Melting Formulas for Sand Casting

Melting costs consist of material cost (see Material Cost and Utilization for Sand Casting), labor cost (see Labor and Setup Costs for Sand Casting and Cycle Time in this section), direct overhead (see Direct Overhead in this section), and metal additive cost (see Additional Direct Costs in this section).

Cycle Time = Process Time * Cycle Time Adjustment Factor

Cycle time is the product of the following:

• Process time (see formula below)

• Cycle time adjustment factor: specified by the cost model variable cycleTimeAdjustmentFactor; 1 in aPriori starting point VPEs.

Process Time = Furnace Melting Time / Number of Parts Per Furnace

This is the per-part time to heat the contents of the selected furnace to the pouring temperature. The cost model assumes that the furnace is filled to capacity or nearly to capacity, so as to accommodate the maximal number of parts. Process time depends on the following:

• Furnace melting time (see formula)

• Number of parts per furnace (see formula)

Furnace Melting Time = Furnace Required Energy / Material Transferred Power

This is the time to heat the contents of the selected furnace from ambient temperature to pouring temperature. The cost model assumes that the furnace is filled so as to accommodate the maximal number of parts. Furnace melting time depends on the following:

• Furnace required energy (see formula)

• Material transferred power: this is the rate of heat transfer through the material in the furnace. The cost model calculates this using Fourier’s law of heat conduction, assuming a cylindrical furnace whose height is twice its diameter.

Furnace Required Energy = (Furnace Required Heat Energy + Furnace Required Melt Energy +

Furnace Required Superheat Energy) * Furnace Factor

This is the energy required to heat the contents of the selected furnace from ambient temperature to pouring temperature. It is the sum of the following:

• Furnace required heat energy (see formula)

• Furnace required melt energy (see formula)

• Furnace required superheat energy (see formula)

• Furnace factor (specified by the machine property Furnace Factor)

Furnace Required Heat Energy = Specific Heat Room Temperature *

(Solidus Temperature – Ambient Temperature) * Total Required Melted Mass

This is the energy required to heat the contents of the selected furnace from ambient temperature to solidus temperature. It depends on the following:

• Specific heat room temperature (specified by the material property Specific Heat at Room Temperature)

• Solidus temperature (specified by the material property Solidus Temp)

• Ambient temperature (specified by the cost model variable ambientTemp, 21 degrees Celsius in starting point VPEs)

• Total required melted mass (see formula)

Furnace Required Melt Energy = Latent Heat * Total Required Melted Mass

This is the energy required to heat the contents of the selected furnace from solidus temperature to liquidus temperature, (that is, heated so that the entirety of contents is liquid). It is the product of the following:

• Latent heat: Energy per unit mass required to change the selected material completely from solid to liquid, once heated to solidus temperature.

• Total required melted mass (see formula)

Furnace Required Superheat Energy = Specific Heat Solidus Temperature *

(Pouring Temperature – Liquidus Temperature) * Total Required Melted Mass

This is the energy required to superheat the contents of the selected furnace from liquidus temperature to pouring temperature. It depends on the following:

• Specific heat solidus temperature (specified by the material property Specific Heat at Solidus Temperature)

• Pouring temperature (specified by the material property Injection Temp)

• Liquidus temperature (specified by the material property Liquidus Temp)

• Total required melted mass (see formula)

Total Required Melted Mass = Number of Parts Per Furnace * Mass Poured

This is the minimum mass of material required to produce the maximum number of parts that can be produced by the selected furnace. It is the product of the following:

• Number of parts per furnace (see formula)

• Mass poured: this is the mass poured per part (see formula).

Number of Parts Per Furnace = rounddown(Furnace Mass Capacity / Mass Poured)

This the maximum number of parts that can be produced by the selected furnace. It depends on the following:

• Furnace mass capacity (product of material density and the machine property Furnace Capacity)

• Mass poured: this is the mass poured per part (see formula).

Direct Overhead Cost = (Mass Poured * Melting Rate) / Final Yield

Direct overhead per part depends on the mass poured per part.

