Formulas and calculations used by the Metal Sintering process are described in the following sections:

Labor cost is a function of the following:

Labor time is the product of the following:

Labor time per part is the powder removal time amortized over the number of parts:

Batch setup cost per part depends on the following:

Cycle time is the product of the following:

Process time is the sum of the following:

Preparation time depends on the following:

This is the time to create the support structures. Support time depends on the following

Support volume depends on the following:

This is the volume of material per unit time sintered by the machine. Sinter rate is the product of the following:

This is the sintering time for the part (not including support structures). Part time depends on the following

This is the time per part for putting fresh powder between layers. Powder is put on top of each layer except the last. Recoat time depends on the following:

This is the number of layers on top of which powder is spread (powder is put on top of each layer except the last). It depends on the following:

This is the time for the recoater blade to travel across the machine bed, plus the time for the blade to return to its starting point. Recoat time per layer depends on the following:

Total powder removal time depends on the following:

The mass of loose bulk powder (powder to be removed) at the end of a cycle is the difference between the following:

This is the mass of the powder initially loaded into the machine. It includes both powder that will be made solid during the machine cycle and powder that will remain in the powdered state. It is calculated based on density of the material in a powdered state, the volume of the build chamber (excluding the portion of the chamber above the top of the part), and an adjustment factor that ensures that the powder feed platform rises enough to cover the build platform. Powder loaded mass is the product of the following:

Solid mass per run is the product of the following:

Solid mass per part is the sum of the following:

Cool time per part depends on the following:

This is the number of parts that are built at one time. By default, this is the maximum number of parts that can fit on the build plate. Users can override the default and specify this number with the setup option Number of Parts per Build Plate.

To calculate the default value, aPriori uses either true-part-shape or rectangular nesting calculations. The cost model assumes a border all around each part whose size, by default, is specified by the cost model variable nestingAllowance (5mm in starting point VPEs). Users can override the default with the setup option Nesting Allowance). aPriori assumes true-part-shape nesting by default, but rectangular nesting is used if you select an option other than True-Part Shape Nesting in the Material Utilization dialog.

With true-part-shape nesting, the cost engine uses an internal algorithm that considers multiple candidate nesting arrangements using a variety of part orientations. By default, the various orientations differ by an angle specified by the cost model variable defaultUtilizationStepAngle (90° in starting point VPEs). With the setup option Step Angle for True-Part Shape Nesting, users can specify a step angle for the cost engine to use in order to generate additional candidate orientations—smaller step angles result in the consideration of a greater number of candidate nesting arrangements (which increases costing time, but may result in more efficient nesting). The algorithm chooses the optimal nesting arrangement from among the considered candidates. (The number of parts is bounded above by the size of a production batch, as specified in the Cost Guide.)

With rectangular nesting, the cost model uses the steps below in order to determine the number of parts that can fit on the build plate.

Material cost depends on the following:

Utilization depends on finish mass (part mass) and rough mass (total, non-reusable material required for one part):

Rough mass is the sum of the following:

Waste mass is the mass of unrecoverable material lost to inefficiencies in the process (for example, material lost due to thermal damage) plus the mass of support-structure material that cannot be removed from the part (for example, because it is inside of an enclosed void). It depends on the following:

This is the per-part amount of powder that has been recycled the maximum allowable number of times, and so must be disposed of. It depends on the following:

Additional direct costs depend on the following:

Nitrogen cost depends on the following:

Note that aPriori converts the times to hours for use in this formula.

Construction time depends on the following:

Geometry extraction creates a number of GCDs to represent support structures, which support overhanging geometries, and provide a base that separates the part from the build platform.

In particular, the structures include the following:

Geometry extraction attempts to choose the height dimension of the part so as to minimize the volume of supports. The cost model assumes that the part is oriented with the height direction normal to the build plate. Users can override the choice of height dimension with the Build Direction tool—see Using the Build Direction Tool to Orient the Part.

The support structures are made with the same material as the part.

If a user considers a particular support structure unnecessary, they can manually assign the GCD to the No Cost operation: right-click on the GCD in the Manufacturing Process pane or Geometric Cost Drivers pane, and select Edit Operation….

Then click No Cost operation in the Operation Sequence Selection dialog, and click OK.

In this case, costs associated with the support structure GCD will not be included.