Tree Box Dimensions

The following sections discuss the calculation of the dimensions of the bounding box of the tree of wax patterns:

Panel Tree: Bounding Box Depth

In starting point Digital Factories, the depth of a panel tree bounding box is the depth required for two wax patterns separated by an allowance. In general, the depth depends on the following:

• Number of wax patterns along the depth dimension: in starting point Digital Factories, this is 2. Administrators can customize the number of wax patterns along the depth dimension with the cost model variable numWaxPatternRowsPerLayer (2 in starting point Digital Factories).

• Space along the tree depth required for one wax pattern: this is the pattern dimension that is aligned with tree depth, that is, dimension not aligned with tree width or height—see Orientation of Wax Pattern in Tree.

• Wax Pattern Spacing Allowance

Panel Tree: Bounding Box Width

By default, the width of a panel tree bounding box is the width required for the maximum number of wax patterns that can fit across the tank for the current Primary Slurry Dipping machine (see Primary Slurry Dipping Machine Selection), given the following constraints and assumptions:

• Each pattern along the width of the tree contributes one of the following to tree box width (whichever is larger):

o Pattern dimension that is aligned with tree width—see Orientation of Wax Pattern in Tree.

o Runner Width

In addition, patterns are separated by a spacing allowance (if more than one fits)—see Wax Pattern Spacing Allowance.

• The tree box width is less than half the slurry tank working diameter. Tank working diameter is the product of the machine property Tank Diameter Less Vertical Paddle and the cost model variable slurryTankSafetyMultiplier_dsiameter (0.8 in starting point Digital Factories).

• Both tree width and tree depth (see Panel Tree: Bounding Box Depth) can be accommodated by the slurry tank opening. That is, the projection of the tree box along the height can fit within a circle whose diameter equals the tank working diameter (see below).

Note that a rectangle circumscribed by a circle has a diagonal that is a diameter of the circle. Therefore, tree width and tree depth must form the legs of a right triangle whose hypotenuse is no greater than the tank working diameter.

The tank working diameter is given by the product of the machine property Tank Diameter Less Vertical Paddle and the cost model the cost model variableslurryTankSafetyMultiplier_dsiameter (0.8 in starting point Digital Factories).

• Single-level tree can be accommodated by the slurry tank working depth, assuming that the tree is tilted so that the diagonal of the front face of its bounding box is vertical. That is, the length of the diagonal is no greater than the tank working depth.

The working depth is the product of the following:

o Cost model variable slurryTankSafetyMultiplier_depth (0.8 in starting point Digital Factories)

o Difference between the machine property Tank Depth and the machine property Horizontal Paddle Height.

The tree diagonal is the hypotenuse of the right triangle whose legs are the tree width and tree height. The tree height for a single-level tree is the sum of the following:

o Pattern dimension that is aligned with tree height—see Orientation of Wax Pattern in Tree.

o Value of the cost model variable runnerLengthAllowance (38.1mm in starting point Digital Factories).

o Twice the value of the cost model variable singleGateHeightAllowance (19.05mm in starting point Digital Factories), provided that Pour Cup Orientation is adjacent (the default in starting point Digital Factories) and Gate Attach Location is top/bottom (the default in starting point Digital Factories).

If the user has specified Number of Wax Patterns per Layer, the width of a panel tree bounding box is the width required for the specified number of patterns divided by the Panel Tree: Number of Wax Patterns Along the Depth Dimension, given the following assumptions:

• Each pattern along the width of the tree contributes one of the following to tree box width (whichever is larger):

o Pattern dimension that is aligned with tree width—see Orientation of Wax Pattern in Tree.

o Runner Width

• Patterns are separated by a spacing allowance (if more than one fits)—see Wax Pattern Spacing Allowance.

Carousel Tree: Bounding Box Width

The width of the bounding box of a carousel tree is generally the sum of the following:

• Twice the wax pattern dimension aligned with tree width (see Orientation of Wax Pattern in Tree)

• Twice the gate length allowance specified by the cost model variable gateLengthAllowance (25.4mm in starting point Digital Factories)

• Runner Width

If the working diameter of the of the current Primary Slurry Dipping machine (see below) cannot accommodate this tree width, one of the following calculations is used instead:

• If the Pour Cup Orientation is adjacent, tree box width is the sum of the following:

o Wax pattern dimension aligned with tree width (see Orientation of Wax Pattern in Tree)

o Gate length allowance specified by the cost model variable gateLengthAllowance (25.4mm in starting point Digital Factories)

o Runner Width

• If the Pour Cup Orientation is centered, tree box width is the wax pattern dimension aligned with tree width (see Orientation of Wax Pattern in Tree)

Slurry tank working diameter is the product of machine property Tank Diameter Less Vertical Paddle and cost model variable slurryTankSafetyMultiplier_diameter (0.8 in starting point Digital Factories).

Tree Bounding Box Maximum Height

The maximum height of the bounding box of a carousel or panel tree is the maximum height that can be accommodated by the working depth of the current Primary Slurry Dipping machine, given the following assumptions:

• Slurry tank working depth is the product of cost model variable slurryTankSafetyMultiplier_depth (0.8 in starting point Digital Factories) and difference between machine property Tank Depth and machine property Horizontal Paddle Height.

• Tree is tilted so that the diagonal of the front face of its bounding box is vertical.

The length of this diagonal is the machine’s working depth. The tree diagonal is the hypotenuse of the right triangle whose legs are the tree width and tree box maximum height (see Panel Tree: Bounding Box Width and Carousel Tree: Bounding Box Width).

The maximum tree height is used to calculate the default Number of Tree Layers. The actual tree height is the height required for the number of wax patterns that can fit along the height dimension, and it may be different from the maximum height.

Wax Pattern Spacing Allowance

Wax patterns in a tree are assumed to be separated by a spacing allowance (see Tree Box Dimensions). The allowance is specified by one of the following cost model variables (depending on part mass):

• waxPatternSpacingAllowance_small (12.7mm in starting point Digital Factories), for parts with mass no greater than partMassSizeThreshold_low (22.68kg in starting point Digital Factories)

• waxPatternSpacingAllowance_medium (15.875mm in starting point Digital Factories), for parts with mass greater than partMassSizeThreshold_low but no greater than partMassSizeThreshold_medium (68.03kg in starting point Digital Factories)

• waxPatternSpacingAllowance_large (19.05mm in starting point Digital Factories), for parts with mass greater than partMassSizeThreshold_medium

Runner Width

By default in starting point Digital Factories, runner width is 38.1mm. Administrators can customize the default with the cost model variable defaultRunnerWidth. Users can override the default on a per-part basis with the setup option Runner Width. Runner width can affect Tree Box Dimensions.