Insert Injection Molding Formulas
Material Cost =
(((Molded Subcomponent Volume * Cost per Volume) / Utilization) / Final Yield)
Material cost is calculated as for Injection Molding in the Plastic Molding process group, except that the volume of the molded subcomponents is used in place of the volume of the whole part. It depends on the following:
• Molded Subcomponent Volume: sum of the values of the Volume property for all Subcomponents whose Is Molded property is true.
• Cost per Volume: this is the product of the values of the material properties Unit Cost and Density for the current material (listed in the Material Selection dialog, which is available from the Production Scenario tab of the Cost Guide).
• Utilization: see IM Material Utilization in the Plastic Molding chapter.
• Final yield: see Yields for Assembly Molding.
Labor Cost = Labor Time * Labor Rate / Final Yield
Labor cost depends on the following:
• Labor time (see formula)
• Labor rate (specified by the machine property Labor Rate)
• Final yield (see Yields for Assembly Molding)
Labor Time = Cycle Time * Number of Operators * Labor Time Standard
Labor time is the product of the following:
• Cycle time (see formula)
• Number of operators: specified by the machine property Number of Operators.
• Labor time standard: specified as the machine property Labor Time Standard. This multiplier is used to account for otherwise unaccounted for factors that affect labor time, such as operator fatigue or time spent by the operator for cleaning or maintenance.
Cycle Time = Process Time * Cycle Time Adjustment Factor
Cycle time is the product of the following
• Process time: see formula.
• Cycle time adjustment factor: specified by the cost model variable cycleTimeAdjustmentFactor (1 in starting point VPEs). Administrators can customize this value in order to globally adjust cycle times for Assembly Molding.
Process Time
The method of process-time calculation depends in the Table Configuration of the current Insert Injection Molding machine.
Process Time No Table =
(Pick and Place Non-idle Time + Insert Injection Molding Non-idle Time) /
Number of Cavities
If the machine selected for Insert Injection Molding has no table (as specified by the machine property Table Configuration), The Insert Injection Molding machine is idle during Pick and Place tasks. In this case, Insert Pick and Place process time depends on the following:
• Pick and Place non-idle time (see formula)
• Insert Injection Molding non-idle time (see formula)
• Number of mold cavities (see Number and Layout of Mold Cavities in the Plastic Molding chapter)
Process Time Shuttle or Rotary =
max (Pick and Place Non-idle Time, Insert Injection Molding Non-idle Time) /
Number of Cavities
If the machine selected for Insert Injection Molding has a rotary or shuttle table (as specified by the machine property Table Configuration), Insert Pick and Place operators can work with one or more lower tools (removing parts and then placing inserts) while Insert Injection Molding operators use another lower tool together with the upper tool (for injection and cooling). Pick and Place Operators are idle during a cycle only if injection and cooling takes longer than removing parts and placing inserts. In this case, the two parallel streams of activity might be represented as follows:
On the other hand, if removing parts and placing inserts takes longer than injection and cooling, Insert Injection Molding operators are idle during each cycle. In this case, the two parallel streams of activity might be represented as follows:
For manual loading (see Manual or Robotic Loading), increasing the number of Insert Pick and Place operators is assumed to decrease the total time required to place inserts.
Insert Pick and Place process time depends on the following:
• Pick and Place non-idle time (see formula)
• Insert Injection Molding non-idle time (see formula)
• Number of mold cavities (see Number and Layout of Mold Cavities in the Plastic Molding chapter)
Pick and Place Non-idle Time =
Part Removal Time +
((Child Operation Times * Number of Cavities) / Number of Operators)
Pick and Place non-idle time is the time required to remove parts from one mold and then place all inserts into it. It depends on the following:
• Part removal time: depends on how the setup option Part Eject Method is set:
o Robotic: part removal time is the value of the cost model variable robotGrabTime (6 seconds in starting point VPEs).
o Manual: part removal time is the value of the cost model variable manualGrabTime (8 seconds in starting point VPEs).
o Gravity: part removal time is the value of the cost model variable gravityDropTime (1.25 seconds in starting point VPEs).
The default in starting point VPEs is Manual. Administrators can customize the default with the cost model variable ejectMethod.
Note that, with multiple cavities, it is assumed that all parts are removed at once, regardless of eject method.
• Child operation cycle times for Insert Pick and Place (see Insert Pick and Place Operation Formulas)
• Number of Mold Cavities (see Number and Layout of Mold Cavities in the Plastic Molding chapter)
• Number of operators for Pick and Place: by default, this is specified by the machine property Number of Operators. Users can override the default with the setup option Number of Operators.
