Injection Molding Formula direct from manufacturer

Core Calculations in Injection Molding

Injection molding is a complex process involving the precise control of several key parameters. Understanding and applying the relevant calculation formulas is crucial for optimizing production, ensuring product quality, and controlling costs. 

1. Clamp Force (F)

Clamp force is the necessary force in the injection molding process to resist the pressure generated by the molten plastic being injected into the mold cavity, ensuring that the mold does not open during injection.

• Formula: F = Am x Pv / 1000
  • F: Clamp Force (in tons)
  • Am: Projected area of the mold cavity on the parting line (in cm²)
  • Pv: Filling pressure or cavity pressure (in kg/cm²)
  • 1000: Unit conversion factor

2. Shot Volume (V)

Shot volume refers to the total volume of plastic injected into the mold during each injection cycle, including the volume of the part itself and the volume of the runner system (if any).

• Formula (based on screw): V = π x (Ds / 2)² x St

  • V: Shot Volume (in cm³)
  • Ds: Diameter of the injection screw (in cm)
  • St: Stroke of the injection screw (in cm)
  • π: Pi (approximately 3.14159)

• Formula (based on part and runner): V = Vp + Vr

  • Vp: Volume of the part (in cm³)
  • Vr: Volume of the runner system (in cm³)

3. Shot Weight (W)

Shot weight is the total mass of plastic injected into the mold during each injection cycle.

• Formula: W = V x ρ

  • W: Shot Weight (in grams)
  • V: Shot Volume (in cm³)
  • ρ: Density of the plastic material (in g/cm³)

• Considering shrinkage and packing factor: W = (Vp + Vr) x ρ x (1 + S) x Pf

  • S: Material shrinkage (as a decimal)
  • Pf: Packing factor (usually slightly greater than 1 to compensate for material packing)

4. Material Consumption per Part (Mc)

This formula is used to calculate the amount of material required to produce a single part.

• Formula: Mc = Wp / Nc

  • Mc: Material Consumption per Part (in grams)
  • Wp: Weight of a single part (in grams)
  • Nc: Number of cavities in the mold

• Considering cold runner waste: Mc = (Wp + (Wr / Nc)) / Nc

  • Wr: Weight of the runner system (in grams)

The Injection Phase and Melt Flow Dynamics

The injection phase is a crucial stage in the injection molding process, directly affecting the quality of the molded product. Understanding the calculation and role of parameters such as injection pressure and speed is essential for optimizing this phase.

5. Injection Pressure (Pi)

Injection pressure is the pressure required by the injection unit to force the molten plastic into the mold cavity.

• Formula: Pi = (Pp x Ai) / As

  • Pi: Injection Pressure (in kg/cm²)
  • Pp: Hydraulic pump pressure (in kg/cm²)
  • Ai: Effective area of the injection cylinder (in cm²)
  • As: Cross-sectional area of the injection screw (in cm²)

• Alternative Formula: Pi = F_injection / As

  • F_injection: Injection force (in kg)

6. Injection Speed (S)

Injection speed refers to the rate at which the molten plastic is injected into the mold cavity.

• Formula: S = Q / A
  • S: Injection Speed (in cm/sec or mm/sec)
  • Q: Volumetric flow rate of the plastic melt (in cm³/sec)
  • A: Cross-sectional area of the injection cylinder (in cm²)

7. Injection Rate (Sv)

Injection rate is the amount of plastic injected into the mold cavity per unit of time.

• Formula: Sv = S x Ao
  • Sv: Injection Rate (in g/sec)
  • S: Injection Speed (as defined above)
  • Ao: Cross-sectional area of the screw (in cm²)

8. Pressure Drop in the Gate (ΔPg)

The gate is a small channel connecting the runner and the cavity, and a pressure drop occurs as the molten plastic flows through it.

• Formula (simplified, for a circular gate): ΔPg ≈ (12 * η * Q * Lg) / (π * dg⁴)
  • ΔPg: Pressure drop across the gate (in Pa or kg/cm²)
  • η: Viscosity of the molten plastic (in Pa·s or poise)
  • Q: Volumetric flow rate through the gate (in m³/s or cm³/s)
  • Lg: Length of the gate (in m or cm)
  • dg: Diameter of the gate (in m or cm)

9. Reynolds Number (Re)

The Reynolds number is a dimensionless quantity that helps predict the flow regime of the molten plastic (laminar or turbulent).

