Runner System Model
For plastic molded parts, aPriori models the mold runner system in order to formulate estimates of runner area and runner volume. These quantities play a key role in the following areas of the cost model:
• Machine selection (see Machine Feasibility and Selection):
o Clamp force required of the machine depends in part on area occupied by the runner system in a mold cross section (parallel to the parting plane). See Required Clamp Force.
o Shot size required of the machine depends in part on runner system volume. See Required Shot Size.
• Material utilization and material cost. See Material Utilization for Plastic Molding.
• Injection time (which affects cycle time). See Times for Plastic Molding.
Note that runner system volume is 0 if hot drops are used (see User Inputs for Plastic Molding).
The following sections further describe the runner system model:
Runner System Calculation Overview
The cost model calculates runner system area and volume based primarily on properties of the runner system layout. In particular, the calculation is based primarily on properties of the straight runner segments (referred to as “branches”) that form the paths from the sprue to the cavities:
• Number of cavities fed by each branch
• Length of each branch relative to various quantities (such as the dimensions of the cavity, sprue, and plastic forming region)
• Diameter of the smallest runner branches (branches that feed a single cavity)
The runner layout is chosen based on the following:
• Cavity layout
• Gate location (see User Inputs for Plastic Molding)
• Cavity orientation
The choice of cavity layout, in turn, depends on the number of cavities and the dimensions of the plastic forming region for a single cavity. See Number and Layout of Mold Cavities for more information.
The plastic forming region for a mold cavity is the portion of the mold containing the mold cavity, as well as the slide mechanisms and temperature control lines that are required for that cavity. The calculation of its dimensions depends on the following:
• Part length and width
• Space allowances for temperature control lines and slide mechanisms, and for inserts
• Cavity orientation
See Dimensions of the Plastic Forming Region for more information.
By default, the cavity is oriented so that the motion of the majority of slides is horizontal. A setup option allows the user to specify the orientation explicitly. See Cavity Orientation for more information.
See Runner System Layout and Runner System Volume and Area for more detailed information on the runner system model.
Runner System Layout
In the course of costing a part, the cost model chooses one of large number of candidate runner system layouts. The runner system is made up of a network of straight runner segments (branches) within the mold that provide paths of flow from the sprue to each cavity.
Information about each possible layout is encoded by the cost model in lookup tables and CSL vectors. (See the Cost Model Workbench User Guide for information on CSL.) This includes information about the cavity layout, as well as the number of runner branches in each path from sprue to cavity, and the number of cavities fed by each branch. It also includes information about the length of each branch relative to various quantities, such as the dimensions of the sprue and plastic forming region.
The following illustrations show a few examples of the various candidate layouts. The first one is annotated and serves as a key for the others. Note that most diagrams show only some of the paths from the sprue to a cavity.
All these layouts show lengthwise-oriented cavities (see Cavity Orientation). There are similar layouts for widthwise cavities as well--see the discussion of equivalences below.
The cost model assumes that each runner network has the following properties:
• The network provides, for each cavity, a path from the sprue to that cavity’s gate. Note that some of the branches of a given path are branches of other paths as well, and so feed multiple cavities.
• By convention, the various branches of a given path are ordered and designated as follows:
o The1st branch is the branch that directly feeds the cavity.
o The last branch is the branch that is fed directly by the sprue.
o For any i between 1 and the number of branches in a path, the ith branch of the path is the branch that is a distance of i branches from the cavity; that is, it is the branch that has i-1 branches between it and the cavity.
• The system is balanced, that is, all the paths have the same form, in the following sense: For any two paths, p1 and p2, from the sprue to a gate
o p1 and p2 have the same number of branches.
o For every i between 1 and the number of branches, the ith branch of p1 has the same length and diameter as the ith branch of p2.
• The diameter of runner branches increases as the number of cavities they feed increases. In particular, the cross-sectional area of a branch is the product of the number of cavities the branch feeds and the cross-sectional area of the 1st branch of a path. So, for example, the cross-sectional area of a runner branch that feeds two cavities is twice that of a branch that feeds one cavity. (These diameters are bounded above by a cost model variable—see the formula for Diameter of an ith Branch in Runner System Volume and Area.)
Note that, for any i, the number of ith branches in the whole runner system is the total number of gates divided by the number of gates fed by a single ith branch.
Each candidate runner layout is represented by the following data structures:
• Row in the lookup table tblRunnerCalculationCoefficients, which, effectively, represents the number of cavities fed by each branch.
• Vector in CSL, which represents branch lengths in terms of sprue, plastic forming region, and runner region dimensions.
The cost model chooses the runner layout that corresponds to the following characteristics:
• Cavity layout (see Number and Layout of Mold Cavities). In tblRunnerCalculationCoefficients, the cavity layout is specified in the column Mold Layout Column. The values in this column have the following form:
number of cavities along the mold base length X number of cavities along the mold base width
For each entry in this table, number of cavities along the mold base length ≥ number of cavities along the mold base width. This means that the only cavity layouts that are explicitly listed in the table are those with at least as many cavities along the mold base length as along the mold base width.
For cavity layouts with more cavities along the mold base width than along the mold base length, an entry for an equivalent runner system is used. See below for an explanation of equivalences among runner system layouts.
• Cavity orientation (see Cavity Orientation): in tblRunnerCalculationCoefficients, the cavity orientation is specified (along with gate location—see below) in the column Cav Orientation and Runner Attachment Side.
• Gate location (see User Inputs for Plastic Molding): indicates whether the gate is on the long side (length) or short side (width) of a cavity. In tblRunnerCalculationCoefficients, the gate location is specified (along with cavity orientation) in the column Cav Orientation and Runner Attachment Side.
In this table, each row actually represents multiple equivalent runner layouts. There are two types of runner layout equivalence. Two runner systems are equivalent if either of the following holds:
• The two runner layouts have the same cavity layout, but differ with regard to both cavity orientation and gate location. Here is an example:
Such layouts are just the same with regard to the number of branches in each path, and with regard to the number of cavities fed by each branch, but are different with regard to branch lengths. So they are the same with regard to the information stored in the lookup table. Branch lengths are represented separately, in CSL vectors.
The following table shows equivalencies for runner layouts that have the same cavity layout:
Cavity Orientation
Gate Location
Is equivalent to
Cavity Orientation
Gate Location
Lengthwise
Long Side
 
