Gating System Model for Die Casting

The properties of the gating system affect material utilization and melting overhead, as well as finishing costs. See the following sections:

• Material Cost and Utilization for Die Casting

• Finishing Formulas for Die Casting

Finishing costs are affected by the cross-sectional area and volume of ingates and risers.

Material utilization and melting costs are affected by the total volume of the gating system. See the following sections:

• Gating System Formulas for High Pressure Die Casting

• Gating System Formulas for Gravity Die Casting

Gating System Formulas for High Pressure Die Casting

The gating system is modeled with the following formulas:

Total Gating Volume = Runner Volume + Total Overflow Volume

The total volume of the gating system is the sum of the following:

• Runner volume (see formula)

• Total overflow volume (see formula)

Runner Volume = Runner Area * Runner Length * Number of Runners

Runner volume is the product of the following:

• Runner area. This is the cross-sectional area of the runner (see formula).

• Runner length: This is the length of the mold base. By default, mold length is based on the part dimensions, the number of cavities, and the number of required side cores. Users can specify the mold length with the setup option Mold Base Size – Length (see High Pressure and Gravity Die Casting Process Inputs).

• Number of runners. By default, this is 1 if the mold has a single cavity; for molds with multiple cavities, the default number of runners is half the number of cavities (rounded up to the nearest whole number of runners). Users can specify the number of runners with the setup option Number of Runners (see High Pressure and Gravity Die Casting Process Inputs).

Runner Area = (Ingate Area * Ingate Area To Runner Area) / Number of Runners

Area of a single runner depends on the following:

• Ingate area (see formula)

• Ingate Area to Runner Area. This is the ratio of the ingate cross-sectional area to the runner cross-sectional area. The ratio is 1.4 in starting point VPEs. VPE administrators can customize this value with the cost model variable ingateAreaToRunnerArea.

• Number of runners. By default, this 1 if the mold has a single cavity; for molds with multiple cavities, the default number of runners is half the number of cavities (rounded up to the nearest whole number of runners). Users can specify the number of runners with the setup option Number of Runners (see High Pressure and Gravity Die Casting Process Inputs).

Ingate Area = (Volume Before Machining + Overflow Volume per Cavity) / (Inject Time * Gate Velocity )

Ingate area is derived, in part, from the optimum pour time. It depends on the following:

• Volume before machining (see formula)

• Overflow volume per cavity (see formula)

• Inject time (see formula)

• Gate velocity. This is looked up by material type and part surface quality in the lookup table tblGateVelocity. By default, part surface quality is 3 (Some porosity, some knit lines), but users can override the default with setup option Surface Quality of Part (see High Pressure and Gravity Die Casting Process Inputs). If there is no matching entry, the table’s minimum gate velocity is used.

Inject Time = Solidification Constant * (Inject Temp – Liquidus Temp +

(Percent Solids * Latent Heat Constant)) / (Liquidus Temp – Mold Temp)) * Average Thickness

This is the optimum time to pour the material. It depends on the following:

• Solidification constant. This is the time per unit thickness required for the mold to solidify the part’s material (that is, the reciprocal of the solidification rate). It is .034 sec/mm in starting point VPEs. VPE administrators can customize the value with the cost model variable solidificationConstantHPDC.

• Inject temperature (temperature of the metal as it enters the cavity, specified by a material property)

• Liquidus temperature (minimum temperature at which the metal can flow, specified by a material property)

• Percent solids: This is the amount of solidification that can occur during injection. It is looked up by part surface quality in the lookup table tblPercentSolids.

By default, part surface quality is Some porosity, some knit lines, but users can override the default with setup option Surface Quality of Part (see High Pressure and Gravity Die Casting Process Inputs).

• Latent heat constant: This is 1% of the size of the current material’s solidification range (that is, the amount of heat that leaves a given mass of the material when the percentage of the mass that is solid is increased by 1). It is looked up by material type in the lookup table latentHeatConstant.

• Mold temperature (die temperature at injection, specified by a material property)

• Average thickness (average part thickness, determined by GCD extraction)

Total Overflow Volume = Overflow Volume per Cavity * Number of Cavities

Total overflow volume is the product of the following:

• Overflow volume per cavity (see formula)

• Number of cavities (see Number of Mold Cavities for Die Casting)

Overflow Volume per Cavity = Volume Before Machining * Overflow to Part Volume Ratio

Overflow Volume per Cavity is the product of the following:

• Volume Before Machining (see formula)

• Overflow to Part Volume Ratio. This is looked up by part wall thickness (the GCD property Average Thickness) in the lookup table tblOverflowDim. aPriori uses the entry with the greatest value in the Wall Thickness column that is less than or equal to the part wall thickness (if there is such an entry). If there is no such entry (that is, if the part thickness is below the table’s range), aPriori uses the entry with the smallest wall thickness. For decorative or highly decorative parts (that is, parts with surface quality less than 3), aPriori uses the value in the column Overflow Volume Ratio High. For parts with surface quality 3 or greater, aPriori uses the value in the column Overflow Volume Ratio Low.