• Formula: Re = (ρ * v * D) / η
  • Re: Reynolds Number
  • ρ: Density of the molten plastic (in kg/m³)
  • v: Velocity of the melt flow (in m/s)
  • D: Characteristic length (e.g., gate diameter or runner diameter) (in m)
  • η: Viscosity of the molten plastic (in Pa·s)

Cooling, Cycle Time, and Advanced Considerations

Beyond injection and flow, other stages and advanced considerations in injection molding are equally important, such as cooling, cycle time, and material properties.

10. Cooling Time (Tc)

Cooling time is the time required for the molded plastic part to solidify sufficiently within the mold cavity to be safely ejected.

• Formula (simplified): Tc ≈ h² / (k / (ρ * Cp))

  • Tc: Cooling Time (in seconds)
  • h: Maximum wall thickness of the part (in cm)
  • k: Thermal conductivity of the plastic material (in W/(m·K))
  • ρ: Density of the plastic material (in kg/m³)
  • Cp: Specific heat capacity of the plastic material (in J/(kg·K))

• Influencing Factors: The actual cooling time is also affected by mold temperature, melt temperature, ejection temperature, and the heat transfer coefficient between the plastic and the mold.

11. Cycle Time (T)

Cycle time is the total time required to complete one injection molding cycle.

• Formula: T = Ti + Tp + Tc + Te
  • T: Cycle Time (in seconds)
  • Ti: Injection time (time taken to fill the cavity)
  • Tp: Packing time (time during which pressure is maintained after filling)
  • Tc: Cooling time
  • Te: Ejection time (time taken to eject the part)

12. Ejection Force (Fe)

Ejection force is the force required to remove the molded plastic part from the mold cavity.

• Formula (approximate): Fe ≈ μ x P_shrinkage x A_part
  • Fe: Ejection Force (in kg or N)
  • μ: Coefficient of friction between the plastic and the mold surface
  • P_shrinkage: Pressure due to material shrinkage onto the mold core
  • A_part: Surface area of the part in contact with the mold core

13. Plasticizing Rate (Screw Speed - N)

Plasticizing rate refers to the speed at which the screw rotates to melt the plastic material and prepare it for the next injection.

• Formula (expressed as melt rate): Melt Rate (kg/hr) ≈ (π x (Ds/2)² x Ld x ρ x N x η) / (60 x 1000)
  • Ds: Diameter of the screw (in cm)
  • Ld: Length of the screw flight per revolution (related to pitch) (in cm)
  • ρ: Density of the plastic material (in kg/cm³)
  • N: Screw speed (in RPM - Revolutions Per Minute)
  • η: Efficiency factor (accounts for leakage and incomplete melting)

14. Holding Pressure (Ph)

Holding pressure is the pressure applied to the molten plastic in the mold cavity after the filling stage is complete. It is used to compensate for the shrinkage of the plastic as it cools and solidifies. It is usually set as a percentage of the injection pressure.

15. Back Pressure (Pb)

Back pressure is the pressure maintained at the front of the screw as it rotates and retracts during the plasticizing phase. It helps ensure proper melting, mixing, and degassing of the plastic material.

16. Mold Temperature (Tm)

Maintaining the correct mold temperature is crucial for the quality and cycle time of the molded part. Mold temperature affects the solidification rate of the plastic, surface finish, dimensional accuracy, and warpage.

17. Machine Capacity Utilization (U)

This helps estimate how much of the injection molding machine's capability is being used for a particular job.

• Clamp Force Utilization: U_clamp = (Required Clamp Force / Maximum Clamp Force of Machine) * 100%
• Shot Volume Utilization: U_volume = (Required Shot Volume / Maximum Shot Volume of Machine) * 100%

18. Melt Flow Rate (MFR) / Melt Flow Index (MFI)

Measures the ease of flow of a thermoplastic melt and is an important material property for selecting processing parameters.

19. Basic Heat Transfer for Cooling (Q)

Describes the basic principles of heat transfer during the cooling process.

• Formula (simplified): Q = h * A * ΔT
  • Q: Rate of heat transfer (in Watts)
  • h: Heat transfer coefficient between the plastic and the mold (in W/(m²·K))
  • A: Heat transfer area (in m²)
  • ΔT: Temperature difference between the plastic and the mold (in K or °C)

20. Cost-Benefit Analysis Model

Formula: Unit Cost = Cmold / N + (Cmachine * Tcycle / 3600) /  + Cmaterial + Clabor

Cmold: mold cost (3D printing mold: $100–$500; steel mold: $5k–$100k)

N: total output

Cmachine: machine hour rate ($/h)

Tcycle: molding cycle (s)

Cmaterial: material cost/piece ($)

Clabor: labor cost/piece ($)

Economies of Scale: For production volumes > 100k parts, mold cost per part decreases to <$0.1/part.