Widthwise
Short Side
Lengthwise
Short Side
 
Widthwise
Long Side
 
• Rotational Equivalence: the two runner layouts differ only with regard to overall rotational orientation. Each runner layout with an nXm cavity layout is a rotation of some runner layout with an mXn cavity layout, and is therefore equivalent for the purposes of runner area and volume calculation. Here are some examples:
In the figure above, the two runner systems on the left are equivalent to one another:
Top left runner layout:
o 1X4 cavity layout
o Widthwise cavity orientation
o Short side gate
Bottom left runner layout:
o 4X1 cavity layout
o Lengthwise cavity orientation
o Short side gate
Similarly, the two runner systems on the right are equivalent to one another:
Top right runner layout:
o 1X4 cavity layout
o Lengthwise cavity orientation
o long side gate
Bottom right runner layout:
o 4X1 cavity layout
o Widthwise cavity orientation
o Long side gate
Here is the list of rotational equivalences:
Cav Orientation and Runner Attachment Side
Mold Layout
Is equivalent to
Cav Orientation and Runner Attachment Side
Mold Layout
WidthwiseShortSide
nXm
 
LengthwiseShortSide
mXn
WidthwiseLongSide
nXm
 
LengthwiseLongSide
mXn
Runner System Volume and Area
The volume of the runner system is given by the following formula:
Runner System Volume =
Runner Volume + Sprue Volume + Pin Point Gate Volume
This is the volume of the entire runner system, including the sprue and gates. It is the sum of the following:
• Runner volume. Runners are assumed to be cylindrical with multiple branches, with a diameter for a given branch that depends on the number of cavities fed by that branch. See formula.
• Sprue volume: assumes a cylindrical sprue with
o Diameter equal to the diameter of a last runner branch (see Runner System Layout). See also the formula below for Diameter of an ith Branch.
o Height: calculated based on part height, water line diameter, and the value of the cost model variable defaultOutboundWaterlineMultiplier.
• Pin point gate volume: not applied for edge gating. See formula.
Note that runner system volume is 0 if hot drops are used (see User Inputs for Plastic Molding).
Pin Point Gate Volume = Pin Point Gate Length *
Pin Point Gate Cross-sectional Area * Number of Cavities
Not applied for edge gating. This value is based on the assumption that each cavity’s gate is cylindrical. It is the product of the following:
• Pin point gate length: this is the difference between the mold base height and the part height.
• Pin point gate cross-sectional area: calculated based on a gate diameter that is 25% greater than the part’s maximum thickness (bounded below by the value of the cost model variable minRunnerDiameter—2.032mm in starting point VPEs).
• Number of cavities (see Number and Layout of Mold Cavities)
Runner Volume = Volume of all ith Branches
This is the volume of the runner system, not including the sprue and gates. It is the sum of the volumes of all the runner branches (see Runner System Layout). The sum is performed by grouping the branches by distance from a cavity (where distance is the count of branches along the path of flow). All the branches in such a group have the same length and diameter. See the formula below.
Volume of all ith Branches = Number of ith Branches *
Cross-sectional Area of an ith Branch * Length of an ith Branch
This is the total volume of all branches that are at a distance of i branches from a cavity (along the path of flow). All such branches feed the same number of cavities and have the same length and diameter. See Runner System Layout for more information. The total volume of all ith branches is the product of the following:
• Number of ith branches (see below)
• Cross-sectional area of an ith branch (see formula)
• Length of each ith branch (see below)
Runner System Area = Runner Area + Pin Point Gate Area
This is the area of the projection of the runner system onto the parting plane. It is the sum of the following:
• Runner Area (see formula)
• Pin point gate area (see formula)
Note that runner system area is 0 if hot drops are used (see User Inputs for Plastic Molding).
Pin Point Gate Area = Pin Point Gate Cross-sectional Area * Number of Cavities
Pin point gate are is 0 if the setup option Gating Type for Cold Runner System is Edge (see User Inputs for Plastic Molding). Otherwise, it is the product of the following:
• Pin point gate cross-sectional area: calculated based on a gate diameter that is 25% greater than the part’s maximum thickness (bounded below by the value of the cost model variable minRunnerDiameter—2.032mm in starting point VPEs).