Insert Injection Molding Non-idle Time =
Mold Close Time +
Injection Time +
Cool Time +
Hydraulic Slide Time +
Mold Open Time +
Ejector Plate Time
Insert Injection Molding non-idle time is the sum of the following:
• Mold close time (see Insert Injection Molding Formulas)
• Injection time (see Insert Injection Molding Formulas)
• Cool time (see Insert Injection Molding Formulas)
• Hydraulic slide time (see Insert Injection Molding Formulas)
• Mold open time (see Insert Injection Molding Formulas)
• Ejector plate time (see Insert Injection Molding Formulas)
Injection Time = ((Number of Cavities * Part Volume) + Runner Volume) / Adjusted Injection Rate
Injection time is function of the following:
• Number of cavities (see Number and Layout of Mold Cavities in the Plastic Molding chapter)
• Part volume (obtained from GCD extraction)
• Runner volume (see Runner Volume and Runner Area for Assembly Molding)
• Adjusted injection rate (see formula below)
Adjusted Injection Rate = Injection Rate * Injection Rate Multiplier
Adjusted injection rate is the product of the following:
• Injection rate: specified by the machine property Injection Rate.
• Injection rate multiplier: specified by the cost model variable injectionRateMultiplier (0.25 in starting point VPEs).
Cool Time = 0 – ((Nominal Wall Thickness^2) / (2 * π * Thermal Diffusivity)
* ln((π/4) * (Eject Deflection Temperature – Mold Temperature) /
(Melting Temperature – Mold Temperature)))
Cool time is a function of the following:
• Nominal wall thickness: see Nominal Wall Thickness.
• Thermal diffusivity: see formula, below.
• Eject deflection temperature: temperature at which the part can be ejected from the mold without deformation, specified by the material property Eject Deflection Temp.
• Melting temperature: specified by the material property Melting Temp.
• Mold temperature: required temperature of the mold to support proper molten polymer flow. This is specified by the material property Mold Temp, increased by the amount specified by the cost model variable defaultMoldTemperatureIncrease (0 in starting point VPEs) or by the override specified by the user with the setup option Local Mold Temperature Increase—see User Inputs for Plastic Molding.
Thermal Diffusivity = Thermal Conductivity / (Density of Melt * Specific Heat)
This is the thermal diffusivity of the current material, in mm2/s. The value is converted from m2/s to mm2/s so that it can be used in the Cool Time formula. The value in m2/s is determined according to this formula by using the following:
• Thermal conductivity: this is the thermal conductivity of the current material, specified in watt/m°C by the material property Thermal Conductivity of Melt.
• Density of melt: this is the melt density of the current material, specified in kg/m3 by the material property Density of Melt.
• Specific heat: this is the specific heat of the current material, specified in joule/g°C by the material property Specific Heat of Melt, and converted to joule/kg°C for use in this formula.
Note: Versions of aPriori prior to 2019 R2 used a value for thermal diffusivity that was provided by the material property Thermal Diffusivity, rather than computing it from thermal conductivity, density of melt, and specific heat. The cost model will continue to use the material property Thermal Diffusivity, if the new material properties Thermal Conductivity of Melt, Density of Melt, and Specific Heat of Melt are not provided; however aPriori recommends that you update older VPEs to use the new properties, as they are reliably found on spec sheets, while thermal diffusivity generally is not.
Nominal Wall Thickness = (2 * Average Wall Thickness + Maximum Wall Thickness) * 1.25/3
Nominal wall thickness is calculated by default, but can be specified by the user with the process-level setup option Nominal Wall Thickness (0.10-15.00 millimeters). If calculated, the following formula is used:
Nominal wall thickness is a linear combination of the following:
• Part average wall thickness (obtained from GCD extraction)
• Part maximum wall thickness (obtained from GCD extraction)
This value is bounded above by part maximum thickness.
Mold Open Time = Travel Distance / Max Machine Velocity
Mold open time depends on the following:
• Travel distance: see Travel Distance, below.
• Max machine velocity: see formula.
