times \pi r^2

  1. Core Diameter for Balanced Filling

d=4Qπvd = \frac{4 Q}{\pi v}

Material Behavior & Rheology (Formulas 241-280)

  1. Shear Rate in Mold

γ˙=4Qπr3\dot{\gamma} = \frac{4Q}{\pi r^3}

  1. Melt Flow Index (MFI)

MFI=WtMFI = \frac{W}{t}

  1. Elastic Modulus (Young’s Modulus)

E=σϵE = \frac{\sigma}{\epsilon}

  1. Tensile Strength

σt=FA\sigma_t = \frac{F}{A}

  1. Poisson’s Ratio

ν=−ϵtransϵlong\nu = -\frac{\epsilon_{trans}}{\epsilon_{long}}

  1. Viscosity at Given Shear Rate

η=k×γ˙n−1\eta = k \times \dot{\gamma}^{n-1}

  1. Shear Stress in Flowing Melt

τ=η×γ˙\tau = \eta \times \dot{\gamma}

  1. Relaxation Modulus

G(t)=σ/ϵ(t)G(t) = \sigma / \epsilon(t)

  1. Stress-Strain Curve Slope (Elastic Region)

m=ΔσΔϵm = \frac{\Delta \sigma}{\Delta \epsilon}

  1. Specific Gravity

SG=ρmaterialρwaterSG = \frac{\rho_{material}}{\rho_{water}}

Thermal and Cooling Analysis (Formulas 281-320)

  1. Cooling Time Based on Thickness

tc=t2π2αt_c = \frac{t^2}{\pi^2 \alpha}

  1. Heat Transfer Rate in Mold

Q=h×A×(Tm−Tc)Q = h \times A \times (T_m – T_c)

  1. Biot Number for Cooling Analysis

Bi=hLckBi = \frac{h L_c}{k}

  1. Reynolds Number (Cooling Flow)

Re=ρvdμRe = \frac{\rho v d}{\mu}

  1. Prandtl Number

Pr=μcpkPr = \frac{\mu c_p}{k}

  1. Nusselt Number for Cooling Channels

Nu=hdkNu = \frac{h d}{k}

  1. Thermal Diffusivity

α=kρcp\alpha = \frac{k}{\rho c_p}

  1. Cooling Channel Flow Rate

Qf=v×AQ_f = v \times A

  1. Energy Loss in Cooling System

El=mcpΔTtE_l = \frac{m c_p \Delta T}{t}

  1. Temperature Rise in Cooling Fluid

ΔT=Qmcp\Delta T = \frac{Q}{m c_p}

Process Efficiency & Cost Analysis (Formulas 321-360)

  1. Overall Equipment Effectiveness (OEE)

OEE=A×P×QOEE = A \times P \times QWhere:
AA = Availability, PP = Performance, QQ = Quality

  1. Cost per Part

Cp=Cm+Cl+CeNC_p = \frac{C_m + C_l + C_e}{N}

  1. Energy Consumption per Shot

Es=P×tE_s = P \times t

  1. Break-Even Point (BEP)

BEP=FixedCostsSellingPrice−VariableCostBEP = \frac{Fixed Costs}{Selling Price – Variable Cost}

  1. Cycle Time Efficiency

Et=tidealtactual×100E_t = \frac{t_{ideal}}{t_{actual}} \times 100

  1. Material Utilization

MU=WeightpartWeighttotal×100MU = \frac{Weight_{part}}{Weight_{total}} \times 100

  1. Scrap Rate

Sr=ScrapWeightTotalMaterialInput×100S_r = \frac{Scrap Weight}{Total Material Input} \times 100

  1. Production Capacity

Pc=3600×OperatingHourstcycleP_c = \frac{3600 \times Operating Hours}{t_{cycle}}

  1. Downtime Percentage

Dt=DowntimeTotalTime×100D_t = \frac{Downtime}{Total Time} \times 100

  1. Profit Margin

PM=Revenue−CostsRevenue×100PM = \frac{Revenue – Costs}{Revenue} \times 100