Gating System Model
The properties of the gating system affect material utilization and melting overhead, as well as degating and finishing costs. See the following sections:
The total volume of the gating system affects material utilization and melting overhead. The cross-sectional area and volume of ingates and risers affect degating and finishing costs. aPriori calculates the volume and cross-sectional areas based on the assumptions described in the following sections:
See also Gating System Formulas.
Gating System Components
The gating system has the following components:
• Pouring basin (or pouring cup): reservoir into which the molten metal is poured, feeding the sprue. The model assumes that the pouring basin volume is the volume of metal that passes in one second, given the optimal pouring time (see Pouring Time and Choke Area). The model also assumes a box-shaped basin with depth equal to width, and length equal to twice the width.
• Sprue: vertical passage through which the molten metal travels from the pouring basin to the sprue well. The model makes the following assumptions about the shape and dimensions of the sprue:
o Sprue is a tapered cone whose axis is parallel to the direction of metal flow.
o The cost model assumes bottom gating, so effective height of the sprue is the flask width for vertical systems and the Cope Height minus half the part height for horizontal systems (see Vertical and Horizontal Systems). Flask width is specified by machine property Flask Width.
o Sprue top area is the fraction of the sprue bottom area given by the square root of the ratio of the effective sprue height to the pouring basin depth.
• Sprue well (or sprue base): reservoir, fed by the sprue, which feeds the runners. The model makes the following assumptions about the sprue well shape and dimensions:
o Cross-sectional area in a plane normal to the direction of metal flow is constant (so the sprue well is cylindrical, for example, or box shaped).
o Cross-sectional area is 3.5 times that of the sprue bottom, in starting point VPEs. This factor is specified by the cost model variable sprueWellAreaToWellBase.
o Height equals runner height.
• Runners: passages through which the molten metal travels from the sprue well to the ingates.
o In starting point VPEs, the runners are assumed to have a width-to-height ratio of 2. The ratio is specified by the cost model variable runnerAspectRatio.
o For vertical gating systems, runner length is assumed to be twice the Cope Height. For horizontal gating systems, runner length is assumed to be the flask width (specified by the moldmaking machine property Flask Width).
o By default, a single runner is assumed 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 Moldmaking Setup Options.
• Ingates: openings through which the molten metal enters the mold cavity. The model makes the following assumptions about ingates:
o Each cavity has at least one ingate.
o 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. You can customize the number of ingates with a setup option—see Moldmaking Setup Options.
o In starting point VPEs, the ingates are assumed to have a width-to-height ratio of 4. The ratio is specified by the cost model variable ingateAspectRatio.
o Length of each is 1/10 of the part length. The fraction of part length is specified by the cost model variable ingateLengthToPartLength.
• Top riser: reservoir on top of the mold cavity, initially fed through the riser base from the cavity. During cooling of the metal in the cavity, the riser feeds the cavity to compensate for shrinkage. The model makes the following assumptions about the riser:
o Riser is a top riser.
o Riser is cylindrical.
o Riser is blind, with a firecracker core.
o Its height is half the diameter of its base.
Vertical and Horizontal Systems
By default in starting point VPEs, the cost model assumes that the gating system is horizontal, unless the moldmaking process is Vertical Automatic. For each moldmaking process, the gating system type is specified by the node attribute gatingSystem. In starting point VPEs, Vertical Automatic is the only process for which gatingSystem is set to vertical; for all other moldmaking processes, it is set to horizontal.
Choke, Sprue, Runner, and Ingate Area Ratios
By default, the cost model makes the following assumptions about the cross-sectional areas of the sprue base, runner, and ingates:
• Runner Area = Sprue Base Area
• Ingates Area (that is, sum of the cross-sectional areas of the ingates) =Sprue Base Area.
The setup option Gating Ratio allows you to override the default and specify ratios for the cross sectional areas—see Moldmaking Setup Options.
If you specify 1:4:4, for example, the cost model assumes that the sprue base is the choke, and makes the following assumptions about the cross-sectional areas of the sprue base, runner, and ingates:
• Runner Area = 4 * Sprue Base Area
• Ingates Area (that is, sum of the cross-sectional areas of the ingates) = 4 * Sprue Base Area.
The multipliers associated with each ratio are recorded in the lookup table tblGatingRatios.
Pouring Time and Choke Area
The cost model assumes a pouring time that is optimal for the pouring weight and material (that is, it assumes the fastest pouring rate that is slow enough to avoid oxidation-causing turbulence). The model then derives the choke area from the pouring time, and then uses the assumptions above to derive the component areas from the choke area. The total system volume is derived from the component areas together with the component shape and dimension assumptions above. See Gating System Formulas.
Optimal pouring time is given by the following formula:
(Optimal pour time for gray iron uses a different formula—see Gating System Formulas.)