Direct overhead depends on the following:

• Mass Poured: mass poured per part (see formula)

• Melting rate: melting cost per unit mass (see formula)

• Final yield (see Yields for Sand Casting)

Mass Poured = Mass Before Machining + Mass Waste + Mass Bad Parts + Mass Loss

Mass poured is the sum of the following:

• Mass before machining (see Material Cost and Utilization for Sand Casting)

• Mass waste (see Material Cost and Utilization for Sand Casting)

• Mass bad parts (see Material Cost and Utilization for Sand Casting)

• Mass loss (see Material Cost and Utilization for Sand Casting)

Melting Rate = Total Annual Factory Cost / Annual Mass Melted Metal

Melting rate depends on the following:

• Total annual factory cost (see formula)

• Annual mass melted metal (see formula)

Total Annual Factory Cost = Annual Labor Cost + Annual Direct Cost + Annual Indirect Cost

Total annual factory cost is the sum of the following:

• Annual labor cost (see formula)

• Annual direct cost (see formula)

• Annual indirect cost (see formula)

Annual Labor Cost = Annual Earned Machine Hours * Number of Operators * Labor Rate

Annual labor cost if the product of the following:

• Annual earned machine hours (see Annual Earned Machine Hours)

• Number of operators (specified by the machine property Number of Operators)

• Labor rate: this is the product of the machine property Labor Rate and cost model variable laborRateAdjustmentFactor (1 in starting point VPEs).

Annual Direct Cost = Depreciation Cost + Maintenance Cost + Annual Energy Cost + Supplies Cost + Imputed Interest Cost

Annual direct cost is the sum of the following:

• Depreciation cost (see Annual Depreciation)

• Maintenance cost (see Annual Maintenance)

• Annual energy cost (see formula)

• Supplies cost (specified by the machine property Supplies Cost)

• Imputed interest cost (see Imputed Interest)

Annual Energy Cost = Annual Mass Melted Metal * Melting Cost Per Mass

Annual energy cost is the product of the following:

• Annual mass melted metal (see formula)

• Melting cost per mass (see formula)

Annual Mass Melted Metal = Furnace Productivity * Material Density * Annual Earned Machine Hours

Annual mass melted metal is the product of the following:

• Furnace productivity: this the machine property Furnace Capacity divided by the furnace melting time (see formula, above)

• Material density (specified by the material property Density)

• Annual earned machine hours (see Annual Earned Machine Hours)

Melting Cost Per Mass = Electricity Rate * Unit Melting Energy

Melting cost per mass is the product of the following:

• Electricity rate (specified by the VPE variable Electricity Rate)

• Unit melting energy (see formula)

Unit Melting Energy = (Latent Heat +

Specific Heat at Solidus Temperature * ( Pouring Temperature - Liquidus Temperature ) +

Specific Heat at Room Temperature * ( Solidus Temperature - Ambient Temperature ) ) *

Furnace Factor

Unit melting energy depends on the following:

• Latent heat (specified by the material property Heat of Fusion)

• Specific heat at solidus temperature (specified by the material property Specific Heat at Solidus Temperature)

• Pouring temperature (specified by the material property Injection Temp)

• Liquidus temperature (specified by the material property Liquidus Temp)

• Specific heat at room temperature (specified by the material property Specific Heat at Room Temperature)

• Solidus temperature (specified by the material property Solidus Temp)

• Ambient temperature (specified by the cost model variable Ambient Temp—21 degrees Celsius in starting point VPEs)

• Furnace factor (specified by the machine property Furnace Factor)

Annual Indirect Cost = Facility Cost + Support Services Cost

Annual indirect cost is the sum of the following:

• Facility cost (see Facilities Cost)

• Support services cost (see Support Services Cost)

Additional Direct Costs = (Rough Mass * Metal Additive Rate) / Final Yield

Additional direct costs consist of metal additive cost, and is the product of the following:

• Rough mass (see Material Cost and Utilization for Sand Casting)

• Metal additive rate is the cost of metal additive per Kg of rough mass. By default, this is looked up by additive type in the table tblMetalAdditives. Additive type is either the additive named Default in the lookup table (with a rate of $0.22 in starting point VPEs), or else the type specified by the user with the PSO Metal Additive Type. You can override the looked-up rate with the PSO Metal Additive Rate (see User Inputs for Sand Casting).

• Final yield (see Yields for Sand Casting)