By default, part surface quality is 3 (Some porosity, some knit lines), but users can override the default with setup option Surface Quality of Part (see High Pressure and Gravity Die Casting Process Inputs).

Volume Before Machining = Part Volume + Metal Chip Volume of Machined Features

Volume before machining is the part volume plus the volume removed by machining. It is the sum of the following:

• Part volume (obtained from GCD extraction)

• Metal chip volume of machined features: derived by summing metal chip volume for each machining operation that is applied to the part. For fully-machined features, this calculation is based on feature volume. For machine-finished features, the calculation is based on the area of the finished surface. The calculation assumes that the depth of material removed during finishing is the value specified by the cost model variable finishAllowance.

Gating System Formulas for Gravity Die Casting

The gating system is modeled with the following formulas:

Total Gating Volume = Riser Volume + Runner Volume +

Ingate Volume + Sprue Volume + Sprue Well Volume + Pouring Basin Volume

The total volume of the gating system is the sum of the following:

• Riser volume (see formula)

• Runner volume (see formula)

• Ingate volume (see formula)

• Sprue volume (see formula)

• Sprue well volume (see formula)

• Pouring basin volume (see formula)

Riser Volume = 1.9 * Shape Factor-0.7 * Part Volume * Contraction Ratio

This formula is based on the NRL (Naval Research Laboratory) method for determination of riser volume. Riser volume depends on the following:

• Shape factor. This is the ratio of the sum of part length and part width to the maximum thickness of the part (determined by geometry extraction).

• Part volume (determined by geometry extraction)

• Contraction ratio. This is the ratio of the contraction volume percentage for the current material to the contraction volume percentage for steel (looked by material type in the lookup table tblSolidificationShrinkage).

Runner Volume = Runner Area * Runner Length * Number of Runners

Runner volume is the product of the following:

• Runner area. This is the cross-sectional area of the runner (see formula).

• Runner length: This is the same as the mold length. It is the product of the number of cavities along the length of the mold (see Number of Mold Cavities for Die Casting) and the part length, supplemented by twice the value of the cost model variable edgeBorderPM (3 inches in starting point VPEs). Additional length is included to accommodate any required slides. The mold length is constrained by the minimum mold length specified by the tool shop variable Mold Min (8 inches in starting point VPEs).

Runner Area = (Choke Area * Gating Ratio Runner Multiplier) / Number of Runners

Runner cross-sectional area depends on the following:

• Choke area (see formula)

• Gating ratio runner multiplier (looked up by gating ratio in the table tblGatingDesign). The gating ratio is 1:2:5 by default, or specified by the setup option Gating Ratio).

Choke Area = Pour Weight /

(Material Density * Fill Time *

Sqrt(2 * Gravitational Acceleration * Effective Sprue Height))

Choke area is derived, in part, from the optimum pour time. It depends on the following:

• Pour weight (see formula)

• Material density (specified by the material property Density)

• Fill time (see formula)

• Gravitational acceleration (9800 mm/sec2)

• Effective sprue height. This is the same as the mold width. It is the product of the number of cavities along the width of the mold (see Number of Mold Cavities for Die Casting) and the part width, supplemented by twice the value of the cost model variable edgeBorderPM (3 inches in starting point VPEs). The value is constrained by the minimum mold length specified by the tool shop variable Mold Min (8 inches in starting point VPEs).

Fill Time = Number of Cavities * (Fill Time Constant + (Part Volume / Fill Rate))

For materials other than gray iron, optimum pour time depends on the following:

• Number of cavities (see Number of Mold Cavities for Die Casting)

• Fill time constant. This is the portion of the per-cavity fill time that is independent of part volume. It is specified by the cost model variable fillTimeConstantGravityDieCasting (15 sec in starting point VPEs).

• Part volume (determined by geometry extraction)

• Fill rate. This is specified by the cost model variable moldFillRateGravityDieCasting (120,000mm3/sec in starting point VPEs).