• Number of cavities (see Number and Layout of Mold Cavities)
Runner Area = Area of all ith Branches
This is the area of the projection of the runners on the parting plane. It is the sum of the areas of all the runner branches (see Runner System Layout). The sum is performed by grouping the branches by distance from a cavity (where distance is the count of branches along the path of flow). All the branches in such a group have the same length and diameter. See the formula below.
Area of all ith branches = Number of ith Branches *
Diameter of an ith Branch * Length of an ith Branch
This is the total area of the rectangular cross-sections of all branches that are at a distance of i branches from a cavity (along the path of flow). All such branches feed the same number of cavities and have the same length and diameter. See Runner System Layout for more information. The total area of all ith branches is the product of the following:
• Number of ith branches (see below)
• Diameter of an ith branch (see formula)
• Length of each ith branch (see below)
Number of ith Branches
The number of ith branches in any runner system layout is the total number of cavities divided by the number of cavities fed by a single ith branch. This quotient is stored in the lookup table tblRunnerCalculationCoefficients. The row representing the current runner layout is looked up by all the following:
• Cavity layout (see Number and Layout of Mold Cavities)
• Cavity orientation (see Cavity Orientation)
• Edge Gate location (see User Inputs for Plastic Molding)
In that row, the number of ith branches is the value in the column Branchi.
See Runner System Layout for more information.
Length of Each ith Branch
This is calculated based on the following:
• CSL vector that is associated with the current runner system layout, which represents branch lengths relative to sprue, plastic forming region, and runner region dimensions. See Runner System Layout.
• Sprue outside diameter: specified by the cost model variable sprueClearanceDia (38.1mm in starting point VPEs).
• Plastic forming region dimensions (see Dimensions of the Plastic Forming Region)
• Cavity dimensions
• Runner region width: this is the width of the region of a multi-cavity mold that contains the sprue. Its length runs either the entire length of the mold or the entire width of the mold (see Runner System Layout). Its width is the same as the sprue diameter.
The illustration below shows some sample of runner length calculations. Note that “PFR” stands for “plastic forming region”:
Runner region width is the same as the sprue diameter.
Note that for single-cavity molds with Center gating (see Gating Type for Cold Runner System in User Inputs for Plastic Molding), the length of the only runner branch is the product of the following:
• Twice the value of the cost model variable runnerRetentionTab (4.7625mm in starting point VPEs)
• 25% greater than the part’s Max Thickness (bounded below by the value of the cost model variable minRunnerDia—2.032mm in starting point VPEs)
Cross-sectional Area of Each ith Branch = π * (Diameter of an ith Branch / 2)2
The cross-sectional area of an ith runner branch is calculated based on its diameter. See the formula below for the calculation of the diameter of an ith branch.
Diameter an ith Branch =
Diameter Coefficient for ith Branches * Diameter of a 1st Branch
The diameter of an ith runner branch is generally the product of the following:
• Diameter coefficient for ith branches: this value is contained in the Diameter Coeff Branch-i column of the lookup table tblRunnerCalculationCoefficients. The row representing the current runner layout is looked up by all the following:
o Cavity orientation (see Cavity Orientation)
o Edge Gate location (see User Inputs for Plastic Molding)
The diameter coefficient is the square root of the number of cavities fed by that branch. This is the factor by which the diameter of a branch must be increased over the diameter of a single-cavity branch (since the number of cavities fed is the factor by which the cross-sectional area must be increased). See Runner System Layout for more information.
• Diameter of a 1st branch: this is 25% greater than the part’s Max Thickness (bounded below by the value of the cost model variable minRunnerDia—2.032mm in starting point VPEs).
The diameter of an ith branch is bounded above by the cross-sectional area of a runner with diameter maxRunnerDia (12.7mm in starting point VPEs).