Travel Distance
Travel distance for mold open or close is generally 3 or 4 times the part height:
• If the setup option Part Eject Method is set to Manual (the default in starting point VPEs) or Gravity, the travel distance is generally the product of part height and the cost model variable nominalHeightFactor (3 in starting point VPEs):
Travel Distance = Part Height * Nominal Height Factor
To accommodate small parts, this value is bounded below by the product of smallHeightPartFactor (1.1 in starting point VPEs) and the length of the plastic forming region (PFR--see Dimensions of the Plastic Forming Region in the Plastic Molding chapter):
Travel Distance = PFR Length * Small Height Factor
In starting point VPEs, this applies when the part height is less than roughly 1/3 of the PFR length.
• If the setup option Part Eject Method is set to Robotic, the travel distance is generally the product of the following:
o Part height
o Sum of the cost model variables nominalHeightFactor (3 in starting point VPEs) and roboticClearanceFactor(1 in starting point VPEs)
Travel Distance = Part Height * (Nominal Height Factor + Robotic Clearance Factor)
To accommodate small parts, this value is bounded below by the product of the following:
o Length of the plastic forming region (PFR--see Dimensions of the Plastic Forming Region in the Plastic Molding chapter)
o Sum of the cost model variables smallHeightPartFactor (1.1 in starting point VPEs) and roboticClearanceFactor (1 in starting point VPEs)
Travel Distance = PFR Length * (Small Height Factor + Robotic Clearance Factor)
In starting point VPEs, this applies when the part height is less than roughly 1/2 the PFR length.
See also Part Eject Method.
Max Machine Velocity = (Machine Max Stroke Length * 2) / Dry Cycle Time
The speed of travel during mold open and close is derived from the following:
• Machine max stroke length: for Vertical machines (see Insert Injection Molding Machine Orientation), this is the value of the machine property Dry Cycle Stroke. For Horizontal machines, see formula.
• Dry cycle time: specified by the machine property Dry Cycle Time.
Machine Max Stroke Length for Horizontal Machines =
Dry Cycle Stroke Factor * Max Tie Bar Distance
• Dry cycle stroke factor: this is the fraction of the maximum tie bar distance that equals the stroke length. The fraction is specified by the cost model variable dryCycleStrokeFactor (0.7 in starting point VPEs—see the Euromap 6 technical recommendation).
• Max tie bar distance: this the larger of the machine properties Tie Bar Distance, H and Tie Bar Distance, V.
Hydraulic Slide Time = (Hydraulic Slide Length / Slide Cycle Rate) * 2
A slide for a given undercut feature is required to be hydraulic (as opposed to mechanical) if the platen movement required to clear the mechanical slide from the undercut exceeds the mold open stroke. The presence of hydraulic slides contributes to the total ejection time because, unlike mechanical slides, hydraulic slides are retracted only after the mold is opened.
Hydraulic slide time depends on the following:
• Hydraulic slide length: this is 0 if hydraulic slides are unnecessary. If hydraulic slides are necessary, the hydraulic slide length is the maximum undercut depth plus some clearance (5mm if there are multiple cavities, 0.5 inch otherwise).
• Cycle rate per slide: this is the rate at which the hydraulic slides can move, specified by the cost model variable slideCycleRate (100mm per second in starting point VPEs).
Hydraulic slides are necessary if and only if the following condition holds:
Max Pin Travel Distance > Machine Opening Stroke
Here, Machine Opening Stroke is the value of the machine property Opening Stroke.
Max Pin Travel Distance is the distance along the draw direction that the platen would have to travel in order to retract a mechanical slide from the part’s deepest undercut. The cost model assumes that a retracting mechanical slide is guided by a pin that makes an angle of 15 degrees with the draw direction. If U is the maximum undercut depth (perpendicular to the draw direction) plus clearance (5mm if there are multiple cavities, 0.5 inch otherwise), then the required platen motion along the draw direction is U/tan(15):
Max Pin Travel Distance = (Max Undercut Depth + Extra Clearance) / tan(15)
If the motion required for a mechanical slide (Max Pin Travel Distance) exceeds the value of the machine property Opening Stroke, then hydraulic slides are necessary for the part.
Ejector Plate Time = (Part Height * Ejector Distance Factor) / Max Machine Velocity
Ejector plate time depends on the following:
• Part height: determined by geometry extraction. Part height is measure along the draw direction.
• Ejector distance factor: this is the multiple of part height that equals the distance an ejector pin should move in order to eject the part. It is specified by the cost model variable ejectorDistanceFactor (3 in starting point VPEs).
• Max machine velocity: see formula.
Mold Close Time = Travel Distance / Max Machine Velocity
Mold close time depends on the following:
• Travel distance: see Travel Distance, above.
• Max machine velocity: see formula.