Pour Weight = (Mass Poured Per Cavity * Number of Cavities) / (Estimated Mold Yield / 100)

Pour weight depends on the following:

• Mass poured per cavity (see formula)

• Number of cavities (see Number of Mold Cavities)

• Estimated mold yield. This is specified by the cost model variable materialYieldGravityDieCasting (70% in starting point VPEs).

Mass Poured Per Cavity = Volume Before Machining * Material Density

Mass Poured per cavity is the product of the following:

• Volume before machining (see formula)

• Material density (specified by the material property Density)

Volume Before Machining = Part Volume + Metal Chip Volume of Machined Features

Volume before machining is the part volume plus the volume removed by machining. It is the sum of the following:

• Part volume (obtained from GCD extraction)

Ingate Volume = Ingate Area * Ingate Length * Number of Ingates

Ingate volume is the product of the following:

• Ingate area (see formula)

• Ingate length (the fraction of part length specified by the cost model variable ingateLengthToPartLength—1/10 in starting point VPEs)

• Number of ingates. By default, there is one ingate for every 6 inches of part length, in starting point VPEs. This distance is specified by the cost model variable ingateGap. This is the maximum distance between ingates for a given cavity. With the setup option Number of Ingates, you can override the default, and specify the number of ingates explicitly.

Ingate Area = (Choke Area * Gating Ratio Ingate Multiplier) / Number of Ingates

Ingate cross-sectional area depends on the following:

• Choke area (see formula)

• Gating ratio ingate multiplier (looked up by gating ratio in the table tblGatingRatios)

Sprue Volume = (PI / 3) * Effective Sprue Height *

((Sprue Bottom Radius^2) + (Sprue Top Radius^2) + (Sprue Bottom Radius * Sprue Top Radius))

Sprue volume depends on the following:

• Sprue bottom radius (see formula)

• Sprue top radius (see formula)

Sprue Bottom Radius = sqrt(Sprue Bottom Area / Pi)

Sprue bottom radius is a function of sprue bottom area (see formula).

Sprue Bottom Area = Choke Area * Gating Ratio Sprue Multiplier

Sprue bottom area is the product of the following:

• Choke area (see formula)

• Gating ratio sprue multiplier (looked up by gating ratio in the table tblGatingRatios)

Sprue Top Radius = sqrt(Sprue Top Area / Pi)

Sprue top radius depends on sprue top area—see formula.

Sprue Top Area = Sprue Bottom Area * sqrt(Effective Sprue Height / Pouring Basin Depth)

Sprue top area depends on the following:

• Sprue bottom area (see formula)

• Effective sprue height: This is the same as the mold width. It is the product of the number of cavities along the width of the mold (see Number of Mold Cavities for Die Casting) and the part width, supplemented by twice the value of the cost model variable edgeBorderPM (3 inches in starting point VPEs). The value is constrained by the minimum mold length specified by the tool shop variable Mold Min (8 inches in starting point VPEs).

• Pouring basin depth (see formula)

Pouring Basin Depth = (Pouring Basin Volume / 2)^(1/3)

The model assumes a box-shaped basin with depth equal to width, and length equal to twice the width, so depth depends only on volume—see formula.

Pouring Basin Volume = (Pour Weight / Metal Density) / Fill Time

Pouring basin volume is assumed to be the volume of metal that passes in one second, given the optimal pouring time. It depends on the following:

• Pour weight (see formula)

• Metal density (specified by the material property Density)

• Fill time (see formula)

Sprue Well Volume = Sprue Well Area * Sprue Well Height

Sprue well volume depends on the following:

• Sprue well area (see formula)

• Sprue well height (see formula)

Sprue Well Height = Runner Height * Sprue Well Height to Runner Height Ratio

Sprue well height is the product of the following:

• Runner height (see formula)

• Sprue well height to runner height ratio. This is specified by the cost model variable sprueWellHeightToRunnerHeight (2 in starting point VPEs).

Runner Height = sqrt(Runner Area / Runner Aspect Ratio)

Runner height depends on the following:

• Runner area (see formula)

• Runner aspect ratio. This is the ratio of runner width to runner height. It is specified by the cost model variable runnerAspectRatio (2 in starting point VPEs).

Sprue Well Area = Pi * ( Sprue Well Radius To Well Base Ratio * Sprue Bottom Radius)2

The cross-sectional area of the sprue well is the product of the following:

• Sprue well radius to well base ratio (specified by the cost model variable sprueWellRadiusToWellBase—3.5 in starting point VPEs)

• Sprue bottom radius (see formula)