The choke area can be derived from the optimal pouring time with the following formula:
See Gating System Formulas for more information.
Gating System Formulas for Sand 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 tblSolidifcationShrinkage).
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: depends on whether the moldmaking process specifies a horizontal or vertical gating system. The gating system is specified by the moldmaking node attribute gatingSystem. In starting point VPEs, Vertical Automatic is the only process for which gatingSystem is set to vertical; for all other moldmaking processes, it is set to horizontal.
For vertical gating systems, runner length is twice the Cope Height.
For horizontal gating systems, runner length is the flask width (specified by the moldmaking machine property Flask Width).
• 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.
Runner Area = (Choke Area * Gating Ratio Runner Multiplier) / Number of Runners
Runner area depends on the following:
• Choke area (see formula)
• Gating ratio runner multiplier. This is looked up by gating ratio in the table tblGatingDesign. (The gating ratio is 1:1:1 by default, or specified by the setup option Gating Ratio--see Choke, Sprue, Runner, and Ingate Area Ratios)
• 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.
Choke Area = Pour Weight /
(Material Density * Optimum Pour Time * Efficiency Coefficient *
Sqrt(2 * Gravitational Acceleration * Effective Sprue Height))
Choke area is derived, in part, from the optimum pour time (see Pouring Time and Choke Area). It depends on the following:
• Pour weight (see formula)
• Material density (specified by the material property Density)
• Optimum pour time (see formula)
• Efficiency coefficient. This is looked up by gating ratio in the lookup table tblGatingRatios. The gating ratio is 1:1:1 by default, or specified by the setup option Gating Ratio--see Choke, Sprue, Runner, and Ingate Area Ratios).
• Gravitational acceleration (9800 mm/sec2)
• Effective sprue height. This is the flask width for vertical systems and the Cope Height minus half the part height for horizontal systems (see Vertical and Horizontal Systems). Flask width is specified by machine property Flask Width.
Optimum Pour Time = Pouring Coefficient * Sqrt( Pour Weight Lbs )
For materials other than gray iron, optimum pour time depends on the following:
• Pouring coefficient. This is looked up in tblPouringCoefficient by material and either part maximum thickness or part weight.
• Pour weight lbs. This is estimated based on material type, part maximum thickness, and number of mold cavities, and converted to pounds—see the formula for Pour Weight.
For gray iron, see the formula below.
Gray Iron Optimum Pour Time = 0.8 * ( 0.95 + (Part Average Thickness in Inches / 0.853) *
Pour Weight in Lbs ) ^ Exponent
For gray iron, optimum pour time depends on the following:
• Part average thickness in inches (determined by geometry extraction)
• Pour weight lbs. This is estimated based on material type, part maximum thickness, and number of mold cavities, and converted to pounds—see the formula for Pour Weight.
• Exponent. This is ½ for parts weighing less than 1000 pounds, and 1/3 for parts weighing 1000 pounds or more.
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 one of the following cost model variables, depending on the current material:
o materialYieldDuctile (for Ductile Iron)
o materialYieldSteel (for Steel or Stainless Steel)
o materialYieldAluminum (for Aluminum or Zinc-Aluminum)
o materialYieldZinc (for Zinc or Lead)
o materialYieldGray (for Gray Iron)
o materialYieldCopper (for all other materials)
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)
• 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.
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—see Choke, Sprue, Runner, and Ingate Area Ratios)
• Number of ingates (4 times the number of cavities—see Number of Mold Cavities)
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:
• Effective sprue height. The cost model assumes bottom gating, so this is the flask width for vertical systems and the Cope Height minus half the part height for horizontal systems (see Vertical and Horizontal Systems). Flask width is specified by the machine property Flask Width.
• 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—see Choke, Sprue, Runner, and Ingate Area Ratios)
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: The cost model assumes bottom gating, so this is the flask width for vertical systems and the Cope Height minus half the part height for horizontal systems (see Vertical and Horizontal Systems). Flask width is specified by the machine property Flask Width.
• 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) / Optimum Pour Time
Pouring basin volume is assumed to be the volume of metal that passes in one second, given the optimal pouring time (see Pouring Time and Choke Area). It depends on the following:
• Pour weight (see formula)
• Metal density (specified by the material property Density)
• Optimum pour time (see formula)
Sprue Well Volume = Sprue Well Area * Runner Height
Sprue well volume depends on the following:
• Sprue well area (see formula)
• Runner height (see formula)
Sprue Well Area = Sprue Well Area to Well Base Ratio * Sprue Bottom Area
The cross-sectional area of the sprue well is the product of the following:
• Sprue well area to well base ratio (specified by the cost model variable sprueWellAreaToWellBase—3.5 in starting point VPEs)
• Sprue bottom area (see formula)
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).