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

Batch setup cost per part depends on the following:

Cycle time is the product of the following:

Process time depends on the following:

Part time is the time to build all the parts on the build platform, and including the time spent putting fresh powder between layers. It depends on the following:

This is the time to build one part (not including the support base). It depends on the following:

Solidification rate is the volume per unit time created by the sintering process. It is the product of the following:

Layer delay is the time spent putting fresh powder between layers. Powder is put on top of each layer except the last. This is the time spent for all the parts on the build platform. The total layer delay depends on the following:

This is the distance in layers from the platform to the top of the parts in the build chamber. It depends on the following:

This depends on the following:

Preparation times depends on the following:

Cool time depends on the following:

Geometry extraction creates a number of GCDs to represent support structures that are required for DMLS, SLA and Material Jetting routings (see Support Structures for Metal Sintering, Additional Direct Costs—Support Structures for Printing and Support Structures for Resin Curing). But these GCDs have no effect on costing for SLS routings. With Laser Sintering, parts are built with a full surrounding of unsintered powder, so supports are unnecessary.

This is the number of parts that are built at one time. By default, this is the maximum number of parts that can fit in the build chamber. 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 first uses either true-part-shape or rectangular nesting calculations in order to determine the number of parts that can fit on the build platform, arranged in the XY plane.

aPriori then calculates the number of vertical layers of n parts so arranged that can be accommodated by the height of the build chamber. The total number of parts that can fit in the build chamber is the product of n and the number of layers.

Note: Note that a layer of whole parts is different from a layer of sintered material created by a single pass over the build chamber (see, for example, Cycle Time Formulas for Laser Sintering).

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 assumed 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.

With rectangular nesting, the cost model uses the steps below in order to determine the number of parts in one layer of parts on the build platform.

With both nesting calculation methods, the number of layers of parts that can fit in the build chamber is the result of rounding down the quotient of the available chamber height and the height required by each part:

Material Cost includes the cost for the material used for the part, as well as un-recoverable, thermally damaged material.

Material cost depends on the following:

Cost per volume is the product of the following:

Utilization depends on the following:

Rough mass depends on the following:

Powder loaded mass is the mass of the powder loaded into the machine chamber per run. It is the depends on the following:

Powder loaded mass is the mass of the powder loaded into the machine chamber per run. It depends on the following:

Virgin powder per machine is the difference between the following:

Recycled mass per machine depends on the following:

Solid mass per run is mass of the sintered material that has been solidified into parts. It is the product of the following:

Additional direct costs depend on the following:

Laser cost depends on the following:

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

Nitrogen cost is 0 for all machines that do not require an external source of Nitrogen (that is, whose machine property Requires External Nitrogen is false). Nitrogen cost depends on the following:

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