Profile 3 Roll Bending

aPriori uses the formulas in the following sections to determine costs associated with this bending process:

Labor Cost for Profile 3 Roll Bending

Labor Cost = (Labor Rate * Labor Time) / Final Yield

Labor cost depends on the following:

  • Labor rate: this is the product of the following:

    • Machine property Labor Rate
    • Cost model variable laborRateAdjustmentFactor (1 in starting point Digital Factories)
    • Machine property Work Center Labor Rate Factor (1 in starting point Digital Factories)

  • Labor time (see formula)

  • Final yield (see Yields for Bar & Tube Fabrication)

Labor Time = Cycle Time *
Number of Operators * Labor Time Standard

Labor time is the product of the following:

  • Cycle time (see formula)

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

  • Labor time standard: specified as the machine property Labor Time Standard. This multiplier is used to account for otherwise unaccounted for factors that affect labor time, such as operator fatigue or time spent by the operator for cleaning or maintenance.

Cycle Time for Profile 3 Roll Bending

Cycle Time = Process Time * Cycle Time Adjustment Factor

Cycle time depends on the following:

  • Process time: this is the sum of the cycle times for each bending operation. See the formula for Operation Cycle Time, below.

  • Cycle time adjustment factor: specified by the cost model variable cycleTimeAdjustmentFactor (1 in starting point Digital Factories). Administrators can customize this value in order to globally adjust cycle times for Bar & Tube.

Operation Cycle Time = (Rolling Time * Number of Passes) +
Prebend Time +  Part Handling Time

Operation cycle time depends on the following:

  • Rolling time: see formula

  • Number of Passes: this is specified by the setup option Number of Passes. By default, this is specified by the formula below.

  • Prebend time: this is specified by the setup option Prebend Time. By default, it is specified by the machine property Prebend Time.

  • Part handling time: this is specified by the setup option Part Handling Time for Bend. By default, it is twice the Load Time specified for the part weight in the lookup table tblMaterialHandling.

Rolling Time = Arc Length / Rolling Speed

Rolling time is the quotient of the following:

  • Arc length: see formula.

  • Rolling speed: This is specified by the setup option Rolling Speed. By default, it is given by the formula below.

Arc Length = Min Bend Radius * Bend Arc Angle in Radians

Arc length is the product of the following:

  • Min bend radius: specified by the GCD property Min Bend Radius.

  • Bend arc angle in radians: the total angle the bend passes through. This is specified in degrees by the GCD property Bend Arc Angle. This is converted to radians for use in this formula.

Rolling Speed = Machine Rolling Speed * Rolling Speed Adjustment Factor

Rolling speed is specified by the setup option Rolling Speed. By default, it is given by the formula above, and is the product of the following:

  • Machine rolling speed: specified by the machine property Rolling Speed.

  • Rolling speed adjustment factor: this is 1 if the material property Tensile Yield Strength is more than 90% of the material Ultimate Tensile Strength. Otherwise, it is specified by the cost model variable rollingSpeedAdjustmentFactor (0.5 in starting point Digital Factories).

Number of Passes =
Pass Material Strength + Overbending Pass + 1

By default, the number of passes depends on the following:

  • Pass material strength: this is 0 if the bend diameter is greater than or equal to Min Pass Diameter (see formula). Otherwise this is the material Tensile Yield Strength divided by 100, rounded off to the nearest whole number.

  • Overbending pass: this is 0 if either of the following holds:

    • Bend diameter is greater than or equal to Min Pass Diameter (see formula).

    • Material Tensile Yield Strength is less than or equal to Machine Reference Yield Strength (see formula).

Otherwise it is 1.

(Bend diameter is twice the GCD property Min Bend Radius.)

Users can override the default with the setup option Number of Passes.

Min Pass Diameter = Machine Min Diameter / Material Strength Ratio

Min pass diameter is the quotient of the following:

  • Machine min diameter: specified by the machine property Top Roller Diameter.

  • Material strength ratio: this is 1 if material Tensile Yield Strength is less than or equal to Machine Reference Yield Strength (see formula). Otherwise, this is specified by the formula below.

Machine Strength Ratio = sqrt(Machine Reference Yield Strength /
Material Tensile Yield Strength)

Machine strength ratio is 1 if material Tensile Yield Strength is less than or equal to Machine Reference Yield Strength (see formula). Otherwise, it is given by the formula above and depends on the following:

  • Machine reference yield strength: see formula

  • Material tensile yield strength: specified by the material property Tensile Yield Strength.

Machine Reference Yield Strength = Machine Bend Force /
Machine Acting Roll Arc

Machine reference yield strength is the quotient of the following:

  • Machine bend force: specified by the machine property Bend Force.

  • Machine acting roll arc: see formula.

Machine Acting Roll Arc = Pi *
Machine Min Diameter * Machine Roller Width * 0.005

Machine acting roll arc depends on the following:

  • Machine min diameter: specified by the machine property Top Roller Diameter.

  • Machine roller width: specified by the machine property Roller Width.

This assumes that 0.5% of roller is in contact with part.

Tooling Cost for Profile 3 Roll Bending

The cost model assumes that the machine’s standard tooling can be used (so hard tooling cost is 0) unless the stock is a custom extrusion (see Extrusion GCDs), which requires custom rollers. Hard tooling cost is given by the formula below.

Hard Tooling Cost = Roller Material Cost *
Special Tooling Multiplier

Hard tooling cost is the product of the following:

  • Roller material cost: this is looked up by Material Type Name in the Roller tool shop. It is specified by the tool shop variable Cost. Material type name is specified by the setup option Roller Material. The default material type name is specified by the tool shop variable Default Tool Material Name.

  • Special tooling multiplier: adjustment factor to account for the cost of custom rollers for extruded stock. This factor can have the following values:

    • 0: if the stock is not a custom extrusion (see Extrusion GCDs). In this case the cost model assumes that the machine’s standard tooling can be used.

    • 1: if the stock is a custom extrusion with no fully-hollow regions and at most one semi-hollow region (see Extrusion GCDs).

    • 1.5: otherwise.