Profile CNC Bend
aPriori uses the formulas in the following sections to determine costs associated with this bending process:
Labor Cost for Profile CNC Bend
Labor Cost = (Labor Rate * Labor Time) / Final Yield
Labor cost depends on the following:
• Labor rate (specified by the machine property Labor Rate)
• 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 CNC Bend
Cycle Time = Process Time * Cycle Time Adjustment Factor
Cycle time depends on the following:
• Process time: see formula.
• 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.
Process Time = Operation Cycle Times + Part Handling Time
Process time is the sum of the following:
• Operation cycle times: sum of the cycle times for all child operations. The cycle time for a child operation is given by Profile 3 Roll Bending Cycle Time or Rotary Draw Bending Cycle Time, below.
• Part handling time: by default, this is twice the Load Time specified for the part weight in the lookup table tblMaterialHandling. Users can override the default with the setup option Part Handling Time.
Profile 3 Roll Bending Cycle Time =
(Rolling Time * Number of Passes) + Prebend Time
Operation cycle time depends on the following:
• Rolling time: see formula.
• Number of Passes: By default, this is specified by the formula below. Users can override the default with the setup option Number of Passes.
• Prebend time: time to move the part (rotationally and translationally) to the position required for the current bend. By default, this is specified by the formula below. Users can override the default with the setup option Prebend Time.
Rolling Time = Arc Length / Rolling Speed
Rolling time is the quotient of the following:
• Arc length: see formula
• Rolling Speed: specified by the setup option Feed Speed. By default, it is given by the formula below.
Arc Length = Min Bend Radius * Bend Angle in Radians
Arc length is the product of the following:
• Min bend radius: specified by the GCD property Min Bend Radius.
• Bend angle in radians: the bend angle is specified in degrees by the GCD property Bend Angle. This is converted to radians for use in this formula.
Rolling Speed = Machine Rolling Speed * Rolling Speed Adjustment Factor
By default, rolling speed is given by the formula above. Users can override the default with the setup option Feed Speed. Default rolling speed is the product of the following:
• Machine rolling speed: specified by the machine property Feed 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:
o Bend diameter is greater than or equal to Min Pass Diameter (see formula).
o 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.
Prebend Time = Clock Angle Rotate Time + Bend Axial Traverse Time
This is the time to move the part (rotationally and translationally) to the position required for the current bend. Prebend time for a subsequent bend depends on its position relative to the previous bend.
By default, prebend time is the sum of the following:
• Clock angle rotate time: time to rotate the part into the orientation required for the current bend. See formula.
• Bend axial traverse time: time to translationally move the part to the position required for the current bend. See formula.
Users can override the default with the setup option Prebend Time.
Clock Angle Rotate Time = Relative Clock Angle / Rotational Speed
Clock angle rotate time is the time to rotate the part into the orientation required for the current bend. For the first bend, this time is included in part handling time (see Process Time above); therefore, clock angle rotate time is 0 for the first bend. For subsequent bends, it depends on the following:
• Relative clock angle: magnitude of the difference between the Clock Angle of the current bend and the Clock Angle of the previous bend. Bends are ordered by their position along the stock piece’s neutral axis (as specified by the geometric property Bar Position From).
• Rotational speed: specified by the machine property Rotational Speed.
Bend Axial Traverse Time = Bend Distance / Machine Rolling Speed
Bend angle traverse time is the time to translationally move the part to the position required for the current bend. It depends on the following:
• Bend distance: magnitude of the difference between the Bar Position From of the current bend and the Bar Position To of the previous bend (or 0 is the current bend is the first bend).
• Machine rolling speed: specified by the machine property Rotational Speed.
Rotary Draw Bending Cycle Time = Prebend Time + Bend Time
Operation cycle time depends on the following:
• Prebend time: time to move the part (rotationally and translationally) to the position required for the current bend. By default, this is specified by the formula above. Users can override the default with the setup option Prebend Time.
• Bend time: see formula
Bend Time = Bend Angle / Rotary Draw Bend Speed
Bend time depends on the following:
• Bend angle: specified in degrees by the geometric property Bend Angle.
• Rotary draw bend speed: specified in degrees per second by the machine property Rotary Draw Bend Speed.
Tooling Cost for Profile CNC Bend
Hard Tooling Cost =
Mandrel Cost + Wiper Cost + First Die Stack Cost + Additional Die Stack Cost
Hard tooling cost is the sum of the following:
• Mandrel cost: see formula.
• Wiper cost: looked up by the Width of the part’s widest bend in the tool shop Tool Materials table. (Maximum bend widths are listed in the column Part Diameter in the materials table.)
• First die stack cost: looked up by the Width of the part’s widest bend in the tool shop Tool Materials table. (Maximum bend widths are listed in the column Part Diameter in the materials table.)
• Additional die stack cost: see formula.
Mandrel Cost = Number of Mandrels * (Mandrel Shank Cost + Mandrel Ball Cost)
Mandrel cost depends on the following:
• Number of mandrels: number of CrossSectionHollow GCDs in the part.
• Mandrel shank cost: looked up by the Width of the part’s widest bend in the tool shop Tool Materials table. (Maximum bend widths are listed in the column Part Diameter in the materials table.)
• Mandrel ball cost: see formula.
Mandrel Ball Cost = Cost per Mandrel Ball * Number of Mandrel Balls
Mandrel ball cost is the product of the following:
• Cost per mandrel ball: looked up by the Width of the part’s widest bend in the tool shop Tool Materials table. (Maximum bend widths are listed in the column Part Diameter in the materials table.)
• Number of mandrel balls: looked up by the Width of the part’s widest bend in the lookup table tblMandrelBalls.
Additional Die Stack Cost =
(Required Number of Rotary Die Stacks – 1) * Cost per Additional Die Stack
The cost for die stacks other than the first die stack depends on the following
• Required number of rotary die stacks: The required number of rotary draw die stacks is the number of equivalence groups of rotary draw bends on the part. See Number of Rotary Draw Die Stacks.
• Cost per additional die stack: looked up by the Width of the part’s widest bend in the tool shop Tool Materials table. (Maximum bend widths are listed in the column Part Diameter in the materials table.)